Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,6,Mod(1,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, 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("294.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.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: | \(47.1528430250\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 294.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −86.0000 | −1.53841 | −0.769207 | − | 0.638999i | \(-0.779349\pi\) | ||||
−0.769207 | + | 0.638999i | \(0.779349\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 344.000 | 1.08782 | ||||||||
\(11\) | 34.0000 | 0.0847222 | 0.0423611 | − | 0.999102i | \(-0.486512\pi\) | ||||
0.0423611 | + | 0.999102i | \(0.486512\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | 3.00000 | 0.00492337 | 0.00246169 | − | 0.999997i | \(-0.499216\pi\) | ||||
0.00246169 | + | 0.999997i | \(0.499216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −774.000 | −0.888204 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1904.00 | 1.59788 | 0.798941 | − | 0.601410i | \(-0.205394\pi\) | ||||
0.798941 | + | 0.601410i | \(0.205394\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | 1489.00 | 0.946260 | 0.473130 | − | 0.880992i | \(-0.343124\pi\) | ||||
0.473130 | + | 0.880992i | \(0.343124\pi\) | |||||||
\(20\) | −1376.00 | −0.769207 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −136.000 | −0.0599076 | ||||||||
\(23\) | −224.000 | −0.0882934 | −0.0441467 | − | 0.999025i | \(-0.514057\pi\) | ||||
−0.0441467 | + | 0.999025i | \(0.514057\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 4271.00 | 1.36672 | ||||||||
\(26\) | −12.0000 | −0.00348135 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6508.00 | −1.43699 | −0.718493 | − | 0.695534i | \(-0.755168\pi\) | ||||
−0.718493 | + | 0.695534i | \(0.755168\pi\) | |||||||
\(30\) | 3096.00 | 0.628055 | ||||||||
\(31\) | −1731.00 | −0.323514 | −0.161757 | − | 0.986831i | \(-0.551716\pi\) | ||||
−0.161757 | + | 0.986831i | \(0.551716\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 306.000 | 0.0489144 | ||||||||
\(34\) | −7616.00 | −1.12987 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −7633.00 | −0.916623 | −0.458312 | − | 0.888792i | \(-0.651546\pi\) | ||||
−0.458312 | + | 0.888792i | \(0.651546\pi\) | |||||||
\(38\) | −5956.00 | −0.669107 | ||||||||
\(39\) | 27.0000 | 0.00284251 | ||||||||
\(40\) | 5504.00 | 0.543912 | ||||||||
\(41\) | −15414.0 | −1.43204 | −0.716021 | − | 0.698079i | \(-0.754039\pi\) | ||||
−0.716021 | + | 0.698079i | \(0.754039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18491.0 | 1.52507 | 0.762534 | − | 0.646948i | \(-0.223955\pi\) | ||||
0.762534 | + | 0.646948i | \(0.223955\pi\) | |||||||
\(44\) | 544.000 | 0.0423611 | ||||||||
\(45\) | −6966.00 | −0.512805 | ||||||||
\(46\) | 896.000 | 0.0624329 | ||||||||
\(47\) | −18462.0 | −1.21909 | −0.609543 | − | 0.792753i | \(-0.708647\pi\) | ||||
−0.609543 | + | 0.792753i | \(0.708647\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −17084.0 | −0.966417 | ||||||||
\(51\) | 17136.0 | 0.922537 | ||||||||
\(52\) | 48.0000 | 0.00246169 | ||||||||
\(53\) | −19956.0 | −0.975852 | −0.487926 | − | 0.872885i | \(-0.662246\pi\) | ||||
−0.487926 | + | 0.872885i | \(0.662246\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | −2924.00 | −0.130338 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13401.0 | 0.546324 | ||||||||
\(58\) | 26032.0 | 1.01610 | ||||||||
\(59\) | 31828.0 | 1.19036 | 0.595181 | − | 0.803591i | \(-0.297080\pi\) | ||||
0.595181 | + | 0.803591i | \(0.297080\pi\) | |||||||
\(60\) | −12384.0 | −0.444102 | ||||||||
\(61\) | 57654.0 | 1.98383 | 0.991916 | − | 0.126897i | \(-0.0405017\pi\) | ||||
0.991916 | + | 0.126897i | \(0.0405017\pi\) | |||||||
\(62\) | 6924.00 | 0.228759 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −258.000 | −0.00757419 | ||||||||
\(66\) | −1224.00 | −0.0345877 | ||||||||
\(67\) | −60563.0 | −1.64824 | −0.824120 | − | 0.566415i | \(-0.808330\pi\) | ||||
−0.824120 | + | 0.566415i | \(0.808330\pi\) | |||||||
\(68\) | 30464.0 | 0.798941 | ||||||||
\(69\) | −2016.00 | −0.0509762 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −44834.0 | −1.05551 | −0.527754 | − | 0.849397i | \(-0.676966\pi\) | ||||
−0.527754 | + | 0.849397i | \(0.676966\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | −20821.0 | −0.457293 | −0.228646 | − | 0.973510i | \(-0.573430\pi\) | ||||
−0.228646 | + | 0.973510i | \(0.573430\pi\) | |||||||
\(74\) | 30532.0 | 0.648151 | ||||||||
\(75\) | 38439.0 | 0.789076 | ||||||||
\(76\) | 23824.0 | 0.473130 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −108.000 | −0.00200996 | ||||||||
\(79\) | −30531.0 | −0.550394 | −0.275197 | − | 0.961388i | \(-0.588743\pi\) | ||||
−0.275197 | + | 0.961388i | \(0.588743\pi\) | |||||||
\(80\) | −22016.0 | −0.384604 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 61656.0 | 1.01261 | ||||||||
\(83\) | −110602. | −1.76225 | −0.881125 | − | 0.472883i | \(-0.843213\pi\) | ||||
−0.881125 | + | 0.472883i | \(0.843213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −163744. | −2.45820 | ||||||||
\(86\) | −73964.0 | −1.07839 | ||||||||
\(87\) | −58572.0 | −0.829644 | ||||||||
\(88\) | −2176.00 | −0.0299538 | ||||||||
\(89\) | 58992.0 | 0.789438 | 0.394719 | − | 0.918802i | \(-0.370842\pi\) | ||||
0.394719 | + | 0.918802i | \(0.370842\pi\) | |||||||
\(90\) | 27864.0 | 0.362608 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3584.00 | −0.0441467 | ||||||||
\(93\) | −15579.0 | −0.186781 | ||||||||
\(94\) | 73848.0 | 0.862023 | ||||||||
\(95\) | −128054. | −1.45574 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | 119846. | 1.29328 | 0.646642 | − | 0.762793i | \(-0.276173\pi\) | ||||
0.646642 | + | 0.762793i | \(0.276173\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2754.00 | 0.0282407 | ||||||||
\(100\) | 68336.0 | 0.683360 | ||||||||
\(101\) | −100010. | −0.975529 | −0.487764 | − | 0.872975i | \(-0.662187\pi\) | ||||
−0.487764 | + | 0.872975i | \(0.662187\pi\) | |||||||
\(102\) | −68544.0 | −0.652332 | ||||||||
\(103\) | −121691. | −1.13023 | −0.565113 | − | 0.825013i | \(-0.691167\pi\) | ||||
−0.565113 | + | 0.825013i | \(0.691167\pi\) | |||||||
\(104\) | −192.000 | −0.00174068 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 79824.0 | 0.690031 | ||||||||
\(107\) | −48648.0 | −0.410776 | −0.205388 | − | 0.978681i | \(-0.565846\pi\) | ||||
−0.205388 | + | 0.978681i | \(0.565846\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | −152075. | −1.22600 | −0.613002 | − | 0.790082i | \(-0.710038\pi\) | ||||
−0.613002 | + | 0.790082i | \(0.710038\pi\) | |||||||
\(110\) | 11696.0 | 0.0921628 | ||||||||
\(111\) | −68697.0 | −0.529213 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −60886.0 | −0.448561 | −0.224280 | − | 0.974525i | \(-0.572003\pi\) | ||||
−0.224280 | + | 0.974525i | \(0.572003\pi\) | |||||||
\(114\) | −53604.0 | −0.386309 | ||||||||
\(115\) | 19264.0 | 0.135832 | ||||||||
\(116\) | −104128. | −0.718493 | ||||||||
\(117\) | 243.000 | 0.00164112 | ||||||||
\(118\) | −127312. | −0.841714 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 49536.0 | 0.314028 | ||||||||
\(121\) | −159895. | −0.992822 | ||||||||
\(122\) | −230616. | −1.40278 | ||||||||
\(123\) | −138726. | −0.826790 | ||||||||
\(124\) | −27696.0 | −0.161757 | ||||||||
\(125\) | −98556.0 | −0.564167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −151965. | −0.836054 | −0.418027 | − | 0.908435i | \(-0.637278\pi\) | ||||
−0.418027 | + | 0.908435i | \(0.637278\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 166419. | 0.880499 | ||||||||
\(130\) | 1032.00 | 0.00535576 | ||||||||
\(131\) | −235502. | −1.19899 | −0.599496 | − | 0.800378i | \(-0.704632\pi\) | ||||
−0.599496 | + | 0.800378i | \(0.704632\pi\) | |||||||
\(132\) | 4896.00 | 0.0244572 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 242252. | 1.16548 | ||||||||
\(135\) | −62694.0 | −0.296068 | ||||||||
\(136\) | −121856. | −0.564937 | ||||||||
\(137\) | 325508. | 1.48170 | 0.740850 | − | 0.671671i | \(-0.234423\pi\) | ||||
0.740850 | + | 0.671671i | \(0.234423\pi\) | |||||||
\(138\) | 8064.00 | 0.0360456 | ||||||||
\(139\) | −3211.00 | −0.0140962 | −0.00704812 | − | 0.999975i | \(-0.502244\pi\) | ||||
−0.00704812 | + | 0.999975i | \(0.502244\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −166158. | −0.703839 | ||||||||
\(142\) | 179336. | 0.746357 | ||||||||
\(143\) | 102.000 | 0.000417119 0 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 559688. | 2.21068 | ||||||||
\(146\) | 83284.0 | 0.323355 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −122128. | −0.458312 | ||||||||
\(149\) | −151884. | −0.560462 | −0.280231 | − | 0.959933i | \(-0.590411\pi\) | ||||
−0.280231 | + | 0.959933i | \(0.590411\pi\) | |||||||
\(150\) | −153756. | −0.557961 | ||||||||
\(151\) | 76648.0 | 0.273564 | 0.136782 | − | 0.990601i | \(-0.456324\pi\) | ||||
0.136782 | + | 0.990601i | \(0.456324\pi\) | |||||||
\(152\) | −95296.0 | −0.334554 | ||||||||
\(153\) | 154224. | 0.532627 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 148866. | 0.497698 | ||||||||
\(156\) | 432.000 | 0.00142126 | ||||||||
\(157\) | 389710. | 1.26181 | 0.630903 | − | 0.775862i | \(-0.282685\pi\) | ||||
0.630903 | + | 0.775862i | \(0.282685\pi\) | |||||||
\(158\) | 122124. | 0.389187 | ||||||||
\(159\) | −179604. | −0.563408 | ||||||||
\(160\) | 88064.0 | 0.271956 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −112372. | −0.331275 | −0.165638 | − | 0.986187i | \(-0.552968\pi\) | ||||
−0.165638 | + | 0.986187i | \(0.552968\pi\) | |||||||
\(164\) | −246624. | −0.716021 | ||||||||
\(165\) | −26316.0 | −0.0752506 | ||||||||
\(166\) | 442408. | 1.24610 | ||||||||
\(167\) | −52550.0 | −0.145808 | −0.0729040 | − | 0.997339i | \(-0.523227\pi\) | ||||
−0.0729040 | + | 0.997339i | \(0.523227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −371284. | −0.999976 | ||||||||
\(170\) | 654976. | 1.73821 | ||||||||
\(171\) | 120609. | 0.315420 | ||||||||
\(172\) | 295856. | 0.762534 | ||||||||
\(173\) | 135256. | 0.343591 | 0.171795 | − | 0.985133i | \(-0.445043\pi\) | ||||
0.171795 | + | 0.985133i | \(0.445043\pi\) | |||||||
\(174\) | 234288. | 0.586647 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8704.00 | 0.0211805 | ||||||||
\(177\) | 286452. | 0.687256 | ||||||||
\(178\) | −235968. | −0.558217 | ||||||||
\(179\) | 250638. | 0.584675 | 0.292337 | − | 0.956315i | \(-0.405567\pi\) | ||||
0.292337 | + | 0.956315i | \(0.405567\pi\) | |||||||
\(180\) | −111456. | −0.256402 | ||||||||
\(181\) | −199233. | −0.452027 | −0.226014 | − | 0.974124i | \(-0.572569\pi\) | ||||
−0.226014 | + | 0.974124i | \(0.572569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 518886. | 1.14537 | ||||||||
\(184\) | 14336.0 | 0.0312164 | ||||||||
\(185\) | 656438. | 1.41015 | ||||||||
\(186\) | 62316.0 | 0.132074 | ||||||||
\(187\) | 64736.0 | 0.135376 | ||||||||
\(188\) | −295392. | −0.609543 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 512216. | 1.02936 | ||||||||
\(191\) | −238770. | −0.473583 | −0.236792 | − | 0.971560i | \(-0.576096\pi\) | ||||
−0.236792 | + | 0.971560i | \(0.576096\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | 85691.0 | 0.165593 | 0.0827965 | − | 0.996566i | \(-0.473615\pi\) | ||||
0.0827965 | + | 0.996566i | \(0.473615\pi\) | |||||||
\(194\) | −479384. | −0.914491 | ||||||||
\(195\) | −2322.00 | −0.00437296 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −71408.0 | −0.131094 | −0.0655468 | − | 0.997849i | \(-0.520879\pi\) | ||||
−0.0655468 | + | 0.997849i | \(0.520879\pi\) | |||||||
\(198\) | −11016.0 | −0.0199692 | ||||||||
\(199\) | 711352. | 1.27336 | 0.636681 | − | 0.771127i | \(-0.280307\pi\) | ||||
0.636681 | + | 0.771127i | \(0.280307\pi\) | |||||||
\(200\) | −273344. | −0.483208 | ||||||||
\(201\) | −545067. | −0.951612 | ||||||||
\(202\) | 400040. | 0.689803 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 274176. | 0.461269 | ||||||||
\(205\) | 1.32560e6 | 2.20307 | ||||||||
\(206\) | 486764. | 0.799191 | ||||||||
\(207\) | −18144.0 | −0.0294311 | ||||||||
\(208\) | 768.000 | 0.00123084 | ||||||||
\(209\) | 50626.0 | 0.0801693 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −260260. | −0.402440 | −0.201220 | − | 0.979546i | \(-0.564491\pi\) | ||||
−0.201220 | + | 0.979546i | \(0.564491\pi\) | |||||||
\(212\) | −319296. | −0.487926 | ||||||||
\(213\) | −403506. | −0.609398 | ||||||||
\(214\) | 194592. | 0.290463 | ||||||||
\(215\) | −1.59023e6 | −2.34619 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 608300. | 0.866915 | ||||||||
\(219\) | −187389. | −0.264018 | ||||||||
\(220\) | −46784.0 | −0.0651689 | ||||||||
\(221\) | 5712.00 | 0.00786697 | ||||||||
\(222\) | 274788. | 0.374210 | ||||||||
\(223\) | −105656. | −0.142276 | −0.0711381 | − | 0.997466i | \(-0.522663\pi\) | ||||
−0.0711381 | + | 0.997466i | \(0.522663\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 345951. | 0.455573 | ||||||||
\(226\) | 243544. | 0.317180 | ||||||||
\(227\) | −654750. | −0.843356 | −0.421678 | − | 0.906746i | \(-0.638559\pi\) | ||||
−0.421678 | + | 0.906746i | \(0.638559\pi\) | |||||||
\(228\) | 214416. | 0.273162 | ||||||||
\(229\) | −557713. | −0.702784 | −0.351392 | − | 0.936228i | \(-0.614292\pi\) | ||||
−0.351392 | + | 0.936228i | \(0.614292\pi\) | |||||||
\(230\) | −77056.0 | −0.0960477 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 416512. | 0.508051 | ||||||||
\(233\) | −1.24759e6 | −1.50551 | −0.752755 | − | 0.658301i | \(-0.771275\pi\) | ||||
−0.752755 | + | 0.658301i | \(0.771275\pi\) | |||||||
\(234\) | −972.000 | −0.00116045 | ||||||||
\(235\) | 1.58773e6 | 1.87546 | ||||||||
\(236\) | 509248. | 0.595181 | ||||||||
\(237\) | −274779. | −0.317770 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −496926. | −0.562726 | −0.281363 | − | 0.959601i | \(-0.590786\pi\) | ||||
−0.281363 | + | 0.959601i | \(0.590786\pi\) | |||||||
\(240\) | −198144. | −0.222051 | ||||||||
\(241\) | 277618. | 0.307897 | 0.153948 | − | 0.988079i | \(-0.450801\pi\) | ||||
0.153948 | + | 0.988079i | \(0.450801\pi\) | |||||||
\(242\) | 639580. | 0.702031 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 922464. | 0.991916 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 554904. | 0.584629 | ||||||||
\(247\) | 4467.00 | 0.00465879 | ||||||||
\(248\) | 110784. | 0.114379 | ||||||||
\(249\) | −995418. | −1.01744 | ||||||||
\(250\) | 394224. | 0.398927 | ||||||||
\(251\) | 308328. | 0.308908 | 0.154454 | − | 0.988000i | \(-0.450638\pi\) | ||||
0.154454 | + | 0.988000i | \(0.450638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7616.00 | −0.00748041 | ||||||||
\(254\) | 607860. | 0.591179 | ||||||||
\(255\) | −1.47370e6 | −1.41925 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −408762. | −0.386045 | −0.193022 | − | 0.981194i | \(-0.561829\pi\) | ||||
−0.193022 | + | 0.981194i | \(0.561829\pi\) | |||||||
\(258\) | −665676. | −0.622606 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4128.00 | −0.00378710 | ||||||||
\(261\) | −527148. | −0.478995 | ||||||||
\(262\) | 942008. | 0.847816 | ||||||||
\(263\) | 1.08812e6 | 0.970039 | 0.485019 | − | 0.874503i | \(-0.338813\pi\) | ||||
0.485019 | + | 0.874503i | \(0.338813\pi\) | |||||||
\(264\) | −19584.0 | −0.0172938 | ||||||||
\(265\) | 1.71622e6 | 1.50126 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 530928. | 0.455782 | ||||||||
\(268\) | −969008. | −0.824120 | ||||||||
\(269\) | 668290. | 0.563098 | 0.281549 | − | 0.959547i | \(-0.409152\pi\) | ||||
0.281549 | + | 0.959547i | \(0.409152\pi\) | |||||||
\(270\) | 250776. | 0.209352 | ||||||||
\(271\) | 830664. | 0.687072 | 0.343536 | − | 0.939140i | \(-0.388375\pi\) | ||||
0.343536 | + | 0.939140i | \(0.388375\pi\) | |||||||
\(272\) | 487424. | 0.399470 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.30203e6 | −1.04772 | ||||||||
\(275\) | 145214. | 0.115792 | ||||||||
\(276\) | −32256.0 | −0.0254881 | ||||||||
\(277\) | 925073. | 0.724397 | 0.362198 | − | 0.932101i | \(-0.382026\pi\) | ||||
0.362198 | + | 0.932101i | \(0.382026\pi\) | |||||||
\(278\) | 12844.0 | 0.00996755 | ||||||||
\(279\) | −140211. | −0.107838 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.33635e6 | 1.00961 | 0.504805 | − | 0.863233i | \(-0.331564\pi\) | ||||
0.504805 | + | 0.863233i | \(0.331564\pi\) | |||||||
\(282\) | 664632. | 0.497689 | ||||||||
\(283\) | 992957. | 0.736995 | 0.368497 | − | 0.929629i | \(-0.379872\pi\) | ||||
0.368497 | + | 0.929629i | \(0.379872\pi\) | |||||||
\(284\) | −717344. | −0.527754 | ||||||||
\(285\) | −1.15249e6 | −0.840473 | ||||||||
\(286\) | −408.000 | −0.000294948 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 2.20536e6 | 1.55323 | ||||||||
\(290\) | −2.23875e6 | −1.56319 | ||||||||
\(291\) | 1.07861e6 | 0.746678 | ||||||||
\(292\) | −333136. | −0.228646 | ||||||||
\(293\) | −563544. | −0.383494 | −0.191747 | − | 0.981444i | \(-0.561415\pi\) | ||||
−0.191747 | + | 0.981444i | \(0.561415\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.73721e6 | −1.83127 | ||||||||
\(296\) | 488512. | 0.324075 | ||||||||
\(297\) | 24786.0 | 0.0163048 | ||||||||
\(298\) | 607536. | 0.396307 | ||||||||
\(299\) | −672.000 | −0.000434702 0 | ||||||||
\(300\) | 615024. | 0.394538 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −306592. | −0.193439 | ||||||||
\(303\) | −900090. | −0.563222 | ||||||||
\(304\) | 381184. | 0.236565 | ||||||||
\(305\) | −4.95824e6 | −3.05196 | ||||||||
\(306\) | −616896. | −0.376624 | ||||||||
\(307\) | −2.82703e6 | −1.71193 | −0.855963 | − | 0.517037i | \(-0.827035\pi\) | ||||
−0.855963 | + | 0.517037i | \(0.827035\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.09522e6 | −0.652536 | ||||||||
\(310\) | −595464. | −0.351926 | ||||||||
\(311\) | 1.12731e6 | 0.660912 | 0.330456 | − | 0.943821i | \(-0.392797\pi\) | ||||
0.330456 | + | 0.943821i | \(0.392797\pi\) | |||||||
\(312\) | −1728.00 | −0.00100498 | ||||||||
\(313\) | 2.36013e6 | 1.36168 | 0.680840 | − | 0.732432i | \(-0.261615\pi\) | ||||
0.680840 | + | 0.732432i | \(0.261615\pi\) | |||||||
\(314\) | −1.55884e6 | −0.892231 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −488496. | −0.275197 | ||||||||
\(317\) | −2.22420e6 | −1.24316 | −0.621578 | − | 0.783352i | \(-0.713508\pi\) | ||||
−0.621578 | + | 0.783352i | \(0.713508\pi\) | |||||||
\(318\) | 718416. | 0.398390 | ||||||||
\(319\) | −221272. | −0.121745 | ||||||||
\(320\) | −352256. | −0.192302 | ||||||||
\(321\) | −437832. | −0.237162 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.83506e6 | 1.51201 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 12813.0 | 0.00672887 | ||||||||
\(326\) | 449488. | 0.234247 | ||||||||
\(327\) | −1.36868e6 | −0.707833 | ||||||||
\(328\) | 986496. | 0.506303 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 105264. | 0.0532102 | ||||||||
\(331\) | −3.70304e6 | −1.85775 | −0.928877 | − | 0.370388i | \(-0.879225\pi\) | ||||
−0.928877 | + | 0.370388i | \(0.879225\pi\) | |||||||
\(332\) | −1.76963e6 | −0.881125 | ||||||||
\(333\) | −618273. | −0.305541 | ||||||||
\(334\) | 210200. | 0.103102 | ||||||||
\(335\) | 5.20842e6 | 2.53568 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.21432e6 | 0.582452 | 0.291226 | − | 0.956654i | \(-0.405937\pi\) | ||||
0.291226 | + | 0.956654i | \(0.405937\pi\) | |||||||
\(338\) | 1.48514e6 | 0.707090 | ||||||||
\(339\) | −547974. | −0.258977 | ||||||||
\(340\) | −2.61990e6 | −1.22910 | ||||||||
\(341\) | −58854.0 | −0.0274088 | ||||||||
\(342\) | −482436. | −0.223036 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.18342e6 | −0.539193 | ||||||||
\(345\) | 173376. | 0.0784226 | ||||||||
\(346\) | −541024. | −0.242955 | ||||||||
\(347\) | −977904. | −0.435986 | −0.217993 | − | 0.975950i | \(-0.569951\pi\) | ||||
−0.217993 | + | 0.975950i | \(0.569951\pi\) | |||||||
\(348\) | −937152. | −0.414822 | ||||||||
\(349\) | −511282. | −0.224697 | −0.112348 | − | 0.993669i | \(-0.535837\pi\) | ||||
−0.112348 | + | 0.993669i | \(0.535837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2187.00 | 0.000947504 0 | ||||||||
\(352\) | −34816.0 | −0.0149769 | ||||||||
\(353\) | −3.02752e6 | −1.29315 | −0.646577 | − | 0.762848i | \(-0.723800\pi\) | ||||
−0.646577 | + | 0.762848i | \(0.723800\pi\) | |||||||
\(354\) | −1.14581e6 | −0.485964 | ||||||||
\(355\) | 3.85572e6 | 1.62381 | ||||||||
\(356\) | 943872. | 0.394719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.00255e6 | −0.413427 | ||||||||
\(359\) | 4.59456e6 | 1.88151 | 0.940757 | − | 0.339082i | \(-0.110116\pi\) | ||||
0.940757 | + | 0.339082i | \(0.110116\pi\) | |||||||
\(360\) | 445824. | 0.181304 | ||||||||
\(361\) | −258978. | −0.104591 | ||||||||
\(362\) | 796932. | 0.319632 | ||||||||
\(363\) | −1.43906e6 | −0.573206 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.79061e6 | 0.703506 | ||||||||
\(366\) | −2.07554e6 | −0.809896 | ||||||||
\(367\) | 1.11273e6 | 0.431246 | 0.215623 | − | 0.976477i | \(-0.430822\pi\) | ||||
0.215623 | + | 0.976477i | \(0.430822\pi\) | |||||||
\(368\) | −57344.0 | −0.0220734 | ||||||||
\(369\) | −1.24853e6 | −0.477347 | ||||||||
\(370\) | −2.62575e6 | −0.997125 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −249264. | −0.0933904 | ||||||||
\(373\) | −2.45895e6 | −0.915119 | −0.457559 | − | 0.889179i | \(-0.651276\pi\) | ||||
−0.457559 | + | 0.889179i | \(0.651276\pi\) | |||||||
\(374\) | −258944. | −0.0957253 | ||||||||
\(375\) | −887004. | −0.325722 | ||||||||
\(376\) | 1.18157e6 | 0.431012 | ||||||||
\(377\) | −19524.0 | −0.00707482 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.10130e6 | −1.46664 | −0.733320 | − | 0.679884i | \(-0.762030\pi\) | ||||
−0.733320 | + | 0.679884i | \(0.762030\pi\) | |||||||
\(380\) | −2.04886e6 | −0.727871 | ||||||||
\(381\) | −1.36768e6 | −0.482696 | ||||||||
\(382\) | 955080. | 0.334874 | ||||||||
\(383\) | 2.59413e6 | 0.903639 | 0.451820 | − | 0.892109i | \(-0.350775\pi\) | ||||
0.451820 | + | 0.892109i | \(0.350775\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −342764. | −0.117092 | ||||||||
\(387\) | 1.49777e6 | 0.508356 | ||||||||
\(388\) | 1.91754e6 | 0.646642 | ||||||||
\(389\) | 2.23407e6 | 0.748552 | 0.374276 | − | 0.927317i | \(-0.377891\pi\) | ||||
0.374276 | + | 0.927317i | \(0.377891\pi\) | |||||||
\(390\) | 9288.00 | 0.00309215 | ||||||||
\(391\) | −426496. | −0.141082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.11952e6 | −0.692238 | ||||||||
\(394\) | 285632. | 0.0926971 | ||||||||
\(395\) | 2.62567e6 | 0.846733 | ||||||||
\(396\) | 44064.0 | 0.0141204 | ||||||||
\(397\) | 2.06400e6 | 0.657253 | 0.328627 | − | 0.944460i | \(-0.393414\pi\) | ||||
0.328627 | + | 0.944460i | \(0.393414\pi\) | |||||||
\(398\) | −2.84541e6 | −0.900403 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.09338e6 | 0.341680 | ||||||||
\(401\) | 1.15283e6 | 0.358017 | 0.179008 | − | 0.983848i | \(-0.442711\pi\) | ||||
0.179008 | + | 0.983848i | \(0.442711\pi\) | |||||||
\(402\) | 2.18027e6 | 0.672891 | ||||||||
\(403\) | −5193.00 | −0.00159278 | ||||||||
\(404\) | −1.60016e6 | −0.487764 | ||||||||
\(405\) | −564246. | −0.170935 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −259522. | −0.0776583 | ||||||||
\(408\) | −1.09670e6 | −0.326166 | ||||||||
\(409\) | −5.93412e6 | −1.75408 | −0.877038 | − | 0.480421i | \(-0.840484\pi\) | ||||
−0.877038 | + | 0.480421i | \(0.840484\pi\) | |||||||
\(410\) | −5.30242e6 | −1.55781 | ||||||||
\(411\) | 2.92957e6 | 0.855460 | ||||||||
\(412\) | −1.94706e6 | −0.565113 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 72576.0 | 0.0208110 | ||||||||
\(415\) | 9.51177e6 | 2.71107 | ||||||||
\(416\) | −3072.00 | −0.000870338 0 | ||||||||
\(417\) | −28899.0 | −0.00813847 | ||||||||
\(418\) | −202504. | −0.0566882 | ||||||||
\(419\) | −771666. | −0.214731 | −0.107365 | − | 0.994220i | \(-0.534241\pi\) | ||||
−0.107365 | + | 0.994220i | \(0.534241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.87542e6 | −0.790671 | −0.395336 | − | 0.918537i | \(-0.629372\pi\) | ||||
−0.395336 | + | 0.918537i | \(0.629372\pi\) | |||||||
\(422\) | 1.04104e6 | 0.284568 | ||||||||
\(423\) | −1.49542e6 | −0.406362 | ||||||||
\(424\) | 1.27718e6 | 0.345016 | ||||||||
\(425\) | 8.13198e6 | 2.18386 | ||||||||
\(426\) | 1.61402e6 | 0.430909 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −778368. | −0.205388 | ||||||||
\(429\) | 918.000 | 0.000240824 0 | ||||||||
\(430\) | 6.36090e6 | 1.65901 | ||||||||
\(431\) | −137862. | −0.0357480 | −0.0178740 | − | 0.999840i | \(-0.505690\pi\) | ||||
−0.0178740 | + | 0.999840i | \(0.505690\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | −1.56526e6 | −0.401204 | −0.200602 | − | 0.979673i | \(-0.564290\pi\) | ||||
−0.200602 | + | 0.979673i | \(0.564290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.03719e6 | 1.27634 | ||||||||
\(436\) | −2.43320e6 | −0.613002 | ||||||||
\(437\) | −333536. | −0.0835486 | ||||||||
\(438\) | 749556. | 0.186689 | ||||||||
\(439\) | −4.88158e6 | −1.20892 | −0.604462 | − | 0.796634i | \(-0.706612\pi\) | ||||
−0.604462 | + | 0.796634i | \(0.706612\pi\) | |||||||
\(440\) | 187136. | 0.0460814 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22848.0 | −0.00556279 | ||||||||
\(443\) | −1.30152e6 | −0.315094 | −0.157547 | − | 0.987511i | \(-0.550359\pi\) | ||||
−0.157547 | + | 0.987511i | \(0.550359\pi\) | |||||||
\(444\) | −1.09915e6 | −0.264606 | ||||||||
\(445\) | −5.07331e6 | −1.21448 | ||||||||
\(446\) | 422624. | 0.100604 | ||||||||
\(447\) | −1.36696e6 | −0.323583 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.13141e6 | −0.733034 | −0.366517 | − | 0.930411i | \(-0.619450\pi\) | ||||
−0.366517 | + | 0.930411i | \(0.619450\pi\) | |||||||
\(450\) | −1.38380e6 | −0.322139 | ||||||||
\(451\) | −524076. | −0.121326 | ||||||||
\(452\) | −974176. | −0.224280 | ||||||||
\(453\) | 689832. | 0.157942 | ||||||||
\(454\) | 2.61900e6 | 0.596343 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −857664. | −0.193155 | ||||||||
\(457\) | 6.49268e6 | 1.45423 | 0.727116 | − | 0.686514i | \(-0.240860\pi\) | ||||
0.727116 | + | 0.686514i | \(0.240860\pi\) | |||||||
\(458\) | 2.23085e6 | 0.496944 | ||||||||
\(459\) | 1.38802e6 | 0.307512 | ||||||||
\(460\) | 308224. | 0.0679160 | ||||||||
\(461\) | −5.34717e6 | −1.17185 | −0.585925 | − | 0.810365i | \(-0.699269\pi\) | ||||
−0.585925 | + | 0.810365i | \(0.699269\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.37285e6 | 0.731215 | 0.365607 | − | 0.930769i | \(-0.380861\pi\) | ||||
0.365607 | + | 0.930769i | \(0.380861\pi\) | |||||||
\(464\) | −1.66605e6 | −0.359247 | ||||||||
\(465\) | 1.33979e6 | 0.287346 | ||||||||
\(466\) | 4.99038e6 | 1.06456 | ||||||||
\(467\) | −2.23452e6 | −0.474125 | −0.237062 | − | 0.971494i | \(-0.576185\pi\) | ||||
−0.237062 | + | 0.971494i | \(0.576185\pi\) | |||||||
\(468\) | 3888.00 | 0.000820562 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.35093e6 | −1.32615 | ||||||||
\(471\) | 3.50739e6 | 0.728504 | ||||||||
\(472\) | −2.03699e6 | −0.420857 | ||||||||
\(473\) | 628694. | 0.129207 | ||||||||
\(474\) | 1.09912e6 | 0.224697 | ||||||||
\(475\) | 6.35952e6 | 1.29327 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.61644e6 | −0.325284 | ||||||||
\(478\) | 1.98770e6 | 0.397907 | ||||||||
\(479\) | 2.52136e6 | 0.502108 | 0.251054 | − | 0.967973i | \(-0.419223\pi\) | ||||
0.251054 | + | 0.967973i | \(0.419223\pi\) | |||||||
\(480\) | 792576. | 0.157014 | ||||||||
\(481\) | −22899.0 | −0.00451288 | ||||||||
\(482\) | −1.11047e6 | −0.217716 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.55832e6 | −0.496411 | ||||||||
\(485\) | −1.03068e7 | −1.98961 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | 1.91672e6 | 0.366215 | 0.183107 | − | 0.983093i | \(-0.441384\pi\) | ||||
0.183107 | + | 0.983093i | \(0.441384\pi\) | |||||||
\(488\) | −3.68986e6 | −0.701390 | ||||||||
\(489\) | −1.01135e6 | −0.191262 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.82875e6 | 1.09112 | 0.545559 | − | 0.838073i | \(-0.316317\pi\) | ||||
0.545559 | + | 0.838073i | \(0.316317\pi\) | |||||||
\(492\) | −2.21962e6 | −0.413395 | ||||||||
\(493\) | −1.23912e7 | −2.29613 | ||||||||
\(494\) | −17868.0 | −0.00329427 | ||||||||
\(495\) | −236844. | −0.0434460 | ||||||||
\(496\) | −443136. | −0.0808785 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.98167e6 | 0.719436 | ||||||||
\(499\) | −1.00049e7 | −1.79870 | −0.899352 | − | 0.437225i | \(-0.855961\pi\) | ||||
−0.899352 | + | 0.437225i | \(0.855961\pi\) | |||||||
\(500\) | −1.57690e6 | −0.282084 | ||||||||
\(501\) | −472950. | −0.0841823 | ||||||||
\(502\) | −1.23331e6 | −0.218431 | ||||||||
\(503\) | −1.13666e6 | −0.200313 | −0.100157 | − | 0.994972i | \(-0.531934\pi\) | ||||
−0.100157 | + | 0.994972i | \(0.531934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.60086e6 | 1.50077 | ||||||||
\(506\) | 30464.0 | 0.00528945 | ||||||||
\(507\) | −3.34156e6 | −0.577336 | ||||||||
\(508\) | −2.43144e6 | −0.418027 | ||||||||
\(509\) | −4.01937e6 | −0.687644 | −0.343822 | − | 0.939035i | \(-0.611722\pi\) | ||||
−0.343822 | + | 0.939035i | \(0.611722\pi\) | |||||||
\(510\) | 5.89478e6 | 1.00356 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 1.08548e6 | 0.182108 | ||||||||
\(514\) | 1.63505e6 | 0.272975 | ||||||||
\(515\) | 1.04654e7 | 1.73876 | ||||||||
\(516\) | 2.66270e6 | 0.440249 | ||||||||
\(517\) | −627708. | −0.103284 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.21730e6 | 0.198372 | ||||||||
\(520\) | 16512.0 | 0.00267788 | ||||||||
\(521\) | 5.52028e6 | 0.890977 | 0.445488 | − | 0.895288i | \(-0.353030\pi\) | ||||
0.445488 | + | 0.895288i | \(0.353030\pi\) | |||||||
\(522\) | 2.10859e6 | 0.338701 | ||||||||
\(523\) | −8.94472e6 | −1.42992 | −0.714961 | − | 0.699164i | \(-0.753556\pi\) | ||||
−0.714961 | + | 0.699164i | \(0.753556\pi\) | |||||||
\(524\) | −3.76803e6 | −0.599496 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.35250e6 | −0.685921 | ||||||||
\(527\) | −3.29582e6 | −0.516937 | ||||||||
\(528\) | 78336.0 | 0.0122286 | ||||||||
\(529\) | −6.38617e6 | −0.992204 | ||||||||
\(530\) | −6.86486e6 | −1.06155 | ||||||||
\(531\) | 2.57807e6 | 0.396788 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46242.0 | −0.00705048 | ||||||||
\(534\) | −2.12371e6 | −0.322287 | ||||||||
\(535\) | 4.18373e6 | 0.631945 | ||||||||
\(536\) | 3.87603e6 | 0.582741 | ||||||||
\(537\) | 2.25574e6 | 0.337562 | ||||||||
\(538\) | −2.67316e6 | −0.398171 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00310e6 | −0.148034 | ||||||||
\(541\) | 849057. | 0.124722 | 0.0623611 | − | 0.998054i | \(-0.480137\pi\) | ||||
0.0623611 | + | 0.998054i | \(0.480137\pi\) | |||||||
\(542\) | −3.32266e6 | −0.485833 | ||||||||
\(543\) | −1.79310e6 | −0.260978 | ||||||||
\(544\) | −1.94970e6 | −0.282468 | ||||||||
\(545\) | 1.30784e7 | 1.88610 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.61340e6 | 1.23085 | 0.615426 | − | 0.788194i | \(-0.288984\pi\) | ||||
0.615426 | + | 0.788194i | \(0.288984\pi\) | |||||||
\(548\) | 5.20813e6 | 0.740850 | ||||||||
\(549\) | 4.66997e6 | 0.661277 | ||||||||
\(550\) | −580856. | −0.0818770 | ||||||||
\(551\) | −9.69041e6 | −1.35976 | ||||||||
\(552\) | 129024. | 0.0180228 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.70029e6 | −0.512226 | ||||||||
\(555\) | 5.90794e6 | 0.814149 | ||||||||
\(556\) | −51376.0 | −0.00704812 | ||||||||
\(557\) | 7.79879e6 | 1.06510 | 0.532549 | − | 0.846399i | \(-0.321234\pi\) | ||||
0.532549 | + | 0.846399i | \(0.321234\pi\) | |||||||
\(558\) | 560844. | 0.0762529 | ||||||||
\(559\) | 55473.0 | 0.00750848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 582624. | 0.0781594 | ||||||||
\(562\) | −5.34539e6 | −0.713902 | ||||||||
\(563\) | −1.07271e6 | −0.142631 | −0.0713153 | − | 0.997454i | \(-0.522720\pi\) | ||||
−0.0713153 | + | 0.997454i | \(0.522720\pi\) | |||||||
\(564\) | −2.65853e6 | −0.351920 | ||||||||
\(565\) | 5.23620e6 | 0.690073 | ||||||||
\(566\) | −3.97183e6 | −0.521134 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.86938e6 | 0.373179 | ||||||||
\(569\) | −1.01524e6 | −0.131459 | −0.0657293 | − | 0.997837i | \(-0.520937\pi\) | ||||
−0.0657293 | + | 0.997837i | \(0.520937\pi\) | |||||||
\(570\) | 4.60994e6 | 0.594304 | ||||||||
\(571\) | −6.78093e6 | −0.870361 | −0.435180 | − | 0.900343i | \(-0.643315\pi\) | ||||
−0.435180 | + | 0.900343i | \(0.643315\pi\) | |||||||
\(572\) | 1632.00 | 0.000208560 0 | ||||||||
\(573\) | −2.14893e6 | −0.273423 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −956704. | −0.120672 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 3.30537e6 | 0.413314 | 0.206657 | − | 0.978413i | \(-0.433742\pi\) | ||||
0.206657 | + | 0.978413i | \(0.433742\pi\) | |||||||
\(578\) | −8.82144e6 | −1.09830 | ||||||||
\(579\) | 771219. | 0.0956052 | ||||||||
\(580\) | 8.95501e6 | 1.10534 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.31446e6 | −0.527981 | ||||||||
\(583\) | −678504. | −0.0826763 | ||||||||
\(584\) | 1.33254e6 | 0.161677 | ||||||||
\(585\) | −20898.0 | −0.00252473 | ||||||||
\(586\) | 2.25418e6 | 0.271171 | ||||||||
\(587\) | 1.19833e7 | 1.43543 | 0.717715 | − | 0.696337i | \(-0.245188\pi\) | ||||
0.717715 | + | 0.696337i | \(0.245188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.57746e6 | −0.306128 | ||||||||
\(590\) | 1.09488e7 | 1.29490 | ||||||||
\(591\) | −642672. | −0.0756869 | ||||||||
\(592\) | −1.95405e6 | −0.229156 | ||||||||
\(593\) | 5.31020e6 | 0.620117 | 0.310059 | − | 0.950717i | \(-0.399651\pi\) | ||||
0.310059 | + | 0.950717i | \(0.399651\pi\) | |||||||
\(594\) | −99144.0 | −0.0115292 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.43014e6 | −0.280231 | ||||||||
\(597\) | 6.40217e6 | 0.735176 | ||||||||
\(598\) | 2688.00 | 0.000307380 0 | ||||||||
\(599\) | 2.42236e6 | 0.275849 | 0.137924 | − | 0.990443i | \(-0.455957\pi\) | ||||
0.137924 | + | 0.990443i | \(0.455957\pi\) | |||||||
\(600\) | −2.46010e6 | −0.278981 | ||||||||
\(601\) | 7.10659e6 | 0.802556 | 0.401278 | − | 0.915956i | \(-0.368566\pi\) | ||||
0.401278 | + | 0.915956i | \(0.368566\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.90560e6 | −0.549413 | ||||||||
\(604\) | 1.22637e6 | 0.136782 | ||||||||
\(605\) | 1.37510e7 | 1.52737 | ||||||||
\(606\) | 3.60036e6 | 0.398258 | ||||||||
\(607\) | −1.79194e7 | −1.97402 | −0.987011 | − | 0.160655i | \(-0.948640\pi\) | ||||
−0.987011 | + | 0.160655i | \(0.948640\pi\) | |||||||
\(608\) | −1.52474e6 | −0.167277 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.98330e7 | 2.15806 | ||||||||
\(611\) | −55386.0 | −0.00600201 | ||||||||
\(612\) | 2.46758e6 | 0.266314 | ||||||||
\(613\) | 1.39790e7 | 1.50254 | 0.751269 | − | 0.659997i | \(-0.229442\pi\) | ||||
0.751269 | + | 0.659997i | \(0.229442\pi\) | |||||||
\(614\) | 1.13081e7 | 1.21051 | ||||||||
\(615\) | 1.19304e7 | 1.27195 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.25594e6 | −0.555824 | −0.277912 | − | 0.960606i | \(-0.589642\pi\) | ||||
−0.277912 | + | 0.960606i | \(0.589642\pi\) | |||||||
\(618\) | 4.38088e6 | 0.461413 | ||||||||
\(619\) | −1.44301e6 | −0.151371 | −0.0756857 | − | 0.997132i | \(-0.524115\pi\) | ||||
−0.0756857 | + | 0.997132i | \(0.524115\pi\) | |||||||
\(620\) | 2.38186e6 | 0.248849 | ||||||||
\(621\) | −163296. | −0.0169921 | ||||||||
\(622\) | −4.50926e6 | −0.467336 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6912.00 | 0.000710628 0 | ||||||||
\(625\) | −4.87106e6 | −0.498796 | ||||||||
\(626\) | −9.44052e6 | −0.962853 | ||||||||
\(627\) | 455634. | 0.0462857 | ||||||||
\(628\) | 6.23536e6 | 0.630903 | ||||||||
\(629\) | −1.45332e7 | −1.46466 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.51723e7 | 1.51697 | 0.758487 | − | 0.651688i | \(-0.225939\pi\) | ||||
0.758487 | + | 0.651688i | \(0.225939\pi\) | |||||||
\(632\) | 1.95398e6 | 0.194593 | ||||||||
\(633\) | −2.34234e6 | −0.232349 | ||||||||
\(634\) | 8.89680e6 | 0.879044 | ||||||||
\(635\) | 1.30690e7 | 1.28620 | ||||||||
\(636\) | −2.87366e6 | −0.281704 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 885088. | 0.0860864 | ||||||||
\(639\) | −3.63155e6 | −0.351836 | ||||||||
\(640\) | 1.40902e6 | 0.135978 | ||||||||
\(641\) | −144848. | −0.0139241 | −0.00696205 | − | 0.999976i | \(-0.502216\pi\) | ||||
−0.00696205 | + | 0.999976i | \(0.502216\pi\) | |||||||
\(642\) | 1.75133e6 | 0.167699 | ||||||||
\(643\) | 27469.0 | 0.00262009 | 0.00131004 | − | 0.999999i | \(-0.499583\pi\) | ||||
0.00131004 | + | 0.999999i | \(0.499583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.43120e7 | −1.35457 | ||||||||
\(646\) | −1.13402e7 | −1.06915 | ||||||||
\(647\) | −8.55783e6 | −0.803717 | −0.401858 | − | 0.915702i | \(-0.631636\pi\) | ||||
−0.401858 | + | 0.915702i | \(0.631636\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 1.08215e6 | 0.100850 | ||||||||
\(650\) | −51252.0 | −0.00475803 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.79795e6 | −0.165638 | ||||||||
\(653\) | 1.25030e7 | 1.14745 | 0.573723 | − | 0.819049i | \(-0.305498\pi\) | ||||
0.573723 | + | 0.819049i | \(0.305498\pi\) | |||||||
\(654\) | 5.47470e6 | 0.500514 | ||||||||
\(655\) | 2.02532e7 | 1.84455 | ||||||||
\(656\) | −3.94598e6 | −0.358010 | ||||||||
\(657\) | −1.68650e6 | −0.152431 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.80471e7 | 1.61880 | 0.809400 | − | 0.587258i | \(-0.199793\pi\) | ||||
0.809400 | + | 0.587258i | \(0.199793\pi\) | |||||||
\(660\) | −421056. | −0.0376253 | ||||||||
\(661\) | −3.34144e6 | −0.297461 | −0.148731 | − | 0.988878i | \(-0.547519\pi\) | ||||
−0.148731 | + | 0.988878i | \(0.547519\pi\) | |||||||
\(662\) | 1.48122e7 | 1.31363 | ||||||||
\(663\) | 51408.0 | 0.00454200 | ||||||||
\(664\) | 7.07853e6 | 0.623050 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.47309e6 | 0.216050 | ||||||||
\(667\) | 1.45779e6 | 0.126876 | ||||||||
\(668\) | −840800. | −0.0729040 | ||||||||
\(669\) | −950904. | −0.0821432 | ||||||||
\(670\) | −2.08337e7 | −1.79299 | ||||||||
\(671\) | 1.96024e6 | 0.168075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.47066e6 | −0.720907 | −0.360454 | − | 0.932777i | \(-0.617378\pi\) | ||||
−0.360454 | + | 0.932777i | \(0.617378\pi\) | |||||||
\(674\) | −4.85730e6 | −0.411856 | ||||||||
\(675\) | 3.11356e6 | 0.263025 | ||||||||
\(676\) | −5.94054e6 | −0.499988 | ||||||||
\(677\) | −1.46553e7 | −1.22892 | −0.614458 | − | 0.788949i | \(-0.710625\pi\) | ||||
−0.614458 | + | 0.788949i | \(0.710625\pi\) | |||||||
\(678\) | 2.19190e6 | 0.183124 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.04796e7 | 0.869107 | ||||||||
\(681\) | −5.89275e6 | −0.486912 | ||||||||
\(682\) | 235416. | 0.0193809 | ||||||||
\(683\) | 1.97616e7 | 1.62095 | 0.810477 | − | 0.585771i | \(-0.199208\pi\) | ||||
0.810477 | + | 0.585771i | \(0.199208\pi\) | |||||||
\(684\) | 1.92974e6 | 0.157710 | ||||||||
\(685\) | −2.79937e7 | −2.27947 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.01942e6 | −0.405753 | ||||||||
\(688\) | 4.73370e6 | 0.381267 | ||||||||
\(689\) | −59868.0 | −0.00480448 | ||||||||
\(690\) | −693504. | −0.0554532 | ||||||||
\(691\) | −1.35832e7 | −1.08220 | −0.541101 | − | 0.840958i | \(-0.681992\pi\) | ||||
−0.541101 | + | 0.840958i | \(0.681992\pi\) | |||||||
\(692\) | 2.16410e6 | 0.171795 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.91162e6 | 0.308289 | ||||||||
\(695\) | 276146. | 0.0216859 | ||||||||
\(696\) | 3.74861e6 | 0.293324 | ||||||||
\(697\) | −2.93483e7 | −2.28823 | ||||||||
\(698\) | 2.04513e6 | 0.158885 | ||||||||
\(699\) | −1.12283e7 | −0.869206 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.29915e7 | −0.998538 | −0.499269 | − | 0.866447i | \(-0.666398\pi\) | ||||
−0.499269 | + | 0.866447i | \(0.666398\pi\) | |||||||
\(702\) | −8748.00 | −0.000669986 0 | ||||||||
\(703\) | −1.13655e7 | −0.867365 | ||||||||
\(704\) | 139264. | 0.0105903 | ||||||||
\(705\) | 1.42896e7 | 1.08280 | ||||||||
\(706\) | 1.21101e7 | 0.914399 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.58323e6 | 0.343628 | ||||||||
\(709\) | 1.90873e6 | 0.142603 | 0.0713017 | − | 0.997455i | \(-0.477285\pi\) | ||||
0.0713017 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(710\) | −1.54229e7 | −1.14821 | ||||||||
\(711\) | −2.47301e6 | −0.183465 | ||||||||
\(712\) | −3.77549e6 | −0.279109 | ||||||||
\(713\) | 387744. | 0.0285641 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8772.00 | −0.000641702 0 | ||||||||
\(716\) | 4.01021e6 | 0.292337 | ||||||||
\(717\) | −4.47233e6 | −0.324890 | ||||||||
\(718\) | −1.83782e7 | −1.33043 | ||||||||
\(719\) | 1.11200e7 | 0.802198 | 0.401099 | − | 0.916035i | \(-0.368628\pi\) | ||||
0.401099 | + | 0.916035i | \(0.368628\pi\) | |||||||
\(720\) | −1.78330e6 | −0.128201 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.03591e6 | 0.0739571 | ||||||||
\(723\) | 2.49856e6 | 0.177764 | ||||||||
\(724\) | −3.18773e6 | −0.226014 | ||||||||
\(725\) | −2.77957e7 | −1.96396 | ||||||||
\(726\) | 5.75622e6 | 0.405318 | ||||||||
\(727\) | −8.37406e6 | −0.587624 | −0.293812 | − | 0.955863i | \(-0.594924\pi\) | ||||
−0.293812 | + | 0.955863i | \(0.594924\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −7.16242e6 | −0.497454 | ||||||||
\(731\) | 3.52069e7 | 2.43688 | ||||||||
\(732\) | 8.30218e6 | 0.572683 | ||||||||
\(733\) | −4.64448e6 | −0.319284 | −0.159642 | − | 0.987175i | \(-0.551034\pi\) | ||||
−0.159642 | + | 0.987175i | \(0.551034\pi\) | |||||||
\(734\) | −4.45092e6 | −0.304937 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 229376. | 0.0156082 | ||||||||
\(737\) | −2.05914e6 | −0.139642 | ||||||||
\(738\) | 4.99414e6 | 0.337536 | ||||||||
\(739\) | −1.10623e7 | −0.745136 | −0.372568 | − | 0.928005i | \(-0.621523\pi\) | ||||
−0.372568 | + | 0.928005i | \(0.621523\pi\) | |||||||
\(740\) | 1.05030e7 | 0.705074 | ||||||||
\(741\) | 40203.0 | 0.00268976 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.97245e6 | 0.131079 | 0.0655395 | − | 0.997850i | \(-0.479123\pi\) | ||||
0.0655395 | + | 0.997850i | \(0.479123\pi\) | |||||||
\(744\) | 997056. | 0.0660370 | ||||||||
\(745\) | 1.30620e7 | 0.862223 | ||||||||
\(746\) | 9.83580e6 | 0.647087 | ||||||||
\(747\) | −8.95876e6 | −0.587417 | ||||||||
\(748\) | 1.03578e6 | 0.0676880 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.54802e6 | 0.230320 | ||||||||
\(751\) | 1.50246e7 | 0.972085 | 0.486042 | − | 0.873935i | \(-0.338440\pi\) | ||||
0.486042 | + | 0.873935i | \(0.338440\pi\) | |||||||
\(752\) | −4.72627e6 | −0.304771 | ||||||||
\(753\) | 2.77495e6 | 0.178348 | ||||||||
\(754\) | 78096.0 | 0.00500265 | ||||||||
\(755\) | −6.59173e6 | −0.420854 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.72426e6 | −0.299636 | −0.149818 | − | 0.988714i | \(-0.547869\pi\) | ||||
−0.149818 | + | 0.988714i | \(0.547869\pi\) | |||||||
\(758\) | 1.64052e7 | 1.03707 | ||||||||
\(759\) | −68544.0 | −0.00431882 | ||||||||
\(760\) | 8.19546e6 | 0.514682 | ||||||||
\(761\) | 8.57835e6 | 0.536960 | 0.268480 | − | 0.963285i | \(-0.413479\pi\) | ||||
0.268480 | + | 0.963285i | \(0.413479\pi\) | |||||||
\(762\) | 5.47074e6 | 0.341318 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.82032e6 | −0.236792 | ||||||||
\(765\) | −1.32633e7 | −0.819402 | ||||||||
\(766\) | −1.03765e7 | −0.638970 | ||||||||
\(767\) | 95484.0 | 0.00586060 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | −1.76168e7 | −1.07426 | −0.537131 | − | 0.843499i | \(-0.680492\pi\) | ||||
−0.537131 | + | 0.843499i | \(0.680492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.67886e6 | −0.222883 | ||||||||
\(772\) | 1.37106e6 | 0.0827965 | ||||||||
\(773\) | 1.25420e6 | 0.0754951 | 0.0377475 | − | 0.999287i | \(-0.487982\pi\) | ||||
0.0377475 | + | 0.999287i | \(0.487982\pi\) | |||||||
\(774\) | −5.99108e6 | −0.359462 | ||||||||
\(775\) | −7.39310e6 | −0.442153 | ||||||||
\(776\) | −7.67014e6 | −0.457245 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.93626e6 | −0.529306 | ||||||||
\(779\) | −2.29514e7 | −1.35508 | ||||||||
\(780\) | −37152.0 | −0.00218648 | ||||||||
\(781\) | −1.52436e6 | −0.0894250 | ||||||||
\(782\) | 1.70598e6 | 0.0997604 | ||||||||
\(783\) | −4.74433e6 | −0.276548 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.35151e7 | −1.94118 | ||||||||
\(786\) | 8.47807e6 | 0.489487 | ||||||||
\(787\) | −7.09121e6 | −0.408116 | −0.204058 | − | 0.978959i | \(-0.565413\pi\) | ||||
−0.204058 | + | 0.978959i | \(0.565413\pi\) | |||||||
\(788\) | −1.14253e6 | −0.0655468 | ||||||||
\(789\) | 9.79312e6 | 0.560052 | ||||||||
\(790\) | −1.05027e7 | −0.598731 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −176256. | −0.00998461 | ||||||||
\(793\) | 172962. | 0.00976715 | ||||||||
\(794\) | −8.25599e6 | −0.464748 | ||||||||
\(795\) | 1.54459e7 | 0.866756 | ||||||||
\(796\) | 1.13816e7 | 0.636681 | ||||||||
\(797\) | 2.71630e6 | 0.151472 | 0.0757358 | − | 0.997128i | \(-0.475869\pi\) | ||||
0.0757358 | + | 0.997128i | \(0.475869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.51516e7 | −1.94795 | ||||||||
\(800\) | −4.37350e6 | −0.241604 | ||||||||
\(801\) | 4.77835e6 | 0.263146 | ||||||||
\(802\) | −4.61131e6 | −0.253156 | ||||||||
\(803\) | −707914. | −0.0387429 | ||||||||
\(804\) | −8.72107e6 | −0.475806 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20772.0 | 0.00112627 | ||||||||
\(807\) | 6.01461e6 | 0.325105 | ||||||||
\(808\) | 6.40064e6 | 0.344901 | ||||||||
\(809\) | −2.18739e7 | −1.17505 | −0.587524 | − | 0.809207i | \(-0.699897\pi\) | ||||
−0.587524 | + | 0.809207i | \(0.699897\pi\) | |||||||
\(810\) | 2.25698e6 | 0.120869 | ||||||||
\(811\) | 1.72352e7 | 0.920164 | 0.460082 | − | 0.887876i | \(-0.347820\pi\) | ||||
0.460082 | + | 0.887876i | \(0.347820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.47598e6 | 0.396681 | ||||||||
\(814\) | 1.03809e6 | 0.0549127 | ||||||||
\(815\) | 9.66399e6 | 0.509639 | ||||||||
\(816\) | 4.38682e6 | 0.230634 | ||||||||
\(817\) | 2.75331e7 | 1.44311 | ||||||||
\(818\) | 2.37365e7 | 1.24032 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.12097e7 | 1.10154 | ||||||||
\(821\) | −2.26191e7 | −1.17116 | −0.585582 | − | 0.810613i | \(-0.699134\pi\) | ||||
−0.585582 | + | 0.810613i | \(0.699134\pi\) | |||||||
\(822\) | −1.17183e7 | −0.604901 | ||||||||
\(823\) | 1.62633e6 | 0.0836967 | 0.0418484 | − | 0.999124i | \(-0.486675\pi\) | ||||
0.0418484 | + | 0.999124i | \(0.486675\pi\) | |||||||
\(824\) | 7.78822e6 | 0.399595 | ||||||||
\(825\) | 1.30693e6 | 0.0668523 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.28304e7 | −1.16078 | −0.580391 | − | 0.814338i | \(-0.697100\pi\) | ||||
−0.580391 | + | 0.814338i | \(0.697100\pi\) | |||||||
\(828\) | −290304. | −0.0147156 | ||||||||
\(829\) | −2.58593e7 | −1.30686 | −0.653432 | − | 0.756985i | \(-0.726672\pi\) | ||||
−0.653432 | + | 0.756985i | \(0.726672\pi\) | |||||||
\(830\) | −3.80471e7 | −1.91702 | ||||||||
\(831\) | 8.32566e6 | 0.418231 | ||||||||
\(832\) | 12288.0 | 0.000615422 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 115596. | 0.00575477 | ||||||||
\(835\) | 4.51930e6 | 0.224313 | ||||||||
\(836\) | 810016. | 0.0400846 | ||||||||
\(837\) | −1.26190e6 | −0.0622603 | ||||||||
\(838\) | 3.08666e6 | 0.151838 | ||||||||
\(839\) | 1.23061e7 | 0.603554 | 0.301777 | − | 0.953379i | \(-0.402420\pi\) | ||||
0.301777 | + | 0.953379i | \(0.402420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.18429e7 | 1.06493 | ||||||||
\(842\) | 1.15017e7 | 0.559089 | ||||||||
\(843\) | 1.20271e7 | 0.582899 | ||||||||
\(844\) | −4.16416e6 | −0.201220 | ||||||||
\(845\) | 3.19304e7 | 1.53838 | ||||||||
\(846\) | 5.98169e6 | 0.287341 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.10874e6 | −0.243963 | ||||||||
\(849\) | 8.93661e6 | 0.425504 | ||||||||
\(850\) | −3.25279e7 | −1.54422 | ||||||||
\(851\) | 1.70979e6 | 0.0809318 | ||||||||
\(852\) | −6.45610e6 | −0.304699 | ||||||||
\(853\) | 1.91416e7 | 0.900753 | 0.450377 | − | 0.892839i | \(-0.351290\pi\) | ||||
0.450377 | + | 0.892839i | \(0.351290\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.03724e7 | −0.485247 | ||||||||
\(856\) | 3.11347e6 | 0.145231 | ||||||||
\(857\) | 4.75507e6 | 0.221159 | 0.110580 | − | 0.993867i | \(-0.464729\pi\) | ||||
0.110580 | + | 0.993867i | \(0.464729\pi\) | |||||||
\(858\) | −3672.00 | −0.000170288 0 | ||||||||
\(859\) | 9.19876e6 | 0.425350 | 0.212675 | − | 0.977123i | \(-0.431782\pi\) | ||||
0.212675 | + | 0.977123i | \(0.431782\pi\) | |||||||
\(860\) | −2.54436e7 | −1.17309 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 551448. | 0.0252776 | ||||||||
\(863\) | −1.73532e7 | −0.793144 | −0.396572 | − | 0.918004i | \(-0.629800\pi\) | ||||
−0.396572 | + | 0.918004i | \(0.629800\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | −1.16320e7 | −0.528585 | ||||||||
\(866\) | 6.26102e6 | 0.283694 | ||||||||
\(867\) | 1.98482e7 | 0.896756 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.03805e6 | −0.0466305 | ||||||||
\(870\) | −2.01488e7 | −0.902507 | ||||||||
\(871\) | −181689. | −0.00811490 | ||||||||
\(872\) | 9.73280e6 | 0.433458 | ||||||||
\(873\) | 9.70753e6 | 0.431095 | ||||||||
\(874\) | 1.33414e6 | 0.0590778 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.99822e6 | −0.132009 | ||||||||
\(877\) | −3.55622e7 | −1.56131 | −0.780655 | − | 0.624962i | \(-0.785115\pi\) | ||||
−0.780655 | + | 0.624962i | \(0.785115\pi\) | |||||||
\(878\) | 1.95263e7 | 0.854838 | ||||||||
\(879\) | −5.07190e6 | −0.221410 | ||||||||
\(880\) | −748544. | −0.0325845 | ||||||||
\(881\) | 2.63056e7 | 1.14185 | 0.570923 | − | 0.821003i | \(-0.306585\pi\) | ||||
0.570923 | + | 0.821003i | \(0.306585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.20394e7 | 0.519642 | 0.259821 | − | 0.965657i | \(-0.416336\pi\) | ||||
0.259821 | + | 0.965657i | \(0.416336\pi\) | |||||||
\(884\) | 91392.0 | 0.00393349 | ||||||||
\(885\) | −2.46349e7 | −1.05729 | ||||||||
\(886\) | 5.20606e6 | 0.222805 | ||||||||
\(887\) | 133590. | 0.00570118 | 0.00285059 | − | 0.999996i | \(-0.499093\pi\) | ||||
0.00285059 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(888\) | 4.39661e6 | 0.187105 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.02932e7 | 0.858769 | ||||||||
\(891\) | 223074. | 0.00941358 | ||||||||
\(892\) | −1.69050e6 | −0.0711381 | ||||||||
\(893\) | −2.74899e7 | −1.15357 | ||||||||
\(894\) | 5.46782e6 | 0.228808 | ||||||||
\(895\) | −2.15549e7 | −0.899472 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6048.00 | −0.000250975 0 | ||||||||
\(898\) | 1.25256e7 | 0.518333 | ||||||||
\(899\) | 1.12653e7 | 0.464885 | ||||||||
\(900\) | 5.53522e6 | 0.227787 | ||||||||
\(901\) | −3.79962e7 | −1.55930 | ||||||||
\(902\) | 2.09630e6 | 0.0857902 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.89670e6 | 0.158590 | ||||||||
\(905\) | 1.71340e7 | 0.695406 | ||||||||
\(906\) | −2.75933e6 | −0.111682 | ||||||||
\(907\) | −1.27476e7 | −0.514529 | −0.257264 | − | 0.966341i | \(-0.582821\pi\) | ||||
−0.257264 | + | 0.966341i | \(0.582821\pi\) | |||||||
\(908\) | −1.04760e7 | −0.421678 | ||||||||
\(909\) | −8.10081e6 | −0.325176 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.43253e7 | 0.971095 | 0.485548 | − | 0.874210i | \(-0.338620\pi\) | ||||
0.485548 | + | 0.874210i | \(0.338620\pi\) | |||||||
\(912\) | 3.43066e6 | 0.136581 | ||||||||
\(913\) | −3.76047e6 | −0.149302 | ||||||||
\(914\) | −2.59707e7 | −1.02830 | ||||||||
\(915\) | −4.46242e7 | −1.76205 | ||||||||
\(916\) | −8.92341e6 | −0.351392 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.55206e6 | −0.217444 | ||||||||
\(919\) | −3.84805e7 | −1.50297 | −0.751487 | − | 0.659748i | \(-0.770663\pi\) | ||||
−0.751487 | + | 0.659748i | \(0.770663\pi\) | |||||||
\(920\) | −1.23290e6 | −0.0480238 | ||||||||
\(921\) | −2.54433e7 | −0.988381 | ||||||||
\(922\) | 2.13887e7 | 0.828623 | ||||||||
\(923\) | −134502. | −0.00519666 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.26005e7 | −1.25277 | ||||||||
\(926\) | −1.34914e7 | −0.517047 | ||||||||
\(927\) | −9.85697e6 | −0.376742 | ||||||||
\(928\) | 6.66419e6 | 0.254026 | ||||||||
\(929\) | −3.96678e7 | −1.50799 | −0.753996 | − | 0.656879i | \(-0.771876\pi\) | ||||
−0.753996 | + | 0.656879i | \(0.771876\pi\) | |||||||
\(930\) | −5.35918e6 | −0.203185 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.99615e7 | −0.752755 | ||||||||
\(933\) | 1.01458e7 | 0.381578 | ||||||||
\(934\) | 8.93809e6 | 0.335257 | ||||||||
\(935\) | −5.56730e6 | −0.208265 | ||||||||
\(936\) | −15552.0 | −0.000580225 0 | ||||||||
\(937\) | −1.48428e7 | −0.552288 | −0.276144 | − | 0.961116i | \(-0.589057\pi\) | ||||
−0.276144 | + | 0.961116i | \(0.589057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.12412e7 | 0.786166 | ||||||||
\(940\) | 2.54037e7 | 0.937729 | ||||||||
\(941\) | −4.67063e7 | −1.71950 | −0.859748 | − | 0.510718i | \(-0.829380\pi\) | ||||
−0.859748 | + | 0.510718i | \(0.829380\pi\) | |||||||
\(942\) | −1.40296e7 | −0.515130 | ||||||||
\(943\) | 3.45274e6 | 0.126440 | ||||||||
\(944\) | 8.14797e6 | 0.297591 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.51478e6 | −0.0913632 | ||||||||
\(947\) | 4.02379e7 | 1.45801 | 0.729006 | − | 0.684508i | \(-0.239983\pi\) | ||||
0.729006 | + | 0.684508i | \(0.239983\pi\) | |||||||
\(948\) | −4.39646e6 | −0.158885 | ||||||||
\(949\) | −62463.0 | −0.00225142 | ||||||||
\(950\) | −2.54381e7 | −0.914482 | ||||||||
\(951\) | −2.00178e7 | −0.717737 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.45579e7 | 0.875908 | 0.437954 | − | 0.898997i | \(-0.355703\pi\) | ||||
0.437954 | + | 0.898997i | \(0.355703\pi\) | |||||||
\(954\) | 6.46574e6 | 0.230010 | ||||||||
\(955\) | 2.05342e7 | 0.728567 | ||||||||
\(956\) | −7.95082e6 | −0.281363 | ||||||||
\(957\) | −1.99145e6 | −0.0702893 | ||||||||
\(958\) | −1.00855e7 | −0.355044 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.17030e6 | −0.111026 | ||||||||
\(961\) | −2.56328e7 | −0.895339 | ||||||||
\(962\) | 91596.0 | 0.00319109 | ||||||||
\(963\) | −3.94049e6 | −0.136925 | ||||||||
\(964\) | 4.44189e6 | 0.153948 | ||||||||
\(965\) | −7.36943e6 | −0.254751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.34313e7 | 1.83751 | 0.918754 | − | 0.394830i | \(-0.129197\pi\) | ||||
0.918754 | + | 0.394830i | \(0.129197\pi\) | |||||||
\(968\) | 1.02333e7 | 0.351016 | ||||||||
\(969\) | 2.55155e7 | 0.872961 | ||||||||
\(970\) | 4.12270e7 | 1.40687 | ||||||||
\(971\) | 2.81485e6 | 0.0958093 | 0.0479046 | − | 0.998852i | \(-0.484746\pi\) | ||||
0.0479046 | + | 0.998852i | \(0.484746\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.66687e6 | −0.258953 | ||||||||
\(975\) | 115317. | 0.00388492 | ||||||||
\(976\) | 1.47594e7 | 0.495958 | ||||||||
\(977\) | 2.54713e7 | 0.853718 | 0.426859 | − | 0.904318i | \(-0.359620\pi\) | ||||
0.426859 | + | 0.904318i | \(0.359620\pi\) | |||||||
\(978\) | 4.04539e6 | 0.135243 | ||||||||
\(979\) | 2.00573e6 | 0.0668829 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.23181e7 | −0.408668 | ||||||||
\(982\) | −2.33150e7 | −0.771537 | ||||||||
\(983\) | 2.90135e6 | 0.0957670 | 0.0478835 | − | 0.998853i | \(-0.484752\pi\) | ||||
0.0478835 | + | 0.998853i | \(0.484752\pi\) | |||||||
\(984\) | 8.87846e6 | 0.292314 | ||||||||
\(985\) | 6.14109e6 | 0.201676 | ||||||||
\(986\) | 4.95649e7 | 1.62361 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 71472.0 | 0.00232940 | ||||||||
\(989\) | −4.14198e6 | −0.134654 | ||||||||
\(990\) | 947376. | 0.0307209 | ||||||||
\(991\) | 2.73784e6 | 0.0885570 | 0.0442785 | − | 0.999019i | \(-0.485901\pi\) | ||||
0.0442785 | + | 0.999019i | \(0.485901\pi\) | |||||||
\(992\) | 1.77254e6 | 0.0571897 | ||||||||
\(993\) | −3.33274e7 | −1.07258 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.11763e7 | −1.95896 | ||||||||
\(996\) | −1.59267e7 | −0.508718 | ||||||||
\(997\) | 2.74079e7 | 0.873249 | 0.436624 | − | 0.899644i | \(-0.356174\pi\) | ||||
0.436624 | + | 0.899644i | \(0.356174\pi\) | |||||||
\(998\) | 4.00194e7 | 1.27188 | ||||||||
\(999\) | −5.56446e6 | −0.176404 |
(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 | 294.6.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 882.6.a.y.1.1 | 1 | |||
7.2 | even | 3 | 294.6.e.m.67.1 | 2 | |||
7.3 | odd | 6 | 42.6.e.b.37.1 | yes | 2 | ||
7.4 | even | 3 | 294.6.e.m.79.1 | 2 | |||
7.5 | odd | 6 | 42.6.e.b.25.1 | ✓ | 2 | ||
7.6 | odd | 2 | 294.6.a.d.1.1 | 1 | |||
21.5 | even | 6 | 126.6.g.b.109.1 | 2 | |||
21.17 | even | 6 | 126.6.g.b.37.1 | 2 | |||
21.20 | even | 2 | 882.6.a.m.1.1 | 1 | |||
28.3 | even | 6 | 336.6.q.a.289.1 | 2 | |||
28.19 | even | 6 | 336.6.q.a.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.e.b.25.1 | ✓ | 2 | 7.5 | odd | 6 | ||
42.6.e.b.37.1 | yes | 2 | 7.3 | odd | 6 | ||
126.6.g.b.37.1 | 2 | 21.17 | even | 6 | |||
126.6.g.b.109.1 | 2 | 21.5 | even | 6 | |||
294.6.a.d.1.1 | 1 | 7.6 | odd | 2 | |||
294.6.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
294.6.e.m.67.1 | 2 | 7.2 | even | 3 | |||
294.6.e.m.79.1 | 2 | 7.4 | even | 3 | |||
336.6.q.a.193.1 | 2 | 28.19 | even | 6 | |||
336.6.q.a.289.1 | 2 | 28.3 | even | 6 | |||
882.6.a.m.1.1 | 1 | 21.20 | even | 2 | |||
882.6.a.y.1.1 | 1 | 3.2 | odd | 2 |