Properties

Label 169.2.i.a.3.12
Level 169169
Weight 22
Character 169.3
Analytic conductor 1.3491.349
Analytic rank 00
Dimension 336336
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,2,Mod(3,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(78))
 
chi = DirichletCharacter(H, H._module([62]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 169=132 169 = 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 169.i (of order 3939, degree 2424, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.349471794161.34947179416
Analytic rank: 00
Dimension: 336336
Relative dimension: 1414 over Q(ζ39)\Q(\zeta_{39})
Twist minimal: yes
Sato-Tate group: SU(2)[C39]\mathrm{SU}(2)[C_{39}]

Embedding invariants

Embedding label 3.12
Character χ\chi == 169.3
Dual form 169.2.i.a.113.12

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.430661.07507i)q2+(0.532083+2.60631i)q3+(0.3345791.15510i)q4+(0.6579000.345292i)q5+(2.04075+4.30078i)q6+(2.44433+0.397242i)q7+(0.506036+1.33431i)q8+(3.749821.59765i)q9+(1.31245+0.213294i)q10+(0.9865780.420341i)q11+(2.83253+1.48663i)q12+(2.641772.45378i)q13+(3.924072.05951i)q14+(1.250001.53097i)q15+(4.19126+2.65040i)q16+(0.9310360.151308i)q17+(7.08231+1.74563i)q18+(2.059423.56703i)q19+(0.618967+0.644413i)q20+(2.33592+6.15931i)q21+(0.9595621.66201i)q22+(3.923106.79501i)q23+(3.74687+0.608926i)q24+(2.526723.66058i)q25+(6.417480.670442i)q26+(1.625902.35552i)q27+(1.276672.69054i)q28+(1.29617+0.974010i)q29+(0.1424213.53414i)q30+(1.92189+2.78434i)q31+(6.000830.484437i)q32+(0.570600+2.79499i)q33+(1.49467+0.784462i)q34+(1.470961.10535i)q35+(3.10005+3.79688i)q36+(5.74077+0.463443i)q37+(0.8884757.31725i)q38+(7.800975.57966i)q39+(0.1278051.05257i)q40+(0.352113+1.72476i)q41+(3.27980+11.3232i)q42+(9.841480.794487i)q43+(0.1554491.28023i)q44+(1.91535+2.34587i)q45+(12.91785.50375i)q46+(0.5934930.146283i)q47+(9.13786+9.51352i)q48+(0.8228260.274700i)q49+(7.550282.52065i)q50+(0.8897452.34606i)q51+(3.71825+2.23053i)q52+(3.97684+10.4861i)q53+(0.2062455.11793i)q54+(0.7942100.0641152i)q55+(0.706874+3.46250i)q56+(8.20101+7.26546i)q57+(0.807253+2.78696i)q58+(10.7661+6.80809i)q59+(1.350201.95610i)q60+(2.21118+2.70820i)q61+(0.243792+6.04963i)q62+(8.531125.39475i)q63+(0.6406940.567606i)q64+(0.890746+2.52653i)q65+(3.82115+3.38525i)q66+(3.1177410.7637i)q67+(0.486282+1.02482i)q68+(19.79736.60932i)q693.29278q70+(4.59941+1.53551i)q71+(0.2342105.81187i)q72+(1.19674+9.85605i)q73+(8.711355.50872i)q74+(10.88504.63769i)q75+(3.431243.57230i)q76+(2.578490.635542i)q77+(5.1620116.3692i)q78+(7.82221+1.92800i)q79+(1.842273.19091i)q80+(3.196473.32787i)q81+(1.35049+2.84610i)q82+(1.36646+1.21058i)q83+(6.33308+4.75900i)q84+(0.560283+0.421025i)q85+(13.225711.7170i)q86+(1.848903.89648i)q87+(1.06011+1.10369i)q88+(6.1865310.7154i)q89+(5.26220+1.29702i)q90+(5.482607.04727i)q91+(9.16151+2.25811i)q92+(6.234266.49055i)q93+(1.00635+0.428767i)q94+(2.58656+1.63564i)q95+(1.93034+15.8978i)q96+(0.2810166.97335i)q97+(1.47251+0.491596i)q984.37104q99+O(q100)q+(1.43066 - 1.07507i) q^{2} +(-0.532083 + 2.60631i) q^{3} +(0.334579 - 1.15510i) q^{4} +(-0.657900 - 0.345292i) q^{5} +(2.04075 + 4.30078i) q^{6} +(2.44433 + 0.397242i) q^{7} +(0.506036 + 1.33431i) q^{8} +(-3.74982 - 1.59765i) q^{9} +(-1.31245 + 0.213294i) q^{10} +(0.986578 - 0.420341i) q^{11} +(2.83253 + 1.48663i) q^{12} +(-2.64177 - 2.45378i) q^{13} +(3.92407 - 2.05951i) q^{14} +(1.25000 - 1.53097i) q^{15} +(4.19126 + 2.65040i) q^{16} +(-0.931036 - 0.151308i) q^{17} +(-7.08231 + 1.74563i) q^{18} +(2.05942 - 3.56703i) q^{19} +(-0.618967 + 0.644413i) q^{20} +(-2.33592 + 6.15931i) q^{21} +(0.959562 - 1.66201i) q^{22} +(-3.92310 - 6.79501i) q^{23} +(-3.74687 + 0.608926i) q^{24} +(-2.52672 - 3.66058i) q^{25} +(-6.41748 - 0.670442i) q^{26} +(1.62590 - 2.35552i) q^{27} +(1.27667 - 2.69054i) q^{28} +(-1.29617 + 0.974010i) q^{29} +(0.142421 - 3.53414i) q^{30} +(-1.92189 + 2.78434i) q^{31} +(6.00083 - 0.484437i) q^{32} +(0.570600 + 2.79499i) q^{33} +(-1.49467 + 0.784462i) q^{34} +(-1.47096 - 1.10535i) q^{35} +(-3.10005 + 3.79688i) q^{36} +(5.74077 + 0.463443i) q^{37} +(-0.888475 - 7.31725i) q^{38} +(7.80097 - 5.57966i) q^{39} +(0.127805 - 1.05257i) q^{40} +(-0.352113 + 1.72476i) q^{41} +(3.27980 + 11.3232i) q^{42} +(9.84148 - 0.794487i) q^{43} +(-0.155449 - 1.28023i) q^{44} +(1.91535 + 2.34587i) q^{45} +(-12.9178 - 5.50375i) q^{46} +(-0.593493 - 0.146283i) q^{47} +(-9.13786 + 9.51352i) q^{48} +(-0.822826 - 0.274700i) q^{49} +(-7.55028 - 2.52065i) q^{50} +(0.889745 - 2.34606i) q^{51} +(-3.71825 + 2.23053i) q^{52} +(3.97684 + 10.4861i) q^{53} +(-0.206245 - 5.11793i) q^{54} +(-0.794210 - 0.0641152i) q^{55} +(0.706874 + 3.46250i) q^{56} +(8.20101 + 7.26546i) q^{57} +(-0.807253 + 2.78696i) q^{58} +(-10.7661 + 6.80809i) q^{59} +(-1.35020 - 1.95610i) q^{60} +(2.21118 + 2.70820i) q^{61} +(0.243792 + 6.04963i) q^{62} +(-8.53112 - 5.39475i) q^{63} +(0.640694 - 0.567606i) q^{64} +(0.890746 + 2.52653i) q^{65} +(3.82115 + 3.38525i) q^{66} +(-3.11774 - 10.7637i) q^{67} +(-0.486282 + 1.02482i) q^{68} +(19.7973 - 6.60932i) q^{69} -3.29278 q^{70} +(-4.59941 + 1.53551i) q^{71} +(0.234210 - 5.81187i) q^{72} +(-1.19674 + 9.85605i) q^{73} +(8.71135 - 5.50872i) q^{74} +(10.8850 - 4.63769i) q^{75} +(-3.43124 - 3.57230i) q^{76} +(2.57849 - 0.635542i) q^{77} +(5.16201 - 16.3692i) q^{78} +(7.82221 + 1.92800i) q^{79} +(-1.84227 - 3.19091i) q^{80} +(-3.19647 - 3.32787i) q^{81} +(1.35049 + 2.84610i) q^{82} +(-1.36646 + 1.21058i) q^{83} +(6.33308 + 4.75900i) q^{84} +(0.560283 + 0.421025i) q^{85} +(13.2257 - 11.7170i) q^{86} +(-1.84890 - 3.89648i) q^{87} +(1.06011 + 1.10369i) q^{88} +(-6.18653 - 10.7154i) q^{89} +(5.26220 + 1.29702i) q^{90} +(-5.48260 - 7.04727i) q^{91} +(-9.16151 + 2.25811i) q^{92} +(-6.23426 - 6.49055i) q^{93} +(-1.00635 + 0.428767i) q^{94} +(-2.58656 + 1.63564i) q^{95} +(-1.93034 + 15.8978i) q^{96} +(0.281016 - 6.97335i) q^{97} +(-1.47251 + 0.491596i) q^{98} -4.37104 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 336q26q226q312q426q526q626q726q812q922q1026q1134q1213q1330q14+26q158q1624q17104q18+52q99+O(q100) 336 q - 26 q^{2} - 26 q^{3} - 12 q^{4} - 26 q^{5} - 26 q^{6} - 26 q^{7} - 26 q^{8} - 12 q^{9} - 22 q^{10} - 26 q^{11} - 34 q^{12} - 13 q^{13} - 30 q^{14} + 26 q^{15} - 8 q^{16} - 24 q^{17} - 104 q^{18}+ \cdots - 52 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/169Z)×\left(\mathbb{Z}/169\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(3139)e\left(\frac{31}{39}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.43066 1.07507i 1.01163 0.760192i 0.0406081 0.999175i 0.487070π-0.487070\pi
0.971024 + 0.238983i 0.0768141π0.0768141\pi
33 −0.532083 + 2.60631i −0.307198 + 1.50476i 0.474030 + 0.880509i 0.342799π0.342799\pi
−0.781228 + 0.624246i 0.785406π0.785406\pi
44 0.334579 1.15510i 0.167290 0.577551i
55 −0.657900 0.345292i −0.294222 0.154419i 0.311154 0.950360i 0.399285π-0.399285\pi
−0.605375 + 0.795940i 0.706977π0.706977\pi
66 2.04075 + 4.30078i 0.833132 + 1.75579i
77 2.44433 + 0.397242i 0.923868 + 0.150143i 0.603695 0.797216i 0.293695π-0.293695\pi
0.320174 + 0.947359i 0.396259π0.396259\pi
88 0.506036 + 1.33431i 0.178911 + 0.471749i
99 −3.74982 1.59765i −1.24994 0.532549i
1010 −1.31245 + 0.213294i −0.415032 + 0.0674493i
1111 0.986578 0.420341i 0.297464 0.126738i −0.238078 0.971246i 0.576517π-0.576517\pi
0.535542 + 0.844508i 0.320107π0.320107\pi
1212 2.83253 + 1.48663i 0.817681 + 0.429152i
1313 −2.64177 2.45378i −0.732695 0.680557i
1414 3.92407 2.05951i 1.04875 0.550428i
1515 1.25000 1.53097i 0.322748 0.395294i
1616 4.19126 + 2.65040i 1.04782 + 0.662599i
1717 −0.931036 0.151308i −0.225810 0.0366976i 0.0464536 0.998920i 0.485208π-0.485208\pi
−0.272263 + 0.962223i 0.587772π0.587772\pi
1818 −7.08231 + 1.74563i −1.66932 + 0.411450i
1919 2.05942 3.56703i 0.472464 0.818332i −0.527039 0.849841i 0.676698π-0.676698\pi
0.999503 + 0.0315087i 0.0100312π0.0100312\pi
2020 −0.618967 + 0.644413i −0.138405 + 0.144095i
2121 −2.33592 + 6.15931i −0.509739 + 1.34407i
2222 0.959562 1.66201i 0.204579 0.354342i
2323 −3.92310 6.79501i −0.818023 1.41686i −0.907137 0.420836i 0.861737π-0.861737\pi
0.0891139 0.996021i 0.471596π-0.471596\pi
2424 −3.74687 + 0.608926i −0.764827 + 0.124297i
2525 −2.52672 3.66058i −0.505344 0.732117i
2626 −6.41748 0.670442i −1.25857 0.131485i
2727 1.62590 2.35552i 0.312905 0.453321i
2828 1.27667 2.69054i 0.241269 0.508463i
2929 −1.29617 + 0.974010i −0.240693 + 0.180869i −0.714243 0.699898i 0.753229π-0.753229\pi
0.473550 + 0.880767i 0.342972π0.342972\pi
3030 0.142421 3.53414i 0.0260024 0.645243i
3131 −1.92189 + 2.78434i −0.345182 + 0.500082i −0.956671 0.291170i 0.905955π-0.905955\pi
0.611489 + 0.791253i 0.290571π0.290571\pi
3232 6.00083 0.484437i 1.06081 0.0856372i
3333 0.570600 + 2.79499i 0.0993288 + 0.486545i
3434 −1.49467 + 0.784462i −0.256333 + 0.134534i
3535 −1.47096 1.10535i −0.248637 0.186839i
3636 −3.10005 + 3.79688i −0.516676 + 0.632813i
3737 5.74077 + 0.463443i 0.943777 + 0.0761896i 0.542766 0.839884i 0.317377π-0.317377\pi
0.401011 + 0.916073i 0.368659π0.368659\pi
3838 −0.888475 7.31725i −0.144130 1.18701i
3939 7.80097 5.57966i 1.24915 0.893461i
4040 0.127805 1.05257i 0.0202078 0.166426i
4141 −0.352113 + 1.72476i −0.0549907 + 0.269363i −0.997985 0.0634457i 0.979791π-0.979791\pi
0.942995 + 0.332808i 0.107996π0.107996\pi
4242 3.27980 + 11.3232i 0.506084 + 1.74721i
4343 9.84148 0.794487i 1.50081 0.121158i 0.697443 0.716640i 0.254321π-0.254321\pi
0.803369 + 0.595482i 0.203039π0.203039\pi
4444 −0.155449 1.28023i −0.0234348 0.193003i
4545 1.91535 + 2.34587i 0.285523 + 0.349702i
4646 −12.9178 5.50375i −1.90462 0.811483i
4747 −0.593493 0.146283i −0.0865698 0.0213375i 0.195793 0.980645i 0.437272π-0.437272\pi
−0.282363 + 0.959308i 0.591118π0.591118\pi
4848 −9.13786 + 9.51352i −1.31894 + 1.37316i
4949 −0.822826 0.274700i −0.117547 0.0392428i
5050 −7.55028 2.52065i −1.06777 0.356474i
5151 0.889745 2.34606i 0.124589 0.328515i
5252 −3.71825 + 2.23053i −0.515628 + 0.309318i
5353 3.97684 + 10.4861i 0.546261 + 1.44037i 0.869442 + 0.494035i 0.164478π0.164478\pi
−0.323181 + 0.946337i 0.604752π0.604752\pi
5454 −0.206245 5.11793i −0.0280664 0.696461i
5555 −0.794210 0.0641152i −0.107091 0.00864530i
5656 0.706874 + 3.46250i 0.0944600 + 0.462696i
5757 8.20101 + 7.26546i 1.08625 + 0.962333i
5858 −0.807253 + 2.78696i −0.105998 + 0.365946i
5959 −10.7661 + 6.80809i −1.40163 + 0.886337i −0.999571 0.0292763i 0.990680π-0.990680\pi
−0.402059 + 0.915614i 0.631705π0.631705\pi
6060 −1.35020 1.95610i −0.174310 0.252532i
6161 2.21118 + 2.70820i 0.283112 + 0.346749i 0.896509 0.443025i 0.146095π-0.146095\pi
−0.613397 + 0.789775i 0.710197π0.710197\pi
6262 0.243792 + 6.04963i 0.0309616 + 0.768304i
6363 −8.53112 5.39475i −1.07482 0.679675i
6464 0.640694 0.567606i 0.0800868 0.0709507i
6565 0.890746 + 2.52653i 0.110483 + 0.313377i
6666 3.82115 + 3.38525i 0.470351 + 0.416695i
6767 −3.11774 10.7637i −0.380893 1.31500i −0.890655 0.454680i 0.849754π-0.849754\pi
0.509762 0.860315i 0.329733π-0.329733\pi
6868 −0.486282 + 1.02482i −0.0589703 + 0.124277i
6969 19.7973 6.60932i 2.38332 0.795669i
7070 −3.29278 −0.393562
7171 −4.59941 + 1.53551i −0.545849 + 0.182231i −0.576201 0.817308i 0.695465π-0.695465\pi
0.0303517 + 0.999539i 0.490337π0.490337\pi
7272 0.234210 5.81187i 0.0276019 0.684935i
7373 −1.19674 + 9.85605i −0.140068 + 1.15356i 0.737923 + 0.674885i 0.235807π0.235807\pi
−0.877991 + 0.478678i 0.841116π0.841116\pi
7474 8.71135 5.50872i 1.01267 0.640376i
7575 10.8850 4.63769i 1.25690 0.535514i
7676 −3.43124 3.57230i −0.393590 0.409771i
7777 2.57849 0.635542i 0.293847 0.0724267i
7878 5.16201 16.3692i 0.584483 1.85345i
7979 7.82221 + 1.92800i 0.880068 + 0.216917i 0.653362 0.757046i 0.273358π-0.273358\pi
0.226706 + 0.973963i 0.427204π0.427204\pi
8080 −1.84227 3.19091i −0.205972 0.356754i
8181 −3.19647 3.32787i −0.355163 0.369764i
8282 1.35049 + 2.84610i 0.149137 + 0.314299i
8383 −1.36646 + 1.21058i −0.149988 + 0.132878i −0.734780 0.678305i 0.762715π-0.762715\pi
0.584792 + 0.811183i 0.301176π0.301176\pi
8484 6.33308 + 4.75900i 0.690996 + 0.519250i
8585 0.560283 + 0.421025i 0.0607712 + 0.0456666i
8686 13.2257 11.7170i 1.42617 1.26347i
8787 −1.84890 3.89648i −0.198223 0.417747i
8888 1.06011 + 1.10369i 0.113008 + 0.117654i
8989 −6.18653 10.7154i −0.655770 1.13583i −0.981700 0.190434i 0.939011π-0.939011\pi
0.325930 0.945394i 0.394323π-0.394323\pi
9090 5.26220 + 1.29702i 0.554685 + 0.136718i
9191 −5.48260 7.04727i −0.574733 0.738755i
9292 −9.16151 + 2.25811i −0.955154 + 0.235424i
9393 −6.23426 6.49055i −0.646462 0.673039i
9494 −1.00635 + 0.428767i −0.103797 + 0.0442239i
9595 −2.58656 + 1.63564i −0.265376 + 0.167813i
9696 −1.93034 + 15.8978i −0.197015 + 1.62256i
9797 0.281016 6.97335i 0.0285329 0.708036i −0.920105 0.391672i 0.871897π-0.871897\pi
0.948638 0.316364i 0.102462π-0.102462\pi
9898 −1.47251 + 0.491596i −0.148746 + 0.0496587i
9999 −4.37104 −0.439306
100100 −5.07373 + 1.69386i −0.507373 + 0.169386i
101101 −8.05077 + 16.9666i −0.801082 + 1.68824i −0.0785457 + 0.996911i 0.525028π0.525028\pi
−0.722536 + 0.691333i 0.757024π0.757024\pi
102102 −1.24927 4.31297i −0.123696 0.427048i
103103 6.49381 + 5.75301i 0.639854 + 0.566861i 0.919426 0.393264i 0.128654π-0.128654\pi
−0.279572 + 0.960125i 0.590193π0.590193\pi
104104 1.93727 4.76663i 0.189965 0.467407i
105105 3.66356 3.24563i 0.357527 0.316742i
106106 16.9628 + 10.7266i 1.64757 + 1.04186i
107107 −0.564488 14.0076i −0.0545711 1.35417i −0.762089 0.647472i 0.775826π-0.775826\pi
0.707518 0.706695i 0.249815π-0.249815\pi
108108 −2.17688 2.66619i −0.209470 0.256554i
109109 6.29872 + 9.12528i 0.603308 + 0.874043i 0.999017 0.0443332i 0.0141163π-0.0141163\pi
−0.395709 + 0.918376i 0.629501π0.629501\pi
110110 −1.20518 + 0.762107i −0.114909 + 0.0726640i
111111 −4.26244 + 14.7157i −0.404573 + 1.39675i
112112 9.19197 + 8.14337i 0.868560 + 0.769477i
113113 −3.21345 15.7405i −0.302296 1.48075i −0.792894 0.609360i 0.791427π-0.791427\pi
0.490598 0.871386i 0.336779π-0.336779\pi
114114 19.5438 + 1.57774i 1.83044 + 0.147769i
115115 0.234742 + 5.82505i 0.0218898 + 0.543189i
116116 0.691408 + 1.82309i 0.0641957 + 0.169270i
117117 5.98587 + 13.4219i 0.553393 + 1.24085i
118118 −8.08351 + 21.3145i −0.744147 + 1.96216i
119119 −2.21565 0.739693i −0.203108 0.0678075i
120120 2.67532 + 0.893154i 0.244223 + 0.0815335i
121121 −6.82332 + 7.10383i −0.620302 + 0.645803i
122122 6.07496 + 1.49734i 0.550001 + 0.135563i
123123 −4.30791 1.83543i −0.388432 0.165495i
124124 2.57317 + 3.15156i 0.231078 + 0.283019i
125125 0.846153 + 6.96870i 0.0756823 + 0.623299i
126126 −18.0049 + 1.45351i −1.60401 + 0.129489i
127127 −4.50920 15.5675i −0.400126 1.38140i −0.867544 0.497360i 0.834303π-0.834303\pi
0.467418 0.884037i 0.345184π-0.345184\pi
128128 −2.10205 + 10.2965i −0.185797 + 0.910093i
129129 −3.16580 + 26.0727i −0.278733 + 2.29557i
130130 3.99056 + 2.65699i 0.349995 + 0.233034i
131131 −0.484839 3.99301i −0.0423605 0.348870i −0.998443 0.0557740i 0.982237π-0.982237\pi
0.956083 0.293096i 0.0946857π-0.0946857\pi
132132 3.41940 + 0.276043i 0.297621 + 0.0240264i
133133 6.45088 7.90089i 0.559362 0.685094i
134134 −16.0322 12.0474i −1.38497 1.04074i
135135 −1.88302 + 0.988287i −0.162065 + 0.0850582i
136136 −0.269246 1.31886i −0.0230877 0.113091i
137137 −12.9976 + 1.04928i −1.11046 + 0.0896456i −0.622057 0.782972i 0.713703π-0.713703\pi
−0.488404 + 0.872618i 0.662421π0.662421\pi
138138 21.2178 30.7393i 1.80618 2.61670i
139139 −0.465818 + 11.5592i −0.0395102 + 0.980435i 0.850914 + 0.525304i 0.176048π0.176048\pi
−0.890425 + 0.455131i 0.849593π0.849593\pi
140140 −1.76895 + 1.32928i −0.149503 + 0.112344i
141141 0.697046 1.46899i 0.0587018 0.123712i
142142 −4.92942 + 7.14150i −0.413668 + 0.599301i
143143 −3.63774 1.31040i −0.304203 0.109581i
144144 −11.4821 16.6347i −0.956839 1.38622i
145145 1.18907 0.193243i 0.0987469 0.0160479i
146146 8.88384 + 15.3873i 0.735232 + 1.27346i
147147 1.15376 1.99838i 0.0951609 0.164823i
148148 2.45607 6.47611i 0.201887 0.532333i
149149 3.81917 3.97618i 0.312879 0.325741i −0.546132 0.837699i 0.683900π-0.683900\pi
0.859010 + 0.511958i 0.171080π0.171080\pi
150150 10.5870 18.3372i 0.864424 1.49723i
151151 −1.78649 + 0.440330i −0.145382 + 0.0358336i −0.311335 0.950300i 0.600776π-0.600776\pi
0.165953 + 0.986134i 0.446930π0.446930\pi
152152 5.80165 + 0.942860i 0.470576 + 0.0764760i
153153 3.24948 + 2.05485i 0.262705 + 0.166124i
154154 3.00570 3.68132i 0.242206 0.296649i
155155 2.22582 1.16820i 0.178782 0.0938323i
156156 −3.83503 10.8777i −0.307048 0.870917i
157157 −13.9445 7.31865i −1.11289 0.584092i −0.194954 0.980812i 0.562456π-0.562456\pi
−0.917939 + 0.396721i 0.870148π0.870148\pi
158158 13.2637 5.65113i 1.05520 0.449580i
159159 −29.4460 + 4.78544i −2.33522 + 0.379510i
160160 −4.11522 1.75333i −0.325337 0.138613i
161161 −6.89008 18.1676i −0.543014 1.43181i
162162 −8.15078 1.32463i −0.640386 0.104073i
163163 7.09054 + 14.9430i 0.555374 + 1.17043i 0.965981 + 0.258613i 0.0832655π0.0832655\pi
−0.410607 + 0.911812i 0.634683π0.634683\pi
164164 1.87446 + 0.983795i 0.146371 + 0.0768215i
165165 0.589690 2.03584i 0.0459073 0.158490i
166166 −0.653482 + 3.20097i −0.0507201 + 0.248443i
167167 0.513690 0.386013i 0.0397505 0.0298706i −0.580681 0.814131i 0.697214π-0.697214\pi
0.620432 + 0.784260i 0.286957π0.286957\pi
168168 −9.40047 −0.725262
169169 0.957889 + 12.9647i 0.0736837 + 0.997282i
170170 1.25421 0.0961935
171171 −13.4213 + 10.0855i −1.02635 + 0.771255i
172172 2.37504 11.6337i 0.181095 0.887064i
173173 0.599250 2.06885i 0.0455602 0.157292i −0.934513 0.355929i 0.884164π-0.884164\pi
0.980073 + 0.198637i 0.0636516π0.0636516\pi
174174 −6.83417 3.58685i −0.518097 0.271918i
175175 −4.72199 9.95138i −0.356949 0.752254i
176176 5.24908 + 0.853058i 0.395664 + 0.0643017i
177177 −12.0155 31.6824i −0.903143 2.38139i
178178 −20.3707 8.67913i −1.52685 0.650528i
179179 25.6314 4.16551i 1.91578 0.311345i 0.919189 0.393817i 0.128846π-0.128846\pi
0.996593 + 0.0824726i 0.0262817π0.0262817\pi
180180 3.35056 1.42754i 0.249736 0.106402i
181181 13.0249 + 6.83600i 0.968133 + 0.508116i 0.873197 0.487368i 0.162043π-0.162043\pi
0.0949366 + 0.995483i 0.469735π0.469735\pi
182182 −15.4201 4.18807i −1.14301 0.310440i
183183 −8.23494 + 4.32203i −0.608744 + 0.319494i
184184 7.08140 8.67313i 0.522047 0.639392i
185185 −3.61683 2.28714i −0.265915 0.168154i
186186 −15.8969 2.58350i −1.16562 0.189432i
187187 −0.982141 + 0.242076i −0.0718213 + 0.0177023i
188188 −0.367542 + 0.636601i −0.0268057 + 0.0464289i
189189 4.90994 5.11179i 0.357146 0.371828i
190190 −1.94206 + 5.12080i −0.140892 + 0.371502i
191191 −2.01270 + 3.48610i −0.145634 + 0.252245i −0.929609 0.368547i 0.879855π-0.879855\pi
0.783975 + 0.620792i 0.213189π0.213189\pi
192192 1.13846 + 1.97186i 0.0821610 + 0.142307i
193193 19.0658 3.09850i 1.37239 0.223035i 0.570888 0.821028i 0.306599π-0.306599\pi
0.801501 + 0.597993i 0.204035π0.204035\pi
194194 −7.09483 10.2786i −0.509379 0.737963i
195195 −7.05887 + 0.977242i −0.505496 + 0.0699818i
196196 −0.592606 + 0.858538i −0.0423290 + 0.0613242i
197197 −10.5112 + 22.1518i −0.748890 + 1.57825i 0.0654434 + 0.997856i 0.479154π0.479154\pi
−0.814334 + 0.580397i 0.802897π0.802897\pi
198198 −6.25349 + 4.69919i −0.444416 + 0.333957i
199199 −0.0284068 + 0.704908i −0.00201371 + 0.0499696i −0.999883 0.0152686i 0.995140π-0.995140\pi
0.997870 + 0.0652381i 0.0207807π0.0207807\pi
200200 3.60573 5.22380i 0.254964 0.369379i
201201 29.7125 2.39864i 2.09576 0.169187i
202202 6.72245 + 32.9287i 0.472990 + 2.31686i
203203 −3.55519 + 1.86591i −0.249525 + 0.130961i
204204 −2.41225 1.81269i −0.168891 0.126914i
205205 0.827202 1.01314i 0.0577743 0.0707607i
206206 15.4754 + 1.24930i 1.07822 + 0.0870429i
207207 3.85488 + 31.7478i 0.267932 + 2.20662i
208208 −4.56886 17.2862i −0.316793 1.19858i
209209 0.532412 4.38481i 0.0368277 0.303304i
210210 1.75203 8.58201i 0.120902 0.592215i
211211 0.619875 + 2.14006i 0.0426740 + 0.147328i 0.979026 0.203734i 0.0653079π-0.0653079\pi
−0.936352 + 0.351062i 0.885821π0.885821\pi
212212 13.4430 1.08523i 0.923271 0.0745342i
213213 −1.55475 12.8045i −0.106530 0.877351i
214214 −15.8668 19.4333i −1.08463 1.32843i
215215 −6.74904 2.87550i −0.460281 0.196107i
216216 3.96575 + 0.977471i 0.269835 + 0.0665085i
217217 −5.80379 + 6.04238i −0.393987 + 0.410184i
218218 18.8217 + 6.28361i 1.27477 + 0.425580i
219219 −25.0512 8.36331i −1.69280 0.565140i
220220 −0.339786 + 0.895941i −0.0229083 + 0.0604043i
221221 2.08831 + 2.68428i 0.140475 + 0.180564i
222222 9.72230 + 25.6356i 0.652518 + 1.72055i
223223 0.208686 + 5.17850i 0.0139747 + 0.346778i 0.991017 + 0.133734i 0.0426967π0.0426967\pi
−0.977043 + 0.213044i 0.931662π0.931662\pi
224224 14.8604 + 1.19966i 0.992904 + 0.0801555i
225225 3.62641 + 17.7633i 0.241760 + 1.18422i
226226 −21.5196 19.0647i −1.43146 1.26817i
227227 −0.588998 + 2.03346i −0.0390932 + 0.134965i −0.977691 0.210047i 0.932638π-0.932638\pi
0.938598 + 0.345013i 0.112125π0.112125\pi
228228 11.1362 7.04212i 0.737514 0.466376i
229229 13.1300 + 19.0220i 0.867652 + 1.25701i 0.965129 + 0.261774i 0.0843074π0.0843074\pi
−0.0974769 + 0.995238i 0.531077π0.531077\pi
230230 6.59820 + 8.08132i 0.435072 + 0.532867i
231231 0.284449 + 7.05852i 0.0187154 + 0.464417i
232232 −1.95554 1.23661i −0.128387 0.0811872i
233233 1.06532 0.943787i 0.0697911 0.0618295i −0.627506 0.778612i 0.715924π-0.715924\pi
0.697297 + 0.716782i 0.254386π0.254386\pi
234234 22.9932 + 12.7669i 1.50312 + 0.834599i
235235 0.339948 + 0.301168i 0.0221758 + 0.0196460i
236236 4.26191 + 14.7138i 0.277427 + 0.957788i
237237 −9.18704 + 19.3613i −0.596762 + 1.25765i
238238 −3.96508 + 1.32374i −0.257018 + 0.0858051i
239239 3.57767 0.231420 0.115710 0.993283i 0.463086π-0.463086\pi
0.115710 + 0.993283i 0.463086π0.463086\pi
240240 9.29674 3.10371i 0.600102 0.200343i
241241 0.425687 10.5633i 0.0274209 0.680443i −0.925772 0.378081i 0.876584π-0.876584\pi
0.953193 0.302361i 0.0977750π-0.0977750\pi
242242 −2.12473 + 17.4988i −0.136583 + 1.12486i
243243 17.6315 11.1495i 1.13106 0.715240i
244244 3.86806 1.64803i 0.247627 0.105504i
245245 0.446485 + 0.464840i 0.0285249 + 0.0296976i
246246 −8.13640 + 2.00544i −0.518758 + 0.127862i
247247 −14.1932 + 4.36988i −0.903094 + 0.278049i
248248 −4.68771 1.15542i −0.297670 0.0733690i
249249 −2.42807 4.20554i −0.153873 0.266515i
250250 8.70243 + 9.06019i 0.550390 + 0.573017i
251251 −0.574490 1.21071i −0.0362615 0.0764195i 0.884511 0.466519i 0.154492π-0.154492\pi
−0.920773 + 0.390099i 0.872441π0.872441\pi
252252 −9.08582 + 8.04934i −0.572353 + 0.507060i
253253 −6.72667 5.05476i −0.422902 0.317790i
254254 −23.1874 17.4242i −1.45491 1.09329i
255255 −1.39544 + 1.23625i −0.0873859 + 0.0774171i
256256 8.79609 + 18.5374i 0.549755 + 1.15858i
257257 −9.21892 9.59791i −0.575061 0.598701i 0.368612 0.929584i 0.379833π-0.379833\pi
−0.943672 + 0.330882i 0.892654π0.892654\pi
258258 23.5009 + 40.7048i 1.46310 + 2.53417i
259259 13.8482 + 3.41328i 0.860486 + 0.212091i
260260 3.21642 0.183579i 0.199474 0.0113851i
261261 6.41653 1.58153i 0.397173 0.0978944i
262262 −4.98642 5.19141i −0.308062 0.320726i
263263 0.667754 0.284503i 0.0411755 0.0175432i −0.371281 0.928521i 0.621081π-0.621081\pi
0.412456 + 0.910977i 0.364671π0.364671\pi
264264 −3.44062 + 2.17572i −0.211756 + 0.133906i
265265 1.00440 8.27195i 0.0616996 0.508142i
266266 0.734994 18.2387i 0.0450654 1.11829i
267267 31.2194 10.4226i 1.91059 0.637850i
268268 −13.4763 −0.823196
269269 15.6040 5.20936i 0.951390 0.317621i 0.201728 0.979442i 0.435344π-0.435344\pi
0.749662 + 0.661821i 0.230216π0.230216\pi
270270 −1.63149 + 3.43830i −0.0992895 + 0.209248i
271271 −5.95705 20.5661i −0.361865 1.24930i −0.910594 0.413302i 0.864375π-0.864375\pi
0.548729 0.836000i 0.315112π-0.315112\pi
272272 −3.50119 3.10179i −0.212291 0.188073i
273273 21.2846 10.5396i 1.28820 0.637888i
274274 −17.4671 + 15.4745i −1.05523 + 0.934851i
275275 −4.03150 2.54937i −0.243109 0.153733i
276276 −1.01066 25.0793i −0.0608346 1.50959i
277277 3.20196 + 3.92169i 0.192387 + 0.235632i 0.861786 0.507271i 0.169346π-0.169346\pi
−0.669399 + 0.742903i 0.733448π0.733448\pi
278278 11.7605 + 17.0381i 0.705349 + 1.02187i
279279 11.6551 7.37026i 0.697774 0.441246i
280280 0.730522 2.52205i 0.0436570 0.150722i
281281 17.3902 + 15.4063i 1.03741 + 0.919065i 0.996786 0.0801098i 0.0255271π-0.0255271\pi
0.0406236 + 0.999175i 0.487066π0.487066\pi
282282 −0.582038 2.85101i −0.0346598 0.169775i
283283 14.8875 + 1.20185i 0.884972 + 0.0714423i 0.514589 0.857437i 0.327944π-0.327944\pi
0.370383 + 0.928879i 0.379226π0.379226\pi
284284 0.234801 + 5.82653i 0.0139329 + 0.345741i
285285 −2.88673 7.61169i −0.170995 0.450877i
286286 −6.61316 + 2.03609i −0.391044 + 0.120397i
287287 −1.54583 + 4.07601i −0.0912472 + 0.240599i
288288 −23.2760 7.77066i −1.37155 0.457891i
289289 −15.2812 5.10161i −0.898893 0.300095i
290290 1.49341 1.55480i 0.0876960 0.0913012i
291291 18.0252 + 4.44281i 1.05666 + 0.260442i
292292 10.9843 + 4.67998i 0.642809 + 0.273875i
293293 −16.8291 20.6119i −0.983166 1.20416i −0.978936 0.204169i 0.934551π-0.934551\pi
−0.00423077 0.999991i 0.501347π-0.501347\pi
294294 −0.497756 4.09939i −0.0290297 0.239081i
295295 9.43381 0.761576i 0.549258 0.0443407i
296296 2.28666 + 7.89447i 0.132909 + 0.458857i
297297 0.613953 3.00734i 0.0356252 0.174504i
298298 1.18926 9.79447i 0.0688922 0.567378i
299299 −6.30956 + 27.5773i −0.364891 + 1.59484i
300300 −1.71509 14.1250i −0.0990206 0.815508i
301301 24.3714 + 1.96746i 1.40474 + 0.113403i
302302 −2.08248 + 2.55057i −0.119833 + 0.146769i
303303 −39.9367 30.0105i −2.29430 1.72406i
304304 18.0856 9.49207i 1.03728 0.544407i
305305 −0.519612 2.54523i −0.0297529 0.145739i
306306 6.85802 0.553637i 0.392047 0.0316493i
307307 19.4564 28.1875i 1.11044 1.60874i 0.381181 0.924500i 0.375517π-0.375517\pi
0.729254 0.684243i 0.239867π-0.239867\pi
308308 0.128595 3.19106i 0.00732740 0.181828i
309309 −18.4494 + 13.8638i −1.04955 + 0.788685i
310310 1.92850 4.06423i 0.109531 0.230833i
311311 17.6707 25.6004i 1.00201 1.45167i 0.113103 0.993583i 0.463921π-0.463921\pi
0.888910 0.458082i 0.151463π-0.151463\pi
312312 11.3925 + 7.58537i 0.644976 + 0.429437i
313313 −14.3412 20.7768i −0.810613 1.17438i −0.981946 0.189162i 0.939423π-0.939423\pi
0.171333 0.985213i 0.445193π-0.445193\pi
314314 −27.8180 + 4.52086i −1.56986 + 0.255127i
315315 3.74985 + 6.49494i 0.211280 + 0.365948i
316316 4.84419 8.39038i 0.272507 0.471996i
317317 −1.39661 + 3.68257i −0.0784417 + 0.206834i −0.968500 0.249012i 0.919894π-0.919894\pi
0.890059 + 0.455846i 0.150663π0.150663\pi
318318 −36.9826 + 38.5029i −2.07388 + 2.15914i
319319 −0.869358 + 1.50577i −0.0486747 + 0.0843070i
320320 −0.617503 + 0.152201i −0.0345194 + 0.00850828i
321321 36.8086 + 5.98198i 2.05446 + 0.333881i
322322 −29.3889 18.5844i −1.63778 1.03567i
323323 −2.45712 + 3.00943i −0.136718 + 0.167449i
324324 −4.91350 + 2.57881i −0.272972 + 0.143267i
325325 −2.30727 + 15.8704i −0.127985 + 0.880334i
326326 26.2090 + 13.7555i 1.45158 + 0.761849i
327327 −27.1348 + 11.5610i −1.50056 + 0.639327i
328328 −2.47954 + 0.402965i −0.136910 + 0.0222500i
329329 −1.39258 0.593323i −0.0767754 0.0327109i
330330 −1.34504 3.54657i −0.0740418 0.195232i
331331 −19.5488 3.17699i −1.07450 0.174623i −0.402682 0.915340i 0.631922π-0.631922\pi
−0.671817 + 0.740717i 0.734486π0.734486\pi
332332 0.941149 + 1.98343i 0.0516523 + 0.108855i
333333 −20.7864 10.9096i −1.13909 0.597840i
334334 0.319925 1.10451i 0.0175055 0.0604361i
335335 −1.66546 + 8.15797i −0.0909939 + 0.445717i
336336 −26.1151 + 19.6242i −1.42469 + 1.07059i
337337 −17.4782 −0.952097 −0.476048 0.879419i 0.657931π-0.657931\pi
−0.476048 + 0.879419i 0.657931π0.657931\pi
338338 15.3084 + 17.5183i 0.832666 + 0.952868i
339339 42.7346 2.32102
340340 0.673786 0.506317i 0.0365412 0.0274589i
341341 −0.725721 + 3.55482i −0.0393000 + 0.192504i
342342 −8.35876 + 28.8578i −0.451990 + 1.56045i
343343 −17.2513 9.05418i −0.931483 0.488880i
344344 6.04023 + 12.7295i 0.325667 + 0.686330i
345345 −15.3068 2.48760i −0.824091 0.133928i
346346 −1.36684 3.60407i −0.0734820 0.193756i
347347 8.50137 + 3.62209i 0.456377 + 0.194444i 0.607907 0.794009i 0.292010π-0.292010\pi
−0.151529 + 0.988453i 0.548420π0.548420\pi
348348 −5.11944 + 0.831990i −0.274431 + 0.0445993i
349349 −8.76694 + 3.73525i −0.469284 + 0.199943i −0.613645 0.789582i 0.710297π-0.710297\pi
0.144361 + 0.989525i 0.453887π0.453887\pi
350350 −17.4540 9.16059i −0.932958 0.489654i
351351 −10.0752 + 2.23314i −0.537775 + 0.119196i
352352 5.71666 3.00033i 0.304699 0.159918i
353353 −4.48762 + 5.49634i −0.238852 + 0.292541i −0.880095 0.474797i 0.842521π-0.842521\pi
0.641243 + 0.767338i 0.278419π0.278419\pi
354354 −51.2511 32.4092i −2.72396 1.72253i
355355 3.55615 + 0.577930i 0.188741 + 0.0306734i
356356 −14.4472 + 3.56092i −0.765702 + 0.188728i
357357 3.10678 5.38110i 0.164428 0.284798i
358358 32.1917 33.5151i 1.70138 1.77133i
359359 −8.64168 + 22.7862i −0.456091 + 1.20261i 0.487976 + 0.872857i 0.337735π0.337735\pi
−0.944067 + 0.329755i 0.893034π0.893034\pi
360360 −2.16088 + 3.74276i −0.113888 + 0.197261i
361361 1.01754 + 1.76243i 0.0535548 + 0.0927597i
362362 25.9835 4.22272i 1.36566 0.221941i
363363 −14.8842 21.5635i −0.781219 1.13179i
364364 −9.97467 + 3.97509i −0.522815 + 0.208351i
365365 4.19055 6.07106i 0.219344 0.317774i
366366 −7.13493 + 15.0365i −0.372949 + 0.785973i
367367 12.8602 9.66385i 0.671300 0.504449i −0.209579 0.977792i 0.567209π-0.567209\pi
0.880878 + 0.473343i 0.156953π0.156953\pi
368368 1.56671 38.8774i 0.0816703 2.02663i
369369 4.07592 5.90499i 0.212184 0.307401i
370370 −7.63331 + 0.616225i −0.396837 + 0.0320360i
371371 5.55519 + 27.2111i 0.288411 + 1.41273i
372372 −9.58309 + 5.02960i −0.496860 + 0.260772i
373373 −4.56777 3.43245i −0.236510 0.177726i 0.475879 0.879511i 0.342130π-0.342130\pi
−0.712389 + 0.701785i 0.752387π0.752387\pi
374374 −1.14486 + 1.40220i −0.0591995 + 0.0725062i
375375 −18.6128 1.50258i −0.961163 0.0775931i
376376 −0.105142 0.865925i −0.00542230 0.0446567i
377377 5.81420 + 0.607416i 0.299446 + 0.0312835i
378378 1.52892 12.5918i 0.0786393 0.647653i
379379 7.48493 36.6636i 0.384475 1.88328i −0.0785042 0.996914i 0.525014π-0.525014\pi
0.462979 0.886369i 0.346780π-0.346780\pi
380380 1.02392 + 3.53499i 0.0525262 + 0.181341i
381381 42.9732 3.46915i 2.20158 0.177730i
382382 0.868317 + 7.15123i 0.0444270 + 0.365889i
383383 22.9103 + 28.0600i 1.17066 + 1.43380i 0.878704 + 0.477368i 0.158409π0.158409\pi
0.291957 + 0.956431i 0.405694π0.405694\pi
384384 −25.7175 10.9572i −1.31239 0.559157i
385385 −1.91584 0.472212i −0.0976402 0.0240661i
386386 23.9457 24.9301i 1.21880 1.26891i
387387 −38.1731 12.7440i −1.94045 0.647816i
388388 −7.96090 2.65774i −0.404154 0.134926i
389389 1.21952 3.21560i 0.0618320 0.163038i −0.900540 0.434773i 0.856828π-0.856828\pi
0.962372 + 0.271736i 0.0875977π0.0875977\pi
390390 −9.04826 + 8.98691i −0.458176 + 0.455070i
391391 2.62441 + 6.92000i 0.132722 + 0.349959i
392392 −0.0498457 1.23691i −0.00251759 0.0624734i
393393 10.6650 + 0.860967i 0.537978 + 0.0434301i
394394 8.77690 + 42.9921i 0.442174 + 2.16591i
395395 −4.48051 3.96938i −0.225439 0.199721i
396396 −1.46246 + 5.04900i −0.0734913 + 0.253722i
397397 15.3821 9.72703i 0.772004 0.488186i −0.0894689 0.995990i 0.528517π-0.528517\pi
0.861473 + 0.507804i 0.169543π0.169543\pi
398398 0.717187 + 1.03903i 0.0359494 + 0.0520816i
399399 17.1598 + 21.0169i 0.859064 + 1.05216i
400400 −0.888153 22.0393i −0.0444076 1.10196i
401401 9.81557 + 6.20699i 0.490166 + 0.309962i 0.756585 0.653895i 0.226866π-0.226866\pi
−0.266419 + 0.963857i 0.585841π0.585841\pi
402402 39.9298 35.3747i 1.99152 1.76433i
403403 11.9094 2.63968i 0.593248 0.131492i
404404 16.9046 + 14.9761i 0.841034 + 0.745091i
405405 0.953865 + 3.29312i 0.0473979 + 0.163637i
406406 −3.08029 + 6.49157i −0.152872 + 0.322171i
407407 5.85852 1.95586i 0.290396 0.0969485i
408408 3.58061 0.177267
409409 −15.1982 + 5.07389i −0.751500 + 0.250888i −0.666512 0.745494i 0.732213π-0.732213\pi
−0.0849883 + 0.996382i 0.527085π0.527085\pi
410410 0.0942489 2.33876i 0.00465462 0.115503i
411411 4.18106 34.4341i 0.206236 1.69851i
412412 8.81800 5.57617i 0.434432 0.274718i
413413 −29.0204 + 12.3644i −1.42800 + 0.608414i
414414 39.6462 + 41.2761i 1.94850 + 2.02861i
415415 1.31699 0.324610i 0.0646487 0.0159345i
416416 −17.0415 13.4450i −0.835529 0.659194i
417417 −29.8789 7.36449i −1.46318 0.360641i
418418 −3.95229 6.84557i −0.193313 0.334828i
419419 −0.0678330 0.0706216i −0.00331386 0.00345009i 0.719543 0.694447i 0.244351π-0.244351\pi
−0.722857 + 0.690997i 0.757172π0.757172\pi
420420 −2.52328 5.31771i −0.123124 0.259478i
421421 −22.5534 + 19.9806i −1.09919 + 0.973794i −0.999774 0.0212519i 0.993235π-0.993235\pi
−0.0994125 + 0.995046i 0.531696π0.531696\pi
422422 3.18755 + 2.39529i 0.155168 + 0.116601i
423423 1.99178 + 1.49673i 0.0968436 + 0.0727733i
424424 −11.9792 + 10.6126i −0.581761 + 0.515396i
425425 1.79859 + 3.79045i 0.0872445 + 0.183864i
426426 −15.9901 16.6475i −0.774724 0.806573i
427427 4.32903 + 7.49809i 0.209496 + 0.362858i
428428 −16.3691 4.03462i −0.791230 0.195021i
429429 5.35090 8.78384i 0.258344 0.424088i
430430 −12.7470 + 3.14185i −0.614714 + 0.151513i
431431 8.69377 + 9.05117i 0.418764 + 0.435980i 0.896851 0.442333i 0.145849π-0.145849\pi
−0.478087 + 0.878313i 0.658670π0.658670\pi
432432 13.0577 5.56334i 0.628237 0.267667i
433433 9.82064 6.21020i 0.471950 0.298443i −0.277237 0.960801i 0.589419π-0.589419\pi
0.749187 + 0.662359i 0.230444π0.230444\pi
434434 −1.80726 + 14.8841i −0.0867512 + 0.714460i
435435 −0.129033 + 3.20191i −0.00618664 + 0.153520i
436436 12.6480 4.22254i 0.605731 0.202223i
437437 −32.3173 −1.54595
438438 −44.8310 + 14.9668i −2.14211 + 0.715140i
439439 9.99425 21.0624i 0.477000 1.00526i −0.512225 0.858851i 0.671179π-0.671179\pi
0.989225 0.146404i 0.0467700π-0.0467700\pi
440440 −0.316349 1.09216i −0.0150814 0.0520669i
441441 2.64657 + 2.34466i 0.126027 + 0.111650i
442442 5.87347 + 1.59522i 0.279372 + 0.0758770i
443443 5.92760 5.25139i 0.281629 0.249501i −0.510468 0.859897i 0.670528π-0.670528\pi
0.792097 + 0.610395i 0.208989π0.208989\pi
444444 15.5719 + 9.84710i 0.739012 + 0.467323i
445445 0.370175 + 9.18580i 0.0175480 + 0.435449i
446446 5.86583 + 7.18433i 0.277755 + 0.340188i
447447 8.33105 + 12.0696i 0.394045 + 0.570873i
448448 1.79154 1.13290i 0.0846424 0.0535246i
449449 −3.67452 + 12.6859i −0.173411 + 0.598686i 0.825977 + 0.563704i 0.190624π0.190624\pi
−0.999388 + 0.0349811i 0.988863π0.988863\pi
450450 24.2850 + 21.5147i 1.14481 + 1.01421i
451451 0.377602 + 1.84962i 0.0177806 + 0.0870951i
452452 −19.2571 1.55459i −0.905777 0.0731219i
453453 −0.197078 4.89044i −0.00925954 0.229773i
454454 1.34346 + 3.54241i 0.0630516 + 0.166254i
455455 1.17363 + 6.52950i 0.0550207 + 0.306108i
456456 −5.54434 + 14.6192i −0.259638 + 0.684608i
457457 20.8863 + 6.97288i 0.977021 + 0.326178i 0.759952 0.649979i 0.225222π-0.225222\pi
0.217069 + 0.976156i 0.430350π0.430350\pi
458458 39.2346 + 13.0985i 1.83331 + 0.612050i
459459 −1.87018 + 1.94707i −0.0872927 + 0.0908813i
460460 6.80706 + 1.67779i 0.317381 + 0.0782274i
461461 −10.2784 4.37922i −0.478714 0.203961i 0.139111 0.990277i 0.455576π-0.455576\pi
−0.617824 + 0.786316i 0.711986π0.711986\pi
462462 7.99538 + 9.79257i 0.371979 + 0.455592i
463463 2.51173 + 20.6859i 0.116730 + 0.961358i 0.926938 + 0.375215i 0.122431π0.122431\pi
−0.810208 + 0.586143i 0.800646π0.800646\pi
464464 −8.01411 + 0.646966i −0.372046 + 0.0300346i
465465 1.86038 + 6.42277i 0.0862730 + 0.297849i
466466 0.509467 2.49553i 0.0236006 0.115603i
467467 −2.57704 + 21.2238i −0.119251 + 0.982122i 0.803120 + 0.595817i 0.203172π0.203172\pi
−0.922371 + 0.386305i 0.873751π0.873751\pi
468468 17.5063 2.42361i 0.809231 0.112031i
469469 −3.34499 27.5485i −0.154457 1.27207i
470470 0.810129 + 0.0654004i 0.0373685 + 0.00301670i
471471 26.4943 32.4496i 1.22079 1.49520i
472472 −14.5321 10.9202i −0.668895 0.502642i
473473 9.37543 4.92061i 0.431083 0.226250i
474474 7.67124 + 37.5762i 0.352352 + 1.72593i
475475 −18.2610 + 1.47418i −0.837872 + 0.0676400i
476476 −1.59573 + 2.31182i −0.0731402 + 0.105962i
477477 1.84061 45.6744i 0.0842760 2.09129i
478478 5.11844 3.84625i 0.234112 0.175924i
479479 −4.15778 + 8.76233i −0.189974 + 0.400361i −0.975981 0.217856i 0.930094π-0.930094\pi
0.786007 + 0.618217i 0.212145π0.212145\pi
480480 6.75936 9.79263i 0.308521 0.446970i
481481 −14.0286 15.3109i −0.639649 0.698118i
482482 −10.7473 15.5702i −0.489527 0.709203i
483483 51.0166 8.29101i 2.32134 0.377254i
484484 5.92270 + 10.2584i 0.269214 + 0.466292i
485485 −2.59273 + 4.49073i −0.117730 + 0.203914i
486486 13.2382 34.9063i 0.600498 1.58338i
487487 9.17143 9.54847i 0.415597 0.432683i −0.480191 0.877164i 0.659433π-0.659433\pi
0.895788 + 0.444481i 0.146612π0.146612\pi
488488 −2.49463 + 4.32083i −0.112927 + 0.195595i
489489 −42.7189 + 10.5293i −1.93181 + 0.476149i
490490 1.13851 + 0.185025i 0.0514325 + 0.00835860i
491491 16.9426 + 10.7139i 0.764610 + 0.483510i 0.858969 0.512028i 0.171106π-0.171106\pi
−0.0943585 + 0.995538i 0.530080π0.530080\pi
492492 −3.56145 + 4.36198i −0.160562 + 0.196653i
493493 1.35416 0.710718i 0.0609883 0.0320091i
494494 −15.6078 + 21.5106i −0.702228 + 0.967808i
495495 2.87571 + 1.50929i 0.129253 + 0.0678374i
496496 −15.4348 + 6.57614i −0.693041 + 0.295277i
497497 −11.8524 + 1.92621i −0.531654 + 0.0864022i
498498 −7.99502 3.40636i −0.358265 0.152643i
499499 −2.63204 6.94013i −0.117827 0.310683i 0.863109 0.505018i 0.168514π-0.168514\pi
−0.980935 + 0.194335i 0.937745π0.937745\pi
500500 8.33266 + 1.35419i 0.372648 + 0.0605612i
501501 0.732745 + 1.54423i 0.0327366 + 0.0689910i
502502 −2.12351 1.11450i −0.0947768 0.0497427i
503503 −0.116889 + 0.403546i −0.00521181 + 0.0179932i −0.963082 0.269209i 0.913238π-0.913238\pi
0.957870 + 0.287202i 0.0927251π0.0927251\pi
504504 2.88120 14.1131i 0.128339 0.628646i
505505 11.1551 8.38248i 0.496393 0.373015i
506506 −15.0578 −0.669403
507507 −34.2996 4.40171i −1.52330 0.195487i
508508 −19.4908 −0.864763
509509 −15.0918 + 11.3407i −0.668932 + 0.502670i −0.880105 0.474779i 0.842528π-0.842528\pi
0.211173 + 0.977449i 0.432272π0.432272\pi
510510 −0.667343 + 3.26886i −0.0295505 + 0.144748i
511511 −6.84046 + 23.6160i −0.302604 + 1.04471i
512512 13.9029 + 7.29681i 0.614428 + 0.322477i
513513 −5.05380 10.6507i −0.223131 0.470238i
514514 −23.5076 3.82036i −1.03688 0.168509i
515515 −2.28580 6.02717i −0.100724 0.265589i
516516 29.0574 + 12.3802i 1.27918 + 0.545008i
517517 −0.647015 + 0.105150i −0.0284557 + 0.00462450i
518518 23.4817 10.0046i 1.03173 0.439577i
519519 5.07323 + 2.66263i 0.222690 + 0.116877i
520520 −2.92041 + 2.46704i −0.128069 + 0.108187i
521521 12.7827 6.70887i 0.560019 0.293921i −0.160865 0.986976i 0.551428π-0.551428\pi
0.720884 + 0.693056i 0.243736π0.243736\pi
522522 7.47963 9.16089i 0.327375 0.400961i
523523 25.7360 + 16.2744i 1.12535 + 0.711631i 0.961487 0.274851i 0.0886285π-0.0886285\pi
0.163868 + 0.986482i 0.447603π0.447603\pi
524524 −4.77454 0.775939i −0.208577 0.0338970i
525525 28.4489 7.01202i 1.24161 0.306030i
526526 0.649469 1.12491i 0.0283182 0.0490485i
527527 2.21064 2.30152i 0.0962972 0.100256i
528528 −5.01628 + 13.2268i −0.218306 + 0.575624i
529529 −19.2814 + 33.3964i −0.838323 + 1.45202i
530530 −7.45600 12.9142i −0.323868 0.560956i
531531 51.2479 8.32860i 2.22397 0.361430i
532532 −6.96800 10.0949i −0.302101 0.437669i
533533 5.16239 3.69241i 0.223608 0.159936i
534534 33.4594 48.4743i 1.44793 2.09769i
535535 −4.46535 + 9.41052i −0.193054 + 0.406852i
536536 12.7844 9.60684i 0.552201 0.414952i
537537 −2.78141 + 69.0199i −0.120027 + 2.97843i
538538 16.7236 24.2282i 0.721004 1.04455i
539539 −0.927249 + 0.0748553i −0.0399394 + 0.00322425i
540540 0.511551 + 2.50574i 0.0220137 + 0.107830i
541541 −20.4545 + 10.7354i −0.879410 + 0.461550i −0.843079 0.537790i 0.819259π-0.819259\pi
−0.0363308 + 0.999340i 0.511567π0.511567\pi
542542 −30.6326 23.0189i −1.31578 0.988747i
543543 −24.7471 + 30.3097i −1.06200 + 1.30071i
544544 −5.66029 0.456946i −0.242683 0.0195914i
545545 −0.993040 8.17842i −0.0425371 0.350325i
546546 19.1202 37.9612i 0.818268 1.62459i
547547 1.06447 8.76666i 0.0455132 0.374835i −0.952100 0.305787i 0.901081π-0.901081\pi
0.997613 0.0690486i 0.0219964π-0.0219964\pi
548548 −3.13671 + 15.3646i −0.133994 + 0.656344i
549549 −3.96476 13.6879i −0.169212 0.584186i
550550 −8.50847 + 0.686875i −0.362803 + 0.0292885i
551551 0.804953 + 6.62938i 0.0342921 + 0.282421i
552552 18.8370 + 23.0712i 0.801757 + 0.981973i
553553 18.3542 + 7.81998i 0.780498 + 0.332539i
554554 8.79704 + 2.16827i 0.373750 + 0.0921212i
555555 7.88546 8.20964i 0.334719 0.348480i
556556 13.1961 + 4.40552i 0.559641 + 0.186836i
557557 −16.4447 5.49006i −0.696785 0.232621i −0.0538584 0.998549i 0.517152π-0.517152\pi
−0.642927 + 0.765927i 0.722280π0.722280\pi
558558 8.75100 23.0745i 0.370459 0.976821i
559559 −27.9484 22.0500i −1.18209 0.932617i
560560 −3.23555 8.53144i −0.136727 0.360519i
561561 −0.108346 2.68857i −0.00457436 0.113512i
562562 41.4424 + 3.34558i 1.74814 + 0.141125i
563563 −3.81516 18.6879i −0.160790 0.787600i −0.977563 0.210642i 0.932445π-0.932445\pi
0.816774 0.576958i 0.195760π-0.195760\pi
564564 −1.46362 1.29665i −0.0616295 0.0545989i
565565 −3.32096 + 11.4653i −0.139714 + 0.482348i
566566 22.5911 14.2858i 0.949576 0.600475i
567567 −6.49124 9.40418i −0.272606 0.394938i
568568 −4.37630 5.36000i −0.183626 0.224901i
569569 0.244956 + 6.07853i 0.0102691 + 0.254825i 0.996167 + 0.0874753i 0.0278799π0.0278799\pi
−0.985898 + 0.167350i 0.946479π0.946479\pi
570570 −12.3131 7.78631i −0.515738 0.326133i
571571 −15.8080 + 14.0047i −0.661544 + 0.586077i −0.925633 0.378421i 0.876467π-0.876467\pi
0.264089 + 0.964498i 0.414929π0.414929\pi
572572 −2.73076 + 3.76352i −0.114179 + 0.157361i
573573 −8.01494 7.10062i −0.334829 0.296633i
574574 2.17045 + 7.49327i 0.0905929 + 0.312763i
575575 −14.9611 + 31.5299i −0.623922 + 1.31489i
576576 −3.30932 + 1.10481i −0.137888 + 0.0460339i
577577 −34.8469 −1.45069 −0.725347 0.688384i 0.758321π-0.758321\pi
−0.725347 + 0.688384i 0.758321π0.758321\pi
578578 −27.3468 + 9.12972i −1.13748 + 0.379746i
579579 −2.06894 + 51.3402i −0.0859821 + 2.13362i
580580 0.174623 1.43815i 0.00725083 0.0597160i
581581 −3.82096 + 2.41623i −0.158520 + 0.100242i
582582 30.5644 13.0223i 1.26693 0.539790i
583583 8.33119 + 8.67368i 0.345043 + 0.359227i
584584 −13.7566 + 3.39069i −0.569251 + 0.140308i
585585 0.696364 10.8971i 0.0287911 0.450540i
586586 −46.2361 11.3962i −1.91000 0.470772i
587587 −0.208841 0.361724i −0.00861981 0.0149299i 0.861683 0.507446i 0.169410π-0.169410\pi
−0.870303 + 0.492516i 0.836077π0.836077\pi
588588 −1.92230 2.00133i −0.0792745 0.0825335i
589589 5.97383 + 12.5896i 0.246147 + 0.518745i
590590 12.6779 11.2316i 0.521939 0.462398i
591591 −52.1418 39.1820i −2.14483 1.61173i
592592 22.8328 + 17.1577i 0.938422 + 0.705178i
593593 18.2958 16.2086i 0.751317 0.665609i −0.197903 0.980222i 0.563413π-0.563413\pi
0.949220 + 0.314613i 0.101875π0.101875\pi
594594 −2.35475 4.96254i −0.0966167 0.203615i
595595 1.20227 + 1.25169i 0.0492881 + 0.0513143i
596596 −3.31507 5.74188i −0.135791 0.235196i
597597 −1.82210 0.449106i −0.0745734 0.0183807i
598598 20.6208 + 46.2371i 0.843246 + 1.89077i
599599 43.0382 10.6080i 1.75849 0.433430i 0.777726 0.628604i 0.216373π-0.216373\pi
0.980769 + 0.195174i 0.0625271π0.0625271\pi
600600 11.6963 + 12.1772i 0.477500 + 0.497130i
601601 1.18719 0.505816i 0.0484267 0.0206327i −0.367617 0.929977i 0.619826π-0.619826\pi
0.416044 + 0.909344i 0.363416π0.363416\pi
602602 36.9824 23.3863i 1.50729 0.953153i
603603 −5.50563 + 45.3429i −0.224207 + 1.84651i
604604 −0.0890963 + 2.21090i −0.00362528 + 0.0899603i
605605 6.94196 2.31757i 0.282231 0.0942225i
606606 −89.3994 −3.63160
607607 −14.6111 + 4.87791i −0.593047 + 0.197988i −0.597321 0.802003i 0.703768π-0.703768\pi
0.00427324 + 0.999991i 0.498640π0.498640\pi
608608 10.6303 22.4028i 0.431114 0.908553i
609609 −2.97148 10.2587i −0.120410 0.415705i
610610 −3.47970 3.08274i −0.140889 0.124817i
611611 1.20892 + 1.84275i 0.0489078 + 0.0745496i
612612 3.46076 3.06597i 0.139893 0.123934i
613613 8.77238 + 5.54732i 0.354313 + 0.224054i 0.699750 0.714388i 0.253295π-0.253295\pi
−0.345437 + 0.938442i 0.612269π0.612269\pi
614614 −2.46804 61.2438i −0.0996021 2.47160i
615615 2.20042 + 2.69502i 0.0887293 + 0.108674i
616616 2.15282 + 3.11890i 0.0867395 + 0.125664i
617617 1.07188 0.677817i 0.0431523 0.0272879i −0.512715 0.858559i 0.671360π-0.671360\pi
0.555868 + 0.831271i 0.312386π0.312386\pi
618618 −11.4902 + 39.6689i −0.462205 + 1.59572i
619619 0.713247 + 0.631881i 0.0286678 + 0.0253975i 0.677335 0.735675i 0.263135π-0.263135\pi
−0.648667 + 0.761072i 0.724673π0.724673\pi
620620 −0.604678 2.96191i −0.0242844 0.118953i
621621 −22.3844 1.80705i −0.898254 0.0725146i
622622 −2.24152 55.6228i −0.0898769 2.23027i
623623 −10.8653 28.6494i −0.435309 1.14781i
624624 47.4842 2.71019i 1.90089 0.108494i
625625 −6.03675 + 15.9176i −0.241470 + 0.636704i
626626 −42.8541 14.3068i −1.71279 0.571814i
627627 11.1449 + 3.72071i 0.445084 + 0.148591i
628628 −13.1193 + 13.6587i −0.523518 + 0.545040i
629629 −5.27474 1.30011i −0.210318 0.0518387i
630630 12.3473 + 5.26070i 0.491929 + 0.209591i
631631 23.4426 + 28.7120i 0.933237 + 1.14301i 0.989492 + 0.144591i 0.0461866π0.0461866\pi
−0.0562550 + 0.998416i 0.517916π0.517916\pi
632632 1.38577 + 11.4129i 0.0551231 + 0.453980i
633633 −5.90748 + 0.476901i −0.234801 + 0.0189551i
634634 1.96095 + 6.76998i 0.0778792 + 0.268870i
635635 −2.40876 + 11.7989i −0.0955886 + 0.468224i
636636 −4.32434 + 35.6142i −0.171471 + 1.41219i
637637 1.49966 + 2.74473i 0.0594188 + 0.108750i
638638 0.375057 + 3.08888i 0.0148487 + 0.122290i
639639 19.7001 + 1.59036i 0.779325 + 0.0629136i
640640 4.93825 6.04826i 0.195202 0.239078i
641641 9.96600 + 7.48897i 0.393633 + 0.295796i 0.779069 0.626939i 0.215692π-0.215692\pi
−0.385435 + 0.922735i 0.625949π0.625949\pi
642642 59.0918 31.0138i 2.33217 1.22402i
643643 −0.534084 2.61612i −0.0210622 0.103170i 0.967901 0.251333i 0.0808689π-0.0808689\pi
−0.988963 + 0.148164i 0.952664π0.952664\pi
644644 −23.2907 + 1.88022i −0.917784 + 0.0740912i
645645 11.0855 16.0601i 0.436491 0.632366i
646646 −0.279957 + 6.94706i −0.0110148 + 0.273328i
647647 31.7679 23.8720i 1.24892 0.938505i 0.249370 0.968408i 0.419776π-0.419776\pi
0.999553 + 0.0299032i 0.00951991π0.00951991\pi
648648 2.82288 5.94909i 0.110893 0.233702i
649649 −7.75990 + 11.2422i −0.304603 + 0.441293i
650650 13.7610 + 25.1857i 0.539749 + 0.987866i
651651 −12.6602 18.3415i −0.496194 0.718861i
652652 19.6330 3.19068i 0.768888 0.124957i
653653 −10.5727 18.3124i −0.413740 0.716619i 0.581555 0.813507i 0.302445π-0.302445\pi
−0.995295 + 0.0968878i 0.969111π0.969111\pi
654654 −26.3917 + 45.7118i −1.03200 + 1.78747i
655655 −1.05978 + 2.79441i −0.0414090 + 0.109187i
656656 −6.04710 + 6.29569i −0.236099 + 0.245806i
657657 20.2340 35.0464i 0.789405 1.36729i
658658 −2.63018 + 0.648281i −0.102535 + 0.0252726i
659659 −0.995262 0.161746i −0.0387699 0.00630072i 0.140995 0.990010i 0.454970π-0.454970\pi
−0.179765 + 0.983710i 0.557534π0.557534\pi
660660 −2.15431 1.36230i −0.0838564 0.0530275i
661661 −3.66786 + 4.49232i −0.142663 + 0.174731i −0.840994 0.541044i 0.818029π-0.818029\pi
0.698331 + 0.715775i 0.253927π0.253927\pi
662662 −31.3832 + 16.4712i −1.21974 + 0.640171i
663663 −8.10723 + 4.01452i −0.314859 + 0.155911i
664664 −2.30675 1.21068i −0.0895194 0.0469834i
665665 −6.97215 + 2.97055i −0.270368 + 0.115193i
666666 −41.4669 + 6.73903i −1.60681 + 0.261132i
667667 11.7034 + 4.98636i 0.453158 + 0.193073i
668668 −0.274014 0.722516i −0.0106019 0.0279550i
669669 −13.6078 2.21149i −0.526109 0.0855010i
670670 6.38770 + 13.4618i 0.246779 + 0.520075i
671671 3.31987 + 1.74240i 0.128162 + 0.0672646i
672672 −11.0337 + 38.0926i −0.425633 + 1.46945i
673673 2.21321 10.8410i 0.0853130 0.417891i −0.914596 0.404370i 0.867491π-0.867491\pi
0.999909 0.0135210i 0.00430400π-0.00430400\pi
674674 −25.0054 + 18.7903i −0.963171 + 0.723776i
675675 −12.7308 −0.490008
676676 15.2960 + 3.23125i 0.588307 + 0.124279i
677677 −10.7526 −0.413256 −0.206628 0.978420i 0.566249π-0.566249\pi
−0.206628 + 0.978420i 0.566249π0.566249\pi
678678 61.1388 45.9428i 2.34802 1.76442i
679679 3.45700 16.9335i 0.132668 0.649848i
680680 −0.278254 + 0.960643i −0.0106705 + 0.0368390i
681681 −4.98643 2.61708i −0.191080 0.100287i
682682 2.78343 + 5.86595i 0.106583 + 0.224619i
683683 −19.2549 3.12922i −0.736767 0.119736i −0.219563 0.975598i 0.570463π-0.570463\pi
−0.517204 + 0.855862i 0.673027π0.673027\pi
684684 7.15924 + 18.8774i 0.273740 + 0.721794i
685685 8.91343 + 3.79766i 0.340565 + 0.145101i
686686 −34.4147 + 5.59294i −1.31396 + 0.213539i
687687 −56.5636 + 24.0995i −2.15804 + 0.919453i
688688 43.3540 + 22.7539i 1.65285 + 0.867485i
689689 15.2246 37.4601i 0.580013 1.42711i
690690 −24.5732 + 12.8970i −0.935487 + 0.490982i
691691 −20.5159 + 25.1275i −0.780463 + 0.955894i −0.999805 0.0197544i 0.993712π-0.993712\pi
0.219342 + 0.975648i 0.429609π0.429609\pi
692692 −2.18924 1.38439i −0.0832223 0.0526266i
693693 −10.6842 1.73636i −0.405861 0.0659588i
694694 16.0566 3.95760i 0.609501 0.150228i
695695 4.29775 7.44392i 0.163023 0.282364i
696696 4.26349 4.43877i 0.161607 0.168251i
697697 0.588800 1.55254i 0.0223024 0.0588066i
698698 −8.52688 + 14.7690i −0.322747 + 0.559015i
699699 1.89297 + 3.27872i 0.0715986 + 0.124012i
700700 −13.0747 + 2.12485i −0.494178 + 0.0803118i
701701 −28.4251 41.1809i −1.07360 1.55538i −0.806058 0.591837i 0.798403π-0.798403\pi
−0.267545 0.963545i 0.586212π-0.586212\pi
702702 −12.0134 + 14.0265i −0.453418 + 0.529395i
703703 13.4758 19.5231i 0.508249 0.736326i
704704 0.393507 0.829298i 0.0148308 0.0312553i
705705 −0.965818 + 0.725765i −0.0363748 + 0.0273339i
706706 −0.511306 + 12.6879i −0.0192433 + 0.477517i
707707 −26.4186 + 38.2739i −0.993572 + 1.43944i
708708 −40.6165 + 3.27890i −1.52646 + 0.123229i
709709 −6.90598 33.8277i −0.259360 1.27043i −0.875665 0.482920i 0.839576π-0.839576\pi
0.616305 0.787508i 0.288629π-0.288629\pi
710710 5.70897 2.99630i 0.214254 0.112449i
711711 −26.2516 19.7268i −0.984511 0.739812i
712712 11.1670 13.6771i 0.418501 0.512570i
713713 26.4594 + 2.13602i 0.990912 + 0.0799947i
714714 −1.34032 11.0386i −0.0501604 0.413108i
715715 1.94079 + 2.11820i 0.0725816 + 0.0792161i
716716 3.76415 31.0006i 0.140673 1.15855i
717717 −1.90361 + 9.32452i −0.0710917 + 0.348230i
718718 12.1336 + 41.8899i 0.452820 + 1.56332i
719719 −17.9737 + 1.45099i −0.670306 + 0.0541127i −0.410934 0.911665i 0.634797π-0.634797\pi
−0.259372 + 0.965778i 0.583515π0.583515\pi
720720 1.81023 + 14.9086i 0.0674634 + 0.555611i
721721 13.5876 + 16.6418i 0.506030 + 0.619775i
722722 3.35051 + 1.42752i 0.124693 + 0.0531267i
723723 27.3048 + 6.73003i 1.01548 + 0.250292i
724724 12.2541 12.7579i 0.455421 0.474144i
725725 6.84051 + 2.28370i 0.254050 + 0.0848144i
726726 −44.4767 14.8485i −1.65069 0.551080i
727727 2.65683 7.00548i 0.0985363 0.259819i −0.876679 0.481075i 0.840246π-0.840246\pi
0.975216 + 0.221256i 0.0710157π0.0710157\pi
728728 6.62882 10.8816i 0.245681 0.403300i
729729 14.7688 + 38.9422i 0.546994 + 1.44230i
730730 −0.531571 13.1908i −0.0196743 0.488214i
731731 −9.28299 0.749401i −0.343344 0.0277176i
732732 2.23714 + 10.9583i 0.0826872 + 0.405029i
733733 7.28926 + 6.45772i 0.269235 + 0.238521i 0.786928 0.617045i 0.211670π-0.211670\pi
−0.517693 + 0.855567i 0.673209π0.673209\pi
734734 8.00934 27.6514i 0.295630 1.02063i
735735 −1.44909 + 0.916346i −0.0534503 + 0.0337999i
736736 −26.8336 38.8752i −0.989100 1.43296i
737737 −7.60033 9.30871i −0.279962 0.342891i
738738 −0.517030 12.8300i −0.0190321 0.472277i
739739 −4.74035 2.99762i −0.174377 0.110269i 0.444426 0.895816i 0.353408π-0.353408\pi
−0.618803 + 0.785546i 0.712382π0.712382\pi
740740 −3.85200 + 3.41257i −0.141602 + 0.125449i
741741 −3.83730 39.3172i −0.140967 1.44435i
742742 37.2016 + 32.9577i 1.36571 + 1.20992i
743743 2.50521 + 8.64899i 0.0919073 + 0.317301i 0.993279 0.115746i 0.0369258π-0.0369258\pi
−0.901372 + 0.433046i 0.857439π0.857439\pi
744744 5.50562 11.6029i 0.201846 0.425381i
745745 −3.88558 + 1.29720i −0.142357 + 0.0475256i
746746 −10.2251 −0.374367
747747 7.05803 2.35632i 0.258240 0.0862131i
748748 −0.0489816 + 1.21547i −0.00179094 + 0.0444418i
749749 4.18462 34.4634i 0.152903 1.25927i
750750 −28.2441 + 17.8605i −1.03133 + 0.652173i
751751 −35.3339 + 15.0544i −1.28935 + 0.549341i −0.924307 0.381649i 0.875356π-0.875356\pi
−0.365044 + 0.930990i 0.618946π0.618946\pi
752752 −2.09978 2.18610i −0.0765710 0.0797189i
753753 3.46117 0.853102i 0.126132 0.0310888i
754754 8.97118 5.38168i 0.326711 0.195989i
755755 1.32737 + 0.327168i 0.0483081 + 0.0119069i
756756 −4.26187 7.38178i −0.155003 0.268473i
757757 −29.3794 30.5872i −1.06781 1.11171i −0.993426 0.114480i 0.963480π-0.963480\pi
−0.0743860 0.997230i 0.523700π-0.523700\pi
758758 −28.7077 60.5001i −1.04271 2.19746i
759759 16.7534 14.8422i 0.608111 0.538739i
760760 −3.49134 2.62357i −0.126644 0.0951670i
761761 −5.35190 4.02169i −0.194006 0.145786i 0.499300 0.866429i 0.333590π-0.333590\pi
−0.693307 + 0.720643i 0.743847π0.743847\pi
762762 57.7505 51.1625i 2.09208 1.85342i
763763 11.7712 + 24.8073i 0.426146 + 0.898083i
764764 3.35339 + 3.49125i 0.121321 + 0.126309i
765765 −1.42831 2.47390i −0.0516406 0.0894441i
766766 62.9435 + 15.5142i 2.27424 + 0.560550i
767767 45.1472 + 8.43236i 1.63017 + 0.304475i
768768 −52.9944 + 13.0619i −1.91227 + 0.471332i
769769 4.96448 + 5.16858i 0.179024 + 0.186384i 0.804668 0.593725i 0.202343π-0.202343\pi
−0.625644 + 0.780109i 0.715164π0.715164\pi
770770 −3.24858 + 1.38409i −0.117071 + 0.0498792i
771771 29.9204 18.9205i 1.07756 0.681406i
772772 2.79995 23.0597i 0.100772 0.829935i
773773 −1.17789 + 29.2290i −0.0423658 + 1.05130i 0.828566 + 0.559891i 0.189157π0.189157\pi
−0.870932 + 0.491404i 0.836484π0.836484\pi
774774 −68.3136 + 22.8064i −2.45548 + 0.819760i
775775 15.0484 0.540554
776776 9.44679 3.15380i 0.339120 0.113215i
777777 −16.2645 + 34.2766i −0.583485 + 1.22967i
778778 −1.71229 5.91152i −0.0613886 0.211938i
779779 5.42712 + 4.80801i 0.194447 + 0.172265i
780780 −1.23294 + 8.48067i −0.0441462 + 0.303657i
781781 −3.89224 + 3.44822i −0.139275 + 0.123387i
782782 11.1942 + 7.07875i 0.400302 + 0.253136i
783783 0.186857 + 4.63681i 0.00667773 + 0.165706i
784784 −2.72062 3.33215i −0.0971649 0.119005i
785785 6.64702 + 9.62987i 0.237242 + 0.343705i
786786 16.1836 10.2339i 0.577251 0.365031i
787787 11.7712 40.6391i 0.419600 1.44863i −0.421045 0.907040i 0.638337π-0.638337\pi
0.840645 0.541587i 0.182176π-0.182176\pi
788788 22.0708 + 19.5530i 0.786240 + 0.696547i
789789 0.386204 + 1.89175i 0.0137492 + 0.0673482i
790790 −10.6775 0.861975i −0.379888 0.0306677i
791791 −1.60193 39.7515i −0.0569582 1.41340i
792792 −2.21190 5.83231i −0.0785965 0.207242i
793793 0.803919 12.5802i 0.0285480 0.446736i
794794 11.5493 30.4530i 0.409869 1.08073i
795795 21.0249 + 7.01913i 0.745675 + 0.248943i
796796 0.804736 + 0.268660i 0.0285231 + 0.00952241i
797797 7.96313 8.29050i 0.282069 0.293665i −0.565063 0.825048i 0.691148π-0.691148\pi
0.847132 + 0.531383i 0.178328π0.178328\pi
798798 47.1446 + 11.6201i 1.66890 + 0.411347i
799799 0.530430 + 0.225995i 0.0187652 + 0.00799512i
800800 −16.9357 20.7425i −0.598769 0.733359i
801801 6.07894 + 50.0646i 0.214789 + 1.76894i
802802 20.7157 1.67235i 0.731498 0.0590526i
803803 2.96223 + 10.2268i 0.104535 + 0.360896i
804804 7.17050 35.1234i 0.252884 1.23871i
805805 −1.74017 + 14.3316i −0.0613329 + 0.505122i
806806 14.2004 16.5799i 0.500189 0.584003i
807807 5.27464 + 43.4406i 0.185676 + 1.52918i
808808 −26.7127 2.15647i −0.939749 0.0758643i
809809 31.9635 39.1482i 1.12378 1.37638i 0.206346 0.978479i 0.433843π-0.433843\pi
0.917430 0.397897i 0.130260π-0.130260\pi
810810 4.90501 + 3.68588i 0.172344 + 0.129508i
811811 −26.7927 + 14.0619i −0.940818 + 0.493779i −0.864126 0.503275i 0.832128π-0.832128\pi
−0.0766919 + 0.997055i 0.524436π0.524436\pi
812812 0.965819 + 4.73089i 0.0338936 + 0.166022i
813813 56.7714 4.58306i 1.99106 0.160735i
814814 6.27888 9.09652i 0.220074 0.318833i
815815 0.494839 12.2793i 0.0173334 0.430125i
816816 9.94715 7.47480i 0.348220 0.261670i
817817 17.4338 36.7410i 0.609933 1.28541i
818818 −16.2886 + 23.5982i −0.569519 + 0.825090i
819819 9.29969 + 35.1852i 0.324957 + 1.22947i
820820 −0.893513 1.29448i −0.0312028 0.0452051i
821821 26.9091 4.37315i 0.939134 0.152624i 0.328471 0.944514i 0.393467π-0.393467\pi
0.610664 + 0.791890i 0.290903π0.290903\pi
822822 −31.0375 53.7586i −1.08256 1.87505i
823823 16.2153 28.0856i 0.565228 0.979004i −0.431800 0.901969i 0.642121π-0.642121\pi
0.997028 0.0770348i 0.0245452π-0.0245452\pi
824824 −4.39018 + 11.5760i −0.152939 + 0.403268i
825825 8.78953 9.15087i 0.306012 0.318593i
826826 −28.2257 + 48.8884i −0.982099 + 1.70104i
827827 0.281668 0.0694250i 0.00979457 0.00241414i −0.234415 0.972137i 0.575318π-0.575318\pi
0.244210 + 0.969722i 0.421471π0.421471\pi
828828 37.9616 + 6.16937i 1.31926 + 0.214400i
829829 35.5396 + 22.4739i 1.23434 + 0.780551i 0.982327 0.187172i 0.0599323π-0.0599323\pi
0.252015 + 0.967723i 0.418907π0.418907\pi
830830 1.53520 1.88027i 0.0532874 0.0652652i
831831 −11.9249 + 6.25865i −0.413669 + 0.217110i
832832 −3.08535 0.0726424i −0.106965 0.00251842i
833833 0.724516 + 0.380256i 0.0251030 + 0.0131751i
834834 −50.6641 + 21.5859i −1.75435 + 0.747460i
835835 −0.471244 + 0.0765846i −0.0163081 + 0.00265032i
836836 −4.88677 2.08206i −0.169012 0.0720094i
837837 3.43378 + 9.05412i 0.118689 + 0.312956i
838838 −0.172970 0.0281103i −0.00597513 0.000971054i
839839 14.0457 + 29.6007i 0.484911 + 1.02193i 0.987532 + 0.157421i 0.0503181π0.0503181\pi
−0.502620 + 0.864507i 0.667631π0.667631\pi
840840 6.18457 + 3.24591i 0.213388 + 0.111995i
841841 −7.33694 + 25.3301i −0.252998 + 0.873450i
842842 −10.7857 + 52.8321i −0.371701 + 1.82071i
843843 −49.4067 + 37.1267i −1.70166 + 1.27871i
844844 2.67938 0.0922281
845845 3.84640 8.86020i 0.132320 0.304800i
846846 4.45866 0.153292
847847 −19.5004 + 14.6536i −0.670040 + 0.503502i
848848 −11.1242 + 54.4901i −0.382007 + 1.87120i
849849 −11.0538 + 38.1621i −0.379365 + 1.30972i
850850 6.64819 + 3.48924i 0.228031 + 0.119680i
851851 −19.3725 40.8267i −0.664082 1.39952i
852852 −15.3107 2.48823i −0.524536 0.0852454i
853853 5.77904 + 15.2381i 0.197871 + 0.521742i 0.996823 0.0796526i 0.0253811π-0.0253811\pi
−0.798952 + 0.601395i 0.794612π0.794612\pi
854854 14.2544 + 6.07323i 0.487775 + 0.207822i
855855 12.3123 2.00095i 0.421072 0.0684309i
856856 18.4048 7.84155i 0.629063 0.268019i
857857 4.46896 + 2.34549i 0.152657 + 0.0801205i 0.539322 0.842100i 0.318681π-0.318681\pi
−0.386665 + 0.922220i 0.626373π0.626373\pi
858858 −1.78794 18.3193i −0.0610393 0.625411i
859859 8.20267 4.30509i 0.279872 0.146888i −0.318947 0.947772i 0.603329π-0.603329\pi
0.598819 + 0.800885i 0.295637π0.295637\pi
860860 −5.57958 + 6.83374i −0.190262 + 0.233029i
861861 −9.80084 6.19768i −0.334012 0.211216i
862862 22.1685 + 3.60274i 0.755063 + 0.122710i
863863 −29.8596 + 7.35974i −1.01643 + 0.250528i −0.712131 0.702047i 0.752270π-0.752270\pi
−0.304303 + 0.952575i 0.598423π0.598423\pi
864864 8.61566 14.9228i 0.293111 0.507682i
865865 −1.10861 + 1.15418i −0.0376937 + 0.0392433i
866866 7.37361 19.4426i 0.250565 0.660687i
867867 21.4272 37.1131i 0.727707 1.26043i
868868 5.03774 + 8.72562i 0.170992 + 0.296167i
869869 8.52764 1.38588i 0.289280 0.0470126i
870870 3.25769 + 4.71957i 0.110446 + 0.160009i
871871 −18.1754 + 36.0855i −0.615851 + 1.22271i
872872 −8.98854 + 13.0221i −0.304390 + 0.440985i
873873 −12.1947 + 25.6998i −0.412728 + 0.869807i
874874 −46.2352 + 34.7435i −1.56393 + 1.17522i
875875 −0.699983 + 17.3699i −0.0236638 + 0.587210i
876876 −18.0421 + 26.1385i −0.609585 + 0.883136i
877877 −5.51633 + 0.445324i −0.186273 + 0.0150375i −0.173251 0.984878i 0.555427π-0.555427\pi
−0.0130220 + 0.999915i 0.504145π0.504145\pi
878878 −8.34527 40.8778i −0.281639 1.37956i
879879 62.6755 32.8947i 2.11399 1.10951i
880880 −3.15881 2.37369i −0.106484 0.0800172i
881881 −2.55624 + 3.13083i −0.0861220 + 0.105480i −0.815868 0.578238i 0.803741π-0.803741\pi
0.729746 + 0.683718i 0.239638π0.239638\pi
882882 6.30703 + 0.509156i 0.212369 + 0.0171442i
883883 −1.72218 14.1834i −0.0579560 0.477310i −0.992573 0.121654i 0.961180π-0.961180\pi
0.934617 0.355657i 0.115743π-0.115743\pi
884884 3.79932 1.51410i 0.127785 0.0509247i
885885 −3.03466 + 24.9927i −0.102009 + 0.840120i
886886 2.83476 13.8856i 0.0952357 0.466495i
887887 10.3958 + 35.8903i 0.349055 + 1.20508i 0.922552 + 0.385872i 0.126099π0.126099\pi
−0.573497 + 0.819208i 0.694414π0.694414\pi
888888 −21.7921 + 1.75924i −0.731296 + 0.0590363i
889889 −4.83787 39.8434i −0.162257 1.33630i
890890 10.4050 + 12.7438i 0.348777 + 0.427174i
891891 −4.55241 1.93960i −0.152511 0.0649790i
892892 6.05151 + 1.49156i 0.202620 + 0.0499412i
893893 −1.74405 + 1.81575i −0.0583623 + 0.0607616i
894894 24.8947 + 8.31106i 0.832602 + 0.277963i
895895 −18.3012 6.10985i −0.611742 0.204230i
896896 −9.22831 + 24.3330i −0.308296 + 0.812910i
897897 −68.5178 31.1181i −2.28774 1.03900i
898898 8.38130 + 22.0997i 0.279687 + 0.737475i
899899 −0.220874 5.48093i −0.00736655 0.182799i
900900 21.7318 + 1.75437i 0.724392 + 0.0584789i
901901 −2.11596 10.3646i −0.0704927 0.345296i
902902 2.52870 + 2.24023i 0.0841965 + 0.0745915i
903903 −18.0954 + 62.4726i −0.602178 + 2.07896i
904904 19.3766 12.2530i 0.644456 0.407529i
905905 −6.20866 8.99480i −0.206383 0.298997i
906906 −5.53954 6.78471i −0.184039 0.225407i
907907 0.00502262 + 0.124635i 0.000166773 + 0.00413844i 0.999270 0.0381966i 0.0121613π-0.0121613\pi
−0.999103 + 0.0423351i 0.986520π0.986520\pi
908908 2.15178 + 1.36071i 0.0714094 + 0.0451566i
909909 57.2956 50.7595i 1.90038 1.68359i
910910 8.69876 + 8.07977i 0.288361 + 0.267842i
911911 22.1989 + 19.6665i 0.735483 + 0.651581i 0.945316 0.326156i 0.105754π-0.105754\pi
−0.209833 + 0.977737i 0.567292π0.567292\pi
912912 15.1163 + 52.1874i 0.500549 + 1.72810i
913913 −0.839261 + 1.76870i −0.0277755 + 0.0585356i
914914 37.3777 12.4785i 1.23634 0.412752i
915915 6.91013 0.228442
916916 26.3654 8.80206i 0.871137 0.290828i
917917 0.401084 9.95281i 0.0132450 0.328671i
918918 −0.582362 + 4.79618i −0.0192208 + 0.158298i
919919 −31.5065 + 19.9235i −1.03930 + 0.657217i −0.941162 0.337956i 0.890265π-0.890265\pi
−0.0981429 + 0.995172i 0.531290π0.531290\pi
920920 −7.65362 + 3.26090i −0.252332 + 0.107509i
921921 63.1129 + 65.7075i 2.07964 + 2.16514i
922922 −19.4129 + 4.78486i −0.639331 + 0.157581i
923923 15.9184 + 7.22950i 0.523960 + 0.237962i
924924 8.24848 + 2.03307i 0.271355 + 0.0668830i
925925 −12.8088 22.1856i −0.421152 0.729457i
926926 25.8324 + 26.8943i 0.848904 + 0.883803i
927927 −15.1593 31.9475i −0.497897 1.04929i
928928 −7.30627 + 6.47279i −0.239840 + 0.212480i
929929 11.1127 + 8.35064i 0.364595 + 0.273976i 0.767213 0.641393i 0.221643π-0.221643\pi
−0.402617 + 0.915368i 0.631899π0.631899\pi
930930 9.56653 + 7.18878i 0.313699 + 0.235729i
931931 −2.67441 + 2.36932i −0.0876502 + 0.0776513i
932932 −0.733737 1.54632i −0.0240344 0.0506514i
933933 57.3204 + 59.6768i 1.87659 + 1.95373i
934934 19.1303 + 33.1347i 0.625963 + 1.08420i
935935 0.729737 + 0.179864i 0.0238650 + 0.00588218i
936936 −14.8798 + 14.7789i −0.486361 + 0.483064i
937937 23.1520 5.70646i 0.756344 0.186422i 0.157755 0.987478i 0.449574π-0.449574\pi
0.598589 + 0.801056i 0.295728π0.295728\pi
938938 −34.4022 35.8165i −1.12327 1.16945i
939939 61.7816 26.3227i 2.01617 0.859008i
940940 0.461619 0.291910i 0.0150564 0.00952106i
941941 3.11786 25.6779i 0.101639 0.837076i −0.849345 0.527838i 0.823003π-0.823003\pi
0.950985 0.309238i 0.100074π-0.100074\pi
942942 3.01868 74.9079i 0.0983540 2.44063i
943943 13.1011 4.37380i 0.426632 0.142431i
944944 −63.1678 −2.05594
945945 −4.99531 + 1.66768i −0.162498 + 0.0542497i
946946 8.12307 17.1190i 0.264104 0.556587i
947947 6.58124 + 22.7211i 0.213862 + 0.738336i 0.993672 + 0.112320i 0.0358282π0.0358282\pi
−0.779810 + 0.626016i 0.784685π0.784685\pi
948948 19.2904 + 17.0898i 0.626525 + 0.555052i
949949 27.3461 23.1009i 0.887693 0.749885i
950950 −24.5405 + 21.7410i −0.796198 + 0.705370i
951951 −8.85481 5.59944i −0.287137 0.181574i
952952 −0.134221 3.33067i −0.00435014 0.107948i
953953 −29.3576 35.9565i −0.950985 1.16475i −0.986232 0.165367i 0.947119π-0.947119\pi
0.0352467 0.999379i 0.488778π-0.488778\pi
954954 −46.4700 67.3235i −1.50452 2.17968i
955955 2.52788 1.59853i 0.0818002 0.0517273i
956956 1.19701 4.13257i 0.0387141 0.133657i
957957 −3.46194 3.06701i −0.111909 0.0991424i
958958 3.47177 + 17.0059i 0.112168 + 0.549434i
959959 −32.1872 2.59842i −1.03938 0.0839073i
960960 −0.0681203 1.69039i −0.00219857 0.0545570i
961961 6.93387 + 18.2831i 0.223673 + 0.589778i
962962 −36.5306 6.82299i −1.17779 0.219982i
963963 −20.2625 + 53.4278i −0.652950 + 1.72169i
964964 −12.0593 4.02598i −0.388403 0.129668i
965965 −13.6133 4.54479i −0.438227 0.146302i
966966 64.0742 66.7083i 2.06155 2.14630i
967967 −20.3389 5.01308i −0.654054 0.161210i −0.101694 0.994816i 0.532426π-0.532426\pi
−0.552360 + 0.833606i 0.686273π0.686273\pi
968968 −12.9315 5.50961i −0.415635 0.177086i
969969 −6.53611 8.00528i −0.209970 0.257167i
970970 1.11855 + 9.21210i 0.0359145 + 0.295783i
971971 18.0689 1.45867i 0.579859 0.0468111i 0.212942 0.977065i 0.431695π-0.431695\pi
0.366917 + 0.930254i 0.380413π0.380413\pi
972972 −6.97966 24.0966i −0.223873 0.772898i
973973 −5.73039 + 28.0693i −0.183708 + 0.899861i
974974 2.85592 23.5206i 0.0915096 0.753649i
975975 −40.1357 14.4579i −1.28537 0.463022i
976976 2.08983 + 17.2113i 0.0668937 + 0.550919i
977977 −56.3146 4.54618i −1.80166 0.145445i −0.866389 0.499370i 0.833565π-0.833565\pi
−0.935274 + 0.353924i 0.884847π0.884847\pi
978978 −49.7966 + 60.9897i −1.59232 + 1.95024i
979979 −10.6076 7.97110i −0.339020 0.254757i
980980 0.686322 0.360210i 0.0219238 0.0115065i
981981 −9.04008 44.2812i −0.288628 1.41379i
982982 35.7574 2.88664i 1.14106 0.0921163i
983983 −11.4094 + 16.5294i −0.363903 + 0.527205i −0.961577 0.274534i 0.911476π-0.911476\pi
0.597674 + 0.801739i 0.296092π0.296092\pi
984984 0.269069 6.67687i 0.00857760 0.212851i
985985 14.5642 10.9443i 0.464053 0.348713i
986986 1.17327 2.47262i 0.0373646 0.0787442i
987987 2.28735 3.31380i 0.0728072 0.105479i
988988 0.298893 + 17.8567i 0.00950906 + 0.568097i
989989 −44.0077 63.7561i −1.39936 2.02733i
990990 5.73676 0.932315i 0.182326 0.0296309i
991991 −22.1392 38.3463i −0.703276 1.21811i −0.967310 0.253597i 0.918386π-0.918386\pi
0.264034 0.964513i 0.414947π-0.414947\pi
992992 −10.1841 + 17.6394i −0.323346 + 0.560051i
993993 18.6818 49.2598i 0.592849 1.56321i
994994 −14.8860 + 15.4980i −0.472156 + 0.491566i
995995 0.262088 0.453950i 0.00830875 0.0143912i
996996 −5.67021 + 1.39758i −0.179667 + 0.0442840i
997997 −48.9446 7.95427i −1.55009 0.251914i −0.675714 0.737164i 0.736165π-0.736165\pi
−0.874376 + 0.485250i 0.838729π0.838729\pi
998998 −11.2267 7.09935i −0.355376 0.224726i
999999 10.4256 12.7690i 0.329851 0.403994i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 169.2.i.a.3.12 336
169.113 even 39 inner 169.2.i.a.113.12 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.2.i.a.3.12 336 1.1 even 1 trivial
169.2.i.a.113.12 yes 336 169.113 even 39 inner