Properties

Label 161.2.g.a.45.11
Level 161161
Weight 22
Character 161.45
Analytic conductor 1.2861.286
Analytic rank 00
Dimension 2828
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [161,2,Mod(45,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.45"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 161=723 161 = 7 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 161.g (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.285591472541.28559147254
Analytic rank: 00
Dimension: 2828
Relative dimension: 1414 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 45.11
Character χ\chi == 161.45
Dual form 161.2.g.a.68.11

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.724735+1.25528i)q2+(2.075261.19815i)q3+(0.0504829+0.0874389i)q4+(1.267812.19591i)q53.47337iq6+(1.915091.82550i)q7+2.75259q8+(1.37113+2.37487i)q9+(1.837663.18291i)q10+(0.9541490.550878i)q11+(0.2095300.120972i)q120.792485iq13+(0.9035753.72697i)q14+6.07612iq15+(2.09587+3.63015i)q16+(1.965663.40463i)q17+(1.98742+3.44231i)q18+(3.54203+6.13498i)q19+0.256011q20+(1.78708+6.08294i)q211.59696iq22+(4.113792.46510i)q23+(5.712353.29803i)q24+(0.714694+1.23789i)q25+(0.9947900.574342i)q26+0.617607iq27+(0.2562990.0752969i)q28+1.18102q29+(7.62723+4.40358i)q30+(4.227842.44094i)q31+(0.285306+0.494164i)q32+(1.32007+2.28643i)q33+5.69834q34+(1.58066+6.51976i)q350.276875q36+(9.917235.72572i)q37+(5.13407+8.89247i)q38+(0.949517+1.64461i)q39+(3.489776.04446i)q40+0.854610iq41+(6.34063+6.65181i)q42+4.03573iq43+(0.09633630.0556198i)q44+(3.476686.02178i)q45+(0.1129846.95050i)q46+(9.870895.69896i)q4710.0447iq48+(0.335124+6.99197i)q492.07186q50+(8.15852+4.71032i)q51+(0.0692940+0.0400069i)q52+(3.141731.81388i)q53+(0.775269+0.447602i)q54+2.79364iq55+(5.271465.02485i)q5616.9756iq57+(0.855928+1.48251i)q58+(4.202832.42650i)q59+(0.5312890.306740i)q60+(5.00067+8.66142i)q617.07616iq62+(1.709487.05109i)q63+7.55639q64+(1.74023+1.00472i)q65+(1.91340+3.31411i)q66+(4.47989+2.58647i)q67+(0.198465+0.343751i)q68+(5.58361+10.0447i)q69+(9.32967+2.74093i)q7010.5645q71+(3.77417+6.53706i)q72+(8.12777+4.69257i)q73+(14.3747+8.29926i)q74+(2.966351.71262i)q750.715248q76+(0.821653+2.79677i)q772.75259q78+(5.615403.24205i)q79+(5.314339.20470i)q80+(4.853398.40631i)q81+(1.07277+0.619366i)q82+5.50430q83+(0.6221030.150824i)q849.96836q85+(5.06597+2.92484i)q86+(2.450921.41504i)q87+(2.626381.51634i)q88+(0.261287+0.452563i)q89+10.0787q90+(1.44668+1.51768i)q91+(0.4232220.235260i)q92+(5.84924+10.1312i)q93+(14.3076+8.26048i)q94+(8.9812615.5560i)q95+(1.184170.683679i)q9611.9199q97+(8.53400+5.48801i)q983.02131iq99+O(q100)q+(0.724735 + 1.25528i) q^{2} +(-2.07526 - 1.19815i) q^{3} +(-0.0504829 + 0.0874389i) q^{4} +(-1.26781 - 2.19591i) q^{5} -3.47337i q^{6} +(-1.91509 - 1.82550i) q^{7} +2.75259 q^{8} +(1.37113 + 2.37487i) q^{9} +(1.83766 - 3.18291i) q^{10} +(-0.954149 - 0.550878i) q^{11} +(0.209530 - 0.120972i) q^{12} -0.792485i q^{13} +(0.903575 - 3.72697i) q^{14} +6.07612i q^{15} +(2.09587 + 3.63015i) q^{16} +(1.96566 - 3.40463i) q^{17} +(-1.98742 + 3.44231i) q^{18} +(3.54203 + 6.13498i) q^{19} +0.256011 q^{20} +(1.78708 + 6.08294i) q^{21} -1.59696i q^{22} +(-4.11379 - 2.46510i) q^{23} +(-5.71235 - 3.29803i) q^{24} +(-0.714694 + 1.23789i) q^{25} +(0.994790 - 0.574342i) q^{26} +0.617607i q^{27} +(0.256299 - 0.0752969i) q^{28} +1.18102 q^{29} +(-7.62723 + 4.40358i) q^{30} +(-4.22784 - 2.44094i) q^{31} +(-0.285306 + 0.494164i) q^{32} +(1.32007 + 2.28643i) q^{33} +5.69834 q^{34} +(-1.58066 + 6.51976i) q^{35} -0.276875 q^{36} +(9.91723 - 5.72572i) q^{37} +(-5.13407 + 8.89247i) q^{38} +(-0.949517 + 1.64461i) q^{39} +(-3.48977 - 6.04446i) q^{40} +0.854610i q^{41} +(-6.34063 + 6.65181i) q^{42} +4.03573i q^{43} +(0.0963363 - 0.0556198i) q^{44} +(3.47668 - 6.02178i) q^{45} +(0.112984 - 6.95050i) q^{46} +(9.87089 - 5.69896i) q^{47} -10.0447i q^{48} +(0.335124 + 6.99197i) q^{49} -2.07186 q^{50} +(-8.15852 + 4.71032i) q^{51} +(0.0692940 + 0.0400069i) q^{52} +(-3.14173 - 1.81388i) q^{53} +(-0.775269 + 0.447602i) q^{54} +2.79364i q^{55} +(-5.27146 - 5.02485i) q^{56} -16.9756i q^{57} +(0.855928 + 1.48251i) q^{58} +(-4.20283 - 2.42650i) q^{59} +(-0.531289 - 0.306740i) q^{60} +(5.00067 + 8.66142i) q^{61} -7.07616i q^{62} +(1.70948 - 7.05109i) q^{63} +7.55639 q^{64} +(-1.74023 + 1.00472i) q^{65} +(-1.91340 + 3.31411i) q^{66} +(4.47989 + 2.58647i) q^{67} +(0.198465 + 0.343751i) q^{68} +(5.58361 + 10.0447i) q^{69} +(-9.32967 + 2.74093i) q^{70} -10.5645 q^{71} +(3.77417 + 6.53706i) q^{72} +(8.12777 + 4.69257i) q^{73} +(14.3747 + 8.29926i) q^{74} +(2.96635 - 1.71262i) q^{75} -0.715248 q^{76} +(0.821653 + 2.79677i) q^{77} -2.75259 q^{78} +(5.61540 - 3.24205i) q^{79} +(5.31433 - 9.20470i) q^{80} +(4.85339 - 8.40631i) q^{81} +(-1.07277 + 0.619366i) q^{82} +5.50430 q^{83} +(-0.622103 - 0.150824i) q^{84} -9.96836 q^{85} +(-5.06597 + 2.92484i) q^{86} +(-2.45092 - 1.41504i) q^{87} +(-2.62638 - 1.51634i) q^{88} +(0.261287 + 0.452563i) q^{89} +10.0787 q^{90} +(-1.44668 + 1.51768i) q^{91} +(0.423222 - 0.235260i) q^{92} +(5.84924 + 10.1312i) q^{93} +(14.3076 + 8.26048i) q^{94} +(8.98126 - 15.5560i) q^{95} +(1.18417 - 0.683679i) q^{96} -11.9199 q^{97} +(-8.53400 + 5.48801i) q^{98} -3.02131i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q4q26q312q4+12q8+4q9+6q12+22q1836q2422q2512q2644q296q3210q3516q39+18q4636q47+28q49+84q50+146q98+O(q100) 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/161Z)×\left(\mathbb{Z}/161\mathbb{Z}\right)^\times.

nn 2424 120120
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) 1-1

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 0.724735 + 1.25528i 0.512465 + 0.887616i 0.999896 + 0.0144540i 0.00460102π0.00460102\pi
−0.487430 + 0.873162i 0.662066π0.662066\pi
33 −2.07526 1.19815i −1.19815 0.691753i −0.238009 0.971263i 0.576495π-0.576495\pi
−0.960143 + 0.279510i 0.909828π0.909828\pi
44 −0.0504829 + 0.0874389i −0.0252414 + 0.0437195i
55 −1.26781 2.19591i −0.566983 0.982043i −0.996862 0.0791566i 0.974777π-0.974777\pi
0.429879 0.902886i 0.358556π-0.358556\pi
66 3.47337i 1.41800i
77 −1.91509 1.82550i −0.723835 0.689973i
88 2.75259 0.973189
99 1.37113 + 2.37487i 0.457044 + 0.791624i
1010 1.83766 3.18291i 0.581118 1.00653i
1111 −0.954149 0.550878i −0.287687 0.166096i 0.349211 0.937044i 0.386449π-0.386449\pi
−0.636898 + 0.770948i 0.719783π0.719783\pi
1212 0.209530 0.120972i 0.0604861 0.0349217i
1313 0.792485i 0.219796i −0.993943 0.109898i 0.964948π-0.964948\pi
0.993943 0.109898i 0.0350524π-0.0350524\pi
1414 0.903575 3.72697i 0.241490 0.996075i
1515 6.07612i 1.56885i
1616 2.09587 + 3.63015i 0.523967 + 0.907538i
1717 1.96566 3.40463i 0.476743 0.825743i −0.522902 0.852393i 0.675151π-0.675151\pi
0.999645 + 0.0266497i 0.00848388π0.00848388\pi
1818 −1.98742 + 3.44231i −0.468439 + 0.811360i
1919 3.54203 + 6.13498i 0.812598 + 1.40746i 0.911040 + 0.412318i 0.135281π0.135281\pi
−0.0984425 + 0.995143i 0.531386π0.531386\pi
2020 0.256011 0.0572458
2121 1.78708 + 6.08294i 0.389973 + 1.32741i
2222 1.59696i 0.340474i
2323 −4.11379 2.46510i −0.857784 0.514010i
2424 −5.71235 3.29803i −1.16603 0.673207i
2525 −0.714694 + 1.23789i −0.142939 + 0.247577i
2626 0.994790 0.574342i 0.195094 0.112638i
2727 0.617607i 0.118859i
2828 0.256299 0.0752969i 0.0484359 0.0142298i
2929 1.18102 0.219310 0.109655 0.993970i 0.465025π-0.465025\pi
0.109655 + 0.993970i 0.465025π0.465025\pi
3030 −7.62723 + 4.40358i −1.39253 + 0.803980i
3131 −4.22784 2.44094i −0.759342 0.438407i 0.0697172 0.997567i 0.477790π-0.477790\pi
−0.829060 + 0.559160i 0.811124π0.811124\pi
3232 −0.285306 + 0.494164i −0.0504354 + 0.0873567i
3333 1.32007 + 2.28643i 0.229795 + 0.398016i
3434 5.69834 0.977257
3535 −1.58066 + 6.51976i −0.267181 + 1.10204i
3636 −0.276875 −0.0461458
3737 9.91723 5.72572i 1.63038 0.941302i 0.646409 0.762991i 0.276270π-0.276270\pi
0.983974 0.178311i 0.0570633π-0.0570633\pi
3838 −5.13407 + 8.89247i −0.832856 + 1.44255i
3939 −0.949517 + 1.64461i −0.152044 + 0.263349i
4040 −3.48977 6.04446i −0.551781 0.955714i
4141 0.854610i 0.133468i 0.997771 + 0.0667338i 0.0212578π0.0212578\pi
−0.997771 + 0.0667338i 0.978742π0.978742\pi
4242 −6.34063 + 6.65181i −0.978380 + 1.02640i
4343 4.03573i 0.615444i 0.951476 + 0.307722i 0.0995666π0.0995666\pi
−0.951476 + 0.307722i 0.900433π0.900433\pi
4444 0.0963363 0.0556198i 0.0145232 0.00838500i
4545 3.47668 6.02178i 0.518273 0.897674i
4646 0.112984 6.95050i 0.0166585 1.02480i
4747 9.87089 5.69896i 1.43982 0.831279i 0.441981 0.897024i 0.354276π-0.354276\pi
0.997836 + 0.0657452i 0.0209425π0.0209425\pi
4848 10.0447i 1.44982i
4949 0.335124 + 6.99197i 0.0478749 + 0.998853i
5050 −2.07186 −0.293005
5151 −8.15852 + 4.71032i −1.14242 + 0.659577i
5252 0.0692940 + 0.0400069i 0.00960935 + 0.00554796i
5353 −3.14173 1.81388i −0.431550 0.249155i 0.268457 0.963292i 0.413486π-0.413486\pi
−0.700007 + 0.714136i 0.746820π0.746820\pi
5454 −0.775269 + 0.447602i −0.105501 + 0.0609109i
5555 2.79364i 0.376694i
5656 −5.27146 5.02485i −0.704429 0.671474i
5757 16.9756i 2.24847i
5858 0.855928 + 1.48251i 0.112389 + 0.194663i
5959 −4.20283 2.42650i −0.547162 0.315904i 0.200815 0.979629i 0.435641π-0.435641\pi
−0.747976 + 0.663725i 0.768974π0.768974\pi
6060 −0.531289 0.306740i −0.0685892 0.0396000i
6161 5.00067 + 8.66142i 0.640270 + 1.10898i 0.985372 + 0.170416i 0.0545110π0.0545110\pi
−0.345102 + 0.938565i 0.612156π0.612156\pi
6262 7.07616i 0.898673i
6363 1.70948 7.05109i 0.215374 0.888354i
6464 7.55639 0.944549
6565 −1.74023 + 1.00472i −0.215849 + 0.124620i
6666 −1.91340 + 3.31411i −0.235524 + 0.407939i
6767 4.47989 + 2.58647i 0.547306 + 0.315987i 0.748035 0.663660i 0.230998π-0.230998\pi
−0.200729 + 0.979647i 0.564331π0.564331\pi
6868 0.198465 + 0.343751i 0.0240674 + 0.0416859i
6969 5.58361 + 10.0447i 0.672188 + 1.20924i
7070 −9.32967 + 2.74093i −1.11511 + 0.327603i
7171 −10.5645 −1.25378 −0.626888 0.779110i 0.715671π-0.715671\pi
−0.626888 + 0.779110i 0.715671π0.715671\pi
7272 3.77417 + 6.53706i 0.444791 + 0.770400i
7373 8.12777 + 4.69257i 0.951283 + 0.549224i 0.893479 0.449104i 0.148257π-0.148257\pi
0.0578041 + 0.998328i 0.481590π0.481590\pi
7474 14.3747 + 8.29926i 1.67103 + 0.964769i
7575 2.96635 1.71262i 0.342525 0.197757i
7676 −0.715248 −0.0820445
7777 0.821653 + 2.79677i 0.0936360 + 0.318722i
7878 −2.75259 −0.311670
7979 5.61540 3.24205i 0.631781 0.364759i −0.149660 0.988737i 0.547818π-0.547818\pi
0.781442 + 0.623978i 0.214485π0.214485\pi
8080 5.31433 9.20470i 0.594161 1.02912i
8181 4.85339 8.40631i 0.539265 0.934035i
8282 −1.07277 + 0.619366i −0.118468 + 0.0683975i
8383 5.50430 0.604175 0.302087 0.953280i 0.402317π-0.402317\pi
0.302087 + 0.953280i 0.402317π0.402317\pi
8484 −0.622103 0.150824i −0.0678770 0.0164562i
8585 −9.96836 −1.08122
8686 −5.06597 + 2.92484i −0.546278 + 0.315394i
8787 −2.45092 1.41504i −0.262767 0.151708i
8888 −2.62638 1.51634i −0.279974 0.161643i
8989 0.261287 + 0.452563i 0.0276964 + 0.0479716i 0.879541 0.475822i 0.157849π-0.157849\pi
−0.851845 + 0.523794i 0.824516π0.824516\pi
9090 10.0787 1.06239
9191 −1.44668 + 1.51768i −0.151653 + 0.159096i
9292 0.423222 0.235260i 0.0441239 0.0245275i
9393 5.84924 + 10.1312i 0.606538 + 1.05055i
9494 14.3076 + 8.26048i 1.47571 + 0.852003i
9595 8.98126 15.5560i 0.921458 1.59601i
9696 1.18417 0.683679i 0.120859 0.0697777i
9797 −11.9199 −1.21028 −0.605139 0.796120i 0.706882π-0.706882\pi
−0.605139 + 0.796120i 0.706882π0.706882\pi
9898 −8.53400 + 5.48801i −0.862064 + 0.554372i
9999 3.02131i 0.303653i
100100 −0.0721596 0.124984i −0.00721596 0.0124984i
101101 −2.64903 1.52942i −0.263588 0.152183i 0.362382 0.932030i 0.381963π-0.381963\pi
−0.625970 + 0.779847i 0.715297π0.715297\pi
102102 −11.8255 6.82747i −1.17090 0.676021i
103103 −7.66969 13.2843i −0.755717 1.30894i −0.945017 0.327022i 0.893955π-0.893955\pi
0.189299 0.981919i 0.439378π-0.439378\pi
104104 2.18139i 0.213903i
105105 11.0919 11.6363i 1.08246 1.13559i
106106 5.25833i 0.510734i
107107 −12.6702 + 7.31513i −1.22487 + 0.707181i −0.965953 0.258718i 0.916700π-0.916700\pi
−0.258920 + 0.965899i 0.583367π0.583367\pi
108108 −0.0540029 0.0311786i −0.00519643 0.00300016i
109109 12.1657 + 7.02387i 1.16526 + 0.672764i 0.952559 0.304353i 0.0984401π-0.0984401\pi
0.212703 + 0.977117i 0.431773π0.431773\pi
110110 −3.50679 + 2.02465i −0.334360 + 0.193043i
111111 −27.4411 −2.60459
112112 2.61306 10.7781i 0.246911 1.01843i
113113 7.95026i 0.747898i −0.927449 0.373949i 0.878004π-0.878004\pi
0.927449 0.373949i 0.121996π-0.121996\pi
114114 21.3091 12.3028i 1.99578 1.15226i
115115 −0.197647 + 12.1588i −0.0184307 + 1.13382i
116116 −0.0596213 + 0.103267i −0.00553570 + 0.00958812i
117117 1.88205 1.08660i 0.173996 0.100456i
118118 7.03429i 0.647559i
119119 −9.97955 + 2.93185i −0.914824 + 0.268762i
120120 16.7251i 1.52679i
121121 −4.89307 8.47504i −0.444824 0.770458i
122122 −7.24833 + 12.5545i −0.656233 + 1.13663i
123123 1.02395 1.77354i 0.0923267 0.159914i
124124 0.426867 0.246452i 0.0383338 0.0221320i
125125 −9.05373 −0.809790
126126 10.0900 2.96430i 0.898889 0.264081i
127127 −6.22806 −0.552651 −0.276325 0.961064i 0.589117π-0.589117\pi
−0.276325 + 0.961064i 0.589117π0.589117\pi
128128 6.04700 + 10.4737i 0.534484 + 0.925753i
129129 4.83542 8.37519i 0.425735 0.737395i
130130 −2.52241 1.45632i −0.221230 0.127727i
131131 13.0632 7.54205i 1.14134 0.658952i 0.194576 0.980887i 0.437667π-0.437667\pi
0.946762 + 0.321936i 0.104334π0.104334\pi
132132 −0.266564 −0.0232014
133133 4.41608 18.2150i 0.382923 1.57944i
134134 7.49802i 0.647730i
135135 1.35621 0.783010i 0.116724 0.0673908i
136136 5.41067 9.37156i 0.463961 0.803604i
137137 −2.81361 1.62444i −0.240383 0.138785i 0.374970 0.927037i 0.377653π-0.377653\pi
−0.615353 + 0.788252i 0.710986π0.710986\pi
138138 −8.56222 + 14.2887i −0.728865 + 1.21634i
139139 15.7497i 1.33587i 0.744220 + 0.667934i 0.232821π0.232821\pi
−0.744220 + 0.667934i 0.767179π0.767179\pi
140140 −0.490284 0.467348i −0.0414366 0.0394981i
141141 −27.3129 −2.30016
142142 −7.65646 13.2614i −0.642516 1.11287i
143143 −0.436563 + 0.756149i −0.0365072 + 0.0632323i
144144 −5.74743 + 9.95484i −0.478953 + 0.829570i
145145 −1.49731 2.59342i −0.124345 0.215372i
146146 13.6035i 1.12583i
147147 7.68197 14.9117i 0.633598 1.22990i
148148 1.15620i 0.0950393i
149149 −5.41098 + 3.12403i −0.443285 + 0.255931i −0.704990 0.709217i 0.749049π-0.749049\pi
0.261705 + 0.965148i 0.415715π0.415715\pi
150150 4.29964 + 2.48240i 0.351064 + 0.202687i
151151 −8.61081 + 14.9144i −0.700738 + 1.21371i 0.267470 + 0.963566i 0.413812π0.413812\pi
−0.968208 + 0.250148i 0.919521π0.919521\pi
152152 9.74978 + 16.8871i 0.790811 + 1.36973i
153153 10.7807 0.871571
154154 −2.91525 + 3.05833i −0.234918 + 0.246447i
155155 12.3786i 0.994276i
156156 −0.0958687 0.166049i −0.00767564 0.0132946i
157157 −2.92731 + 5.07024i −0.233624 + 0.404649i −0.958872 0.283839i 0.908392π-0.908392\pi
0.725248 + 0.688488i 0.241725π0.241725\pi
158158 8.13935 + 4.69926i 0.647532 + 0.373853i
159159 4.34660 + 7.52853i 0.344708 + 0.597051i
160160 1.44686 0.114384
161161 3.37823 + 12.2306i 0.266242 + 0.963906i
162162 14.0697 1.10542
163163 −2.38556 4.13192i −0.186852 0.323637i 0.757347 0.653012i 0.226495π-0.226495\pi
−0.944199 + 0.329376i 0.893162π0.893162\pi
164164 −0.0747262 0.0431432i −0.00583513 0.00336892i
165165 3.34720 5.79752i 0.260579 0.451337i
166166 3.98916 + 6.90942i 0.309619 + 0.536275i
167167 17.9409i 1.38831i 0.719824 + 0.694156i 0.244222π0.244222\pi
−0.719824 + 0.694156i 0.755778π0.755778\pi
168168 4.91911 + 16.7439i 0.379518 + 1.29182i
169169 12.3720 0.951690
170170 −7.22442 12.5131i −0.554088 0.959708i
171171 −9.71319 + 16.8237i −0.742786 + 1.28654i
172172 −0.352880 0.203735i −0.0269069 0.0155347i
173173 −3.83381 + 2.21345i −0.291479 + 0.168286i −0.638609 0.769532i 0.720490π-0.720490\pi
0.347130 + 0.937817i 0.387156π0.387156\pi
174174 4.10212i 0.310981i
175175 3.62846 1.06599i 0.274286 0.0805813i
176176 4.61827i 0.348115i
177177 5.81464 + 10.0712i 0.437055 + 0.757001i
178178 −0.378729 + 0.655977i −0.0283869 + 0.0491676i
179179 −6.72869 + 11.6544i −0.502926 + 0.871093i 0.497068 + 0.867711i 0.334410π0.334410\pi
−0.999994 + 0.00338176i 0.998924π0.998924\pi
180180 0.351025 + 0.607994i 0.0261639 + 0.0453172i
181181 12.4838 0.927917 0.463958 0.885857i 0.346429π-0.346429\pi
0.463958 + 0.885857i 0.346429π0.346429\pi
182182 −2.95357 0.716069i −0.218933 0.0530786i
183183 23.9662i 1.77164i
184184 −11.3236 6.78543i −0.834786 0.500229i
185185 −25.1464 14.5183i −1.84880 1.06740i
186186 −8.47830 + 14.6849i −0.621659 + 1.07675i
187187 −3.75107 + 2.16568i −0.274305 + 0.158370i
188188 1.15080i 0.0839307i
189189 1.12744 1.18277i 0.0820092 0.0860340i
190190 26.0361 1.88886
191191 9.37119 5.41046i 0.678076 0.391487i −0.121054 0.992646i 0.538627π-0.538627\pi
0.799130 + 0.601159i 0.205294π0.205294\pi
192192 −15.6815 9.05370i −1.13171 0.653394i
193193 −3.58582 + 6.21083i −0.258113 + 0.447065i −0.965736 0.259525i 0.916434π-0.916434\pi
0.707623 + 0.706590i 0.249767π0.249767\pi
194194 −8.63874 14.9627i −0.620225 1.07426i
195195 4.81524 0.344826
196196 −0.628289 0.323672i −0.0448778 0.0231194i
197197 −4.56103 −0.324960 −0.162480 0.986712i 0.551949π-0.551949\pi
−0.162480 + 0.986712i 0.551949π0.551949\pi
198198 3.79258 2.18965i 0.269527 0.155612i
199199 1.72033 2.97970i 0.121951 0.211226i −0.798586 0.601881i 0.794418π-0.794418\pi
0.920537 + 0.390655i 0.127752π0.127752\pi
200200 −1.96726 + 3.40740i −0.139107 + 0.240940i
201201 −6.19796 10.7352i −0.437170 0.757201i
202202 4.43369i 0.311953i
203203 −2.26176 2.15595i −0.158744 0.151318i
204204 0.951162i 0.0665947i
205205 1.87665 1.08348i 0.131071 0.0756739i
206206 11.1170 19.2552i 0.774558 1.34157i
207207 0.213755 13.1497i 0.0148570 0.913968i
208208 2.87684 1.66094i 0.199473 0.115166i
209209 7.80491i 0.539877i
210210 22.6455 + 5.49023i 1.56269 + 0.378862i
211211 9.49610 0.653739 0.326869 0.945070i 0.394006π-0.394006\pi
0.326869 + 0.945070i 0.394006π0.394006\pi
212212 0.317207 0.183140i 0.0217859 0.0125781i
213213 21.9241 + 12.6579i 1.50221 + 0.867303i
214214 −18.3651 10.6031i −1.25541 0.724811i
215215 8.86213 5.11655i 0.604392 0.348946i
216216 1.70002i 0.115672i
217217 3.64075 + 12.3925i 0.247150 + 0.841260i
218218 20.3618i 1.37907i
219219 −11.2448 19.4766i −0.759854 1.31611i
220220 −0.244273 0.141031i −0.0164689 0.00950830i
221221 −2.69812 1.55776i −0.181495 0.104786i
222222 −19.8875 34.4462i −1.33476 2.31188i
223223 15.3821i 1.03006i −0.857171 0.515032i 0.827780π-0.827780\pi
0.857171 0.515032i 0.172220π-0.172220\pi
224224 1.44848 0.425543i 0.0967807 0.0284328i
225225 −3.91976 −0.261318
226226 9.97979 5.76184i 0.663846 0.383272i
227227 12.3428 21.3784i 0.819222 1.41893i −0.0870336 0.996205i 0.527739π-0.527739\pi
0.906256 0.422729i 0.138928π-0.138928\pi
228228 1.48432 + 0.856975i 0.0983018 + 0.0567545i
229229 6.24731 + 10.8207i 0.412834 + 0.715050i 0.995198 0.0978783i 0.0312056π-0.0312056\pi
−0.582364 + 0.812928i 0.697872π0.697872\pi
230230 −15.4059 + 8.56382i −1.01584 + 0.564682i
231231 1.64582 6.78850i 0.108287 0.446650i
232232 3.25087 0.213430
233233 13.0198 + 22.5509i 0.852954 + 1.47736i 0.878530 + 0.477687i 0.158525π0.158525\pi
−0.0255758 + 0.999673i 0.508142π0.508142\pi
234234 2.72798 + 1.57500i 0.178334 + 0.102961i
235235 −25.0289 14.4504i −1.63270 0.942642i
236236 0.424342 0.244994i 0.0276223 0.0159477i
237237 −15.5379 −1.00929
238238 −10.9128 10.4023i −0.707373 0.674281i
239239 25.2986 1.63643 0.818215 0.574912i 0.194964π-0.194964\pi
0.818215 + 0.574912i 0.194964π0.194964\pi
240240 −22.0572 + 12.7348i −1.42379 + 0.822025i
241241 −14.4451 + 25.0196i −0.930490 + 1.61166i −0.148004 + 0.988987i 0.547285π0.547285\pi
−0.782486 + 0.622668i 0.786049π0.786049\pi
242242 7.09236 12.2843i 0.455914 0.789666i
243243 −18.5395 + 10.7038i −1.18931 + 0.686647i
244244 −1.00979 −0.0646454
245245 14.9289 9.60041i 0.953773 0.613348i
246246 2.96838 0.189257
247247 4.86188 2.80701i 0.309354 0.178606i
248248 −11.6375 6.71893i −0.738984 0.426653i
249249 −11.4228 6.59498i −0.723893 0.417940i
250250 −6.56156 11.3650i −0.414989 0.718783i
251251 2.54584 0.160692 0.0803459 0.996767i 0.474398π-0.474398\pi
0.0803459 + 0.996767i 0.474398π0.474398\pi
252252 0.530240 + 0.505434i 0.0334020 + 0.0318394i
253253 2.56719 + 4.61827i 0.161398 + 0.290348i
254254 −4.51370 7.81795i −0.283214 0.490542i
255255 20.6869 + 11.9436i 1.29547 + 0.747937i
256256 −1.20855 + 2.09328i −0.0755346 + 0.130830i
257257 0.243730 0.140718i 0.0152035 0.00877774i −0.492379 0.870381i 0.663873π-0.663873\pi
0.507582 + 0.861603i 0.330539π0.330539\pi
258258 14.0176 0.872698
259259 −29.4447 7.13862i −1.82960 0.443572i
260260 0.202885i 0.0125824i
261261 1.61934 + 2.80477i 0.100234 + 0.173611i
262262 18.9347 + 10.9320i 1.16979 + 0.675380i
263263 25.3650 + 14.6445i 1.56407 + 0.903018i 0.996838 + 0.0794624i 0.0253204π0.0253204\pi
0.567235 + 0.823556i 0.308013π0.308013\pi
264264 3.63362 + 6.29361i 0.223634 + 0.387345i
265265 9.19862i 0.565067i
266266 26.0654 7.65764i 1.59817 0.469520i
267267 1.25225i 0.0766363i
268268 −0.452316 + 0.261145i −0.0276296 + 0.0159519i
269269 −1.57794 0.911022i −0.0962085 0.0555460i 0.451124 0.892461i 0.351023π-0.351023\pi
−0.547332 + 0.836915i 0.684357π0.684357\pi
270270 1.96579 + 1.13495i 0.119634 + 0.0690709i
271271 −2.06198 + 1.19048i −0.125256 + 0.0723167i −0.561319 0.827600i 0.689706π-0.689706\pi
0.436063 + 0.899916i 0.356373π0.356373\pi
272272 16.4791 0.999191
273273 4.82064 1.41624i 0.291759 0.0857145i
274274 4.70916i 0.284491i
275275 1.36385 0.787419i 0.0822432 0.0474831i
276276 −1.16017 0.0188591i −0.0698341 0.00113519i
277277 −1.93244 + 3.34708i −0.116109 + 0.201107i −0.918223 0.396065i 0.870376π-0.870376\pi
0.802113 + 0.597172i 0.203709π0.203709\pi
278278 −19.7702 + 11.4143i −1.18574 + 0.684586i
279279 13.3874i 0.801485i
280280 −4.35093 + 17.9462i −0.260018 + 1.07249i
281281 21.8412i 1.30294i −0.758675 0.651470i 0.774153π-0.774153\pi
0.758675 0.651470i 0.225847π-0.225847\pi
282282 −19.7946 34.2853i −1.17875 2.04166i
283283 7.71377 13.3606i 0.458536 0.794208i −0.540348 0.841442i 0.681707π-0.681707\pi
0.998884 + 0.0472339i 0.0150406π0.0150406\pi
284284 0.533326 0.923748i 0.0316471 0.0548144i
285285 −37.2769 + 21.5218i −2.20809 + 1.27484i
286286 −1.26557 −0.0748347
287287 1.56009 1.63665i 0.0920891 0.0966086i
288288 −1.56477 −0.0922049
289289 0.772346 + 1.33774i 0.0454321 + 0.0786907i
290290 2.17031 3.75909i 0.127445 0.220741i
291291 24.7368 + 14.2818i 1.45010 + 0.837213i
292292 −0.820626 + 0.473789i −0.0480235 + 0.0277264i
293293 −7.77950 −0.454484 −0.227242 0.973838i 0.572971π-0.572971\pi
−0.227242 + 0.973838i 0.572971π0.572971\pi
294294 24.2857 1.16401i 1.41637 0.0678865i
295295 12.3054i 0.716448i
296296 27.2981 15.7606i 1.58667 0.916065i
297297 0.340226 0.589289i 0.0197419 0.0341940i
298298 −7.84306 4.52819i −0.454336 0.262311i
299299 −1.95356 + 3.26012i −0.112977 + 0.188537i
300300 0.345833i 0.0199667i
301301 7.36722 7.72879i 0.424640 0.445480i
302302 −24.9622 −1.43642
303303 3.66494 + 6.34787i 0.210545 + 0.364675i
304304 −14.8473 + 25.7162i −0.851549 + 1.47493i
305305 12.6798 21.9621i 0.726044 1.25755i
306306 7.81318 + 13.5328i 0.446650 + 0.773620i
307307 4.61716i 0.263515i 0.991282 + 0.131758i 0.0420621π0.0420621\pi
−0.991282 + 0.131758i 0.957938π0.957938\pi
308308 −0.286026 0.0693448i −0.0162979 0.00395129i
309309 36.7578i 2.09108i
310310 −15.5386 + 8.97123i −0.882535 + 0.509532i
311311 20.4727 + 11.8199i 1.16090 + 0.670246i 0.951520 0.307588i 0.0995217π-0.0995217\pi
0.209381 + 0.977834i 0.432855π0.432855\pi
312312 −2.61364 + 4.52695i −0.147968 + 0.256288i
313313 −5.35830 9.28084i −0.302869 0.524584i 0.673916 0.738808i 0.264611π-0.264611\pi
−0.976785 + 0.214224i 0.931278π0.931278\pi
314314 −8.48609 −0.478898
315315 −17.6509 + 5.18558i −0.994515 + 0.292174i
316316 0.654672i 0.0368282i
317317 5.84074 + 10.1165i 0.328049 + 0.568197i 0.982125 0.188232i 0.0602757π-0.0602757\pi
−0.654076 + 0.756429i 0.726942π0.726942\pi
318318 −6.30027 + 10.9124i −0.353302 + 0.611936i
319319 −1.12687 0.650599i −0.0630926 0.0364265i
320320 −9.58008 16.5932i −0.535543 0.927587i
321321 35.0586 1.95678
322322 −12.9045 + 13.1046i −0.719139 + 0.730289i
323323 27.8497 1.54960
324324 0.490026 + 0.848750i 0.0272237 + 0.0471528i
325325 0.981007 + 0.566385i 0.0544165 + 0.0314174i
326326 3.45780 5.98909i 0.191510 0.331705i
327327 −16.8313 29.1527i −0.930773 1.61215i
328328 2.35239i 0.129889i
329329 −29.3071 7.10527i −1.61575 0.391726i
330330 9.70334 0.534151
331331 −13.9316 24.1303i −0.765751 1.32632i −0.939849 0.341591i 0.889034π-0.889034\pi
0.174098 0.984728i 0.444299π-0.444299\pi
332332 −0.277873 + 0.481290i −0.0152502 + 0.0264142i
333333 27.1957 + 15.7014i 1.49032 + 0.860434i
334334 −22.5209 + 13.0024i −1.23229 + 0.711462i
335335 13.1166i 0.716637i
336336 −18.3365 + 19.2364i −1.00034 + 1.04943i
337337 3.40512i 0.185489i 0.995690 + 0.0927444i 0.0295639π0.0295639\pi
−0.995690 + 0.0927444i 0.970436π0.970436\pi
338338 8.96640 + 15.5303i 0.487708 + 0.844735i
339339 −9.52562 + 16.4989i −0.517360 + 0.896095i
340340 0.503231 0.871622i 0.0272916 0.0472704i
341341 2.68932 + 4.65805i 0.145635 + 0.252247i
342342 −28.1580 −1.52261
343343 12.1220 14.0020i 0.654528 0.756038i
344344 11.1087i 0.598943i
345345 14.9783 24.9959i 0.806403 1.34573i
346346 −5.55700 3.20833i −0.298746 0.172481i
347347 −3.25674 + 5.64083i −0.174831 + 0.302816i −0.940103 0.340891i 0.889271π-0.889271\pi
0.765272 + 0.643707i 0.222604π0.222604\pi
348348 0.247459 0.142871i 0.0132652 0.00765868i
349349 13.7110i 0.733931i −0.930234 0.366966i 0.880397π-0.880397\pi
0.930234 0.366966i 0.119603π-0.119603\pi
350350 3.96779 + 3.78217i 0.212087 + 0.202165i
351351 0.489445 0.0261246
352352 0.544448 0.314337i 0.0290192 0.0167542i
353353 −10.4296 6.02155i −0.555113 0.320495i 0.196069 0.980590i 0.437182π-0.437182\pi
−0.751182 + 0.660096i 0.770516π0.770516\pi
354354 −8.42815 + 14.5980i −0.447951 + 0.775874i
355355 13.3938 + 23.1987i 0.710869 + 1.23126i
356356 −0.0527622 −0.00279639
357357 24.2230 + 5.87266i 1.28201 + 0.310814i
358358 −19.5061 −1.03093
359359 13.1144 7.57162i 0.692153 0.399615i −0.112265 0.993678i 0.535811π-0.535811\pi
0.804418 + 0.594064i 0.202477π0.202477\pi
360360 9.56989 16.5755i 0.504377 0.873607i
361361 −15.5920 + 27.0061i −0.820630 + 1.42137i
362362 9.04748 + 15.6707i 0.475525 + 0.823634i
363363 23.4505i 1.23083i
364364 −0.0596717 0.203113i −0.00312764 0.0106460i
365365 23.7972i 1.24560i
366366 30.0843 17.3692i 1.57253 0.907902i
367367 −15.2658 + 26.4412i −0.796870 + 1.38022i 0.124775 + 0.992185i 0.460179π0.460179\pi
−0.921645 + 0.388034i 0.873154π0.873154\pi
368368 0.326738 20.1002i 0.0170324 1.04780i
369369 −2.02959 + 1.17178i −0.105656 + 0.0610006i
370370 42.0876i 2.18803i
371371 2.70546 + 9.20895i 0.140460 + 0.478105i
372372 −1.18115 −0.0612396
373373 −5.76974 + 3.33116i −0.298746 + 0.172481i −0.641879 0.766806i 0.721845π-0.721845\pi
0.343134 + 0.939287i 0.388512π0.388512\pi
374374 −5.43706 3.13909i −0.281144 0.162318i
375375 18.7888 + 10.8477i 0.970251 + 0.560175i
376376 27.1706 15.6869i 1.40122 0.808992i
377377 0.935942i 0.0482035i
378378 2.30180 + 0.558054i 0.118392 + 0.0287032i
379379 24.8693i 1.27745i 0.769434 + 0.638726i 0.220538π0.220538\pi
−0.769434 + 0.638726i 0.779462π0.779462\pi
380380 0.906799 + 1.57062i 0.0465178 + 0.0805712i
381381 12.9248 + 7.46216i 0.662159 + 0.382298i
382382 13.5833 + 7.84231i 0.694981 + 0.401247i
383383 −5.34052 9.25006i −0.272888 0.472656i 0.696712 0.717351i 0.254646π-0.254646\pi
−0.969600 + 0.244695i 0.921312π0.921312\pi
384384 28.9809i 1.47892i
385385 5.09978 5.35006i 0.259909 0.272665i
386386 −10.3951 −0.529096
387387 −9.58436 + 5.53353i −0.487200 + 0.281285i
388388 0.601748 1.04226i 0.0305491 0.0529127i
389389 −24.9946 14.4306i −1.26728 0.731663i −0.292805 0.956172i 0.594589π-0.594589\pi
−0.974472 + 0.224510i 0.927922π0.927922\pi
390390 3.48977 + 6.04446i 0.176712 + 0.306073i
391391 −16.4791 + 9.16035i −0.833383 + 0.463259i
392392 0.922461 + 19.2461i 0.0465913 + 0.972073i
393393 −36.1461 −1.82333
394394 −3.30554 5.72536i −0.166531 0.288440i
395395 −14.2385 8.22062i −0.716418 0.413624i
396396 0.264180 + 0.152524i 0.0132755 + 0.00766464i
397397 −0.919722 + 0.531001i −0.0461595 + 0.0266502i −0.522902 0.852393i 0.675151π-0.675151\pi
0.476743 + 0.879043i 0.341817π0.341817\pi
398398 4.98714 0.249983
399399 −30.9888 + 32.5097i −1.55138 + 1.62752i
400400 −5.99162 −0.299581
401401 −21.0551 + 12.1562i −1.05144 + 0.607050i −0.923053 0.384674i 0.874314π-0.874314\pi
−0.128389 + 0.991724i 0.540981π0.540981\pi
402402 8.98376 15.5603i 0.448069 0.776079i
403403 −1.93441 + 3.35050i −0.0963599 + 0.166900i
404404 0.267461 0.154419i 0.0133067 0.00768261i
405405 −24.6127 −1.22302
406406 1.06714 4.40163i 0.0529613 0.218449i
407407 −12.6167 −0.625386
408408 −22.4571 + 12.9656i −1.11179 + 0.641893i
409409 0.535872 + 0.309386i 0.0264972 + 0.0152981i 0.513190 0.858275i 0.328464π-0.328464\pi
−0.486693 + 0.873573i 0.661797π0.661797\pi
410410 2.72015 + 1.57048i 0.134339 + 0.0775605i
411411 3.89265 + 6.74227i 0.192010 + 0.332572i
412412 1.54875 0.0763016
413413 3.61921 + 12.3192i 0.178090 + 0.606189i
414414 16.6615 9.26174i 0.818866 0.455190i
415415 −6.97841 12.0870i −0.342557 0.593326i
416416 0.391618 + 0.226101i 0.0192006 + 0.0110855i
417417 18.8705 32.6846i 0.924091 1.60057i
418418 9.79733 5.65649i 0.479203 0.276668i
419419 13.8170 0.675005 0.337502 0.941325i 0.390418π-0.390418\pi
0.337502 + 0.941325i 0.390418π0.390418\pi
420420 0.457513 + 1.55730i 0.0223244 + 0.0759885i
421421 1.48319i 0.0722863i −0.999347 0.0361432i 0.988493π-0.988493\pi
0.999347 0.0361432i 0.0115072π-0.0115072\pi
422422 6.88216 + 11.9203i 0.335018 + 0.580269i
423423 27.0686 + 15.6281i 1.31612 + 0.759863i
424424 −8.64790 4.99287i −0.419979 0.242475i
425425 2.80969 + 4.86653i 0.136290 + 0.236062i
426426 36.6944i 1.77785i
427427 6.23466 25.7161i 0.301716 1.24449i
428428 1.47716i 0.0714010i
429429 1.81196 1.04614i 0.0874823 0.0505079i
430430 12.8454 + 7.41629i 0.619460 + 0.357645i
431431 −30.4482 17.5793i −1.46664 0.846763i −0.467333 0.884081i 0.654785π-0.654785\pi
−0.999303 + 0.0373185i 0.988118π0.988118\pi
432432 −2.24201 + 1.29442i −0.107869 + 0.0622780i
433433 12.5373 0.602505 0.301252 0.953544i 0.402595π-0.402595\pi
0.301252 + 0.953544i 0.402595π0.402595\pi
434434 −12.9175 + 13.5515i −0.620060 + 0.650491i
435435 7.17603i 0.344064i
436436 −1.22832 + 0.709170i −0.0588258 + 0.0339631i
437437 0.552190 33.9695i 0.0264148 1.62498i
438438 16.2990 28.2308i 0.778798 1.34892i
439439 21.8276 12.6022i 1.04177 0.601469i 0.121439 0.992599i 0.461249π-0.461249\pi
0.920335 + 0.391130i 0.127916π0.127916\pi
440440 7.68976i 0.366595i
441441 −16.1455 + 10.3828i −0.768835 + 0.494419i
442442 4.51585i 0.214797i
443443 −4.17328 7.22834i −0.198279 0.343429i 0.749692 0.661787i 0.230202π-0.230202\pi
−0.947970 + 0.318359i 0.896868π0.896868\pi
444444 1.38531 2.39942i 0.0657437 0.113871i
445445 0.662527 1.14753i 0.0314068 0.0543981i
446446 19.3089 11.1480i 0.914302 0.527872i
447447 14.9723 0.708163
448448 −14.4712 13.7942i −0.683698 0.651713i
449449 4.40940 0.208092 0.104046 0.994572i 0.466821π-0.466821\pi
0.104046 + 0.994572i 0.466821π0.466821\pi
450450 −2.84079 4.92040i −0.133916 0.231950i
451451 0.470786 0.815425i 0.0221684 0.0383969i
452452 0.695162 + 0.401352i 0.0326977 + 0.0188780i
453453 35.7393 20.6341i 1.67918 0.969475i
454454 35.7811 1.67929
455455 5.16681 + 1.25265i 0.242224 + 0.0587252i
456456 46.7268i 2.18818i
457457 −27.4739 + 15.8620i −1.28517 + 0.741995i −0.977789 0.209590i 0.932787π-0.932787\pi
−0.307384 + 0.951585i 0.599454π0.599454\pi
458458 −9.05530 + 15.6842i −0.423126 + 0.732876i
459459 2.10272 + 1.21401i 0.0981467 + 0.0566650i
460460 −1.05318 0.631094i −0.0491046 0.0294249i
461461 34.4607i 1.60500i 0.596654 + 0.802498i 0.296496π0.296496\pi
−0.596654 + 0.802498i 0.703504π0.703504\pi
462462 9.71424 2.85390i 0.451947 0.132776i
463463 −3.47708 −0.161594 −0.0807968 0.996731i 0.525746π-0.525746\pi
−0.0807968 + 0.996731i 0.525746π0.525746\pi
464464 2.47527 + 4.28729i 0.114911 + 0.199032i
465465 14.8315 25.6889i 0.687793 1.19129i
466466 −18.8718 + 32.6869i −0.874219 + 1.51419i
467467 11.4593 + 19.8481i 0.530274 + 0.918461i 0.999376 + 0.0353171i 0.0112441π0.0112441\pi
−0.469103 + 0.883144i 0.655423π0.655423\pi
468468 0.219419i 0.0101427i
469469 −3.85780 13.1313i −0.178137 0.606349i
470470 41.8909i 1.93228i
471471 12.1498 7.01471i 0.559835 0.323221i
472472 −11.5687 6.67918i −0.532492 0.307434i
473473 2.22320 3.85069i 0.102223 0.177055i
474474 −11.2608 19.5044i −0.517228 0.895865i
475475 −10.1259 −0.464607
476476 0.247439 1.02061i 0.0113413 0.0467795i
477477 9.94827i 0.455500i
478478 18.3348 + 31.7568i 0.838614 + 1.45252i
479479 3.86417 6.69295i 0.176559 0.305809i −0.764141 0.645049i 0.776837π-0.776837\pi
0.940700 + 0.339241i 0.110170π0.110170\pi
480480 −3.00260 1.73355i −0.137049 0.0791255i
481481 −4.53755 7.85926i −0.206894 0.358351i
482482 −41.8755 −1.90737
483483 7.64341 29.4293i 0.347787 1.33908i
484484 0.988064 0.0449120
485485 15.1121 + 26.1750i 0.686207 + 1.18854i
486486 −26.8724 15.5148i −1.21896 0.703766i
487487 −1.40999 + 2.44217i −0.0638926 + 0.110665i −0.896202 0.443646i 0.853685π-0.853685\pi
0.832310 + 0.554311i 0.187018π0.187018\pi
488488 13.7648 + 23.8414i 0.623104 + 1.07925i
489489 11.4331i 0.517021i
490490 22.8707 + 11.7822i 1.03319 + 0.532264i
491491 −6.06047 −0.273505 −0.136753 0.990605i 0.543667π-0.543667\pi
−0.136753 + 0.990605i 0.543667π0.543667\pi
492492 0.103384 + 0.179066i 0.00466091 + 0.00807294i
493493 2.32149 4.02094i 0.104555 0.181094i
494494 7.04715 + 4.06867i 0.317066 + 0.183058i
495495 −6.63454 + 3.83045i −0.298200 + 0.172166i
496496 20.4636i 0.918843i
497497 20.2319 + 19.2855i 0.907527 + 0.865071i
498498 19.1185i 0.856719i
499499 6.95553 + 12.0473i 0.311372 + 0.539313i 0.978660 0.205488i 0.0658780π-0.0658780\pi
−0.667287 + 0.744800i 0.732545π0.732545\pi
500500 0.457058 0.791648i 0.0204403 0.0354036i
501501 21.4960 37.2321i 0.960369 1.66341i
502502 1.84506 + 3.19573i 0.0823490 + 0.142633i
503503 18.7223 0.834788 0.417394 0.908726i 0.362944π-0.362944\pi
0.417394 + 0.908726i 0.362944π0.362944\pi
504504 4.70551 19.4088i 0.209600 0.864536i
505505 7.75605i 0.345139i
506506 −3.93668 + 6.56957i −0.175007 + 0.292053i
507507 −25.6750 14.8235i −1.14027 0.658334i
508508 0.314410 0.544575i 0.0139497 0.0241616i
509509 10.7975 6.23394i 0.478591 0.276315i −0.241238 0.970466i 0.577553π-0.577553\pi
0.719829 + 0.694151i 0.244220π0.244220\pi
510510 34.6238i 1.53317i
511511 −6.99912 23.8239i −0.309623 1.05391i
512512 20.6845 0.914132
513513 −3.78901 + 2.18758i −0.167289 + 0.0965842i
514514 0.353280 + 0.203966i 0.0155825 + 0.00899657i
515515 −19.4475 + 33.6840i −0.856957 + 1.48429i
516516 0.488212 + 0.845608i 0.0214923 + 0.0372258i
517517 −12.5577 −0.552288
518518 −12.3786 42.1349i −0.543885 1.85130i
519519 10.6082 0.465648
520520 −4.79015 + 2.76559i −0.210062 + 0.121279i
521521 4.25588 7.37140i 0.186453 0.322947i −0.757612 0.652705i 0.773634π-0.773634\pi
0.944065 + 0.329758i 0.106967π0.106967\pi
522522 −2.34718 + 4.06544i −0.102733 + 0.177939i
523523 −2.22225 3.84905i −0.0971721 0.168307i 0.813341 0.581787i 0.197646π-0.197646\pi
−0.910513 + 0.413480i 0.864313π0.864313\pi
524524 1.52298i 0.0665315i
525525 −8.80721 2.13524i −0.384378 0.0931895i
526526 42.4535i 1.85106i
527527 −16.6210 + 9.59614i −0.724022 + 0.418015i
528528 −5.53339 + 9.58411i −0.240810 + 0.417095i
529529 10.8465 + 20.2818i 0.471588 + 0.881819i
530530 −11.5468 + 6.66657i −0.501562 + 0.289577i
531531 13.3082i 0.577528i
532532 1.36976 + 1.30568i 0.0593867 + 0.0566085i
533533 0.677266 0.0293356
534534 1.57192 0.907548i 0.0680236 0.0392735i
535535 32.1268 + 18.5484i 1.38896 + 0.801919i
536536 12.3313 + 7.11950i 0.532632 + 0.307515i
537537 27.9275 16.1240i 1.20516 0.695801i
538538 2.64100i 0.113862i
539539 3.53197 6.85599i 0.152133 0.295309i
540540 0.158114i 0.00680416i
541541 −14.0046 24.2567i −0.602105 1.04288i −0.992502 0.122230i 0.960995π-0.960995\pi
0.390396 0.920647i 0.372338π-0.372338\pi
542542 −2.98878 1.72557i −0.128379 0.0741196i
543543 −25.9072 14.9575i −1.11178 0.641889i
544544 1.12163 + 1.94272i 0.0480895 + 0.0832934i
545545 35.6198i 1.52578i
546546 5.27146 + 5.02485i 0.225598 + 0.215044i
547547 −15.7527 −0.673539 −0.336769 0.941587i 0.609334π-0.609334\pi
−0.336769 + 0.941587i 0.609334π0.609334\pi
548548 0.284079 0.164013i 0.0121352 0.00700628i
549549 −13.7132 + 23.7519i −0.585264 + 1.01371i
550550 1.97686 + 1.14134i 0.0842936 + 0.0486669i
551551 4.18321 + 7.24554i 0.178211 + 0.308670i
552552 15.3694 + 27.6489i 0.654166 + 1.17682i
553553 −16.6723 4.04208i −0.708980 0.171887i
554554 −5.60203 −0.238007
555555 34.7902 + 60.2583i 1.47676 + 2.55782i
556556 −1.37713 0.795088i −0.0584035 0.0337193i
557557 5.53273 + 3.19432i 0.234429 + 0.135348i 0.612614 0.790383i 0.290118π-0.290118\pi
−0.378185 + 0.925730i 0.623452π0.623452\pi
558558 16.8050 9.70235i 0.711411 0.410733i
559559 3.19826 0.135272
560560 −26.9806 + 7.92651i −1.14014 + 0.334956i
561561 10.3792 0.438212
562562 27.4168 15.8291i 1.15651 0.667711i
563563 −1.50242 + 2.60227i −0.0633194 + 0.109672i −0.895947 0.444160i 0.853502π-0.853502\pi
0.832628 + 0.553833i 0.186835π0.186835\pi
564564 1.37883 2.38821i 0.0580593 0.100562i
565565 −17.4581 + 10.0794i −0.734468 + 0.424045i
566566 22.3618 0.939936
567567 −24.6404 + 7.23899i −1.03480 + 0.304009i
568568 −29.0798 −1.22016
569569 −6.67438 + 3.85345i −0.279804 + 0.161545i −0.633335 0.773878i 0.718314π-0.718314\pi
0.353530 + 0.935423i 0.384981π0.384981\pi
570570 −54.0317 31.1952i −2.26314 1.30662i
571571 −17.3049 9.99099i −0.724188 0.418110i 0.0921042 0.995749i 0.470641π-0.470641\pi
−0.816292 + 0.577639i 0.803974π0.803974\pi
572572 −0.0440779 0.0763451i −0.00184299 0.00319215i
573573 −25.9302 −1.08325
574574 3.18511 + 0.772204i 0.132944 + 0.0322312i
575575 5.99162 3.33061i 0.249868 0.138896i
576576 10.3608 + 17.9455i 0.431701 + 0.747728i
577577 −18.0693 10.4323i −0.752236 0.434304i 0.0742654 0.997239i 0.476339π-0.476339\pi
−0.826501 + 0.562935i 0.809672π0.809672\pi
578578 −1.11949 + 1.93902i −0.0465647 + 0.0806525i
579579 14.8830 8.59272i 0.618517 0.357101i
580580 0.302355 0.0125546
581581 −10.5412 10.0481i −0.437323 0.416864i
582582 41.4021i 1.71617i
583583 1.99845 + 3.46142i 0.0827674 + 0.143357i
584584 22.3725 + 12.9167i 0.925779 + 0.534499i
585585 −4.77217 2.75522i −0.197305 0.113914i
586586 −5.63808 9.76545i −0.232907 0.403407i
587587 6.07612i 0.250788i 0.992107 + 0.125394i 0.0400196π0.0400196\pi
−0.992107 + 0.125394i 0.959980π0.959980\pi
588588 0.916053 + 1.42449i 0.0377774 + 0.0587449i
589589 34.5836i 1.42499i
590590 −15.4467 + 8.91816i −0.635931 + 0.367155i
591591 9.46532 + 5.46480i 0.389351 + 0.224792i
592592 41.5704 + 24.0007i 1.70853 + 0.986423i
593593 −14.8284 + 8.56116i −0.608928 + 0.351565i −0.772546 0.634959i 0.781017π-0.781017\pi
0.163618 + 0.986524i 0.447684π0.447684\pi
594594 0.986296 0.0404682
595595 19.0903 + 18.1972i 0.782625 + 0.746013i
596596 0.630840i 0.0258402i
597597 −7.14027 + 4.12244i −0.292232 + 0.168720i
598598 −5.50817 0.0895379i −0.225246 0.00366148i
599599 12.6564 21.9216i 0.517128 0.895693i −0.482674 0.875800i 0.660334π-0.660334\pi
0.999802 0.0198925i 0.00633239π-0.00633239\pi
600600 8.16516 4.71416i 0.333341 0.192455i
601601 27.7769i 1.13304i −0.824047 0.566522i 0.808289π-0.808289\pi
0.824047 0.566522i 0.191711π-0.191711\pi
602602 15.0411 + 3.64659i 0.613028 + 0.148624i
603603 14.1856i 0.577681i
604604 −0.869397 1.50584i −0.0353753 0.0612718i
605605 −12.4070 + 21.4895i −0.504415 + 0.873673i
606606 −5.31223 + 9.20105i −0.215795 + 0.373767i
607607 11.2012 6.46699i 0.454641 0.262487i −0.255147 0.966902i 0.582124π-0.582124\pi
0.709788 + 0.704415i 0.248791π0.248791\pi
608608 −4.04225 −0.163935
609609 2.11058 + 7.18409i 0.0855251 + 0.291114i
610610 36.7581 1.48829
611611 −4.51634 7.82254i −0.182712 0.316466i
612612 −0.544243 + 0.942656i −0.0219997 + 0.0381046i
613613 −22.0172 12.7117i −0.889268 0.513419i −0.0155649 0.999879i 0.504955π-0.504955\pi
−0.873703 + 0.486460i 0.838288π0.838288\pi
614614 −5.79582 + 3.34622i −0.233900 + 0.135042i
615615 −5.19271 −0.209390
616616 2.26168 + 7.69839i 0.0911256 + 0.310177i
617617 23.3062i 0.938271i 0.883126 + 0.469135i 0.155434π0.155434\pi
−0.883126 + 0.469135i 0.844566π0.844566\pi
618618 −46.1413 + 26.6397i −1.85608 + 1.07161i
619619 6.18042 10.7048i 0.248412 0.430262i −0.714673 0.699458i 0.753425π-0.753425\pi
0.963085 + 0.269196i 0.0867579π0.0867579\pi
620620 −1.08237 0.624909i −0.0434692 0.0250969i
621621 1.52247 2.54071i 0.0610945 0.101955i
622622 34.2653i 1.37391i
623623 0.325764 1.34368i 0.0130515 0.0538333i
624624 −7.96025 −0.318665
625625 15.0519 + 26.0706i 0.602076 + 1.04283i
626626 7.76669 13.4523i 0.310419 0.537662i
627627 −9.35146 + 16.1972i −0.373461 + 0.646854i
628628 −0.295558 0.511921i −0.0117940 0.0204279i
629629 45.0193i 1.79504i
630630 −19.3016 18.3986i −0.768993 0.733018i
631631 33.1168i 1.31836i −0.751985 0.659180i 0.770903π-0.770903\pi
0.751985 0.659180i 0.229097π-0.229097\pi
632632 15.4569 8.92405i 0.614843 0.354980i
633633 −19.7069 11.3778i −0.783278 0.452226i
634634 −8.46598 + 14.6635i −0.336227 + 0.582362i
635635 7.89601 + 13.6763i 0.313344 + 0.542727i
636636 −0.877715 −0.0348037
637637 5.54103 0.265581i 0.219544 0.0105227i
638638 1.88605i 0.0746693i
639639 −14.4853 25.0893i −0.573031 0.992519i
640640 15.3329 26.5574i 0.606086 1.04977i
641641 16.6053 + 9.58710i 0.655871 + 0.378668i 0.790702 0.612201i 0.209716π-0.209716\pi
−0.134831 + 0.990869i 0.543049π0.543049\pi
642642 25.4082 + 44.0082i 1.00278 + 1.73687i
643643 −33.6042 −1.32522 −0.662610 0.748965i 0.730551π-0.730551\pi
−0.662610 + 0.748965i 0.730551π0.730551\pi
644644 −1.23997 0.322047i −0.0488618 0.0126904i
645645 −24.5216 −0.965538
646646 20.1837 + 34.9592i 0.794117 + 1.37545i
647647 −40.7198 23.5096i −1.60086 0.924258i −0.991315 0.131507i 0.958019π-0.958019\pi
−0.609546 0.792751i 0.708648π-0.708648\pi
648648 13.3594 23.1392i 0.524807 0.908993i
649649 2.67341 + 4.63049i 0.104941 + 0.181763i
650650 1.64192i 0.0644012i
651651 7.29263 30.0799i 0.285821 1.17892i
652652 0.481720 0.0188656
653653 −6.83605 11.8404i −0.267515 0.463350i 0.700704 0.713452i 0.252869π-0.252869\pi
−0.968220 + 0.250102i 0.919536π0.919536\pi
654654 24.3965 42.2560i 0.953978 1.65234i
655655 −33.1234 19.1238i −1.29424 0.747228i
656656 −3.10236 + 1.79115i −0.121127 + 0.0699327i
657657 25.7366i 1.00408i
658658 −12.3208 41.9380i −0.480314 1.63491i
659659 24.5743i 0.957280i 0.878011 + 0.478640i 0.158870π0.158870\pi
−0.878011 + 0.478640i 0.841130π0.841130\pi
660660 0.337953 + 0.585351i 0.0131548 + 0.0227848i
661661 7.59564 13.1560i 0.295436 0.511710i −0.679650 0.733536i 0.737868π-0.737868\pi
0.975086 + 0.221826i 0.0712017π0.0712017\pi
662662 20.1935 34.9761i 0.784841 1.35939i
663663 3.73286 + 6.46550i 0.144972 + 0.251099i
664664 15.1511 0.587977
665665 −45.5973 + 13.3958i −1.76819 + 0.519469i
666666 45.5176i 1.76377i
667667 −4.85847 2.91134i −0.188121 0.112728i
668668 −1.56874 0.905711i −0.0606963 0.0350430i
669669 −18.4301 + 31.9219i −0.712550 + 1.23417i
670670 16.4650 9.50608i 0.636099 0.367252i
671671 11.0190i 0.425385i
672672 −3.51584 0.852387i −0.135626 0.0328815i
673673 −0.379942 −0.0146457 −0.00732284 0.999973i 0.502331π-0.502331\pi
−0.00732284 + 0.999973i 0.502331π0.502331\pi
674674 −4.27437 + 2.46781i −0.164643 + 0.0950565i
675675 −0.764528 0.441400i −0.0294267 0.0169895i
676676 −0.624572 + 1.08179i −0.0240220 + 0.0416074i
677677 −14.8652 25.7473i −0.571317 0.989550i −0.996431 0.0844105i 0.973099π-0.973099\pi
0.425114 0.905140i 0.360234π-0.360234\pi
678678 −27.6142 −1.06052
679679 22.8276 + 21.7597i 0.876042 + 0.835059i
680680 −27.4389 −1.05223
681681 −51.2291 + 29.5772i −1.96310 + 1.13340i
682682 −3.89810 + 6.75170i −0.149266 + 0.258536i
683683 −19.7761 + 34.2532i −0.756710 + 1.31066i 0.187809 + 0.982206i 0.439861π0.439861\pi
−0.944520 + 0.328455i 0.893472π0.893472\pi
684684 −0.980700 1.69862i −0.0374980 0.0649484i
685685 8.23794i 0.314756i
686686 26.3617 + 5.06877i 1.00649 + 0.193527i
687687 29.9409i 1.14232i
688688 −14.6503 + 8.45837i −0.558538 + 0.322472i
689689 −1.43747 + 2.48977i −0.0547633 + 0.0948528i
690690 42.2321 + 0.686503i 1.60775 + 0.0261347i
691691 30.1036 17.3803i 1.14520 0.661180i 0.197484 0.980306i 0.436723π-0.436723\pi
0.947712 + 0.319127i 0.103389π0.103389\pi
692692 0.446966i 0.0169911i
693693 −5.51539 + 5.78607i −0.209512 + 0.219795i
694694 −9.44109 −0.358379
695695 34.5849 19.9676i 1.31188 0.757415i
696696 −6.74640 3.89504i −0.255722 0.147641i
697697 2.90963 + 1.67987i 0.110210 + 0.0636298i
698698 17.2111 9.93683i 0.651449 0.376114i
699699 62.3987i 2.36013i
700700 −0.0899661 + 0.371083i −0.00340040 + 0.0140256i
701701 2.33382i 0.0881471i 0.999028 + 0.0440735i 0.0140336π0.0140336\pi
−0.999028 + 0.0440735i 0.985966π0.985966\pi
702702 0.354718 + 0.614389i 0.0133880 + 0.0231886i
703703 70.2543 + 40.5613i 2.64969 + 1.52980i
704704 −7.20992 4.16265i −0.271734 0.156886i
705705 34.6276 + 59.9768i 1.30415 + 2.25886i
706706 17.4561i 0.656970i
707707 2.28117 + 7.76475i 0.0857924 + 0.292024i
708708 −1.17416 −0.0441276
709709 23.0680 13.3183i 0.866339 0.500181i 0.000208831 1.00000i 0.499934π-0.499934\pi
0.866130 + 0.499819i 0.166600π0.166600\pi
710710 −19.4139 + 33.6259i −0.728591 + 1.26196i
711711 15.3989 + 8.89057i 0.577504 + 0.333422i
712712 0.719219 + 1.24572i 0.0269539 + 0.0466854i
713713 11.3753 + 20.4636i 0.426007 + 0.766368i
714714 10.1834 + 34.6627i 0.381104 + 1.29722i
715715 2.21392 0.0827958
716716 −0.679367 1.17670i −0.0253891 0.0439753i
717717 −52.5012 30.3116i −1.96069 1.13201i
718718 19.0090 + 10.9748i 0.709409 + 0.409577i
719719 −24.0839 + 13.9049i −0.898179 + 0.518564i −0.876609 0.481203i 0.840200π-0.840200\pi
−0.0215704 + 0.999767i 0.506867π0.506867\pi
720720 29.1466 1.08623
721721 −9.56231 + 39.4416i −0.356119 + 1.46888i
722722 −45.2002 −1.68218
723723 59.9546 34.6148i 2.22973 1.28734i
724724 −0.630220 + 1.09157i −0.0234219 + 0.0405680i
725725 −0.844069 + 1.46197i −0.0313479 + 0.0542962i
726726 −29.4370 + 16.9954i −1.09251 + 0.630760i
727727 52.1718 1.93494 0.967472 0.252980i 0.0814106π-0.0814106\pi
0.967472 + 0.252980i 0.0814106π0.0814106\pi
728728 −3.98212 + 4.17755i −0.147587 + 0.154830i
729729 22.1786 0.821431
730730 29.8721 17.2467i 1.10562 0.638328i
731731 13.7402 + 7.93289i 0.508199 + 0.293409i
732732 2.09558 + 1.20988i 0.0774549 + 0.0447186i
733733 −1.09544 1.89736i −0.0404610 0.0700806i 0.845086 0.534631i 0.179549π-0.179549\pi
−0.885547 + 0.464550i 0.846216π0.846216\pi
734734 −44.2548 −1.63347
735735 −42.4841 + 2.03626i −1.56705 + 0.0751084i
736736 2.39185 1.32958i 0.0881649 0.0490089i
737737 −2.84966 4.93575i −0.104968 0.181811i
738738 −2.94183 1.69847i −0.108290 0.0625214i
739739 −18.1785 + 31.4861i −0.668707 + 1.15823i 0.309559 + 0.950880i 0.399819π0.399819\pi
−0.978266 + 0.207354i 0.933515π0.933515\pi
740740 2.53892 1.46585i 0.0933326 0.0538856i
741741 −13.4529 −0.494204
742742 −9.59906 + 10.0702i −0.352392 + 0.369687i
743743 9.56263i 0.350819i −0.984496 0.175410i 0.943875π-0.943875\pi
0.984496 0.175410i 0.0561249π-0.0561249\pi
744744 16.1006 + 27.8870i 0.590276 + 1.02239i
745745 13.7202 + 7.92137i 0.502670 + 0.290217i
746746 −8.36307 4.82842i −0.306194 0.176781i
747747 7.54712 + 13.0720i 0.276135 + 0.478279i
748748 0.437319i 0.0159900i
749749 37.6183 + 9.12025i 1.37454 + 0.333247i
750750 31.4470i 1.14828i
751751 17.9493 10.3630i 0.654978 0.378152i −0.135383 0.990793i 0.543227π-0.543227\pi
0.790361 + 0.612642i 0.209893π0.209893\pi
752752 41.3762 + 23.8886i 1.50883 + 0.871126i
753753 −5.28327 3.05030i −0.192533 0.111159i
754754 1.17487 0.678310i 0.0427862 0.0247026i
755755 43.6676 1.58923
756756 0.0465039 + 0.158292i 0.00169133 + 0.00575702i
757757 30.8300i 1.12054i 0.828312 + 0.560268i 0.189302π0.189302\pi
−0.828312 + 0.560268i 0.810698π0.810698\pi
758758 −31.2179 + 18.0237i −1.13389 + 0.654650i
759759 0.205794 12.6600i 0.00746986 0.459529i
760760 24.7218 42.8194i 0.896753 1.55322i
761761 25.2474 14.5766i 0.915218 0.528402i 0.0331119 0.999452i 0.489458π-0.489458\pi
0.882106 + 0.471050i 0.156125π0.156125\pi
762762 21.6324i 0.783658i
763763 −10.4763 35.6598i −0.379269 1.29097i
764764 1.09254i 0.0395268i
765765 −13.6679 23.6736i −0.494166 0.855920i
766766 7.74093 13.4077i 0.279691 0.484439i
767767 −1.92297 + 3.33068i −0.0694343 + 0.120264i
768768 5.01612 2.89606i 0.181004 0.104503i
769769 1.49923 0.0540637 0.0270318 0.999635i 0.491394π-0.491394\pi
0.0270318 + 0.999635i 0.491394π0.491394\pi
770770 10.4118 + 2.52426i 0.375216 + 0.0909681i
771771 −0.674405 −0.0242881
772772 −0.362045 0.627081i −0.0130303 0.0225691i
773773 −6.31015 + 10.9295i −0.226960 + 0.393107i −0.956906 0.290399i 0.906212π-0.906212\pi
0.729945 + 0.683505i 0.239545π0.239545\pi
774774 −13.8922 8.02069i −0.499346 0.288298i
775775 6.04322 3.48906i 0.217079 0.125331i
776776 −32.8105 −1.17783
777777 52.5521 + 50.0936i 1.88530 + 1.79710i
778778 41.8336i 1.49981i
779779 −5.24301 + 3.02705i −0.187850 + 0.108456i
780780 −0.243087 + 0.421039i −0.00870391 + 0.0150756i
781781 10.0801 + 5.81975i 0.360694 + 0.208247i
782782 −23.4418 14.0470i −0.838276 0.502320i
783783 0.729407i 0.0260669i
784784 −24.6795 + 15.8708i −0.881412 + 0.566815i
785785 14.8451 0.529844
786786 −26.1963 45.3734i −0.934392 1.61841i
787787 5.38671 9.33005i 0.192015 0.332580i −0.753903 0.656986i 0.771831π-0.771831\pi
0.945918 + 0.324406i 0.105164π0.105164\pi
788788 0.230254 0.398811i 0.00820245 0.0142071i
789789 −35.0926 60.7822i −1.24933 2.16390i
790790 23.8311i 0.847873i
791791 −14.5132 + 15.2254i −0.516029 + 0.541355i
792792 8.31644i 0.295512i
793793 6.86404 3.96296i 0.243749 0.140729i
794794 −1.33311 0.769671i −0.0473103 0.0273146i
795795 11.0213 19.0895i 0.390887 0.677036i
796796 0.173695 + 0.300848i 0.00615644 + 0.0106633i
797797 −1.15594 −0.0409457 −0.0204728 0.999790i 0.506517π-0.506517\pi
−0.0204728 + 0.999790i 0.506517π0.506517\pi
798798 −63.2674 15.3387i −2.23964 0.542983i
799799 44.8089i 1.58523i
800800 −0.407813 0.706353i −0.0144184 0.0249733i
801801 −0.716520 + 1.24105i −0.0253170 + 0.0438503i
802802 −30.5188 17.6200i −1.07765 0.622184i
803803 −5.17007 8.95482i −0.182448 0.316009i
804804 1.25156 0.0441392
805805 22.5744 22.9244i 0.795643 0.807979i
806806 −5.60775 −0.197524
807807 2.18309 + 3.78122i 0.0768483 + 0.133105i
808808 −7.29169 4.20986i −0.256521 0.148102i
809809 −7.05670 + 12.2226i −0.248100 + 0.429722i −0.962999 0.269506i 0.913140π-0.913140\pi
0.714898 + 0.699228i 0.246473π0.246473\pi
810810 −17.8377 30.8958i −0.626753 1.08557i
811811 36.0451i 1.26572i −0.774268 0.632858i 0.781882π-0.781882\pi
0.774268 0.632858i 0.218118π-0.218118\pi
812812 0.302694 0.0889272i 0.0106225 0.00312073i
813813 5.70552 0.200101
814814 −9.14376 15.8375i −0.320489 0.555103i
815815 −6.04889 + 10.4770i −0.211883 + 0.366993i
816816 −34.1984 19.7444i −1.19718 0.691193i
817817 −24.7591 + 14.2947i −0.866213 + 0.500108i
818818 0.896891i 0.0313591i
819819 −5.58788 1.35474i −0.195256 0.0473384i
820820 0.218790i 0.00764047i
821821 −11.4197 19.7796i −0.398552 0.690312i 0.594996 0.803729i 0.297154π-0.297154\pi
−0.993548 + 0.113417i 0.963820π0.963820\pi
822822 −5.64229 + 9.77272i −0.196797 + 0.340863i
823823 26.4562 45.8235i 0.922206 1.59731i 0.126211 0.992003i 0.459718π-0.459718\pi
0.795995 0.605304i 0.206948π-0.206948\pi
824824 −21.1116 36.5663i −0.735456 1.27385i
825825 −3.77379 −0.131386
826826 −12.8411 + 13.4713i −0.446798 + 0.468726i
827827 24.4927i 0.851694i −0.904795 0.425847i 0.859976π-0.859976\pi
0.904795 0.425847i 0.140024π-0.140024\pi
828828 1.13901 + 0.682526i 0.0395832 + 0.0237194i
829829 −1.46534 0.846013i −0.0508933 0.0293833i 0.474337 0.880343i 0.342688π-0.342688\pi
−0.525231 + 0.850960i 0.676021π0.676021\pi
830830 10.1150 17.5197i 0.351097 0.608118i
831831 8.02063 4.63071i 0.278232 0.160638i
832832 5.98833i 0.207608i
833833 24.4638 + 12.6029i 0.847620 + 0.436664i
834834 54.7044 1.89426
835835 39.3968 22.7457i 1.36338 0.787149i
836836 0.682453 + 0.394014i 0.0236031 + 0.0136273i
837837 1.50755 2.61114i 0.0521084 0.0902544i
838838 10.0137 + 17.3442i 0.345916 + 0.599145i
839839 35.3581 1.22070 0.610349 0.792133i 0.291029π-0.291029\pi
0.610349 + 0.792133i 0.291029π0.291029\pi
840840 30.5316 32.0300i 1.05344 1.10514i
841841 −27.6052 −0.951903
842842 1.86182 1.07492i 0.0641625 0.0370442i
843843 −26.1691 + 45.3262i −0.901312 + 1.56112i
844844 −0.479391 + 0.830329i −0.0165013 + 0.0285811i
845845 −15.6853 27.1678i −0.539592 0.934600i
846846 45.3049i 1.55761i
847847 −6.10050 + 25.1627i −0.209616 + 0.864601i
848848 15.2066i 0.522197i
849849 −32.0162 + 18.4845i −1.09879 + 0.634388i
850850 −4.07257 + 7.05390i −0.139688 + 0.241947i
851851 −54.9119 0.892619i −1.88236 0.0305986i
852852 −2.21358 + 1.27801i −0.0758360 + 0.0437839i
853853 22.6660i 0.776071i 0.921645 + 0.388035i 0.126846π0.126846\pi
−0.921645 + 0.388035i 0.873154π0.873154\pi
854854 36.7993 10.8111i 1.25925 0.369949i
855855 49.2580 1.68459
856856 −34.8759 + 20.1356i −1.19203 + 0.688221i
857857 12.9065 + 7.45159i 0.440879 + 0.254542i 0.703970 0.710229i 0.251409π-0.251409\pi
−0.263091 + 0.964771i 0.584742π0.584742\pi
858858 2.62638 + 1.51634i 0.0896633 + 0.0517671i
859859 −6.14530 + 3.54799i −0.209675 + 0.121056i −0.601160 0.799128i 0.705295π-0.705295\pi
0.391485 + 0.920184i 0.371961π0.371961\pi
860860 1.03319i 0.0352316i
861861 −5.19854 + 1.52726i −0.177166 + 0.0520488i
862862 50.9612i 1.73575i
863863 −11.0652 19.1655i −0.376663 0.652400i 0.613911 0.789375i 0.289595π-0.289595\pi
−0.990574 + 0.136975i 0.956262π0.956262\pi
864864 −0.305199 0.176207i −0.0103831 0.00599468i
865865 9.72110 + 5.61248i 0.330527 + 0.190830i
866866 9.08623 + 15.7378i 0.308763 + 0.534793i
867867 3.70155i 0.125711i
868868 −1.26738 0.307267i −0.0430178 0.0104293i
869869 −7.14390 −0.242340
870870 −9.00792 + 5.20072i −0.305397 + 0.176321i
871871 2.04974 3.55025i 0.0694527 0.120296i
872872 33.4872 + 19.3339i 1.13402 + 0.654727i
873873 −16.3437 28.3081i −0.553151 0.958085i
874874 43.0414 23.9257i 1.45590 0.809300i
875875 17.3387 + 16.5275i 0.586155 + 0.558733i
876876 2.27068 0.0767193
877877 18.1869 + 31.5006i 0.614127 + 1.06370i 0.990537 + 0.137245i 0.0438249π0.0438249\pi
−0.376410 + 0.926453i 0.622842π0.622842\pi
878878 31.6385 + 18.2665i 1.06775 + 0.616464i
879879 16.1445 + 9.32102i 0.544540 + 0.314390i
880880 −10.1413 + 5.85510i −0.341864 + 0.197375i
881881 −28.1227 −0.947479 −0.473739 0.880665i 0.657096π-0.657096\pi
−0.473739 + 0.880665i 0.657096π0.657096\pi
882882 −24.7346 12.7424i −0.832856 0.429058i
883883 40.3739 1.35869 0.679345 0.733819i 0.262264π-0.262264\pi
0.679345 + 0.733819i 0.262264π0.262264\pi
884884 0.272417 0.157280i 0.00916238 0.00528991i
885885 14.7437 25.5369i 0.495605 0.858413i
886886 6.04905 10.4773i 0.203222 0.351990i
887887 −40.6923 + 23.4937i −1.36631 + 0.788842i −0.990455 0.137835i 0.955986π-0.955986\pi
−0.375859 + 0.926677i 0.622652π0.622652\pi
888888 −75.5342 −2.53476
889889 11.9273 + 11.3693i 0.400028 + 0.381314i
890890 1.92063 0.0643795
891891 −9.26171 + 5.34725i −0.310279 + 0.179140i
892892 1.34500 + 0.776535i 0.0450339 + 0.0260003i
893893 69.9260 + 40.3718i 2.33998 + 1.35099i
894894 10.8509 + 18.7943i 0.362909 + 0.628577i
895895 34.1228 1.14060
896896 7.53918 31.0968i 0.251866 1.03887i
897897 7.96025 4.42493i 0.265785 0.147744i
898898 3.19564 + 5.53502i 0.106640 + 0.184706i
899899 −4.99317 2.88281i −0.166531 0.0961470i
900900 0.197881 0.342740i 0.00659603 0.0114247i
901901 −12.3512 + 7.13094i −0.411477 + 0.237566i
902902 1.36478 0.0454422
903903 −24.5491 + 7.21219i −0.816944 + 0.240007i
904904 21.8838i 0.727846i
905905 −15.8272 27.4134i −0.526113 0.911254i
906906 51.8031 + 29.9085i 1.72104 + 0.993645i
907907 14.0079 + 8.08749i 0.465126 + 0.268541i 0.714197 0.699945i 0.246792π-0.246792\pi
−0.249071 + 0.968485i 0.580125π0.580125\pi
908908 1.24620 + 2.15849i 0.0413567 + 0.0716319i
909909 8.38813i 0.278217i
910910 2.17214 + 7.39363i 0.0720058 + 0.245096i
911911 54.7724i 1.81469i 0.420385 + 0.907346i 0.361895π0.361895\pi
−0.420385 + 0.907346i 0.638105π0.638105\pi
912912 61.6238 35.5785i 2.04057 1.17812i
913913 −5.25192 3.03220i −0.173813 0.100351i
914914 −39.8226 22.9916i −1.31721 0.760494i
915915 −52.6278 + 30.3847i −1.73982 + 1.00449i
916916 −1.26153 −0.0416821
917917 −38.7852 9.40316i −1.28080 0.310520i
918918 3.51934i 0.116155i
919919 −44.2701 + 25.5594i −1.46034 + 0.843125i −0.999026 0.0441143i 0.985953π-0.985953\pi
−0.461309 + 0.887239i 0.652620π0.652620\pi
920920 −0.544043 + 33.4683i −0.0179366 + 1.10342i
921921 5.53206 9.58181i 0.182288 0.315731i
922922 −43.2578 + 24.9749i −1.42462 + 0.822505i
923923 8.37221i 0.275575i
924924 0.510493 + 0.486611i 0.0167940 + 0.0160083i
925925 16.3685i 0.538195i
926926 −2.51996 4.36471i −0.0828112 0.143433i
927927 21.0323 36.4291i 0.690793 1.19649i
928928 −0.336952 + 0.583618i −0.0110610 + 0.0191582i
929929 −36.3178 + 20.9681i −1.19155 + 0.687941i −0.958658 0.284562i 0.908152π-0.908152\pi
−0.232891 + 0.972503i 0.574819π0.574819\pi
930930 42.9956 1.40988
931931 −41.7086 + 26.8218i −1.36694 + 0.879048i
932932 −2.62910 −0.0861192
933933 −28.3241 49.0588i −0.927290 1.60611i
934934 −16.6099 + 28.7693i −0.543494 + 0.941359i
935935 9.51130 + 5.49135i 0.311053 + 0.179586i
936936 5.18052 2.99098i 0.169331 0.0977631i
937937 35.9442 1.17425 0.587123 0.809498i 0.300261π-0.300261\pi
0.587123 + 0.809498i 0.300261π0.300261\pi
938938 13.6876 14.3594i 0.446916 0.468850i
939939 25.6802i 0.838041i
940940 2.52706 1.45900i 0.0824236 0.0475873i
941941 −14.9692 + 25.9274i −0.487981 + 0.845208i −0.999904 0.0138228i 0.995600π-0.995600\pi
0.511923 + 0.859031i 0.328933π0.328933\pi
942942 17.6108 + 10.1676i 0.573792 + 0.331279i
943943 2.10670 3.51569i 0.0686037 0.114486i
944944 20.3425i 0.662093i
945945 −4.02665 0.976229i −0.130987 0.0317567i
946946 6.44492 0.209542
947947 23.2755 + 40.3144i 0.756353 + 1.31004i 0.944699 + 0.327939i 0.106354π0.106354\pi
−0.188346 + 0.982103i 0.560313π0.560313\pi
948948 0.784396 1.35861i 0.0254760 0.0441257i
949949 3.71879 6.44114i 0.120717 0.209088i
950950 −7.33858 12.7108i −0.238095 0.412393i
951951 27.9924i 0.907714i
952952 −27.4697 + 8.07020i −0.890297 + 0.261557i
953953 46.6808i 1.51214i 0.654492 + 0.756069i 0.272883π0.272883\pi
−0.654492 + 0.756069i 0.727117π0.727117\pi
954954 12.4879 7.20987i 0.404309 0.233428i
955955 −23.7618 13.7189i −0.768914 0.443933i
956956 −1.27715 + 2.21208i −0.0413059 + 0.0715439i
957957 1.55903 + 2.70032i 0.0503963 + 0.0872890i
958958 11.2020 0.361921
959959 2.42291 + 8.24719i 0.0782398 + 0.266316i
960960 45.9135i 1.48185i
961961 −3.58358 6.20695i −0.115599 0.200224i
962962 6.57704 11.3918i 0.212052 0.367285i
963963 −34.7450 20.0600i −1.11964 0.646426i
964964 −1.45846 2.52612i −0.0469738 0.0813610i
965965 18.1846 0.585383
966966 42.4814 11.7338i 1.36682 0.377530i
967967 −27.1443 −0.872902 −0.436451 0.899728i 0.643765π-0.643765\pi
−0.436451 + 0.899728i 0.643765π0.643765\pi
968968 −13.4686 23.3284i −0.432898 0.749802i
969969 −57.7954 33.3682i −1.85666 1.07194i
970970 −21.9046 + 37.9399i −0.703314 + 1.21818i
971971 8.26330 + 14.3125i 0.265182 + 0.459309i 0.967611 0.252445i 0.0812346π-0.0812346\pi
−0.702429 + 0.711754i 0.747901π0.747901\pi
972972 2.16143i 0.0693279i
973973 28.7510 30.1620i 0.921713 0.966949i
974974 −4.08747 −0.130971
975975 −1.35723 2.35079i −0.0434661 0.0752855i
976976 −20.9615 + 36.3064i −0.670961 + 1.16214i
977977 27.2815 + 15.7510i 0.872813 + 0.503919i 0.868282 0.496071i 0.165224π-0.165224\pi
0.00453074 + 0.999990i 0.498558π0.498558\pi
978978 −14.3517 + 8.28594i −0.458916 + 0.264955i
979979 0.575750i 0.0184011i
980980 0.0857956 + 1.79002i 0.00274064 + 0.0571802i
981981 38.5226i 1.22993i
982982 −4.39224 7.60758i −0.140162 0.242768i
983983 15.8593 27.4691i 0.505833 0.876129i −0.494144 0.869380i 0.664518π-0.664518\pi
0.999977 0.00674862i 0.00214817π-0.00214817\pi
984984 2.81853 4.88183i 0.0898513 0.155627i
985985 5.78253 + 10.0156i 0.184247 + 0.319124i
986986 6.72986 0.214322
987987 52.3066 + 49.8596i 1.66494 + 1.58705i
988988 0.566823i 0.0180330i
989989 9.94851 16.6022i 0.316344 0.527918i
990990 −9.61657 5.55213i −0.305635 0.176458i
991991 −7.74129 + 13.4083i −0.245910 + 0.425929i −0.962387 0.271682i 0.912420π-0.912420\pi
0.716477 + 0.697611i 0.245753π0.245753\pi
992992 2.41245 1.39283i 0.0765955 0.0442224i
993993 66.7687i 2.11884i
994994 −9.54581 + 39.3736i −0.302775 + 1.24885i
995995 −8.72423 −0.276577
996996 1.15332 0.665867i 0.0365442 0.0210988i
997997 35.6689 + 20.5935i 1.12965 + 0.652202i 0.943846 0.330386i 0.107179π-0.107179\pi
0.185800 + 0.982588i 0.440512π0.440512\pi
998998 −10.0818 + 17.4623i −0.319135 + 0.552758i
999999 3.53624 + 6.12496i 0.111882 + 0.193785i
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 161.2.g.a.45.11 28
7.3 odd 6 1127.2.c.c.1126.8 28
7.4 even 3 1127.2.c.c.1126.6 28
7.5 odd 6 inner 161.2.g.a.68.12 yes 28
23.22 odd 2 inner 161.2.g.a.45.12 yes 28
161.45 even 6 1127.2.c.c.1126.7 28
161.68 even 6 inner 161.2.g.a.68.11 yes 28
161.137 odd 6 1127.2.c.c.1126.5 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.2.g.a.45.11 28 1.1 even 1 trivial
161.2.g.a.45.12 yes 28 23.22 odd 2 inner
161.2.g.a.68.11 yes 28 161.68 even 6 inner
161.2.g.a.68.12 yes 28 7.5 odd 6 inner
1127.2.c.c.1126.5 28 161.137 odd 6
1127.2.c.c.1126.6 28 7.4 even 3
1127.2.c.c.1126.7 28 161.45 even 6
1127.2.c.c.1126.8 28 7.3 odd 6