Properties

Label 220.2.l.c.23.5
Level 220220
Weight 22
Character 220.23
Analytic conductor 1.7571.757
Analytic rank 00
Dimension 2828
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [220,2,Mod(23,220)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(220, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("220.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 220=22511 220 = 2^{2} \cdot 5 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 220.l (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.756708844471.75670884447
Analytic rank: 00
Dimension: 2828
Relative dimension: 1414 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 23.5
Character χ\chi == 220.23
Dual form 220.2.l.c.67.5

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.892874+1.09671i)q2+(1.635231.63523i)q3+(0.4055511.95845i)q4+(2.22762+0.194242i)q5+(0.333320+3.25343i)q6+(2.273232.27323i)q7+(2.50996+1.30388i)q82.34794iq9+(2.20201+2.26962i)q101.00000iq11+(3.865682.53934i)q12+(0.7239930.723993i)q13+(4.522780.463369i)q14+(3.960293.32503i)q15+(3.67106+1.58850i)q16+(0.922419+0.922419i)q17+(2.57501+2.09641i)q18+1.41633q19+(0.5229994.44145i)q207.43450q21+(1.09671+0.892874i)q22+(3.571163.57116i)q23+(6.236491.97222i)q24+(4.92454+0.865394i)q25+(1.440450.147577i)q26+(1.06627+1.06627i)q27+(3.53010+5.37392i)q28+9.64395iq29+(0.110556+7.31213i)q30+7.64876iq31+(1.535665.44442i)q32+(1.635231.63523i)q33+(0.1880231.83523i)q34+(4.622325.50544i)q35+(4.59832+0.952210i)q36+(1.95305+1.95305i)q37+(1.26460+1.55330i)q382.36779q39+(5.33796+3.39208i)q40+8.11796q41+(6.638078.15350i)q42+(3.57789+3.57789i)q43+(1.95845+0.405551i)q44+(0.4560695.23031i)q45+(0.727934+7.10512i)q46+(8.619198.61919i)q47+(3.40545+8.60058i)q48+3.33515iq49+(5.34608+4.62811i)q50+3.01673iq51+(1.12429+1.71152i)q52+(7.927647.92764i)q53+(2.12143+0.217345i)q54+(0.1942422.22762i)q55+(2.741718.66973i)q56+(2.316012.31601i)q57+(10.57668.61084i)q582.51199q59+(8.118006.40756i)q603.54775q61+(8.388486.82938i)q62+(5.33741+5.33741i)q63+(4.59981+6.54536i)q64+(1.472151.75341i)q65+(3.253430.333320i)q66+(7.01754+7.01754i)q67+(2.18060+1.43242i)q6811.6793iq69+(10.16500.153691i)q70+14.9871iq71+(3.061435.89324i)q72+(1.98983+1.98983i)q73+(0.3981043.88576i)q74+(9.467866.63763i)q75+(0.5743932.77380i)q76+(2.27323+2.27323i)q77+(2.114142.59678i)q7814.1444q79+(8.48626+2.82550i)q80+10.5310q81+(7.24831+8.90305i)q82+(3.375073.37507i)q83+(3.01507+14.5601i)q84+(2.23397+1.87562i)q85+(0.7293067.11851i)q86+(15.7701+15.7701i)q87+(1.303882.50996i)q88+4.70719iq89+(5.32892+5.17018i)q90+3.29161iq91+(8.442225.54565i)q92+(12.5075+12.5075i)q93+(17.14861.75691i)q94+(3.15503+0.275110i)q95+(6.3917211.4140i)q96+(0.3096890.309689i)q97+(3.657692.97787i)q982.34794q99+O(q100)q+(-0.892874 + 1.09671i) q^{2} +(1.63523 - 1.63523i) q^{3} +(-0.405551 - 1.95845i) q^{4} +(2.22762 + 0.194242i) q^{5} +(0.333320 + 3.25343i) q^{6} +(-2.27323 - 2.27323i) q^{7} +(2.50996 + 1.30388i) q^{8} -2.34794i q^{9} +(-2.20201 + 2.26962i) q^{10} -1.00000i q^{11} +(-3.86568 - 2.53934i) q^{12} +(-0.723993 - 0.723993i) q^{13} +(4.52278 - 0.463369i) q^{14} +(3.96029 - 3.32503i) q^{15} +(-3.67106 + 1.58850i) q^{16} +(-0.922419 + 0.922419i) q^{17} +(2.57501 + 2.09641i) q^{18} +1.41633 q^{19} +(-0.522999 - 4.44145i) q^{20} -7.43450 q^{21} +(1.09671 + 0.892874i) q^{22} +(3.57116 - 3.57116i) q^{23} +(6.23649 - 1.97222i) q^{24} +(4.92454 + 0.865394i) q^{25} +(1.44045 - 0.147577i) q^{26} +(1.06627 + 1.06627i) q^{27} +(-3.53010 + 5.37392i) q^{28} +9.64395i q^{29} +(0.110556 + 7.31213i) q^{30} +7.64876i q^{31} +(1.53566 - 5.44442i) q^{32} +(-1.63523 - 1.63523i) q^{33} +(-0.188023 - 1.83523i) q^{34} +(-4.62232 - 5.50544i) q^{35} +(-4.59832 + 0.952210i) q^{36} +(-1.95305 + 1.95305i) q^{37} +(-1.26460 + 1.55330i) q^{38} -2.36779 q^{39} +(5.33796 + 3.39208i) q^{40} +8.11796 q^{41} +(6.63807 - 8.15350i) q^{42} +(-3.57789 + 3.57789i) q^{43} +(-1.95845 + 0.405551i) q^{44} +(0.456069 - 5.23031i) q^{45} +(0.727934 + 7.10512i) q^{46} +(-8.61919 - 8.61919i) q^{47} +(-3.40545 + 8.60058i) q^{48} +3.33515i q^{49} +(-5.34608 + 4.62811i) q^{50} +3.01673i q^{51} +(-1.12429 + 1.71152i) q^{52} +(-7.92764 - 7.92764i) q^{53} +(-2.12143 + 0.217345i) q^{54} +(0.194242 - 2.22762i) q^{55} +(-2.74171 - 8.66973i) q^{56} +(2.31601 - 2.31601i) q^{57} +(-10.5766 - 8.61084i) q^{58} -2.51199 q^{59} +(-8.11800 - 6.40756i) q^{60} -3.54775 q^{61} +(-8.38848 - 6.82938i) q^{62} +(-5.33741 + 5.33741i) q^{63} +(4.59981 + 6.54536i) q^{64} +(-1.47215 - 1.75341i) q^{65} +(3.25343 - 0.333320i) q^{66} +(7.01754 + 7.01754i) q^{67} +(2.18060 + 1.43242i) q^{68} -11.6793i q^{69} +(10.1650 - 0.153691i) q^{70} +14.9871i q^{71} +(3.06143 - 5.89324i) q^{72} +(1.98983 + 1.98983i) q^{73} +(-0.398104 - 3.88576i) q^{74} +(9.46786 - 6.63763i) q^{75} +(-0.574393 - 2.77380i) q^{76} +(-2.27323 + 2.27323i) q^{77} +(2.11414 - 2.59678i) q^{78} -14.1444 q^{79} +(-8.48626 + 2.82550i) q^{80} +10.5310 q^{81} +(-7.24831 + 8.90305i) q^{82} +(3.37507 - 3.37507i) q^{83} +(3.01507 + 14.5601i) q^{84} +(-2.23397 + 1.87562i) q^{85} +(-0.729306 - 7.11851i) q^{86} +(15.7701 + 15.7701i) q^{87} +(1.30388 - 2.50996i) q^{88} +4.70719i q^{89} +(5.32892 + 5.17018i) q^{90} +3.29161i q^{91} +(-8.44222 - 5.54565i) q^{92} +(12.5075 + 12.5075i) q^{93} +(17.1486 - 1.75691i) q^{94} +(3.15503 + 0.275110i) q^{95} +(-6.39172 - 11.4140i) q^{96} +(0.309689 - 0.309689i) q^{97} +(-3.65769 - 2.97787i) q^{98} -2.34794 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q2q24q3+4q4+2q512q62q714q8+6q108q12+6q1320q14+8q15+8q1614q17+34q18+4q19+8q2016q21+20q99+O(q100) 28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/220Z)×\left(\mathbb{Z}/220\mathbb{Z}\right)^\times.

nn 101101 111111 177177
χ(n)\chi(n) 11 1-1 e(34)e\left(\frac{3}{4}\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 −0.892874 + 1.09671i −0.631357 + 0.775492i
33 1.63523 1.63523i 0.944099 0.944099i −0.0544190 0.998518i 0.517331π-0.517331\pi
0.998518 + 0.0544190i 0.0173307π0.0173307\pi
44 −0.405551 1.95845i −0.202776 0.979225i
55 2.22762 + 0.194242i 0.996220 + 0.0868678i
66 0.333320 + 3.25343i 0.136077 + 1.32821i
77 −2.27323 2.27323i −0.859200 0.859200i 0.132044 0.991244i 0.457846π-0.457846\pi
−0.991244 + 0.132044i 0.957846π0.957846\pi
88 2.50996 + 1.30388i 0.887405 + 0.460990i
99 2.34794i 0.782647i
1010 −2.20201 + 2.26962i −0.696336 + 0.717716i
1111 1.00000i 0.301511i
1212 −3.86568 2.53934i −1.11593 0.733045i
1313 −0.723993 0.723993i −0.200800 0.200800i 0.599543 0.800343i 0.295349π-0.295349\pi
−0.800343 + 0.599543i 0.795349π0.795349\pi
1414 4.52278 0.463369i 1.20877 0.123840i
1515 3.96029 3.32503i 1.02254 0.858519i
1616 −3.67106 + 1.58850i −0.917764 + 0.397126i
1717 −0.922419 + 0.922419i −0.223720 + 0.223720i −0.810063 0.586343i 0.800567π-0.800567\pi
0.586343 + 0.810063i 0.300567π0.300567\pi
1818 2.57501 + 2.09641i 0.606936 + 0.494130i
1919 1.41633 0.324927 0.162464 0.986715i 0.448056π-0.448056\pi
0.162464 + 0.986715i 0.448056π0.448056\pi
2020 −0.522999 4.44145i −0.116946 0.993138i
2121 −7.43450 −1.62234
2222 1.09671 + 0.892874i 0.233820 + 0.190361i
2323 3.57116 3.57116i 0.744638 0.744638i −0.228829 0.973467i 0.573490π-0.573490\pi
0.973467 + 0.228829i 0.0734896π0.0734896\pi
2424 6.23649 1.97222i 1.27302 0.402578i
2525 4.92454 + 0.865394i 0.984908 + 0.173079i
2626 1.44045 0.147577i 0.282495 0.0289422i
2727 1.06627 + 1.06627i 0.205203 + 0.205203i
2828 −3.53010 + 5.37392i −0.667126 + 1.01558i
2929 9.64395i 1.79084i 0.445225 + 0.895419i 0.353124π0.353124\pi
−0.445225 + 0.895419i 0.646876π0.646876\pi
3030 0.110556 + 7.31213i 0.0201847 + 1.33501i
3131 7.64876i 1.37376i 0.726772 + 0.686879i 0.241020π0.241020\pi
−0.726772 + 0.686879i 0.758980π0.758980\pi
3232 1.53566 5.44442i 0.271469 0.962447i
3333 −1.63523 1.63523i −0.284657 0.284657i
3434 −0.188023 1.83523i −0.0322457 0.314740i
3535 −4.62232 5.50544i −0.781315 0.930589i
3636 −4.59832 + 0.952210i −0.766387 + 0.158702i
3737 −1.95305 + 1.95305i −0.321080 + 0.321080i −0.849181 0.528102i 0.822904π-0.822904\pi
0.528102 + 0.849181i 0.322904π0.322904\pi
3838 −1.26460 + 1.55330i −0.205145 + 0.251979i
3939 −2.36779 −0.379149
4040 5.33796 + 3.39208i 0.844006 + 0.536335i
4141 8.11796 1.26781 0.633906 0.773410i 0.281451π-0.281451\pi
0.633906 + 0.773410i 0.281451π0.281451\pi
4242 6.63807 8.15350i 1.02428 1.25811i
4343 −3.57789 + 3.57789i −0.545623 + 0.545623i −0.925172 0.379549i 0.876079π-0.876079\pi
0.379549 + 0.925172i 0.376079π0.376079\pi
4444 −1.95845 + 0.405551i −0.295248 + 0.0611392i
4545 0.456069 5.23031i 0.0679868 0.779688i
4646 0.727934 + 7.10512i 0.107328 + 1.04759i
4747 −8.61919 8.61919i −1.25724 1.25724i −0.952406 0.304833i 0.901399π-0.901399\pi
−0.304833 0.952406i 0.598601π-0.598601\pi
4848 −3.40545 + 8.60058i −0.491534 + 1.24139i
4949 3.33515i 0.476450i
5050 −5.34608 + 4.62811i −0.756050 + 0.654514i
5151 3.01673i 0.422427i
5252 −1.12429 + 1.71152i −0.155911 + 0.237345i
5353 −7.92764 7.92764i −1.08894 1.08894i −0.995637 0.0933073i 0.970256π-0.970256\pi
−0.0933073 0.995637i 0.529744π-0.529744\pi
5454 −2.12143 + 0.217345i −0.288690 + 0.0295769i
5555 0.194242 2.22762i 0.0261916 0.300372i
5656 −2.74171 8.66973i −0.366376 1.15854i
5757 2.31601 2.31601i 0.306764 0.306764i
5858 −10.5766 8.61084i −1.38878 1.13066i
5959 −2.51199 −0.327034 −0.163517 0.986541i 0.552284π-0.552284\pi
−0.163517 + 0.986541i 0.552284π0.552284\pi
6060 −8.11800 6.40756i −1.04803 0.827212i
6161 −3.54775 −0.454243 −0.227122 0.973866i 0.572931π-0.572931\pi
−0.227122 + 0.973866i 0.572931π0.572931\pi
6262 −8.38848 6.82938i −1.06534 0.867332i
6363 −5.33741 + 5.33741i −0.672450 + 0.672450i
6464 4.59981 + 6.54536i 0.574976 + 0.818170i
6565 −1.47215 1.75341i −0.182598 0.217484i
6666 3.25343 0.333320i 0.400469 0.0410289i
6767 7.01754 + 7.01754i 0.857329 + 0.857329i 0.991023 0.133693i 0.0426837π-0.0426837\pi
−0.133693 + 0.991023i 0.542684π0.542684\pi
6868 2.18060 + 1.43242i 0.264437 + 0.173707i
6969 11.6793i 1.40602i
7070 10.1650 0.153691i 1.21495 0.0183696i
7171 14.9871i 1.77864i 0.457284 + 0.889321i 0.348822π0.348822\pi
−0.457284 + 0.889321i 0.651178π0.651178\pi
7272 3.06143 5.89324i 0.360792 0.694525i
7373 1.98983 + 1.98983i 0.232891 + 0.232891i 0.813899 0.581007i 0.197341π-0.197341\pi
−0.581007 + 0.813899i 0.697341π0.697341\pi
7474 −0.398104 3.88576i −0.0462787 0.451711i
7575 9.46786 6.63763i 1.09325 0.766447i
7676 −0.574393 2.77380i −0.0658873 0.318177i
7777 −2.27323 + 2.27323i −0.259059 + 0.259059i
7878 2.11414 2.59678i 0.239379 0.294027i
7979 −14.1444 −1.59136 −0.795682 0.605714i 0.792888π-0.792888\pi
−0.795682 + 0.605714i 0.792888π0.792888\pi
8080 −8.48626 + 2.82550i −0.948792 + 0.315901i
8181 10.5310 1.17011
8282 −7.24831 + 8.90305i −0.800442 + 0.983178i
8383 3.37507 3.37507i 0.370462 0.370462i −0.497183 0.867645i 0.665632π-0.665632\pi
0.867645 + 0.497183i 0.165632π0.165632\pi
8484 3.01507 + 14.5601i 0.328971 + 1.58864i
8585 −2.23397 + 1.87562i −0.242308 + 0.203440i
8686 −0.729306 7.11851i −0.0786431 0.767609i
8787 15.7701 + 15.7701i 1.69073 + 1.69073i
8888 1.30388 2.50996i 0.138994 0.267563i
8989 4.70719i 0.498961i 0.968380 + 0.249481i 0.0802599π0.0802599\pi
−0.968380 + 0.249481i 0.919740π0.919740\pi
9090 5.32892 + 5.17018i 0.561718 + 0.544985i
9191 3.29161i 0.345054i
9292 −8.44222 5.54565i −0.880162 0.578174i
9393 12.5075 + 12.5075i 1.29696 + 1.29696i
9494 17.1486 1.75691i 1.76875 0.181212i
9595 3.15503 + 0.275110i 0.323699 + 0.0282257i
9696 −6.39172 11.4140i −0.652352 1.16494i
9797 0.309689 0.309689i 0.0314442 0.0314442i −0.691210 0.722654i 0.742922π-0.742922\pi
0.722654 + 0.691210i 0.242922π0.242922\pi
9898 −3.65769 2.97787i −0.369483 0.300810i
9999 −2.34794 −0.235977
100100 −0.302323 9.99543i −0.0302323 0.999543i
101101 8.34044 0.829905 0.414952 0.909843i 0.363798π-0.363798\pi
0.414952 + 0.909843i 0.363798π0.363798\pi
102102 −3.30848 2.69356i −0.327589 0.266702i
103103 −9.04433 + 9.04433i −0.891164 + 0.891164i −0.994633 0.103469i 0.967006π-0.967006\pi
0.103469 + 0.994633i 0.467006π0.467006\pi
104104 −0.873196 2.76119i −0.0856240 0.270757i
105105 −16.5612 1.44409i −1.61621 0.140929i
106106 15.7727 1.61595i 1.53198 0.156955i
107107 −0.464738 0.464738i −0.0449280 0.0449280i 0.684286 0.729214i 0.260114π-0.260114\pi
−0.729214 + 0.684286i 0.760114π0.760114\pi
108108 1.65580 2.52066i 0.159330 0.242550i
109109 6.78445i 0.649832i −0.945743 0.324916i 0.894664π-0.894664\pi
0.945743 0.324916i 0.105336π-0.105336\pi
110110 2.26962 + 2.20201i 0.216399 + 0.209953i
111111 6.38737i 0.606262i
112112 11.9562 + 4.73412i 1.12975 + 0.447332i
113113 −3.36794 3.36794i −0.316829 0.316829i 0.530719 0.847548i 0.321922π-0.321922\pi
−0.847548 + 0.530719i 0.821922π0.821922\pi
114114 0.472090 + 4.60791i 0.0442152 + 0.431570i
115115 8.64883 7.26149i 0.806508 0.677138i
116116 18.8872 3.91112i 1.75363 0.363138i
117117 −1.69989 + 1.69989i −0.157155 + 0.157155i
118118 2.24290 2.75493i 0.206475 0.253612i
119119 4.19374 0.384440
120120 14.2756 3.18196i 1.30318 0.290472i
121121 −1.00000 −0.0909091
122122 3.16770 3.89086i 0.286790 0.352262i
123123 13.2747 13.2747i 1.19694 1.19694i
124124 14.9797 3.10197i 1.34522 0.278565i
125125 10.8019 + 2.88432i 0.966150 + 0.257981i
126126 −1.08796 10.6192i −0.0969233 0.946036i
127127 −5.74732 5.74732i −0.509992 0.509992i 0.404532 0.914524i 0.367434π-0.367434\pi
−0.914524 + 0.404532i 0.867434π0.867434\pi
128128 −11.2854 0.799523i −0.997500 0.0706685i
129129 11.7013i 1.03024i
130130 3.23743 0.0489485i 0.283941 0.00429307i
131131 18.0937i 1.58085i −0.612556 0.790427i 0.709859π-0.709859\pi
0.612556 0.790427i 0.290141π-0.290141\pi
132132 −2.53934 + 3.86568i −0.221022 + 0.336464i
133133 −3.21963 3.21963i −0.279178 0.279178i
134134 −13.9620 + 1.43044i −1.20613 + 0.123571i
135135 2.16812 + 2.58235i 0.186602 + 0.222253i
136136 −3.51796 + 1.11252i −0.301662 + 0.0953974i
137137 6.35346 6.35346i 0.542812 0.542812i −0.381540 0.924352i 0.624606π-0.624606\pi
0.924352 + 0.381540i 0.124606π0.124606\pi
138138 12.8088 + 10.4282i 1.09036 + 0.887704i
139139 −0.935850 −0.0793778 −0.0396889 0.999212i 0.512637π-0.512637\pi
−0.0396889 + 0.999212i 0.512637π0.512637\pi
140140 −8.90754 + 11.2853i −0.752824 + 0.953785i
141141 −28.1887 −2.37392
142142 −16.4365 13.3816i −1.37932 1.12296i
143143 −0.723993 + 0.723993i −0.0605433 + 0.0605433i
144144 3.72971 + 8.61942i 0.310809 + 0.718285i
145145 −1.87326 + 21.4830i −0.155566 + 1.78407i
146146 −3.95893 + 0.405600i −0.327643 + 0.0335677i
147147 5.45373 + 5.45373i 0.449816 + 0.449816i
148148 4.61702 + 3.03289i 0.379516 + 0.249302i
149149 12.5283i 1.02636i −0.858281 0.513180i 0.828467π-0.828467\pi
0.858281 0.513180i 0.171533π-0.171533\pi
150150 −1.17405 + 16.3101i −0.0958605 + 1.33171i
151151 11.6081i 0.944655i −0.881423 0.472328i 0.843414π-0.843414\pi
0.881423 0.472328i 0.156586π-0.156586\pi
152152 3.55492 + 1.84671i 0.288342 + 0.149788i
153153 2.16579 + 2.16579i 0.175093 + 0.175093i
154154 −0.463369 4.52278i −0.0373393 0.364456i
155155 −1.48571 + 17.0385i −0.119335 + 1.36857i
156156 0.960259 + 4.63719i 0.0768823 + 0.371273i
157157 2.67425 2.67425i 0.213428 0.213428i −0.592294 0.805722i 0.701778π-0.701778\pi
0.805722 + 0.592294i 0.201778π0.201778\pi
158158 12.6291 15.5123i 1.00472 1.23409i
159159 −25.9270 −2.05614
160160 4.47840 11.8298i 0.354049 0.935227i
161161 −16.2361 −1.27959
162162 −9.40286 + 11.5495i −0.738758 + 0.907412i
163163 −5.14228 + 5.14228i −0.402775 + 0.402775i −0.879210 0.476435i 0.841929π-0.841929\pi
0.476435 + 0.879210i 0.341929π0.341929\pi
164164 −3.29225 15.8986i −0.257081 1.24147i
165165 −3.32503 3.96029i −0.258853 0.308308i
166166 0.687964 + 6.71499i 0.0533964 + 0.521184i
167167 10.2219 + 10.2219i 0.790991 + 0.790991i 0.981655 0.190665i 0.0610643π-0.0610643\pi
−0.190665 + 0.981655i 0.561064π0.561064\pi
168168 −18.6603 9.69367i −1.43967 0.747883i
169169 11.9517i 0.919359i
170170 −0.0623640 4.12471i −0.00478310 0.316351i
171171 3.32545i 0.254303i
172172 8.45813 + 5.55610i 0.644927 + 0.423649i
173173 13.4480 + 13.4480i 1.02244 + 1.02244i 0.999742 + 0.0226936i 0.00722423π0.00722423\pi
0.0226936 + 0.999742i 0.492776π0.492776\pi
174174 −31.3759 + 3.21452i −2.37860 + 0.243692i
175175 −9.22737 13.1618i −0.697524 0.994942i
176176 1.58850 + 3.67106i 0.119738 + 0.276716i
177177 −4.10768 + 4.10768i −0.308752 + 0.308752i
178178 −5.16243 4.20293i −0.386941 0.315023i
179179 5.08038 0.379725 0.189863 0.981811i 0.439196π-0.439196\pi
0.189863 + 0.981811i 0.439196π0.439196\pi
180180 −10.4283 + 1.22797i −0.777276 + 0.0915274i
181181 −9.69715 −0.720783 −0.360392 0.932801i 0.617357π-0.617357\pi
−0.360392 + 0.932801i 0.617357π0.617357\pi
182182 −3.60994 2.93899i −0.267587 0.217852i
183183 −5.80138 + 5.80138i −0.428851 + 0.428851i
184184 13.6198 4.30711i 1.00407 0.317525i
185185 −4.73001 + 3.97128i −0.347757 + 0.291974i
186186 −24.8847 + 2.54949i −1.82463 + 0.186937i
187187 0.922419 + 0.922419i 0.0674540 + 0.0674540i
188188 −13.3847 + 20.3758i −0.976183 + 1.48606i
189189 4.84774i 0.352621i
190190 −3.11876 + 3.21452i −0.226259 + 0.233206i
191191 6.59943i 0.477518i 0.971079 + 0.238759i 0.0767405π0.0767405\pi
−0.971079 + 0.238759i 0.923259π0.923259\pi
192192 18.2249 + 3.18142i 1.31527 + 0.229599i
193193 −7.19452 7.19452i −0.517873 0.517873i 0.399054 0.916927i 0.369338π-0.369338\pi
−0.916927 + 0.399054i 0.869338π0.869338\pi
194194 0.0631262 + 0.616153i 0.00453219 + 0.0442372i
195195 −5.27452 0.459924i −0.377716 0.0329359i
196196 6.53172 1.35257i 0.466551 0.0966124i
197197 14.8919 14.8919i 1.06100 1.06100i 0.0629865 0.998014i 0.479937π-0.479937\pi
0.998014 0.0629865i 0.0200625π-0.0200625\pi
198198 2.09641 2.57501i 0.148986 0.182998i
199199 −20.8386 −1.47721 −0.738605 0.674139i 0.764515π-0.764515\pi
−0.738605 + 0.674139i 0.764515π0.764515\pi
200200 11.2320 + 8.59310i 0.794225 + 0.607624i
201201 22.9506 1.61881
202202 −7.44696 + 9.14705i −0.523966 + 0.643584i
203203 21.9229 21.9229i 1.53869 1.53869i
204204 5.90812 1.22344i 0.413651 0.0856579i
205205 18.0837 + 1.57685i 1.26302 + 0.110132i
206206 −1.84357 17.9945i −0.128448 1.25373i
207207 −8.38486 8.38486i −0.582788 0.582788i
208208 3.80789 + 1.50775i 0.264029 + 0.104544i
209209 1.41633i 0.0979693i
210210 16.3708 16.8735i 1.12969 1.16438i
211211 1.74833i 0.120360i 0.998188 + 0.0601799i 0.0191674π0.0191674\pi
−0.998188 + 0.0601799i 0.980833π0.980833\pi
212212 −12.3108 + 18.7409i −0.845511 + 1.28713i
213213 24.5073 + 24.5073i 1.67921 + 1.67921i
214214 0.924637 0.0947309i 0.0632069 0.00647567i
215215 −8.66514 + 7.27518i −0.590957 + 0.496163i
216216 1.28601 + 4.06657i 0.0875017 + 0.276695i
217217 17.3874 17.3874i 1.18033 1.18033i
218218 7.44058 + 6.05766i 0.503940 + 0.410276i
219219 6.50764 0.439745
220220 −4.44145 + 0.522999i −0.299442 + 0.0352606i
221221 1.33565 0.0898456
222222 −7.00510 5.70312i −0.470151 0.382768i
223223 4.01382 4.01382i 0.268785 0.268785i −0.559825 0.828611i 0.689132π-0.689132\pi
0.828611 + 0.559825i 0.189132π0.189132\pi
224224 −15.8673 + 8.88551i −1.06018 + 0.593688i
225225 2.03189 11.5625i 0.135460 0.770835i
226226 6.70080 0.686511i 0.445731 0.0456660i
227227 7.34061 + 7.34061i 0.487213 + 0.487213i 0.907426 0.420213i 0.138044π-0.138044\pi
−0.420213 + 0.907426i 0.638044π0.638044\pi
228228 −5.47506 3.59654i −0.362595 0.238186i
229229 1.92059i 0.126916i −0.997985 0.0634581i 0.979787π-0.979787\pi
0.997985 0.0634581i 0.0202129π-0.0202129\pi
230230 0.241443 + 15.9689i 0.0159203 + 1.05296i
231231 7.43450i 0.489154i
232232 −12.5745 + 24.2059i −0.825558 + 1.58920i
233233 −15.6936 15.6936i −1.02812 1.02812i −0.999593 0.0285271i 0.990918π-0.990918\pi
−0.0285271 0.999593i 0.509082π-0.509082\pi
234234 −0.346501 3.38208i −0.0226515 0.221094i
235235 −17.5260 20.8745i −1.14327 1.36170i
236236 1.01874 + 4.91962i 0.0663145 + 0.320240i
237237 −23.1293 + 23.1293i −1.50241 + 1.50241i
238238 −3.74448 + 4.59932i −0.242719 + 0.298130i
239239 24.5204 1.58609 0.793047 0.609161i 0.208494π-0.208494\pi
0.793047 + 0.609161i 0.208494π0.208494\pi
240240 −9.25662 + 18.4973i −0.597512 + 1.19400i
241241 5.52210 0.355710 0.177855 0.984057i 0.443084π-0.443084\pi
0.177855 + 0.984057i 0.443084π0.443084\pi
242242 0.892874 1.09671i 0.0573961 0.0704993i
243243 14.0218 14.0218i 0.899498 0.899498i
244244 1.43880 + 6.94810i 0.0921095 + 0.444806i
245245 −0.647826 + 7.42942i −0.0413881 + 0.474649i
246246 2.70588 + 26.4112i 0.172520 + 1.68391i
247247 −1.02541 1.02541i −0.0652453 0.0652453i
248248 −9.97305 + 19.1981i −0.633289 + 1.21908i
249249 11.0380i 0.699506i
250250 −12.8080 + 9.27122i −0.810048 + 0.586363i
251251 13.1078i 0.827357i −0.910423 0.413678i 0.864244π-0.864244\pi
0.910423 0.413678i 0.135756π-0.135756\pi
252252 12.6176 + 8.28845i 0.794837 + 0.522124i
253253 −3.57116 3.57116i −0.224517 0.224517i
254254 11.4348 1.17152i 0.717482 0.0735075i
255255 −0.585977 + 6.72012i −0.0366953 + 0.420830i
256256 10.9533 11.6630i 0.684582 0.728936i
257257 −20.6594 + 20.6594i −1.28870 + 1.28870i −0.353121 + 0.935578i 0.614880π0.614880\pi
−0.935578 + 0.353121i 0.885120π0.885120\pi
258258 −12.8330 10.4478i −0.798946 0.650452i
259259 8.87947 0.551743
260260 −2.83693 + 3.59423i −0.175939 + 0.222904i
261261 22.6434 1.40159
262262 19.8436 + 16.1554i 1.22594 + 0.998084i
263263 −5.86258 + 5.86258i −0.361502 + 0.361502i −0.864366 0.502864i 0.832280π-0.832280\pi
0.502864 + 0.864366i 0.332280π0.332280\pi
264264 −1.97222 6.23649i −0.121382 0.383830i
265265 −16.1198 19.1996i −0.990234 1.17942i
266266 6.40574 0.656281i 0.392761 0.0402391i
267267 7.69733 + 7.69733i 0.471069 + 0.471069i
268268 10.8975 16.5895i 0.665673 1.01336i
269269 12.8329i 0.782437i −0.920298 0.391219i 0.872054π-0.872054\pi
0.920298 0.391219i 0.127946π-0.127946\pi
270270 −4.76795 + 0.0720893i −0.290168 + 0.00438722i
271271 18.6929i 1.13551i −0.823196 0.567757i 0.807811π-0.807811\pi
0.823196 0.567757i 0.192189π-0.192189\pi
272272 1.92099 4.85152i 0.116477 0.294167i
273273 5.38252 + 5.38252i 0.325765 + 0.325765i
274274 1.29507 + 12.6407i 0.0782380 + 0.763655i
275275 0.865394 4.92454i 0.0521852 0.296961i
276276 −22.8734 + 4.73656i −1.37681 + 0.285107i
277277 −6.37661 + 6.37661i −0.383133 + 0.383133i −0.872230 0.489097i 0.837327π-0.837327\pi
0.489097 + 0.872230i 0.337327π0.337327\pi
278278 0.835597 1.02636i 0.0501158 0.0615568i
279279 17.9588 1.07517
280280 −4.42344 19.8454i −0.264351 1.18599i
281281 −16.5985 −0.990183 −0.495092 0.868841i 0.664866π-0.664866\pi
−0.495092 + 0.868841i 0.664866π0.664866\pi
282282 25.1690 30.9149i 1.49879 1.84095i
283283 −10.6084 + 10.6084i −0.630606 + 0.630606i −0.948220 0.317614i 0.897118π-0.897118\pi
0.317614 + 0.948220i 0.397118π0.397118\pi
284284 29.3515 6.07804i 1.74169 0.360665i
285285 5.60906 4.70932i 0.332252 0.278956i
286286 −0.147577 1.44045i −0.00872639 0.0851754i
287287 −18.4540 18.4540i −1.08930 1.08930i
288288 −12.7832 3.60564i −0.753256 0.212464i
289289 15.2983i 0.899899i
290290 −21.8881 21.2361i −1.28531 1.24702i
291291 1.01283i 0.0593729i
292292 3.09000 4.70395i 0.180828 0.275278i
293293 −15.3588 15.3588i −0.897270 0.897270i 0.0979236 0.995194i 0.468780π-0.468780\pi
−0.995194 + 0.0979236i 0.968780π0.968780\pi
294294 −10.8507 + 1.11167i −0.632823 + 0.0648340i
295295 −5.59576 0.487935i −0.325798 0.0284087i
296296 −7.44862 + 2.35554i −0.432942 + 0.136913i
297297 1.06627 1.06627i 0.0618711 0.0618711i
298298 13.7399 + 11.1862i 0.795933 + 0.647999i
299299 −5.17099 −0.299046
300300 −16.8392 15.8504i −0.972210 0.915125i
301301 16.2667 0.937598
302302 12.7308 + 10.3646i 0.732573 + 0.596415i
303303 13.6385 13.6385i 0.783512 0.783512i
304304 −5.19941 + 2.24984i −0.298207 + 0.129037i
305305 −7.90303 0.689123i −0.452526 0.0394591i
306306 −4.30902 + 0.441467i −0.246330 + 0.0252370i
307307 0.975912 + 0.975912i 0.0556982 + 0.0556982i 0.734407 0.678709i 0.237460π-0.237460\pi
−0.678709 + 0.734407i 0.737460π0.737460\pi
308308 5.37392 + 3.53010i 0.306207 + 0.201146i
309309 29.5791i 1.68269i
310310 −17.3598 16.8426i −0.985968 0.956597i
311311 5.31250i 0.301244i 0.988591 + 0.150622i 0.0481277π0.0481277\pi
−0.988591 + 0.150622i 0.951872π0.951872\pi
312312 −5.94305 3.08730i −0.336459 0.174784i
313313 4.06321 + 4.06321i 0.229666 + 0.229666i 0.812553 0.582887i 0.198077π-0.198077\pi
−0.582887 + 0.812553i 0.698077π0.698077\pi
314314 0.545110 + 5.32064i 0.0307624 + 0.300261i
315315 −12.9264 + 10.8529i −0.728322 + 0.611494i
316316 5.73626 + 27.7010i 0.322690 + 1.55830i
317317 −7.01485 + 7.01485i −0.393993 + 0.393993i −0.876108 0.482115i 0.839869π-0.839869\pi
0.482115 + 0.876108i 0.339869π0.339869\pi
318318 23.1495 28.4344i 1.29816 1.59452i
319319 9.64395 0.539958
320320 8.97522 + 15.4740i 0.501730 + 0.865024i
321321 −1.51991 −0.0848329
322322 14.4968 17.8063i 0.807876 0.992308i
323323 −1.30645 + 1.30645i −0.0726926 + 0.0726926i
324324 −4.27086 20.6244i −0.237270 1.14580i
325325 −2.93879 4.19187i −0.163015 0.232523i
326326 −1.04819 10.2310i −0.0580537 0.566643i
327327 −11.0941 11.0941i −0.613506 0.613506i
328328 20.3758 + 10.5848i 1.12506 + 0.584449i
329329 39.1868i 2.16044i
330330 7.31213 0.110556i 0.402519 0.00608592i
331331 25.0017i 1.37422i −0.726556 0.687108i 0.758880π-0.758880\pi
0.726556 0.687108i 0.241120π-0.241120\pi
332332 −7.97867 5.24114i −0.437886 0.287645i
333333 4.58565 + 4.58565i 0.251292 + 0.251292i
334334 −20.3372 + 2.08359i −1.11280 + 0.114009i
335335 14.2693 + 16.9955i 0.779614 + 0.928563i
336336 27.2925 11.8097i 1.48893 0.644274i
337337 2.87545 2.87545i 0.156636 0.156636i −0.624438 0.781074i 0.714672π-0.714672\pi
0.781074 + 0.624438i 0.214672π0.214672\pi
338338 13.1075 + 10.6713i 0.712956 + 0.580444i
339339 −11.0147 −0.598236
340340 4.57930 + 3.61446i 0.248348 + 0.196021i
341341 7.64876 0.414204
342342 3.64706 + 2.96921i 0.197210 + 0.160556i
343343 −8.33105 + 8.33105i −0.449835 + 0.449835i
344344 −13.6455 + 4.31523i −0.735715 + 0.232662i
345345 2.26862 26.0170i 0.122138 1.40071i
346346 −26.7560 + 2.74121i −1.43841 + 0.147368i
347347 0.444682 + 0.444682i 0.0238718 + 0.0238718i 0.718942 0.695070i 0.244627π-0.244627\pi
−0.695070 + 0.718942i 0.744627π0.744627\pi
348348 24.4893 37.2805i 1.31277 1.99844i
349349 11.1765i 0.598262i 0.954212 + 0.299131i 0.0966968π0.0966968\pi
−0.954212 + 0.299131i 0.903303π0.903303\pi
350350 22.6736 + 1.63211i 1.21196 + 0.0872401i
351351 1.54394i 0.0824094i
352352 −5.44442 1.53566i −0.290189 0.0818510i
353353 9.52218 + 9.52218i 0.506814 + 0.506814i 0.913547 0.406733i 0.133332π-0.133332\pi
−0.406733 + 0.913547i 0.633332π0.633332\pi
354354 −0.837298 8.17259i −0.0445019 0.434368i
355355 −2.91113 + 33.3855i −0.154507 + 1.77192i
356356 9.21880 1.90901i 0.488596 0.101177i
357357 6.85772 6.85772i 0.362949 0.362949i
358358 −4.53614 + 5.57171i −0.239742 + 0.294474i
359359 23.9996 1.26665 0.633326 0.773885i 0.281689π-0.281689\pi
0.633326 + 0.773885i 0.281689π0.281689\pi
360360 7.96439 12.5332i 0.419760 0.660558i
361361 −16.9940 −0.894422
362362 8.65833 10.6350i 0.455072 0.558962i
363363 −1.63523 + 1.63523i −0.0858272 + 0.0858272i
364364 6.44645 1.33491i 0.337886 0.0699686i
365365 4.04606 + 4.81907i 0.211780 + 0.252242i
366366 −1.18254 11.5424i −0.0618122 0.603328i
367367 10.7096 + 10.7096i 0.559038 + 0.559038i 0.929033 0.369996i 0.120641π-0.120641\pi
−0.369996 + 0.929033i 0.620641π0.620641\pi
368368 −7.43712 + 18.7827i −0.387687 + 0.979117i
369369 19.0605i 0.992249i
370370 −0.132044 8.73331i −0.00686464 0.454023i
371371 36.0427i 1.87124i
372372 19.4228 29.5677i 1.00703 1.53301i
373373 −12.7491 12.7491i −0.660125 0.660125i 0.295284 0.955409i 0.404586π-0.404586\pi
−0.955409 + 0.295284i 0.904586π0.904586\pi
374374 −1.83523 + 0.188023i −0.0948976 + 0.00972245i
375375 22.3801 12.9470i 1.15570 0.668581i
376376 −10.3955 32.8722i −0.536105 1.69526i
377377 6.98216 6.98216i 0.359599 0.359599i
378378 5.31657 + 4.32842i 0.273455 + 0.222630i
379379 −11.9690 −0.614804 −0.307402 0.951580i 0.599460π-0.599460\pi
−0.307402 + 0.951580i 0.599460π0.599460\pi
380380 −0.740736 6.29054i −0.0379990 0.322698i
381381 −18.7963 −0.962966
382382 −7.23766 5.89246i −0.370311 0.301484i
383383 −0.0817471 + 0.0817471i −0.00417708 + 0.00417708i −0.709192 0.705015i 0.750940π-0.750940\pi
0.705015 + 0.709192i 0.250940π0.250940\pi
384384 −19.7616 + 17.1468i −1.00846 + 0.875021i
385385 −5.50544 + 4.62232i −0.280583 + 0.235575i
386386 14.3141 1.46651i 0.728569 0.0746434i
387387 8.40067 + 8.40067i 0.427030 + 0.427030i
388388 −0.732106 0.480916i −0.0371671 0.0244148i
389389 13.0833i 0.663347i −0.943394 0.331674i 0.892387π-0.892387\pi
0.943394 0.331674i 0.107613π-0.107613\pi
390390 5.21389 5.37397i 0.264015 0.272122i
391391 6.58821i 0.333180i
392392 −4.34862 + 8.37109i −0.219639 + 0.422804i
393393 −29.5873 29.5873i −1.49248 1.49248i
394394 3.03551 + 29.6286i 0.152927 + 1.49267i
395395 −31.5082 2.74743i −1.58535 0.138238i
396396 0.952210 + 4.59832i 0.0478504 + 0.231074i
397397 13.8205 13.8205i 0.693631 0.693631i −0.269398 0.963029i 0.586825π-0.586825\pi
0.963029 + 0.269398i 0.0868248π0.0868248\pi
398398 18.6063 22.8539i 0.932647 1.14556i
399399 −10.5297 −0.527143
400400 −19.4529 + 4.64574i −0.972647 + 0.232287i
401401 29.9011 1.49319 0.746595 0.665279i 0.231687π-0.231687\pi
0.746595 + 0.665279i 0.231687π0.231687\pi
402402 −20.4920 + 25.1701i −1.02205 + 1.25537i
403403 5.53765 5.53765i 0.275850 0.275850i
404404 −3.38248 16.3343i −0.168284 0.812664i
405405 23.4590 + 2.04556i 1.16569 + 0.101645i
406406 4.46870 + 43.6175i 0.221778 + 2.16470i
407407 1.95305 + 1.95305i 0.0968091 + 0.0968091i
408408 −3.93345 + 7.57188i −0.194735 + 0.374864i
409409 25.5845i 1.26507i 0.774531 + 0.632536i 0.217986π0.217986\pi
−0.774531 + 0.632536i 0.782014π0.782014\pi
410410 −17.8758 + 18.4247i −0.882823 + 0.909929i
411411 20.7787i 1.02494i
412412 21.3808 + 14.0449i 1.05336 + 0.691944i
413413 5.71034 + 5.71034i 0.280988 + 0.280988i
414414 16.6824 1.70915i 0.819895 0.0839999i
415415 8.17394 6.86277i 0.401243 0.336880i
416416 −5.05353 + 2.82992i −0.247770 + 0.138748i
417417 −1.53033 + 1.53033i −0.0749405 + 0.0749405i
418418 1.55330 + 1.26460i 0.0759744 + 0.0618536i
419419 −5.31123 −0.259470 −0.129735 0.991549i 0.541413π-0.541413\pi
−0.129735 + 0.991549i 0.541413π0.541413\pi
420420 3.88823 + 33.0199i 0.189726 + 1.61121i
421421 14.3707 0.700385 0.350192 0.936678i 0.386116π-0.386116\pi
0.350192 + 0.936678i 0.386116π0.386116\pi
422422 −1.91741 1.56104i −0.0933381 0.0759900i
423423 −20.2374 + 20.2374i −0.983974 + 0.983974i
424424 −9.56139 30.2347i −0.464342 1.46833i
425425 −5.34075 + 3.74424i −0.259064 + 0.181622i
426426 −48.7594 + 4.99550i −2.36240 + 0.242033i
427427 8.06486 + 8.06486i 0.390286 + 0.390286i
428428 −0.721692 + 1.09864i −0.0348843 + 0.0531049i
429429 2.36779i 0.114318i
430430 −0.241898 15.9990i −0.0116653 0.771539i
431431 38.3768i 1.84854i 0.381734 + 0.924272i 0.375327π0.375327\pi
−0.381734 + 0.924272i 0.624673π0.624673\pi
432432 −5.60809 2.22056i −0.269820 0.106837i
433433 −6.38327 6.38327i −0.306760 0.306760i 0.536891 0.843651i 0.319599π-0.319599\pi
−0.843651 + 0.536891i 0.819599π0.819599\pi
434434 3.54420 + 34.5937i 0.170127 + 1.66055i
435435 32.0664 + 38.1928i 1.53747 + 1.83121i
436436 −13.2870 + 2.75144i −0.636332 + 0.131770i
437437 5.05792 5.05792i 0.241953 0.241953i
438438 −5.81050 + 7.13700i −0.277636 + 0.341019i
439439 16.3392 0.779827 0.389913 0.920852i 0.372505π-0.372505\pi
0.389913 + 0.920852i 0.372505π0.372505\pi
440440 3.39208 5.33796i 0.161711 0.254477i
441441 7.83073 0.372892
442442 −1.19257 + 1.46482i −0.0567247 + 0.0696745i
443443 6.87247 6.87247i 0.326521 0.326521i −0.524741 0.851262i 0.675838π-0.675838\pi
0.851262 + 0.524741i 0.175838π0.175838\pi
444444 12.5093 2.59040i 0.593667 0.122935i
445445 −0.914335 + 10.4858i −0.0433437 + 0.497075i
446446 0.818166 + 7.98584i 0.0387413 + 0.378141i
447447 −20.4866 20.4866i −0.968985 0.968985i
448448 4.42269 25.3355i 0.208952 1.19699i
449449 4.44137i 0.209601i 0.994493 + 0.104801i 0.0334204π0.0334204\pi
−0.994493 + 0.104801i 0.966580π0.966580\pi
450450 10.8665 + 12.5523i 0.512253 + 0.591720i
451451 8.11796i 0.382260i
452452 −5.23007 + 7.96181i −0.246002 + 0.374492i
453453 −18.9819 18.9819i −0.891848 0.891848i
454454 −14.6048 + 1.49629i −0.685436 + 0.0702243i
455455 −0.639369 + 7.33243i −0.0299741 + 0.343750i
456456 8.83291 2.79331i 0.413639 0.130809i
457457 −11.8533 + 11.8533i −0.554476 + 0.554476i −0.927729 0.373254i 0.878242π-0.878242\pi
0.373254 + 0.927729i 0.378242π0.378242\pi
458458 2.10633 + 1.71485i 0.0984225 + 0.0801295i
459459 −1.96709 −0.0918159
460460 −17.7288 13.9934i −0.826611 0.652446i
461461 −25.5894 −1.19182 −0.595909 0.803052i 0.703208π-0.703208\pi
−0.595909 + 0.803052i 0.703208π0.703208\pi
462462 −8.15350 6.63807i −0.379335 0.308831i
463463 −16.4285 + 16.4285i −0.763499 + 0.763499i −0.976953 0.213454i 0.931529π-0.931529\pi
0.213454 + 0.976953i 0.431529π0.431529\pi
464464 −15.3195 35.4035i −0.711188 1.64357i
465465 25.4324 + 30.2913i 1.17940 + 1.40473i
466466 31.2237 3.19893i 1.44641 0.148188i
467467 −19.5335 19.5335i −0.903901 0.903901i 0.0918697 0.995771i 0.470716π-0.470716\pi
−0.995771 + 0.0918697i 0.970716π0.970716\pi
468468 4.01855 + 2.63976i 0.185757 + 0.122023i
469469 31.9050i 1.47323i
470470 38.5418 0.582736i 1.77780 0.0268796i
471471 8.74600i 0.402995i
472472 −6.30501 3.27533i −0.290212 0.150759i
473473 3.57789 + 3.57789i 0.164511 + 0.164511i
474474 −4.71460 46.0176i −0.216549 2.11366i
475475 6.97475 + 1.22568i 0.320024 + 0.0562380i
476476 −1.70078 8.21324i −0.0779550 0.376453i
477477 −18.6136 + 18.6136i −0.852259 + 0.852259i
478478 −21.8936 + 26.8918i −1.00139 + 1.23000i
479479 −1.19428 −0.0545681 −0.0272840 0.999628i 0.508686π-0.508686\pi
−0.0272840 + 0.999628i 0.508686π0.508686\pi
480480 −12.0212 26.6676i −0.548690 1.21720i
481481 2.82799 0.128945
482482 −4.93054 + 6.05615i −0.224580 + 0.275850i
483483 −26.5498 + 26.5498i −1.20806 + 1.20806i
484484 0.405551 + 1.95845i 0.0184341 + 0.0890205i
485485 0.750023 0.629714i 0.0340568 0.0285938i
486486 2.85816 + 27.8975i 0.129649 + 1.26546i
487487 −3.24221 3.24221i −0.146919 0.146919i 0.629821 0.776740i 0.283128π-0.283128\pi
−0.776740 + 0.629821i 0.783128π0.783128\pi
488488 −8.90472 4.62583i −0.403098 0.209402i
489489 16.8176i 0.760518i
490490 −7.56951 7.34402i −0.341955 0.331769i
491491 11.6132i 0.524095i −0.965055 0.262047i 0.915602π-0.915602\pi
0.965055 0.262047i 0.0843977π-0.0843977\pi
492492 −31.3814 20.6143i −1.41478 0.929364i
493493 −8.89577 8.89577i −0.400645 0.400645i
494494 2.04014 0.209017i 0.0917903 0.00940410i
495495 −5.23031 0.456069i −0.235085 0.0204988i
496496 −12.1501 28.0790i −0.545555 1.26079i
497497 34.0691 34.0691i 1.52821 1.52821i
498498 12.1055 + 9.85556i 0.542461 + 0.441638i
499499 16.5509 0.740919 0.370459 0.928849i 0.379200π-0.379200\pi
0.370459 + 0.928849i 0.379200π0.379200\pi
500500 1.26808 22.3247i 0.0567101 0.998391i
501501 33.4301 1.49355
502502 14.3755 + 11.7036i 0.641608 + 0.522358i
503503 −2.09623 + 2.09623i −0.0934662 + 0.0934662i −0.752294 0.658828i 0.771053π-0.771053\pi
0.658828 + 0.752294i 0.271053π0.271053\pi
504504 −20.3560 + 6.43736i −0.906729 + 0.286743i
505505 18.5793 + 1.62007i 0.826767 + 0.0720920i
506506 7.10512 0.727934i 0.315861 0.0323606i
507507 −19.5437 19.5437i −0.867966 0.867966i
508508 −8.92500 + 13.5867i −0.395983 + 0.602811i
509509 34.7631i 1.54085i −0.637533 0.770423i 0.720045π-0.720045\pi
0.637533 0.770423i 0.279955π-0.279955\pi
510510 −6.84683 6.64287i −0.303183 0.294151i
511511 9.04666i 0.400201i
512512 3.01099 + 22.4262i 0.133068 + 0.991107i
513513 1.51018 + 1.51018i 0.0666761 + 0.0666761i
514514 −4.21115 41.1037i −0.185746 1.81301i
515515 −21.9041 + 18.3905i −0.965209 + 0.810382i
516516 22.9165 4.74549i 1.00884 0.208908i
517517 −8.61919 + 8.61919i −0.379072 + 0.379072i
518518 −7.92825 + 9.73821i −0.348347 + 0.427872i
519519 43.9812 1.93056
520520 −1.40881 6.32049i −0.0617802 0.277172i
521521 −28.2376 −1.23711 −0.618555 0.785741i 0.712282π-0.712282\pi
−0.618555 + 0.785741i 0.712282π0.712282\pi
522522 −20.2177 + 24.8333i −0.884906 + 1.08692i
523523 −23.3918 + 23.3918i −1.02285 + 1.02285i −0.0231215 + 0.999733i 0.507360π0.507360\pi
−0.999733 + 0.0231215i 0.992640π0.992640\pi
524524 −35.4356 + 7.33793i −1.54801 + 0.320559i
525525 −36.6115 6.43377i −1.59786 0.280793i
526526 −1.19501 11.6641i −0.0521049 0.508579i
527527 −7.05537 7.05537i −0.307337 0.307337i
528528 8.60058 + 3.40545i 0.374292 + 0.148203i
529529 2.50633i 0.108971i
530530 35.4494 0.535980i 1.53982 0.0232815i
531531 5.89801i 0.255952i
532532 −4.99977 + 7.61122i −0.216767 + 0.329988i
533533 −5.87734 5.87734i −0.254576 0.254576i
534534 −15.3145 + 1.56900i −0.662723 + 0.0678973i
535535 −0.944987 1.12553i −0.0408553 0.0486609i
536536 8.46374 + 26.7638i 0.365578 + 1.15602i
537537 8.30757 8.30757i 0.358498 0.358498i
538538 14.0740 + 11.4582i 0.606774 + 0.493997i
539539 3.33515 0.143655
540540 4.17811 5.29343i 0.179797 0.227793i
541541 −21.3400 −0.917478 −0.458739 0.888571i 0.651699π-0.651699\pi
−0.458739 + 0.888571i 0.651699π0.651699\pi
542542 20.5008 + 16.6904i 0.880583 + 0.716916i
543543 −15.8570 + 15.8570i −0.680491 + 0.680491i
544544 3.60552 + 6.43857i 0.154585 + 0.276051i
545545 1.31783 15.1131i 0.0564495 0.647376i
546546 −10.7090 + 1.09716i −0.458303 + 0.0469540i
547547 17.5485 + 17.5485i 0.750320 + 0.750320i 0.974539 0.224219i 0.0719830π-0.0719830\pi
−0.224219 + 0.974539i 0.571983π0.571983\pi
548548 −15.0196 9.86628i −0.641605 0.421466i
549549 8.32991i 0.355512i
550550 4.62811 + 5.34608i 0.197343 + 0.227958i
551551 13.6590i 0.581892i
552552 15.2284 29.3146i 0.648163 1.24771i
553553 32.1534 + 32.1534i 1.36730 + 1.36730i
554554 −1.29979 12.6868i −0.0552227 0.539011i
555555 −1.24070 + 14.2286i −0.0526646 + 0.603970i
556556 0.379535 + 1.83282i 0.0160959 + 0.0777287i
557557 −5.97438 + 5.97438i −0.253143 + 0.253143i −0.822258 0.569115i 0.807286π-0.807286\pi
0.569115 + 0.822258i 0.307286π0.307286\pi
558558 −16.0350 + 19.6957i −0.678815 + 0.833784i
559559 5.18073 0.219122
560560 25.7142 + 12.8682i 1.08662 + 0.543780i
561561 3.01673 0.127367
562562 14.8204 18.2038i 0.625160 0.767879i
563563 5.46575 5.46575i 0.230354 0.230354i −0.582486 0.812840i 0.697920π-0.697920\pi
0.812840 + 0.582486i 0.197920π0.197920\pi
564564 11.4320 + 55.2062i 0.481372 + 2.32460i
565565 −6.84828 8.15667i −0.288109 0.343154i
566566 −2.16239 21.1064i −0.0908921 0.887168i
567567 −23.9394 23.9394i −1.00536 1.00536i
568568 −19.5413 + 37.6170i −0.819936 + 1.57838i
569569 35.6456i 1.49434i 0.664632 + 0.747171i 0.268588π0.268588\pi
−0.664632 + 0.747171i 0.731412π0.731412\pi
570570 0.156584 + 10.3563i 0.00655857 + 0.433780i
571571 0.929679i 0.0389059i 0.999811 + 0.0194529i 0.00619245π0.00619245\pi
−0.999811 + 0.0194529i 0.993808π0.993808\pi
572572 1.71152 + 1.12429i 0.0715623 + 0.0470089i
573573 10.7916 + 10.7916i 0.450824 + 0.450824i
574574 36.7158 3.76161i 1.53249 0.157006i
575575 20.6768 14.4958i 0.862281 0.604519i
576576 15.3681 10.8001i 0.640338 0.450003i
577577 −21.1801 + 21.1801i −0.881740 + 0.881740i −0.993711 0.111972i 0.964283π-0.964283\pi
0.111972 + 0.993711i 0.464283π0.464283\pi
578578 −16.7778 13.6594i −0.697865 0.568158i
579579 −23.5294 −0.977847
580580 42.8331 5.04377i 1.77855 0.209431i
581581 −15.3446 −0.636602
582582 1.11078 + 0.904325i 0.0460432 + 0.0374855i
583583 −7.92764 + 7.92764i −0.328329 + 0.328329i
584584 2.39990 + 7.58887i 0.0993084 + 0.314030i
585585 −4.11690 + 3.45652i −0.170213 + 0.142909i
586586 30.5576 3.13069i 1.26232 0.129328i
587587 −9.39519 9.39519i −0.387781 0.387781i 0.486114 0.873895i 0.338414π-0.338414\pi
−0.873895 + 0.486114i 0.838414π0.838414\pi
588588 8.46909 12.8926i 0.349259 0.531683i
589589 10.8331i 0.446372i
590590 5.53143 5.70127i 0.227725 0.234717i
591591 48.7032i 2.00338i
592592 4.06733 10.2722i 0.167166 0.422184i
593593 22.6726 + 22.6726i 0.931054 + 0.931054i 0.997772 0.0667183i 0.0212529π-0.0212529\pi
−0.0667183 + 0.997772i 0.521253π0.521253\pi
594594 0.217345 + 2.12143i 0.00891776 + 0.0870433i
595595 9.34205 + 0.814602i 0.382987 + 0.0333954i
596596 −24.5361 + 5.08087i −1.00504 + 0.208121i
597597 −34.0759 + 34.0759i −1.39463 + 1.39463i
598598 4.61704 5.67108i 0.188805 0.231908i
599599 17.6219 0.720011 0.360006 0.932950i 0.382775π-0.382775\pi
0.360006 + 0.932950i 0.382775π0.382775\pi
600600 32.4186 4.31526i 1.32348 0.176170i
601601 −9.95444 −0.406050 −0.203025 0.979174i 0.565077π-0.565077\pi
−0.203025 + 0.979174i 0.565077π0.565077\pi
602602 −14.5241 + 17.8399i −0.591960 + 0.727100i
603603 16.4768 16.4768i 0.670986 0.670986i
604604 −22.7339 + 4.70769i −0.925030 + 0.191553i
605605 −2.22762 0.194242i −0.0905654 0.00789707i
606606 2.78004 + 27.1350i 0.112931 + 1.10228i
607607 −30.5524 30.5524i −1.24008 1.24008i −0.959966 0.280116i 0.909627π-0.909627\pi
−0.280116 0.959966i 0.590373π-0.590373\pi
608608 2.17500 7.71107i 0.0882077 0.312725i
609609 71.6979i 2.90535i
610610 7.81218 8.05204i 0.316306 0.326018i
611611 12.4805i 0.504906i
612612 3.36325 5.11992i 0.135951 0.206961i
613613 −15.5026 15.5026i −0.626145 0.626145i 0.320951 0.947096i 0.395998π-0.395998\pi
−0.947096 + 0.320951i 0.895998π0.895998\pi
614614 −1.94166 + 0.198927i −0.0783590 + 0.00802804i
615615 32.1495 26.9924i 1.29639 1.08844i
616616 −8.66973 + 2.74171i −0.349313 + 0.110466i
617617 25.9842 25.9842i 1.04608 1.04608i 0.0471977 0.998886i 0.484971π-0.484971\pi
0.998886 0.0471977i 0.0150291π-0.0150291\pi
618618 −32.4397 26.4104i −1.30492 1.06238i
619619 8.25617 0.331843 0.165922 0.986139i 0.446940π-0.446940\pi
0.165922 + 0.986139i 0.446940π0.446940\pi
620620 33.9716 4.00029i 1.36433 0.160656i
621621 7.61561 0.305604
622622 −5.82628 4.74339i −0.233613 0.190193i
623623 10.7005 10.7005i 0.428708 0.428708i
624624 8.69228 3.76124i 0.347970 0.150570i
625625 23.5022 + 8.52333i 0.940087 + 0.340933i
626626 −8.08410 + 0.828233i −0.323106 + 0.0331028i
627627 −2.31601 2.31601i −0.0924927 0.0924927i
628628 −6.32192 4.15283i −0.252272 0.165716i
629629 3.60306i 0.143664i
630630 −0.360857 23.8669i −0.0143769 0.950879i
631631 10.1166i 0.402735i −0.979516 0.201367i 0.935462π-0.935462\pi
0.979516 0.201367i 0.0645385π-0.0645385\pi
632632 −35.5018 18.4425i −1.41219 0.733604i
633633 2.85891 + 2.85891i 0.113632 + 0.113632i
634634 −1.42989 13.9566i −0.0567880 0.554289i
635635 −11.6864 13.9192i −0.463762 0.552366i
636636 10.5147 + 50.7767i 0.416936 + 2.01343i
637637 2.41462 2.41462i 0.0956709 0.0956709i
638638 −8.61084 + 10.5766i −0.340906 + 0.418733i
639639 35.1888 1.39205
640640 −24.9843 3.97314i −0.987590 0.157052i
641641 −33.6135 −1.32765 −0.663827 0.747886i 0.731069π-0.731069\pi
−0.663827 + 0.747886i 0.731069π0.731069\pi
642642 1.35709 1.66690i 0.0535599 0.0657872i
643643 29.4474 29.4474i 1.16129 1.16129i 0.177097 0.984193i 0.443329π-0.443329\pi
0.984193 0.177097i 0.0566706π-0.0566706\pi
644644 6.58458 + 31.7976i 0.259469 + 1.25300i
645645 −2.27289 + 26.0660i −0.0894950 + 1.02635i
646646 −0.266302 2.59929i −0.0104775 0.102268i
647647 5.15400 + 5.15400i 0.202625 + 0.202625i 0.801124 0.598499i 0.204236π-0.204236\pi
−0.598499 + 0.801124i 0.704236π0.704236\pi
648648 26.4324 + 13.7311i 1.03836 + 0.539410i
649649 2.51199i 0.0986044i
650650 7.22125 + 0.519806i 0.283241 + 0.0203885i
651651 56.8647i 2.22870i
652652 12.1564 + 7.98545i 0.476080 + 0.312734i
653653 16.9805 + 16.9805i 0.664498 + 0.664498i 0.956437 0.291939i 0.0943004π-0.0943004\pi
−0.291939 + 0.956437i 0.594300π0.594300\pi
654654 22.0727 2.26139i 0.863111 0.0884275i
655655 3.51456 40.3058i 0.137325 1.57488i
656656 −29.8015 + 12.8954i −1.16355 + 0.503481i
657657 4.67199 4.67199i 0.182272 0.182272i
658658 −42.9766 34.9889i −1.67540 1.36401i
659659 38.6928 1.50726 0.753629 0.657300i 0.228301π-0.228301\pi
0.753629 + 0.657300i 0.228301π0.228301\pi
660660 −6.40756 + 8.11800i −0.249414 + 0.315993i
661661 3.52220 0.136998 0.0684988 0.997651i 0.478179π-0.478179\pi
0.0684988 + 0.997651i 0.478179π0.478179\pi
662662 27.4196 + 22.3233i 1.06569 + 0.867621i
663663 2.18409 2.18409i 0.0848231 0.0848231i
664664 12.8720 4.07062i 0.499529 0.157971i
665665 −6.54672 7.79749i −0.253871 0.302374i
666666 −9.12354 + 0.934725i −0.353530 + 0.0362198i
667667 34.4401 + 34.4401i 1.33352 + 1.33352i
668668 15.8735 24.1645i 0.614164 0.934952i
669669 13.1270i 0.507520i
670670 −31.3798 + 0.474450i −1.21231 + 0.0183296i
671671 3.54775i 0.136960i
672672 −11.4169 + 40.4765i −0.440415 + 1.56142i
673673 −2.73473 2.73473i −0.105416 0.105416i 0.652432 0.757848i 0.273749π-0.273749\pi
−0.757848 + 0.652432i 0.773749π0.773749\pi
674674 0.586124 + 5.72096i 0.0225766 + 0.220363i
675675 4.32813 + 6.17361i 0.166590 + 0.237623i
676676 −23.4067 + 4.84701i −0.900260 + 0.186424i
677677 3.78865 3.78865i 0.145610 0.145610i −0.630544 0.776154i 0.717168π-0.717168\pi
0.776154 + 0.630544i 0.217168π0.217168\pi
678678 9.83474 12.0799i 0.377701 0.463927i
679679 −1.40799 −0.0540337
680680 −8.05276 + 1.79492i −0.308809 + 0.0688320i
681681 24.0071 0.919955
682682 −6.82938 + 8.38848i −0.261511 + 0.321212i
683683 −13.7937 + 13.7937i −0.527802 + 0.527802i −0.919916 0.392115i 0.871744π-0.871744\pi
0.392115 + 0.919916i 0.371744π0.371744\pi
684684 −6.51272 + 1.34864i −0.249020 + 0.0515665i
685685 15.3872 12.9189i 0.587913 0.493608i
686686 −1.69818 16.5753i −0.0648367 0.632849i
687687 −3.14060 3.14060i −0.119822 0.119822i
688688 7.45114 18.8181i 0.284072 0.717434i
689689 11.4791i 0.437319i
690690 26.5076 + 25.7179i 1.00913 + 0.979065i
691691 22.1562i 0.842861i −0.906861 0.421431i 0.861528π-0.861528\pi
0.906861 0.421431i 0.138472π-0.138472\pi
692692 20.8835 31.7912i 0.793870 1.20852i
693693 5.33741 + 5.33741i 0.202751 + 0.202751i
694694 −0.884733 + 0.0906427i −0.0335840 + 0.00344075i
695695 −2.08471 0.181782i −0.0790777 0.00689537i
696696 19.0200 + 60.1445i 0.720952 + 2.27977i
697697 −7.48816 + 7.48816i −0.283634 + 0.283634i
698698 −12.2573 9.97917i −0.463948 0.377717i
699699 −51.3251 −1.94129
700700 −22.0347 + 23.4092i −0.832832 + 0.884783i
701701 3.91585 0.147899 0.0739497 0.997262i 0.476440π-0.476440\pi
0.0739497 + 0.997262i 0.476440π0.476440\pi
702702 1.69326 + 1.37854i 0.0639078 + 0.0520298i
703703 −2.76616 + 2.76616i −0.104328 + 0.104328i
704704 6.54536 4.59981i 0.246688 0.173362i
705705 −62.7936 5.47543i −2.36494 0.206217i
706706 −18.9452 + 1.94097i −0.713011 + 0.0730495i
707707 −18.9597 18.9597i −0.713054 0.713054i
708708 9.71057 + 6.37882i 0.364946 + 0.239731i
709709 14.8137i 0.556341i 0.960532 + 0.278170i 0.0897280π0.0897280\pi
−0.960532 + 0.278170i 0.910272π0.910272\pi
710710 −34.0150 33.0017i −1.27656 1.23853i
711711 33.2101i 1.24548i
712712 −6.13760 + 11.8149i −0.230016 + 0.442781i
713713 27.3149 + 27.3149i 1.02295 + 1.02295i
714714 1.39786 + 13.6440i 0.0523135 + 0.510615i
715715 −1.75341 + 1.47215i −0.0655738 + 0.0550552i
716716 −2.06035 9.94966i −0.0769990 0.371836i
717717 40.0965 40.0965i 1.49743 1.49743i
718718 −21.4286 + 26.3206i −0.799710 + 0.982278i
719719 10.4233 0.388724 0.194362 0.980930i 0.437736π-0.437736\pi
0.194362 + 0.980930i 0.437736π0.437736\pi
720720 6.63411 + 19.9252i 0.247239 + 0.742569i
721721 41.1197 1.53138
722722 15.1735 18.6375i 0.564700 0.693617i
723723 9.02990 9.02990i 0.335825 0.335825i
724724 3.93269 + 18.9914i 0.146157 + 0.705809i
725725 −8.34582 + 47.4920i −0.309956 + 1.76381i
726726 −0.333320 3.25343i −0.0123707 0.120746i
727727 21.3788 + 21.3788i 0.792897 + 0.792897i 0.981964 0.189067i 0.0605465π-0.0605465\pi
−0.189067 + 0.981964i 0.560546π0.560546\pi
728728 −4.29185 + 8.26180i −0.159067 + 0.306203i
729729 14.2646i 0.528319i
730730 −8.89775 + 0.134530i −0.329321 + 0.00497919i
731731 6.60063i 0.244133i
732732 13.7145 + 9.00897i 0.506902 + 0.332981i
733733 1.02633 + 1.02633i 0.0379083 + 0.0379083i 0.725807 0.687899i 0.241467π-0.241467\pi
−0.687899 + 0.725807i 0.741467π0.741467\pi
734734 −21.3077 + 2.18302i −0.786482 + 0.0805766i
735735 11.0895 + 13.2081i 0.409041 + 0.487190i
736736 −13.9588 24.9270i −0.514528 0.918821i
737737 7.01754 7.01754i 0.258495 0.258495i
738738 20.9038 + 17.0186i 0.769481 + 0.626464i
739739 −5.29534 −0.194792 −0.0973961 0.995246i 0.531051π-0.531051\pi
−0.0973961 + 0.995246i 0.531051π0.531051\pi
740740 9.69582 + 7.65293i 0.356425 + 0.281327i
741741 −3.35356 −0.123196
742742 −39.5284 32.1816i −1.45113 1.18142i
743743 32.9662 32.9662i 1.20941 1.20941i 0.238196 0.971217i 0.423444π-0.423444\pi
0.971217 0.238196i 0.0765560π-0.0765560\pi
744744 15.0851 + 47.7015i 0.553045 + 1.74882i
745745 2.43353 27.9083i 0.0891575 1.02248i
746746 25.3655 2.59875i 0.928697 0.0951469i
747747 −7.92446 7.92446i −0.289941 0.289941i
748748 1.43242 2.18060i 0.0523746 0.0797307i
749749 2.11291i 0.0772042i
750750 −5.78343 + 36.1045i −0.211181 + 1.31835i
751751 21.6289i 0.789249i −0.918842 0.394625i 0.870875π-0.870875\pi
0.918842 0.394625i 0.129125π-0.129125\pi
752752 45.3332 + 17.9499i 1.65313 + 0.654566i
753753 −21.4342 21.4342i −0.781107 0.781107i
754754 1.42322 + 13.8916i 0.0518307 + 0.505902i
755755 2.25479 25.8584i 0.0820601 0.941084i
756756 −9.49406 + 1.96601i −0.345295 + 0.0715030i
757757 18.2612 18.2612i 0.663714 0.663714i −0.292539 0.956254i 0.594500π-0.594500\pi
0.956254 + 0.292539i 0.0945002π0.0945002\pi
758758 10.6868 13.1265i 0.388161 0.476776i
759759 −11.6793 −0.423932
760760 7.56029 + 4.80429i 0.274240 + 0.174270i
761761 10.6344 0.385497 0.192749 0.981248i 0.438260π-0.438260\pi
0.192749 + 0.981248i 0.438260π0.438260\pi
762762 16.7828 20.6142i 0.607976 0.746772i
763763 −15.4226 + 15.4226i −0.558336 + 0.558336i
764764 12.9246 2.67641i 0.467597 0.0968290i
765765 4.40385 + 5.24522i 0.159222 + 0.189641i
766766 −0.0166631 0.162643i −0.000602062 0.00587653i
767767 1.81867 + 1.81867i 0.0656683 + 0.0656683i
768768 −1.16047 36.9828i −0.0418748 1.33450i
769769 23.9199i 0.862572i −0.902215 0.431286i 0.858060π-0.858060\pi
0.902215 0.431286i 0.141940π-0.141940\pi
770770 −0.153691 10.1650i −0.00553864 0.366322i
771771 67.5657i 2.43332i
772772 −11.1724 + 17.0079i −0.402102 + 0.612126i
773773 0.715023 + 0.715023i 0.0257176 + 0.0257176i 0.719849 0.694131i 0.244211π-0.244211\pi
−0.694131 + 0.719849i 0.744211π0.744211\pi
774774 −16.7138 + 1.71237i −0.600767 + 0.0615498i
775775 −6.61919 + 37.6666i −0.237768 + 1.35303i
776776 1.18110 0.373511i 0.0423992 0.0134083i
777777 14.5200 14.5200i 0.520900 0.520900i
778778 14.3486 + 11.6817i 0.514421 + 0.418809i
779779 11.4977 0.411947
780780 1.23835 + 10.5164i 0.0443400 + 0.376548i
781781 14.9871 0.536280
782782 −7.22536 5.88244i −0.258378 0.210356i
783783 −10.2830 + 10.2830i −0.367485 + 0.367485i
784784 −5.29790 12.2435i −0.189211 0.437268i
785785 6.47664 5.43774i 0.231161 0.194081i
786786 58.8665 6.03100i 2.09970 0.215119i
787787 6.63240 + 6.63240i 0.236420 + 0.236420i 0.815366 0.578946i 0.196536π-0.196536\pi
−0.578946 + 0.815366i 0.696536π0.696536\pi
788788 −35.2044 23.1256i −1.25410 0.823814i
789789 19.1733i 0.682587i
790790 31.1460 32.1023i 1.10812 1.14215i
791791 15.3122i 0.544439i
792792 −5.89324 3.06143i −0.209407 0.108783i
793793 2.56855 + 2.56855i 0.0912119 + 0.0912119i
794794 2.81713 + 27.4971i 0.0999762 + 0.975834i
795795 −57.7553 5.03611i −2.04837 0.178613i
796796 8.45112 + 40.8114i 0.299542 + 1.44652i
797797 2.54383 2.54383i 0.0901071 0.0901071i −0.660616 0.750724i 0.729705π-0.729705\pi
0.750724 + 0.660616i 0.229705π0.229705\pi
798798 9.40167 11.5480i 0.332815 0.408795i
799799 15.9010 0.562538
800800 12.2740 25.4823i 0.433951 0.900936i
801801 11.0522 0.390510
802802 −26.6979 + 32.7929i −0.942736 + 1.15796i
803803 1.98983 1.98983i 0.0702194 0.0702194i
804804 −9.30763 44.9475i −0.328255 1.58518i
805805 −36.1678 3.15374i −1.27475 0.111155i
806806 1.12878 + 11.0176i 0.0397595 + 0.388080i
807807 −20.9848 20.9848i −0.738698 0.738698i
808808 20.9342 + 10.8749i 0.736462 + 0.382578i
809809 6.12905i 0.215486i −0.994179 0.107743i 0.965638π-0.965638\pi
0.994179 0.107743i 0.0343624π-0.0343624\pi
810810 −23.1893 + 23.9013i −0.814790 + 0.839807i
811811 16.4078i 0.576156i 0.957607 + 0.288078i 0.0930163π0.0930163\pi
−0.957607 + 0.288078i 0.906984π0.906984\pi
812812 −51.8258 34.0441i −1.81873 1.19471i
813813 −30.5672 30.5672i −1.07204 1.07204i
814814 −3.88576 + 0.398104i −0.136196 + 0.0139535i
815815 −12.4539 + 10.4562i −0.436240 + 0.366264i
816816 −4.79209 11.0746i −0.167757 0.387688i
817817 −5.06745 + 5.06745i −0.177288 + 0.177288i
818818 −28.0588 22.8437i −0.981053 0.798712i
819819 7.72849 0.270055
820820 −4.24568 36.0555i −0.148266 1.25911i
821821 1.10741 0.0386488 0.0193244 0.999813i 0.493848π-0.493848\pi
0.0193244 + 0.999813i 0.493848π0.493848\pi
822822 22.7882 + 18.5528i 0.794831 + 0.647102i
823823 2.63390 2.63390i 0.0918121 0.0918121i −0.659709 0.751521i 0.729320π-0.729320\pi
0.751521 + 0.659709i 0.229320π0.229320\pi
824824 −34.4936 + 10.9082i −1.20164 + 0.380006i
825825 −6.63763 9.46786i −0.231093 0.329629i
826826 −11.3612 + 1.16398i −0.395307 + 0.0405000i
827827 −23.9250 23.9250i −0.831955 0.831955i 0.155829 0.987784i 0.450195π-0.450195\pi
−0.987784 + 0.155829i 0.950195π0.950195\pi
828828 −13.0208 + 19.8218i −0.452506 + 0.688856i
829829 7.35056i 0.255296i 0.991820 + 0.127648i 0.0407427π0.0407427\pi
−0.991820 + 0.127648i 0.959257π0.959257\pi
830830 0.228185 + 15.0920i 0.00792043 + 0.523852i
831831 20.8544i 0.723431i
832832 1.40857 8.06903i 0.0488333 0.279743i
833833 −3.07640 3.07640i −0.106591 0.106591i
834834 −0.311938 3.04472i −0.0108015 0.105430i
835835 20.7848 + 24.7559i 0.719289 + 0.856712i
836836 −2.77380 + 0.574393i −0.0959340 + 0.0198658i
837837 −8.15562 + 8.15562i −0.281900 + 0.281900i
838838 4.74226 5.82488i 0.163819 0.201217i
839839 −43.5458 −1.50337 −0.751684 0.659523i 0.770758π-0.770758\pi
−0.751684 + 0.659523i 0.770758π0.770758\pi
840840 −39.6850 25.2184i −1.36926 0.870117i
841841 −64.0058 −2.20710
842842 −12.8312 + 15.7605i −0.442193 + 0.543143i
843843 −27.1423 + 27.1423i −0.934831 + 0.934831i
844844 3.42401 0.709036i 0.117859 0.0244060i
845845 2.32152 26.6237i 0.0798627 0.915884i
846846 −4.12512 40.2639i −0.141825 1.38430i
847847 2.27323 + 2.27323i 0.0781091 + 0.0781091i
848848 41.6959 + 16.5097i 1.43184 + 0.566946i
849849 34.6944i 1.19071i
850850 0.662271 9.20039i 0.0227157 0.315571i
851851 13.9493i 0.478176i
852852 38.0574 57.9353i 1.30382 1.98483i
853853 37.1733 + 37.1733i 1.27279 + 1.27279i 0.944617 + 0.328174i 0.106433π0.106433\pi
0.328174 + 0.944617i 0.393567π0.393567\pi
854854 −16.0457 + 1.64392i −0.549073 + 0.0562537i
855855 0.645942 7.40782i 0.0220908 0.253342i
856856 −0.560513 1.77244i −0.0191580 0.0605807i
857857 −12.1732 + 12.1732i −0.415830 + 0.415830i −0.883763 0.467934i 0.844999π-0.844999\pi
0.467934 + 0.883763i 0.344999π0.344999\pi
858858 −2.59678 2.11414i −0.0886526 0.0721754i
859859 −9.73794 −0.332254 −0.166127 0.986104i 0.553126π-0.553126\pi
−0.166127 + 0.986104i 0.553126π0.553126\pi
860860 17.7622 + 14.0198i 0.605687 + 0.478070i
861861 −60.3529 −2.05682
862862 −42.0882 34.2656i −1.43353 1.16709i
863863 9.20125 9.20125i 0.313214 0.313214i −0.532939 0.846154i 0.678913π-0.678913\pi
0.846154 + 0.532939i 0.178913π0.178913\pi
864864 7.44263 4.16778i 0.253203 0.141791i
865865 27.3449 + 32.5693i 0.929754 + 1.10739i
866866 12.7001 1.30115i 0.431565 0.0442148i
867867 25.0162 + 25.0162i 0.849594 + 0.849594i
868868 −41.1038 27.0009i −1.39515 0.916469i
869869 14.1444i 0.479815i
870870 −70.5178 + 1.06620i −2.39078 + 0.0361476i
871871 10.1613i 0.344303i
872872 8.84609 17.0287i 0.299566 0.576665i
873873 −0.727132 0.727132i −0.0246097 0.0246097i
874874 1.03099 + 10.0632i 0.0348738 + 0.340392i
875875 −17.9984 31.1119i −0.608459 1.05177i
876876 −2.63918 12.7449i −0.0891696 0.430610i
877877 17.7574 17.7574i 0.599624 0.599624i −0.340588 0.940213i 0.610626π-0.610626\pi
0.940213 + 0.340588i 0.110626π0.110626\pi
878878 −14.5888 + 17.9194i −0.492349 + 0.604749i
879879 −50.2303 −1.69422
880880 2.82550 + 8.48626i 0.0952477 + 0.286072i
881881 27.2559 0.918274 0.459137 0.888365i 0.348159π-0.348159\pi
0.459137 + 0.888365i 0.348159π0.348159\pi
882882 −6.99185 + 8.58804i −0.235428 + 0.289175i
883883 −8.06986 + 8.06986i −0.271573 + 0.271573i −0.829733 0.558160i 0.811507π-0.811507\pi
0.558160 + 0.829733i 0.311507π0.311507\pi
884884 −0.541675 2.61581i −0.0182185 0.0879791i
885885 −9.94823 + 8.35245i −0.334406 + 0.280765i
886886 1.40086 + 13.6734i 0.0470629 + 0.459366i
887887 0.528230 + 0.528230i 0.0177362 + 0.0177362i 0.715919 0.698183i 0.246008π-0.246008\pi
−0.698183 + 0.715919i 0.746008π0.746008\pi
888888 −8.32834 + 16.0320i −0.279481 + 0.538000i
889889 26.1299i 0.876370i
890890 −10.6835 10.3653i −0.358112 0.347445i
891891 10.5310i 0.352802i
892892 −9.48868 6.23306i −0.317705 0.208698i
893893 −12.2076 12.2076i −0.408511 0.408511i
894894 40.7599 4.17594i 1.36322 0.139664i
895895 11.3171 + 0.986823i 0.378290 + 0.0329859i
896896 23.8369 + 27.4719i 0.796334 + 0.917770i
897897 −8.45574 + 8.45574i −0.282329 + 0.282329i
898898 −4.87090 3.96558i −0.162544 0.132333i
899899 −73.7643 −2.46018
900900 −23.4687 + 0.709835i −0.782289 + 0.0236612i
901901 14.6252 0.487236
902902 8.90305 + 7.24831i 0.296439 + 0.241342i
903903 26.5998 26.5998i 0.885186 0.885186i
904904 −4.06202 12.8448i −0.135101 0.427211i
905905 −21.6015 1.88359i −0.718058 0.0626128i
906906 37.7661 3.86922i 1.25470 0.128546i
907907 1.27942 + 1.27942i 0.0424825 + 0.0424825i 0.728029 0.685546i 0.240437π-0.240437\pi
−0.685546 + 0.728029i 0.740437π0.740437\pi
908908 11.3992 17.3532i 0.378296 0.575886i
909909 19.5828i 0.649522i
910910 −7.47068 7.24814i −0.247651 0.240274i
911911 39.0054i 1.29231i 0.763208 + 0.646153i 0.223623π0.223623\pi
−0.763208 + 0.646153i 0.776377π0.776377\pi
912912 −4.82322 + 12.1812i −0.159713 + 0.403360i
913913 −3.37507 3.37507i −0.111698 0.111698i
914914 −2.41615 23.5832i −0.0799191 0.780064i
915915 −14.0501 + 11.7964i −0.464483 + 0.389976i
916916 −3.76138 + 0.778898i −0.124280 + 0.0257355i
917917 −41.1312 + 41.1312i −1.35827 + 1.35827i
918918 1.75636 2.15733i 0.0579687 0.0712025i
919919 44.5397 1.46923 0.734615 0.678484i 0.237363π-0.237363\pi
0.734615 + 0.678484i 0.237363π0.237363\pi
920920 31.1763 6.94905i 1.02785 0.229103i
921921 3.19168 0.105169
922922 22.8481 28.0642i 0.752463 0.924245i
923923 10.8506 10.8506i 0.357150 0.357150i
924924 14.5601 3.01507i 0.478992 0.0991885i
925925 −11.3080 + 7.92772i −0.371806 + 0.260662i
926926 −3.34875 32.6860i −0.110047 1.07413i
927927 21.2355 + 21.2355i 0.697467 + 0.697467i
928928 52.5058 + 14.8098i 1.72359 + 0.486157i
929929 38.4798i 1.26248i −0.775587 0.631241i 0.782546π-0.782546\pi
0.775587 0.631241i 0.217454π-0.217454\pi
930930 −55.9287 + 0.845619i −1.83397 + 0.0277289i
931931 4.72365i 0.154811i
932932 −24.3705 + 37.0996i −0.798283 + 1.21524i
933933 8.68715 + 8.68715i 0.284404 + 0.284404i
934934 38.8635 3.98165i 1.27165 0.130283i
935935 1.87562 + 2.23397i 0.0613394 + 0.0730586i
936936 −6.48311 + 2.05021i −0.211907 + 0.0670133i
937937 −12.6310 + 12.6310i −0.412637 + 0.412637i −0.882656 0.470019i 0.844247π-0.844247\pi
0.470019 + 0.882656i 0.344247π0.344247\pi
938938 34.9905 + 28.4871i 1.14248 + 0.930138i
939939 13.2885 0.433655
940940 −33.7739 + 42.7895i −1.10158 + 1.39564i
941941 −0.184281 −0.00600739 −0.00300370 0.999995i 0.500956π-0.500956\pi
−0.00300370 + 0.999995i 0.500956π0.500956\pi
942942 9.59184 + 7.80908i 0.312519 + 0.254434i
943943 28.9905 28.9905i 0.944060 0.944060i
944944 9.22167 3.99031i 0.300140 0.129874i
945945 0.941636 10.7989i 0.0306314 0.351288i
946946 −7.11851 + 0.729306i −0.231443 + 0.0237118i
947947 29.9611 + 29.9611i 0.973605 + 0.973605i 0.999660 0.0260556i 0.00829470π-0.00829470\pi
−0.0260556 + 0.999660i 0.508295π0.508295\pi
948948 54.6776 + 35.9174i 1.77585 + 1.16654i
949949 2.88124i 0.0935290i
950950 −7.57179 + 6.55491i −0.245661 + 0.212669i
951951 22.9417i 0.743937i
952952 10.5261 + 5.46813i 0.341154 + 0.177223i
953953 25.4062 + 25.4062i 0.822988 + 0.822988i 0.986535 0.163548i 0.0522938π-0.0522938\pi
−0.163548 + 0.986535i 0.552294π0.552294\pi
954954 −3.79414 37.0334i −0.122840 1.19900i
955955 −1.28189 + 14.7010i −0.0414809 + 0.475713i
956956 −9.94429 48.0220i −0.321621 1.55314i
957957 15.7701 15.7701i 0.509774 0.509774i
958958 1.06634 1.30978i 0.0344520 0.0423171i
959959 −28.8857 −0.932769
960960 39.9801 + 10.6270i 1.29035 + 0.342986i
961961 −27.5036 −0.887212
962962 −2.52504 + 3.10149i −0.0814106 + 0.0999960i
963963 −1.09118 + 1.09118i −0.0351627 + 0.0351627i
964964 −2.23950 10.8148i −0.0721293 0.348320i
965965 −14.6291 17.4241i −0.470929 0.560902i
966966 −5.41182 52.8230i −0.174123 1.69955i
967967 14.3306 + 14.3306i 0.460842 + 0.460842i 0.898931 0.438089i 0.144345π-0.144345\pi
−0.438089 + 0.898931i 0.644345π0.644345\pi
968968 −2.50996 1.30388i −0.0806732 0.0419082i
969969 4.27267i 0.137258i
970970 0.0209378 + 1.38481i 0.000672273 + 0.0444637i
971971 27.6798i 0.888287i 0.895956 + 0.444143i 0.146492π0.146492\pi
−0.895956 + 0.444143i 0.853508π0.853508\pi
972972 −33.1475 21.7744i −1.06321 0.698415i
973973 2.12740 + 2.12740i 0.0682014 + 0.0682014i
974974 6.45065 0.660882i 0.206692 0.0211760i
975975 −11.6603 2.04907i −0.373427 0.0656227i
976976 13.0240 5.63562i 0.416888 0.180392i
977977 −10.8893 + 10.8893i −0.348381 + 0.348381i −0.859506 0.511125i 0.829229π-0.829229\pi
0.511125 + 0.859506i 0.329229π0.329229\pi
978978 −18.4441 15.0160i −0.589776 0.480159i
979979 4.70719 0.150443
980980 14.8129 1.74428i 0.473180 0.0557189i
981981 −15.9295 −0.508589
982982 12.7363 + 10.3691i 0.406431 + 0.330891i
983983 −1.95471 + 1.95471i −0.0623455 + 0.0623455i −0.737592 0.675247i 0.764037π-0.764037\pi
0.675247 + 0.737592i 0.264037π0.264037\pi
984984 50.6276 16.0104i 1.61395 0.510393i
985985 36.0660 30.2807i 1.14916 0.964823i
986986 17.6989 1.81329i 0.563648 0.0577468i
987987 64.0794 + 64.0794i 2.03967 + 2.03967i
988988 −1.59236 + 2.42407i −0.0506597 + 0.0771200i
989989 25.5544i 0.812583i
990990 5.17018 5.32892i 0.164319 0.169364i
991991 0.700492i 0.0222519i −0.999938 0.0111259i 0.996458π-0.996458\pi
0.999938 0.0111259i 0.00354157π-0.00354157\pi
992992 41.6431 + 11.7459i 1.32217 + 0.372933i
993993 −40.8834 40.8834i −1.29740 1.29740i
994994 6.94455 + 67.7834i 0.220268 + 2.14996i
995995 −46.4204 4.04774i −1.47163 0.128322i
996996 −21.6174 + 4.47648i −0.684974 + 0.141843i
997997 4.80082 4.80082i 0.152044 0.152044i −0.626987 0.779030i 0.715712π-0.715712\pi
0.779030 + 0.626987i 0.215712π0.215712\pi
998998 −14.7778 + 18.1515i −0.467785 + 0.574577i
999999 −4.16495 −0.131773
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 220.2.l.c.23.5 28
4.3 odd 2 220.2.l.d.23.3 yes 28
5.2 odd 4 220.2.l.d.67.3 yes 28
20.7 even 4 inner 220.2.l.c.67.5 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
220.2.l.c.23.5 28 1.1 even 1 trivial
220.2.l.c.67.5 yes 28 20.7 even 4 inner
220.2.l.d.23.3 yes 28 4.3 odd 2
220.2.l.d.67.3 yes 28 5.2 odd 4