Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1535279252\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{31}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 31 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 20) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.56776\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 11.1355 | 0.714345 | 0.357172 | − | 0.934039i | \(-0.383741\pi\) | ||||
0.357172 | + | 0.934039i | \(0.383741\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −122.491 | −0.944840 | −0.472420 | − | 0.881373i | \(-0.656620\pi\) | ||||
−0.472420 | + | 0.881373i | \(0.656620\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −119.000 | −0.489712 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 100.000 | 0.249183 | 0.124591 | − | 0.992208i | \(-0.460238\pi\) | ||||
0.124591 | + | 0.992208i | \(0.460238\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 734.945 | 1.20614 | 0.603068 | − | 0.797690i | \(-0.293945\pi\) | ||||
0.603068 | + | 0.797690i | \(0.293945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −979.927 | −0.822377 | −0.411189 | − | 0.911550i | \(-0.634886\pi\) | ||||
−0.411189 | + | 0.911550i | \(0.634886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2244.00 | 1.42606 | 0.713032 | − | 0.701132i | \(-0.247322\pi\) | ||||
0.713032 | + | 0.701132i | \(0.247322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1364.00 | −0.674942 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3418.61 | 1.34750 | 0.673751 | − | 0.738958i | \(-0.264682\pi\) | ||||
0.673751 | + | 0.738958i | \(0.264682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4031.06 | −1.06417 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7854.00 | −1.73419 | −0.867093 | − | 0.498146i | \(-0.834015\pi\) | ||||
−0.867093 | + | 0.498146i | \(0.834015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2144.00 | 0.400701 | 0.200351 | − | 0.979724i | \(-0.435792\pi\) | ||||
0.200351 | + | 0.979724i | \(0.435792\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1113.55 | 0.178002 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10400.6 | −1.24897 | −0.624487 | − | 0.781035i | \(-0.714692\pi\) | ||||
−0.624487 | + | 0.781035i | \(0.714692\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8184.00 | 0.861597 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7414.00 | −0.688800 | −0.344400 | − | 0.938823i | \(-0.611918\pi\) | ||||
−0.344400 | + | 0.938823i | \(0.611918\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17761.2 | −1.46487 | −0.732437 | − | 0.680835i | \(-0.761617\pi\) | ||||
−0.732437 | + | 0.680835i | \(0.761617\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9431.79 | −0.622801 | −0.311401 | − | 0.950279i | \(-0.600798\pi\) | ||||
−0.311401 | + | 0.950279i | \(0.600798\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1803.00 | −0.107277 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10912.0 | −0.587461 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −24253.2 | −1.18598 | −0.592992 | − | 0.805208i | \(-0.702054\pi\) | ||||
−0.592992 | + | 0.805208i | \(0.702054\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24988.1 | 1.01870 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25972.0 | −0.971349 | −0.485675 | − | 0.874140i | \(-0.661426\pi\) | ||||
−0.485675 | + | 0.874140i | \(0.661426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3058.00 | −0.105224 | −0.0526118 | − | 0.998615i | \(-0.516755\pi\) | ||||
−0.0526118 | + | 0.998615i | \(0.516755\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14576.4 | 0.462700 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 58784.5 | 1.59984 | 0.799918 | − | 0.600109i | \(-0.204876\pi\) | ||||
0.799918 | + | 0.600109i | \(0.204876\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 38068.0 | 0.962581 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −37608.0 | −0.885389 | −0.442695 | − | 0.896672i | \(-0.645977\pi\) | ||||
−0.442695 | + | 0.896672i | \(0.645977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24008.2 | 0.527294 | 0.263647 | − | 0.964619i | \(-0.415075\pi\) | ||||
0.263647 | + | 0.964619i | \(0.415075\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12249.1 | −0.235438 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −79728.0 | −1.43729 | −0.718643 | − | 0.695379i | \(-0.755236\pi\) | ||||
−0.718643 | + | 0.695379i | \(0.755236\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −15971.0 | −0.270470 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16291.3 | −0.259573 | −0.129787 | − | 0.991542i | \(-0.541429\pi\) | ||||
−0.129787 | + | 0.991542i | \(0.541429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −87458.4 | −1.23881 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −826.000 | −0.0110536 | −0.00552682 | − | 0.999985i | \(-0.501759\pi\) | ||||
−0.00552682 | + | 0.999985i | \(0.501759\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −90024.0 | −1.13961 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23874.6 | 0.286239 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 37593.5 | 0.405680 | 0.202840 | − | 0.979212i | \(-0.434983\pi\) | ||||
0.202840 | + | 0.979212i | \(0.434983\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11900.0 | −0.122028 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −143594. | −1.40066 | −0.700330 | − | 0.713819i | \(-0.746964\pi\) | ||||
−0.700330 | + | 0.713819i | \(0.746964\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 111834. | 1.03868 | 0.519339 | − | 0.854568i | \(-0.326178\pi\) | ||||
0.519339 | + | 0.854568i | \(0.326178\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 92235.6 | 0.778824 | 0.389412 | − | 0.921064i | \(-0.372678\pi\) | ||||
0.389412 | + | 0.921064i | \(0.372678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −106238. | −0.856473 | −0.428236 | − | 0.903667i | \(-0.640865\pi\) | ||||
−0.428236 | + | 0.903667i | \(0.640865\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −115816. | −0.892198 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 113048. | 0.832849 | 0.416425 | − | 0.909170i | \(-0.363283\pi\) | ||||
0.416425 | + | 0.909170i | \(0.363283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −87458.4 | −0.590659 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 120032. | 0.777015 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −151051. | −0.937908 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −82558.8 | −0.492040 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −51568.6 | −0.283711 | −0.141856 | − | 0.989887i | \(-0.545307\pi\) | ||||
−0.141856 | + | 0.989887i | \(0.545307\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −197780. | −1.04642 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 89100.0 | 0.453628 | 0.226814 | − | 0.973938i | \(-0.427169\pi\) | ||||
0.226814 | + | 0.973938i | \(0.427169\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −274869. | −1.34740 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 38350.8 | 0.174571 | 0.0872856 | − | 0.996183i | \(-0.472181\pi\) | ||||
0.0872856 | + | 0.996183i | \(0.472181\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 134684. | 0.591261 | 0.295630 | − | 0.955302i | \(-0.404470\pi\) | ||||
0.295630 | + | 0.955302i | \(0.404470\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −105028. | −0.444895 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 73494.5 | 0.300549 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20077.4 | −0.0766325 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −248006. | −0.915159 | −0.457579 | − | 0.889169i | \(-0.651283\pi\) | ||||
−0.457579 | + | 0.889169i | \(0.651283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −313720. | −1.11970 | −0.559848 | − | 0.828596i | \(-0.689140\pi\) | ||||
−0.559848 | + | 0.828596i | \(0.689140\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 116611. | 0.402728 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 245583. | 0.795150 | 0.397575 | − | 0.917570i | \(-0.369852\pi\) | ||||
0.397575 | + | 0.917570i | \(0.369852\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −270072. | −0.847202 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −418748. | −1.27317 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −397483. | −1.17179 | −0.585894 | − | 0.810388i | \(-0.699257\pi\) | ||||
−0.585894 | + | 0.810388i | \(0.699257\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 189983. | 0.527138 | 0.263569 | − | 0.964641i | \(-0.415100\pi\) | ||||
0.263569 | + | 0.964641i | \(0.415100\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168851. | 0.454765 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −267036. | −0.698360 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 81088.9 | 0.205990 | 0.102995 | − | 0.994682i | \(-0.467157\pi\) | ||||
0.102995 | + | 0.994682i | \(0.467157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −289212. | −0.693878 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −142108. | −0.331502 | −0.165751 | − | 0.986168i | \(-0.553005\pi\) | ||||
−0.165751 | + | 0.986168i | \(0.553005\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 250790. | 0.569002 | 0.284501 | − | 0.958676i | \(-0.408172\pi\) | ||||
0.284501 | + | 0.958676i | \(0.408172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −34052.4 | −0.0751659 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −97992.7 | −0.204922 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 493768. | 1.00547 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 209472. | 0.415473 | 0.207736 | − | 0.978185i | \(-0.433390\pi\) | ||||
0.207736 | + | 0.978185i | \(0.433390\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −356693. | −0.689289 | −0.344645 | − | 0.938733i | \(-0.612001\pi\) | ||||
−0.344645 | + | 0.938733i | \(0.612001\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −86478.5 | −0.158761 | −0.0793803 | − | 0.996844i | \(-0.525294\pi\) | ||||
−0.0793803 | + | 0.996844i | \(0.525294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −749208. | −1.34113 | −0.670563 | − | 0.741852i | \(-0.733947\pi\) | ||||
−0.670563 | + | 0.741852i | \(0.733947\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 654596. | 1.14283 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 962043. | 1.63853 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −406814. | −0.659888 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 224400. | 0.355351 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −287364. | −0.444351 | −0.222176 | − | 0.975007i | \(-0.571316\pi\) | ||||
−0.222176 | + | 0.975007i | \(0.571316\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −418785. | −0.632473 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −262620. | −0.378599 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 267344. | 0.376669 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −720192. | −0.991899 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.18866e6 | −1.60065 | −0.800325 | − | 0.599567i | \(-0.795340\pi\) | ||||
−0.800325 | + | 0.599567i | \(0.795340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −978334. | −1.26015 | −0.630075 | − | 0.776534i | \(-0.716976\pi\) | ||||
−0.630075 | + | 0.776534i | \(0.716976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 506474. | 0.638217 | 0.319109 | − | 0.947718i | \(-0.396617\pi\) | ||||
0.319109 | + | 0.947718i | \(0.396617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −136400. | −0.168184 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.55465e6 | 1.87605 | 0.938024 | − | 0.346571i | \(-0.112654\pi\) | ||||
0.938024 | + | 0.346571i | \(0.112654\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −887813. | −1.02672 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 374704. | 0.424320 | 0.212160 | − | 0.977235i | \(-0.431950\pi\) | ||||
0.212160 | + | 0.977235i | \(0.431950\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 843634. | 0.935646 | 0.467823 | − | 0.883822i | \(-0.345039\pi\) | ||||
0.467823 | + | 0.883822i | \(0.345039\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 801702. | 0.870959 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.64922e6 | 1.72003 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −181412. | −0.185425 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.72050e6 | 1.72373 | 0.861867 | − | 0.507134i | \(-0.169295\pi\) | ||||
0.861867 | + | 0.507134i | \(0.169295\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 341861. | 0.335775 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.55220e6 | 1.46594 | 0.732969 | − | 0.680262i | \(-0.238134\pi\) | ||||
0.732969 | + | 0.680262i | \(0.238134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.27398e6 | 1.18008 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 934626. | 0.849252 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 407772. | 0.363520 | 0.181760 | − | 0.983343i | \(-0.441821\pi\) | ||||
0.181760 | + | 0.983343i | \(0.441821\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9197.95 | −0.00789610 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.82710e6 | −1.53951 | −0.769754 | − | 0.638340i | \(-0.779621\pi\) | ||||
−0.769754 | + | 0.638340i | \(0.779621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 616880. | 0.510243 | 0.255122 | − | 0.966909i | \(-0.417884\pi\) | ||||
0.255122 | + | 0.966909i | \(0.417884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.00246e6 | −0.814071 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.83712e6 | 1.43859 | 0.719296 | − | 0.694704i | \(-0.244465\pi\) | ||||
0.719296 | + | 0.694704i | \(0.244465\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −255136. | −0.196228 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.22093e6 | −0.922415 | −0.461208 | − | 0.887292i | \(-0.652584\pi\) | ||||
−0.461208 | + | 0.887292i | \(0.652584\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 688766. | 0.511217 | 0.255609 | − | 0.966780i | \(-0.417724\pi\) | ||||
0.255609 | + | 0.966780i | \(0.417724\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 908147. | 0.650806 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −459601. | −0.323695 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 418624. | 0.289796 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −856211. | −0.582655 | −0.291328 | − | 0.956623i | \(-0.594097\pi\) | ||||
−0.291328 | + | 0.956623i | \(0.594097\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −403106. | −0.265172 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.51249e6 | 1.62527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.17558e6 | 1.38407 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.59900e6 | −1.00055 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.09617e6 | 0.663792 | 0.331896 | − | 0.943316i | \(-0.392312\pi\) | ||||
0.331896 | + | 0.943316i | \(0.392312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.24533e6 | 0.741974 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.12465e6 | 1.24562 | 0.622811 | − | 0.782373i | \(-0.285991\pi\) | ||||
0.622811 | + | 0.782373i | \(0.285991\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −294824. | −0.170099 | −0.0850496 | − | 0.996377i | \(-0.527105\pi\) | ||||
−0.0850496 | + | 0.996377i | \(0.527105\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.53153e6 | −1.41493 | −0.707465 | − | 0.706749i | \(-0.750161\pi\) | ||||
−0.707465 | + | 0.706749i | \(0.750161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −785400. | −0.432130 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.02709e6 | 0.556348 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.19896e6 | −1.17276 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.18302e6 | −0.611817 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.15531e6 | 0.588448 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.17021e6 | 0.587076 | 0.293538 | − | 0.955947i | \(-0.405167\pi\) | ||||
0.293538 | + | 0.955947i | \(0.405167\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.23767e6 | 0.611637 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.86872e6 | 0.896333 | 0.448167 | − | 0.893950i | \(-0.352077\pi\) | ||||
0.448167 | + | 0.893950i | \(0.352077\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.25885e6 | 0.594941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 214400. | 0.0998479 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.27955e6 | 1.04620 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.63342e6 | −0.728237 | −0.364119 | − | 0.931353i | \(-0.618630\pi\) | ||||
−0.364119 | + | 0.931353i | \(0.618630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00629e6 | 0.881719 | 0.440859 | − | 0.897576i | \(-0.354674\pi\) | ||||
0.440859 | + | 0.897576i | \(0.354674\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.96261e6 | −1.28353 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.80859e6 | −0.772508 | −0.386254 | − | 0.922392i | \(-0.626231\pi\) | ||||
−0.386254 | + | 0.922392i | \(0.626231\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.33662e6 | 0.555057 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.50674e6 | −1.84555 | −0.922777 | − | 0.385334i | \(-0.874086\pi\) | ||||
−0.922777 | + | 0.385334i | \(0.874086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.55944e6 | 1.03366 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.68203e6 | −0.669989 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.02796e6 | −1.17351 | −0.586753 | − | 0.809766i | \(-0.699594\pi\) | ||||
−0.586753 | + | 0.809766i | \(0.699594\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 882266. | 0.337313 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.97079e6 | 1.12057 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.16342e6 | 0.432976 | 0.216488 | − | 0.976285i | \(-0.430540\pi\) | ||||
0.216488 | + | 0.976285i | \(0.430540\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.77226e6 | −2.09167 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −832052. | −0.297545 | −0.148772 | − | 0.988871i | \(-0.547532\pi\) | ||||
−0.148772 | + | 0.988871i | \(0.547532\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −574244. | −0.202667 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.86948e6 | 0.999554 | 0.499777 | − | 0.866154i | \(-0.333415\pi\) | ||||
0.499777 | + | 0.866154i | \(0.333415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.11358e6 | 0.717366 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −311926. | −0.104515 | −0.0522574 | − | 0.998634i | \(-0.516642\pi\) | ||||
−0.0522574 | + | 0.998634i | \(0.516642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.34998e6 | −1.10816 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 992176. | 0.324046 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.95619e6 | −0.941362 | −0.470681 | − | 0.882304i | \(-0.655992\pi\) | ||||
−0.470681 | + | 0.882304i | \(0.655992\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.06082e6 | −0.962509 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2770.00 | 0.000860238 0 | 0.000430119 | − | 1.00000i | \(-0.499863\pi\) | ||||
0.000430119 | 1.00000i | \(0.499863\pi\) | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.57572e6 | 0.483300 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.04006e6 | −0.311223 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.97985e6 | 0.585225 | 0.292613 | − | 0.956231i | \(-0.405475\pi\) | ||||
0.292613 | + | 0.956231i | \(0.405475\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 427056. | 0.124704 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.18133e6 | 0.917770 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.49978e6 | 0.422364 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.10120e6 | 1.41951 | 0.709754 | − | 0.704450i | \(-0.248806\pi\) | ||||
0.709754 | + | 0.704450i | \(0.248806\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.43223e6 | −0.668806 | −0.334403 | − | 0.942430i | \(-0.608535\pi\) | ||||
−0.334403 | + | 0.942430i | \(0.608535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.12238e6 | 0.304993 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 374577. | 0.0994194 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 818400. | 0.214695 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −918896. | −0.238272 | −0.119136 | − | 0.992878i | \(-0.538012\pi\) | ||||
−0.119136 | + | 0.992878i | \(0.538012\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.05455e6 | −0.526619 | −0.263310 | − | 0.964711i | \(-0.584814\pi\) | ||||
−0.263310 | + | 0.964711i | \(0.584814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.67135e6 | 1.92162 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 676632. | 0.167568 | 0.0837840 | − | 0.996484i | \(-0.473299\pi\) | ||||
0.0837840 | + | 0.996484i | \(0.473299\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 214557. | 0.0525347 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.53092e6 | −0.612729 | −0.306365 | − | 0.951914i | \(-0.599113\pi\) | ||||
−0.306365 | + | 0.951914i | \(0.599113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.76168e6 | −0.653739 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.17619e6 | −1.21170 | −0.605849 | − | 0.795579i | \(-0.707167\pi\) | ||||
−0.605849 | + | 0.795579i | \(0.707167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −741400. | −0.171637 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.49344e6 | −0.799848 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.11274e6 | −0.697191 | −0.348596 | − | 0.937273i | \(-0.613341\pi\) | ||||
−0.348596 | + | 0.937273i | \(0.613341\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.95014e6 | 0.875147 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.64957e6 | −0.580662 | −0.290331 | − | 0.956926i | \(-0.593765\pi\) | ||||
−0.290331 | + | 0.956926i | \(0.593765\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.59165e6 | −0.561854 | −0.280927 | − | 0.959729i | \(-0.590642\pi\) | ||||
−0.280927 | + | 0.959729i | \(0.590642\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.62135e6 | 1.40493 | 0.702465 | − | 0.711719i | \(-0.252083\pi\) | ||||
0.702465 | + | 0.711719i | \(0.252083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.20056e6 | −1.51159 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.73470e6 | 0.568011 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.77612e6 | −0.365022 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.88613e6 | 0.580791 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.89322e6 | −1.37272 | −0.686362 | − | 0.727260i | \(-0.740793\pi\) | ||||
−0.686362 | + | 0.727260i | \(0.740793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.64386e6 | −1.50643 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.66298e6 | −0.909485 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.65370e6 | 1.08021 | 0.540107 | − | 0.841596i | \(-0.318384\pi\) | ||||
0.540107 | + | 0.841596i | \(0.318384\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.42618e6 | −0.837061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.88390e6 | −1.10144 | −0.550721 | − | 0.834689i | \(-0.685647\pi\) | ||||
−0.550721 | + | 0.834689i | \(0.685647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.69634e6 | 1.42616 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.60663e6 | 0.836552 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.72080e6 | 1.20829 | 0.604143 | − | 0.796876i | \(-0.293515\pi\) | ||||
0.604143 | + | 0.796876i | \(0.293515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.11556e6 | 0.376558 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −469262. | −0.0826981 | −0.0413491 | − | 0.999145i | \(-0.513166\pi\) | ||||
−0.0413491 | + | 0.999145i | \(0.513166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.88025e6 | 0.324859 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −294414. | −0.0503691 | −0.0251845 | − | 0.999683i | \(-0.508017\pi\) | ||||
−0.0251845 | + | 0.999683i | \(0.508017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.94078e6 | −0.498208 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.04570e6 | −1.51757 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −943179. | −0.155191 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 902968. | 0.147148 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.10025e6 | −1.14599 | −0.572993 | − | 0.819560i | \(-0.694218\pi\) | ||||
−0.572993 | + | 0.819560i | \(0.694218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.96567e6 | 0.953685 | 0.476843 | − | 0.878989i | \(-0.341781\pi\) | ||||
0.476843 | + | 0.878989i | \(0.341781\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.10096e6 | −0.329528 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.25053e6 | 0.815763 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.09067e6 | 0.475681 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.44888e6 | −0.830786 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.58245e6 | −0.236807 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −180300. | −0.0267315 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.72367e6 | −0.400093 | −0.200046 | − | 0.979786i | \(-0.564109\pi\) | ||||
−0.200046 | + | 0.979786i | \(0.564109\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.79268e6 | 0.406463 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.22148e6 | −1.31775 | −0.658874 | − | 0.752254i | \(-0.728967\pi\) | ||||
−0.658874 | + | 0.752254i | \(0.728967\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 363902. | 0.0515292 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.76244e7 | −2.47306 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.76595e6 | 1.35801 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.42852e6 | −0.468240 | −0.234120 | − | 0.972208i | \(-0.575221\pi\) | ||||
−0.234120 | + | 0.972208i | \(0.575221\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.30535e7 | −1.76684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.09120e6 | −0.146385 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.77899e6 | 0.768389 | 0.384195 | − | 0.923252i | \(-0.374479\pi\) | ||||
0.384195 | + | 0.923252i | \(0.374479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.95630e6 | 0.255551 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.89257e6 | −0.504029 | −0.252015 | − | 0.967723i | \(-0.581093\pi\) | ||||
−0.252015 | + | 0.967723i | \(0.581093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.06277e6 | 0.649828 | 0.324914 | − | 0.945744i | \(-0.394665\pi\) | ||||
0.324914 | + | 0.945744i | \(0.394665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.33258e6 | 0.296791 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.30075e6 | −0.412737 | −0.206368 | − | 0.978474i | \(-0.566164\pi\) | ||||
−0.206368 | + | 0.978474i | \(0.566164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.97197e6 | −0.492390 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.99553e6 | 0.245255 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.42532e6 | −0.295527 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.16997e6 | −0.619288 | −0.309644 | − | 0.950853i | \(-0.600210\pi\) | ||||
−0.309644 | + | 0.950853i | \(0.600210\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.81114e6 | 0.571425 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −962984. | −0.113410 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.58484e7 | 1.85075 | 0.925374 | − | 0.379055i | \(-0.123751\pi\) | ||||
0.925374 | + | 0.379055i | \(0.123751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.34283e6 | −0.958026 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.66146e7 | −1.89201 | −0.946004 | − | 0.324156i | \(-0.894920\pi\) | ||||
−0.946004 | + | 0.324156i | \(0.894920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.88249e6 | 0.890179 | 0.445089 | − | 0.895486i | \(-0.353172\pi\) | ||||
0.445089 | + | 0.895486i | \(0.353172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.99535e6 | −0.783459 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −782594. | −0.0862114 | −0.0431057 | − | 0.999071i | \(-0.513725\pi\) | ||||
−0.0431057 | + | 0.999071i | \(0.513725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.07129e7 | 1.17047 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.93185e6 | −0.751183 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.41233e6 | −0.259290 | −0.129645 | − | 0.991560i | \(-0.541384\pi\) | ||||
−0.129645 | + | 0.991560i | \(0.541384\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.66355e6 | 1.02194 | 0.510968 | − | 0.859600i | \(-0.329287\pi\) | ||||
0.510968 | + | 0.859600i | \(0.329287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.80036e7 | 1.88857 | 0.944283 | − | 0.329134i | \(-0.106757\pi\) | ||||
0.944283 | + | 0.329134i | \(0.106757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.37806e7 | −1.43397 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 101177. | 0.0104439 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.49881e6 | 0.253843 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.01918e7 | 1.02713 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.80081e6 | 0.480000 | 0.240000 | − | 0.970773i | \(-0.422853\pi\) | ||||
0.240000 | + | 0.970773i | \(0.422853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.19995e6 | −0.317420 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.32511e6 | −0.129390 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.47535e6 | 0.433586 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.44950e7 | 1.39340 | 0.696698 | − | 0.717365i | \(-0.254652\pi\) | ||||
0.696698 | + | 0.717365i | \(0.254652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.82430e7 | 1.74008 | 0.870041 | − | 0.492979i | \(-0.164092\pi\) | ||||
0.870041 | + | 0.492979i | \(0.164092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.64592e6 | 0.905905 | 0.452953 | − | 0.891535i | \(-0.350371\pi\) | ||||
0.452953 | + | 0.891535i | \(0.350371\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.59720e6 | −0.242044 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.92442e6 | −0.270450 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.92807e7 | −1.76945 | −0.884726 | − | 0.466111i | \(-0.845655\pi\) | ||||
−0.884726 | + | 0.466111i | \(0.845655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.85698e6 | −0.258222 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.70592e6 | −0.870609 | −0.435304 | − | 0.900283i | \(-0.643359\pi\) | ||||
−0.435304 | + | 0.900283i | \(0.643359\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.28396e6 | −0.381366 | −0.190683 | − | 0.981652i | \(-0.561070\pi\) | ||||
−0.190683 | + | 0.981652i | \(0.561070\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.01972e6 | −0.708558 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.68497e7 | −2.33682 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.32364e7 | −1.14342 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −305800. | −0.0262199 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.30585e7 | −1.11136 | −0.555681 | − | 0.831395i | \(-0.687542\pi\) | ||||
−0.555681 | + | 0.831395i | \(0.687542\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.42565e6 | −0.706532 | −0.353266 | − | 0.935523i | \(-0.614929\pi\) | ||||
−0.353266 | + | 0.935523i | \(0.614929\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.60486e6 | −0.383303 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.08943e7 | −0.900182 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.64100e7 | −1.34603 | −0.673017 | − | 0.739627i | \(-0.735002\pi\) | ||||
−0.673017 | + | 0.739627i | \(0.735002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.63986e6 | 0.455907 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.78248e7 | −1.43046 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.12139e7 | 0.893428 | 0.446714 | − | 0.894677i | \(-0.352594\pi\) | ||||
0.446714 | + | 0.894677i | \(0.352594\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.45764e6 | 0.115297 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.26518e6 | 0.566453 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.73119e7 | 1.34014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.04707e7 | 1.57339 | 0.786696 | − | 0.617340i | \(-0.211790\pi\) | ||||
0.786696 | + | 0.617340i | \(0.211790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.33389e7 | −1.78112 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.75889e7 | 1.32340 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −81654.0 | −0.00610045 | −0.00305023 | − | 0.999995i | \(-0.500971\pi\) | ||||
−0.00305023 | + | 0.999995i | \(0.500971\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.48763e6 | 0.703856 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.32949e6 | 0.539946 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.17253e6 | 0.303111 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.61006e6 | 0.621132 | 0.310566 | − | 0.950552i | \(-0.399481\pi\) | ||||
0.310566 | + | 0.950552i | \(0.399481\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.36987e7 | −0.981386 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.39431e6 | 0.668373 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17682e7 | 0.825796 | 0.412898 | − | 0.910777i | \(-0.364517\pi\) | ||||
0.412898 | + | 0.910777i | \(0.364517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.28083e7 | 0.892635 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.74046e7 | 1.20468 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.93759e6 | −0.270689 | −0.135344 | − | 0.990799i | \(-0.543214\pi\) | ||||
−0.135344 | + | 0.990799i | \(0.543214\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.87845e6 | 0.398652 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.30602e7 | 1.55329 | 0.776643 | − | 0.629941i | \(-0.216921\pi\) | ||||
0.776643 | + | 0.629941i | \(0.216921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.83649e7 | 1.22869 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.72675e6 | 0.114751 | 0.0573757 | − | 0.998353i | \(-0.481727\pi\) | ||||
0.0573757 | + | 0.998353i | \(0.481727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.93866e6 | 0.127116 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.12980e7 | −0.735864 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.58030e6 | 0.166944 | 0.0834720 | − | 0.996510i | \(-0.473399\pi\) | ||||
0.0834720 | + | 0.996510i | \(0.473399\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.91587e7 | 1.23134 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.75878e6 | 0.365251 | 0.182625 | − | 0.983183i | \(-0.441540\pi\) | ||||
0.182625 | + | 0.983183i | \(0.441540\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.80680e6 | 0.239859 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.40499e7 | 0.879450 | 0.439725 | − | 0.898133i | \(-0.355076\pi\) | ||||
0.439725 | + | 0.898133i | \(0.355076\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.30132e7 | 0.809230 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.90880e7 | −1.17158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.59898e6 | −0.341423 | −0.170712 | − | 0.985321i | \(-0.554607\pi\) | ||||
−0.170712 | + | 0.985321i | \(0.554607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.72846e7 | 1.04719 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.34625e6 | 0.382004 | 0.191002 | − | 0.981590i | \(-0.438826\pi\) | ||||
0.191002 | + | 0.981590i | \(0.438826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.41864e7 | 0.842984 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.66370e7 | −0.982272 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.76080e6 | −0.220624 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.16600e7 | 1.84547 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.73688e7 | 0.999617 | 0.499809 | − | 0.866136i | \(-0.333404\pi\) | ||||
0.499809 | + | 0.866136i | \(0.333404\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.54076e6 | 0.259678 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.38473e7 | −0.786909 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.24746e6 | −0.126914 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.06932e6 | 0.449978 | 0.224989 | − | 0.974361i | \(-0.427765\pi\) | ||||
0.224989 | + | 0.974361i | \(0.427765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.24246e6 | 0.512178 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 98294.0 | 0.00541310 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.40082e6 | 0.131393 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.03457e7 | −1.09974 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.94554e7 | 1.04513 | 0.522564 | − | 0.852600i | \(-0.324976\pi\) | ||||
0.522564 | + | 0.852600i | \(0.324976\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.85204e6 | 0.152266 | 0.0761330 | − | 0.997098i | \(-0.475743\pi\) | ||||
0.0761330 | + | 0.997098i | \(0.475743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.86928e6 | 0.364490 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.98561e7 | −2.08900 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.07129e7 | 0.558079 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.48431e6 | −0.283965 | −0.141982 | − | 0.989869i | \(-0.545348\pi\) | ||||
−0.141982 | + | 0.989869i | \(0.545348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.57652e6 | −0.338452 | −0.169226 | − | 0.985577i | \(-0.554127\pi\) | ||||
−0.169226 | + | 0.985577i | \(0.554127\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.19715e6 | 0.213398 | 0.106699 | − | 0.994291i | \(-0.465972\pi\) | ||||
0.106699 | + | 0.994291i | \(0.465972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.78889e7 | 1.40943 | 0.704717 | − | 0.709488i | \(-0.251074\pi\) | ||||
0.704717 | + | 0.709488i | \(0.251074\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.04573e7 | 1.02765 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.76681e6 | 0.0882220 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.64260e6 | −0.426413 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.27752e7 | −0.626560 | −0.313280 | − | 0.949661i | \(-0.601428\pi\) | ||||
−0.313280 | + | 0.949661i | \(0.601428\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.11742e7 | 2.00740 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.35957e7 | −0.658922 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.85024e7 | 0.886173 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.66977e6 | 0.365185 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.55555e7 | −1.68300 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.37122e6 | 0.252755 | 0.126378 | − | 0.991982i | \(-0.459665\pi\) | ||||
0.126378 | + | 0.991982i | \(0.459665\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.61585e7 | −0.751535 | −0.375767 | − | 0.926714i | \(-0.622621\pi\) | ||||
−0.375767 | + | 0.926714i | \(0.622621\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.34643e7 | −1.54739 | −0.773693 | − | 0.633561i | \(-0.781593\pi\) | ||||
−0.773693 | + | 0.633561i | \(0.781593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.01127e7 | 0.464899 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.51788e7 | 1.15082 | 0.575412 | − | 0.817864i | \(-0.304842\pi\) | ||||
0.575412 | + | 0.817864i | \(0.304842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.11790e6 | −0.231230 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.97280e6 | −0.358147 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.32033e7 | 1.92962 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.47363e6 | −0.198666 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.46327e7 | 1.08146 | 0.540732 | − | 0.841195i | \(-0.318147\pi\) | ||||
0.540732 | + | 0.841195i | \(0.318147\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.53436e6 | −0.416217 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.10564e7 | −0.479926 | −0.239963 | − | 0.970782i | \(-0.577135\pi\) | ||||
−0.239963 | + | 0.970782i | \(0.577135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.74671e7 | −1.61714 | −0.808572 | − | 0.588398i | \(-0.799759\pi\) | ||||
−0.808572 | + | 0.588398i | \(0.799759\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.96341e7 | −1.26469 | −0.632343 | − | 0.774689i | \(-0.717906\pi\) | ||||
−0.632343 | + | 0.774689i | \(0.717906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.31668e6 | 0.268062 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.59710e6 | −0.0673966 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.11649e7 | −0.888154 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.79779e7 | 1.16100 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.68390e7 | −0.694891 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.37663e7 | 0.975327 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.42262e7 | 0.988705 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.94430e6 | 0.0784773 | 0.0392387 | − | 0.999230i | \(-0.487507\pi\) | ||||
0.0392387 | + | 0.999230i | \(0.487507\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.70877e7 | 0.685920 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.28064e7 | −0.511245 | −0.255623 | − | 0.966777i | \(-0.582280\pi\) | ||||
−0.255623 | + | 0.966777i | \(0.582280\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.62913e6 | −0.0646812 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.09139e7 | −0.428606 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.58404e7 | 1.39986 | 0.699929 | − | 0.714213i | \(-0.253215\pi\) | ||||
0.699929 | + | 0.714213i | \(0.253215\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.22064e7 | 0.474176 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.76398e7 | −1.06790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.33083e7 | −0.508653 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.47792e6 | −0.322292 | −0.161146 | − | 0.986931i | \(-0.551519\pi\) | ||||
−0.161146 | + | 0.986931i | \(0.551519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.04593e6 | −0.152983 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.36591e7 | 0.889803 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.60566e7 | 0.597454 | 0.298727 | − | 0.954339i | \(-0.403438\pi\) | ||||
0.298727 | + | 0.954339i | \(0.403438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.28302e6 | −0.121509 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.24675e7 | −1.56344 | −0.781722 | − | 0.623627i | \(-0.785658\pi\) | ||||
−0.781722 | + | 0.623627i | \(0.785658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.53456e7 | −0.928159 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.78877e7 | 1.01050 | 0.505252 | − | 0.862972i | \(-0.331400\pi\) | ||||
0.505252 | + | 0.862972i | \(0.331400\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.76447e7 | 0.635988 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.81899e7 | −1.01075 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.77895e7 | −1.70451 | −0.852257 | − | 0.523123i | \(-0.824767\pi\) | ||||
−0.852257 | + | 0.523123i | \(0.824767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.74584e6 | −0.308690 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.69762e6 | −0.164942 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.40324e7 | −0.839439 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.09760e7 | −0.381399 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.51588e7 | 1.55302 | 0.776509 | − | 0.630107i | \(-0.216989\pi\) | ||||
0.776509 | + | 0.630107i | \(0.216989\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.44865e7 | −0.837756 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.70901e7 | 0.922067 | 0.461033 | − | 0.887383i | \(-0.347479\pi\) | ||||
0.461033 | + | 0.887383i | \(0.347479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.64976e7 | −0.558647 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.34630e7 | −1.45675 | −0.728373 | − | 0.685181i | \(-0.759723\pi\) | ||||
−0.728373 | + | 0.685181i | \(0.759723\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −82600.0 | −0.00275438 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.26423e7 | 0.419425 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.56037e6 | 0.216543 | 0.108272 | − | 0.994121i | \(-0.465468\pi\) | ||||
0.108272 | + | 0.994121i | \(0.465468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.28650e7 | 0.420355 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.07185e7 | −1.97392 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.72942e7 | −0.559391 | −0.279696 | − | 0.960089i | \(-0.590234\pi\) | ||||
−0.279696 | + | 0.960089i | \(0.590234\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.30309e7 | 0.419375 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.24107e7 | 0.714031 | 0.357015 | − | 0.934098i | \(-0.383794\pi\) | ||||
0.357015 | + | 0.934098i | \(0.383794\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.19254e7 | 1.32912 |
(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 | 400.6.a.s.1.2 | 2 | ||
4.3 | odd | 2 | 100.6.a.d.1.1 | 2 | |||
5.2 | odd | 4 | 80.6.c.b.49.1 | 2 | |||
5.3 | odd | 4 | 80.6.c.b.49.2 | 2 | |||
5.4 | even | 2 | inner | 400.6.a.s.1.1 | 2 | ||
12.11 | even | 2 | 900.6.a.q.1.2 | 2 | |||
15.2 | even | 4 | 720.6.f.d.289.1 | 2 | |||
15.8 | even | 4 | 720.6.f.d.289.2 | 2 | |||
20.3 | even | 4 | 20.6.c.a.9.1 | ✓ | 2 | ||
20.7 | even | 4 | 20.6.c.a.9.2 | yes | 2 | ||
20.19 | odd | 2 | 100.6.a.d.1.2 | 2 | |||
40.3 | even | 4 | 320.6.c.e.129.2 | 2 | |||
40.13 | odd | 4 | 320.6.c.d.129.1 | 2 | |||
40.27 | even | 4 | 320.6.c.e.129.1 | 2 | |||
40.37 | odd | 4 | 320.6.c.d.129.2 | 2 | |||
60.23 | odd | 4 | 180.6.d.b.109.2 | 2 | |||
60.47 | odd | 4 | 180.6.d.b.109.1 | 2 | |||
60.59 | even | 2 | 900.6.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.6.c.a.9.1 | ✓ | 2 | 20.3 | even | 4 | ||
20.6.c.a.9.2 | yes | 2 | 20.7 | even | 4 | ||
80.6.c.b.49.1 | 2 | 5.2 | odd | 4 | |||
80.6.c.b.49.2 | 2 | 5.3 | odd | 4 | |||
100.6.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
100.6.a.d.1.2 | 2 | 20.19 | odd | 2 | |||
180.6.d.b.109.1 | 2 | 60.47 | odd | 4 | |||
180.6.d.b.109.2 | 2 | 60.23 | odd | 4 | |||
320.6.c.d.129.1 | 2 | 40.13 | odd | 4 | |||
320.6.c.d.129.2 | 2 | 40.37 | odd | 4 | |||
320.6.c.e.129.1 | 2 | 40.27 | even | 4 | |||
320.6.c.e.129.2 | 2 | 40.3 | even | 4 | |||
400.6.a.s.1.1 | 2 | 5.4 | even | 2 | inner | ||
400.6.a.s.1.2 | 2 | 1.1 | even | 1 | trivial | ||
720.6.f.d.289.1 | 2 | 15.2 | even | 4 | |||
720.6.f.d.289.2 | 2 | 15.8 | even | 4 | |||
900.6.a.q.1.1 | 2 | 60.59 | even | 2 | |||
900.6.a.q.1.2 | 2 | 12.11 | even | 2 |