Properties

Label 637.2.cc.a.5.2
Level 637637
Weight 22
Character 637.5
Analytic conductor 5.0865.086
Analytic rank 00
Dimension 15361536
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(5,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(84))
 
chi = DirichletCharacter(H, H._module([58, 63]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.cc (of order 8484, 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: 5.086470608765.08647060876
Analytic rank: 00
Dimension: 15361536
Relative dimension: 6464 over Q(ζ84)\Q(\zeta_{84})
Twist minimal: yes
Sato-Tate group: SU(2)[C84]\mathrm{SU}(2)[C_{84}]

Embedding invariants

Embedding label 5.2
Character χ\chi == 637.5
Dual form 637.2.cc.a.255.2

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+(1.60364+2.17285i)q2+(1.54581+2.26729i)q3+(1.560135.05780i)q4+(1.554931.33812i)q5+(2.447576.99474i)q6+(2.20094+1.46828i)q7+(8.39375+2.93710i)q8+(1.655054.21700i)q9+(0.414004+5.52450i)q10+(1.62882+0.710645i)q11+(13.8792+4.28116i)q12+(3.57611+0.459857i)q13+(6.71988+2.42773i)q14+(0.630289+5.59397i)q15+(11.0959+7.56509i)q16+(1.91962+1.78115i)q17+(11.8170+3.16636i)q18+(3.07140+0.822980i)q19+(9.193865.77688i)q20+(6.73127+2.72049i)q21+(1.067914.67880i)q22+(0.397623+0.428536i)q23+(19.6344+14.4909i)q24+(0.117985+0.782779i)q25+(6.73399+7.03291i)q26+(4.09362+0.934343i)q27+(3.9925413.4226i)q28+(2.254369.87698i)q29+(13.16567.60118i)q30+(2.58254+9.63818i)q31+(0.69104018.4684i)q32+(0.9066054.79152i)q33+(0.7917947.02737i)q34+(5.387050.662058i)q35+(18.7467+14.9500i)q36+(4.45792+8.43479i)q37+(3.137217.99347i)q38+(6.57062+7.39722i)q39+(16.98196.66490i)q40+(7.39484+2.58757i)q41+(4.8833118.9887i)q42+(4.50742+9.35975i)q43+(6.13546+7.12954i)q44+(8.216354.34247i)q45+(0.2935021.55119i)q46+(2.16156+2.92881i)q4736.8520iq48+(2.68829+6.46321i)q49+(1.511661.51166i)q50+(1.071007.10565i)q51+(3.2533118.8047i)q52+(7.89106+2.43407i)q53+(8.59489+7.39650i)q54+(1.58176+3.28456i)q55+(14.1617+18.7888i)q56+(2.881888.23594i)q57+(25.0764+10.9407i)q58+(1.258591.08310i)q59+(27.309911.9152i)q60+(2.116636.86195i)q61+(16.800921.0676i)q62+(2.5490811.7114i)q63+(18.0219+14.3720i)q64+(6.175934.07023i)q65+(8.95742+9.65380i)q66+(3.49793+0.937267i)q67+(12.0035+6.93024i)q68+(0.3569651.56396i)q69+(7.20033+12.7670i)q70+(2.342483.72804i)q71+(1.5063340.2575i)q72+(0.5555090.409985i)q73+(25.47653.83996i)q74+(1.592401.47754i)q75+(8.95425+14.2506i)q76+(4.628360.827474i)q77+(5.5361826.1395i)q78+(0.441303+0.764359i)q79+(7.13038+26.6109i)q80+(1.516101.40673i)q81+(17.4811+11.9184i)q82+(2.450690.276126i)q83+(24.2613+29.8012i)q84+(0.601475+5.33824i)q85+(13.109124.8036i)q86+(25.8788+10.1567i)q87+(15.7591+1.18098i)q88+(3.109251.35655i)q89+(22.611610.8892i)q90+(7.19560+6.26285i)q91+(2.78779+1.34253i)q92+(17.860420.7542i)q93+(2.897519.39351i)q94+(3.67456+5.38959i)q95+(40.8051+30.1155i)q96+(9.675439.67543i)q97+(18.35474.52340i)q98+(5.69256+5.69256i)q99+O(q100)q+(-1.60364 + 2.17285i) q^{2} +(-1.54581 + 2.26729i) q^{3} +(-1.56013 - 5.05780i) q^{4} +(1.55493 - 1.33812i) q^{5} +(-2.44757 - 6.99474i) q^{6} +(2.20094 + 1.46828i) q^{7} +(8.39375 + 2.93710i) q^{8} +(-1.65505 - 4.21700i) q^{9} +(0.414004 + 5.52450i) q^{10} +(-1.62882 + 0.710645i) q^{11} +(13.8792 + 4.28116i) q^{12} +(3.57611 + 0.459857i) q^{13} +(-6.71988 + 2.42773i) q^{14} +(0.630289 + 5.59397i) q^{15} +(-11.0959 + 7.56509i) q^{16} +(-1.91962 + 1.78115i) q^{17} +(11.8170 + 3.16636i) q^{18} +(-3.07140 + 0.822980i) q^{19} +(-9.19386 - 5.77688i) q^{20} +(-6.73127 + 2.72049i) q^{21} +(1.06791 - 4.67880i) q^{22} +(-0.397623 + 0.428536i) q^{23} +(-19.6344 + 14.4909i) q^{24} +(-0.117985 + 0.782779i) q^{25} +(-6.73399 + 7.03291i) q^{26} +(4.09362 + 0.934343i) q^{27} +(3.99254 - 13.4226i) q^{28} +(-2.25436 - 9.87698i) q^{29} +(-13.1656 - 7.60118i) q^{30} +(-2.58254 + 9.63818i) q^{31} +(0.691040 - 18.4684i) q^{32} +(0.906605 - 4.79152i) q^{33} +(-0.791794 - 7.02737i) q^{34} +(5.38705 - 0.662058i) q^{35} +(-18.7467 + 14.9500i) q^{36} +(4.45792 + 8.43479i) q^{37} +(3.13721 - 7.99347i) q^{38} +(-6.57062 + 7.39722i) q^{39} +(16.9819 - 6.66490i) q^{40} +(7.39484 + 2.58757i) q^{41} +(4.88331 - 18.9887i) q^{42} +(-4.50742 + 9.35975i) q^{43} +(6.13546 + 7.12954i) q^{44} +(-8.21635 - 4.34247i) q^{45} +(-0.293502 - 1.55119i) q^{46} +(-2.16156 + 2.92881i) q^{47} -36.8520i q^{48} +(2.68829 + 6.46321i) q^{49} +(-1.51166 - 1.51166i) q^{50} +(-1.07100 - 7.10565i) q^{51} +(-3.25331 - 18.8047i) q^{52} +(-7.89106 + 2.43407i) q^{53} +(-8.59489 + 7.39650i) q^{54} +(-1.58176 + 3.28456i) q^{55} +(14.1617 + 18.7888i) q^{56} +(2.88188 - 8.23594i) q^{57} +(25.0764 + 10.9407i) q^{58} +(-1.25859 - 1.08310i) q^{59} +(27.3099 - 11.9152i) q^{60} +(2.11663 - 6.86195i) q^{61} +(-16.8009 - 21.0676i) q^{62} +(2.54908 - 11.7114i) q^{63} +(18.0219 + 14.3720i) q^{64} +(6.17593 - 4.07023i) q^{65} +(8.95742 + 9.65380i) q^{66} +(3.49793 + 0.937267i) q^{67} +(12.0035 + 6.93024i) q^{68} +(-0.356965 - 1.56396i) q^{69} +(-7.20033 + 12.7670i) q^{70} +(-2.34248 - 3.72804i) q^{71} +(-1.50633 - 40.2575i) q^{72} +(0.555509 - 0.409985i) q^{73} +(-25.4765 - 3.83996i) q^{74} +(-1.59240 - 1.47754i) q^{75} +(8.95425 + 14.2506i) q^{76} +(-4.62836 - 0.827474i) q^{77} +(-5.53618 - 26.1395i) q^{78} +(-0.441303 + 0.764359i) q^{79} +(-7.13038 + 26.6109i) q^{80} +(1.51610 - 1.40673i) q^{81} +(-17.4811 + 11.9184i) q^{82} +(2.45069 - 0.276126i) q^{83} +(24.2613 + 29.8012i) q^{84} +(-0.601475 + 5.33824i) q^{85} +(-13.1091 - 24.8036i) q^{86} +(25.8788 + 10.1567i) q^{87} +(-15.7591 + 1.18098i) q^{88} +(-3.10925 - 1.35655i) q^{89} +(22.6116 - 10.8892i) q^{90} +(7.19560 + 6.26285i) q^{91} +(2.78779 + 1.34253i) q^{92} +(-17.8604 - 20.7542i) q^{93} +(-2.89751 - 9.39351i) q^{94} +(-3.67456 + 5.38959i) q^{95} +(40.8051 + 30.1155i) q^{96} +(-9.67543 - 9.67543i) q^{97} +(-18.3547 - 4.52340i) q^{98} +(5.69256 + 5.69256i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 1536q26q244q322q528q622q712q8176q922q1128q1384q148q15180q1618q1854q1928q202q2148q22+32q99+O(q100) 1536 q - 26 q^{2} - 44 q^{3} - 22 q^{5} - 28 q^{6} - 22 q^{7} - 12 q^{8} - 176 q^{9} - 22 q^{11} - 28 q^{13} - 84 q^{14} - 8 q^{15} - 180 q^{16} - 18 q^{18} - 54 q^{19} - 28 q^{20} - 2 q^{21} - 48 q^{22}+ \cdots - 32 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/637Z)×\left(\mathbb{Z}/637\mathbb{Z}\right)^\times.

nn 197197 248248
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) e(2942)e\left(\frac{29}{42}\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 −1.60364 + 2.17285i −1.13394 + 1.53644i −0.327774 + 0.944756i 0.606299π0.606299\pi
−0.806170 + 0.591684i 0.798463π0.798463\pi
33 −1.54581 + 2.26729i −0.892476 + 1.30902i 0.0580303 + 0.998315i 0.481518π0.481518\pi
−0.950506 + 0.310706i 0.899434π0.899434\pi
44 −1.56013 5.05780i −0.780063 2.52890i
55 1.55493 1.33812i 0.695385 0.598427i −0.231919 0.972735i 0.574501π-0.574501\pi
0.927305 + 0.374308i 0.122120π0.122120\pi
66 −2.44757 6.99474i −0.999215 2.85559i
77 2.20094 + 1.46828i 0.831878 + 0.554959i
88 8.39375 + 2.93710i 2.96764 + 1.03842i
99 −1.65505 4.21700i −0.551683 1.40567i
1010 0.414004 + 5.52450i 0.130920 + 1.74700i
1111 −1.62882 + 0.710645i −0.491106 + 0.214268i −0.630827 0.775923i 0.717284π-0.717284\pi
0.139721 + 0.990191i 0.455380π0.455380\pi
1212 13.8792 + 4.28116i 4.00657 + 1.23586i
1313 3.57611 + 0.459857i 0.991833 + 0.127541i
1414 −6.71988 + 2.42773i −1.79596 + 0.648838i
1515 0.630289 + 5.59397i 0.162740 + 1.44436i
1616 −11.0959 + 7.56509i −2.77399 + 1.89127i
1717 −1.91962 + 1.78115i −0.465576 + 0.431991i −0.877754 0.479112i 0.840959π-0.840959\pi
0.412178 + 0.911103i 0.364768π0.364768\pi
1818 11.8170 + 3.16636i 2.78530 + 0.746318i
1919 −3.07140 + 0.822980i −0.704628 + 0.188804i −0.593303 0.804980i 0.702176π-0.702176\pi
−0.111325 + 0.993784i 0.535510π0.535510\pi
2020 −9.19386 5.77688i −2.05581 1.29175i
2121 −6.73127 + 2.72049i −1.46888 + 0.593659i
2222 1.06791 4.67880i 0.227678 0.997523i
2323 −0.397623 + 0.428536i −0.0829102 + 0.0893559i −0.773144 0.634230i 0.781317π-0.781317\pi
0.690234 + 0.723586i 0.257508π0.257508\pi
2424 −19.6344 + 14.4909i −4.00786 + 2.95794i
2525 −0.117985 + 0.782779i −0.0235970 + 0.156556i
2626 −6.73399 + 7.03291i −1.32064 + 1.37927i
2727 4.09362 + 0.934343i 0.787818 + 0.179814i
2828 3.99254 13.4226i 0.754520 2.53664i
2929 −2.25436 9.87698i −0.418623 1.83411i −0.540213 0.841528i 0.681656π-0.681656\pi
0.121589 0.992580i 0.461201π-0.461201\pi
3030 −13.1656 7.60118i −2.40370 1.38778i
3131 −2.58254 + 9.63818i −0.463838 + 1.73107i 0.196874 + 0.980429i 0.436921π0.436921\pi
−0.660713 + 0.750639i 0.729746π0.729746\pi
3232 0.691040 18.4684i 0.122160 3.26479i
3333 0.906605 4.79152i 0.157820 0.834097i
3434 −0.791794 7.02737i −0.135792 1.20518i
3535 5.38705 0.662058i 0.910578 0.111908i
3636 −18.7467 + 14.9500i −3.12444 + 2.49166i
3737 4.45792 + 8.43479i 0.732877 + 1.38667i 0.915024 + 0.403400i 0.132172π0.132172\pi
−0.182147 + 0.983271i 0.558305π0.558305\pi
3838 3.13721 7.99347i 0.508922 1.29671i
3939 −6.57062 + 7.39722i −1.05214 + 1.18450i
4040 16.9819 6.66490i 2.68507 1.05381i
4141 7.39484 + 2.58757i 1.15488 + 0.404110i 0.838702 0.544590i 0.183315π-0.183315\pi
0.316177 + 0.948700i 0.397601π0.397601\pi
4242 4.88331 18.9887i 0.753512 2.93003i
4343 −4.50742 + 9.35975i −0.687375 + 1.42735i 0.206235 + 0.978503i 0.433879π0.433879\pi
−0.893609 + 0.448845i 0.851835π0.851835\pi
4444 6.13546 + 7.12954i 0.924956 + 1.07482i
4545 −8.21635 4.34247i −1.22482 0.647337i
4646 −0.293502 1.55119i −0.0432745 0.228711i
4747 −2.16156 + 2.92881i −0.315296 + 0.427211i −0.933374 0.358906i 0.883150π-0.883150\pi
0.618078 + 0.786117i 0.287912π0.287912\pi
4848 36.8520i 5.31912i
4949 2.68829 + 6.46321i 0.384041 + 0.923316i
5050 −1.51166 1.51166i −0.213781 0.213781i
5151 −1.07100 7.10565i −0.149971 0.994990i
5252 −3.25331 18.8047i −0.451153 2.60774i
5353 −7.89106 + 2.43407i −1.08392 + 0.334345i −0.784723 0.619846i 0.787195π-0.787195\pi
−0.299197 + 0.954191i 0.596719π0.596719\pi
5454 −8.59489 + 7.39650i −1.16962 + 1.00654i
5555 −1.58176 + 3.28456i −0.213285 + 0.442890i
5656 14.1617 + 18.7888i 1.89243 + 2.51076i
5757 2.88188 8.23594i 0.381714 1.09088i
5858 25.0764 + 10.9407i 3.29269 + 1.43659i
5959 −1.25859 1.08310i −0.163854 0.141008i 0.566539 0.824035i 0.308282π-0.308282\pi
−0.730393 + 0.683027i 0.760663π0.760663\pi
6060 27.3099 11.9152i 3.52569 1.53824i
6161 2.11663 6.86195i 0.271007 0.878582i −0.713109 0.701053i 0.752713π-0.752713\pi
0.984116 0.177529i 0.0568104π-0.0568104\pi
6262 −16.8009 21.0676i −2.13371 2.67559i
6363 2.54908 11.7114i 0.321154 1.47550i
6464 18.0219 + 14.3720i 2.25273 + 1.79649i
6565 6.17593 4.07023i 0.766030 0.504850i
6666 8.95742 + 9.65380i 1.10258 + 1.18830i
6767 3.49793 + 0.937267i 0.427340 + 0.114505i 0.466077 0.884744i 0.345667π-0.345667\pi
−0.0387373 + 0.999249i 0.512334π0.512334\pi
6868 12.0035 + 6.93024i 1.45564 + 0.840415i
6969 −0.356965 1.56396i −0.0429735 0.188279i
7070 −7.20033 + 12.7670i −0.860605 + 1.52595i
7171 −2.34248 3.72804i −0.278002 0.442437i 0.678314 0.734772i 0.262711π-0.262711\pi
−0.956316 + 0.292335i 0.905568π0.905568\pi
7272 −1.50633 40.2575i −0.177522 4.74439i
7373 0.555509 0.409985i 0.0650175 0.0479851i −0.560827 0.827933i 0.689517π-0.689517\pi
0.625844 + 0.779948i 0.284755π0.284755\pi
7474 −25.4765 3.83996i −2.96158 0.446386i
7575 −1.59240 1.47754i −0.183875 0.170611i
7676 8.95425 + 14.2506i 1.02712 + 1.63466i
7777 −4.62836 0.827474i −0.527450 0.0942994i
7878 −5.53618 26.1395i −0.626849 2.95971i
7979 −0.441303 + 0.764359i −0.0496504 + 0.0859971i −0.889783 0.456385i 0.849144π-0.849144\pi
0.840132 + 0.542382i 0.182477π0.182477\pi
8080 −7.13038 + 26.6109i −0.797201 + 2.97519i
8181 1.51610 1.40673i 0.168455 0.156304i
8282 −17.4811 + 11.9184i −1.93046 + 1.31617i
8383 2.45069 0.276126i 0.268998 0.0303088i 0.0235647 0.999722i 0.492498π-0.492498\pi
0.245433 + 0.969414i 0.421070π0.421070\pi
8484 24.2613 + 29.8012i 2.64713 + 3.25157i
8585 −0.601475 + 5.33824i −0.0652392 + 0.579014i
8686 −13.1091 24.8036i −1.41359 2.67464i
8787 25.8788 + 10.1567i 2.77450 + 1.08891i
8888 −15.7591 + 1.18098i −1.67993 + 0.125893i
8989 −3.10925 1.35655i −0.329580 0.143794i 0.228586 0.973524i 0.426590π-0.426590\pi
−0.558166 + 0.829729i 0.688495π0.688495\pi
9090 22.6116 10.8892i 2.38347 1.14782i
9191 7.19560 + 6.26285i 0.754304 + 0.656525i
9292 2.78779 + 1.34253i 0.290648 + 0.139968i
9393 −17.8604 20.7542i −1.85204 2.15211i
9494 −2.89751 9.39351i −0.298856 0.968867i
9595 −3.67456 + 5.38959i −0.377002 + 0.552961i
9696 40.8051 + 30.1155i 4.16465 + 3.07365i
9797 −9.67543 9.67543i −0.982391 0.982391i 0.0174565 0.999848i 0.494443π-0.494443\pi
−0.999848 + 0.0174565i 0.994443π0.994443\pi
9898 −18.3547 4.52340i −1.85410 0.456932i
9999 5.69256 + 5.69256i 0.572124 + 0.572124i
100100 4.14321 0.624489i 0.414321 0.0624489i
101101 1.99807 + 1.36226i 0.198815 + 0.135550i 0.658636 0.752462i 0.271134π-0.271134\pi
−0.459820 + 0.888012i 0.652086π0.652086\pi
102102 17.1571 + 9.06777i 1.69880 + 0.897843i
103103 0.262686 3.50530i 0.0258832 0.345388i −0.969195 0.246295i 0.920787π-0.920787\pi
0.995078 0.0990928i 0.0315941π-0.0315941\pi
104104 28.6663 + 14.3633i 2.81096 + 1.40844i
105105 −6.82630 + 13.2374i −0.666178 + 1.29184i
106106 7.36554 21.0495i 0.715404 2.04451i
107107 −3.05492 7.78382i −0.295331 0.752490i −0.999114 0.0420760i 0.986603π-0.986603\pi
0.703784 0.710414i 0.251492π-0.251492\pi
108108 −1.66084 22.1624i −0.159815 2.13258i
109109 −1.32999 3.04838i −0.127390 0.291982i 0.841166 0.540777i 0.181870π-0.181870\pi
−0.968556 + 0.248796i 0.919965π0.919965\pi
110110 −4.60030 8.70419i −0.438621 0.829912i
111111 −26.0152 2.93121i −2.46926 0.278218i
112112 −35.5292 + 0.358328i −3.35720 + 0.0338588i
113113 −8.15707 + 10.2286i −0.767353 + 0.962230i −0.999946 0.0103443i 0.996707π-0.996707\pi
0.232594 + 0.972574i 0.425279π0.425279\pi
114114 13.2740 + 19.4694i 1.24322 + 1.82347i
115115 −0.0448414 + 1.19841i −0.00418148 + 0.111752i
116116 −46.4388 + 26.8114i −4.31173 + 2.48938i
117117 −3.97942 15.8415i −0.367897 1.46455i
118118 4.37174 0.997821i 0.402451 0.0918569i
119119 −6.84019 + 1.10165i −0.627040 + 0.100989i
120120 −11.1396 + 48.8056i −1.01690 + 4.45532i
121121 −5.33388 + 5.74855i −0.484898 + 0.522596i
122122 11.5157 + 15.6032i 1.04258 + 1.41265i
123123 −17.2978 + 12.7664i −1.55969 + 1.15110i
124124 52.7771 1.97478i 4.73952 0.177340i
125125 6.32114 + 10.0600i 0.565380 + 0.899797i
126126 21.3595 + 24.3197i 1.90285 + 2.16657i
127127 9.20188 2.10027i 0.816535 0.186369i 0.206198 0.978510i 0.433891π-0.433891\pi
0.610337 + 0.792142i 0.291034π0.291034\pi
128128 −24.4255 + 6.54480i −2.15893 + 0.578484i
129129 −14.2536 24.6880i −1.25496 2.17366i
130130 −1.05996 + 19.9466i −0.0929644 + 1.74943i
131131 7.27838 + 10.6754i 0.635915 + 0.932717i 0.999999 + 0.00135029i 0.000429809π0.000429809\pi
−0.364084 + 0.931366i 0.618618π0.618618\pi
132132 −25.6490 + 2.88995i −2.23246 + 0.251538i
133133 −7.96834 2.69836i −0.690943 0.233977i
134134 −7.64596 + 6.09745i −0.660510 + 0.526739i
135135 7.61556 4.02494i 0.655443 0.346412i
136136 −21.3442 + 9.31238i −1.83025 + 0.798530i
137137 −8.85057 + 10.2846i −0.756156 + 0.878669i −0.995740 0.0922069i 0.970608π-0.970608\pi
0.239584 + 0.970876i 0.422989π0.422989\pi
138138 3.97071 + 1.73240i 0.338009 + 0.147472i
139139 6.78128 + 14.0815i 0.575181 + 1.19438i 0.962210 + 0.272308i 0.0877870π0.0877870\pi
−0.387029 + 0.922068i 0.626499π0.626499\pi
140140 −11.7530 26.2138i −0.993313 2.21547i
141141 −3.29910 9.42828i −0.277834 0.794004i
142142 11.8570 + 0.888559i 0.995017 + 0.0745662i
143143 −6.15161 + 1.79232i −0.514424 + 0.149881i
144144 50.2663 + 34.2710i 4.18886 + 2.85592i
145145 −16.7220 12.3414i −1.38869 1.02490i
146146 1.86451i 0.154308i
147147 −18.8096 3.89578i −1.55139 0.321319i
148148 35.7066 35.7066i 2.93507 2.93507i
149149 3.35431 4.54492i 0.274795 0.372335i −0.645366 0.763873i 0.723295π-0.723295\pi
0.920162 + 0.391539i 0.128057π0.128057\pi
150150 5.76411 1.09063i 0.470638 0.0890495i
151151 −7.59174 4.01235i −0.617807 0.326521i 0.128916 0.991656i 0.458850π-0.458850\pi
−0.746723 + 0.665135i 0.768374π0.768374\pi
152152 −28.1978 2.11313i −2.28714 0.171397i
153153 10.6881 + 5.14714i 0.864085 + 0.416122i
154154 9.22020 8.72977i 0.742985 0.703465i
155155 8.88141 + 18.4424i 0.713372 + 1.48133i
156156 47.6647 + 21.6923i 3.81623 + 1.73678i
157157 1.73472 0.129999i 0.138446 0.0103751i −0.00532691 0.999986i 0.501696π-0.501696\pi
0.143773 + 0.989611i 0.454077π0.454077\pi
158158 −0.953150 2.18464i −0.0758285 0.173801i
159159 6.67936 21.6539i 0.529708 1.71727i
160160 −23.6385 29.6418i −1.86879 2.34339i
161161 −1.50436 + 0.359359i −0.118560 + 0.0283215i
162162 0.625352 + 5.55016i 0.0491323 + 0.436061i
163163 5.51592 + 1.04367i 0.432041 + 0.0817465i 0.397383 0.917653i 0.369918π-0.369918\pi
0.0346574 + 0.999399i 0.488966π0.488966\pi
164164 1.55052 41.4386i 0.121075 3.23581i
165165 −5.00195 8.66363i −0.389401 0.674463i
166166 −3.33004 + 5.76779i −0.258461 + 0.447667i
167167 −10.9097 6.85502i −0.844218 0.530458i 0.0390977 0.999235i 0.487552π-0.487552\pi
−0.883316 + 0.468778i 0.844695π0.844695\pi
168168 −64.4909 + 3.06466i −4.97558 + 0.236443i
169169 12.5771 + 3.28899i 0.967466 + 0.252999i
170170 −10.6347 9.86753i −0.815642 0.756805i
171171 8.55382 + 11.5900i 0.654127 + 0.886311i
172172 54.3719 + 8.19525i 4.14582 + 0.624882i
173173 0.317118 + 0.294243i 0.0241101 + 0.0223709i 0.692136 0.721767i 0.256670π-0.256670\pi
−0.668026 + 0.744138i 0.732860π0.732860\pi
174174 −63.5693 + 39.9432i −4.81917 + 3.02809i
175175 −1.40902 + 1.54962i −0.106512 + 0.117140i
176176 12.6972 20.2074i 0.957085 1.52319i
177177 4.40124 1.17931i 0.330818 0.0886424i
178178 7.93371 4.58053i 0.594657 0.343325i
179179 −0.362720 0.390919i −0.0271110 0.0292187i 0.719351 0.694647i 0.244439π-0.244439\pi
−0.746462 + 0.665428i 0.768249π0.768249\pi
180180 −9.14481 + 48.3315i −0.681614 + 3.60242i
181181 7.30816 9.16414i 0.543211 0.681165i −0.432145 0.901804i 0.642243π-0.642243\pi
0.975355 + 0.220639i 0.0708144π0.0708144\pi
182182 −25.1474 + 5.59163i −1.86405 + 0.414479i
183183 12.2861 + 15.4063i 0.908216 + 1.13887i
184184 −4.59620 + 2.42916i −0.338837 + 0.179080i
185185 18.2185 + 7.15025i 1.33945 + 0.525697i
186186 73.7375 5.52586i 5.40670 0.405176i
187187 1.86094 4.26533i 0.136086 0.311911i
188188 18.1857 + 6.36344i 1.32633 + 0.464101i
189189 7.63795 + 8.06703i 0.555579 + 0.586790i
190190 −5.81813 16.6273i −0.422091 1.20627i
191191 −0.324282 + 4.32724i −0.0234642 + 0.313108i 0.973106 + 0.230357i 0.0739895π0.0739895\pi
−0.996570 + 0.0827505i 0.973630π0.973630\pi
192192 −60.4439 + 18.6445i −4.36216 + 1.34555i
193193 1.36516 + 7.21502i 0.0982660 + 0.519348i 0.996765 + 0.0803726i 0.0256110π0.0256110\pi
−0.898499 + 0.438976i 0.855341π0.855341\pi
194194 36.5392 5.50740i 2.62336 0.395408i
195195 −0.318445 + 20.2945i −0.0228043 + 1.45332i
196196 28.4956 23.6803i 2.03540 1.69145i
197197 −6.46692 + 6.46692i −0.460749 + 0.460749i −0.898901 0.438152i 0.855633π-0.855633\pi
0.438152 + 0.898901i 0.355633π0.355633\pi
198198 −21.4979 + 3.24029i −1.52779 + 0.230277i
199199 −1.03556 0.706033i −0.0734089 0.0500494i 0.526059 0.850448i 0.323669π-0.323669\pi
−0.599468 + 0.800398i 0.704621π0.704621\pi
200200 −3.28944 + 6.22392i −0.232598 + 0.440097i
201201 −7.53220 + 6.48198i −0.531280 + 0.457204i
202202 −6.16418 + 2.15694i −0.433710 + 0.151762i
203203 9.54050 25.0487i 0.669611 1.75807i
204204 −34.2681 + 16.5026i −2.39925 + 1.15542i
205205 14.9609 5.87173i 1.04492 0.410100i
206206 7.19525 + 6.19202i 0.501317 + 0.431418i
207207 2.46522 + 0.967528i 0.171345 + 0.0672478i
208208 −43.1591 + 21.9510i −2.99255 + 1.52203i
209209 4.41790 3.52316i 0.305593 0.243702i
210210 −17.8161 36.0606i −1.22943 2.48842i
211211 −11.5115 + 14.4350i −0.792485 + 0.993745i 0.207395 + 0.978257i 0.433502π0.433502\pi
−0.999880 + 0.0154877i 0.995070π0.995070\pi
212212 24.6221 + 36.1140i 1.69105 + 2.48032i
213213 12.0736 + 0.451762i 0.827269 + 0.0309542i
214214 21.8121 + 5.84454i 1.49104 + 0.399524i
215215 5.51579 + 20.5852i 0.376174 + 1.40390i
216216 31.6166 + 19.8660i 2.15124 + 1.35171i
217217 −19.8356 + 17.4212i −1.34653 + 1.18263i
218218 8.75651 + 1.99862i 0.593066 + 0.135363i
219219 0.0708408 + 1.89326i 0.00478698 + 0.127935i
220220 19.0804 + 2.87591i 1.28640 + 0.193894i
221221 −7.68383 + 5.48682i −0.516870 + 0.369083i
222222 48.0882 51.8267i 3.22747 3.47838i
223223 23.2279 14.5951i 1.55546 0.977357i 0.567368 0.823464i 0.307962π-0.307962\pi
0.988087 0.153893i 0.0491812π-0.0491812\pi
224224 28.6378 39.6333i 1.91345 2.64811i
225225 3.49625 0.797995i 0.233083 0.0531997i
226226 −9.14435 34.1272i −0.608273 2.27011i
227227 3.68083 13.7370i 0.244305 0.911759i −0.729426 0.684060i 0.760213π-0.760213\pi
0.973731 0.227700i 0.0731205π-0.0731205\pi
228228 −46.1519 1.72688i −3.05648 0.114365i
229229 5.18168 27.3858i 0.342415 1.80971i −0.211777 0.977318i 0.567925π-0.567925\pi
0.554192 0.832389i 0.313027π-0.313027\pi
230230 −2.53207 2.01925i −0.166959 0.133146i
231231 9.03070 9.21471i 0.594176 0.606284i
232232 10.0872 89.5262i 0.662256 5.87768i
233233 −8.16314 + 26.4643i −0.534785 + 1.73373i 0.134681 + 0.990889i 0.456999π0.456999\pi
−0.669466 + 0.742843i 0.733477π0.733477\pi
234234 40.8028 + 16.7574i 2.66737 + 1.09546i
235235 0.558040 + 7.44653i 0.0364025 + 0.485758i
236236 −3.51456 + 8.05546i −0.228778 + 0.524366i
237237 −1.05085 2.18212i −0.0682602 0.141744i
238238 8.57547 16.6294i 0.555865 1.07792i
239239 14.7301 5.15430i 0.952814 0.333404i 0.191285 0.981535i 0.438735π-0.438735\pi
0.761529 + 0.648130i 0.224449π0.224449\pi
240240 −49.3125 57.3022i −3.18311 3.69884i
241241 0.581376 1.10002i 0.0374497 0.0708584i −0.864680 0.502322i 0.832479π-0.832479\pi
0.902130 + 0.431464i 0.142003π0.142003\pi
242242 −3.93715 20.8083i −0.253090 1.33761i
243243 2.72331 + 18.0680i 0.174700 + 1.15906i
244244 −38.0086 −2.43325
245245 12.8287 + 6.45257i 0.819594 + 0.412239i
246246 58.0582i 3.70166i
247247 −11.3621 + 1.53066i −0.722954 + 0.0973934i
248248 −49.9855 + 73.3153i −3.17408 + 4.65552i
249249 −3.16225 + 5.98326i −0.200399 + 0.379174i
250250 −31.9958 2.39776i −2.02359 0.151647i
251251 11.3341 + 5.45822i 0.715402 + 0.344520i 0.755924 0.654659i 0.227188π-0.227188\pi
−0.0405220 + 0.999179i 0.512902π0.512902\pi
252252 −63.2111 + 5.37859i −3.98192 + 0.338819i
253253 0.343118 0.980575i 0.0215716 0.0616482i
254254 −10.1929 + 23.3624i −0.639561 + 1.46589i
255255 −11.1736 9.61564i −0.699717 0.602155i
256256 8.10600 20.6538i 0.506625 1.29086i
257257 0.422044 + 0.130183i 0.0263264 + 0.00812062i 0.307890 0.951422i 0.400377π-0.400377\pi
−0.281564 + 0.959542i 0.590853π0.590853\pi
258258 76.5012 + 8.61962i 4.76276 + 0.536634i
259259 −2.57305 + 25.1100i −0.159881 + 1.56026i
260260 −30.2217 24.8866i −1.87427 1.54340i
261261 −37.9201 + 25.8535i −2.34720 + 1.60029i
262262 −34.8681 1.30467i −2.15416 0.0806028i
263263 −14.8057 25.6443i −0.912961 1.58130i −0.809859 0.586625i 0.800456π-0.800456\pi
−0.103102 0.994671i 0.532877π-0.532877\pi
264264 21.6830 37.5561i 1.33450 2.31142i
265265 −9.01295 + 14.3440i −0.553661 + 0.881146i
266266 18.6415 12.9869i 1.14298 0.796275i
267267 7.88202 4.95260i 0.482372 0.303094i
268268 −0.716695 19.1541i −0.0437791 1.17002i
269269 2.28196 15.1398i 0.139133 0.923090i −0.804940 0.593356i 0.797803π-0.797803\pi
0.944074 0.329734i 0.106959π-0.106959\pi
270270 −3.46700 + 23.0020i −0.210995 + 1.39986i
271271 −19.9661 + 0.747079i −1.21285 + 0.0453818i −0.636146 0.771568i 0.719473π-0.719473\pi
−0.576708 + 0.816950i 0.695663π0.695663\pi
272272 7.82546 34.2856i 0.474488 2.07887i
273273 −25.3228 + 6.63332i −1.53260 + 0.401467i
274274 −8.15371 35.7237i −0.492583 2.15815i
275275 −0.364102 1.35885i −0.0219562 0.0819416i
276276 −7.35331 + 4.24544i −0.442618 + 0.255545i
277277 16.3914 + 17.6657i 0.984861 + 1.06143i 0.998106 + 0.0615153i 0.0195933π0.0195933\pi
−0.0132452 + 0.999912i 0.504216π0.504216\pi
278278 −41.4717 7.84688i −2.48731 0.470624i
279279 44.9184 5.06109i 2.68919 0.302999i
280280 47.1621 + 10.2652i 2.81847 + 0.613461i
281281 −1.91339 + 16.9818i −0.114143 + 1.01305i 0.797853 + 0.602852i 0.205969π0.205969\pi
−0.911996 + 0.410198i 0.865460π0.865460\pi
282282 25.7768 + 7.95110i 1.53499 + 0.473481i
283283 4.82250 12.2875i 0.286668 0.730418i −0.712907 0.701259i 0.752622π-0.752622\pi
0.999575 0.0291593i 0.00928301π-0.00928301\pi
284284 −15.2011 + 17.6640i −0.902022 + 1.04817i
285285 −6.53959 16.6626i −0.387372 0.987008i
286286 5.97052 16.2408i 0.353044 0.960338i
287287 12.4763 + 16.5528i 0.736454 + 0.977081i
288288 −79.0250 + 27.6520i −4.65659 + 1.62941i
289289 −0.757956 + 10.1142i −0.0445857 + 0.594954i
290290 53.6321 16.5433i 3.14938 0.971456i
291291 36.8934 6.98061i 2.16273 0.409211i
292292 −2.94029 2.17003i −0.172067 0.126991i
293293 21.9466 21.9466i 1.28213 1.28213i 0.342682 0.939452i 0.388665π-0.388665\pi
0.939452 0.342682i 0.111335π-0.111335\pi
294294 38.6287 34.6230i 2.25287 2.01926i
295295 −3.40634 −0.198324
296296 12.6448 + 83.8929i 0.734965 + 4.87618i
297297 −7.33174 + 1.38724i −0.425431 + 0.0804959i
298298 4.49636 + 14.5768i 0.260467 + 0.844414i
299299 −1.61901 + 1.34964i −0.0936296 + 0.0780517i
300300 −4.98873 + 10.3592i −0.288025 + 0.598090i
301301 −23.6633 + 13.9821i −1.36393 + 0.805914i
302302 20.8927 10.0614i 1.20224 0.578967i
303303 −6.17728 + 2.42440i −0.354876 + 0.139278i
304304 27.8542 32.3672i 1.59755 1.85638i
305305 −5.89093 13.5022i −0.337314 0.773131i
306306 −28.3239 + 14.9696i −1.61917 + 0.855757i
307307 24.4832 + 2.75860i 1.39733 + 0.157441i 0.778284 0.627912i 0.216090π-0.216090\pi
0.619047 + 0.785354i 0.287519π0.287519\pi
308308 3.03562 + 24.7003i 0.172970 + 1.40743i
309309 7.54147 + 6.01413i 0.429020 + 0.342132i
310310 −54.3153 10.2770i −3.08490 0.583695i
311311 −12.2403 + 11.3573i −0.694083 + 0.644015i −0.946163 0.323692i 0.895076π-0.895076\pi
0.252080 + 0.967707i 0.418886π0.418886\pi
312312 −76.8785 + 42.7919i −4.35239 + 2.42261i
313313 22.4311 + 12.9506i 1.26788 + 0.732011i 0.974586 0.224012i 0.0719155π-0.0719155\pi
0.293293 + 0.956023i 0.405249π0.405249\pi
314314 −2.49940 + 3.97777i −0.141049 + 0.224478i
315315 −11.7077 21.6214i −0.659656 1.21823i
316316 4.55446 + 1.03953i 0.256209 + 0.0584780i
317317 −0.830970 + 0.0310927i −0.0466719 + 0.00174634i −0.0607170 0.998155i 0.519339π-0.519339\pi
0.0140450 + 0.999901i 0.495529π0.495529\pi
318318 36.3396 + 49.2384i 2.03782 + 2.76115i
319319 10.6910 + 14.4857i 0.598579 + 0.811045i
320320 47.2542 1.76813i 2.64159 0.0988413i
321321 22.3705 + 5.10593i 1.24860 + 0.284985i
322322 1.63161 3.84503i 0.0909262 0.214275i
323323 4.43007 7.05042i 0.246496 0.392296i
324324 −9.48029 5.47345i −0.526683 0.304081i
325325 −0.781893 + 2.74504i −0.0433716 + 0.152268i
326326 −11.1133 + 10.3116i −0.615509 + 0.571108i
327327 8.96748 + 1.69674i 0.495903 + 0.0938299i
328328 54.4705 + 43.4388i 3.00763 + 2.39850i
329329 −9.05779 + 3.27236i −0.499372 + 0.180411i
330330 26.8461 + 3.02483i 1.47783 + 0.166512i
331331 −14.4690 + 7.64710i −0.795290 + 0.420323i −0.814984 0.579483i 0.803254π-0.803254\pi
0.0196946 + 0.999806i 0.493731π0.493731\pi
332332 −5.21997 11.9643i −0.286483 0.656626i
333333 28.1914 32.7590i 1.54488 1.79518i
334334 32.3902 12.7122i 1.77231 0.695582i
335335 6.69321 3.22328i 0.365689 0.176107i
336336 54.1091 81.1090i 2.95189 4.42486i
337337 −12.6672 + 26.3036i −0.690024 + 1.43285i 0.201321 + 0.979525i 0.435476π0.435476\pi
−0.891345 + 0.453325i 0.850238π0.850238\pi
338338 −27.3156 + 22.0538i −1.48577 + 1.19957i
339339 −10.5820 34.3060i −0.574736 1.86325i
340340 27.9382 5.28619i 1.51516 0.286684i
341341 −2.64284 17.5341i −0.143118 0.949524i
342342 −38.9007 −2.10351
343343 −3.57305 + 18.1723i −0.192927 + 0.981213i
344344 −65.3246 + 65.3246i −3.52207 + 3.52207i
345345 −2.64783 1.95419i −0.142555 0.105210i
346346 −1.14789 + 0.217193i −0.0617110 + 0.0116763i
347347 19.2941 5.95145i 1.03576 0.319491i 0.270168 0.962813i 0.412921π-0.412921\pi
0.765595 + 0.643322i 0.222444π0.222444\pi
348348 10.9963 146.736i 0.589464 7.86586i
349349 −23.6428 + 8.27299i −1.26557 + 0.442843i −0.877851 0.478934i 0.841023π-0.841023\pi
−0.387721 + 0.921777i 0.626738π0.626738\pi
350350 −1.10753 5.54662i −0.0592000 0.296479i
351351 14.2096 + 5.22379i 0.758450 + 0.278825i
352352 11.9989 + 30.5728i 0.639545 + 1.62953i
353353 13.6168 15.8230i 0.724748 0.842172i −0.267870 0.963455i 0.586320π-0.586320\pi
0.992618 + 0.121283i 0.0387008π0.0387008\pi
354354 −4.49554 + 11.4545i −0.238935 + 0.608797i
355355 −8.63098 2.66230i −0.458085 0.141300i
356356 −2.01035 + 17.8424i −0.106549 + 0.945645i
357357 8.07589 17.2117i 0.427421 0.910938i
358358 1.43108 0.161244i 0.0756351 0.00852203i
359359 −2.50802 0.474543i −0.132368 0.0250454i 0.119305 0.992858i 0.461933π-0.461933\pi
−0.251673 + 0.967812i 0.580981π0.580981\pi
360360 −56.2117 60.5818i −2.96262 3.19294i
361361 −7.69827 + 4.44460i −0.405172 + 0.233926i
362362 8.19269 + 30.5755i 0.430598 + 1.60701i
363363 −4.78846 20.9796i −0.251329 1.10115i
364364 20.4502 46.1648i 1.07188 2.41969i
365365 0.315167 1.38084i 0.0164966 0.0722763i
366366 −53.1782 + 1.98979i −2.77967 + 0.104008i
367367 3.99739 26.5210i 0.208662 1.38438i −0.601826 0.798627i 0.705560π-0.705560\pi
0.810488 0.585755i 0.199202π-0.199202\pi
368368 1.17009 7.76307i 0.0609954 0.404678i
369369 −1.32706 35.4665i −0.0690842 1.84631i
370370 −44.7524 + 28.1198i −2.32657 + 1.46188i
371371 −20.9417 6.22906i −1.08724 0.323397i
372372 −77.1061 + 122.714i −3.99777 + 6.36241i
373373 11.9499 20.6978i 0.618742 1.07169i −0.370974 0.928643i 0.620976π-0.620976\pi
0.989716 0.143049i 0.0456906π-0.0456906\pi
374374 6.28365 + 10.8836i 0.324920 + 0.562778i
375375 −32.5803 1.21907i −1.68244 0.0629525i
376376 −26.7458 + 18.2350i −1.37931 + 0.940397i
377377 −3.51982 36.3578i −0.181280 1.87252i
378378 −29.7770 + 3.65953i −1.53156 + 0.188226i
379379 20.4854 + 2.30815i 1.05227 + 0.118562i 0.621116 0.783719i 0.286680π-0.286680\pi
0.431150 + 0.902280i 0.358108π0.358108\pi
380380 32.9923 + 10.1768i 1.69247 + 0.522057i
381381 −9.46247 + 24.1100i −0.484777 + 1.23519i
382382 −8.88242 7.64394i −0.454464 0.391098i
383383 1.78507 4.09142i 0.0912128 0.209062i −0.864976 0.501814i 0.832666π-0.832666\pi
0.956188 + 0.292752i 0.0945710π0.0945710\pi
384384 22.9183 65.4968i 1.16955 3.34237i
385385 −8.30403 + 4.90665i −0.423212 + 0.250066i
386386 −17.8664 8.60401i −0.909376 0.437932i
387387 46.9300 + 3.51692i 2.38559 + 0.178775i
388388 −33.8415 + 64.0313i −1.71804 + 3.25070i
389389 12.5628 18.4263i 0.636960 0.934249i −0.363036 0.931775i 0.618260π-0.618260\pi
0.999997 0.00247452i 0.000787664π-0.000787664\pi
390390 −43.5862 33.2369i −2.20707 1.68302i
391391 1.53085i 0.0774184i
392392 3.58173 + 62.1464i 0.180905 + 3.13886i
393393 −35.4553 −1.78848
394394 −3.68107 24.4223i −0.185450 1.23038i
395395 0.336613 + 1.77904i 0.0169368 + 0.0895133i
396396 19.9107 37.6730i 1.00055 1.89314i
397397 −2.16678 2.51784i −0.108747 0.126367i 0.700960 0.713201i 0.252755π-0.252755\pi
−0.809707 + 0.586834i 0.800374π0.800374\pi
398398 3.19477 1.11790i 0.160139 0.0560352i
399399 18.4355 13.8954i 0.922931 0.695640i
400400 −4.61264 9.57824i −0.230632 0.478912i
401401 −3.91114 + 8.96443i −0.195313 + 0.447662i −0.986468 0.163953i 0.947575π-0.947575\pi
0.791155 + 0.611616i 0.209480π0.209480\pi
402402 −2.00547 26.7611i −0.100024 1.33472i
403403 −13.6676 + 33.2795i −0.680833 + 1.65777i
404404 3.77281 12.2311i 0.187704 0.608522i
405405 0.475040 4.21610i 0.0236049 0.209500i
406406 39.1276 + 60.8992i 1.94187 + 3.02238i
407407 −13.2553 10.5707i −0.657039 0.523971i
408408 11.8803 62.7887i 0.588161 3.10850i
409409 7.28752 + 0.272680i 0.360344 + 0.0134831i 0.216951 0.976183i 0.430389π-0.430389\pi
0.143394 + 0.989666i 0.454198π0.454198\pi
410410 −11.2335 + 41.9241i −0.554784 + 2.07048i
411411 −9.63675 35.9648i −0.475346 1.77401i
412412 −18.1390 + 4.14010i −0.893642 + 0.203968i
413413 −1.17978 4.23180i −0.0580530 0.208233i
414414 −6.05562 + 3.80500i −0.297618 + 0.187005i
415415 3.44115 3.70868i 0.168919 0.182052i
416416 10.9641 65.7273i 0.537558 3.22255i
417417 −42.4094 6.39219i −2.07680 0.313027i
418418 0.570590 + 15.2493i 0.0279085 + 0.745869i
419419 16.3520 + 3.73224i 0.798849 + 0.182332i 0.602413 0.798185i 0.294206π-0.294206\pi
0.196436 + 0.980517i 0.437063π0.437063\pi
420420 77.6023 + 13.8740i 3.78660 + 0.676982i
421421 −7.10838 4.46649i −0.346441 0.217683i 0.347559 0.937658i 0.387011π-0.387011\pi
−0.694000 + 0.719975i 0.744153π0.744153\pi
422422 −12.9048 48.1613i −0.628196 2.34446i
423423 15.9283 + 4.26797i 0.774459 + 0.207516i
424424 −73.3847 2.74586i −3.56388 0.133351i
425425 −1.16776 1.71278i −0.0566445 0.0830823i
426426 −20.3433 + 25.5097i −0.985637 + 1.23595i
427427 14.7339 11.9949i 0.713022 0.580476i
428428 −34.6030 + 27.5950i −1.67260 + 1.33385i
429429 5.44553 16.7181i 0.262913 0.807157i
430430 −53.5740 21.0263i −2.58357 1.01398i
431431 18.2730 + 15.7252i 0.880181 + 0.757457i 0.971168 0.238395i 0.0766213π-0.0766213\pi
−0.0909873 + 0.995852i 0.529002π0.529002\pi
432432 −52.4910 + 20.6012i −2.52548 + 0.991176i
433433 −5.68432 + 2.73743i −0.273171 + 0.131552i −0.565455 0.824779i 0.691299π-0.691299\pi
0.292283 + 0.956332i 0.405585π0.405585\pi
434434 −6.04451 71.0371i −0.290146 3.40989i
435435 53.8306 18.8361i 2.58098 0.903124i
436436 −13.3431 + 11.4827i −0.639020 + 0.549921i
437437 0.868584 1.64344i 0.0415500 0.0786165i
438438 −4.22738 2.88218i −0.201992 0.137716i
439439 9.72055 1.46514i 0.463936 0.0699272i 0.0870850 0.996201i 0.472245π-0.472245\pi
0.376851 + 0.926274i 0.377007π0.377007\pi
440440 −22.9240 + 22.9240i −1.09286 + 1.09286i
441441 22.8061 22.0334i 1.08600 1.04921i
442442 0.400043 25.4947i 0.0190281 1.21266i
443443 −11.8530 + 1.78656i −0.563155 + 0.0848820i −0.424449 0.905452i 0.639532π-0.639532\pi
−0.138706 + 0.990334i 0.544294π0.544294\pi
444444 25.7615 + 136.153i 1.22259 + 6.46154i
445445 −6.64990 + 2.05122i −0.315236 + 0.0972373i
446446 −5.53625 + 73.8761i −0.262149 + 3.49813i
447447 5.11954 + 14.6308i 0.242146 + 0.692013i
448448 18.5630 + 58.0930i 0.877018 + 2.74464i
449449 −0.800174 0.279993i −0.0377625 0.0132137i 0.311332 0.950301i 0.399225π-0.399225\pi
−0.349094 + 0.937088i 0.613511π0.613511\pi
450450 −3.87279 + 8.87653i −0.182565 + 0.418444i
451451 −13.8837 + 1.04044i −0.653756 + 0.0489923i
452452 64.4605 + 25.2989i 3.03197 + 1.18996i
453453 20.8326 11.0103i 0.978800 0.517311i
454454 23.9459 + 30.0272i 1.12384 + 1.40924i
455455 19.5691 + 0.109682i 0.917415 + 0.00514199i
456456 48.3795 60.6660i 2.26558 2.84095i
457457 1.13099 5.97740i 0.0529053 0.279611i −0.946117 0.323826i 0.895031π-0.895031\pi
0.999022 + 0.0442145i 0.0140785π0.0140785\pi
458458 51.1959 + 55.1760i 2.39223 + 2.57821i
459459 −9.52239 + 5.49776i −0.444467 + 0.256613i
460460 6.13129 1.64287i 0.285873 0.0765994i
461461 −7.97274 + 12.6885i −0.371328 + 0.590965i −0.979157 0.203103i 0.934897π-0.934897\pi
0.607830 + 0.794067i 0.292040π0.292040\pi
462462 5.54024 + 34.3995i 0.257755 + 1.60041i
463463 17.6606 11.0969i 0.820757 0.515716i −0.0549897 0.998487i 0.517513π-0.517513\pi
0.875746 + 0.482771i 0.160370π0.160370\pi
464464 99.7345 + 92.5401i 4.63006 + 4.29606i
465465 −55.5434 8.37182i −2.57576 0.388234i
466466 −44.4123 60.1765i −2.05736 2.78762i
467467 23.2343 + 21.5583i 1.07515 + 0.997597i 1.00000 0.000425134i 0.000135324π0.000135324\pi
0.0751540 + 0.997172i 0.476055π0.476055\pi
468468 −73.9149 + 44.8419i −3.41672 + 2.07282i
469469 6.32256 + 7.19882i 0.291949 + 0.332411i
470470 −17.0751 10.7290i −0.787616 0.494892i
471471 −2.38681 + 4.13407i −0.109978 + 0.190488i
472472 −7.38308 12.7879i −0.339834 0.588610i
473473 0.690293 18.4485i 0.0317397 0.848262i
474474 6.42661 + 1.21598i 0.295184 + 0.0558518i
475475 −0.281832 2.50133i −0.0129313 0.114769i
476476 16.2435 + 32.8776i 0.744521 + 1.50694i
477477 23.3246 + 29.2481i 1.06796 + 1.33918i
478478 −12.4223 + 40.2721i −0.568183 + 1.84200i
479479 −4.31963 9.90070i −0.197369 0.452374i 0.789530 0.613711i 0.210324π-0.210324\pi
−0.986899 + 0.161337i 0.948419π0.948419\pi
480480 103.747 7.77479i 4.73540 0.354869i
481481 12.0632 + 32.2137i 0.550034 + 1.46882i
482482 1.45786 + 3.02728i 0.0664037 + 0.137889i
483483 1.51068 3.96632i 0.0687385 0.180474i
484484 37.3966 + 18.0092i 1.69984 + 0.818602i
485485 −27.9915 2.09768i −1.27103 0.0952505i
486486 −43.6263 23.0572i −1.97893 1.04589i
487487 −10.8236 + 2.04794i −0.490466 + 0.0928011i −0.425261 0.905071i 0.639818π-0.639818\pi
−0.0652047 + 0.997872i 0.520770π0.520770\pi
488488 37.9207 51.3807i 1.71659 2.32590i
489489 −10.8929 + 10.8929i −0.492594 + 0.492594i
490490 −34.5931 + 17.5273i −1.56276 + 0.791801i
491491 1.82479i 0.0823515i −0.999152 0.0411758i 0.986890π-0.986890\pi
0.999152 0.0411758i 0.0131104π-0.0131104\pi
492492 91.5565 + 67.5718i 4.12769 + 3.04637i
493493 21.9198 + 14.9447i 0.987220 + 0.673075i
494494 14.8948 27.1428i 0.670150 1.22121i
495495 16.4689 + 1.23417i 0.740221 + 0.0554719i
496496 −44.2579 126.482i −1.98724 5.67920i
497497 0.318150 11.6446i 0.0142710 0.522333i
498498 −7.92965 16.4661i −0.355336 0.737863i
499499 −29.0274 12.6645i −1.29945 0.566943i −0.367664 0.929959i 0.619842π-0.619842\pi
−0.931783 + 0.363016i 0.881747π0.881747\pi
500500 41.0199 47.6660i 1.83447 2.13169i
501501 32.4067 14.1389i 1.44782 0.631679i
502502 −30.0357 + 15.8743i −1.34056 + 0.708507i
503503 −28.9898 + 23.1186i −1.29259 + 1.03081i −0.295443 + 0.955361i 0.595467π0.595467\pi
−0.997150 + 0.0754475i 0.975961π0.975961\pi
504504 55.7940 90.8160i 2.48526 4.04527i
505505 4.92973 0.555447i 0.219370 0.0247171i
506506 1.58041 + 2.31803i 0.0702577 + 0.103049i
507507 −26.8989 + 23.4317i −1.19462 + 1.04064i
508508 −24.9789 43.2646i −1.10826 1.91956i
509509 11.3183 3.03273i 0.501675 0.134423i 0.000897769 1.00000i 0.499714π-0.499714\pi
0.500777 + 0.865576i 0.333048π0.333048\pi
510510 38.8118 8.85854i 1.71862 0.392263i
511511 1.82462 0.0867072i 0.0807163 0.00383570i
512512 4.97135 + 7.91185i 0.219705 + 0.349658i
513513 −13.3421 + 0.499226i −0.589068 + 0.0220414i
514514 −0.959676 + 0.708273i −0.0423295 + 0.0312406i
515515 −4.28207 5.80200i −0.188691 0.255667i
516516 −102.630 + 110.609i −4.51803 + 4.86927i
517517 1.43944 6.30659i 0.0633065 0.277364i
518518 −50.4341 45.8582i −2.21595 2.01489i
519519 −1.15734 + 0.264155i −0.0508016 + 0.0115951i
520520 63.7939 16.0251i 2.79755 0.702749i
521521 30.6630 17.7033i 1.34337 0.775595i 0.356069 0.934460i 0.384117π-0.384117\pi
0.987300 + 0.158865i 0.0507834π0.0507834\pi
522522 4.63431 123.855i 0.202838 5.42097i
523523 16.0253 + 23.5049i 0.700739 + 1.02780i 0.997347 + 0.0727965i 0.0231923π0.0231923\pi
−0.296607 + 0.955000i 0.595855π0.595855\pi
524524 42.6390 53.4677i 1.86269 2.33575i
525525 −1.33535 5.59007i −0.0582794 0.243971i
526526 79.4644 + 8.95349i 3.46481 + 0.390391i
527527 −12.2095 23.1015i −0.531854 1.00632i
528528 26.1887 + 60.0251i 1.13972 + 2.61226i
529529 1.69325 + 22.5949i 0.0736197 + 0.982387i
530530 −16.7140 42.5865i −0.726008 1.84984i
531531 −2.48441 + 7.10004i −0.107814 + 0.308115i
532532 −1.21614 + 44.5121i −0.0527264 + 1.92984i
533533 25.2548 + 12.6540i 1.09391 + 0.548104i
534534 −1.87864 + 25.0687i −0.0812966 + 1.08483i
535535 −15.1659 8.01542i −0.655679 0.346537i
536536 26.6079 + 18.1409i 1.14929 + 0.783570i
537537 1.44703 0.218104i 0.0624438 0.00941189i
538538 29.2372 + 29.2372i 1.26050 + 1.26050i
539539 −8.97178 8.61696i −0.386442 0.371159i
540540 −32.2386 32.2386i −1.38733 1.38733i
541541 15.0760 + 11.1266i 0.648168 + 0.478370i 0.867603 0.497257i 0.165660π-0.165660\pi
−0.219435 + 0.975627i 0.570421π0.570421\pi
542542 30.3951 44.5815i 1.30558 1.91494i
543543 9.48073 + 30.7358i 0.406857 + 1.31900i
544544 31.5684 + 36.6832i 1.35349 + 1.57278i
545545 −6.14715 2.96031i −0.263315 0.126806i
546546 26.1953 65.6601i 1.12106 2.80999i
547547 4.60885 2.21951i 0.197060 0.0948992i −0.332751 0.943015i 0.607977π-0.607977\pi
0.529811 + 0.848115i 0.322263π0.322263\pi
548548 65.8253 + 28.7193i 2.81192 + 1.22683i
549549 −32.4399 + 2.43104i −1.38450 + 0.103754i
550550 3.53647 + 1.38796i 0.150795 + 0.0591829i
551551 15.0526 + 28.4809i 0.641262 + 1.21333i
552552 1.59725 14.1760i 0.0679834 0.603369i
553553 −2.09358 + 1.03435i −0.0890279 + 0.0439851i
554554 −64.6708 + 7.28664i −2.74760 + 0.309580i
555555 −44.3742 + 30.2538i −1.88358 + 1.28420i
556556 60.6417 56.2673i 2.57178 2.38627i
557557 −2.61227 + 9.74913i −0.110686 + 0.413084i −0.998928 0.0462909i 0.985260π-0.985260\pi
0.888242 + 0.459375i 0.151927π0.151927\pi
558558 −61.0359 + 105.717i −2.58386 + 4.47537i
559559 −20.4231 + 31.3987i −0.863807 + 1.32802i
560560 −54.7659 + 48.0997i −2.31428 + 2.03258i
561561 6.79407 + 10.8127i 0.286846 + 0.456512i
562562 −33.8306 31.3902i −1.42706 1.32412i
563563 −19.3841 2.92168i −0.816942 0.123134i −0.272739 0.962088i 0.587930π-0.587930\pi
−0.544203 + 0.838954i 0.683168π0.683168\pi
564564 −42.5394 + 31.3955i −1.79123 + 1.32199i
565565 1.00353 + 26.8200i 0.0422189 + 1.12833i
566566 18.9655 + 30.1834i 0.797178 + 1.26870i
567567 5.40233 0.870078i 0.226877 0.0365398i
568568 −8.71259 38.1724i −0.365572 1.60168i
569569 24.1531 + 13.9448i 1.01255 + 0.584597i 0.911938 0.410329i 0.134586π-0.134586\pi
0.100614 + 0.994926i 0.467919π0.467919\pi
570570 46.6926 + 12.5112i 1.95574 + 0.524038i
571571 −4.54638 4.89983i −0.190260 0.205051i 0.630717 0.776013i 0.282761π-0.282761\pi
−0.820977 + 0.570962i 0.806570π0.806570\pi
572572 18.6625 + 28.3174i 0.780318 + 1.18401i
573573 −9.30983 7.42434i −0.388924 0.310156i
574574 −55.9743 + 0.564527i −2.33632 + 0.0235629i
575575 −0.288535 0.361812i −0.0120328 0.0150886i
576576 30.7794 99.7844i 1.28248 4.15769i
577577 30.1298 13.1455i 1.25432 0.547254i 0.335541 0.942026i 0.391081π-0.391081\pi
0.918780 + 0.394771i 0.129176π0.129176\pi
578578 −20.7612 17.8665i −0.863554 0.743148i
579579 −18.4688 8.05787i −0.767538 0.334873i
580580 −36.3319 + 103.831i −1.50860 + 4.31133i
581581 5.79925 + 2.99056i 0.240593 + 0.124070i
582582 −43.9959 + 91.3584i −1.82369 + 3.78693i
583583 11.1233 9.57239i 0.460681 0.396448i
584584 5.86697 1.80972i 0.242777 0.0748868i
585585 −27.3856 19.3075i −1.13226 0.798265i
586586 12.4923 + 82.8812i 0.516053 + 3.42379i
587587 −3.55145 3.55145i −0.146584 0.146584i 0.630006 0.776590i 0.283052π-0.283052\pi
−0.776590 + 0.630006i 0.783052π0.783052\pi
588588 9.64121 + 101.213i 0.397597 + 4.17396i
589589 31.7281i 1.30733i
590590 5.46253 7.40147i 0.224889 0.304714i
591591 −4.66574 24.6590i −0.191923 1.01434i
592592 −113.275 59.8675i −4.65557 2.46054i
593593 11.2669 + 13.0924i 0.462678 + 0.537641i 0.940039 0.341066i 0.110788π-0.110788\pi
−0.477362 + 0.878707i 0.658407π0.658407\pi
594594 8.74320 18.1554i 0.358738 0.744927i
595595 −9.16186 + 10.8660i −0.375600 + 0.445464i
596596 −28.2205 9.87477i −1.15596 0.404486i
597597 3.20157 1.25652i 0.131031 0.0514260i
598598 −0.336266 5.68220i −0.0137509 0.232363i
599599 12.0439 30.6873i 0.492100 1.25385i −0.442057 0.896987i 0.645751π-0.645751\pi
0.934157 0.356863i 0.116154π-0.116154\pi
600600 −9.02658 17.0791i −0.368508 0.697252i
601601 7.59102 6.05364i 0.309644 0.246933i −0.456321 0.889815i 0.650833π-0.650833\pi
0.765965 + 0.642882i 0.222262π0.222262\pi
602602 7.56638 73.8392i 0.308383 3.00946i
603603 −1.83679 16.3020i −0.0747999 0.663868i
604604 −8.44962 + 44.6573i −0.343810 + 1.81708i
605605 −0.601521 + 16.0760i −0.0244553 + 0.653581i
606606 4.63826 17.3102i 0.188416 0.703179i
607607 −6.61851 3.82120i −0.268637 0.155098i 0.359631 0.933095i 0.382903π-0.382903\pi
−0.628268 + 0.777997i 0.716236π0.716236\pi
608608 13.0767 + 57.2927i 0.530330 + 2.32353i
609609 42.0449 + 60.3517i 1.70374 + 2.44557i
610610 38.7851 + 8.85246i 1.57036 + 0.358425i
611611 −9.07680 + 9.47973i −0.367208 + 0.383509i
612612 9.35837 62.0887i 0.378290 2.50979i
613613 24.1849 17.8492i 0.976818 0.720924i 0.0165091 0.999864i 0.494745π-0.494745\pi
0.960309 + 0.278939i 0.0899829π0.0899829\pi
614614 −45.2563 + 48.7747i −1.82640 + 1.96839i
615615 −9.81387 + 42.9974i −0.395734 + 1.73382i
616616 −36.4189 20.5396i −1.46736 0.827562i
617617 25.5737 + 16.0690i 1.02956 + 0.646914i 0.937193 0.348811i 0.113415π-0.113415\pi
0.0923645 + 0.995725i 0.470557π0.470557\pi
618618 −25.1616 + 6.74204i −1.01215 + 0.271205i
619619 8.62258 + 2.31041i 0.346571 + 0.0928633i 0.427905 0.903824i 0.359252π-0.359252\pi
−0.0813348 + 0.996687i 0.525918π0.525918\pi
620620 79.4221 73.6930i 3.18967 2.95958i
621621 −2.02812 + 1.38275i −0.0813856 + 0.0554878i
622622 −5.04881 44.8094i −0.202439 1.79669i
623623 −4.85148 7.55096i −0.194370 0.302523i
624624 16.9466 131.787i 0.678408 5.27568i
625625 19.5082 + 6.01750i 0.780330 + 0.240700i
626626 −64.1111 + 27.9714i −2.56240 + 1.11796i
627627 1.15878 + 15.4628i 0.0462771 + 0.617525i
628628 −3.36390 8.57107i −0.134234 0.342023i
629629 −23.5811 8.25138i −0.940240 0.329004i
630630 65.7552 + 9.23380i 2.61975 + 0.367883i
631631 −1.28540 3.67347i −0.0511711 0.146239i 0.915461 0.402406i 0.131826π-0.131826\pi
−0.966632 + 0.256167i 0.917540π0.917540\pi
632632 −5.94918 + 5.11969i −0.236646 + 0.203650i
633633 −14.9337 48.4137i −0.593560 1.92427i
634634 1.26502 1.85544i 0.0502402 0.0736889i
635635 11.4978 15.5790i 0.456278 0.618235i
636636 −119.942 −4.75601
637637 6.64146 + 24.3494i 0.263144 + 0.964757i
638638 −48.6198 −1.92488
639639 −11.8442 + 16.0483i −0.468550 + 0.634862i
640640 −29.2222 + 42.8611i −1.15511 + 1.69423i
641641 −8.35667 27.0917i −0.330069 1.07006i −0.956782 0.290806i 0.906076π-0.906076\pi
0.626713 0.779250i 0.284400π-0.284400\pi
642642 −46.9687 + 40.4198i −1.85371 + 1.59524i
643643 −9.49932 27.1475i −0.374617 1.07059i −0.964723 0.263267i 0.915200π-0.915200\pi
0.590106 0.807326i 0.299086π-0.299086\pi
644644 4.16456 + 7.04810i 0.164106 + 0.277734i
645645 −55.1991 19.3150i −2.17346 0.760527i
646646 8.21530 + 20.9322i 0.323227 + 0.823568i
647647 0.0926362 + 1.23614i 0.00364190 + 0.0485978i 0.998729 0.0504090i 0.0160525π-0.0160525\pi
−0.995087 + 0.0990068i 0.968433π0.968433\pi
648648 16.8575 7.35484i 0.662224 0.288925i
649649 2.81971 + 0.869764i 0.110683 + 0.0341412i
650650 −4.71071 6.10100i −0.184769 0.239301i
651651 −8.83673 71.9029i −0.346339 2.81810i
652652 −3.32686 29.5267i −0.130290 1.15636i
653653 −5.53030 + 3.77050i −0.216417 + 0.147551i −0.666677 0.745347i 0.732284π-0.732284\pi
0.450259 + 0.892898i 0.351331π0.351331\pi
654654 −18.0674 + 16.7641i −0.706490 + 0.655527i
655655 25.6024 + 6.86015i 1.00037 + 0.268048i
656656 −101.628 + 27.2311i −3.96790 + 1.06320i
657657 −2.64830 1.66404i −0.103320 0.0649202i
658658 7.41507 24.9289i 0.289070 0.971831i
659659 9.21020 40.3525i 0.358779 1.57191i −0.397462 0.917618i 0.630109π-0.630109\pi
0.756241 0.654293i 0.227034π-0.227034\pi
660660 −36.0153 + 38.8152i −1.40189 + 1.51088i
661661 −16.1881 + 11.9473i −0.629643 + 0.464697i −0.861298 0.508101i 0.830348π-0.830348\pi
0.231655 + 0.972798i 0.425586π0.425586\pi
662662 6.58706 43.7023i 0.256013 1.69854i
663663 −0.562444 25.9031i −0.0218435 1.00599i
664664 21.3815 + 4.88018i 0.829762 + 0.189388i
665665 −16.0009 + 6.46688i −0.620490 + 0.250775i
666666 25.9717 + 113.789i 1.00638 + 4.40925i
667667 5.12902 + 2.96124i 0.198597 + 0.114660i
668668 −17.6509 + 65.8739i −0.682932 + 2.54874i
669669 −2.81475 + 75.2257i −0.108824 + 2.90839i
670670 −3.72978 + 19.7123i −0.144094 + 0.761554i
671671 1.42881 + 12.6810i 0.0551585 + 0.489545i
672672 45.5915 + 126.196i 1.75873 + 4.86812i
673673 −0.562031 + 0.448204i −0.0216647 + 0.0172770i −0.634262 0.773118i 0.718696π-0.718696\pi
0.612598 + 0.790395i 0.290125π0.290125\pi
674674 −36.8404 69.7054i −1.41904 2.68495i
675675 −1.21437 + 3.09416i −0.0467411 + 0.119094i
676676 −2.98672 68.7436i −0.114874 2.64398i
677677 −5.82194 + 2.28494i −0.223755 + 0.0878175i −0.474571 0.880217i 0.657397π-0.657397\pi
0.250815 + 0.968035i 0.419301π0.419301\pi
678678 91.5117 + 32.0213i 3.51449 + 1.22977i
679679 −7.08879 35.5013i −0.272043 1.36242i
680680 −20.7276 + 43.0413i −0.794867 + 1.65056i
681681 25.4560 + 29.5804i 0.975476 + 1.13352i
682682 42.3372 + 22.3758i 1.62117 + 0.856816i
683683 0.984594 + 5.20370i 0.0376744 + 0.199114i 0.996347 0.0853977i 0.0272161π-0.0272161\pi
−0.958673 + 0.284512i 0.908168π0.908168\pi
684684 45.2750 61.3455i 1.73113 2.34560i
685685 27.8349i 1.06352i
686686 −33.7559 36.9056i −1.28881 1.40906i
687687 54.0818 + 54.0818i 2.06335 + 2.06335i
688688 −20.7933 137.954i −0.792736 5.25946i
689689 −29.3386 + 5.07573i −1.11771 + 0.193370i
690690 8.49234 2.61954i 0.323298 0.0997242i
691691 29.5234 25.4070i 1.12312 0.966526i 0.123457 0.992350i 0.460602π-0.460602\pi
0.999667 + 0.0258238i 0.00822088π0.00822088\pi
692692 0.993479 2.06298i 0.0377664 0.0784227i
693693 4.17070 + 20.8873i 0.158432 + 0.793442i
694694 −18.0092 + 51.4673i −0.683620 + 1.95367i
695695 29.3872 + 12.8215i 1.11472 + 0.486347i
696696 187.389 + 161.261i 7.10296 + 6.11259i
697697 −18.8041 + 8.20414i −0.712256 + 0.310754i
698698 19.9386 64.6394i 0.754687 2.44664i
699699 −47.3835 59.4170i −1.79221 2.24736i
700700 10.0359 + 4.70895i 0.379321 + 0.177981i
701701 −13.3954 10.6825i −0.505939 0.403473i 0.336981 0.941511i 0.390594π-0.390594\pi
−0.842920 + 0.538039i 0.819165π0.819165\pi
702702 −34.1375 + 22.4982i −1.28844 + 0.849141i
703703 −20.6337 22.2379i −0.778216 0.838717i
704704 −39.5677 10.6021i −1.49126 0.399583i
705705 −17.7461 10.2457i −0.668356 0.385875i
706706 12.5446 + 54.9616i 0.472124 + 2.06851i
707707 2.39745 + 5.93199i 0.0901654 + 0.223095i
708708 −12.8312 20.4208i −0.482227 0.767459i
709709 −1.31998 35.2771i −0.0495727 1.32486i −0.772977 0.634434i 0.781233π-0.781233\pi
0.723404 0.690425i 0.242576π-0.242576\pi
710710 19.6258 14.4845i 0.736542 0.543593i
711711 3.95368 + 0.595921i 0.148274 + 0.0223488i
712712 −22.1140 20.5188i −0.828756 0.768973i
713713 −3.10343 4.93907i −0.116224 0.184970i
714714 24.4476 + 45.1490i 0.914929 + 1.68966i
715715 −7.16697 + 11.0186i −0.268030 + 0.412070i
716716 −1.41131 + 2.44445i −0.0527429 + 0.0913535i
717717 −11.0838 + 41.3651i −0.413930 + 1.54481i
718718 5.05307 4.68856i 0.188579 0.174976i
719719 −10.4472 + 7.12281i −0.389617 + 0.265636i −0.742247 0.670127i 0.766240π-0.766240\pi
0.352630 + 0.935763i 0.385287π0.385287\pi
720720 124.019 13.9736i 4.62193 0.520766i
721721 5.72493 7.32927i 0.213208 0.272956i
722722 2.68778 23.8547i 0.100029 0.887782i
723723 1.59536 + 3.01857i 0.0593321 + 0.112262i
724724 −57.7521 22.6660i −2.14634 0.842376i
725725 7.99747 0.599327i 0.297019 0.0222585i
726726 53.2647 + 23.2391i 1.97684 + 0.862485i
727727 11.9059 5.73356i 0.441564 0.212646i −0.199873 0.979822i 0.564053π-0.564053\pi
0.641437 + 0.767176i 0.278339π0.278339\pi
728728 42.0034 + 73.7030i 1.55675 + 2.73162i
729729 −39.5850 19.0631i −1.46611 0.706041i
730730 2.49494 + 2.89918i 0.0923420 + 0.107303i
731731 −8.01855 25.9955i −0.296577 0.961479i
732732 58.7542 86.1766i 2.17162 3.18518i
733733 −5.91943 4.36874i −0.218639 0.161363i 0.478994 0.877818i 0.341002π-0.341002\pi
−0.697633 + 0.716455i 0.745763π0.745763\pi
734734 51.2158 + 51.2158i 1.89041 + 1.89041i
735735 −34.4606 + 19.1119i −1.27110 + 0.704953i
736736 7.63961 + 7.63961i 0.281600 + 0.281600i
737737 −6.36354 + 0.959150i −0.234404 + 0.0353307i
738738 79.1918 + 53.9920i 2.91509 + 1.98747i
739739 29.9625 + 15.8356i 1.10219 + 0.582523i 0.916479 0.400082i 0.131018π-0.131018\pi
0.185708 + 0.982605i 0.440542π0.440542\pi
740740 7.74135 103.301i 0.284578 3.79743i
741741 14.0933 28.1273i 0.517729 1.03328i
742742 47.1177 35.5140i 1.72975 1.30376i
743743 −0.919691 + 2.62832i −0.0337402 + 0.0964239i −0.959521 0.281636i 0.909123π-0.909123\pi
0.925781 + 0.378060i 0.123409π0.123409\pi
744744 −88.9588 226.663i −3.26139 8.30988i
745745 −0.865966 11.5555i −0.0317265 0.423361i
746746 25.8100 + 59.1572i 0.944972 + 2.16590i
747747 −5.22043 9.87753i −0.191006 0.361400i
748748 −24.4765 2.75784i −0.894949 0.100837i
749749 4.70514 21.6172i 0.171922 0.789876i
750750 54.8960 68.8374i 2.00452 2.51359i
751751 −23.2201 34.0577i −0.847314 1.24278i −0.968216 0.250117i 0.919531π-0.919531\pi
0.120901 0.992665i 0.461422π-0.461422\pi
752752 1.82785 48.8503i 0.0666548 1.78139i
753753 −29.8958 + 17.2603i −1.08946 + 0.629001i
754754 84.6447 + 50.6568i 3.08258 + 1.84481i
755755 −17.1736 + 3.91977i −0.625013 + 0.142655i
756756 28.8853 51.2168i 1.05055 1.86274i
757757 2.11007 9.24484i 0.0766920 0.336009i −0.921997 0.387197i 0.873443π-0.873443\pi
0.998689 + 0.0511873i 0.0163006π0.0163006\pi
758758 −37.8665 + 40.8104i −1.37537 + 1.48230i
759759 1.69285 + 2.29373i 0.0614467 + 0.0832573i
760760 −46.6731 + 34.4463i −1.69301 + 1.24950i
761761 −24.0144 + 0.898556i −0.870522 + 0.0325726i −0.468919 0.883241i 0.655356π-0.655356\pi
−0.401603 + 0.915814i 0.631547π0.631547\pi
762762 −37.2131 59.2243i −1.34809 2.14547i
763763 1.54864 8.66211i 0.0560646 0.313589i
764764 22.3922 5.11088i 0.810123 0.184905i
765765 23.5068 6.29863i 0.849891 0.227728i
766766 6.02746 + 10.4399i 0.217781 + 0.377208i
767767 −4.00277 4.45205i −0.144531 0.160754i
768768 34.2977 + 50.3055i 1.23761 + 1.81524i
769769 −10.9916 + 1.23845i −0.396366 + 0.0446597i −0.307898 0.951419i 0.599626π-0.599626\pi
−0.0884676 + 0.996079i 0.528197π0.528197\pi
770770 2.65522 25.9119i 0.0956876 0.933802i
771771 −0.947565 + 0.755658i −0.0341257 + 0.0272144i
772772 34.3623 18.1610i 1.23673 0.653630i
773773 13.2944 5.80030i 0.478168 0.208622i −0.146964 0.989142i 0.546950π-0.546950\pi
0.625132 + 0.780519i 0.285045π0.285045\pi
774774 −82.9006 + 96.3322i −2.97980 + 3.46259i
775775 −7.23986 3.15872i −0.260063 0.113464i
776776 −52.7954 109.631i −1.89525 3.93552i
777777 −52.9542 44.6492i −1.89972 1.60178i
778778 19.8914 + 56.8463i 0.713141 + 2.03804i
779779 −24.8420 1.86165i −0.890058 0.0667006i
780780 103.142 30.0513i 3.69308 1.07601i
781781 6.46479 + 4.40762i 0.231328 + 0.157717i
782782 3.32631 + 2.45493i 0.118949 + 0.0877882i
783783 42.5390i 1.52022i
784784 −78.7239 51.3783i −2.81157 1.83494i
785785 2.52341 2.52341i 0.0900645 0.0900645i
786786 56.8576 77.0393i 2.02804 2.74790i
787787 13.8736 2.62503i 0.494541 0.0935721i 0.0673420 0.997730i 0.478548π-0.478548\pi
0.427199 + 0.904158i 0.359501π0.359501\pi
788788 42.7976 + 22.6192i 1.52460 + 0.805776i
789789 81.0300 + 6.07236i 2.88474 + 0.216182i
790790 −4.40540 2.12153i −0.156737 0.0754807i
791791 −32.9718 + 10.5358i −1.17234 + 0.374608i
792792 31.0623 + 64.5015i 1.10375 + 2.29196i
793793 10.7248 23.5657i 0.380849 0.836843i
794794 8.94563 0.670382i 0.317469 0.0237910i
795795 −18.5897 42.6082i −0.659310 1.51116i
796796 −1.95537 + 6.33916i −0.0693063 + 0.224686i
797797 23.2140 + 29.1094i 0.822282 + 1.03111i 0.998903 + 0.0468301i 0.0149119π0.0149119\pi
−0.176621 + 0.984279i 0.556517π0.556517\pi
798798 0.628737 + 62.3409i 0.0222570 + 2.20685i
799799 −1.06727 9.47225i −0.0377572 0.335104i
800800 14.3752 + 2.71993i 0.508239 + 0.0961640i
801801 −0.574613 + 15.3569i −0.0203030 + 0.542608i
802802 −13.2063 22.8741i −0.466332 0.807711i
803803 −0.613469 + 1.06256i −0.0216488 + 0.0374969i
804804 44.5358 + 27.9837i 1.57066 + 0.986908i
805805 −1.85830 + 2.57179i −0.0654965 + 0.0906439i
806806 −50.3937 83.0661i −1.77504 2.92588i
807807 30.7989 + 28.5772i 1.08417 + 1.00596i
808808 12.7702 + 17.3030i 0.449254 + 0.608718i
809809 32.7543 + 4.93692i 1.15158 + 0.173573i 0.696958 0.717112i 0.254536π-0.254536\pi
0.454622 + 0.890684i 0.349774π0.349774\pi
810810 8.39918 + 7.79330i 0.295117 + 0.273829i
811811 −22.4533 + 14.1084i −0.788443 + 0.495412i −0.865072 0.501648i 0.832727π-0.832727\pi
0.0766286 + 0.997060i 0.475584π0.475584\pi
812812 −141.576 9.17485i −4.96834 0.321974i
813813 29.1700 46.4238i 1.02304 1.62815i
814814 44.2253 11.8501i 1.55010 0.415347i
815815 9.97343 5.75816i 0.349354 0.201700i
816816 65.6387 + 70.7417i 2.29781 + 2.47646i
817817 6.14121 32.4571i 0.214854 1.13553i
818818 −12.2790 + 15.3974i −0.429327 + 0.538359i
819819 14.5014 40.7091i 0.506718 1.42249i
820820 −53.0390 66.5088i −1.85220 2.32259i
821821 −9.77918 + 5.16845i −0.341296 + 0.180380i −0.629130 0.777300i 0.716589π-0.716589\pi
0.287834 + 0.957680i 0.407065π0.407065\pi
822822 93.6002 + 36.7354i 3.26468 + 1.28129i
823823 −23.5452 + 1.76447i −0.820733 + 0.0615054i −0.478476 0.878101i 0.658811π-0.658811\pi
−0.342257 + 0.939606i 0.611191π0.611191\pi
824824 12.5003 28.6511i 0.435470 0.998108i
825825 3.64374 + 1.27500i 0.126859 + 0.0443898i
826826 11.0870 + 4.22280i 0.385767 + 0.146930i
827827 9.92884 + 28.3750i 0.345260 + 0.986695i 0.977318 + 0.211775i 0.0679244π0.0679244\pi
−0.632059 + 0.774920i 0.717790π0.717790\pi
828828 1.04751 13.9781i 0.0364035 0.485771i
829829 −10.3602 + 3.19569i −0.359824 + 0.110991i −0.469396 0.882988i 0.655528π-0.655528\pi
0.109572 + 0.993979i 0.465052π0.465052\pi
830830 2.54005 + 13.4245i 0.0881666 + 0.465971i
831831 −65.3912 + 9.85614i −2.26840 + 0.341906i
832832 57.8391 + 59.6831i 2.00521 + 2.06914i
833833 −16.6724 7.61866i −0.577665 0.263971i
834834 81.8987 81.8987i 2.83592 2.83592i
835835 −26.1367 + 3.93947i −0.904497 + 0.136331i
836836 −24.7119 16.8483i −0.854680 0.582711i
837837 −19.5773 + 37.0421i −0.676691 + 1.28036i
838838 −34.3324 + 29.5454i −1.18599 + 1.02063i
839839 −7.99604 + 2.79794i −0.276054 + 0.0965954i −0.464756 0.885439i 0.653858π-0.653858\pi
0.188702 + 0.982034i 0.439572π0.439572\pi
840840 −96.1779 + 91.0622i −3.31845 + 3.14194i
841841 −66.3445 + 31.9498i −2.28774 + 1.10172i
842842 21.1043 8.28283i 0.727303 0.285445i
843843 −35.5450 30.5889i −1.22423 1.05354i
844844 90.9687 + 35.7026i 3.13127 + 1.22893i
845845 23.9575 11.7155i 0.824164 0.403026i
846846 −34.8169 + 27.7655i −1.19703 + 0.954599i
847847 −20.1801 + 4.82059i −0.693395 + 0.165637i
848848 69.1448 86.7049i 2.37444 2.97746i
849849 20.4047 + 29.9282i 0.700289 + 1.02713i
850850 5.59429 + 0.209324i 0.191883 + 0.00717974i
851851 −5.38718 1.44349i −0.184670 0.0494822i
852852 −16.5514 61.7707i −0.567042 2.11623i
853853 15.6605 + 9.84017i 0.536207 + 0.336921i 0.772761 0.634697i 0.218875π-0.218875\pi
−0.236554 + 0.971618i 0.576018π0.576018\pi
854854 2.43544 + 51.2501i 0.0833391 + 1.75374i
855855 28.8095 + 6.57557i 0.985263 + 0.224880i
856856 −2.78041 74.3081i −0.0950325 2.53980i
857857 −2.73412 0.412102i −0.0933956 0.0140771i 0.102178 0.994766i 0.467419π-0.467419\pi
−0.195574 + 0.980689i 0.562657π0.562657\pi
858858 27.5933 + 38.6421i 0.942020 + 1.31922i
859859 −0.0848854 + 0.0914847i −0.00289625 + 0.00312142i −0.734498 0.678610i 0.762582π-0.762582\pi
0.731602 + 0.681732i 0.238773π0.238773\pi
860860 95.5107 60.0133i 3.25689 2.04644i
861861 −56.8161 + 2.69994i −1.93629 + 0.0920138i
862862 −63.4720 + 14.4871i −2.16186 + 0.493431i
863863 9.67148 + 36.0944i 0.329221 + 1.22867i 0.910000 + 0.414608i 0.136081π0.136081\pi
−0.580779 + 0.814061i 0.697252π0.697252\pi
864864 20.0847 74.9571i 0.683295 2.55009i
865865 0.886830 + 0.0331828i 0.0301531 + 0.00112825i
866866 3.16758 16.7411i 0.107639 0.568884i
867867 −21.7602 17.3532i −0.739016 0.589346i
868868 119.059 + 73.1454i 4.04112 + 2.48272i
869869 0.175613 1.55861i 0.00595727 0.0528722i
870870 −45.3967 + 147.172i −1.53909 + 4.98961i
871871 12.0780 + 4.96031i 0.409246 + 0.168074i
872872 −2.21024 29.4936i −0.0748483 0.998781i
873873 −24.7879 + 56.8146i −0.838945 + 1.92288i
874874 2.17806 + 4.52280i 0.0736741 + 0.152986i
875875 −0.858520 + 31.4228i −0.0290233 + 1.06228i
876876 9.46522 3.31203i 0.319800 0.111903i
877877 −18.2350 21.1895i −0.615753 0.715518i 0.360352 0.932816i 0.382657π-0.382657\pi
−0.976105 + 0.217298i 0.930276π0.930276\pi
878878 −12.4047 + 23.4709i −0.418639 + 0.792104i
879879 15.8340 + 83.6846i 0.534067 + 2.82261i
880880 −7.29686 48.4115i −0.245977 1.63195i
881881 21.0350 0.708687 0.354344 0.935115i 0.384704π-0.384704\pi
0.354344 + 0.935115i 0.384704π0.384704\pi
882882 11.3027 + 84.8880i 0.380582 + 2.85833i
883883 27.0503i 0.910316i 0.890411 + 0.455158i 0.150417π0.150417\pi
−0.890411 + 0.455158i 0.849583π0.849583\pi
884884 39.7390 + 30.3032i 1.33657 + 1.01921i
885885 5.26556 7.72315i 0.177000 0.259611i
886886 15.1261 28.6199i 0.508170 0.961505i
887887 −13.2728 0.994657i −0.445656 0.0333973i −0.149988 0.988688i 0.547923π-0.547923\pi
−0.295669 + 0.955291i 0.595542π0.595542\pi
888888 −209.756 101.013i −7.03896 3.38978i
889889 23.3366 + 8.88840i 0.782684 + 0.298107i
890890 6.20704 17.7387i 0.208060 0.594602i
891891 −1.46976 + 3.36872i −0.0492387 + 0.112856i
892892 −110.057 94.7121i −3.68500 3.17119i
893893 4.22867 10.7745i 0.141507 0.360554i
894894 −40.0005 12.3385i −1.33782 0.412662i
895895 −1.08710 0.122487i −0.0363378 0.00409429i
896896 −63.3688 21.4589i −2.11700 0.716890i
897897 −0.557344 5.75705i −0.0186092 0.192222i
898898 1.89157 1.28965i 0.0631227 0.0430363i
899899 101.018 + 3.77983i 3.36914 + 0.126064i
900900 −9.49069 16.4384i −0.316356 0.547945i
901901 10.8124 18.7276i 0.360213 0.623907i
902902 20.0037 31.8357i 0.666050 1.06001i
903903 4.87759 75.2653i 0.162316 2.50467i
904904 −98.5109 + 61.8985i −3.27643 + 2.05871i
905905 −0.899094 24.0288i −0.0298869 0.798744i
906906 −9.48409 + 62.9228i −0.315088 + 2.09047i
907907 3.27571 21.7329i 0.108768 0.721629i −0.866268 0.499580i 0.833488π-0.833488\pi
0.975036 0.222048i 0.0712743π-0.0712743\pi
908908 −75.2218 + 2.81460i −2.49632 + 0.0934059i
909909 2.43774 10.6805i 0.0808549 0.354248i
910910 −31.6201 + 42.3450i −1.04820 + 1.40372i
911911 −1.02200 4.47769i −0.0338605 0.148353i 0.955172 0.296052i 0.0956702π-0.0956702\pi
−0.989032 + 0.147700i 0.952813π0.952813\pi
912912 30.3284 + 113.187i 1.00427 + 3.74800i
913913 −3.79549 + 2.19133i −0.125612 + 0.0725223i
914914 11.1743 + 12.0431i 0.369614 + 0.398349i
915915 39.7196 + 7.51535i 1.31309 + 0.248450i
916916 −146.596 + 16.5174i −4.84368 + 0.545751i
917917 0.344748 + 34.1827i 0.0113846 + 1.12881i
918918 3.32466 29.5072i 0.109730 0.973883i
919919 44.7507 + 13.8038i 1.47619 + 0.455344i 0.925301 0.379234i 0.123812π-0.123812\pi
0.550889 + 0.834578i 0.314289π0.314289\pi
920920 −3.89624 + 9.92747i −0.128455 + 0.327299i
921921 −44.1010 + 51.2463i −1.45318 + 1.68862i
922922 −14.7850 37.6715i −0.486917 1.24064i
923923 −6.66261 14.4091i −0.219302 0.474281i
924924 −60.6952 31.2994i −1.99673 1.02967i
925925 −7.12854 + 2.49438i −0.234385 + 0.0820149i
926926 −4.20930 + 56.1693i −0.138326 + 1.84584i
927927 −15.2166 + 4.69370i −0.499779 + 0.154161i
928928 −183.970 + 34.8090i −6.03912 + 1.14266i
929929 22.5910 + 16.6729i 0.741187 + 0.547021i 0.897675 0.440659i 0.145255π-0.145255\pi
−0.156487 + 0.987680i 0.550017π0.550017\pi
930930 107.262 107.262i 3.51727 3.51727i
931931 −13.5759 17.6387i −0.444932 0.578085i
932932 146.587 4.80160
933933 −6.82917 45.3086i −0.223577 1.48334i
934934 −84.1023 + 15.9130i −2.75191 + 0.520690i
935935 −2.81390 9.12245i −0.0920245 0.298336i
936936 13.1259 144.658i 0.429033 4.72828i
937937 −19.1278 + 39.7194i −0.624879 + 1.29758i 0.312716 + 0.949847i 0.398761π0.398761\pi
−0.937595 + 0.347729i 0.886953π0.886953\pi
938938 −25.7811 + 2.19370i −0.841783 + 0.0716268i
939939 −64.0370 + 30.8386i −2.08977 + 1.00638i
940940 36.7925 14.4400i 1.20004 0.470980i
941941 15.6455 18.1804i 0.510028 0.592664i −0.442631 0.896704i 0.645955π-0.645955\pi
0.952659 + 0.304040i 0.0983357π0.0983357\pi
942942 −5.15516 11.8158i −0.167964 0.384978i
943943 −4.04922 + 2.14008i −0.131861 + 0.0696905i
944944 22.1590 + 2.49672i 0.721213 + 0.0812612i
945945 22.6711 + 2.32314i 0.737493 + 0.0755716i
946946 38.9789 + 31.0846i 1.26731 + 1.01065i
947947 −22.9970 4.35127i −0.747302 0.141397i −0.201707 0.979446i 0.564649π-0.564649\pi
−0.545595 + 0.838049i 0.683696π0.683696\pi
948948 −9.39726 + 8.71938i −0.305209 + 0.283192i
949949 2.17509 1.21069i 0.0706066 0.0393008i
950950 5.88698 + 3.39885i 0.190999 + 0.110273i
951951 1.21403 1.93211i 0.0393676 0.0626531i
952952 −60.6506 10.8433i −1.96570 0.351434i
953953 −33.2547 7.59017i −1.07723 0.245870i −0.353133 0.935573i 0.614884π-0.614884\pi
−0.724092 + 0.689703i 0.757741π0.757741\pi
954954 −100.956 + 3.77751i −3.26857 + 0.122301i
955955 5.28615 + 7.16247i 0.171056 + 0.231772i
956956 −49.0503 66.4609i −1.58640 2.14950i
957957 −49.3696 + 1.84728i −1.59589 + 0.0597141i
958958 28.4399 + 6.49122i 0.918852 + 0.209722i
959959 −34.5802 + 9.64056i −1.11665 + 0.311310i
960960 −69.0373 + 109.872i −2.22817 + 3.54611i
961961 −59.3781 34.2820i −1.91542 1.10587i
962962 −89.3407 25.4476i −2.88046 0.820464i
963963 −27.7683 + 25.7652i −0.894821 + 0.830272i
964964 −6.47070 1.22432i −0.208407 0.0394327i
965965 11.7773 + 9.39209i 0.379125 + 0.302342i
966966 6.19564 + 9.64304i 0.199341 + 0.310260i
967967 45.8751 + 5.16889i 1.47524 + 0.166220i 0.812647 0.582756i 0.198025π-0.198025\pi
0.662597 + 0.748976i 0.269454π0.269454\pi
968968 −61.6553 + 32.5858i −1.98168 + 1.04735i
969969 9.13729 + 20.9429i 0.293532 + 0.672783i
970970 49.4463 57.4576i 1.58762 1.84485i
971971 −6.86444 + 2.69410i −0.220290 + 0.0864576i −0.472920 0.881106i 0.656800π-0.656800\pi
0.252629 + 0.967563i 0.418705π0.418705\pi
972972 87.1356 41.9623i 2.79488 1.34594i
973973 −5.75039 + 40.9494i −0.184349 + 1.31278i
974974 12.9073 26.8023i 0.413577 0.858802i
975975 −5.01515 6.01610i −0.160613 0.192669i
976976 28.4252 + 92.1523i 0.909870 + 2.94972i
977977 9.54595 1.80619i 0.305402 0.0577852i −0.0309518 0.999521i 0.509854π-0.509854\pi
0.336354 + 0.941736i 0.390806π0.390806\pi
978978 −6.20040 41.1369i −0.198267 1.31541i
979979 6.02843 0.192669
980980 12.6215 74.9518i 0.403178 2.39425i
981981 −10.6538 + 10.6538i −0.340149 + 0.340149i
982982 3.96500 + 2.92630i 0.126528 + 0.0933821i
983983 −5.52033 + 1.04450i −0.176071 + 0.0333145i −0.273199 0.961957i 0.588082π-0.588082\pi
0.0971283 + 0.995272i 0.469034π0.469034\pi
984984 −182.689 + 56.3522i −5.82393 + 1.79644i
985985 −1.40206 + 18.7091i −0.0446732 + 0.596123i
986986 −67.6242 + 23.6627i −2.15359 + 0.753575i
987987 6.58226 25.5951i 0.209516 0.814701i
988988 25.4681 + 55.0793i 0.810248 + 1.75231i
989989 −2.21873 5.65324i −0.0705516 0.179763i
990990 −29.0918 + 33.8053i −0.924598 + 1.07440i
991991 2.83204 7.21592i 0.0899627 0.229221i −0.878810 0.477172i 0.841662π-0.841662\pi
0.968773 + 0.247951i 0.0797571π0.0797571\pi
992992 176.217 + 54.3559i 5.59491 + 1.72580i
993993 5.02820 44.6265i 0.159565 1.41618i
994994 24.7919 + 19.3651i 0.786351 + 0.614223i
995995 −2.55498 + 0.287877i −0.0809984 + 0.00912633i
996996 35.1957 + 6.65938i 1.11522 + 0.211010i
997997 10.3499 + 11.1545i 0.327784 + 0.353267i 0.875345 0.483499i 0.160634π-0.160634\pi
−0.547561 + 0.836766i 0.684444π0.684444\pi
998998 74.0678 42.7630i 2.34457 1.35364i
999999 10.3680 + 38.6941i 0.328030 + 1.22423i
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 637.2.cc.a.5.2 1536
13.8 odd 4 inner 637.2.cc.a.593.2 yes 1536
49.10 odd 42 inner 637.2.cc.a.304.2 yes 1536
637.255 even 84 inner 637.2.cc.a.255.2 yes 1536
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.cc.a.5.2 1536 1.1 even 1 trivial
637.2.cc.a.255.2 yes 1536 637.255 even 84 inner
637.2.cc.a.304.2 yes 1536 49.10 odd 42 inner
637.2.cc.a.593.2 yes 1536 13.8 odd 4 inner