Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,35,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 35, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 35);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 35 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (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: | \(36.6128270213\) |
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 | 2.8 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.35.c.a.3.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8626.63 | + | 8626.63i | 0.0658160 | + | 0.0658160i | 0.739249 | − | 0.673433i | \(-0.235181\pi\) |
−0.673433 | + | 0.739249i | \(0.735181\pi\) | |||||||
\(3\) | 9.89110e7 | − | 9.89110e7i | 0.765920 | − | 0.765920i | −0.211465 | − | 0.977385i | \(-0.567824\pi\) |
0.977385 | + | 0.211465i | \(0.0678236\pi\) | |||||||
\(4\) | − | 1.70310e10i | − | 0.991337i | ||||||
\(5\) | −8.06672e10 | + | 7.58663e11i | −0.105732 | + | 0.994395i | ||||
\(6\) | 1.70654e12 | 0.100820 | ||||||||
\(7\) | 1.10848e14 | + | 1.10848e14i | 0.476498 | + | 0.476498i | 0.904010 | − | 0.427512i | \(-0.140610\pi\) |
−0.427512 | + | 0.904010i | \(0.640610\pi\) | |||||||
\(8\) | 2.95125e14 | − | 2.95125e14i | 0.131062 | − | 0.131062i | ||||
\(9\) | − | 2.88960e15i | − | 0.173267i | ||||||
\(10\) | −7.24059e15 | + | 5.84882e15i | −0.0724059 | + | 0.0584882i | ||||
\(11\) | −6.88211e17 | −1.36159 | −0.680794 | − | 0.732475i | \(-0.738365\pi\) | ||||
−0.680794 | + | 0.732475i | \(0.738365\pi\) | |||||||
\(12\) | −1.68456e18 | − | 1.68456e18i | −0.759284 | − | 0.759284i | ||||
\(13\) | −6.48947e18 | + | 6.48947e18i | −0.750191 | + | 0.750191i | −0.974515 | − | 0.224323i | \(-0.927983\pi\) |
0.224323 | + | 0.974515i | \(0.427983\pi\) | |||||||
\(14\) | 1.91249e18i | 0.0627223i | ||||||||
\(15\) | 6.70613e19 | + | 8.30190e19i | 0.680644 | + | 0.842609i | ||||
\(16\) | −2.87499e20 | −0.974085 | ||||||||
\(17\) | −2.93589e20 | − | 2.93589e20i | −0.354902 | − | 0.354902i | 0.507028 | − | 0.861930i | \(-0.330744\pi\) |
−0.861930 | + | 0.507028i | \(0.830744\pi\) | |||||||
\(18\) | 2.49275e19 | − | 2.49275e19i | 0.0114037 | − | 0.0114037i | ||||
\(19\) | − | 1.21721e21i | − | 0.222104i | −0.993815 | − | 0.111052i | \(-0.964578\pi\) | ||
0.993815 | − | 0.111052i | \(-0.0354219\pi\) | |||||||
\(20\) | 1.29208e22 | + | 1.37385e21i | 0.985780 | + | 0.104816i | ||||
\(21\) | 2.19282e22 | 0.729919 | ||||||||
\(22\) | −5.93694e21 | − | 5.93694e21i | −0.0896142 | − | 0.0896142i | ||||
\(23\) | −1.01208e23 | + | 1.01208e23i | −0.717531 | + | 0.717531i | −0.968099 | − | 0.250568i | \(-0.919383\pi\) |
0.250568 | + | 0.968099i | \(0.419383\pi\) | |||||||
\(24\) | − | 5.83822e22i | − | 0.200766i | ||||||
\(25\) | −5.69062e23 | − | 1.22398e23i | −0.977641 | − | 0.210279i | ||||
\(26\) | −1.11964e23 | −0.0987491 | ||||||||
\(27\) | 1.36374e24 | + | 1.36374e24i | 0.633211 | + | 0.633211i | ||||
\(28\) | 1.88786e24 | − | 1.88786e24i | 0.472370 | − | 0.472370i | ||||
\(29\) | − | 1.11720e23i | − | 0.0153945i | −0.999970 | − | 0.00769726i | \(-0.997550\pi\) | ||
0.999970 | − | 0.00769726i | \(-0.00245014\pi\) | |||||||
\(30\) | −1.37662e23 | + | 1.29469e24i | −0.0106599 | + | 0.100254i | ||||
\(31\) | 5.21184e24 | 0.231123 | 0.115561 | − | 0.993300i | \(-0.463133\pi\) | ||||
0.115561 | + | 0.993300i | \(0.463133\pi\) | |||||||
\(32\) | −7.55035e24 | − | 7.55035e24i | −0.195172 | − | 0.195172i | ||||
\(33\) | −6.80716e25 | + | 6.80716e25i | −1.04287 | + | 1.04287i | ||||
\(34\) | − | 5.06537e24i | − | 0.0467164i | ||||||
\(35\) | −9.30380e25 | + | 7.51545e25i | −0.524208 | + | 0.423446i | ||||
\(36\) | −4.92129e25 | −0.171766 | ||||||||
\(37\) | 3.43768e26 | + | 3.43768e26i | 0.753071 | + | 0.753071i | 0.975051 | − | 0.221980i | \(-0.0712520\pi\) |
−0.221980 | + | 0.975051i | \(0.571252\pi\) | |||||||
\(38\) | 1.05005e25 | − | 1.05005e25i | 0.0146180 | − | 0.0146180i | ||||
\(39\) | 1.28376e27i | 1.14917i | ||||||||
\(40\) | 2.00093e26 | + | 2.47707e26i | 0.116470 | + | 0.144184i | ||||
\(41\) | −3.54150e27 | −1.35476 | −0.677378 | − | 0.735635i | \(-0.736884\pi\) | ||||
−0.677378 | + | 0.735635i | \(0.736884\pi\) | |||||||
\(42\) | 1.89166e26 | + | 1.89166e26i | 0.0480403 | + | 0.0480403i | ||||
\(43\) | −7.17056e27 | + | 7.17056e27i | −1.22065 | + | 1.22065i | −0.253242 | + | 0.967403i | \(0.581497\pi\) |
−0.967403 | + | 0.253242i | \(0.918503\pi\) | |||||||
\(44\) | 1.17209e28i | 1.34979i | ||||||||
\(45\) | 2.19223e27 | + | 2.33096e26i | 0.172296 | + | 0.0183199i | ||||
\(46\) | −1.74616e27 | −0.0944500 | ||||||||
\(47\) | 1.36485e28 | + | 1.36485e28i | 0.512177 | + | 0.512177i | 0.915193 | − | 0.403016i | \(-0.132038\pi\) |
−0.403016 | + | 0.915193i | \(0.632038\pi\) | |||||||
\(48\) | −2.84368e28 | + | 2.84368e28i | −0.746071 | + | 0.746071i | ||||
\(49\) | − | 2.95424e28i | − | 0.545899i | ||||||
\(50\) | −3.85320e27 | − | 5.96497e27i | −0.0505047 | − | 0.0781841i | ||||
\(51\) | −5.80784e28 | −0.543653 | ||||||||
\(52\) | 1.10522e29 | + | 1.10522e29i | 0.743692 | + | 0.743692i | ||||
\(53\) | −2.76365e28 | + | 2.76365e28i | −0.134522 | + | 0.134522i | −0.771161 | − | 0.636640i | \(-0.780324\pi\) |
0.636640 | + | 0.771161i | \(0.280324\pi\) | |||||||
\(54\) | 2.35290e28i | 0.0833508i | ||||||||
\(55\) | 5.55160e28 | − | 5.22120e29i | 0.143964 | − | 1.35396i | ||||
\(56\) | 6.54280e28 | 0.124901 | ||||||||
\(57\) | −1.20396e29 | − | 1.20396e29i | −0.170114 | − | 0.170114i | ||||
\(58\) | 9.63769e26 | − | 9.63769e26i | 0.00101320 | − | 0.00101320i | ||||
\(59\) | − | 1.87864e30i | − | 1.47692i | −0.674295 | − | 0.738462i | \(-0.735552\pi\) | ||
0.674295 | − | 0.738462i | \(-0.264448\pi\) | |||||||
\(60\) | 1.41390e30 | − | 1.14212e30i | 0.835309 | − | 0.674748i | ||||
\(61\) | 2.15476e30 | 0.961150 | 0.480575 | − | 0.876954i | \(-0.340428\pi\) | ||||
0.480575 | + | 0.876954i | \(0.340428\pi\) | |||||||
\(62\) | 4.49607e28 | + | 4.49607e28i | 0.0152116 | + | 0.0152116i | ||||
\(63\) | 3.20307e29 | − | 3.20307e29i | 0.0825613 | − | 0.0825613i | ||||
\(64\) | 4.80893e30i | 0.948394i | ||||||||
\(65\) | −4.39983e30 | − | 5.44680e30i | −0.666667 | − | 0.825305i | ||||
\(66\) | −1.17446e30 | −0.137275 | ||||||||
\(67\) | −6.36486e30 | − | 6.36486e30i | −0.576125 | − | 0.576125i | 0.357708 | − | 0.933833i | \(-0.383558\pi\) |
−0.933833 | + | 0.357708i | \(0.883558\pi\) | |||||||
\(68\) | −5.00013e30 | + | 5.00013e30i | −0.351827 | + | 0.351827i | ||||
\(69\) | 2.00211e31i | 1.09914i | ||||||||
\(70\) | −1.45093e30 | − | 1.54275e29i | −0.0623708 | − | 0.00663176i | ||||
\(71\) | 5.86667e31 | 1.98153 | 0.990763 | − | 0.135603i | \(-0.0432973\pi\) | ||||
0.990763 | + | 0.135603i | \(0.0432973\pi\) | |||||||
\(72\) | −8.52793e29 | − | 8.52793e29i | −0.0227086 | − | 0.0227086i | ||||
\(73\) | −5.09535e31 | + | 5.09535e31i | −1.07321 | + | 1.07321i | −0.0761120 | + | 0.997099i | \(0.524251\pi\) |
−0.997099 | + | 0.0761120i | \(0.975749\pi\) | |||||||
\(74\) | 5.93112e30i | 0.0991282i | ||||||||
\(75\) | −6.83931e31 | + | 4.41800e31i | −0.909852 | + | 0.587738i | ||||
\(76\) | −2.07304e31 | −0.220179 | ||||||||
\(77\) | −7.62868e31 | − | 7.62868e31i | −0.648794 | − | 0.648794i | ||||
\(78\) | −1.10745e31 | + | 1.10745e31i | −0.0756339 | + | 0.0756339i | ||||
\(79\) | 3.07734e32i | 1.69245i | 0.532828 | + | 0.846223i | \(0.321129\pi\) | ||||
−0.532828 | + | 0.846223i | \(0.678871\pi\) | |||||||
\(80\) | 2.31917e31 | − | 2.18115e32i | 0.102992 | − | 0.968625i | ||||
\(81\) | 3.17969e32 | 1.14325 | ||||||||
\(82\) | −3.05512e31 | − | 3.05512e31i | −0.0891646 | − | 0.0891646i | ||||
\(83\) | 2.32954e32 | − | 2.32954e32i | 0.553277 | − | 0.553277i | −0.374108 | − | 0.927385i | \(-0.622051\pi\) |
0.927385 | + | 0.374108i | \(0.122051\pi\) | |||||||
\(84\) | − | 3.73459e32i | − | 0.723595i | ||||||
\(85\) | 2.46418e32 | − | 1.99052e32i | 0.390437 | − | 0.315388i | ||||
\(86\) | −1.23716e32 | −0.160676 | ||||||||
\(87\) | −1.10504e31 | − | 1.10504e31i | −0.0117910 | − | 0.0117910i | ||||
\(88\) | −2.03108e32 | + | 2.03108e32i | −0.178452 | + | 0.178452i | ||||
\(89\) | − | 2.13775e33i | − | 1.54998i | −0.631972 | − | 0.774991i | \(-0.717754\pi\) | ||
0.631972 | − | 0.774991i | \(-0.282246\pi\) | |||||||
\(90\) | 1.69008e31 | + | 2.09224e31i | 0.0101341 | + | 0.0125455i | ||||
\(91\) | −1.43869e33 | −0.714929 | ||||||||
\(92\) | 1.72367e33 | + | 1.72367e33i | 0.711315 | + | 0.711315i | ||||
\(93\) | 5.15509e32 | − | 5.15509e32i | 0.177022 | − | 0.177022i | ||||
\(94\) | 2.35480e32i | 0.0674188i | ||||||||
\(95\) | 9.23455e32 | + | 9.81892e31i | 0.220859 | + | 0.0234835i | ||||
\(96\) | −1.49363e33 | −0.298972 | ||||||||
\(97\) | 2.18835e33 | + | 2.18835e33i | 0.367280 | + | 0.367280i | 0.866484 | − | 0.499204i | \(-0.166374\pi\) |
−0.499204 | + | 0.866484i | \(0.666374\pi\) | |||||||
\(98\) | 2.54851e32 | − | 2.54851e32i | 0.0359289 | − | 0.0359289i | ||||
\(99\) | 1.98866e33i | 0.235918i | ||||||||
\(100\) | −2.08457e33 | + | 9.69172e33i | −0.208457 | + | 0.969172i | ||||
\(101\) | −1.31831e34 | −1.11315 | −0.556577 | − | 0.830796i | \(-0.687886\pi\) | ||||
−0.556577 | + | 0.830796i | \(0.687886\pi\) | |||||||
\(102\) | −5.01021e32 | − | 5.01021e32i | −0.0357810 | − | 0.0357810i | ||||
\(103\) | −6.45435e33 | + | 6.45435e33i | −0.390499 | + | 0.390499i | −0.874865 | − | 0.484366i | \(-0.839050\pi\) |
0.484366 | + | 0.874865i | \(0.339050\pi\) | |||||||
\(104\) | 3.83040e33i | 0.196643i | ||||||||
\(105\) | −1.76888e33 | + | 1.66361e34i | −0.0771758 | + | 0.725827i | ||||
\(106\) | −4.76819e32 | −0.0177074 | ||||||||
\(107\) | −3.45225e33 | − | 3.45225e33i | −0.109290 | − | 0.109290i | 0.650347 | − | 0.759637i | \(-0.274623\pi\) |
−0.759637 | + | 0.650347i | \(0.774623\pi\) | |||||||
\(108\) | 2.32260e34 | − | 2.32260e34i | 0.627726 | − | 0.627726i | ||||
\(109\) | − | 1.36483e34i | − | 0.315376i | −0.987489 | − | 0.157688i | \(-0.949596\pi\) | ||
0.987489 | − | 0.157688i | \(-0.0504040\pi\) | |||||||
\(110\) | 4.98305e33 | − | 4.02522e33i | 0.0985870 | − | 0.0796368i | ||||
\(111\) | 6.80049e34 | 1.15358 | ||||||||
\(112\) | −3.18687e34 | − | 3.18687e34i | −0.464149 | − | 0.464149i | ||||
\(113\) | 2.28365e34 | − | 2.28365e34i | 0.285954 | − | 0.285954i | −0.549524 | − | 0.835478i | \(-0.685191\pi\) |
0.835478 | + | 0.549524i | \(0.185191\pi\) | |||||||
\(114\) | − | 2.07722e33i | − | 0.0223924i | ||||||
\(115\) | −6.86185e34 | − | 8.49468e34i | −0.637643 | − | 0.789375i | ||||
\(116\) | −1.90271e33 | −0.0152611 | ||||||||
\(117\) | 1.87520e34 | + | 1.87520e34i | 0.129983 | + | 0.129983i | ||||
\(118\) | 1.62063e34 | − | 1.62063e34i | 0.0972052 | − | 0.0972052i | ||||
\(119\) | − | 6.50875e34i | − | 0.338220i | ||||||
\(120\) | 4.42924e34 | + | 4.70953e33i | 0.199640 | + | 0.0212274i | ||||
\(121\) | 2.18157e35 | 0.853923 | ||||||||
\(122\) | 1.85883e34 | + | 1.85883e34i | 0.0632590 | + | 0.0632590i | ||||
\(123\) | −3.50293e35 | + | 3.50293e35i | −1.03763 | + | 1.03763i | ||||
\(124\) | − | 8.87631e34i | − | 0.229120i | ||||||
\(125\) | 1.38764e35 | − | 4.21853e35i | 0.312468 | − | 0.949928i | ||||
\(126\) | 5.52633e33 | 0.0108677 | ||||||||
\(127\) | −1.54642e35 | − | 1.54642e35i | −0.265866 | − | 0.265866i | 0.561566 | − | 0.827432i | \(-0.310199\pi\) |
−0.827432 | + | 0.561566i | \(0.810199\pi\) | |||||||
\(128\) | −1.71199e35 | + | 1.71199e35i | −0.257591 | + | 0.257591i | ||||
\(129\) | 1.41850e36i | 1.86983i | ||||||||
\(130\) | 9.03185e33 | − | 8.49433e34i | 0.0104409 | − | 0.0981956i | ||||
\(131\) | −1.06496e36 | −1.08074 | −0.540369 | − | 0.841428i | \(-0.681716\pi\) | ||||
−0.540369 | + | 0.841428i | \(0.681716\pi\) | |||||||
\(132\) | 1.15933e36 | + | 1.15933e36i | 1.03383 | + | 1.03383i | ||||
\(133\) | 1.34926e35 | − | 1.34926e35i | 0.105832 | − | 0.105832i | ||||
\(134\) | − | 1.09815e35i | − | 0.0758365i | ||||||
\(135\) | −1.14463e36 | + | 9.24612e35i | −0.696613 | + | 0.562711i | ||||
\(136\) | −1.73291e35 | −0.0930281 | ||||||||
\(137\) | −1.32213e36 | − | 1.32213e36i | −0.626649 | − | 0.626649i | 0.320574 | − | 0.947223i | \(-0.396124\pi\) |
−0.947223 | + | 0.320574i | \(0.896124\pi\) | |||||||
\(138\) | −1.72715e35 | + | 1.72715e35i | −0.0723412 | + | 0.0723412i | ||||
\(139\) | − | 3.82962e36i | − | 1.41875i | −0.704834 | − | 0.709373i | \(-0.748978\pi\) | ||
0.704834 | − | 0.709373i | \(-0.251022\pi\) | |||||||
\(140\) | 1.27996e36 | + | 1.58453e36i | 0.419777 | + | 0.519667i | ||||
\(141\) | 2.69997e36 | 0.784573 | ||||||||
\(142\) | 5.06096e35 | + | 5.06096e35i | 0.130416 | + | 0.130416i | ||||
\(143\) | 4.46612e36 | − | 4.46612e36i | 1.02145 | − | 1.02145i | ||||
\(144\) | 8.30758e35i | 0.168777i | ||||||||
\(145\) | 8.47580e34 | + | 9.01216e33i | 0.0153082 | + | 0.00162769i | ||||
\(146\) | −8.79114e35 | −0.141269 | ||||||||
\(147\) | −2.92207e36 | − | 2.92207e36i | −0.418115 | − | 0.418115i | ||||
\(148\) | 5.85472e36 | − | 5.85472e36i | 0.746547 | − | 0.746547i | ||||
\(149\) | 1.85717e36i | 0.211196i | 0.994409 | + | 0.105598i | \(0.0336757\pi\) | ||||
−0.994409 | + | 0.105598i | \(0.966324\pi\) | |||||||
\(150\) | −9.71126e35 | − | 2.08877e35i | −0.0985653 | − | 0.0212002i | ||||
\(151\) | −1.84957e37 | −1.67673 | −0.838365 | − | 0.545109i | \(-0.816488\pi\) | ||||
−0.838365 | + | 0.545109i | \(0.816488\pi\) | |||||||
\(152\) | −3.59230e35 | − | 3.59230e35i | −0.0291093 | − | 0.0291093i | ||||
\(153\) | −8.48356e35 | + | 8.48356e35i | −0.0614927 | + | 0.0614927i | ||||
\(154\) | − | 1.31620e36i | − | 0.0854020i | ||||||
\(155\) | −4.20425e35 | + | 3.95403e36i | −0.0244371 | + | 0.229827i | ||||
\(156\) | 2.18638e37 | 1.13922 | ||||||||
\(157\) | 1.80278e37 | + | 1.80278e37i | 0.842654 | + | 0.842654i | 0.989203 | − | 0.146549i | \(-0.0468167\pi\) |
−0.146549 | + | 0.989203i | \(0.546817\pi\) | |||||||
\(158\) | −2.65471e36 | + | 2.65471e36i | −0.111390 | + | 0.111390i | ||||
\(159\) | 5.46710e36i | 0.206066i | ||||||||
\(160\) | 6.33724e36 | − | 5.11911e36i | 0.214714 | − | 0.173442i | ||||
\(161\) | −2.24374e37 | −0.683804 | ||||||||
\(162\) | 2.74300e36 | + | 2.74300e36i | 0.0752438 | + | 0.0752438i | ||||
\(163\) | −4.47489e37 | + | 4.47489e37i | −1.10559 | + | 1.10559i | −0.111864 | + | 0.993724i | \(0.535682\pi\) |
−0.993724 | + | 0.111864i | \(0.964318\pi\) | |||||||
\(164\) | 6.03153e37i | 1.34302i | ||||||||
\(165\) | −4.61523e37 | − | 5.71346e37i | −0.926758 | − | 1.14729i | ||||
\(166\) | 4.01921e36 | 0.0728289 | ||||||||
\(167\) | −2.48709e37 | − | 2.48709e37i | −0.406923 | − | 0.406923i | 0.473741 | − | 0.880664i | \(-0.342903\pi\) |
−0.880664 | + | 0.473741i | \(0.842903\pi\) | |||||||
\(168\) | 6.47155e36 | − | 6.47155e36i | 0.0956644 | − | 0.0956644i | ||||
\(169\) | − | 9.39665e36i | − | 0.125574i | ||||||
\(170\) | 3.84291e36 | + | 4.08609e35i | 0.0464546 | + | 0.00493942i | ||||
\(171\) | −3.51726e36 | −0.0384832 | ||||||||
\(172\) | 1.22122e38 | + | 1.22122e38i | 1.21007 | + | 1.21007i | ||||
\(173\) | 1.23631e38 | − | 1.23631e38i | 1.11005 | − | 1.11005i | 0.116910 | − | 0.993142i | \(-0.462701\pi\) |
0.993142 | − | 0.116910i | \(-0.0372990\pi\) | |||||||
\(174\) | − | 1.90655e35i | − | 0.00155207i | ||||||
\(175\) | −4.95118e37 | − | 7.66470e37i | −0.365647 | − | 0.566042i | ||||
\(176\) | 1.97860e38 | 1.32630 | ||||||||
\(177\) | −1.85818e38 | − | 1.85818e38i | −1.13121 | − | 1.13121i | ||||
\(178\) | 1.84416e37 | − | 1.84416e37i | 0.102014 | − | 0.102014i | ||||
\(179\) | 2.20634e37i | 0.110961i | 0.998460 | + | 0.0554805i | \(0.0176691\pi\) | ||||
−0.998460 | + | 0.0554805i | \(0.982331\pi\) | |||||||
\(180\) | 3.96987e36 | − | 3.73360e37i | 0.0181611 | − | 0.170803i | ||||
\(181\) | −2.18507e38 | −0.909765 | −0.454882 | − | 0.890552i | \(-0.650319\pi\) | ||||
−0.454882 | + | 0.890552i | \(0.650319\pi\) | |||||||
\(182\) | −1.24110e37 | − | 1.24110e37i | −0.0470538 | − | 0.0470538i | ||||
\(183\) | 2.13129e38 | − | 2.13129e38i | 0.736164 | − | 0.736164i | ||||
\(184\) | 5.97379e37i | 0.188082i | ||||||||
\(185\) | −2.88535e38 | + | 2.33073e38i | −0.828474 | + | 0.669226i | ||||
\(186\) | 8.89421e36 | 0.0233017 | ||||||||
\(187\) | 2.02051e38 | + | 2.02051e38i | 0.483230 | + | 0.483230i | ||||
\(188\) | 2.32447e38 | − | 2.32447e38i | 0.507740 | − | 0.507740i | ||||
\(189\) | 3.02336e38i | 0.603448i | ||||||||
\(190\) | 7.11926e36 | + | 8.81334e36i | 0.0129904 | + | 0.0160816i | ||||
\(191\) | −6.99811e38 | −1.16792 | −0.583961 | − | 0.811782i | \(-0.698498\pi\) | ||||
−0.583961 | + | 0.811782i | \(0.698498\pi\) | |||||||
\(192\) | 4.75656e38 | + | 4.75656e38i | 0.726394 | + | 0.726394i | ||||
\(193\) | 3.14898e38 | − | 3.14898e38i | 0.440246 | − | 0.440246i | −0.451849 | − | 0.892095i | \(-0.649235\pi\) |
0.892095 | + | 0.451849i | \(0.149235\pi\) | |||||||
\(194\) | 3.77562e37i | 0.0483458i | ||||||||
\(195\) | −9.73941e38 | − | 1.03557e38i | −1.14273 | − | 0.121504i | ||||
\(196\) | −5.03138e38 | −0.541170 | ||||||||
\(197\) | 1.03468e39 | + | 1.03468e39i | 1.02065 | + | 1.02065i | 0.999782 | + | 0.0208725i | \(0.00664439\pi\) |
0.0208725 | + | 0.999782i | \(0.493356\pi\) | |||||||
\(198\) | −1.71554e37 | + | 1.71554e37i | −0.0155272 | + | 0.0155272i | ||||
\(199\) | 7.40998e38i | 0.615623i | 0.951447 | + | 0.307811i | \(0.0995965\pi\) | ||||
−0.951447 | + | 0.307811i | \(0.900403\pi\) | |||||||
\(200\) | −2.04067e38 | + | 1.31822e38i | −0.155691 | + | 0.100572i | ||||
\(201\) | −1.25911e39 | −0.882532 | ||||||||
\(202\) | −1.13726e38 | − | 1.13726e38i | −0.0732633 | − | 0.0732633i | ||||
\(203\) | 1.23840e37 | − | 1.23840e37i | 0.00733545 | − | 0.00733545i | ||||
\(204\) | 9.89135e38i | 0.538943i | ||||||||
\(205\) | 2.85682e38 | − | 2.68680e39i | 0.143241 | − | 1.34716i | ||||
\(206\) | −1.11359e38 | −0.0514021 | ||||||||
\(207\) | 2.92450e38 | + | 2.92450e38i | 0.124324 | + | 0.124324i | ||||
\(208\) | 1.86572e39 | − | 1.86572e39i | 0.730750 | − | 0.730750i | ||||
\(209\) | 8.37700e38i | 0.302414i | ||||||||
\(210\) | −1.58773e38 | + | 1.28254e38i | −0.0528504 | + | 0.0426916i | ||||
\(211\) | 6.75889e38 | 0.207527 | 0.103763 | − | 0.994602i | \(-0.466912\pi\) | ||||
0.103763 | + | 0.994602i | \(0.466912\pi\) | |||||||
\(212\) | 4.70677e38 | + | 4.70677e38i | 0.133356 | + | 0.133356i | ||||
\(213\) | 5.80279e39 | − | 5.80279e39i | 1.51769 | − | 1.51769i | ||||
\(214\) | − | 5.95626e37i | − | 0.0143860i | ||||||
\(215\) | −4.86161e39 | − | 6.01847e39i | −1.08474 | − | 1.34286i | ||||
\(216\) | 8.04949e38 | 0.165980 | ||||||||
\(217\) | 5.77722e38 | + | 5.77722e38i | 0.110130 | + | 0.110130i | ||||
\(218\) | 1.17739e38 | − | 1.17739e38i | 0.0207568 | − | 0.0207568i | ||||
\(219\) | 1.00797e40i | 1.64399i | ||||||||
\(220\) | −8.89224e39 | − | 9.45495e38i | −1.34223 | − | 0.142716i | ||||
\(221\) | 3.81047e39 | 0.532489 | ||||||||
\(222\) | 5.86653e38 | + | 5.86653e38i | 0.0759243 | + | 0.0759243i | ||||
\(223\) | −1.10093e38 | + | 1.10093e38i | −0.0132000 | + | 0.0132000i | −0.713676 | − | 0.700476i | \(-0.752971\pi\) |
0.700476 | + | 0.713676i | \(0.252971\pi\) | |||||||
\(224\) | − | 1.67388e39i | − | 0.185998i | ||||||
\(225\) | −3.53683e38 | + | 1.64436e39i | −0.0364343 | + | 0.169393i | ||||
\(226\) | 3.94004e38 | 0.0376406 | ||||||||
\(227\) | 1.35925e39 | + | 1.35925e39i | 0.120465 | + | 0.120465i | 0.764769 | − | 0.644304i | \(-0.222853\pi\) |
−0.644304 | + | 0.764769i | \(0.722853\pi\) | |||||||
\(228\) | −2.05047e39 | + | 2.05047e39i | −0.168640 | + | 0.168640i | ||||
\(229\) | 2.17155e40i | 1.65793i | 0.559300 | + | 0.828965i | \(0.311070\pi\) | ||||
−0.559300 | + | 0.828965i | \(0.688930\pi\) | |||||||
\(230\) | 1.40858e38 | − | 1.32475e39i | 0.00998640 | − | 0.0939206i | ||||
\(231\) | −1.50912e40 | −0.993849 | ||||||||
\(232\) | −3.29714e37 | − | 3.29714e37i | −0.00201763 | − | 0.00201763i | ||||
\(233\) | 2.44949e40 | − | 2.44949e40i | 1.39324 | − | 1.39324i | 0.575277 | − | 0.817959i | \(-0.304894\pi\) |
0.817959 | − | 0.575277i | \(-0.195106\pi\) | |||||||
\(234\) | 3.23533e38i | 0.0171099i | ||||||||
\(235\) | −1.14556e40 | + | 9.25359e39i | −0.563459 | + | 0.455152i | ||||
\(236\) | −3.19951e40 | −1.46413 | ||||||||
\(237\) | 3.04383e40 | + | 3.04383e40i | 1.29628 | + | 1.29628i | ||||
\(238\) | 5.61486e38 | − | 5.61486e38i | 0.0222603 | − | 0.0222603i | ||||
\(239\) | 1.57577e40i | 0.581739i | 0.956763 | + | 0.290869i | \(0.0939445\pi\) | ||||
−0.956763 | + | 0.290869i | \(0.906056\pi\) | |||||||
\(240\) | −1.92800e40 | − | 2.38679e40i | −0.663005 | − | 0.820772i | ||||
\(241\) | −3.80121e38 | −0.0121796 | −0.00608979 | − | 0.999981i | \(-0.501938\pi\) | ||||
−0.00608979 | + | 0.999981i | \(0.501938\pi\) | |||||||
\(242\) | 1.88196e39 | + | 1.88196e39i | 0.0562018 | + | 0.0562018i | ||||
\(243\) | 8.70724e39 | − | 8.70724e39i | 0.242423 | − | 0.242423i | ||||
\(244\) | − | 3.66978e40i | − | 0.952824i | ||||||
\(245\) | 2.24127e40 | + | 2.38310e39i | 0.542839 | + | 0.0577191i | ||||
\(246\) | −6.04370e39 | −0.136586 | ||||||||
\(247\) | 7.89907e39 | + | 7.89907e39i | 0.166620 | + | 0.166620i | ||||
\(248\) | 1.53814e39 | − | 1.53814e39i | 0.0302913 | − | 0.0302913i | ||||
\(249\) | − | 4.60834e40i | − | 0.847531i | ||||||
\(250\) | 4.83623e39 | − | 2.44211e39i | 0.0830858 | − | 0.0419550i | ||||
\(251\) | −2.78328e40 | −0.446790 | −0.223395 | − | 0.974728i | \(-0.571714\pi\) | ||||
−0.223395 | + | 0.974728i | \(0.571714\pi\) | |||||||
\(252\) | −5.45515e39 | − | 5.45515e39i | −0.0818460 | − | 0.0818460i | ||||
\(253\) | 6.96523e40 | − | 6.96523e40i | 0.976982 | − | 0.976982i | ||||
\(254\) | − | 2.66807e39i | − | 0.0349965i | ||||||
\(255\) | 4.68502e39 | − | 4.40619e40i | 0.0574815 | − | 0.540605i | ||||
\(256\) | 7.96630e40 | 0.914486 | ||||||||
\(257\) | 2.10479e40 | + | 2.10479e40i | 0.226123 | + | 0.226123i | 0.811071 | − | 0.584948i | \(-0.198885\pi\) |
−0.584948 | + | 0.811071i | \(0.698885\pi\) | |||||||
\(258\) | −1.22368e40 | + | 1.22368e40i | −0.123065 | + | 0.123065i | ||||
\(259\) | 7.62120e40i | 0.717674i | ||||||||
\(260\) | −9.27647e40 | + | 7.49337e40i | −0.818155 | + | 0.660891i | ||||
\(261\) | −3.22827e38 | −0.00266736 | ||||||||
\(262\) | −9.18700e39 | − | 9.18700e39i | −0.0711299 | − | 0.0711299i | ||||
\(263\) | −7.49213e40 | + | 7.49213e40i | −0.543698 | + | 0.543698i | −0.924611 | − | 0.380913i | \(-0.875610\pi\) |
0.380913 | + | 0.924611i | \(0.375610\pi\) | |||||||
\(264\) | 4.01793e40i | 0.273360i | ||||||||
\(265\) | −1.87374e40 | − | 2.31961e40i | −0.119544 | − | 0.147991i | ||||
\(266\) | 2.32791e39 | 0.0139309 | ||||||||
\(267\) | −2.11447e41 | − | 2.11447e41i | −1.18716 | − | 1.18716i | ||||
\(268\) | −1.08400e41 | + | 1.08400e41i | −0.571134 | + | 0.571134i | ||||
\(269\) | 1.84932e41i | 0.914584i | 0.889317 | + | 0.457292i | \(0.151181\pi\) | ||||
−0.889317 | + | 0.457292i | \(0.848819\pi\) | |||||||
\(270\) | −1.78506e40 | − | 1.89802e39i | −0.0828836 | − | 0.00881286i | ||||
\(271\) | 1.72179e41 | 0.750763 | 0.375381 | − | 0.926870i | \(-0.377512\pi\) | ||||
0.375381 | + | 0.926870i | \(0.377512\pi\) | |||||||
\(272\) | 8.44066e40 | + | 8.44066e40i | 0.345704 | + | 0.345704i | ||||
\(273\) | −1.42302e41 | + | 1.42302e41i | −0.547579 | + | 0.547579i | ||||
\(274\) | − | 2.28111e40i | − | 0.0824871i | ||||||
\(275\) | 3.91635e41 | + | 8.42359e40i | 1.33115 | + | 0.286313i | ||||
\(276\) | 3.40981e41 | 1.08962 | ||||||||
\(277\) | −8.97098e40 | − | 8.97098e40i | −0.269578 | − | 0.269578i | 0.559352 | − | 0.828930i | \(-0.311050\pi\) |
−0.828930 | + | 0.559352i | \(0.811050\pi\) | |||||||
\(278\) | 3.30367e40 | − | 3.30367e40i | 0.0933761 | − | 0.0933761i | ||||
\(279\) | − | 1.50602e40i | − | 0.0400459i | ||||||
\(280\) | −5.27789e39 | + | 4.96378e40i | −0.0132061 | + | 0.124201i | ||||
\(281\) | −5.12786e41 | −1.20762 | −0.603808 | − | 0.797130i | \(-0.706350\pi\) | ||||
−0.603808 | + | 0.797130i | \(0.706350\pi\) | |||||||
\(282\) | 2.32916e40 | + | 2.32916e40i | 0.0516374 | + | 0.0516374i | ||||
\(283\) | −3.74105e41 | + | 3.74105e41i | −0.780951 | + | 0.780951i | −0.979991 | − | 0.199040i | \(-0.936218\pi\) |
0.199040 | + | 0.979991i | \(0.436218\pi\) | |||||||
\(284\) | − | 9.99155e41i | − | 1.96436i | ||||||
\(285\) | 1.01052e41 | − | 8.16279e40i | 0.187146 | − | 0.151174i | ||||
\(286\) | 7.70551e40 | 0.134456 | ||||||||
\(287\) | −3.92568e41 | − | 3.92568e41i | −0.645539 | − | 0.645539i | ||||
\(288\) | −2.18175e40 | + | 2.18175e40i | −0.0338168 | + | 0.0338168i | ||||
\(289\) | − | 5.11937e41i | − | 0.748089i | ||||||
\(290\) | 6.53431e38 | + | 8.08920e38i | 0.000900397 | + | 0.00111465i | ||||
\(291\) | 4.32904e41 | 0.562614 | ||||||||
\(292\) | 8.67790e41 | + | 8.67790e41i | 1.06391 | + | 1.06391i | ||||
\(293\) | 3.38770e41 | − | 3.38770e41i | 0.391882 | − | 0.391882i | −0.483476 | − | 0.875358i | \(-0.660626\pi\) |
0.875358 | + | 0.483476i | \(0.160626\pi\) | |||||||
\(294\) | − | 5.04152e40i | − | 0.0550373i | ||||||
\(295\) | 1.42525e42 | + | 1.51544e41i | 1.46865 | + | 0.156158i | ||||
\(296\) | 2.02909e41 | 0.197398 | ||||||||
\(297\) | −9.38543e41 | − | 9.38543e41i | −0.862173 | − | 0.862173i | ||||
\(298\) | −1.60211e40 | + | 1.60211e40i | −0.0139001 | + | 0.0139001i | ||||
\(299\) | − | 1.31357e42i | − | 1.07657i | ||||||
\(300\) | 7.52431e41 | + | 1.16480e42i | 0.582647 | + | 0.901969i | ||||
\(301\) | −1.58968e42 | −1.16327 | ||||||||
\(302\) | −1.59556e41 | − | 1.59556e41i | −0.110356 | − | 0.110356i | ||||
\(303\) | −1.30396e42 | + | 1.30396e42i | −0.852587 | + | 0.852587i | ||||
\(304\) | 3.49948e41i | 0.216348i | ||||||||
\(305\) | −1.73818e41 | + | 1.63474e42i | −0.101624 | + | 0.955763i | ||||
\(306\) | −1.46369e40 | −0.00809440 | ||||||||
\(307\) | −1.28758e42 | − | 1.28758e42i | −0.673632 | − | 0.673632i | 0.284919 | − | 0.958552i | \(-0.408033\pi\) |
−0.958552 | + | 0.284919i | \(0.908033\pi\) | |||||||
\(308\) | −1.29924e42 | + | 1.29924e42i | −0.643173 | + | 0.643173i | ||||
\(309\) | 1.27681e42i | 0.598182i | ||||||||
\(310\) | −3.77368e40 | + | 3.04831e40i | −0.0167346 | + | 0.0135179i | ||||
\(311\) | 1.33809e42 | 0.561770 | 0.280885 | − | 0.959741i | \(-0.409372\pi\) | ||||
0.280885 | + | 0.959741i | \(0.409372\pi\) | |||||||
\(312\) | 3.78869e41 | + | 3.78869e41i | 0.150613 | + | 0.150613i | ||||
\(313\) | −7.38120e41 | + | 7.38120e41i | −0.277890 | + | 0.277890i | −0.832266 | − | 0.554376i | \(-0.812957\pi\) |
0.554376 | + | 0.832266i | \(0.312957\pi\) | |||||||
\(314\) | 3.11039e41i | 0.110920i | ||||||||
\(315\) | 2.17166e41 | + | 2.68843e41i | 0.0733691 | + | 0.0908279i | ||||
\(316\) | 5.24103e42 | 1.67778 | ||||||||
\(317\) | −5.15270e41 | − | 5.15270e41i | −0.156324 | − | 0.156324i | 0.624611 | − | 0.780936i | \(-0.285257\pi\) |
−0.780936 | + | 0.624611i | \(0.785257\pi\) | |||||||
\(318\) | −4.71627e40 | + | 4.71627e40i | −0.0135624 | + | 0.0135624i | ||||
\(319\) | 7.68871e40i | 0.0209610i | ||||||||
\(320\) | −3.64836e42 | − | 3.87923e41i | −0.943078 | − | 0.100276i | ||||
\(321\) | −6.82932e41 | −0.167414 | ||||||||
\(322\) | −1.93559e41 | − | 1.93559e41i | −0.0450052 | − | 0.0450052i | ||||
\(323\) | −3.57361e41 | + | 3.57361e41i | −0.0788250 | + | 0.0788250i | ||||
\(324\) | − | 5.41534e42i | − | 1.13334i | ||||||
\(325\) | 4.48721e42 | − | 2.89861e42i | 0.891167 | − | 0.575669i | ||||
\(326\) | −7.72064e41 | −0.145531 | ||||||||
\(327\) | −1.34997e42 | − | 1.34997e42i | −0.241553 | − | 0.241553i | ||||
\(328\) | −1.04518e42 | + | 1.04518e42i | −0.177557 | + | 0.177557i | ||||
\(329\) | 3.02581e42i | 0.488102i | ||||||||
\(330\) | 9.47402e40 | − | 8.91017e41i | 0.0145143 | − | 0.136505i | ||||
\(331\) | 5.10169e42 | 0.742400 | 0.371200 | − | 0.928553i | \(-0.378946\pi\) | ||||
0.371200 | + | 0.928553i | \(0.378946\pi\) | |||||||
\(332\) | −3.96744e42 | − | 3.96744e42i | −0.548483 | − | 0.548483i | ||||
\(333\) | 9.93352e41 | − | 9.93352e41i | 0.130482 | − | 0.130482i | ||||
\(334\) | − | 4.29105e41i | − | 0.0535640i | ||||||
\(335\) | 5.34222e42 | − | 4.31535e42i | 0.633811 | − | 0.511981i | ||||
\(336\) | −6.30433e42 | −0.711002 | ||||||||
\(337\) | 9.90128e42 | + | 9.90128e42i | 1.06165 | + | 1.06165i | 0.997970 | + | 0.0636835i | \(0.0202848\pi\) |
0.0636835 | + | 0.997970i | \(0.479715\pi\) | |||||||
\(338\) | 8.10614e40 | − | 8.10614e40i | 0.00826476 | − | 0.00826476i | ||||
\(339\) | − | 4.51756e42i | − | 0.438035i | ||||||
\(340\) | −3.39006e42 | − | 4.19676e42i | −0.312656 | − | 0.387054i | ||||
\(341\) | −3.58685e42 | −0.314694 | ||||||||
\(342\) | −3.03421e40 | − | 3.03421e40i | −0.00253281 | − | 0.00253281i | ||||
\(343\) | 9.27347e42 | − | 9.27347e42i | 0.736618 | − | 0.736618i | ||||
\(344\) | 4.23242e42i | 0.319960i | ||||||||
\(345\) | −1.51893e43 | − | 1.61505e42i | −1.09298 | − | 0.116215i | ||||
\(346\) | 2.13304e42 | 0.146118 | ||||||||
\(347\) | 8.35946e42 | + | 8.35946e42i | 0.545227 | + | 0.545227i | 0.925056 | − | 0.379830i | \(-0.124017\pi\) |
−0.379830 | + | 0.925056i | \(0.624017\pi\) | |||||||
\(348\) | −1.88199e41 | + | 1.88199e41i | −0.0116888 | + | 0.0116888i | ||||
\(349\) | 2.09009e43i | 1.23633i | 0.786050 | + | 0.618163i | \(0.212123\pi\) | ||||
−0.786050 | + | 0.618163i | \(0.787877\pi\) | |||||||
\(350\) | 2.34085e41 | − | 1.08833e42i | 0.0131892 | − | 0.0613200i | ||||
\(351\) | −1.76999e43 | −0.950059 | ||||||||
\(352\) | 5.19623e42 | + | 5.19623e42i | 0.265744 | + | 0.265744i | ||||
\(353\) | 5.49957e42 | − | 5.49957e42i | 0.268015 | − | 0.268015i | −0.560285 | − | 0.828300i | \(-0.689308\pi\) |
0.828300 | + | 0.560285i | \(0.189308\pi\) | |||||||
\(354\) | − | 3.20596e42i | − | 0.148903i | ||||||
\(355\) | −4.73248e42 | + | 4.45083e43i | −0.209511 | + | 1.97042i | ||||
\(356\) | −3.64081e43 | −1.53655 | ||||||||
\(357\) | −6.43787e42 | − | 6.43787e42i | −0.259049 | − | 0.259049i | ||||
\(358\) | −1.90333e41 | + | 1.90333e41i | −0.00730301 | + | 0.00730301i | ||||
\(359\) | 2.05726e42i | 0.0752808i | 0.999291 | + | 0.0376404i | \(0.0119841\pi\) | ||||
−0.999291 | + | 0.0376404i | \(0.988016\pi\) | |||||||
\(360\) | 7.15775e41 | − | 5.78190e41i | 0.0249824 | − | 0.0201803i | ||||
\(361\) | 2.85530e43 | 0.950670 | ||||||||
\(362\) | −1.88498e42 | − | 1.88498e42i | −0.0598770 | − | 0.0598770i | ||||
\(363\) | 2.15782e43 | − | 2.15782e43i | 0.654037 | − | 0.654037i | ||||
\(364\) | 2.45023e43i | 0.708735i | ||||||||
\(365\) | −3.45462e43 | − | 4.27668e43i | −0.953723 | − | 1.18067i | ||||
\(366\) | 3.67718e42 | 0.0969027 | ||||||||
\(367\) | 2.70483e43 | + | 2.70483e43i | 0.680482 | + | 0.680482i | 0.960109 | − | 0.279627i | \(-0.0902107\pi\) |
−0.279627 | + | 0.960109i | \(0.590211\pi\) | |||||||
\(368\) | 2.90972e43 | − | 2.90972e43i | 0.698936 | − | 0.698936i | ||||
\(369\) | 1.02335e43i | 0.234734i | ||||||||
\(370\) | −4.49972e42 | − | 4.78446e41i | −0.0985726 | − | 0.0104810i | ||||
\(371\) | −6.12689e42 | −0.128199 | ||||||||
\(372\) | −8.77965e42 | − | 8.77965e42i | −0.175488 | − | 0.175488i | ||||
\(373\) | 5.29128e43 | − | 5.29128e43i | 1.01044 | − | 1.01044i | 0.0104958 | − | 0.999945i | \(-0.496659\pi\) |
0.999945 | − | 0.0104958i | \(-0.00334098\pi\) | |||||||
\(374\) | 3.48604e42i | 0.0636085i | ||||||||
\(375\) | −2.80006e43 | − | 5.54512e43i | −0.488243 | − | 0.966895i | ||||
\(376\) | 8.05599e42 | 0.134254 | ||||||||
\(377\) | 7.25005e41 | + | 7.25005e41i | 0.0115488 | + | 0.0115488i | ||||
\(378\) | −2.60814e42 | + | 2.60814e42i | −0.0397165 | + | 0.0397165i | ||||
\(379\) | 1.09800e43i | 0.159858i | 0.996801 | + | 0.0799291i | \(0.0254694\pi\) | ||||
−0.996801 | + | 0.0799291i | \(0.974531\pi\) | |||||||
\(380\) | 1.67226e42 | − | 1.57274e43i | 0.0232800 | − | 0.218945i | ||||
\(381\) | −3.05915e43 | −0.407264 | ||||||||
\(382\) | −6.03701e42 | − | 6.03701e42i | −0.0768678 | − | 0.0768678i | ||||
\(383\) | −5.71132e43 | + | 5.71132e43i | −0.695597 | + | 0.695597i | −0.963458 | − | 0.267861i | \(-0.913683\pi\) |
0.267861 | + | 0.963458i | \(0.413683\pi\) | |||||||
\(384\) | 3.38669e43i | 0.394589i | ||||||||
\(385\) | 6.40298e43 | − | 5.17221e43i | 0.713756 | − | 0.576559i | ||||
\(386\) | 5.43301e42 | 0.0579504 | ||||||||
\(387\) | 2.07201e43 | + | 2.07201e43i | 0.211497 | + | 0.211497i | ||||
\(388\) | 3.72699e43 | − | 3.72699e43i | 0.364098 | − | 0.364098i | ||||
\(389\) | − | 8.74993e42i | − | 0.0818203i | −0.999163 | − | 0.0409102i | \(-0.986974\pi\) | ||
0.999163 | − | 0.0409102i | \(-0.0130257\pi\) | |||||||
\(390\) | −7.50848e42 | − | 9.29518e42i | −0.0672130 | − | 0.0832069i | ||||
\(391\) | 5.94270e43 | 0.509306 | ||||||||
\(392\) | −8.71870e42 | − | 8.71870e42i | −0.0715465 | − | 0.0715465i | ||||
\(393\) | −1.05336e44 | + | 1.05336e44i | −0.827759 | + | 0.827759i | ||||
\(394\) | 1.78515e43i | 0.134351i | ||||||||
\(395\) | −2.33466e44 | − | 2.48240e43i | −1.68296 | − | 0.178946i | ||||
\(396\) | 3.38689e43 | 0.233874 | ||||||||
\(397\) | 1.62610e44 | + | 1.62610e44i | 1.07575 | + | 1.07575i | 0.996886 | + | 0.0788600i | \(0.0251280\pi\) |
0.0788600 | + | 0.996886i | \(0.474872\pi\) | |||||||
\(398\) | −6.39231e42 | + | 6.39231e42i | −0.0405178 | + | 0.0405178i | ||||
\(399\) | − | 2.66913e43i | − | 0.162118i | ||||||
\(400\) | 1.63605e44 | + | 3.51894e43i | 0.952306 | + | 0.204829i | ||||
\(401\) | −9.96116e43 | −0.555719 | −0.277860 | − | 0.960622i | \(-0.589625\pi\) | ||||
−0.277860 | + | 0.960622i | \(0.589625\pi\) | |||||||
\(402\) | −1.08619e43 | − | 1.08619e43i | −0.0580847 | − | 0.0580847i | ||||
\(403\) | −3.38221e43 | + | 3.38221e43i | −0.173386 | + | 0.173386i | ||||
\(404\) | 2.24522e44i | 1.10351i | ||||||||
\(405\) | −2.56497e43 | + | 2.41231e44i | −0.120878 | + | 1.13684i | ||||
\(406\) | 2.13664e41 | 0.000965580 | ||||||||
\(407\) | −2.36585e44 | − | 2.36585e44i | −1.02537 | − | 1.02537i | ||||
\(408\) | −1.71404e43 | + | 1.71404e43i | −0.0712521 | + | 0.0712521i | ||||
\(409\) | − | 2.51915e44i | − | 1.00452i | −0.864718 | − | 0.502258i | \(-0.832503\pi\) | ||
0.864718 | − | 0.502258i | \(-0.167497\pi\) | |||||||
\(410\) | 2.56425e43 | − | 2.07136e43i | 0.0980923 | − | 0.0792372i | ||||
\(411\) | −2.61547e44 | −0.959926 | ||||||||
\(412\) | 1.09924e44 | + | 1.09924e44i | 0.387116 | + | 0.387116i | ||||
\(413\) | 2.08243e44 | − | 2.08243e44i | 0.703752 | − | 0.703752i | ||||
\(414\) | 5.04572e42i | 0.0163651i | ||||||||
\(415\) | 1.57942e44 | + | 1.95525e44i | 0.491676 | + | 0.608674i | ||||
\(416\) | 9.79955e43 | 0.292833 | ||||||||
\(417\) | −3.78792e44 | − | 3.78792e44i | −1.08665 | − | 1.08665i | ||||
\(418\) | −7.22652e42 | + | 7.22652e42i | −0.0199036 | + | 0.0199036i | ||||
\(419\) | − | 4.91478e44i | − | 1.29977i | −0.760034 | − | 0.649883i | \(-0.774818\pi\) | ||
0.760034 | − | 0.649883i | \(-0.225182\pi\) | |||||||
\(420\) | 2.83330e44 | + | 3.01259e43i | 0.719539 | + | 0.0765072i | ||||
\(421\) | 6.36896e44 | 1.55336 | 0.776681 | − | 0.629894i | \(-0.216902\pi\) | ||||
0.776681 | + | 0.629894i | \(0.216902\pi\) | |||||||
\(422\) | 5.83065e42 | + | 5.83065e42i | 0.0136586 | + | 0.0136586i | ||||
\(423\) | 3.94386e43 | − | 3.94386e43i | 0.0887432 | − | 0.0887432i | ||||
\(424\) | 1.63124e43i | 0.0352613i | ||||||||
\(425\) | 1.31136e44 | + | 2.03005e44i | 0.272338 | + | 0.421595i | ||||
\(426\) | 1.00117e44 | 0.199777 | ||||||||
\(427\) | 2.38851e44 | + | 2.38851e44i | 0.457986 | + | 0.457986i | ||||
\(428\) | −5.87954e43 | + | 5.87954e43i | −0.108343 | + | 0.108343i | ||||
\(429\) | − | 8.83497e44i | − | 1.56470i | ||||||
\(430\) | 9.97978e42 | − | 9.38584e43i | 0.0169886 | − | 0.159775i | ||||
\(431\) | −2.33203e44 | −0.381611 | −0.190806 | − | 0.981628i | \(-0.561110\pi\) | ||||
−0.190806 | + | 0.981628i | \(0.561110\pi\) | |||||||
\(432\) | −3.92075e44 | − | 3.92075e44i | −0.616802 | − | 0.616802i | ||||
\(433\) | −8.82179e44 | + | 8.82179e44i | −1.33433 | + | 1.33433i | −0.432872 | + | 0.901455i | \(0.642500\pi\) |
−0.901455 | + | 0.432872i | \(0.857500\pi\) | |||||||
\(434\) | 9.96759e42i | 0.0144966i | ||||||||
\(435\) | 9.27490e42 | − | 7.49210e42i | 0.0129716 | − | 0.0104782i | ||||
\(436\) | −2.32445e44 | −0.312643 | ||||||||
\(437\) | 1.23192e44 | + | 1.23192e44i | 0.159366 | + | 0.159366i | ||||
\(438\) | −8.69540e43 | + | 8.69540e43i | −0.108201 | + | 0.108201i | ||||
\(439\) | 8.30089e44i | 0.993637i | 0.867854 | + | 0.496819i | \(0.165499\pi\) | ||||
−0.867854 | + | 0.496819i | \(0.834501\pi\) | |||||||
\(440\) | −1.37706e44 | − | 1.70475e44i | −0.158584 | − | 0.196320i | ||||
\(441\) | −8.53658e43 | −0.0945862 | ||||||||
\(442\) | 3.28715e43 | + | 3.28715e43i | 0.0350462 | + | 0.0350462i | ||||
\(443\) | −3.24616e44 | + | 3.24616e44i | −0.333047 | + | 0.333047i | −0.853743 | − | 0.520695i | \(-0.825673\pi\) |
0.520695 | + | 0.853743i | \(0.325673\pi\) | |||||||
\(444\) | − | 1.15819e45i | − | 1.14359i | ||||||
\(445\) | 1.62183e45 | + | 1.72446e44i | 1.54129 | + | 0.163883i | ||||
\(446\) | −1.89945e42 | −0.00173755 | ||||||||
\(447\) | 1.83695e44 | + | 1.83695e44i | 0.161759 | + | 0.161759i | ||||
\(448\) | −5.33060e44 | + | 5.33060e44i | −0.451908 | + | 0.451908i | ||||
\(449\) | 1.90869e45i | 1.55793i | 0.627069 | + | 0.778963i | \(0.284254\pi\) | ||||
−0.627069 | + | 0.778963i | \(0.715746\pi\) | |||||||
\(450\) | −1.72364e43 | + | 1.11342e43i | −0.0135467 | + | 0.00875079i | ||||
\(451\) | 2.43730e45 | 1.84462 | ||||||||
\(452\) | −3.88929e44 | − | 3.88929e44i | −0.283476 | − | 0.283476i | ||||
\(453\) | −1.82943e45 | + | 1.82943e45i | −1.28424 | + | 1.28424i | ||||
\(454\) | 2.34515e43i | 0.0158570i | ||||||||
\(455\) | 1.16055e44 | − | 1.09148e45i | 0.0755909 | − | 0.710922i | ||||
\(456\) | −7.10636e43 | −0.0445908 | ||||||||
\(457\) | −1.66802e45 | − | 1.66802e45i | −1.00838 | − | 1.00838i | −0.999965 | − | 0.00841722i | \(-0.997321\pi\) |
−0.00841722 | − | 0.999965i | \(-0.502679\pi\) | |||||||
\(458\) | −1.87331e44 | + | 1.87331e44i | −0.109118 | + | 0.109118i | ||||
\(459\) | − | 8.00761e44i | − | 0.449456i | ||||||
\(460\) | −1.44673e45 | + | 1.16864e45i | −0.782537 | + | 0.632119i | ||||
\(461\) | −2.23128e45 | −1.16316 | −0.581578 | − | 0.813491i | \(-0.697565\pi\) | ||||
−0.581578 | + | 0.813491i | \(0.697565\pi\) | |||||||
\(462\) | −1.30186e44 | − | 1.30186e44i | −0.0654111 | − | 0.0654111i | ||||
\(463\) | 2.05040e45 | − | 2.05040e45i | 0.993028 | − | 0.993028i | −0.00694820 | − | 0.999976i | \(-0.502212\pi\) |
0.999976 | + | 0.00694820i | \(0.00221170\pi\) | |||||||
\(464\) | 3.21195e43i | 0.0149956i | ||||||||
\(465\) | 3.49513e44 | + | 4.32682e44i | 0.157312 | + | 0.194746i | ||||
\(466\) | 4.22616e44 | 0.183394 | ||||||||
\(467\) | 1.85050e45 | + | 1.85050e45i | 0.774286 | + | 0.774286i | 0.978853 | − | 0.204567i | \(-0.0655786\pi\) |
−0.204567 | + | 0.978853i | \(0.565579\pi\) | |||||||
\(468\) | 3.19365e44 | − | 3.19365e44i | 0.128857 | − | 0.128857i | ||||
\(469\) | − | 1.41106e45i | − | 0.549045i | ||||||
\(470\) | −1.78650e44 | − | 1.89955e43i | −0.0670409 | − | 0.00712833i | ||||
\(471\) | 3.56630e45 | 1.29081 | ||||||||
\(472\) | −5.54432e44 | − | 5.54432e44i | −0.193568 | − | 0.193568i | ||||
\(473\) | 4.93486e45 | − | 4.93486e45i | 1.66202 | − | 1.66202i | ||||
\(474\) | 5.25160e44i | 0.170632i | ||||||||
\(475\) | −1.48985e44 | + | 6.92670e44i | −0.0467037 | + | 0.217138i | ||||
\(476\) | −1.10851e45 | −0.335290 | ||||||||
\(477\) | 7.98584e43 | + | 7.98584e43i | 0.0233082 | + | 0.0233082i | ||||
\(478\) | −1.35936e44 | + | 1.35936e44i | −0.0382877 | + | 0.0382877i | ||||
\(479\) | − | 2.03171e45i | − | 0.552279i | −0.961118 | − | 0.276140i | \(-0.910945\pi\) | ||
0.961118 | − | 0.276140i | \(-0.0890553\pi\) | |||||||
\(480\) | 1.20487e44 | − | 1.13316e45i | 0.0316110 | − | 0.297296i | ||||
\(481\) | −4.46174e45 | −1.12989 | ||||||||
\(482\) | −3.27916e42 | − | 3.27916e42i | −0.000801610 | − | 0.000801610i | ||||
\(483\) | −2.21930e45 | + | 2.21930e45i | −0.523739 | + | 0.523739i | ||||
\(484\) | − | 3.71545e45i | − | 0.846525i | ||||||
\(485\) | −1.83675e45 | + | 1.48369e45i | −0.404055 | + | 0.326388i | ||||
\(486\) | 1.50228e44 | 0.0319106 | ||||||||
\(487\) | −1.24569e45 | − | 1.24569e45i | −0.255515 | − | 0.255515i | 0.567712 | − | 0.823227i | \(-0.307829\pi\) |
−0.823227 | + | 0.567712i | \(0.807829\pi\) | |||||||
\(488\) | 6.35923e44 | − | 6.35923e44i | 0.125970 | − | 0.125970i | ||||
\(489\) | 8.85232e45i | 1.69358i | ||||||||
\(490\) | 1.72788e44 | + | 2.13904e44i | 0.0319287 | + | 0.0395263i | ||||
\(491\) | −4.38681e45 | −0.783004 | −0.391502 | − | 0.920177i | \(-0.628044\pi\) | ||||
−0.391502 | + | 0.920177i | \(0.628044\pi\) | |||||||
\(492\) | 5.96585e45 | + | 5.96585e45i | 1.02865 | + | 1.02865i | ||||
\(493\) | −3.27998e43 | + | 3.27998e43i | −0.00546354 | + | 0.00546354i | ||||
\(494\) | 1.36285e44i | 0.0219325i | ||||||||
\(495\) | −1.50872e45 | − | 1.60419e44i | −0.234596 | − | 0.0249441i | ||||
\(496\) | −1.49840e45 | −0.225133 | ||||||||
\(497\) | 6.50309e45 | + | 6.50309e45i | 0.944193 | + | 0.944193i | ||||
\(498\) | 3.97545e44 | − | 3.97545e44i | 0.0557811 | − | 0.0557811i | ||||
\(499\) | 6.97705e45i | 0.946156i | 0.881021 | + | 0.473078i | \(0.156857\pi\) | ||||
−0.881021 | + | 0.473078i | \(0.843143\pi\) | |||||||
\(500\) | −7.18459e45 | − | 2.36329e45i | −0.941699 | − | 0.309761i | ||||
\(501\) | −4.92002e45 | −0.623341 | ||||||||
\(502\) | −2.40103e44 | − | 2.40103e44i | −0.0294059 | − | 0.0294059i | ||||
\(503\) | 7.50300e45 | − | 7.50300e45i | 0.888339 | − | 0.888339i | −0.106024 | − | 0.994364i | \(-0.533812\pi\) |
0.994364 | + | 0.106024i | \(0.0338121\pi\) | |||||||
\(504\) | − | 1.89061e44i | − | 0.0216412i | ||||||
\(505\) | 1.06345e45 | − | 1.00016e46i | 0.117696 | − | 1.10691i | ||||
\(506\) | 1.20173e45 | 0.128602 | ||||||||
\(507\) | −9.29432e44 | − | 9.29432e44i | −0.0961795 | − | 0.0961795i | ||||
\(508\) | −2.63371e45 | + | 2.63371e45i | −0.263563 | + | 0.263563i | ||||
\(509\) | 1.40793e46i | 1.36263i | 0.731989 | + | 0.681317i | \(0.238592\pi\) | ||||
−0.731989 | + | 0.681317i | \(0.761408\pi\) | |||||||
\(510\) | 4.20522e44 | − | 3.39690e44i | 0.0393637 | − | 0.0317973i | ||||
\(511\) | −1.12962e46 | −1.02277 | ||||||||
\(512\) | 3.62840e45 | + | 3.62840e45i | 0.317779 | + | 0.317779i | ||||
\(513\) | 1.65997e45 | − | 1.65997e45i | 0.140639 | − | 0.140639i | ||||
\(514\) | 3.63145e44i | 0.0297651i | ||||||||
\(515\) | −4.37602e45 | − | 5.41733e45i | −0.347022 | − | 0.429598i | ||||
\(516\) | 2.41584e46 | 1.85363 | ||||||||
\(517\) | −9.39301e45 | − | 9.39301e45i | −0.697374 | − | 0.697374i | ||||
\(518\) | −6.57452e44 | + | 6.57452e44i | −0.0472344 | + | 0.0472344i | ||||
\(519\) | − | 2.44569e46i | − | 1.70042i | ||||||
\(520\) | −2.90599e45 | − | 3.08988e44i | −0.195540 | − | 0.0207914i | ||||
\(521\) | 1.41254e46 | 0.919943 | 0.459971 | − | 0.887934i | \(-0.347860\pi\) | ||||
0.459971 | + | 0.887934i | \(0.347860\pi\) | |||||||
\(522\) | −2.78491e42 | − | 2.78491e42i | −0.000175555 | − | 0.000175555i | ||||
\(523\) | −5.47989e45 | + | 5.47989e45i | −0.334382 | + | 0.334382i | −0.854248 | − | 0.519866i | \(-0.825982\pi\) |
0.519866 | + | 0.854248i | \(0.325982\pi\) | |||||||
\(524\) | 1.81373e46i | 1.07138i | ||||||||
\(525\) | −1.24785e46 | − | 2.68397e45i | −0.713599 | − | 0.153486i | ||||
\(526\) | −1.29264e45 | −0.0715680 | ||||||||
\(527\) | −1.53014e45 | − | 1.53014e45i | −0.0820259 | − | 0.0820259i | ||||
\(528\) | 1.95705e46 | − | 1.95705e46i | 1.01584 | − | 1.01584i | ||||
\(529\) | − | 5.90935e44i | − | 0.0297025i | ||||||
\(530\) | 3.84636e43 | − | 3.61745e44i | 0.00187224 | − | 0.0176081i | ||||
\(531\) | −5.42851e45 | −0.255902 | ||||||||
\(532\) | −2.29792e45 | − | 2.29792e45i | −0.104915 | − | 0.104915i | ||||
\(533\) | 2.29824e46 | − | 2.29824e46i | 1.01633 | − | 1.01633i | ||||
\(534\) | − | 3.64815e45i | − | 0.156268i | ||||||
\(535\) | 2.89758e45 | − | 2.34061e45i | 0.120232 | − | 0.0971215i | ||||
\(536\) | −3.75685e45 | −0.151016 | ||||||||
\(537\) | 2.18231e45 | + | 2.18231e45i | 0.0849873 | + | 0.0849873i | ||||
\(538\) | −1.59534e45 | + | 1.59534e45i | −0.0601942 | + | 0.0601942i | ||||
\(539\) | 2.03314e46i | 0.743290i | ||||||||
\(540\) | 1.57471e46 | + | 1.94942e46i | 0.557836 | + | 0.690578i | ||||
\(541\) | −2.04665e46 | −0.702570 | −0.351285 | − | 0.936269i | \(-0.614255\pi\) | ||||
−0.351285 | + | 0.936269i | \(0.614255\pi\) | |||||||
\(542\) | 1.48533e45 | + | 1.48533e45i | 0.0494122 | + | 0.0494122i | ||||
\(543\) | −2.16127e46 | + | 2.16127e46i | −0.696807 | + | 0.696807i | ||||
\(544\) | 4.43340e45i | 0.138534i | ||||||||
\(545\) | 1.03545e46 | + | 1.10097e45i | 0.313608 | + | 0.0333453i | ||||
\(546\) | −2.45518e45 | −0.0720788 | ||||||||
\(547\) | −1.15910e46 | − | 1.15910e46i | −0.329865 | − | 0.329865i | 0.522670 | − | 0.852535i | \(-0.324936\pi\) |
−0.852535 | + | 0.522670i | \(0.824936\pi\) | |||||||
\(548\) | −2.25172e46 | + | 2.25172e46i | −0.621220 | + | 0.621220i | ||||
\(549\) | − | 6.22639e45i | − | 0.166535i | ||||||
\(550\) | 2.65182e45 | + | 4.10516e45i | 0.0687666 | + | 0.106455i | ||||
\(551\) | −1.35987e44 | −0.00341918 | ||||||||
\(552\) | 5.90873e45 | + | 5.90873e45i | 0.144056 | + | 0.144056i | ||||
\(553\) | −3.41117e46 | + | 3.41117e46i | −0.806447 | + | 0.806447i | ||||
\(554\) | − | 1.54779e45i | − | 0.0354850i | ||||||
\(555\) | −5.48576e45 | + | 5.15928e46i | −0.121971 | + | 1.14712i | ||||
\(556\) | −6.52224e46 | −1.40645 | ||||||||
\(557\) | 3.58600e46 | + | 3.58600e46i | 0.750019 | + | 0.750019i | 0.974483 | − | 0.224463i | \(-0.0720629\pi\) |
−0.224463 | + | 0.974483i | \(0.572063\pi\) | |||||||
\(558\) | 1.29918e44 | − | 1.29918e44i | 0.00263566 | − | 0.00263566i | ||||
\(559\) | − | 9.30663e46i | − | 1.83143i | ||||||
\(560\) | 2.67483e46 | − | 2.16068e46i | 0.510623 | − | 0.412472i | ||||
\(561\) | 3.99702e46 | 0.740231 | ||||||||
\(562\) | −4.42361e45 | − | 4.42361e45i | −0.0794804 | − | 0.0794804i | ||||
\(563\) | 7.99935e45 | − | 7.99935e45i | 0.139448 | − | 0.139448i | −0.633937 | − | 0.773385i | \(-0.718562\pi\) |
0.773385 | + | 0.633937i | \(0.218562\pi\) | |||||||
\(564\) | − | 4.59832e46i | − | 0.777776i | ||||||
\(565\) | 1.54830e46 | + | 1.91673e46i | 0.254116 | + | 0.314585i | ||||
\(566\) | −6.45453e45 | −0.102798 | ||||||||
\(567\) | 3.52462e46 | + | 3.52462e46i | 0.544754 | + | 0.544754i | ||||
\(568\) | 1.73140e46 | − | 1.73140e46i | 0.259702 | − | 0.259702i | ||||
\(569\) | 3.85724e46i | 0.561524i | 0.959777 | + | 0.280762i | \(0.0905871\pi\) | ||||
−0.959777 | + | 0.280762i | \(0.909413\pi\) | |||||||
\(570\) | 1.57591e45 | + | 1.67563e44i | 0.0222669 | + | 0.00236759i | ||||
\(571\) | 8.26224e46 | 1.13314 | 0.566570 | − | 0.824013i | \(-0.308270\pi\) | ||||
0.566570 | + | 0.824013i | \(0.308270\pi\) | |||||||
\(572\) | −7.60626e46 | − | 7.60626e46i | −1.01260 | − | 1.01260i | ||||
\(573\) | −6.92190e46 | + | 6.92190e46i | −0.894534 | + | 0.894534i | ||||
\(574\) | − | 6.77307e45i | − | 0.0849735i | ||||||
\(575\) | 6.99812e46 | − | 4.52059e46i | 0.852370 | − | 0.550607i | ||||
\(576\) | 1.38959e46 | 0.164325 | ||||||||
\(577\) | −7.95956e46 | − | 7.95956e46i | −0.913904 | − | 0.913904i | 0.0826730 | − | 0.996577i | \(-0.473654\pi\) |
−0.996577 | + | 0.0826730i | \(0.973654\pi\) | |||||||
\(578\) | 4.41629e45 | − | 4.41629e45i | 0.0492362 | − | 0.0492362i | ||||
\(579\) | − | 6.22937e46i | − | 0.674386i | ||||||
\(580\) | 1.53486e44 | − | 1.44352e45i | 0.00161359 | − | 0.0151756i | ||||
\(581\) | 5.16449e46 | 0.527270 | ||||||||
\(582\) | 3.73450e45 | + | 3.73450e45i | 0.0370290 | + | 0.0370290i | ||||
\(583\) | 1.90197e46 | − | 1.90197e46i | 0.183163 | − | 0.183163i | ||||
\(584\) | 3.00753e46i | 0.281314i | ||||||||
\(585\) | −1.57391e46 | + | 1.27138e46i | −0.142998 | + | 0.115511i | ||||
\(586\) | 5.84489e45 | 0.0515842 | ||||||||
\(587\) | −4.99373e46 | − | 4.99373e46i | −0.428132 | − | 0.428132i | 0.459860 | − | 0.887992i | \(-0.347900\pi\) |
−0.887992 | + | 0.459860i | \(0.847900\pi\) | |||||||
\(588\) | −4.97659e46 | + | 4.97659e46i | −0.414493 | + | 0.414493i | ||||
\(589\) | − | 6.34393e45i | − | 0.0513332i | ||||||
\(590\) | 1.09878e46 | + | 1.36024e46i | 0.0863826 | + | 0.106938i | ||||
\(591\) | 2.04682e47 | 1.56348 | ||||||||
\(592\) | −9.88329e46 | − | 9.88329e46i | −0.733555 | − | 0.733555i | ||||
\(593\) | −9.05166e46 | + | 9.05166e46i | −0.652828 | + | 0.652828i | −0.953673 | − | 0.300845i | \(-0.902731\pi\) |
0.300845 | + | 0.953673i | \(0.402731\pi\) | |||||||
\(594\) | − | 1.61929e46i | − | 0.113490i | ||||||
\(595\) | 4.93795e46 | + | 5.25042e45i | 0.336324 | + | 0.0357607i | ||||
\(596\) | 3.16296e46 | 0.209366 | ||||||||
\(597\) | 7.32928e46 | + | 7.32928e46i | 0.471518 | + | 0.471518i | ||||
\(598\) | 1.13317e46 | − | 1.13317e46i | 0.0708556 | − | 0.0708556i | ||||
\(599\) | − | 1.24561e47i | − | 0.757056i | −0.925590 | − | 0.378528i | \(-0.876430\pi\) | ||
0.925590 | − | 0.378528i | \(-0.123570\pi\) | |||||||
\(600\) | −7.14588e45 | + | 3.32231e46i | −0.0422167 | + | 0.196277i | ||||
\(601\) | −1.14125e47 | −0.655413 | −0.327706 | − | 0.944780i | \(-0.606276\pi\) | ||||
−0.327706 | + | 0.944780i | \(0.606276\pi\) | |||||||
\(602\) | −1.37136e46 | − | 1.37136e46i | −0.0765617 | − | 0.0765617i | ||||
\(603\) | −1.83919e46 | + | 1.83919e46i | −0.0998234 | + | 0.0998234i | ||||
\(604\) | 3.15001e47i | 1.66220i | ||||||||
\(605\) | −1.75981e46 | + | 1.65508e47i | −0.0902870 | + | 0.849136i | ||||
\(606\) | −2.24975e46 | −0.112228 | ||||||||
\(607\) | 1.03338e47 | + | 1.03338e47i | 0.501248 | + | 0.501248i | 0.911826 | − | 0.410578i | \(-0.134673\pi\) |
−0.410578 | + | 0.911826i | \(0.634673\pi\) | |||||||
\(608\) | −9.19039e45 | + | 9.19039e45i | −0.0433484 | + | 0.0433484i | ||||
\(609\) | − | 2.44982e45i | − | 0.0112367i | ||||||
\(610\) | −1.56017e46 | + | 1.26028e46i | −0.0695930 | + | 0.0562159i | ||||
\(611\) | −1.77142e47 | −0.768461 | ||||||||
\(612\) | 1.44484e46 | + | 1.44484e46i | 0.0609600 | + | 0.0609600i | ||||
\(613\) | −1.09951e47 | + | 1.09951e47i | −0.451202 | + | 0.451202i | −0.895753 | − | 0.444551i | \(-0.853363\pi\) |
0.444551 | + | 0.895753i | \(0.353363\pi\) | |||||||
\(614\) | − | 2.22150e46i | − | 0.0886715i | ||||||
\(615\) | −2.37497e47 | − | 2.94011e47i | −0.922107 | − | 1.14153i | ||||
\(616\) | −4.50282e46 | −0.170064 | ||||||||
\(617\) | 8.87754e46 | + | 8.87754e46i | 0.326171 | + | 0.326171i | 0.851128 | − | 0.524958i | \(-0.175919\pi\) |
−0.524958 | + | 0.851128i | \(0.675919\pi\) | |||||||
\(618\) | −1.10146e46 | + | 1.10146e46i | −0.0393699 | + | 0.0393699i | ||||
\(619\) | 1.48801e47i | 0.517445i | 0.965952 | + | 0.258722i | \(0.0833015\pi\) | ||||
−0.965952 | + | 0.258722i | \(0.916699\pi\) | |||||||
\(620\) | 6.73413e46 | + | 7.16027e45i | 0.227836 | + | 0.0242254i | ||||
\(621\) | −2.76043e47 | −0.908698 | ||||||||
\(622\) | 1.15432e46 | + | 1.15432e46i | 0.0369735 | + | 0.0369735i | ||||
\(623\) | 2.36965e47 | − | 2.36965e47i | 0.738563 | − | 0.738563i | ||||
\(624\) | − | 3.69080e47i | − | 1.11939i | ||||||
\(625\) | 3.08850e47 | + | 1.39305e47i | 0.911566 | + | 0.411155i | ||||
\(626\) | −1.27350e46 | −0.0365792 | ||||||||
\(627\) | 8.28577e46 | + | 8.28577e46i | 0.231625 | + | 0.231625i | ||||
\(628\) | 3.07033e47 | − | 3.07033e47i | 0.835354 | − | 0.835354i | ||||
\(629\) | − | 2.01853e47i | − | 0.534533i | ||||||
\(630\) | −4.45793e44 | + | 4.19262e45i | −0.00114906 | + | 0.0108068i | ||||
\(631\) | 1.74047e47 | 0.436684 | 0.218342 | − | 0.975872i | \(-0.429935\pi\) | ||||
0.218342 | + | 0.975872i | \(0.429935\pi\) | |||||||
\(632\) | 9.08199e46 | + | 9.08199e46i | 0.221815 | + | 0.221815i | ||||
\(633\) | 6.68529e46 | − | 6.68529e46i | 0.158949 | − | 0.158949i | ||||
\(634\) | − | 8.89008e45i | − | 0.0205773i | ||||||
\(635\) | 1.29795e47 | − | 1.04846e47i | 0.292486 | − | 0.236265i | ||||
\(636\) | 9.31104e46 | 0.204281 | ||||||||
\(637\) | 1.91714e47 | + | 1.91714e47i | 0.409529 | + | 0.409529i | ||||
\(638\) | −6.63276e44 | + | 6.63276e44i | −0.00137957 | + | 0.00137957i | ||||
\(639\) | − | 1.69523e47i | − | 0.343333i | ||||||
\(640\) | −1.16072e47 | − | 1.43692e47i | −0.228912 | − | 0.283383i | ||||
\(641\) | −8.86274e47 | −1.70209 | −0.851043 | − | 0.525097i | \(-0.824029\pi\) | ||||
−0.851043 | + | 0.525097i | \(0.824029\pi\) | |||||||
\(642\) | −5.89140e45 | − | 5.89140e45i | −0.0110185 | − | 0.0110185i | ||||
\(643\) | 7.26265e47 | − | 7.26265e47i | 1.32284 | − | 1.32284i | 0.411378 | − | 0.911465i | \(-0.365048\pi\) |
0.911465 | − | 0.411378i | \(-0.134952\pi\) | |||||||
\(644\) | 3.82131e47i | 0.677880i | ||||||||
\(645\) | −1.07616e48 | − | 1.14426e47i | −1.85935 | − | 0.197701i | ||||
\(646\) | −6.16564e45 | −0.0103759 | ||||||||
\(647\) | −8.10865e47 | − | 8.10865e47i | −1.32916 | − | 1.32916i | −0.906107 | − | 0.423049i | \(-0.860960\pi\) |
−0.423049 | − | 0.906107i | \(-0.639040\pi\) | |||||||
\(648\) | 9.38405e46 | − | 9.38405e46i | 0.149836 | − | 0.149836i | ||||
\(649\) | 1.29290e48i | 2.01096i | ||||||||
\(650\) | 6.37147e46 | + | 1.37043e46i | 0.0965412 | + | 0.0207648i | ||||
\(651\) | 1.14286e47 | 0.168701 | ||||||||
\(652\) | 7.62120e47 | + | 7.62120e47i | 1.09601 | + | 1.09601i | ||||
\(653\) | −3.01980e47 | + | 3.01980e47i | −0.423111 | + | 0.423111i | −0.886273 | − | 0.463162i | \(-0.846715\pi\) |
0.463162 | + | 0.886273i | \(0.346715\pi\) | |||||||
\(654\) | − | 2.32913e46i | − | 0.0317960i | ||||||
\(655\) | 8.59072e46 | − | 8.07945e47i | 0.114269 | − | 1.07468i | ||||
\(656\) | 1.01818e48 | 1.31965 | ||||||||
\(657\) | 1.47235e47 | + | 1.47235e47i | 0.185952 | + | 0.185952i | ||||
\(658\) | −2.61025e46 | + | 2.61025e46i | −0.0321249 | + | 0.0321249i | ||||
\(659\) | 6.14945e47i | 0.737538i | 0.929521 | + | 0.368769i | \(0.120221\pi\) | ||||
−0.929521 | + | 0.368769i | \(0.879779\pi\) | |||||||
\(660\) | −9.73061e47 | + | 7.86021e47i | −1.13735 | + | 0.918729i | ||||
\(661\) | 6.68918e47 | 0.761988 | 0.380994 | − | 0.924578i | \(-0.375582\pi\) | ||||
0.380994 | + | 0.924578i | \(0.375582\pi\) | |||||||
\(662\) | 4.40104e46 | + | 4.40104e46i | 0.0488618 | + | 0.0488618i | ||||
\(663\) | 3.76898e47 | − | 3.76898e47i | 0.407844 | − | 0.407844i | ||||
\(664\) | − | 1.37501e47i | − | 0.145027i | ||||||
\(665\) | 9.14790e46 | + | 1.13247e47i | 0.0940489 | + | 0.116429i | ||||
\(666\) | 1.71386e46 | 0.0171756 | ||||||||
\(667\) | 1.13070e46 | + | 1.13070e46i | 0.0110460 | + | 0.0110460i | ||||
\(668\) | −4.23578e47 | + | 4.23578e47i | −0.403398 | + | 0.403398i | ||||
\(669\) | 2.17787e46i | 0.0202203i | ||||||||
\(670\) | 8.33122e46 | + | 8.85842e45i | 0.0754114 | + | 0.00801835i | ||||
\(671\) | −1.48293e48 | −1.30869 | ||||||||
\(672\) | −1.65565e47 | − | 1.65565e47i | −0.142460 | − | 0.142460i | ||||
\(673\) | −1.10617e48 | + | 1.10617e48i | −0.928036 | + | 0.928036i | −0.997579 | − | 0.0695425i | \(-0.977846\pi\) |
0.0695425 | + | 0.997579i | \(0.477846\pi\) | |||||||
\(674\) | 1.70829e47i | 0.139748i | ||||||||
\(675\) | −6.09135e47 | − | 9.42975e47i | −0.485903 | − | 0.752205i | ||||
\(676\) | −1.60035e47 | −0.124486 | ||||||||
\(677\) | −1.38585e47 | − | 1.38585e47i | −0.105126 | − | 0.105126i | 0.652588 | − | 0.757713i | \(-0.273683\pi\) |
−0.757713 | + | 0.652588i | \(0.773683\pi\) | |||||||
\(678\) | 3.89713e46 | − | 3.89713e46i | 0.0288297 | − | 0.0288297i | ||||
\(679\) | 4.85148e47i | 0.350016i | ||||||||
\(680\) | 1.39789e46 | − | 1.31469e47i | 0.00983605 | − | 0.0925066i | ||||
\(681\) | 2.68890e47 | 0.184533 | ||||||||
\(682\) | −3.09424e46 | − | 3.09424e46i | −0.0207119 | − | 0.0207119i | ||||
\(683\) | 4.62921e47 | − | 4.62921e47i | 0.302242 | − | 0.302242i | −0.539648 | − | 0.841890i | \(-0.681443\pi\) |
0.841890 | + | 0.539648i | \(0.181443\pi\) | |||||||
\(684\) | 5.99026e46i | 0.0381498i | ||||||||
\(685\) | 1.10970e48 | − | 8.96399e47i | 0.689394 | − | 0.556880i | ||||
\(686\) | 1.59998e47 | 0.0969624 | ||||||||
\(687\) | 2.14790e48 | + | 2.14790e48i | 1.26984 | + | 1.26984i | ||||
\(688\) | 2.06153e48 | − | 2.06153e48i | 1.18901 | − | 1.18901i | ||||
\(689\) | − | 3.58692e47i | − | 0.201834i | ||||||
\(690\) | −1.17100e47 | − | 1.44965e47i | −0.0642869 | − | 0.0795844i | ||||
\(691\) | −6.73289e47 | −0.360641 | −0.180320 | − | 0.983608i | \(-0.557713\pi\) | ||||
−0.180320 | + | 0.983608i | \(0.557713\pi\) | |||||||
\(692\) | −2.10556e48 | − | 2.10556e48i | −1.10044 | − | 1.10044i | ||||
\(693\) | −2.20438e47 | + | 2.20438e47i | −0.112414 | + | 0.112414i | ||||
\(694\) | 1.44228e47i | 0.0717693i | ||||||||
\(695\) | 2.90539e48 | + | 3.08925e47i | 1.41079 | + | 0.150007i | ||||
\(696\) | −6.52247e45 | −0.00309069 | ||||||||
\(697\) | 1.03974e48 | + | 1.03974e48i | 0.480806 | + | 0.480806i | ||||
\(698\) | −1.80304e47 | + | 1.80304e47i | −0.0813700 | + | 0.0813700i | ||||
\(699\) | − | 4.84563e48i | − | 2.13421i | ||||||
\(700\) | −1.30538e48 | + | 8.43237e47i | −0.561138 | + | 0.362479i | ||||
\(701\) | −1.79285e47 | −0.0752207 | −0.0376103 | − | 0.999292i | \(-0.511975\pi\) | ||||
−0.0376103 | + | 0.999292i | \(0.511975\pi\) | |||||||
\(702\) | −1.52691e47 | − | 1.52691e47i | −0.0625291 | − | 0.0625291i | ||||
\(703\) | 4.18439e47 | − | 4.18439e47i | 0.167260 | − | 0.167260i | ||||
\(704\) | − | 3.30956e48i | − | 1.29132i | ||||||
\(705\) | −2.17799e47 | + | 2.04836e48i | −0.0829545 | + | 0.780175i | ||||
\(706\) | 9.48854e46 | 0.0352793 | ||||||||
\(707\) | −1.46132e48 | − | 1.46132e48i | −0.530416 | − | 0.530416i | ||||
\(708\) | −3.16467e48 | + | 3.16467e48i | −1.12141 | + | 1.12141i | ||||
\(709\) | 1.28578e48i | 0.444818i | 0.974953 | + | 0.222409i | \(0.0713920\pi\) | ||||
−0.974953 | + | 0.222409i | \(0.928608\pi\) | |||||||
\(710\) | −4.24782e47 | + | 3.43131e47i | −0.143474 | + | 0.115896i | ||||
\(711\) | 8.89229e47 | 0.293245 | ||||||||
\(712\) | −6.30903e47 | − | 6.30903e47i | −0.203143 | − | 0.203143i | ||||
\(713\) | −5.27480e47 | + | 5.27480e47i | −0.165838 | + | 0.165838i | ||||
\(714\) | − | 1.11074e47i | − | 0.0340992i | ||||||
\(715\) | 3.02801e48 | + | 3.74855e48i | 0.907726 | + | 1.12373i | ||||
\(716\) | 3.75762e47 | 0.110000 | ||||||||
\(717\) | 1.55861e48 | + | 1.55861e48i | 0.445565 | + | 0.445565i | ||||
\(718\) | −1.77472e46 | + | 1.77472e46i | −0.00495468 | + | 0.00495468i | ||||
\(719\) | 1.36709e48i | 0.372739i | 0.982480 | + | 0.186369i | \(0.0596721\pi\) | ||||
−0.982480 | + | 0.186369i | \(0.940328\pi\) | |||||||
\(720\) | −6.30265e47 | − | 6.70149e46i | −0.167830 | − | 0.0178451i | ||||
\(721\) | −1.43090e48 | −0.372144 | ||||||||
\(722\) | 2.46316e47 | + | 2.46316e47i | 0.0625693 | + | 0.0625693i | ||||
\(723\) | −3.75982e46 | + | 3.75982e46i | −0.00932858 | + | 0.00932858i | ||||
\(724\) | 3.72140e48i | 0.901883i | ||||||||
\(725\) | −1.36744e46 | + | 6.35758e46i | −0.00323714 | + | 0.0150503i | ||||
\(726\) | 3.72294e47 | 0.0860921 | ||||||||
\(727\) | −5.67334e48 | − | 5.67334e48i | −1.28160 | − | 1.28160i | −0.939754 | − | 0.341850i | \(-0.888946\pi\) |
−0.341850 | − | 0.939754i | \(-0.611054\pi\) | |||||||
\(728\) | −4.24593e47 | + | 4.24593e47i | −0.0936999 | + | 0.0936999i | ||||
\(729\) | 3.58034e48i | 0.771892i | ||||||||
\(730\) | 7.09156e46 | − | 6.66951e47i | 0.0149366 | − | 0.140477i | ||||
\(731\) | 4.21040e48 | 0.866419 | ||||||||
\(732\) | −3.62981e48 | − | 3.62981e48i | −0.729787 | − | 0.729787i | ||||
\(733\) | −4.46120e48 | + | 4.46120e48i | −0.876364 | + | 0.876364i | −0.993156 | − | 0.116792i | \(-0.962739\pi\) |
0.116792 | + | 0.993156i | \(0.462739\pi\) | |||||||
\(734\) | 4.66671e47i | 0.0895731i | ||||||||
\(735\) | 2.45258e48 | − | 1.98115e48i | 0.459980 | − | 0.371563i | ||||
\(736\) | 1.52831e48 | 0.280084 | ||||||||
\(737\) | 4.38036e48 | + | 4.38036e48i | 0.784446 | + | 0.784446i | ||||
\(738\) | −8.82807e46 | + | 8.82807e46i | −0.0154493 | + | 0.0154493i | ||||
\(739\) | − | 9.62849e48i | − | 1.64666i | −0.567566 | − | 0.823328i | \(-0.692115\pi\) | ||
0.567566 | − | 0.823328i | \(-0.307885\pi\) | |||||||
\(740\) | 3.96948e48 | + | 4.91404e48i | 0.663428 | + | 0.821296i | ||||
\(741\) | 1.56261e48 | 0.255235 | ||||||||
\(742\) | −5.28544e46 | − | 5.28544e46i | −0.00843752 | − | 0.00843752i | ||||
\(743\) | −5.77556e48 | + | 5.77556e48i | −0.901124 | + | 0.901124i | −0.995533 | − | 0.0944098i | \(-0.969904\pi\) |
0.0944098 | + | 0.995533i | \(0.469904\pi\) | |||||||
\(744\) | − | 3.04279e47i | − | 0.0464015i | ||||||
\(745\) | −1.40897e48 | − | 1.49813e47i | −0.210012 | − | 0.0223302i | ||||
\(746\) | 9.12919e47 | 0.133006 | ||||||||
\(747\) | −6.73144e47 | − | 6.73144e47i | −0.0958645 | − | 0.0958645i | ||||
\(748\) | 3.44114e48 | − | 3.44114e48i | 0.479044 | − | 0.479044i | ||||
\(749\) | − | 7.65351e47i | − | 0.104152i | ||||||
\(750\) | 2.36806e47 | − | 7.19908e47i | 0.0315029 | − | 0.0957713i | ||||
\(751\) | 6.94009e47 | 0.0902581 | 0.0451291 | − | 0.998981i | \(-0.485630\pi\) | ||||
0.0451291 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(752\) | −3.92392e48 | − | 3.92392e48i | −0.498904 | − | 0.498904i | ||||
\(753\) | −2.75297e48 | + | 2.75297e48i | −0.342206 | + | 0.342206i | ||||
\(754\) | 1.25087e46i | 0.00152019i | ||||||||
\(755\) | 1.49200e48 | − | 1.40320e49i | 0.177284 | − | 1.66733i | ||||
\(756\) | 5.14910e48 | 0.598220 | ||||||||
\(757\) | −9.35810e46 | − | 9.35810e46i | −0.0106306 | − | 0.0106306i | 0.701772 | − | 0.712402i | \(-0.252393\pi\) |
−0.712402 | + | 0.701772i | \(0.752393\pi\) | |||||||
\(758\) | −9.47202e46 | + | 9.47202e46i | −0.0105212 | + | 0.0105212i | ||||
\(759\) | − | 1.37788e49i | − | 1.49658i | ||||||
\(760\) | 3.01512e47 | − | 2.43556e47i | 0.0320239 | − | 0.0258683i | ||||
\(761\) | −2.45174e48 | −0.254645 | −0.127323 | − | 0.991861i | \(-0.540638\pi\) | ||||
−0.127323 | + | 0.991861i | \(0.540638\pi\) | |||||||
\(762\) | −2.63902e47 | − | 2.63902e47i | −0.0268045 | − | 0.0268045i | ||||
\(763\) | 1.51289e48 | − | 1.51289e48i | 0.150276 | − | 0.150276i | ||||
\(764\) | 1.19185e49i | 1.15780i | ||||||||
\(765\) | −5.75182e47 | − | 7.12050e47i | −0.0546463 | − | 0.0676498i | ||||
\(766\) | −9.85389e47 | −0.0915627 | ||||||||
\(767\) | 1.21913e49 | + | 1.21913e49i | 1.10798 | + | 1.10798i | ||||
\(768\) | 7.87955e48 | − | 7.87955e48i | 0.700423 | − | 0.700423i | ||||
\(769\) | − | 4.88746e48i | − | 0.424947i | −0.977167 | − | 0.212474i | \(-0.931848\pi\) | ||
0.977167 | − | 0.212474i | \(-0.0681520\pi\) | |||||||
\(770\) | 9.98549e47 | + | 1.06174e47i | 0.0849233 | + | 0.00902973i | ||||
\(771\) | 4.16374e48 | 0.346385 | ||||||||
\(772\) | −5.36303e48 | − | 5.36303e48i | −0.436432 | − | 0.436432i | ||||
\(773\) | −1.15100e48 | + | 1.15100e48i | −0.0916267 | + | 0.0916267i | −0.751434 | − | 0.659808i | \(-0.770638\pi\) |
0.659808 | + | 0.751434i | \(0.270638\pi\) | |||||||
\(774\) | 3.57489e47i | 0.0278398i | ||||||||
\(775\) | −2.96586e48 | − | 6.37921e47i | −0.225955 | − | 0.0486002i | ||||
\(776\) | 1.29167e48 | 0.0962727 | ||||||||
\(777\) | 7.53820e48 | + | 7.53820e48i | 0.549681 | + | 0.549681i | ||||
\(778\) | 7.54824e46 | − | 7.54824e46i | 0.00538508 | − | 0.00538508i | ||||
\(779\) | 4.31076e48i | 0.300896i | ||||||||
\(780\) | −1.76369e48 | + | 1.65872e49i | −0.120452 | + | 1.13283i | ||||
\(781\) | −4.03751e49 | −2.69802 | ||||||||
\(782\) | 5.12655e47 | + | 5.12655e47i | 0.0335205 | + | 0.0335205i | ||||
\(783\) | 1.52358e47 | − | 1.52358e47i | 0.00974798 | − | 0.00974798i | ||||
\(784\) | 8.49342e48i | 0.531752i | ||||||||
\(785\) | −1.51313e49 | + | 1.22228e49i | −0.927026 | + | 0.748835i | ||||
\(786\) | −1.81739e48 | −0.108960 | ||||||||
\(787\) | 1.52690e48 | + | 1.52690e48i | 0.0895862 | + | 0.0895862i | 0.750480 | − | 0.660893i | \(-0.229823\pi\) |
−0.660893 | + | 0.750480i | \(0.729823\pi\) | |||||||
\(788\) | 1.76216e49 | − | 1.76216e49i | 1.01181 | − | 1.01181i | ||||
\(789\) | 1.48211e49i | 0.832858i | ||||||||
\(790\) | −1.79988e48 | − | 2.22818e48i | −0.0989881 | − | 0.122543i | ||||
\(791\) | 5.06276e48 | 0.272513 | ||||||||
\(792\) | 5.86901e47 | + | 5.86901e47i | 0.0309198 | + | 0.0309198i | ||||
\(793\) | −1.39832e49 | + | 1.39832e49i | −0.721047 | + | 0.721047i | ||||
\(794\) | 2.80556e48i | 0.141602i | ||||||||
\(795\) | −4.14769e48 | − | 4.41016e47i | −0.204911 | − | 0.0217878i | ||||
\(796\) | 1.26200e49 | 0.610289 | ||||||||
\(797\) | −8.97419e48 | − | 8.97419e48i | −0.424819 | − | 0.424819i | 0.462040 | − | 0.886859i | \(-0.347118\pi\) |
−0.886859 | + | 0.462040i | \(0.847118\pi\) | |||||||
\(798\) | 2.30256e47 | − | 2.30256e47i | 0.0106699 | − | 0.0106699i | ||||
\(799\) | − | 8.01408e48i | − | 0.363545i | ||||||
\(800\) | 3.37247e48 | + | 5.22077e48i | 0.149768 | + | 0.231849i | ||||
\(801\) | −6.17724e48 | −0.268560 | ||||||||
\(802\) | −8.59312e47 | − | 8.59312e47i | −0.0365752 | − | 0.0365752i | ||||
\(803\) | 3.50667e49 | − | 3.50667e49i | 1.46127 | − | 1.46127i | ||||
\(804\) | 2.14439e49i | 0.874886i | ||||||||
\(805\) | 1.80996e48 | − | 1.70224e49i | 0.0723001 | − | 0.679972i | ||||
\(806\) | −5.83541e47 | −0.0228232 | ||||||||
\(807\) | 1.82918e49 | + | 1.82918e49i | 0.700498 | + | 0.700498i | ||||
\(808\) | −3.89067e48 | + | 3.89067e48i | −0.145892 | + | 0.145892i | ||||
\(809\) | 2.24166e48i | 0.0823086i | 0.999153 | + | 0.0411543i | \(0.0131035\pi\) | ||||
−0.999153 | + | 0.0411543i | \(0.986896\pi\) | |||||||
\(810\) | −2.30228e48 | + | 1.85974e48i | −0.0827777 | + | 0.0668663i | ||||
\(811\) | −8.22977e48 | −0.289756 | −0.144878 | − | 0.989450i | \(-0.546279\pi\) | ||||
−0.144878 | + | 0.989450i | \(0.546279\pi\) | |||||||
\(812\) | −2.10912e47 | − | 2.10912e47i | −0.00727190 | − | 0.00727190i | ||||
\(813\) | 1.70304e49 | − | 1.70304e49i | 0.575024 | − | 0.575024i | ||||
\(814\) | − | 4.08186e48i | − | 0.134972i | ||||||
\(815\) | −3.03396e49 | − | 3.75591e49i | −0.982494 | − | 1.21629i | ||||
\(816\) | 1.66975e49 | 0.529564 | ||||||||
\(817\) | 8.72811e48 | + | 8.72811e48i | 0.271110 | + | 0.271110i | ||||
\(818\) | 2.17317e48 | − | 2.17317e48i | 0.0661132 | − | 0.0661132i | ||||
\(819\) | 4.15724e48i | 0.123873i | ||||||||
\(820\) | −4.57590e49 | − | 4.86547e48i | −1.33549 | − | 0.142000i | ||||
\(821\) | −8.16350e48 | −0.233369 | −0.116684 | − | 0.993169i | \(-0.537227\pi\) | ||||
−0.116684 | + | 0.993169i | \(0.537227\pi\) | |||||||
\(822\) | −2.25626e48 | − | 2.25626e48i | −0.0631785 | − | 0.0631785i | ||||
\(823\) | −6.61773e48 | + | 6.61773e48i | −0.181515 | + | 0.181515i | −0.792016 | − | 0.610501i | \(-0.790968\pi\) |
0.610501 | + | 0.792016i | \(0.290968\pi\) | |||||||
\(824\) | 3.80968e48i | 0.102359i | ||||||||
\(825\) | 4.70689e49 | − | 3.04051e49i | 1.23884 | − | 0.800258i | ||||
\(826\) | 3.59287e48 | 0.0926362 | ||||||||
\(827\) | 2.35491e49 | + | 2.35491e49i | 0.594813 | + | 0.594813i | 0.938928 | − | 0.344115i | \(-0.111821\pi\) |
−0.344115 | + | 0.938928i | \(0.611821\pi\) | |||||||
\(828\) | 4.98073e48 | − | 4.98073e48i | 0.123247 | − | 0.123247i | ||||
\(829\) | − | 3.09117e49i | − | 0.749370i | −0.927152 | − | 0.374685i | \(-0.877751\pi\) | ||
0.927152 | − | 0.374685i | \(-0.122249\pi\) | |||||||
\(830\) | −3.24219e47 | + | 3.04923e48i | −0.00770035 | + | 0.0724206i | ||||
\(831\) | −1.77466e49 | −0.412950 | ||||||||
\(832\) | −3.12074e49 | − | 3.12074e49i | −0.711477 | − | 0.711477i | ||||
\(833\) | −8.67333e48 | + | 8.67333e48i | −0.193741 | + | 0.193741i | ||||
\(834\) | − | 6.53539e48i | − | 0.143037i | ||||||
\(835\) | 2.08749e49 | − | 1.68624e49i | 0.447667 | − | 0.361617i | ||||
\(836\) | 1.42669e49 | 0.299794 | ||||||||
\(837\) | 7.10762e48 | + | 7.10762e48i | 0.146350 | + | 0.146350i | ||||
\(838\) | 4.23980e48 | − | 4.23980e48i | 0.0855454 | − | 0.0855454i | ||||
\(839\) | 5.36205e49i | 1.06018i | 0.847943 | + | 0.530088i | \(0.177841\pi\) | ||||
−0.847943 | + | 0.530088i | \(0.822159\pi\) | |||||||
\(840\) | 4.38768e48 | + | 5.43176e48i | 0.0850134 | + | 0.105243i | ||||
\(841\) | 5.26537e49 | 0.999763 | ||||||||
\(842\) | 5.49427e48 | + | 5.49427e48i | 0.102236 | + | 0.102236i | ||||
\(843\) | −5.07202e49 | + | 5.07202e49i | −0.924937 | + | 0.924937i | ||||
\(844\) | − | 1.15111e49i | − | 0.205729i | ||||||
\(845\) | 7.12889e48 | + | 7.58001e47i | 0.124870 | + | 0.0132772i | ||||
\(846\) | 6.80444e47 | 0.0116814 | ||||||||
\(847\) | 2.41823e49 | + | 2.41823e49i | 0.406893 | + | 0.406893i | ||||
\(848\) | 7.94545e48 | − | 7.94545e48i | 0.131036 | − | 0.131036i | ||||
\(849\) | 7.40062e49i | 1.19629i | ||||||||
\(850\) | −6.19993e47 | + | 2.88251e48i | −0.00982347 | + | 0.0456719i | ||||
\(851\) | −6.95840e49 | −1.08070 | ||||||||
\(852\) | −9.88274e49 | − | 9.88274e49i | −1.50454 | − | 1.50454i | ||||
\(853\) | 1.43630e49 | − | 1.43630e49i | 0.214344 | − | 0.214344i | −0.591766 | − | 0.806110i | \(-0.701569\pi\) |
0.806110 | + | 0.591766i | \(0.201569\pi\) | |||||||
\(854\) | 4.12095e48i | 0.0602856i | ||||||||
\(855\) | 2.83728e47 | − | 2.66842e48i | 0.00406891 | − | 0.0382675i | ||||
\(856\) | −2.03769e48 | −0.0286473 | ||||||||
\(857\) | 8.96598e49 | + | 8.96598e49i | 1.23573 | + | 1.23573i | 0.961730 | + | 0.274000i | \(0.0883469\pi\) |
0.274000 | + | 0.961730i | \(0.411653\pi\) | |||||||
\(858\) | 7.62160e48 | − | 7.62160e48i | 0.102982 | − | 0.102982i | ||||
\(859\) | 2.22565e49i | 0.294831i | 0.989075 | + | 0.147416i | \(0.0470955\pi\) | ||||
−0.989075 | + | 0.147416i | \(0.952904\pi\) | |||||||
\(860\) | −1.02501e50 | + | 8.27983e49i | −1.33123 | + | 1.07534i | ||||
\(861\) | −7.76585e49 | −0.988862 | ||||||||
\(862\) | −2.01176e48 | − | 2.01176e48i | −0.0251161 | − | 0.0251161i | ||||
\(863\) | −5.63347e49 | + | 5.63347e49i | −0.689593 | + | 0.689593i | −0.962142 | − | 0.272549i | \(-0.912133\pi\) |
0.272549 | + | 0.962142i | \(0.412133\pi\) | |||||||
\(864\) | − | 2.05935e49i | − | 0.247170i | ||||||
\(865\) | 8.38213e49 | + | 1.03767e50i | 0.986462 | + | 1.22120i | ||||
\(866\) | −1.52205e49 | −0.175640 | ||||||||
\(867\) | −5.06362e49 | − | 5.06362e49i | −0.572977 | − | 0.572977i | ||||
\(868\) | 9.83921e48 | − | 9.83921e48i | 0.109175 | − | 0.109175i | ||||
\(869\) | − | 2.11786e50i | − | 2.30442i | ||||||
\(870\) | 1.44643e47 | + | 1.53796e46i | 0.00154337 | + | 0.000164103i | ||||
\(871\) | 8.26090e49 | 0.864408 | ||||||||
\(872\) | −4.02795e48 | − | 4.02795e48i | −0.0413337 | − | 0.0413337i | ||||
\(873\) | 6.32346e48 | − | 6.32346e48i | 0.0636374 | − | 0.0636374i | ||||
\(874\) | 2.12546e48i | 0.0209777i | ||||||||
\(875\) | 6.21432e49 | − | 3.13799e49i | 0.601529 | − | 0.303748i | ||||
\(876\) | 1.71668e50 | 1.62975 | ||||||||
\(877\) | −9.40692e48 | − | 9.40692e48i | −0.0875899 | − | 0.0875899i | 0.661954 | − | 0.749544i | \(-0.269727\pi\) |
−0.749544 | + | 0.661954i | \(0.769727\pi\) | |||||||
\(878\) | −7.16087e48 | + | 7.16087e48i | −0.0653972 | + | 0.0653972i | ||||
\(879\) | − | 6.70162e49i | − | 0.600301i | ||||||
\(880\) | −1.59608e49 | + | 1.50109e50i | −0.140233 | + | 1.31887i | ||||
\(881\) | 6.90094e49 | 0.594727 | 0.297363 | − | 0.954764i | \(-0.403893\pi\) | ||||
0.297363 | + | 0.954764i | \(0.403893\pi\) | |||||||
\(882\) | −7.36419e47 | − | 7.36419e47i | −0.00622528 | − | 0.00622528i | ||||
\(883\) | −1.42424e49 | + | 1.42424e49i | −0.118100 | + | 0.118100i | −0.763687 | − | 0.645587i | \(-0.776613\pi\) |
0.645587 | + | 0.763687i | \(0.276613\pi\) | |||||||
\(884\) | − | 6.48963e49i | − | 0.527875i | ||||||
\(885\) | 1.55962e50 | − | 1.25984e50i | 1.24447 | − | 1.00526i | ||||
\(886\) | −5.60068e48 | −0.0438397 | ||||||||
\(887\) | −7.62444e49 | − | 7.62444e49i | −0.585472 | − | 0.585472i | 0.350930 | − | 0.936402i | \(-0.385866\pi\) |
−0.936402 | + | 0.350930i | \(0.885866\pi\) | |||||||
\(888\) | 2.00699e49 | − | 2.00699e49i | 0.151191 | − | 0.151191i | ||||
\(889\) | − | 3.42834e49i | − | 0.253369i | ||||||
\(890\) | 1.25033e49 | + | 1.54786e49i | 0.0906556 | + | 0.112228i | ||||
\(891\) | −2.18830e50 | −1.55663 | ||||||||
\(892\) | 1.87499e48 | + | 1.87499e48i | 0.0130857 | + | 0.0130857i | ||||
\(893\) | 1.66131e49 | − | 1.66131e49i | 0.113756 | − | 0.113756i | ||||
\(894\) | 3.16933e48i | 0.0212927i | ||||||||
\(895\) | −1.67387e49 | − | 1.77979e48i | −0.110339 | − | 0.0117321i | ||||
\(896\) | −3.79541e49 | −0.245484 | ||||||||
\(897\) | −1.29927e50 | − | 1.29927e50i | −0.824568 | − | 0.824568i | ||||
\(898\) | −1.64655e49 | + | 1.64655e49i | −0.102536 | + | 0.102536i | ||||
\(899\) | − | 5.82269e47i | − | 0.00355802i | ||||||
\(900\) | 2.80052e49 | + | 6.02358e48i | 0.167925 | + | 0.0361187i | ||||
\(901\) | 1.62275e49 | 0.0954841 | ||||||||
\(902\) | 2.10256e49 | + | 2.10256e49i | 0.121405 | + | 0.121405i | ||||
\(903\) | −1.57237e50 | + | 1.57237e50i | −0.890972 | + | 0.890972i | ||||
\(904\) | − | 1.34792e49i | − | 0.0749552i | ||||||
\(905\) | 1.76263e49 | − | 1.65773e50i | 0.0961913 | − | 0.904665i | ||||
\(906\) | −3.15637e49 | −0.169047 | ||||||||
\(907\) | 2.31119e50 | + | 2.31119e50i | 1.21482 | + | 1.21482i | 0.969423 | + | 0.245394i | \(0.0789173\pi\) |
0.245394 | + | 0.969423i | \(0.421083\pi\) | |||||||
\(908\) | 2.31494e49 | − | 2.31494e49i | 0.119421 | − | 0.119421i | ||||
\(909\) | 3.80940e49i | 0.192873i | ||||||||
\(910\) | 1.04170e49 | − | 8.41463e48i | 0.0517651 | − | 0.0418149i | ||||
\(911\) | 2.16120e50 | 1.05410 | 0.527051 | − | 0.849834i | \(-0.323298\pi\) | ||||
0.527051 | + | 0.849834i | \(0.323298\pi\) | |||||||
\(912\) | 3.46137e49 | + | 3.46137e49i | 0.165705 | + | 0.165705i | ||||
\(913\) | −1.60321e50 | + | 1.60321e50i | −0.753335 | + | 0.753335i | ||||
\(914\) | − | 2.87787e49i | − | 0.132735i | ||||||
\(915\) | 1.44501e50 | + | 1.78886e50i | 0.654202 | + | 0.809874i | ||||
\(916\) | 3.69837e50 | 1.64357 | ||||||||
\(917\) | −1.18049e50 | − | 1.18049e50i | −0.514970 | − | 0.514970i | ||||
\(918\) | 6.90786e48 | − | 6.90786e48i | 0.0295814 | − | 0.0295814i | ||||
\(919\) | − | 2.08883e49i | − | 0.0878090i | −0.999036 | − | 0.0439045i | \(-0.986020\pi\) | ||
0.999036 | − | 0.0439045i | \(-0.0139797\pi\) | |||||||
\(920\) | −4.53209e49 | − | 4.81888e48i | −0.187028 | − | 0.0198863i | ||||
\(921\) | −2.54712e50 | −1.03190 | ||||||||
\(922\) | −1.92484e49 | − | 1.92484e49i | −0.0765542 | − | 0.0765542i | ||||
\(923\) | −3.80716e50 | + | 3.80716e50i | −1.48652 | + | 1.48652i | ||||
\(924\) | 2.57019e50i | 0.985239i | ||||||||
\(925\) | −1.53549e50 | − | 2.37702e50i | −0.577879 | − | 0.894589i | ||||
\(926\) | 3.53760e49 | 0.130714 | ||||||||
\(927\) | 1.86505e49 | + | 1.86505e49i | 0.0676605 | + | 0.0676605i | ||||
\(928\) | −8.43527e47 | + | 8.43527e47i | −0.00300458 | + | 0.00300458i | ||||
\(929\) | − | 2.69117e49i | − | 0.0941184i | −0.998892 | − | 0.0470592i | \(-0.985015\pi\) | ||
0.998892 | − | 0.0470592i | \(-0.0149849\pi\) | |||||||
\(930\) | −7.17471e47 | + | 6.74771e48i | −0.00246374 | + | 0.0231711i | ||||
\(931\) | −3.59594e49 | −0.121246 | ||||||||
\(932\) | −4.17173e50 | − | 4.17173e50i | −1.38117 | − | 1.38117i | ||||
\(933\) | 1.32352e50 | − | 1.32352e50i | 0.430271 | − | 0.430271i | ||||
\(934\) | 3.19271e49i | 0.101921i | ||||||||
\(935\) | −1.69588e50 | + | 1.36990e50i | −0.531615 | + | 0.429429i | ||||
\(936\) | 1.10683e49 | 0.0340717 | ||||||||
\(937\) | 3.20211e50 | + | 3.20211e50i | 0.967973 | + | 0.967973i | 0.999503 | − | 0.0315298i | \(-0.0100379\pi\) |
−0.0315298 | + | 0.999503i | \(0.510038\pi\) | |||||||
\(938\) | 1.21727e49 | − | 1.21727e49i | 0.0361359 | − | 0.0361359i | ||||
\(939\) | 1.46016e50i | 0.425683i | ||||||||
\(940\) | 1.57598e50 | + | 1.95100e50i | 0.451209 | + | 0.558578i | ||||
\(941\) | −2.06156e50 | −0.579659 | −0.289829 | − | 0.957078i | \(-0.593599\pi\) | ||||
−0.289829 | + | 0.957078i | \(0.593599\pi\) | |||||||
\(942\) | 3.07652e49 | + | 3.07652e49i | 0.0849560 | + | 0.0849560i | ||||
\(943\) | 3.58427e50 | − | 3.58427e50i | 0.972080 | − | 0.972080i | ||||
\(944\) | 5.40106e50i | 1.43865i | ||||||||
\(945\) | −2.29371e50 | − | 2.43886e49i | −0.600065 | − | 0.0638038i | ||||
\(946\) | 8.51424e49 | 0.218774 | ||||||||
\(947\) | 7.39230e49 | + | 7.39230e49i | 0.186565 | + | 0.186565i | 0.794209 | − | 0.607644i | \(-0.207885\pi\) |
−0.607644 | + | 0.794209i | \(0.707885\pi\) | |||||||
\(948\) | 5.18395e50 | − | 5.18395e50i | 1.28505 | − | 1.28505i | ||||
\(949\) | − | 6.61322e50i | − | 1.61023i | ||||||
\(950\) | −7.26065e48 | + | 4.69017e48i | −0.0173650 | + | 0.0112173i | ||||
\(951\) | −1.01932e50 | −0.239464 | ||||||||
\(952\) | −1.92089e49 | − | 1.92089e49i | −0.0443277 | − | 0.0443277i | ||||
\(953\) | 3.22463e50 | − | 3.22463e50i | 0.730972 | − | 0.730972i | −0.239840 | − | 0.970812i | \(-0.577095\pi\) |
0.970812 | + | 0.239840i | \(0.0770951\pi\) | |||||||
\(954\) | 1.37782e48i | 0.00306810i | ||||||||
\(955\) | 5.64518e49 | − | 5.30921e50i | 0.123487 | − | 1.16137i | ||||
\(956\) | 2.68369e50 | 0.576699 | ||||||||
\(957\) | 7.60498e48 | + | 7.60498e48i | 0.0160544 | + | 0.0160544i | ||||
\(958\) | 1.75268e49 | − | 1.75268e49i | 0.0363488 | − | 0.0363488i | ||||
\(959\) | − | 2.93111e50i | − | 0.597194i | ||||||
\(960\) | −3.99232e50 | + | 3.22493e50i | −0.799125 | + | 0.645519i | ||||
\(961\) | −4.81344e50 | −0.946582 | ||||||||
\(962\) | −3.84898e49 | − | 3.84898e49i | −0.0743651 | − | 0.0743651i | ||||
\(963\) | −9.97564e48 | + | 9.97564e48i | −0.0189362 | + | 0.0189362i | ||||
\(964\) | 6.47385e48i | 0.0120741i | ||||||||
\(965\) | 2.13499e50 | + | 2.64303e50i | 0.391230 | + | 0.484326i | ||||
\(966\) | −3.82902e49 | −0.0689408 | ||||||||
\(967\) | 1.51137e50 | + | 1.51137e50i | 0.267374 | + | 0.267374i | 0.828041 | − | 0.560667i | \(-0.189455\pi\) |
−0.560667 | + | 0.828041i | \(0.689455\pi\) | |||||||
\(968\) | 6.43837e49 | − | 6.43837e49i | 0.111917 | − | 0.111917i | ||||
\(969\) | 7.06938e49i | 0.120747i | ||||||||
\(970\) | −2.86442e49 | − | 3.04568e48i | −0.0480748 | − | 0.00511170i | ||||
\(971\) | −1.84274e50 | −0.303904 | −0.151952 | − | 0.988388i | \(-0.548556\pi\) | ||||
−0.151952 | + | 0.988388i | \(0.548556\pi\) | |||||||
\(972\) | −1.48293e50 | − | 1.48293e50i | −0.240323 | − | 0.240323i | ||||
\(973\) | 4.24506e50 | − | 4.24506e50i | 0.676029 | − | 0.676029i | ||||
\(974\) | − | 2.14922e49i | − | 0.0336340i | ||||||
\(975\) | 1.57130e50 | − | 7.30539e50i | 0.241647 | − | 1.12348i | ||||
\(976\) | −6.19491e50 | −0.936242 | ||||||||
\(977\) | 8.60809e50 | + | 8.60809e50i | 1.27850 | + | 1.27850i | 0.941510 | + | 0.336986i | \(0.109408\pi\) |
0.336986 | + | 0.941510i | \(0.390592\pi\) | |||||||
\(978\) | −7.63657e49 | + | 7.63657e49i | −0.111465 | + | 0.111465i | ||||
\(979\) | 1.47122e51i | 2.11044i | ||||||||
\(980\) | 4.05867e49 | − | 3.81712e50i | 0.0572190 | − | 0.538137i | ||||
\(981\) | −3.94382e49 | −0.0546441 | ||||||||
\(982\) | −3.78434e49 | − | 3.78434e49i | −0.0515341 | − | 0.0515341i | ||||
\(983\) | −7.39214e50 | + | 7.39214e50i | −0.989374 | + | 0.989374i | −0.999944 | − | 0.0105700i | \(-0.996635\pi\) |
0.0105700 | + | 0.999944i | \(0.496635\pi\) | |||||||
\(984\) | 2.06760e50i | 0.271988i | ||||||||
\(985\) | −8.68435e50 | + | 7.01506e50i | −1.12285 | + | 0.907018i | ||||
\(986\) | −5.65904e47 | −0.000719176 | ||||||||
\(987\) | 2.99286e50 | + | 2.99286e50i | 0.373847 | + | 0.373847i | ||||
\(988\) | 1.34529e50 | − | 1.34529e50i | 0.165177 | − | 0.165177i | ||||
\(989\) | − | 1.45143e51i | − | 1.75170i | ||||||
\(990\) | −1.16313e49 | − | 1.43990e49i | −0.0137984 | − | 0.0170819i | ||||
\(991\) | −2.59004e50 | −0.302033 | −0.151016 | − | 0.988531i | \(-0.548255\pi\) | ||||
−0.151016 | + | 0.988531i | \(0.548255\pi\) | |||||||
\(992\) | −3.93513e49 | − | 3.93513e49i | −0.0451087 | − | 0.0451087i | ||||
\(993\) | 5.04613e50 | − | 5.04613e50i | 0.568619 | − | 0.568619i | ||||
\(994\) | 1.12199e50i | 0.124286i | ||||||||
\(995\) | −5.62167e50 | − | 5.97742e49i | −0.612172 | − | 0.0650910i | ||||
\(996\) | −7.84848e50 | −0.840189 | ||||||||
\(997\) | 6.19129e50 | + | 6.19129e50i | 0.651574 | + | 0.651574i | 0.953372 | − | 0.301798i | \(-0.0975868\pi\) |
−0.301798 | + | 0.953372i | \(0.597587\pi\) | |||||||
\(998\) | −6.01884e49 | + | 6.01884e49i | −0.0622721 | + | 0.0622721i | ||||
\(999\) | 9.37623e50i | 0.953707i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 5.35.c.a.2.8 | ✓ | 32 | |
5.2 | odd | 4 | 25.35.c.b.18.9 | 32 | |||
5.3 | odd | 4 | inner | 5.35.c.a.3.8 | yes | 32 | |
5.4 | even | 2 | 25.35.c.b.7.9 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.35.c.a.2.8 | ✓ | 32 | 1.1 | even | 1 | trivial | |
5.35.c.a.3.8 | yes | 32 | 5.3 | odd | 4 | inner | |
25.35.c.b.7.9 | 32 | 5.4 | even | 2 | |||
25.35.c.b.18.9 | 32 | 5.2 | odd | 4 |