Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,8,Mod(257,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.257");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.i (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: | \(93.7155076452\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 132 x^{14} - 784 x^{13} + 5524236 x^{12} - 33135588 x^{11} - 49457570 x^{10} + \cdots + 18\!\cdots\!21 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{44}\cdot 3^{12}\cdot 5^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.7 | ||
Root | \(-19.4848 - 23.5555i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.257 |
Dual form | 300.8.i.c.293.7 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 40.5650 | + | 23.2698i | 0.867415 | + | 0.497586i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −208.115 | − | 208.115i | −0.229330 | − | 0.229330i | 0.583083 | − | 0.812413i | \(-0.301846\pi\) |
−0.812413 | + | 0.583083i | \(0.801846\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1104.03 | + | 1887.88i | 0.504817 | + | 0.863227i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7004.41i | 1.58671i | 0.608760 | + | 0.793354i | \(0.291667\pi\) | ||||
−0.608760 | + | 0.793354i | \(0.708333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9873.16 | − | 9873.16i | 1.24639 | − | 1.24639i | 0.289089 | − | 0.957302i | \(-0.406648\pi\) |
0.957302 | − | 0.289089i | \(-0.0933522\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17509.4 | − | 17509.4i | 0.864369 | − | 0.864369i | −0.127473 | − | 0.991842i | \(-0.540687\pi\) |
0.991842 | + | 0.127473i | \(0.0406865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 24385.0i | − | 0.815616i | −0.913068 | − | 0.407808i | \(-0.866293\pi\) | ||
0.913068 | − | 0.407808i | \(-0.133707\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3599.39 | − | 13285.0i | −0.0848129 | − | 0.313036i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15785.8 | − | 15785.8i | −0.270533 | − | 0.270533i | 0.558782 | − | 0.829315i | \(-0.311269\pi\) |
−0.829315 | + | 0.558782i | \(0.811269\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 854.643 | + | 102272.i | 0.00835625 | + | 0.999965i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −122497. | −0.932678 | −0.466339 | − | 0.884606i | \(-0.654427\pi\) | ||||
−0.466339 | + | 0.884606i | \(0.654427\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 228108. | 1.37523 | 0.687613 | − | 0.726078i | \(-0.258659\pi\) | ||||
0.687613 | + | 0.726078i | \(0.258659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −162991. | + | 284134.i | −0.789524 | + | 1.37633i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −155115. | − | 155115.i | −0.503439 | − | 0.503439i | 0.409066 | − | 0.912505i | \(-0.365855\pi\) |
−0.912505 | + | 0.409066i | \(0.865855\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 630251. | − | 170758.i | 1.70132 | − | 0.460951i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 725519.i | 1.64401i | 0.569478 | + | 0.822007i | \(0.307145\pi\) | ||||
−0.569478 | + | 0.822007i | \(0.692855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 430632. | − | 430632.i | 0.825974 | − | 0.825974i | −0.160983 | − | 0.986957i | \(-0.551466\pi\) |
0.986957 | + | 0.160983i | \(0.0514664\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −24323.9 | + | 24323.9i | −0.0341736 | + | 0.0341736i | −0.723987 | − | 0.689813i | \(-0.757693\pi\) |
0.689813 | + | 0.723987i | \(0.257693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 736919.i | − | 0.894816i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.11771e6 | − | 302828.i | 1.17986 | − | 0.319669i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 464100. | + | 464100.i | 0.428200 | + | 0.428200i | 0.888015 | − | 0.459815i | \(-0.152084\pi\) |
−0.459815 | + | 0.888015i | \(0.652084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 567434. | − | 989178.i | 0.405839 | − | 0.707477i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 78012.9 | 0.0494521 | 0.0247260 | − | 0.999694i | \(-0.492129\pi\) | ||||
0.0247260 | + | 0.999694i | \(0.492129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.98833e6 | 1.12159 | 0.560795 | − | 0.827954i | \(-0.310495\pi\) | ||||
0.560795 | + | 0.827954i | \(0.310495\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 163130. | − | 622662.i | 0.0821941 | − | 0.313733i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.14870e6 | + | 2.14870e6i | 0.872797 | + | 0.872797i | 0.992776 | − | 0.119980i | \(-0.0382829\pi\) |
−0.119980 | + | 0.992776i | \(0.538283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −273019. | − | 1.00768e6i | −0.100051 | − | 0.369278i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 870154.i | 0.288531i | 0.989539 | + | 0.144265i | \(0.0460819\pi\) | ||||
−0.989539 | + | 0.144265i | \(0.953918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.29108e6 | + | 3.29108e6i | −0.990165 | + | 0.990165i | −0.999952 | − | 0.00978664i | \(-0.996885\pi\) |
0.00978664 | + | 0.999952i | \(0.496885\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.45772e6 | − | 1.45772e6i | 0.363880 | − | 0.363880i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 450479.i | − | 0.102797i | −0.998678 | − | 0.0513985i | \(-0.983632\pi\) | ||
0.998678 | − | 0.0513985i | \(-0.0163679\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.34519e6 | + | 4.16856e6i | −0.490320 | + | 0.871542i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.28119e6 | + | 4.28119e6i | 0.821847 | + | 0.821847i | 0.986373 | − | 0.164525i | \(-0.0526093\pi\) |
−0.164525 | + | 0.986373i | \(0.552609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.96908e6 | − | 2.85047e6i | −0.809019 | − | 0.464087i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.27320e6 | 0.792883 | 0.396441 | − | 0.918060i | \(-0.370245\pi\) | ||||
0.396441 | + | 0.918060i | \(0.370245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.10951e6 | −0.571670 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.25318e6 | + | 5.30802e6i | 1.19289 | + | 0.684293i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −471574. | − | 471574.i | −0.0524624 | − | 0.0524624i | 0.680389 | − | 0.732851i | \(-0.261811\pi\) |
−0.732851 | + | 0.680389i | \(0.761811\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.32235e7 | + | 7.73311e6i | −1.36969 | + | 0.800997i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.64755e7i | − | 1.59116i | −0.605848 | − | 0.795581i | \(-0.707166\pi\) | ||
0.605848 | − | 0.795581i | \(-0.292834\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.84694e6 | − | 1.84694e6i | 0.166541 | − | 0.166541i | −0.618916 | − | 0.785457i | \(-0.712428\pi\) |
0.785457 | + | 0.618916i | \(0.212428\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.43575e7 | − | 1.43575e7i | 1.13301 | − | 1.13301i | 0.143340 | − | 0.989673i | \(-0.454216\pi\) |
0.989673 | − | 0.143340i | \(-0.0457844\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.20147e6i | 0.606595i | 0.952896 | + | 0.303298i | \(0.0980876\pi\) | ||||
−0.952896 | + | 0.303298i | \(0.901912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.68274e6 | − | 9.90172e6i | −0.186187 | − | 0.687195i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.48391e7 | + | 1.48391e7i | 0.967457 | + | 0.967457i | 0.999487 | − | 0.0320296i | \(-0.0101971\pi\) |
−0.0320296 | + | 0.999487i | \(0.510197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.95396e7 | + | 7.73900e6i | 1.70512 | + | 0.446719i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.28794e6 | −0.396452 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.95746e7 | −1.51764 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.68827e7 | + | 2.94307e7i | −0.818038 | + | 1.42604i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.01955e6 | + | 3.01955e6i | 0.130807 | + | 0.130807i | 0.769479 | − | 0.638672i | \(-0.220516\pi\) |
−0.638672 | + | 0.769479i | \(0.720516\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.74893e7 | − | 7.44786e6i | 1.12746 | − | 0.305469i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00934e7i | 0.780915i | 0.920621 | + | 0.390458i | \(0.127683\pi\) | ||||
−0.920621 | + | 0.390458i | \(0.872317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.07490e6 | + | 5.07490e6i | −0.187045 | + | 0.187045i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.47844e6 | − | 9.47844e6i | 0.314931 | − | 0.314931i | −0.531886 | − | 0.846816i | \(-0.678516\pi\) |
0.846816 | + | 0.531886i | \(0.178516\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.38424e7i | 0.437180i | 0.975817 | + | 0.218590i | \(0.0701458\pi\) | ||||
−0.975817 | + | 0.218590i | \(0.929854\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.55271e6 | + | 420687.i | −0.0466470 | + | 0.0126384i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.91556e7 | + | 6.91556e7i | 1.97766 | + | 1.97766i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.71479e7 | − | 2.98931e7i | 0.445247 | − | 0.776176i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.65482e7 | −1.15279 | −0.576396 | − | 0.817170i | \(-0.695542\pi\) | ||||
−0.576396 | + | 0.817170i | \(0.695542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.01802e7 | 0.949714 | 0.474857 | − | 0.880063i | \(-0.342500\pi\) | ||||
0.474857 | + | 0.880063i | \(0.342500\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.23865e7 | + | 1.37246e7i | 1.18249 | + | 0.309798i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.05276e7 | − | 2.05276e7i | −0.423340 | − | 0.423340i | 0.463012 | − | 0.886352i | \(-0.346769\pi\) |
−0.886352 | + | 0.463012i | \(0.846769\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.02670e6 | + | 2.96257e7i | 0.158361 | + | 0.584493i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.57055e6i | 0.124083i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.27257e7 | + | 3.27257e7i | −0.591879 | + | 0.591879i | −0.938139 | − | 0.346260i | \(-0.887451\pi\) |
0.346260 | + | 0.938139i | \(0.387451\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.86557e7 | − | 5.86557e7i | 0.974546 | − | 0.974546i | −0.0251383 | − | 0.999684i | \(-0.508003\pi\) |
0.999684 | + | 0.0251383i | \(0.00800260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.32210e8i | − | 2.10698i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.60359e7 | − | 2.69219e7i | 0.704061 | − | 0.411737i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.72521e7 | + | 5.72521e7i | 0.840679 | + | 0.840679i | 0.988947 | − | 0.148268i | \(-0.0473698\pi\) |
−0.148268 | + | 0.988947i | \(0.547370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.16459e6 | + | 1.81534e6i | 0.0428954 | + | 0.0246066i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.51415e7 | 0.848930 | 0.424465 | − | 0.905444i | \(-0.360462\pi\) | ||||
0.424465 | + | 0.905444i | \(0.360462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.65856e7 | 0.583951 | 0.291976 | − | 0.956426i | \(-0.405687\pi\) | ||||
0.291976 | + | 0.956426i | \(0.405687\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.06566e7 | + | 4.62681e7i | 0.972885 | + | 0.558088i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.22643e8 | + | 1.22643e8i | 1.37150 | + | 1.37150i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.11066e7 | − | 2.14623e7i | 0.227406 | − | 0.231238i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.17412e8i | 1.21926i | 0.792685 | + | 0.609631i | \(0.208682\pi\) | ||||
−0.792685 | + | 0.609631i | \(0.791318\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.10869e8 | + | 1.10869e8i | −1.11010 | + | 1.11010i | −0.116961 | + | 0.993136i | \(0.537315\pi\) |
−0.993136 | + | 0.116961i | \(0.962685\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.03739e8 | − | 1.03739e8i | 0.966739 | − | 0.966739i | −0.0327254 | − | 0.999464i | \(-0.510419\pi\) |
0.999464 | + | 0.0327254i | \(0.0104187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.08544e7i | 0.727307i | 0.931534 | + | 0.363654i | \(0.118471\pi\) | ||||
−0.931534 | + | 0.363654i | \(0.881529\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.71621e7 | + | 1.37161e8i | 0.322786 | + | 1.19137i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.54935e7 | + | 2.54935e7i | 0.213891 | + | 0.213891i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.23736e7 | − | 4.72298e7i | 0.0969616 | − | 0.370101i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.70803e8 | 1.29414 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.34222e6 | 0.0611355 | 0.0305677 | − | 0.999533i | \(-0.490268\pi\) | ||||
0.0305677 | + | 0.999533i | \(0.490268\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.02483e7 | + | 3.52978e7i | −0.143569 | + | 0.250276i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.74727e7 | − | 4.74727e7i | −0.315381 | − | 0.315381i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.10085e8 | + | 5.69198e7i | −1.35158 | + | 0.366192i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.45746e8i | − | 2.15468i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.74036e8 | − | 1.74036e8i | 1.05092 | − | 1.05092i | 0.0522927 | − | 0.998632i | \(-0.483347\pi\) |
0.998632 | − | 0.0522927i | \(-0.0166529\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.22939e7 | + | 7.22939e7i | −0.410215 | + | 0.410215i | −0.881813 | − | 0.471599i | \(-0.843677\pi\) |
0.471599 | + | 0.881813i | \(0.343677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.01557e8i | − | 1.10911i | −0.832148 | − | 0.554554i | \(-0.812889\pi\) | ||
0.832148 | − | 0.554554i | \(-0.187111\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.30535e7 | − | 2.52116e7i | 0.496696 | − | 0.134573i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.06022e8 | + | 2.06022e8i | 1.06701 | + | 1.06701i | 0.997587 | + | 0.0694233i | \(0.0221159\pi\) |
0.0694233 | + | 0.997587i | \(0.477884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.04826e7 | − | 1.82737e7i | 0.0511503 | − | 0.0891676i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.20720e8 | −1.04580 | −0.522899 | − | 0.852394i | \(-0.675150\pi\) | ||||
−0.522899 | + | 0.852394i | \(0.675150\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.25054e8 | −1.95607 | −0.978035 | − | 0.208440i | \(-0.933161\pi\) | ||||
−0.978035 | + | 0.208440i | \(0.933161\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.92134e8 | + | 1.14526e8i | −0.858978 | + | 0.512012i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.40757e8 | − | 2.40757e8i | −1.01658 | − | 1.01658i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.40440e7 | + | 2.73289e8i | 0.303943 | + | 1.12182i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.74762e8i | 0.697573i | 0.937202 | + | 0.348787i | \(0.113406\pi\) | ||||
−0.937202 | + | 0.348787i | \(0.886594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.10570e8 | − | 1.10570e8i | 0.429257 | − | 0.429257i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.89089e8 | + | 1.89089e8i | −0.694864 | + | 0.694864i | −0.963298 | − | 0.268434i | \(-0.913494\pi\) |
0.268434 | + | 0.963298i | \(0.413494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.45635e7i | 0.230908i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.35241e8 | − | 2.31259e8i | −0.470832 | − | 0.805112i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.69233e8 | − | 3.69233e8i | −1.25157 | − | 1.25157i | −0.955015 | − | 0.296556i | \(-0.904162\pi\) |
−0.296556 | − | 0.955015i | \(-0.595838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.13907e8 | + | 1.22706e8i | 0.687758 | + | 0.394527i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.90340e7 | −0.278884 | −0.139442 | − | 0.990230i | \(-0.544531\pi\) | ||||
−0.139442 | + | 0.990230i | \(0.544531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.21578e8 | −0.371076 | −0.185538 | − | 0.982637i | \(-0.559403\pi\) | ||||
−0.185538 | + | 0.982637i | \(0.559403\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.66702e8 | − | 9.56274e7i | −0.495875 | − | 0.284455i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.68927e8 | + | 4.68927e8i | 1.32564 | + | 1.32564i | 0.909131 | + | 0.416511i | \(0.136747\pi\) |
0.416511 | + | 0.909131i | \(0.363253\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.51839e8 | + | 4.30639e8i | 0.694237 | + | 1.18713i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.39688e8i | 0.644427i | 0.946667 | + | 0.322214i | \(0.104427\pi\) | ||||
−0.946667 | + | 0.322214i | \(0.895573\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.76790e8 | + | 1.76790e8i | −0.463665 | + | 0.463665i | −0.899855 | − | 0.436190i | \(-0.856328\pi\) |
0.436190 | + | 0.899855i | \(0.356328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.50992e8 | − | 1.50992e8i | 0.377022 | − | 0.377022i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 2.02818e8i | − | 0.494269i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.15596e6 | − | 3.01028e7i | −0.0194021 | − | 0.0716113i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.55883e8 | − | 4.55883e8i | −1.05881 | − | 1.05881i | −0.998159 | − | 0.0606464i | \(-0.980684\pi\) |
−0.0606464 | − | 0.998159i | \(-0.519316\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.16357e8 | + | 5.98627e6i | −1.58665 | + | 0.0132589i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.11712e8 | −0.674380 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.79242e8 | −0.378841 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.83382e8 | − | 6.68329e8i | 0.791739 | − | 1.38020i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.07641e8 | − | 4.07641e8i | −0.804068 | − | 0.804068i | 0.179660 | − | 0.983729i | \(-0.442500\pi\) |
−0.983729 | + | 0.179660i | \(0.942500\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.17899e8 | − | 3.19431e7i | 0.227329 | − | 0.0615918i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.42251e8i | − | 1.58774i | −0.608086 | − | 0.793871i | \(-0.708062\pi\) | ||
0.608086 | − | 0.793871i | \(-0.291938\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.45437e8 | − | 2.45437e8i | 0.452414 | − | 0.452414i | −0.443741 | − | 0.896155i | \(-0.646349\pi\) |
0.896155 | + | 0.443741i | \(0.146349\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.61944e8 | + | 5.61944e8i | −0.990799 | + | 0.990799i | −0.999958 | − | 0.00915869i | \(-0.997085\pi\) |
0.00915869 | + | 0.999958i | \(0.497085\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.58018e8i | − | 1.47989i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.16507e8 | − | 2.48315e8i | 1.54656 | − | 0.419021i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.26967e8 | − | 4.26967e8i | −0.704994 | − | 0.704994i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.90846e8 | + | 3.32692e8i | −0.301833 | + | 0.526169i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.01244e7 | 0.0156741 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.41804e8 | −0.366494 | −0.183247 | − | 0.983067i | \(-0.558661\pi\) | ||||
−0.183247 | + | 0.983067i | \(0.558661\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.21586e8 | − | 4.64090e8i | 0.180438 | − | 0.688727i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.29724e8 | − | 4.29724e8i | −0.611625 | − | 0.611625i | 0.331744 | − | 0.943369i | \(-0.392363\pi\) |
−0.943369 | + | 0.331744i | \(0.892363\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.56644e8 | + | 9.47248e8i | 0.357794 | + | 1.32058i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.59776e9i | 2.18208i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.24756e8 | + | 3.24756e8i | −0.434538 | + | 0.434538i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.11375e8 | + | 3.11375e8i | −0.400065 | + | 0.400065i | −0.878256 | − | 0.478191i | \(-0.841293\pi\) |
0.478191 | + | 0.878256i | \(0.341293\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.50967e8i | − | 1.07158i | −0.844352 | − | 0.535789i | \(-0.820014\pi\) | ||
0.844352 | − | 0.535789i | \(-0.179986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.01819e9 | + | 1.00131e9i | 1.25676 | + | 1.23593i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.66049e8 | − | 6.66049e8i | −0.805925 | − | 0.805925i | 0.178090 | − | 0.984014i | \(-0.443008\pi\) |
−0.984014 | + | 0.178090i | \(0.943008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.95635e8 | − | 1.69589e8i | −0.343888 | − | 0.197269i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.30978e9 | 1.49406 | 0.747029 | − | 0.664791i | \(-0.231480\pi\) | ||||
0.747029 | + | 0.664791i | \(0.231480\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.99242e8 | 0.334770 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.19969e9 | − | 6.88194e8i | −1.31643 | − | 0.755158i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.61703e8 | + | 7.61703e8i | 0.804367 | + | 0.804367i | 0.983775 | − | 0.179408i | \(-0.0574181\pi\) |
−0.179408 | + | 0.983775i | \(0.557418\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.36969e9 | + | 8.00998e8i | −1.41916 | + | 0.829925i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.93173e8i | − | 0.196398i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.12129e7 | − | 2.12129e7i | 0.0211650 | − | 0.0211650i | −0.696445 | − | 0.717610i | \(-0.745236\pi\) |
0.717610 | + | 0.696445i | \(0.245236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.20943e9 | + | 1.20943e9i | −1.16248 | + | 1.16248i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.01580e9i | − | 1.90200i | −0.309195 | − | 0.950999i | \(-0.600060\pi\) | ||
0.309195 | − | 0.950999i | \(-0.399940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.22237e7 | + | 1.92752e8i | 0.0483760 | + | 0.178551i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.64823e8 | − | 6.64823e8i | −0.604658 | − | 0.604658i | 0.336887 | − | 0.941545i | \(-0.390626\pi\) |
−0.941545 | + | 0.336887i | \(0.890626\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.28841e9 | + | 3.37547e8i | 1.12997 | + | 0.296037i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.81809e8 | 0.673406 | 0.336703 | − | 0.941611i | \(-0.390688\pi\) | ||||
0.336703 | + | 0.941611i | \(0.390688\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.52800e8 | −0.467681 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.67569e8 | + | 8.15088e8i | −0.388572 | + | 0.677377i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.04364e9 | − | 1.04364e9i | −0.837110 | − | 0.837110i | 0.151367 | − | 0.988478i | \(-0.451632\pi\) |
−0.988478 | + | 0.151367i | \(0.951632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.23955e8 | + | 8.77713e7i | −0.255317 | + | 0.0691747i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.04506e9i | − | 1.58380i | −0.610649 | − | 0.791901i | \(-0.709091\pi\) | ||
0.610649 | − | 0.791901i | \(-0.290909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.25214e9 | − | 2.25214e9i | 1.71407 | − | 1.71407i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.08649e9 | − | 1.08649e9i | 0.798812 | − | 0.798812i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.59201e8i | − | 0.115058i | −0.998344 | − | 0.0575288i | \(-0.981678\pi\) | ||
0.998344 | − | 0.0575288i | \(-0.0183221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.05054e8 | − | 1.63931e8i | 0.429880 | − | 0.116470i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.62357e7 | − | 1.62357e7i | −0.0113408 | − | 0.0113408i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.22110e8 | + | 5.61518e8i | −0.217535 | + | 0.379217i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.84493e9 | −1.22527 | −0.612635 | − | 0.790366i | \(-0.709890\pi\) | ||||
−0.612635 | + | 0.790366i | \(0.709890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.31405e8 | −0.412402 | −0.206201 | − | 0.978510i | \(-0.566110\pi\) | ||||
−0.206201 | + | 0.978510i | \(0.566110\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.27750e7 | − | 1.90661e7i | −0.0467510 | − | 0.0122482i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.13802e8 | − | 4.13802e8i | −0.257214 | − | 0.257214i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.19606e9 | + | 4.41453e9i | 0.731396 | + | 2.69951i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.92656e8i | 0.356560i | 0.983980 | + | 0.178280i | \(0.0570532\pi\) | ||||
−0.983980 | + | 0.178280i | \(0.942947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.10579e8 | + | 4.10579e8i | −0.243046 | + | 0.243046i | −0.818109 | − | 0.575063i | \(-0.804978\pi\) |
0.575063 | + | 0.818109i | \(0.304978\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.84938e8 | + | 3.84938e8i | −0.220651 | + | 0.220651i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.00227e9i | − | 1.12953i | −0.825252 | − | 0.564764i | \(-0.808967\pi\) | ||
0.825252 | − | 0.564764i | \(-0.191033\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.39121e9 | − | 8.13584e8i | 0.772428 | − | 0.451718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.16030e8 | + | 2.16030e8i | 0.118059 | + | 0.118059i | 0.763668 | − | 0.645609i | \(-0.223396\pi\) |
−0.645609 | + | 0.763668i | \(0.723396\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.88823e9 | − | 1.08317e9i | −0.999950 | − | 0.573613i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.11732e8 | −0.266797 | −0.133398 | − | 0.991062i | \(-0.542589\pi\) | ||||
−0.133398 | + | 0.991062i | \(0.542589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.08183e9 | −2.60857 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.62991e9 | + | 9.34985e8i | 0.823796 | + | 0.472564i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.62621e8 | + | 8.62621e8i | 0.422779 | + | 0.422779i | 0.886159 | − | 0.463380i | \(-0.153364\pi\) |
−0.463380 | + | 0.886159i | \(0.653364\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.80569e9 | + | 1.77576e9i | 0.871562 | + | 0.857116i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.93234e9i | 0.918609i | 0.888279 | + | 0.459304i | \(0.151901\pi\) | ||||
−0.888279 | + | 0.459304i | \(0.848099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.48394e9 | + | 2.48394e9i | −1.16308 | + | 1.16308i | −0.179276 | + | 0.983799i | \(0.557376\pi\) |
−0.983799 | + | 0.179276i | \(0.942624\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.66432e9 | − | 1.66432e9i | 0.756183 | − | 0.756183i | −0.219443 | − | 0.975625i | \(-0.570424\pi\) |
0.975625 | + | 0.219443i | \(0.0704239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.94353e8i | − | 0.400317i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.55029e8 | − | 1.31037e9i | −0.156563 | − | 0.577859i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.01632e9 | + | 3.01632e9i | 1.31058 | + | 1.31058i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.63781e8 | + | 1.38855e9i | −0.153471 | + | 0.585796i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.04923e8 | 0.0436213 | 0.0218106 | − | 0.999762i | \(-0.493057\pi\) | ||||
0.0218106 | + | 0.999762i | \(0.493057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.06295e9 | −1.25496 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.52895e8 | + | 2.66534e8i | −0.0617417 | + | 0.107631i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.88946e9 | + | 2.88946e9i | 1.13362 | + | 1.13362i | 0.989571 | + | 0.144044i | \(0.0460108\pi\) |
0.144044 | + | 0.989571i | \(0.453989\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.08904e9 | + | 5.65998e8i | −0.807915 | + | 0.218894i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.35081e9i | − | 0.896258i | −0.893969 | − | 0.448129i | \(-0.852090\pi\) | ||
0.893969 | − | 0.448129i | \(-0.147910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.14484e9 | + | 2.14484e9i | −0.806178 | + | 0.806178i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.81092e8 | − | 1.81092e8i | 0.0661687 | − | 0.0661687i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.74159e9i | − | 0.627471i | −0.949510 | − | 0.313736i | \(-0.898419\pi\) | ||
0.949510 | − | 0.313736i | \(-0.101581\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.74427e9 | − | 1.01446e9i | 1.33026 | − | 0.360415i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.07332e9 | − | 1.07332e9i | −0.376046 | − | 0.376046i | 0.493628 | − | 0.869673i | \(-0.335671\pi\) |
−0.869673 | + | 0.493628i | \(0.835671\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.07650e9 | − | 5.36309e9i | 1.04840 | − | 1.82763i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.65019e9 | −1.89911 | −0.949556 | − | 0.313598i | \(-0.898466\pi\) | ||||
−0.949556 | + | 0.313598i | \(0.898466\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.36985e9 | 0.454149 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.49391e9 | − | 2.08405e7i | 0.815588 | − | 0.00681549i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.70375e8 | − | 1.70375e8i | −0.0542236 | − | 0.0542236i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.90186e8 | + | 3.65468e9i | 0.310908 | + | 1.14753i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.72735e8i | 0.0535118i | 0.999642 | + | 0.0267559i | \(0.00851768\pi\) | ||||
−0.999642 | + | 0.0267559i | \(0.991482\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.43183e9 | − | 2.43183e9i | 0.743324 | − | 0.743324i | −0.229892 | − | 0.973216i | \(-0.573837\pi\) |
0.973216 | + | 0.229892i | \(0.0738375\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.99402e9 | − | 3.99402e9i | 1.18870 | − | 1.18870i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 2.90644e9i | − | 0.853624i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.61289e7 | + | 1.47279e8i | 0.0249642 | + | 0.0426883i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.16316e9 | + | 7.16316e9i | 2.04908 | + | 2.04908i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.64246e9 | + | 1.51583e9i | 0.736374 | + | 0.422415i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.16168e9 | 1.41981 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.02142e8 | 0.0277340 | 0.0138670 | − | 0.999904i | \(-0.495586\pi\) | ||||
0.0138670 | + | 0.999904i | \(0.495586\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.88974e9 | + | 1.08404e9i | 0.506528 | + | 0.290566i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.32606e9 | − | 1.32606e9i | −0.346425 | − | 0.346425i | 0.512351 | − | 0.858776i | \(-0.328775\pi\) |
−0.858776 | + | 0.512351i | \(0.828775\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.19519e9 | + | 3.75373e9i | 0.566198 | + | 0.968187i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.98709e9i | 0.760707i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.37517e7 | + | 9.37517e7i | −0.0235744 | + | 0.0235744i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.99637e9 | + | 2.99637e9i | −0.734686 | + | 0.734686i | −0.971544 | − | 0.236858i | \(-0.923882\pi\) |
0.236858 | + | 0.971544i | \(0.423882\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.50339e9i | − | 2.05897i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.12113e9 | + | 7.82887e9i | 0.507221 | + | 1.87210i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.93345e9 | + | 1.93345e9i | 0.456619 | + | 0.456619i | 0.897544 | − | 0.440925i | \(-0.145349\pi\) |
−0.440925 | + | 0.897544i | \(0.645349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.35561e9 | − | 3.79472e8i | 0.312316 | − | 0.0874257i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.47404e9 | 1.47327 | 0.736635 | − | 0.676291i | \(-0.236414\pi\) | ||||
0.736635 | + | 0.676291i | \(0.236414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.26336e9 | 0.283988 | 0.141994 | − | 0.989868i | \(-0.454649\pi\) | ||||
0.141994 | + | 0.989868i | \(0.454649\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.73216e9 | + | 4.76283e9i | −0.606688 | + | 1.05761i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.72702e9 | − | 3.72702e9i | −0.807694 | − | 0.807694i | 0.176591 | − | 0.984284i | \(-0.443493\pi\) |
−0.984284 | + | 0.176591i | \(0.943493\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.07732e9 | + | 1.91751e9i | −1.51528 | + | 0.410546i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.78196e9i | − | 0.376949i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.25075e9 | + | 3.25075e9i | −0.679428 | + | 0.679428i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.89458e9 | − | 4.89458e9i | 0.998809 | − | 0.998809i | −0.00119025 | − | 0.999999i | \(-0.500379\pi\) |
0.999999 | + | 0.00119025i | \(0.000378869\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.56241e9i | − | 1.12166i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.62214e9 | − | 1.79418e9i | 1.31960 | − | 0.357528i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.78642e9 | + | 1.78642e9i | 0.351797 | + | 0.351797i | 0.860778 | − | 0.508981i | \(-0.169978\pi\) |
−0.508981 | + | 0.860778i | \(0.669978\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.88146e9 | + | 3.27986e9i | −0.361898 | + | 0.630877i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.07984e9 | 0.965731 | 0.482865 | − | 0.875695i | \(-0.339596\pi\) | ||||
0.482865 | + | 0.875695i | \(0.339596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.30990e9 | −0.246138 | −0.123069 | − | 0.992398i | \(-0.539274\pi\) | ||||
−0.123069 | + | 0.992398i | \(0.539274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.68424e9 | + | 6.42871e9i | −0.312819 | + | 1.19402i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.46174e9 | + | 6.46174e9i | 1.17271 | + | 1.17271i | 0.981562 | + | 0.191144i | \(0.0612196\pi\) |
0.191144 | + | 0.981562i | \(0.438780\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.40914e8 | + | 1.62737e9i | 0.0791031 | + | 0.291961i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.80308e8i | 0.0851874i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.40772e9 | − | 1.40772e9i | 0.246834 | − | 0.246834i | −0.572836 | − | 0.819670i | \(-0.694157\pi\) |
0.819670 | + | 0.572836i | \(0.194157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.28198e8 | + | 2.28198e8i | −0.0391123 | + | 0.0391123i | −0.726392 | − | 0.687280i | \(-0.758804\pi\) |
0.687280 | + | 0.726392i | \(0.258804\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.44766e9i | 0.414795i | 0.978257 | + | 0.207398i | \(0.0664994\pi\) | ||||
−0.978257 | + | 0.207398i | \(0.933501\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.60096e9 | − | 1.62794e9i | 0.268263 | − | 0.272784i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.09743e9 | − | 1.09743e9i | −0.181832 | − | 0.181832i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.92861e9 | + | 3.97454e9i | 1.12256 | + | 0.643948i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.43193e9 | −0.870315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.12819e9 | 0.337216 | 0.168608 | − | 0.985683i | \(-0.446073\pi\) | ||||
0.168608 | + | 0.985683i | \(0.446073\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.38402e8 | + | 1.94122e8i | 0.0530298 | + | 0.0304201i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.27572e9 | − | 7.27572e9i | −1.11529 | − | 1.11529i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.64274e9 | + | 9.60680e8i | −0.249067 | + | 0.145655i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.56635e9i | − | 0.834771i | −0.908730 | − | 0.417385i | \(-0.862947\pi\) | ||
0.908730 | − | 0.417385i | \(-0.137053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.31903e9 | − | 3.31903e9i | 0.492349 | − | 0.492349i | −0.416697 | − | 0.909046i | \(-0.636812\pi\) |
0.909046 | + | 0.416697i | \(0.136812\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.59584e9 | − | 6.59584e9i | 0.957425 | − | 0.957425i | −0.0417046 | − | 0.999130i | \(-0.513279\pi\) |
0.999130 | + | 0.0417046i | \(0.0132788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.46434e8i | 0.0784660i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.21049e8 | − | 3.03041e9i | −0.116637 | − | 0.430495i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.48024e7 | − | 1.48024e7i | −0.00208035 | − | 0.00208035i | 0.706066 | − | 0.708146i | \(-0.250468\pi\) |
−0.708146 | + | 0.706066i | \(0.750468\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.84660e9 | − | 2.57968e9i | −1.35459 | − | 0.354885i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.36101e10 | −1.85252 | −0.926261 | − | 0.376882i | \(-0.876996\pi\) | ||||
−0.926261 | + | 0.376882i | \(0.876996\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.92029e9 | −0.932008 | −0.466004 | − | 0.884783i | \(-0.654307\pi\) | ||||
−0.466004 | + | 0.884783i | \(0.654307\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.04542e9 | − | 1.40252e10i | 1.07214 | − | 1.86900i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.93371e9 | + | 1.93371e9i | 0.252320 | + | 0.252320i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.11095e10 | − | 3.00998e9i | 1.43451 | − | 0.388662i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.39271e10i | 1.77964i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.28430e9 | + | 2.28430e9i | −0.288869 | + | 0.288869i | −0.836633 | − | 0.547764i | \(-0.815479\pi\) |
0.547764 | + | 0.836633i | \(0.315479\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.48446e9 | + | 8.48446e9i | −1.05091 | + | 1.05091i | −0.0522733 | + | 0.998633i | \(0.516647\pi\) |
−0.998633 | + | 0.0522733i | \(0.983353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.96283e8i | 0.0240624i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.61487e9 | + | 1.25034e9i | −0.559944 | + | 0.151709i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.90325e9 | − | 4.90325e9i | −0.588860 | − | 0.588860i | 0.348463 | − | 0.937323i | \(-0.386704\pi\) |
−0.937323 | + | 0.348463i | \(0.886704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.69019e9 | − | 8.17616e9i | 0.551877 | − | 0.962057i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.16427e9 | 1.06741 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.48616e10 | −1.71353 | −0.856765 | − | 0.515707i | \(-0.827529\pi\) | ||||
−0.856765 | + | 0.515707i | \(0.827529\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.36138e9 | + | 1.14263e9i | 0.497803 | + | 0.130418i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.27034e10 | + | 1.27034e10i | 1.42103 | + | 1.42103i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.56320e9 | + | 1.31514e10i | 0.394611 | + | 1.45647i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.00461e9i | − | 0.658372i | −0.944265 | − | 0.329186i | \(-0.893226\pi\) | ||
0.944265 | − | 0.329186i | \(-0.106774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.78248e9 | + | 3.78248e9i | −0.410613 | + | 0.410613i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.42881e9 | + | 3.42881e9i | −0.364901 | + | 0.364901i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.62435e9i | − | 0.381916i | −0.981598 | − | 0.190958i | \(-0.938840\pi\) | ||
0.981598 | − | 0.190958i | \(-0.0611595\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.50449e8 | − | 4.97345e8i | 0.0887370 | − | 0.0518936i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.60087e9 | − | 3.60087e9i | −0.372044 | − | 0.372044i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.95348e9 | − | 5.13610e9i | −0.907141 | − | 0.520375i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.29081e10 | −1.29512 | −0.647562 | − | 0.762013i | \(-0.724211\pi\) | ||||
−0.647562 | + | 0.762013i | \(0.724211\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.68751e8 | −0.0763858 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.72423e10 | − | 9.89092e9i | −1.69672 | − | 0.973313i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.33372e10 | − | 1.33372e10i | −1.28734 | − | 1.28734i | −0.936397 | − | 0.350942i | \(-0.885861\pi\) |
−0.350942 | − | 0.936397i | \(-0.614139\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04589e10 | + | 1.74813e8i | −0.999860 | + | 0.0167119i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.50802e10i | − | 1.42789i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.38410e9 | + | 1.38410e9i | −0.129809 | + | 0.129809i | −0.769026 | − | 0.639217i | \(-0.779258\pi\) |
0.639217 | + | 0.769026i | \(0.279258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.50503e10 | + | 1.50503e10i | −1.38487 | + | 1.38487i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.46663e10i | 1.33680i | 0.743804 | + | 0.668398i | \(0.233020\pi\) | ||||
−0.743804 | + | 0.668398i | \(0.766980\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.16394e9 | − | 1.53687e10i | −0.375959 | − | 1.38763i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.03403e10 | − | 1.03403e10i | −0.924854 | − | 0.924854i | 0.0725133 | − | 0.997367i | \(-0.476898\pi\) |
−0.997367 | + | 0.0725133i | \(0.976898\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.35578e9 | + | 1.28089e10i | −0.294558 | + | 1.12432i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.97603e9 | −0.519668 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.75881e10 | 1.51524 | 0.757618 | − | 0.652698i | \(-0.226363\pi\) | ||||
0.757618 | + | 0.652698i | \(0.226363\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.06668e9 | + | 7.08923e9i | −0.347103 | + | 0.605085i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.99031e9 | + | 5.99031e9i | 0.501896 | + | 0.501896i | 0.912027 | − | 0.410131i | \(-0.134517\pi\) |
−0.410131 | + | 0.912027i | \(0.634517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.05824e9 | − | 1.91234e9i | 0.585936 | − | 0.158752i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.12357e10i | 0.924173i | 0.886835 | + | 0.462087i | \(0.152899\pi\) | ||||
−0.886835 | + | 0.462087i | \(0.847101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.70685e9 | − | 1.70685e9i | 0.139110 | − | 0.139110i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.70234e8 | − | 7.70234e8i | 0.0616366 | − | 0.0616366i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.11702e9i | − | 0.0885762i | −0.999019 | − | 0.0442881i | \(-0.985898\pi\) | ||
0.999019 | − | 0.0442881i | \(-0.0141020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.20704e10 | + | 3.27033e9i | −0.948490 | + | 0.256981i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.05235e8 | − | 3.05235e8i | −0.0237687 | − | 0.0237687i | 0.695123 | − | 0.718891i | \(-0.255350\pi\) |
−0.718891 | + | 0.695123i | \(0.755350\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.50238e9 | + | 2.61902e9i | −0.114896 | + | 0.200293i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.76918e10 | 1.34088 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.09492e9 | −0.457814 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.04691e8 | − | 1.25280e10i | −0.00779369 | − | 0.932646i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.84014e9 | − | 5.84014e9i | −0.427083 | − | 0.427083i | 0.460551 | − | 0.887633i | \(-0.347652\pi\) |
−0.887633 | + | 0.460551i | \(0.847652\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.38596e9 | − | 2.35699e10i | −0.462867 | − | 1.70840i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.17647e9i | − | 0.443734i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.96311e10 | − | 1.96311e10i | 1.39794 | − | 1.39794i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.64740e9 | + | 2.64740e9i | −0.185232 | + | 0.185232i | −0.793631 | − | 0.608399i | \(-0.791812\pi\) |
0.608399 | + | 0.793631i | \(0.291812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.51793e8i | 0.0590773i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.82179e9 | + | 9.95514e9i | 0.400260 | + | 0.684437i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.30520e10 | − | 2.30520e10i | −1.57110 | − | 1.57110i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.61166e9 | − | 2.07180e9i | −0.241908 | − | 0.138768i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.14300e10 | 0.758970 | 0.379485 | − | 0.925198i | \(-0.376101\pi\) | ||||
0.379485 | + | 0.925198i | \(0.376101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.36707e10 | 0.899950 | 0.449975 | − | 0.893041i | \(-0.351433\pi\) | ||||
0.449975 | + | 0.893041i | \(0.351433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.93182e9 | − | 2.82910e9i | −0.321877 | − | 0.184642i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.05010e10 | − | 1.05010e10i | −0.673678 | − | 0.673678i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.53704e9 | − | 7.75825e9i | −0.288588 | − | 0.493480i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.04807e10i | 0.660979i | 0.943810 | + | 0.330489i | \(0.107214\pi\) | ||||
−0.943810 | + | 0.330489i | \(0.892786\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.74134e10 | − | 1.74134e10i | 1.08889 | − | 1.08889i | 0.0932472 | − | 0.995643i | \(-0.470275\pi\) |
0.995643 | − | 0.0932472i | \(-0.0297247\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.41202e10 | − | 1.41202e10i | 0.868102 | − | 0.868102i | −0.124160 | − | 0.992262i | \(-0.539624\pi\) |
0.992262 | + | 0.124160i | \(0.0396237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.04559e10i | 0.637413i | 0.947853 | + | 0.318706i | \(0.103248\pi\) | ||||
−0.947853 | + | 0.318706i | \(0.896752\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.11018e9 | + | 2.99338e10i | 0.490261 | + | 1.80950i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.29030e10 | − | 1.29030e10i | −0.773451 | − | 0.773451i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.94951e8 | + | 2.33291e10i | 0.0114917 | + | 1.37518i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.09527e10 | 0.640256 | 0.320128 | − | 0.947374i | \(-0.396274\pi\) | ||||
0.320128 | + | 0.947374i | \(0.396274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.24441e9 | −0.130112 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.57748e9 | + | 9.72293e9i | −0.320658 | + | 0.558986i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.15492e9 | + | 6.15492e9i | 0.348041 | + | 0.348041i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.12853e10 | + | 3.05761e9i | −0.632903 | + | 0.171477i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89723e9i | 0.272394i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.67601e9 | + | 7.67601e9i | −0.423462 | + | 0.423462i | −0.886394 | − | 0.462932i | \(-0.846797\pi\) |
0.462932 | + | 0.886394i | \(0.346797\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.66912e10 | + | 1.66912e10i | −0.905845 | + | 0.905845i | −0.995934 | − | 0.0900883i | \(-0.971285\pi\) |
0.0900883 | + | 0.995934i | \(0.471285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.18465e9i | 0.225259i | 0.993637 | + | 0.112630i | \(0.0359274\pi\) | ||||
−0.993637 | + | 0.112630i | \(0.964073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.63851e9 | − | 2.61143e9i | 0.514635 | − | 0.139433i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.76521e9 | + | 4.76521e9i | 0.252374 | + | 0.252374i | 0.821943 | − | 0.569569i | \(-0.192890\pi\) |
−0.569569 | + | 0.821943i | \(0.692890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.71952e9 | − | 8.22729e9i | 0.245941 | − | 0.428736i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.15534e9 | 0.163109 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.24288e10 | 2.17569 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.69639e8 | − | 1.41091e9i | 0.0188031 | − | 0.0717709i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.04742e10 | − | 1.04742e10i | −0.524352 | − | 0.524352i | 0.394531 | − | 0.918883i | \(-0.370907\pi\) |
−0.918883 | + | 0.394531i | \(0.870907\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.88457e9 | − | 2.91012e10i | −0.391577 | − | 1.44527i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.12337e10i | − | 1.04619i | −0.852274 | − | 0.523095i | \(-0.824777\pi\) | ||
0.852274 | − | 0.523095i | \(-0.175223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.40155e10 | + | 1.40155e10i | −0.685087 | + | 0.685087i | −0.961142 | − | 0.276055i | \(-0.910973\pi\) |
0.276055 | + | 0.961142i | \(0.410973\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.82610e10 | + | 1.82610e10i | −0.878602 | + | 0.878602i | −0.993390 | − | 0.114788i | \(-0.963381\pi\) |
0.114788 | + | 0.993390i | \(0.463381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.25683e9i | − | 0.0599957i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.91983e10 | − | 1.64266e10i | −1.38288 | − | 0.777995i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.93139e8 | + | 5.93139e8i | 0.0278726 | + | 0.0278726i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.26446e10 | − | 7.25347e9i | −0.584967 | − | 0.335562i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.79425e10 | −1.28264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.62522e10 | 0.740245 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.27095e9 | − | 4.17093e9i | −0.328613 | − | 0.188506i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.18663e10 | + | 2.18663e10i | 0.973083 | + | 0.973083i | 0.999647 | − | 0.0265641i | \(-0.00845661\pi\) |
−0.0265641 | + | 0.999647i | \(0.508457\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.11037e10 | − | 1.81895e10i | 1.37353 | − | 0.803245i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.80144e9i | 0.341869i | 0.985282 | + | 0.170935i | \(0.0546787\pi\) | ||||
−0.985282 | + | 0.170935i | \(0.945321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.99872e10 | + | 2.99872e10i | −1.30403 | + | 1.30403i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.18174e9 | − | 4.18174e9i | 0.179087 | − | 0.179087i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.03762e9i | 0.171602i | 0.996312 | + | 0.0858008i | \(0.0273448\pi\) | ||||
−0.996312 | + | 0.0858008i | \(0.972655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.05022e9 | − | 2.60216e10i | −0.297368 | − | 1.09755i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.59117e9 | + | 8.59117e9i | 0.359622 | + | 0.359622i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.52587e9 | + | 1.44771e9i | 0.227836 | + | 0.0596900i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.97159e9 | 0.244363 | 0.122181 | − | 0.992508i | \(-0.461011\pi\) | ||||
0.122181 | + | 0.992508i | \(0.461011\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.79698e10 | −0.729826 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.95990e10 | − | 3.41659e10i | 0.790038 | − | 1.37723i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.91067e10 | − | 1.91067e10i | −0.758746 | − | 0.758746i | 0.217348 | − | 0.976094i | \(-0.430259\pi\) |
−0.976094 | + | 0.217348i | \(0.930259\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.56674e10 | − | 4.24489e9i | 0.617545 | − | 0.167316i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.02986e10i | 1.96785i | 0.178577 | + | 0.983926i | \(0.442851\pi\) | ||||
−0.178577 | + | 0.983926i | \(0.557149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.14529e10 | − | 1.14529e10i | 0.444760 | − | 0.444760i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.11199e10 | − | 1.11199e10i | 0.425478 | − | 0.425478i | −0.461607 | − | 0.887085i | \(-0.652727\pi\) |
0.887085 | + | 0.461607i | \(0.152727\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.49866e10i | 2.46827i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.58716e10 | + | 9.71893e9i | −1.35244 | + | 0.366426i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.33786e10 | + | 2.33786e10i | 0.874970 | + | 0.874970i | 0.993009 | − | 0.118039i | \(-0.0376609\pi\) |
−0.118039 | + | 0.993009i | \(0.537661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.99659e10 | − | 3.48055e10i | 0.736371 | − | 1.28368i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.94522e9 | −0.144446 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.45205e10 | 0.891246 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.29563e10 | + | 1.12540e10i | 1.55001 | + | 0.406083i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.62361e9 | + | 5.62361e9i | 0.199997 | + | 0.199997i | 0.799999 | − | 0.600002i | \(-0.204834\pi\) |
−0.600002 | + | 0.799999i | \(0.704834\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.38447e9 | − | 2.72553e10i | −0.260727 | − | 0.962317i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.42386e10i | − | 0.849650i | −0.905275 | − | 0.424825i | \(-0.860336\pi\) | ||
0.905275 | − | 0.424825i | \(-0.139664\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.88082e9 | − | 2.88082e9i | 0.100259 | − | 0.100259i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.12025e10 | − | 2.12025e10i | 0.727371 | − | 0.727371i | −0.242724 | − | 0.970095i | \(-0.578041\pi\) |
0.970095 | + | 0.242724i | \(0.0780411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.69356e10i | 1.25807i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.54834e10 | + | 9.05470e9i | −0.523629 | + | 0.306219i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.22993e10 | + | 1.22993e10i | 0.412993 | + | 0.412993i | 0.882780 | − | 0.469787i | \(-0.155669\pi\) |
−0.469787 | + | 0.882780i | \(0.655669\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.10694e8 | + | 2.35592e8i | 0.0135959 | + | 0.00779920i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.35958e10 | −0.446906 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.44732e10 | −0.472397 | −0.236199 | − | 0.971705i | \(-0.575902\pi\) | ||||
−0.236199 | + | 0.971705i | \(0.575902\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.80879e9 | − | 5.62674e9i | −0.317902 | − | 0.182362i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.78256e10 | + | 2.78256e10i | 0.889224 | + | 0.889224i | 0.994448 | − | 0.105225i | \(-0.0335561\pi\) |
−0.105225 | + | 0.994448i | \(0.533556\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.57314e10 | − | 1.59965e10i | 0.499215 | − | 0.507629i |
(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 | 300.8.i.c.257.7 | yes | 16 | |
3.2 | odd | 2 | inner | 300.8.i.c.257.3 | yes | 16 | |
5.2 | odd | 4 | inner | 300.8.i.c.293.6 | yes | 16 | |
5.3 | odd | 4 | inner | 300.8.i.c.293.3 | yes | 16 | |
5.4 | even | 2 | inner | 300.8.i.c.257.2 | ✓ | 16 | |
15.2 | even | 4 | inner | 300.8.i.c.293.2 | yes | 16 | |
15.8 | even | 4 | inner | 300.8.i.c.293.7 | yes | 16 | |
15.14 | odd | 2 | inner | 300.8.i.c.257.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.8.i.c.257.2 | ✓ | 16 | 5.4 | even | 2 | inner | |
300.8.i.c.257.3 | yes | 16 | 3.2 | odd | 2 | inner | |
300.8.i.c.257.6 | yes | 16 | 15.14 | odd | 2 | inner | |
300.8.i.c.257.7 | yes | 16 | 1.1 | even | 1 | trivial | |
300.8.i.c.293.2 | yes | 16 | 15.2 | even | 4 | inner | |
300.8.i.c.293.3 | yes | 16 | 5.3 | odd | 4 | inner | |
300.8.i.c.293.6 | yes | 16 | 5.2 | odd | 4 | inner | |
300.8.i.c.293.7 | yes | 16 | 15.8 | even | 4 | inner |