Properties

Label 22.14.c.b.9.3
Level 2222
Weight 1414
Character 22.9
Analytic conductor 23.59123.591
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] = [22,14,Mod(3,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.3");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: N N == 22=211 22 = 2 \cdot 11
Weight: k k == 14 14
Character orbit: [χ][\chi] == 22.c (of order 55, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 23.590804369423.5908043694
Analytic rank: 00
Dimension: 2828
Relative dimension: 77 over Q(ζ5)\Q(\zeta_{5})
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 9.3
Character χ\chi == 22.9
Dual form 22.14.c.b.5.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(19.777160.8676i)q2+(501.424+364.306i)q3+(3313.732407.57i)q4+(17458.1+53730.4i)q5+(12257.7+37725.4i)q6+(385628.280175.i)q7+(212079.+154084.i)q8+(373966.+1.15095e6i)q9+3.61571e6q10+(5.87360e6+153242.i)q11+2.53868e6q12+(6.48230e61.99505e7i)q13+(2.46802e7+1.79312e7i)q14+(2.83282e72.05816e7i)q15+(5.18444e6+1.59561e7i)q16+(3.88058e71.19432e8i)q17+(6.26595e7+4.55248e7i)q18+(9.84864e77.15545e7i)q19+(7.15083e72.20080e8i)q20+2.95432e8q21+(1.25490e83.54482e8i)q225.82343e8q23+(5.02076e71.54523e8i)q24+(1.59461e9+1.15855e9i)q25+(1.08614e97.89124e8i)q26+(5.37137e81.65314e9i)q27+(6.03327e8+1.85685e9i)q28+(2.19265e91.59305e9i)q29+(1.81301e9+1.31723e9i)q30+(1.11280e93.42483e9i)q31+1.07374e9q32+(3.00099e9+2.06295e9i)q338.03700e9q34+(8.32161e92.56113e10i)q35+(4.01021e92.91359e9i)q36+(8.13105e95.90756e9i)q37+(2.40758e97.40977e9i)q38+(4.01769e9+1.23652e10i)q39+(1.19815e108.70508e9i)q40+(1.26905e10+9.22015e9i)q41+(5.84279e91.79823e10i)q42+2.91315e10q43+(1.90946e101.46489e10i)q446.83697e10q45+(1.15170e10+3.54458e10i)q46+(1.17541e118.53986e10i)q47+(8.41250e96.11204e9i)q48+(4.02704e10+1.23940e11i)q49+(3.89815e10+1.19973e11i)q50+(6.29679e10+4.57488e10i)q51+(6.95127e10+5.05039e10i)q52+(5.45008e101.67736e11i)q531.11246e11q54+(9.43081e10+3.18267e11i)q55+1.24954e11q56+(2.33157e10+7.17583e10i)q57+(1.40330e11+1.01955e11i)q58+(4.46985e113.24754e11i)q59+(4.43204e10+1.36404e11i)q60+(1.87571e11+5.77285e11i)q61+(1.86453e111.35466e11i)q62+(4.66678e113.39062e11i)q63+(2.12355e106.53561e10i)q64+1.18512e12q65+(6.62159e10+2.23462e11i)q66+4.94624e11q67+(1.58948e11+4.89193e11i)q68+(2.92001e112.12151e11i)q69+(1.39432e121.01303e12i)q70+(2.72872e11+8.39813e11i)q71+(9.80329e103.01714e11i)q72+(7.40121e115.37729e11i)q73+(5.20387e11+3.78084e11i)q74+(3.77507e111.16185e12i)q754.98630e11q76+(2.22209e121.70473e12i)q77+8.32097e11q78+(1.44237e11+4.43915e11i)q79+(7.66817e11+5.57125e11i)q80+(6.89348e115.00841e11i)q81+(3.10229e11+9.54785e11i)q82+(3.93195e111.21013e12i)q83+(9.78984e117.11274e11i)q84+(5.73965e124.17010e12i)q85+(5.76136e111.77317e12i)q86+1.67980e12q87+(1.26928e12+8.72531e11i)q887.38624e12q89+(1.35215e12+4.16150e12i)q90+(8.08937e12+5.87727e12i)q91+(1.92973e12+1.40203e12i)q92+(6.89704e11+2.12269e12i)q93+(2.87339e128.84338e12i)q94+(5.56404e12+4.04251e12i)q95+(5.38400e11+3.91170e11i)q96+(1.49344e124.59634e12i)q97+8.34034e12q98+(2.37290e12+6.70291e12i)q99+O(q100)q+(19.7771 - 60.8676i) q^{2} +(-501.424 + 364.306i) q^{3} +(-3313.73 - 2407.57i) q^{4} +(17458.1 + 53730.4i) q^{5} +(12257.7 + 37725.4i) q^{6} +(-385628. - 280175. i) q^{7} +(-212079. + 154084. i) q^{8} +(-373966. + 1.15095e6i) q^{9} +3.61571e6 q^{10} +(5.87360e6 + 153242. i) q^{11} +2.53868e6 q^{12} +(6.48230e6 - 1.99505e7i) q^{13} +(-2.46802e7 + 1.79312e7i) q^{14} +(-2.83282e7 - 2.05816e7i) q^{15} +(5.18444e6 + 1.59561e7i) q^{16} +(-3.88058e7 - 1.19432e8i) q^{17} +(6.26595e7 + 4.55248e7i) q^{18} +(9.84864e7 - 7.15545e7i) q^{19} +(7.15083e7 - 2.20080e8i) q^{20} +2.95432e8 q^{21} +(1.25490e8 - 3.54482e8i) q^{22} -5.82343e8 q^{23} +(5.02076e7 - 1.54523e8i) q^{24} +(-1.59461e9 + 1.15855e9i) q^{25} +(-1.08614e9 - 7.89124e8i) q^{26} +(-5.37137e8 - 1.65314e9i) q^{27} +(6.03327e8 + 1.85685e9i) q^{28} +(-2.19265e9 - 1.59305e9i) q^{29} +(-1.81301e9 + 1.31723e9i) q^{30} +(1.11280e9 - 3.42483e9i) q^{31} +1.07374e9 q^{32} +(-3.00099e9 + 2.06295e9i) q^{33} -8.03700e9 q^{34} +(8.32161e9 - 2.56113e10i) q^{35} +(4.01021e9 - 2.91359e9i) q^{36} +(-8.13105e9 - 5.90756e9i) q^{37} +(-2.40758e9 - 7.40977e9i) q^{38} +(4.01769e9 + 1.23652e10i) q^{39} +(-1.19815e10 - 8.70508e9i) q^{40} +(-1.26905e10 + 9.22015e9i) q^{41} +(5.84279e9 - 1.79823e10i) q^{42} +2.91315e10 q^{43} +(-1.90946e10 - 1.46489e10i) q^{44} -6.83697e10 q^{45} +(-1.15170e10 + 3.54458e10i) q^{46} +(1.17541e11 - 8.53986e10i) q^{47} +(-8.41250e9 - 6.11204e9i) q^{48} +(4.02704e10 + 1.23940e11i) q^{49} +(3.89815e10 + 1.19973e11i) q^{50} +(6.29679e10 + 4.57488e10i) q^{51} +(-6.95127e10 + 5.05039e10i) q^{52} +(5.45008e10 - 1.67736e11i) q^{53} -1.11246e11 q^{54} +(9.43081e10 + 3.18267e11i) q^{55} +1.24954e11 q^{56} +(-2.33157e10 + 7.17583e10i) q^{57} +(-1.40330e11 + 1.01955e11i) q^{58} +(-4.46985e11 - 3.24754e11i) q^{59} +(4.43204e10 + 1.36404e11i) q^{60} +(1.87571e11 + 5.77285e11i) q^{61} +(-1.86453e11 - 1.35466e11i) q^{62} +(4.66678e11 - 3.39062e11i) q^{63} +(2.12355e10 - 6.53561e10i) q^{64} +1.18512e12 q^{65} +(6.62159e10 + 2.23462e11i) q^{66} +4.94624e11 q^{67} +(-1.58948e11 + 4.89193e11i) q^{68} +(2.92001e11 - 2.12151e11i) q^{69} +(-1.39432e12 - 1.01303e12i) q^{70} +(2.72872e11 + 8.39813e11i) q^{71} +(-9.80329e10 - 3.01714e11i) q^{72} +(-7.40121e11 - 5.37729e11i) q^{73} +(-5.20387e11 + 3.78084e11i) q^{74} +(3.77507e11 - 1.16185e12i) q^{75} -4.98630e11 q^{76} +(-2.22209e12 - 1.70473e12i) q^{77} +8.32097e11 q^{78} +(-1.44237e11 + 4.43915e11i) q^{79} +(-7.66817e11 + 5.57125e11i) q^{80} +(-6.89348e11 - 5.00841e11i) q^{81} +(3.10229e11 + 9.54785e11i) q^{82} +(-3.93195e11 - 1.21013e12i) q^{83} +(-9.78984e11 - 7.11274e11i) q^{84} +(5.73965e12 - 4.17010e12i) q^{85} +(5.76136e11 - 1.77317e12i) q^{86} +1.67980e12 q^{87} +(-1.26928e12 + 8.72531e11i) q^{88} -7.38624e12 q^{89} +(-1.35215e12 + 4.16150e12i) q^{90} +(-8.08937e12 + 5.87727e12i) q^{91} +(1.92973e12 + 1.40203e12i) q^{92} +(6.89704e11 + 2.12269e12i) q^{93} +(-2.87339e12 - 8.84338e12i) q^{94} +(5.56404e12 + 4.04251e12i) q^{95} +(-5.38400e11 + 3.91170e11i) q^{96} +(1.49344e12 - 4.59634e12i) q^{97} +8.34034e12 q^{98} +(-2.37290e12 + 6.70291e12i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q448q21248q328672q4+71554q5+99008q6+361734q71835008q88615367q9+2898176q10+8699239q112449408q12+32373940q13+23150976q14++71382923151637q99+O(q100) 28 q - 448 q^{2} - 1248 q^{3} - 28672 q^{4} + 71554 q^{5} + 99008 q^{6} + 361734 q^{7} - 1835008 q^{8} - 8615367 q^{9} + 2898176 q^{10} + 8699239 q^{11} - 2449408 q^{12} + 32373940 q^{13} + 23150976 q^{14}+ \cdots + 71382923151637 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/22Z)×\left(\mathbb{Z}/22\mathbb{Z}\right)^\times.

nn 1313
χ(n)\chi(n) e(35)e\left(\frac{3}{5}\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 19.7771 60.8676i 0.218508 0.672499i
33 −501.424 + 364.306i −0.397115 + 0.288521i −0.768365 0.640012i 0.778929π-0.778929\pi
0.371250 + 0.928533i 0.378929π0.378929\pi
44 −3313.73 2407.57i −0.404508 0.293893i
55 17458.1 + 53730.4i 0.499679 + 1.53785i 0.809535 + 0.587071i 0.199719π0.199719\pi
−0.309856 + 0.950784i 0.600281π0.600281\pi
66 12257.7 + 37725.4i 0.107257 + 0.330104i
77 −385628. 280175.i −1.23889 0.900103i −0.241362 0.970435i 0.577594π-0.577594\pi
−0.997524 + 0.0703325i 0.977594π0.977594\pi
88 −212079. + 154084.i −0.286031 + 0.207813i
99 −373966. + 1.15095e6i −0.234561 + 0.721904i
1010 3.61571e6 1.14339
1111 5.87360e6 + 153242.i 0.999660 + 0.0260811i
1212 2.53868e6 0.245431
1313 6.48230e6 1.99505e7i 0.372475 1.14636i −0.572692 0.819771i 0.694101π-0.694101\pi
0.945166 0.326589i 0.105899π-0.105899\pi
1414 −2.46802e7 + 1.79312e7i −0.876024 + 0.636469i
1515 −2.83282e7 2.05816e7i −0.642134 0.466538i
1616 5.18444e6 + 1.59561e7i 0.0772542 + 0.237764i
1717 −3.88058e7 1.19432e8i −0.389922 1.20006i −0.932846 0.360276i 0.882683π-0.882683\pi
0.542923 0.839782i 0.317317π-0.317317\pi
1818 6.26595e7 + 4.55248e7i 0.434226 + 0.315484i
1919 9.84864e7 7.15545e7i 0.480261 0.348930i −0.321165 0.947023i 0.604075π-0.604075\pi
0.801427 + 0.598093i 0.204075π0.204075\pi
2020 7.15083e7 2.20080e8i 0.249840 0.768927i
2121 2.95432e8 0.751679
2222 1.25490e8 3.54482e8i 0.235973 0.666571i
2323 −5.82343e8 −0.820253 −0.410126 0.912029i 0.634515π-0.634515\pi
−0.410126 + 0.912029i 0.634515π0.634515\pi
2424 5.02076e7 1.54523e8i 0.0536286 0.165052i
2525 −1.59461e9 + 1.15855e9i −1.30630 + 0.949083i
2626 −1.08614e9 7.89124e8i −0.689537 0.500978i
2727 −5.37137e8 1.65314e9i −0.266822 0.821192i
2828 6.03327e8 + 1.85685e9i 0.236606 + 0.728198i
2929 −2.19265e9 1.59305e9i −0.684514 0.497328i 0.190338 0.981719i 0.439041π-0.439041\pi
−0.874852 + 0.484390i 0.839041π0.839041\pi
3030 −1.81301e9 + 1.31723e9i −0.454058 + 0.329892i
3131 1.11280e9 3.42483e9i 0.225198 0.693088i −0.773074 0.634316i 0.781282π-0.781282\pi
0.998271 0.0587714i 0.0187183π-0.0187183\pi
3232 1.07374e9 0.176777
3333 −3.00099e9 + 2.06295e9i −0.404505 + 0.278066i
3434 −8.03700e9 −0.892238
3535 8.32161e9 2.56113e10i 0.765182 2.35499i
3636 4.01021e9 2.91359e9i 0.307044 0.223081i
3737 −8.13105e9 5.90756e9i −0.520997 0.378527i 0.295982 0.955193i 0.404353π-0.404353\pi
−0.816979 + 0.576667i 0.804353π0.804353\pi
3838 −2.40758e9 7.40977e9i −0.129714 0.399219i
3939 4.01769e9 + 1.23652e10i 0.182834 + 0.562704i
4040 −1.19815e10 8.70508e9i −0.462511 0.336034i
4141 −1.26905e10 + 9.22015e9i −0.417236 + 0.303140i −0.776525 0.630087i 0.783019π-0.783019\pi
0.359289 + 0.933226i 0.383019π0.383019\pi
4242 5.84279e9 1.79823e10i 0.164248 0.505503i
4343 2.91315e10 0.702778 0.351389 0.936230i 0.385709π-0.385709\pi
0.351389 + 0.936230i 0.385709π0.385709\pi
4444 −1.90946e10 1.46489e10i −0.396706 0.304343i
4545 −6.83697e10 −1.22739
4646 −1.15170e10 + 3.54458e10i −0.179232 + 0.551619i
4747 1.17541e11 8.53986e10i 1.59057 1.15562i 0.687456 0.726226i 0.258728π-0.258728\pi
0.903118 0.429393i 0.141272π-0.141272\pi
4848 −8.41250e9 6.11204e9i −0.0992789 0.0721303i
4949 4.02704e10 + 1.23940e11i 0.415634 + 1.27919i
5050 3.89815e10 + 1.19973e11i 0.352820 + 1.08587i
5151 6.29679e10 + 4.57488e10i 0.501087 + 0.364061i
5252 −6.95127e10 + 5.05039e10i −0.487576 + 0.354245i
5353 5.45008e10 1.67736e11i 0.337761 1.03952i −0.627584 0.778548i 0.715956π-0.715956\pi
0.965346 0.260974i 0.0840437π-0.0840437\pi
5454 −1.11246e11 −0.610553
5555 9.43081e10 + 3.18267e11i 0.459400 + 1.55036i
5656 1.24954e11 0.541413
5757 −2.33157e10 + 7.17583e10i −0.0900454 + 0.277131i
5858 −1.40330e11 + 1.01955e11i −0.484024 + 0.351664i
5959 −4.46985e11 3.24754e11i −1.37961 1.00234i −0.996917 0.0784661i 0.974998π-0.974998\pi
−0.382690 0.923877i 0.625002π-0.625002\pi
6060 4.43204e10 + 1.36404e11i 0.122637 + 0.377437i
6161 1.87571e11 + 5.77285e11i 0.466146 + 1.43465i 0.857535 + 0.514426i 0.171995π0.171995\pi
−0.391389 + 0.920226i 0.628005π0.628005\pi
6262 −1.86453e11 1.35466e11i −0.416893 0.302890i
6363 4.66678e11 3.39062e11i 0.940382 0.683227i
6464 2.12355e10 6.53561e10i 0.0386271 0.118882i
6565 1.18512e12 1.94905
6666 6.62159e10 + 2.23462e11i 0.0986113 + 0.332789i
6767 4.94624e11 0.668019 0.334009 0.942570i 0.391598π-0.391598\pi
0.334009 + 0.942570i 0.391598π0.391598\pi
6868 −1.58948e11 + 4.89193e11i −0.194961 + 0.600029i
6969 2.92001e11 2.12151e11i 0.325735 0.236660i
7070 −1.39432e12 1.01303e12i −1.41653 1.02917i
7171 2.72872e11 + 8.39813e11i 0.252801 + 0.778042i 0.994255 + 0.107038i 0.0341367π0.0341367\pi
−0.741454 + 0.671004i 0.765863π0.765863\pi
7272 −9.80329e10 3.01714e11i −0.0829298 0.255232i
7373 −7.40121e11 5.37729e11i −0.572406 0.415877i 0.263573 0.964640i 0.415099π-0.415099\pi
−0.835978 + 0.548762i 0.815099π0.815099\pi
7474 −5.20387e11 + 3.78084e11i −0.368401 + 0.267659i
7575 3.77507e11 1.16185e12i 0.244922 0.753792i
7676 −4.98630e11 −0.296818
7777 −2.22209e12 1.70473e12i −1.21499 0.932108i
7878 8.32097e11 0.418368
7979 −1.44237e11 + 4.43915e11i −0.0667575 + 0.205458i −0.978871 0.204480i 0.934450π-0.934450\pi
0.912113 + 0.409938i 0.134450π0.134450\pi
8080 −7.66817e11 + 5.57125e11i −0.327044 + 0.237612i
8181 −6.89348e11 5.00841e11i −0.271198 0.197037i
8282 3.10229e11 + 9.54785e11i 0.112692 + 0.346829i
8383 −3.93195e11 1.21013e12i −0.132008 0.406279i 0.863105 0.505025i 0.168517π-0.168517\pi
−0.995113 + 0.0987460i 0.968517π0.968517\pi
8484 −9.78984e11 7.11274e11i −0.304061 0.220913i
8585 5.73965e12 4.17010e12i 1.65068 1.19929i
8686 5.76136e11 1.77317e12i 0.153563 0.472617i
8787 1.67980e12 0.415321
8888 −1.26928e12 + 8.72531e11i −0.291353 + 0.200283i
8989 −7.38624e12 −1.57539 −0.787695 0.616065i 0.788726π-0.788726\pi
−0.787695 + 0.616065i 0.788726π0.788726\pi
9090 −1.35215e12 + 4.16150e12i −0.268194 + 0.825417i
9191 −8.08937e12 + 5.87727e12i −1.49330 + 1.08494i
9292 1.92973e12 + 1.40203e12i 0.331799 + 0.241066i
9393 6.89704e11 + 2.12269e12i 0.110541 + 0.340210i
9494 −2.87339e12 8.84338e12i −0.429599 1.32217i
9595 5.56404e12 + 4.04251e12i 0.776581 + 0.564219i
9696 −5.38400e11 + 3.91170e11i −0.0702008 + 0.0510038i
9797 1.49344e12 4.59634e12i 0.182042 0.560268i −0.817843 0.575442i 0.804830π-0.804830\pi
0.999885 + 0.0151736i 0.00483008π0.00483008\pi
9898 8.34034e12 0.951074
9999 −2.37290e12 + 6.70291e12i −0.253309 + 0.715541i
100100 8.07339e12 0.807339
101101 3.65812e12 1.12585e13i 0.342901 1.05534i −0.619797 0.784762i 0.712785π-0.712785\pi
0.962698 0.270579i 0.0872150π-0.0872150\pi
102102 4.02994e12 2.92792e12i 0.354322 0.257430i
103103 4.30461e12 + 3.12748e12i 0.355216 + 0.258079i 0.751054 0.660241i 0.229546π-0.229546\pi
−0.395838 + 0.918320i 0.629546π0.629546\pi
104104 1.69929e12 + 5.22989e12i 0.131690 + 0.405299i
105105 5.15768e12 + 1.58737e13i 0.375599 + 1.15597i
106106 −9.13184e12 6.63467e12i −0.625274 0.454288i
107107 6.27081e12 4.55601e12i 0.403951 0.293488i −0.367197 0.930143i 0.619683π-0.619683\pi
0.771149 + 0.636655i 0.219683π0.219683\pi
108108 −2.20011e12 + 6.77126e12i −0.133411 + 0.410596i
109109 −1.23082e13 −0.702946 −0.351473 0.936198i 0.614319π-0.614319\pi
−0.351473 + 0.936198i 0.614319π0.614319\pi
110110 2.12373e13 + 5.54081e11i 1.14300 + 0.0298209i
111111 6.22926e12 0.316109
112112 2.47123e12 7.60566e12i 0.118303 0.364099i
113113 −2.91515e13 + 2.11798e13i −1.31720 + 0.956999i −0.317233 + 0.948348i 0.602754π0.602754\pi
−0.999963 + 0.00865116i 0.997246π0.997246\pi
114114 3.90664e12 + 2.83834e12i 0.166695 + 0.121111i
115115 −1.01666e13 3.12895e13i −0.409863 1.26143i
116116 3.43047e12 + 1.05579e13i 0.130730 + 0.402347i
117117 2.05378e13 + 1.49216e13i 0.740194 + 0.537782i
118118 −2.86071e13 + 2.07843e13i −0.975529 + 0.708764i
119119 −1.84972e13 + 5.69287e13i −0.597106 + 1.83770i
120120 9.17913e12 0.280623
121121 3.44757e13 + 1.80017e12i 0.998640 + 0.0521445i
122122 3.88476e13 1.06666
123123 3.00434e12 9.24641e12i 0.0782287 0.240763i
124124 −1.19330e13 + 8.66985e12i −0.294788 + 0.214176i
125125 −3.42949e13 2.49167e13i −0.804107 0.584218i
126126 −1.14083e13 3.51113e13i −0.253988 0.781696i
127127 −2.02053e12 6.21854e12i −0.0427307 0.131512i 0.927415 0.374033i 0.122025π-0.122025\pi
−0.970146 + 0.242522i 0.922025π0.922025\pi
128128 −3.55809e12 2.58511e12i −0.0715077 0.0519534i
129129 −1.46072e13 + 1.06128e13i −0.279084 + 0.202766i
130130 2.34381e13 7.21351e13i 0.425884 1.31074i
131131 −7.46859e13 −1.29114 −0.645572 0.763699i 0.723381π-0.723381\pi
−0.645572 + 0.763699i 0.723381π0.723381\pi
132132 1.49112e13 + 3.89033e11i 0.245347 + 0.00640112i
133133 −5.80269e13 −0.909062
134134 9.78221e12 3.01066e13i 0.145967 0.449242i
135135 7.94465e13 5.77213e13i 1.12955 0.820666i
136136 2.66325e13 + 1.93496e13i 0.360918 + 0.262222i
137137 −1.75485e13 5.40086e13i −0.226754 0.697877i −0.998109 0.0614718i 0.980421π-0.980421\pi
0.771355 0.636405i 0.219579π-0.219579\pi
138138 −7.13820e12 2.19691e13i −0.0879781 0.270769i
139139 −1.93287e13 1.40431e13i −0.227304 0.165146i 0.468304 0.883567i 0.344865π-0.344865\pi
−0.695608 + 0.718421i 0.744865π0.744865\pi
140140 −8.92365e13 + 6.48341e13i −1.00164 + 0.727731i
141141 −2.78267e13 + 8.56418e13i −0.298221 + 0.917829i
142142 5.65140e13 0.578471
143143 4.11317e13 1.16188e14i 0.402247 1.13626i
144144 −2.03034e13 −0.189764
145145 4.73160e13 1.45624e14i 0.422781 1.30119i
146146 −4.73677e13 + 3.44147e13i −0.404752 + 0.294070i
147147 −6.53444e13 4.74755e13i −0.534129 0.388067i
148148 1.27213e13 + 3.91521e13i 0.0995016 + 0.306235i
149149 2.11187e13 + 6.49966e13i 0.158109 + 0.486609i 0.998463 0.0554296i 0.0176528π-0.0176528\pi
−0.840354 + 0.542038i 0.817653π0.817653\pi
150150 −6.32529e13 4.59560e13i −0.453406 0.329419i
151151 1.15205e14 8.37013e13i 0.790899 0.574622i −0.117331 0.993093i 0.537434π-0.537434\pi
0.908230 + 0.418471i 0.137434π0.137434\pi
152152 −9.86145e12 + 3.03504e13i −0.0648571 + 0.199610i
153153 1.51972e14 0.957787
154154 −1.47709e14 + 1.01539e14i −0.892326 + 0.613405i
155155 2.03445e14 1.17840
156156 1.64564e13 5.06477e13i 0.0914168 0.281352i
157157 −2.56944e14 + 1.86681e14i −1.36928 + 0.994838i −0.371485 + 0.928439i 0.621151π0.621151\pi
−0.997793 + 0.0663993i 0.978849π0.978849\pi
158158 2.41675e13 + 1.75587e13i 0.123583 + 0.0897886i
159159 3.37793e13 + 1.03962e14i 0.165794 + 0.510262i
160160 1.87455e13 + 5.76926e13i 0.0883317 + 0.271857i
161161 2.24568e14 + 1.63158e14i 1.01620 + 0.738312i
162162 −4.41183e13 + 3.20538e13i −0.191766 + 0.139326i
163163 −6.27053e13 + 1.92987e14i −0.261870 + 0.805952i 0.730528 + 0.682882i 0.239274π0.239274\pi
−0.992398 + 0.123070i 0.960726π0.960726\pi
164164 6.42509e13 0.257866
165165 −1.63235e14 1.25230e14i −0.629748 0.483127i
166166 −8.14340e13 −0.302067
167167 −1.64221e14 + 5.05419e14i −0.585829 + 1.80300i 0.0100872 + 0.999949i 0.496789π0.496789\pi
−0.595916 + 0.803047i 0.703211π0.703211\pi
168168 −6.26550e13 + 4.55215e13i −0.215003 + 0.156209i
169169 −1.10969e14 8.06239e13i −0.366386 0.266195i
170170 −1.40311e14 4.31831e14i −0.445833 1.37213i
171171 4.55250e13 + 1.40112e14i 0.139244 + 0.428548i
172172 −9.65341e13 7.01361e13i −0.284280 0.206541i
173173 4.17155e14 3.03081e14i 1.18304 0.859526i 0.190525 0.981682i 0.438981π-0.438981\pi
0.992511 + 0.122157i 0.0389811π0.0389811\pi
174174 3.32216e13 1.02246e14i 0.0907509 0.279303i
175175 9.39521e14 2.47263
176176 2.80062e13 + 9.45142e13i 0.0710268 + 0.239698i
177177 3.42439e14 0.837060
178178 −1.46078e14 + 4.49583e14i −0.344236 + 1.05945i
179179 −9.98088e13 + 7.25153e13i −0.226790 + 0.164773i −0.695378 0.718644i 0.744763π-0.744763\pi
0.468588 + 0.883417i 0.344763π0.344763\pi
180180 2.26559e14 + 1.64605e14i 0.496489 + 0.360721i
181181 −1.21799e14 3.74858e14i −0.257473 0.792422i −0.993332 0.115287i 0.963221π-0.963221\pi
0.735859 0.677135i 0.236779π-0.236779\pi
182182 1.97751e14 + 6.08616e14i 0.403325 + 1.24131i
183183 −3.04361e14 2.21131e14i −0.599041 0.435229i
184184 1.23503e14 8.97299e13i 0.234618 0.170460i
185185 1.75463e14 5.40020e14i 0.321788 0.990360i
186186 1.42843e14 0.252945
187187 −2.09628e14 7.07442e14i −0.358491 1.20982i
188188 −5.95103e14 −0.983028
189189 −2.56033e14 + 7.87989e14i −0.408596 + 1.25753i
190190 3.56099e14 2.58721e14i 0.549126 0.398963i
191191 −3.32812e14 2.41802e14i −0.496001 0.360366i 0.311486 0.950251i 0.399173π-0.399173\pi
−0.807487 + 0.589885i 0.799173π0.799173\pi
192192 1.31616e13 + 4.05073e13i 0.0189606 + 0.0583547i
193193 −1.17079e13 3.60332e13i −0.0163063 0.0501858i 0.942572 0.334002i 0.108399π-0.108399\pi
−0.958879 + 0.283817i 0.908399π0.908399\pi
194194 −2.50232e14 1.81805e14i −0.337002 0.244846i
195195 −5.94245e14 + 4.31744e14i −0.773999 + 0.562343i
196196 1.64948e14 5.07657e14i 0.207817 0.639596i
197197 −1.33018e15 −1.62137 −0.810683 0.585485i 0.800904π-0.800904\pi
−0.810683 + 0.585485i 0.800904π0.800904\pi
198198 3.61061e14 + 2.76997e14i 0.425850 + 0.326701i
199199 3.05984e14 0.349264 0.174632 0.984634i 0.444126π-0.444126\pi
0.174632 + 0.984634i 0.444126π0.444126\pi
200200 1.59668e14 4.91408e14i 0.176410 0.542934i
201201 −2.48016e14 + 1.80194e14i −0.265281 + 0.192738i
202202 −6.12933e14 4.45322e14i −0.634788 0.461201i
203203 3.99213e14 + 1.22865e15i 0.400387 + 1.23227i
204204 −9.85153e13 3.03199e14i −0.0956990 0.294531i
205205 −7.16954e14 5.20897e14i −0.674669 0.490176i
206206 2.75495e14 2.00159e14i 0.251175 0.182490i
207207 2.17776e14 6.70246e14i 0.192399 0.592144i
208208 3.51938e14 0.301339
209209 5.89435e14 4.05191e14i 0.489199 0.336286i
210210 1.06820e15 0.859462
211211 4.09851e14 1.26139e15i 0.319735 0.984044i −0.654026 0.756472i 0.726921π-0.726921\pi
0.973761 0.227572i 0.0730787π-0.0730787\pi
212212 −5.84438e14 + 4.24619e14i −0.442135 + 0.321230i
213213 −4.42773e14 3.21693e14i −0.324873 0.236034i
214214 −1.53295e14 4.71794e14i −0.109104 0.335786i
215215 5.08580e14 + 1.56525e15i 0.351164 + 1.08077i
216216 3.68638e14 + 2.67831e14i 0.246974 + 0.179437i
217217 −1.38868e15 + 1.00893e15i −0.902844 + 0.655955i
218218 −2.43420e14 + 7.49170e14i −0.153599 + 0.472730i
219219 5.67012e14 0.347301
220220 4.53737e14 1.28170e15i 0.269809 0.762150i
221221 −2.63427e15 −1.52093
222222 1.23197e14 3.79160e14i 0.0690724 0.212583i
223223 −3.33492e13 + 2.42296e13i −0.0181595 + 0.0131937i −0.596828 0.802369i 0.703573π-0.703573\pi
0.578668 + 0.815563i 0.303573π0.303573\pi
224224 −4.14065e14 3.00836e14i −0.219006 0.159117i
225225 −7.37102e14 2.26857e15i −0.378740 1.16564i
226226 7.12631e14 + 2.19325e15i 0.355762 + 1.09492i
227227 −1.07978e15 7.84509e14i −0.523804 0.380566i 0.294231 0.955734i 0.404936π-0.404936\pi
−0.818035 + 0.575169i 0.804936π0.804936\pi
228228 2.50025e14 1.81654e14i 0.117871 0.0856383i
229229 −6.43487e14 + 1.98045e15i −0.294855 + 0.907472i 0.688414 + 0.725318i 0.258307π0.258307\pi
−0.983270 + 0.182154i 0.941693π0.941693\pi
230230 −2.10559e15 −0.937868
231231 1.73525e15 + 4.52728e13i 0.751424 + 0.0196046i
232232 7.10479e14 0.299143
233233 3.19710e14 9.83967e14i 0.130901 0.402872i −0.864029 0.503442i 0.832067π-0.832067\pi
0.994930 + 0.100570i 0.0320667π0.0320667\pi
234234 1.31442e15 9.54981e14i 0.523396 0.380269i
235235 6.64055e15 + 4.82464e15i 2.57195 + 1.86863i
236236 6.99323e14 + 2.15230e15i 0.263481 + 0.810912i
237237 −8.93971e13 2.75136e14i −0.0327687 0.100852i
238238 3.09929e15 + 2.25177e15i 1.10538 + 0.803106i
239239 9.00380e14 6.54164e14i 0.312492 0.227039i −0.420473 0.907305i 0.638136π-0.638136\pi
0.732965 + 0.680266i 0.238136π0.238136\pi
240240 1.81536e14 5.58712e14i 0.0613184 0.188719i
241241 3.30381e13 0.0108619 0.00543093 0.999985i 0.498271π-0.498271\pi
0.00543093 + 0.999985i 0.498271π0.498271\pi
242242 7.91402e14 2.06285e15i 0.253278 0.660190i
243243 3.29939e15 1.02800
244244 7.68292e14 2.36456e15i 0.233073 0.717326i
245245 −5.95628e15 + 4.32749e15i −1.75953 + 1.27837i
246246 −5.03390e14 3.65734e14i −0.144819 0.105217i
247247 −7.89128e14 2.42869e15i −0.221114 0.680520i
248248 2.91713e14 + 8.97799e14i 0.0796195 + 0.245043i
249249 6.38015e14 + 4.63545e14i 0.169643 + 0.123253i
250250 −2.19487e15 + 1.59467e15i −0.568590 + 0.413104i
251251 1.32229e15 4.06959e15i 0.333770 1.02724i −0.633554 0.773698i 0.718405π-0.718405\pi
0.967325 0.253541i 0.0815954π-0.0815954\pi
252252 −2.36276e15 −0.581188
253253 −3.42045e15 8.92396e13i −0.819974 0.0213931i
254254 −4.18468e14 −0.0977784
255255 −1.35881e15 + 4.18198e15i −0.309490 + 0.952512i
256256 −2.27718e14 + 1.65447e14i −0.0505636 + 0.0367366i
257257 8.02671e14 + 5.83174e14i 0.173769 + 0.126251i 0.671270 0.741213i 0.265749π-0.265749\pi
−0.497501 + 0.867463i 0.665749π0.665749\pi
258258 3.57086e14 + 1.09900e15i 0.0753780 + 0.231990i
259259 1.48041e15 + 4.55623e15i 0.304743 + 0.937902i
260260 −3.92716e15 2.85325e15i −0.788409 0.572812i
261261 2.65350e15 1.92788e15i 0.519583 0.377499i
262262 −1.47707e15 + 4.54595e15i −0.282126 + 0.868293i
263263 −7.54164e15 −1.40525 −0.702624 0.711561i 0.747989π-0.747989\pi
−0.702624 + 0.711561i 0.747989π0.747989\pi
264264 3.18579e14 8.99914e14i 0.0579151 0.163597i
265265 9.96402e15 1.76741
266266 −1.14760e15 + 3.53196e15i −0.198637 + 0.611343i
267267 3.70364e15 2.69085e15i 0.625612 0.454534i
268268 −1.63905e15 1.19084e15i −0.270219 0.196326i
269269 −1.72316e15 5.30334e15i −0.277291 0.853415i −0.988604 0.150539i 0.951899π-0.951899\pi
0.711313 0.702876i 0.248101π-0.248101\pi
270270 −1.94214e15 5.97728e15i −0.305081 0.938942i
271271 1.08618e15 + 7.89154e14i 0.166571 + 0.121021i 0.667948 0.744208i 0.267173π-0.267173\pi
−0.501377 + 0.865229i 0.667173π0.667173\pi
272272 1.70448e15 1.23838e15i 0.255208 0.185419i
273273 1.91508e15 5.89401e15i 0.279982 0.861695i
274274 −3.63443e15 −0.518869
275275 −9.54362e15 + 6.56050e15i −1.33061 + 0.914691i
276276 −1.47838e15 −0.201315
277277 2.97984e15 9.17100e15i 0.396346 1.21983i −0.531562 0.847019i 0.678395π-0.678395\pi
0.927908 0.372808i 0.121605π-0.121605\pi
278278 −1.23704e15 + 8.98761e14i −0.160728 + 0.116776i
279279 3.52566e15 + 2.56154e15i 0.447520 + 0.325142i
280280 2.18146e15 + 6.71384e15i 0.270533 + 0.832614i
281281 −3.37226e15 1.03788e16i −0.408630 1.25763i −0.917826 0.396983i 0.870057π-0.870057\pi
0.509196 0.860651i 0.329943π-0.329943\pi
282282 4.66248e15 + 3.38749e15i 0.552075 + 0.401106i
283283 1.80631e15 1.31236e15i 0.209017 0.151860i −0.478352 0.878168i 0.658766π-0.658766\pi
0.687369 + 0.726309i 0.258766π0.258766\pi
284284 1.11768e15 3.43987e15i 0.126401 0.389021i
285285 −4.26265e15 −0.471182
286286 −6.25860e15 4.80144e15i −0.676236 0.518791i
287287 7.47705e15 0.789765
288288 −4.01543e14 + 1.23582e15i −0.0414649 + 0.127616i
289289 −4.74511e15 + 3.44753e15i −0.479083 + 0.348074i
290290 −7.92799e15 5.76002e15i −0.782665 0.568640i
291291 9.25626e14 + 2.84879e15i 0.0893576 + 0.275014i
292292 1.15794e15 + 3.56378e15i 0.109320 + 0.336452i
293293 1.01844e16 + 7.39938e15i 0.940362 + 0.683213i 0.948508 0.316754i 0.102593π-0.102593\pi
−0.00814615 + 0.999967i 0.502593π0.502593\pi
294294 −4.18204e15 + 3.03843e15i −0.377686 + 0.274405i
295295 9.64566e15 2.96863e16i 0.852097 2.62249i
296296 2.63469e15 0.227684
297297 −2.90160e15 9.79220e15i −0.245313 0.827872i
298298 4.37385e15 0.361792
299299 −3.77492e15 + 1.16180e16i −0.305524 + 0.940305i
300300 −4.04819e15 + 2.94118e15i −0.320607 + 0.232934i
301301 −1.12339e16 8.16192e15i −0.870661 0.632572i
302302 −2.81628e15 8.66762e15i −0.213614 0.657438i
303303 2.26728e15 + 6.97797e15i 0.168317 + 0.518026i
304304 1.65233e15 + 1.20049e15i 0.120065 + 0.0872326i
305305 −2.77431e16 + 2.01566e16i −1.97336 + 1.43373i
306306 3.00556e15 9.25017e15i 0.209284 0.644110i
307307 1.78233e16 1.21504 0.607519 0.794305i 0.292165π-0.292165\pi
0.607519 + 0.794305i 0.292165π0.292165\pi
308308 3.25916e15 + 1.09989e16i 0.217533 + 0.734122i
309309 −3.29780e15 −0.215523
310310 4.02355e15 1.23832e16i 0.257489 0.792469i
311311 −6.81975e14 + 4.95484e14i −0.0427392 + 0.0310518i −0.608950 0.793209i 0.708409π-0.708409\pi
0.566211 + 0.824261i 0.308409π0.308409\pi
312312 −2.75735e15 2.00333e15i −0.169234 0.122955i
313313 7.43561e15 + 2.28845e16i 0.446970 + 1.37563i 0.880309 + 0.474401i 0.157335π0.157335\pi
−0.433339 + 0.901231i 0.642665π0.642665\pi
314314 6.28122e15 + 1.93316e16i 0.369829 + 1.13822i
315315 2.63652e16 + 1.91555e16i 1.52059 + 1.10478i
316316 1.54672e15 1.12376e15i 0.0873867 0.0634901i
317317 −1.61508e14 + 4.97070e14i −0.00893940 + 0.0275126i −0.955427 0.295228i 0.904604π-0.904604\pi
0.946487 + 0.322741i 0.104604π0.104604\pi
318318 6.99597e15 0.379378
319319 −1.26346e16 9.69297e15i −0.671310 0.515012i
320320 3.88234e15 0.202125
321321 −1.48455e15 + 4.56898e15i −0.0757379 + 0.233097i
322322 1.43723e16 1.04421e16i 0.718561 0.522065i
323323 −1.23677e16 8.98568e15i −0.606001 0.440286i
324324 1.07851e15 + 3.31931e15i 0.0517942 + 0.159406i
325325 1.27769e16 + 3.93232e16i 0.601427 + 1.85100i
326326 1.05065e16 + 7.63345e15i 0.484781 + 0.352214i
327327 6.17162e15 4.48394e15i 0.279151 0.202815i
328328 1.27070e15 3.91080e15i 0.0563458 0.173415i
329329 −6.92537e16 −3.01071
330330 −1.08507e16 + 7.45903e15i −0.462507 + 0.317938i
331331 1.67407e16 0.699667 0.349834 0.936812i 0.386238π-0.386238\pi
0.349834 + 0.936812i 0.386238π0.386238\pi
332332 −1.61053e15 + 4.95670e15i −0.0660041 + 0.203140i
333333 9.84002e15 7.14920e15i 0.395466 0.287323i
334334 2.75159e16 + 1.99914e16i 1.08450 + 0.787938i
335335 8.63518e15 + 2.65763e16i 0.333795 + 1.02732i
336336 1.53165e15 + 4.71394e15i 0.0580704 + 0.178722i
337337 −1.53308e16 1.11385e16i −0.570126 0.414221i 0.265025 0.964241i 0.414620π-0.414620\pi
−0.835151 + 0.550021i 0.814620π0.814620\pi
338338 −7.10204e15 + 5.15993e15i −0.259074 + 0.188229i
339339 6.90132e15 2.12401e16i 0.246964 0.760078i
340340 −2.90595e16 −1.02018
341341 7.06095e15 1.99456e16i 0.243198 0.686978i
342342 9.42861e15 0.318624
343343 4.92395e15 1.51544e16i 0.163268 0.502488i
344344 −6.17818e15 + 4.48871e15i −0.201016 + 0.146047i
345345 1.64967e16 + 1.19856e16i 0.526713 + 0.382679i
346346 −1.01977e16 3.13853e16i −0.319527 0.983403i
347347 −7.11293e15 2.18914e16i −0.218729 0.673180i −0.998868 0.0475728i 0.984851π-0.984851\pi
0.780138 0.625607i 0.215149π-0.215149\pi
348348 −5.56642e15 4.04424e15i −0.168001 0.122060i
349349 2.82948e16 2.05574e16i 0.838187 0.608978i −0.0836767 0.996493i 0.526666π-0.526666\pi
0.921864 + 0.387515i 0.126666π0.126666\pi
350350 1.85810e16 5.71864e16i 0.540289 1.66284i
351351 −3.64628e16 −1.04077
352352 6.30673e15 + 1.64543e14i 0.176717 + 0.00461054i
353353 2.24884e16 0.618618 0.309309 0.950962i 0.399902π-0.399902\pi
0.309309 + 0.950962i 0.399902π0.399902\pi
354354 6.77244e15 2.08434e16i 0.182904 0.562922i
355355 −4.03597e16 + 2.93230e16i −1.07020 + 0.777543i
356356 2.44760e16 + 1.77829e16i 0.637259 + 0.462996i
357357 −1.14645e16 3.52840e16i −0.293097 0.902059i
358358 2.43991e15 + 7.50926e15i 0.0612539 + 0.188520i
359359 4.76481e16 + 3.46183e16i 1.17471 + 0.853478i 0.991565 0.129607i 0.0413717π-0.0413717\pi
0.183147 + 0.983086i 0.441372π0.441372\pi
360360 1.44998e16 1.05347e16i 0.351071 0.255068i
361361 −8.41557e15 + 2.59005e16i −0.200118 + 0.615901i
362362 −2.52256e16 −0.589162
363363 −1.79428e16 + 1.16571e16i −0.411620 + 0.267421i
364364 4.09560e16 0.922907
365365 1.59713e16 4.91547e16i 0.353539 1.08808i
366366 −1.94791e16 + 1.41524e16i −0.423586 + 0.307753i
367367 −2.24537e16 1.63136e16i −0.479687 0.348513i 0.321517 0.946904i 0.395807π-0.395807\pi
−0.801205 + 0.598391i 0.795807π0.795807\pi
368368 −3.01912e15 9.29191e15i −0.0633680 0.195027i
369369 −5.86612e15 1.80541e16i −0.120971 0.372309i
370370 −2.93996e16 2.13600e16i −0.595703 0.432803i
371371 −6.80125e16 + 4.94140e16i −1.35412 + 0.983829i
372372 2.82503e15 8.69454e15i 0.0552705 0.170105i
373373 −7.82976e16 −1.50536 −0.752681 0.658386i 0.771240π-0.771240\pi
−0.752681 + 0.658386i 0.771240π0.771240\pi
374374 −4.72061e16 1.23161e15i −0.891935 0.0232706i
375375 2.62735e16 0.487883
376376 −1.17694e16 + 3.62225e16i −0.214800 + 0.661085i
377377 −4.59955e16 + 3.34177e16i −0.825081 + 0.599457i
378378 4.28994e16 + 3.11682e16i 0.756405 + 0.549561i
379379 −4.03511e15 1.24188e16i −0.0699360 0.215241i 0.909980 0.414653i 0.136097π-0.136097\pi
−0.979916 + 0.199412i 0.936097π0.936097\pi
380380 −8.70512e15 2.67916e16i −0.148314 0.456463i
381381 3.27859e15 + 2.38204e15i 0.0549130 + 0.0398966i
382382 −2.13000e16 + 1.54753e16i −0.350726 + 0.254817i
383383 2.06618e16 6.35904e16i 0.334484 1.02944i −0.632491 0.774568i 0.717968π-0.717968\pi
0.966975 0.254869i 0.0820325π-0.0820325\pi
384384 2.72588e15 0.0433865
385385 5.28025e16 1.49155e17i 0.826343 2.33423i
386386 −2.42480e15 −0.0373129
387387 −1.08942e16 + 3.35289e16i −0.164844 + 0.507338i
388388 −1.60149e16 + 1.16355e16i −0.238296 + 0.173132i
389389 9.65637e16 + 7.01576e16i 1.41300 + 1.02660i 0.992878 + 0.119134i 0.0380117π0.0380117\pi
0.420119 + 0.907469i 0.361988π0.361988\pi
390390 1.45268e16 + 4.47089e16i 0.209050 + 0.643390i
391391 2.25983e16 + 6.95503e16i 0.319835 + 0.984351i
392392 −2.76377e16 2.00799e16i −0.384717 0.279514i
393393 3.74493e16 2.72085e16i 0.512734 0.372523i
394394 −2.63072e16 + 8.09651e16i −0.354281 + 1.09037i
395395 −2.63699e16 −0.349323
396396 2.40009e16 1.64987e16i 0.312758 0.214997i
397397 1.04546e17 1.34020 0.670102 0.742269i 0.266250π-0.266250\pi
0.670102 + 0.742269i 0.266250π0.266250\pi
398398 6.05148e15 1.86245e16i 0.0763171 0.234880i
399399 2.90961e16 2.11395e16i 0.361003 0.262284i
400400 −2.67531e16 1.94372e16i −0.326575 0.237271i
401401 −1.14128e16 3.51249e16i −0.137073 0.421868i 0.858834 0.512255i 0.171190π-0.171190\pi
−0.995907 + 0.0903870i 0.971190π0.971190\pi
402402 6.06296e15 + 1.86599e16i 0.0716498 + 0.220515i
403403 −6.11135e16 4.44015e16i −0.710647 0.516316i
404404 −3.92277e16 + 2.85006e16i −0.448863 + 0.326118i
405405 1.48757e16 4.57827e16i 0.167502 0.515518i
406406 8.26803e16 0.916184
407407 −4.68533e16 3.59447e16i −0.510948 0.391986i
408408 −2.04033e16 −0.218983
409409 −1.57282e16 + 4.84064e16i −0.166141 + 0.511330i −0.999119 0.0419771i 0.986634π-0.986634\pi
0.832977 + 0.553307i 0.186634π0.186634\pi
410410 −4.58850e16 + 3.33374e16i −0.477063 + 0.346607i
411411 2.84748e16 + 2.06882e16i 0.291400 + 0.211714i
412412 −6.73471e15 2.07273e16i −0.0678402 0.208791i
413413 8.13821e16 + 2.50468e17i 0.806963 + 2.48358i
414414 −3.64893e16 2.65110e16i −0.356175 0.258776i
415415 5.81564e16 4.22531e16i 0.558837 0.406019i
416416 6.96031e15 2.14216e16i 0.0658449 0.202650i
417417 1.48079e16 0.137914
418418 −1.30057e16 4.38910e16i −0.119258 0.402466i
419419 −2.12629e16 −0.191969 −0.0959847 0.995383i 0.530600π-0.530600\pi
−0.0959847 + 0.995383i 0.530600π0.530600\pi
420420 2.11259e16 6.50187e16i 0.187799 0.577987i
421421 −5.47646e16 + 3.97888e16i −0.479365 + 0.348279i −0.801080 0.598557i 0.795741π-0.795741\pi
0.321715 + 0.946837i 0.395741π0.395741\pi
422422 −6.86723e16 4.98934e16i −0.591903 0.430043i
423423 5.43330e16 + 1.67220e17i 0.461160 + 1.41930i
424424 1.42871e16 + 4.39711e16i 0.119417 + 0.367527i
425425 2.00248e17 + 1.45488e17i 1.64831 + 1.19757i
426426 −2.83375e16 + 2.05884e16i −0.229720 + 0.166901i
427427 8.94081e16 2.75170e17i 0.713832 2.19695i
428428 −3.17487e16 −0.249656
429429 2.17034e16 + 7.32438e16i 0.168096 + 0.567281i
430430 1.05331e17 0.803549
431431 5.44682e15 1.67636e16i 0.0409299 0.125969i −0.928504 0.371323i 0.878904π-0.878904\pi
0.969434 + 0.245354i 0.0789042π0.0789042\pi
432432 2.35929e16 1.71412e16i 0.174637 0.126881i
433433 −7.65130e15 5.55899e15i −0.0557910 0.0405345i 0.559540 0.828803i 0.310978π-0.310978\pi
−0.615331 + 0.788269i 0.710978π0.710978\pi
434434 3.39473e16 + 1.04479e17i 0.243850 + 0.750493i
435435 2.93262e16 + 9.02566e16i 0.207527 + 0.638703i
436436 4.07860e16 + 2.96328e16i 0.284347 + 0.206591i
437437 −5.73528e16 + 4.16693e16i −0.393936 + 0.286211i
438438 1.12138e16 3.45127e16i 0.0758880 0.233559i
439439 −1.34634e16 −0.0897708 −0.0448854 0.998992i 0.514292π-0.514292\pi
−0.0448854 + 0.998992i 0.514292π0.514292\pi
440440 −6.90407e16 5.29663e16i −0.453589 0.347982i
441441 −1.57708e17 −1.02094
442442 −5.20982e16 + 1.60342e17i −0.332336 + 1.02283i
443443 7.07962e16 5.14365e16i 0.445027 0.323331i −0.342602 0.939480i 0.611308π-0.611308\pi
0.787629 + 0.616150i 0.211308π0.211308\pi
444444 −2.06421e16 1.49974e16i −0.127869 0.0929022i
445445 −1.28950e17 3.96866e17i −0.787190 2.42272i
446446 8.15250e14 + 2.50908e15i 0.00490472 + 0.0150952i
447447 −3.42680e16 2.48972e16i −0.203184 0.147622i
448448 −2.65001e16 + 1.92535e16i −0.154861 + 0.112513i
449449 2.11200e16 6.50006e16i 0.121644 0.374383i −0.871630 0.490164i 0.836937π-0.836937\pi
0.993275 + 0.115781i 0.0369370π0.0369370\pi
450450 −1.52660e17 −0.866650
451451 −7.59516e16 + 5.22108e16i −0.425000 + 0.292155i
452452 1.47592e17 0.814072
453453 −2.72736e16 + 8.39397e16i −0.148288 + 0.456382i
454454 −6.91062e16 + 5.02086e16i −0.370385 + 0.269101i
455455 −4.57013e17 3.32040e17i −2.41465 1.75435i
456456 −6.11207e15 1.88110e16i −0.0318359 0.0979807i
457457 8.46297e16 + 2.60463e17i 0.434578 + 1.33749i 0.893519 + 0.449026i 0.148229π0.148229\pi
−0.458941 + 0.888467i 0.651771π0.651771\pi
458458 1.07819e17 + 7.83351e16i 0.545845 + 0.396580i
459459 −1.76593e17 + 1.28303e17i −0.881439 + 0.640403i
460460 −4.16423e16 + 1.28162e17i −0.204932 + 0.630715i
461461 3.51258e17 1.70439 0.852197 0.523221i 0.175270π-0.175270\pi
0.852197 + 0.523221i 0.175270π0.175270\pi
462462 3.70739e16 1.04725e17i 0.177376 0.501047i
463463 −7.93735e16 −0.374455 −0.187227 0.982317i 0.559950π-0.559950\pi
−0.187227 + 0.982317i 0.559950π0.559950\pi
464464 1.40512e16 4.32452e16i 0.0653652 0.201173i
465465 −1.02012e17 + 7.41162e16i −0.467959 + 0.339992i
466466 −5.35688e16 3.89200e16i −0.242328 0.176062i
467467 −6.00673e16 1.84868e17i −0.267965 0.824712i −0.990995 0.133896i 0.957251π-0.957251\pi
0.723030 0.690816i 0.242749π-0.242749\pi
468468 −3.21320e16 9.88922e16i −0.141364 0.435075i
469469 −1.90741e17 1.38581e17i −0.827598 0.601285i
470470 4.24995e17 3.08777e17i 1.81864 1.32132i
471471 6.08291e16 1.87213e17i 0.256729 0.790132i
472472 1.44836e17 0.602910
473473 1.71107e17 + 4.46418e15i 0.702539 + 0.0183292i
474474 −1.85149e16 −0.0749828
475475 −7.41475e16 + 2.28203e17i −0.296202 + 0.911616i
476476 1.98355e17 1.44113e17i 0.781622 0.567882i
477477 1.72674e17 + 1.25455e17i 0.671210 + 0.487662i
478478 −2.20105e16 6.77414e16i −0.0844013 0.259760i
479479 −1.01261e17 3.11650e17i −0.383056 1.17892i −0.937881 0.346958i 0.887215π-0.887215\pi
0.554825 0.831967i 0.312785π-0.312785\pi
480480 −3.04172e16 2.20994e16i −0.113514 0.0824730i
481481 −1.70566e17 + 1.23924e17i −0.627986 + 0.456259i
482482 6.53398e14 2.01095e15i 0.00237340 0.00730459i
483483 −1.72043e17 −0.616567
484484 −1.09909e17 8.89680e16i −0.388633 0.314586i
485485 2.73036e17 0.952574
486486 6.52523e16 2.00826e17i 0.224626 0.691328i
487487 −2.90904e17 + 2.11354e17i −0.988125 + 0.717915i −0.959510 0.281676i 0.909110π-0.909110\pi
−0.0286152 + 0.999591i 0.509110π0.509110\pi
488488 −1.28731e17 9.35282e16i −0.431472 0.313483i
489489 −3.88644e16 1.19612e17i −0.128542 0.395611i
490490 1.45606e17 + 4.48130e17i 0.475232 + 1.46261i
491491 1.58162e17 + 1.14911e17i 0.509415 + 0.370112i 0.812602 0.582820i 0.198051π-0.198051\pi
−0.303187 + 0.952931i 0.598051π0.598051\pi
492492 −3.22169e16 + 2.34070e16i −0.102403 + 0.0743999i
493493 −1.05174e17 + 3.23692e17i −0.329915 + 1.01538i
494494 −1.63435e17 −0.505964
495495 −4.01576e17 1.04771e16i −1.22697 0.0320117i
496496 6.04161e16 0.182189
497497 1.30068e17 4.00307e17i 0.387126 1.19145i
498498 4.08330e16 2.96669e16i 0.119956 0.0871528i
499499 2.89875e17 + 2.10606e17i 0.840538 + 0.610686i 0.922521 0.385947i 0.126125π-0.126125\pi
−0.0819832 + 0.996634i 0.526125π0.526125\pi
500500 5.36554e16 + 1.65134e17i 0.153571 + 0.472642i
501501 −1.01783e17 3.13256e17i −0.287561 0.885022i
502502 −2.21555e17 1.60969e17i −0.617886 0.448920i
503503 9.70042e16 7.04776e16i 0.267054 0.194026i −0.446197 0.894935i 0.647222π-0.647222\pi
0.713251 + 0.700909i 0.247222π0.247222\pi
504504 −4.67286e16 + 1.43816e17i −0.126994 + 0.390848i
505505 6.68789e17 1.79430
506506 −7.30784e16 + 2.06430e17i −0.193558 + 0.546757i
507507 8.50144e16 0.222301
508508 −8.27608e15 + 2.54711e16i −0.0213654 + 0.0657558i
509509 −5.03024e17 + 3.65468e17i −1.28210 + 0.931502i −0.999614 0.0277684i 0.991160π-0.991160\pi
−0.282489 + 0.959271i 0.591160π0.591160\pi
510510 2.27674e17 + 1.65415e17i 0.572937 + 0.416263i
511511 1.34753e17 + 4.14727e17i 0.334813 + 1.03045i
512512 5.56676e15 + 1.71327e16i 0.0136568 + 0.0420312i
513513 −1.71190e17 1.24377e17i −0.414683 0.301285i
514514 5.13709e16 3.73232e16i 0.122873 0.0892726i
515515 −9.28909e16 + 2.85889e17i −0.219395 + 0.675227i
516516 7.39555e16 0.172483
517517 7.03477e17 4.83585e17i 1.62017 1.11374i
518518 3.06605e17 0.697327
519519 −9.87574e16 + 3.03944e17i −0.221810 + 0.682662i
520520 −2.51338e17 + 1.82608e17i −0.557489 + 0.405040i
521521 5.80225e17 + 4.21558e17i 1.27102 + 0.923448i 0.999243 0.0389133i 0.0123896π-0.0123896\pi
0.271774 + 0.962361i 0.412390π0.412390\pi
522522 −6.48669e16 1.99640e17i −0.140335 0.431906i
523523 −1.88538e17 5.80260e17i −0.402844 1.23983i −0.922682 0.385562i 0.874007π-0.874007\pi
0.519837 0.854265i 0.325993π-0.325993\pi
524524 2.47489e17 + 1.79811e17i 0.522279 + 0.379458i
525525 −4.71098e17 + 3.42273e17i −0.981920 + 0.713406i
526526 −1.49152e17 + 4.59041e17i −0.307058 + 0.945028i
527527 −4.52217e17 −0.919555
528528 −4.84751e16 3.71888e16i −0.0973639 0.0746951i
529529 −1.64913e17 −0.327185
530530 1.97059e17 6.06486e17i 0.386193 1.18858i
531531 5.40932e17 3.93010e17i 1.04720 0.760833i
532532 1.92286e17 + 1.39704e17i 0.367723 + 0.267167i
533533 1.01683e17 + 3.12948e17i 0.192097 + 0.591215i
534534 −9.05384e16 2.78649e17i −0.168972 0.520042i
535535 3.54273e17 + 2.57394e17i 0.653188 + 0.474569i
536536 −1.04899e17 + 7.62138e16i −0.191074 + 0.138823i
537537 2.36287e16 7.27218e16i 0.0425214 0.130867i
538538 −3.56881e17 −0.634510
539539 2.17540e17 + 7.34143e17i 0.382130 + 1.28960i
540540 −4.02232e17 −0.698100
541541 −5.54540e16 + 1.70670e17i −0.0950935 + 0.292668i −0.987278 0.159003i 0.949172π-0.949172\pi
0.892185 + 0.451671i 0.149172π0.149172\pi
542542 6.95153e16 5.05059e16i 0.117784 0.0855749i
543543 1.97636e17 + 1.43591e17i 0.330877 + 0.240396i
544544 −4.16674e16 1.28239e17i −0.0689292 0.212142i
545545 −2.14877e17 6.61324e17i −0.351247 1.08103i
546546 −3.20880e17 2.33133e17i −0.518310 0.376575i
547547 2.83800e17 2.06193e17i 0.452997 0.329121i −0.337781 0.941225i 0.609676π-0.609676\pi
0.790778 + 0.612103i 0.209676π0.209676\pi
548548 −7.18785e16 + 2.21219e17i −0.113377 + 0.348939i
549549 −7.34570e17 −1.14502
550550 2.10577e17 + 7.10645e17i 0.324379 + 1.09470i
551551 −3.29936e17 −0.502278
552552 −2.92380e16 + 8.99855e16i −0.0439890 + 0.135384i
553553 1.79996e17 1.30774e17i 0.267639 0.194451i
554554 −4.99285e17 3.62752e17i −0.733727 0.533084i
555555 1.08751e17 + 3.34701e17i 0.157953 + 0.486130i
556556 3.02404e16 + 9.30705e16i 0.0434112 + 0.133606i
557557 5.09309e17 + 3.70034e17i 0.722641 + 0.525029i 0.887227 0.461334i 0.152629π-0.152629\pi
−0.164586 + 0.986363i 0.552629π0.552629\pi
558558 2.25642e17 1.63938e17i 0.316445 0.229910i
559559 1.88839e17 5.81187e17i 0.261767 0.805636i
560560 4.51798e17 0.619045
561561 3.62838e17 + 2.78360e17i 0.491421 + 0.377006i
562562 −6.98424e17 −0.935046
563563 3.42691e17 1.05469e18i 0.453522 1.39580i −0.419340 0.907829i 0.637738π-0.637738\pi
0.872862 0.487968i 0.162262π-0.162262\pi
564564 2.98399e17 2.16799e17i 0.390376 0.283625i
565565 −1.64693e18 1.19656e18i −2.12990 1.54746i
566566 −4.41568e16 1.35901e17i −0.0564535 0.173746i
567567 1.25509e17 + 3.86276e17i 0.158630 + 0.488212i
568568 −1.87272e17 1.36061e17i −0.233997 0.170008i
569569 7.48111e17 5.43535e17i 0.924137 0.671425i −0.0204132 0.999792i 0.506498π-0.506498\pi
0.944550 + 0.328367i 0.106498π0.106498\pi
570570 −8.43028e16 + 2.59457e17i −0.102957 + 0.316869i
571571 −1.45652e17 −0.175866 −0.0879330 0.996126i 0.528026π-0.528026\pi
−0.0879330 + 0.996126i 0.528026π0.528026\pi
572572 −4.16029e17 + 2.85988e17i −0.496649 + 0.341408i
573573 2.54970e17 0.300943
574574 1.47874e17 4.55110e17i 0.172570 0.531116i
575575 9.28607e17 6.74673e17i 1.07150 0.778489i
576576 6.72801e16 + 4.88819e16i 0.0767610 + 0.0557701i
577577 −4.37476e17 1.34641e18i −0.493527 1.51892i −0.819239 0.573452i 0.805604π-0.805604\pi
0.325712 0.945469i 0.394396π-0.394396\pi
578578 1.15998e17 + 3.57006e17i 0.129396 + 0.398239i
579579 1.89977e16 + 1.38027e16i 0.0209552 + 0.0152248i
580580 −5.07391e17 + 3.68641e17i −0.553428 + 0.402089i
581581 −1.87421e17 + 5.76824e17i −0.202150 + 0.622154i
582582 1.91705e17 0.204472
583583 3.45821e17 9.76865e17i 0.364758 1.03036i
584584 2.39820e17 0.250151
585585 −4.43192e17 + 1.36401e18i −0.457172 + 1.40703i
586586 6.51800e17 4.73560e17i 0.664936 0.483104i
587587 4.09634e17 + 2.97616e17i 0.413284 + 0.300268i 0.774930 0.632047i 0.217785π-0.217785\pi
−0.361646 + 0.932315i 0.617785π0.617785\pi
588588 1.02234e17 + 3.14642e17i 0.102010 + 0.313953i
589589 −1.35467e17 4.16925e17i −0.133685 0.411442i
590590 −1.61617e18 1.17422e18i −1.57743 1.14607i
591591 6.66986e17 4.84593e17i 0.643870 0.467799i
592592 5.21064e16 1.60367e17i 0.0497508 0.153117i
593593 1.11813e18 1.05593 0.527965 0.849266i 0.322955π-0.322955\pi
0.527965 + 0.849266i 0.322955π0.322955\pi
594594 −6.53413e17 1.70475e16i −0.610346 0.0159239i
595595 −3.38173e18 −3.12448
596596 8.65021e16 2.66226e17i 0.0790543 0.243304i
597597 −1.53428e17 + 1.11472e17i −0.138698 + 0.100770i
598598 6.32503e17 + 4.59541e17i 0.565594 + 0.410928i
599599 4.31239e17 + 1.32722e18i 0.381455 + 1.17400i 0.939019 + 0.343865i 0.111736π0.111736\pi
−0.557564 + 0.830134i 0.688264π0.688264\pi
600600 9.89613e16 + 3.04572e17i 0.0865929 + 0.266506i
601601 −8.38603e17 6.09281e17i −0.725893 0.527392i 0.162369 0.986730i 0.448087π-0.448087\pi
−0.888261 + 0.459338i 0.848087π0.848087\pi
602602 −7.18971e17 + 5.22363e17i −0.615650 + 0.447296i
603603 −1.84972e17 + 5.69286e17i −0.156691 + 0.482245i
604604 −5.83275e17 −0.488802
605605 5.05156e17 + 1.88382e18i 0.418809 + 1.56182i
606606 4.69572e17 0.385151
607607 −7.30892e17 + 2.24945e18i −0.593098 + 1.82537i −0.0291246 + 0.999576i 0.509272π0.509272\pi
−0.563974 + 0.825793i 0.690728π0.690728\pi
608608 1.05749e17 7.68311e16i 0.0848990 0.0616828i
609609 −6.47779e17 4.70639e17i −0.514535 0.373831i
610610 6.78204e17 + 2.08730e18i 0.532987 + 1.64036i
611611 −9.41805e17 2.89858e18i −0.732307 2.25381i
612612 −5.03594e17 3.65883e17i −0.387433 0.281487i
613613 7.95285e17 5.77808e17i 0.605382 0.439836i −0.242403 0.970176i 0.577936π-0.577936\pi
0.847785 + 0.530340i 0.177936π0.177936\pi
614614 3.52494e17 1.08486e18i 0.265495 0.817111i
615615 5.49264e17 0.409348
616616 7.33931e17 + 1.91483e16i 0.541228 + 0.0141207i
617617 −1.64010e18 −1.19678 −0.598392 0.801204i 0.704193π-0.704193\pi
−0.598392 + 0.801204i 0.704193π0.704193\pi
618618 −6.52208e16 + 2.00729e17i −0.0470935 + 0.144939i
619619 1.74505e18 1.26785e18i 1.24686 0.905897i 0.248824 0.968549i 0.419956π-0.419956\pi
0.998035 + 0.0626519i 0.0199558π0.0199558\pi
620620 −6.74162e17 4.89808e17i −0.476671 0.346322i
621621 3.12798e17 + 9.62694e17i 0.218861 + 0.673585i
622622 1.66715e16 + 5.13095e16i 0.0115435 + 0.0355271i
623623 2.84834e18 + 2.06944e18i 1.95173 + 1.41801i
624624 −1.76470e17 + 1.28213e17i −0.119666 + 0.0869426i
625625 −3.45104e15 + 1.06212e16i −0.00231595 + 0.00712777i
626626 1.53998e18 1.02278
627627 −1.47944e17 + 4.17907e17i −0.0972427 + 0.274689i
628628 1.30089e18 0.846260
629629 −3.90019e17 + 1.20035e18i −0.251105 + 0.772823i
630630 1.68738e18 1.22595e18i 1.07522 0.781195i
631631 1.14974e18 + 8.35336e17i 0.725119 + 0.526830i 0.888015 0.459814i 0.152084π-0.152084\pi
−0.162897 + 0.986643i 0.552084π0.552084\pi
632632 −3.78108e16 1.16370e17i −0.0236023 0.0726405i
633633 2.54023e17 + 7.81804e17i 0.156946 + 0.483029i
634634 2.70613e16 + 1.96612e16i 0.0165489 + 0.0120235i
635635 2.98850e17 2.17128e17i 0.180894 0.131427i
636636 1.38360e17 4.25828e17i 0.0828971 0.255131i
637637 2.73370e18 1.62123
638638 −8.39864e17 + 5.77341e17i −0.493031 + 0.338921i
639639 −1.06863e18 −0.620969
640640 7.67814e16 2.36309e17i 0.0441658 0.135928i
641641 −2.39882e18 + 1.74285e18i −1.36591 + 0.992388i −0.367861 + 0.929881i 0.619910π0.619910\pi
−0.998044 + 0.0625077i 0.980090π0.980090\pi
642642 2.48743e17 + 1.80722e17i 0.140208 + 0.101867i
643643 4.48104e17 + 1.37912e18i 0.250039 + 0.769540i 0.994767 + 0.102172i 0.0325792π0.0325792\pi
−0.744728 + 0.667368i 0.767421π0.767421\pi
644644 −3.51343e17 1.08132e18i −0.194077 0.597307i
645645 −8.25243e17 5.99574e17i −0.451278 0.327872i
646646 −7.91535e17 + 5.75084e17i −0.428508 + 0.311329i
647647 −4.93014e17 + 1.51734e18i −0.264230 + 0.813215i 0.727640 + 0.685959i 0.240617π0.240617\pi
−0.991870 + 0.127256i 0.959383π0.959383\pi
648648 2.23368e17 0.118518
649649 −2.57565e18 1.97597e18i −1.35300 1.03798i
650650 2.64620e18 1.37621
651651 3.28756e17 1.01181e18i 0.169277 0.520980i
652652 6.72419e17 4.88541e17i 0.342792 0.249053i
653653 −1.17859e18 8.56294e17i −0.594875 0.432202i 0.249181 0.968457i 0.419839π-0.419839\pi
−0.844056 + 0.536255i 0.819839π0.819839\pi
654654 −1.50870e17 4.64331e17i −0.0753960 0.232045i
655655 −1.30387e18 4.01290e18i −0.645158 1.98559i
656656 −2.12910e17 1.54688e17i −0.104309 0.0757850i
657657 8.95678e17 6.50748e17i 0.434487 0.315674i
658658 −1.36964e18 + 4.21531e18i −0.657865 + 2.02470i
659659 −1.46633e18 −0.697390 −0.348695 0.937236i 0.613375π-0.613375\pi
−0.348695 + 0.937236i 0.613375π0.613375\pi
660660 2.39418e17 + 8.07976e17i 0.112751 + 0.380507i
661661 −1.85286e18 −0.864036 −0.432018 0.901865i 0.642198π-0.642198\pi
−0.432018 + 0.901865i 0.642198π0.642198\pi
662662 3.31082e17 1.01897e18i 0.152883 0.470525i
663663 1.32089e18 9.59680e17i 0.603987 0.438822i
664664 2.69851e17 + 1.96058e17i 0.122189 + 0.0887753i
665665 −1.01304e18 3.11781e18i −0.454239 1.39801i
666666 −2.40548e17 7.40329e17i −0.106812 0.328732i
667667 1.27687e18 + 9.27703e17i 0.561474 + 0.407935i
668668 1.76101e18 1.27945e18i 0.766860 0.557156i
669669 7.89511e15 2.42986e16i 0.00340477 0.0104788i
670670 1.78842e18 0.763805
671671 1.01325e18 + 3.41949e18i 0.428571 + 1.44632i
672672 3.17218e17 0.132879
673673 −6.97940e17 + 2.14804e18i −0.289548 + 0.891136i 0.695451 + 0.718574i 0.255205π0.255205\pi
−0.984999 + 0.172562i 0.944795π0.944795\pi
674674 −9.81171e17 + 7.12863e17i −0.403140 + 0.292898i
675675 2.77177e18 + 2.01381e18i 1.12793 + 0.819489i
676676 1.73615e17 + 5.34332e17i 0.0699736 + 0.215357i
677677 7.74183e16 + 2.38269e17i 0.0309042 + 0.0951133i 0.965319 0.261074i 0.0840766π-0.0840766\pi
−0.934415 + 0.356187i 0.884077π0.884077\pi
678678 −1.15635e18 8.40134e17i −0.457188 0.332166i
679679 −1.86369e18 + 1.35405e18i −0.729828 + 0.530251i
680680 −5.74712e17 + 1.76878e18i −0.222917 + 0.686067i
681681 8.27230e17 0.317812
682682 −1.07439e18 8.24248e17i −0.408851 0.313660i
683683 −5.32396e17 −0.200678 −0.100339 0.994953i 0.531993π-0.531993\pi
−0.100339 + 0.994953i 0.531993π0.531993\pi
684684 1.86471e17 5.73897e17i 0.0696218 0.214274i
685685 2.59554e18 1.88577e18i 0.959930 0.697430i
686686 −8.25028e17 5.99418e17i −0.302247 0.219595i
687687 −3.98829e17 1.22747e18i −0.144733 0.445443i
688688 1.51031e17 + 4.64825e17i 0.0542926 + 0.167095i
689689 −2.99312e18 2.17463e18i −1.06586 0.774392i
690690 1.05579e18 7.67077e17i 0.372442 0.270595i
691691 −1.39430e17 + 4.29122e17i −0.0487247 + 0.149959i −0.972459 0.233075i 0.925121π-0.925121\pi
0.923734 + 0.383035i 0.125121π0.125121\pi
692692 −2.11203e18 −0.731156
693693 2.79304e18 1.92000e18i 0.957881 0.658469i
694694 −1.47315e18 −0.500507
695695 4.17102e17 1.28371e18i 0.140392 0.432081i
696696 −3.56251e17 + 2.58832e17i −0.118794 + 0.0863092i
697697 1.59364e18 + 1.15785e18i 0.526475 + 0.382507i
698698 −6.91689e17 2.12880e18i −0.226387 0.696746i
699699 1.98154e17 + 6.09857e17i 0.0642543 + 0.197754i
700700 −3.11332e18 2.26196e18i −1.00020 0.726688i
701701 −7.18462e17 + 5.21993e17i −0.228684 + 0.166149i −0.696227 0.717821i 0.745139π-0.745139\pi
0.467543 + 0.883970i 0.345139π0.345139\pi
702702 −7.21127e17 + 2.21940e18i −0.227416 + 0.699914i
703703 −1.22351e18 −0.382294
704704 1.34744e17 3.80622e17i 0.0417146 0.117834i
705705 −5.08737e18 −1.56050
706706 4.44754e17 1.36881e18i 0.135173 0.416020i
707707 −4.56503e18 + 3.31669e18i −1.37473 + 0.998800i
708708 −1.13475e18 8.24445e17i −0.338598 0.246006i
709709 −1.12013e18 3.44742e18i −0.331184 1.01928i −0.968571 0.248736i 0.919985π-0.919985\pi
0.637388 0.770543i 0.280015π-0.280015\pi
710710 9.86626e17 + 3.03652e18i 0.289050 + 0.889605i
711711 −4.56984e17 3.32018e17i −0.132663 0.0963850i
712712 1.56647e18 1.13810e18i 0.450610 0.327387i
713713 −6.48028e17 + 1.99443e18i −0.184719 + 0.568507i
714714 −2.37439e18 −0.670677
715715 6.96090e18 + 1.81610e17i 1.94839 + 0.0508335i
716716 5.05325e17 0.140164
717717 −2.13156e17 + 6.56027e17i −0.0585900 + 0.180321i
718718 3.04948e18 2.21557e18i 0.830647 0.603500i
719719 −4.04353e18 2.93780e18i −1.09150 0.793020i −0.111847 0.993725i 0.535677π-0.535677\pi
−0.979652 + 0.200706i 0.935677π0.935677\pi
720720 −3.54459e17 1.09091e18i −0.0948210 0.291829i
721721 −7.83736e17 2.41209e18i −0.207774 0.639461i
722722 1.41006e18 + 1.02447e18i 0.370465 + 0.269159i
723723 −1.65661e16 + 1.20360e16i −0.00431341 + 0.00313388i
724724 −4.98888e17 + 1.53542e18i −0.128737 + 0.396211i
725725 5.34204e18 1.36619
726726 3.54682e17 + 1.32268e18i 0.0898982 + 0.335248i
727727 6.95566e18 1.74729 0.873645 0.486564i 0.161750π-0.161750\pi
0.873645 + 0.486564i 0.161750π0.161750\pi
728728 8.09989e17 2.49289e18i 0.201663 0.620654i
729729 −5.55348e17 + 4.03484e17i −0.137036 + 0.0995628i
730730 −2.67607e18 1.94428e18i −0.654483 0.475509i
731731 −1.13047e18 3.47923e18i −0.274029 0.843374i
732732 4.76183e17 + 1.46554e18i 0.114407 + 0.352108i
733733 4.86370e18 + 3.53369e18i 1.15822 + 0.841496i 0.989552 0.144177i 0.0460535π-0.0460535\pi
0.168668 + 0.985673i 0.446053π0.446053\pi
734734 −1.43704e18 + 1.04407e18i −0.339190 + 0.246436i
735735 1.41009e18 4.33982e18i 0.329898 1.01532i
736736 −6.25286e17 −0.145002
737737 2.90522e18 + 7.57973e16i 0.667791 + 0.0174227i
738738 −1.21492e18 −0.276810
739739 1.65805e18 5.10295e18i 0.374462 1.15248i −0.569378 0.822076i 0.692816π-0.692816\pi
0.943841 0.330401i 0.107184π-0.107184\pi
740740 −1.88157e18 + 1.36704e18i −0.421225 + 0.306038i
741741 1.28047e18 + 9.30317e17i 0.284153 + 0.206449i
742742 1.66262e18 + 5.11703e18i 0.365737 + 1.12562i
743743 −8.39468e17 2.58362e18i −0.183053 0.563379i 0.816856 0.576841i 0.195715π-0.195715\pi
−0.999909 + 0.0134620i 0.995715π0.995715\pi
744744 −4.73345e17 3.43905e17i −0.102318 0.0743387i
745745 −3.12360e18 + 2.26943e18i −0.669330 + 0.486296i
746746 −1.54850e18 + 4.76579e18i −0.328934 + 1.01235i
747747 1.53984e18 0.324259
748748 −1.00857e18 + 2.84897e18i −0.210544 + 0.594740i
749749 −3.69468e18 −0.764619
750750 5.19614e17 1.59921e18i 0.106606 0.328100i
751751 −9.97283e17 + 7.24569e17i −0.202842 + 0.147374i −0.684569 0.728948i 0.740010π-0.740010\pi
0.481727 + 0.876321i 0.340010π0.340010\pi
752752 1.97201e18 + 1.43275e18i 0.397643 + 0.288905i
753753 8.19548e17 + 2.52231e18i 0.163835 + 0.504233i
754754 1.12440e18 + 3.46054e18i 0.222847 + 0.685852i
755755 6.50856e18 + 4.72875e18i 1.27888 + 0.929161i
756756 2.74556e18 1.99477e18i 0.534859 0.388598i
757757 2.20650e18 6.79092e18i 0.426168 1.31161i −0.475703 0.879606i 0.657806π-0.657806\pi
0.901871 0.432005i 0.142194π-0.142194\pi
758758 −8.35706e17 −0.160031
759759 1.74761e18 1.20134e18i 0.331797 0.228084i
760760 −1.80290e18 −0.339378
761761 −1.20347e18 + 3.70391e18i −0.224614 + 0.691291i 0.773717 + 0.633532i 0.218395π0.218395\pi
−0.998331 + 0.0577587i 0.981605π0.981605\pi
762762 2.09830e17 1.52450e17i 0.0388293 0.0282112i
763763 4.74638e18 + 3.44844e18i 0.870869 + 0.632723i
764764 5.20696e17 + 1.60254e18i 0.0947278 + 0.291542i
765765 2.65314e18 + 8.16552e18i 0.478586 + 1.47294i
766766 −3.46197e18 2.51527e18i −0.619207 0.449880i
767767 −9.37648e18 + 6.81241e18i −1.66291 + 1.20818i
768768 5.39100e16 1.65918e17i 0.00948029 0.0291773i
769769 −1.23890e18 −0.216030 −0.108015 0.994149i 0.534450π-0.534450\pi
−0.108015 + 0.994149i 0.534450π0.534450\pi
770770 −8.03444e18 6.16382e18i −1.38920 1.06576i
771771 −6.14932e17 −0.105432
772772 −4.79556e16 + 1.47592e17i −0.00815317 + 0.0250929i
773773 −3.91192e18 + 2.84218e18i −0.659514 + 0.479165i −0.866499 0.499179i 0.833635π-0.833635\pi
0.206985 + 0.978344i 0.433635π0.433635\pi
774774 1.82537e18 + 1.32621e18i 0.305164 + 0.221715i
775775 2.19337e18 + 6.75048e18i 0.363622 + 1.11911i
776776 3.91497e17 + 1.20490e18i 0.0643616 + 0.198085i
777777 −2.40218e18 1.74528e18i −0.391623 0.284531i
778778 6.18007e18 4.49009e18i 0.999140 0.725918i
779779 −5.90093e17 + 1.81612e18i −0.0946078 + 0.291173i
780780 3.00862e18 0.478358
781781 1.47405e18 + 4.97454e18i 0.232423 + 0.784371i
782782 4.68029e18 0.731861
783783 −1.45578e18 + 4.48044e18i −0.225759 + 0.694815i
784784 −1.76881e18 + 1.28512e18i −0.272036 + 0.197646i
785785 −1.45162e19 1.05466e19i −2.21412 1.60865i
786786 −9.15478e17 2.81755e18i −0.138485 0.426212i
787787 −9.37110e17 2.88413e18i −0.140590 0.432692i 0.855827 0.517261i 0.173049π-0.173049\pi
−0.996418 + 0.0845694i 0.973049π0.973049\pi
788788 4.40787e18 + 3.20251e18i 0.655856 + 0.476507i
789789 3.78156e18 2.74746e18i 0.558046 0.405444i
790790 −5.21519e17 + 1.60507e18i −0.0763298 + 0.234919i
791791 1.71757e19 2.49325
792792 −5.29571e17 1.78717e18i −0.0762448 0.257308i
793793 1.27330e19 1.81825
794794 2.06763e18 6.36350e18i 0.292845 0.901286i
795795 −4.99620e18 + 3.62995e18i −0.701865 + 0.509935i
796796 −1.01395e18 7.36678e17i −0.141280 0.102646i
797797 3.05825e17 + 9.41232e17i 0.0422663 + 0.130082i 0.969963 0.243252i 0.0782143π-0.0782143\pi
−0.927697 + 0.373335i 0.878214π0.878214\pi
798798 −7.11277e17 2.18909e18i −0.0975035 0.300085i
799799 −1.47606e19 1.07242e19i −2.00701 1.45818i
800800 −1.71220e18 + 1.24398e18i −0.230924 + 0.167776i
801801 2.76220e18 8.50118e18i 0.369525 1.13728i
802802 −2.36368e18 −0.313657
803803 −4.26477e18 3.27183e18i −0.561365 0.430665i
804804 1.25569e18 0.163952
805805 −4.84603e18 + 1.49145e19i −0.627643 + 1.93169i
806806 −3.91126e18 + 2.84170e18i −0.502504 + 0.365090i
807807 2.79607e18 + 2.03147e18i 0.356345 + 0.258900i
808808 9.58954e17 + 2.95136e18i 0.121234 + 0.373119i
809809 −2.07739e18 6.39356e18i −0.260527 0.801821i −0.992690 0.120691i 0.961489π-0.961489\pi
0.732163 0.681130i 0.238511π-0.238511\pi
810810 −2.49249e18 1.81090e18i −0.310085 0.225290i
811811 3.92597e18 2.85238e18i 0.484519 0.352024i −0.318553 0.947905i 0.603197π-0.603197\pi
0.803073 + 0.595881i 0.203197π0.203197\pi
812812 1.63518e18 5.03255e18i 0.200194 0.616133i
813813 −8.32129e17 −0.101065
814814 −3.11449e18 + 2.14097e18i −0.375256 + 0.257959i
815815 −1.14640e19 −1.37029
816816 −4.03519e17 + 1.24190e18i −0.0478495 + 0.147266i
817817 2.86906e18 2.08449e18i 0.337517 0.245221i
818818 2.63532e18 + 1.91467e18i 0.307565 + 0.223459i
819819 −3.73929e18 1.15083e19i −0.432956 1.33250i
820820 1.12170e18 + 3.45223e18i 0.128850 + 0.396561i
821821 6.82410e18 + 4.95800e18i 0.777705 + 0.565036i 0.904289 0.426920i 0.140401π-0.140401\pi
−0.126584 + 0.991956i 0.540401π0.540401\pi
822822 1.82239e18 1.32404e18i 0.206051 0.149705i
823823 2.96062e18 9.11186e18i 0.332112 1.02213i −0.636016 0.771676i 0.719419π-0.719419\pi
0.968127 0.250458i 0.0805813π-0.0805813\pi
824824 −1.39481e18 −0.155235
825825 2.39537e18 6.76639e18i 0.264498 0.747147i
826826 1.68549e19 1.84653
827827 −1.80337e18 + 5.55022e18i −0.196020 + 0.603287i 0.803943 + 0.594706i 0.202732π0.202732\pi
−0.999963 + 0.00858129i 0.997268π0.997268\pi
828828 −2.33532e18 + 1.69671e18i −0.251854 + 0.182983i
829829 7.49355e17 + 5.44438e17i 0.0801831 + 0.0582565i 0.627155 0.778895i 0.284219π-0.284219\pi
−0.546972 + 0.837151i 0.684219π0.684219\pi
830830 −1.42168e18 4.37549e18i −0.150937 0.464535i
831831 1.84689e18 + 5.68413e18i 0.194551 + 0.598767i
832832 −1.16623e18 8.47315e17i −0.121894 0.0885612i
833833 1.32396e19 9.61914e18i 1.37304 0.997571i
834834 2.92857e17 9.01321e17i 0.0301353 0.0927470i
835835 −3.00234e19 −3.06547
836836 −2.92876e18 7.64113e16i −0.296717 0.00774135i
837837 −6.25945e18 −0.629246
838838 −4.20519e17 + 1.29422e18i −0.0419468 + 0.129099i
839839 −5.48645e18 + 3.98614e18i −0.543049 + 0.394548i −0.825216 0.564817i 0.808947π-0.808947\pi
0.282167 + 0.959365i 0.408947π0.408947\pi
840840 −3.53973e18 2.57176e18i −0.347660 0.252590i
841841 −9.00817e17 2.77243e18i −0.0877936 0.270201i
842842 1.33877e18 + 4.12030e18i 0.129472 + 0.398474i
843843 5.47197e18 + 3.97562e18i 0.525127 + 0.381527i
844844 −4.39503e18 + 3.19317e18i −0.418539 + 0.304086i
845845 2.39465e18 7.36997e18i 0.226294 0.696461i
846846 1.12528e19 1.05525
847847 −1.27904e19 1.03534e19i −1.19026 0.963479i
848848 2.95897e18 0.273255
849849 −4.27627e17 + 1.31610e18i −0.0391891 + 0.120612i
850850 1.28158e19 9.31126e18i 1.16553 0.846809i
851851 4.73506e18 + 3.44022e18i 0.427350 + 0.310488i
852852 6.92733e17 + 2.13201e18i 0.0620452 + 0.190956i
853853 3.71885e18 + 1.14455e19i 0.330552 + 1.01734i 0.968872 + 0.247564i 0.0796300π0.0796300\pi
−0.638319 + 0.769772i 0.720370π0.720370\pi
854854 −1.49807e19 1.08841e19i −1.32147 0.960101i
855855 −6.73348e18 + 4.89216e18i −0.589467 + 0.428273i
856856 −6.27897e17 + 1.93247e18i −0.0545518 + 0.167893i
857857 −9.75331e18 −0.840963 −0.420481 0.907301i 0.638139π-0.638139\pi
−0.420481 + 0.907301i 0.638139π0.638139\pi
858858 4.88741e18 + 1.27512e17i 0.418226 + 0.0109115i
859859 −1.06763e19 −0.906707 −0.453353 0.891331i 0.649772π-0.649772\pi
−0.453353 + 0.891331i 0.649772π0.649772\pi
860860 2.08314e18 6.41126e18i 0.175582 0.540385i
861861 −3.74917e18 + 2.72393e18i −0.313628 + 0.227864i
862862 −9.12638e17 6.63070e17i −0.0757707 0.0550506i
863863 −2.84113e18 8.74411e18i −0.234111 0.720519i −0.997238 0.0742706i 0.976337π-0.976337\pi
0.763127 0.646248i 0.223663π-0.223663\pi
864864 −5.76747e17 1.77504e18i −0.0471678 0.145168i
865865 2.35674e19 + 1.71227e19i 1.91296 + 1.38985i
866866 −4.89683e17 + 3.55776e17i −0.0394502 + 0.0286622i
867867 1.12336e18 3.45734e18i 0.0898244 0.276451i
868868 7.03078e18 0.557989
869869 −9.15217e17 + 2.58528e18i −0.0720934 + 0.203647i
870870 6.07369e18 0.474873
871871 3.20630e18 9.86796e18i 0.248820 0.765790i
872872 2.61031e18 1.89650e18i 0.201064 0.146082i
873873 4.73166e18 + 3.43775e18i 0.361760 + 0.262834i
874874 1.40204e18 + 4.31503e18i 0.106398 + 0.327461i
875875 6.24402e18 + 1.92171e19i 0.470340 + 1.44756i
876876 −1.87893e18 1.36512e18i −0.140486 0.102069i
877877 −8.73214e18 + 6.34427e18i −0.648072 + 0.470852i −0.862614 0.505863i 0.831174π-0.831174\pi
0.214542 + 0.976715i 0.431174π0.431174\pi
878878 −2.66267e17 + 8.19485e17i −0.0196156 + 0.0603707i
879879 −7.80233e18 −0.570554
880880 −4.58935e18 + 3.15482e18i −0.333130 + 0.229001i
881881 1.31967e19 0.950871 0.475435 0.879751i 0.342291π-0.342291\pi
0.475435 + 0.879751i 0.342291π0.342291\pi
882882 −3.11900e18 + 9.59930e18i −0.223085 + 0.686584i
883883 2.84301e18 2.06556e18i 0.201852 0.146654i −0.482267 0.876024i 0.660187π-0.660187\pi
0.684120 + 0.729370i 0.260187π0.260187\pi
884884 8.72927e18 + 6.34219e18i 0.615231 + 0.446991i
885885 5.97832e18 + 1.83994e19i 0.418262 + 1.28728i
886886 −1.73067e18 5.32646e18i −0.120198 0.369930i
887887 1.49805e19 + 1.08840e19i 1.03282 + 0.750386i 0.968871 0.247567i 0.0796310π-0.0796310\pi
0.0639474 + 0.997953i 0.479631π0.479631\pi
888888 −1.32109e18 + 9.59832e17i −0.0904169 + 0.0656917i
889889 −9.63109e17 + 2.96414e18i −0.0654356 + 0.201390i
890890 −2.67065e19 −1.80128
891891 −3.97221e18 3.04738e18i −0.265967 0.204043i
892892 1.68845e17 0.0112232
893893 5.46554e18 1.68212e19i 0.360660 1.11000i
894894 −2.19315e18 + 1.59342e18i −0.143673 + 0.104385i
895895 −5.63875e18 4.09679e18i −0.366719 0.266437i
896896 6.47818e17 + 1.99378e18i 0.0418264 + 0.128729i
897897 −2.33967e18 7.20077e18i −0.149970 0.461560i
898898 −3.53874e18 2.57104e18i −0.225192 0.163611i
899899 −7.89590e18 + 5.73671e18i −0.498843 + 0.362431i
900900 −3.01917e18 + 9.29205e18i −0.189370 + 0.582821i
901901 −2.21480e19 −1.37919
902902 1.67585e18 + 5.65557e18i 0.103608 + 0.349650i
903903 8.60639e18 0.528264
904904 2.91894e18 8.98357e18i 0.177881 0.547462i
905905 1.80149e19 1.30886e19i 1.08998 0.791914i
906906 4.56981e18 + 3.32016e18i 0.274514 + 0.199446i
907907 1.21660e18 + 3.74432e18i 0.0725608 + 0.223319i 0.980759 0.195220i 0.0625422π-0.0625422\pi
−0.908199 + 0.418539i 0.862542π0.862542\pi
908908 1.68936e18 + 5.19931e18i 0.100038 + 0.307884i
909909 1.15900e19 + 8.42061e18i 0.681424 + 0.495083i
910910 −2.92488e19 + 2.12505e19i −1.70742 + 1.24051i
911911 2.85024e18 8.77215e18i 0.165201 0.508436i −0.833850 0.551991i 0.813868π-0.813868\pi
0.999051 + 0.0435548i 0.0138683π0.0138683\pi
912912 −1.26586e18 −0.0728483
913913 −2.12403e18 7.16808e18i −0.121367 0.409584i
914914 1.75275e19 0.994421
915915 6.56792e18 2.02140e19i 0.369991 1.13871i
916916 6.90041e18 5.01344e18i 0.385971 0.280424i
917917 2.88009e19 + 2.09251e19i 1.59958 + 1.16216i
918918 4.31697e18 + 1.32863e19i 0.238068 + 0.732699i
919919 7.34834e17 + 2.26159e18i 0.0402382 + 0.123840i 0.969158 0.246441i 0.0792612π-0.0792612\pi
−0.928920 + 0.370282i 0.879261π0.879261\pi
920920 6.97735e18 + 5.06934e18i 0.379376 + 0.275633i
921921 −8.93705e18 + 6.49314e18i −0.482510 + 0.350564i
922922 6.94685e18 2.13802e19i 0.372424 1.14620i
923923 1.85235e19 0.986078
924924 −5.64117e18 4.32776e18i −0.298196 0.228768i
925925 1.98100e19 1.03983
926926 −1.56978e18 + 4.83128e18i −0.0818213 + 0.251820i
927927 −5.20935e18 + 3.78481e18i −0.269628 + 0.195896i
928928 −2.35434e18 1.71053e18i −0.121006 0.0879160i
929929 −3.91212e18 1.20403e19i −0.199669 0.614517i −0.999890 0.0148128i 0.995285π-0.995285\pi
0.800221 0.599705i 0.204715π-0.204715\pi
930930 2.49377e18 + 7.67504e18i 0.126391 + 0.388993i
931931 1.28345e19 + 9.32483e18i 0.645962 + 0.469319i
932932 −3.42840e18 + 2.49088e18i −0.171352 + 0.124494i
933933 1.61451e17 4.96895e17i 0.00801328 0.0246623i
934934 −1.24404e19 −0.613170
935935 3.43515e19 2.36140e19i 1.68140 1.15583i
936936 −6.65481e18 −0.323477
937937 −2.96385e18 + 9.12179e18i −0.143070 + 0.440324i −0.996758 0.0804609i 0.974361π-0.974361\pi
0.853688 + 0.520785i 0.174361π0.174361\pi
938938 −1.22074e19 + 8.86919e18i −0.585200 + 0.425173i
939939 −1.20653e19 8.76598e18i −0.574398 0.417325i
940940 −1.03894e19 3.19751e19i −0.491199 1.51176i
941941 2.51071e18 + 7.72718e18i 0.117887 + 0.362818i 0.992538 0.121935i 0.0389098π-0.0389098\pi
−0.874652 + 0.484752i 0.838910π0.838910\pi
942942 −1.01922e19 7.40504e18i −0.475265 0.345300i
943943 7.39019e18 5.36929e18i 0.342239 0.248651i
944944 2.86443e18 8.81580e18i 0.131741 0.405456i
945945 −4.68088e19 −2.13807
946946 3.65572e18 1.03266e19i 0.165837 0.468451i
947947 −3.93632e19 −1.77344 −0.886718 0.462311i 0.847021π-0.847021\pi
−0.886718 + 0.462311i 0.847021π0.847021\pi
948948 −3.66171e17 + 1.12696e18i −0.0163843 + 0.0504258i
949949 −1.55256e19 + 1.12800e19i −0.689952 + 0.501279i
950950 1.24237e19 + 9.02637e18i 0.548338 + 0.398391i
951951 −1.00102e17 3.08081e17i −0.00438801 0.0135049i
952952 −4.84894e18 1.49235e19i −0.211109 0.649727i
953953 −1.64810e19 1.19741e19i −0.712655 0.517774i 0.171374 0.985206i 0.445179π-0.445179\pi
−0.884029 + 0.467432i 0.845179π0.845179\pi
954954 1.10512e19 8.02914e18i 0.474617 0.344829i
955955 7.18188e18 2.21036e19i 0.306349 0.942845i
956956 −4.55856e18 −0.193131
957957 9.86651e18 + 2.57417e17i 0.415179 + 0.0108320i
958958 −2.09720e19 −0.876526
959959 −8.36468e18 + 2.57438e19i −0.347239 + 1.06869i
960960 −1.94670e18 + 1.41436e18i −0.0802668 + 0.0583172i
961961 9.26305e18 + 6.73000e18i 0.379361 + 0.275622i
962962 4.16963e18 + 1.28328e19i 0.169613 + 0.522016i
963963 2.89866e18 + 8.92117e18i 0.117119 + 0.360455i
964964 −1.09479e17 7.95415e16i −0.00439372 0.00319222i
965965 1.73168e18 1.25814e18i 0.0690305 0.0501536i
966966 −3.40251e18 + 1.04718e19i −0.134725 + 0.414641i
967967 1.80292e19 0.709093 0.354547 0.935038i 0.384635π-0.384635\pi
0.354547 + 0.935038i 0.384635π0.384635\pi
968968 −7.58896e18 + 4.93040e18i −0.296478 + 0.192616i
969969 9.47501e18 0.367684
970970 5.39986e18 1.66191e19i 0.208145 0.640605i
971971 2.83999e18 2.06337e18i 0.108741 0.0790047i −0.532086 0.846690i 0.678592π-0.678592\pi
0.640827 + 0.767686i 0.278592π0.278592\pi
972972 −1.09333e19 7.94350e18i −0.415834 0.302121i
973973 3.51916e18 + 1.08309e19i 0.132955 + 0.409194i
974974 7.11139e18 + 2.18866e19i 0.266883 + 0.821383i
975975 −2.07323e19 1.50629e19i −0.772889 0.561537i
976976 −8.23875e18 + 5.98580e18i −0.305097 + 0.221666i
977977 9.91026e18 3.05006e19i 0.364561 1.12200i −0.585694 0.810532i 0.699178π-0.699178\pi
0.950255 0.311472i 0.100822π-0.100822\pi
978978 −8.04914e18 −0.294135
979979 −4.33838e19 1.13188e18i −1.57485 0.0410880i
980980 3.01563e19 1.08745
981981 4.60284e18 1.41661e19i 0.164883 0.507459i
982982 1.01224e19 7.35432e18i 0.360211 0.261708i
983983 −3.41072e18 2.47803e18i −0.120572 0.0876009i 0.525865 0.850568i 0.323742π-0.323742\pi
−0.646437 + 0.762967i 0.723742π0.723742\pi
984984 7.87570e17 + 2.42389e18i 0.0276580 + 0.0851226i
985985 −2.32224e19 7.14713e19i −0.810163 2.49343i
986986 1.76223e19 + 1.28034e19i 0.610749 + 0.443735i
987987 3.47254e19 2.52295e19i 1.19560 0.868655i
988988 −3.23227e18 + 9.94789e18i −0.110557 + 0.340260i
989989 −1.69645e19 −0.576456
990990 −8.57973e18 + 2.42358e19i −0.289631 + 0.818142i
991991 4.45272e19 1.49330 0.746649 0.665218i 0.231662π-0.231662\pi
0.746649 + 0.665218i 0.231662π0.231662\pi
992992 1.19485e18 3.67738e18i 0.0398097 0.122522i
993993 −8.39419e18 + 6.09873e18i −0.277849 + 0.201869i
994994 −2.17934e19 1.58338e19i −0.716659 0.520684i
995995 5.34190e18 + 1.64407e19i 0.174520 + 0.537118i
996996 −9.98196e17 3.07213e18i −0.0323989 0.0997135i
997997 2.53865e19 + 1.84444e19i 0.818624 + 0.594765i 0.916318 0.400451i 0.131147π-0.131147\pi
−0.0976939 + 0.995217i 0.531147π0.531147\pi
998998 1.85520e19 1.34788e19i 0.594350 0.431820i
999999 −5.39852e18 + 1.66149e19i −0.171830 + 0.528838i
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 22.14.c.b.9.3 yes 28
11.5 even 5 inner 22.14.c.b.5.3 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.14.c.b.5.3 28 11.5 even 5 inner
22.14.c.b.9.3 yes 28 1.1 even 1 trivial