Inspired by Pi Approximation Day.
In [1]:
from math import pi
In [2]:
from fractions import Fraction
In [3]:
pi
Out[3]:
3.141592653589793
In [4]:
pi_fraction = Fraction(3141592653589793, 1000000000000000)
float(pi_fraction)
Out[4]:
3.141592653589793
In [5]:
def get_approximations(x, type_=None, n=None):
"""yields (numerator, denominator) tuples
that approximate x with increasing accuracy.
Up to n approximations are yielded.
n defaults to 10.
type_ defaults to float."""
x = abs(x)
if n is None:
n = 10
if type_ is None:
type_ = float
numerators = [0, 1]
denominators = [1, 0]
for _ in range(n):
# It is fun to play with continued fractions.
integer, fraction = divmod(x, 1)
integer = int(integer)
numerators.append(integer*numerators[-1] + numerators[-2])
denominators.append(integer*denominators[-1] + denominators[-2])
yield numerators[-1], denominators[-1]
if fraction == 0:
break
x = type_(1) / fraction
In [6]:
def show_float_approximations(x, n=None):
for i, (numerator, denominator) in enumerate(get_approximations(x, float, n), 1):
error = numerator / denominator - x
error_fraction = Fraction(numerator, denominator) - Fraction(x)
print(f'{i} {numerator}/{denominator} ({100*error:.3}% error) ({float(100*error_fraction):.3}% error)')
In [7]:
x = pi
show_float_approximations(x)
1 3/1 (-14.2% error) (-14.2% error)
2 22/7 (0.126% error) (0.126% error)
3 333/106 (-0.00832% error) (-0.00832% error)
4 355/113 (2.67e-05% error) (2.67e-05% error)
5 103993/33102 (-5.78e-08% error) (-5.78e-08% error)
6 104348/33215 (3.32e-08% error) (3.32e-08% error)
7 208341/66317 (-1.22e-08% error) (-1.22e-08% error)
8 312689/99532 (2.91e-09% error) (2.91e-09% error)
9 833719/265381 (-8.72e-10% error) (-8.72e-10% error)
10 1146408/364913 (1.61e-10% error) (1.61e-10% error)
In [8]:
def show_fraction_approximations(x, n=None):
print(repr(x))
for i, (numerator, denominator) in enumerate(get_approximations(x, Fraction, n), 1):
error = Fraction(numerator, denominator) - x
print(f'{i} {numerator}/{denominator} ({float(100*error):.3}% error)')
In [9]:
# Python floats have limited precision.
x = pi_fraction
show_float_approximations(x, 20)
1 3/1 (-14.2% error) (-14.2% error)
2 22/7 (0.126% error) (0.126% error)
3 333/106 (-0.00832% error) (-0.00832% error)
4 355/113 (2.67e-05% error) (2.67e-05% error)
5 103993/33102 (-5.78e-08% error) (-5.78e-08% error)
6 104348/33215 (3.32e-08% error) (3.32e-08% error)
7 208341/66317 (-1.22e-08% error) (-1.22e-08% error)
8 312689/99532 (2.91e-09% error) (2.91e-09% error)
9 833719/265381 (-8.72e-10% error) (-8.72e-10% error)
10 1146408/364913 (1.61e-10% error) (1.61e-10% error)
11 4272943/1360120 (-4.04e-11% error) (-4.04e-11% error)
12 5419351/1725033 (2.22e-12% error) (2.24e-12% error)
13 80143857/25510582 (-4.44e-14% error) (-3.41e-14% error)
14 325994779/103767361 (0.0% error) (3.71e-15% error)
15 732133415/233045304 (0.0% error) (-4.21e-16% error)
16 1058128194/336812665 (0.0% error) (8.53e-16% error)
17 1790261609/569857969 (0.0% error) (3.32e-16% error)
18 2848389803/906670634 (0.0% error) (5.25e-16% error)
19 10335431018/3289869871 (0.0% error) (4.92e-16% error)
20 116538131001/37095239215 (0.0% error) (4.92e-16% error)
In [10]:
# Python fractions have arbitrary precision.
x = pi_fraction
show_fraction_approximations(x, 20)
Fraction(3141592653589793, 1000000000000000)
1 3/1 (-14.2% error)
2 22/7 (0.126% error)
3 333/106 (-0.00832% error)
4 355/113 (2.67e-05% error)
5 103993/33102 (-5.78e-08% error)
6 104348/33215 (3.32e-08% error)
7 208341/66317 (-1.22e-08% error)
8 312689/99532 (2.91e-09% error)
9 833719/265381 (-8.72e-10% error)
10 1146408/364913 (1.61e-10% error)
11 4272943/1360120 (-4.04e-11% error)
12 5419351/1725033 (2.24e-12% error)
13 80143857/25510582 (-3.41e-14% error)
14 325994779/103767361 (3.71e-15% error)
15 732133415/233045304 (-4.21e-16% error)
16 2522395024/802903273 (1.13e-16% error)
17 3254528439/1035948577 (-7.2e-18% error)
18 41576736292/13234286197 (9.66e-20% error)
19 211138209899/67207379562 (-1.59e-20% error)
20 252714946191/80441665759 (2.63e-21% error)
In [11]:
# let's try some more digits
pi_long = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679'
i = pi_long.rindex('.')
pi_just_digits = pi_long[:i] + pi_long[i+1:]
pi_fraction = Fraction(int(pi_just_digits), 10**(len(pi_long) - (i+1)))
pi_fraction
Out[11]:
Fraction(31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679, 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
In [12]:
x = pi_fraction
show_float_approximations(x, 300)
1 3/1 (-14.2% error) (-14.2% error)
2 22/7 (0.126% error) (0.126% error)
3 333/106 (-0.00832% error) (-0.00832% error)
4 355/113 (2.67e-05% error) (2.67e-05% error)
5 103993/33102 (-5.78e-08% error) (-5.78e-08% error)
6 104348/33215 (3.32e-08% error) (3.32e-08% error)
7 208341/66317 (-1.22e-08% error) (-1.22e-08% error)
8 312689/99532 (2.91e-09% error) (2.91e-09% error)
9 833719/265381 (-8.72e-10% error) (-8.72e-10% error)
10 1146408/364913 (1.61e-10% error) (1.61e-10% error)
11 4272943/1360120 (-4.04e-11% error) (-4.04e-11% error)
12 5419351/1725033 (2.22e-12% error) (2.21e-12% error)
13 80143857/25510582 (-4.44e-14% error) (-5.79e-14% error)
14 165707065/52746197 (4.44e-14% error) (1.64e-14% error)
15 245850922/78256779 (0.0% error) (-7.82e-15% error)
16 657408909/209259755 (0.0% error) (-1.71e-15% error)
17 5505122194/1752334819 (0.0% error) (-1.98e-15% error)
18 22677897685/7218599031 (0.0% error) (-1.98e-15% error)
19 50860917564/16189532881 (0.0% error) (-1.98e-15% error)
20 582147990889/185303460722 (0.0% error) (-1.98e-15% error)
21 633008908453/201492993603 (0.0% error) (-1.98e-15% error)
22 6912237075419/2200233396752 (0.0% error) (-1.98e-15% error)
23 7545245983872/2401726390355 (0.0% error) (-1.98e-15% error)
24 14457483059291/4601959787107 (0.0% error) (-1.98e-15% error)
25 79832661280327/25411525325890 (0.0% error) (-1.98e-15% error)
26 94290144339618/30013485112997 (0.0% error) (-1.98e-15% error)
27 174122805619945/55425010438887 (0.0% error) (-1.98e-15% error)
28 1139026978059288/362563547746319 (0.0% error) (-1.98e-15% error)
29 2452176761738521/780552105931525 (0.0% error) (-1.98e-15% error)
30 6043380501536330/1923667759609369 (0.0% error) (-1.98e-15% error)
31 14538937764811181/4627887625150263 (0.0% error) (-1.98e-15% error)
32 20582318266347511/6551555384759632 (0.0% error) (-1.98e-15% error)
33 35121256031158692/11179443009909895 (0.0% error) (-1.98e-15% error)
34 196188598422140971/62448770434309107 (0.0% error) (-1.98e-15% error)
35 427498452875440634/136076983878528109 (0.0% error) (-1.98e-15% error)
36 623687051297581605/198525754312837216 (0.0% error) (-1.98e-15% error)
37 1674872555470603844/533128492504202541 (0.0% error) (-1.98e-15% error)
38 2298559606768185449/731654246817039757 (0.0% error) (-1.98e-15% error)
39 13167670589311531089/4191399726589401326 (0.0% error) (-1.98e-15% error)
40 15466230196079716538/4923053973406441083 (0.0% error) (-1.98e-15% error)
41 136897512157949263393/43575831513840929990 (0.0% error) (-1.98e-15% error)
42 426158766669927506717/135650548514929231053 (0.0% error) (-1.98e-15% error)
43 563056278827876770110/179226380028770161043 (0.0% error) (-1.98e-15% error)
44 1552271324325681046937/494103308572469553139 (0.0% error) (-1.98e-15% error)
45 12981226873433325145606/4132052848608526586155 (0.0% error) (-1.98e-15% error)
46 14533498197759006192543/4626156157180996139294 (0.0% error) (-1.98e-15% error)
47 463519671003962517114439/147542893721219406904269 (0.0% error) (-1.98e-15% error)
48 69542484148792136573358393/22136060214340092031779644 (0.0% error) (-1.98e-15% error)
49 139548487968588235663831225/44419663322401403470463557 (0.0% error) (-1.98e-15% error)
50 2162769803677615671530826768/688431010050361144088732999 (0.0% error) (-1.98e-15% error)
51 4465088095323819578725484761/1421281683423123691647929555 (0.0% error) (-1.98e-15% error)
52 11092945994325254828981796290/3530994376896608527384592109 (0.0% error) (-1.98e-15% error)
53 15558034089649074407707281051/4952276060319732219032521664 (0.0% error) (-1.98e-15% error)
54 104441150532219701275225482596/33244650738815001841579722093 (0.0% error) (-1.98e-15% error)
55 224440335154088476958158246243/71441577537949735902191965850 (0.0% error) (-1.98e-15% error)
56 328881485686308178233383728839/104686228276764737743771687943 (0.0% error) (-1.98e-15% error)
57 1539966277899321189891693161599/490186490645008686877278717622 (0.0% error) (-1.98e-15% error)
58 252883351061174983320471062231075/80495270694058189385617481377951 (0.0% error) (-1.98e-15% error)
59 254423317339074304510362755392674/80985457184703198072494760095573 (0.0% error) (-1.98e-15% error)
60 2033846572434695114893010349979793/647393470986980575893080802046962 (0.0% error) (-1.98e-15% error)
61 2288269889773769419403373105372467/728378928171683773965575562142535 (0.0% error) (-1.98e-15% error)
62 4322116462208464534296383455352260/1375772399158664349858656364189497 (0.0% error) (-1.98e-15% error)
63 6610386351982233953699756560724727/2104151327330348123824231926332032 (0.0% error) (-1.98e-15% error)
64 10932502814190698487996140016076987/3479923726489012473682888290521529 (0.0% error) (-1.98e-15% error)
65 28475391980363630929692036592878701/9063998780308373071190008507375090 (0.0% error) (-1.98e-15% error)
66 67883286774917960347380213201834389/21607921287105758616062905305271709 (0.0% error) (-1.98e-15% error)
67 435775112629871393013973315803885035/138711526502942924767567440339005344 (0.0% error) (-1.98e-15% error)
68 1375208624664532139389300160613489494/437742500795934532918765226322287741 (0.0% error) (-1.98e-15% error)
69 18313487233268789205074875403779248457/5829364036850091852711515382528745977 (0.0% error) (-1.98e-15% error)
70 312704491590233948625662182024860713263/99536931127247496029014526729310969350 (0.0% error) (-1.98e-15% error)
71 331017978823502737830737057428639961720/105366295164097587881726042111839715327 (0.0% error) (-1.98e-15% error)
72 643722470413736686456399239453500674983/204903226291345083910740568841150684677 (0.0% error) (-1.98e-15% error)
73 974740449237239424287136296882140636703/310269521455442671792466610952990400004 (0.0% error) (-1.98e-15% error)
74 35734378642954355960793305927210563596291/11374605998687281268439538563148805084821 (0.0% error) (-1.98e-15% error)
75 36709119092191595385080442224092704232994/11684875520142723940232005174101795484825 (0.0% error) (-1.98e-15% error)
76 109152616827337546730954190375395972062279/34744357038972729148903548911352396054471 (0.0% error) (-1.98e-15% error)
77 255014352746866688846988822974884648357552/81173589598088182238039102996806587593767 (0.0% error) (-1.98e-15% error)
78 874195675067937613271920659300049917134935/278265125833237275863020857901772158835772 (0.0% error) (-1.98e-15% error)
79 3751797053018617141934671460175084316897292/1194234092931037285690122534603895222936855 (0.0% error) (-1.98e-15% error)
80 12129586834123789039075935039825302867826811/3860967404626349132933388461713457827646337 (0.0% error) (-1.98e-15% error)
81 15881383887142406181010606500000387184724103/5055201497557386418623510996317353050583192 (0.0% error) (-1.98e-15% error)
82 75655122382693413763118361039826851606723223/24081773394855894807427432446982870029979105 (0.0% error) (-1.98e-15% error)
83 91536506269835819944128967539827238791447326/29136974892413281226050943443300223080562297 (0.0% error) (-1.98e-15% error)
84 3737115373176126211528277062632916403264616263/1189560769091387143849465170178991793252470985 (0.0% error) (-1.98e-15% error)
85 44936920984383350358283453719134824077966842482/14303866203989059007419632985591201742110214117 (0.0% error) (-1.98e-15% error)
86 93610957341942826928095184500902564559198301227/29797293177069505158688731141361395277472899219 (0.0% error) (-1.98e-15% error)
87 138547878326326177286378638220037388637165143709/44101159381058564166108364126952597019583113336 (0.0% error) (-1.98e-15% error)
88 1617637618931530777078260204921313839568014882026/514910046368713710985880736537839962492887145915 (0.0% error) (-1.98e-15% error)
89 3373823116189387731442899048062665067773194907761/1073921252118485986137869837202632522005357405166 (0.0% error) (-1.98e-15% error)
90 15112930083689081702849856397171974110660794513070/4810595054842657655537360085348370050514316766579 (0.0% error) (-1.98e-15% error)
91 18486753199878469434292755445234639178433989420831/5884516306961143641675229922551002572519674171745 (0.0% error) (-1.98e-15% error)
92 717609551679070920205974563316088262891152392504648/228422214719366116039196097142286467806261935292889 (0.0% error) (-1.98e-15% error)
93 5759363166632445831082089261973940742307653129458015/1833262234061890071955244007060842745022615156514857 (0.0% error) (-1.98e-15% error)
94 52551878051371083399944777921081554943660030557626783/16727782321276376763636392160689871173009798343926602 (0.0% error) (-1.98e-15% error)
95 110863119269374612630971645104137050629627714244711581/35288826876614643599228028328440585091042211844368061 (0.0% error) (-1.98e-15% error)
96 496004355128869533923831358337629757462170887536473107/157883089827734951160548505474452211537178645721398846 (0.0% error) (-1.98e-15% error)
97 28383111361614938046289359070349033225973368303823678680/9034624947057506859750492840372216642710225017964102283 (0.0% error) (-1.98e-15% error)
98 397859563417738002181974858343224094921089327141067974627/126642632348632830987667448270685485209480328897218830808 (0.0% error) (-1.98e-15% error)
99 824102238197090942410239075756797223068152022585959627934/262319889644323168835085389381743187061670882812401763899 (0.0% error) (-1.98e-15% error)
100 1221961801614828944592213934100021317989241349727027602561/388962521992955999822752837652428672271151211709620594707 (0.0% error) (-1.98e-15% error)
101 2046064039811919887002453009856818541057393372312987230495/651282411637279168657838227034171859332822094522022358606 (0.0% error) (-1.98e-15% error)
102 3268025841426748831594666943956839859046634722040014833056/1040244933630235168480591064686600531603973306231642953313 (0.0% error) (-1.98e-15% error)
103 5314089881238668718597119953813658400104028094353002063551/1691527345267514337138429291720772390936795400753665311919 (0.0% error) (-1.98e-15% error)
104 24524385366381423705983146759211473459462747099452023087260/7806354314700292517034308231569690095351154909246304200989 (0.0% error) (-1.98e-15% error)
105 152460402079527210954496000509082499156880510691065140587111/48529653233469269439344278681138912963043724856231490517853 (0.0% error) (-1.98e-15% error)
106 176984787445908634660479147268293972616343257790517163674371/56336007548169561956378586912708603058394879765477794718842 (0.0% error) (-1.98e-15% error)
107 1037384339309070384256891736850552362238596799643650958958966/330209690974317079221237213244681928255018123683620464112063 (0.0% error) (-1.98e-15% error)
108 3289137805373119787431154357819951059332133656721470040551269/1046965080471120799620090226646754387823449250816339187055031 (0.0% error) (-1.98e-15% error)
109 4326522144682190171688046094670503421570730456365120999510235/1377174771445437878841327439891436316078467374499959651167094 (0.0% error) (-1.98e-15% error)
110 16268704239419690302495292641831461324044325025816833039081974/5178489394807434436144072546321063336058851374316218140556313 (0.0% error) (-1.98e-15% error)
111 20595226384101880474183338736501964745615055482181954038592209/6555664166252872314985399986212499652137318748816177791723407 (0.0% error) (-1.98e-15% error)
112 98649609775827212199228647587839320306504546954544649193450810/31401146059818923696085672491171061944608126369580929307449941 (0.0% error) (-1.98e-15% error)
113 119244836159929092673411986324341285052119602436726603232043019/37956810226071796011071072477383561596745445118397107099173348 (0.0% error) (-1.98e-15% error)
114 25140065203360936673615745775699509181251621058667131327922484800/8002331293534896086021010892741718997261151601232973420133853021 (0.0% error) (-1.98e-15% error)
115 25259310039520865766289157762023850466303740661103857931154527819/8040288103760967882032081965219102558857897046351370527233026369 (0.0% error) (-1.98e-15% error)
116 201955235480006997037639850109866462445377805686394136846004179533/64284348019861671260245584649275436909266430925692567110765037604 (0.0% error) (-1.98e-15% error)
117 429169780999534859841568857981756775357059352033892131623162886885/136608984143484310402523251263769976377390758897736504748763101577 (0.0% error) (-1.98e-15% error)
118 631125016479541856879208708091623237802437157720286268469167066418/200893332163345981662768835913045413286657189823429071859528139181 (0.0% error) (-1.98e-15% error)
119 24411920407222125421251499765463439811849671345404770333451511410769/7770555606350631613587739015959495681270363972188041235410832390455 (0.0% error) (-1.98e-15% error)
120 25043045423701667278130708473555063049652108503125056601920678477187/7971448938513977595250507851872541094557021162011470307270360529636 (0.0% error) (-1.98e-15% error)
121 99541056678327127255643625186128628960805996854779940139213546842330/31684902421892564399339262571577118964941427458222452157221913979363 (0.0% error) (-1.98e-15% error)
122 224125158780355921789417958845812320971264102212684936880347772161847/71341253782299106393929032995026779024439876078456374621714188488362 (0.0% error) (-1.98e-15% error)
123 323666215458683049045061584031940949932070099067464877019561319004177/103026156204191670793268295566603897989381303536678826778936102467725 (0.0% error) (-1.98e-15% error)
124 2489788666991137265104849047069398970495754795684939076017277005191086/792524347211640801946807101961254064950109000835208162074266905762437 (0.0% error) (-1.98e-15% error)
125 7793032216432094844359608725240137861419334486122282105071392334577435/2480599197839114076633689601450366092839708306042303313001736819755036 (0.0% error) (-1.98e-15% error)
126 10282820883423232109464457772309536831915089281807221181088669339768521/3273123545050754878580496703411620157789817306877511475076003725517473 (0.0% error) (-1.98e-15% error)
127 172318166351203808595790933082192727172060762995037821002490101770873771/54850575918651192133921636856036288617476785216082486914217796428034604 (0.0% error) (-1.98e-15% error)
128 354919153585830849301046323936694991176036615271882863186068872881516063/112974275382353139146423770415484197392743387739042485303511596581586681 (0.0% error) (-1.98e-15% error)
129 882156473522865507197883580955582709524133993538803547374627847533905897/280799126683357470426769177687004683402963560694167457521240989591207966 (0.0% error) (-1.98e-15% error)
130 3001388574154427370894697066803443119748438595888293505309952415483233754/955371655432425550426731303476498247601634069821544857867234565355210579 (0.0% error) (-1.98e-15% error)
131 9886322195986147619881974781365912068769449781203684063304485093983607159/3146914092980634121706963088116499426207865770158802031122944685656839703 (0.0% error) (-1.98e-15% error)
132 141409899317960494049242344005926212082520735532739870391572743731253733980/45012168957161303254324214537107490214511754852044773293588460164550966421 (0.0% error) (-1.98e-15% error)
133 999755617421709605964578382822849396646414598510382776804313691212759745019/318232096793109756901976464847868930927790149734472215086242165837513604650 (0.0% error) (-1.98e-15% error)
134 2140921134161379705978399109651625005375349932553505424000200126156773224018/681476362543380817058277144232845352070092054320989203466072791839578175721 (0.0% error) (-1.98e-15% error)
135 5281597885744469017921376602126099407397114463617393624804713943526306193055/1681184821879871391018530753313559635067974258376450622018387749516669956092 (0.0% error) (-1.98e-15% error)
136 12704116905650317741821152313903823820169578859788292673609628013209385610128/4043846006303123599095338650859964622206040571073890447502848290872918087905 (0.0% error) (-1.98e-15% error)
137 43393948602695422243384833543837570867905851042982271645633597983154463023439/13812722840789242188304546705893453501686095971598121964526932622135424219807 (0.0% error) (-1.98e-15% error)
138 273067808521822851202130153576929249027604685117681922547411215912136163750762/86920183051038576728922618886220685632322616400662622234664444023685463406747 (0.0% error) (-1.98e-15% error)
139 316461757124518273445514987120766819895510536160664194193044813895290626774201/100732905891827818917227165592114139134008712372260744199191376645820887626554 (0.0% error) (-1.98e-15% error)
140 589529565646341124647645140697696068923115221278346116740456029807426790524963/187653088942866395646149784478334824766331328772923366433855820669506351033301 (0.0% error) (-1.98e-15% error)
141 41583531352368396998780674835959491644513576025644892366024966900415165963521611/13236449131892475514147712079075551872777201726476896394569098823511265459957624 (0.0% error) (-1.98e-15% error)
142 250090717679856723117331694156454645936004571375147700312890257432298422571654629/79606347880297719480532422258931646061429541687634301733848448761737099110779045 (0.0% error) (-1.98e-15% error)
143 291674249032225120116112368992414137580518147400792592678915224332713588535176240/92842797012190194994680134338007197934206743414111198128417547585248364570736669 (0.0% error) (-1.98e-15% error)
144 19500591153806714650780748047655787726250202299827458817121295063391395265893286469/6207230950684850589129421288567406709719074607018973378209406589388129160779399199 (0.0% error) (-1.98e-15% error)
145 58793447710452369072458356511959777316331125046883169044042800414506899386215035647/18714535649066741962382944000040227327091430564471031332756637315749635846908934266 (0.0% error) (-1.98e-15% error)
146 137087486574711452795697461071575342358912452393593796905206895892405194038323357763/43636302248818334513895309288647861363901935735961036043722681220887400854597267731 (0.0% error) (-1.98e-15% error)
147 332968420859875274663853278655110462034156029834070762854456592199317287462861751173/105987140146703410990173562577335950054895302036393103420201999757524437556103469728 (0.0% error) (-1.98e-15% error)
148 470055907434586727459550739726685804393068482227664559759663488091722481501185108936/149623442395521745504068871865983811418797237772354139463924680978411838410700737459 (0.0% error) (-1.98e-15% error)
149 4563471587771155821799809936195282701571772369883051800691427985024819620973527731597/1452598121706399120526793409371190252824070441987580358595524128563230983252410106859 (0.0% error) (-1.98e-15% error)
150 68922129724001924054456699782655926327969654030473441570131083263464016796104101082891/21938595267991508553405970012433837603779853867586059518396786609426876587196852340344 (0.0% error) (-1.98e-15% error)
151 73485601311773079876256509718851209029541426400356493370822511248488836417077628814488/23391193389697907673932763421805027856603924309573639876992310737990107570449262447203 (0.0% error) (-1.98e-15% error)
152 215893332347548083806969719220358344387052506831186428311776105760441689630259358711867/68720982047387323901271496856043893316987702486733339272381408085407091728095377234750 (0.0% error) (-1.98e-15% error)
153 5254925577652927091243529771007451474318801590348830772853449049499089387543302237899296/1672694762526993681304448687966858467464308783991173782414146104787760309044738316081203 (0.0% error) (-1.98e-15% error)
154 42255297953570964813755207887279970138937465229621832611139368501753156789976677261906235/13450279082263336774336861000590911633031457974416123598585550246387489564086001905884374 (0.0% error) (-1.98e-15% error)
155 808105586695501258552592479629326884114130640953163650384501450582809068397100170214117761/257227997325530392393704807699194179495062010297897522155539600786150062026678774527884309 (0.0% error) (-1.98e-15% error)
156 4082783231431077257576717606033914390709590669995440084533646621415798498775477528332495040/1299590265709915298742860899496561809108341509463903734376283554177137799697479874545305919 (0.0% error) (-1.98e-15% error)
157 4890888818126578516129310085663241274823721310948603734918148071998607567172577698546612801/1556818263035445691136565707195755988603403519761801256531823154963287861724158649073190228 (0.0% error) (-1.98e-15% error)
158 8973672049557655773706027691697155665533311980944043819451794693414406065948055226879107841/2856408528745360989879426606692317797711745029225704990908106709140425661421638523618496147 (0.0% error) (-1.98e-15% error)
159 327943082602202186369546306986760845234022952624934181235182757034917225941302565866194495077/104387525297868441326795923548119196706226224571887180929223664684018611672903145499339051520 (0.0% error) (-1.98e-15% error)
160 336916754651759842143252334678458000899556264605878225054634551728331632007250621093073602918/107243933826613802316675350154811514503937969601112885920131771393159037334324784022957547667 (0.0% error) (-1.98e-15% error)
161 1001776591905721870656050976343676847033135481836690631344451860491580489955803808052341700913/318875392951096045960146623857742225714102163774112952769487207470336686341552713545254146854 (0.0% error) (-1.98e-15% error)
162 21374225184671919125920322837895671788595401383176381483288123622051521921079130590192249322091/6803627185799630767479754451167398254500083408857484894079363128270229450506931768473294631601 (0.0% error) (-1.98e-15% error)
163 65124452145921479248417019490030692212819339631365835081208822726646146253193195578629089667186/20729756950349988348399409977359936989214352390346567635007576592281025037862348018965138041657 (0.0% error) (-1.98e-15% error)
164 216747581622436356871171381307987748427053420277273886726914591801989960680658717326079518323649/68992898036849595812677984383247209222143140579897187799102092905113304564093975825368708756572 (0.0% error) (-1.98e-15% error)
165 281872033768357836119588400798018440639872759908639721808123414528636106933851912904708607990835/89722654987199584161077394360607146211357492970243755434109669497394329601956323844333846798229 (0.0% error) (-1.98e-15% error)
166 780491649159152029110348182904024629706798940094553330343161420859262174548362543135496734305319/248438208011248764134832773104461501644858126520384698667321431899901963768006623514036402353030 (0.0% error) (-1.98e-15% error)
167 1062363682927509865229936583702043070346671700003193052151284835387898281482214456040205342296154/338160862998448348295910167465068647856215619490628454101431101397296293369962947358370249151259 (0.0% error) (-1.98e-15% error)
168 15653583210144290142329460354732627614560202740139256060461149116289838115299364927698371526451475/4982690289989525640277575117615422571631876799389183056087356851462050070947487886531219890470656 (0.0% error) (-1.98e-15% error)
169 16715946893071800007559396938434670684906874440142449112612433951677736396781579383738576868747629/5320851152987973988573485285080491219488092418879811510188787952859346364317450833889590139621915 (0.0% error) (-1.98e-15% error)
170 49085476996287890157448254231601968984373951620424154285686017019645310908862523695175525263946733/15624392595965473617424545687776405010608061637148806076464932757180742799582389554310400169714486 (0.0% error) (-1.98e-15% error)
171 114886900885647580322455905401638608653654777680990757683984467990968358214506626774089627396641095/36569636344918921223422576660633301240704215693177423663118653467220831963482229942510390479050887 (0.0% error) (-1.98e-15% error)
172 163972377881935470479904159633240577638028729301414911969670485010613669123369150469265152660587828/52194028940884394840847122348409706251312277330326229739583586224401574763064619496820790648765373 (0.0% error) (-1.98e-15% error)
173 1590638301823066814641593342100803807395913341393724965411018833086491380324828980997476001341931547/506315896812878474791046677796320657502514711666113491319370929486835004831063805413897506317939244 (0.0% error) (-1.98e-15% error)
174 12889078792466469987612650896439671036805335460451214635257821149702544711722000998449073163396040204/4102721203443912193169220544718974966271429970659234160294551022119081613411575062808000841192279325 (0.0% error) (-1.98e-15% error)
175 27368795886756006789866895134980145881006584262296154235926661132491580803768830977895622328134011955/8711758303700702861129487767234270590045374652984581811908472973724998231654213931029899188702497894 (0.0% error) (-1.98e-15% error)
176 1080272118375950734792421561160665360396062121690001229836397605316874196058706409136378343960622506449/343861295047771323777219243466855527978041041437057924824724996997394012647925918372974069200589697191 (0.0% error) (-1.98e-15% error)
177 1107640914262706741582288456295645506277068705952297384072324266449365776862475240114273966288756518404/352573053351472026638348731234089798568086416090042506636633469971119010879580132304003968389292195085 (0.0% error) (-1.98e-15% error)
178 6618476689689484442703863842638892891781405651451488150198018937563703080371082609707748175404405098469/2106726561805131456968962899637304520818473121887270458007892346852989067045826579892993911147050672616 (0.0% error) (-1.98e-15% error)
179 7726117603952191184286152298934538398058474357403785534270343204013068857233557849822022141693161616873/2459299615156603483607311630871394319386559537977312964644525816824108077925406712196997879536342867701 (0.0% error) (-1.98e-15% error)
180 22070711897593866811276168440507969687898354366259059218738705345589840794838198309351792458790728332215/7025325792118338424183586161380093159591592197841896387296943980501205222896640004286989670219736408018 (0.0% error) (-1.98e-15% error)
181 140150388989515392051943162941982356525448600554958140846702575277552113626262747705932776894437531610163/44611254367866634028708828599151953276936112725028691288426189699831339415305246737918935900854761315809 (0.0% error) (-1.98e-15% error)
182 162221100887109258863219331382490326213346954921217200065441280623141954421100946015284569353228259942378/51636580159984972452892414760532046436527704922870587675723133680332544638201886742205925571074497723827 (0.0% error) (-1.98e-15% error)
183 1437919196086389462957697814001904966232224239924695741370232820262687748995070315828209331720263611149187/457703895647746413651848146683408324769157752107993392694211259142491696520920340675566340469450743106425 (0.0% error) (-1.98e-15% error)
184 1600140296973498721820917145384395292445571194845912941435674100885829703416171261843493901073491871091565/509340475807731386104740561443940371205685457030863980369934392822824241159122227417772266040525240830252 (0.0% error) (-1.98e-15% error)
185 3038059493059888184778614959386300258677795434770608682805906921148517452411241577671703232793755482240752/967044371455477799756588708127348695974843209138857373064145651965315937680042568093338606509975983936677 (0.0% error) (-1.98e-15% error)
186 25904616241452604200049836820474797361867934673010782403882929470073969322706103883217119763423535729017581/8245695447451553784157450226462729939004431130141722964883099608545351742599462772164481118120333112323668 (0.0% error) (-1.98e-15% error)
187 28942675734512492384828451779861097620545730107781391086688836391222486775117345460888822996217291211258333/9212739818907031583914038934590078634979274339280580337947245260510667680279505340257819724630309096260345 (0.0% error) (-1.98e-15% error)
188 112732643444990081354535192160058090223505124996354955663949438643741429648058140265883588752075409362792580/35883914904172648535899567030232965843942254147983463978724835390077354783437978792937940292011260401104703 (0.0% error) (-1.98e-15% error)
189 141675319179502573739363643939919187844050855104136346750638275034963916423175485726772411748292700574050913/45096654723079680119813605964823044478921528487264044316672080650588022463717484133195760016641569497365048 (0.0% error) (-1.98e-15% error)
190 254407962624492655093898836099977278067555980100491302414587713678705346071233625992656000500368109936843493/80980569627252328655713172995056010322863782635247508295396916040665377247155462926133700308652829898469751 (0.0% error) (-1.98e-15% error)
191 1413715132301965849208857824439805578181830755606592858823576843428490646779343615690052414250133250258268378/449999502859341323398379470940103096093240441663501585793656660853914908699494798763864261559905718989713803 (0.0% error) (-1.98e-15% error)
192 3081838227228424353511614484979588434431217491313677020061741400535686639629920857372760829000634610453380249/980979575345934975452472114875262202509344665962250679882710237748495194646145060453862223428464267877897357 (0.0% error) (-1.98e-15% error)
193 4495553359530390202720472309419394012613048246920269878885318243964177286409264473062813243250767860711648627/1430979078205276298850851585815365298602585107625752265676366898602410103345639859217726484988369986867611160 (0.0% error) (-1.98e-15% error)
194 12072944946289204758952559103818376459657313985154216777832377888464041212448449803498387315502170331876677503/3842937731756487573154175286505992799714514881213755211235444034953315401337424778889315193405204241613119677 (0.0% error) (-1.98e-15% error)
195 16568498305819594961673031413237770472270362232074486656717696132428218498857714276561200558752938192588326130/5273916809961763872005026872321358098317099988839507476911810933555725504683064638107041678393574228480730837 (0.0% error) (-1.98e-15% error)
196 45209941557928394682298621930293917404198038449303190091267770153320478210163878356620788433008046717053329763/14390771351680015317164229031148708996348714858892770165059065902064766410703554055103398550192352698574581351 (0.0% error) (-1.98e-15% error)
197 152198322979604779008568897204119522684864477579984056930521006592389653129349349346423565857777078343748315419/48446230865001809823497713965767485087363244565517817972089008639750024736793726803417237328970632324204474890 (0.0% error) (-1.98e-15% error)
198 1871589817313185742785125388379728189622571769409111873257519849261996315762356070513703578726332986842033114791/595745541731701733199136796620358530044707649645106585830127169579065063252228275696110246497839940589028280031 (0.0% error) (-1.98e-15% error)
199 2023788140292790521793694285583847712307436246989095930188040855854385968891705419860127144584110065185781430210/644191772596703543022634510586126015132070894210624403802216178218815087989022002499527483826810572913232754921 (0.0% error) (-1.98e-15% error)
200 50442505184340158265833788242392073285001041697147414197770500389767259569163286147156755048744974551300787439831/16056348084052586765742365050687382893214409110700092277083315446830627174988756335684769858341293690506614398135 (0.0% error) (-1.98e-15% error)
201 52466293324632948787627482527975920997308477944136510127958541245621645538054991567016882193329084616486568870041/16700539856649290308764999561273508908346480004910716680885531625049442262977778338184297342168104263419847153056 (0.0% error) (-1.98e-15% error)
202 312773971807504902203971200882271678271543431417829964837563206617875487259438243982241166015390397633733631790036/99559047367299038309567362857054927434946809135253675681510973572077838489877648026606256569181815007605850163415 (0.0% error) (-1.98e-15% error)
203 365240265132137850991598683410247599268851909361966474965521747863497132797493235549258048208719482250220200660077/116259587223948328618332362418328436343293289140164392362396505197127280752855426364790553911349919271025697316471 (0.0% error) (-1.98e-15% error)
204 12000462456035916133935129070010194854874804531000757163734259138249783736779221781558498708694413829640780052912500/3819865838533645554096202960243564890420332061620514231278199139880150822581251291699903981732379231680428164290487 (0.0% error) (-1.98e-15% error)
205 12365702721168053984926727753420442454143656440362723638699780886113280869576715017107756756903133311891000253572577/3936125425757593882714535322661893326763625350760678623640595645077278103334106718064694535643729150951453861606958 (0.0% error) (-1.98e-15% error)
206 24366165177203970118861856823430637309018460971363480802434040024363064606355936798666255465597547141531780306485077/7755991264291239436810738282905458217183957412381192854918794784957428925915358009764598517376108382631882025897445 (0.0% error) (-1.98e-15% error)
207 36731867898372024103788584576851079763162117411726204441133820910476345475932651815774012222500680453422780560057654/11692116690048833319525273605567351543947582763141871478559390430034707029249464727829293053019837533583335887504403 (0.0% error) (-1.98e-15% error)
208 208025504669064090637804779707686036124829048029994503008103144576744791986019195877536316578100949408645683106773347/66216574714535406034437106310742215936921871228090550247715746935130964072162681648911063782475296050548561463419460 (0.0% error) (-1.98e-15% error)
209 868833886574628386655007703407595224262478309531704216473546399217455513420009435325919278534904478088005512987151042/276558415548190457457273698848536215291635067675504072469422378170558563317900191323473548182921021735777581741182243 (0.0% error) (-1.98e-15% error)
210 1076859391243692477292812483115281260387307357561698719481649543794200305406028631203455595113005427496651196093924389/342774990262725863491710805159278431228556938903594622717138125105689527390062872972384611965396317786326143204601703 (0.0% error) (-1.98e-15% error)
211 12714287190255245636875945017675689088522859242710390130771691380953658872886324378563930824777964180551168670020319321/4047083308438174955866092555600598958805761395615044922357941754333143364608591794019704279802280517385365156991800976 (0.0% error) (-1.98e-15% error)
212 51934008152264675024796592553818037614478744328403259242568415067608835796951326145459178894224862149701325876175201673/16531108224015425686956081027561674266451602521363774312148905142438262985824430049051201731174518387327786771171805607 (0.0% error) (-1.98e-15% error)
213 1518800523605930821355977129078398779908406444766404908165255728341609896984474782596880118757298966521889619079101167838/483449221804885519877592442354889152685902234515164499974676190885042769953517063216504554483863313749891181520974163579 (0.0% error) (-1.98e-15% error)
214 1570734531758195496380773721632216817522885189094808167407824143409218732781426108742339297651523828671590944955276369511/499980330028900945564548523382450826952353837036528274286825096027481032939341493265555756215037832137218968292145969186 (0.0% error) (-1.98e-15% error)
215 36074960222286231741732999004987168765411880604852184591137386883344422018175849174928344667090823197296890408095181297080/11483016482440706322297659956768807345637686649318786534284828303489625494619029915058731191214695620768708483948185485671 (0.0% error) (-1.98e-15% error)
216 145870575420903122463312769741580891879170407608503546531957371676786906805484822808455717966014816617859152577336001557831/46432046259791726234755188350457680209503100434311674411426138309985983011415461153500480521073820315212052904084887911870 (0.0% error) (-1.98e-15% error)
217 473686686484995599131671308229729844402923103430362824187009501913705142434630317600295498565135273050874348140103185970573/150779155261815885026563225008141847974146987952253809768563243233447574528865413375560172754436156566404867196202849221281 (0.0% error) (-1.98e-15% error)
218 619557261905898721594984077971310736282093511038866370718966873590492049240115140408751216531150089668733500717439187528404/197211201521607611261318413358599528183650088386565484179989381543433557540280874529060653275509976881616920100287737133151 (0.0% error) (-1.98e-15% error)
219 2332358472202691763916623542143662053249203636546961936343910122685181290154975738826549148158585542057074850292420748555785/742412759826638718810518465083940432525097253111950262308531387863748247149708036962742132580966087211255627497066060620734 (0.0% error) (-1.98e-15% error)
220 12281349622919357541178101788689621002528111693773676052438517487016398500014993834541496957324077799954107752179542930307329/3909275000654801205313910738778301690809136353946316795722646320862174793288821059342771316180340412937895057585618040236821 (0.0% error) (-1.98e-15% error)
221 14613708095122049305094725330833283055777315330320637988782427609701579790169969573368046105482663342011182602471963678863114/4651687760481439924124429203862242123334233607058267058031177708725923040438529096305513448761306500149150685082684100857555 (0.0% error) (-1.98e-15% error)
222 41508765813163456151367552450356187114082742354414952030003372706419558080354932981277589168289404483976472957123470288033557/13212650521617681053562769146502785937477603568062850911785001738314020874165879251953798213702953413236196427750986241951931 (0.0% error) (-1.98e-15% error)
223 56122473908285505456462277781189470169860057684735590018785800316121137870524902554645635273772067825987655559595433966896671/17864338282099120977687198350365028060811837175121117969816179447039943914604408348259311662464259913385347112833670342809486 (0.0% error) (-1.98e-15% error)
224 322121135354590983433678941356303537963383030778092902123932374287025247432979445754505765537149743613914750755100640122516912/102534341932113285941998760898327926241536789443668440760865898973513740447187920993250356526024252980162931991919337955999361 (0.0% error) (-1.98e-15% error)
225 378243609262876488890141219137493008133243088462828492142718174603146385303504348309151400810921811439902406314696074089413583/120398680214212406919685959248692954302348626618789558730682078420553684361792329341509668188488512893548279104753008298808847 (0.0% error) (-1.98e-15% error)
226 18856057989235538939050598679093460936492294365456689017117122929841198127304692512902924405272318504169132660175208270503782479/6002069672428521225006610764084282687056619493764356818564287741580644274175012058727224097761961384764028608124816744597632864 (0.0% error) (-1.98e-15% error)
227 19234301598498415427940739898230953944625537453919517509259841104444344512608196861212075806083240315609035066489904344593196062/6122468352642733631926296723332975641358968120383146377294969820001197958536804388068733765950449897657576887229569752896441711 (0.0% error) (-1.98e-15% error)
228 38090359587733954366991338577324414881117831819376206526376964034285542639912889374115000211355558819778167726665112615096978541/12124538025071254856932907487417258328415587614147503195859257561581842232711816446795957863712411282421605495354386497494074575 (0.0% error) (-1.98e-15% error)
229 57324661186232369794932078475555368825743369273295724035636805138729887152521086235327076017438799135387202793155016959690174603/18247006377713988488859204210750233969774555734530649573154227381583040191248620834864691629662861180079182382583956250390516286 (0.0% error) (-1.98e-15% error)
230 152739681960198693956855495528435152532604570365967654597650574311745316944955061844769152246233157090552573312975146534477327747/48618550780499231834651315908917726267964699083208802342167712324747922615209058116525341123038133642579970260522298998275107147 (0.0% error) (-1.98e-15% error)
231 515543707066828451665498565060860826423557080371198687828588528073965837987386271769634532756138270407044922732080456563122157844/164102658719211683992813151937503412773668652984157056599657364355826808036875795184440714998777262107819093164150853245215837727 (0.0% error) (-1.98e-15% error)
232 668283389027027145622354060589295978956161650737166342426239102385711154932341333614403685002371427497597496045055603097599485591/212721209499710915827464467846421139041633352067365858941825076680574730652084853300966056121815395750399063424673152243490944874 (0.0% error) (-1.98e-15% error)
233 1183827096093855597287852625650156805379718731108365030254827630459676992919727605384038217758509697904642418777136059660721643435/376823868218922599820277619783924551815302005051522915541482441036401538688960648485406771120592657858218156588824005488706782601 (0.0% error) (-1.98e-15% error)
234 515633070189854211965838246218407506319133809682875954503276258352345203075013849675671028409954090016017049664099241555511514379816/164131103884731041837648229073853601178698005549479834119486686927515244060349966944452911493579621564075297179563115539830941376309 (0.0% error) (-1.98e-15% error)
235 516816897285948067563126098844057663124513528413984319533531085982804880067933577281055066627712599713921692082876377615172236023251/164507927752949964437468506693637525730513307554531357035028169368551645599038927592938318264700214221933515336151939545319648158910 (0.0% error) (-1.98e-15% error)
236 2066083762047698414655216542750580495692674394924828913103869516300759843278814581518836228293091889157782125912728374401028222449569/657654887143580935150053749154766178370237928213073905224571195033170180857466749723267866287680264229875843188018934175789885853039 (0.0% error) (-1.98e-15% error)
237 4648984421381344896873559184345218654509862318263642145741270118584324566625562740318727523213896378029485943908333126417228680922389/1479817702040111834737576005003169882470989163980679167484170559434892007313972427039474050840060742681685201712189807896899419864988 (0.0% error) (-1.98e-15% error)
238 43906943554479802486517249201857548386281435259297608224775300583559680942908879244387383937218159291423155621087726512156086350751070/13976014205504587447788237794183295120609140404039186412582106229947198246683218593078534323848226948365042658597727205247884664637931 (0.0% error) (-1.98e-15% error)
239 48555927975861147383390808386202767040791297577561250370516570702144005509534441984706111460432055669452641564996059638573315031673459/15455831907544699282525813799186465003080129568019865580066276789382090253997191020118008374688287691046727860309917013144784084502919 (0.0% error) (-1.98e-15% error)
240 92462871530340949869908057588060315427072732836858858595291871285703686452443321229093495397650214960875797186083786150729401382424529/29431846113049286730314051593369760123689269972059051992648383019329288500680409613196542698536514639411770518907644218392668749140850 (0.0% error) (-1.98e-15% error)
241 141018799506202097253298865974263082467864030414420108965808441987847691961977763213799606858082270630328438751079845789302716414097988/44887678020593986012839865392556225126769399540078917572714659808711378754677600633314551073224802330458498379217561231537452833643769 (0.0% error) (-1.98e-15% error)
242 1079594468073755630643000119407901892702120945737799621355950965200637530186287663725690743404226109373174868443642706675848416281110445/343645592257207188820193109341263336011075066752611475001651001680308939783423614046398400211110130952621259173430572839154838584647233 (0.0% error) (-1.98e-15% error)
243 1220613267579957727896298985382164975169984976152219730321759407188485222148265426939490350262308380003503307194722552465151132695208433/388533270277801174833032974733819561137844466292690392574365661489020318538101214679712951284334933283079757552648134070692291418291002 (0.0% error) (-1.98e-15% error)
244 19388793481773121549087484900140376520251895588021095576182342073027915862410269067818045997338851809425724476364480993653115406709236940/6171644646424224811315687730348556753078742061142967363617135924015613717854941834242092669476134130198817622463152583899539209859012263 (0.0% error) (-1.98e-15% error)
245 39998200231126200826071268785662918015673776152194410882686443553244316946968803562575582344940011998854952259923684539771381946113682313/12731822563126250797464408435430933067295328588578625119808637509520247754247984883163898290236603193680715002478953301869770711136315528 (0.0% error) (-1.98e-15% error)
246 59386993712899322375158753685803294535925671740215506458868785626272232809379072630393628342278863808280676736288165533424497352822919253/18903467209550475608780096165779489820374070649721592483425773433535861472102926717405990959712737323879532624942105885769309920995327791 (0.0% error) (-1.98e-15% error)
247 336933168795622812701865037214679390695302134853271943177030371684605480993864166714543724056334331040258335941364512206893868710228278578/107249158610878628841364889264328382169165681837186587536937504677199555114762618470193853088800289813078378127189482730716320316112954483 (0.0% error) (-1.98e-15% error)
248 396320162508522135077023790900482685231227806593487449635899157310877713803243239344937352398613194848539012677652677740318366063051197831/126152625820429104450144985430107871989539752486908180020363278110735416586865545187599844048513027136957910752131588616485630237108282274 (0.0% error) (-1.98e-15% error)
249 2318533981338233488086983991717092816851441167820709191356526158238994050010080363439230486049400305282953399329627900908485699025484267733/738012287713024151092089816414867742116864444271727487638753895230876638049090344408193073331365425497867931887847425813144471501654365853 (0.0% error) (-1.98e-15% error)
250 2714854143846755623164007782617575502082668974414196640992425315549871763813323602784167838448013500131492412007280578648804065088535465564/864164913533453255542234801844975614106404196758635667659117173341612054635955889595792917379878452634825842639979014429630101738762648127 (0.0% error) (-1.98e-15% error)
251 5033388125184989111250991774334668318934110142234905832348951473788865813823403966223398324497413805414445811336908479557289764114019733297/1602177201246477406634324618259843356223268641030363155297871068572488692685046234003985990711243878132693774527826440242774573240417013980 (0.0% error) (-1.98e-15% error)
252 93315840397176559625681859720641605242896651534642501623273551843749456412634594994805337679401461997591517016071633210680019819140890664910/29703354535970046574960077930522156026125239735305172463020796407646408522966788101667540750182268259023313784140854938799572420066268899767 (0.0% error) (-1.98e-15% error)
253 98349228522361548736932851494976273561830761676877407455622503317538322226457998961028736003898875803005962827408541690237309583254910398207/31305531737216523981594402548781999382348508376335535618318667476218897215651834335671526740893512137156007558668681379042346993306685913747 (0.0% error) (-1.98e-15% error)
254 191665068919538108362614711215617878804727413211519909078896055161287778639092593955834073683300337800597479843480174900917329402395801063117/61008886273186570556554480479304155408473748111640708081339463883865305738618622437339067491075780396179321342809536317841919413372954813514 (0.0% error) (-1.98e-15% error)
255 481679366361437765462162273926212031171285588099917225613414613640113879504643186872696883370499551404200922514368891492071968388046512524441/153323304283589665094703363507390310199296004599616951780997595243949508692889079210349661723045072929514650244287754014726185820052595540775 (0.0% error) (-1.98e-15% error)
256 673344435280975873824776985141829909976013001311437134692310668801401658143735780828530957053799889204798402357849066392989297790442313587558/214332190556776235651257843986694465607769752711257659862337059127814814431507701647688729214120853325693971587097290332568105233425550354289 (0.0% error) (-1.98e-15% error)
257 1155023801642413639286939259068041941147298589411354360305725282441515537648378967701227840424299440608999324872217957885061266178488826111999/367655494840365900745961207494084775807065757310874611643334654371764323124396780858038390937165926255208621831385044347294291053478145895064 (0.0% error) (-1.98e-15% error)
258 4138415840208216791685594762345955733417908769545500215609486516125948271088872683932214478326698211031796376974502940048173096325908791923555/1317298675077873937889141466468948793028967024643881494792341022243107783804698044221803902025618632091319837081252423374450978393859988039481 (0.0% error) (-1.98e-15% error)
259 5293439641850630430972534021413997674565207358956854575915211798567463808737251651633442318750997651640795701846720897933234362504397618035554/1684954169918239838635102673963033568836032781954756106435675676614872106929094825079842292962784558346528458912637467721745269447338133934545 (0.0% error) (-1.98e-15% error)
260 9431855482058847222658128783759953407983116128502354791524698314693412079826124335565656797077695862672592078821223837981407458830306409959109/3002252844996113776524244140431982361864999806598637601228016698857979890733792869301646194988403190437848295993889891096196247841198121974026 (0.0% error) (-1.98e-15% error)
261 14725295123909477653630662805173951082548323487459209367439910113260875888563375987199099115828693514313387780667944735914641821334704027994663/4687207014914353615159346814395015930701032588553393707663692375472851997662887694381488487951187748784376754906527358817941517288536255908571 (0.0% error) (-1.98e-15% error)
262 24157150605968324876288791588933904490531439615961564158964608427954287968389500322764755912906389376985979859489168573896049280165010437953772/7689459859910467391683590954826998292566032395152031308891709074330831888396680563683134682939590939222225050900417249914137765129734377882597 (0.0% error) (-1.98e-15% error)
263 38882445729877802529919454394107855573079763103420773526404518541215163856952876309963855028735082891299367640157113309810691101499714465948435/12376666874824821006842937769222014223267064983705425016555401449803683886059568258064623170890778688006601805806944608732079282418270633791168 (0.0% error) (-1.98e-15% error)
264 101922042065723929936127700377149615636690965822803111211773645510384615682295252942692465970376555159584715139803395193517431483164439369850642/32442793609560109405369466493271026739100162362562881342002511973938199660515817079812381024721148315235428662514306467378296329966275645464933 (0.0% error) (-1.98e-15% error)
265 344648571927049592338302555525556702483152660571830107161725455072369010903838635138041252939864748370053513059567298890362985550993032575500361/109705047703505149222951337249035094440567552071394069042562937371618282867607019497501766245054223633712887793349864010866968272317097570185967 (0.0% error) (-1.98e-15% error)
266 446570613992773522274430255902706318119843626394633218373499100582753626586133888080733718910241303529638228199370694083880417034157471945351003/142147841313065258628320803742306121179667714433956950384565449345556482528122836577314147269775371948948316455864170478245264602283373215650900 (0.0% error) (-1.98e-15% error)
267 2130931027898143681436023579136381974962527166150362980655721857403383517248374187460976128580829962488606425857050075225884653687622920356904373/678296412955766183736234552218259579159238409807221870580824734753844212980098365806758355324155711429506153616806545923848026681450590432789567 (0.0% error) (-1.98e-15% error)
268 6839363697687204566582500993311852243007425124845722160340664672792904178331256450463662104652731190995457505770520919761534378097026233016064122/2177037080180363809837024460397084858657382943855622562127039653607089121468417933997589213242242506237466777306283808249789344646635144514019601 (0.0% error) (-1.98e-15% error)
269 8970294725585348248018524572448234217969952290996085140996386530196287695579630637924638233233561153484063931627570994987419031784649153372968495/2855333493136129993573259012615344437816621353662844432707864388360933334448516299804347568566398217666972930923090354173637371328085734946809168 (0.0% error) (-1.98e-15% error)
270 15809658423272552814601025565760086460977377415841807301337051202989191873910887088388300337886292344479521437398091914748953409881675386389032617/5032370573316493803410283473012429296474004297518466994834904041968022455916934233801936781808640723904439708229374162423426715974720879460828769 (0.0% error) (-1.98e-15% error)
271 214495854228128534837831856927329358210675858696939580058378052169055782056421162786972542625755361631717842617802765886723813360246429176430392516/68276150946250549437906944161776925291978677221402915365561616933945225261368661339229525732078727628424689137904954465678184678999457167937583165 (0.0% error) (-1.98e-15% error)
272 444801366879529622490264739420418802882329094809720967418093155541100755986753212662333385589397015607915206673003623688196580130374533739249817649/141584672465817592679224171796566279880431358740324297725958137909858472978654256912260988245966095980753817984039283093779796073973635215335995099 (0.0% error) (-1.98e-15% error)
273 2438502688625776647289155554029423372622321332745544417148843829874559561990187226098639470572740439671293875982820884327706714012119097872679480761/776199513275338512834027803144608324694135470923024403995352306483237590154639945900534466961909207532193779058101369934577165048867633244617558660 (0.0% error) (-1.98e-15% error)
274 5321806744131082917068575847479265548126971760300809801715780815290219879967127664859612326734877894950502958638645392343610008154612729484608779171/1693983699016494618347279778085782929268702300586373105716662750876333653287934148713329922169784511045141376100242022962934126171708901704571112419 (0.0% error) (-1.98e-15% error)
275 7760309432756859564357731401508688920749293093046354218864624645164779441957314890958251797307618334621796834621466276671316722166731827357288259932/2470183212291833131181307581230391253962837771509397509712015057359571243442574094613864389131693718577335155158343392897511291220576534949188671079 (0.0% error) (-1.98e-15% error)
276 36363044475158521174499501453514021231124144132486226677174279395949337647796387228692619515965351233437690297124510499028876896821540038913761818899/11574716548183827143072510103007347945120053386623963144564722980314618627058230527168787478696559385354481996733615594552979291054015041501325796735 (0.0% error) (-1.98e-15% error)
277 80486398383073901913356734308536731382997581358018807573213183437063454737550089348343490829238320801497177428870487274729070515809811905184811897730/25619616308659487417326327787245087144202944544757323798841461017988808497559035148951439346524812489286299148625574582003469873328606617951840264549 (0.0% error) (-1.98e-15% error)
278 438795036390528030741283172996197678146112050922580264543240196581266611335546833970410073662156955240923577441476946872674229475870599564837821307549/139672798091481264229704149039232783666134776110410582138772028070258661114853406271925984211320621831785977739861488504570328657697048131260527119480 (0.0% error) (-1.98e-15% error)
279 958076471164129963395923080300932087675221683203179336659693576599596677408643757289163638153552231283344332311824381020077529467551011034860454512828/304965212491622015876734625865710654476472496765578488076385517158506130727265847692803407769166056152858254628348551591144127188722702880472894503509 (0.0% error) (-1.98e-15% error)
280 1396871507554657994137206253297129765821333734125759601202933773180863288744190591259573711815709186524267909753301327892751758943421610599698275820377/444638010583103280106438774904943438142607272875989070215157545228764791842119253964729391980486677984644232368210040095714455846419751011733421622989 (0.0% error) (-1.98e-15% error)
281 121089026120864717459195660863854091948309922818018505040111998070153839509409034605612502854304542272370384571095738579796728798601809522608912175065250/38543834122638504105030469267690846334740697964100638526579934406832278229149521688659531118091020362832262238294411999822587329980821289889547154080563 (0.0% error) (-1.98e-15% error)
282 122485897628419375453332867117151221714131256552144264641314931843334702798153225196872076566120251458894652480849039907689480557545231133208610450885627/38988472133221607385136908042595789772883305236976627596795091952061043020991640942624260510071507040816906470662622039918301785827241040901280575703552 (0.0% error) (-1.98e-15% error)
283 1100976207148219721085858597801063865661359975235172622170631452816831461894634836180589115383266553943527604417888057841312573258963658588277795782150266/350451611188411363186125733608457164517807139859913659300940670023320622397082649229653615198663076689367514003595388319169001616598749617099791759708979 (0.0% error) (-1.98e-15% error)
284 2324438311924858817625050062719278953036851207022489508982577837476997626587422897558050307332653359345949861316625155590314627075472548309764202015186159/739891694510044333757388375259510118808497584956803946198676431998702287815156939401931490907397660419551934477853398678256305019024740275100864095121510 (0.0% error) (-1.98e-15% error)
285 3425414519073078538710908660520342818698211182257662131153209290293829088482057733738639422715919913289477465734513213431627200334436206898041997797336425/1090343305698455696943514108867967283326304724816717605499617102022022910212239588631585106106060737108919448481448786997425306635623489892200655854830489 (0.0% error) (-1.98e-15% error)
286 9175267350071015895046867383759964590433273571537813771288996418064655803551538365035329152764493185924904792785651582453569027744344962105848197609859009/2920578305906955727644416592995444685461107034590239157197910636042748108239636116665101703119519134637390831440750972673106918290271720059502175804782488 (0.0% error) (-1.98e-15% error)
287 21775949219215110328804643428040271999564758325333289673731202126423140695585134463809297728244906285139287051305816378338765255823126131109738393017054443/6931499917512367152232347294858856654248518793997195919895438374107519126691511821961788512345099006383701111362950732343639143216166930011205007464395465 (0.0% error) (-1.98e-15% error)
288 30951216569286126223851510811800236589998031896871103445020198544487796499136672828844626881009399471064191844091467960792334283567471093215586590626913452/9852078223419322879876763887854301339709625828587435077093349010150267234931147938626890215464618141021091942803701705016746061506438650070707183269177953 (0.0% error) (-1.98e-15% error)
289 114629598927073489000359175863440981769558854015946600008791797759886530192995152950343178371273104698331862583580220260715768106525539410756498164897794799/36487734587770335791862638958421760673377396279759501151175485404558320831484955637842459158738953429446976939774055847393877327735482880223326557271929324 (0.0% error) (-1.98e-15% error)
290 145580815496359615224210686675241218359556885912817703453811996304374326692131825779187805252282504169396054427671688221508102390093010503972084755524708251/46339812811189658671739402846276062013087022108346936228268834414708588066416103576469349374203571570468068882577757552410623389241921530294033740541107277 (0.0% error) (-1.98e-15% error)
291 260210414423433104224569862538682200129115739928764303462603794064260856885126978729530983623555608867727917011251908482223870496618549914728582920422503050/82827547398959994463602041804697822686464418388106437379444319819266908897901059214311808532942524999915045822351813399804500716977404410517360297813036601 (0.0% error) (-1.98e-15% error)
292 405791229919792719448780549213923418488672625841582006916415790368635183577258804508718788875838113037123971438923596703731972886711560418700667675947211301/129167360210149653135341444650973884699551440496453373607713154233975496964317162790781157907146096570383114704929570952215124106219325940811394038354143878 (0.0% error) (-1.98e-15% error)
293 1477584104182811262570911510180452455595133617453510324211851165170166407616903392255687350251069947979099831328022698593419789156753231170830585948264136953/470329628029408953869626375757619476785118739877466558202583782521193399790852547586655282254380814711064389937140526256449873035635382232951542412875468235 (0.0% error) (-1.98e-15% error)
294 1883375334102603982019692059394375874083806243295092331128266955538801591194162196764406139126908061016223802766946295297151762043464791589531253624211348254/599496988239558607004967820408593361484670180373919931810296936755168896755169710377436440161526911281447504642070097208664997141854708173762936451229612113 (0.0% error) (-1.98e-15% error)
295 10894460774695831172669371807152331826014164833928971979853185942864174363587714376077718045885610253060218845162754175079178599374077189118486854069320878223/3467814569227201988894465477800586284208469641747066217254068466297037883566701099473837483062015371118301913147491012299774858744908923101766224669023528800 (0.0% error) (-1.98e-15% error)
296 12777836108798435154689063866546707700097971077224064310981452898402975954781876572842124185012518314076442647929700470376330361417541980708018107693532226477/4067311557466760595899433298209179645693139822120986149064365403052206780321870809851273923223542282399749417789561109508439855886763631275529161120253140913 (0.0% error) (-1.98e-15% error)
297 23672296883494266327358435673699039526112135911153036290834638841267150318369590948919842230898128567136661493092454645455508960791619169826504961762853104700/7535126126693962584793898776009765929901609463868052366318433869349244663888571909325111406285557653518051330937052121808214714631672554377295385789276669713 (0.0% error) (-1.98e-15% error)
298 36450132992292701482047499540245747226210106988377100601816091739670126273151467521761966415910646881213104141022155115831839322209161150534523069456385331177/11602437684160723180693332074218945575594749285989038515382799272401451444210442719176385329509099935917800748726613231316654570518436185652824546909529810626 (0.0% error) (-1.98e-15% error)
299 862025355706226400414450925099351225728944596643826350132604748853680054600853343949445069796843006835038056736602022309587813371602325632120535559259715721771/274391192862390595740740536483045514168580843041615938220122817134582627880728754450381973984994856179627468551649156442091269836555704824392259964708462314111 (0.0% error) (-1.98e-15% error)
300 4346576911523424703554302125037001875870933090207508851264839836008070399277418187268987315400125681056403387824032266663770906180220789311137200865754963940032/1383558401996113701884396014489446516418498964494068729615996884945314590847854214971086255254483380834055143506972395441773003753296960307614124370451841381181 (0.0% error) (-1.98e-15% error)
In [13]:
x = pi_fraction
show_fraction_approximations(x, 300)
Fraction(31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679, 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
1 3/1 (-14.2% error)
2 22/7 (0.126% error)
3 333/106 (-0.00832% error)
4 355/113 (2.67e-05% error)
5 103993/33102 (-5.78e-08% error)
6 104348/33215 (3.32e-08% error)
7 208341/66317 (-1.22e-08% error)
8 312689/99532 (2.91e-09% error)
9 833719/265381 (-8.72e-10% error)
10 1146408/364913 (1.61e-10% error)
11 4272943/1360120 (-4.04e-11% error)
12 5419351/1725033 (2.21e-12% error)
13 80143857/25510582 (-5.79e-14% error)
14 165707065/52746197 (1.64e-14% error)
15 245850922/78256779 (-7.82e-15% error)
16 411557987/131002976 (1.94e-15% error)
17 1068966896/340262731 (-3.07e-16% error)
18 2549491779/811528438 (5.51e-17% error)
19 6167950454/1963319607 (-7.63e-18% error)
20 14885392687/4738167652 (3.12e-18% error)
21 21053343141/6701487259 (-2.62e-20% error)
22 1783366216531/567663097408 (1.23e-22% error)
23 3587785776203/1142027682075 (-3.15e-23% error)
24 5371151992734/1709690779483 (1.97e-23% error)
25 8958937768937/2851718461558 (-7.72e-25% error)
26 139755218526789/44485467702853 (1.61e-26% error)
27 428224593349304/136308121570117 (-3.81e-28% error)
28 5706674932067741/1816491048114374 (2.33e-29% error)
29 6134899525417045/1952799169684491 (-4.86e-30% error)
30 30246273033735921/9627687726852338 (4.56e-31% error)
31 66627445592888887/21208174623389167 (-3.36e-32% error)
32 430010946591069243/136876735467187340 (8.66e-34% error)
33 2646693125139304345/842468587426513207 (-1.41e-36% error)
34 262452630335382199398/83541266890691994833 (1.01e-38% error)
35 265099323460521503743/84383735478118508040 (-4.07e-39% error)
36 792651277256425206884/252308737846929010913 (6.3e-40% error)
37 1850401877973371917511/589001211171976529866 (-4.27e-41% error)
38 11895062545096656711950/3786316004878788190109 (2.09e-42% error)
39 37535589513263342053361/11947949225808341100193 (-1.2e-43% error)
40 199573010111413366978755/63526062133920493691074 (1.21e-44% error)
41 237108599624676709032116/75474011359728834791267 (-8.75e-45% error)
42 436681609736090076010871/139000073493649328482341 (7.78e-46% error)
43 2857198258041217165097342/909474452321624805685313 (-1.34e-47% error)
44 23294267674065827396789607/7414795692066647773964845 (1.45e-48% error)
45 26151465932107044561886949/8324270144388272579650158 (-1.68e-49% error)
46 206354529198815139329998250/65684686702784555831515951 (1.49e-50% error)
47 232505995130922183891885199/74008956847172828411166109 (-5.69e-51% error)
48 671366519460659507113768648/213702600397130212653848169 (6.3e-52% error)
49 2246605553512900705233191143/715116758038563466372710616 (-2.44e-53% error)
50 16397605394050964443746106649/5219519906667074477262822481 (2.39e-54% error)
51 18644210947563865148979297792/5934636664705637943635533097 (-8.35e-55% error)
52 53686027289178694741704702233/17088793236078350364533888675 (1.51e-55% error)
53 72330238236742559890684000025/23023429900783988308169421772 (-1.04e-55% error)
54 126016265525921254632388702258/40112223136862338672703310447 (4.7e-57% error)
55 1584525424547797615479348427121/504370107543132052380609147136 (-2.39e-58% error)
56 1710541690073718870111737129379/544482330679994391053312457583 (1.25e-58% error)
57 3295067114621516485591085556500/1048852438223126443433921604719 (-5.04e-59% error)
58 5005608804695235355702822685879/1593334768903120834487234062302 (9.41e-60% error)
59 18311893528707222552699553614137/5828856744932488946895623791625 (-1.36e-60% error)
60 23317502333402457908402376300016/7422191513835609781382857853927 (9.54e-61% error)
61 41629395862109680461101929914153/13251048258768098728278481645552 (-6.23e-62% error)
62 356352669230279901597217815613240/113430577583980399607610711018343 (4.18e-63% error)
63 397982065092389582058319745527393/126681625842748498335889192663895 (-2.78e-63% error)
64 754334734322669483655537561140633/240112203426728897943499903682238 (5.11e-64% error)
65 1906651533737728549369394867808659/606906032696206294222889000028371 (-1.75e-64% error)
66 2660986268060398033024932428949292/847018236122935192166388903710609 (1.92e-65% error)
67 17872569142100116747518989441504411/5689015449433817447221222422292025 (-1.55e-66% error)
68 20533555410160514780543921870453703/6536033685556752639387611326002634 (1.14e-66% error)
69 38406124552260631528062911311958114/12225049134990570086608833748294659 (-1.13e-67% error)
70 212564178171463672420858478430244273/67661279360509603072431780067475929 (8.33e-69% error)
71 463534480895187976369779868172446660/147547607856009776231472393883246517 (-1.68e-69% error)
72 1139633139961839625160418214775137593/362756495072529155535376567833968963 (1.85e-70% error)
73 3882433900780706851851034512497859439/1235817093073597242837602097385153406 (-3.76e-71% error)
74 5022067040742546477011452727272997032/1598573588146126398372978665219122369 (1.3e-71% error)
75 13926567982265799805873939967043853503/4432964269365850039583559427823398144 (-1.1e-72% error)
76 60728338969805745700507212595448411044/19330430665609526556707216376512714945 (6.24e-74% error)
77 256839923861488782607902790348837497679/81754686931803956266412424933874257924 (-8.68e-76% error)
78 4170167120753626267426951858176848373908/1327405421574472826819306015318500841729 (5.31e-77% error)
79 4427007044615115050034854648525685871587/1409160108506276783085718440252375099653 (-3.11e-79% error)
80 716918301303787149323038550270812273699415/228202182891085034903619974895950891885862 (4.18e-83% error)
81 32265750565715036834586769616835078002345262/10270507390207332847445984588758042509963443 (-8.89e-85% error)
82 32982668867018823983909808167105890276044677/10498709573098417882349604563653993401849305 (3.83e-86% error)
83 757884465640129164480602549293164664075328156/241242117998372526259137284989145897350648153 (-1.17e-87% error)
84 790867134507147988464512357460270554351372833/251740827571470944141486889552799890752497458 (4.76e-88% error)
85 2339618734654425141409627264213705772778073822/744723773141314414542111064094745678855643069 (-5.7e-89% error)
86 5470104603815998271283766885887682099907520477/1741188373854099773225709017742291248463783596 (2.01e-89% error)
87 7809723338470423412693394150101387872685594299/2485912146995414187767820081837036927319426665 (-3.01e-90% error)
88 36708997957697691922057343486293233590649897673/11684836961835756524296989345090438957741490256 (4.3e-91% error)
89 44518721296168115334750737636394621463335491972/14170749108831170712064809426927475885060916921 (-1.74e-91% error)
90 125746440550033922591558818759082476517320881617/40026335179498097948426608198945390727863324098 (2.49e-93% error)
91 3062433294496982257532162387854374057879036650780/974802793416785521474303406201616853353780695273 (-7.52e-95% error)
92 3188179735047016180123721206613456534396357532397/1014829128596283619422730014400562244081644019371 (2.59e-95% error)
93 9438792764591014617779604801081287126671751715574/3004461050609352760319763435002741341517068734015 (-6.89e-96% error)
94 12626972499638030797903326007694743661068109247971/4019290179205636379742493449403303585598712753386 (1.4e-96% error)
95 47319710263505107011489582824165518109876079459487/15062331588226261899547243783212652098313206994173 (-2.57e-97% error)
96 59946682763143137809392908831860261770944188707458/19081621767431898279289737232615955683911919747559 (9.11e-98% error)
97 167213075789791382630275400487886041651764456874403/53225575123090058458126718248444563466137046489291 (-7.33e-99% error)
98 728798985922308668330494510783404428378002016205070/231983922259792132111796610226394209548460105704723 (7.72e-100% error)
99 1624811047634408719291264422054694898407768489284543/517193419642674322681719938701232982563057257898737 (-6.16e-101% error)
100 8852854224094352264786816621056878920416844462627785/2817951020473163745520396303732559122363746395198408 (6.99e-102% error)
101 10477665271728760984078081043111573818824612951912328/3335144440115838068202116242433792104926803653097145 (-3.65e-102% error)
102 19330519495823113248864897664168452739241457414540113/6153095460589001813722512546166351227290550048295553 (1.22e-102% error)
103 29808184767551874232942978707280026558066070366452441/9488239900704839881924628788600143332217353701392698 (-4.88e-103% error)
104 49138704263374987481807876371448479297307527780992554/15641335361293841695647141334766494559507903749688251 (1.86e-103% error)
105 78946889030926861714750855078728505855373598147444995/25129575261998681577571770123366637891725257451080949 (-6.88e-104% error)
106 128085593294301849196558731450176985152681125928437549/40770910623292523273218911458133132451233161200769200 (2.88e-104% error)
107 207032482325228710911309586528905491008054724075882544/65900485885291204850790681581499770342958418651850149 (-8.45e-105% error)
108 542150557944759271019177904507987967168790574080202637/172571882393874932974800274621132673137149998504469498 (3.47e-106% error)
109 5086387503828062150083910727100797195527169890797706277/1619047427430165601623993153171693828577308405192075631 (-1.05e-107% error)
110 15801313069428945721270910085810379553750300246473321468/5029714164684371737846779734136214158869075214080696391 (1.74e-108% error)
111 20887700573257007871354820812911176749277470137271027745/6648761592114537339470772887307907987446383619272772022 (-1.25e-108% error)
112 36689013642685953592625730898721556303027770383744349213/11678475756798909077317552621444122146315458833353468413 (4.22e-110% error)
113 607911918856232265353366515192456077597721796277180615153/193504373700897082576551614830413862328493724952928266630 (-2.06e-111% error)
114 644600932498918218945992246091177633900749566660924964366/205182849457695991653869167451857984474809183786281735043 (4.57e-112% error)
115 3186315648851905141137335499557166613200720062920880472617/1014235771531681049192028284637845800227730460098055206802 (-2.36e-113% error)
116 10203547879054633642357998744762677473502909755423566382217/3247890164052739139229954021365395385158000564080447355449 (6.77e-114% error)
117 13389863527906538783495334244319844086703629818344446854834/4262125935584420188421982306003241185385731024178502562251 (-4.56e-115% error)
118 157492046686026560260806675432280962427242837757212481785391/50131275455481361211871759387401048424401041830043975540210 (1.22e-116% error)
119 485866003585986219565915360541162731368432143089981892211007/154655952302028503824037260468206386458588856514310429182881 (-6.49e-118% error)
120 3072688068201943877656298838679257350637835696297103835051433/978066989267652384156095322196639367175934180915906550637496 (1.19e-119% error)
121 25067370549201537240816306069975221536471117713466812572622471/7979191866443247577072799838041321323866062303841562834282849 (-9.51e-121% error)
122 28140058617403481118472604908654478887108953409763916407673904/8957258855710899961228895160237960691041996484757469384920345 (4.48e-121% error)
123 53207429166605018359288910978629700423580071123230728980296375/16936450722154147538301694998279282014908058788599032219203194 (-2.11e-121% error)
124 81347487784008499477761515887284179310689024532994645387970279/25893709577865047499530590158517242705950055273356501604123539 (1.67e-122% error)
125 703987331438673014181381038076903134909092267387187892084058607/224086127345074527534546416266417223662508500975451045052191506 (-5.68e-124% error)
126 2193309482100027542021904630117993584037965826694558321640146100/698152091613088630103169838957768913693475558199709636760698057 (7.17e-125% error)
127 5090606295638728098225190298312890302985023920776304535364350807/1620390310571251787740886094181955051049459617374870318573587620 (-1.67e-125% error)
128 7283915777738755640247094928430883887022989747470862857004496907/2318542402184340417844055933139723964742935175574579955334285677 (9.92e-126% error)
129 12374522073377483738472285226743774190008013668247167392368847714/3938932712755592205584942027321679015792394792949450273907873297 (-1.03e-126% error)
130 69156526144626174332608521062149754837063058088706699818848735477/22013205965962301445768766069748119043704909140321831324873652162 (1.21e-127% error)
131 81531048218003658071080806288893529027071071756953867211217583191/25952138678717893651353708097069798059497303933271281598781525459 (-5.45e-128% error)
132 150687574362629832403689327351043283864134129845660567030066318668/47965344644680195097122474166817917103202213073593112923655177621 (2.58e-128% error)
133 232218622580633490474770133639936812891205201602614434241283901859/73917483323398088748476182263887715162699517006864394522436703080 (-2.38e-129% error)
134 1776217932427064265727080262830600974102570541063961606719053631681/565387727908466816336455750014031923242098832121643874580712099181 (9.32e-132% error)
135 58847410392673754259468418807049768958276033056713347455970053747332/18731712504302803027851515932726941182151960977021112255685935976053 (-1.2e-133% error)
136 119471038717774572784663917876930138890654636654490656518659161126345/38028812736514072872039487615467914287546020786163868385952584051287 (2.07e-134% error)
137 297789487828222899828796254560910046739585306365694660493288376000022/94789337977330948771930491163662769757244002549348849027591104078627 (-7.02e-135% error)
138 417260526545997472613460172437840185630239943020185317011947537126367/132818150713845021643969978779130684044790023335512717413543688129914 (9.2e-136% error)
139 2384092120558210262896097116750110974890785021466621245553026061631857/758880091546556056991780385059316189981194119226912436095309544728197 (-7.26e-137% error)
140 5185444767662417998405654405938062135411809985953427808117999660390081/1650578333806957135627530748897763064007178261789337589604162777586308 (7.21e-138% error)
141 23125871191207882256518714740502359516538024965280332478025024703192181/7361193426774384599501903380650368446009907166384262794511960655073429 (-1.02e-138% error)
142 28311315958870300254924369146440421651949834951233760286143024363582262/9011771760581341735129434129548131510017085428173600384116123432659737 (4.84e-139% error)
143 51437187150078182511443083886942781168487859916514092764168049066774443/16372965187355726334631337510198499956026992594557863178628084087733166 (-1.94e-139% error)
144 79748503108948482766367453033383202820437694867747853050311073430356705/25384736947937068069760771639746631466044078022731463562744207520392903 (4.69e-140% error)
145 210934193367975148044177989953709186809363249652009798864790195927487853/67142439083229862474152880789691762888115148640020790304116499128518972 (-1.17e-140% error)
146 290682696476923630810545442987092389629800944519757651915101269357844558/92527176031166930543913652429438394354159226662752253866860706648911875 (4.35e-141% error)
147 501616889844898778854723432940801576439164194171767450779891465285332411/159669615114396793018066533219130157242274375302773044170977205777430847 (-2.41e-141% error)
148 792299586321822409665268875927893966068965138691525102694992734643176969/252196791145563723561980185648568551596433601965525298037837912426342722 (6.93e-143% error)
149 17932207788924991791490638703354468829956397245385319710069731627435225729/5707999020316798711381630617487638292363813618544329601003411279156970731 (-1.7e-145% error)
150 323572039786971674656496765536308332905284115555627279883950162028477240091/102996179156847940528431331300426057814145078735763458116099240937251815880 (5.84e-148% error)
151 5195084844380471786295438887284287795314502246135421797853272324083071067185/1653646865529883847166282931424304563318685073390759659458591266275186024811 (-3.13e-150% error)
152 57469505327972161323906324525663474081364808823045267056269945726942258979126/18293111699985570259357543576967776254319680886034119712160603169964298088801 (1.74e-151% error)
153 62664590172352633110201763412947761876679311069180688854123218051025330046311/19946758565515454106523826508392080817638365959424879371619194436239484113612 (-1e-151% error)
154 120134095500324794434108087938611235958044119892225955910393163777967589025437/38239870265501024365881370085359857071958046845458999083779797606203782202413 (3.06e-152% error)
155 182798685672677427544309851351558997834723430961406644764516381828992919071748/58186628831016478472405196593751937889596412804883878455398992042443266316025 (-1.43e-152% error)
156 302932781173002221978417939290170233792767550853632600674909545606960508097185/96426499096517502838286566679111794961554459650342877539178789648647048518438 (3.49e-153% error)
157 788664248018681871501145729931899465420258532668671846114335473042913935266118/251039627024051484148978329951975527812705332105569633533756571339737363352901 (-6.4e-154% error)
158 1880261277210365964980709399153969164633284616190976292903580491692788378629421/598505753144620471136243226583062850586965123861482144606691932328121775224240 (2.55e-155% error)
159 19591277020122341521308239721471591111753104694578434775150140389970797721560328/6236097158470256195511410595782604033682356570720391079600675894620955115595301 (-1.25e-156% error)
160 21471538297332707486288949120625560276386389310769411068053720881663586100189749/6834602911614876666647653822365666884269321694581873224207367826949076890819541 (1.09e-156% error)
161 41062815317455049007597188842097151388139494005347845843203861271634383821750077/13070700070085132862159064418148270917951678265302264303808043721570032006414842 (-2.68e-158% error)
162 883790659963888736645829914804665739427315763423074173775334807585985646356941366/281319304383402666771988006603479356161254565265929423604176285979919749025531223 (3.62e-160% error)
163 2692434795209121258945086933256094369670086784274570367169208284029591322892574175/857028613220293133178123084228586339401715374063090535116336901661329279083008511 (-5.32e-161% error)
164 6268660250382131254536003781316854478767489331972214908113751375645168292142089716/1995376530823988933128234175060652034964685313392110493836850089302578307191548245 (5.3e-162% error)
165 27767075796737646277089102058523512284740044112163429999624213786610264491460933039/8838534736516248865691059784471194479260456627631532510463737258871642507849201491 (-3.65e-163% error)
166 89569887640595070085803309956887391332987621668462504906986392735475961766524888833/28510980740372735530201413528474235472746055196286708025228061865917505830739152718 (3.14e-164% error)
167 296476738718522856534499031929185686283702909117550944720583391993038149791035599538/94371476957634455456295300369893900897498622216491656586147922856624160000066659645 (-5.73e-165% error)
168 386046626359117926620302341886073077616690530786013449627569784728514111557560488371/122882457698007190986496713898368136370244677412778364611375984722541665830805812363 (2.89e-165% error)
169 682523365077640783154801373815258763900393439903564394348153176721552261348596087909/217253934655641646442792014268262037267743299629270021197523907579165825830872472008 (-8.52e-166% error)
170 1068569991436758709775103715701331841517083970689577843975722961450066372906156576280/340136392353648837429288728166630173637987977042048385808899892301707491661678284371 (5.02e-166% error)
171 1751093356514399492929905089516590605417477410593142238323876138171618634254752664189/557390327009290483872080742434892210905731276671318407006423799880873317492550756379 (-2.58e-167% error)
172 20330596913095153132004059700383828501109335487214142465538360481337871349708435882359/6471429989455844160022176894950444493601032020426550862879561690991313984079736604540 (1.97e-168% error)
173 22081690269609552624933964789900419106526812897807284703862236619509489983963188546548/7028820316465134643894257637385336704506763297097869269885985490872187301572287360919 (-2.27e-169% error)
174 174902428800362021506541813229686762246797025771865135392574016817904301237450755708195/55673172204711786667281980356647801425148375100111635752081460127096625095085748130973 (2.81e-170% error)
175 196984119069971574131475778019587181353323838669672420096436253437413791221413944254743/62701992521176921311176237994033138129655138397209505021967445617968812396658035491892 (-5.75e-172% error)
176 8645219548809139709160000268071935560439722088567779199539332914626697323758250358662144/2751858850615319403047860214100072741000319326180120351696681621699755558151381274282329 (5.05e-174% error)
177 17487423216688250992451476314163458302232768015805230819175102082690808438737914661579031/5566419693751815727406896666194178620130293790757450208415330689017479928699420584056550 (-1.48e-174% error)
178 26132642765497390701611476582235393862672490104373010018714434997317505762496165020241175/8318278544367135130454756880294251361130613116937570560112012310717235486850801858338879 (6.8e-175% error)
179 43620065982185641694062952896398852164905258120178240837889537080008314201234079681820206/13884698238118950857861653546488429981260906907695020768527342999734715415550222442395429 (-1.86e-175% error)
180 113372774729868674089737382375033098192483006344729491694493509157334134164964324383881587/36087675020605036846178063973271111323652426932327612097166698310186666317951246743129737 (1.36e-176% error)
181 610483939631529012142749864771564343127320289843825699310357082866678985026055701601228141/194323073341144135088751973412843986599523041569333081254360834550668047005306456158044114 (-6.59e-178% error)
182 1944824593624455710517986976689726127574443875876206589625564757757371089243131429187566010/619056895044037442112433984211803071122221551640326855860249201962190807333870615217262079 (1.72e-178% error)
183 2555308533255984722660736841461290470701764165720032288935921840624050074269187130788794151/813379968385181577201185957624647057721744593209659937114610036512858854339177071375306193 (-2.63e-179% error)
184 12166058726648394601160934342534888010381500538756335745369252120253571386319879952342742614/3872576768584763750917177814710391302009199924478966604318689348013626224690578900718486851 (5.45e-180% error)
185 14721367259904379323821671183996178481083264704476368034305173960877621460589067083131536765/4685956736969945328118363772335038359730944517688626541433299384526485079029755972093793044 (-5.75e-182% error)
186 1160432704999189981859251286694236809534876147487913042421172821068708045312267112436602610284/369377202252240499344149552056843383361022872304191836836116041341079462389011544724034344283 (2.47e-184% error)
187 2335586777258284343042324244572469797550835559680302452876650816098293712085123291956336757333/743440361241450944016417467886021805081776689126072300213665382066685409857052845420162481610 (-1.17e-184% error)
188 3496019482257474324901575531266706607085711707168215495297823637167001757397390404392939367617/1112817563493691443360567019942865188442799561430264137049781423407764872246064390144196825893 (3.67e-186% error)
189 75751995904665245165975410401173308546350781410212827854130947196605330617430321784208063477290/24112609194608971254588324886686190762380567479161619178259075273629747727024405038448295825363 (-5.45e-188% error)
190 230752007196253209822827806734786632246138055937806699057690665226982993609688355757017129799487/73450645147320605207125541680001437475584501998915121671827007244297008053319279505489084301982 (1.94e-189% error)
191 2152520060670944133571425671014252998761593284850473119373346934239452273104625523597362231672673/685168415520494418118718200006699128042641085469397714224702140472302820206897920587850054543201 (-5.08e-191% error)
192 8840832249880029744108530490791798627292511195339699176551078402184792086028190450146466056490179/2814124307229298277681998341706797949646148843876505978570635569133508288880910961856889302474786 (1.09e-192% error)
193 99401674809351271318765261069724037898979216433587164061435209358272165219414720475208488853064642/31640535795042775472620699958781476574150278368110963478501693400940893997896918501013632381765847 (-3.57e-194% error)
194 207644181868582572381639052630239874425250944062514027299421497118729122524857631400563443762619463/66095195897314849222923398259269751097946705580098432935574022371015296284674747963884154066006480 (1.21e-194% error)
195 307045856677933843700404313699963912324230160496101191360856706477001287744272351875771932615684105/97735731692357624695544098218051227672096983948209396414075715771956190282571666464897786447772327 (-3.38e-195% error)
196 821735895224450259782447680030167699073711265054716410021134910072731698013402335152107308993987673/261566659282030098614011594695372206442140673476517225763725453914927676849818080893679726961551134 (5.35e-196% error)
197 1950517647126834363265299673760299310471652690605534011403126526622464683771077022179986550603659451/620869050256417821923567287608795640556378330901243847941526623601811543982207828252257240370874595 (-8.05e-197% error)
198 4722771189478118986313047027550766320017016646265784432827387963317661065555556379512080410201306575/1503304759794865742461146169912963487554897335279004921646778701118550764814233737398194207703300324 (2.66e-197% error)
199 6673288836604953349578346701311065630488669336871318444230514489940125749326633401692066960804966026/2124173810051283564384713457521759128111275666180248769588305324720362308796441565650451448074174919 (-4.71e-198% error)
200 31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (0.0% error)
Content source: james-prior/cohpy
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