Properties

Label 825.2.cb.a.169.14
Level 825825
Weight 22
Character 825.169
Analytic conductor 6.5886.588
Analytic rank 00
Dimension 240240
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(169,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 825=35211 825 = 3 \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 825.cb (of order 1010, 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: 6.587658166766.58765816676
Analytic rank: 00
Dimension: 240240
Relative dimension: 6060 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 169.14
Character χ\chi == 825.169
Dual form 825.2.cb.a.454.14

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+(1.750580.568798i)q2+(0.951057+0.309017i)q3+(1.12297+0.815886i)q4+(2.124420.697744i)q5+1.84067q6+(0.1614770.0524671i)q7+(0.662061+0.911249i)q8+(0.8090170.587785i)q9+(4.11584+0.0130915i)q10+(2.62986+2.02085i)q11+(1.320130.428937i)q12+(3.85838+5.31060i)q130.312522q14+(1.80483+1.32008i)q15+(1.498554.61206i)q161.03771iq17+(1.75058+0.568798i)q18+(3.38755+2.46120i)q19+(2.95494+0.949737i)q20+(0.137361+0.0997983i)q21+(5.753242.04180i)q22+(5.22698+1.69835i)q23+(0.9112490.662061i)q24+(4.026312.96460i)q25+(3.7337411.4913i)q26+(0.587785+0.809017i)q27+(0.224141+0.0728279i)q28+(0.5958470.432909i)q29+(3.910351.28432i)q30+(0.09086530.279655i)q31+6.67342iq32+(1.876672.73461i)q33+(0.590249+1.81660i)q34+(0.3064360.224132i)q35+1.38807q36+3.82856iq37+(7.330122.38170i)q38+(5.310603.85838i)q39+(2.04231+1.47392i)q40+(9.891087.18629i)q41+(0.2972260.0965746i)q42+1.43140iq43+(4.60204+0.123687i)q44+(1.308571.81319i)q45+10.1163q46+(5.744081.86636i)q47+(2.85041+3.92325i)q48+(5.63980+4.09755i)q49+(8.73464+2.89962i)q50+(0.320671+0.986923i)q51+9.11164iq52+2.20721iq53+(1.489131.08192i)q54+(4.17689+6.12810i)q55+(0.154718+0.112409i)q56+(2.461203.38755i)q57+(0.796842+1.09676i)q5814.3049q59+(3.10380+0.00987244i)q60+(11.1996+8.13701i)q61+0.541242iq62+(0.09979830.137361i)q63+(0.7987372.45826i)q64+(11.9022+8.58978i)q65+(4.84071+3.71972i)q66+(6.82297+9.39102i)q67+(0.8466551.16532i)q68+(4.446343.23045i)q69+(0.663927+0.218060i)q70+(0.682027+2.09906i)q71+(1.07124+0.348066i)q72+(8.57381+11.8008i)q73+(2.177686.70220i)q74+(2.91313+4.06370i)q755.81218q76+(0.318634+0.464302i)q77+(7.10200+9.77506i)q78+11.1282q79+(6.401588.75234i)q80+(0.3090170.951057i)q81+(13.2276+18.2062i)q82+14.1599iq830.235676q84+(0.7240572.20453i)q85+(0.8141812.50579i)q86+(0.700461+0.227593i)q87+(3.582621.05853i)q88+(0.142074+0.437258i)q89+(3.32209+2.42982i)q90+(0.901671+0.655102i)q91+(7.255412.35742i)q92+(0.172836+0.237888i)q9311.1171q94+(5.47929+7.59227i)q95+(2.062206.34680i)q96+4.61724iq97+(12.20363.96519i)q98+(0.939777+3.18069i)q99+O(q100)q+(-1.75058 - 0.568798i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(1.12297 + 0.815886i) q^{4} +(2.12442 - 0.697744i) q^{5} +1.84067 q^{6} +(0.161477 - 0.0524671i) q^{7} +(0.662061 + 0.911249i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-4.11584 + 0.0130915i) q^{10} +(-2.62986 + 2.02085i) q^{11} +(-1.32013 - 0.428937i) q^{12} +(3.85838 + 5.31060i) q^{13} -0.312522 q^{14} +(-1.80483 + 1.32008i) q^{15} +(-1.49855 - 4.61206i) q^{16} -1.03771i q^{17} +(-1.75058 + 0.568798i) q^{18} +(-3.38755 + 2.46120i) q^{19} +(2.95494 + 0.949737i) q^{20} +(-0.137361 + 0.0997983i) q^{21} +(5.75324 - 2.04180i) q^{22} +(-5.22698 + 1.69835i) q^{23} +(-0.911249 - 0.662061i) q^{24} +(4.02631 - 2.96460i) q^{25} +(-3.73374 - 11.4913i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(0.224141 + 0.0728279i) q^{28} +(-0.595847 - 0.432909i) q^{29} +(3.91035 - 1.28432i) q^{30} +(-0.0908653 - 0.279655i) q^{31} +6.67342i q^{32} +(1.87667 - 2.73461i) q^{33} +(-0.590249 + 1.81660i) q^{34} +(0.306436 - 0.224132i) q^{35} +1.38807 q^{36} +3.82856i q^{37} +(7.33012 - 2.38170i) q^{38} +(-5.31060 - 3.85838i) q^{39} +(2.04231 + 1.47392i) q^{40} +(-9.89108 - 7.18629i) q^{41} +(0.297226 - 0.0965746i) q^{42} +1.43140i q^{43} +(-4.60204 + 0.123687i) q^{44} +(1.30857 - 1.81319i) q^{45} +10.1163 q^{46} +(5.74408 - 1.86636i) q^{47} +(2.85041 + 3.92325i) q^{48} +(-5.63980 + 4.09755i) q^{49} +(-8.73464 + 2.89962i) q^{50} +(0.320671 + 0.986923i) q^{51} +9.11164i q^{52} +2.20721i q^{53} +(1.48913 - 1.08192i) q^{54} +(-4.17689 + 6.12810i) q^{55} +(0.154718 + 0.112409i) q^{56} +(2.46120 - 3.38755i) q^{57} +(0.796842 + 1.09676i) q^{58} -14.3049 q^{59} +(-3.10380 + 0.00987244i) q^{60} +(11.1996 + 8.13701i) q^{61} +0.541242i q^{62} +(0.0997983 - 0.137361i) q^{63} +(0.798737 - 2.45826i) q^{64} +(11.9022 + 8.58978i) q^{65} +(-4.84071 + 3.71972i) q^{66} +(-6.82297 + 9.39102i) q^{67} +(0.846655 - 1.16532i) q^{68} +(4.44634 - 3.23045i) q^{69} +(-0.663927 + 0.218060i) q^{70} +(-0.682027 + 2.09906i) q^{71} +(1.07124 + 0.348066i) q^{72} +(8.57381 + 11.8008i) q^{73} +(2.17768 - 6.70220i) q^{74} +(-2.91313 + 4.06370i) q^{75} -5.81218 q^{76} +(-0.318634 + 0.464302i) q^{77} +(7.10200 + 9.77506i) q^{78} +11.1282 q^{79} +(-6.40158 - 8.75234i) q^{80} +(0.309017 - 0.951057i) q^{81} +(13.2276 + 18.2062i) q^{82} +14.1599i q^{83} -0.235676 q^{84} +(-0.724057 - 2.20453i) q^{85} +(0.814181 - 2.50579i) q^{86} +(0.700461 + 0.227593i) q^{87} +(-3.58262 - 1.05853i) q^{88} +(0.142074 + 0.437258i) q^{89} +(-3.32209 + 2.42982i) q^{90} +(0.901671 + 0.655102i) q^{91} +(-7.25541 - 2.35742i) q^{92} +(0.172836 + 0.237888i) q^{93} -11.1171 q^{94} +(-5.47929 + 7.59227i) q^{95} +(-2.06220 - 6.34680i) q^{96} +4.61724i q^{97} +(12.2036 - 3.96519i) q^{98} +(-0.939777 + 3.18069i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 240q+60q4+6q516q6+10q7+60q9+8q10+4q1120q1264q1624q1944q20+8q2140q22+40q2312q24+4q25+40q26+30q28+4q99+O(q100) 240 q + 60 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{7} + 60 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 64 q^{16} - 24 q^{19} - 44 q^{20} + 8 q^{21} - 40 q^{22} + 40 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{26} + 30 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/825Z)×\left(\mathbb{Z}/825\mathbb{Z}\right)^\times.

nn 376376 551551 727727
χ(n)\chi(n) e(15)e\left(\frac{1}{5}\right) 11 e(910)e\left(\frac{9}{10}\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 −1.75058 0.568798i −1.23785 0.402201i −0.384297 0.923210i 0.625556π-0.625556\pi
−0.853552 + 0.521008i 0.825556π0.825556\pi
33 −0.951057 + 0.309017i −0.549093 + 0.178411i
44 1.12297 + 0.815886i 0.561485 + 0.407943i
55 2.12442 0.697744i 0.950069 0.312040i
66 1.84067 0.751451
77 0.161477 0.0524671i 0.0610326 0.0198307i −0.278342 0.960482i 0.589785π-0.589785\pi
0.339374 + 0.940651i 0.389785π0.389785\pi
88 0.662061 + 0.911249i 0.234074 + 0.322175i
99 0.809017 0.587785i 0.269672 0.195928i
1010 −4.11584 + 0.0130915i −1.30154 + 0.00413990i
1111 −2.62986 + 2.02085i −0.792933 + 0.609309i
1212 −1.32013 0.428937i −0.381089 0.123823i
1313 3.85838 + 5.31060i 1.07012 + 1.47290i 0.869954 + 0.493133i 0.164149π0.164149\pi
0.200167 + 0.979762i 0.435851π0.435851\pi
1414 −0.312522 −0.0835250
1515 −1.80483 + 1.32008i −0.466004 + 0.340842i
1616 −1.49855 4.61206i −0.374637 1.15301i
1717 1.03771i 0.251682i −0.992050 0.125841i 0.959837π-0.959837\pi
0.992050 0.125841i 0.0401629π-0.0401629\pi
1818 −1.75058 + 0.568798i −0.412616 + 0.134067i
1919 −3.38755 + 2.46120i −0.777158 + 0.564638i −0.904125 0.427269i 0.859476π-0.859476\pi
0.126967 + 0.991907i 0.459476π0.459476\pi
2020 2.95494 + 0.949737i 0.660744 + 0.212368i
2121 −0.137361 + 0.0997983i −0.0299745 + 0.0217778i
2222 5.75324 2.04180i 1.22660 0.435313i
2323 −5.22698 + 1.69835i −1.08990 + 0.354130i −0.798208 0.602382i 0.794219π-0.794219\pi
−0.291693 + 0.956512i 0.594219π0.594219\pi
2424 −0.911249 0.662061i −0.186008 0.135143i
2525 4.02631 2.96460i 0.805261 0.592920i
2626 −3.73374 11.4913i −0.732247 2.25362i
2727 −0.587785 + 0.809017i −0.113119 + 0.155695i
2828 0.224141 + 0.0728279i 0.0423587 + 0.0137632i
2929 −0.595847 0.432909i −0.110646 0.0803891i 0.531086 0.847318i 0.321784π-0.321784\pi
−0.641732 + 0.766929i 0.721784π0.721784\pi
3030 3.91035 1.28432i 0.713930 0.234483i
3131 −0.0908653 0.279655i −0.0163199 0.0502274i 0.942565 0.334023i 0.108406π-0.108406\pi
−0.958885 + 0.283796i 0.908406π0.908406\pi
3232 6.67342i 1.17971i
3333 1.87667 2.73461i 0.326686 0.476035i
3434 −0.590249 + 1.81660i −0.101227 + 0.311544i
3535 0.306436 0.224132i 0.0517972 0.0378852i
3636 1.38807 0.231345
3737 3.82856i 0.629411i 0.949189 + 0.314705i 0.101906π0.101906\pi
−0.949189 + 0.314705i 0.898094π0.898094\pi
3838 7.33012 2.38170i 1.18910 0.386363i
3939 −5.31060 3.85838i −0.850376 0.617835i
4040 2.04231 + 1.47392i 0.322918 + 0.233048i
4141 −9.89108 7.18629i −1.54473 1.12231i −0.947282 0.320400i 0.896183π-0.896183\pi
−0.597445 0.801910i 0.703817π-0.703817\pi
4242 0.297226 0.0965746i 0.0458630 0.0149018i
4343 1.43140i 0.218287i 0.994026 + 0.109144i 0.0348108π0.0348108\pi
−0.994026 + 0.109144i 0.965189π0.965189\pi
4444 −4.60204 + 0.123687i −0.693783 + 0.0186465i
4545 1.30857 1.81319i 0.195070 0.270294i
4646 10.1163 1.49156
4747 5.74408 1.86636i 0.837860 0.272237i 0.141508 0.989937i 0.454805π-0.454805\pi
0.696353 + 0.717700i 0.254805π0.254805\pi
4848 2.85041 + 3.92325i 0.411421 + 0.566272i
4949 −5.63980 + 4.09755i −0.805685 + 0.585365i
5050 −8.73464 + 2.89962i −1.23526 + 0.410068i
5151 0.320671 + 0.986923i 0.0449029 + 0.138197i
5252 9.11164i 1.26356i
5353 2.20721i 0.303183i 0.988443 + 0.151592i 0.0484398π0.0484398\pi
−0.988443 + 0.151592i 0.951560π0.951560\pi
5454 1.48913 1.08192i 0.202645 0.147231i
5555 −4.17689 + 6.12810i −0.563212 + 0.826313i
5656 0.154718 + 0.112409i 0.0206751 + 0.0150213i
5757 2.46120 3.38755i 0.325994 0.448692i
5858 0.796842 + 1.09676i 0.104630 + 0.144011i
5959 −14.3049 −1.86234 −0.931172 0.364581i 0.881212π-0.881212\pi
−0.931172 + 0.364581i 0.881212π0.881212\pi
6060 −3.10380 + 0.00987244i −0.400699 + 0.00127453i
6161 11.1996 + 8.13701i 1.43397 + 1.04184i 0.989261 + 0.146161i 0.0466916π0.0466916\pi
0.444705 + 0.895677i 0.353308π0.353308\pi
6262 0.541242i 0.0687378i
6363 0.0997983 0.137361i 0.0125734 0.0173058i
6464 0.798737 2.45826i 0.0998421 0.307282i
6565 11.9022 + 8.58978i 1.47629 + 1.06543i
6666 −4.84071 + 3.71972i −0.595850 + 0.457865i
6767 −6.82297 + 9.39102i −0.833559 + 1.14730i 0.153691 + 0.988119i 0.450884π0.450884\pi
−0.987250 + 0.159176i 0.949116π0.949116\pi
6868 0.846655 1.16532i 0.102672 0.141316i
6969 4.44634 3.23045i 0.535276 0.388901i
7070 −0.663927 + 0.218060i −0.0793545 + 0.0260632i
7171 −0.682027 + 2.09906i −0.0809417 + 0.249113i −0.983336 0.181799i 0.941808π-0.941808\pi
0.902394 + 0.430912i 0.141808π0.141808\pi
7272 1.07124 + 0.348066i 0.126247 + 0.0410200i
7373 8.57381 + 11.8008i 1.00349 + 1.38118i 0.923160 + 0.384415i 0.125597π0.125597\pi
0.0803281 + 0.996768i 0.474403π0.474403\pi
7474 2.17768 6.70220i 0.253150 0.779115i
7575 −2.91313 + 4.06370i −0.336380 + 0.469236i
7676 −5.81218 −0.666703
7777 −0.318634 + 0.464302i −0.0363117 + 0.0529121i
7878 7.10200 + 9.77506i 0.804143 + 1.10681i
7979 11.1282 1.25202 0.626008 0.779817i 0.284688π-0.284688\pi
0.626008 + 0.779817i 0.284688π0.284688\pi
8080 −6.40158 8.75234i −0.715718 0.978541i
8181 0.309017 0.951057i 0.0343352 0.105673i
8282 13.2276 + 18.2062i 1.46074 + 2.01054i
8383 14.1599i 1.55425i 0.629344 + 0.777127i 0.283324π0.283324\pi
−0.629344 + 0.777127i 0.716676π0.716676\pi
8484 −0.235676 −0.0257143
8585 −0.724057 2.20453i −0.0785350 0.239115i
8686 0.814181 2.50579i 0.0877954 0.270206i
8787 0.700461 + 0.227593i 0.0750973 + 0.0244006i
8888 −3.58262 1.05853i −0.381909 0.112840i
8989 0.142074 + 0.437258i 0.0150598 + 0.0463492i 0.958304 0.285751i 0.0922429π-0.0922429\pi
−0.943244 + 0.332100i 0.892243π0.892243\pi
9090 −3.32209 + 2.42982i −0.350179 + 0.256126i
9191 0.901671 + 0.655102i 0.0945208 + 0.0686734i
9292 −7.25541 2.35742i −0.756429 0.245779i
9393 0.172836 + 0.237888i 0.0179223 + 0.0246679i
9494 −11.1171 −1.14664
9595 −5.47929 + 7.59227i −0.562164 + 0.778950i
9696 −2.06220 6.34680i −0.210473 0.647768i
9797 4.61724i 0.468810i 0.972139 + 0.234405i 0.0753141π0.0753141\pi
−0.972139 + 0.234405i 0.924686π0.924686\pi
9898 12.2036 3.96519i 1.23275 0.400545i
9999 −0.939777 + 3.18069i −0.0944512 + 0.319672i
100100 6.94020 0.0441507i 0.694020 0.00441507i
101101 −0.268477 0.195060i −0.0267145 0.0194092i 0.574348 0.818611i 0.305256π-0.305256\pi
−0.601062 + 0.799202i 0.705256π0.705256\pi
102102 1.91009i 0.189127i
103103 4.13076 5.68551i 0.407016 0.560210i −0.555471 0.831536i 0.687462π-0.687462\pi
0.962487 + 0.271326i 0.0874622π0.0874622\pi
104104 −2.28480 + 7.03188i −0.224043 + 0.689533i
105105 −0.222178 + 0.307856i −0.0216823 + 0.0300437i
106106 1.25546 3.86390i 0.121941 0.375295i
107107 0.706648 + 0.229604i 0.0683142 + 0.0221966i 0.342975 0.939345i 0.388565π-0.388565\pi
−0.274661 + 0.961541i 0.588565π0.588565\pi
108108 −1.32013 + 0.428937i −0.127030 + 0.0412744i
109109 1.47491 4.53931i 0.141271 0.434787i −0.855242 0.518229i 0.826591π-0.826591\pi
0.996513 + 0.0834422i 0.0265914π0.0265914\pi
110110 10.7976 8.35193i 1.02951 0.796325i
111111 −1.18309 3.64117i −0.112294 0.345605i
112112 −0.483962 0.666117i −0.0457301 0.0629421i
113113 5.13705 7.07054i 0.483253 0.665140i −0.495873 0.868395i 0.665152π-0.665152\pi
0.979126 + 0.203255i 0.0651520π0.0651520\pi
114114 −6.23537 + 4.53026i −0.583996 + 0.424298i
115115 −9.91929 + 7.25510i −0.924978 + 0.676542i
116116 −0.315915 0.972287i −0.0293320 0.0902746i
117117 6.24298 + 2.02847i 0.577164 + 0.187532i
118118 25.0419 + 8.13662i 2.30530 + 0.749037i
119119 −0.0544457 0.167567i −0.00499103 0.0153608i
120120 −2.39782 0.770676i −0.218890 0.0703528i
121121 2.83234 10.6291i 0.257485 0.966282i
122122 −14.9776 20.6148i −1.35600 1.86638i
123123 11.6277 + 3.77806i 1.04843 + 0.340656i
124124 0.126127 0.388179i 0.0113266 0.0348595i
125125 6.48503 9.10738i 0.580039 0.814589i
126126 −0.252836 + 0.183696i −0.0225244 + 0.0163649i
127127 −2.15422 + 2.96504i −0.191157 + 0.263104i −0.893828 0.448410i 0.851990π-0.851990\pi
0.702671 + 0.711515i 0.251990π0.251990\pi
128128 5.04857 6.94876i 0.446235 0.614190i
129129 −0.442328 1.36135i −0.0389448 0.119860i
130130 −15.9500 21.8071i −1.39891 1.91261i
131131 14.5629 + 10.5806i 1.27237 + 0.924430i 0.999294 0.0375625i 0.0119593π-0.0119593\pi
0.273075 + 0.961993i 0.411959π0.411959\pi
132132 4.33858 1.53974i 0.377625 0.134017i
133133 −0.417880 + 0.575163i −0.0362348 + 0.0498729i
134134 17.2858 12.5588i 1.49326 1.08492i
135135 −0.684215 + 2.12881i −0.0588879 + 0.183219i
136136 0.945614 0.687029i 0.0810857 0.0589122i
137137 −12.1727 + 3.95515i −1.03998 + 0.337911i −0.778730 0.627359i 0.784136π-0.784136\pi
−0.261254 + 0.965270i 0.584136π0.584136\pi
138138 −9.62115 + 3.12610i −0.819007 + 0.266112i
139139 −9.79416 + 7.11588i −0.830730 + 0.603561i −0.919766 0.392468i 0.871621π-0.871621\pi
0.0890357 + 0.996028i 0.471621π0.471621\pi
140140 0.526985 0.00167621i 0.0445383 0.000141666i
141141 −4.88621 + 3.55004i −0.411493 + 0.298967i
142142 2.38789 3.28664i 0.200387 0.275809i
143143 −20.8789 6.16894i −1.74598 0.515873i
144144 −3.92325 2.85041i −0.326937 0.237534i
145145 −1.56789 0.503930i −0.130206 0.0418491i
146146 −8.29686 25.5351i −0.686653 2.11330i
147147 4.09755 5.63980i 0.337960 0.465163i
148148 −3.12366 + 4.29936i −0.256764 + 0.353405i
149149 −11.8481 + 8.60817i −0.970636 + 0.705208i −0.955596 0.294679i 0.904787π-0.904787\pi
−0.0150396 + 0.999887i 0.504787π0.504787\pi
150150 7.41111 5.45685i 0.605114 0.445550i
151151 3.45685 10.6391i 0.281315 0.865797i −0.706165 0.708048i 0.749576π-0.749576\pi
0.987479 0.157749i 0.0504238π-0.0504238\pi
152152 −4.48553 1.45744i −0.363825 0.118214i
153153 −0.609952 0.839527i −0.0493117 0.0678717i
154154 0.821889 0.631560i 0.0662297 0.0508925i
155155 −0.388163 0.530703i −0.0311780 0.0426271i
156156 −2.81565 8.66568i −0.225433 0.693810i
157157 −8.90719 2.89412i −0.710871 0.230976i −0.0688104 0.997630i 0.521920π-0.521920\pi
−0.642061 + 0.766654i 0.721920π0.721920\pi
158158 −19.4807 6.32968i −1.54980 0.503562i
159159 −0.682064 2.09918i −0.0540912 0.166476i
160160 4.65634 + 14.1771i 0.368116 + 1.12080i
161161 −0.754930 + 0.548489i −0.0594968 + 0.0432270i
162162 −1.08192 + 1.48913i −0.0850036 + 0.116997i
163163 −11.8460 16.3046i −0.927848 1.27707i −0.960693 0.277613i 0.910457π-0.910457\pi
0.0328447 0.999460i 0.489543π-0.489543\pi
164164 −5.24420 16.1400i −0.409503 1.26032i
165165 2.07877 7.11890i 0.161832 0.554205i
166166 8.05415 24.7881i 0.625123 1.92393i
167167 21.8120 7.08714i 1.68786 0.548420i 0.701451 0.712717i 0.252536π-0.252536\pi
0.986411 + 0.164298i 0.0525358π0.0525358\pi
168168 −0.181882 0.0590971i −0.0140325 0.00455944i
169169 −9.29817 + 28.6168i −0.715244 + 2.20129i
170170 0.0135852 + 4.27106i 0.00104194 + 0.327575i
171171 −1.29393 + 3.98231i −0.0989493 + 0.304535i
172172 −1.16786 + 1.60743i −0.0890487 + 0.122565i
173173 15.2451i 1.15907i 0.814949 + 0.579533i 0.196765π0.196765\pi
−0.814949 + 0.579533i 0.803235π0.803235\pi
174174 −1.09676 0.796842i −0.0831451 0.0604084i
175175 0.494612 0.689963i 0.0373892 0.0521563i
176176 13.2612 + 9.10073i 0.999604 + 0.685993i
177177 13.6048 4.42047i 1.02260 0.332263i
178178 0.846267i 0.0634304i
179179 2.87221 + 8.83975i 0.214679 + 0.660714i 0.999176 + 0.0405818i 0.0129211π0.0129211\pi
−0.784497 + 0.620132i 0.787079π0.787079\pi
180180 2.94884 0.968516i 0.219793 0.0721889i
181181 3.75534 0.279132 0.139566 0.990213i 0.455429π-0.455429\pi
0.139566 + 0.990213i 0.455429π0.455429\pi
182182 −1.20583 1.65968i −0.0893819 0.123024i
183183 −13.1660 4.27788i −0.973256 0.316230i
184184 −5.00820 3.63867i −0.369209 0.268246i
185185 2.67135 + 8.13345i 0.196402 + 0.597983i
186186 −0.167253 0.514752i −0.0122636 0.0377434i
187187 2.09706 + 2.72904i 0.153352 + 0.199567i
188188 7.97317 + 2.59064i 0.581503 + 0.188942i
189189 −0.0524671 + 0.161477i −0.00381642 + 0.0117457i
190190 13.9104 10.1743i 1.00917 0.738119i
191191 25.4592 1.84216 0.921081 0.389371i 0.127307π-0.127307\pi
0.921081 + 0.389371i 0.127307π0.127307\pi
192192 2.58477i 0.186539i
193193 −4.65416 6.40591i −0.335014 0.461107i 0.607963 0.793965i 0.291987π-0.291987\pi
−0.942977 + 0.332858i 0.891987π0.891987\pi
194194 2.62628 8.08285i 0.188556 0.580315i
195195 −13.9741 4.49137i −1.00071 0.321634i
196196 −9.67646 −0.691176
197197 4.73782 + 6.52105i 0.337556 + 0.464606i 0.943726 0.330730i 0.107295π-0.107295\pi
−0.606170 + 0.795335i 0.707295π0.707295\pi
198198 3.45433 5.03352i 0.245489 0.357717i
199199 −15.2117 −1.07833 −0.539163 0.842201i 0.681259π-0.681259\pi
−0.539163 + 0.842201i 0.681259π0.681259\pi
200200 5.36715 + 1.70622i 0.379515 + 0.120648i
201201 3.58705 11.0398i 0.253011 0.778688i
202202 0.359042 + 0.494179i 0.0252621 + 0.0347703i
203203 −0.118929 0.0386424i −0.00834719 0.00271217i
204204 −0.445113 + 1.36992i −0.0311641 + 0.0959133i
205205 −26.0270 8.36525i −1.81780 0.584254i
206206 −10.4651 + 7.60337i −0.729141 + 0.529752i
207207 −3.23045 + 4.44634i −0.224532 + 0.309042i
208208 18.7108 25.7532i 1.29736 1.78567i
209209 3.93508 13.3184i 0.272195 0.921250i
210210 0.564048 0.412552i 0.0389230 0.0284688i
211211 3.33692 10.2700i 0.229723 0.707016i −0.768054 0.640385i 0.778775π-0.778775\pi
0.997778 0.0666311i 0.0212251π-0.0212251\pi
212212 −1.80083 + 2.47863i −0.123681 + 0.170233i
213213 2.20708i 0.151227i
214214 −1.10645 0.803881i −0.0756351 0.0549521i
215215 0.998754 + 3.04090i 0.0681144 + 0.207388i
216216 −1.12637 −0.0766395
217217 −0.0293453 0.0403904i −0.00199209 0.00274188i
218218 −5.16391 + 7.10751i −0.349744 + 0.481381i
219219 −11.8008 8.57381i −0.797427 0.579364i
220220 −9.69035 + 3.47381i −0.653324 + 0.234204i
221221 5.51087 4.00388i 0.370701 0.269330i
222222 7.04711i 0.472971i
223223 6.72487i 0.450331i −0.974321 0.225165i 0.927708π-0.927708\pi
0.974321 0.225165i 0.0722922π-0.0722922\pi
224224 0.350135 + 1.07760i 0.0233944 + 0.0720005i
225225 1.51480 4.76502i 0.100987 0.317668i
226226 −13.0145 + 9.45561i −0.865713 + 0.628978i
227227 −7.99327 11.0018i −0.530532 0.730215i 0.456679 0.889631i 0.349039π-0.349039\pi
−0.987211 + 0.159416i 0.949039π0.949039\pi
228228 5.52771 1.79606i 0.366082 0.118947i
229229 7.24194 0.478561 0.239280 0.970951i 0.423088π-0.423088\pi
0.239280 + 0.970951i 0.423088π0.423088\pi
230230 21.4912 7.05857i 1.41709 0.465428i
231231 0.159562 0.540041i 0.0104984 0.0355321i
232232 0.829577i 0.0544644i
233233 −15.5173 + 5.04188i −1.01657 + 0.330304i −0.769469 0.638685i 0.779479π-0.779479\pi
−0.247104 + 0.968989i 0.579479π0.579479\pi
234234 −9.77506 7.10200i −0.639016 0.464272i
235235 10.9006 7.97284i 0.711076 0.520090i
236236 −16.0640 11.6712i −1.04568 0.759730i
237237 −10.5835 + 3.43879i −0.687472 + 0.223373i
238238 0.324308i 0.0210218i
239239 −1.58661 −0.102629 −0.0513145 0.998683i 0.516341π-0.516341\pi
−0.0513145 + 0.998683i 0.516341π0.516341\pi
240240 8.79288 + 6.34577i 0.567578 + 0.409618i
241241 6.51807 20.0606i 0.419866 1.29221i −0.487960 0.872866i 0.662259π-0.662259\pi
0.907825 0.419348i 0.137741π-0.137741\pi
242242 −11.0041 + 16.9961i −0.707368 + 1.09255i
243243 1.00000i 0.0641500i
244244 5.93799 + 18.2752i 0.380141 + 1.16995i
245245 −9.12225 + 12.6400i −0.582799 + 0.807543i
246246 −18.2062 13.2276i −1.16079 0.843361i
247247 −26.1409 8.49370i −1.66331 0.540441i
248248 0.194676 0.267949i 0.0123620 0.0170148i
249249 −4.37566 13.4669i −0.277296 0.853430i
250250 −16.5328 + 12.2545i −1.04563 + 0.775045i
251251 6.69050 + 4.86093i 0.422301 + 0.306819i 0.778563 0.627567i 0.215949π-0.215949\pi
−0.356262 + 0.934386i 0.615949π0.615949\pi
252252 0.224141 0.0728279i 0.0141196 0.00458772i
253253 10.3141 15.0294i 0.648444 0.944888i
254254 5.45765 3.96522i 0.342444 0.248800i
255255 1.36986 + 1.87289i 0.0857838 + 0.117285i
256256 −16.9726 + 12.3313i −1.06079 + 0.770708i
257257 −2.37472 + 0.771595i −0.148131 + 0.0481308i −0.382144 0.924103i 0.624814π-0.624814\pi
0.234013 + 0.972233i 0.424814π0.424814\pi
258258 2.63474i 0.164032i
259259 0.200873 + 0.618224i 0.0124816 + 0.0384146i
260260 6.35759 + 19.3569i 0.394281 + 1.20047i
261261 −0.736508 −0.0455887
262262 −19.4754 26.8056i −1.20319 1.65605i
263263 −4.74448 1.54157i −0.292557 0.0950575i 0.159062 0.987269i 0.449153π-0.449153\pi
−0.451618 + 0.892211i 0.649153π0.649153\pi
264264 3.73438 0.100367i 0.229835 0.00617719i
265265 1.54006 + 4.68903i 0.0946054 + 0.288045i
266266 1.05868 0.769180i 0.0649121 0.0471614i
267267 −0.270240 0.371954i −0.0165384 0.0227632i
268268 −15.3240 + 4.97907i −0.936062 + 0.304145i
269269 5.18045 0.315858 0.157929 0.987450i 0.449518π-0.449518\pi
0.157929 + 0.987450i 0.449518π0.449518\pi
270270 2.40864 3.33748i 0.146585 0.203113i
271271 12.8910 + 9.36583i 0.783070 + 0.568934i 0.905899 0.423494i 0.139197π-0.139197\pi
−0.122829 + 0.992428i 0.539197π0.539197\pi
272272 −4.78599 + 1.55506i −0.290193 + 0.0942894i
273273 −1.05998 0.344408i −0.0641528 0.0208445i
274274 23.5590 1.42325
275275 −4.59762 + 15.9330i −0.277247 + 0.960799i
276276 7.62879 0.459199
277277 21.0866 + 6.85147i 1.26697 + 0.411665i 0.863974 0.503536i 0.167968π-0.167968\pi
0.402999 + 0.915200i 0.367968π0.367968\pi
278278 21.1930 6.88602i 1.27107 0.412996i
279279 −0.237888 0.172836i −0.0142420 0.0103474i
280280 0.407119 + 0.130851i 0.0243300 + 0.00781983i
281281 −23.8147 −1.42067 −0.710334 0.703865i 0.751456π-0.751456\pi
−0.710334 + 0.703865i 0.751456π0.751456\pi
282282 10.5730 3.43536i 0.629611 0.204573i
283283 −0.498218 0.685738i −0.0296160 0.0407629i 0.793952 0.607980i 0.208020π-0.208020\pi
−0.823568 + 0.567217i 0.808020π0.808020\pi
284284 −2.47849 + 1.80073i −0.147071 + 0.106854i
285285 2.86498 8.91387i 0.169707 0.528012i
286286 33.0414 + 22.6751i 1.95378 + 1.34081i
287287 −1.97423 0.641465i −0.116535 0.0378645i
288288 3.92254 + 5.39891i 0.231138 + 0.318134i
289289 15.9232 0.936656
290290 2.45808 + 1.77398i 0.144344 + 0.104172i
291291 −1.42681 4.39125i −0.0836408 0.257420i
292292 20.2472i 1.18488i
293293 8.18800 2.66044i 0.478348 0.155425i −0.0599118 0.998204i 0.519082π-0.519082\pi
0.538260 + 0.842779i 0.319082π0.319082\pi
294294 −10.3810 + 7.54224i −0.605433 + 0.439873i
295295 −30.3897 + 9.98118i −1.76935 + 0.581126i
296296 −3.48877 + 2.53474i −0.202780 + 0.147329i
297297 −0.0891073 3.31543i −0.00517053 0.192381i
298298 25.6374 8.33010i 1.48514 0.482550i
299299 −29.1869 21.2055i −1.68792 1.22635i
300300 −6.58688 + 2.18663i −0.380294 + 0.126245i
301301 0.0751016 + 0.231139i 0.00432879 + 0.0133226i
302302 −12.1030 + 16.6583i −0.696449 + 0.958580i
303303 0.315614 + 0.102549i 0.0181316 + 0.00589130i
304304 16.4276 + 11.9354i 0.942188 + 0.684540i
305305 29.4703 + 9.47194i 1.68746 + 0.542362i
306306 0.590249 + 1.81660i 0.0337423 + 0.103848i
307307 21.6951i 1.23820i 0.785310 + 0.619102i 0.212503π0.212503\pi
−0.785310 + 0.619102i 0.787497π0.787497\pi
308308 −0.736634 + 0.261428i −0.0419736 + 0.0148962i
309309 −2.17167 + 6.68371i −0.123542 + 0.380223i
310310 0.377648 + 1.14982i 0.0214490 + 0.0653057i
311311 −7.17017 −0.406583 −0.203291 0.979118i 0.565164π-0.565164\pi
−0.203291 + 0.979118i 0.565164π0.565164\pi
312312 7.39376i 0.418589i
313313 12.8673 4.18084i 0.727303 0.236315i 0.0781165 0.996944i 0.475109π-0.475109\pi
0.649187 + 0.760629i 0.275109π0.275109\pi
314314 13.9466 + 10.1328i 0.787052 + 0.571827i
315315 0.116171 0.361445i 0.00654549 0.0203651i
316316 12.4966 + 9.07930i 0.702988 + 0.510751i
317317 17.2917 5.61840i 0.971196 0.315561i 0.219898 0.975523i 0.429428π-0.429428\pi
0.751299 + 0.659962i 0.229428π0.229428\pi
318318 4.06274i 0.227827i
319319 2.44184 0.0656283i 0.136717 0.00367448i
320320 −0.0183838 5.77968i −0.00102768 0.323094i
321321 −0.743014 −0.0414710
322322 1.63355 0.530772i 0.0910340 0.0295787i
323323 2.55402 + 3.51530i 0.142109 + 0.195597i
324324 1.12297 0.815886i 0.0623873 0.0453270i
325325 31.2788 + 9.94356i 1.73504 + 0.551570i
326326 11.4633 + 35.2805i 0.634895 + 1.95400i
327327 4.77291i 0.263943i
328328 13.7710i 0.760376i
329329 0.829614 0.602750i 0.0457381 0.0332307i
330330 −7.68828 + 11.2798i −0.423226 + 0.620933i
331331 −13.4577 9.77759i −0.739702 0.537425i 0.152916 0.988239i 0.451134π-0.451134\pi
−0.892618 + 0.450814i 0.851134π0.851134\pi
332332 −11.5529 + 15.9012i −0.634047 + 0.872691i
333333 2.25037 + 3.09737i 0.123319 + 0.169735i
334334 −42.2148 −2.30989
335335 −7.94233 + 24.7111i −0.433936 + 1.35011i
336336 0.666117 + 0.483962i 0.0363397 + 0.0264023i
337337 19.3394i 1.05348i 0.850025 + 0.526742i 0.176587π0.176587\pi
−0.850025 + 0.526742i 0.823413π0.823413\pi
338338 32.5544 44.8073i 1.77073 2.43720i
339339 −2.70070 + 8.31191i −0.146682 + 0.451441i
340340 0.985554 3.06638i 0.0534492 0.166298i
341341 0.804103 + 0.551828i 0.0435446 + 0.0298831i
342342 4.53026 6.23537i 0.244968 0.337170i
343343 −1.39430 + 1.91909i −0.0752851 + 0.103621i
344344 −1.30437 + 0.947677i −0.0703267 + 0.0510953i
345345 7.19185 9.96524i 0.387196 0.536510i
346346 8.67141 26.6879i 0.466178 1.43475i
347347 −4.09731 1.33130i −0.219955 0.0714677i 0.196967 0.980410i 0.436891π-0.436891\pi
−0.416921 + 0.908943i 0.636891π0.636891\pi
348348 0.600906 + 0.827077i 0.0322120 + 0.0443360i
349349 7.56819 23.2925i 0.405116 1.24682i −0.515683 0.856780i 0.672462π-0.672462\pi
0.920799 0.390038i 0.127538π-0.127538\pi
350350 −1.25831 + 0.926502i −0.0672595 + 0.0495236i
351351 −6.56426 −0.350374
352352 −13.4860 17.5502i −0.718805 0.935428i
353353 −7.47823 10.2929i −0.398026 0.547836i 0.562221 0.826987i 0.309947π-0.309947\pi
−0.960247 + 0.279151i 0.909947π0.909947\pi
354354 −26.3307 −1.39946
355355 0.0156976 + 4.93517i 0.000833141 + 0.261931i
356356 −0.197208 + 0.606944i −0.0104520 + 0.0321680i
357357 0.103562 + 0.142541i 0.00548108 + 0.00754406i
358358 17.1084i 0.904208i
359359 31.5526 1.66528 0.832642 0.553812i 0.186827π-0.186827\pi
0.832642 + 0.553812i 0.186827π0.186827\pi
360360 2.51862 0.00801112i 0.132743 0.000422223i
361361 −0.453318 + 1.39517i −0.0238589 + 0.0734300i
362362 −6.57403 2.13603i −0.345524 0.112267i
363363 0.590858 + 10.9841i 0.0310120 + 0.576517i
364364 0.478061 + 1.47132i 0.0250572 + 0.0771182i
365365 26.4483 + 19.0876i 1.38437 + 0.999090i
366366 20.6148 + 14.9776i 1.07755 + 0.782889i
367367 9.16660 + 2.97841i 0.478493 + 0.155472i 0.538326 0.842737i 0.319057π-0.319057\pi
−0.0598333 + 0.998208i 0.519057π0.519057\pi
368368 15.6658 + 21.5621i 0.816635 + 1.12400i
369369 −12.2260 −0.636463
370370 −0.0501216 15.7577i −0.00260570 0.819206i
371371 0.115806 + 0.356413i 0.00601233 + 0.0185041i
372372 0.408156i 0.0211619i
373373 −29.3061 + 9.52212i −1.51741 + 0.493037i −0.945039 0.326957i 0.893977π-0.893977\pi
−0.572372 + 0.819994i 0.693977π0.693977\pi
374374 −2.11880 5.97021i −0.109561 0.308712i
375375 −3.35330 + 10.6656i −0.173163 + 0.550770i
376376 5.50365 + 3.99864i 0.283829 + 0.206214i
377377 4.83463i 0.248996i
378378 0.183696 0.252836i 0.00944829 0.0130045i
379379 5.02204 15.4562i 0.257965 0.793934i −0.735266 0.677778i 0.762943π-0.762943\pi
0.993231 0.116155i 0.0370571π-0.0370571\pi
380380 −12.3475 + 4.05541i −0.633414 + 0.208038i
381381 1.13254 3.48561i 0.0580219 0.178573i
382382 −44.5684 14.4811i −2.28032 0.740920i
383383 −11.2220 + 3.64625i −0.573418 + 0.186315i −0.581350 0.813654i 0.697475π-0.697475\pi
0.00793171 + 0.999969i 0.497475π0.497475\pi
384384 −2.65419 + 8.16876i −0.135446 + 0.416860i
385385 −0.352949 + 1.20870i −0.0179879 + 0.0616009i
386386 4.50382 + 13.8613i 0.229239 + 0.705524i
387387 0.841359 + 1.15803i 0.0427687 + 0.0588660i
388388 −3.76714 + 5.18502i −0.191248 + 0.263230i
389389 16.4315 11.9382i 0.833111 0.605291i −0.0873265 0.996180i 0.527832π-0.527832\pi
0.920438 + 0.390889i 0.127832π0.127832\pi
390390 21.9081 + 15.8109i 1.10936 + 0.800618i
391391 1.76240 + 5.42410i 0.0891283 + 0.274309i
392392 −7.46778 2.42643i −0.377180 0.122553i
393393 −17.1198 5.56254i −0.863577 0.280593i
394394 −4.58478 14.1105i −0.230978 0.710877i
395395 23.6409 7.76460i 1.18950 0.390679i
396396 −3.65043 + 2.80508i −0.183441 + 0.140960i
397397 11.2736 + 15.5168i 0.565808 + 0.778768i 0.992050 0.125841i 0.0401630π-0.0401630\pi
−0.426243 + 0.904609i 0.640163π0.640163\pi
398398 26.6293 + 8.65237i 1.33480 + 0.433704i
399399 0.219693 0.676144i 0.0109984 0.0338495i
400400 −19.7065 14.1270i −0.985326 0.706348i
401401 −3.93580 + 2.85952i −0.196544 + 0.142798i −0.681705 0.731627i 0.738761π-0.738761\pi
0.485161 + 0.874425i 0.338761π0.338761\pi
402402 −12.5588 + 17.2858i −0.626378 + 0.862136i
403403 1.13454 1.56156i 0.0565155 0.0777869i
404404 −0.142345 0.438094i −0.00708195 0.0217960i
405405 −0.00711236 2.23606i −0.000353416 0.111111i
406406 0.186215 + 0.135293i 0.00924172 + 0.00671450i
407407 −7.73693 10.0686i −0.383505 0.499080i
408408 −0.687029 + 0.945614i −0.0340130 + 0.0468149i
409409 −20.2251 + 14.6944i −1.00007 + 0.726592i −0.962103 0.272687i 0.912088π-0.912088\pi
−0.0379653 + 0.999279i 0.512088π0.512088\pi
410410 40.8042 + 29.4482i 2.01518 + 1.45434i
411411 10.3547 7.52314i 0.510761 0.371089i
412412 9.27745 3.01443i 0.457067 0.148510i
413413 −2.30992 + 0.750538i −0.113664 + 0.0369315i
414414 8.18424 5.94620i 0.402234 0.292240i
415415 9.88000 + 30.0816i 0.484990 + 1.47665i
416416 −35.4399 + 25.7486i −1.73758 + 1.26243i
417417 7.11588 9.79416i 0.348466 0.479622i
418418 −14.4641 + 21.0766i −0.707464 + 1.03089i
419419 15.5801 + 11.3196i 0.761137 + 0.552998i 0.899259 0.437417i 0.144107π-0.144107\pi
−0.138122 + 0.990415i 0.544107π0.544107\pi
420420 −0.500674 + 0.164441i −0.0244304 + 0.00802392i
421421 −6.73317 20.7226i −0.328155 1.00996i −0.969996 0.243119i 0.921829π-0.921829\pi
0.641842 0.766837i 0.278171π-0.278171\pi
422422 −11.6831 + 16.0804i −0.568725 + 0.782783i
423423 3.55004 4.88621i 0.172609 0.237575i
424424 −2.01131 + 1.46131i −0.0976781 + 0.0709673i
425425 −3.07640 4.17815i −0.149227 0.202670i
426426 −1.25539 + 3.86368i −0.0608237 + 0.187196i
427427 2.23541 + 0.726328i 0.108179 + 0.0351495i
428428 0.606214 + 0.834382i 0.0293025 + 0.0403314i
429429 21.7633 0.584924i 1.05074 0.0282404i
430430 −0.0187393 5.89144i −0.000903687 0.284110i
431431 −5.26351 16.1994i −0.253534 0.780298i −0.994115 0.108331i 0.965449π-0.965449\pi
0.740581 0.671967i 0.234551π-0.234551\pi
432432 4.61206 + 1.49855i 0.221898 + 0.0720989i
433433 −14.7305 4.78624i −0.707905 0.230012i −0.0671334 0.997744i 0.521385π-0.521385\pi
−0.640771 + 0.767732i 0.721385π0.721385\pi
434434 0.0283974 + 0.0873982i 0.00136312 + 0.00419525i
435435 1.64687 0.00523831i 0.0789615 0.000251158i
436436 5.35984 3.89415i 0.256690 0.186496i
437437 13.5267 18.6179i 0.647070 0.890615i
438438 15.7816 + 21.7215i 0.754072 + 1.03789i
439439 −0.0733759 0.225828i −0.00350204 0.0107782i 0.949290 0.314401i 0.101804π-0.101804\pi
−0.952792 + 0.303623i 0.901804π0.901804\pi
440440 −8.34958 + 0.250988i −0.398050 + 0.0119654i
441441 −2.15421 + 6.62998i −0.102581 + 0.315713i
442442 −11.9246 + 3.87455i −0.567197 + 0.184293i
443443 −16.4961 5.35991i −0.783753 0.254657i −0.110311 0.993897i 0.535185π-0.535185\pi
−0.673442 + 0.739240i 0.735185π0.735185\pi
444444 1.64221 5.05420i 0.0779357 0.239861i
445445 0.606918 + 0.829788i 0.0287707 + 0.0393357i
446446 −3.82510 + 11.7724i −0.181124 + 0.557441i
447447 8.60817 11.8481i 0.407152 0.560397i
448448 0.438860i 0.0207342i
449449 −31.1915 22.6619i −1.47202 1.06948i −0.980023 0.198884i 0.936268π-0.936268\pi
−0.491993 0.870599i 0.663732π-0.663732\pi
450450 −5.36212 + 7.47993i −0.252773 + 0.352607i
451451 40.5346 1.08943i 1.90870 0.0512993i
452452 11.5375 3.74876i 0.542678 0.176327i
453453 11.1866i 0.525593i
454454 7.73507 + 23.8061i 0.363025 + 1.11728i
455455 2.37262 + 0.762576i 0.111230 + 0.0357501i
456456 4.71637 0.220864
457457 5.19064 + 7.14430i 0.242808 + 0.334196i 0.912976 0.408013i 0.133778π-0.133778\pi
−0.670168 + 0.742209i 0.733778π0.733778\pi
458458 −12.6776 4.11920i −0.592386 0.192478i
459459 0.839527 + 0.609952i 0.0391857 + 0.0284701i
460460 −17.0584 + 0.0542587i −0.795352 + 0.00252982i
461461 4.71859 + 14.5223i 0.219766 + 0.676372i 0.998781 + 0.0493655i 0.0157199π0.0157199\pi
−0.779014 + 0.627006i 0.784280π0.784280\pi
462462 −0.586501 + 0.854627i −0.0272865 + 0.0397608i
463463 6.31940 + 2.05330i 0.293688 + 0.0954249i 0.452155 0.891939i 0.350655π-0.350655\pi
−0.158468 + 0.987364i 0.550655π0.550655\pi
464464 −1.10369 + 3.39682i −0.0512376 + 0.157693i
465465 0.533161 + 0.384779i 0.0247248 + 0.0178437i
466466 30.0321 1.39121
467467 20.2368i 0.936445i −0.883611 0.468223i 0.844895π-0.844895\pi
0.883611 0.468223i 0.155105π-0.155105\pi
468468 5.35569 + 7.37147i 0.247567 + 0.340746i
469469 −0.609034 + 1.87442i −0.0281226 + 0.0865524i
470470 −23.6173 + 7.75686i −1.08938 + 0.357797i
471471 9.36558 0.431543
472472 −9.47073 13.0353i −0.435926 0.600001i
473473 −2.89265 3.76440i −0.133004 0.173087i
474474 20.4833 0.940828
475475 −6.34285 + 19.9523i −0.291030 + 0.915474i
476476 0.0755743 0.232594i 0.00346394 0.0106609i
477477 1.29736 + 1.78567i 0.0594022 + 0.0817601i
478478 2.77748 + 0.902459i 0.127039 + 0.0412775i
479479 −7.80533 + 24.0223i −0.356635 + 1.09761i 0.598421 + 0.801182i 0.295795π0.295795\pi
−0.955056 + 0.296427i 0.904205π0.904205\pi
480480 −8.80942 12.0444i −0.402093 0.549748i
481481 −20.3319 + 14.7720i −0.927056 + 0.673546i
482482 −22.8208 + 31.4102i −1.03946 + 1.43069i
483483 0.548489 0.754930i 0.0249571 0.0343505i
484484 11.8528 9.62530i 0.538762 0.437514i
485485 3.22165 + 9.80895i 0.146288 + 0.445401i
486486 0.568798 1.75058i 0.0258012 0.0794080i
487487 −7.12353 + 9.80470i −0.322798 + 0.444293i −0.939319 0.343045i 0.888542π-0.888542\pi
0.616521 + 0.787338i 0.288542π0.288542\pi
488488 15.5929i 0.705855i
489489 16.3046 + 11.8460i 0.737319 + 0.535693i
490490 23.1589 16.9387i 1.04621 0.765213i
491491 −17.0511 −0.769506 −0.384753 0.923019i 0.625713π-0.625713\pi
−0.384753 + 0.923019i 0.625713π0.625713\pi
492492 9.97506 + 13.7295i 0.449710 + 0.618973i
493493 −0.449234 + 0.618318i −0.0202325 + 0.0278476i
494494 40.9306 + 29.7378i 1.84155 + 1.33797i
495495 0.222830 + 7.41285i 0.0100154 + 0.333183i
496496 −1.15362 + 0.838151i −0.0517989 + 0.0376341i
497497 0.374734i 0.0168091i
498498 26.0638i 1.16795i
499499 −8.26293 25.4307i −0.369900 1.13843i −0.946856 0.321659i 0.895760π-0.895760\pi
0.576956 0.816775i 0.304240π-0.304240\pi
500500 14.7131 4.93628i 0.657989 0.220757i
501501 −18.5544 + 13.4805i −0.828949 + 0.602267i
502502 −8.94737 12.3150i −0.399341 0.549646i
503503 21.2717 6.91161i 0.948460 0.308173i 0.206370 0.978474i 0.433835π-0.433835\pi
0.742090 + 0.670301i 0.233835π0.233835\pi
504504 0.191242 0.00851861
505505 −0.706461 0.227061i −0.0314371 0.0101041i
506506 −26.6044 + 20.4435i −1.18271 + 0.908823i
507507 30.0895i 1.33632i
508508 −4.83826 + 1.57205i −0.214663 + 0.0697483i
509509 19.1469 + 13.9110i 0.848672 + 0.616596i 0.924779 0.380504i 0.124249π-0.124249\pi
−0.0761078 + 0.997100i 0.524249π0.524249\pi
510510 −1.33275 4.05782i −0.0590152 0.179683i
511511 2.00363 + 1.45572i 0.0886353 + 0.0643973i
512512 20.3885 6.62462i 0.901052 0.292770i
513513 4.18725i 0.184871i
514514 4.59603 0.202722
515515 4.80844 14.9606i 0.211885 0.659243i
516516 0.613982 1.88964i 0.0270290 0.0831868i
517517 −11.3345 + 16.5162i −0.498490 + 0.726382i
518518 1.19651i 0.0525715i
519519 −4.71101 14.4990i −0.206790 0.636435i
520520 0.0525871 + 16.5329i 0.00230609 + 0.725014i
521521 −8.39742 6.10108i −0.367898 0.267293i 0.388441 0.921474i 0.373014π-0.373014\pi
−0.756339 + 0.654180i 0.773014π0.773014\pi
522522 1.28932 + 0.418925i 0.0564319 + 0.0183358i
523523 −22.1299 + 30.4592i −0.967672 + 1.33189i −0.0244586 + 0.999701i 0.507786π0.507786\pi
−0.943214 + 0.332186i 0.892214π0.892214\pi
524524 7.72119 + 23.7634i 0.337302 + 1.03811i
525525 −0.257194 + 0.809038i −0.0112249 + 0.0353093i
526526 7.42875 + 5.39730i 0.323909 + 0.235334i
527527 −0.290201 + 0.0942920i −0.0126413 + 0.00410742i
528528 −15.4245 4.55736i −0.671264 0.198334i
529529 5.82957 4.23543i 0.253460 0.184149i
530530 −0.0288957 9.08452i −0.00125515 0.394606i
531531 −11.5729 + 8.40823i −0.502222 + 0.364886i
532532 −0.938534 + 0.304948i −0.0406906 + 0.0132212i
533533 80.2550i 3.47623i
534534 0.261511 + 0.804848i 0.0113167 + 0.0348292i
535535 1.66142 0.00528458i 0.0718295 0.000228472i
536536 −13.0748 −0.564744
537537 −5.46327 7.51954i −0.235757 0.324492i
538538 −9.06881 2.94663i −0.390984 0.127038i
539539 6.55135 22.1732i 0.282187 0.955066i
540540 −2.50522 + 1.83235i −0.107808 + 0.0788520i
541541 −12.2679 + 8.91312i −0.527437 + 0.383205i −0.819398 0.573225i 0.805692π-0.805692\pi
0.291961 + 0.956430i 0.405692π0.405692\pi
542542 −17.2394 23.7280i −0.740496 1.01921i
543543 −3.57154 + 1.16046i −0.153270 + 0.0498003i
544544 6.92509 0.296911
545545 −0.0339467 10.6725i −0.00145412 0.457160i
546546 1.65968 + 1.20583i 0.0710277 + 0.0516046i
547547 −10.4861 + 3.40715i −0.448354 + 0.145679i −0.524487 0.851419i 0.675743π-0.675743\pi
0.0761327 + 0.997098i 0.475743π0.475743\pi
548548 −16.8965 5.49002i −0.721784 0.234522i
549549 13.8435 0.590827
550550 17.1112 25.2770i 0.729624 1.07781i
551551 3.08394 0.131380
552552 5.88749 + 1.91296i 0.250588 + 0.0814211i
553553 1.79694 0.583862i 0.0764137 0.0248283i
554554 −33.0168 23.9881i −1.40275 1.01916i
555555 −5.05398 6.90988i −0.214530 0.293308i
556556 −16.8043 −0.712661
557557 2.99540 0.973265i 0.126919 0.0412385i −0.244869 0.969556i 0.578745π-0.578745\pi
0.371788 + 0.928318i 0.378745π0.378745\pi
558558 0.318134 + 0.437874i 0.0134677 + 0.0185367i
559559 −7.60162 + 5.52290i −0.321514 + 0.233594i
560560 −1.49292 1.07743i −0.0630873 0.0455297i
561561 −2.83774 1.94744i −0.119810 0.0822211i
562562 41.6896 + 13.5458i 1.75857 + 0.571394i
563563 −14.1738 19.5086i −0.597354 0.822188i 0.398108 0.917338i 0.369667π-0.369667\pi
−0.995463 + 0.0951505i 0.969667π0.969667\pi
564564 −8.38349 −0.353009
565565 5.97981 18.6051i 0.251573 0.782723i
566566 0.482124 + 1.48383i 0.0202652 + 0.0623698i
567567 0.169787i 0.00713038i
568568 −2.36431 + 0.768211i −0.0992043 + 0.0322334i
569569 12.0524 8.75661i 0.505264 0.367096i −0.305760 0.952109i 0.598910π-0.598910\pi
0.811024 + 0.585013i 0.198910π0.198910\pi
570570 −10.0856 + 13.9749i −0.422438 + 0.585342i
571571 −20.2290 + 14.6972i −0.846558 + 0.615060i −0.924195 0.381921i 0.875263π-0.875263\pi
0.0776369 + 0.996982i 0.475263π0.475263\pi
572572 −18.4132 23.9623i −0.769897 1.00192i
573573 −24.2131 + 7.86732i −1.01152 + 0.328662i
574574 3.09118 + 2.24587i 0.129023 + 0.0937410i
575575 −16.0105 + 22.3340i −0.667685 + 0.931392i
576576 −0.798737 2.45826i −0.0332807 0.102427i
577577 11.5147 15.8486i 0.479362 0.659785i −0.499020 0.866590i 0.666307π-0.666307\pi
0.978382 + 0.206806i 0.0663067π0.0663067\pi
578578 −27.8748 9.05707i −1.15944 0.376724i
579579 6.40591 + 4.65416i 0.266220 + 0.193420i
580580 −1.34954 1.84512i −0.0560367 0.0766143i
581581 0.742930 + 2.28650i 0.0308219 + 0.0948602i
582582 8.49881i 0.352287i
583583 −4.46043 5.80465i −0.184732 0.240404i
584584 −5.07711 + 15.6257i −0.210092 + 0.646598i
585585 14.6781 0.0466874i 0.606863 0.00193029i
586586 −15.8470 −0.654634
587587 35.4324i 1.46245i 0.682135 + 0.731226i 0.261052π0.261052\pi
−0.682135 + 0.731226i 0.738948π0.738948\pi
588588 9.20286 2.99019i 0.379520 0.123313i
589589 0.996097 + 0.723707i 0.0410435 + 0.0298198i
590590 58.8769 0.187273i 2.42392 0.00770991i
591591 −6.52105 4.73782i −0.268240 0.194888i
592592 17.6575 5.73727i 0.725719 0.235801i
593593 14.2924i 0.586919i −0.955971 0.293460i 0.905193π-0.905193\pi
0.955971 0.293460i 0.0948066π-0.0948066\pi
594594 −1.72982 + 5.85461i −0.0709754 + 0.240218i
595595 −0.232584 0.317993i −0.00953502 0.0130364i
596596 −20.3284 −0.832683
597597 14.4672 4.70066i 0.592101 0.192385i
598598 39.0324 + 53.7235i 1.59615 + 2.19692i
599599 −0.110576 + 0.0803381i −0.00451801 + 0.00328253i −0.590042 0.807373i 0.700889π-0.700889\pi
0.585524 + 0.810655i 0.300889π0.300889\pi
600600 −5.63171 + 0.0358266i −0.229914 + 0.00146262i
601601 −6.36934 19.6028i −0.259811 0.799616i −0.992844 0.119422i 0.961896π-0.961896\pi
0.733033 0.680193i 0.238104π-0.238104\pi
602602 0.447345i 0.0182324i
603603 11.6079i 0.472712i
604604 12.5622 9.12699i 0.511150 0.371372i
605605 −1.39931 24.5569i −0.0568902 0.998380i
606606 −0.494179 0.359042i −0.0200746 0.0145851i
607607 16.5997 22.8475i 0.673759 0.927350i −0.326079 0.945343i 0.605727π-0.605727\pi
0.999838 + 0.0179925i 0.00572749π0.00572749\pi
608608 −16.4246 22.6066i −0.666107 0.916818i
609609 0.125049 0.00506726
610610 −46.2025 33.3440i −1.87068 1.35006i
611611 32.0743 + 23.3034i 1.29759 + 0.942753i
612612 1.44041i 0.0582253i
613613 25.4451 35.0221i 1.02772 1.41453i 0.121068 0.992644i 0.461368π-0.461368\pi
0.906649 0.421886i 0.138632π-0.138632\pi
614614 12.3401 37.9790i 0.498008 1.53271i
615615 27.3381 0.0869561i 1.10238 0.00350641i
616616 −0.634050 + 0.0170411i −0.0255466 + 0.000686605i
617617 16.9406 23.3167i 0.682003 0.938696i −0.317953 0.948106i 0.602995π-0.602995\pi
0.999956 + 0.00941037i 0.00299546π0.00299546\pi
618618 7.60337 10.4651i 0.305852 0.420970i
619619 −19.8287 + 14.4064i −0.796981 + 0.579041i −0.910027 0.414549i 0.863939π-0.863939\pi
0.113046 + 0.993590i 0.463939π0.463939\pi
620620 −0.00290295 0.912660i −0.000116585 0.0366533i
621621 1.69835 5.22698i 0.0681524 0.209752i
622622 12.5520 + 4.07838i 0.503288 + 0.163528i
623623 0.0458833 + 0.0631529i 0.00183828 + 0.00253017i
624624 −9.83686 + 30.2747i −0.393790 + 1.21196i
625625 7.42230 23.8728i 0.296892 0.954911i
626626 −24.9033 −0.995337
627627 0.373114 + 13.8825i 0.0149008 + 0.554414i
628628 −7.64124 10.5173i −0.304919 0.419685i
629629 3.97294 0.158411
630630 −0.408956 + 0.566661i −0.0162932 + 0.0225763i
631631 2.16032 6.64878i 0.0860010 0.264684i −0.898803 0.438352i 0.855562π-0.855562\pi
0.984804 + 0.173669i 0.0555622π0.0555622\pi
632632 7.36752 + 10.1405i 0.293064 + 0.403368i
633633 10.7985i 0.429202i
634634 −33.4662 −1.32911
635635 −2.50764 + 7.80207i −0.0995126 + 0.309616i
636636 0.946752 2.91380i 0.0375411 0.115540i
637637 −43.5209 14.1408i −1.72436 0.560279i
638638 −4.31197 1.27403i −0.170712 0.0504392i
639639 0.682027 + 2.09906i 0.0269806 + 0.0830376i
640640 5.87682 18.2847i 0.232302 0.722766i
641641 28.7440 + 20.8837i 1.13532 + 0.824858i 0.986460 0.164001i 0.0524400π-0.0524400\pi
0.148859 + 0.988858i 0.452440π0.452440\pi
642642 1.30071 + 0.422625i 0.0513348 + 0.0166797i
643643 −17.8094 24.5126i −0.702336 0.966682i −0.999928 0.0119894i 0.996184π-0.996184\pi
0.297592 0.954693i 0.403816π-0.403816\pi
644644 −1.29527 −0.0510407
645645 −1.88956 2.58344i −0.0744014 0.101723i
646646 −2.47152 7.60655i −0.0972406 0.299276i
647647 3.20788i 0.126115i 0.998010 + 0.0630574i 0.0200851π0.0200851\pi
−0.998010 + 0.0630574i 0.979915π0.979915\pi
648648 1.07124 0.348066i 0.0420822 0.0136733i
649649 37.6200 28.9081i 1.47671 1.13474i
650650 −49.1002 35.1984i −1.92587 1.38059i
651651 0.0403904 + 0.0293453i 0.00158302 + 0.00115013i
652652 27.9745i 1.09557i
653653 −1.24524 + 1.71393i −0.0487300 + 0.0670711i −0.832687 0.553744i 0.813198π-0.813198\pi
0.783957 + 0.620816i 0.213198π0.213198\pi
654654 2.71483 8.35538i 0.106158 0.326721i
655655 38.3203 + 12.3164i 1.49730 + 0.481242i
656656 −18.3213 + 56.3872i −0.715327 + 2.20155i
657657 13.8727 + 4.50752i 0.541226 + 0.175855i
658658 −1.79515 + 0.583280i −0.0699823 + 0.0227386i
659659 11.7034 36.0195i 0.455901 1.40312i −0.414172 0.910198i 0.635929π-0.635929\pi
0.870074 0.492922i 0.164071π-0.164071\pi
660660 8.14261 6.29827i 0.316951 0.245160i
661661 −5.41391 16.6623i −0.210577 0.648088i −0.999438 0.0335171i 0.989329π-0.989329\pi
0.788862 0.614571i 0.210671π-0.210671\pi
662662 17.9973 + 24.7712i 0.699486 + 0.962760i
663663 −4.00388 + 5.51087i −0.155498 + 0.214025i
664664 −12.9032 + 9.37474i −0.500742 + 0.363810i
665665 −0.486436 + 1.51346i −0.0188632 + 0.0586894i
666666 −2.17768 6.70220i −0.0843833 0.259705i
667667 3.84971 + 1.25085i 0.149062 + 0.0484330i
668668 30.2765 + 9.83744i 1.17143 + 0.380622i
669669 2.07810 + 6.39573i 0.0803440 + 0.247273i
670670 27.9593 38.7413i 1.08016 1.49671i
671671 −45.8972 + 1.23356i −1.77184 + 0.0476210i
672672 −0.665996 0.916665i −0.0256914 0.0353611i
673673 24.7789 + 8.05116i 0.955158 + 0.310350i 0.744810 0.667277i 0.232540π-0.232540\pi
0.210348 + 0.977627i 0.432540π0.432540\pi
674674 11.0002 33.8552i 0.423713 1.30405i
675675 0.0318073 + 4.99990i 0.00122426 + 0.192446i
676676 −33.7896 + 24.5496i −1.29960 + 0.944216i
677677 −18.0136 + 24.7936i −0.692320 + 0.952896i 0.307679 + 0.951490i 0.400448π0.400448\pi
−0.999999 + 0.00140604i 0.999552π0.999552\pi
678678 9.45561 13.0145i 0.363140 0.499820i
679679 0.242253 + 0.745578i 0.00929682 + 0.0286127i
680680 1.52951 2.11933i 0.0586540 0.0812727i
681681 11.0018 + 7.99327i 0.421590 + 0.306303i
682682 −1.09377 1.42339i −0.0418826 0.0545045i
683683 −5.48949 + 7.55563i −0.210049 + 0.289108i −0.901023 0.433772i 0.857182π-0.857182\pi
0.690973 + 0.722880i 0.257182π0.257182\pi
684684 −4.70215 + 3.41631i −0.179791 + 0.130626i
685685 −23.1002 + 16.8958i −0.882614 + 0.645556i
686686 3.53241 2.56645i 0.134868 0.0979873i
687687 −6.88749 + 2.23788i −0.262774 + 0.0853805i
688688 6.60172 2.14503i 0.251688 0.0817785i
689689 −11.7216 + 8.51623i −0.446557 + 0.324443i
690690 −18.2581 + 13.3542i −0.695075 + 0.508388i
691691 −5.99100 + 4.35272i −0.227908 + 0.165585i −0.695879 0.718159i 0.744985π-0.744985\pi
0.467971 + 0.883744i 0.344985π0.344985\pi
692692 −12.4383 + 17.1198i −0.472833 + 0.650799i
693693 0.0151293 + 0.562917i 0.000574713 + 0.0213834i
694694 6.41543 + 4.66108i 0.243526 + 0.176932i
695695 −15.8418 + 21.9509i −0.600915 + 0.832646i
696696 0.256353 + 0.788975i 0.00971705 + 0.0299060i
697697 −7.45730 + 10.2641i −0.282465 + 0.388780i
698698 −26.4975 + 36.4706i −1.00294 + 1.38043i
699699 13.1998 9.59022i 0.499263 0.362736i
700700 1.11837 0.371261i 0.0422703 0.0140324i
701701 2.56749 7.90192i 0.0969727 0.298451i −0.890790 0.454415i 0.849848π-0.849848\pi
0.987763 + 0.155964i 0.0498483π0.0498483\pi
702702 11.4913 + 3.73374i 0.433710 + 0.140921i
703703 −9.42285 12.9694i −0.355389 0.489152i
704704 2.86720 + 8.07901i 0.108062 + 0.304489i
705705 −7.90333 + 10.9511i −0.297657 + 0.412442i
706706 7.23667 + 22.2722i 0.272356 + 0.838225i
707707 −0.0535872 0.0174115i −0.00201535 0.000654828i
708708 18.8844 + 6.13591i 0.709718 + 0.230602i
709709 10.2149 + 31.4382i 0.383628 + 1.18069i 0.937470 + 0.348065i 0.113161π0.113161\pi
−0.553842 + 0.832622i 0.686839π0.686839\pi
710710 2.77964 8.64834i 0.104318 0.324566i
711711 9.00287 6.54096i 0.337634 0.245305i
712712 −0.304389 + 0.418956i −0.0114075 + 0.0157010i
713713 0.949902 + 1.30743i 0.0355741 + 0.0489636i
714714 −0.100217 0.308435i −0.00375051 0.0115429i
715715 −48.6599 + 1.46271i −1.81978 + 0.0547023i
716716 −3.98682 + 12.2702i −0.148995 + 0.458558i
717717 1.50895 0.490288i 0.0563528 0.0183101i
718718 −55.2354 17.9471i −2.06137 0.669779i
719719 6.90112 21.2395i 0.257368 0.792098i −0.735986 0.676997i 0.763281π-0.763281\pi
0.993354 0.115101i 0.0367191π-0.0367191\pi
720720 −10.3235 3.31804i −0.384733 0.123656i
721721 0.368721 1.13481i 0.0137319 0.0422624i
722722 1.58714 2.18451i 0.0590673 0.0812991i
723723 21.0929i 0.784454i
724724 4.21714 + 3.06393i 0.156729 + 0.113870i
725725 −3.68247 + 0.0234263i −0.136763 + 0.000870032i
726726 5.21341 19.5647i 0.193488 0.726113i
727727 40.3074 13.0967i 1.49492 0.485729i 0.556388 0.830923i 0.312187π-0.312187\pi
0.938531 + 0.345194i 0.112187π0.112187\pi
728728 1.25536i 0.0465269i
729729 −0.309017 0.951057i −0.0114451 0.0352243i
730730 −35.4430 48.4582i −1.31180 1.79352i
731731 1.48539 0.0549390
732732 −11.2947 15.5459i −0.417465 0.574591i
733733 −12.6821 4.12068i −0.468425 0.152201i 0.0652872 0.997867i 0.479204π-0.479204\pi
−0.533713 + 0.845666i 0.679204π0.679204\pi
734734 −14.3528 10.4279i −0.529770 0.384901i
735735 4.76978 14.8403i 0.175936 0.547394i
736736 −11.3338 34.8819i −0.417770 1.28576i
737737 −1.03435 38.4853i −0.0381009 1.41762i
738738 21.4027 + 6.95416i 0.787844 + 0.255986i
739739 7.65463 23.5585i 0.281580 0.866614i −0.705823 0.708388i 0.749423π-0.749423\pi
0.987403 0.158226i 0.0505774π-0.0505774\pi
740740 −3.63612 + 11.3131i −0.133666 + 0.415880i
741741 27.4862 1.00973
742742 0.689801i 0.0253234i
743743 10.1482 + 13.9678i 0.372303 + 0.512431i 0.953525 0.301314i 0.0974253π-0.0974253\pi
−0.581222 + 0.813745i 0.697425π0.697425\pi
744744 −0.102347 + 0.314993i −0.00375224 + 0.0115482i
745745 −19.1641 + 26.5543i −0.702117 + 0.972874i
746746 56.7188 2.07662
747747 8.32300 + 11.4556i 0.304523 + 0.419139i
748748 0.128352 + 4.77559i 0.00469300 + 0.174613i
749749 0.126154 0.00460957
750750 11.9368 16.7637i 0.435870 0.612123i
751751 −1.49197 + 4.59180i −0.0544426 + 0.167557i −0.974581 0.224037i 0.928076π-0.928076\pi
0.920138 + 0.391594i 0.128076π0.128076\pi
752752 −17.2156 23.6952i −0.627787 0.864074i
753753 −7.86515 2.55554i −0.286622 0.0931292i
754754 −2.74993 + 8.46342i −0.100147 + 0.308219i
755755 −0.0795632 25.0139i −0.00289560 0.910348i
756756 −0.190666 + 0.138527i −0.00693445 + 0.00503817i
757757 27.7779 38.2329i 1.00960 1.38960i 0.0903603 0.995909i 0.471198π-0.471198\pi
0.919243 0.393691i 0.128802π-0.128802\pi
758758 −17.5830 + 24.2009i −0.638642 + 0.879016i
759759 −5.16499 + 17.4810i −0.187477 + 0.634521i
760760 −10.5461 + 0.0335445i −0.382546 + 0.00121679i
761761 3.00956 9.26247i 0.109096 0.335764i −0.881574 0.472047i 0.843515π-0.843515\pi
0.990670 + 0.136282i 0.0435154π0.0435154\pi
762762 −3.96522 + 5.45765i −0.143645 + 0.197710i
763763 0.810379i 0.0293377i
764764 28.5899 + 20.7718i 1.03435 + 0.751497i
765765 −1.88157 1.35792i −0.0680282 0.0490956i
766766 21.7190 0.784741
767767 −55.1938 75.9677i −1.99293 2.74304i
768768 12.3313 16.9726i 0.444969 0.612447i
769769 0.0643186 + 0.0467302i 0.00231939 + 0.00168513i 0.588944 0.808174i 0.299544π-0.299544\pi
−0.586625 + 0.809859i 0.699544π0.699544\pi
770770 1.30537 1.91517i 0.0470423 0.0690178i
771771 2.02006 1.46766i 0.0727507 0.0528565i
772772 10.9909i 0.395572i
773773 28.5769i 1.02784i −0.857839 0.513919i 0.828193π-0.828193\pi
0.857839 0.513919i 0.171807π-0.171807\pi
774774 −0.814181 2.50579i −0.0292651 0.0900688i
775775 −1.19492 0.856596i −0.0429226 0.0307698i
776776 −4.20745 + 3.05689i −0.151039 + 0.109736i
777777 −0.382083 0.525893i −0.0137072 0.0188663i
778778 −35.5552 + 11.5526i −1.27471 + 0.414180i
779779 51.1935 1.83420
780780 −12.0280 16.4449i −0.430673 0.588823i
781781 −2.44825 6.89852i −0.0876053 0.246848i
782782 10.4978i 0.375400i
783783 0.700461 0.227593i 0.0250324 0.00813353i
784784 27.3496 + 19.8707i 0.976773 + 0.709667i
785785 −20.9420 + 0.0666113i −0.747451 + 0.00237746i
786786 26.8056 + 19.4754i 0.956123 + 0.694664i
787787 16.5535 5.37857i 0.590070 0.191725i 0.00126306 0.999999i 0.499598π-0.499598\pi
0.588807 + 0.808274i 0.299598π0.299598\pi
788788 11.1885i 0.398573i
789789 4.98864 0.177600
790790 −45.8017 + 0.145684i −1.62955 + 0.00518322i
791791 0.458545 1.41126i 0.0163040 0.0501785i
792792 −3.52059 + 1.24944i −0.125099 + 0.0443970i
793793 90.8724i 3.22697i
794794 −10.9095 33.5759i −0.387163 1.19156i
795795 −2.91368 3.98363i −0.103338 0.141285i
796796 −17.0822 12.4110i −0.605464 0.439896i
797797 38.6615 + 12.5619i 1.36946 + 0.444965i 0.899191 0.437557i 0.144156π-0.144156\pi
0.470271 + 0.882522i 0.344156π0.344156\pi
798798 −0.769180 + 1.05868i −0.0272287 + 0.0374770i
799799 −1.93675 5.96070i −0.0685173 0.210874i
800800 19.7840 + 26.8693i 0.699471 + 0.949971i
801801 0.371954 + 0.270240i 0.0131423 + 0.00954847i
802802 8.51643 2.76716i 0.300726 0.0977116i
803803 −46.3956 13.7082i −1.63727 0.483752i
804804 13.0354 9.47075i 0.459722 0.334008i
805805 −1.22108 + 1.69197i −0.0430375 + 0.0596340i
806806 −2.87432 + 2.08832i −0.101244 + 0.0735578i
807807 −4.92690 + 1.60085i −0.173435 + 0.0563525i
808808 0.373792i 0.0131499i
809809 −13.6739 42.0839i −0.480748 1.47959i −0.838046 0.545600i 0.816302π-0.816302\pi
0.357297 0.933991i 0.383698π-0.383698\pi
810810 −1.25941 + 3.91845i −0.0442513 + 0.137680i
811811 48.8543 1.71551 0.857754 0.514061i 0.171859π-0.171859\pi
0.857754 + 0.514061i 0.171859π0.171859\pi
812812 −0.102026 0.140427i −0.00358041 0.00492802i
813813 −15.1542 4.92391i −0.531482 0.172689i
814814 7.81714 + 22.0266i 0.273991 + 0.772032i
815815 −36.5422 26.3723i −1.28002 0.923782i
816816 4.07120 2.95790i 0.142521 0.103547i
817817 −3.52298 4.84896i −0.123253 0.169644i
818818 43.7639 14.2198i 1.53017 0.497182i
819819 1.11453 0.0389447
820820 −22.4024 30.6290i −0.782327 1.06961i
821821 8.61385 + 6.25833i 0.300626 + 0.218417i 0.727864 0.685722i 0.240513π-0.240513\pi
−0.427238 + 0.904139i 0.640513π0.640513\pi
822822 −22.4059 + 7.28013i −0.781497 + 0.253924i
823823 25.4043 + 8.25436i 0.885538 + 0.287729i 0.716255 0.697839i 0.245855π-0.245855\pi
0.169283 + 0.985567i 0.445855π0.445855\pi
824824 7.91573 0.275757
825825 −0.550982 16.5740i −0.0191827 0.577032i
826826 4.47060 0.155552
827827 32.5497 + 10.5761i 1.13187 + 0.367765i 0.814285 0.580466i 0.197129π-0.197129\pi
0.317581 + 0.948231i 0.397129π0.397129\pi
828828 −7.25541 + 2.35742i −0.252143 + 0.0819262i
829829 −19.8391 14.4139i −0.689039 0.500616i 0.187305 0.982302i 0.440025π-0.440025\pi
−0.876344 + 0.481685i 0.840025π0.840025\pi
830830 −0.185375 58.2801i −0.00643446 2.02293i
831831 −22.1718 −0.769132
832832 16.1367 5.24312i 0.559438 0.181772i
833833 4.25208 + 5.85249i 0.147326 + 0.202777i
834834 −18.0278 + 13.0980i −0.624253 + 0.453546i
835835 41.3928 30.2752i 1.43246 1.04772i
836836 15.2852 11.7455i 0.528651 0.406228i
837837 0.279655 + 0.0908653i 0.00966627 + 0.00314076i
838838 −20.8356 28.6778i −0.719755 0.990658i
839839 50.0182 1.72682 0.863410 0.504503i 0.168324π-0.168324\pi
0.863410 + 0.504503i 0.168324π0.168324\pi
840840 −0.427628 + 0.00136018i −0.0147546 + 4.69308e-5i
841841 −8.79387 27.0647i −0.303237 0.933267i
842842 40.1064i 1.38216i
843843 22.6491 7.35915i 0.780078 0.253463i
844844 12.1264 8.81036i 0.417408 0.303265i
845845 0.214008 + 67.2819i 0.00736208 + 2.31457i
846846 −8.99390 + 6.53445i −0.309217 + 0.224659i
847847 −0.100320 1.86496i −0.00344704 0.0640808i
848848 10.1798 3.30761i 0.349575 0.113584i
849849 0.685738 + 0.498218i 0.0235345 + 0.0170988i
850850 3.00897 + 9.06404i 0.103207 + 0.310894i
851851 −6.50223 20.0118i −0.222893 0.685996i
852852 1.80073 2.47849i 0.0616920 0.0849117i
853853 −13.9458 4.53125i −0.477494 0.155147i 0.0603749 0.998176i 0.480770π-0.480770\pi
−0.537869 + 0.843029i 0.680770π0.680770\pi
854854 −3.50013 2.54299i −0.119772 0.0870195i
855855 0.0297812 + 9.36292i 0.00101850 + 0.320205i
856856 0.258618 + 0.795944i 0.00883937 + 0.0272048i
857857 33.8924i 1.15774i 0.815419 + 0.578872i 0.196507π0.196507\pi
−0.815419 + 0.578872i 0.803493π0.803493\pi
858858 −38.4312 11.3550i −1.31202 0.387653i
859859 8.55901 26.3419i 0.292030 0.898775i −0.692173 0.721731i 0.743347π-0.743347\pi
0.984203 0.177044i 0.0566534π-0.0566534\pi
860860 −1.35946 + 4.22971i −0.0463571 + 0.144232i
861861 2.07582 0.0707439
862862 31.3523i 1.06786i
863863 −24.9315 + 8.10073i −0.848678 + 0.275752i −0.700892 0.713267i 0.747215π-0.747215\pi
−0.147786 + 0.989019i 0.547215π0.547215\pi
864864 −5.39891 3.92254i −0.183675 0.133448i
865865 10.6372 + 32.3871i 0.361676 + 1.10119i
866866 23.0646 + 16.7574i 0.783767 + 0.569440i
867867 −15.1438 + 4.92053i −0.514311 + 0.167110i
868868 0.0692996i 0.00235218i
869869 −29.2655 + 22.4883i −0.992764 + 0.762864i
870870 −2.88597 0.927569i −0.0978434 0.0314475i
871871 −76.1975 −2.58185
872872 5.11292 1.66129i 0.173145 0.0562583i
873873 2.71394 + 3.73542i 0.0918531 + 0.126425i
874874 −34.2694 + 24.8982i −1.15918 + 0.842194i
875875 0.569346 1.81088i 0.0192474 0.0612190i
876876 −6.25674 19.2563i −0.211396 0.650609i
877877 18.0791i 0.610488i −0.952274 0.305244i 0.901262π-0.901262\pi
0.952274 0.305244i 0.0987380π-0.0987380\pi
878878 0.437066i 0.0147503i
879879 −6.96513 + 5.06046i −0.234928 + 0.170685i
880880 34.5224 + 10.0808i 1.16375 + 0.339824i
881881 −1.18473 0.860754i −0.0399144 0.0289995i 0.567649 0.823271i 0.307853π-0.307853\pi
−0.607564 + 0.794271i 0.707853π0.707853\pi
882882 7.54224 10.3810i 0.253961 0.349547i
883883 22.7800 + 31.3540i 0.766609 + 1.05515i 0.996635 + 0.0819624i 0.0261188π0.0261188\pi
−0.230026 + 0.973184i 0.573881π0.573881\pi
884884 9.45526 0.318015
885885 25.8179 18.8836i 0.867860 0.634765i
886886 25.8291 + 18.7659i 0.867744 + 0.630453i
887887 35.4553i 1.19047i 0.803551 + 0.595235i 0.202941π0.202941\pi
−0.803551 + 0.595235i 0.797059π0.797059\pi
888888 2.53474 3.48877i 0.0850602 0.117075i
889889 −0.192291 + 0.591811i −0.00644924 + 0.0198487i
890890 −0.590478 1.79783i −0.0197929 0.0602632i
891891 1.10927 + 3.12562i 0.0371619 + 0.104712i
892892 5.48673 7.55183i 0.183709 0.252854i
893893 −14.8649 + 20.4597i −0.497434 + 0.684659i
894894 −21.8085 + 15.8448i −0.729385 + 0.529929i
895895 12.2697 + 16.7753i 0.410129 + 0.560735i
896896 0.450647 1.38695i 0.0150551 0.0463347i
897897 34.3113 + 11.1484i 1.14562 + 0.372235i
898898 41.7131 + 57.4132i 1.39199 + 1.91590i
899899 −0.0669230 + 0.205968i −0.00223201 + 0.00686941i
900900 5.58879 4.11507i 0.186293 0.137169i
901901 2.29045 0.0763058
902902 −71.5788 21.1489i −2.38331 0.704180i
903903 −0.142852 0.196619i −0.00475381 0.00654306i
904904 9.84405 0.327408
905905 7.97792 2.62027i 0.265195 0.0871006i
906906 6.36292 19.5831i 0.211394 0.650604i
907907 9.25599 + 12.7398i 0.307340 + 0.423018i 0.934549 0.355833i 0.115803π-0.115803\pi
−0.627209 + 0.778851i 0.715803π0.715803\pi
908908 18.8763i 0.626432i
909909 −0.331856 −0.0110070
910910 −3.71971 2.68449i −0.123307 0.0889901i
911911 −8.97759 + 27.6302i −0.297441 + 0.915429i 0.684950 + 0.728590i 0.259824π0.259824\pi
−0.982391 + 0.186838i 0.940176π0.940176\pi
912912 −19.3118 6.27479i −0.639478 0.207779i
913913 −28.6151 37.2387i −0.947021 1.23242i
914914 −5.02297 15.4591i −0.166145 0.511342i
915915 −30.9549 + 0.0984600i −1.02334 + 0.00325499i
916916 8.13248 + 5.90860i 0.268705 + 0.195226i
917917 2.90671 + 0.944448i 0.0959881 + 0.0311884i
918918 −1.12272 1.54529i −0.0370553 0.0510022i
919919 5.35833 0.176755 0.0883774 0.996087i 0.471832π-0.471832\pi
0.0883774 + 0.996087i 0.471832π0.471832\pi
920920 −13.1784 4.23562i −0.434478 0.139644i
921921 −6.70416 20.6333i −0.220909 0.679889i
922922 28.1064i 0.925636i
923923 −13.7788 + 4.47700i −0.453534 + 0.147362i
924924 0.619795 0.476265i 0.0203898 0.0156680i
925925 11.3501 + 15.4149i 0.373190 + 0.506840i
926926 −9.89472 7.18893i −0.325161 0.236243i
927927 7.02767i 0.230819i
928928 2.88898 3.97634i 0.0948355 0.130530i
929929 −10.8562 + 33.4118i −0.356179 + 1.09621i 0.599144 + 0.800642i 0.295508π0.295508\pi
−0.955323 + 0.295565i 0.904492π0.904492\pi
930930 −0.714480 0.976849i −0.0234287 0.0320321i
931931 9.02021 27.7614i 0.295625 0.909842i
932932 −21.5391 6.99847i −0.705536 0.229243i
933933 6.81924 2.21570i 0.223252 0.0725389i
934934 −11.5106 + 35.4261i −0.376639 + 1.15918i
935935 6.35920 + 4.33441i 0.207968 + 0.141750i
936936 2.28480 + 7.03188i 0.0746809 + 0.229844i
937937 −2.57505 3.54425i −0.0841231 0.115785i 0.764881 0.644171i 0.222798π-0.222798\pi
−0.849004 + 0.528386i 0.822798π0.822798\pi
938938 2.13233 2.93490i 0.0696230 0.0958278i
939939 −10.9456 + 7.95243i −0.357196 + 0.259518i
940940 18.7460 0.0596264i 0.611426 0.00194480i
941941 3.53728 + 10.8866i 0.115312 + 0.354894i 0.992012 0.126144i 0.0402601π-0.0402601\pi
−0.876700 + 0.481038i 0.840260π0.840260\pi
942942 −16.3952 5.32712i −0.534185 0.173567i
943943 63.9053 + 20.7641i 2.08104 + 0.676172i
944944 21.4366 + 65.9751i 0.697703 + 2.14731i
945945 0.00120759 + 0.379653i 3.92828e−5 + 0.0123501i
946946 2.92264 + 8.23522i 0.0950233 + 0.267750i
947947 0.266870 + 0.367315i 0.00867211 + 0.0119361i 0.813331 0.581801i 0.197652π-0.197652\pi
−0.804659 + 0.593737i 0.797652π0.797652\pi
948948 −14.6906 4.77327i −0.477129 0.155029i
949949 −29.5885 + 91.0641i −0.960484 + 2.95607i
950950 22.4525 31.3203i 0.728456 1.01617i
951951 −14.7092 + 10.6868i −0.476977 + 0.346544i
952952 0.116649 0.160553i 0.00378060 0.00520355i
953953 4.89019 6.73076i 0.158409 0.218031i −0.722434 0.691440i 0.756977π-0.756977\pi
0.880843 + 0.473409i 0.156977π0.156977\pi
954954 −1.25546 3.86390i −0.0406469 0.125098i
955955 54.0860 17.7640i 1.75018 0.574829i
956956 −1.78171 1.29449i −0.0576247 0.0418668i
957957 −2.30205 + 0.816986i −0.0744146 + 0.0264094i
958958 27.3277 37.6134i 0.882919 1.21523i
959959 −1.75810 + 1.27733i −0.0567719 + 0.0412472i
960960 1.80350 + 5.49112i 0.0582079 + 0.177225i
961961 25.0096 18.1705i 0.806761 0.586146i
962962 43.9950 14.2948i 1.41846 0.460884i
963963 0.706648 0.229604i 0.0227714 0.00739888i
964964 23.6867 17.2094i 0.762898 0.554278i
965965 −14.3571 10.3614i −0.462170 0.333546i
966966 −1.38958 + 1.00959i −0.0447089 + 0.0324829i
967967 −29.3942 + 40.4576i −0.945253 + 1.30103i 0.00835079 + 0.999965i 0.497342π0.497342\pi
−0.953604 + 0.301064i 0.902658π0.902658\pi
968968 11.5609 4.45615i 0.371583 0.143226i
969969 −3.51530 2.55402i −0.112928 0.0820469i
970970 −0.0604466 19.0038i −0.00194082 0.610176i
971971 1.13395 + 3.48995i 0.0363903 + 0.111998i 0.967602 0.252482i 0.0812468π-0.0812468\pi
−0.931211 + 0.364480i 0.881247π0.881247\pi
972972 −0.815886 + 1.12297i −0.0261696 + 0.0360193i
973973 −1.20818 + 1.66292i −0.0387326 + 0.0533108i
974974 18.0472 13.1121i 0.578270 0.420138i
975975 −32.8206 + 0.208791i −1.05110 + 0.00668667i
976976 20.7452 63.8471i 0.664037 2.04369i
977977 29.7646 + 9.67111i 0.952254 + 0.309406i 0.743631 0.668590i 0.233102π-0.233102\pi
0.208623 + 0.977996i 0.433102π0.433102\pi
978978 −21.8045 30.0114i −0.697232 0.959658i
979979 −1.25727 0.862818i −0.0401824 0.0275758i
980980 −20.5569 + 6.75169i −0.656665 + 0.215675i
981981 −1.47491 4.53931i −0.0470903 0.144929i
982982 29.8494 + 9.69865i 0.952532 + 0.309496i
983983 −3.12263 1.01460i −0.0995964 0.0323608i 0.258795 0.965932i 0.416675π-0.416675\pi
−0.358391 + 0.933571i 0.616675π0.616675\pi
984984 4.25547 + 13.0970i 0.135659 + 0.417517i
985985 14.6151 + 10.5477i 0.465677 + 0.336076i
986986 1.13812 0.826893i 0.0362451 0.0263336i
987987 −0.602750 + 0.829614i −0.0191857 + 0.0264069i
988988 −22.4256 30.8662i −0.713453 0.981984i
989989 −2.43103 7.48193i −0.0773021 0.237911i
990990 3.82634 13.1035i 0.121609 0.416458i
991991 −12.6780 + 39.0188i −0.402729 + 1.23947i 0.520047 + 0.854138i 0.325914π0.325914\pi
−0.922776 + 0.385336i 0.874086π0.874086\pi
992992 1.86625 0.606382i 0.0592536 0.0192527i
993993 15.8205 + 5.14039i 0.502048 + 0.163125i
994994 0.213148 0.656003i 0.00676065 0.0208072i
995995 −32.3159 + 10.6138i −1.02448 + 0.336481i
996996 6.07371 18.6930i 0.192453 0.592309i
997997 −12.8104 + 17.6320i −0.405709 + 0.558411i −0.962165 0.272466i 0.912161π-0.912161\pi
0.556456 + 0.830877i 0.312161π0.312161\pi
998998 49.2184i 1.55798i
999999 −3.09737 2.25037i −0.0979963 0.0711985i
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 825.2.cb.a.169.14 yes 240
11.3 even 5 825.2.by.a.619.14 yes 240
25.4 even 10 825.2.by.a.4.14 240
275.179 even 10 inner 825.2.cb.a.454.14 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
825.2.by.a.4.14 240 25.4 even 10
825.2.by.a.619.14 yes 240 11.3 even 5
825.2.cb.a.169.14 yes 240 1.1 even 1 trivial
825.2.cb.a.454.14 yes 240 275.179 even 10 inner