Properties

Label 627.2.j.a.58.3
Level 627627
Weight 22
Character 627.58
Analytic conductor 5.0075.007
Analytic rank 00
Dimension 2424
Inner twists 22

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [627,2,Mod(58,627)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(627, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("627.58");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 627=31119 627 = 3 \cdot 11 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 627.j (of order 55, degree 44, 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: 5.006620206735.00662020673
Analytic rank: 00
Dimension: 2424
Relative dimension: 66 over Q(ζ5)\Q(\zeta_{5})
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 58.3
Character χ\chi == 627.58
Dual form 627.2.j.a.400.3

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+(0.2714540.197223i)q2+(0.309017+0.951057i)q3+(0.583244+1.79504i)q4+(2.016161.46483i)q5+(0.271454+0.197223i)q6+(0.281064+0.865027i)q7+(0.403072+1.24053i)q8+(0.809017+0.587785i)q90.836193q10+(1.01652+3.15701i)q111.88742q12+(2.011191.46121i)q13+(0.0943071+0.290248i)q14+(0.7701052.37014i)q15+(2.699831.96154i)q16+(6.323084.59398i)q17+(0.103686+0.319114i)q18+(0.309017+0.951057i)q19+(3.805342.76474i)q200.909543q21+(0.346695+1.05746i)q227.23909q23+(1.05526+0.766688i)q24+(0.374105+1.15138i)q25+(0.2577610.793306i)q26+(0.8090170.587785i)q27+(1.388831.00904i)q28+(2.19995+6.77075i)q29+(0.2583980.795267i)q30+(4.669743.39276i)q313.72848q32+(3.31661+0.00879787i)q332.62247q34+(1.833791.33232i)q35+(0.5832441.79504i)q36+(3.12139+9.60665i)q37+(0.271454+0.197223i)q38+(2.01119+1.46121i)q39+(1.004503.09153i)q40+(1.33433+4.10663i)q41+(0.246899+0.179383i)q421.26242q43+(5.074073.66600i)q44+2.49211q45+(1.96508+1.42772i)q46+(3.5215010.8381i)q47+(1.031243.17384i)q48+(4.99384+3.62824i)q49+(0.328630+0.238764i)q50+(2.415207.43322i)q51+(1.44992+4.46241i)q52+(3.84930+2.79668i)q530.335536q54+(6.673944.87600i)q551.18638q56+(0.809017+0.587785i)q57+(0.738163+2.27183i)q58+(0.7967762.45222i)q59+(3.80534+2.76474i)q60+(7.300735.30429i)q61+(0.5984891.84196i)q62+(0.2810640.865027i)q63+(4.387543.18774i)q646.19531q65+(0.898574+0.656501i)q66+2.84348q67+(11.93438.67076i)q68+(2.237006.88479i)q69+(0.2350240.723330i)q70+(10.9767+7.97503i)q71+(1.055260.766688i)q72+(2.83023+8.71055i)q73+(1.04734+3.22338i)q74+(0.979419+0.711589i)q751.88742q76+(2.445191.76664i)q77+0.834131q78+(6.73616+4.89411i)q79+(2.56997+7.90956i)q80+(0.3090170.951057i)q81+(1.17213+0.851604i)q82+(10.8732+7.89986i)q83+(0.5304851.63266i)q84+(6.01895+18.5244i)q85+(0.342688+0.248977i)q867.11919q87+(4.32608+0.0114757i)q88+8.67792q89+(0.6764950.491502i)q90+(0.698716+2.15043i)q91+(4.2221512.9945i)q92+(4.66974+3.39276i)q93+(3.093442.24752i)q94+(0.7701052.37014i)q95+(1.152163.54599i)q96+(10.4341+7.58082i)q97+2.07117q98+(1.033263.15157i)q99+O(q100)q+(0.271454 - 0.197223i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.583244 + 1.79504i) q^{4} +(-2.01616 - 1.46483i) q^{5} +(0.271454 + 0.197223i) q^{6} +(-0.281064 + 0.865027i) q^{7} +(0.403072 + 1.24053i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.836193 q^{10} +(-1.01652 + 3.15701i) q^{11} -1.88742 q^{12} +(2.01119 - 1.46121i) q^{13} +(0.0943071 + 0.290248i) q^{14} +(0.770105 - 2.37014i) q^{15} +(-2.69983 - 1.96154i) q^{16} +(-6.32308 - 4.59398i) q^{17} +(-0.103686 + 0.319114i) q^{18} +(0.309017 + 0.951057i) q^{19} +(3.80534 - 2.76474i) q^{20} -0.909543 q^{21} +(0.346695 + 1.05746i) q^{22} -7.23909 q^{23} +(-1.05526 + 0.766688i) q^{24} +(0.374105 + 1.15138i) q^{25} +(0.257761 - 0.793306i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.38883 - 1.00904i) q^{28} +(-2.19995 + 6.77075i) q^{29} +(-0.258398 - 0.795267i) q^{30} +(4.66974 - 3.39276i) q^{31} -3.72848 q^{32} +(-3.31661 + 0.00879787i) q^{33} -2.62247 q^{34} +(1.83379 - 1.33232i) q^{35} +(-0.583244 - 1.79504i) q^{36} +(-3.12139 + 9.60665i) q^{37} +(0.271454 + 0.197223i) q^{38} +(2.01119 + 1.46121i) q^{39} +(1.00450 - 3.09153i) q^{40} +(1.33433 + 4.10663i) q^{41} +(-0.246899 + 0.179383i) q^{42} -1.26242 q^{43} +(-5.07407 - 3.66600i) q^{44} +2.49211 q^{45} +(-1.96508 + 1.42772i) q^{46} +(-3.52150 - 10.8381i) q^{47} +(1.03124 - 3.17384i) q^{48} +(4.99384 + 3.62824i) q^{49} +(0.328630 + 0.238764i) q^{50} +(2.41520 - 7.43322i) q^{51} +(1.44992 + 4.46241i) q^{52} +(-3.84930 + 2.79668i) q^{53} -0.335536 q^{54} +(6.67394 - 4.87600i) q^{55} -1.18638 q^{56} +(-0.809017 + 0.587785i) q^{57} +(0.738163 + 2.27183i) q^{58} +(0.796776 - 2.45222i) q^{59} +(3.80534 + 2.76474i) q^{60} +(-7.30073 - 5.30429i) q^{61} +(0.598489 - 1.84196i) q^{62} +(-0.281064 - 0.865027i) q^{63} +(4.38754 - 3.18774i) q^{64} -6.19531 q^{65} +(-0.898574 + 0.656501i) q^{66} +2.84348 q^{67} +(11.9343 - 8.67076i) q^{68} +(-2.23700 - 6.88479i) q^{69} +(0.235024 - 0.723330i) q^{70} +(10.9767 + 7.97503i) q^{71} +(-1.05526 - 0.766688i) q^{72} +(-2.83023 + 8.71055i) q^{73} +(1.04734 + 3.22338i) q^{74} +(-0.979419 + 0.711589i) q^{75} -1.88742 q^{76} +(-2.44519 - 1.76664i) q^{77} +0.834131 q^{78} +(-6.73616 + 4.89411i) q^{79} +(2.56997 + 7.90956i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.17213 + 0.851604i) q^{82} +(10.8732 + 7.89986i) q^{83} +(0.530485 - 1.63266i) q^{84} +(6.01895 + 18.5244i) q^{85} +(-0.342688 + 0.248977i) q^{86} -7.11919 q^{87} +(-4.32608 + 0.0114757i) q^{88} +8.67792 q^{89} +(0.676495 - 0.491502i) q^{90} +(0.698716 + 2.15043i) q^{91} +(4.22215 - 12.9945i) q^{92} +(4.66974 + 3.39276i) q^{93} +(-3.09344 - 2.24752i) q^{94} +(0.770105 - 2.37014i) q^{95} +(-1.15216 - 3.54599i) q^{96} +(-10.4341 + 7.58082i) q^{97} +2.07117 q^{98} +(-1.03326 - 3.15157i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+3q26q35q4+8q5+3q6+q7+5q86q9+2q1010q11+10q12+6q13+12q142q15+11q168q172q186q19+9q20+22q98+O(q100) 24 q + 3 q^{2} - 6 q^{3} - 5 q^{4} + 8 q^{5} + 3 q^{6} + q^{7} + 5 q^{8} - 6 q^{9} + 2 q^{10} - 10 q^{11} + 10 q^{12} + 6 q^{13} + 12 q^{14} - 2 q^{15} + 11 q^{16} - 8 q^{17} - 2 q^{18} - 6 q^{19} + 9 q^{20}+ \cdots - 22 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/627Z)×\left(\mathbb{Z}/627\mathbb{Z}\right)^\times.

nn 343343 419419 496496
χ(n)\chi(n) e(45)e\left(\frac{4}{5}\right) 11 11

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 0.271454 0.197223i 0.191947 0.139458i −0.487661 0.873033i 0.662150π-0.662150\pi
0.679608 + 0.733575i 0.262150π0.262150\pi
33 0.309017 + 0.951057i 0.178411 + 0.549093i
44 −0.583244 + 1.79504i −0.291622 + 0.897519i
55 −2.01616 1.46483i −0.901655 0.655091i 0.0372355 0.999307i 0.488145π-0.488145\pi
−0.938891 + 0.344216i 0.888145π0.888145\pi
66 0.271454 + 0.197223i 0.110821 + 0.0805160i
77 −0.281064 + 0.865027i −0.106232 + 0.326949i −0.990018 0.140943i 0.954987π-0.954987\pi
0.883785 + 0.467892i 0.154987π0.154987\pi
88 0.403072 + 1.24053i 0.142507 + 0.438593i
99 −0.809017 + 0.587785i −0.269672 + 0.195928i
1010 −0.836193 −0.264428
1111 −1.01652 + 3.15701i −0.306493 + 0.951873i
1212 −1.88742 −0.544850
1313 2.01119 1.46121i 0.557804 0.405268i −0.272851 0.962056i 0.587967π-0.587967\pi
0.830654 + 0.556788i 0.187967π0.187967\pi
1414 0.0943071 + 0.290248i 0.0252046 + 0.0775719i
1515 0.770105 2.37014i 0.198840 0.611968i
1616 −2.69983 1.96154i −0.674957 0.490385i
1717 −6.32308 4.59398i −1.53357 1.11420i −0.954211 0.299133i 0.903303π-0.903303\pi
−0.579360 0.815072i 0.696697π-0.696697\pi
1818 −0.103686 + 0.319114i −0.0244391 + 0.0752158i
1919 0.309017 + 0.951057i 0.0708934 + 0.218187i
2020 3.80534 2.76474i 0.850899 0.618214i
2121 −0.909543 −0.198479
2222 0.346695 + 1.05746i 0.0739156 + 0.225452i
2323 −7.23909 −1.50946 −0.754728 0.656038i 0.772231π-0.772231\pi
−0.754728 + 0.656038i 0.772231π0.772231\pi
2424 −1.05526 + 0.766688i −0.215403 + 0.156500i
2525 0.374105 + 1.15138i 0.0748209 + 0.230275i
2626 0.257761 0.793306i 0.0505510 0.155580i
2727 −0.809017 0.587785i −0.155695 0.113119i
2828 −1.38883 1.00904i −0.262464 0.190691i
2929 −2.19995 + 6.77075i −0.408521 + 1.25730i 0.509399 + 0.860531i 0.329868π0.329868\pi
−0.917919 + 0.396767i 0.870132π0.870132\pi
3030 −0.258398 0.795267i −0.0471768 0.145195i
3131 4.66974 3.39276i 0.838710 0.609358i −0.0833004 0.996524i 0.526546π-0.526546\pi
0.922010 + 0.387166i 0.126546π0.126546\pi
3232 −3.72848 −0.659107
3333 −3.31661 + 0.00879787i −0.577348 + 0.00153151i
3434 −2.62247 −0.449749
3535 1.83379 1.33232i 0.309966 0.225204i
3636 −0.583244 1.79504i −0.0972073 0.299173i
3737 −3.12139 + 9.60665i −0.513153 + 1.57932i 0.273464 + 0.961882i 0.411831π0.411831\pi
−0.786617 + 0.617441i 0.788169π0.788169\pi
3838 0.271454 + 0.197223i 0.0440357 + 0.0319938i
3939 2.01119 + 1.46121i 0.322048 + 0.233982i
4040 1.00450 3.09153i 0.158825 0.488814i
4141 1.33433 + 4.10663i 0.208387 + 0.641349i 0.999557 + 0.0297530i 0.00947206π0.00947206\pi
−0.791170 + 0.611596i 0.790528π0.790528\pi
4242 −0.246899 + 0.179383i −0.0380974 + 0.0276794i
4343 −1.26242 −0.192517 −0.0962583 0.995356i 0.530687π-0.530687\pi
−0.0962583 + 0.995356i 0.530687π0.530687\pi
4444 −5.07407 3.66600i −0.764944 0.552670i
4545 2.49211 0.371502
4646 −1.96508 + 1.42772i −0.289736 + 0.210505i
4747 −3.52150 10.8381i −0.513664 1.58089i −0.785700 0.618607i 0.787697π-0.787697\pi
0.272037 0.962287i 0.412303π-0.412303\pi
4848 1.03124 3.17384i 0.148847 0.458104i
4949 4.99384 + 3.62824i 0.713406 + 0.518320i
5050 0.328630 + 0.238764i 0.0464753 + 0.0337663i
5151 2.41520 7.43322i 0.338196 1.04086i
5252 1.44992 + 4.46241i 0.201068 + 0.618824i
5353 −3.84930 + 2.79668i −0.528743 + 0.384154i −0.819887 0.572525i 0.805964π-0.805964\pi
0.291145 + 0.956679i 0.405964π0.405964\pi
5454 −0.335536 −0.0456607
5555 6.67394 4.87600i 0.899914 0.657480i
5656 −1.18638 −0.158536
5757 −0.809017 + 0.587785i −0.107157 + 0.0778541i
5858 0.738163 + 2.27183i 0.0969255 + 0.298306i
5959 0.796776 2.45222i 0.103731 0.319252i −0.885699 0.464259i 0.846321π-0.846321\pi
0.989431 + 0.145007i 0.0463205π0.0463205\pi
6060 3.80534 + 2.76474i 0.491267 + 0.356926i
6161 −7.30073 5.30429i −0.934763 0.679145i 0.0123914 0.999923i 0.496056π-0.496056\pi
−0.947154 + 0.320778i 0.896056π0.896056\pi
6262 0.598489 1.84196i 0.0760082 0.233929i
6363 −0.281064 0.865027i −0.0354108 0.108983i
6464 4.38754 3.18774i 0.548443 0.398467i
6565 −6.19531 −0.768434
6666 −0.898574 + 0.656501i −0.110607 + 0.0808097i
6767 2.84348 0.347386 0.173693 0.984800i 0.444430π-0.444430\pi
0.173693 + 0.984800i 0.444430π0.444430\pi
6868 11.9343 8.67076i 1.44724 1.05148i
6969 −2.23700 6.88479i −0.269303 0.828831i
7070 0.235024 0.723330i 0.0280907 0.0864544i
7171 10.9767 + 7.97503i 1.30269 + 0.946462i 0.999978 0.00661910i 0.00210694π-0.00210694\pi
0.302715 + 0.953081i 0.402107π0.402107\pi
7272 −1.05526 0.766688i −0.124363 0.0903550i
7373 −2.83023 + 8.71055i −0.331253 + 1.01949i 0.637285 + 0.770628i 0.280057π0.280057\pi
−0.968538 + 0.248864i 0.919943π0.919943\pi
7474 1.04734 + 3.22338i 0.121751 + 0.374710i
7575 −0.979419 + 0.711589i −0.113094 + 0.0821673i
7676 −1.88742 −0.216501
7777 −2.44519 1.76664i −0.278655 0.201327i
7878 0.834131 0.0944467
7979 −6.73616 + 4.89411i −0.757877 + 0.550630i −0.898259 0.439467i 0.855167π-0.855167\pi
0.140381 + 0.990098i 0.455167π0.455167\pi
8080 2.56997 + 7.90956i 0.287332 + 0.884316i
8181 0.309017 0.951057i 0.0343352 0.105673i
8282 1.17213 + 0.851604i 0.129440 + 0.0940439i
8383 10.8732 + 7.89986i 1.19349 + 0.867123i 0.993629 0.112701i 0.0359503π-0.0359503\pi
0.199863 + 0.979824i 0.435950π0.435950\pi
8484 0.530485 1.63266i 0.0578807 0.178138i
8585 6.01895 + 18.5244i 0.652847 + 2.00926i
8686 −0.342688 + 0.248977i −0.0369530 + 0.0268479i
8787 −7.11919 −0.763258
8888 −4.32608 + 0.0114757i −0.461162 + 0.00122331i
8989 8.67792 0.919858 0.459929 0.887956i 0.347875π-0.347875\pi
0.459929 + 0.887956i 0.347875π0.347875\pi
9090 0.676495 0.491502i 0.0713088 0.0518089i
9191 0.698716 + 2.15043i 0.0732454 + 0.225426i
9292 4.22215 12.9945i 0.440190 1.35477i
9393 4.66974 + 3.39276i 0.484229 + 0.351813i
9494 −3.09344 2.24752i −0.319064 0.231814i
9595 0.770105 2.37014i 0.0790111 0.243171i
9696 −1.15216 3.54599i −0.117592 0.361911i
9797 −10.4341 + 7.58082i −1.05942 + 0.769716i −0.973982 0.226627i 0.927230π-0.927230\pi
−0.0854414 + 0.996343i 0.527230π0.527230\pi
9898 2.07117 0.209220
9999 −1.03326 3.15157i −0.103846 0.316744i
100100 −2.28496 −0.228496
101101 5.99526 4.35581i 0.596550 0.433419i −0.248102 0.968734i 0.579807π-0.579807\pi
0.844653 + 0.535315i 0.179807π0.179807\pi
102102 −0.810386 2.49411i −0.0802402 0.246954i
103103 −1.25217 + 3.85378i −0.123380 + 0.379724i −0.993602 0.112935i 0.963975π-0.963975\pi
0.870223 + 0.492659i 0.163975π0.163975\pi
104104 2.62333 + 1.90596i 0.257239 + 0.186895i
105105 1.83379 + 1.33232i 0.178959 + 0.130021i
106106 −0.493340 + 1.51834i −0.0479174 + 0.147475i
107107 3.68781 + 11.3499i 0.356514 + 1.09724i 0.955126 + 0.296198i 0.0957189π0.0957189\pi
−0.598612 + 0.801039i 0.704281π0.704281\pi
108108 1.52695 1.10940i 0.146931 0.106752i
109109 15.3614 1.47135 0.735676 0.677334i 0.236865π-0.236865\pi
0.735676 + 0.677334i 0.236865π0.236865\pi
110110 0.850009 2.63987i 0.0810452 0.251701i
111111 −10.1010 −0.958747
112112 2.45561 1.78410i 0.232033 0.168582i
113113 0.0328895 + 0.101224i 0.00309399 + 0.00952231i 0.952592 0.304252i 0.0984065π-0.0984065\pi
−0.949498 + 0.313774i 0.898406π0.898406\pi
114114 −0.103686 + 0.319114i −0.00971111 + 0.0298877i
115115 14.5952 + 10.6040i 1.36101 + 0.988830i
116116 −10.8707 7.89800i −1.00932 0.733311i
117117 −0.768206 + 2.36429i −0.0710207 + 0.218579i
118118 −0.267347 0.822809i −0.0246113 0.0757457i
119119 5.75111 4.17843i 0.527203 0.383036i
120120 3.25063 0.296741
121121 −8.93336 6.41833i −0.812124 0.583485i
122122 −3.02794 −0.274137
123123 −3.49331 + 2.53804i −0.314981 + 0.228847i
124124 3.36655 + 10.3612i 0.302325 + 0.930460i
125125 −2.91822 + 8.98134i −0.261013 + 0.803316i
126126 −0.246899 0.179383i −0.0219955 0.0159807i
127127 −3.19548 2.32165i −0.283553 0.206013i 0.436913 0.899504i 0.356072π-0.356072\pi
−0.720466 + 0.693491i 0.756072π0.756072\pi
128128 2.86665 8.82263i 0.253378 0.779818i
129129 −0.390108 1.20063i −0.0343471 0.105709i
130130 −1.68174 + 1.22186i −0.147499 + 0.107164i
131131 −12.0449 −1.05237 −0.526185 0.850370i 0.676378π-0.676378\pi
−0.526185 + 0.850370i 0.676378π0.676378\pi
132132 1.91860 5.95858i 0.166993 0.518628i
133133 −0.909543 −0.0788674
134134 0.771874 0.560799i 0.0666797 0.0484457i
135135 0.770105 + 2.37014i 0.0662801 + 0.203989i
136136 3.15031 9.69565i 0.270137 0.831395i
137137 3.74838 + 2.72336i 0.320246 + 0.232672i 0.736280 0.676677i 0.236580π-0.236580\pi
−0.416035 + 0.909349i 0.636580π0.636580\pi
138138 −1.96508 1.42772i −0.167279 0.121535i
139139 0.340778 1.04881i 0.0289044 0.0889587i −0.935564 0.353158i 0.885108π-0.885108\pi
0.964468 + 0.264199i 0.0851077π0.0851077\pi
140140 1.32203 + 4.06879i 0.111732 + 0.343875i
141141 9.21941 6.69829i 0.776414 0.564098i
142142 4.55253 0.382040
143143 2.56864 + 7.83469i 0.214801 + 0.655170i
144144 3.33717 0.278097
145145 14.3534 10.4284i 1.19199 0.866030i
146146 0.949643 + 2.92270i 0.0785930 + 0.241885i
147147 −1.90748 + 5.87062i −0.157326 + 0.484200i
148148 −15.4238 11.2060i −1.26783 0.921130i
149149 −12.9895 9.43744i −1.06414 0.773145i −0.0892925 0.996005i 0.528461π-0.528461\pi
−0.974850 + 0.222860i 0.928461π0.928461\pi
150150 −0.125526 + 0.386328i −0.0102491 + 0.0315435i
151151 −1.59843 4.91947i −0.130079 0.400341i 0.864714 0.502265i 0.167500π-0.167500\pi
−0.994792 + 0.101925i 0.967500π0.967500\pi
152152 −1.05526 + 0.766688i −0.0855925 + 0.0621866i
153153 7.81575 0.631866
154154 −1.01218 + 0.00268497i −0.0815636 + 0.000216361i
155155 −14.3848 −1.15541
156156 −3.79595 + 2.75792i −0.303919 + 0.220810i
157157 4.67828 + 14.3983i 0.373367 + 1.14911i 0.944574 + 0.328300i 0.106476π0.106476\pi
−0.571206 + 0.820806i 0.693524π0.693524\pi
158158 −0.863329 + 2.65705i −0.0686827 + 0.211384i
159159 −3.84930 2.79668i −0.305270 0.221791i
160160 7.51721 + 5.46157i 0.594288 + 0.431775i
161161 2.03465 6.26201i 0.160353 0.493515i
162162 −0.103686 0.319114i −0.00814636 0.0250719i
163163 3.11617 2.26403i 0.244077 0.177332i −0.459021 0.888426i 0.651800π-0.651800\pi
0.703098 + 0.711093i 0.251800π0.251800\pi
164164 −8.14981 −0.636393
165165 6.69972 + 4.84053i 0.521572 + 0.376835i
166166 4.50962 0.350014
167167 3.36122 2.44207i 0.260099 0.188973i −0.450092 0.892982i 0.648609π-0.648609\pi
0.710191 + 0.704009i 0.248609π0.248609\pi
168168 −0.366611 1.12831i −0.0282847 0.0870512i
169169 −2.10749 + 6.48618i −0.162114 + 0.498937i
170170 5.28732 + 3.84146i 0.405519 + 0.294626i
171171 −0.809017 0.587785i −0.0618671 0.0449491i
172172 0.736296 2.26609i 0.0561420 0.172787i
173173 −7.35968 22.6508i −0.559546 1.72211i −0.683625 0.729833i 0.739598π-0.739598\pi
0.124080 0.992272i 0.460402π-0.460402\pi
174174 −1.93253 + 1.40407i −0.146505 + 0.106442i
175175 −1.10112 −0.0832367
176176 8.93702 6.52942i 0.673653 0.492173i
177177 2.57842 0.193806
178178 2.35566 1.71149i 0.176564 0.128281i
179179 1.06971 + 3.29223i 0.0799538 + 0.246073i 0.983041 0.183384i 0.0587051π-0.0587051\pi
−0.903088 + 0.429457i 0.858705π0.858705\pi
180180 −1.45351 + 4.47344i −0.108338 + 0.333431i
181181 15.3514 + 11.1534i 1.14106 + 0.829028i 0.987266 0.159076i 0.0508513π-0.0508513\pi
0.153792 + 0.988103i 0.450851π0.450851\pi
182182 0.613783 + 0.445940i 0.0454966 + 0.0330552i
183183 2.78863 8.58253i 0.206142 0.634439i
184184 −2.91787 8.98029i −0.215108 0.662036i
185185 20.3653 14.7963i 1.49729 1.08784i
186186 1.93675 0.142009
187187 20.9308 15.2921i 1.53061 1.11827i
188188 21.5086 1.56868
189189 0.735836 0.534616i 0.0535242 0.0388876i
190190 −0.258398 0.795267i −0.0187462 0.0576947i
191191 2.05731 6.33173i 0.148861 0.458148i −0.848626 0.528993i 0.822570π-0.822570\pi
0.997487 + 0.0708452i 0.0225696π0.0225696\pi
192192 4.38754 + 3.18774i 0.316644 + 0.230055i
193193 5.29086 + 3.84404i 0.380845 + 0.276700i 0.761693 0.647938i 0.224368π-0.224368\pi
−0.380849 + 0.924637i 0.624368π0.624368\pi
194194 −1.33727 + 4.11569i −0.0960104 + 0.295490i
195195 −1.91446 5.89209i −0.137097 0.421941i
196196 −9.42546 + 6.84800i −0.673247 + 0.489143i
197197 −19.7664 −1.40829 −0.704147 0.710054i 0.748671π-0.748671\pi
−0.704147 + 0.710054i 0.748671π0.748671\pi
198198 −0.902044 0.651724i −0.0641055 0.0463160i
199199 −3.62149 −0.256721 −0.128360 0.991728i 0.540971π-0.540971\pi
−0.128360 + 0.991728i 0.540971π0.540971\pi
200200 −1.27752 + 0.928174i −0.0903344 + 0.0656318i
201201 0.878682 + 2.70431i 0.0619775 + 0.190747i
202202 0.768372 2.36481i 0.0540625 0.166387i
203203 −5.23856 3.80603i −0.367675 0.267131i
204204 11.9343 + 8.67076i 0.835566 + 0.607074i
205205 3.32529 10.2342i 0.232249 0.714787i
206206 0.420147 + 1.29308i 0.0292730 + 0.0900932i
207207 5.85655 4.25503i 0.407058 0.295745i
208208 −8.29609 −0.575230
209209 −3.31661 + 0.00879787i −0.229415 + 0.000608562i
210210 0.760554 0.0524832
211211 7.41500 5.38731i 0.510470 0.370878i −0.302532 0.953139i 0.597832π-0.597832\pi
0.813002 + 0.582261i 0.197832π0.197832\pi
212212 −2.77507 8.54080i −0.190593 0.586584i
213213 −4.19272 + 12.9039i −0.287281 + 0.884159i
214214 3.23954 + 2.35366i 0.221450 + 0.160893i
215215 2.54523 + 1.84922i 0.173584 + 0.126116i
216216 0.403072 1.24053i 0.0274256 0.0844072i
217217 1.62233 + 4.99303i 0.110131 + 0.338949i
218218 4.16991 3.02961i 0.282422 0.205191i
219219 −9.15881 −0.618895
220220 4.86008 + 14.8239i 0.327667 + 0.999426i
221221 −19.4297 −1.30698
222222 −2.74197 + 1.99216i −0.184029 + 0.133705i
223223 −8.09236 24.9057i −0.541904 1.66781i −0.728239 0.685324i 0.759661π-0.759661\pi
0.186334 0.982486i 0.440339π-0.440339\pi
224224 1.04794 3.22523i 0.0700185 0.215495i
225225 −0.979419 0.711589i −0.0652946 0.0474393i
226226 0.0288916 + 0.0209910i 0.00192184 + 0.00139630i
227227 −5.10864 + 15.7228i −0.339072 + 1.04356i 0.625609 + 0.780137i 0.284851π0.284851\pi
−0.964681 + 0.263421i 0.915149π0.915149\pi
228228 −0.583244 1.79504i −0.0386262 0.118879i
229229 −22.3355 + 16.2277i −1.47597 + 1.07236i −0.497144 + 0.867668i 0.665618π0.665618\pi
−0.978827 + 0.204688i 0.934382π0.934382\pi
230230 6.05328 0.399142
231231 0.924571 2.87143i 0.0608323 0.188926i
232232 −9.28604 −0.609659
233233 −6.81202 + 4.94922i −0.446270 + 0.324234i −0.788121 0.615520i 0.788946π-0.788946\pi
0.341851 + 0.939754i 0.388946π0.388946\pi
234234 0.257761 + 0.793306i 0.0168503 + 0.0518600i
235235 −8.77598 + 27.0097i −0.572482 + 1.76192i
236236 3.93712 + 2.86049i 0.256285 + 0.186202i
237237 −6.73616 4.89411i −0.437561 0.317906i
238238 0.737081 2.26850i 0.0477779 0.147045i
239239 3.57299 + 10.9965i 0.231117 + 0.711306i 0.997613 + 0.0690562i 0.0219988π0.0219988\pi
−0.766495 + 0.642250i 0.778001π0.778001\pi
240240 −6.72827 + 4.88838i −0.434308 + 0.315543i
241241 −10.9212 −0.703494 −0.351747 0.936095i 0.614412π-0.614412\pi
−0.351747 + 0.936095i 0.614412π0.614412\pi
242242 −3.69084 + 0.0195813i −0.237256 + 0.00125873i
243243 1.00000 0.0641500
244244 13.7795 10.0114i 0.882143 0.640915i
245245 −4.75365 14.6302i −0.303700 0.934692i
246246 −0.447714 + 1.37792i −0.0285452 + 0.0878532i
247247 2.01119 + 1.46121i 0.127969 + 0.0929748i
248248 6.09105 + 4.42541i 0.386782 + 0.281014i
249249 −4.15320 + 12.7822i −0.263199 + 0.810042i
250250 0.979166 + 3.01356i 0.0619279 + 0.190594i
251251 4.02364 2.92335i 0.253970 0.184520i −0.453514 0.891249i 0.649830π-0.649830\pi
0.707484 + 0.706729i 0.249830π0.249830\pi
252252 1.71669 0.108141
253253 7.35870 22.8539i 0.462638 1.43681i
254254 −1.32531 −0.0831573
255255 −15.7578 + 11.4487i −0.986793 + 0.716947i
256256 2.38992 + 7.35542i 0.149370 + 0.459714i
257257 −6.72861 + 20.7085i −0.419719 + 1.29176i 0.488242 + 0.872708i 0.337638π0.337638\pi
−0.907961 + 0.419054i 0.862362π0.862362\pi
258258 −0.342688 0.248977i −0.0213348 0.0155007i
259259 −7.43270 5.40017i −0.461845 0.335550i
260260 3.61337 11.1208i 0.224092 0.689684i
261261 −2.19995 6.77075i −0.136174 0.419099i
262262 −3.26964 + 2.37554i −0.201999 + 0.146761i
263263 −15.9746 −0.985035 −0.492518 0.870303i 0.663923π-0.663923\pi
−0.492518 + 0.870303i 0.663923π0.663923\pi
264264 −1.34775 4.11080i −0.0829481 0.253002i
265265 11.8575 0.728399
266266 −0.246899 + 0.179383i −0.0151384 + 0.0109987i
267267 2.68162 + 8.25319i 0.164113 + 0.505087i
268268 −1.65844 + 5.10415i −0.101305 + 0.311786i
269269 22.9479 + 16.6726i 1.39916 + 1.01655i 0.994790 + 0.101949i 0.0325078π0.0325078\pi
0.404366 + 0.914597i 0.367492π0.367492\pi
270270 0.676495 + 0.491502i 0.0411702 + 0.0299119i
271271 6.86783 21.1370i 0.417191 1.28398i −0.493085 0.869981i 0.664131π-0.664131\pi
0.910276 0.414001i 0.135869π-0.135869\pi
272272 8.05993 + 24.8059i 0.488705 + 1.50408i
273273 −1.82926 + 1.32904i −0.110712 + 0.0804370i
274274 1.55462 0.0939182
275275 −4.01519 + 0.0106510i −0.242125 + 0.000642277i
276276 13.6632 0.822427
277277 −0.661635 + 0.480706i −0.0397538 + 0.0288828i −0.607485 0.794331i 0.707821π-0.707821\pi
0.567731 + 0.823214i 0.307821π0.307821\pi
278278 −0.114343 0.351913i −0.00685786 0.0211063i
279279 −1.78368 + 5.48961i −0.106786 + 0.328654i
280280 2.39193 + 1.73784i 0.142945 + 0.103856i
281281 −2.17276 1.57860i −0.129616 0.0941714i 0.521088 0.853503i 0.325526π-0.325526\pi
−0.650704 + 0.759331i 0.725526π0.725526\pi
282282 1.18159 3.63656i 0.0703627 0.216554i
283283 −5.98851 18.4307i −0.355980 1.09559i −0.955439 0.295188i 0.904618π-0.904618\pi
0.599459 0.800405i 0.295382π-0.295382\pi
284284 −20.7176 + 15.0522i −1.22936 + 0.893184i
285285 2.49211 0.147620
286286 2.24245 + 1.62016i 0.132599 + 0.0958024i
287287 −3.92738 −0.231826
288288 3.01640 2.19154i 0.177743 0.129138i
289289 13.6233 + 41.9283i 0.801372 + 2.46637i
290290 1.83958 5.66166i 0.108024 0.332464i
291291 −10.4341 7.58082i −0.611658 0.444396i
292292 −13.9851 10.1607i −0.818414 0.594612i
293293 4.45105 13.6989i 0.260033 0.800300i −0.732763 0.680484i 0.761770π-0.761770\pi
0.992796 0.119816i 0.0382304π-0.0382304\pi
294294 0.640028 + 1.96980i 0.0373272 + 0.114881i
295295 −5.19851 + 3.77694i −0.302669 + 0.219902i
296296 −13.1755 −0.765808
297297 2.67803 1.95657i 0.155395 0.113532i
298298 −5.38734 −0.312080
299299 −14.5592 + 10.5779i −0.841979 + 0.611734i
300300 −0.706091 2.17312i −0.0407662 0.125465i
301301 0.354820 1.09202i 0.0204515 0.0629432i
302302 −1.40413 1.02016i −0.0807988 0.0587038i
303303 5.99526 + 4.35581i 0.344419 + 0.250235i
304304 1.03124 3.17384i 0.0591458 0.182032i
305305 6.94959 + 21.3886i 0.397932 + 1.22471i
306306 2.12162 1.54145i 0.121285 0.0881186i
307307 0.0689145 0.00393316 0.00196658 0.999998i 0.499374π-0.499374\pi
0.00196658 + 0.999998i 0.499374π0.499374\pi
308308 4.59733 3.35882i 0.261957 0.191387i
309309 −4.05210 −0.230516
310310 −3.90480 + 2.83701i −0.221778 + 0.161131i
311311 −2.54209 7.82376i −0.144149 0.443645i 0.852752 0.522317i 0.174932π-0.174932\pi
−0.996901 + 0.0786719i 0.974932π0.974932\pi
312312 −1.00202 + 3.08391i −0.0567284 + 0.174592i
313313 −24.5962 17.8702i −1.39026 1.01008i −0.995837 0.0911551i 0.970944π-0.970944\pi
−0.394424 0.918929i 0.629056π-0.629056\pi
314314 4.10961 + 2.98580i 0.231919 + 0.168499i
315315 −0.700444 + 2.15574i −0.0394655 + 0.121462i
316316 −4.85629 14.9461i −0.273188 0.840785i
317317 23.4277 17.0212i 1.31583 0.956006i 0.315856 0.948807i 0.397708π-0.397708\pi
0.999974 0.00719913i 0.00229157π-0.00229157\pi
318318 −1.59648 −0.0895262
319319 −19.1390 13.8279i −1.07158 0.774213i
320320 −13.5155 −0.755538
321321 −9.65481 + 7.01463i −0.538879 + 0.391518i
322322 −0.682698 2.10113i −0.0380453 0.117091i
323323 2.41520 7.43322i 0.134385 0.413596i
324324 1.52695 + 1.10940i 0.0848306 + 0.0616331i
325325 2.43480 + 1.76899i 0.135059 + 0.0981258i
326326 0.399378 1.22916i 0.0221195 0.0680769i
327327 4.74692 + 14.6095i 0.262505 + 0.807909i
328328 −4.55656 + 3.31054i −0.251594 + 0.182794i
329329 10.3650 0.571440
330330 2.77333 0.00735672i 0.152667 0.000404974i
331331 −2.46229 −0.135340 −0.0676698 0.997708i 0.521556π-0.521556\pi
−0.0676698 + 0.997708i 0.521556π0.521556\pi
332332 −20.5223 + 14.9103i −1.12631 + 0.818310i
333333 −3.12139 9.60665i −0.171051 0.526441i
334334 0.430785 1.32582i 0.0235715 0.0725456i
335335 −5.73291 4.16520i −0.313222 0.227569i
336336 2.45561 + 1.78410i 0.133964 + 0.0973308i
337337 1.09642 3.37445i 0.0597260 0.183818i −0.916742 0.399480i 0.869191π-0.869191\pi
0.976468 + 0.215662i 0.0691909π0.0691909\pi
338338 0.707137 + 2.17635i 0.0384632 + 0.118378i
339339 −0.0861059 + 0.0625596i −0.00467663 + 0.00339777i
340340 −36.7626 −1.99373
341341 5.96408 + 18.1912i 0.322973 + 0.985109i
342342 −0.335536 −0.0181437
343343 −9.69297 + 7.04235i −0.523371 + 0.380251i
344344 −0.508844 1.56606i −0.0274350 0.0844363i
345345 −5.57486 + 17.1577i −0.300141 + 0.923738i
346346 −6.46507 4.69715i −0.347564 0.252520i
347347 −22.4427 16.3056i −1.20479 0.875330i −0.210041 0.977692i 0.567360π-0.567360\pi
−0.994747 + 0.102362i 0.967360π0.967360\pi
348348 4.15222 12.7792i 0.222583 0.685039i
349349 −9.62177 29.6128i −0.515041 1.58513i −0.783207 0.621761i 0.786417π-0.786417\pi
0.268165 0.963373i 0.413583π-0.413583\pi
350350 −0.298903 + 0.217166i −0.0159770 + 0.0116080i
351351 −2.48597 −0.132691
352352 3.79008 11.7708i 0.202012 0.627387i
353353 0.921389 0.0490406 0.0245203 0.999699i 0.492194π-0.492194\pi
0.0245203 + 0.999699i 0.492194π0.492194\pi
354354 0.699923 0.508524i 0.0372005 0.0270277i
355355 −10.4487 32.1579i −0.554561 1.70676i
356356 −5.06134 + 15.5772i −0.268250 + 0.825590i
357357 5.75111 + 4.17843i 0.304381 + 0.221146i
358358 0.939680 + 0.682718i 0.0496636 + 0.0360827i
359359 3.53828 10.8897i 0.186743 0.574737i −0.813231 0.581942i 0.802293π-0.802293\pi
0.999974 + 0.00720437i 0.00229324π0.00229324\pi
360360 1.00450 + 3.09153i 0.0529418 + 0.162938i
361361 −0.809017 + 0.587785i −0.0425798 + 0.0309361i
362362 6.36691 0.334637
363363 3.34364 10.4795i 0.175495 0.550032i
364364 −4.26762 −0.223684
365365 18.4656 13.4161i 0.966536 0.702230i
366366 −0.935686 2.87975i −0.0489091 0.150527i
367367 −6.29823 + 19.3839i −0.328765 + 1.01183i 0.640948 + 0.767584i 0.278541π0.278541\pi
−0.969712 + 0.244249i 0.921459π0.921459\pi
368368 19.5443 + 14.1998i 1.01882 + 0.740214i
369369 −3.49331 2.53804i −0.181855 0.132125i
370370 2.61009 8.03302i 0.135692 0.417617i
371371 −1.33730 4.11580i −0.0694294 0.213682i
372372 −8.81373 + 6.40355i −0.456971 + 0.332009i
373373 38.3906 1.98779 0.993894 0.110341i 0.0351944π-0.0351944\pi
0.993894 + 0.110341i 0.0351944π0.0351944\pi
374374 2.66580 8.27914i 0.137845 0.428104i
375375 −9.44354 −0.487662
376376 12.0255 8.73703i 0.620168 0.450578i
377377 5.46901 + 16.8319i 0.281668 + 0.866885i
378378 0.0943071 0.290248i 0.00485064 0.0149287i
379379 9.00630 + 6.54346i 0.462623 + 0.336115i 0.794559 0.607187i 0.207702π-0.207702\pi
−0.331937 + 0.943302i 0.607702π0.607702\pi
380380 3.80534 + 2.76474i 0.195210 + 0.141828i
381381 1.22056 3.75651i 0.0625314 0.192452i
382382 −0.690300 2.12452i −0.0353188 0.108700i
383383 −18.0630 + 13.1236i −0.922977 + 0.670582i −0.944263 0.329191i 0.893224π-0.893224\pi
0.0212860 + 0.999773i 0.493224π0.493224\pi
384384 9.27666 0.473398
385385 2.34207 + 7.14361i 0.119363 + 0.364072i
386386 2.19436 0.111690
387387 1.02132 0.742029i 0.0519164 0.0377195i
388388 −7.52225 23.1511i −0.381884 1.17532i
389389 2.06915 6.36819i 0.104910 0.322880i −0.884799 0.465972i 0.845705π-0.845705\pi
0.989709 + 0.143092i 0.0457046π0.0457046\pi
390390 −1.68174 1.22186i −0.0851584 0.0618712i
391391 45.7733 + 33.2563i 2.31486 + 1.68184i
392392 −2.48805 + 7.65744i −0.125666 + 0.386759i
393393 −3.72208 11.4554i −0.187754 0.577848i
394394 −5.36566 + 3.89838i −0.270318 + 0.196398i
395395 20.7502 1.04406
396396 6.25983 0.0166052i 0.314568 0.000834445i
397397 −12.2071 −0.612658 −0.306329 0.951926i 0.599101π-0.599101\pi
−0.306329 + 0.951926i 0.599101π0.599101\pi
398398 −0.983070 + 0.714242i −0.0492769 + 0.0358017i
399399 −0.281064 0.865027i −0.0140708 0.0433055i
400400 1.24845 3.84234i 0.0624225 0.192117i
401401 12.8248 + 9.31778i 0.640441 + 0.465308i 0.860002 0.510291i 0.170462π-0.170462\pi
−0.219560 + 0.975599i 0.570462π0.570462\pi
402402 0.771874 + 0.560799i 0.0384976 + 0.0279701i
403403 4.43417 13.6470i 0.220882 0.679804i
404404 4.32215 + 13.3022i 0.215035 + 0.661810i
405405 −2.01616 + 1.46483i −0.100184 + 0.0727879i
406406 −2.17267 −0.107828
407407 −27.1553 19.6196i −1.34604 0.972508i
408408 10.1946 0.504709
409409 −16.6896 + 12.1257i −0.825248 + 0.599578i −0.918211 0.396092i 0.870366π-0.870366\pi
0.0929631 + 0.995670i 0.470366π0.470366\pi
410410 −1.11576 3.43394i −0.0551032 0.169590i
411411 −1.43175 + 4.40648i −0.0706232 + 0.217356i
412412 −6.18736 4.49538i −0.304829 0.221471i
413413 1.89729 + 1.37846i 0.0933597 + 0.0678298i
414414 0.750595 2.31009i 0.0368897 0.113535i
415415 −10.3503 31.8548i −0.508074 1.56369i
416416 −7.49867 + 5.44810i −0.367652 + 0.267115i
417417 1.10278 0.0540035
418418 −0.898574 + 0.656501i −0.0439507 + 0.0321105i
419419 11.2902 0.551561 0.275781 0.961221i 0.411064π-0.411064\pi
0.275781 + 0.961221i 0.411064π0.411064\pi
420420 −3.46112 + 2.51465i −0.168885 + 0.122702i
421421 −7.47758 23.0136i −0.364435 1.12161i −0.950334 0.311231i 0.899259π-0.899259\pi
0.585900 0.810384i 0.300741π-0.300741\pi
422422 0.950331 2.92482i 0.0462614 0.142378i
423423 9.21941 + 6.69829i 0.448263 + 0.325682i
424424 −5.02091 3.64790i −0.243837 0.177158i
425425 2.92391 8.99887i 0.141830 0.436509i
426426 1.40681 + 4.32971i 0.0681601 + 0.209775i
427427 6.64033 4.82448i 0.321348 0.233473i
428428 −22.5244 −1.08876
429429 −6.65748 + 4.86398i −0.321426 + 0.234835i
430430 1.05562 0.0509067
431431 7.73133 5.61714i 0.372405 0.270568i −0.385802 0.922581i 0.626075π-0.626075\pi
0.758208 + 0.652013i 0.226075π0.226075\pi
432432 1.03124 + 3.17384i 0.0496157 + 0.152701i
433433 −5.30049 + 16.3132i −0.254725 + 0.783963i 0.739159 + 0.673532i 0.235223π0.235223\pi
−0.993884 + 0.110432i 0.964777π0.964777\pi
434434 1.42513 + 1.03542i 0.0684084 + 0.0497016i
435435 14.3534 + 10.4284i 0.688195 + 0.500003i
436436 −8.95942 + 27.5742i −0.429078 + 1.32057i
437437 −2.23700 6.88479i −0.107010 0.329344i
438438 −2.48620 + 1.80633i −0.118795 + 0.0863097i
439439 5.10608 0.243700 0.121850 0.992549i 0.461117π-0.461117\pi
0.121850 + 0.992549i 0.461117π0.461117\pi
440440 8.73889 + 6.31383i 0.416610 + 0.301000i
441441 −6.17273 −0.293940
442442 −5.27427 + 3.83198i −0.250872 + 0.182269i
443443 6.45197 + 19.8571i 0.306542 + 0.943440i 0.979097 + 0.203393i 0.0651968π0.0651968\pi
−0.672555 + 0.740047i 0.734803π0.734803\pi
444444 5.89136 18.1317i 0.279592 0.860494i
445445 −17.4961 12.7117i −0.829394 0.602590i
446446 −7.10869 5.16476i −0.336606 0.244559i
447447 4.96155 15.2701i 0.234673 0.722251i
448448 1.52430 + 4.69130i 0.0720162 + 0.221643i
449449 −23.0551 + 16.7505i −1.08804 + 0.790505i −0.979067 0.203540i 0.934755π-0.934755\pi
−0.108970 + 0.994045i 0.534755π0.534755\pi
450450 −0.406209 −0.0191489
451451 −14.3210 + 0.0379890i −0.674351 + 0.00178883i
452452 −0.200883 −0.00944873
453453 4.18475 3.04040i 0.196617 0.142850i
454454 1.71413 + 5.27556i 0.0804482 + 0.247594i
455455 1.74128 5.35911i 0.0816325 0.251239i
456456 −1.05526 0.766688i −0.0494169 0.0359035i
457457 23.1030 + 16.7853i 1.08071 + 0.785185i 0.977807 0.209506i 0.0671856π-0.0671856\pi
0.102907 + 0.994691i 0.467186π0.467186\pi
458458 −2.86259 + 8.81015i −0.133760 + 0.411671i
459459 2.41520 + 7.43322i 0.112732 + 0.346953i
460460 −27.5472 + 20.0142i −1.28439 + 0.933167i
461461 0.799377 0.0372307 0.0186154 0.999827i 0.494074π-0.494074\pi
0.0186154 + 0.999827i 0.494074π0.494074\pi
462462 −0.315334 0.961809i −0.0146707 0.0447474i
463463 −23.3696 −1.08608 −0.543038 0.839708i 0.682726π-0.682726\pi
−0.543038 + 0.839708i 0.682726π0.682726\pi
464464 19.2206 13.9646i 0.892293 0.648289i
465465 −4.44513 13.6807i −0.206138 0.634428i
466466 −0.873051 + 2.68697i −0.0404433 + 0.124472i
467467 2.18138 + 1.58487i 0.100942 + 0.0733389i 0.637111 0.770772i 0.280129π-0.280129\pi
−0.536169 + 0.844111i 0.680129π0.680129\pi
468468 −3.79595 2.75792i −0.175468 0.127485i
469469 −0.799199 + 2.45968i −0.0369036 + 0.113578i
470470 2.94466 + 9.06272i 0.135827 + 0.418032i
471471 −12.2479 + 8.89861i −0.564353 + 0.410026i
472472 3.36321 0.154804
473473 1.28327 3.98545i 0.0590050 0.183251i
474474 −2.79379 −0.128323
475475 −0.979419 + 0.711589i −0.0449388 + 0.0326500i
476476 4.14614 + 12.7605i 0.190038 + 0.584877i
477477 1.47030 4.52513i 0.0673206 0.207191i
478478 3.13867 + 2.28038i 0.143559 + 0.104302i
479479 15.6140 + 11.3442i 0.713423 + 0.518332i 0.884276 0.466965i 0.154652π-0.154652\pi
−0.170853 + 0.985296i 0.554652π0.554652\pi
480480 −2.87132 + 8.83701i −0.131057 + 0.403352i
481481 7.75967 + 23.8818i 0.353810 + 1.08892i
482482 −2.96460 + 2.15390i −0.135034 + 0.0981077i
483483 6.58427 0.299594
484484 16.7315 12.2923i 0.760522 0.558740i
485485 32.1414 1.45947
486486 0.271454 0.197223i 0.0123134 0.00894622i
487487 −4.48727 13.8104i −0.203338 0.625809i −0.999778 0.0210915i 0.993286π-0.993286\pi
0.796440 0.604718i 0.206714π-0.206714\pi
488488 3.63740 11.1948i 0.164657 0.506763i
489489 3.11617 + 2.26403i 0.140918 + 0.102383i
490490 −4.17582 3.03391i −0.188644 0.137058i
491491 5.57486 17.1577i 0.251590 0.774314i −0.742892 0.669411i 0.766547π-0.766547\pi
0.994482 0.104904i 0.0334534π-0.0334534\pi
492492 −2.51843 7.75093i −0.113540 0.349439i
493493 45.0152 32.7055i 2.02738 1.47298i
494494 0.834131 0.0375293
495495 −2.53329 + 7.86761i −0.113863 + 0.353623i
496496 −19.2625 −0.864912
497497 −9.98377 + 7.25363i −0.447833 + 0.325370i
498498 1.39355 + 4.28890i 0.0624464 + 0.192190i
499499 −6.76893 + 20.8326i −0.303019 + 0.932597i 0.677390 + 0.735624i 0.263111π0.263111\pi
−0.980409 + 0.196973i 0.936889π0.936889\pi
500500 −14.4198 10.4766i −0.644874 0.468529i
501501 3.36122 + 2.44207i 0.150168 + 0.109104i
502502 0.515683 1.58711i 0.0230161 0.0708362i
503503 5.90754 + 18.1815i 0.263404 + 0.810674i 0.992057 + 0.125791i 0.0401468π0.0401468\pi
−0.728653 + 0.684883i 0.759853π0.759853\pi
504504 0.959800 0.697336i 0.0427529 0.0310618i
505505 −18.4679 −0.821812
506506 −2.50976 7.65508i −0.111572 0.340310i
507507 −6.81997 −0.302886
508508 6.03120 4.38192i 0.267591 0.194416i
509509 6.88543 + 21.1912i 0.305191 + 0.939282i 0.979606 + 0.200929i 0.0643962π0.0643962\pi
−0.674414 + 0.738353i 0.735604π0.735604\pi
510510 −2.01957 + 6.21561i −0.0894283 + 0.275232i
511511 −6.73938 4.89645i −0.298133 0.216606i
512512 17.1094 + 12.4307i 0.756134 + 0.549364i
513513 0.309017 0.951057i 0.0136434 0.0419902i
514514 2.25769 + 6.94846i 0.0995824 + 0.306483i
515515 8.16969 5.93563i 0.360000 0.261555i
516516 2.38270 0.104893
517517 37.7955 0.100259i 1.66224 0.00440938i
518518 −3.08268 −0.135445
519519 19.2679 13.9989i 0.845766 0.614485i
520520 −2.49715 7.68545i −0.109507 0.337029i
521521 9.71578 29.9021i 0.425656 1.31004i −0.476708 0.879061i 0.658170π-0.658170\pi
0.902365 0.430974i 0.141830π-0.141830\pi
522522 −1.93253 1.40407i −0.0845848 0.0614544i
523523 −26.2367 19.0621i −1.14725 0.833528i −0.159140 0.987256i 0.550872π-0.550872\pi
−0.988113 + 0.153728i 0.950872π0.950872\pi
524524 7.02512 21.6211i 0.306894 0.944522i
525525 −0.340264 1.04723i −0.0148503 0.0457047i
526526 −4.33637 + 3.15056i −0.189075 + 0.137371i
527527 −45.1134 −1.96517
528528 8.97154 + 6.48191i 0.390436 + 0.282089i
529529 29.4045 1.27846
530530 3.21876 2.33857i 0.139814 0.101581i
531531 0.796776 + 2.45222i 0.0345771 + 0.106417i
532532 0.530485 1.63266i 0.0229994 0.0707850i
533533 8.68426 + 6.30948i 0.376157 + 0.273294i
534534 2.35566 + 1.71149i 0.101939 + 0.0740632i
535535 9.19044 28.2853i 0.397337 1.22288i
536536 1.14612 + 3.52741i 0.0495051 + 0.152361i
537537 −2.80054 + 2.03471i −0.120852 + 0.0878041i
538538 9.51751 0.410329
539539 −16.5307 + 12.0774i −0.712029 + 0.520211i
540540 −4.70365 −0.202413
541541 21.9417 15.9415i 0.943346 0.685381i −0.00587804 0.999983i 0.501871π-0.501871\pi
0.949224 + 0.314602i 0.101871π0.101871\pi
542542 −2.30440 7.09223i −0.0989826 0.304637i
543543 −5.86370 + 18.0466i −0.251636 + 0.774455i
544544 23.5754 + 17.1286i 1.01079 + 0.734381i
545545 −30.9710 22.5017i −1.32665 0.963869i
546546 −0.234444 + 0.721546i −0.0100333 + 0.0308793i
547547 −8.32831 25.6319i −0.356093 1.09594i −0.955373 0.295402i 0.904547π-0.904547\pi
0.599280 0.800539i 0.295453π-0.295453\pi
548548 −7.07475 + 5.14011i −0.302218 + 0.219575i
549549 9.02420 0.385144
550550 −1.08784 + 0.794778i −0.0463856 + 0.0338895i
551551 −7.11919 −0.303288
552552 7.63909 5.55013i 0.325141 0.236229i
553553 −2.34024 7.20252i −0.0995171 0.306282i
554554 −0.0847973 + 0.260979i −0.00360269 + 0.0110879i
555555 20.3653 + 14.7963i 0.864459 + 0.628066i
556556 1.68389 + 1.22342i 0.0714130 + 0.0518846i
557557 −3.12482 + 9.61721i −0.132403 + 0.407494i −0.995177 0.0980954i 0.968725π-0.968725\pi
0.862774 + 0.505590i 0.168725π0.168725\pi
558558 0.598489 + 1.84196i 0.0253361 + 0.0779764i
559559 −2.53896 + 1.84466i −0.107386 + 0.0780208i
560560 −7.56431 −0.319650
561561 21.0116 + 15.1808i 0.887111 + 0.640935i
562562 −0.901141 −0.0380123
563563 −3.59582 + 2.61252i −0.151546 + 0.110104i −0.660974 0.750408i 0.729857π-0.729857\pi
0.509429 + 0.860513i 0.329857π0.329857\pi
564564 6.64654 + 20.4559i 0.279870 + 0.861350i
565565 0.0819644 0.252260i 0.00344827 0.0106127i
566566 −5.26057 3.82203i −0.221118 0.160652i
567567 0.735836 + 0.534616i 0.0309022 + 0.0224518i
568568 −5.46885 + 16.8314i −0.229468 + 0.706229i
569569 −2.10035 6.46422i −0.0880513 0.270994i 0.897329 0.441362i 0.145504π-0.145504\pi
−0.985381 + 0.170368i 0.945504π0.945504\pi
570570 0.676495 0.491502i 0.0283352 0.0205868i
571571 −16.1697 −0.676681 −0.338341 0.941024i 0.609866π-0.609866\pi
−0.338341 + 0.941024i 0.609866π0.609866\pi
572572 −15.5617 + 0.0412801i −0.650668 + 0.00172601i
573573 6.65758 0.278124
574574 −1.06610 + 0.774570i −0.0444983 + 0.0323299i
575575 −2.70818 8.33492i −0.112939 0.347590i
576576 −1.67589 + 5.15787i −0.0698288 + 0.214911i
577577 0.750345 + 0.545157i 0.0312373 + 0.0226952i 0.603294 0.797519i 0.293854π-0.293854\pi
−0.572057 + 0.820214i 0.693854π0.693854\pi
578578 11.9673 + 8.69477i 0.497775 + 0.361655i
579579 −2.02093 + 6.21978i −0.0839869 + 0.258485i
580580 10.3478 + 31.8473i 0.429669 + 1.32239i
581581 −9.88967 + 7.18526i −0.410293 + 0.298095i
582582 −4.32750 −0.179380
583583 −4.91624 14.9952i −0.203610 0.621036i
584584 −11.9465 −0.494348
585585 5.01211 3.64151i 0.207225 0.150558i
586586 −1.49349 4.59648i −0.0616954 0.189879i
587587 −2.11236 + 6.50118i −0.0871865 + 0.268333i −0.985139 0.171760i 0.945055π-0.945055\pi
0.897952 + 0.440093i 0.145055π0.145055\pi
588588 −9.42546 6.84800i −0.388699 0.282407i
589589 4.66974 + 3.39276i 0.192413 + 0.139796i
590590 −0.666259 + 2.05053i −0.0274294 + 0.0844191i
591591 −6.10814 18.7989i −0.251255 0.773284i
592592 27.2710 19.8136i 1.12083 0.814332i
593593 30.4399 1.25002 0.625009 0.780617i 0.285095π-0.285095\pi
0.625009 + 0.780617i 0.285095π0.285095\pi
594594 0.341080 1.05929i 0.0139947 0.0434631i
595595 −17.7158 −0.726279
596596 24.5166 17.8124i 1.00424 0.729623i
597597 −1.11910 3.44425i −0.0458019 0.140964i
598598 −1.86595 + 5.74281i −0.0763045 + 0.234841i
599599 20.1262 + 14.6226i 0.822336 + 0.597462i 0.917381 0.398011i 0.130299π-0.130299\pi
−0.0950446 + 0.995473i 0.530299π0.530299\pi
600600 −1.27752 0.928174i −0.0521546 0.0378925i
601601 −3.86863 + 11.9064i −0.157805 + 0.485672i −0.998434 0.0559379i 0.982185π-0.982185\pi
0.840630 + 0.541610i 0.182185π0.182185\pi
602602 −0.119055 0.366413i −0.00485231 0.0149339i
603603 −2.30042 + 1.67135i −0.0936804 + 0.0680628i
604604 9.76291 0.397247
605605 8.60936 + 26.0262i 0.350020 + 1.05812i
606606 2.48650 0.101007
607607 22.3187 16.2155i 0.905887 0.658166i −0.0340841 0.999419i 0.510851π-0.510851\pi
0.939971 + 0.341253i 0.110851π0.110851\pi
608608 −1.15216 3.54599i −0.0467263 0.143809i
609609 2.00095 6.15829i 0.0810826 0.249547i
610610 6.10482 + 4.43541i 0.247177 + 0.179585i
611611 −22.9191 16.6517i −0.927209 0.673657i
612612 −4.55849 + 14.0296i −0.184266 + 0.567112i
613613 9.06521 + 27.8998i 0.366140 + 1.12686i 0.949264 + 0.314481i 0.101830π0.101830\pi
−0.583124 + 0.812383i 0.698170π0.698170\pi
614614 0.0187071 0.0135915i 0.000754959 0.000548510i
615615 10.7609 0.433920
616616 1.20598 3.74540i 0.0485903 0.150907i
617617 12.7952 0.515114 0.257557 0.966263i 0.417082π-0.417082\pi
0.257557 + 0.966263i 0.417082π0.417082\pi
618618 −1.09996 + 0.799168i −0.0442469 + 0.0321472i
619619 7.35983 + 22.6512i 0.295817 + 0.910430i 0.982946 + 0.183895i 0.0588706π0.0588706\pi
−0.687129 + 0.726535i 0.741129π0.741129\pi
620620 8.38982 25.8212i 0.336943 1.03700i
621621 5.85655 + 4.25503i 0.235015 + 0.170749i
622622 −2.23309 1.62243i −0.0895387 0.0650536i
623623 −2.43905 + 7.50663i −0.0977186 + 0.300747i
624624 −2.56363 7.89005i −0.102627 0.315855i
625625 23.9368 17.3911i 0.957472 0.695644i
626626 −10.2012 −0.407721
627627 −1.03326 3.15157i −0.0412643 0.125861i
628628 −28.5740 −1.14023
629629 63.8696 46.4040i 2.54665 1.85025i
630630 0.235024 + 0.723330i 0.00936358 + 0.0288181i
631631 −1.55033 + 4.77141i −0.0617175 + 0.189947i −0.977161 0.212499i 0.931840π-0.931840\pi
0.915444 + 0.402446i 0.131840π0.131840\pi
632632 −8.78643 6.38371i −0.349505 0.253931i
633633 7.41500 + 5.38731i 0.294720 + 0.214126i
634634 3.00257 9.24096i 0.119247 0.367005i
635635 3.04179 + 9.36165i 0.120710 + 0.371506i
636636 7.26524 5.27850i 0.288085 0.209306i
637637 15.3452 0.607999
638638 −7.92254 + 0.0210159i −0.313656 + 0.000832026i
639639 −13.5679 −0.536739
640640 −18.7033 + 13.5887i −0.739311 + 0.537141i
641641 5.21881 + 16.0618i 0.206131 + 0.634404i 0.999665 + 0.0258793i 0.00823856π0.00823856\pi
−0.793535 + 0.608525i 0.791761π0.791761\pi
642642 −1.23739 + 3.80830i −0.0488360 + 0.150302i
643643 2.40085 + 1.74432i 0.0946804 + 0.0687893i 0.634118 0.773236i 0.281363π-0.281363\pi
−0.539438 + 0.842025i 0.681363π0.681363\pi
644644 10.0539 + 7.30455i 0.396177 + 0.287840i
645645 −0.972193 + 2.99210i −0.0382801 + 0.117814i
646646 −0.810386 2.49411i −0.0318842 0.0981296i
647647 −0.209243 + 0.152024i −0.00822619 + 0.00597668i −0.591891 0.806018i 0.701618π-0.701618\pi
0.583665 + 0.811995i 0.301618π0.301618\pi
648648 1.30437 0.0512404
649649 6.93174 + 5.00816i 0.272095 + 0.196588i
650650 1.00982 0.0396085
651651 −4.24733 + 3.08586i −0.166466 + 0.120945i
652652 2.24653 + 6.91412i 0.0879810 + 0.270778i
653653 6.56923 20.2180i 0.257074 0.791192i −0.736340 0.676612i 0.763448π-0.763448\pi
0.993414 0.114581i 0.0365524π-0.0365524\pi
654654 4.16991 + 3.02961i 0.163056 + 0.118467i
655655 24.2845 + 17.6437i 0.948874 + 0.689397i
656656 4.45287 13.7045i 0.173856 0.535072i
657657 −2.83023 8.71055i −0.110418 0.339831i
658658 2.81362 2.04421i 0.109686 0.0796917i
659659 −37.2792 −1.45219 −0.726095 0.687594i 0.758667π-0.758667\pi
−0.726095 + 0.687594i 0.758667π0.758667\pi
660660 −12.5965 + 9.20305i −0.490318 + 0.358228i
661661 −18.5045 −0.719740 −0.359870 0.933002i 0.617179π-0.617179\pi
−0.359870 + 0.933002i 0.617179π0.617179\pi
662662 −0.668398 + 0.485620i −0.0259780 + 0.0188741i
663663 −6.00411 18.4787i −0.233180 0.717655i
664664 −5.41730 + 16.6727i −0.210232 + 0.647028i
665665 1.83379 + 1.33232i 0.0711112 + 0.0516653i
666666 −2.74197 1.99216i −0.106249 0.0771945i
667667 15.9257 49.0141i 0.616644 1.89783i
668668 2.42320 + 7.45784i 0.0937564 + 0.288552i
669669 21.1861 15.3926i 0.819101 0.595111i
670670 −2.37770 −0.0918584
671671 24.1670 17.6565i 0.932958 0.681622i
672672 3.39121 0.130819
673673 −18.4531 + 13.4070i −0.711315 + 0.516801i −0.883598 0.468247i 0.844886π-0.844886\pi
0.172283 + 0.985048i 0.444886π0.444886\pi
674674 −0.367890 1.13225i −0.0141706 0.0436125i
675675 0.374105 1.15138i 0.0143993 0.0443165i
676676 −10.4138 7.56604i −0.400529 0.291002i
677677 19.5315 + 14.1905i 0.750658 + 0.545385i 0.896031 0.443992i 0.146438π-0.146438\pi
−0.145373 + 0.989377i 0.546438π0.546438\pi
678678 −0.0110356 + 0.0339641i −0.000423820 + 0.00130438i
679679 −3.62496 11.1565i −0.139113 0.428146i
680680 −20.5540 + 14.9333i −0.788210 + 0.572668i
681681 −16.5319 −0.633504
682682 5.20670 + 3.76183i 0.199375 + 0.144048i
683683 −0.588022 −0.0225000 −0.0112500 0.999937i 0.503581π-0.503581\pi
−0.0112500 + 0.999937i 0.503581π0.503581\pi
684684 1.52695 1.10940i 0.0583844 0.0424188i
685685 −3.56809 10.9815i −0.136330 0.419580i
686686 −1.24228 + 3.82335i −0.0474306 + 0.145976i
687687 −22.3355 16.2277i −0.852152 0.619125i
688688 3.40830 + 2.47628i 0.129940 + 0.0944072i
689689 −3.65513 + 11.2493i −0.139249 + 0.428565i
690690 1.87057 + 5.75701i 0.0712113 + 0.219166i
691691 32.0314 23.2722i 1.21853 0.885316i 0.222555 0.974920i 0.428560π-0.428560\pi
0.995977 + 0.0896044i 0.0285603π0.0285603\pi
692692 44.9515 1.70880
693693 3.01660 0.00800204i 0.114591 0.000303972i
694694 −9.30801 −0.353327
695695 −2.22339 + 1.61539i −0.0843379 + 0.0612750i
696696 −2.86955 8.83155i −0.108770 0.334759i
697697 10.4288 32.0964i 0.395018 1.21574i
698698 −8.45219 6.14087i −0.319920 0.232435i
699699 −6.81202 4.94922i −0.257654 0.187197i
700700 0.642220 1.97655i 0.0242736 0.0747066i
701701 8.42736 + 25.9367i 0.318297 + 0.979617i 0.974376 + 0.224925i 0.0722137π0.0722137\pi
−0.656079 + 0.754692i 0.727786π0.727786\pi
702702 −0.674826 + 0.490290i −0.0254697 + 0.0185048i
703703 −10.1010 −0.380968
704704 5.60366 + 17.0919i 0.211196 + 0.644175i
705705 −28.3997 −1.06959
706706 0.250115 0.181719i 0.00941320 0.00683909i
707707 2.08284 + 6.41032i 0.0783332 + 0.241085i
708708 −1.50385 + 4.62836i −0.0565180 + 0.173945i
709709 25.8021 + 18.7463i 0.969018 + 0.704032i 0.955227 0.295872i 0.0956103π-0.0956103\pi
0.0137901 + 0.999905i 0.495610π0.495610\pi
710710 −9.17863 6.66867i −0.344468 0.250271i
711711 2.57298 7.91883i 0.0964945 0.296979i
712712 3.49782 + 10.7652i 0.131086 + 0.403443i
713713 −33.8047 + 24.5605i −1.26599 + 0.919799i
714714 2.38524 0.0892655
715715 6.29767 19.5586i 0.235520 0.731451i
716716 −6.53358 −0.244171
717717 −9.35420 + 6.79623i −0.349339 + 0.253810i
718718 −1.18722 3.65389i −0.0443067 0.136362i
719719 1.49569 4.60326i 0.0557798 0.171673i −0.919285 0.393592i 0.871232π-0.871232\pi
0.975065 + 0.221920i 0.0712322π0.0712322\pi
720720 −6.72827 4.88838i −0.250748 0.182179i
721721 −2.98168 2.16632i −0.111044 0.0806779i
722722 −0.103686 + 0.319114i −0.00385880 + 0.0118762i
723723 −3.37482 10.3866i −0.125511 0.386283i
724724 −28.9744 + 21.0512i −1.07683 + 0.782360i
725725 −8.61869 −0.320090
726726 −1.15916 3.50415i −0.0430203 0.130051i
727727 39.8974 1.47971 0.739856 0.672765i 0.234894π-0.234894\pi
0.739856 + 0.672765i 0.234894π0.234894\pi
728728 −2.38603 + 1.73355i −0.0884322 + 0.0642497i
729729 0.309017 + 0.951057i 0.0114451 + 0.0352243i
730730 2.36662 7.28370i 0.0875925 0.269582i
731731 7.98235 + 5.79952i 0.295238 + 0.214503i
732732 13.7795 + 10.0114i 0.509306 + 0.370032i
733733 8.20512 25.2527i 0.303063 0.932732i −0.677330 0.735679i 0.736863π-0.736863\pi
0.980393 0.197052i 0.0631369π-0.0631369\pi
734734 2.11328 + 6.50401i 0.0780026 + 0.240067i
735735 12.4452 9.04199i 0.459049 0.333519i
736736 26.9908 0.994893
737737 −2.89046 + 8.97687i −0.106471 + 0.330667i
738738 −1.44883 −0.0533323
739739 −4.94872 + 3.59545i −0.182042 + 0.132261i −0.675074 0.737750i 0.735888π-0.735888\pi
0.493033 + 0.870011i 0.335888π0.335888\pi
740740 14.6819 + 45.1863i 0.539719 + 1.66108i
741741 −0.768206 + 2.36429i −0.0282207 + 0.0868545i
742742 −1.17475 0.853504i −0.0431263 0.0313331i
743743 −12.7683 9.27670i −0.468423 0.340329i 0.328403 0.944538i 0.393489π-0.393489\pi
−0.796826 + 0.604208i 0.793489π0.793489\pi
744744 −2.32658 + 7.16046i −0.0852964 + 0.262515i
745745 12.3648 + 38.0548i 0.453010 + 1.39422i
746746 10.4213 7.57150i 0.381550 0.277212i
747747 −13.4401 −0.491746
748748 15.2422 + 46.4906i 0.557309 + 1.69986i
749749 −10.8545 −0.396614
750750 −2.56349 + 1.86248i −0.0936054 + 0.0680083i
751751 −4.02308 12.3818i −0.146804 0.451818i 0.850434 0.526081i 0.176339π-0.176339\pi
−0.997239 + 0.0742638i 0.976339π0.976339\pi
752752 −11.7518 + 36.1685i −0.428546 + 1.31893i
753753 4.02364 + 2.92335i 0.146630 + 0.106533i
754754 4.80422 + 3.49047i 0.174959 + 0.127115i
755755 −3.98347 + 12.2599i −0.144973 + 0.446182i
756756 0.530485 + 1.63266i 0.0192936 + 0.0593794i
757757 10.3390 7.51176i 0.375779 0.273019i −0.383824 0.923406i 0.625393π-0.625393\pi
0.759603 + 0.650387i 0.225393π0.225393\pi
758758 3.73532 0.135673
759759 24.0093 0.0636886i 0.871481 0.00231175i
760760 3.25063 0.117913
761761 −16.1178 + 11.7102i −0.584269 + 0.424496i −0.840261 0.542183i 0.817598π-0.817598\pi
0.255992 + 0.966679i 0.417598π0.417598\pi
762762 −0.409543 1.26044i −0.0148362 0.0456611i
763763 −4.31753 + 13.2880i −0.156305 + 0.481057i
764764 10.1658 + 7.38589i 0.367786 + 0.267212i
765765 −15.7578 11.4487i −0.569725 0.413930i
766766 −2.31502 + 7.12489i −0.0836450 + 0.257433i
767767 −1.98076 6.09614i −0.0715210 0.220119i
768768 −6.25690 + 4.54590i −0.225776 + 0.164036i
769769 −32.2343 −1.16240 −0.581199 0.813762i 0.697416π-0.697416\pi
−0.581199 + 0.813762i 0.697416π0.697416\pi
770770 2.04465 + 1.47725i 0.0736840 + 0.0532365i
771771 −21.7742 −0.784180
772772 −9.98605 + 7.25529i −0.359406 + 0.261124i
773773 −12.9520 39.8622i −0.465852 1.43374i −0.857908 0.513803i 0.828236π-0.828236\pi
0.392057 0.919941i 0.371764π-0.371764\pi
774774 0.130895 0.402854i 0.00470493 0.0144803i
775775 5.65331 + 4.10737i 0.203073 + 0.147541i
776776 −13.6099 9.88818i −0.488567 0.354965i
777777 2.83904 8.73766i 0.101850 0.313462i
778778 −0.694274 2.13676i −0.0248909 0.0766064i
779779 −3.49331 + 2.53804i −0.125161 + 0.0909347i
780780 11.6931 0.418681
781781 −36.3353 + 26.5467i −1.30018 + 0.949914i
782782 18.9843 0.678876
783783 5.75955 4.18456i 0.205829 0.149544i
784784 −6.36558 19.5912i −0.227342 0.699687i
785785 11.6588 35.8821i 0.416120 1.28069i
786786 −3.26964 2.37554i −0.116624 0.0847325i
787787 −5.63792 4.09619i −0.200970 0.146013i 0.482749 0.875759i 0.339639π-0.339639\pi
−0.683719 + 0.729746i 0.739639π0.739639\pi
788788 11.5286 35.4814i 0.410689 1.26397i
789789 −4.93642 15.1927i −0.175741 0.540876i
790790 5.63273 4.09242i 0.200404 0.145602i
791791 −0.0968051 −0.00344199
792792 3.49313 2.55209i 0.124123 0.0906846i
793793 −22.4339 −0.796650
794794 −3.31368 + 2.40753i −0.117598 + 0.0854400i
795795 3.66416 + 11.2771i 0.129954 + 0.399959i
796796 2.11221 6.50072i 0.0748654 0.230412i
797797 −0.209047 0.151882i −0.00740484 0.00537993i 0.584077 0.811698i 0.301457π-0.301457\pi
−0.591482 + 0.806319i 0.701457π0.701457\pi
798798 −0.246899 0.179383i −0.00874014 0.00635008i
799799 −27.5232 + 84.7076i −0.973700 + 2.99674i
800800 −1.39484 4.29288i −0.0493150 0.151776i
801801 −7.02058 + 5.10075i −0.248060 + 0.180226i
802802 5.31904 0.187822
803803 −24.6223 17.7895i −0.868900 0.627778i
804804 −5.36682 −0.189273
805805 −13.2749 + 9.64481i −0.467880 + 0.339935i
806806 −1.48782 4.57905i −0.0524063 0.161290i
807807 −8.76530 + 26.9768i −0.308553 + 0.949629i
808808 7.82002 + 5.68158i 0.275107 + 0.199877i
809809 −7.58656 5.51196i −0.266729 0.193790i 0.446379 0.894844i 0.352713π-0.352713\pi
−0.713108 + 0.701054i 0.752713π0.752713\pi
810810 −0.258398 + 0.795267i −0.00907918 + 0.0279428i
811811 9.69501 + 29.8382i 0.340438 + 1.04776i 0.963981 + 0.265971i 0.0856925π0.0856925\pi
−0.623543 + 0.781789i 0.714308π0.714308\pi
812812 9.88733 7.18357i 0.346977 0.252094i
813813 22.2248 0.779457
814814 −11.2409 + 0.0298183i −0.393992 + 0.00104513i
815815 −9.59911 −0.336242
816816 −21.1012 + 15.3309i −0.738689 + 0.536689i
817817 −0.390108 1.20063i −0.0136481 0.0420047i
818818 −2.13899 + 6.58315i −0.0747882 + 0.230174i
819819 −1.82926 1.32904i −0.0639196 0.0464403i
820820 16.4313 + 11.9381i 0.573807 + 0.416895i
821821 −14.5043 + 44.6397i −0.506204 + 1.55794i 0.292532 + 0.956256i 0.405502π0.405502\pi
−0.798737 + 0.601681i 0.794498π0.794498\pi
822822 0.480405 + 1.47853i 0.0167560 + 0.0515698i
823823 10.8974 7.91742i 0.379859 0.275984i −0.381428 0.924398i 0.624568π-0.624568\pi
0.761287 + 0.648415i 0.224568π0.224568\pi
824824 −5.28543 −0.184127
825825 −1.25089 3.81538i −0.0435504 0.132834i
826826 0.786893 0.0273795
827827 13.9279 10.1192i 0.484319 0.351878i −0.318676 0.947864i 0.603238π-0.603238\pi
0.802995 + 0.595985i 0.203238π0.203238\pi
828828 4.22215 + 12.9945i 0.146730 + 0.451588i
829829 7.44421 22.9109i 0.258548 0.795729i −0.734562 0.678542i 0.762612π-0.762612\pi
0.993110 0.117187i 0.0373878π-0.0373878\pi
830830 −9.09212 6.60581i −0.315592 0.229291i
831831 −0.661635 0.480706i −0.0229519 0.0166755i
832832 4.16621 12.8223i 0.144437 0.444533i
833833 −14.9084 45.8833i −0.516545 1.58976i
834834 0.299355 0.217494i 0.0103658 0.00753120i
835835 −10.3540 −0.358314
836836 1.91860 5.95858i 0.0663562 0.206082i
837837 −5.77211 −0.199513
838838 3.06477 2.22668i 0.105871 0.0769195i
839839 8.13283 + 25.0303i 0.280776 + 0.864141i 0.987633 + 0.156784i 0.0501126π0.0501126\pi
−0.706857 + 0.707357i 0.749887π0.749887\pi
840840 −0.913636 + 2.81188i −0.0315234 + 0.0970192i
841841 −17.5418 12.7449i −0.604891 0.439479i
842842 −6.56863 4.77239i −0.226370 0.164467i
843843 0.829920 2.55423i 0.0285840 0.0879724i
844844 5.34568 + 16.4523i 0.184006 + 0.566312i
845845 13.7502 9.99008i 0.473020 0.343669i
846846 3.82371 0.131462
847847 8.06288 5.92363i 0.277044 0.203538i
848848 15.8783 0.545262
849849 15.6781 11.3908i 0.538072 0.390932i
850850 −0.981077 3.01944i −0.0336506 0.103566i
851851 22.5960 69.5434i 0.774582 2.38392i
852852 −20.7176 15.0522i −0.709772 0.515680i
853853 −29.4040 21.3633i −1.00677 0.731464i −0.0432443 0.999065i 0.513769π-0.513769\pi
−0.963530 + 0.267600i 0.913769π0.913769\pi
854854 0.851047 2.61925i 0.0291222 0.0896290i
855855 0.770105 + 2.37014i 0.0263370 + 0.0810571i
856856 −12.5934 + 9.14965i −0.430434 + 0.312729i
857857 −21.7298 −0.742274 −0.371137 0.928578i 0.621032π-0.621032\pi
−0.371137 + 0.928578i 0.621032π0.621032\pi
858858 −0.847913 + 2.63336i −0.0289473 + 0.0899013i
859859 20.4025 0.696123 0.348061 0.937472i 0.386840π-0.386840\pi
0.348061 + 0.937472i 0.386840π0.386840\pi
860860 −4.80391 + 3.49025i −0.163812 + 0.119016i
861861 −1.21363 3.73516i −0.0413603 0.127294i
862862 0.990873 3.04959i 0.0337493 0.103870i
863863 −2.17317 1.57890i −0.0739754 0.0537463i 0.550183 0.835044i 0.314558π-0.314558\pi
−0.624158 + 0.781298i 0.714558π0.714558\pi
864864 3.01640 + 2.19154i 0.102620 + 0.0745578i
865865 −18.3411 + 56.4483i −0.623618 + 1.91930i
866866 1.77850 + 5.47367i 0.0604360 + 0.186003i
867867 −35.6663 + 25.9131i −1.21129 + 0.880055i
868868 −9.90890 −0.336330
869869 −8.60326 26.2411i −0.291846 0.890167i
870870 5.95302 0.201826
871871 5.71877 4.15493i 0.193773 0.140784i
872872 6.19173 + 19.0562i 0.209678 + 0.645324i
873873 3.98547 12.2660i 0.134888 0.415142i
874874 −1.96508 1.42772i −0.0664699 0.0482932i
875875 −6.94890 5.04867i −0.234916 0.170676i
876876 5.34182 16.4404i 0.180483 0.555470i
877877 −10.4871 32.2760i −0.354125 1.08988i −0.956515 0.291683i 0.905785π-0.905785\pi
0.602390 0.798202i 0.294215π-0.294215\pi
878878 1.38607 1.00704i 0.0467775 0.0339859i
879879 14.4039 0.485832
880880 −27.5830 + 0.0731684i −0.929821 + 0.00246651i
881881 1.74919 0.0589318 0.0294659 0.999566i 0.490619π-0.490619\pi
0.0294659 + 0.999566i 0.490619π0.490619\pi
882882 −1.67561 + 1.21740i −0.0564209 + 0.0409922i
883883 −4.99716 15.3797i −0.168168 0.517567i 0.831088 0.556141i 0.187719π-0.187719\pi
−0.999256 + 0.0385738i 0.987719π0.987719\pi
884884 11.3322 34.8771i 0.381145 1.17304i
885885 −5.19851 3.77694i −0.174746 0.126960i
886886 5.66769 + 4.11782i 0.190410 + 0.138341i
887887 −10.7122 + 32.9688i −0.359681 + 1.10698i 0.593564 + 0.804787i 0.297720π0.297720\pi
−0.953245 + 0.302198i 0.902280π0.902280\pi
888888 −4.07144 12.5306i −0.136629 0.420499i
889889 2.90643 2.11164i 0.0974784 0.0708222i
890890 −7.25642 −0.243236
891891 2.68837 + 1.94234i 0.0900637 + 0.0650708i
892892 49.4265 1.65492
893893 9.21941 6.69829i 0.308516 0.224150i
894894 −1.66478 5.12367i −0.0556786 0.171361i
895895 2.66584 8.20460i 0.0891091 0.274250i
896896 6.82610 + 4.95945i 0.228044 + 0.165684i
897897 −14.5592 10.5779i −0.486117 0.353185i
898898 −2.95482 + 9.09399i −0.0986035 + 0.303470i
899899 12.6984 + 39.0816i 0.423514 + 1.30344i
900900 1.84857 1.34306i 0.0616190 0.0447688i
901901 37.1874 1.23889
902902 −3.88002 + 2.83475i −0.129190 + 0.0943869i
903903 1.14822 0.0382104
904904 −0.112314 + 0.0816007i −0.00373550 + 0.00271400i
905905 −14.6130 44.9742i −0.485753 1.49499i
906906 0.536331 1.65066i 0.0178184 0.0548395i
907907 27.6465 + 20.0863i 0.917986 + 0.666956i 0.943022 0.332731i 0.107970π-0.107970\pi
−0.0250361 + 0.999687i 0.507970π0.507970\pi
908908 −25.2434 18.3404i −0.837732 0.608648i
909909 −2.28998 + 7.04785i −0.0759540 + 0.233762i
910910 −0.584262 1.79817i −0.0193681 0.0596089i
911911 20.7519 15.0771i 0.687541 0.499528i −0.188310 0.982110i 0.560301π-0.560301\pi
0.875851 + 0.482582i 0.160301π0.160301\pi
912912 3.33717 0.110505
913913 −35.9928 + 26.2965i −1.19119 + 0.870286i
914914 9.58187 0.316940
915915 −18.1943 + 13.2189i −0.601483 + 0.437003i
916916 −16.1023 49.5578i −0.532035 1.63744i
917917 3.38540 10.4192i 0.111796 0.344071i
918918 2.12162 + 1.54145i 0.0700239 + 0.0508753i
919919 −13.8058 10.0305i −0.455410 0.330875i 0.336318 0.941749i 0.390818π-0.390818\pi
−0.791728 + 0.610874i 0.790818π0.790818\pi
920920 −7.27167 + 22.3799i −0.239740 + 0.737844i
921921 0.0212958 + 0.0655416i 0.000701719 + 0.00215967i
922922 0.216994 0.157656i 0.00714633 0.00519211i
923923 33.7294 1.11022
924924 4.61508 + 3.33438i 0.151825 + 0.109693i
925925 −12.2286 −0.402074
926926 −6.34377 + 4.60902i −0.208469 + 0.151462i
927927 −1.25217 3.85378i −0.0411266 0.126575i
928928 8.20246 25.2446i 0.269259 0.828694i
929929 −5.74928 4.17710i −0.188628 0.137046i 0.489464 0.872024i 0.337193π-0.337193\pi
−0.678091 + 0.734978i 0.737193π0.737193\pi
930930 −3.90480 2.83701i −0.128044 0.0930291i
931931 −1.90748 + 5.87062i −0.0625151 + 0.192402i
932932 −4.91098 15.1144i −0.160864 0.495090i
933933 6.65529 4.83535i 0.217884 0.158302i
934934 0.904718 0.0296033
935935 −64.6001 + 0.171363i −2.11265 + 0.00560416i
936936 −3.24261 −0.105988
937937 −48.5665 + 35.2857i −1.58660 + 1.15273i −0.678001 + 0.735061i 0.737154π0.737154\pi
−0.908598 + 0.417671i 0.862846π0.862846\pi
938938 0.268160 + 0.825312i 0.00875574 + 0.0269474i
939939 9.39492 28.9146i 0.306592 0.943592i
940940 −43.3649 31.5064i −1.41441 1.02763i
941941 −13.6447 9.91349i −0.444806 0.323171i 0.342736 0.939432i 0.388646π-0.388646\pi
−0.787542 + 0.616261i 0.788646π0.788646\pi
942942 −1.56973 + 4.83113i −0.0511446 + 0.157407i
943943 −9.65931 29.7283i −0.314551 0.968087i
944944 −6.96129 + 5.05767i −0.226571 + 0.164613i
945945 −2.26668 −0.0737352
946946 −0.437673 1.33496i −0.0142300 0.0434033i
947947 20.1240 0.653942 0.326971 0.945034i 0.393972π-0.393972\pi
0.326971 + 0.945034i 0.393972π0.393972\pi
948948 12.7139 9.23721i 0.412929 0.300011i
949949 7.03585 + 21.6541i 0.228393 + 0.702923i
950950 −0.125526 + 0.386328i −0.00407259 + 0.0125341i
951951 23.4277 + 17.0212i 0.759695 + 0.551951i
952952 7.50156 + 5.45020i 0.243127 + 0.176642i
953953 −10.8384 + 33.3570i −0.351089 + 1.08054i 0.607154 + 0.794584i 0.292311π0.292311\pi
−0.958243 + 0.285956i 0.907689π0.907689\pi
954954 −0.493340 1.51834i −0.0159725 0.0491582i
955955 −13.4228 + 9.75221i −0.434350 + 0.315574i
956956 −21.8231 −0.705810
957957 7.23682 22.4753i 0.233933 0.726524i
958958 6.47584 0.209225
959959 −3.40931 + 2.47701i −0.110092 + 0.0799868i
960960 −4.17651 12.8540i −0.134796 0.414861i
961961 0.716079 2.20386i 0.0230993 0.0710924i
962962 6.81644 + 4.95243i 0.219771 + 0.159673i
963963 −9.65481 7.01463i −0.311122 0.226043i
964964 6.36970 19.6039i 0.205154 0.631399i
965965 −5.03638 15.5004i −0.162127 0.498975i
966966 1.78733 1.29857i 0.0575063 0.0417808i
967967 −32.6003 −1.04836 −0.524178 0.851609i 0.675627π-0.675627\pi
−0.524178 + 0.851609i 0.675627π0.675627\pi
968968 4.36133 13.6691i 0.140179 0.439342i
969969 7.81575 0.251078
970970 8.72493 6.33903i 0.280141 0.203534i
971971 14.1133 + 43.4364i 0.452918 + 1.39394i 0.873562 + 0.486713i 0.161804π0.161804\pi
−0.420643 + 0.907226i 0.638196π0.638196\pi
972972 −0.583244 + 1.79504i −0.0187075 + 0.0575759i
973973 0.811466 + 0.589565i 0.0260144 + 0.0189006i
974974 −3.94182 2.86390i −0.126304 0.0917653i
975975 −0.930012 + 2.86228i −0.0297842 + 0.0916664i
976976 9.30614 + 28.6413i 0.297882 + 0.916787i
977977 −1.62488 + 1.18054i −0.0519845 + 0.0377690i −0.613474 0.789715i 0.710228π-0.710228\pi
0.561490 + 0.827484i 0.310228π0.310228\pi
978978 1.29241 0.0413269
979979 −8.82130 + 27.3962i −0.281930 + 0.875587i
980980 29.0344 0.927470
981981 −12.4276 + 9.02918i −0.396783 + 0.288280i
982982 −1.87057 5.75701i −0.0596922 0.183714i
983983 6.05736 18.6426i 0.193200 0.594608i −0.806793 0.590834i 0.798799π-0.798799\pi
0.999993 0.00377358i 0.00120117π-0.00120117\pi
984984 −4.55656 3.31054i −0.145258 0.105536i
985985 39.8522 + 28.9543i 1.26980 + 0.922561i
986986 5.76930 17.7561i 0.183732 0.565468i
987987 3.20296 + 9.85768i 0.101951 + 0.313774i
988988 −3.79595 + 2.75792i −0.120765 + 0.0877411i
989989 9.13874 0.290595
990990 0.864003 + 2.63532i 0.0274598 + 0.0837560i
991991 45.3764 1.44143 0.720714 0.693232i 0.243814π-0.243814\pi
0.720714 + 0.693232i 0.243814π0.243814\pi
992992 −17.4110 + 12.6498i −0.552800 + 0.401633i
993993 −0.760888 2.34177i −0.0241461 0.0743139i
994994 −1.27955 + 3.93806i −0.0405850 + 0.124908i
995995 7.30152 + 5.30486i 0.231474 + 0.168176i
996996 −20.5223 14.9103i −0.650274 0.472452i
997997 1.01618 3.12749i 0.0321829 0.0990486i −0.933675 0.358122i 0.883417π-0.883417\pi
0.965858 + 0.259073i 0.0834172π0.0834172\pi
998998 2.27122 + 6.99010i 0.0718942 + 0.221268i
999999 8.17190 5.93724i 0.258548 0.187846i
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 627.2.j.a.58.3 24
11.2 odd 10 6897.2.a.bg.1.7 12
11.4 even 5 inner 627.2.j.a.400.3 yes 24
11.9 even 5 6897.2.a.bf.1.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
627.2.j.a.58.3 24 1.1 even 1 trivial
627.2.j.a.400.3 yes 24 11.4 even 5 inner
6897.2.a.bf.1.6 12 11.9 even 5
6897.2.a.bg.1.7 12 11.2 odd 10