Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(197,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.197");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.c (of order \(2\), degree \(1\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4002260 x^{14} + 6534459751956 x^{12} + \cdots + 19\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{37}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.7 | ||
Root | \(-348.567i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.197 |
Dual form | 252.9.c.a.197.10 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 348.567i | − 0.557707i | −0.960334 | − | 0.278853i | \(-0.910046\pi\) | ||||
0.960334 | − | 0.278853i | \(-0.0899544\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 907.493 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11889.3i | 0.812056i | 0.913861 | + | 0.406028i | \(0.133087\pi\) | ||||
−0.913861 | + | 0.406028i | \(0.866913\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4095.93 | −0.143410 | −0.0717049 | − | 0.997426i | \(-0.522844\pi\) | ||||
−0.0717049 | + | 0.997426i | \(0.522844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 67449.6i | − 0.807576i | −0.914852 | − | 0.403788i | \(-0.867693\pi\) | ||||
0.914852 | − | 0.403788i | \(-0.132307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −116874. | −0.896816 | −0.448408 | − | 0.893829i | \(-0.648009\pi\) | ||||
−0.448408 | + | 0.893829i | \(0.648009\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 68357.8i | 0.244274i | 0.992513 | + | 0.122137i | \(0.0389747\pi\) | ||||
−0.992513 | + | 0.122137i | \(0.961025\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 269126. | 0.688963 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 774693.i | − 1.09531i | −0.836704 | − | 0.547656i | \(-0.815520\pi\) | ||||
0.836704 | − | 0.547656i | \(-0.184480\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 807878. | 0.874781 | 0.437390 | − | 0.899272i | \(-0.355903\pi\) | ||||
0.437390 | + | 0.899272i | \(0.355903\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 316322.i | − 0.210793i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.02479e6 | 0.546799 | 0.273399 | − | 0.961901i | \(-0.411852\pi\) | ||||
0.273399 | + | 0.961901i | \(0.411852\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 850867.i | − 0.301111i | −0.988602 | − | 0.150555i | \(-0.951894\pi\) | ||||
0.988602 | − | 0.150555i | \(-0.0481062\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.69010e6 | −1.07936 | −0.539678 | − | 0.841872i | \(-0.681454\pi\) | ||||
−0.539678 | + | 0.841872i | \(0.681454\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.47190e6i | 1.12137i | 0.828031 | + | 0.560683i | \(0.189461\pi\) | ||||
−0.828031 | + | 0.560683i | \(0.810539\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 823543. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 541263.i | 0.0685969i | 0.999412 | + | 0.0342984i | \(0.0109197\pi\) | ||||
−0.999412 | + | 0.0342984i | \(0.989080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.14422e6 | 0.452889 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 8.95168e6i | − 0.738748i | −0.929281 | − | 0.369374i | \(-0.879572\pi\) | ||||
0.929281 | − | 0.369374i | \(-0.120428\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 650282. | 0.0469659 | 0.0234829 | − | 0.999724i | \(-0.492524\pi\) | ||||
0.0234829 | + | 0.999724i | \(0.492524\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.42770e6i | 0.0799806i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.39158e7 | −1.68307 | −0.841536 | − | 0.540201i | \(-0.818348\pi\) | ||||
−0.841536 | + | 0.540201i | \(0.818348\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1.63485e7i | − 0.643346i | −0.946851 | − | 0.321673i | \(-0.895755\pi\) | ||||
0.946851 | − | 0.321673i | \(-0.104245\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.67469e7 | 0.589716 | 0.294858 | − | 0.955541i | \(-0.404728\pi\) | ||||
0.294858 | + | 0.955541i | \(0.404728\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.07895e7i | 0.306928i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.38232e7 | −0.354895 | −0.177448 | − | 0.984130i | \(-0.556784\pi\) | ||||
−0.177448 | + | 0.984130i | \(0.556784\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.98832e6i | − 0.0418961i | −0.999781 | − | 0.0209480i | \(-0.993332\pi\) | ||||
0.999781 | − | 0.0209480i | \(-0.00666845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.35107e7 | −0.450391 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 6.05729e7i | − 0.965424i | −0.875779 | − | 0.482712i | \(-0.839652\pi\) | ||||
0.875779 | − | 0.482712i | \(-0.160348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.71702e6 | −0.0542038 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.07384e7i | 0.500160i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.52027e7 | −0.397639 | −0.198819 | − | 0.980036i | \(-0.563711\pi\) | ||||
−0.198819 | + | 0.980036i | \(0.563711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.19699e8i | − 1.15029i | −0.818053 | − | 0.575143i | \(-0.804946\pi\) | ||||
0.818053 | − | 0.575143i | \(-0.195054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.19816e7 | 0.106455 | 0.0532273 | − | 0.998582i | \(-0.483049\pi\) | ||||
0.0532273 | + | 0.998582i | \(0.483049\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.98152e8i | − 1.51169i | −0.654749 | − | 0.755846i | \(-0.727226\pi\) | ||||
0.654749 | − | 0.755846i | \(-0.272774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.18524e7 | −0.154808 | −0.0774038 | − | 0.997000i | \(-0.524663\pi\) | ||||
−0.0774038 | + | 0.997000i | \(0.524663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.09321e8i | 0.670485i | 0.942132 | + | 0.335243i | \(0.108818\pi\) | ||||
−0.942132 | + | 0.335243i | \(0.891182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.38272e7 | 0.136233 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 6.12100e7i | − 0.305235i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.30030e7 | 0.340564 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.29967e8i | − 0.941946i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.13988e8 | −1.20698 | −0.603488 | − | 0.797372i | \(-0.706223\pi\) | ||||
−0.603488 | + | 0.797372i | \(0.706223\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.95386e8i | − 0.663451i | −0.943376 | − | 0.331726i | \(-0.892369\pi\) | ||||
0.943376 | − | 0.331726i | \(-0.107631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.06062e8 | −0.338964 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 4.32944e8i | − 1.22899i | −0.788919 | − | 0.614497i | \(-0.789359\pi\) | ||||
0.788919 | − | 0.614497i | \(-0.210641\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.25420e8 | −1.40750 | −0.703748 | − | 0.710450i | \(-0.748492\pi\) | ||||
−0.703748 | + | 0.710450i | \(0.748492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 4.86978e7i | − 0.116457i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.70032e8 | −0.610863 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.49656e8i | − 0.506521i | −0.967398 | − | 0.253261i | \(-0.918497\pi\) | ||||
0.967398 | − | 0.253261i | \(-0.0815030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.90108e8 | −0.365672 | −0.182836 | − | 0.983143i | \(-0.558528\pi\) | ||||
−0.182836 | + | 0.983143i | \(0.558528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.81599e8i | − 0.487871i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.70501e8 | −0.774393 | −0.387197 | − | 0.921997i | \(-0.626557\pi\) | ||||
−0.387197 | + | 0.921997i | \(0.626557\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.20342e7i | 0.0923267i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.63201e8 | −0.656174 | −0.328087 | − | 0.944648i | \(-0.606404\pi\) | ||||
−0.328087 | + | 0.944648i | \(0.606404\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 4.36026e8i | − 0.560592i | −0.959914 | − | 0.280296i | \(-0.909567\pi\) | ||||
0.959914 | − | 0.280296i | \(-0.0904325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.98954e8 | −0.979434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.28581e9i | − 1.43546i | −0.696322 | − | 0.717729i | \(-0.745181\pi\) | ||||
0.696322 | − | 0.717729i | \(-0.254819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.44230e8 | 0.260404 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 5.77990e8i | − 0.562999i | −0.959561 | − | 0.281500i | \(-0.909168\pi\) | ||||
0.959561 | − | 0.281500i | \(-0.0908318\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.36134e9 | 1.26839 | 0.634195 | − | 0.773173i | \(-0.281332\pi\) | ||||
0.634195 | + | 0.773173i | \(0.281332\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 3.57207e8i | − 0.304953i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.01930e8 | 0.655798 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 3.97105e8i | − 0.298381i | −0.988808 | − | 0.149191i | \(-0.952333\pi\) | ||||
0.988808 | − | 0.149191i | \(-0.0476668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.44780e9 | −1.04347 | −0.521734 | − | 0.853108i | \(-0.674715\pi\) | ||||
−0.521734 | + | 0.853108i | \(0.674715\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.27633e9i | − 0.847420i | −0.905798 | − | 0.423710i | \(-0.860728\pi\) | ||||
0.905798 | − | 0.423710i | \(-0.139272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.33138e9 | −1.48663 | −0.743313 | − | 0.668944i | \(-0.766746\pi\) | ||||
−0.743313 | + | 0.668944i | \(0.766746\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 7.03029e8i | − 0.413989i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.96584e8 | −0.167931 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 1.38955e9i | − 0.728265i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.69510e8 | −0.287324 | −0.143662 | − | 0.989627i | \(-0.545888\pi\) | ||||
−0.143662 | + | 0.989627i | \(0.545888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.28625e9i | 0.601964i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.33144e8 | 0.330636 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.76269e8i | 0.115814i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.10060e8 | −0.0445049 | −0.0222525 | − | 0.999752i | \(-0.507084\pi\) | ||||
−0.0222525 | + | 0.999752i | \(0.507084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.62031e9i | − 0.610232i | −0.952315 | − | 0.305116i | \(-0.901305\pi\) | ||||
0.952315 | − | 0.305116i | \(-0.0986953\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.86805e9 | −0.679278 | −0.339639 | − | 0.940556i | \(-0.610305\pi\) | ||||
−0.339639 | + | 0.940556i | \(0.610305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1.23197e9i | − 0.417999i | −0.977916 | − | 0.209000i | \(-0.932979\pi\) | ||||
0.977916 | − | 0.209000i | \(-0.0670207\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.90732e9 | 0.625393 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.64262e9i | 0.503437i | 0.967800 | + | 0.251719i | \(0.0809958\pi\) | ||||
−0.967800 | + | 0.251719i | \(0.919004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.10426e9 | −0.327342 | −0.163671 | − | 0.986515i | \(-0.552334\pi\) | ||||
−0.163671 | + | 0.986515i | \(0.552334\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.87060e8i | − 0.0796724i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.78707e8 | 0.128612 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.57251e9i | − 0.396187i | −0.980183 | − | 0.198093i | \(-0.936525\pi\) | ||||
0.980183 | − | 0.198093i | \(-0.0634749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.12727e8 | −0.198364 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1.88202e9i | − 0.431412i | −0.976458 | − | 0.215706i | \(-0.930795\pi\) | ||||
0.976458 | − | 0.215706i | \(-0.0692053\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.29989e8 | 0.206671 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.28482e9i | 0.268547i | 0.990944 | + | 0.134274i | \(0.0428701\pi\) | ||||
−0.990944 | + | 0.134274i | \(0.957130\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.88666e8 | 0.0382570 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.82675e9i | 1.87673i | 0.345652 | + | 0.938363i | \(0.387658\pi\) | ||||
−0.345652 | + | 0.938363i | \(0.612342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.37009e9 | 0.439428 | 0.219714 | − | 0.975564i | \(-0.429488\pi\) | ||||
0.219714 | + | 0.975564i | \(0.429488\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.19973e9i | 0.559477i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.04785e9 | −0.517695 | −0.258847 | − | 0.965918i | \(-0.583343\pi\) | ||||
−0.258847 | + | 0.965918i | \(0.583343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.73650e9i | 1.24085i | 0.784266 | + | 0.620425i | \(0.213040\pi\) | ||||
−0.784266 | + | 0.620425i | \(0.786960\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.94321e9 | 0.926564 | 0.463282 | − | 0.886211i | \(-0.346672\pi\) | ||||
0.463282 | + | 0.886211i | \(0.346672\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 7.72155e8i | − 0.113809i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.42631e9 | 0.347820 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.90739e9i | 0.530172i | 0.964225 | + | 0.265086i | \(0.0854003\pi\) | ||||
−0.964225 | + | 0.265086i | \(0.914600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.12026e9 | −0.412005 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 2.79988e8i | − 0.0350312i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.34874e9 | −0.407958 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 2.26667e8i | − 0.0261932i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.72279e9 | 0.756826 | 0.378413 | − | 0.925637i | \(-0.376470\pi\) | ||||
0.378413 | + | 0.925637i | \(0.376470\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 7.74568e8i | − 0.0827977i | −0.999143 | − | 0.0413988i | \(-0.986819\pi\) | ||||
0.999143 | − | 0.0413988i | \(-0.0131814\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.68797e10 | 1.75868 | 0.879339 | − | 0.476197i | \(-0.157985\pi\) | ||||
0.879339 | + | 0.476197i | \(0.157985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6.08895e9i | − 0.602983i | −0.953469 | − | 0.301492i | \(-0.902515\pi\) | ||||
0.953469 | − | 0.301492i | \(-0.0974845\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.21058e9 | 0.889455 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.88310e9i | 0.724247i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.10232e9 | −0.0988041 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.96571e9i | 0.423836i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.68142e9 | 0.556618 | 0.278309 | − | 0.960492i | \(-0.410226\pi\) | ||||
0.278309 | + | 0.960492i | \(0.410226\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.18219e10i | 0.938661i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.18497e9 | 0.634596 | 0.317298 | − | 0.948326i | \(-0.397224\pi\) | ||||
0.317298 | + | 0.948326i | \(0.397224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.60512e9i | 0.710371i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.47359e8 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.41926e10i | 0.978916i | 0.872027 | + | 0.489458i | \(0.162805\pi\) | ||||
−0.872027 | + | 0.489458i | \(0.837195\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.87708e9 | −0.328744 | −0.164372 | − | 0.986398i | \(-0.552560\pi\) | ||||
−0.164372 | + | 0.986398i | \(0.552560\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.09772e10i | − 0.706957i | −0.935443 | − | 0.353479i | \(-0.884999\pi\) | ||||
0.935443 | − | 0.353479i | \(-0.115001\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.69854e9 | −0.358798 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.83944e10i | 1.10741i | 0.832713 | + | 0.553704i | \(0.186786\pi\) | ||||
−0.832713 | + | 0.553704i | \(0.813214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.32406e9 | −0.195722 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.83741e9i | − 0.328889i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.73627e10 | 0.957093 | 0.478547 | − | 0.878062i | \(-0.341164\pi\) | ||||
0.478547 | + | 0.878062i | \(0.341164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.91192e8i | 0.0259272i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.25097e9 | 0.426255 | 0.213128 | − | 0.977024i | \(-0.431635\pi\) | ||||
0.213128 | + | 0.977024i | \(0.431635\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.17309e9i | 0.157078i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.09004e10 | −0.528308 | −0.264154 | − | 0.964481i | \(-0.585093\pi\) | ||||
−0.264154 | + | 0.964481i | \(0.585093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.93716e10i | 1.36500i | 0.730886 | + | 0.682500i | \(0.239107\pi\) | ||||
−0.730886 | + | 0.682500i | \(0.760893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.76085e9 | 0.171176 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.08142e9i | 0.352931i | 0.984307 | + | 0.176465i | \(0.0564663\pi\) | ||||
−0.984307 | + | 0.176465i | \(0.943534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.61070e9 | 0.197270 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.81831e9i | 0.197928i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.23249e9 | −0.170386 | −0.0851930 | − | 0.996364i | \(-0.527151\pi\) | ||||
−0.0851930 | + | 0.996364i | \(0.527151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.74199e9i | 0.144719i | 0.997379 | + | 0.0723595i | \(0.0230529\pi\) | ||||
−0.997379 | + | 0.0723595i | \(0.976947\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.30901e9 | −0.125452 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.21840e10i | 0.444032i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.46732e9 | −0.338325 | −0.169162 | − | 0.985588i | \(-0.554106\pi\) | ||||
−0.169162 | + | 0.985588i | \(0.554106\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8.12358e9i | − 0.279221i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.93061e8 | −0.0233657 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.06975e10i | 0.671525i | 0.941947 | + | 0.335762i | \(0.108994\pi\) | ||||
−0.941947 | + | 0.335762i | \(0.891006\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.83855e10 | 0.903582 | 0.451791 | − | 0.892124i | \(-0.350785\pi\) | ||||
0.451791 | + | 0.892124i | \(0.350785\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 1.81525e10i | − 0.556390i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.90126e8 | 0.0177514 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 3.33726e10i | − 0.967123i | −0.875310 | − | 0.483561i | \(-0.839343\pi\) | ||||
0.875310 | − | 0.483561i | \(-0.160657\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.35508e10 | 0.385490 | 0.192745 | − | 0.981249i | \(-0.438261\pi\) | ||||
0.192745 | + | 0.981249i | \(0.438261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.98924e9i | − 0.219068i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.08521e10 | −0.292183 | −0.146091 | − | 0.989271i | \(-0.546669\pi\) | ||||
−0.146091 | + | 0.989271i | \(0.546669\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.77764e10i | − 0.721209i | −0.932719 | − | 0.360605i | \(-0.882570\pi\) | ||||
0.932719 | − | 0.360605i | \(-0.117430\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.11137e10 | −0.538424 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 4.44594e10i | − 1.09390i | −0.837165 | − | 0.546950i | \(-0.815789\pi\) | ||||
0.837165 | − | 0.546950i | \(-0.184211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.01162e10 | 0.244519 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.29563e9i | 0.0302298i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.26792e10 | −1.89553 | −0.947766 | − | 0.318966i | \(-0.896665\pi\) | ||||
−0.947766 | + | 0.318966i | \(0.896665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 5.06508e10i | − 1.12146i | −0.828000 | − | 0.560728i | \(-0.810521\pi\) | ||||
0.828000 | − | 0.560728i | \(-0.189479\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.76023e10 | 1.68869 | 0.844346 | − | 0.535798i | \(-0.179989\pi\) | ||||
0.844346 | + | 0.535798i | \(0.179989\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.58099e10i | 0.542648i | 0.962488 | + | 0.271324i | \(0.0874615\pi\) | ||||
−0.962488 | + | 0.271324i | \(0.912539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.07783e10 | −0.636142 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4.38728e10i | − 0.876497i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.14538e10 | −0.617873 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.61244e10i | 0.686213i | 0.939296 | + | 0.343107i | \(0.111479\pi\) | ||||
−0.939296 | + | 0.343107i | \(0.888521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.19746e9 | −0.0784163 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.22705e10i | 0.221766i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.41764e9 | 0.167427 | 0.0837137 | − | 0.996490i | \(-0.473322\pi\) | ||||
0.0837137 | + | 0.996490i | \(0.473322\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.29411e10i | − 0.394720i | −0.980331 | − | 0.197360i | \(-0.936763\pi\) | ||||
0.980331 | − | 0.197360i | \(-0.0632368\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.22528e10 | −0.884548 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1.48361e10i | − 0.243162i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.95129e10 | 0.314717 | 0.157359 | − | 0.987542i | \(-0.449702\pi\) | ||||
0.157359 | + | 0.987542i | \(0.449702\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.96172e10i | − 0.306454i | −0.988191 | − | 0.153227i | \(-0.951033\pi\) | ||||
0.988191 | − | 0.153227i | \(-0.0489666\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.17232e10 | −0.641522 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 5.09459e10i | − 0.758993i | −0.925193 | − | 0.379496i | \(-0.876097\pi\) | ||||
0.925193 | − | 0.379496i | \(-0.123903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.51977e10 | 0.222892 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.17638e9i | − 0.0593705i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.50572e10 | −0.910612 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 1.02686e11i | − 1.39368i | −0.717229 | − | 0.696838i | \(-0.754590\pi\) | ||||
0.717229 | − | 0.696838i | \(-0.245410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.84556e10 | −0.513987 | −0.256994 | − | 0.966413i | \(-0.582732\pi\) | ||||
−0.256994 | + | 0.966413i | \(0.582732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 5.44911e10i | − 0.706452i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.36382e10 | 0.940330 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.48509e9i | 0.0431822i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.90692e10 | −0.843081 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.79136e9i | 0.116008i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.67196e10 | −0.778869 | −0.389434 | − | 0.921054i | \(-0.627329\pi\) | ||||
−0.389434 | + | 0.921054i | \(0.627329\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.61701e9i | 0.0863373i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.55267e10 | −0.173432 | −0.0867158 | − | 0.996233i | \(-0.527637\pi\) | ||||
−0.0867158 | + | 0.996233i | \(0.527637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.05414e10i | 0.982293i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.25445e10 | −0.134138 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.18540e11i | − 1.23152i | −0.787933 | − | 0.615762i | \(-0.788848\pi\) | ||||
0.787933 | − | 0.615762i | \(-0.211152\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.51144e10 | 0.154790 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7.71879e10i | − 0.768273i | −0.923276 | − | 0.384136i | \(-0.874499\pi\) | ||||
0.923276 | − | 0.384136i | \(-0.125501\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.81056e10 | 0.373934 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 1.17585e11i | − 1.12177i | −0.827895 | − | 0.560883i | \(-0.810462\pi\) | ||||
0.827895 | − | 0.560883i | \(-0.189538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.04156e11 | −0.979807 | −0.489904 | − | 0.871777i | \(-0.662968\pi\) | ||||
−0.489904 | + | 0.871777i | \(0.662968\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.83969e10i | 0.168295i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.22534e10 | −0.290986 | −0.145493 | − | 0.989359i | \(-0.546477\pi\) | ||||
−0.145493 | + | 0.989359i | \(0.546477\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.80438e9i | − 0.0158352i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.43524e9 | −0.0557045 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.16532e11i | 0.981509i | 0.871298 | + | 0.490754i | \(0.163279\pi\) | ||||
−0.871298 | + | 0.490754i | \(0.836721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.44199e10 | −0.784517 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.84175e10i | 0.472415i | 0.971703 | + | 0.236208i | \(0.0759046\pi\) | ||||
−0.971703 | + | 0.236208i | \(0.924095\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.13358e10 | −0.170232 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 4.11787e10i | − 0.319864i | −0.987128 | − | 0.159932i | \(-0.948873\pi\) | ||||
0.987128 | − | 0.159932i | \(-0.0511275\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.25375e10 | −0.555987 | −0.277994 | − | 0.960583i | \(-0.589669\pi\) | ||||
−0.277994 | + | 0.960583i | \(0.589669\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2.54464e10i | − 0.189935i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.61757e10 | 0.634790 | 0.317395 | − | 0.948293i | \(-0.397192\pi\) | ||||
0.317395 | + | 0.948293i | \(0.397192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.24125e10i | − 0.160815i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.89534e11 | −1.34229 | −0.671143 | − | 0.741328i | \(-0.734196\pi\) | ||||
−0.671143 | + | 0.741328i | \(0.734196\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1.36770e11i | − 0.943739i | −0.881669 | − | 0.471869i | \(-0.843579\pi\) | ||||
0.881669 | − | 0.471869i | \(-0.156421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.05400e11 | 1.39907 | 0.699534 | − | 0.714599i | \(-0.253391\pi\) | ||||
0.699534 | + | 0.714599i | \(0.253391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5.49695e10i | − 0.364896i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.49685e10 | 0.163633 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 6.91216e10i | − 0.441582i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.44468e11 | 0.911288 | 0.455644 | − | 0.890162i | \(-0.349409\pi\) | ||||
0.455644 | + | 0.890162i | \(0.349409\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.09446e11i | 0.673138i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.37317e9 | −0.0204871 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1.48167e10i | − 0.0877648i | −0.999037 | − | 0.0438824i | \(-0.986027\pi\) | ||||
0.999037 | − | 0.0438824i | \(-0.0139727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.20057e11 | 1.87234 | 0.936168 | − | 0.351553i | \(-0.114346\pi\) | ||||
0.936168 | + | 0.351553i | \(0.114346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.36291e10i | − 0.134843i | −0.997725 | − | 0.0674216i | \(-0.978523\pi\) | ||||
0.997725 | − | 0.0674216i | \(-0.0214773\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.06429e11 | 0.599905 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.18818e10i | − 0.0653473i | −0.999466 | − | 0.0326737i | \(-0.989598\pi\) | ||||
0.999466 | − | 0.0326737i | \(-0.0104022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.81052e10 | −0.370011 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.02462e11i | 1.60372i | 0.597510 | + | 0.801862i | \(0.296157\pi\) | ||||
−0.597510 | + | 0.801862i | \(0.703843\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.94947e8 | −0.00102120 | −0.000510600 | − | 1.00000i | \(-0.500163\pi\) | ||||
−0.000510600 | 1.00000i | \(0.500163\pi\) | ||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.69698e10i | 0.189043i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.29563e10 | 0.267556 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.73141e9i | 0.0381389i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.04705e10 | −0.246024 | −0.123012 | − | 0.992405i | \(-0.539255\pi\) | ||||
−0.123012 | + | 0.992405i | \(0.539255\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 9.18944e10i | − 0.437456i | −0.975786 | − | 0.218728i | \(-0.929809\pi\) | ||||
0.975786 | − | 0.218728i | \(-0.0701907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.19462e10 | −0.150293 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.76743e11i | 1.27173i | 0.771802 | + | 0.635863i | \(0.219356\pi\) | ||||
−0.771802 | + | 0.635863i | \(0.780644\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.50910e11 | −0.685418 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 2.21697e9i | − 0.00983747i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.33822e11 | 1.46421 | 0.732104 | − | 0.681193i | \(-0.238538\pi\) | ||||
0.732104 | + | 0.681193i | \(0.238538\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.83144e11i | 0.784970i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.73906e10 | −0.243170 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.07724e11i | 1.68847i | 0.535971 | + | 0.844236i | \(0.319945\pi\) | ||||
−0.535971 | + | 0.844236i | \(0.680055\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.19771e11 | −0.490378 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.08626e11i | − 0.434767i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.90558e10 | −0.194136 | −0.0970678 | − | 0.995278i | \(-0.530946\pi\) | ||||
−0.0970678 | + | 0.995278i | \(0.530946\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.52248e10i | 0.213686i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.69744e10 | −0.0649488 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.69821e11i | 1.75799i | 0.476830 | + | 0.878996i | \(0.341786\pi\) | ||||
−0.476830 | + | 0.878996i | \(0.658214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.08732e10 | 0.0402361 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.08490e11i | − 0.754630i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.92122e11 | 0.687764 | 0.343882 | − | 0.939013i | \(-0.388258\pi\) | ||||
0.343882 | + | 0.939013i | \(0.388258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.48896e11i | 0.871662i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.47278e10 | 0.258861 | 0.129430 | − | 0.991589i | \(-0.458685\pi\) | ||||
0.129430 | + | 0.991589i | \(0.458685\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 4.03236e11i | − 1.36675i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.49064e11 | 0.499799 | 0.249900 | − | 0.968272i | \(-0.419602\pi\) | ||||
0.249900 | + | 0.968272i | \(0.419602\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.90655e11i | 0.953723i | 0.878978 | + | 0.476862i | \(0.158226\pi\) | ||||
−0.878978 | + | 0.476862i | \(0.841774\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.70219e10 | −0.282490 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.79822e11i | − 0.571366i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.85693e10 | −0.121250 | −0.0606250 | − | 0.998161i | \(-0.519309\pi\) | ||||
−0.0606250 | + | 0.998161i | \(0.519309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.62652e10i | 0.203938i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.75336e11 | 0.533934 | 0.266967 | − | 0.963706i | \(-0.413979\pi\) | ||||
0.266967 | + | 0.963706i | \(0.413979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.42227e11i | 1.61675i | 0.588668 | + | 0.808375i | \(0.299653\pi\) | ||||
−0.588668 | + | 0.808375i | \(0.700347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.98309e10 | −0.0585118 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.66654e10i | 0.105944i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.67008e11 | 0.763517 | 0.381759 | − | 0.924262i | \(-0.375319\pi\) | ||||
0.381759 | + | 0.924262i | \(0.375319\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.93424e11i | − 0.541743i | −0.962616 | − | 0.270871i | \(-0.912688\pi\) | ||||
0.962616 | − | 0.270871i | \(-0.0873118\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.17421e11 | 0.602692 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.94441e10i | 0.270041i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.94372e11 | 0.522433 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.64001e11i | 0.431884i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.52841e10 | −0.222315 | −0.111158 | − | 0.993803i | \(-0.535456\pi\) | ||||
−0.111158 | + | 0.993803i | \(0.535456\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.92079e10i | 0.253420i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.66351e9 | −0.00673536 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.61423e11i | 1.63925i | 0.572897 | + | 0.819627i | \(0.305819\pi\) | ||||
−0.572897 | + | 0.819627i | \(0.694181\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.69078e11 | 0.905588 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.99109e11i | 0.478883i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.16231e10 | 0.0514913 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 8.13264e11i | − 1.89862i | −0.314344 | − | 0.949309i | \(-0.601785\pi\) | ||||
0.314344 | − | 0.949309i | \(-0.398215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.22085e10 | 0.0975702 | 0.0487851 | − | 0.998809i | \(-0.484465\pi\) | ||||
0.0487851 | + | 0.998809i | \(0.484465\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.61456e11i | 0.365953i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.31277e11 | 0.967983 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 5.27883e11i | − 1.16189i | −0.813943 | − | 0.580945i | \(-0.802683\pi\) | ||||
0.813943 | − | 0.580945i | \(-0.197317\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.78060e10 | −0.191393 | −0.0956963 | − | 0.995411i | \(-0.530508\pi\) | ||||
−0.0956963 | + | 0.995411i | \(0.530508\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.95035e11i | 0.416955i | 0.978027 | + | 0.208478i | \(0.0668509\pi\) | ||||
−0.978027 | + | 0.208478i | \(0.933149\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.56585e11 | −1.60192 | −0.800958 | − | 0.598720i | \(-0.795676\pi\) | ||||
−0.800958 | + | 0.598720i | \(0.795676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5.55476e10i | − 0.115368i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.51984e11 | −0.312646 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.44106e10i | 0.170353i | 0.996366 | + | 0.0851763i | \(0.0271454\pi\) | ||||
−0.996366 | + | 0.0851763i | \(0.972855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.99034e10 | −0.199708 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.78489e11i | 0.546237i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.62497e10 | 0.128721 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.00523e10i | 0.133569i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.56707e11 | 0.862664 | 0.431332 | − | 0.902193i | \(-0.358044\pi\) | ||||
0.431332 | + | 0.902193i | \(0.358044\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.28440e11i | 0.608881i | 0.952531 | + | 0.304440i | \(0.0984694\pi\) | ||||
−0.952531 | + | 0.304440i | \(0.901531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.00764e12 | 1.85069 | 0.925344 | − | 0.379129i | \(-0.123776\pi\) | ||||
0.925344 | + | 0.379129i | \(0.123776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.82398e11i | 0.869685i | 0.900507 | + | 0.434842i | \(0.143196\pi\) | ||||
−0.900507 | + | 0.434842i | \(0.856804\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.48189e11 | −0.800565 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.64348e11i | − 0.288195i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.38917e11 | 0.241369 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.08694e11i | − 0.356022i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.47431e10 | −0.0249225 | −0.0124613 | − | 0.999922i | \(-0.503967\pi\) | ||||
−0.0124613 | + | 0.999922i | \(0.503967\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 6.80542e11i | − 1.12967i | −0.825204 | − | 0.564835i | \(-0.808940\pi\) | ||||
0.825204 | − | 0.564835i | \(-0.191060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.59710e11 | −0.262717 | −0.131358 | − | 0.991335i | \(-0.541934\pi\) | ||||
−0.131358 | + | 0.991335i | \(0.541934\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.26548e11i | 1.01218i | 0.862479 | + | 0.506092i | \(0.168911\pi\) | ||||
−0.862479 | + | 0.506092i | \(0.831089\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.84942e11 | −0.456194 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6.39523e11i | − 1.00566i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.01468e11 | −0.313989 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 6.25858e11i | − 0.958158i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.65079e10 | 0.0553972 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 4.74519e11i | − 0.707390i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.67535e11 | −1.42968 | −0.714838 | − | 0.699290i | \(-0.753500\pi\) | ||||
−0.714838 | + | 0.699290i | \(0.753500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 5.30084e11i | − 0.769611i | −0.922998 | − | 0.384805i | \(-0.874269\pi\) | ||||
0.922998 | − | 0.384805i | \(-0.125731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.36397e10 | 0.0340220 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.77312e11i | − 0.250761i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.29433e12 | −1.81461 | −0.907304 | − | 0.420476i | \(-0.861863\pi\) | ||||
−0.907304 | + | 0.420476i | \(0.861863\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.69623e10i | 0.0922621i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.75798e11 | 0.376724 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.17539e12i | 1.57804i | 0.614369 | + | 0.789019i | \(0.289411\pi\) | ||||
−0.614369 | + | 0.789019i | \(0.710589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.62507e10 | −0.128117 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2.79526e11i | − 0.365743i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.22945e11 | −0.937880 | −0.468940 | − | 0.883230i | \(-0.655364\pi\) | ||||
−0.468940 | + | 0.883230i | \(0.655364\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.19339e12i | − 1.52203i | −0.648733 | − | 0.761016i | \(-0.724701\pi\) | ||||
0.648733 | − | 0.761016i | \(-0.275299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.81633e10 | 0.0735534 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.56063e12i | − 1.94044i | −0.242226 | − | 0.970220i | \(-0.577877\pi\) | ||||
0.242226 | − | 0.970220i | \(-0.422123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.85941e10 | −0.0845711 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.68527e11i | 1.05296i | 0.850188 | + | 0.526480i | \(0.176488\pi\) | ||||
−0.850188 | + | 0.526480i | \(0.823512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.38418e11 | −0.166409 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 3.92894e11i | − 0.464516i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00224e11 | −0.234759 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.04655e11i | 0.581949i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.38012e12 | 1.57838 | 0.789189 | − | 0.614151i | \(-0.210501\pi\) | ||||
0.789189 | + | 0.614151i | \(0.210501\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.75507e11i | 0.984879i | 0.870347 | + | 0.492439i | \(0.163895\pi\) | ||||
−0.870347 | + | 0.492439i | \(0.836105\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.76815e11 | −0.531984 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 7.13074e11i | − 0.782630i | −0.920257 | − | 0.391315i | \(-0.872020\pi\) | ||||
0.920257 | − | 0.391315i | \(-0.127980\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.20170e11 | 0.783979 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.62031e12i | − 1.73534i | −0.497140 | − | 0.867670i | \(-0.665617\pi\) | ||||
0.497140 | − | 0.867670i | \(-0.334383\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.44887e11 | −0.472612 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2.52247e11i | − 0.263658i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.45491e12 | −1.50849 | −0.754243 | − | 0.656595i | \(-0.771996\pi\) | ||||
−0.754243 | + | 0.656595i | \(0.771996\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.12643e11i | 0.829101i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.93410e11 | −0.296958 | −0.148479 | − | 0.988916i | \(-0.547438\pi\) | ||||
−0.148479 | + | 0.988916i | \(0.547438\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.9.c.a.197.7 | ✓ | 16 | |
3.2 | odd | 2 | inner | 252.9.c.a.197.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.c.a.197.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
252.9.c.a.197.10 | yes | 16 | 3.2 | odd | 2 | inner |