Properties

Label 22.13.d.a.13.1
Level 2222
Weight 1313
Character 22.13
Analytic conductor 20.10820.108
Analytic rank 00
Dimension 4848
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [22,13,Mod(7,22)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 13, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("22.7"); S:= CuspForms(chi, 13); N := Newforms(S);
 
Level: N N == 22=211 22 = 2 \cdot 11
Weight: k k == 13 13
Character orbit: [χ][\chi] == 22.d (of order 1010, degree 44, 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: 20.107863980120.1078639801
Analytic rank: 00
Dimension: 4848
Relative dimension: 1212 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 13.1
Character χ\chi == 22.13
Dual form 22.13.d.a.17.1

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+(43.039913.9845i)q2+(974.141+707.755i)q3+(1656.87+1203.78i)q4+(1693.39+5211.73i)q5+(51824.516838.8i)q6+(23282.732045.9i)q7+(54477.174981.2i)q8+(283809.873474.i)q9247993.iq10+(1.16794e61.33205e6i)q112.46600e6q12+(235938.+76660.8i)q13+(1.45023e6+1.05366e6i)q14+(5.33823e63.87845e6i)q15+(1.29611e6+3.98902e6i)q16+(2.12124e6689234.i)q17+(2.44302e7+3.36253e7i)q18+(2.20372e7+3.03315e7i)q19+(3.46807e6+1.06736e7i)q20+4.76957e7iq21+(6.88959e7+4.09983e7i)q22+1.00113e8q23+(1.06137e8+3.44859e7i)q24+(1.73219e81.25851e8i)q25+(9.08267e66.59894e6i)q26+(1.43992e8+4.43163e8i)q27+(7.71528e72.50685e7i)q28+(4.32401e8+5.95150e8i)q29+(1.75519e8+2.41581e8i)q30+(4.11680e8+1.26702e9i)q311.89813e8iq32+(1.94969e8+2.12421e9i)q331.00937e8q34+(2.06441e8+6.70769e7i)q35+(1.52171e91.10559e9i)q36+(2.35478e91.71085e9i)q37+(5.24305e81.61365e9i)q38+(2.84093e8+9.23075e7i)q39+(2.98531e84.10892e8i)q40+(1.26771e9+1.74485e9i)q41+(6.67001e82.05282e9i)q429.05523e9iq43+(3.53861e98.01086e8i)q44+5.03291e9q45+(4.30886e91.40003e9i)q46+(7.45605e8+5.41714e8i)q47+(4.08584e92.96854e9i)q48+(3.79234e9+1.16716e10i)q49+(9.21532e9+2.99424e9i)q50+(1.57858e9+2.17273e9i)q51+(2.98634e8+4.11035e8i)q52+(2.64627e98.14439e9i)q532.10874e10iq54+(8.92005e9+3.83128e9i)q553.67122e9q56+(4.29346e101.39503e10i)q57+(2.69334e101.95683e10i)q58+(2.86614e10+2.08237e10i)q59+(4.17591e91.28521e10i)q60+(6.78713e10+2.20527e10i)q61+(3.54374e104.87754e10i)q62+(2.13835e102.94318e10i)q63+(2.65444e9+8.16951e9i)q64+1.35946e9iq65+(3.80976e108.86995e10i)q66+1.76414e11q67+(4.34431e9+1.41155e9i)q68+(9.75242e10+7.08555e10i)q69+(7.94718e95.77397e9i)q70+(4.91313e10+1.51211e11i)q71+(8.09553e10+2.63040e10i)q72+(1.65141e11+2.27297e11i)q73+(7.74241e10+1.06565e11i)q74+(7.96682e10+2.45194e11i)q75+7.67833e10iq76+(1.54940e106.84413e10i)q77+1.35182e10q78+(1.34835e11+4.38105e10i)q79+(1.85949e10+1.35100e10i)q80+(5.90474e104.29004e10i)q81+(3.01611e109.28263e10i)q82+(4.31001e111.40041e11i)q83+(5.74153e10+7.90254e10i)q84+(7.18419e9+9.88819e9i)q85+(1.26633e11+3.89736e11i)q868.85793e11iq87+(1.63504e111.50071e10i)q88+6.81851e11q89+(2.16616e117.03828e10i)q90+(7.94994e95.77597e9i)q91+(1.65874e11+1.20515e11i)q92+(4.95706e111.52563e12i)q93+(3.96664e101.28884e10i)q94+(1.20762e11+1.66215e11i)q95+(1.34341e11+1.84904e11i)q96+(3.33707e11+1.02704e12i)q975.55379e11iq98+(8.32040e111.39821e12i)q99+O(q100)q+(-43.0399 - 13.9845i) q^{2} +(-974.141 + 707.755i) q^{3} +(1656.87 + 1203.78i) q^{4} +(1693.39 + 5211.73i) q^{5} +(51824.5 - 16838.8i) q^{6} +(23282.7 - 32045.9i) q^{7} +(-54477.1 - 74981.2i) q^{8} +(283809. - 873474. i) q^{9} -247993. i q^{10} +(1.16794e6 - 1.33205e6i) q^{11} -2.46600e6 q^{12} +(235938. + 76660.8i) q^{13} +(-1.45023e6 + 1.05366e6i) q^{14} +(-5.33823e6 - 3.87845e6i) q^{15} +(1.29611e6 + 3.98902e6i) q^{16} +(2.12124e6 - 689234. i) q^{17} +(-2.44302e7 + 3.36253e7i) q^{18} +(2.20372e7 + 3.03315e7i) q^{19} +(-3.46807e6 + 1.06736e7i) q^{20} +4.76957e7i q^{21} +(-6.88959e7 + 4.09983e7i) q^{22} +1.00113e8 q^{23} +(1.06137e8 + 3.44859e7i) q^{24} +(1.73219e8 - 1.25851e8i) q^{25} +(-9.08267e6 - 6.59894e6i) q^{26} +(1.43992e8 + 4.43163e8i) q^{27} +(7.71528e7 - 2.50685e7i) q^{28} +(-4.32401e8 + 5.95150e8i) q^{29} +(1.75519e8 + 2.41581e8i) q^{30} +(-4.11680e8 + 1.26702e9i) q^{31} -1.89813e8i q^{32} +(-1.94969e8 + 2.12421e9i) q^{33} -1.00937e8 q^{34} +(2.06441e8 + 6.70769e7i) q^{35} +(1.52171e9 - 1.10559e9i) q^{36} +(-2.35478e9 - 1.71085e9i) q^{37} +(-5.24305e8 - 1.61365e9i) q^{38} +(-2.84093e8 + 9.23075e7i) q^{39} +(2.98531e8 - 4.10892e8i) q^{40} +(1.26771e9 + 1.74485e9i) q^{41} +(6.67001e8 - 2.05282e9i) q^{42} -9.05523e9i q^{43} +(3.53861e9 - 8.01086e8i) q^{44} +5.03291e9 q^{45} +(-4.30886e9 - 1.40003e9i) q^{46} +(-7.45605e8 + 5.41714e8i) q^{47} +(-4.08584e9 - 2.96854e9i) q^{48} +(3.79234e9 + 1.16716e10i) q^{49} +(-9.21532e9 + 2.99424e9i) q^{50} +(-1.57858e9 + 2.17273e9i) q^{51} +(2.98634e8 + 4.11035e8i) q^{52} +(2.64627e9 - 8.14439e9i) q^{53} -2.10874e10i q^{54} +(8.92005e9 + 3.83128e9i) q^{55} -3.67122e9 q^{56} +(-4.29346e10 - 1.39503e10i) q^{57} +(2.69334e10 - 1.95683e10i) q^{58} +(2.86614e10 + 2.08237e10i) q^{59} +(-4.17591e9 - 1.28521e10i) q^{60} +(-6.78713e10 + 2.20527e10i) q^{61} +(3.54374e10 - 4.87754e10i) q^{62} +(-2.13835e10 - 2.94318e10i) q^{63} +(-2.65444e9 + 8.16951e9i) q^{64} +1.35946e9i q^{65} +(3.80976e10 - 8.86995e10i) q^{66} +1.76414e11 q^{67} +(4.34431e9 + 1.41155e9i) q^{68} +(-9.75242e10 + 7.08555e10i) q^{69} +(-7.94718e9 - 5.77397e9i) q^{70} +(4.91313e10 + 1.51211e11i) q^{71} +(-8.09553e10 + 2.63040e10i) q^{72} +(-1.65141e11 + 2.27297e11i) q^{73} +(7.74241e10 + 1.06565e11i) q^{74} +(-7.96682e10 + 2.45194e11i) q^{75} +7.67833e10i q^{76} +(-1.54940e10 - 6.84413e10i) q^{77} +1.35182e10 q^{78} +(1.34835e11 + 4.38105e10i) q^{79} +(-1.85949e10 + 1.35100e10i) q^{80} +(-5.90474e10 - 4.29004e10i) q^{81} +(-3.01611e10 - 9.28263e10i) q^{82} +(4.31001e11 - 1.40041e11i) q^{83} +(-5.74153e10 + 7.90254e10i) q^{84} +(7.18419e9 + 9.88819e9i) q^{85} +(-1.26633e11 + 3.89736e11i) q^{86} -8.85793e11i q^{87} +(-1.63504e11 - 1.50071e10i) q^{88} +6.81851e11 q^{89} +(-2.16616e11 - 7.03828e10i) q^{90} +(7.94994e9 - 5.77597e9i) q^{91} +(1.65874e11 + 1.20515e11i) q^{92} +(-4.95706e11 - 1.52563e12i) q^{93} +(3.96664e10 - 1.28884e10i) q^{94} +(-1.20762e11 + 1.66215e11i) q^{95} +(1.34341e11 + 1.84904e11i) q^{96} +(-3.33707e11 + 1.02704e12i) q^{97} -5.55379e11i q^{98} +(-8.32040e11 - 1.39821e12i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q+1240q3+24576q4+1440q5147200q6+439200q7+563348q97317468q11+737280q12+13341600q137524864q1429808888q1550331648q16+29458800q17+5181480396620q99+O(q100) 48 q + 1240 q^{3} + 24576 q^{4} + 1440 q^{5} - 147200 q^{6} + 439200 q^{7} + 563348 q^{9} - 7317468 q^{11} + 737280 q^{12} + 13341600 q^{13} - 7524864 q^{14} - 29808888 q^{15} - 50331648 q^{16} + 29458800 q^{17}+ \cdots - 5181480396620 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(110)e\left(\frac{1}{10}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −43.0399 13.9845i −0.672499 0.218508i
33 −974.141 + 707.755i −1.33627 + 0.970857i −0.336697 + 0.941613i 0.609310π0.609310\pi
−0.999572 + 0.0292437i 0.990690π0.990690\pi
44 1656.87 + 1203.78i 0.404508 + 0.293893i
55 1693.39 + 5211.73i 0.108377 + 0.333550i 0.990508 0.137453i 0.0438918π-0.0438918\pi
−0.882131 + 0.471004i 0.843892π0.843892\pi
66 51824.5 16838.8i 1.11078 0.360914i
77 23282.7 32045.9i 0.197900 0.272386i −0.698521 0.715590i 0.746158π-0.746158\pi
0.896421 + 0.443204i 0.146158π0.146158\pi
88 −54477.1 74981.2i −0.207813 0.286031i
99 283809. 873474.i 0.534037 1.64360i
1010 247993.i 0.247993i
1111 1.16794e6 1.33205e6i 0.659269 0.751907i
1212 −2.46600e6 −0.825860
1313 235938. + 76660.8i 0.0488806 + 0.0158823i 0.333355 0.942801i 0.391819π-0.391819\pi
−0.284475 + 0.958684i 0.591819π0.591819\pi
1414 −1.45023e6 + 1.05366e6i −0.192606 + 0.139936i
1515 −5.33823e6 3.87845e6i −0.468651 0.340495i
1616 1.29611e6 + 3.98902e6i 0.0772542 + 0.237764i
1717 2.12124e6 689234.i 0.0878814 0.0285544i −0.264746 0.964318i 0.585288π-0.585288\pi
0.352628 + 0.935764i 0.385288π0.385288\pi
1818 −2.44302e7 + 3.36253e7i −0.718278 + 0.988625i
1919 2.20372e7 + 3.03315e7i 0.468418 + 0.644723i 0.976228 0.216747i 0.0695446π-0.0695446\pi
−0.507809 + 0.861469i 0.669545π0.669545\pi
2020 −3.46807e6 + 1.06736e7i −0.0541886 + 0.166775i
2121 4.76957e7i 0.556114i
2222 −6.88959e7 + 4.09983e7i −0.607655 + 0.361601i
2323 1.00113e8 0.676276 0.338138 0.941097i 0.390203π-0.390203\pi
0.338138 + 0.941097i 0.390203π0.390203\pi
2424 1.06137e8 + 3.44859e7i 0.555390 + 0.180457i
2525 1.73219e8 1.25851e8i 0.709507 0.515487i
2626 −9.08267e6 6.59894e6i −0.0294018 0.0213616i
2727 1.43992e8 + 4.43163e8i 0.371670 + 1.14388i
2828 7.71528e7 2.50685e7i 0.160104 0.0520211i
2929 −4.32401e8 + 5.95150e8i −0.726941 + 1.00055i 0.272324 + 0.962206i 0.412208π0.412208\pi
−0.999265 + 0.0383427i 0.987792π0.987792\pi
3030 1.75519e8 + 2.41581e8i 0.240766 + 0.331386i
3131 −4.11680e8 + 1.26702e9i −0.463863 + 1.42762i 0.396543 + 0.918016i 0.370210π0.370210\pi
−0.860406 + 0.509609i 0.829790π0.829790\pi
3232 1.89813e8i 0.176777i
3333 −1.94969e8 + 2.12421e9i −0.150967 + 1.64481i
3434 −1.00937e8 −0.0653395
3535 2.06441e8 + 6.70769e7i 0.112302 + 0.0364892i
3636 1.52171e9 1.10559e9i 0.699063 0.507899i
3737 −2.35478e9 1.71085e9i −0.917782 0.666808i 0.0251886 0.999683i 0.491981π-0.491981\pi
−0.942971 + 0.332875i 0.891981π0.891981\pi
3838 −5.24305e8 1.61365e9i −0.174134 0.535928i
3939 −2.84093e8 + 9.23075e7i −0.0807371 + 0.0262331i
4040 2.98531e8 4.10892e8i 0.0728835 0.100315i
4141 1.26771e9 + 1.74485e9i 0.266880 + 0.367328i 0.921333 0.388774i 0.127101π-0.127101\pi
−0.654454 + 0.756102i 0.727101π0.727101\pi
4242 6.67001e8 2.05282e9i 0.121515 0.373986i
4343 9.05523e9i 1.43248i −0.697854 0.716240i 0.745862π-0.745862\pi
0.697854 0.716240i 0.254138π-0.254138\pi
4444 3.53861e9 8.01086e8i 0.487660 0.110399i
4545 5.03291e9 0.606100
4646 −4.30886e9 1.40003e9i −0.454794 0.147772i
4747 −7.45605e8 + 5.41714e8i −0.0691707 + 0.0502554i −0.621833 0.783150i 0.713612π-0.713612\pi
0.552663 + 0.833405i 0.313612π0.313612\pi
4848 −4.08584e9 2.96854e9i −0.334067 0.242714i
4949 3.79234e9 + 1.16716e10i 0.273987 + 0.843246i
5050 −9.21532e9 + 2.99424e9i −0.589780 + 0.191631i
5151 −1.57858e9 + 2.17273e9i −0.0897110 + 0.123477i
5252 2.98634e8 + 4.11035e8i 0.0151050 + 0.0207902i
5353 2.64627e9 8.14439e9i 0.119393 0.367454i −0.873445 0.486923i 0.838119π-0.838119\pi
0.992838 + 0.119469i 0.0381192π0.0381192\pi
5454 2.10874e10i 0.850471i
5555 8.92005e9 + 3.83128e9i 0.322249 + 0.138410i
5656 −3.67122e9 −0.119037
5757 −4.29346e10 1.39503e10i −1.25187 0.406756i
5858 2.69334e10 1.95683e10i 0.707495 0.514025i
5959 2.86614e10 + 2.08237e10i 0.679493 + 0.493680i 0.873189 0.487381i 0.162048π-0.162048\pi
−0.193697 + 0.981061i 0.562048π0.562048\pi
6060 −4.17591e9 1.28521e10i −0.0895043 0.275466i
6161 −6.78713e10 + 2.20527e10i −1.31737 + 0.428039i −0.881590 0.472016i 0.843527π-0.843527\pi
−0.435778 + 0.900054i 0.643527π0.643527\pi
6262 3.54374e10 4.87754e10i 0.623895 0.858718i
6363 −2.13835e10 2.94318e10i −0.342007 0.470732i
6464 −2.65444e9 + 8.16951e9i −0.0386271 + 0.118882i
6565 1.35946e9i 0.0180254i
6666 3.80976e10 8.86995e10i 0.460928 1.07314i
6767 1.76414e11 1.95022 0.975110 0.221722i 0.0711678π-0.0711678\pi
0.975110 + 0.221722i 0.0711678π0.0711678\pi
6868 4.34431e9 + 1.41155e9i 0.0439407 + 0.0142772i
6969 −9.75242e10 + 7.08555e10i −0.903687 + 0.656567i
7070 −7.94718e9 5.77397e9i −0.0675499 0.0490779i
7171 4.91313e10 + 1.51211e11i 0.383538 + 1.18041i 0.937535 + 0.347890i 0.113102π0.113102\pi
−0.553997 + 0.832519i 0.686898π0.686898\pi
7272 −8.09553e10 + 2.63040e10i −0.581099 + 0.188810i
7373 −1.65141e11 + 2.27297e11i −1.09123 + 1.50196i −0.244717 + 0.969595i 0.578695π0.578695\pi
−0.846518 + 0.532360i 0.821305π0.821305\pi
7474 7.74241e10 + 1.06565e11i 0.471504 + 0.648970i
7575 −7.96682e10 + 2.45194e11i −0.447628 + 1.37766i
7676 7.67833e10i 0.398460i
7777 −1.54940e10 6.84413e10i −0.0743396 0.328378i
7878 1.35182e10 0.0600277
7979 1.34835e11 + 4.38105e10i 0.554676 + 0.180225i 0.572924 0.819608i 0.305809π-0.305809\pi
−0.0182483 + 0.999833i 0.505809π0.505809\pi
8080 −1.85949e10 + 1.35100e10i −0.0709337 + 0.0515364i
8181 −5.90474e10 4.29004e10i −0.209069 0.151898i
8282 −3.01611e10 9.28263e10i −0.0992120 0.305343i
8383 4.31001e11 1.40041e11i 1.31829 0.428337i 0.436381 0.899762i 0.356260π-0.356260\pi
0.881906 + 0.471425i 0.156260π0.156260\pi
8484 −5.74153e10 + 7.90254e10i −0.163438 + 0.224953i
8585 7.18419e9 + 9.88819e9i 0.0190487 + 0.0262182i
8686 −1.26633e11 + 3.89736e11i −0.313008 + 0.963341i
8787 8.85793e11i 2.04276i
8888 −1.63504e11 1.50071e10i −0.352074 0.0323147i
8989 6.81851e11 1.37199 0.685993 0.727608i 0.259368π-0.259368\pi
0.685993 + 0.727608i 0.259368π0.259368\pi
9090 −2.16616e11 7.03828e10i −0.407601 0.132438i
9191 7.94994e9 5.77597e9i 0.0139996 0.0101713i
9292 1.65874e11 + 1.20515e11i 0.273559 + 0.198752i
9393 −4.95706e11 1.52563e12i −0.766172 2.35804i
9494 3.96664e10 1.28884e10i 0.0574984 0.0186824i
9595 −1.20762e11 + 1.66215e11i −0.164282 + 0.226114i
9696 1.34341e11 + 1.84904e11i 0.171625 + 0.236221i
9797 −3.33707e11 + 1.02704e12i −0.400622 + 1.23299i 0.523874 + 0.851796i 0.324486π0.324486\pi
−0.924496 + 0.381191i 0.875514π0.875514\pi
9898 5.55379e11i 0.626950i
9999 −8.32040e11 1.39821e12i −0.883758 1.48512i
100100 4.38499e11 0.438499
101101 −7.74626e11 2.51691e11i −0.729733 0.237105i −0.0794951 0.996835i 0.525331π-0.525331\pi
−0.650238 + 0.759731i 0.725331π0.725331\pi
102102 9.83265e10 7.14384e10i 0.0873111 0.0634353i
103103 −2.81320e11 2.04391e11i −0.235601 0.171174i 0.463720 0.885982i 0.346514π-0.346514\pi
−0.699321 + 0.714808i 0.746514π0.746514\pi
104104 −7.10506e9 2.18671e10i −0.00561524 0.0172819i
105105 −2.48577e11 + 8.07676e10i −0.185492 + 0.0602700i
106106 −2.27791e11 + 3.13527e11i −0.160583 + 0.221024i
107107 7.64275e11 + 1.05193e12i 0.509269 + 0.700948i 0.983796 0.179293i 0.0573809π-0.0573809\pi
−0.474527 + 0.880241i 0.657381π0.657381\pi
108108 −2.94896e11 + 9.07598e11i −0.185835 + 0.571941i
109109 5.20080e11i 0.310106i −0.987906 0.155053i 0.950445π-0.950445\pi
0.987906 0.155053i 0.0495549π-0.0495549\pi
110110 −3.30340e11 2.89640e11i −0.186468 0.163494i
111111 3.50474e12 1.87378
112112 1.58009e11 + 5.13402e10i 0.0800522 + 0.0260105i
113113 −2.00771e11 + 1.45869e11i −0.0964340 + 0.0700634i −0.634957 0.772547i 0.718982π-0.718982\pi
0.538523 + 0.842611i 0.318982π0.318982\pi
114114 1.65281e12 + 1.20084e12i 0.752999 + 0.547086i
115115 1.69531e11 + 5.21762e11i 0.0732928 + 0.225572i
116116 −1.43286e12 + 4.65565e11i −0.588108 + 0.191088i
117117 1.33922e11 1.84328e11i 0.0522081 0.0718583i
118118 −9.42373e11 1.29706e12i −0.349085 0.480474i
119119 2.73012e10 8.40245e10i 0.00961391 0.0295886i
120120 6.11553e11i 0.204808i
121121 −4.10283e11 3.11149e12i −0.130729 0.991418i
122122 3.22957e12 0.979458
123123 −2.46985e12 8.02502e11i −0.713246 0.231748i
124124 −2.20732e12 + 1.60371e12i −0.607205 + 0.441160i
125125 2.03159e12 + 1.47604e12i 0.532570 + 0.386935i
126126 5.08752e11 + 1.56578e12i 0.127140 + 0.391298i
127127 −5.70964e12 + 1.85517e12i −1.36077 + 0.442142i −0.896301 0.443445i 0.853756π-0.853756\pi
−0.464473 + 0.885588i 0.653756π0.653756\pi
128128 2.28493e11 3.14494e11i 0.0519534 0.0715077i
129129 6.40888e12 + 8.82106e12i 1.39073 + 1.91418i
130130 1.90114e10 5.85110e10i 0.00393870 0.0121221i
131131 1.57710e12i 0.312054i −0.987753 0.156027i 0.950131π-0.950131\pi
0.987753 0.156027i 0.0498688π-0.0498688\pi
132132 −2.88013e12 + 3.28484e12i −0.544464 + 0.620970i
133133 1.48509e12 0.268313
134134 −7.59283e12 2.46706e12i −1.31152 0.426139i
135135 −2.06581e12 + 1.50090e12i −0.341262 + 0.247941i
136136 −1.67239e11 1.21506e11i −0.0264304 0.0192028i
137137 1.68660e12 + 5.19081e12i 0.255087 + 0.785076i 0.993813 + 0.111070i 0.0354278π0.0354278\pi
−0.738726 + 0.674006i 0.764572π0.764572\pi
138138 5.18831e12 1.68579e12i 0.751193 0.244077i
139139 −1.51726e12 + 2.08832e12i −0.210363 + 0.289540i −0.901140 0.433528i 0.857269π-0.857269\pi
0.690777 + 0.723068i 0.257269π0.257269\pi
140140 2.61300e11 + 3.59648e11i 0.0347033 + 0.0477650i
141141 3.42924e11 1.05541e12i 0.0436398 0.134310i
142142 7.19517e12i 0.877629i
143143 3.77676e11 2.24746e11i 0.0441675 0.0262830i
144144 3.85215e12 0.432045
145145 −3.83398e12 1.24574e12i −0.412517 0.134035i
146146 1.02863e13 7.47343e12i 1.06204 0.771619i
147147 −1.19549e13 8.68575e12i −1.18479 0.860802i
148148 −1.84206e12 5.66929e12i −0.175281 0.539459i
149149 1.24111e13 4.03260e12i 1.13420 0.368525i 0.319032 0.947744i 0.396642π-0.396642\pi
0.815172 + 0.579218i 0.196642π0.196642\pi
150150 6.85783e12 9.43899e12i 0.602059 0.828663i
151151 3.90947e12 + 5.38093e12i 0.329804 + 0.453937i 0.941429 0.337211i 0.109484π-0.109484\pi
−0.611625 + 0.791148i 0.709484π0.709484\pi
152152 1.07378e12 3.30475e12i 0.0870668 0.267964i
153153 2.04846e12i 0.159691i
154154 −2.90257e11 + 3.16239e12i −0.0217599 + 0.237078i
155155 −7.30051e12 −0.526457
156156 −5.81823e11 1.89046e11i −0.0403686 0.0131165i
157157 −1.92589e13 + 1.39924e13i −1.28598 + 0.934316i −0.999716 0.0238356i 0.992412π-0.992412\pi
−0.286260 + 0.958152i 0.592412π0.592412\pi
158158 −5.19061e12 3.77120e12i −0.333638 0.242402i
159159 3.18639e12 + 9.80669e12i 0.197204 + 0.606931i
160160 9.89251e11 3.21427e11i 0.0589640 0.0191585i
161161 2.33091e12 3.20822e12i 0.133835 0.184208i
162162 1.94145e12 + 2.67218e12i 0.107408 + 0.147834i
163163 5.11922e12 1.57553e13i 0.272947 0.840044i −0.716808 0.697270i 0.754398π-0.754398\pi
0.989755 0.142774i 0.0456022π-0.0456022\pi
164164 4.41702e12i 0.227021i
165165 −1.14010e13 + 2.58100e12i −0.564987 + 0.127904i
166166 −2.05087e13 −0.980141
167167 3.00766e13 + 9.77248e12i 1.38653 + 0.450511i 0.904811 0.425814i 0.140012π-0.140012\pi
0.481720 + 0.876325i 0.340012π0.340012\pi
168168 3.57628e12 2.59832e12i 0.159066 0.115568i
169169 −1.87988e13 1.36581e13i −0.806880 0.586233i
170170 −1.70925e11 5.26054e11i −0.00708130 0.0217940i
171171 3.27482e13 1.06405e13i 1.30982 0.425585i
172172 1.09005e13 1.50033e13i 0.420995 0.579450i
173173 −1.01792e13 1.40105e13i −0.379698 0.522610i 0.575806 0.817586i 0.304688π-0.304688\pi
−0.955505 + 0.294976i 0.904688π0.904688\pi
174174 −1.23874e13 + 3.81245e13i −0.446359 + 1.37375i
175175 8.48114e12i 0.295275i
176176 6.82735e12 + 2.93243e12i 0.229708 + 0.0986625i
177177 −4.26583e13 −1.38728
178178 −2.93468e13 9.53535e12i −0.922658 0.299790i
179179 −1.04848e13 + 7.61762e12i −0.318743 + 0.231580i −0.735639 0.677374i 0.763118π-0.763118\pi
0.416896 + 0.908954i 0.363118π0.363118\pi
180180 8.33886e12 + 6.05854e12i 0.245172 + 0.178128i
181181 1.58445e13 + 4.87643e13i 0.450616 + 1.38685i 0.876206 + 0.481937i 0.160066π0.160066\pi
−0.425590 + 0.904916i 0.639934π0.639934\pi
182182 −4.22939e11 + 1.37421e11i −0.0116372 + 0.00378116i
183183 5.05083e13 6.95187e13i 1.34479 1.85095i
184184 −5.45387e12 7.50660e12i −0.140539 0.193436i
185185 4.92890e12 1.51696e13i 0.122948 0.378393i
186186 7.25950e13i 1.75319i
187187 1.55938e12 3.63058e12i 0.0364672 0.0849037i
188188 −1.88748e12 −0.0427498
189189 1.75541e13 + 5.70368e12i 0.385131 + 0.125137i
190190 7.52202e12 5.46507e12i 0.159887 0.116165i
191191 4.46377e13 + 3.24312e13i 0.919393 + 0.667978i 0.943373 0.331734i 0.107634π-0.107634\pi
−0.0239799 + 0.999712i 0.507634π0.507634\pi
192192 −3.19622e12 9.83694e12i −0.0638012 0.196360i
193193 1.77814e13 5.77751e12i 0.344050 0.111789i −0.131895 0.991264i 0.542106π-0.542106\pi
0.475945 + 0.879475i 0.342106π0.342106\pi
194194 2.87254e13 3.95371e13i 0.538835 0.741643i
195195 −9.62163e11 1.32430e12i −0.0175001 0.0240868i
196196 −7.76671e12 + 2.39035e13i −0.136994 + 0.421623i
197197 6.13561e13i 1.04969i 0.851198 + 0.524844i 0.175876π0.175876\pi
−0.851198 + 0.524844i 0.824124π0.824124\pi
198198 1.62577e13 + 7.18145e13i 0.269816 + 1.19185i
199199 −5.68662e13 −0.915664 −0.457832 0.889039i 0.651374π-0.651374\pi
−0.457832 + 0.889039i 0.651374π0.651374\pi
200200 −1.88730e13 6.13220e12i −0.294890 0.0958156i
201201 −1.71852e14 + 1.24858e14i −2.60602 + 1.89338i
202202 2.98201e13 + 2.16655e13i 0.438935 + 0.318905i
203203 9.00464e12 + 2.77134e13i 0.128674 + 0.396017i
204204 −5.23100e12 + 1.69965e12i −0.0725777 + 0.0235819i
205205 −6.94694e12 + 9.56165e12i −0.0935989 + 0.128828i
206206 9.24967e12 + 1.27311e13i 0.121038 + 0.166595i
207207 2.84130e13 8.74462e13i 0.361156 1.11152i
208208 1.04052e12i 0.0128490i
209209 6.61411e13 + 6.07070e12i 0.793585 + 0.0728385i
210210 1.18282e13 0.137913
211211 9.07678e13 + 2.94922e13i 1.02858 + 0.334205i 0.774228 0.632907i 0.218139π-0.218139\pi
0.254350 + 0.967112i 0.418139π0.418139\pi
212212 1.41886e13 1.03086e13i 0.156288 0.113550i
213213 −1.54881e14 1.12528e14i −1.65852 1.20498i
214214 −1.81835e13 5.59632e13i −0.189320 0.582666i
215215 4.71934e13 1.53341e13i 0.477805 0.155248i
216216 2.53846e13 3.49389e13i 0.249947 0.344023i
217217 3.10179e13 + 4.26924e13i 0.297066 + 0.408877i
218218 −7.27306e12 + 2.23842e13i −0.0677607 + 0.208546i
219219 3.38299e14i 3.06645i
220220 1.01673e13 + 1.70857e13i 0.0896747 + 0.150695i
221221 5.53318e11 0.00474921
222222 −1.50844e14 4.90121e13i −1.26011 0.409436i
223223 7.60121e13 5.52260e13i 0.618093 0.449071i −0.234162 0.972198i 0.575235π-0.575235\pi
0.852255 + 0.523127i 0.175235π0.175235\pi
224224 −6.08272e12 4.41936e12i −0.0481515 0.0349841i
225225 −6.07666e13 1.87020e14i −0.468349 1.44143i
226226 1.06811e13 3.47049e12i 0.0801612 0.0260459i
227227 1.88292e13 2.59162e13i 0.137619 0.189416i −0.734645 0.678452i 0.762651π-0.762651\pi
0.872264 + 0.489036i 0.162651π0.162651\pi
228228 −5.43437e13 7.47977e13i −0.386848 0.532451i
229229 3.59682e12 1.10699e13i 0.0249405 0.0767590i −0.937812 0.347145i 0.887151π-0.887151\pi
0.962752 + 0.270386i 0.0871512π0.0871512\pi
230230 2.48274e13i 0.167712i
231231 6.35330e13 + 5.57055e13i 0.418146 + 0.366628i
232232 6.81810e13 0.437256
233233 6.40053e13 + 2.07966e13i 0.400019 + 0.129974i 0.502116 0.864800i 0.332555π-0.332555\pi
−0.102097 + 0.994774i 0.532555π0.532555\pi
234234 −8.34175e12 + 6.06064e12i −0.0508115 + 0.0369167i
235235 −4.08587e12 2.96856e12i −0.0242592 0.0176254i
236236 2.24208e13 + 6.90042e13i 0.129772 + 0.399396i
237237 −1.62355e14 + 5.27524e13i −0.916169 + 0.297681i
238238 −2.35008e12 + 3.23461e12i −0.0129307 + 0.0177976i
239239 2.01973e14 + 2.77992e14i 1.08369 + 1.49157i 0.855392 + 0.517982i 0.173317π0.173317\pi
0.228299 + 0.973591i 0.426683π0.426683\pi
240240 8.55227e12 2.63212e13i 0.0447522 0.137733i
241241 3.45260e13i 0.176215i 0.996111 + 0.0881077i 0.0280820π0.0280820\pi
−0.996111 + 0.0881077i 0.971918π0.971918\pi
242242 −2.58542e13 + 1.39656e14i −0.128718 + 0.695293i
243243 −1.59752e14 −0.775904
244244 −1.39000e14 4.51640e13i −0.658684 0.214019i
245245 −5.44073e13 + 3.95292e13i −0.251571 + 0.182777i
246246 9.50794e13 + 6.90792e13i 0.429018 + 0.311700i
247247 2.87415e12 + 8.84573e12i 0.0126569 + 0.0389540i
248248 1.17430e14 3.81553e13i 0.504742 0.164000i
249249 −3.20741e14 + 4.41463e14i −1.34573 + 1.85224i
250250 −6.67979e13 9.19394e13i −0.273604 0.376584i
251251 −3.12760e13 + 9.62575e13i −0.125074 + 0.384939i −0.993915 0.110153i 0.964866π-0.964866\pi
0.868840 + 0.495093i 0.164866π0.164866\pi
252252 7.45056e13i 0.290928i
253253 1.16926e14 1.33356e14i 0.445848 0.508497i
254254 2.71686e14 1.01173
255255 −1.39968e13 4.54785e12i −0.0509083 0.0165411i
256256 −1.42324e13 + 1.03404e13i −0.0505636 + 0.0367366i
257257 3.75455e14 + 2.72784e14i 1.30304 + 0.946717i 0.999980 0.00625283i 0.00199035π-0.00199035\pi
0.303064 + 0.952970i 0.401990π0.401990\pi
258258 −1.52479e14 4.69283e14i −0.517002 1.59117i
259259 −1.09651e14 + 3.56279e13i −0.363258 + 0.118030i
260260 −1.63649e12 + 2.25244e12i −0.00529754 + 0.00729144i
261261 3.97128e14 + 5.46600e14i 1.25628 + 1.72913i
262262 −2.20549e13 + 6.78781e13i −0.0681864 + 0.209856i
263263 5.47581e14i 1.65468i −0.561702 0.827340i 0.689853π-0.689853\pi
0.561702 0.827340i 0.310147π-0.310147\pi
264264 1.69898e14 1.01102e14i 0.501838 0.298632i
265265 4.69275e13 0.135504
266266 −6.39180e13 2.07682e13i −0.180440 0.0586286i
267267 −6.64219e14 + 4.82583e14i −1.83334 + 1.33200i
268268 2.92294e14 + 2.12364e14i 0.788880 + 0.573155i
269269 −4.17119e13 1.28376e14i −0.110090 0.338821i 0.880802 0.473485i 0.157004π-0.157004\pi
−0.990891 + 0.134664i 0.957004π0.957004\pi
270270 1.09902e14 3.57092e13i 0.283675 0.0921716i
271271 −1.60128e14 + 2.20397e14i −0.404251 + 0.556403i −0.961804 0.273738i 0.911740π-0.911740\pi
0.557554 + 0.830141i 0.311740π0.311740\pi
272272 5.49873e12 + 7.56836e12i 0.0135784 + 0.0186891i
273273 −3.65639e12 + 1.12532e13i −0.00883236 + 0.0271832i
274274 2.46998e14i 0.583701i
275275 3.46690e13 3.77723e14i 0.0801576 0.873328i
276276 −2.46879e14 −0.558509
277277 −6.09254e14 1.97959e14i −1.34871 0.438224i −0.456454 0.889747i 0.650881π-0.650881\pi
−0.892259 + 0.451523i 0.850881π0.850881\pi
278278 9.45067e13 6.86631e13i 0.204736 0.148749i
279279 9.89873e14 + 7.19185e14i 2.09872 + 1.52481i
280280 −6.21681e12 1.91334e13i −0.0129009 0.0397049i
281281 3.44036e14 1.11784e14i 0.698820 0.227060i 0.0620039 0.998076i 0.480251π-0.480251\pi
0.636816 + 0.771015i 0.280251π0.280251\pi
282282 −2.95188e13 + 4.06292e13i −0.0586954 + 0.0807873i
283283 −2.53813e14 3.49344e14i −0.494078 0.680040i 0.487056 0.873371i 0.338071π-0.338071\pi
−0.981134 + 0.193331i 0.938071π0.938071\pi
284284 −1.00621e14 + 3.09680e14i −0.191769 + 0.590204i
285285 2.47387e14i 0.461644i
286286 −1.93981e13 + 4.39142e12i −0.0354456 + 0.00802433i
287287 8.54310e13 0.152871
288288 −1.65796e14 5.38705e13i −0.290549 0.0944052i
289289 −4.67327e14 + 3.39533e14i −0.802109 + 0.582766i
290290 1.47593e14 + 1.07233e14i 0.248129 + 0.180277i
291291 −4.01818e14 1.23667e15i −0.661715 2.03655i
292292 −5.47234e14 + 1.77807e14i −0.882827 + 0.286848i
293293 2.84557e13 3.91659e13i 0.0449742 0.0619017i −0.785938 0.618306i 0.787819π-0.787819\pi
0.830912 + 0.556404i 0.187819π0.187819\pi
294294 3.93072e14 + 5.41017e14i 0.608679 + 0.837774i
295295 −5.99925e13 + 1.84638e14i −0.0910258 + 0.280149i
296296 2.69766e14i 0.401086i
297297 7.58489e14 + 3.25781e14i 1.10512 + 0.474665i
298298 −5.90565e14 −0.843277
299299 2.36204e13 + 7.67475e12i 0.0330568 + 0.0107408i
300300 −4.27160e14 + 3.10350e14i −0.585953 + 0.425720i
301301 −2.90183e14 2.10830e14i −0.390188 0.283488i
302302 −9.30137e13 2.86267e14i −0.122604 0.377337i
303303 9.32731e14 3.03063e14i 1.20531 0.391630i
304304 −9.24305e13 + 1.27220e14i −0.117105 + 0.161181i
305305 −2.29865e14 3.16383e14i −0.285545 0.393019i
306306 −2.86467e13 + 8.81656e13i −0.0348937 + 0.107392i
307307 1.26988e15i 1.51681i −0.651783 0.758405i 0.725979π-0.725979\pi
0.651783 0.758405i 0.274021π-0.274021\pi
308308 5.67170e13 1.32050e14i 0.0664369 0.154680i
309309 4.18704e14 0.481012
310310 3.14213e14 + 1.02094e14i 0.354042 + 0.115035i
311311 7.06857e14 5.13562e14i 0.781213 0.567584i −0.124130 0.992266i 0.539614π-0.539614\pi
0.905343 + 0.424682i 0.139614π0.139614\pi
312312 2.23979e13 + 1.62730e13i 0.0242817 + 0.0176417i
313313 −3.63311e14 1.11816e15i −0.386378 1.18915i −0.935476 0.353391i 0.885029π-0.885029\pi
0.549098 0.835758i 0.314971π-0.314971\pi
314314 1.02458e15 3.32905e14i 1.06897 0.347330i
315315 1.17180e14 1.61284e14i 0.119947 0.165093i
316316 1.70665e14 + 2.34900e14i 0.171404 + 0.235918i
317317 1.75058e14 5.38772e14i 0.172514 0.530945i −0.826997 0.562207i 0.809953π-0.809953\pi
0.999511 + 0.0312617i 0.00995253π0.00995253\pi
318318 4.66639e14i 0.451251i
319319 2.87752e14 + 1.27108e15i 0.273070 + 1.20622i
320320 −4.70723e13 −0.0438395
321321 −1.48902e15 4.83813e14i −1.36104 0.442229i
322322 −1.45187e14 + 1.05485e14i −0.130255 + 0.0946356i
323323 6.76517e13 + 4.91518e13i 0.0595749 + 0.0432837i
324324 −4.61908e13 1.42161e14i −0.0399287 0.122888i
325325 5.05168e13 1.64139e13i 0.0428683 0.0139287i
326326 −4.40661e14 + 6.06518e14i −0.367113 + 0.505287i
327327 3.68089e14 + 5.06631e14i 0.301069 + 0.414386i
328328 6.17699e13 1.90108e14i 0.0496060 0.152672i
329329 3.65062e13i 0.0287867i
330330 5.26791e14 + 4.83511e13i 0.407901 + 0.0374388i
331331 −1.48833e15 −1.13170 −0.565849 0.824509i 0.691452π-0.691452\pi
−0.565849 + 0.824509i 0.691452π0.691452\pi
332332 8.82691e14 + 2.86804e14i 0.659144 + 0.214169i
333333 −2.16269e15 + 1.57128e15i −1.58609 + 1.15236i
334334 −1.15783e15 8.41213e14i −0.834000 0.605936i
335335 2.98738e14 + 9.19420e14i 0.211359 + 0.650497i
336336 −1.90259e14 + 6.18189e13i −0.132224 + 0.0429621i
337337 6.74345e14 9.28157e14i 0.460366 0.633639i −0.514219 0.857659i 0.671918π-0.671918\pi
0.974585 + 0.224020i 0.0719181π0.0719181\pi
338338 6.18095e14 + 8.50735e14i 0.414529 + 0.570550i
339339 9.23400e13 2.84193e14i 0.0608403 0.187247i
340340 2.50316e13i 0.0162038i
341341 1.20692e15 + 2.02818e15i 0.767630 + 1.28997i
342342 −1.55828e15 −0.973843
343343 9.83756e14 + 3.19642e14i 0.604119 + 0.196290i
344344 −6.78972e14 + 4.93302e14i −0.409733 + 0.297689i
345345 −5.34426e14 3.88283e14i −0.316937 0.230268i
346346 2.42183e14 + 7.45363e14i 0.141152 + 0.434421i
347347 −1.86497e15 + 6.05966e14i −1.06831 + 0.347114i −0.789828 0.613329i 0.789830π-0.789830\pi
−0.278478 + 0.960443i 0.589830π0.589830\pi
348348 1.06630e15 1.46764e15i 0.600351 0.826313i
349349 1.07095e15 + 1.47404e15i 0.592677 + 0.815750i 0.995013 0.0997420i 0.0318018π-0.0318018\pi
−0.402336 + 0.915492i 0.631802π0.631802\pi
350350 −1.18605e14 + 3.65027e14i −0.0645198 + 0.198572i
351351 1.15597e14i 0.0618166i
352352 −2.52840e14 2.21689e14i −0.132920 0.116543i
353353 −5.19563e14 −0.268528 −0.134264 0.990946i 0.542867π-0.542867\pi
−0.134264 + 0.990946i 0.542867π0.542867\pi
354354 1.83601e15 + 5.96555e14i 0.932942 + 0.303131i
355355 −7.04870e14 + 5.12118e14i −0.352159 + 0.255859i
356356 1.12974e15 + 8.20802e14i 0.554980 + 0.403216i
357357 3.28735e13 + 1.01174e14i 0.0158795 + 0.0488720i
358358 5.57792e14 1.81237e14i 0.264956 0.0860894i
359359 1.94378e15 2.67539e15i 0.907990 1.24974i −0.0598578 0.998207i 0.519065π-0.519065\pi
0.967848 0.251535i 0.0809353π-0.0809353\pi
360360 −2.74178e14 3.77374e14i −0.125956 0.173363i
361361 2.49586e14 7.68146e14i 0.112766 0.347057i
362362 2.32039e15i 1.03112i
363363 2.60185e15 + 2.74065e15i 1.13721 + 1.19788i
364364 2.01250e13 0.00865222
365365 −1.46426e15 4.75767e14i −0.619243 0.201204i
366366 −3.14606e15 + 2.28574e15i −1.30882 + 0.950913i
367367 2.00886e15 + 1.45953e15i 0.822156 + 0.597331i 0.917329 0.398130i 0.130341π-0.130341\pi
−0.0951734 + 0.995461i 0.530341π0.530341\pi
368368 1.29758e14 + 3.99353e14i 0.0522452 + 0.160794i
369369 1.88387e15 6.12105e14i 0.746263 0.242476i
370370 −4.24279e14 + 5.83970e14i −0.165364 + 0.227604i
371371 −1.99382e14 2.74426e14i −0.0764615 0.105240i
372372 1.01521e15 3.12448e15i 0.383086 1.17902i
373373 1.44012e15i 0.534745i 0.963593 + 0.267372i 0.0861554π0.0861554\pi
−0.963593 + 0.267372i 0.913845π0.913845\pi
374374 −1.17888e14 + 1.34453e14i −0.0430763 + 0.0491292i
375375 −3.02373e15 −1.08732
376376 8.12368e13 + 2.63954e13i 0.0287492 + 0.00934118i
377377 −1.47644e14 + 1.07270e14i −0.0514243 + 0.0373620i
378378 −6.75764e14 4.90972e14i −0.231656 0.168308i
379379 6.29413e14 + 1.93713e15i 0.212374 + 0.653619i 0.999330 + 0.0366097i 0.0116558π0.0116558\pi
−0.786956 + 0.617009i 0.788344π0.788344\pi
380380 −4.00174e14 + 1.30024e14i −0.132907 + 0.0431840i
381381 4.24898e15 5.84822e15i 1.38910 1.91194i
382382 −1.46767e15 2.02007e15i −0.472332 0.650109i
383383 −1.18596e15 + 3.65000e15i −0.375730 + 1.15638i 0.567254 + 0.823543i 0.308006π0.308006\pi
−0.942985 + 0.332836i 0.891994π0.891994\pi
384384 4.68079e14i 0.145993i
385385 3.30460e14 1.96649e14i 0.101474 0.0603847i
386386 −8.46104e14 −0.255800
387387 −7.90951e15 2.56996e15i −2.35442 0.764997i
388388 −1.78925e15 + 1.29996e15i −0.524421 + 0.381014i
389389 −9.33881e14 6.78504e14i −0.269522 0.195819i 0.444812 0.895624i 0.353270π-0.353270\pi
−0.714334 + 0.699805i 0.753270π0.753270\pi
390390 2.28917e13 + 7.04533e13i 0.00650563 + 0.0200223i
391391 2.12364e14 6.90013e13i 0.0594321 0.0193106i
392392 6.68557e14 9.20189e14i 0.184256 0.253607i
393393 1.11620e15 + 1.53631e15i 0.302960 + 0.416989i
394394 8.58035e14 2.64076e15i 0.229365 0.705914i
395395 7.76910e14i 0.204545i
396396 3.04562e14 3.31824e15i 0.0789777 0.860473i
397397 −1.23343e15 −0.315045 −0.157523 0.987515i 0.550351π-0.550351\pi
−0.157523 + 0.987515i 0.550351π0.550351\pi
398398 2.44752e15 + 7.95247e14i 0.615783 + 0.200080i
399399 −1.44668e15 + 1.05108e15i −0.358539 + 0.260494i
400400 7.26535e14 + 5.27858e14i 0.177377 + 0.128872i
401401 −1.24434e15 3.82970e15i −0.299278 0.921082i −0.981751 0.190171i 0.939096π-0.939096\pi
0.682473 0.730911i 0.260904π-0.260904\pi
402402 9.14256e15 2.97060e15i 2.16626 0.703862i
403403 −1.94262e14 + 2.67378e14i −0.0453479 + 0.0624160i
404404 −9.80471e14 1.34950e15i −0.225500 0.310374i
405405 1.23595e14 3.80386e14i 0.0280073 0.0861975i
406406 1.31871e15i 0.294437i
407407 −5.02916e15 + 1.13852e15i −1.10644 + 0.250481i
408408 2.48910e14 0.0539613
409409 5.40230e15 + 1.75531e15i 1.15409 + 0.374986i 0.822682 0.568502i 0.192477π-0.192477\pi
0.331406 + 0.943488i 0.392477π0.392477\pi
410410 4.32711e14 3.14383e14i 0.0910950 0.0661844i
411411 −5.31680e15 3.86288e15i −1.10306 0.801420i
412412 −2.20067e14 6.77297e14i −0.0449958 0.138483i
413413 1.33463e15 4.33647e14i 0.268943 0.0873849i
414414 −2.44579e15 + 3.36633e15i −0.485754 + 0.668583i
415415 1.45971e15 + 2.00912e15i 0.285744 + 0.393293i
416416 1.45512e13 4.47839e13i 0.00280762 0.00864096i
417417 3.10816e15i 0.591136i
418418 −2.76181e15 1.18623e15i −0.517769 0.222389i
419419 1.99139e15 0.368021 0.184010 0.982924i 0.441092π-0.441092\pi
0.184010 + 0.982924i 0.441092π0.441092\pi
420420 −5.09086e14 1.65412e14i −0.0927460 0.0301350i
421421 7.15656e15 5.19955e15i 1.28532 0.933841i 0.285622 0.958342i 0.407800π-0.407800\pi
0.999700 + 0.0245012i 0.00779975π0.00779975\pi
422422 −3.49420e15 2.53869e15i −0.618690 0.449505i
423423 2.61564e14 + 8.05010e14i 0.0456599 + 0.140527i
424424 −7.54837e14 + 2.45261e14i −0.129915 + 0.0422118i
425425 2.80700e14 3.86350e14i 0.0476330 0.0655612i
426426 5.09242e15 + 7.00911e15i 0.852052 + 1.17275i
427427 −8.73529e14 + 2.68845e15i −0.144115 + 0.443541i
428428 2.66294e15i 0.433210i
429429 −2.08844e14 + 4.86236e14i −0.0335027 + 0.0780015i
430430 −2.24564e15 −0.355246
431431 −8.48409e15 2.75665e15i −1.32355 0.430049i −0.439840 0.898076i 0.644965π-0.644965\pi
−0.883714 + 0.468027i 0.844965π0.844965\pi
432432 −1.58116e15 + 1.14878e15i −0.243261 + 0.176739i
433433 7.71807e15 + 5.60751e15i 1.17107 + 0.850829i 0.991136 0.132850i 0.0424129π-0.0424129\pi
0.179930 + 0.983679i 0.442413π0.442413\pi
434434 −7.37973e14 2.27125e15i −0.110434 0.339880i
435435 4.61651e15 1.50000e15i 0.681363 0.221388i
436436 6.26064e14 8.61703e14i 0.0911380 0.125441i
437437 2.20621e15 + 3.03658e15i 0.316780 + 0.436010i
438438 −4.73094e15 + 1.45603e16i −0.670044 + 2.06218i
439439 2.81649e15i 0.393478i −0.980456 0.196739i 0.936965π-0.936965\pi
0.980456 0.196739i 0.0630352π-0.0630352\pi
440440 −1.98664e14 8.77553e14i −0.0273781 0.120936i
441441 1.12712e16 1.53228
442442 −2.38148e13 7.73788e12i −0.00319384 0.00103774i
443443 −5.92081e15 + 4.30172e15i −0.783355 + 0.569141i −0.905984 0.423312i 0.860867π-0.860867\pi
0.122629 + 0.992453i 0.460867π0.460867\pi
444444 5.80690e15 + 4.21896e15i 0.757960 + 0.550690i
445445 1.15464e15 + 3.55362e15i 0.148692 + 0.457626i
446446 −4.04386e15 + 1.31393e15i −0.513792 + 0.166941i
447447 −9.23603e15 + 1.27123e16i −1.15782 + 1.59360i
448448 1.99997e14 + 2.75273e14i 0.0247375 + 0.0340482i
449449 −1.92283e15 + 5.91788e15i −0.234673 + 0.722250i 0.762491 + 0.646999i 0.223976π0.223976\pi
−0.997165 + 0.0752518i 0.976024π0.976024\pi
450450 8.89913e15i 1.07170i
451451 3.80482e15 + 3.49222e14i 0.452142 + 0.0414995i
452452 −5.08245e14 −0.0595995
453453 −7.61675e15 2.47483e15i −0.881415 0.286389i
454454 −1.17283e15 + 8.52114e14i −0.133937 + 0.0973112i
455455 4.35651e13 + 3.16519e13i 0.00490988 + 0.00356723i
456456 1.29294e15 + 3.97926e15i 0.143810 + 0.442602i
457457 −7.17258e15 + 2.33051e15i −0.787369 + 0.255832i −0.674983 0.737833i 0.735849π-0.735849\pi
−0.112385 + 0.993665i 0.535849π0.535849\pi
458458 −3.09613e14 + 4.26146e14i −0.0335449 + 0.0461706i
459459 6.10886e14 + 8.40812e14i 0.0653257 + 0.0899131i
460460 −3.47199e14 + 1.06857e15i −0.0366464 + 0.112786i
461461 1.86103e16i 1.93887i −0.245358 0.969433i 0.578905π-0.578905\pi
0.245358 0.969433i 0.421095π-0.421095\pi
462462 −1.95544e15 3.28604e15i −0.201091 0.337925i
463463 1.69597e16 1.72160 0.860800 0.508943i 0.169964π-0.169964\pi
0.860800 + 0.508943i 0.169964π0.169964\pi
464464 −2.93450e15 9.53478e14i −0.294054 0.0955439i
465465 7.11172e15 5.16697e15i 0.703489 0.511114i
466466 −2.46395e15 1.79017e15i −0.240612 0.174815i
467467 −7.91408e14 2.43570e15i −0.0762955 0.234813i 0.905634 0.424060i 0.139395π-0.139395\pi
−0.981930 + 0.189247i 0.939395π0.939395\pi
468468 4.43783e14 1.44194e14i 0.0422373 0.0137237i
469469 4.10739e15 5.65334e15i 0.385948 0.531213i
470470 1.34342e14 + 1.84905e14i 0.0124630 + 0.0171539i
471471 8.85767e15 2.72611e16i 0.811324 2.49700i
472472 3.28348e15i 0.296949i
473473 −1.20620e16 1.05759e16i −1.07709 0.944390i
474474 7.72546e15 0.681168
475475 7.63453e15 + 2.48061e15i 0.664692 + 0.215971i
476476 1.46382e14 1.06353e14i 0.0125848 0.00914337i
477477 −6.36288e15 4.62290e15i −0.540186 0.392468i
478478 −4.80531e15 1.47892e16i −0.402860 1.23988i
479479 −1.96054e16 + 6.37020e15i −1.62317 + 0.527399i −0.972687 0.232122i 0.925433π-0.925433\pi
−0.650482 + 0.759522i 0.725433π0.725433\pi
480480 −7.36178e14 + 1.01326e15i −0.0601915 + 0.0828465i
481481 −4.24426e14 5.84172e14i −0.0342714 0.0471705i
482482 4.82829e14 1.48600e15i 0.0385045 0.118505i
483483 4.77497e15i 0.376086i
484484 3.06578e15 5.64922e15i 0.238490 0.439457i
485485 −5.91777e15 −0.454682
486486 6.87570e15 + 2.23405e15i 0.521794 + 0.169541i
487487 −1.43615e15 + 1.04343e15i −0.107653 + 0.0782146i −0.640309 0.768117i 0.721194π-0.721194\pi
0.532656 + 0.846332i 0.321194π0.321194\pi
488488 5.35097e15 + 3.88771e15i 0.396199 + 0.287855i
489489 6.16407e15 + 1.89711e16i 0.450832 + 1.38752i
490490 2.89448e15 9.40475e14i 0.209120 0.0679471i
491491 −7.56260e15 + 1.04090e16i −0.539737 + 0.742884i −0.988575 0.150729i 0.951838π-0.951838\pi
0.448838 + 0.893613i 0.351838π0.351838\pi
492492 −3.12617e15 4.30280e15i −0.220405 0.303362i
493493 −5.07031e14 + 1.56048e15i −0.0353145 + 0.108687i
494494 4.20913e14i 0.0289622i
495495 5.87811e15 6.70408e15i 0.399583 0.455731i
496496 −5.58776e15 −0.375273
497497 5.98960e15 + 1.94614e15i 0.397429 + 0.129133i
498498 1.99783e16 1.45151e16i 1.30973 0.951577i
499499 9.87065e15 + 7.17144e15i 0.639355 + 0.464519i 0.859629 0.510919i 0.170695π-0.170695\pi
−0.220273 + 0.975438i 0.570695π0.570695\pi
500500 1.58925e15 + 4.89120e15i 0.101712 + 0.313037i
501501 −3.62153e16 + 1.17671e16i −2.29016 + 0.744119i
502502 2.69223e15 3.70553e15i 0.168225 0.231541i
503503 −1.10218e16 1.51702e16i −0.680524 0.936661i 0.319416 0.947615i 0.396513π-0.396513\pi
−0.999940 + 0.0109539i 0.996513π0.996513\pi
504504 −1.04193e15 + 3.20672e15i −0.0635702 + 0.195649i
505505 4.46335e15i 0.269100i
506506 −6.89738e15 + 4.10446e15i −0.410943 + 0.244542i
507507 2.79792e16 1.64736
508508 −1.16933e16 3.79939e15i −0.680387 0.221071i
509509 4.35537e15 3.16436e15i 0.250449 0.181962i −0.455477 0.890248i 0.650531π-0.650531\pi
0.705926 + 0.708286i 0.250531π0.250531\pi
510510 5.38823e14 + 3.91478e14i 0.0306214 + 0.0222477i
511511 3.43902e15 + 1.05842e16i 0.193156 + 0.594474i
512512 7.57166e14 2.46018e14i 0.0420312 0.0136568i
513513 −1.02686e16 + 1.41336e16i −0.563389 + 0.775439i
514514 −1.23448e16 1.69912e16i −0.669430 0.921392i
515515 5.88844e14 1.81228e15i 0.0315614 0.0971362i
516516 2.23302e16i 1.18303i
517517 −1.49229e14 + 1.62587e15i −0.00781466 + 0.0851418i
518518 5.21762e15 0.270081
519519 1.98320e16 + 6.44381e15i 1.01476 + 0.329715i
520520 1.01934e14 7.40593e13i 0.00515583 0.00374593i
521521 −1.99717e16 1.45103e16i −0.998592 0.725519i −0.0368058 0.999322i 0.511718π-0.511718\pi
−0.961786 + 0.273803i 0.911718π0.911718\pi
522522 −9.44843e15 2.90793e16i −0.467021 1.43734i
523523 2.98859e15 9.71051e14i 0.146035 0.0474495i −0.235088 0.971974i 0.575538π-0.575538\pi
0.381122 + 0.924525i 0.375538π0.375538\pi
524524 1.89848e15 2.61304e15i 0.0917105 0.126229i
525525 6.00257e15 + 8.26182e15i 0.286669 + 0.394566i
526526 −7.65765e15 + 2.35678e16i −0.361561 + 1.11277i
527527 2.97141e15i 0.138707i
528528 −8.72624e15 + 1.97548e15i −0.402739 + 0.0911737i
529529 −1.18920e16 −0.542651
530530 −2.01975e15 6.56258e14i −0.0911262 0.0296087i
531531 2.63233e16 1.91250e16i 1.17428 0.853168i
532532 2.46059e15 + 1.78773e15i 0.108535 + 0.0788553i
533533 1.65338e14 + 5.08858e14i 0.00721124 + 0.0221939i
534534 3.53366e16 1.14816e16i 1.52397 0.495169i
535535 −4.18818e15 + 5.76453e15i −0.178609 + 0.245834i
536536 −9.61050e15 1.32277e16i −0.405282 0.557823i
537537 4.82222e15 1.48413e16i 0.201095 0.618907i
538538 6.10862e15i 0.251912i
539539 1.99764e16 + 8.58011e15i 0.814674 + 0.349913i
540540 −5.22953e15 −0.210911
541541 3.26755e16 + 1.06169e16i 1.30328 + 0.423463i 0.876723 0.480996i 0.159725π-0.159725\pi
0.426561 + 0.904459i 0.359725π0.359725\pi
542542 9.97402e15 7.24655e15i 0.393436 0.285848i
543543 −4.99479e16 3.62893e16i −1.94858 1.41573i
544544 −1.30825e14 4.02638e14i −0.00504775 0.0155354i
545545 2.71051e15 8.80699e14i 0.103436 0.0336084i
546546 3.14741e14 4.33204e14i 0.0118795 0.0163507i
547547 −5.45185e15 7.50383e15i −0.203526 0.280129i 0.695037 0.718974i 0.255388π-0.255388\pi
−0.898563 + 0.438844i 0.855388π0.855388\pi
548548 −3.45415e15 + 1.06308e16i −0.127543 + 0.392538i
549549 6.55426e16i 2.39381i
550550 −6.77442e15 + 1.57723e16i −0.244735 + 0.569796i
551551 −2.75807e16 −0.985589
552552 1.06257e16 + 3.45249e15i 0.375597 + 0.122039i
553553 4.54327e15 3.30088e15i 0.158861 0.115419i
554554 2.34539e16 + 1.70402e16i 0.811253 + 0.589410i
555555 5.93491e15 + 1.82658e16i 0.203075 + 0.625000i
556556 −5.02778e15 + 1.63362e15i −0.170187 + 0.0552972i
557557 −1.44683e16 + 1.99138e16i −0.484490 + 0.666843i −0.979360 0.202124i 0.935216π-0.935216\pi
0.494870 + 0.868967i 0.335216π0.335216\pi
558558 −3.25466e16 4.47965e16i −1.07820 1.48402i
559559 6.94181e14 2.13647e15i 0.0227511 0.0700206i
560560 9.10438e14i 0.0295204i
561561 1.05050e15 + 4.64035e15i 0.0336993 + 0.148859i
562562 −1.63705e16 −0.519570
563563 3.42050e16 + 1.11139e16i 1.07409 + 0.348991i 0.792077 0.610421i 0.209000π-0.209000\pi
0.282008 + 0.959412i 0.409000π0.409000\pi
564564 1.83867e15 1.33587e15i 0.0571253 0.0415039i
565565 −1.10021e15 7.99351e14i −0.0338209 0.0245723i
566566 6.03869e15 + 1.85852e16i 0.183673 + 0.565286i
567567 −2.74957e15 + 8.93389e14i −0.0827497 + 0.0268870i
568568 8.66144e15 1.19214e16i 0.257929 0.355009i
569569 1.44488e16 + 1.98870e16i 0.425752 + 0.585997i 0.966972 0.254884i 0.0820372π-0.0820372\pi
−0.541220 + 0.840881i 0.682037π0.682037\pi
570570 −3.45958e15 + 1.06475e16i −0.100873 + 0.310455i
571571 3.11031e16i 0.897403i 0.893682 + 0.448701i 0.148113π0.148113\pi
−0.893682 + 0.448701i 0.851887π0.851887\pi
572572 8.96304e14 + 8.22664e13i 0.0255905 + 0.00234880i
573573 −6.64366e16 −1.87707
574574 −3.67694e15 1.19471e15i −0.102805 0.0334034i
575575 1.73415e16 1.25994e16i 0.479822 0.348611i
576576 6.38251e15 + 4.63716e15i 0.174766 + 0.126975i
577577 1.28427e16 + 3.95257e16i 0.348018 + 1.07109i 0.959948 + 0.280177i 0.0903930π0.0903930\pi
−0.611931 + 0.790911i 0.709607π0.709607\pi
578578 2.48619e16 8.07812e15i 0.666756 0.216642i
579579 −1.32325e16 + 1.82130e16i −0.351213 + 0.483403i
580580 −4.85280e15 6.67931e15i −0.127475 0.175454i
581581 5.54715e15 1.70724e16i 0.144216 0.443851i
582582 5.88453e16i 1.51417i
583583 −7.75805e15 1.30371e16i −0.197579 0.332024i
584584 2.60394e16 0.656378
585585 1.18745e15 + 3.85827e14i 0.0296265 + 0.00962625i
586586 −1.77245e15 + 1.28776e15i −0.0437711 + 0.0318016i
587587 1.75546e16 + 1.27542e16i 0.429105 + 0.311763i 0.781291 0.624167i 0.214562π-0.214562\pi
−0.352186 + 0.935930i 0.614562π0.614562\pi
588588 −9.35192e15 2.87823e16i −0.226275 0.696403i
589589 −4.75030e16 + 1.54347e16i −1.13770 + 0.369662i
590590 5.16414e15 7.10783e15i 0.122429 0.168510i
591591 −4.34250e16 5.97694e16i −1.01910 1.40267i
592592 3.77255e15 1.16107e16i 0.0876404 0.269729i
593593 4.46367e16i 1.02651i −0.858236 0.513256i 0.828439π-0.828439\pi
0.858236 0.513256i 0.171561π-0.171561\pi
594594 −2.80894e16 2.46287e16i −0.639475 0.560689i
595595 4.84144e14 0.0109112
596596 2.54179e16 + 8.25876e15i 0.567102 + 0.184263i
597597 5.53957e16 4.02473e16i 1.22357 0.888978i
598598 −9.09294e14 6.60641e14i −0.0198837 0.0144464i
599599 9.91535e15 + 3.05163e16i 0.214658 + 0.660649i 0.999178 + 0.0405454i 0.0129095π0.0129095\pi
−0.784520 + 0.620104i 0.787090π0.787090\pi
600600 2.27250e16 7.38380e15i 0.487076 0.158261i
601601 3.70136e16 5.09449e16i 0.785443 1.08107i −0.209218 0.977869i 0.567092π-0.567092\pi
0.994661 0.103200i 0.0329082π-0.0329082\pi
602602 9.54110e15 + 1.31322e16i 0.200456 + 0.275904i
603603 5.00678e16 1.54093e17i 1.04149 3.20537i
604604 1.36216e16i 0.280548i
605605 1.55215e16 7.40726e15i 0.316520 0.151052i
606606 −4.43828e16 −0.896147
607607 −1.50430e16 4.88778e15i −0.300749 0.0977192i 0.154756 0.987953i 0.450541π-0.450541\pi
−0.455504 + 0.890234i 0.650541π0.650541\pi
608608 5.75731e15 4.18293e15i 0.113972 0.0828055i
609609 −2.83861e16 2.06237e16i −0.556419 0.404262i
610610 5.46893e15 + 1.68316e16i 0.106151 + 0.326699i
611611 −2.17445e14 + 7.06520e13i −0.00417928 + 0.00135793i
612612 2.46591e15 3.39403e15i 0.0469319 0.0645962i
613613 −2.86752e16 3.94680e16i −0.540435 0.743844i 0.448241 0.893913i 0.352051π-0.352051\pi
−0.988676 + 0.150068i 0.952051π0.952051\pi
614614 −1.77586e16 + 5.46554e16i −0.331435 + 1.02005i
615615 1.42311e16i 0.263020i
616616 −4.28775e15 + 4.89024e15i −0.0784774 + 0.0895048i
617617 6.47599e16 1.17380 0.586902 0.809658i 0.300347π-0.300347\pi
0.586902 + 0.809658i 0.300347π0.300347\pi
618618 −1.80210e16 5.85536e15i −0.323480 0.105105i
619619 2.29737e15 1.66914e15i 0.0408401 0.0296721i −0.567178 0.823595i 0.691965π-0.691965\pi
0.608018 + 0.793923i 0.291965π0.291965\pi
620620 −1.20960e16 8.78824e15i −0.212956 0.154722i
621621 1.44155e16 + 4.43664e16i 0.251351 + 0.773579i
622622 −3.76050e16 + 1.22186e16i −0.649386 + 0.210998i
623623 1.58754e16 2.18506e16i 0.271516 0.373710i
624624 −7.36433e14 1.01361e15i −0.0124746 0.0171698i
625625 1.19009e16 3.66271e16i 0.199664 0.614501i
626626 5.32061e16i 0.884128i
627627 −6.87273e16 + 4.08979e16i −1.13116 + 0.673126i
628628 −4.87532e16 −0.794777
629629 −6.17423e15 2.00613e15i −0.0996963 0.0323933i
630630 −7.29889e15 + 5.30296e15i −0.116738 + 0.0848154i
631631 −2.50610e16 1.82079e16i −0.397028 0.288458i 0.371301 0.928513i 0.378912π-0.378912\pi
−0.768330 + 0.640055i 0.778912π0.778912\pi
632632 −4.06044e15 1.24967e16i −0.0637192 0.196108i
633633 −1.09294e17 + 3.55117e16i −1.69892 + 0.552013i
634634 −1.50689e16 + 2.07406e16i −0.232031 + 0.319364i
635635 −1.93373e16 2.66155e16i −0.294954 0.405969i
636636 −6.52572e15 + 2.00841e16i −0.0986020 + 0.303466i
637637 3.04449e15i 0.0455700i
638638 5.39058e15 5.87311e16i 0.0799302 0.870851i
639639 1.46023e17 2.14494
640640 2.02599e15 + 6.58283e14i 0.0294820 + 0.00957927i
641641 2.06063e16 1.49713e16i 0.297065 0.215830i −0.429262 0.903180i 0.641226π-0.641226\pi
0.726326 + 0.687350i 0.241226π0.241226\pi
642642 5.73215e16 + 4.16465e16i 0.818667 + 0.594797i
643643 1.57101e16 + 4.83508e16i 0.222287 + 0.684129i 0.998556 + 0.0537268i 0.0171100π0.0171100\pi
−0.776269 + 0.630402i 0.782890π0.782890\pi
644644 7.72400e15 2.50968e15i 0.108275 0.0351806i
645645 −3.51202e16 + 4.83388e16i −0.487752 + 0.671333i
646646 −2.22436e15 3.06157e15i −0.0306062 0.0421258i
647647 −1.21526e16 + 3.74019e16i −0.165670 + 0.509880i −0.999085 0.0427677i 0.986382π-0.986382\pi
0.833415 + 0.552648i 0.186382π0.186382\pi
648648 6.76454e15i 0.0913667i
649649 6.12128e16 1.38576e16i 0.819170 0.185447i
650650 −2.40378e15 −0.0318724
651651 −6.04315e16 1.96354e16i −0.793922 0.257961i
652652 2.74479e16 1.99421e16i 0.357292 0.259588i
653653 −8.24907e16 5.99330e16i −1.06396 0.773014i −0.0891447 0.996019i 0.528413π-0.528413\pi
−0.974817 + 0.223005i 0.928413π0.928413\pi
654654 −8.75752e15 2.69529e16i −0.111922 0.344460i
655655 8.21939e15 2.67064e15i 0.104086 0.0338196i
656656 −5.31714e15 + 7.31842e15i −0.0667199 + 0.0918321i
657657 1.51670e17 + 2.08756e17i 1.88585 + 2.59565i
658658 5.10522e14 1.57122e15i 0.00629012 0.0193590i
659659 1.15685e17i 1.41242i −0.708001 0.706211i 0.750403π-0.750403\pi
0.708001 0.706211i 0.249597π-0.249597\pi
660660 −2.19969e16 9.44795e15i −0.266132 0.114307i
661661 −7.83616e15 −0.0939495 −0.0469747 0.998896i 0.514958π-0.514958\pi
−0.0469747 + 0.998896i 0.514958π0.514958\pi
662662 6.40575e16 + 2.08135e16i 0.761066 + 0.247285i
663663 −5.39010e14 + 3.91613e14i −0.00634622 + 0.00461080i
664664 −3.39801e16 2.46880e16i −0.396475 0.288056i
665665 2.51484e15 + 7.73987e15i 0.0290790 + 0.0894961i
666666 1.15056e17 3.73838e16i 1.31845 0.428389i
667667 −4.32890e16 + 5.95823e16i −0.491613 + 0.676647i
668668 3.80689e16 + 5.23974e16i 0.428462 + 0.589727i
669669 −3.49600e16 + 1.07596e17i −0.389955 + 1.20016i
670670 4.37495e16i 0.483642i
671671 −4.98940e16 + 1.16164e17i −0.546654 + 1.27273i
672672 9.05324e15 0.0983079
673673 −7.26572e16 2.36078e16i −0.781967 0.254076i −0.109287 0.994010i 0.534857π-0.534857\pi
−0.672680 + 0.739934i 0.734857π0.734857\pi
674674 −4.20036e16 + 3.05174e16i −0.448051 + 0.325528i
675675 8.07149e16 + 5.86428e16i 0.853358 + 0.620001i
676676 −1.47056e16 4.52593e16i −0.154100 0.474272i
677677 −1.38363e16 + 4.49570e15i −0.143711 + 0.0466944i −0.379989 0.924991i 0.624072π-0.624072\pi
0.236278 + 0.971685i 0.424072π0.424072\pi
678678 −7.94861e15 + 1.09403e16i −0.0818301 + 0.112629i
679679 2.51430e16 + 3.46063e16i 0.256565 + 0.353132i
680680 3.50055e14 1.07736e15i 0.00354065 0.0108970i
681681 3.85725e16i 0.386719i
682682 −2.35826e16 1.04171e17i −0.234361 1.03524i
683683 1.56197e17 1.53868 0.769339 0.638841i 0.220586π-0.220586\pi
0.769339 + 0.638841i 0.220586π0.220586\pi
684684 6.70682e16 + 2.17918e16i 0.654908 + 0.212793i
685685 −2.41970e16 + 1.75802e16i −0.234217 + 0.170169i
686686 −3.78707e16 2.75147e16i −0.363378 0.264010i
687687 4.33094e15 + 1.33293e16i 0.0411947 + 0.126784i
688688 3.61215e16 1.17366e16i 0.340592 0.110665i
689689 1.24871e15 1.71870e15i 0.0116720 0.0160652i
690690 1.75717e16 + 2.41854e16i 0.162824 + 0.224108i
691691 −3.37390e16 + 1.03838e17i −0.309930 + 0.953866i 0.667862 + 0.744286i 0.267210π0.267210\pi
−0.977791 + 0.209580i 0.932790π0.932790\pi
692692 3.54672e16i 0.322991i
693693 −6.41791e16 5.89062e15i −0.579421 0.0531816i
694694 8.87424e16 0.794281
695695 −1.34531e16 4.37117e15i −0.119375 0.0387872i
696696 −6.64179e16 + 4.82554e16i −0.584291 + 0.424513i
697697 3.89172e15 + 2.82750e15i 0.0339426 + 0.0246607i
698698 −2.54800e16 7.84193e16i −0.220327 0.678095i
699699 −7.70690e16 + 2.50413e16i −0.660719 + 0.214681i
700700 1.02095e16 1.40521e16i 0.0867790 0.119441i
701701 −2.19654e16 3.02328e16i −0.185111 0.254783i 0.706369 0.707844i 0.250332π-0.250332\pi
−0.891480 + 0.453061i 0.850332π0.850332\pi
702702 1.61657e15 4.97530e15i 0.0135074 0.0415716i
703703 1.09126e17i 0.904060i
704704 7.78199e15 + 1.30773e16i 0.0639226 + 0.107419i
705705 6.08122e15 0.0495286
706706 2.23619e16 + 7.26583e15i 0.180585 + 0.0586755i
707707 −2.61011e16 + 1.89636e16i −0.208998 + 0.151846i
708708 −7.06790e16 5.13513e16i −0.561166 0.407711i
709709 −4.34990e16 1.33876e17i −0.342454 1.05396i −0.962933 0.269741i 0.913062π-0.913062\pi
0.620479 0.784223i 0.286938π-0.286938\pi
710710 3.74993e16 1.21843e16i 0.292734 0.0951149i
711711 7.65346e16 1.05341e17i 0.592435 0.815416i
712712 −3.71452e16 5.11260e16i −0.285117 0.392430i
713713 −4.12146e16 + 1.26846e17i −0.313700 + 0.965468i
714714 4.81425e15i 0.0363362i
715715 1.81087e15 + 1.58776e15i 0.0135535 + 0.0118836i
716716 −2.65418e16 −0.196994
717717 −3.93500e17 1.27856e17i −2.89621 0.941035i
718718 −1.21074e17 + 8.79656e16i −0.883701 + 0.642046i
719719 1.47267e17 + 1.06996e17i 1.06594 + 0.774452i 0.975178 0.221421i 0.0710695π-0.0710695\pi
0.0907628 + 0.995873i 0.471069π0.471069\pi
720720 6.52321e15 + 2.00764e16i 0.0468238 + 0.144109i
721721 −1.30998e16 + 4.25638e15i −0.0932508 + 0.0302990i
722722 −2.14843e16 + 2.95706e16i −0.151669 + 0.208755i
723723 −2.44359e16 3.36332e16i −0.171080 0.235471i
724724 −3.24495e16 + 9.98692e16i −0.225308 + 0.693426i
725725 1.57510e17i 1.08462i
726726 −7.36566e16 1.54343e17i −0.503028 1.05406i
727727 1.55067e17 1.05030 0.525148 0.851011i 0.324010π-0.324010\pi
0.525148 + 0.851011i 0.324010π0.324010\pi
728728 −8.66178e14 2.81438e14i −0.00581861 0.00189058i
729729 1.87001e17 1.35864e17i 1.24589 0.905189i
730730 5.63682e16 + 4.09539e16i 0.372475 + 0.270619i
731731 −6.24117e15 1.92083e16i −0.0409036 0.125888i
732732 1.67371e17 5.43821e16i 1.08796 0.353500i
733733 1.53237e17 2.10912e17i 0.987958 1.35981i 0.0555283 0.998457i 0.482316π-0.482316\pi
0.932430 0.361351i 0.117684π-0.117684\pi
734734 −6.60506e16 9.09108e16i −0.422377 0.581352i
735735 2.50234e16 7.70141e16i 0.158717 0.488479i
736736 1.90027e16i 0.119550i
737737 2.06040e17 2.34992e17i 1.28572 1.46638i
738738 −8.96414e16 −0.554844
739739 4.72986e16 + 1.53682e16i 0.290390 + 0.0943534i 0.450590 0.892731i 0.351214π-0.351214\pi
−0.160200 + 0.987085i 0.551214π0.551214\pi
740740 2.64275e16 1.92007e16i 0.160940 0.116930i
741741 −9.06044e15 6.58279e15i −0.0547318 0.0397650i
742742 4.74367e15 + 1.45995e16i 0.0284244 + 0.0874813i
743743 −3.81547e16 + 1.23972e16i −0.226785 + 0.0736870i −0.420205 0.907429i 0.638042π-0.638042\pi
0.193420 + 0.981116i 0.438042π0.438042\pi
744744 −8.73887e16 + 1.20280e17i −0.515250 + 0.709181i
745745 4.20336e16 + 5.78543e16i 0.245844 + 0.338375i
746746 2.01394e16 6.19828e16i 0.116846 0.359615i
747747 4.16213e17i 2.39548i
748748 6.95412e15 4.13823e15i 0.0397039 0.0236268i
749749 5.15046e16 0.291713
750750 1.30141e17 + 4.22854e16i 0.731218 + 0.237587i
751751 −2.35866e17 + 1.71366e17i −1.31469 + 0.955182i −0.314713 + 0.949187i 0.601908π0.601908\pi
−0.999982 + 0.00599447i 0.998092π0.998092\pi
752752 −3.12730e15 2.27211e15i −0.0172927 0.0125639i
753753 −3.76595e16 1.15904e17i −0.206588 0.635812i
754754 7.85472e15 2.55215e15i 0.0427467 0.0138892i
755755 −2.14236e16 + 2.94871e16i −0.115668 + 0.159203i
756756 2.22188e16 + 3.05816e16i 0.119012 + 0.163806i
757757 −2.33111e16 + 7.17441e16i −0.123876 + 0.381251i −0.993695 0.112121i 0.964236π-0.964236\pi
0.869819 + 0.493371i 0.164236π0.164236\pi
758758 9.21761e16i 0.485963i
759759 −1.95190e16 + 2.12662e17i −0.102095 + 1.11234i
760760 1.90418e16 0.0988156
761761 1.63673e17 + 5.31807e16i 0.842695 + 0.273808i 0.698383 0.715724i 0.253903π-0.253903\pi
0.144312 + 0.989532i 0.453903π0.453903\pi
762762 −2.64660e17 + 1.92287e17i −1.35194 + 0.982245i
763763 −1.66664e16 1.21089e16i −0.0844687 0.0613701i
764764 3.49185e16 + 1.07468e17i 0.175588 + 0.540406i
765765 1.06760e16 3.46885e15i 0.0532649 0.0173068i
766766 1.02087e17 1.40511e17i 0.505356 0.695563i
767767 5.16593e15 + 7.11029e15i 0.0253733 + 0.0349233i
768768 6.54585e15 2.01461e16i 0.0319006 0.0981799i
769769 1.03619e17i 0.501052i 0.968110 + 0.250526i 0.0806036π0.0806036\pi
−0.968110 + 0.250526i 0.919396π0.919396\pi
770770 −1.69730e16 + 3.84242e15i −0.0814356 + 0.0184357i
771771 −5.58810e17 −2.66035
772772 3.64162e16 + 1.18324e16i 0.172025 + 0.0558943i
773773 −1.25040e17 + 9.08467e16i −0.586100 + 0.425826i −0.840918 0.541163i 0.817984π-0.817984\pi
0.254818 + 0.966989i 0.417984π0.417984\pi
774774 3.04485e17 + 2.21221e17i 1.41619 + 1.02892i
775775 8.81453e16 + 2.71283e17i 0.406807 + 1.25202i
776776 9.51884e16 3.09286e16i 0.435927 0.141641i
777777 8.16001e16 1.12313e17i 0.370821 0.510391i
778778 3.07056e16 + 4.22626e16i 0.138465 + 0.190581i
779779 −2.49873e16 + 7.69030e16i −0.111814 + 0.344127i
780780 3.35243e15i 0.0148865i
781781 2.58802e17 + 1.11159e17i 1.14041 + 0.489822i
782782 −1.01051e16 −0.0441875
783783 −3.26011e17 1.05927e17i −1.41469 0.459661i
784784 −4.16430e16 + 3.02554e16i −0.179327 + 0.130289i
785785 −1.05537e17 7.66774e16i −0.451012 0.327679i
786786 −2.65564e16 8.17322e16i −0.112625 0.346624i
787787 −1.76251e17 + 5.72674e16i −0.741794 + 0.241023i −0.655446 0.755242i 0.727519π-0.727519\pi
−0.0863473 + 0.996265i 0.527519π0.527519\pi
788788 −7.38595e16 + 1.01659e17i −0.308496 + 0.424608i
789789 3.87553e17 + 5.33421e17i 1.60646 + 2.21110i
790790 1.08647e16 3.34381e16i 0.0446947 0.137556i
791791 9.83012e15i 0.0401328i
792792 −5.95123e16 + 1.38558e17i −0.241133 + 0.561409i
793793 −1.77040e16 −0.0711920
794794 5.30869e16 + 1.72490e16i 0.211867 + 0.0688399i
795795 −4.57140e16 + 3.32131e16i −0.181070 + 0.131555i
796796 −9.42198e16 6.84547e16i −0.370394 0.269107i
797797 −7.55037e16 2.32377e17i −0.294590 0.906656i −0.983359 0.181674i 0.941848π-0.941848\pi
0.688768 0.724981i 0.258152π-0.258152\pi
798798 7.69640e16 2.50071e16i 0.298037 0.0968381i
799799 −1.20824e15 + 1.66300e15i −0.00464380 + 0.00639164i
800800 −2.38881e16 3.28792e16i −0.0911260 0.125424i
801801 1.93515e17 5.95579e17i 0.732691 2.25499i
802802 1.82231e17i 0.684821i
803803 1.09897e17 + 4.85445e17i 0.409914 + 1.81070i
804804 −4.35037e17 −1.61061
805805 2.06675e16 + 6.71528e15i 0.0759473 + 0.0246768i
806806 1.21002e16 8.79128e15i 0.0441348 0.0320658i
807807 1.31492e17 + 9.55346e16i 0.476056 + 0.345875i
808808 2.33272e16 + 7.17938e16i 0.0838292 + 0.258000i
809809 2.42349e17 7.87440e16i 0.864471 0.280884i 0.156976 0.987602i 0.449825π-0.449825\pi
0.707495 + 0.706719i 0.249825π0.249825\pi
810810 −1.06390e16 + 1.46434e16i −0.0376697 + 0.0518479i
811811 −2.92446e17 4.02518e17i −1.02783 1.41469i −0.906565 0.422065i 0.861305π-0.861305\pi
−0.121264 0.992620i 0.538695π-0.538695\pi
812812 −1.84415e16 + 5.67571e16i −0.0643369 + 0.198009i
813813 3.28029e17i 1.13597i
814814 2.32376e17 + 2.13284e16i 0.798814 + 0.0733184i
815815 9.07814e16 0.309778
816816 −1.07131e16 3.48089e15i −0.0362889 0.0117910i
817817 2.74659e17 1.99551e17i 0.923552 0.671000i
818818 −2.07967e17 1.51097e17i −0.694185 0.504355i
819819 −2.78890e15 8.58334e15i −0.00924121 0.0284415i
820820 −2.30203e16 + 7.47976e15i −0.0757231 + 0.0246039i
821821 1.01678e17 1.39947e17i 0.332022 0.456989i −0.610068 0.792349i 0.708858π-0.708858\pi
0.942090 + 0.335360i 0.108858π0.108858\pi
822822 1.74814e17 + 2.40611e17i 0.566690 + 0.779982i
823823 3.62093e16 1.11441e17i 0.116525 0.358628i −0.875737 0.482789i 0.839624π-0.839624\pi
0.992262 + 0.124161i 0.0396238π0.0396238\pi
824824 3.22283e16i 0.102961i
825825 2.33563e17 + 3.92492e17i 0.740764 + 1.24482i
826826 −6.35067e16 −0.199958
827827 −1.76869e17 5.74681e16i −0.552864 0.179636i 0.0192441 0.999815i 0.493874π-0.493874\pi
−0.572108 + 0.820179i 0.693874π0.693874\pi
828828 1.52343e17 1.10684e17i 0.472760 0.343480i
829829 −1.62988e17 1.18418e17i −0.502144 0.364829i 0.307692 0.951486i 0.400444π-0.400444\pi
−0.809835 + 0.586657i 0.800444π0.800444\pi
830830 −3.47292e16 1.06886e17i −0.106225 0.326927i
831831 7.33605e17 2.38363e17i 2.22770 0.723823i
832832 −1.25256e15 + 1.72400e15i −0.00377624 + 0.00519755i
833833 1.60889e16 + 2.21445e16i 0.0481568 + 0.0662821i
834834 −4.34662e16 + 1.33775e17i −0.129168 + 0.397538i
835835 1.73300e17i 0.511303i
836836 1.02279e17 + 8.96779e16i 0.299605 + 0.262693i
837837 −6.20776e17 −1.80544
838838 −8.57093e16 2.78486e16i −0.247493 0.0804155i
839839 −4.42586e17 + 3.21558e17i −1.26890 + 0.921907i −0.999158 0.0410263i 0.986937π-0.986937\pi
−0.269739 + 0.962934i 0.586937π0.586937\pi
840840 1.95978e16 + 1.42386e16i 0.0557868 + 0.0405315i
841841 −5.78972e16 1.78189e17i −0.163637 0.503623i
842842 −3.80731e17 + 1.23707e17i −1.06843 + 0.347154i
843843 −2.56023e17 + 3.52386e17i −0.713369 + 0.981868i
844844 1.14888e17 + 1.58129e17i 0.317848 + 0.437480i
845845 3.93486e16 1.21102e17i 0.108091 0.332669i
846846 3.83054e16i 0.104481i
847847 −1.09263e17 5.92962e16i −0.295920 0.160593i
848848 3.59180e16 0.0965910
849849 4.94499e17 + 1.60673e17i 1.32044 + 0.429038i
850850 −1.74842e16 + 1.27030e16i −0.0463588 + 0.0336816i
851851 −2.35744e17 1.71278e17i −0.620674 0.450946i
852852 −1.21158e17 3.72886e17i −0.316749 0.974853i
853853 −5.55091e17 + 1.80360e17i −1.44102 + 0.468216i −0.922215 0.386677i 0.873623π-0.873623\pi
−0.518804 + 0.854893i 0.673623π0.673623\pi
854854 7.51932e16 1.03495e17i 0.193835 0.266791i
855855 1.10911e17 + 1.52656e17i 0.283908 + 0.390766i
856856 3.72399e16 1.14613e17i 0.0946598 0.291333i
857857 1.27318e17i 0.321369i −0.987006 0.160684i 0.948630π-0.948630\pi
0.987006 0.160684i 0.0513701π-0.0513701\pi
858858 1.57884e16 1.80069e16i 0.0395744 0.0451353i
859859 2.87699e17 0.716109 0.358055 0.933701i 0.383440π-0.383440\pi
0.358055 + 0.933701i 0.383440π0.383440\pi
860860 9.66520e16 + 3.14041e16i 0.238902 + 0.0776240i
861861 −8.32218e16 + 6.04641e16i −0.204276 + 0.148415i
862862 3.26604e17 + 2.37292e17i 0.796119 + 0.578415i
863863 8.14957e16 + 2.50818e17i 0.197274 + 0.607147i 0.999943 + 0.0107217i 0.00341290π0.00341290\pi
−0.802668 + 0.596426i 0.796587π0.796587\pi
864864 8.41179e16 2.73316e16i 0.202212 0.0657025i
865865 5.57815e16 7.67767e16i 0.133166 0.183287i
866866 −2.53767e17 3.49280e17i −0.601627 0.828069i
867867 2.14936e17 6.61505e17i 0.506051 1.55747i
868868 1.08074e17i 0.252700i
869869 2.15836e17 1.28439e17i 0.501193 0.298248i
870870 −2.19671e17 −0.506591
871871 4.16226e16 + 1.35240e16i 0.0953280 + 0.0309739i
872872 −3.89962e16 + 2.83324e16i −0.0887000 + 0.0644443i
873873 8.02387e17 + 5.82968e17i 1.81259 + 1.31692i
874874 −5.24898e16 1.61547e17i −0.117762 0.362435i
875875 9.46021e16 3.07381e16i 0.210791 0.0684902i
876876 4.07239e17 5.60516e17i 0.901207 1.24040i
877877 −6.67984e16 9.19401e16i −0.146814 0.202073i 0.729276 0.684220i 0.239857π-0.239857\pi
−0.876090 + 0.482147i 0.839857π0.839857\pi
878878 −3.93872e16 + 1.21221e17i −0.0859781 + 0.264613i
879879 5.82928e16i 0.126381i
880880 −3.72166e15 + 4.05480e16i −0.00801385 + 0.0873119i
881881 −7.71080e17 −1.64909 −0.824544 0.565798i 0.808568π-0.808568\pi
−0.824544 + 0.565798i 0.808568π0.808568\pi
882882 −4.85109e17 1.57622e17i −1.03045 0.334814i
883883 −5.62566e17 + 4.08728e17i −1.18689 + 0.862323i −0.992932 0.118688i 0.962131π-0.962131\pi
−0.193954 + 0.981011i 0.562131π0.562131\pi
884884 9.16774e14 + 6.66075e14i 0.00192109 + 0.00139576i
885885 −7.22372e16 2.22323e17i −0.150349 0.462727i
886886 3.14988e17 1.02346e17i 0.651167 0.211577i
887887 8.06316e15 1.10980e16i 0.0165563 0.0227878i −0.800659 0.599121i 0.795517π-0.795517\pi
0.817215 + 0.576333i 0.195517π0.195517\pi
888888 −1.90928e17 2.62790e17i −0.389397 0.535959i
889889 −7.34852e16 + 2.26164e17i −0.148864 + 0.458156i
890890 1.69095e17i 0.340243i
891891 −1.26109e17 + 2.85491e16i −0.252046 + 0.0570593i
892892 1.92422e17 0.382002
893893 −3.28620e16 1.06775e16i −0.0648016 0.0210553i
894894 5.75293e17 4.17975e17i 1.12684 0.818701i
895895 −5.74558e16 4.17441e16i −0.111788 0.0812188i
896896 −4.75831e15 1.46446e16i −0.00919612 0.0283027i
897897 −2.84415e16 + 9.24119e15i −0.0546006 + 0.0177408i
898898 1.65517e17 2.27815e17i 0.315635 0.434434i
899899 −5.76056e17 7.92874e17i −1.09121 1.50192i
900900 1.24450e17 3.83018e17i 0.234175 0.720716i
901901 1.91001e16i 0.0357016i
902902 −1.58875e17 6.82391e16i −0.294997 0.126705i
903903 4.31896e17 0.796622
904904 2.18748e16 + 7.10756e15i 0.0400806 + 0.0130230i
905905 −2.27315e17 + 1.65154e17i −0.413749 + 0.300606i
906906 2.93215e17 + 2.13033e17i 0.530172 + 0.385192i
907907 −1.50465e17 4.63084e17i −0.270266 0.831794i −0.990433 0.137993i 0.955935π-0.955935\pi
0.720167 0.693801i 0.244065π-0.244065\pi
908908 6.23951e16 2.02734e16i 0.111336 0.0361752i
909909 −4.39692e17 + 6.05184e17i −0.779409 + 1.07276i
910910 −1.43240e15 1.97153e15i −0.00252242 0.00347181i
911911 −5.53223e16 + 1.70265e17i −0.0967810 + 0.297861i −0.987714 0.156274i 0.950052π-0.950052\pi
0.890933 + 0.454135i 0.150052π0.150052\pi
912912 1.89348e17i 0.329073i
913913 3.16840e17 7.37674e17i 0.547036 1.27362i
914914 3.41298e17 0.585405
915915 4.47843e17 + 1.45513e17i 0.763130 + 0.247956i
916916 1.92852e16 1.40115e16i 0.0326476 0.0237198i
917917 −5.05395e16 3.67191e16i −0.0849993 0.0617556i
918918 −1.45341e16 4.47314e16i −0.0242847 0.0747406i
919919 3.71426e17 1.20684e17i 0.616566 0.200334i 0.0159507 0.999873i 0.494923π-0.494923\pi
0.600615 + 0.799538i 0.294923π0.294923\pi
920920 2.98868e16 4.11357e16i 0.0492893 0.0678409i
921921 8.98761e17 + 1.23704e18i 1.47261 + 2.02687i
922922 −2.60256e17 + 8.00985e17i −0.423658 + 1.30388i
923923 3.94427e16i 0.0637906i
924924 3.82084e16 + 1.68777e17i 0.0613941 + 0.271194i
925925 −6.23206e17 −0.994903
926926 −7.29944e17 2.37173e17i −1.15777 0.376183i
927927 −2.58371e17 + 1.87718e17i −0.407161 + 0.295819i
928928 1.12967e17 + 8.20752e16i 0.176874 + 0.128506i
929929 −1.24148e17 3.82090e17i −0.193129 0.594389i −0.999993 0.00365286i 0.998837π-0.998837\pi
0.806865 0.590737i 0.201163π-0.201163\pi
930930 −3.78345e17 + 1.22932e17i −0.584778 + 0.190006i
931931 −2.70446e17 + 3.72237e17i −0.415319 + 0.571638i
932932 8.10137e16 + 1.11506e17i 0.123613 + 0.170138i
933933 −3.25102e17 + 1.00056e18i −0.492868 + 1.51689i
934934 1.15900e17i 0.174583i
935935 2.15622e16 + 1.97907e15i 0.0322719 + 0.00296204i
936936 −2.11169e16 −0.0314032
937937 6.46530e17 + 2.10070e17i 0.955325 + 0.310404i 0.744878 0.667201i 0.232508π-0.232508\pi
0.210448 + 0.977605i 0.432508π0.432508\pi
938938 −2.55841e17 + 1.85879e17i −0.375624 + 0.272907i
939939 1.14530e18 + 8.32106e17i 1.67080 + 1.21391i
940940 −3.19624e15 9.83701e15i −0.00463310 0.0142592i
941941 −1.02103e18 + 3.31752e17i −1.47062 + 0.477833i −0.931295 0.364265i 0.881320π-0.881320\pi
−0.539324 + 0.842098i 0.681320π0.681320\pi
942942 −7.62467e17 + 1.04945e18i −1.09123 + 1.50195i
943943 1.26914e17 + 1.74682e17i 0.180484 + 0.248415i
944944 −4.59178e16 + 1.41321e17i −0.0648858 + 0.199698i
945945 1.01146e17i 0.142022i
946946 3.71249e17 + 6.23868e17i 0.517986 + 0.870454i
947947 1.39804e18 1.93830 0.969151 0.246470i 0.0792705π-0.0792705\pi
0.969151 + 0.246470i 0.0792705π0.0792705\pi
948948 −3.32503e17 1.08037e17i −0.458085 0.148841i
949949 −5.63878e16 + 4.09681e16i −0.0771947 + 0.0560852i
950950 −2.93899e17 2.13530e17i −0.399813 0.290481i
951951 2.10788e17 + 6.48738e17i 0.284946 + 0.876973i
952952 −7.78755e15 + 2.53033e15i −0.0104611 + 0.00339903i
953953 2.07585e17 2.85717e17i 0.277102 0.381398i −0.647669 0.761922i 0.724256π-0.724256\pi
0.924771 + 0.380523i 0.124256π0.124256\pi
954954 2.09209e17 + 2.87951e17i 0.277517 + 0.381969i
955955 −9.34332e16 + 2.87558e17i −0.123163 + 0.379058i
956956 7.03727e17i 0.921843i
957957 −1.17992e18 1.03455e18i −1.53596 1.34673i
958958 9.32901e17 1.20682
959959 2.05613e17 + 6.68077e16i 0.264325 + 0.0858845i
960960 4.58550e16 3.33156e16i 0.0585813 0.0425618i
961961 −7.98632e17 5.80240e17i −1.01393 0.736660i
962962 1.00979e16 + 3.10781e16i 0.0127403 + 0.0392106i
963963 1.13575e18 3.69026e17i 1.42404 0.462700i
964964 −4.15619e16 + 5.72050e16i −0.0517884 + 0.0712807i
965965 6.02217e16 + 8.28880e16i 0.0745742 + 0.102643i
966966 6.67756e16 2.05514e17i 0.0821779 0.252917i
967967 1.56875e18i 1.91865i −0.282304 0.959325i 0.591099π-0.591099\pi
0.282304 0.959325i 0.408901π-0.408901\pi
968968 −2.10953e17 + 2.00269e17i −0.256409 + 0.243422i
969969 −1.00690e17 −0.121630
970970 2.54700e17 + 8.27571e16i 0.305773 + 0.0993516i
971971 4.56504e17 3.31670e17i 0.544665 0.395722i −0.281150 0.959664i 0.590716π-0.590716\pi
0.825815 + 0.563942i 0.190716π0.190716\pi
972972 −2.64687e17 1.92307e17i −0.313860 0.228032i
973973 3.15964e16 + 9.72437e16i 0.0372358 + 0.114600i
974974 7.64036e16 2.48250e16i 0.0894871 0.0290761i
975975 −3.75935e16 + 5.17430e16i −0.0437607 + 0.0602315i
976976 −1.75937e17 2.42157e17i −0.203545 0.280155i
977977 −3.67118e17 + 1.12987e18i −0.422122 + 1.29916i 0.483602 + 0.875288i 0.339328π0.339328\pi
−0.905723 + 0.423869i 0.860672π0.860672\pi
978978 9.02714e17i 1.03161i
979979 7.96358e17 9.08259e17i 0.904507 1.03161i
980980 −1.37730e17 −0.155480
981981 −4.54276e17 1.47603e17i −0.509690 0.165608i
982982 4.71059e17 3.42244e17i 0.525298 0.381652i
983983 −1.28240e18 9.31719e17i −1.42136 1.03268i −0.991546 0.129757i 0.958580π-0.958580\pi
−0.429811 0.902919i 0.641420π-0.641420\pi
984984 7.43774e16 + 2.28910e17i 0.0819352 + 0.252171i
985985 −3.19771e17 + 1.03900e17i −0.350124 + 0.113762i
986986 4.36452e16 6.00724e16i 0.0474979 0.0653753i
987987 −2.58374e16 3.55622e16i −0.0279477 0.0384667i
988988 −5.88627e15 + 1.81161e16i −0.00632846 + 0.0194770i
989989 9.06547e17i 0.968752i
990990 −3.46747e17 + 2.06341e17i −0.368300 + 0.219166i
991991 1.95954e17 0.206877 0.103439 0.994636i 0.467015π-0.467015\pi
0.103439 + 0.994636i 0.467015π0.467015\pi
992992 2.40497e17 + 7.81421e16i 0.252371 + 0.0820002i
993993 1.44984e18 1.05337e18i 1.51225 1.09872i
994994 −2.30576e17 1.67523e17i −0.239054 0.173683i
995995 −9.62969e16 2.96371e17i −0.0992370 0.305420i
996996 −1.06285e18 + 3.45341e17i −1.08872 + 0.353747i
997997 −2.66021e17 + 3.66146e17i −0.270860 + 0.372806i −0.922680 0.385567i 0.874006π-0.874006\pi
0.651820 + 0.758374i 0.274006π0.274006\pi
998998 −3.24543e17 4.46694e17i −0.328464 0.452093i
999999 4.19114e17 1.28990e18i 0.421637 1.29767i
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 22.13.d.a.13.1 48
11.6 odd 10 inner 22.13.d.a.17.1 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.13.d.a.13.1 48 1.1 even 1 trivial
22.13.d.a.17.1 yes 48 11.6 odd 10 inner