Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, 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("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 7) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −25.6495 | −1.64542 | −0.822708 | − | 0.568464i | \(-0.807538\pi\) | ||||
−0.822708 | + | 0.568464i | \(0.807538\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −28.7492 | −0.514281 | −0.257140 | − | 0.966374i | \(-0.582780\pi\) | ||||
−0.257140 | + | 0.966374i | \(0.582780\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 414.897 | 1.70740 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 270.090 | 0.673018 | 0.336509 | − | 0.941680i | \(-0.390754\pi\) | ||||
0.336509 | + | 0.941680i | \(0.390754\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −300.640 | −0.493387 | −0.246694 | − | 0.969094i | \(-0.579344\pi\) | ||||
−0.246694 | + | 0.969094i | \(0.579344\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 737.402 | 0.846206 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −613.106 | −0.514533 | −0.257267 | − | 0.966340i | \(-0.582822\pi\) | ||||
−0.257267 | + | 0.966340i | \(0.582822\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1700.95 | −1.08095 | −0.540477 | − | 0.841359i | \(-0.681756\pi\) | ||||
−0.540477 | + | 0.841359i | \(0.681756\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3188.15 | −1.25667 | −0.628333 | − | 0.777945i | \(-0.716262\pi\) | ||||
−0.628333 | + | 0.777945i | \(0.716262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2298.49 | −0.735515 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4409.07 | −1.16396 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4299.28 | 0.949294 | 0.474647 | − | 0.880176i | \(-0.342576\pi\) | ||||
0.474647 | + | 0.880176i | \(0.342576\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2028.46 | 0.379106 | 0.189553 | − | 0.981870i | \(-0.439296\pi\) | ||||
0.189553 | + | 0.981870i | \(0.439296\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6927.67 | −1.10739 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5154.46 | 0.618983 | 0.309491 | − | 0.950902i | \(-0.399841\pi\) | ||||
0.309491 | + | 0.950902i | \(0.399841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7711.26 | 0.811827 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7146.21 | 0.663921 | 0.331960 | − | 0.943293i | \(-0.392290\pi\) | ||||
0.331960 | + | 0.943293i | \(0.392290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19584.3 | 1.61524 | 0.807620 | − | 0.589703i | \(-0.200755\pi\) | ||||
0.807620 | + | 0.589703i | \(0.200755\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11927.9 | −0.878081 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 19998.4 | 1.32054 | 0.660268 | − | 0.751030i | \(-0.270443\pi\) | ||||
0.660268 | + | 0.751030i | \(0.270443\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15725.9 | 0.846621 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3948.82 | 0.193098 | 0.0965489 | − | 0.995328i | \(-0.469220\pi\) | ||||
0.0965489 | + | 0.995328i | \(0.469220\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7764.86 | −0.346120 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 43628.5 | 1.77862 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −29707.6 | −1.11106 | −0.555530 | − | 0.831497i | \(-0.687484\pi\) | ||||
−0.555530 | + | 0.831497i | \(0.687484\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 50519.3 | 1.73833 | 0.869165 | − | 0.494522i | \(-0.164657\pi\) | ||||
0.869165 | + | 0.494522i | \(0.164657\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8643.14 | 0.253740 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5053.56 | −0.137534 | −0.0687671 | − | 0.997633i | \(-0.521907\pi\) | ||||
−0.0687671 | + | 0.997633i | \(0.521907\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 81774.5 | 2.06774 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −32853.3 | −0.773453 | −0.386726 | − | 0.922195i | \(-0.626394\pi\) | ||||
−0.386726 | + | 0.922195i | \(0.626394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11115.0 | 0.244119 | 0.122059 | − | 0.992523i | \(-0.461050\pi\) | ||||
0.122059 | + | 0.992523i | \(0.461050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 58955.0 | 1.21023 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −81889.4 | −1.47625 | −0.738125 | − | 0.674664i | \(-0.764288\pi\) | ||||
−0.738125 | + | 0.674664i | \(0.764288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 12270.6 | 0.207803 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 118234. | 1.88385 | 0.941926 | − | 0.335819i | \(-0.109013\pi\) | ||||
0.941926 | + | 0.335819i | \(0.109013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17626.3 | 0.264615 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −110274. | −1.56198 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 41695.4 | 0.557972 | 0.278986 | − | 0.960295i | \(-0.410002\pi\) | ||||
0.278986 | + | 0.960295i | \(0.410002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −52028.9 | −0.623788 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 48900.9 | 0.555914 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −43682.8 | −0.471391 | −0.235695 | − | 0.971827i | \(-0.575737\pi\) | ||||
−0.235695 | + | 0.971827i | \(0.575737\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 112059. | 1.14911 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −25648.1 | −0.250179 | −0.125090 | − | 0.992145i | \(-0.539922\pi\) | ||||
−0.125090 | + | 0.992145i | \(0.539922\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14320.0 | −0.133000 | −0.0664999 | − | 0.997786i | \(-0.521183\pi\) | ||||
−0.0664999 | + | 0.997786i | \(0.521183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17201.8 | −0.145249 | −0.0726247 | − | 0.997359i | \(-0.523138\pi\) | ||||
−0.0726247 | + | 0.997359i | \(0.523138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −86017.6 | −0.693459 | −0.346730 | − | 0.937965i | \(-0.612708\pi\) | ||||
−0.346730 | + | 0.937965i | \(0.612708\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −132209. | −1.01848 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 137568. | 1.01349 | 0.506745 | − | 0.862096i | \(-0.330848\pi\) | ||||
0.506745 | + | 0.862096i | \(0.330848\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 91656.8 | 0.646279 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −124734. | −0.842407 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −88102.5 | −0.547047 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −183297. | −1.09243 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 155921. | 0.892542 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 70567.1 | 0.388233 | 0.194117 | − | 0.980978i | \(-0.437816\pi\) | ||||
0.194117 | + | 0.980978i | \(0.437816\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −502328. | −2.65774 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −173712. | −0.884408 | −0.442204 | − | 0.896914i | \(-0.645803\pi\) | ||||
−0.442204 | + | 0.896914i | \(0.645803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 126757. | 0.598602 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1989.94 | −0.00905813 | −0.00452907 | − | 0.999990i | \(-0.501442\pi\) | ||||
−0.00452907 | + | 0.999990i | \(0.501442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 366409. | 1.60853 | 0.804264 | − | 0.594272i | \(-0.202560\pi\) | ||||
0.804264 | + | 0.594272i | \(0.202560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −512949. | −2.17283 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −81199.7 | −0.332058 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −123601. | −0.488204 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 140719. | 0.519261 | 0.259631 | − | 0.965708i | \(-0.416399\pi\) | ||||
0.259631 | + | 0.965708i | \(0.416399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −50064.6 | −0.178685 | −0.0893425 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893425 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −254376. | −0.878512 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −58316.4 | −0.194967 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 89794.6 | 0.290738 | 0.145369 | − | 0.989378i | \(-0.453563\pi\) | ||||
0.145369 | + | 0.989378i | \(0.453563\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −101285. | −0.317726 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 481230. | 1.41868 | 0.709339 | − | 0.704867i | \(-0.248994\pi\) | ||||
0.709339 | + | 0.704867i | \(0.248994\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 199165. | 0.569512 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −86572.7 | −0.240209 | −0.120105 | − | 0.992761i | \(-0.538323\pi\) | ||||
−0.120105 | + | 0.992761i | \(0.538323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −280909. | −0.756569 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −705718. | −1.84562 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 58137.4 | 0.147686 | 0.0738432 | − | 0.997270i | \(-0.476474\pi\) | ||||
0.0738432 | + | 0.997270i | \(0.476474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 761985. | 1.82816 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 209380. | 0.488431 | 0.244215 | − | 0.969721i | \(-0.421470\pi\) | ||||
0.244215 | + | 0.969721i | \(0.421470\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −278996. | −0.632996 | −0.316498 | − | 0.948593i | \(-0.602507\pi\) | ||||
−0.316498 | + | 0.948593i | \(0.602507\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.29579e6 | −2.86028 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −148186. | −0.318331 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −165594. | −0.346290 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 445132. | 0.882888 | 0.441444 | − | 0.897289i | \(-0.354466\pi\) | ||||
0.441444 | + | 0.897289i | \(0.354466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −726811. | −1.40452 | −0.702260 | − | 0.711920i | \(-0.747826\pi\) | ||||
−0.702260 | + | 0.711920i | \(0.747826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −221692. | −0.417507 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −364897. | −0.669892 | −0.334946 | − | 0.942237i | \(-0.608718\pi\) | ||||
−0.334946 | + | 0.942237i | \(0.608718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 289307. | 0.517877 | 0.258938 | − | 0.965894i | \(-0.416627\pi\) | ||||
0.258938 | + | 0.965894i | \(0.416627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 129621. | 0.226301 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −205448. | −0.341442 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.32276e6 | −2.14562 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −459409. | −0.727501 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −750147. | −1.15995 | −0.579976 | − | 0.814633i | \(-0.696938\pi\) | ||||
−0.579976 | + | 0.814633i | \(0.696938\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 842672. | 1.27265 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −563033. | −0.830687 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −285093. | −0.401677 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 184324. | 0.253864 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 534398. | 0.719619 | 0.359810 | − | 0.933026i | \(-0.382842\pi\) | ||||
0.359810 | + | 0.933026i | \(0.382842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −953635. | −1.25582 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −410624. | −0.528907 | −0.264453 | − | 0.964398i | \(-0.585192\pi\) | ||||
−0.264453 | + | 0.964398i | \(0.585192\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.03036e6 | −1.29838 | −0.649189 | − | 0.760627i | \(-0.724892\pi\) | ||||
−0.649189 | + | 0.760627i | \(0.724892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −119211. | −0.143856 | −0.0719278 | − | 0.997410i | \(-0.522915\pi\) | ||||
−0.0719278 | + | 0.997410i | \(0.522915\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −574937. | −0.679127 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.10042e6 | 2.42905 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 254090. | 0.287735 | 0.143868 | − | 0.989597i | \(-0.454046\pi\) | ||||
0.143868 | + | 0.989597i | \(0.454046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.41251e6 | −1.56656 | −0.783282 | − | 0.621667i | \(-0.786456\pi\) | ||||
−0.783282 | + | 0.621667i | \(0.786456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 756671. | 0.822037 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 511372. | 0.533329 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.03264e6 | −3.09972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.67542e6 | −1.67857 | −0.839286 | − | 0.543690i | \(-0.817027\pi\) | ||||
−0.839286 | + | 0.543690i | \(0.817027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −861087. | −0.845758 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −452106. | −0.435401 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −726996. | −0.686593 | −0.343296 | − | 0.939227i | \(-0.611544\pi\) | ||||
−0.343296 | + | 0.939227i | \(0.611544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.78376e6 | 1.62082 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 225880. | 0.201367 | 0.100684 | − | 0.994918i | \(-0.467897\pi\) | ||||
0.100684 | + | 0.994918i | \(0.467897\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −113525. | −0.0993065 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.06947e6 | −0.918097 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.80527e6 | −1.52111 | −0.760557 | − | 0.649272i | \(-0.775074\pi\) | ||||
−0.760557 | + | 0.649272i | \(0.775074\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.71380e6 | −1.41754 | −0.708771 | − | 0.705439i | \(-0.750750\pi\) | ||||
−0.708771 | + | 0.705439i | \(0.750750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −620797. | −0.495015 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.23055e6 | 1.74668 | 0.873338 | − | 0.487115i | \(-0.161951\pi\) | ||||
0.873338 | + | 0.487115i | \(0.161951\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 841600. | 0.647285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.67140e6 | 1.26274 | 0.631371 | − | 0.775481i | \(-0.282493\pi\) | ||||
0.631371 | + | 0.775481i | \(0.282493\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −396152. | −0.294033 | −0.147016 | − | 0.989134i | \(-0.546967\pi\) | ||||
−0.147016 | + | 0.989134i | \(0.546967\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.25428e6 | −0.914710 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.04396e6 | −0.735256 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.12044e6 | 0.775634 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 929465. | 0.632505 | 0.316252 | − | 0.948675i | \(-0.397575\pi\) | ||||
0.316252 | + | 0.948675i | \(0.397575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 854068. | 0.571397 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.19085e6 | −0.783365 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 958485. | 0.620022 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 657860. | 0.411649 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.45239e6 | −0.893990 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.83295e6 | 1.10995 | 0.554976 | − | 0.831866i | \(-0.312727\pi\) | ||||
0.554976 | + | 0.831866i | \(0.312727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 367302. | 0.218840 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.29685e6 | −1.34658 | −0.673289 | − | 0.739379i | \(-0.735119\pi\) | ||||
−0.673289 | + | 0.739379i | \(0.735119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.42470e6 | 1.97589 | 0.987943 | − | 0.154817i | \(-0.0494787\pi\) | ||||
0.987943 | + | 0.154817i | \(0.0494787\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.94305e6 | 1.64494 | 0.822470 | − | 0.568808i | \(-0.192595\pi\) | ||||
0.822470 | + | 0.568808i | \(0.192595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.16119e6 | 0.638891 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 441217. | 0.238996 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.04286e6 | 0.556187 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 691016. | 0.362894 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.20631e6 | 1.14103 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −966164. | −0.484709 | −0.242354 | − | 0.970188i | \(-0.577920\pi\) | ||||
−0.242354 | + | 0.970188i | \(0.577920\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.13857e6 | 1.05685 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 145286. | 0.0707312 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 136417. | 0.0654327 | 0.0327163 | − | 0.999465i | \(-0.489584\pi\) | ||||
0.0327163 | + | 0.999465i | \(0.489584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.52854e6 | −1.66761 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 547865. | 0.255145 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.35095e6 | −1.06340 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −355408. | −0.158454 | −0.0792270 | − | 0.996857i | \(-0.525245\pi\) | ||||
−0.0792270 | + | 0.996857i | \(0.525245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 140128. | 0.0615830 | 0.0307915 | − | 0.999526i | \(-0.490197\pi\) | ||||
0.0307915 | + | 0.999526i | \(0.490197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.32554e6 | 0.574283 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.48141e6 | −1.48703 | −0.743514 | − | 0.668721i | \(-0.766842\pi\) | ||||
−0.743514 | + | 0.668721i | \(0.766842\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 944507. | 0.397772 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.75285e6 | −0.717810 | −0.358905 | − | 0.933374i | \(-0.616850\pi\) | ||||
−0.358905 | + | 0.933374i | \(0.616850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 417127. | 0.168461 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.25979e6 | 0.900121 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −319546. | −0.125546 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.76939e6 | −0.685738 | −0.342869 | − | 0.939383i | \(-0.611399\pi\) | ||||
−0.342869 | + | 0.939383i | \(0.611399\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.96494e6 | 1.13357 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.16212e6 | −1.54897 | −0.774485 | − | 0.632592i | \(-0.781991\pi\) | ||||
−0.774485 | + | 0.632592i | \(0.781991\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.99929e6 | −1.46860 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.29253e6 | −0.468369 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −618163. | −0.221057 | −0.110529 | − | 0.993873i | \(-0.535254\pi\) | ||||
−0.110529 | + | 0.993873i | \(0.535254\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.81001e6 | −0.638805 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.11163e6 | −1.43225 | −0.716123 | − | 0.697974i | \(-0.754085\pi\) | ||||
−0.716123 | + | 0.697974i | \(0.754085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.12547e6 | 2.75785 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.62076e6 | 1.54824 | 0.774122 | − | 0.633037i | \(-0.218192\pi\) | ||||
0.774122 | + | 0.633037i | \(0.218192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.95468e6 | 0.646596 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.45564e6 | 1.45522 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.35425e6 | 0.759207 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.07349e6 | −1.61559 | −0.807794 | − | 0.589465i | \(-0.799339\pi\) | ||||
−0.807794 | + | 0.589465i | \(0.799339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.48056e6 | −0.459795 | −0.229898 | − | 0.973215i | \(-0.573839\pi\) | ||||
−0.229898 | + | 0.973215i | \(0.573839\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −609834. | −0.187046 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −352768. | −0.106869 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.39217e6 | 0.416586 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.53379e6 | 1.34015 | 0.670075 | − | 0.742294i | \(-0.266262\pi\) | ||||
0.670075 | + | 0.742294i | \(0.266262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 51041.0 | 0.0149044 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.39913e6 | −0.968829 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.39820e6 | −2.64670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 111026. | 0.0308952 | 0.0154476 | − | 0.999881i | \(-0.495083\pi\) | ||||
0.0154476 | + | 0.999881i | \(0.495083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.41151e6 | −0.388132 | −0.194066 | − | 0.980988i | \(-0.562168\pi\) | ||||
−0.194066 | + | 0.980988i | \(0.562168\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.29727e6 | 2.25468 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.40922e6 | 0.378447 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.08273e6 | 0.546374 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.07640e6 | −0.279113 | −0.139557 | − | 0.990214i | \(-0.544568\pi\) | ||||
−0.139557 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 310172. | 0.0795029 | 0.0397515 | − | 0.999210i | \(-0.487343\pi\) | ||||
0.0397515 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.17030e6 | 0.803298 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.42288e6 | 1.35840 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.67650e6 | 1.40579 | 0.702893 | − | 0.711296i | \(-0.251891\pi\) | ||||
0.702893 | + | 0.711296i | \(0.251891\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.05966e6 | −0.982834 | −0.491417 | − | 0.870924i | \(-0.663521\pi\) | ||||
−0.491417 | + | 0.870924i | \(0.663521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.19871e6 | −0.286955 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.60936e6 | −0.854401 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.96544e6 | −1.63054 | −0.815272 | − | 0.579078i | \(-0.803413\pi\) | ||||
−0.815272 | + | 0.579078i | \(0.803413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.93012e6 | 0.446830 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.28413e6 | 0.294011 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.79523e6 | 0.402096 | 0.201048 | − | 0.979581i | \(-0.435565\pi\) | ||||
0.201048 | + | 0.979581i | \(0.435565\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.70323e6 | 0.598896 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.11294e6 | 0.463058 | 0.231529 | − | 0.972828i | \(-0.425627\pi\) | ||||
0.231529 | + | 0.972828i | \(0.425627\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.26223e6 | −0.273643 | −0.136822 | − | 0.990596i | \(-0.543689\pi\) | ||||
−0.136822 | + | 0.990596i | \(0.543689\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.49579e6 | 0.320802 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.58926e6 | −0.761576 | −0.380788 | − | 0.924662i | \(-0.624347\pi\) | ||||
−0.380788 | + | 0.924662i | \(0.624347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.30319e6 | −0.478384 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.28952e6 | 1.08708 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.90960e6 | 0.795058 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.63835e6 | 0.329694 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.41693e6 | −0.481311 | −0.240655 | − | 0.970611i | \(-0.577362\pi\) | ||||
−0.240655 | + | 0.970611i | \(0.577362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.54963e6 | −0.305398 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.25584e6 | 0.242427 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.19403e6 | 0.992388 | 0.496194 | − | 0.868212i | \(-0.334730\pi\) | ||||
0.496194 | + | 0.868212i | \(0.334730\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.23433e7 | −2.33432 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.38961e6 | −1.00891 | −0.504456 | − | 0.863437i | \(-0.668307\pi\) | ||||
−0.504456 | + | 0.863437i | \(0.668307\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.63592e6 | −0.488443 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.22162e6 | −0.590964 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.29606e6 | 0.592576 | 0.296288 | − | 0.955099i | \(-0.404251\pi\) | ||||
0.296288 | + | 0.955099i | \(0.404251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.22055e6 | 0.395244 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.06512e7 | −1.87706 | −0.938528 | − | 0.345204i | \(-0.887810\pi\) | ||||
−0.938528 | + | 0.345204i | \(0.887810\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 737361. | 0.128662 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.20517e6 | 1.24487 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.74268e6 | 0.469225 | 0.234612 | − | 0.972089i | \(-0.424618\pi\) | ||||
0.234612 | + | 0.972089i | \(0.424618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.49961e6 | 1.25819 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 411689. | 0.0683992 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.40136e6 | 0.888744 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.49120e6 | −0.243006 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.97077e6 | −0.802286 | −0.401143 | − | 0.916015i | \(-0.631387\pi\) | ||||
−0.401143 | + | 0.916015i | \(0.631387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.41579e6 | 0.386193 | 0.193096 | − | 0.981180i | \(-0.438147\pi\) | ||||
0.193096 | + | 0.981180i | \(0.438147\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.24366e6 | −0.195063 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.72798e6 | 0.579207 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.23256e7 | −1.89702 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.14843e6 | −0.327570 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 494537. | 0.0746989 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.37050e6 | −0.803672 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 472165. | 0.0693587 | 0.0346794 | − | 0.999398i | \(-0.488959\pi\) | ||||
0.0346794 | + | 0.999398i | \(0.488959\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.15610e6 | 1.04154 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.47293e6 | 0.356633 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.63716e6 | −1.09135 | −0.545675 | − | 0.837997i | \(-0.683727\pi\) | ||||
−0.545675 | + | 0.837997i | \(0.683727\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.09603e7 | 2.96802 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.31285e6 | −1.02614 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.80091e6 | 0.523787 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.48807e6 | −0.612946 | −0.306473 | − | 0.951879i | \(-0.599149\pi\) | ||||
−0.306473 | + | 0.951879i | \(0.599149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.88782e6 | −0.796938 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.24740e6 | 0.569791 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.16500e6 | −0.287864 | −0.143932 | − | 0.989588i | \(-0.545975\pi\) | ||||
−0.143932 | + | 0.989588i | \(0.545975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.95495e6 | −0.521219 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.13325e7 | −1.46739 | −0.733696 | − | 0.679478i | \(-0.762206\pi\) | ||||
−0.733696 | + | 0.679478i | \(0.762206\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 843773. | 0.108302 | 0.0541509 | − | 0.998533i | \(-0.482755\pi\) | ||||
0.0541509 | + | 0.998533i | \(0.482755\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.14174e7 | −1.45272 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.32792e6 | 0.924296 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.23784e6 | 0.279827 | 0.139914 | − | 0.990164i | \(-0.455318\pi\) | ||||
0.139914 | + | 0.990164i | \(0.455318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.86423e7 | 2.31102 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.06653e6 | 0.129958 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.58601e6 | 0.433234 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.21190e7 | 1.45168 | 0.725839 | − | 0.687864i | \(-0.241452\pi\) | ||||
0.725839 | + | 0.687864i | \(0.241452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.45030e6 | −0.409797 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.35942e6 | 1.10225 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.00167e6 | −0.934424 | −0.467212 | − | 0.884145i | \(-0.654742\pi\) | ||||
−0.467212 | + | 0.884145i | \(0.654742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.42058e6 | −0.852123 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.45899e7 | −1.66144 | −0.830719 | − | 0.556692i | \(-0.812070\pi\) | ||||
−0.830719 | + | 0.556692i | \(0.812070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.67178e6 | 0.979314 | 0.489657 | − | 0.871915i | \(-0.337122\pi\) | ||||
0.489657 | + | 0.871915i | \(0.337122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.09671e6 | −0.234825 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.53287e6 | 0.281336 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.33059e7 | −1.46580 | −0.732898 | − | 0.680339i | \(-0.761833\pi\) | ||||
−0.732898 | + | 0.680339i | \(0.761833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.01231e6 | −0.651536 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.35101e6 | 0.252699 | 0.126350 | − | 0.991986i | \(-0.459674\pi\) | ||||
0.126350 | + | 0.991986i | \(0.459674\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.26963e6 | 0.561814 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.63523e6 | 1.01894 | 0.509470 | − | 0.860488i | \(-0.329841\pi\) | ||||
0.509470 | + | 0.860488i | \(0.329841\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.86148e6 | −0.509967 | −0.254983 | − | 0.966945i | \(-0.582070\pi\) | ||||
−0.254983 | + | 0.966945i | \(0.582070\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.40568e7 | 1.46271 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.70017e6 | 0.276498 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.17836e7 | 1.19704 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.16023e6 | −0.318487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.59770e6 | 0.659659 | 0.329829 | − | 0.944041i | \(-0.393009\pi\) | ||||
0.329829 | + | 0.944041i | \(0.393009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.92409e7 | 1.90860 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.02874e6 | −0.199661 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.36308e7 | −1.32059 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.44525e7 | 1.38930 | 0.694651 | − | 0.719347i | \(-0.255559\pi\) | ||||
0.694651 | + | 0.719347i | \(0.255559\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.54720e7 | −1.47577 | −0.737886 | − | 0.674926i | \(-0.764176\pi\) | ||||
−0.737886 | + | 0.674926i | \(0.764176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.44415e7 | 1.36683 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.66647e7 | 1.56508 | 0.782540 | − | 0.622601i | \(-0.213924\pi\) | ||||
0.782540 | + | 0.622601i | \(0.213924\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.02371e6 | −0.747762 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.33451e7 | −1.22472 | −0.612361 | − | 0.790578i | \(-0.709780\pi\) | ||||
−0.612361 | + | 0.790578i | \(0.709780\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.99409e6 | 0.454834 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.61157e6 | 0.416807 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.00667e6 | 0.359393 | 0.179697 | − | 0.983722i | \(-0.442488\pi\) | ||||
0.179697 | + | 0.983722i | \(0.442488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.08005e7 | −0.961478 | −0.480739 | − | 0.876864i | \(-0.659632\pi\) | ||||
−0.480739 | + | 0.876864i | \(0.659632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.72782e6 | −0.417712 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.37068e7 | −1.19294 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.37070e7 | −1.18407 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.36447e7 | 1.16993 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.09119e7 | 0.928676 | 0.464338 | − | 0.885658i | \(-0.346292\pi\) | ||||
0.464338 | + | 0.885658i | \(0.346292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.01342e7 | 0.856110 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.35765e7 | 1.13846 | 0.569229 | − | 0.822179i | \(-0.307242\pi\) | ||||
0.569229 | + | 0.822179i | \(0.307242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.05323e7 | 0.870272 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.26726e7 | 1.03948 | 0.519738 | − | 0.854326i | \(-0.326030\pi\) | ||||
0.519738 | + | 0.854326i | \(0.326030\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57209.2 | 0.00465843 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.64283e7 | 2.13637 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.18717e6 | −0.0952720 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.11964e6 | 0.567235 | 0.283617 | − | 0.958938i | \(-0.408465\pi\) | ||||
0.283617 | + | 0.958938i | \(0.408465\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.05339e7 | −0.827235 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.38139e6 | −0.341609 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.05770e6 | 0.236702 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.00155e7 | −0.769803 | −0.384902 | − | 0.922958i | \(-0.625765\pi\) | ||||
−0.384902 | + | 0.922958i | \(0.625765\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.76746e6 | −0.669092 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.47469e7 | 1.11745 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.84454e6 | −0.660784 | −0.330392 | − | 0.943844i | \(-0.607181\pi\) | ||||
−0.330392 | + | 0.943844i | \(0.607181\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.39757e7 | −2.52054 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.46703e6 | −0.476410 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.33442e6 | 0.170771 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.51728e6 | −0.473444 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.58086e6 | 0.474745 | 0.237373 | − | 0.971419i | \(-0.423714\pi\) | ||||
0.237373 | + | 0.971419i | \(0.423714\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.62301e7 | 2.57765 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.88183e6 | −0.698220 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.88401e7 | 1.32205 | 0.661023 | − | 0.750365i | \(-0.270122\pi\) | ||||
0.661023 | + | 0.750365i | \(0.270122\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.23900e7 | −1.56040 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.20073e7 | −0.831095 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.78330e6 | 0.191337 | 0.0956687 | − | 0.995413i | \(-0.469501\pi\) | ||||
0.0956687 | + | 0.995413i | \(0.469501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.36491e6 | −0.0925629 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.48970e7 | 1.67701 | 0.838505 | − | 0.544894i | \(-0.183430\pi\) | ||||
0.838505 | + | 0.544894i | \(0.183430\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.31164e7 | −0.877548 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.86085e6 | 0.256573 | 0.128286 | − | 0.991737i | \(-0.459052\pi\) | ||||
0.128286 | + | 0.991737i | \(0.459052\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.04554e6 | −0.267046 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.90549e7 | 3.21648 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.72737e6 | −0.435257 | −0.217628 | − | 0.976032i | \(-0.569832\pi\) | ||||
−0.217628 | + | 0.976032i | \(0.569832\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.29737e7 | 2.76195 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.43932e6 | 0.0918943 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.17782e7 | 1.38128 | 0.690642 | − | 0.723197i | \(-0.257328\pi\) | ||||
0.690642 | + | 0.723197i | \(0.257328\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.20865e7 | 1.39162 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.57074e7 | 1.60915 | 0.804575 | − | 0.593851i | \(-0.202393\pi\) | ||||
0.804575 | + | 0.593851i | \(0.202393\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.31310e6 | 0.451802 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.93127e6 | 0.548182 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.34375e7 | 0.819413 | 0.409706 | − | 0.912217i | \(-0.365631\pi\) | ||||
0.409706 | + | 0.912217i | \(0.365631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.86471e7 | 1.12973 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.05572e7 | −1.83935 | −0.919674 | − | 0.392682i | \(-0.871547\pi\) | ||||
−0.919674 | + | 0.392682i | \(0.871547\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.66237e6 | −0.278839 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.21553e7 | −0.717667 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.87335e6 | −0.520547 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.89558e7 | −1.10494 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.58152e6 | −0.149521 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.07672e6 | −0.119520 | −0.0597602 | − | 0.998213i | \(-0.519034\pi\) | ||||
−0.0597602 | + | 0.998213i | \(0.519034\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.79372e6 | −0.331333 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.51881e7 | −0.857670 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.91187e6 | 0.163401 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.98563e6 | 0.333783 | 0.166892 | − | 0.985975i | \(-0.446627\pi\) | ||||
0.166892 | + | 0.985975i | \(0.446627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.22611e7 | −0.679460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.72993e7 | 0.952679 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.00204e6 | 0.164296 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.63043e7 | 2.50286 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.96864e7 | 1.05754 | 0.528769 | − | 0.848766i | \(-0.322654\pi\) | ||||
0.528769 | + | 0.848766i | \(0.322654\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.50101e6 | 0.453856 | 0.226928 | − | 0.973912i | \(-0.427132\pi\) | ||||
0.226928 | + | 0.973912i | \(0.427132\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.39580e7 | 2.33245 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.38350e7 | −0.729599 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.33119e7 | −1.74600 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.36199e6 | −0.0705204 | −0.0352602 | − | 0.999378i | \(-0.511226\pi\) | ||||
−0.0352602 | + | 0.999378i | \(0.511226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.35934e6 | 0.0699566 | 0.0349783 | − | 0.999388i | \(-0.488864\pi\) | ||||
0.0349783 | + | 0.999388i | \(0.488864\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.59231e7 | 0.814505 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.00727e7 | −0.512132 | −0.256066 | − | 0.966659i | \(-0.582426\pi\) | ||||
−0.256066 | + | 0.966659i | \(0.582426\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.63984e6 | 0.285023 | 0.142512 | − | 0.989793i | \(-0.454482\pi\) | ||||
0.142512 | + | 0.989793i | \(0.454482\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.72125e7 | −2.87401 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.48889e6 | 0.123535 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.94361e6 | −0.441265 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.16351e7 | −0.570642 | −0.285321 | − | 0.958432i | \(-0.592100\pi\) | ||||
−0.285321 | + | 0.958432i | \(0.592100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.02735e6 | −0.0988413 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.28706e7 | −2.07774 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.07590e6 | 0.389089 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.01611e7 | 0.483806 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.64332e7 | −0.777854 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.85205e7 | −1.34210 | −0.671049 | − | 0.741413i | \(-0.734156\pi\) | ||||
−0.671049 | + | 0.741413i | \(0.734156\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.02888e7 | 0.949165 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.95725e6 | 0.463113 | 0.231557 | − | 0.972821i | \(-0.425618\pi\) | ||||
0.231557 | + | 0.972821i | \(0.425618\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.49322e7 | −0.690463 | −0.345232 | − | 0.938517i | \(-0.612200\pi\) | ||||
−0.345232 | + | 0.938517i | \(0.612200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.84933e7 | −1.75937 | −0.879687 | − | 0.475553i | \(-0.842248\pi\) | ||||
−0.879687 | + | 0.475553i | \(0.842248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.67140e6 | −0.0759523 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.67770e7 | 1.20980 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.21175e7 | −0.993542 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.51930e6 | 0.0678576 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.81239e7 | −0.804850 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.40311e6 | 0.412831 | 0.206416 | − | 0.978464i | \(-0.433820\pi\) | ||||
0.206416 | + | 0.978464i | \(0.433820\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.38403e7 | −1.04073 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.10395e6 | −0.0479194 | −0.0239597 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239597 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.06579e6 | −0.348133 | −0.174067 | − | 0.984734i | \(-0.555691\pi\) | ||||
−0.174067 | + | 0.984734i | \(0.555691\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.19064e7 | −0.940185 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.49902e7 | −0.639732 | −0.319866 | − | 0.947463i | \(-0.603638\pi\) | ||||
−0.319866 | + | 0.947463i | \(0.603638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.31415e6 | 0.139855 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.40162e7 | −1.42744 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.01950e6 | −0.251190 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.45847e7 | −1.02019 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.72090e6 | 0.359883 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.42104e6 | −0.0993553 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.02089e6 | 0.325538 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.12622e6 | −0.166546 | −0.0832730 | − | 0.996527i | \(-0.526537\pi\) | ||||
−0.0832730 | + | 0.996527i | \(0.526537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.06413e7 | −0.427155 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.04272e7 | −1.61391 | −0.806953 | − | 0.590616i | \(-0.798885\pi\) | ||||
−0.806953 | + | 0.590616i | \(0.798885\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.19338e7 | 1.26787 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.72530e7 | 1.47099 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.18546e7 | −0.853600 | −0.426800 | − | 0.904346i | \(-0.640359\pi\) | ||||
−0.426800 | + | 0.904346i | \(0.640359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.70142e7 | −1.82633 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.87702e6 | 0.381612 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.18474e7 | −0.455271 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.94134e6 | −0.227083 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.06843e7 | −0.406169 | −0.203085 | − | 0.979161i | \(-0.565097\pi\) | ||||
−0.203085 | + | 0.979161i | \(0.565097\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.89130e7 | 2.21568 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.76068e6 | 0.178090 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.99105e7 | 1.48504 | 0.742521 | − | 0.669823i | \(-0.233630\pi\) | ||||
0.742521 | + | 0.669823i | \(0.233630\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.78419e7 | −3.25116 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.32350e6 | −0.0487248 | −0.0243624 | − | 0.999703i | \(-0.507756\pi\) | ||||
−0.0243624 | + | 0.999703i | \(0.507756\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.27832e7 | −0.834326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.76322e7 | 1.00124 | 0.500622 | − | 0.865666i | \(-0.333105\pi\) | ||||
0.500622 | + | 0.865666i | \(0.333105\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.34160e6 | −0.120445 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.54879e7 | −2.70661 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.07901e7 | −1.09819 | −0.549096 | − | 0.835759i | \(-0.685028\pi\) | ||||
−0.549096 | + | 0.835759i | \(0.685028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.27972e7 | −0.454053 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.97840e7 | −1.05124 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.45145e7 | −0.856278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.13697e6 | −0.247998 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.08952e7 | 0.722318 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.92557e6 | −0.100611 | −0.0503055 | − | 0.998734i | \(-0.516019\pi\) | ||||
−0.0503055 | + | 0.998734i | \(0.516019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.67489e7 | −0.915159 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.78109e6 | 0.0946601 | 0.0473301 | − | 0.998879i | \(-0.484929\pi\) | ||||
0.0473301 | + | 0.998879i | \(0.484929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.77242e7 | −0.597111 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.48673e6 | 0.250932 | 0.125466 | − | 0.992098i | \(-0.459957\pi\) | ||||
0.125466 | + | 0.992098i | \(0.459957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.12615e7 | 0.375525 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.56884e7 | −1.18401 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.79815e7 | 0.593528 | 0.296764 | − | 0.954951i | \(-0.404093\pi\) | ||||
0.296764 | + | 0.954951i | \(0.404093\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.04905e7 | 0.344512 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.24378e7 | −2.02982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.72778e7 | −1.20578 | −0.602888 | − | 0.797826i | \(-0.705983\pi\) | ||||
−0.602888 | + | 0.797826i | \(0.705983\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.47816e7 | 0.797548 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.31734e6 | −0.266334 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.87422e7 | −1.55298 | −0.776492 | − | 0.630128i | \(-0.783003\pi\) | ||||
−0.776492 | + | 0.630128i | \(0.783003\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.27264e7 | −0.720471 |
(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 | 784.6.a.v.1.1 | 2 | ||
4.3 | odd | 2 | 49.6.a.f.1.2 | 2 | |||
7.6 | odd | 2 | 112.6.a.h.1.2 | 2 | |||
12.11 | even | 2 | 441.6.a.l.1.1 | 2 | |||
21.20 | even | 2 | 1008.6.a.bq.1.1 | 2 | |||
28.3 | even | 6 | 49.6.c.e.30.1 | 4 | |||
28.11 | odd | 6 | 49.6.c.d.30.1 | 4 | |||
28.19 | even | 6 | 49.6.c.e.18.1 | 4 | |||
28.23 | odd | 6 | 49.6.c.d.18.1 | 4 | |||
28.27 | even | 2 | 7.6.a.b.1.2 | ✓ | 2 | ||
56.13 | odd | 2 | 448.6.a.u.1.1 | 2 | |||
56.27 | even | 2 | 448.6.a.w.1.2 | 2 | |||
84.83 | odd | 2 | 63.6.a.f.1.1 | 2 | |||
140.27 | odd | 4 | 175.6.b.c.99.4 | 4 | |||
140.83 | odd | 4 | 175.6.b.c.99.1 | 4 | |||
140.139 | even | 2 | 175.6.a.c.1.1 | 2 | |||
308.307 | odd | 2 | 847.6.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.b.1.2 | ✓ | 2 | 28.27 | even | 2 | ||
49.6.a.f.1.2 | 2 | 4.3 | odd | 2 | |||
49.6.c.d.18.1 | 4 | 28.23 | odd | 6 | |||
49.6.c.d.30.1 | 4 | 28.11 | odd | 6 | |||
49.6.c.e.18.1 | 4 | 28.19 | even | 6 | |||
49.6.c.e.30.1 | 4 | 28.3 | even | 6 | |||
63.6.a.f.1.1 | 2 | 84.83 | odd | 2 | |||
112.6.a.h.1.2 | 2 | 7.6 | odd | 2 | |||
175.6.a.c.1.1 | 2 | 140.139 | even | 2 | |||
175.6.b.c.99.1 | 4 | 140.83 | odd | 4 | |||
175.6.b.c.99.4 | 4 | 140.27 | odd | 4 | |||
441.6.a.l.1.1 | 2 | 12.11 | even | 2 | |||
448.6.a.u.1.1 | 2 | 56.13 | odd | 2 | |||
448.6.a.w.1.2 | 2 | 56.27 | even | 2 | |||
784.6.a.v.1.1 | 2 | 1.1 | even | 1 | trivial | ||
847.6.a.c.1.1 | 2 | 308.307 | odd | 2 | |||
1008.6.a.bq.1.1 | 2 | 21.20 | even | 2 |