Properties

Label 15.10.e.a.2.5
Level $15$
Weight $10$
Character 15.2
Analytic conductor $7.726$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,10,Mod(2,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 15.e (of order \(4\), degree \(2\), 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: \(7.72553754246\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2.5
Character \(\chi\) \(=\) 15.2
Dual form 15.10.e.a.8.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-13.8737 + 13.8737i) q^{2} +(-55.7208 + 128.756i) q^{3} +127.039i q^{4} +(-919.994 + 1052.02i) q^{5} +(-1013.28 - 2559.39i) q^{6} +(6797.28 + 6797.28i) q^{7} +(-8865.86 - 8865.86i) q^{8} +(-13473.4 - 14348.8i) q^{9} +O(q^{10})\) \(q+(-13.8737 + 13.8737i) q^{2} +(-55.7208 + 128.756i) q^{3} +127.039i q^{4} +(-919.994 + 1052.02i) q^{5} +(-1013.28 - 2559.39i) q^{6} +(6797.28 + 6797.28i) q^{7} +(-8865.86 - 8865.86i) q^{8} +(-13473.4 - 14348.8i) q^{9} +(-1831.63 - 27359.1i) q^{10} -28401.8i q^{11} +(-16357.1 - 7078.71i) q^{12} +(28203.0 - 28203.0i) q^{13} -188607. q^{14} +(-84190.9 - 177074. i) q^{15} +180961. q^{16} +(21103.5 - 21103.5i) q^{17} +(385998. + 12145.4i) q^{18} +759794. i q^{19} +(-133647. - 116875. i) q^{20} +(-1.25394e6 + 496443. i) q^{21} +(394039. + 394039. i) q^{22} +(1.18196e6 + 1.18196e6i) q^{23} +(1.63555e6 - 647523. i) q^{24} +(-260348. - 1.93570e6i) q^{25} +782563. i q^{26} +(2.59825e6 - 935257. i) q^{27} +(-863519. + 863519. i) q^{28} -6.93799e6 q^{29} +(3.62472e6 + 1.28864e6i) q^{30} -1.45656e6 q^{31} +(2.02871e6 - 2.02871e6i) q^{32} +(3.65691e6 + 1.58257e6i) q^{33} +585568. i q^{34} +(-1.34043e7 + 897387. i) q^{35} +(1.82286e6 - 1.71164e6i) q^{36} +(-8.18291e6 - 8.18291e6i) q^{37} +(-1.05412e7 - 1.05412e7i) q^{38} +(2.05982e6 + 5.20282e6i) q^{39} +(1.74836e7 - 1.17048e6i) q^{40} +7.44760e6i q^{41} +(1.05093e7 - 2.42844e7i) q^{42} +(6.21407e6 - 6.21407e6i) q^{43} +3.60813e6 q^{44} +(2.74906e7 - 973394. i) q^{45} -3.27964e7 q^{46} +(-1.95906e7 + 1.95906e7i) q^{47} +(-1.00833e7 + 2.32999e7i) q^{48} +5.20524e7i q^{49} +(3.04673e7 + 2.32433e7i) q^{50} +(1.54130e6 + 3.89311e6i) q^{51} +(3.58288e6 + 3.58288e6i) q^{52} +(4.55510e7 + 4.55510e7i) q^{53} +(-2.30719e7 + 4.90229e7i) q^{54} +(2.98791e7 + 2.61295e7i) q^{55} -1.20527e8i q^{56} +(-9.78283e7 - 4.23363e7i) q^{57} +(9.62559e7 - 9.62559e7i) q^{58} -3.03496e7 q^{59} +(2.24953e7 - 1.06955e7i) q^{60} -5.71850e7 q^{61} +(2.02079e7 - 2.02079e7i) q^{62} +(5.95048e6 - 1.89115e8i) q^{63} +1.48944e8i q^{64} +(3.72341e6 + 5.56167e7i) q^{65} +(-7.26911e7 + 2.87788e7i) q^{66} +(-1.30797e8 - 1.30797e8i) q^{67} +(2.68096e6 + 2.68096e6i) q^{68} +(-2.18044e8 + 8.63250e7i) q^{69} +(1.73518e8 - 1.98418e8i) q^{70} -1.62406e8i q^{71} +(-7.76136e6 + 2.46668e8i) q^{72} +(-1.40481e8 + 1.40481e8i) q^{73} +2.27055e8 q^{74} +(2.63740e8 + 7.43371e7i) q^{75} -9.65235e7 q^{76} +(1.93055e8 - 1.93055e8i) q^{77} +(-1.00760e8 - 4.36050e7i) q^{78} +4.65848e7i q^{79} +(-1.66483e8 + 1.90374e8i) q^{80} +(-2.43562e7 + 3.86654e8i) q^{81} +(-1.03326e8 - 1.03326e8i) q^{82} +(4.75271e8 + 4.75271e8i) q^{83} +(-6.30676e7 - 1.59300e8i) q^{84} +(2.78611e6 + 4.16163e7i) q^{85} +1.72425e8i q^{86} +(3.86590e8 - 8.93311e8i) q^{87} +(-2.51806e8 + 2.51806e8i) q^{88} +1.99838e8 q^{89} +(-3.67893e8 + 3.94902e8i) q^{90} +3.83408e8 q^{91} +(-1.50155e8 + 1.50155e8i) q^{92} +(8.11605e7 - 1.87541e8i) q^{93} -5.43591e8i q^{94} +(-7.99315e8 - 6.99006e8i) q^{95} +(1.48168e8 + 3.74251e8i) q^{96} +(9.83386e8 + 9.83386e8i) q^{97} +(-7.22161e8 - 7.22161e8i) q^{98} +(-4.07532e8 + 3.82668e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 150 q^{3} - 4548 q^{6} - 9760 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 150 q^{3} - 4548 q^{6} - 9760 q^{7} - 39820 q^{10} + 191940 q^{12} + 114260 q^{13} - 40230 q^{15} - 1494724 q^{16} + 994800 q^{18} + 592212 q^{21} + 308260 q^{22} + 5808020 q^{25} + 4786830 q^{27} - 12953300 q^{28} - 17343060 q^{30} + 16124104 q^{31} + 19638120 q^{33} - 48943956 q^{36} - 35578660 q^{37} + 144132840 q^{40} + 46648260 q^{42} - 118721020 q^{43} - 129688380 q^{45} + 3145024 q^{46} + 275395140 q^{48} - 64226868 q^{51} - 157103680 q^{52} + 144539740 q^{55} + 48163500 q^{57} - 209634300 q^{58} - 140815620 q^{60} + 63607744 q^{61} + 89858580 q^{63} + 358931400 q^{66} + 153311540 q^{67} + 420519420 q^{70} - 1534046760 q^{72} + 628070360 q^{73} + 138090210 q^{75} - 2457023472 q^{76} - 403337880 q^{78} + 2250542952 q^{81} + 4138031440 q^{82} + 108907340 q^{85} - 2878139760 q^{87} - 595851300 q^{88} + 693868920 q^{90} - 4369040216 q^{91} - 293672640 q^{93} + 7291125636 q^{96} + 3987642200 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −13.8737 + 13.8737i −0.613138 + 0.613138i −0.943762 0.330624i \(-0.892741\pi\)
0.330624 + 0.943762i \(0.392741\pi\)
\(3\) −55.7208 + 128.756i −0.397166 + 0.917747i
\(4\) 127.039i 0.248123i
\(5\) −919.994 + 1052.02i −0.658294 + 0.752761i
\(6\) −1013.28 2559.39i −0.319188 0.806223i
\(7\) 6797.28 + 6797.28i 1.07002 + 1.07002i 0.997356 + 0.0726688i \(0.0231516\pi\)
0.0726688 + 0.997356i \(0.476848\pi\)
\(8\) −8865.86 8865.86i −0.765272 0.765272i
\(9\) −13473.4 14348.8i −0.684519 0.728995i
\(10\) −1831.63 27359.1i −0.0579213 0.865172i
\(11\) 28401.8i 0.584895i −0.956282 0.292448i \(-0.905530\pi\)
0.956282 0.292448i \(-0.0944698\pi\)
\(12\) −16357.1 7078.71i −0.227714 0.0985459i
\(13\) 28203.0 28203.0i 0.273874 0.273874i −0.556784 0.830658i \(-0.687965\pi\)
0.830658 + 0.556784i \(0.187965\pi\)
\(14\) −188607. −1.31215
\(15\) −84190.9 177074.i −0.429392 0.903118i
\(16\) 180961. 0.690312
\(17\) 21103.5 21103.5i 0.0612822 0.0612822i −0.675802 0.737084i \(-0.736202\pi\)
0.737084 + 0.675802i \(0.236202\pi\)
\(18\) 385998. + 12145.4i 0.866680 + 0.0272700i
\(19\) 759794.i 1.33753i 0.743472 + 0.668767i \(0.233178\pi\)
−0.743472 + 0.668767i \(0.766822\pi\)
\(20\) −133647. 116875.i −0.186777 0.163338i
\(21\) −1.25394e6 + 496443.i −1.40699 + 0.557035i
\(22\) 394039. + 394039.i 0.358622 + 0.358622i
\(23\) 1.18196e6 + 1.18196e6i 0.880698 + 0.880698i 0.993606 0.112907i \(-0.0360164\pi\)
−0.112907 + 0.993606i \(0.536016\pi\)
\(24\) 1.63555e6 647523.i 1.00627 0.398386i
\(25\) −260348. 1.93570e6i −0.133298 0.991076i
\(26\) 782563.i 0.335845i
\(27\) 2.59825e6 935257.i 0.940900 0.338684i
\(28\) −863519. + 863519.i −0.265498 + 0.265498i
\(29\) −6.93799e6 −1.82156 −0.910779 0.412895i \(-0.864518\pi\)
−0.910779 + 0.412895i \(0.864518\pi\)
\(30\) 3.62472e6 + 1.28864e6i 0.817013 + 0.290459i
\(31\) −1.45656e6 −0.283270 −0.141635 0.989919i \(-0.545236\pi\)
−0.141635 + 0.989919i \(0.545236\pi\)
\(32\) 2.02871e6 2.02871e6i 0.342015 0.342015i
\(33\) 3.65691e6 + 1.58257e6i 0.536786 + 0.232300i
\(34\) 585568.i 0.0751489i
\(35\) −1.34043e7 + 897387.i −1.50986 + 0.101082i
\(36\) 1.82286e6 1.71164e6i 0.180880 0.169845i
\(37\) −8.18291e6 8.18291e6i −0.717795 0.717795i 0.250359 0.968153i \(-0.419452\pi\)
−0.968153 + 0.250359i \(0.919452\pi\)
\(38\) −1.05412e7 1.05412e7i −0.820093 0.820093i
\(39\) 2.05982e6 + 5.20282e6i 0.142574 + 0.360120i
\(40\) 1.74836e7 1.17048e6i 1.07984 0.0722929i
\(41\) 7.44760e6i 0.411613i 0.978593 + 0.205806i \(0.0659817\pi\)
−0.978593 + 0.205806i \(0.934018\pi\)
\(42\) 1.05093e7 2.42844e7i 0.521139 1.20422i
\(43\) 6.21407e6 6.21407e6i 0.277184 0.277184i −0.554800 0.831984i \(-0.687205\pi\)
0.831984 + 0.554800i \(0.187205\pi\)
\(44\) 3.60813e6 0.145126
\(45\) 2.74906e7 973394.i 0.999374 0.0353861i
\(46\) −3.27964e7 −1.07998
\(47\) −1.95906e7 + 1.95906e7i −0.585610 + 0.585610i −0.936439 0.350830i \(-0.885900\pi\)
0.350830 + 0.936439i \(0.385900\pi\)
\(48\) −1.00833e7 + 2.32999e7i −0.274168 + 0.633532i
\(49\) 5.20524e7i 1.28991i
\(50\) 3.04673e7 + 2.32433e7i 0.689397 + 0.525937i
\(51\) 1.54130e6 + 3.89311e6i 0.0319024 + 0.0805807i
\(52\) 3.58288e6 + 3.58288e6i 0.0679544 + 0.0679544i
\(53\) 4.55510e7 + 4.55510e7i 0.792969 + 0.792969i 0.981976 0.189006i \(-0.0605267\pi\)
−0.189006 + 0.981976i \(0.560527\pi\)
\(54\) −2.30719e7 + 4.90229e7i −0.369242 + 0.784562i
\(55\) 2.98791e7 + 2.61295e7i 0.440286 + 0.385033i
\(56\) 1.20527e8i 1.63772i
\(57\) −9.78283e7 4.23363e7i −1.22752 0.531222i
\(58\) 9.62559e7 9.62559e7i 1.11687 1.11687i
\(59\) −3.03496e7 −0.326076 −0.163038 0.986620i \(-0.552129\pi\)
−0.163038 + 0.986620i \(0.552129\pi\)
\(60\) 2.24953e7 1.06955e7i 0.224084 0.106542i
\(61\) −5.71850e7 −0.528808 −0.264404 0.964412i \(-0.585175\pi\)
−0.264404 + 0.964412i \(0.585175\pi\)
\(62\) 2.02079e7 2.02079e7i 0.173683 0.173683i
\(63\) 5.95048e6 1.89115e8i 0.0475905 1.51250i
\(64\) 1.48944e8i 1.10972i
\(65\) 3.72341e6 + 5.56167e7i 0.0258720 + 0.386451i
\(66\) −7.26911e7 + 2.87788e7i −0.471556 + 0.186692i
\(67\) −1.30797e8 1.30797e8i −0.792978 0.792978i 0.188999 0.981977i \(-0.439476\pi\)
−0.981977 + 0.188999i \(0.939476\pi\)
\(68\) 2.68096e6 + 2.68096e6i 0.0152055 + 0.0152055i
\(69\) −2.18044e8 + 8.63250e7i −1.15804 + 0.458475i
\(70\) 1.73518e8 1.98418e8i 0.863778 0.987733i
\(71\) 1.62406e8i 0.758471i −0.925300 0.379236i \(-0.876187\pi\)
0.925300 0.379236i \(-0.123813\pi\)
\(72\) −7.76136e6 + 2.46668e8i −0.0340363 + 1.08172i
\(73\) −1.40481e8 + 1.40481e8i −0.578980 + 0.578980i −0.934622 0.355642i \(-0.884262\pi\)
0.355642 + 0.934622i \(0.384262\pi\)
\(74\) 2.27055e8 0.880215
\(75\) 2.63740e8 + 7.43371e7i 0.962498 + 0.271287i
\(76\) −9.65235e7 −0.331873
\(77\) 1.93055e8 1.93055e8i 0.625853 0.625853i
\(78\) −1.00760e8 4.36050e7i −0.308221 0.133386i
\(79\) 4.65848e7i 0.134562i 0.997734 + 0.0672810i \(0.0214324\pi\)
−0.997734 + 0.0672810i \(0.978568\pi\)
\(80\) −1.66483e8 + 1.90374e8i −0.454428 + 0.519640i
\(81\) −2.43562e7 + 3.86654e8i −0.0628675 + 0.998022i
\(82\) −1.03326e8 1.03326e8i −0.252375 0.252375i
\(83\) 4.75271e8 + 4.75271e8i 1.09923 + 1.09923i 0.994500 + 0.104733i \(0.0333989\pi\)
0.104733 + 0.994500i \(0.466601\pi\)
\(84\) −6.30676e7 1.59300e8i −0.138213 0.349106i
\(85\) 2.78611e6 + 4.16163e7i 0.00578914 + 0.0864725i
\(86\) 1.72425e8i 0.339904i
\(87\) 3.86590e8 8.93311e8i 0.723460 1.67173i
\(88\) −2.51806e8 + 2.51806e8i −0.447604 + 0.447604i
\(89\) 1.99838e8 0.337616 0.168808 0.985649i \(-0.446008\pi\)
0.168808 + 0.985649i \(0.446008\pi\)
\(90\) −3.67893e8 + 3.94902e8i −0.591058 + 0.634451i
\(91\) 3.83408e8 0.586104
\(92\) −1.50155e8 + 1.50155e8i −0.218521 + 0.218521i
\(93\) 8.11605e7 1.87541e8i 0.112505 0.259970i
\(94\) 5.43591e8i 0.718119i
\(95\) −7.99315e8 6.99006e8i −1.00684 0.880491i
\(96\) 1.48168e8 + 3.74251e8i 0.178047 + 0.449720i
\(97\) 9.83386e8 + 9.83386e8i 1.12785 + 1.12785i 0.990526 + 0.137323i \(0.0438498\pi\)
0.137323 + 0.990526i \(0.456150\pi\)
\(98\) −7.22161e8 7.22161e8i −0.790891 0.790891i
\(99\) −4.07532e8 + 3.82668e8i −0.426386 + 0.400372i
\(100\) 2.45909e8 3.30743e7i 0.245909 0.0330743i
\(101\) 3.93761e8i 0.376519i −0.982119 0.188259i \(-0.939715\pi\)
0.982119 0.188259i \(-0.0602845\pi\)
\(102\) −7.53956e7 3.26283e7i −0.0689677 0.0298465i
\(103\) 8.08640e7 8.08640e7i 0.0707926 0.0707926i −0.670824 0.741617i \(-0.734059\pi\)
0.741617 + 0.670824i \(0.234059\pi\)
\(104\) −5.00088e8 −0.419176
\(105\) 6.31354e8 1.77589e9i 0.506898 1.42582i
\(106\) −1.26392e9 −0.972400
\(107\) −1.59491e9 + 1.59491e9i −1.17627 + 1.17627i −0.195587 + 0.980686i \(0.562661\pi\)
−0.980686 + 0.195587i \(0.937339\pi\)
\(108\) 1.18814e8 + 3.30079e8i 0.0840351 + 0.233459i
\(109\) 1.78913e9i 1.21401i −0.794697 0.607006i \(-0.792370\pi\)
0.794697 0.607006i \(-0.207630\pi\)
\(110\) −7.77048e8 + 5.20216e7i −0.506035 + 0.0338779i
\(111\) 1.50956e9 5.97644e8i 0.943837 0.373671i
\(112\) 1.23004e9 + 1.23004e9i 0.738651 + 0.738651i
\(113\) 8.48948e8 + 8.48948e8i 0.489810 + 0.489810i 0.908246 0.418436i \(-0.137422\pi\)
−0.418436 + 0.908246i \(0.637422\pi\)
\(114\) 1.94461e9 7.69881e8i 1.07835 0.426925i
\(115\) −2.33083e9 + 1.56044e8i −1.24271 + 0.0831968i
\(116\) 8.81395e8i 0.451970i
\(117\) −7.84671e8 2.46895e7i −0.387125 0.0121808i
\(118\) 4.21062e8 4.21062e8i 0.199930 0.199930i
\(119\) 2.86893e8 0.131147
\(120\) −8.23490e8 + 2.31634e9i −0.362529 + 1.01973i
\(121\) 1.55129e9 0.657897
\(122\) 7.93370e8 7.93370e8i 0.324232 0.324232i
\(123\) −9.58925e8 4.14986e8i −0.377756 0.163478i
\(124\) 1.85040e8i 0.0702857i
\(125\) 2.27590e9 + 1.50694e9i 0.833793 + 0.552078i
\(126\) 2.54118e9 + 2.70629e9i 0.898189 + 0.956548i
\(127\) −1.38222e8 1.38222e8i −0.0471477 0.0471477i 0.683140 0.730288i \(-0.260614\pi\)
−0.730288 + 0.683140i \(0.760614\pi\)
\(128\) −1.02771e9 1.02771e9i −0.338395 0.338395i
\(129\) 4.53848e8 + 1.14635e9i 0.144297 + 0.364473i
\(130\) −8.23268e8 7.19953e8i −0.252811 0.221085i
\(131\) 1.46746e9i 0.435357i 0.976021 + 0.217679i \(0.0698484\pi\)
−0.976021 + 0.217679i \(0.930152\pi\)
\(132\) −2.01048e8 + 4.64570e8i −0.0576390 + 0.133189i
\(133\) −5.16453e9 + 5.16453e9i −1.43119 + 1.43119i
\(134\) 3.62928e9 0.972410
\(135\) −1.40647e9 + 3.59383e9i −0.364441 + 0.931226i
\(136\) −3.74201e8 −0.0937950
\(137\) −2.10946e9 + 2.10946e9i −0.511597 + 0.511597i −0.915016 0.403418i \(-0.867822\pi\)
0.403418 + 0.915016i \(0.367822\pi\)
\(138\) 1.82744e9 4.22274e9i 0.428931 0.991148i
\(139\) 4.89284e9i 1.11172i −0.831277 0.555859i \(-0.812390\pi\)
0.831277 0.555859i \(-0.187610\pi\)
\(140\) −1.14003e8 1.70287e9i −0.0250807 0.374632i
\(141\) −1.43081e9 3.61402e9i −0.304857 0.770025i
\(142\) 2.25318e9 + 2.25318e9i 0.465048 + 0.465048i
\(143\) −8.01016e8 8.01016e8i −0.160188 0.160188i
\(144\) −2.43816e9 2.59658e9i −0.472532 0.503234i
\(145\) 6.38291e9 7.29888e9i 1.19912 1.37120i
\(146\) 3.89798e9i 0.709989i
\(147\) −6.70207e9 2.90040e9i −1.18381 0.512307i
\(148\) 1.03955e9 1.03955e9i 0.178101 0.178101i
\(149\) −8.48172e8 −0.140976 −0.0704881 0.997513i \(-0.522456\pi\)
−0.0704881 + 0.997513i \(0.522456\pi\)
\(150\) −4.69039e9 + 2.62772e9i −0.756481 + 0.423808i
\(151\) −6.40697e8 −0.100290 −0.0501448 0.998742i \(-0.515968\pi\)
−0.0501448 + 0.998742i \(0.515968\pi\)
\(152\) 6.73623e9 6.73623e9i 1.02358 1.02358i
\(153\) −5.87145e8 1.84744e7i −0.0866232 0.00272559i
\(154\) 5.35678e9i 0.767469i
\(155\) 1.34002e9 1.53232e9i 0.186475 0.213234i
\(156\) −6.60960e8 + 2.61678e8i −0.0893541 + 0.0353758i
\(157\) 5.12078e9 + 5.12078e9i 0.672647 + 0.672647i 0.958326 0.285678i \(-0.0922189\pi\)
−0.285678 + 0.958326i \(0.592219\pi\)
\(158\) −6.46306e8 6.46306e8i −0.0825052 0.0825052i
\(159\) −8.40312e9 + 3.32684e9i −1.04269 + 0.412805i
\(160\) 2.67834e8 + 4.00064e9i 0.0323091 + 0.482602i
\(161\) 1.60682e10i 1.88474i
\(162\) −5.02643e9 5.70225e9i −0.573379 0.650472i
\(163\) 2.16838e9 2.16838e9i 0.240597 0.240597i −0.576500 0.817097i \(-0.695582\pi\)
0.817097 + 0.576500i \(0.195582\pi\)
\(164\) −9.46135e8 −0.102131
\(165\) −5.02922e9 + 2.39117e9i −0.528230 + 0.251150i
\(166\) −1.31876e10 −1.34796
\(167\) 6.10389e9 6.10389e9i 0.607271 0.607271i −0.334961 0.942232i \(-0.608723\pi\)
0.942232 + 0.334961i \(0.108723\pi\)
\(168\) 1.55187e10 + 6.71588e9i 1.50301 + 0.650446i
\(169\) 9.01368e9i 0.849986i
\(170\) −6.16027e8 5.38719e8i −0.0565691 0.0494701i
\(171\) 1.09021e10 1.02370e10i 0.975056 0.915567i
\(172\) 7.89429e8 + 7.89429e8i 0.0687757 + 0.0687757i
\(173\) 9.83053e9 + 9.83053e9i 0.834391 + 0.834391i 0.988114 0.153723i \(-0.0491264\pi\)
−0.153723 + 0.988114i \(0.549126\pi\)
\(174\) 7.03010e9 + 1.77570e10i 0.581420 + 1.46858i
\(175\) 1.13878e10 1.49271e10i 0.917844 1.20311i
\(176\) 5.13962e9i 0.403760i
\(177\) 1.69110e9 3.90770e9i 0.129506 0.299255i
\(178\) −2.77250e9 + 2.77250e9i −0.207005 + 0.207005i
\(179\) −1.60454e10 −1.16819 −0.584093 0.811687i \(-0.698550\pi\)
−0.584093 + 0.811687i \(0.698550\pi\)
\(180\) 1.23659e8 + 3.49238e9i 0.00878010 + 0.247968i
\(181\) −2.57147e10 −1.78085 −0.890427 0.455126i \(-0.849594\pi\)
−0.890427 + 0.455126i \(0.849594\pi\)
\(182\) −5.31930e9 + 5.31930e9i −0.359363 + 0.359363i
\(183\) 3.18639e9 7.36293e9i 0.210024 0.485312i
\(184\) 2.09582e10i 1.34795i
\(185\) 1.61368e10 1.08032e9i 1.01285 0.0678078i
\(186\) 1.47589e9 + 3.72789e9i 0.0904164 + 0.228379i
\(187\) −5.99376e8 5.99376e8i −0.0358437 0.0358437i
\(188\) −2.48877e9 2.48877e9i −0.145303 0.145303i
\(189\) 2.40182e10 + 1.13038e10i 1.36919 + 0.644387i
\(190\) 2.07873e10 1.39166e9i 1.15720 0.0774717i
\(191\) 4.55097e9i 0.247431i −0.992318 0.123715i \(-0.960519\pi\)
0.992318 0.123715i \(-0.0394810\pi\)
\(192\) −1.91774e10 8.29926e9i −1.01844 0.440742i
\(193\) −4.90333e9 + 4.90333e9i −0.254380 + 0.254380i −0.822764 0.568383i \(-0.807569\pi\)
0.568383 + 0.822764i \(0.307569\pi\)
\(194\) −2.72865e10 −1.38305
\(195\) −7.36847e9 2.61959e9i −0.364940 0.129741i
\(196\) −6.61268e9 −0.320055
\(197\) −5.03000e9 + 5.03000e9i −0.237941 + 0.237941i −0.815997 0.578056i \(-0.803812\pi\)
0.578056 + 0.815997i \(0.303812\pi\)
\(198\) 3.44950e8 1.09630e10i 0.0159501 0.506917i
\(199\) 3.17333e10i 1.43442i 0.696858 + 0.717210i \(0.254581\pi\)
−0.696858 + 0.717210i \(0.745419\pi\)
\(200\) −1.48534e10 + 1.94698e10i −0.656433 + 0.860452i
\(201\) 2.41290e10 9.55283e9i 1.04270 0.412809i
\(202\) 5.46294e9 + 5.46294e9i 0.230858 + 0.230858i
\(203\) −4.71595e10 4.71595e10i −1.94911 1.94911i
\(204\) −4.94577e8 + 1.95806e8i −0.0199939 + 0.00791571i
\(205\) −7.83498e9 6.85174e9i −0.309846 0.270962i
\(206\) 2.24377e9i 0.0868113i
\(207\) 1.03471e9 3.28847e10i 0.0391699 1.24488i
\(208\) 5.10366e9 5.10366e9i 0.189059 0.189059i
\(209\) 2.15795e10 0.782318
\(210\) 1.58790e10 + 3.33975e10i 0.563426 + 1.18502i
\(211\) 4.25545e10 1.47800 0.739000 0.673705i \(-0.235298\pi\)
0.739000 + 0.673705i \(0.235298\pi\)
\(212\) −5.78675e9 + 5.78675e9i −0.196754 + 0.196754i
\(213\) 2.09108e10 + 9.04938e9i 0.696085 + 0.301239i
\(214\) 4.42546e10i 1.44244i
\(215\) 8.20391e8 + 1.22542e10i 0.0261847 + 0.391122i
\(216\) −3.13275e10 1.47438e10i −0.979230 0.460860i
\(217\) −9.90063e9 9.90063e9i −0.303106 0.303106i
\(218\) 2.48219e10 + 2.48219e10i 0.744357 + 0.744357i
\(219\) −1.02601e10 2.59154e10i −0.301406 0.761308i
\(220\) −3.31946e9 + 3.79581e9i −0.0955356 + 0.109245i
\(221\) 1.19037e9i 0.0335672i
\(222\) −1.26517e10 + 2.92348e10i −0.349591 + 0.807814i
\(223\) −3.92420e10 + 3.92420e10i −1.06262 + 1.06262i −0.0647183 + 0.997904i \(0.520615\pi\)
−0.997904 + 0.0647183i \(0.979385\pi\)
\(224\) 2.75794e10 0.731930
\(225\) −2.42672e10 + 2.98161e10i −0.631244 + 0.775584i
\(226\) −2.35562e10 −0.600643
\(227\) 1.60894e9 1.60894e9i 0.0402182 0.0402182i −0.686712 0.726930i \(-0.740947\pi\)
0.726930 + 0.686712i \(0.240947\pi\)
\(228\) 5.37836e9 1.24280e10i 0.131808 0.304575i
\(229\) 1.31989e10i 0.317159i 0.987346 + 0.158579i \(0.0506914\pi\)
−0.987346 + 0.158579i \(0.949309\pi\)
\(230\) 3.01725e10 3.45023e10i 0.710944 0.812966i
\(231\) 1.40999e10 + 3.56142e10i 0.325807 + 0.822942i
\(232\) 6.15113e10 + 6.15113e10i 1.39399 + 1.39399i
\(233\) 3.10211e10 + 3.10211e10i 0.689533 + 0.689533i 0.962129 0.272596i \(-0.0878821\pi\)
−0.272596 + 0.962129i \(0.587882\pi\)
\(234\) 1.12288e10 1.05438e10i 0.244830 0.229892i
\(235\) −2.58638e9 3.86329e10i −0.0553207 0.826327i
\(236\) 3.85558e9i 0.0809069i
\(237\) −5.99809e9 2.59574e9i −0.123494 0.0534434i
\(238\) −3.98027e9 + 3.98027e9i −0.0804112 + 0.0804112i
\(239\) 3.88560e10 0.770313 0.385156 0.922851i \(-0.374147\pi\)
0.385156 + 0.922851i \(0.374147\pi\)
\(240\) −1.52353e10 3.20435e10i −0.296415 0.623433i
\(241\) 2.24178e10 0.428072 0.214036 0.976826i \(-0.431339\pi\)
0.214036 + 0.976826i \(0.431339\pi\)
\(242\) −2.15221e10 + 2.15221e10i −0.403382 + 0.403382i
\(243\) −4.84270e10 2.46807e10i −0.890963 0.454076i
\(244\) 7.26472e9i 0.131209i
\(245\) −5.47599e10 4.78879e10i −0.970991 0.849138i
\(246\) 1.90613e10 7.54647e9i 0.331852 0.131382i
\(247\) 2.14285e10 + 2.14285e10i 0.366316 + 0.366316i
\(248\) 1.29136e10 + 1.29136e10i 0.216778 + 0.216778i
\(249\) −8.76766e10 + 3.47117e10i −1.44540 + 0.572241i
\(250\) −5.24821e10 + 1.06684e10i −0.849730 + 0.172730i
\(251\) 5.40224e10i 0.859097i 0.903044 + 0.429548i \(0.141327\pi\)
−0.903044 + 0.429548i \(0.858673\pi\)
\(252\) 2.40250e10 + 7.55943e8i 0.375285 + 0.0118083i
\(253\) 3.35697e10 3.35697e10i 0.515116 0.515116i
\(254\) 3.83531e9 0.0578161
\(255\) −5.51360e9 1.96016e9i −0.0816591 0.0290309i
\(256\) −4.77430e10 −0.694751
\(257\) 5.32745e10 5.32745e10i 0.761764 0.761764i −0.214877 0.976641i \(-0.568935\pi\)
0.976641 + 0.214877i \(0.0689351\pi\)
\(258\) −2.22008e10 9.60765e9i −0.311946 0.134998i
\(259\) 1.11243e11i 1.53612i
\(260\) −7.06548e9 + 4.73018e8i −0.0958874 + 0.00641944i
\(261\) 9.34783e10 + 9.95519e10i 1.24689 + 1.32791i
\(262\) −2.03592e10 2.03592e10i −0.266934 0.266934i
\(263\) −4.07549e9 4.07549e9i −0.0525266 0.0525266i 0.680356 0.732882i \(-0.261825\pi\)
−0.732882 + 0.680356i \(0.761825\pi\)
\(264\) −1.83908e10 4.64524e10i −0.233014 0.588560i
\(265\) −8.98270e10 + 6.01371e9i −1.11892 + 0.0749094i
\(266\) 1.43303e11i 1.75504i
\(267\) −1.11351e10 + 2.57304e10i −0.134090 + 0.309846i
\(268\) 1.66163e10 1.66163e10i 0.196756 0.196756i
\(269\) −7.72429e8 −0.00899442 −0.00449721 0.999990i \(-0.501432\pi\)
−0.00449721 + 0.999990i \(0.501432\pi\)
\(270\) −3.03469e10 6.93728e10i −0.347518 0.794423i
\(271\) 2.60396e10 0.293274 0.146637 0.989190i \(-0.453155\pi\)
0.146637 + 0.989190i \(0.453155\pi\)
\(272\) 3.81891e9 3.81891e9i 0.0423038 0.0423038i
\(273\) −2.13638e10 + 4.93662e10i −0.232780 + 0.537895i
\(274\) 5.85321e10i 0.627360i
\(275\) −5.49772e10 + 7.39433e9i −0.579676 + 0.0779654i
\(276\) −1.09666e10 2.77001e10i −0.113758 0.287337i
\(277\) 1.73407e10 + 1.73407e10i 0.176974 + 0.176974i 0.790035 0.613062i \(-0.210062\pi\)
−0.613062 + 0.790035i \(0.710062\pi\)
\(278\) 6.78820e10 + 6.78820e10i 0.681636 + 0.681636i
\(279\) 1.96248e10 + 2.08999e10i 0.193903 + 0.206502i
\(280\) 1.26797e11 + 1.10884e11i 1.23281 + 1.07810i
\(281\) 1.47652e10i 0.141273i 0.997502 + 0.0706366i \(0.0225031\pi\)
−0.997502 + 0.0706366i \(0.977497\pi\)
\(282\) 6.99907e10 + 3.02893e10i 0.659052 + 0.285212i
\(283\) −8.06665e10 + 8.06665e10i −0.747574 + 0.747574i −0.974023 0.226449i \(-0.927288\pi\)
0.226449 + 0.974023i \(0.427288\pi\)
\(284\) 2.06319e10 0.188194
\(285\) 1.34540e11 6.39677e10i 1.20795 0.574327i
\(286\) 2.22262e10 0.196434
\(287\) −5.06234e10 + 5.06234e10i −0.440436 + 0.440436i
\(288\) −5.64432e10 1.77598e9i −0.483443 0.0152115i
\(289\) 1.17697e11i 0.992489i
\(290\) 1.27078e10 + 1.89817e11i 0.105507 + 1.57596i
\(291\) −1.81412e11 + 7.18221e10i −1.48302 + 0.587137i
\(292\) −1.78465e10 1.78465e10i −0.143658 0.143658i
\(293\) −1.17190e11 1.17190e11i −0.928940 0.928940i 0.0686973 0.997638i \(-0.478116\pi\)
−0.997638 + 0.0686973i \(0.978116\pi\)
\(294\) 1.33222e11 5.27434e10i 1.03995 0.411723i
\(295\) 2.79214e10 3.19282e10i 0.214654 0.245457i
\(296\) 1.45097e11i 1.09862i
\(297\) −2.65630e10 7.37948e10i −0.198094 0.550328i
\(298\) 1.17673e10 1.17673e10i 0.0864379 0.0864379i
\(299\) 6.66697e10 0.482401
\(300\) −9.44370e9 + 3.35052e10i −0.0673126 + 0.238818i
\(301\) 8.44776e10 0.593188
\(302\) 8.88886e9 8.88886e9i 0.0614914 0.0614914i
\(303\) 5.06992e10 + 2.19407e10i 0.345549 + 0.149540i
\(304\) 1.37493e11i 0.923316i
\(305\) 5.26099e10 6.01595e10i 0.348111 0.398066i
\(306\) 8.40221e9 7.88959e9i 0.0547832 0.0514408i
\(307\) −1.50347e11 1.50347e11i −0.965987 0.965987i 0.0334536 0.999440i \(-0.489349\pi\)
−0.999440 + 0.0334536i \(0.989349\pi\)
\(308\) 2.45255e10 + 2.45255e10i 0.155288 + 0.155288i
\(309\) 5.90595e9 + 1.49176e10i 0.0368533 + 0.0930860i
\(310\) 2.66788e9 + 3.98502e10i 0.0164073 + 0.245077i
\(311\) 2.76803e11i 1.67784i −0.544259 0.838918i \(-0.683189\pi\)
0.544259 0.838918i \(-0.316811\pi\)
\(312\) 2.78653e10 6.43895e10i 0.166482 0.384698i
\(313\) 1.77661e11 1.77661e11i 1.04626 1.04626i 0.0473879 0.998877i \(-0.484910\pi\)
0.998877 0.0473879i \(-0.0150897\pi\)
\(314\) −1.42089e11 −0.824852
\(315\) 1.93478e11 + 1.80245e11i 1.10722 + 1.03149i
\(316\) −5.91809e9 −0.0333879
\(317\) −1.65689e11 + 1.65689e11i −0.921568 + 0.921568i −0.997140 0.0755723i \(-0.975922\pi\)
0.0755723 + 0.997140i \(0.475922\pi\)
\(318\) 7.04269e10 1.62738e11i 0.386204 0.892417i
\(319\) 1.97051e11i 1.06542i
\(320\) −1.56691e11 1.37027e11i −0.835352 0.730520i
\(321\) −1.16485e11 2.94224e11i −0.612346 1.54670i
\(322\) −2.22926e11 2.22926e11i −1.15560 1.15560i
\(323\) 1.60343e10 + 1.60343e10i 0.0819670 + 0.0819670i
\(324\) −4.91201e10 3.09418e9i −0.247632 0.0155989i
\(325\) −6.19351e10 4.72499e10i −0.307937 0.234923i
\(326\) 6.01670e10i 0.295039i
\(327\) 2.30362e11 + 9.96918e10i 1.11416 + 0.482164i
\(328\) 6.60293e10 6.60293e10i 0.314996 0.314996i
\(329\) −2.66326e11 −1.25323
\(330\) 3.65996e10 1.02949e11i 0.169888 0.477867i
\(331\) 2.21445e11 1.01400 0.507002 0.861945i \(-0.330754\pi\)
0.507002 + 0.861945i \(0.330754\pi\)
\(332\) −6.03779e10 + 6.03779e10i −0.272745 + 0.272745i
\(333\) −7.16350e9 + 2.27667e11i −0.0319247 + 1.01461i
\(334\) 1.69367e11i 0.744682i
\(335\) 2.57933e11 1.72680e10i 1.11894 0.0749101i
\(336\) −2.26915e11 + 8.98369e10i −0.971262 + 0.384528i
\(337\) 1.22542e10 + 1.22542e10i 0.0517549 + 0.0517549i 0.732511 0.680756i \(-0.238348\pi\)
−0.680756 + 0.732511i \(0.738348\pi\)
\(338\) −1.25053e11 1.25053e11i −0.521159 0.521159i
\(339\) −1.56611e11 + 6.20034e10i −0.644058 + 0.254986i
\(340\) −5.28689e9 + 3.53945e8i −0.0214558 + 0.00143642i
\(341\) 4.13688e10i 0.165683i
\(342\) −9.22798e9 + 2.93279e11i −0.0364745 + 1.15921i
\(343\) −7.95199e10 + 7.95199e10i −0.310207 + 0.310207i
\(344\) −1.10186e11 −0.424242
\(345\) 1.09784e11 3.08804e11i 0.417209 1.17354i
\(346\) −2.72772e11 −1.02319
\(347\) 2.70672e11 2.70672e11i 1.00221 1.00221i 0.00221640 0.999998i \(-0.499294\pi\)
0.999998 0.00221640i \(-0.000705503\pi\)
\(348\) 1.13485e11 + 4.91120e10i 0.414794 + 0.179507i
\(349\) 8.22110e10i 0.296630i −0.988940 0.148315i \(-0.952615\pi\)
0.988940 0.148315i \(-0.0473850\pi\)
\(350\) 4.91035e10 + 3.65086e11i 0.174906 + 1.30044i
\(351\) 4.69014e10 9.96556e10i 0.164932 0.350445i
\(352\) −5.76190e10 5.76190e10i −0.200043 0.200043i
\(353\) 7.63738e10 + 7.63738e10i 0.261793 + 0.261793i 0.825782 0.563989i \(-0.190734\pi\)
−0.563989 + 0.825782i \(0.690734\pi\)
\(354\) 3.07525e10 + 7.76763e10i 0.104080 + 0.262890i
\(355\) 1.70853e11 + 1.49412e11i 0.570948 + 0.499297i
\(356\) 2.53872e10i 0.0837703i
\(357\) −1.59859e10 + 3.69392e10i −0.0520870 + 0.120360i
\(358\) 2.22610e11 2.22610e11i 0.716260 0.716260i
\(359\) 5.59194e11 1.77679 0.888397 0.459076i \(-0.151819\pi\)
0.888397 + 0.459076i \(0.151819\pi\)
\(360\) −2.52358e11 2.35098e11i −0.791873 0.737713i
\(361\) −2.54600e11 −0.788997
\(362\) 3.56759e11 3.56759e11i 1.09191 1.09191i
\(363\) −8.64390e10 + 1.99738e11i −0.261294 + 0.603783i
\(364\) 4.87077e10i 0.145426i
\(365\) −1.85464e10 2.77029e11i −0.0546944 0.816972i
\(366\) 5.79442e10 + 1.46359e11i 0.168789 + 0.426337i
\(367\) −1.90433e11 1.90433e11i −0.547956 0.547956i 0.377893 0.925849i \(-0.376649\pi\)
−0.925849 + 0.377893i \(0.876649\pi\)
\(368\) 2.13889e11 + 2.13889e11i 0.607956 + 0.607956i
\(369\) 1.06864e11 1.00344e11i 0.300064 0.281757i
\(370\) −2.08889e11 + 2.38866e11i −0.579440 + 0.662591i
\(371\) 6.19246e11i 1.69699i
\(372\) 2.38250e10 + 1.03105e10i 0.0645045 + 0.0279151i
\(373\) 8.34593e10 8.34593e10i 0.223247 0.223247i −0.586618 0.809864i \(-0.699541\pi\)
0.809864 + 0.586618i \(0.199541\pi\)
\(374\) 1.66312e10 0.0439542
\(375\) −3.20843e11 + 2.09069e11i −0.837822 + 0.545944i
\(376\) 3.47376e11 0.896301
\(377\) −1.95673e11 + 1.95673e11i −0.498877 + 0.498877i
\(378\) −4.90048e11 + 1.76396e11i −1.23460 + 0.444402i
\(379\) 5.62115e10i 0.139942i −0.997549 0.0699711i \(-0.977709\pi\)
0.997549 0.0699711i \(-0.0222907\pi\)
\(380\) 8.88010e10 1.01544e11i 0.218470 0.249821i
\(381\) 2.54988e10 1.00951e10i 0.0619951 0.0245442i
\(382\) 6.31390e10 + 6.31390e10i 0.151709 + 0.151709i
\(383\) 6.81602e10 + 6.81602e10i 0.161859 + 0.161859i 0.783390 0.621531i \(-0.213489\pi\)
−0.621531 + 0.783390i \(0.713489\pi\)
\(384\) 1.89588e11 7.50590e10i 0.444960 0.176162i
\(385\) 2.54874e10 + 3.80706e11i 0.0591224 + 0.883113i
\(386\) 1.36055e11i 0.311941i
\(387\) −1.72889e11 5.43993e9i −0.391804 0.0123280i
\(388\) −1.24928e11 + 1.24928e11i −0.279845 + 0.279845i
\(389\) −5.84018e11 −1.29316 −0.646581 0.762845i \(-0.723802\pi\)
−0.646581 + 0.762845i \(0.723802\pi\)
\(390\) 1.38572e11 6.58847e10i 0.303308 0.144209i
\(391\) 4.98869e10 0.107942
\(392\) 4.61489e11 4.61489e11i 0.987129 0.987129i
\(393\) −1.88945e11 8.17680e10i −0.399548 0.172909i
\(394\) 1.39570e11i 0.291782i
\(395\) −4.90080e10 4.28578e10i −0.101293 0.0885814i
\(396\) −4.86137e10 5.17724e10i −0.0993415 0.105796i
\(397\) 3.89039e11 + 3.89039e11i 0.786024 + 0.786024i 0.980840 0.194816i \(-0.0624109\pi\)
−0.194816 + 0.980840i \(0.562411\pi\)
\(398\) −4.40259e11 4.40259e11i −0.879497 0.879497i
\(399\) −3.77195e11 9.52738e11i −0.745053 1.88190i
\(400\) −4.71128e10 3.50286e11i −0.0920172 0.684152i
\(401\) 2.18705e11i 0.422385i −0.977445 0.211192i \(-0.932265\pi\)
0.977445 0.211192i \(-0.0677347\pi\)
\(402\) −2.02227e11 + 4.67293e11i −0.386208 + 0.892426i
\(403\) −4.10794e10 + 4.10794e10i −0.0775802 + 0.0775802i
\(404\) 5.00230e10 0.0934229
\(405\) −3.84359e11 3.81342e11i −0.709887 0.704316i
\(406\) 1.30856e12 2.39015
\(407\) −2.32409e11 + 2.32409e11i −0.419835 + 0.419835i
\(408\) 2.08508e10 4.81808e10i 0.0372522 0.0860801i
\(409\) 2.80172e11i 0.495074i −0.968878 0.247537i \(-0.920379\pi\)
0.968878 0.247537i \(-0.0796212\pi\)
\(410\) 2.03760e11 1.36412e10i 0.356116 0.0238411i
\(411\) −1.54065e11 3.89147e11i −0.266328 0.672706i
\(412\) 1.02729e10 + 1.02729e10i 0.0175653 + 0.0175653i
\(413\) −2.06295e11 2.06295e11i −0.348909 0.348909i
\(414\) 4.41878e11 + 4.70589e11i 0.739266 + 0.787300i
\(415\) −9.37239e11 + 6.27460e10i −1.55108 + 0.103841i
\(416\) 1.14432e11i 0.187338i
\(417\) 6.29984e11 + 2.72633e11i 1.02028 + 0.441536i
\(418\) −2.99388e11 + 2.99388e11i −0.479669 + 0.479669i
\(419\) 4.77789e11 0.757309 0.378654 0.925538i \(-0.376387\pi\)
0.378654 + 0.925538i \(0.376387\pi\)
\(420\) 2.25607e11 + 8.02065e10i 0.353778 + 0.125773i
\(421\) −6.62033e11 −1.02709 −0.513547 0.858062i \(-0.671669\pi\)
−0.513547 + 0.858062i \(0.671669\pi\)
\(422\) −5.90390e11 + 5.90390e11i −0.906219 + 0.906219i
\(423\) 5.45055e11 + 1.71501e10i 0.827767 + 0.0260456i
\(424\) 8.07697e11i 1.21367i
\(425\) −4.63442e10 3.53557e10i −0.0689041 0.0525665i
\(426\) −4.15659e11 + 1.64562e11i −0.611497 + 0.242095i
\(427\) −3.88703e11 3.88703e11i −0.565838 0.565838i
\(428\) −2.02615e11 2.02615e11i −0.291860 0.291860i
\(429\) 1.47769e11 5.85027e10i 0.210633 0.0833907i
\(430\) −1.81394e11 1.58630e11i −0.255867 0.223757i
\(431\) 1.11904e12i 1.56206i 0.624496 + 0.781028i \(0.285304\pi\)
−0.624496 + 0.781028i \(0.714696\pi\)
\(432\) 4.70182e11 1.69245e11i 0.649515 0.233797i
\(433\) 5.97670e11 5.97670e11i 0.817083 0.817083i −0.168602 0.985684i \(-0.553925\pi\)
0.985684 + 0.168602i \(0.0539252\pi\)
\(434\) 2.74717e11 0.371691
\(435\) 5.84116e11 + 1.22854e12i 0.782163 + 1.64508i
\(436\) 2.27289e11 0.301224
\(437\) −8.98045e11 + 8.98045e11i −1.17796 + 1.17796i
\(438\) 5.01890e11 + 2.17198e11i 0.651590 + 0.281983i
\(439\) 1.32725e12i 1.70554i 0.522285 + 0.852771i \(0.325080\pi\)
−0.522285 + 0.852771i \(0.674920\pi\)
\(440\) −3.32438e10 4.96564e11i −0.0422838 0.631594i
\(441\) 7.46890e11 7.01322e11i 0.940336 0.882966i
\(442\) 1.65148e10 + 1.65148e10i 0.0205813 + 0.0205813i
\(443\) 5.29633e11 + 5.29633e11i 0.653369 + 0.653369i 0.953803 0.300434i \(-0.0971314\pi\)
−0.300434 + 0.953803i \(0.597131\pi\)
\(444\) 7.59240e10 + 1.91773e11i 0.0927162 + 0.234188i
\(445\) −1.83850e11 + 2.10233e11i −0.222251 + 0.254144i
\(446\) 1.08886e12i 1.30307i
\(447\) 4.72608e10 1.09208e11i 0.0559909 0.129380i
\(448\) −1.01241e12 + 1.01241e12i −1.18743 + 1.18743i
\(449\) 4.03309e11 0.468306 0.234153 0.972200i \(-0.424768\pi\)
0.234153 + 0.972200i \(0.424768\pi\)
\(450\) −7.69839e10 7.50336e11i −0.0885000 0.862580i
\(451\) 2.11525e11 0.240750
\(452\) −1.07849e11 + 1.07849e11i −0.121533 + 0.121533i
\(453\) 3.57001e10 8.24938e10i 0.0398316 0.0920406i
\(454\) 4.46439e10i 0.0493186i
\(455\) −3.52733e11 + 4.03351e11i −0.385829 + 0.441196i
\(456\) 4.91984e11 + 1.24268e12i 0.532855 + 1.34591i
\(457\) 3.18544e11 + 3.18544e11i 0.341623 + 0.341623i 0.856977 0.515354i \(-0.172340\pi\)
−0.515354 + 0.856977i \(0.672340\pi\)
\(458\) −1.83118e11 1.83118e11i −0.194462 0.194462i
\(459\) 3.50949e10 7.45693e10i 0.0369052 0.0784157i
\(460\) −1.98237e10 2.96107e11i −0.0206430 0.308346i
\(461\) 3.17205e11i 0.327104i −0.986535 0.163552i \(-0.947705\pi\)
0.986535 0.163552i \(-0.0522951\pi\)
\(462\) −6.89719e11 2.98484e11i −0.704342 0.304812i
\(463\) 7.62052e11 7.62052e11i 0.770673 0.770673i −0.207551 0.978224i \(-0.566549\pi\)
0.978224 + 0.207551i \(0.0665492\pi\)
\(464\) −1.25551e12 −1.25744
\(465\) 1.22629e11 + 2.57919e11i 0.121634 + 0.255826i
\(466\) −8.60756e11 −0.845558
\(467\) 8.83707e11 8.83707e11i 0.859771 0.859771i −0.131540 0.991311i \(-0.541992\pi\)
0.991311 + 0.131540i \(0.0419923\pi\)
\(468\) 3.13653e9 9.96837e10i 0.00302234 0.0960545i
\(469\) 1.77813e12i 1.69701i
\(470\) 5.71866e11 + 5.00100e11i 0.540572 + 0.472734i
\(471\) −9.44666e11 + 3.73999e11i −0.884472 + 0.350168i
\(472\) 2.69075e11 + 2.69075e11i 0.249537 + 0.249537i
\(473\) −1.76491e11 1.76491e11i −0.162124 0.162124i
\(474\) 1.19229e11 4.72033e10i 0.108487 0.0429506i
\(475\) 1.47073e12 1.97811e11i 1.32560 0.178291i
\(476\) 3.64465e10i 0.0325405i
\(477\) 3.98763e10 1.26733e12i 0.0352681 1.12087i
\(478\) −5.39077e11 + 5.39077e11i −0.472308 + 0.472308i
\(479\) −1.64692e11 −0.142943 −0.0714716 0.997443i \(-0.522770\pi\)
−0.0714716 + 0.997443i \(0.522770\pi\)
\(480\) −5.30031e11 1.88433e11i −0.455739 0.162021i
\(481\) −4.61566e11 −0.393171
\(482\) −3.11019e11 + 3.11019e11i −0.262468 + 0.262468i
\(483\) −2.06888e12 8.95333e11i −1.72971 0.748553i
\(484\) 1.97074e11i 0.163239i
\(485\) −1.93925e12 + 1.29828e11i −1.59146 + 0.106544i
\(486\) 1.01428e12 3.29450e11i 0.824695 0.267872i
\(487\) 7.10366e11 + 7.10366e11i 0.572271 + 0.572271i 0.932763 0.360491i \(-0.117391\pi\)
−0.360491 + 0.932763i \(0.617391\pi\)
\(488\) 5.06994e11 + 5.06994e11i 0.404682 + 0.404682i
\(489\) 1.58369e11 + 4.00016e11i 0.125250 + 0.316364i
\(490\) 1.42411e12 9.53408e10i 1.11599 0.0747130i
\(491\) 1.44637e12i 1.12308i −0.827449 0.561541i \(-0.810209\pi\)
0.827449 0.561541i \(-0.189791\pi\)
\(492\) 5.27194e10 1.21821e11i 0.0405627 0.0937300i
\(493\) −1.46416e11 + 1.46416e11i −0.111629 + 0.111629i
\(494\) −5.94587e11 −0.449204
\(495\) −2.76461e10 7.80782e11i −0.0206972 0.584529i
\(496\) −2.63580e11 −0.195544
\(497\) 1.10392e12 1.10392e12i 0.811583 0.811583i
\(498\) 7.34822e11 1.69798e12i 0.535365 1.23709i
\(499\) 3.54572e11i 0.256007i 0.991774 + 0.128004i \(0.0408569\pi\)
−0.991774 + 0.128004i \(0.959143\pi\)
\(500\) −1.91440e11 + 2.89128e11i −0.136983 + 0.206883i
\(501\) 4.45801e11 + 1.12603e12i 0.316134 + 0.798508i
\(502\) −7.49492e11 7.49492e11i −0.526745 0.526745i
\(503\) 3.04846e11 + 3.04846e11i 0.212336 + 0.212336i 0.805259 0.592923i \(-0.202026\pi\)
−0.592923 + 0.805259i \(0.702026\pi\)
\(504\) −1.72942e12 + 1.62391e12i −1.19389 + 1.12105i
\(505\) 4.14243e11 + 3.62258e11i 0.283429 + 0.247860i
\(506\) 9.31475e11i 0.631675i
\(507\) −1.16057e12 5.02249e11i −0.780072 0.337585i
\(508\) 1.75596e10 1.75596e10i 0.0116984 0.0116984i
\(509\) 2.24323e12 1.48130 0.740652 0.671889i \(-0.234517\pi\)
0.740652 + 0.671889i \(0.234517\pi\)
\(510\) 1.03689e11 4.92995e10i 0.0678683 0.0322684i
\(511\) −1.90977e12 −1.23905
\(512\) 1.18856e12 1.18856e12i 0.764374 0.764374i
\(513\) 7.10603e11 + 1.97413e12i 0.453001 + 1.25849i
\(514\) 1.47823e12i 0.934133i
\(515\) 1.06758e10 + 1.59465e11i 0.00668755 + 0.0998922i
\(516\) −1.45632e11 + 5.76564e10i −0.0904341 + 0.0358034i
\(517\) 5.56409e11 + 5.56409e11i 0.342520 + 0.342520i
\(518\) 1.54336e12 + 1.54336e12i 0.941852 + 0.941852i
\(519\) −1.81351e12 + 7.17978e11i −1.09715 + 0.434368i
\(520\) 4.60078e11 5.26101e11i 0.275941 0.315539i
\(521\) 8.77749e10i 0.0521916i −0.999659 0.0260958i \(-0.991693\pi\)
0.999659 0.0260958i \(-0.00830750\pi\)
\(522\) −2.67805e12 8.42645e10i −1.57871 0.0496738i
\(523\) 3.06455e11 3.06455e11i 0.179106 0.179106i −0.611860 0.790966i \(-0.709578\pi\)
0.790966 + 0.611860i \(0.209578\pi\)
\(524\) −1.86425e11 −0.108022
\(525\) 1.28742e12 + 2.29800e12i 0.739613 + 1.32018i
\(526\) 1.13085e11 0.0644121
\(527\) −3.07384e10 + 3.07384e10i −0.0173594 + 0.0173594i
\(528\) 6.61758e11 + 2.86384e11i 0.370550 + 0.160360i
\(529\) 9.92900e11i 0.551258i
\(530\) 1.16280e12 1.32967e12i 0.640125 0.731985i
\(531\) 4.08912e11 + 4.35480e11i 0.223205 + 0.237708i
\(532\) −6.56097e11 6.56097e11i −0.355112 0.355112i
\(533\) 2.10045e11 + 2.10045e11i 0.112730 + 0.112730i
\(534\) −2.02491e11 5.11463e11i −0.107763 0.272194i
\(535\) −2.10562e11 3.14517e12i −0.111119 1.65979i
\(536\) 2.31925e12i 1.21369i
\(537\) 8.94063e11 2.06595e12i 0.463963 1.07210i
\(538\) 1.07165e10 1.07165e10i 0.00551483 0.00551483i
\(539\) 1.47838e12 0.754461
\(540\) −4.56556e11 1.78676e11i −0.231059 0.0904263i
\(541\) −2.50327e12 −1.25638 −0.628189 0.778061i \(-0.716203\pi\)
−0.628189 + 0.778061i \(0.716203\pi\)
\(542\) −3.61267e11 + 3.61267e11i −0.179817 + 0.179817i
\(543\) 1.43284e12 3.31093e12i 0.707294 1.63437i
\(544\) 8.56258e10i 0.0419189i
\(545\) 1.88219e12 + 1.64599e12i 0.913860 + 0.799177i
\(546\) −3.88498e11 9.81289e11i −0.187078 0.472531i
\(547\) 1.69084e12 + 1.69084e12i 0.807532 + 0.807532i 0.984260 0.176727i \(-0.0565511\pi\)
−0.176727 + 0.984260i \(0.556551\pi\)
\(548\) −2.67983e11 2.67983e11i −0.126939 0.126939i
\(549\) 7.70476e11 + 8.20537e11i 0.361979 + 0.385498i
\(550\) 6.60152e11 8.65326e11i 0.307618 0.403225i
\(551\) 5.27145e12i 2.43640i
\(552\) 2.69850e12 + 1.16780e12i 1.23707 + 0.535358i
\(553\) −3.16650e11 + 3.16650e11i −0.143985 + 0.143985i
\(554\) −4.81161e11 −0.217019
\(555\) −7.60056e11 + 2.13791e12i −0.340038 + 0.956469i
\(556\) 6.21581e11 0.275843
\(557\) −2.97369e12 + 2.97369e12i −1.30902 + 1.30902i −0.386905 + 0.922119i \(0.626456\pi\)
−0.922119 + 0.386905i \(0.873544\pi\)
\(558\) −5.62228e11 1.76904e10i −0.245504 0.00772475i
\(559\) 3.50512e11i 0.151827i
\(560\) −2.42566e12 + 1.62392e11i −1.04228 + 0.0697781i
\(561\) 1.10571e11 4.37758e10i 0.0471313 0.0186595i
\(562\) −2.04848e11 2.04848e11i −0.0866200 0.0866200i
\(563\) −5.00667e11 5.00667e11i −0.210020 0.210020i 0.594256 0.804276i \(-0.297447\pi\)
−0.804276 + 0.594256i \(0.797447\pi\)
\(564\) 4.59122e11 1.81769e11i 0.191061 0.0756421i
\(565\) −1.67413e12 + 1.12079e11i −0.691149 + 0.0462709i
\(566\) 2.23829e12i 0.916732i
\(567\) −2.79375e12 + 2.46264e12i −1.13518 + 1.00064i
\(568\) −1.43987e12 + 1.43987e12i −0.580437 + 0.580437i
\(569\) −3.50215e12 −1.40065 −0.700326 0.713823i \(-0.746962\pi\)
−0.700326 + 0.713823i \(0.746962\pi\)
\(570\) −9.79100e11 + 2.75404e12i −0.388499 + 1.09278i
\(571\) −6.74836e11 −0.265666 −0.132833 0.991138i \(-0.542407\pi\)
−0.132833 + 0.991138i \(0.542407\pi\)
\(572\) 1.01760e11 1.01760e11i 0.0397462 0.0397462i
\(573\) 5.85966e11 + 2.53584e11i 0.227079 + 0.0982710i
\(574\) 1.40467e12i 0.540096i
\(575\) 1.98019e12 2.59563e12i 0.755443 0.990234i
\(576\) 2.13717e12 2.00678e12i 0.808978 0.759623i
\(577\) 5.21939e11 + 5.21939e11i 0.196033 + 0.196033i 0.798297 0.602264i \(-0.205735\pi\)
−0.602264 + 0.798297i \(0.705735\pi\)
\(578\) −1.63290e12 1.63290e12i −0.608533 0.608533i
\(579\) −3.58118e11 9.04553e11i −0.132426 0.334488i
\(580\) 9.27241e11 + 8.10878e11i 0.340225 + 0.297529i
\(581\) 6.46110e12i 2.35241i
\(582\) 1.52042e12 3.51330e12i 0.549302 1.26929i
\(583\) 1.29373e12 1.29373e12i 0.463804 0.463804i
\(584\) 2.49096e12 0.886154
\(585\) 7.47866e11 8.02771e11i 0.264011 0.283394i
\(586\) 3.25174e12 1.13914
\(587\) 4.42151e11 4.42151e11i 0.153709 0.153709i −0.626063 0.779772i \(-0.715335\pi\)
0.779772 + 0.626063i \(0.215335\pi\)
\(588\) 3.68464e11 8.51424e11i 0.127115 0.293730i
\(589\) 1.10668e12i 0.378883i
\(590\) 5.55893e10 + 8.30338e11i 0.0188867 + 0.282112i
\(591\) −3.67369e11 9.27919e11i −0.123868 0.312872i
\(592\) −1.48079e12 1.48079e12i −0.495502 0.495502i
\(593\) −3.56617e12 3.56617e12i −1.18428 1.18428i −0.978624 0.205659i \(-0.934066\pi\)
−0.205659 0.978624i \(-0.565934\pi\)
\(594\) 1.39234e12 + 6.55283e11i 0.458887 + 0.215968i
\(595\) −2.63939e11 + 3.01815e11i −0.0863332 + 0.0987222i
\(596\) 1.07751e11i 0.0349794i
\(597\) −4.08586e12 1.76820e12i −1.31643 0.569702i
\(598\) −9.24957e11 + 9.24957e11i −0.295778 + 0.295778i
\(599\) −4.70831e12 −1.49432 −0.747161 0.664644i \(-0.768583\pi\)
−0.747161 + 0.664644i \(0.768583\pi\)
\(600\) −1.67922e12 2.99734e12i −0.528964 0.944182i
\(601\) 4.62688e12 1.44661 0.723307 0.690526i \(-0.242621\pi\)
0.723307 + 0.690526i \(0.242621\pi\)
\(602\) −1.17202e12 + 1.17202e12i −0.363706 + 0.363706i
\(603\) −1.14502e11 + 3.63906e12i −0.0352685 + 1.12089i
\(604\) 8.13934e10i 0.0248842i
\(605\) −1.42717e12 + 1.63198e12i −0.433090 + 0.495239i
\(606\) −1.00779e12 + 3.98989e11i −0.303558 + 0.120180i
\(607\) 2.35211e12 + 2.35211e12i 0.703247 + 0.703247i 0.965106 0.261859i \(-0.0843356\pi\)
−0.261859 + 0.965106i \(0.584336\pi\)
\(608\) 1.54140e12 + 1.54140e12i 0.457457 + 0.457457i
\(609\) 8.69984e12 3.44432e12i 2.56291 1.01467i
\(610\) 1.04742e11 + 1.56453e12i 0.0306292 + 0.457510i
\(611\) 1.10503e12i 0.320766i
\(612\) 2.34697e9 7.45903e10i 0.000676281 0.0214932i
\(613\) −1.73213e12 + 1.73213e12i −0.495459 + 0.495459i −0.910021 0.414562i \(-0.863935\pi\)
0.414562 + 0.910021i \(0.363935\pi\)
\(614\) 4.17174e12 1.18457
\(615\) 1.31878e12 6.27019e11i 0.371735 0.176743i
\(616\) −3.42319e12 −0.957895
\(617\) 2.29690e12 2.29690e12i 0.638057 0.638057i −0.312019 0.950076i \(-0.601005\pi\)
0.950076 + 0.312019i \(0.101005\pi\)
\(618\) −2.88900e11 1.25025e11i −0.0796708 0.0344784i
\(619\) 2.90444e12i 0.795160i −0.917567 0.397580i \(-0.869850\pi\)
0.917567 0.397580i \(-0.130150\pi\)
\(620\) 1.94664e11 + 1.70235e11i 0.0529083 + 0.0462687i
\(621\) 4.17646e12 + 1.96559e12i 1.12693 + 0.530371i
\(622\) 3.84029e12 + 3.84029e12i 1.02874 + 1.02874i
\(623\) 1.35836e12 + 1.35836e12i 0.361258 + 0.361258i
\(624\) 3.72748e11 + 9.41508e11i 0.0984204 + 0.248595i
\(625\) −3.67914e12 + 1.00791e12i −0.964463 + 0.264217i
\(626\) 4.92963e12i 1.28301i
\(627\) −1.20243e12 + 2.77850e12i −0.310710 + 0.717970i
\(628\) −6.50538e11 + 6.50538e11i −0.166899 + 0.166899i
\(629\) −3.45376e11 −0.0879760
\(630\) −5.18493e12 + 1.83589e11i −1.31132 + 0.0464317i
\(631\) −4.43420e12 −1.11348 −0.556742 0.830686i \(-0.687949\pi\)
−0.556742 + 0.830686i \(0.687949\pi\)
\(632\) 4.13015e11 4.13015e11i 0.102977 0.102977i
\(633\) −2.37117e12 + 5.47916e12i −0.587011 + 1.35643i
\(634\) 4.59745e12i 1.13010i
\(635\) 2.72575e11 1.82483e10i 0.0665280 0.00445389i
\(636\) −4.22638e11 1.06752e12i −0.102426 0.258714i
\(637\) 1.46804e12 + 1.46804e12i 0.353272 + 0.353272i
\(638\) −2.73384e12 2.73384e12i −0.653250 0.653250i
\(639\) −2.33033e12 + 2.18816e12i −0.552922 + 0.519188i
\(640\) 2.02664e12 1.35679e11i 0.477494 0.0319671i
\(641\) 2.50250e12i 0.585482i −0.956192 0.292741i \(-0.905433\pi\)
0.956192 0.292741i \(-0.0945673\pi\)
\(642\) 5.69806e12 + 2.46590e12i 1.32379 + 0.572886i
\(643\) −1.41508e12 + 1.41508e12i −0.326461 + 0.326461i −0.851239 0.524778i \(-0.824148\pi\)
0.524778 + 0.851239i \(0.324148\pi\)
\(644\) −2.04129e12 −0.467647
\(645\) −1.62352e12 5.77184e11i −0.369351 0.131309i
\(646\) −4.44912e11 −0.100514
\(647\) 2.28194e12 2.28194e12i 0.511960 0.511960i −0.403167 0.915127i \(-0.632091\pi\)
0.915127 + 0.403167i \(0.132091\pi\)
\(648\) 3.64396e12 3.21208e12i 0.811869 0.715647i
\(649\) 8.61982e11i 0.190720i
\(650\) 1.51480e12 2.03738e11i 0.332848 0.0447675i
\(651\) 1.82644e12 7.23098e11i 0.398557 0.157791i
\(652\) 2.75468e11 + 2.75468e11i 0.0596977 + 0.0596977i
\(653\) 2.35221e12 + 2.35221e12i 0.506252 + 0.506252i 0.913374 0.407122i \(-0.133468\pi\)
−0.407122 + 0.913374i \(0.633468\pi\)
\(654\) −4.57908e12 + 1.81288e12i −0.978764 + 0.387498i
\(655\) −1.54379e12 1.35005e12i −0.327720 0.286593i
\(656\) 1.34773e12i 0.284141i
\(657\) 3.90848e12 + 1.22980e11i 0.818396 + 0.0257507i
\(658\) 3.69494e12 3.69494e12i 0.768406 0.768406i
\(659\) −1.43151e12 −0.295673 −0.147836 0.989012i \(-0.547231\pi\)
−0.147836 + 0.989012i \(0.547231\pi\)
\(660\) −3.03772e11 6.38907e11i −0.0623160 0.131066i
\(661\) 6.21365e12 1.26602 0.633009 0.774144i \(-0.281819\pi\)
0.633009 + 0.774144i \(0.281819\pi\)
\(662\) −3.07226e12 + 3.07226e12i −0.621724 + 0.621724i
\(663\) 1.53267e11 + 6.63281e10i 0.0308062 + 0.0133317i
\(664\) 8.42737e12i 1.68243i
\(665\) −6.81829e11 1.01845e13i −0.135201 2.01949i
\(666\) −3.05920e12 3.25797e12i −0.602524 0.641672i
\(667\) −8.20042e12 8.20042e12i −1.60424 1.60424i
\(668\) 7.75431e11 + 7.75431e11i 0.150678 + 0.150678i
\(669\) −2.86606e12 7.23924e12i −0.553181 1.39725i
\(670\) −3.33892e12 + 3.81806e12i −0.640132 + 0.731992i
\(671\) 1.62416e12i 0.309297i
\(672\) −1.53675e12 + 3.55103e12i −0.290697 + 0.671726i
\(673\) 6.01077e10 6.01077e10i 0.0112944 0.0112944i −0.701437 0.712731i \(-0.747458\pi\)
0.712731 + 0.701437i \(0.247458\pi\)
\(674\) −3.40024e11 −0.0634659
\(675\) −2.48682e12 4.78592e12i −0.461081 0.887358i
\(676\) −1.14509e12 −0.210901
\(677\) 1.60635e12 1.60635e12i 0.293894 0.293894i −0.544723 0.838616i \(-0.683365\pi\)
0.838616 + 0.544723i \(0.183365\pi\)
\(678\) 1.31257e12 3.03300e12i 0.238555 0.551238i
\(679\) 1.33687e13i 2.41365i
\(680\) 3.44263e11 3.93665e11i 0.0617447 0.0706052i
\(681\) 1.17510e11 + 2.96812e11i 0.0209368 + 0.0528834i
\(682\) −5.73940e11 5.73940e11i −0.101587 0.101587i
\(683\) 1.16448e12 + 1.16448e12i 0.204757 + 0.204757i 0.802034 0.597278i \(-0.203751\pi\)
−0.597278 + 0.802034i \(0.703751\pi\)
\(684\) 1.30050e12 + 1.38500e12i 0.227173 + 0.241934i
\(685\) −2.78494e11 4.15987e12i −0.0483290 0.721892i
\(686\) 2.20647e12i 0.380400i
\(687\) −1.69944e12 7.35451e11i −0.291072 0.125965i
\(688\) 1.12451e12 1.12451e12i 0.191344 0.191344i
\(689\) 2.56935e12 0.434347
\(690\) 2.76115e12 + 5.80739e12i 0.463735 + 0.975349i
\(691\) 4.63663e12 0.773661 0.386831 0.922151i \(-0.373570\pi\)
0.386831 + 0.922151i \(0.373570\pi\)
\(692\) −1.24886e12 + 1.24886e12i −0.207032 + 0.207032i
\(693\) −5.37121e12 1.69004e11i −0.884652 0.0278354i
\(694\) 7.51046e12i 1.22899i
\(695\) 5.14734e12 + 4.50138e12i 0.836857 + 0.731837i
\(696\) −1.13474e13 + 4.49251e12i −1.83297 + 0.725684i
\(697\) 1.57170e11 + 1.57170e11i 0.0252245 + 0.0252245i
\(698\) 1.14057e12 + 1.14057e12i 0.181875 + 0.181875i
\(699\) −5.72268e12 + 2.26564e12i −0.906676 + 0.358958i
\(700\) 1.89632e12 + 1.44669e12i 0.298519 + 0.227738i
\(701\) 2.76654e12i 0.432719i −0.976314 0.216360i \(-0.930582\pi\)
0.976314 0.216360i \(-0.0694184\pi\)
\(702\) 7.31898e11 + 2.03329e12i 0.113745 + 0.315997i
\(703\) 6.21733e12 6.21733e12i 0.960075 0.960075i
\(704\) 4.23027e12 0.649069
\(705\) 5.11835e12 + 1.81964e12i 0.780331 + 0.277418i
\(706\) −2.11918e12 −0.321031
\(707\) 2.67650e12 2.67650e12i 0.402884 0.402884i
\(708\) 4.96430e11 + 2.14836e11i 0.0742521 + 0.0321334i
\(709\) 2.72772e12i 0.405407i 0.979240 + 0.202703i \(0.0649727\pi\)
−0.979240 + 0.202703i \(0.935027\pi\)
\(710\) −4.44328e12 + 2.97468e11i −0.656208 + 0.0439316i
\(711\) 6.68437e11 6.27656e11i 0.0980951 0.0921103i
\(712\) −1.77174e12 1.77174e12i −0.258368 0.258368i
\(713\) −1.72159e12 1.72159e12i −0.249475 0.249475i
\(714\) −2.90701e11 7.34269e11i −0.0418606 0.105734i
\(715\) 1.57961e12 1.05751e11i 0.226034 0.0151324i
\(716\) 2.03839e12i 0.289854i
\(717\) −2.16509e12 + 5.00295e12i −0.305942 + 0.706952i
\(718\) −7.75810e12 + 7.75810e12i −1.08942 + 1.08942i
\(719\) 7.38296e12 1.03027 0.515134 0.857109i \(-0.327742\pi\)
0.515134 + 0.857109i \(0.327742\pi\)
\(720\) 4.97473e12 1.76147e11i 0.689880 0.0244274i
\(721\) 1.09931e12 0.151500
\(722\) 3.53225e12 3.53225e12i 0.483764 0.483764i
\(723\) −1.24914e12 + 2.88644e12i −0.170016 + 0.392862i
\(724\) 3.26677e12i 0.441871i
\(725\) 1.80629e12 + 1.34298e13i 0.242810 + 1.80530i
\(726\) −1.57188e12 3.97034e12i −0.209993 0.530412i
\(727\) −2.42923e12 2.42923e12i −0.322525 0.322525i 0.527210 0.849735i \(-0.323238\pi\)
−0.849735 + 0.527210i \(0.823238\pi\)
\(728\) −3.39924e12 3.39924e12i −0.448529 0.448529i
\(729\) 5.87619e12 4.86006e12i 0.770587 0.637335i
\(730\) 4.10073e12 + 3.58612e12i 0.534452 + 0.467382i
\(731\) 2.62277e11i 0.0339729i
\(732\) 9.35379e11 + 4.04796e11i 0.120417 + 0.0521119i
\(733\) 1.70574e12 1.70574e12i 0.218246 0.218246i −0.589513 0.807759i \(-0.700680\pi\)
0.807759 + 0.589513i \(0.200680\pi\)
\(734\) 5.28404e12 0.671945
\(735\) 9.21713e12 4.38233e12i 1.16494 0.553876i
\(736\) 4.79571e12 0.602424
\(737\) −3.71486e12 + 3.71486e12i −0.463809 + 0.463809i
\(738\) −9.04538e10 + 2.87476e12i −0.0112247 + 0.356736i
\(739\) 1.37205e13i 1.69227i 0.532970 + 0.846134i \(0.321076\pi\)
−0.532970 + 0.846134i \(0.678924\pi\)
\(740\) 1.37243e11 + 2.05000e12i 0.0168247 + 0.251311i
\(741\) −3.95307e12 + 1.56504e12i −0.481673 + 0.190697i
\(742\) −8.59125e12 8.59125e12i −1.04049 1.04049i
\(743\) 5.78641e12 + 5.78641e12i 0.696562 + 0.696562i 0.963667 0.267105i \(-0.0860672\pi\)
−0.267105 + 0.963667i \(0.586067\pi\)
\(744\) −2.38227e12 + 9.43154e11i −0.285045 + 0.112851i
\(745\) 7.80313e11 8.92290e11i 0.0928038 0.106121i
\(746\) 2.31578e12i 0.273762i
\(747\) 4.16063e11 1.32231e13i 0.0488895 1.55378i
\(748\) 7.61441e10 7.61441e10i 0.00889363 0.00889363i
\(749\) −2.16821e13 −2.51728
\(750\) 1.55072e12 7.35185e12i 0.178961 0.848440i
\(751\) 6.40009e11 0.0734186 0.0367093 0.999326i \(-0.488312\pi\)
0.0367093 + 0.999326i \(0.488312\pi\)
\(752\) −3.54514e12 + 3.54514e12i −0.404253 + 0.404253i
\(753\) −6.95572e12 3.01017e12i −0.788433 0.341204i
\(754\) 5.42942e12i 0.611762i
\(755\) 5.89437e11 6.74023e11i 0.0660201 0.0754942i
\(756\) −1.43602e12 + 3.05125e12i −0.159887 + 0.339727i
\(757\) −3.74748e12 3.74748e12i −0.414770 0.414770i 0.468626 0.883396i \(-0.344749\pi\)
−0.883396 + 0.468626i \(0.844749\pi\)
\(758\) 7.79863e11 + 7.79863e11i 0.0858039 + 0.0858039i
\(759\) 2.45178e12 + 6.19284e12i 0.268160 + 0.677333i
\(760\) 8.89327e11 + 1.32839e13i 0.0966942 + 1.44432i
\(761\) 1.13276e13i 1.22435i −0.790721 0.612176i \(-0.790294\pi\)
0.790721 0.612176i \(-0.209706\pi\)
\(762\) −2.13706e11 + 4.93820e11i −0.0229626 + 0.0530605i
\(763\) 1.21612e13 1.21612e13i 1.29902 1.29902i
\(764\) 5.78150e11 0.0613933
\(765\) 5.59606e11 6.00690e11i 0.0590752 0.0634123i
\(766\) −1.89127e12 −0.198484
\(767\) −8.55951e11 + 8.55951e11i −0.0893037 + 0.0893037i
\(768\) 2.66028e12 6.14721e12i 0.275931 0.637606i
\(769\) 6.02880e11i 0.0621674i −0.999517 0.0310837i \(-0.990104\pi\)
0.999517 0.0310837i \(-0.00989584\pi\)
\(770\) −5.63542e12 4.92820e12i −0.577720 0.505220i
\(771\) 3.89093e12 + 9.82793e12i 0.396560 + 1.00165i
\(772\) −6.22914e11 6.22914e11i −0.0631176 0.0631176i
\(773\) −4.09904e12 4.09904e12i −0.412928 0.412928i 0.469829 0.882757i \(-0.344315\pi\)
−0.882757 + 0.469829i \(0.844315\pi\)
\(774\) 2.47409e12 2.32315e12i 0.247789 0.232671i
\(775\) 3.79211e11 + 2.81945e12i 0.0377593 + 0.280742i
\(776\) 1.74371e13i 1.72622i
\(777\) 1.43233e13 + 6.19855e12i 1.40977 + 0.610093i
\(778\) 8.10251e12 8.10251e12i 0.792887 0.792887i
\(779\) −5.65864e12 −0.550546
\(780\) 3.32790e11 9.36082e11i 0.0321918 0.0905500i
\(781\) −4.61261e12 −0.443626
\(782\) −6.92118e11 + 6.92118e11i −0.0661835 + 0.0661835i
\(783\) −1.80266e13 + 6.48881e12i −1.71390 + 0.616931i
\(784\) 9.41946e12i 0.890438i
\(785\) −1.00982e13 + 6.76053e11i −0.949142 + 0.0635429i
\(786\) 3.75580e12 1.48694e12i 0.350995 0.138961i
\(787\) −2.67793e12 2.67793e12i −0.248836 0.248836i 0.571657 0.820493i \(-0.306301\pi\)
−0.820493 + 0.571657i \(0.806301\pi\)
\(788\) −6.39006e11 6.39006e11i −0.0590387 0.0590387i
\(789\) 7.51835e11 2.97656e11i 0.0690679 0.0273444i
\(790\) 1.27452e12 8.53262e10i 0.116419 0.00779401i
\(791\) 1.15411e13i 1.04822i
\(792\) 7.00580e12 + 2.20436e11i 0.632695 + 0.0199077i
\(793\) −1.61279e12 + 1.61279e12i −0.144827 + 0.144827i
\(794\) −1.07948e13 −0.963883
\(795\) 4.23093e12 1.19009e13i 0.375650 1.05664i
\(796\) −4.03136e12 −0.355912
\(797\) −9.34648e12 + 9.34648e12i −0.820513 + 0.820513i −0.986182 0.165668i \(-0.947022\pi\)
0.165668 + 0.986182i \(0.447022\pi\)
\(798\) 1.84511e13 + 7.98494e12i 1.61068 + 0.697042i
\(799\) 8.26861e11i 0.0717748i
\(800\) −4.45514e12 3.39880e12i −0.384553 0.293373i
\(801\) −2.69250e12 2.86744e12i −0.231105 0.246121i
\(802\) 3.03425e12 + 3.03425e12i 0.258980 + 0.258980i
\(803\) 3.98990e12 + 3.98990e12i 0.338643 + 0.338643i
\(804\) 1.21358e12 + 3.06533e12i 0.102427 + 0.258717i
\(805\) −1.69040e13 1.47826e13i −1.41876 1.24071i
\(806\) 1.13985e12i 0.0951348i
\(807\) 4.30404e10 9.94551e10i 0.00357228 0.00825460i
\(808\) −3.49103e12 + 3.49103e12i −0.288139 + 0.288139i
\(809\) 2.30195e13 1.88942 0.944709 0.327909i \(-0.106344\pi\)
0.944709 + 0.327909i \(0.106344\pi\)
\(810\) 1.06231e13 4.18446e10i 0.867102 0.00341552i
\(811\) −1.59125e13 −1.29165 −0.645823 0.763487i \(-0.723486\pi\)
−0.645823 + 0.763487i \(0.723486\pi\)
\(812\) 5.99109e12 5.99109e12i 0.483619 0.483619i
\(813\) −1.45095e12 + 3.35277e12i −0.116478 + 0.269151i
\(814\) 6.44877e12i 0.514834i
\(815\) 2.86272e11 + 4.27606e12i 0.0227285 + 0.339496i
\(816\) 2.78916e11 + 7.04502e11i 0.0220226 + 0.0556258i
\(817\) 4.72142e12 + 4.72142e12i 0.370743 + 0.370743i
\(818\) 3.88704e12 + 3.88704e12i 0.303549 + 0.303549i
\(819\) −5.16580e12 5.50145e12i −0.401199 0.427267i
\(820\) 8.70438e11 9.95348e11i 0.0672319 0.0768799i
\(821\) 2.43606e13i 1.87130i 0.352925 + 0.935652i \(0.385187\pi\)
−0.352925 + 0.935652i \(0.614813\pi\)
\(822\) 7.53638e12 + 3.26145e12i 0.575757 + 0.249166i
\(823\) −9.88955e11 + 9.88955e11i −0.0751410 + 0.0751410i −0.743678 0.668537i \(-0.766921\pi\)
0.668537 + 0.743678i \(0.266921\pi\)
\(824\) −1.43386e12 −0.108351
\(825\) 2.11130e12 7.49068e12i 0.158675 0.562961i
\(826\) 5.72415e12 0.427859
\(827\) −1.22483e11 + 1.22483e11i −0.00910544 + 0.00910544i −0.711645 0.702539i \(-0.752049\pi\)
0.702539 + 0.711645i \(0.252049\pi\)
\(828\) 4.17764e12 + 1.31449e11i 0.308883 + 0.00971896i
\(829\) 2.28000e13i 1.67664i −0.545181 0.838319i \(-0.683539\pi\)
0.545181 0.838319i \(-0.316461\pi\)
\(830\) 1.21325e13 1.38735e13i 0.887357 1.01469i
\(831\) −3.19897e12 + 1.26649e12i −0.232705 + 0.0921292i
\(832\) 4.20067e12 + 4.20067e12i 0.303923 + 0.303923i
\(833\) 1.09849e12 + 1.09849e12i 0.0790483 + 0.0790483i
\(834\) −1.25227e13 + 4.95780e12i −0.896292 + 0.354847i
\(835\) 8.05844e11 + 1.20369e13i 0.0573670 + 0.856892i
\(836\) 2.74144e12i 0.194111i
\(837\) −3.78450e12 + 1.36226e12i −0.266529 + 0.0959388i
\(838\) −6.62872e12 + 6.62872e12i −0.464335 + 0.464335i
\(839\) 4.70641e12 0.327915 0.163957 0.986467i \(-0.447574\pi\)
0.163957 + 0.986467i \(0.447574\pi\)
\(840\) −2.13423e13 + 1.01473e13i −1.47905 + 0.703224i
\(841\) 3.36286e13 2.31807
\(842\) 9.18487e12 9.18487e12i 0.629750 0.629750i
\(843\) −1.90111e12 8.22726e11i −0.129653 0.0561088i
\(844\) 5.40608e12i 0.366726i
\(845\) −9.48253e12 8.29253e12i −0.639836 0.559541i
\(846\) −7.79988e12 + 7.32401e12i −0.523505 + 0.491566i
\(847\) 1.05445e13 + 1.05445e13i 0.703966 + 0.703966i
\(848\) 8.24296e12 + 8.24296e12i 0.547396 + 0.547396i
\(849\) −5.89152e12 1.48811e13i −0.389173 0.982994i
\(850\) 1.13348e12 1.52451e11i 0.0744783 0.0100172i
\(851\) 1.93437e13i 1.26432i
\(852\) −1.14962e12 + 2.65648e12i −0.0747442 + 0.172715i
\(853\) −1.78295e13 + 1.78295e13i −1.15310 + 1.15310i −0.167178 + 0.985927i \(0.553465\pi\)
−0.985927 + 0.167178i \(0.946535\pi\)
\(854\) 1.07855e13 0.693874
\(855\) 7.39579e11 + 2.08872e13i 0.0473301 + 1.33670i
\(856\) 2.82804e13 1.80034
\(857\) 6.52749e12 6.52749e12i 0.413364 0.413364i −0.469545 0.882909i \(-0.655582\pi\)
0.882909 + 0.469545i \(0.155582\pi\)
\(858\) −1.23846e12 + 2.86176e12i −0.0780170 + 0.180277i
\(859\) 1.79258e13i 1.12334i 0.827363 + 0.561668i \(0.189840\pi\)
−0.827363 + 0.561668i \(0.810160\pi\)
\(860\) −1.55676e12 + 1.04222e11i −0.0970463 + 0.00649703i
\(861\) −3.69731e12 9.33886e12i −0.229283 0.579135i
\(862\) −1.55252e13 1.55252e13i −0.957756 0.957756i
\(863\) 8.49589e11 + 8.49589e11i 0.0521387 + 0.0521387i 0.732695 0.680557i \(-0.238262\pi\)
−0.680557 + 0.732695i \(0.738262\pi\)
\(864\) 3.37373e12 7.16846e12i 0.205967 0.437637i
\(865\) −1.93859e13 + 1.29784e12i −1.17737 + 0.0788223i
\(866\) 1.65838e13i 1.00197i
\(867\) −1.51543e13 6.55818e12i −0.910854 0.394182i
\(868\) 1.25777e12 1.25777e12i 0.0752075 0.0752075i
\(869\) 1.32309e12 0.0787048
\(870\) −2.51483e13 8.94056e12i −1.48824 0.529088i
\(871\) −7.37774e12 −0.434352
\(872\) −1.58622e13 + 1.58622e13i −0.929049 + 0.929049i
\(873\) 8.60877e11 2.73599e13i 0.0501622 1.59423i
\(874\) 2.49185e13i 1.44451i
\(875\) 5.22684e12 + 2.57130e13i 0.301442 + 1.48292i
\(876\) 3.29227e12 1.30343e12i 0.188898 0.0747857i
\(877\) 1.38367e13 + 1.38367e13i 0.789830 + 0.789830i 0.981466 0.191636i \(-0.0613794\pi\)
−0.191636 + 0.981466i \(0.561379\pi\)
\(878\) −1.84139e13 1.84139e13i −1.04573 1.04573i
\(879\) 2.16190e13 8.55907e12i 1.22148 0.483589i
\(880\) 5.40696e12 + 4.72842e12i 0.303935 + 0.265793i
\(881\) 4.62011e12i 0.258381i 0.991620 + 0.129191i \(0.0412379\pi\)
−0.991620 + 0.129191i \(0.958762\pi\)
\(882\) −6.32195e11 + 2.00921e13i −0.0351757 + 1.11794i
\(883\) 5.86096e12 5.86096e12i 0.324448 0.324448i −0.526022 0.850471i \(-0.676317\pi\)
0.850471 + 0.526022i \(0.176317\pi\)
\(884\) 1.51223e11 0.00832879
\(885\) 2.55516e12 + 5.37413e12i 0.140014 + 0.294485i
\(886\) −1.46960e13 −0.801211
\(887\) 1.48535e13 1.48535e13i 0.805698 0.805698i −0.178281 0.983980i \(-0.557054\pi\)
0.983980 + 0.178281i \(0.0570536\pi\)
\(888\) −1.86822e13 8.08492e12i −1.00825 0.436333i
\(889\) 1.87907e12i 0.100898i
\(890\) −3.66030e11 5.46740e12i −0.0195552 0.292096i
\(891\) 1.09817e13 + 6.91758e11i 0.583739 + 0.0367709i
\(892\) −4.98526e12 4.98526e12i −0.263661 0.263661i
\(893\) −1.48849e13 1.48849e13i −0.783273 0.783273i
\(894\) 8.59432e11 + 2.17080e12i 0.0449980 + 0.113658i
\(895\) 1.47617e13 1.68800e13i 0.769010 0.879365i
\(896\) 1.39712e13i 0.724182i
\(897\) −3.71489e12 + 8.58414e12i −0.191593 + 0.442722i
\(898\) −5.59541e12 + 5.59541e12i −0.287136 + 0.287136i
\(899\) 1.01056e13 0.515992
\(900\) −3.78780e12 3.08287e12i −0.192440 0.156626i
\(901\) 1.92257e12 0.0971898
\(902\) −2.93464e12 + 2.93464e12i −0.147613 + 0.147613i
\(903\) −4.70716e12 + 1.08770e13i −0.235594 + 0.544396i
\(904\) 1.50533e13i 0.749676i
\(905\) 2.36574e13 2.70523e13i 1.17233 1.34056i
\(906\) 6.49203e11 + 1.63979e12i 0.0320113 + 0.0808559i
\(907\) 5.88750e11 + 5.88750e11i 0.0288867 + 0.0288867i 0.721403 0.692516i \(-0.243498\pi\)
−0.692516 + 0.721403i \(0.743498\pi\)
\(908\) 2.04398e11 + 2.04398e11i 0.00997905 + 0.00997905i
\(909\) −5.65000e12 + 5.30529e12i −0.274480 + 0.257734i
\(910\) −7.02262e11 1.04897e13i −0.0339479 0.507081i
\(911\) 1.60365e13i 0.771394i −0.922625 0.385697i \(-0.873961\pi\)
0.922625 0.385697i \(-0.126039\pi\)
\(912\) −1.77031e13 7.66123e12i −0.847370 0.366709i
\(913\) 1.34985e13 1.34985e13i 0.642937 0.642937i
\(914\) −8.83879e12 −0.418924
\(915\) 4.81446e12 + 1.01260e13i 0.227066 + 0.477576i
\(916\) −1.67677e12 −0.0786944
\(917\) −9.97474e12 + 9.97474e12i −0.465843 + 0.465843i
\(918\) 5.47657e11 + 1.52145e12i 0.0254517 + 0.0707076i
\(919\) 1.93950e13i 0.896954i −0.893794 0.448477i \(-0.851967\pi\)
0.893794 0.448477i \(-0.148033\pi\)
\(920\) 2.20483e13 + 1.92814e13i 1.01468 + 0.887345i
\(921\) 2.77355e13 1.09807e13i 1.27019 0.502875i
\(922\) 4.40082e12 + 4.40082e12i 0.200560 + 0.200560i
\(923\) −4.58034e12 4.58034e12i −0.207726 0.207726i
\(924\) −4.52439e12 + 1.79123e12i −0.204191 + 0.0808403i
\(925\) −1.37092e13 + 1.79700e13i −0.615709 + 0.807070i
\(926\) 2.11450e13i 0.945059i
\(927\) −2.24981e12 7.07901e10i −0.100066 0.00314857i
\(928\) −1.40752e13 + 1.40752e13i −0.623000 + 0.623000i
\(929\) −3.21275e12 −0.141516 −0.0707580 0.997494i \(-0.522542\pi\)
−0.0707580 + 0.997494i \(0.522542\pi\)
\(930\) −5.27962e12 1.87698e12i −0.231435 0.0822783i
\(931\) −3.95491e13 −1.72529
\(932\) −3.94088e12 + 3.94088e12i −0.171089 + 0.171089i
\(933\) 3.56402e13 + 1.54237e13i 1.53983 + 0.666378i
\(934\) 2.45206e13i 1.05432i
\(935\) 1.18198e12 7.91306e10i 0.0505774 0.00338604i
\(936\) 6.73788e12 + 7.17567e12i 0.286934 + 0.305577i
\(937\) 2.31245e13 + 2.31245e13i 0.980039 + 0.980039i 0.999805 0.0197656i \(-0.00629198\pi\)
−0.0197656 + 0.999805i \(0.506292\pi\)
\(938\) 2.46693e13 + 2.46693e13i 1.04050 + 1.04050i
\(939\) 1.29755e13 + 3.27743e13i 0.544666 + 1.37575i
\(940\) 4.90788e12 3.28572e11i 0.205031 0.0137263i
\(941\) 4.53540e12i 0.188566i −0.995545 0.0942828i \(-0.969944\pi\)
0.995545 0.0942828i \(-0.0300558\pi\)
\(942\) 7.91729e12 1.82948e13i 0.327603 0.757005i
\(943\) −8.80275e12 + 8.80275e12i −0.362506 + 0.362506i
\(944\) −5.49210e12 −0.225094
\(945\) −3.39884e13 + 1.48681e13i −1.38640 + 0.606474i
\(946\) 4.89717e12 0.198809
\(947\) −1.56187e12 + 1.56187e12i −0.0631060 + 0.0631060i −0.737955 0.674849i \(-0.764209\pi\)
0.674849 + 0.737955i \(0.264209\pi\)
\(948\) 3.29761e11 7.61991e11i 0.0132605 0.0306417i
\(949\) 7.92396e12i 0.317135i
\(950\) −1.76601e13 + 2.31489e13i −0.703458 + 0.922092i
\(951\) −1.21012e13 3.05659e13i −0.479751 1.21178i
\(952\) −2.54355e12 2.54355e12i −0.100363 0.100363i
\(953\) 1.16298e13 + 1.16298e13i 0.456726 + 0.456726i 0.897579 0.440853i \(-0.145324\pi\)
−0.440853 + 0.897579i \(0.645324\pi\)
\(954\) 1.70293e13 + 1.81358e13i 0.665626 + 0.708875i
\(955\) 4.78769e12 + 4.18686e12i 0.186256 + 0.162882i
\(956\) 4.93622e12i 0.191132i
\(957\) −2.53716e13 1.09799e13i −0.977787 0.423148i
\(958\) 2.28490e12 2.28490e12i 0.0876440 0.0876440i
\(959\) −2.86771e13 −1.09484
\(960\) 2.63741e13 1.25397e13i 1.00221 0.476504i
\(961\) −2.43181e13 −0.919758
\(962\) 6.40365e12 6.40365e12i 0.241068 0.241068i
\(963\) 4.43738e13 + 1.39622e12i 1.66268 + 0.0523160i
\(964\) 2.84794e12i 0.106215i
\(965\) −6.47345e11 9.66942e12i −0.0240305 0.358945i
\(966\) 4.11248e13 1.62815e13i 1.51952 0.601586i
\(967\) −1.76340e13 1.76340e13i −0.648531 0.648531i 0.304107 0.952638i \(-0.401642\pi\)
−0.952638 + 0.304107i \(0.901642\pi\)
\(968\) −1.37535e13 1.37535e13i −0.503470 0.503470i
\(969\) −2.95796e12 + 1.17107e12i −0.107779 + 0.0426705i
\(970\) 2.51034e13 2.87058e13i 0.910457 1.04111i
\(971\) 4.02821e13i 1.45420i 0.686529 + 0.727102i \(0.259133\pi\)
−0.686529 + 0.727102i \(0.740867\pi\)
\(972\) 3.13541e12 6.15212e12i 0.112667 0.221068i
\(973\) 3.32580e13 3.32580e13i 1.18957 1.18957i
\(974\) −1.97109e13 −0.701763
\(975\) 9.53480e12 5.34173e12i 0.337902 0.189305i
\(976\) −1.03483e13 −0.365043
\(977\) 2.20794e13 2.20794e13i 0.775284 0.775284i −0.203741 0.979025i \(-0.565310\pi\)
0.979025 + 0.203741i \(0.0653099\pi\)
\(978\) −7.74688e12 3.35255e12i −0.270771 0.117179i
\(979\) 5.67576e12i 0.197470i
\(980\) 6.08362e12 6.95664e12i 0.210691 0.240925i
\(981\) −2.56719e13 + 2.41057e13i −0.885008 + 0.831014i
\(982\) 2.00665e13 + 2.00665e13i 0.688605 + 0.688605i
\(983\) −3.07300e13 3.07300e13i −1.04972 1.04972i −0.998698 0.0510177i \(-0.983753\pi\)
−0.0510177 0.998698i \(-0.516247\pi\)
\(984\) 4.82249e12 + 1.21809e13i 0.163981 + 0.414192i
\(985\) −6.64068e11 9.91920e12i −0.0224776 0.335748i
\(986\) 4.06267e12i 0.136888i
\(987\) 1.48399e13 3.42912e13i 0.497741 1.15015i
\(988\) −2.72226e12 + 2.72226e12i −0.0908914 + 0.0908914i
\(989\) 1.46896e13 0.488231
\(990\) 1.12159e13 + 1.04488e13i 0.371087 + 0.345707i
\(991\) −1.98605e13 −0.654123 −0.327062 0.945003i \(-0.606058\pi\)
−0.327062 + 0.945003i \(0.606058\pi\)
\(992\) −2.95494e12 + 2.95494e12i −0.0968825 + 0.0968825i
\(993\) −1.23391e13 + 2.85124e13i −0.402727 + 0.930598i
\(994\) 3.06309e13i 0.995225i
\(995\) −3.33839e13 2.91944e13i −1.07977 0.944270i
\(996\) −4.40974e12 1.11383e13i −0.141986 0.358636i
\(997\) 3.85580e12 + 3.85580e12i 0.123591 + 0.123591i 0.766197 0.642606i \(-0.222147\pi\)
−0.642606 + 0.766197i \(0.722147\pi\)
\(998\) −4.91924e12 4.91924e12i −0.156968 0.156968i
\(999\) −2.89144e13 1.36081e13i −0.918478 0.432268i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 15.10.e.a.2.5 32
3.2 odd 2 inner 15.10.e.a.2.12 yes 32
5.2 odd 4 75.10.e.f.68.5 32
5.3 odd 4 inner 15.10.e.a.8.12 yes 32
5.4 even 2 75.10.e.f.32.12 32
15.2 even 4 75.10.e.f.68.12 32
15.8 even 4 inner 15.10.e.a.8.5 yes 32
15.14 odd 2 75.10.e.f.32.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.10.e.a.2.5 32 1.1 even 1 trivial
15.10.e.a.2.12 yes 32 3.2 odd 2 inner
15.10.e.a.8.5 yes 32 15.8 even 4 inner
15.10.e.a.8.12 yes 32 5.3 odd 4 inner
75.10.e.f.32.5 32 15.14 odd 2
75.10.e.f.32.12 32 5.4 even 2
75.10.e.f.68.5 32 5.2 odd 4
75.10.e.f.68.12 32 15.2 even 4