Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(70.7292645375\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 146x^{6} + 5453x^{4} - 40868x^{2} + 3844 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 7^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.308653\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.12599 | −1.43649 | −0.718243 | − | 0.695792i | \(-0.755053\pi\) | ||||
−0.718243 | + | 0.695792i | \(0.755053\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 34.0317 | 1.06349 | ||||||||
\(5\) | 17.4201 | 0.311621 | 0.155811 | − | 0.987787i | \(-0.450201\pi\) | ||||
0.155811 | + | 0.987787i | \(0.450201\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −16.5098 | −0.0912047 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −141.556 | −0.447639 | ||||||||
\(11\) | 114.280 | 0.284765 | 0.142383 | − | 0.989812i | \(-0.454524\pi\) | ||||
0.142383 | + | 0.989812i | \(0.454524\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 205.240 | 0.336825 | 0.168413 | − | 0.985717i | \(-0.446136\pi\) | ||||
0.168413 | + | 0.985717i | \(0.446136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −954.857 | −0.932477 | ||||||||
\(17\) | −757.277 | −0.635524 | −0.317762 | − | 0.948170i | \(-0.602931\pi\) | ||||
−0.317762 | + | 0.948170i | \(0.602931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1013.65 | 0.644178 | 0.322089 | − | 0.946709i | \(-0.395615\pi\) | ||||
0.322089 | + | 0.946709i | \(0.395615\pi\) | |||||||
\(20\) | 592.838 | 0.331406 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −928.635 | −0.409061 | ||||||||
\(23\) | 916.299 | 0.361175 | 0.180587 | − | 0.983559i | \(-0.442200\pi\) | ||||
0.180587 | + | 0.983559i | \(0.442200\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2821.54 | −0.902892 | ||||||||
\(26\) | −1667.78 | −0.483845 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1095.47 | 0.241883 | 0.120942 | − | 0.992660i | \(-0.461409\pi\) | ||||
0.120942 | + | 0.992660i | \(0.461409\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8233.32 | −1.53876 | −0.769380 | − | 0.638791i | \(-0.779435\pi\) | ||||
−0.769380 | + | 0.638791i | \(0.779435\pi\) | |||||||
\(32\) | 8287.47 | 1.43070 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6153.62 | 0.912922 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10716.4 | −1.28690 | −0.643448 | − | 0.765490i | \(-0.722497\pi\) | ||||
−0.643448 | + | 0.765490i | \(0.722497\pi\) | |||||||
\(38\) | −8236.94 | −0.925352 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −287.604 | −0.0284213 | ||||||||
\(41\) | 18758.1 | 1.74273 | 0.871365 | − | 0.490636i | \(-0.163235\pi\) | ||||
0.871365 | + | 0.490636i | \(0.163235\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4643.49 | −0.382978 | −0.191489 | − | 0.981495i | \(-0.561332\pi\) | ||||
−0.191489 | + | 0.981495i | \(0.561332\pi\) | |||||||
\(44\) | 3889.13 | 0.302845 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7445.84 | −0.518823 | ||||||||
\(47\) | −13969.4 | −0.922428 | −0.461214 | − | 0.887289i | \(-0.652586\pi\) | ||||
−0.461214 | + | 0.887289i | \(0.652586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 22927.8 | 1.29699 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6984.69 | 0.358211 | ||||||||
\(53\) | 29306.0 | 1.43307 | 0.716533 | − | 0.697553i | \(-0.245728\pi\) | ||||
0.716533 | + | 0.697553i | \(0.245728\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1990.77 | 0.0887388 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8901.78 | −0.347462 | ||||||||
\(59\) | −30378.0 | −1.13613 | −0.568067 | − | 0.822983i | \(-0.692308\pi\) | ||||
−0.568067 | + | 0.822983i | \(0.692308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18658.2 | −0.642014 | −0.321007 | − | 0.947077i | \(-0.604021\pi\) | ||||
−0.321007 | + | 0.947077i | \(0.604021\pi\) | |||||||
\(62\) | 66903.9 | 2.21041 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −36788.5 | −1.12270 | ||||||||
\(65\) | 3575.32 | 0.104962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 19933.4 | 0.542493 | 0.271246 | − | 0.962510i | \(-0.412564\pi\) | ||||
0.271246 | + | 0.962510i | \(0.412564\pi\) | |||||||
\(68\) | −25771.4 | −0.675875 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 57338.5 | 1.34990 | 0.674948 | − | 0.737866i | \(-0.264166\pi\) | ||||
0.674948 | + | 0.737866i | \(0.264166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 60194.4 | 1.32205 | 0.661027 | − | 0.750362i | \(-0.270121\pi\) | ||||
0.661027 | + | 0.750362i | \(0.270121\pi\) | |||||||
\(74\) | 87081.2 | 1.84861 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 34496.4 | 0.685078 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35715.5 | 0.643857 | 0.321928 | − | 0.946764i | \(-0.395669\pi\) | ||||
0.321928 | + | 0.946764i | \(0.395669\pi\) | |||||||
\(80\) | −16633.7 | −0.290580 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −152428. | −2.50341 | ||||||||
\(83\) | 86641.2 | 1.38048 | 0.690239 | − | 0.723582i | \(-0.257506\pi\) | ||||
0.690239 | + | 0.723582i | \(0.257506\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13191.9 | −0.198043 | ||||||||
\(86\) | 37733.0 | 0.550142 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1886.73 | −0.0259719 | ||||||||
\(89\) | −42941.7 | −0.574651 | −0.287326 | − | 0.957833i | \(-0.592766\pi\) | ||||
−0.287326 | + | 0.957833i | \(0.592766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 31183.2 | 0.384107 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 113515. | 1.32506 | ||||||||
\(95\) | 17658.0 | 0.200739 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −20619.4 | −0.222508 | −0.111254 | − | 0.993792i | \(-0.535487\pi\) | ||||
−0.111254 | + | 0.993792i | \(0.535487\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −96021.8 | −0.960218 | ||||||||
\(101\) | −106588. | −1.03970 | −0.519848 | − | 0.854259i | \(-0.674012\pi\) | ||||
−0.519848 | + | 0.854259i | \(0.674012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −87392.9 | −0.811677 | −0.405839 | − | 0.913945i | \(-0.633020\pi\) | ||||
−0.405839 | + | 0.913945i | \(0.633020\pi\) | |||||||
\(104\) | −3388.48 | −0.0307201 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −238140. | −2.05858 | ||||||||
\(107\) | −39306.9 | −0.331902 | −0.165951 | − | 0.986134i | \(-0.553069\pi\) | ||||
−0.165951 | + | 0.986134i | \(0.553069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −44341.3 | −0.357472 | −0.178736 | − | 0.983897i | \(-0.557201\pi\) | ||||
−0.178736 | + | 0.983897i | \(0.557201\pi\) | |||||||
\(110\) | −16177.0 | −0.127472 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −64665.1 | −0.476402 | −0.238201 | − | 0.971216i | \(-0.576558\pi\) | ||||
−0.238201 | + | 0.971216i | \(0.576558\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15962.1 | 0.112550 | ||||||||
\(116\) | 37280.7 | 0.257241 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 246851. | 1.63204 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −147991. | −0.918909 | ||||||||
\(122\) | 151616. | 0.922244 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −280194. | −1.63646 | ||||||||
\(125\) | −103590. | −0.592981 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −155448. | −0.855215 | −0.427607 | − | 0.903965i | \(-0.640643\pi\) | ||||
−0.427607 | + | 0.903965i | \(0.640643\pi\) | |||||||
\(128\) | 33744.0 | 0.182042 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −29053.0 | −0.150776 | ||||||||
\(131\) | 189150. | 0.963002 | 0.481501 | − | 0.876446i | \(-0.340092\pi\) | ||||
0.481501 | + | 0.876446i | \(0.340092\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −161978. | −0.779283 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12502.5 | 0.0579628 | ||||||||
\(137\) | −344445. | −1.56790 | −0.783950 | − | 0.620824i | \(-0.786798\pi\) | ||||
−0.783950 | + | 0.620824i | \(0.786798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 270646. | 1.18813 | 0.594065 | − | 0.804417i | \(-0.297522\pi\) | ||||
0.594065 | + | 0.804417i | \(0.297522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −465932. | −1.93911 | ||||||||
\(143\) | 23454.8 | 0.0959161 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19083.2 | 0.0753759 | ||||||||
\(146\) | −489139. | −1.89911 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −364697. | −1.36860 | ||||||||
\(149\) | −131911. | −0.486759 | −0.243379 | − | 0.969931i | \(-0.578256\pi\) | ||||
−0.243379 | + | 0.969931i | \(0.578256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −322961. | −1.15268 | −0.576338 | − | 0.817211i | \(-0.695519\pi\) | ||||
−0.576338 | + | 0.817211i | \(0.695519\pi\) | |||||||
\(152\) | −16735.2 | −0.0587521 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −143426. | −0.479510 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −181881. | −0.588894 | −0.294447 | − | 0.955668i | \(-0.595135\pi\) | ||||
−0.294447 | + | 0.955668i | \(0.595135\pi\) | |||||||
\(158\) | −290224. | −0.924891 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 144369. | 0.445835 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −196117. | −0.578157 | −0.289078 | − | 0.957305i | \(-0.593349\pi\) | ||||
−0.289078 | + | 0.957305i | \(0.593349\pi\) | |||||||
\(164\) | 638372. | 1.85338 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −704046. | −1.98304 | ||||||||
\(167\) | −293276. | −0.813741 | −0.406870 | − | 0.913486i | \(-0.633380\pi\) | ||||
−0.406870 | + | 0.913486i | \(0.633380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −329169. | −0.886549 | ||||||||
\(170\) | 107197. | 0.284486 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −158026. | −0.407294 | ||||||||
\(173\) | 442828. | 1.12492 | 0.562458 | − | 0.826826i | \(-0.309856\pi\) | ||||
0.562458 | + | 0.826826i | \(0.309856\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −109121. | −0.265537 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 348944. | 0.825479 | ||||||||
\(179\) | −661446. | −1.54298 | −0.771492 | − | 0.636239i | \(-0.780489\pi\) | ||||
−0.771492 | + | 0.636239i | \(0.780489\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −139700. | −0.316956 | −0.158478 | − | 0.987363i | \(-0.550659\pi\) | ||||
−0.158478 | + | 0.987363i | \(0.550659\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15127.9 | −0.0329409 | ||||||||
\(185\) | −186681. | −0.401024 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −86541.2 | −0.180975 | ||||||||
\(188\) | −475402. | −0.980995 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −143489. | −0.288359 | ||||||||
\(191\) | −751907. | −1.49135 | −0.745677 | − | 0.666308i | \(-0.767874\pi\) | ||||
−0.745677 | + | 0.666308i | \(0.767874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 464929. | 0.898449 | 0.449224 | − | 0.893419i | \(-0.351700\pi\) | ||||
0.449224 | + | 0.893419i | \(0.351700\pi\) | |||||||
\(194\) | 167553. | 0.319630 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −518493. | −0.951870 | −0.475935 | − | 0.879480i | \(-0.657890\pi\) | ||||
−0.475935 | + | 0.879480i | \(0.657890\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 590287. | 1.05665 | 0.528324 | − | 0.849043i | \(-0.322821\pi\) | ||||
0.528324 | + | 0.849043i | \(0.322821\pi\) | |||||||
\(200\) | 46583.1 | 0.0823480 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 866137. | 1.49351 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 326770. | 0.543071 | ||||||||
\(206\) | 710154. | 1.16596 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −195975. | −0.314082 | ||||||||
\(209\) | 115840. | 0.183439 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 207037. | 0.320142 | 0.160071 | − | 0.987106i | \(-0.448828\pi\) | ||||
0.160071 | + | 0.987106i | \(0.448828\pi\) | |||||||
\(212\) | 997333. | 1.52405 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 319408. | 0.476772 | ||||||||
\(215\) | −80890.3 | −0.119344 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 360317. | 0.513503 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 67749.2 | 0.0943730 | ||||||||
\(221\) | −155424. | −0.214061 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.23347e6 | −1.66098 | −0.830491 | − | 0.557033i | \(-0.811940\pi\) | ||||
−0.830491 | + | 0.557033i | \(0.811940\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 525468. | 0.684345 | ||||||||
\(227\) | −1.12039e6 | −1.44312 | −0.721562 | − | 0.692350i | \(-0.756576\pi\) | ||||
−0.721562 | + | 0.692350i | \(0.756576\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −412271. | −0.519510 | −0.259755 | − | 0.965675i | \(-0.583642\pi\) | ||||
−0.259755 | + | 0.965675i | \(0.583642\pi\) | |||||||
\(230\) | −129708. | −0.161676 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18086.0 | −0.0220609 | ||||||||
\(233\) | −836448. | −1.00937 | −0.504684 | − | 0.863304i | \(-0.668391\pi\) | ||||
−0.504684 | + | 0.863304i | \(0.668391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −243349. | −0.287448 | ||||||||
\(236\) | −1.03382e6 | −1.20827 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 319694. | 0.362026 | 0.181013 | − | 0.983481i | \(-0.442062\pi\) | ||||
0.181013 | + | 0.983481i | \(0.442062\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 965937. | 1.07129 | 0.535644 | − | 0.844444i | \(-0.320069\pi\) | ||||
0.535644 | + | 0.844444i | \(0.320069\pi\) | |||||||
\(242\) | 1.20258e6 | 1.32000 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −634970. | −0.682776 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 208043. | 0.216975 | ||||||||
\(248\) | 135931. | 0.140342 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 841768. | 0.851809 | ||||||||
\(251\) | 1.60171e6 | 1.60472 | 0.802361 | − | 0.596839i | \(-0.203577\pi\) | ||||
0.802361 | + | 0.596839i | \(0.203577\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 104714. | 0.102850 | ||||||||
\(254\) | 1.26317e6 | 1.22850 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 903029. | 0.861196 | ||||||||
\(257\) | 1.08451e6 | 1.02424 | 0.512120 | − | 0.858914i | \(-0.328860\pi\) | ||||
0.512120 | + | 0.858914i | \(0.328860\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 121674. | 0.111626 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.53703e6 | −1.38334 | ||||||||
\(263\) | 1.04604e6 | 0.932517 | 0.466259 | − | 0.884648i | \(-0.345602\pi\) | ||||
0.466259 | + | 0.884648i | \(0.345602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 510514. | 0.446574 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 678368. | 0.576937 | ||||||||
\(269\) | −1.41567e6 | −1.19284 | −0.596419 | − | 0.802673i | \(-0.703410\pi\) | ||||
−0.596419 | + | 0.802673i | \(0.703410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 884078. | 0.731252 | 0.365626 | − | 0.930762i | \(-0.380855\pi\) | ||||
0.365626 | + | 0.930762i | \(0.380855\pi\) | |||||||
\(272\) | 723091. | 0.592612 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.79896e6 | 2.25227 | ||||||||
\(275\) | −322444. | −0.257112 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.77062e6 | −1.38652 | −0.693258 | − | 0.720690i | \(-0.743825\pi\) | ||||
−0.693258 | + | 0.720690i | \(0.743825\pi\) | |||||||
\(278\) | −2.19926e6 | −1.70673 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 802195. | 0.606058 | 0.303029 | − | 0.952981i | \(-0.402002\pi\) | ||||
0.303029 | + | 0.952981i | \(0.402002\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.81693e6 | −1.34856 | −0.674282 | − | 0.738474i | \(-0.735547\pi\) | ||||
−0.674282 | + | 0.738474i | \(0.735547\pi\) | |||||||
\(284\) | 1.95133e6 | 1.43560 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −190593. | −0.137782 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −846389. | −0.596109 | ||||||||
\(290\) | −155070. | −0.108276 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.04852e6 | 1.40599 | ||||||||
\(293\) | 2.34122e6 | 1.59321 | 0.796605 | − | 0.604500i | \(-0.206627\pi\) | ||||
0.796605 | + | 0.604500i | \(0.206627\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −529189. | −0.354043 | ||||||||
\(296\) | 176925. | 0.117371 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.07190e6 | 0.699222 | ||||||||
\(299\) | 188062. | 0.121653 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.62438e6 | 1.65580 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −967894. | −0.600681 | ||||||||
\(305\) | −325028. | −0.200065 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −855540. | −0.518077 | −0.259039 | − | 0.965867i | \(-0.583406\pi\) | ||||
−0.259039 | + | 0.965867i | \(0.583406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.16548e6 | 0.688809 | ||||||||
\(311\) | −2.58071e6 | −1.51300 | −0.756498 | − | 0.653996i | \(-0.773091\pi\) | ||||
−0.756498 | + | 0.653996i | \(0.773091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.03363e6 | 1.75026 | 0.875129 | − | 0.483889i | \(-0.160776\pi\) | ||||
0.875129 | + | 0.483889i | \(0.160776\pi\) | |||||||
\(314\) | 1.47796e6 | 0.845938 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.21546e6 | 0.684736 | ||||||||
\(317\) | −751440. | −0.419997 | −0.209999 | − | 0.977702i | \(-0.567346\pi\) | ||||
−0.209999 | + | 0.977702i | \(0.567346\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 125190. | 0.0688799 | ||||||||
\(320\) | −640861. | −0.349856 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −767616. | −0.409391 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −579094. | −0.304117 | ||||||||
\(326\) | 1.59364e6 | 0.830514 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −309693. | −0.158945 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −726862. | −0.364655 | −0.182327 | − | 0.983238i | \(-0.558363\pi\) | ||||
−0.182327 | + | 0.983238i | \(0.558363\pi\) | |||||||
\(332\) | 2.94855e6 | 1.46813 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.38316e6 | 1.16893 | ||||||||
\(335\) | 347243. | 0.169052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 650213. | 0.311875 | 0.155938 | − | 0.987767i | \(-0.450160\pi\) | ||||
0.155938 | + | 0.987767i | \(0.450160\pi\) | |||||||
\(338\) | 2.67483e6 | 1.27351 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −448942. | −0.210617 | ||||||||
\(341\) | −940900. | −0.438185 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 76663.2 | 0.0349294 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.59842e6 | −1.61593 | ||||||||
\(347\) | −60293.3 | −0.0268810 | −0.0134405 | − | 0.999910i | \(-0.504278\pi\) | ||||
−0.0134405 | + | 0.999910i | \(0.504278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.61218e6 | −1.58747 | −0.793735 | − | 0.608263i | \(-0.791866\pi\) | ||||
−0.793735 | + | 0.608263i | \(0.791866\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 947088. | 0.407412 | ||||||||
\(353\) | −681893. | −0.291259 | −0.145629 | − | 0.989339i | \(-0.546521\pi\) | ||||
−0.145629 | + | 0.989339i | \(0.546521\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 998844. | 0.420656 | ||||||||
\(356\) | −1.46138e6 | −0.611137 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.37490e6 | 2.21648 | ||||||||
\(359\) | −3.14620e6 | −1.28840 | −0.644200 | − | 0.764857i | \(-0.722810\pi\) | ||||
−0.644200 | + | 0.764857i | \(0.722810\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.44860e6 | −0.585035 | ||||||||
\(362\) | 1.13520e6 | 0.455303 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.04860e6 | 0.411980 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.97099e6 | 1.15143 | 0.575714 | − | 0.817651i | \(-0.304724\pi\) | ||||
0.575714 | + | 0.817651i | \(0.304724\pi\) | |||||||
\(368\) | −874934. | −0.336787 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.51697e6 | 0.576066 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00412e6 | 1.11801 | 0.559005 | − | 0.829164i | \(-0.311183\pi\) | ||||
0.559005 | + | 0.829164i | \(0.311183\pi\) | |||||||
\(374\) | 703233. | 0.259968 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 230632. | 0.0841298 | ||||||||
\(377\) | 224835. | 0.0814723 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −754946. | −0.269972 | −0.134986 | − | 0.990848i | \(-0.543099\pi\) | ||||
−0.134986 | + | 0.990848i | \(0.543099\pi\) | |||||||
\(380\) | 600932. | 0.213485 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.10999e6 | 2.14231 | ||||||||
\(383\) | 3.66829e6 | 1.27781 | 0.638905 | − | 0.769286i | \(-0.279388\pi\) | ||||
0.638905 | + | 0.769286i | \(0.279388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.77801e6 | −1.29061 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −701712. | −0.236635 | ||||||||
\(389\) | −3.00960e6 | −1.00841 | −0.504203 | − | 0.863585i | \(-0.668214\pi\) | ||||
−0.504203 | + | 0.863585i | \(0.668214\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −693892. | −0.229536 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.21327e6 | 1.36735 | ||||||||
\(395\) | 622170. | 0.200639 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −287204. | −0.0914564 | −0.0457282 | − | 0.998954i | \(-0.514561\pi\) | ||||
−0.0457282 | + | 0.998954i | \(0.514561\pi\) | |||||||
\(398\) | −4.79666e6 | −1.51786 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.69416e6 | 0.841927 | ||||||||
\(401\) | 863171. | 0.268063 | 0.134031 | − | 0.990977i | \(-0.457208\pi\) | ||||
0.134031 | + | 0.990977i | \(0.457208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.68981e6 | −0.518293 | ||||||||
\(404\) | −3.62739e6 | −1.10571 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.22466e6 | −0.366463 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.82932e6 | 0.836321 | 0.418161 | − | 0.908373i | \(-0.362675\pi\) | ||||
0.418161 | + | 0.908373i | \(0.362675\pi\) | |||||||
\(410\) | −2.65533e6 | −0.780114 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.97413e6 | −0.863212 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.50930e6 | 0.430186 | ||||||||
\(416\) | 1.70092e6 | 0.481894 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −941314. | −0.263508 | ||||||||
\(419\) | −7.08132e6 | −1.97051 | −0.985256 | − | 0.171089i | \(-0.945272\pi\) | ||||
−0.985256 | + | 0.171089i | \(0.945272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.95296e6 | −0.811994 | −0.405997 | − | 0.913874i | \(-0.633076\pi\) | ||||
−0.405997 | + | 0.913874i | \(0.633076\pi\) | |||||||
\(422\) | −1.68238e6 | −0.459879 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −483836. | −0.130702 | ||||||||
\(425\) | 2.13668e6 | 0.573810 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.33768e6 | −0.352975 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 657314. | 0.171436 | ||||||||
\(431\) | −4.47340e6 | −1.15996 | −0.579981 | − | 0.814630i | \(-0.696940\pi\) | ||||
−0.579981 | + | 0.814630i | \(0.696940\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.11279e6 | −1.31050 | −0.655252 | − | 0.755411i | \(-0.727437\pi\) | ||||
−0.655252 | + | 0.755411i | \(0.727437\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.50901e6 | −0.380168 | ||||||||
\(437\) | 928810. | 0.232661 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 590666. | 0.146279 | 0.0731393 | − | 0.997322i | \(-0.476698\pi\) | ||||
0.0731393 | + | 0.997322i | \(0.476698\pi\) | |||||||
\(440\) | −32867.2 | −0.00809340 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.26297e6 | 0.307495 | ||||||||
\(443\) | −160765. | −0.0389209 | −0.0194605 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194605 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −748051. | −0.179073 | ||||||||
\(446\) | 1.00231e7 | 2.38598 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.98274e6 | −1.86869 | −0.934343 | − | 0.356376i | \(-0.884012\pi\) | ||||
−0.934343 | + | 0.356376i | \(0.884012\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.14367e6 | 0.496269 | ||||||||
\(452\) | −2.20067e6 | −0.506650 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.10426e6 | 2.07303 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.22463e6 | −0.274292 | −0.137146 | − | 0.990551i | \(-0.543793\pi\) | ||||
−0.137146 | + | 0.990551i | \(0.543793\pi\) | |||||||
\(458\) | 3.35011e6 | 0.746269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 543217. | 0.119696 | ||||||||
\(461\) | −1.99446e6 | −0.437091 | −0.218546 | − | 0.975827i | \(-0.570131\pi\) | ||||
−0.218546 | + | 0.975827i | \(0.570131\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −125144. | −0.0271304 | −0.0135652 | − | 0.999908i | \(-0.504318\pi\) | ||||
−0.0135652 | + | 0.999908i | \(0.504318\pi\) | |||||||
\(464\) | −1.04602e6 | −0.225550 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.79697e6 | 1.44994 | ||||||||
\(467\) | −7.06372e6 | −1.49879 | −0.749396 | − | 0.662122i | \(-0.769656\pi\) | ||||
−0.749396 | + | 0.662122i | \(0.769656\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.97745e6 | 0.412915 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 501535. | 0.103621 | ||||||||
\(473\) | −530656. | −0.109059 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.86006e6 | −0.581623 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.59783e6 | −0.520045 | ||||||||
\(479\) | 4.64810e6 | 0.925629 | 0.462814 | − | 0.886455i | \(-0.346840\pi\) | ||||
0.462814 | + | 0.886455i | \(0.346840\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.19943e6 | −0.433459 | ||||||||
\(482\) | −7.84919e6 | −1.53889 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.03640e6 | −0.977252 | ||||||||
\(485\) | −359192. | −0.0693382 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.57906e6 | −1.06595 | −0.532977 | − | 0.846130i | \(-0.678927\pi\) | ||||
−0.532977 | + | 0.846130i | \(0.678927\pi\) | |||||||
\(488\) | 308043. | 0.0585547 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.81454e6 | 1.08846 | 0.544229 | − | 0.838937i | \(-0.316822\pi\) | ||||
0.544229 | + | 0.838937i | \(0.316822\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −829574. | −0.153723 | ||||||||
\(494\) | −1.69055e6 | −0.311682 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.86164e6 | 1.43486 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.17797e6 | −1.29048 | −0.645238 | − | 0.763982i | \(-0.723242\pi\) | ||||
−0.645238 | + | 0.763982i | \(0.723242\pi\) | |||||||
\(500\) | −3.52533e6 | −0.630631 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.30155e7 | −2.30516 | ||||||||
\(503\) | 3.00238e6 | 0.529109 | 0.264555 | − | 0.964371i | \(-0.414775\pi\) | ||||
0.264555 | + | 0.964371i | \(0.414775\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.85679e6 | −0.323991 | ||||||||
\(506\) | −850907. | −0.147743 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.29016e6 | −0.909514 | ||||||||
\(509\) | 3.52386e6 | 0.602870 | 0.301435 | − | 0.953487i | \(-0.402534\pi\) | ||||
0.301435 | + | 0.953487i | \(0.402534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8.41781e6 | −1.41914 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.81274e6 | −1.47131 | ||||||||
\(515\) | −1.52240e6 | −0.252936 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.59641e6 | −0.262675 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −59027.9 | −0.00957302 | ||||||||
\(521\) | 3.20451e6 | 0.517210 | 0.258605 | − | 0.965983i | \(-0.416737\pi\) | ||||
0.258605 | + | 0.965983i | \(0.416737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.14584e6 | 1.30221 | 0.651106 | − | 0.758987i | \(-0.274305\pi\) | ||||
0.651106 | + | 0.758987i | \(0.274305\pi\) | |||||||
\(524\) | 6.43709e6 | 1.02414 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.50007e6 | −1.33955 | ||||||||
\(527\) | 6.23490e6 | 0.977920 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.59674e6 | −0.869553 | ||||||||
\(530\) | −4.14843e6 | −0.641497 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.84993e6 | 0.586995 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −684733. | −0.103428 | ||||||||
\(536\) | −329097. | −0.0494779 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.15037e7 | 1.71349 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.33721e6 | −1.37159 | −0.685794 | − | 0.727795i | \(-0.740545\pi\) | ||||
−0.685794 | + | 0.727795i | \(0.740545\pi\) | |||||||
\(542\) | −7.18401e6 | −1.05043 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.27591e6 | −0.909242 | ||||||||
\(545\) | −772432. | −0.111396 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.27605e6 | −1.03975 | −0.519873 | − | 0.854244i | \(-0.674021\pi\) | ||||
−0.519873 | + | 0.854244i | \(0.674021\pi\) | |||||||
\(548\) | −1.17221e7 | −1.66745 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.62018e6 | 0.369338 | ||||||||
\(551\) | 1.11043e6 | 0.155816 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.43880e7 | 1.99171 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.21054e6 | 1.26357 | ||||||||
\(557\) | 9.10577e6 | 1.24359 | 0.621797 | − | 0.783178i | \(-0.286403\pi\) | ||||
0.621797 | + | 0.783178i | \(0.286403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −953032. | −0.128997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.51863e6 | −0.870594 | ||||||||
\(563\) | −1.93485e6 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.12648e6 | −0.148457 | ||||||||
\(566\) | 1.47643e7 | 1.93719 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −946648. | −0.123117 | ||||||||
\(569\) | 8.73948e6 | 1.13163 | 0.565816 | − | 0.824532i | \(-0.308561\pi\) | ||||
0.565816 | + | 0.824532i | \(0.308561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.03137e7 | −1.32380 | −0.661902 | − | 0.749591i | \(-0.730250\pi\) | ||||
−0.661902 | + | 0.749591i | \(0.730250\pi\) | |||||||
\(572\) | 798207. | 0.102006 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.58537e6 | −0.326102 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.56614e6 | 0.696009 | 0.348004 | − | 0.937493i | \(-0.386859\pi\) | ||||
0.348004 | + | 0.937493i | \(0.386859\pi\) | |||||||
\(578\) | 6.87775e6 | 0.856302 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 649436. | 0.0801616 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.34907e6 | 0.408087 | ||||||||
\(584\) | −993799. | −0.120578 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.90247e7 | −2.28862 | ||||||||
\(587\) | 1.57310e6 | 0.188435 | 0.0942173 | − | 0.995552i | \(-0.469965\pi\) | ||||
0.0942173 | + | 0.995552i | \(0.469965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.34574e6 | −0.991235 | ||||||||
\(590\) | 4.30019e6 | 0.508578 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.02326e7 | 1.20000 | ||||||||
\(593\) | −1.62461e7 | −1.89720 | −0.948599 | − | 0.316481i | \(-0.897499\pi\) | ||||
−0.948599 | + | 0.316481i | \(0.897499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.48914e6 | −0.517664 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.52819e6 | −0.174753 | ||||||||
\(599\) | 1.69388e7 | 1.92893 | 0.964465 | − | 0.264210i | \(-0.0851113\pi\) | ||||
0.964465 | + | 0.264210i | \(0.0851113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 700155. | 0.0790693 | 0.0395347 | − | 0.999218i | \(-0.487412\pi\) | ||||
0.0395347 | + | 0.999218i | \(0.487412\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.09909e7 | −1.22586 | ||||||||
\(605\) | −2.57803e6 | −0.286351 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.13306e6 | −0.345141 | −0.172570 | − | 0.984997i | \(-0.555207\pi\) | ||||
−0.172570 | + | 0.984997i | \(0.555207\pi\) | |||||||
\(608\) | 8.40063e6 | 0.921622 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.64118e6 | 0.287391 | ||||||||
\(611\) | −2.86708e6 | −0.310697 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.65140e6 | 0.284986 | 0.142493 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142493 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(614\) | 6.95211e6 | 0.744210 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.47657e7 | 1.56149 | 0.780747 | − | 0.624848i | \(-0.214839\pi\) | ||||
0.780747 | + | 0.624848i | \(0.214839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.33398e6 | 0.874230 | 0.437115 | − | 0.899406i | \(-0.356000\pi\) | ||||
0.437115 | + | 0.899406i | \(0.356000\pi\) | |||||||
\(620\) | −4.88103e6 | −0.509955 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.09708e7 | 2.17340 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.01276e6 | 0.718107 | ||||||||
\(626\) | −2.46513e7 | −2.51422 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.18971e6 | −0.626284 | ||||||||
\(629\) | 8.11526e6 | 0.817854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.17243e7 | −1.17223 | −0.586116 | − | 0.810227i | \(-0.699344\pi\) | ||||
−0.586116 | + | 0.810227i | \(0.699344\pi\) | |||||||
\(632\) | −589657. | −0.0587228 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.10620e6 | 0.603320 | ||||||||
\(635\) | −2.70792e6 | −0.266503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.01729e6 | −0.0989449 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 587825. | 0.0567281 | ||||||||
\(641\) | 8.58605e6 | 0.825369 | 0.412685 | − | 0.910874i | \(-0.364591\pi\) | ||||
0.412685 | + | 0.910874i | \(0.364591\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.87633e7 | −1.78970 | −0.894852 | − | 0.446364i | \(-0.852719\pi\) | ||||
−0.894852 | + | 0.446364i | \(0.852719\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.23764e6 | 0.588084 | ||||||||
\(647\) | 1.59559e7 | 1.49851 | 0.749255 | − | 0.662282i | \(-0.230412\pi\) | ||||
0.749255 | + | 0.662282i | \(0.230412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.47159e6 | −0.323531 | ||||||||
\(650\) | 4.70571e6 | 0.436860 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.67419e6 | −0.614865 | ||||||||
\(653\) | 1.36524e7 | 1.25293 | 0.626464 | − | 0.779451i | \(-0.284502\pi\) | ||||
0.626464 | + | 0.779451i | \(0.284502\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.29501e6 | 0.300092 | ||||||||
\(656\) | −1.79113e7 | −1.62506 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.32613e6 | 0.388049 | 0.194024 | − | 0.980997i | \(-0.437846\pi\) | ||||
0.194024 | + | 0.980997i | \(0.437846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.97317e7 | 1.75655 | 0.878275 | − | 0.478157i | \(-0.158695\pi\) | ||||
0.878275 | + | 0.478157i | \(0.158695\pi\) | |||||||
\(662\) | 5.90647e6 | 0.523821 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.43043e6 | −0.125906 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00378e6 | 0.0873621 | ||||||||
\(668\) | −9.98070e6 | −0.865406 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.82169e6 | −0.242841 | ||||||||
\(671\) | −2.13225e6 | −0.182823 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.88089e6 | 0.840927 | 0.420464 | − | 0.907309i | \(-0.361867\pi\) | ||||
0.420464 | + | 0.907309i | \(0.361867\pi\) | |||||||
\(674\) | −5.28362e6 | −0.448004 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.12022e7 | −0.942837 | ||||||||
\(677\) | −2.22205e6 | −0.186329 | −0.0931647 | − | 0.995651i | \(-0.529698\pi\) | ||||
−0.0931647 | + | 0.995651i | \(0.529698\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 217795. | 0.0180624 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.64575e6 | 0.629447 | ||||||||
\(683\) | 5.54335e6 | 0.454695 | 0.227347 | − | 0.973814i | \(-0.426995\pi\) | ||||
0.227347 | + | 0.973814i | \(0.426995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00028e6 | −0.488591 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.43387e6 | 0.357118 | ||||||||
\(689\) | 6.01477e6 | 0.482693 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.43508e7 | −1.14335 | −0.571677 | − | 0.820478i | \(-0.693707\pi\) | ||||
−0.571677 | + | 0.820478i | \(0.693707\pi\) | |||||||
\(692\) | 1.50702e7 | 1.19634 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 489943. | 0.0386142 | ||||||||
\(695\) | 4.71469e6 | 0.370246 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.42051e7 | −1.10755 | ||||||||
\(698\) | 2.93525e7 | 2.28038 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.50894e7 | −1.15978 | −0.579891 | − | 0.814694i | \(-0.696905\pi\) | ||||
−0.579891 | + | 0.814694i | \(0.696905\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.08627e7 | −0.828990 | ||||||||
\(704\) | −4.20417e6 | −0.319705 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.54105e6 | 0.418389 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.04016e7 | 0.777115 | 0.388557 | − | 0.921425i | \(-0.372974\pi\) | ||||
0.388557 | + | 0.921425i | \(0.372974\pi\) | |||||||
\(710\) | −8.11660e6 | −0.604266 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 708960. | 0.0524109 | ||||||||
\(713\) | −7.54419e6 | −0.555762 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 408586. | 0.0298895 | ||||||||
\(716\) | −2.25101e7 | −1.64095 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.55660e7 | 1.85077 | ||||||||
\(719\) | −1.11331e7 | −0.803145 | −0.401572 | − | 0.915827i | \(-0.631536\pi\) | ||||
−0.401572 | + | 0.915827i | \(0.631536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.17713e7 | 0.840395 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.75422e6 | −0.337080 | ||||||||
\(725\) | −3.09091e6 | −0.218394 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.95327e6 | 0.628269 | 0.314135 | − | 0.949378i | \(-0.398286\pi\) | ||||
0.314135 | + | 0.949378i | \(0.398286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.52088e6 | −0.591803 | ||||||||
\(731\) | 3.51641e6 | 0.243392 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.60536e7 | 1.79105 | 0.895524 | − | 0.445014i | \(-0.146801\pi\) | ||||
0.895524 | + | 0.445014i | \(0.146801\pi\) | |||||||
\(734\) | −2.41423e7 | −1.65401 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.59380e6 | 0.516731 | ||||||||
\(737\) | 2.27798e6 | 0.154483 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.97111e6 | −0.402202 | −0.201101 | − | 0.979571i | \(-0.564452\pi\) | ||||
−0.201101 | + | 0.979571i | \(0.564452\pi\) | |||||||
\(740\) | −6.35307e6 | −0.426486 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.80330e6 | 0.452114 | 0.226057 | − | 0.974114i | \(-0.427417\pi\) | ||||
0.226057 | + | 0.974114i | \(0.427417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.29790e6 | −0.151684 | ||||||||
\(746\) | −2.44115e7 | −1.60601 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.94515e6 | −0.192466 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.12648e7 | −1.37582 | −0.687911 | − | 0.725795i | \(-0.741472\pi\) | ||||
−0.687911 | + | 0.725795i | \(0.741472\pi\) | |||||||
\(752\) | 1.33388e7 | 0.860143 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.82701e6 | −0.117034 | ||||||||
\(755\) | −5.62602e6 | −0.359198 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.49238e6 | −0.602054 | −0.301027 | − | 0.953616i | \(-0.597329\pi\) | ||||
−0.301027 | + | 0.953616i | \(0.597329\pi\) | |||||||
\(758\) | 6.13469e6 | 0.387810 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −291530. | −0.0183084 | ||||||||
\(761\) | 1.71806e7 | 1.07542 | 0.537710 | − | 0.843130i | \(-0.319290\pi\) | ||||
0.537710 | + | 0.843130i | \(0.319290\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.55887e7 | −1.58604 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.98085e7 | −1.83556 | ||||||||
\(767\) | −6.23480e6 | −0.382678 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.39968e7 | −0.853517 | −0.426758 | − | 0.904366i | \(-0.640345\pi\) | ||||
−0.426758 | + | 0.904366i | \(0.640345\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.58223e7 | 0.955493 | ||||||||
\(773\) | 2.54449e7 | 1.53162 | 0.765812 | − | 0.643065i | \(-0.222337\pi\) | ||||
0.765812 | + | 0.643065i | \(0.222337\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.32306e7 | 1.38933 | ||||||||
\(776\) | 340422. | 0.0202938 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.44560e7 | 1.44856 | ||||||||
\(779\) | 1.90143e7 | 1.12263 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.55261e6 | 0.384403 | ||||||||
\(782\) | 5.63856e6 | 0.329725 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.16839e6 | −0.183512 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.95632e6 | −0.573010 | −0.286505 | − | 0.958079i | \(-0.592493\pi\) | ||||
−0.286505 | + | 0.958079i | \(0.592493\pi\) | |||||||
\(788\) | −1.76452e7 | −1.01231 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.05575e6 | −0.288216 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.82941e6 | −0.216246 | ||||||||
\(794\) | 2.33382e6 | 0.131376 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00885e7 | 1.12374 | ||||||||
\(797\) | −2.19815e7 | −1.22578 | −0.612888 | − | 0.790170i | \(-0.709992\pi\) | ||||
−0.612888 | + | 0.790170i | \(0.709992\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.05787e7 | 0.586226 | ||||||||
\(800\) | −2.33834e7 | −1.29176 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.01412e6 | −0.385068 | ||||||||
\(803\) | 6.87899e6 | 0.376475 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.37314e7 | 0.744521 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.75976e6 | 0.0948253 | ||||||||
\(809\) | −1.01820e7 | −0.546969 | −0.273485 | − | 0.961876i | \(-0.588176\pi\) | ||||
−0.273485 | + | 0.961876i | \(0.588176\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.06750e7 | 0.569923 | 0.284961 | − | 0.958539i | \(-0.408019\pi\) | ||||
0.284961 | + | 0.958539i | \(0.408019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.95160e6 | 0.526419 | ||||||||
\(815\) | −3.41638e6 | −0.180166 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.70689e6 | −0.246706 | ||||||||
\(818\) | −2.29910e7 | −1.20136 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.11205e7 | 0.577552 | ||||||||
\(821\) | −2.22260e7 | −1.15081 | −0.575404 | − | 0.817869i | \(-0.695155\pi\) | ||||
−0.575404 | + | 0.817869i | \(0.695155\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.42908e7 | −1.25009 | −0.625046 | − | 0.780588i | \(-0.714920\pi\) | ||||
−0.625046 | + | 0.780588i | \(0.714920\pi\) | |||||||
\(824\) | 1.44284e6 | 0.0740288 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.66722e7 | −1.35611 | −0.678055 | − | 0.735011i | \(-0.737177\pi\) | ||||
−0.678055 | + | 0.735011i | \(0.737177\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.78413e6 | −0.342853 | −0.171427 | − | 0.985197i | \(-0.554838\pi\) | ||||
−0.171427 | + | 0.985197i | \(0.554838\pi\) | |||||||
\(830\) | −1.22646e7 | −0.617956 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.55049e6 | −0.378152 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.10892e6 | −0.253579 | ||||||||
\(836\) | 3.94223e6 | 0.195086 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.75427e7 | 2.83061 | ||||||||
\(839\) | −1.88975e7 | −0.926830 | −0.463415 | − | 0.886141i | \(-0.653376\pi\) | ||||
−0.463415 | + | 0.886141i | \(0.653376\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.93111e7 | −0.941493 | ||||||||
\(842\) | 2.39958e7 | 1.16642 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.04584e6 | 0.340468 | ||||||||
\(845\) | −5.73418e6 | −0.276267 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.79830e7 | −1.33630 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.73627e7 | −0.824270 | ||||||||
\(851\) | −9.81941e6 | −0.464795 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.69205e7 | −0.796235 | −0.398118 | − | 0.917334i | \(-0.630336\pi\) | ||||
−0.398118 | + | 0.917334i | \(0.630336\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 648950. | 0.0302710 | ||||||||
\(857\) | 2.87564e7 | 1.33747 | 0.668733 | − | 0.743502i | \(-0.266837\pi\) | ||||
0.668733 | + | 0.743502i | \(0.266837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.92517e6 | 0.412699 | 0.206350 | − | 0.978478i | \(-0.433842\pi\) | ||||
0.206350 | + | 0.978478i | \(0.433842\pi\) | |||||||
\(860\) | −2.75284e6 | −0.126921 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.63508e7 | 1.66627 | ||||||||
\(863\) | −7.18205e6 | −0.328262 | −0.164131 | − | 0.986439i | \(-0.552482\pi\) | ||||
−0.164131 | + | 0.986439i | \(0.552482\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.71413e6 | 0.350547 | ||||||||
\(866\) | 4.15465e7 | 1.88252 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.08155e6 | 0.183348 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.09114e6 | 0.182725 | ||||||||
\(872\) | 732066. | 0.0326031 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.54750e6 | −0.334214 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.05341e6 | 0.221863 | 0.110932 | − | 0.993828i | \(-0.464617\pi\) | ||||
0.110932 | + | 0.993828i | \(0.464617\pi\) | |||||||
\(878\) | −4.79975e6 | −0.210127 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.90090e6 | −0.0827469 | ||||||||
\(881\) | −3.15002e6 | −0.136733 | −0.0683665 | − | 0.997660i | \(-0.521779\pi\) | ||||
−0.0683665 | + | 0.997660i | \(0.521779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.33141e7 | 1.43789 | 0.718946 | − | 0.695066i | \(-0.244625\pi\) | ||||
0.718946 | + | 0.695066i | \(0.244625\pi\) | |||||||
\(884\) | −5.28934e6 | −0.227652 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.30638e6 | 0.0559094 | ||||||||
\(887\) | −2.04549e6 | −0.0872946 | −0.0436473 | − | 0.999047i | \(-0.513898\pi\) | ||||
−0.0436473 | + | 0.999047i | \(0.513898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.07866e6 | 0.257237 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.19770e7 | −1.76644 | ||||||||
\(893\) | −1.41601e7 | −0.594208 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.15225e7 | −0.480827 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.48677e7 | 2.68434 | ||||||||
\(899\) | −9.01936e6 | −0.372200 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.21927e7 | −0.910749 | ||||||||
\(902\) | −1.74195e7 | −0.712883 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.06761e6 | 0.0434502 | ||||||||
\(905\) | −2.43359e6 | −0.0987702 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.69774e7 | 1.08888 | 0.544442 | − | 0.838798i | \(-0.316741\pi\) | ||||
0.544442 | + | 0.838798i | \(0.316741\pi\) | |||||||
\(908\) | −3.81287e7 | −1.53475 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.42821e6 | 0.216701 | 0.108350 | − | 0.994113i | \(-0.465443\pi\) | ||||
0.108350 | + | 0.994113i | \(0.465443\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.90132e6 | 0.393112 | ||||||||
\(914\) | 9.95129e6 | 0.394016 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.40303e7 | −0.552495 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.41696e6 | 0.367809 | 0.183904 | − | 0.982944i | \(-0.441126\pi\) | ||||
0.183904 | + | 0.982944i | \(0.441126\pi\) | |||||||
\(920\) | −263531. | −0.0102651 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.62069e7 | 0.627876 | ||||||||
\(923\) | 1.17682e7 | 0.454679 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.02367e7 | 1.16193 | ||||||||
\(926\) | 1.01692e6 | 0.0389724 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.07868e6 | 0.346061 | ||||||||
\(929\) | −8.43871e6 | −0.320802 | −0.160401 | − | 0.987052i | \(-0.551279\pi\) | ||||
−0.160401 | + | 0.987052i | \(0.551279\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.84658e7 | −1.07345 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.73997e7 | 2.15299 | ||||||||
\(935\) | −1.50756e6 | −0.0563957 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 683755. | 0.0254420 | 0.0127210 | − | 0.999919i | \(-0.495951\pi\) | ||||
0.0127210 | + | 0.999919i | \(0.495951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.28158e6 | −0.305699 | ||||||||
\(941\) | −4.97436e7 | −1.83132 | −0.915658 | − | 0.401958i | \(-0.868330\pi\) | ||||
−0.915658 | + | 0.401958i | \(0.868330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.71881e7 | 0.629430 | ||||||||
\(944\) | 2.90066e7 | 1.05942 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.31211e6 | 0.156661 | ||||||||
\(947\) | 2.21967e7 | 0.804292 | 0.402146 | − | 0.915575i | \(-0.368264\pi\) | ||||
0.402146 | + | 0.915575i | \(0.368264\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.23543e7 | 0.445301 | ||||||||
\(950\) | 2.32408e7 | 0.835493 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.34934e7 | 0.481270 | 0.240635 | − | 0.970616i | \(-0.422644\pi\) | ||||
0.240635 | + | 0.970616i | \(0.422644\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.30983e7 | −0.464737 | ||||||||
\(956\) | 1.08797e7 | 0.385012 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.77704e7 | −1.32965 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.91585e7 | 1.36778 | ||||||||
\(962\) | 1.78726e7 | 0.622658 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.28725e7 | 1.13931 | ||||||||
\(965\) | 8.09913e6 | 0.279976 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.59641e7 | −0.549008 | −0.274504 | − | 0.961586i | \(-0.588514\pi\) | ||||
−0.274504 | + | 0.961586i | \(0.588514\pi\) | |||||||
\(968\) | 2.44331e6 | 0.0838088 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.91879e6 | 0.0996033 | ||||||||
\(971\) | 2.03921e7 | 0.694087 | 0.347043 | − | 0.937849i | \(-0.387186\pi\) | ||||
0.347043 | + | 0.937849i | \(0.387186\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.53354e7 | 1.53123 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.78159e7 | 0.598663 | ||||||||
\(977\) | 2.62595e7 | 0.880136 | 0.440068 | − | 0.897964i | \(-0.354954\pi\) | ||||
0.440068 | + | 0.897964i | \(0.354954\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.90736e6 | −0.163641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.72489e7 | −1.56355 | ||||||||
\(983\) | −8.01076e6 | −0.264417 | −0.132209 | − | 0.991222i | \(-0.542207\pi\) | ||||
−0.132209 | + | 0.991222i | \(0.542207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.03223e6 | −0.296623 | ||||||||
\(986\) | 6.74111e6 | 0.220820 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.08006e6 | 0.230751 | ||||||||
\(989\) | −4.25483e6 | −0.138322 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.60083e7 | −0.517798 | −0.258899 | − | 0.965904i | \(-0.583360\pi\) | ||||
−0.258899 | + | 0.965904i | \(0.583360\pi\) | |||||||
\(992\) | −6.82334e7 | −2.20150 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.02829e7 | 0.329274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.97034e7 | 0.946386 | 0.473193 | − | 0.880959i | \(-0.343101\pi\) | ||||
0.473193 | + | 0.880959i | \(0.343101\pi\) | |||||||
\(998\) | 5.83281e7 | 1.85375 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.6.a.be.1.2 | yes | 8 | |
3.2 | odd | 2 | inner | 441.6.a.be.1.7 | yes | 8 | |
7.6 | odd | 2 | inner | 441.6.a.be.1.1 | ✓ | 8 | |
21.20 | even | 2 | inner | 441.6.a.be.1.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.6.a.be.1.1 | ✓ | 8 | 7.6 | odd | 2 | inner | |
441.6.a.be.1.2 | yes | 8 | 1.1 | even | 1 | trivial | |
441.6.a.be.1.7 | yes | 8 | 3.2 | odd | 2 | inner | |
441.6.a.be.1.8 | yes | 8 | 21.20 | even | 2 | inner |