Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,6,Mod(1,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("688.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.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: | \(110.344068031\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(11.5305\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −27.4953 | −1.76382 | −0.881911 | − | 0.471417i | \(-0.843743\pi\) | ||||
−0.881911 | + | 0.471417i | \(0.843743\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 86.8464 | 1.55356 | 0.776778 | − | 0.629775i | \(-0.216853\pi\) | ||||
0.776778 | + | 0.629775i | \(0.216853\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 19.8137 | 0.152834 | 0.0764171 | − | 0.997076i | \(-0.475652\pi\) | ||||
0.0764171 | + | 0.997076i | \(0.475652\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 512.989 | 2.11107 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 85.3712 | 0.212730 | 0.106365 | − | 0.994327i | \(-0.466079\pi\) | ||||
0.106365 | + | 0.994327i | \(0.466079\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −229.081 | −0.375951 | −0.187975 | − | 0.982174i | \(-0.560193\pi\) | ||||
−0.187975 | + | 0.982174i | \(0.560193\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2387.86 | −2.74019 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1356.51 | 1.13841 | 0.569207 | − | 0.822194i | \(-0.307250\pi\) | ||||
0.569207 | + | 0.822194i | \(0.307250\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2795.35 | 1.77645 | 0.888223 | − | 0.459413i | \(-0.151940\pi\) | ||||
0.888223 | + | 0.459413i | \(0.151940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −544.783 | −0.269572 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1856.11 | 0.731618 | 0.365809 | − | 0.930690i | \(-0.380792\pi\) | ||||
0.365809 | + | 0.930690i | \(0.380792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4417.29 | 1.41353 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7423.41 | −1.95972 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7312.96 | 1.61472 | 0.807362 | − | 0.590057i | \(-0.200895\pi\) | ||||
0.807362 | + | 0.590057i | \(0.200895\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2937.36 | 0.548975 | 0.274488 | − | 0.961591i | \(-0.411492\pi\) | ||||
0.274488 | + | 0.961591i | \(0.411492\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2347.30 | −0.375218 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1720.75 | 0.237436 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2577.36 | 0.309507 | 0.154754 | − | 0.987953i | \(-0.450542\pi\) | ||||
0.154754 | + | 0.987953i | \(0.450542\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6298.65 | 0.663110 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3532.54 | −0.328192 | −0.164096 | − | 0.986444i | \(-0.552471\pi\) | ||||
−0.164096 | + | 0.986444i | \(0.552471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1849.00 | −0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 44551.2 | 3.27966 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7065.73 | 0.466566 | 0.233283 | − | 0.972409i | \(-0.425053\pi\) | ||||
0.233283 | + | 0.972409i | \(0.425053\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16414.4 | −0.976642 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −37297.6 | −2.00796 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3852.63 | −0.188394 | −0.0941972 | − | 0.995554i | \(-0.530028\pi\) | ||||
−0.0941972 | + | 0.995554i | \(0.530028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7414.18 | 0.330488 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −76858.8 | −3.13333 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −27996.1 | −1.04705 | −0.523524 | − | 0.852011i | \(-0.675383\pi\) | ||||
−0.523524 | + | 0.852011i | \(0.675383\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39244.4 | −1.35037 | −0.675186 | − | 0.737648i | \(-0.735937\pi\) | ||||
−0.675186 | + | 0.737648i | \(0.735937\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10164.2 | 0.322643 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −19894.9 | −0.584060 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14809.1 | 0.403034 | 0.201517 | − | 0.979485i | \(-0.435413\pi\) | ||||
0.201517 | + | 0.979485i | \(0.435413\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −51034.2 | −1.29044 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8956.13 | −0.210850 | −0.105425 | − | 0.994427i | \(-0.533620\pi\) | ||||
−0.105425 | + | 0.994427i | \(0.533620\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35168.6 | 0.772411 | 0.386205 | − | 0.922413i | \(-0.373786\pi\) | ||||
0.386205 | + | 0.922413i | \(0.373786\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −121455. | −2.49322 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1691.52 | 0.0325125 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13263.6 | 0.239108 | 0.119554 | − | 0.992828i | \(-0.461854\pi\) | ||||
0.119554 | + | 0.992828i | \(0.461854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79452.3 | 1.34553 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9812.47 | 0.156345 | 0.0781724 | − | 0.996940i | \(-0.475092\pi\) | ||||
0.0781724 | + | 0.996940i | \(0.475092\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 117808. | 1.76859 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −201072. | −2.84808 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −87124.9 | −1.16592 | −0.582958 | − | 0.812502i | \(-0.698105\pi\) | ||||
−0.582958 | + | 0.812502i | \(0.698105\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4538.95 | −0.0574581 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −80763.5 | −0.968295 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 242766. | 2.75981 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 83982.4 | 0.906272 | 0.453136 | − | 0.891441i | \(-0.350305\pi\) | ||||
0.453136 | + | 0.891441i | \(0.350305\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43794.5 | 0.449088 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 74775.4 | 0.729382 | 0.364691 | − | 0.931129i | \(-0.381175\pi\) | ||||
0.364691 | + | 0.931129i | \(0.381175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −29400.7 | −0.273064 | −0.136532 | − | 0.990636i | \(-0.543596\pi\) | ||||
−0.136532 | + | 0.990636i | \(0.543596\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −47312.4 | −0.418795 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 199822. | 1.68727 | 0.843635 | − | 0.536917i | \(-0.180411\pi\) | ||||
0.843635 | + | 0.536917i | \(0.180411\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −39465.7 | −0.318166 | −0.159083 | − | 0.987265i | \(-0.550854\pi\) | ||||
−0.159083 | + | 0.987265i | \(0.550854\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −70865.2 | −0.545915 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 41487.8 | 0.305650 | 0.152825 | − | 0.988253i | \(-0.451163\pi\) | ||||
0.152825 | + | 0.988253i | \(0.451163\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 161196. | 1.13661 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117516. | −0.793657 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26877.5 | 0.173989 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −153763. | −0.954746 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 97128.1 | 0.578871 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 112231. | 0.642448 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −357769. | −1.96831 | −0.984156 | − | 0.177305i | \(-0.943262\pi\) | ||||
−0.984156 | + | 0.177305i | \(0.943262\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 50838.7 | 0.268980 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 61207.9 | 0.311623 | 0.155811 | − | 0.987787i | \(-0.450201\pi\) | ||||
0.155811 | + | 0.987787i | \(0.450201\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 55386.2 | 0.271502 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −644697. | −3.04453 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −309777. | −1.41009 | −0.705047 | − | 0.709161i | \(-0.749074\pi\) | ||||
−0.705047 | + | 0.709161i | \(0.749074\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 193740. | 0.850517 | 0.425259 | − | 0.905072i | \(-0.360183\pi\) | ||||
0.425259 | + | 0.905072i | \(0.360183\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −194274. | −0.822938 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19556.9 | −0.0799762 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 635104. | 2.50856 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 451319. | 1.72262 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −455017. | −1.67904 | −0.839521 | − | 0.543327i | \(-0.817164\pi\) | ||||
−0.839521 | + | 0.543327i | \(0.817164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 505868. | 1.80549 | 0.902744 | − | 0.430179i | \(-0.141549\pi\) | ||||
0.902744 | + | 0.430179i | \(0.141549\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 695874. | 2.40327 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 255099. | 0.852864 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 348495. | 1.12836 | 0.564179 | − | 0.825652i | \(-0.309193\pi\) | ||||
0.564179 | + | 0.825652i | \(0.309193\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 105929. | 0.332294 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 36776.4 | 0.111816 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −104915. | −0.309291 | −0.154645 | − | 0.987970i | \(-0.549424\pi\) | ||||
−0.154645 | + | 0.987970i | \(0.549424\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −203855. | −0.582923 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −186982. | −0.518809 | −0.259405 | − | 0.965769i | \(-0.583526\pi\) | ||||
−0.259405 | + | 0.965769i | \(0.583526\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −318815. | −0.858661 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.43398e6 | 3.75019 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 491718. | 1.24911 | 0.624555 | − | 0.780981i | \(-0.285280\pi\) | ||||
0.624555 | + | 0.780981i | \(0.285280\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 87522.9 | 0.216036 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 769758. | 1.84681 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −374509. | −0.873634 | −0.436817 | − | 0.899550i | \(-0.643894\pi\) | ||||
−0.436817 | + | 0.899550i | \(0.643894\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 460794. | 1.04547 | 0.522733 | − | 0.852496i | \(-0.324912\pi\) | ||||
0.522733 | + | 0.852496i | \(0.324912\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.07904e6 | 2.38181 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 223834. | 0.480837 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 115807. | 0.242175 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −147085. | −0.299512 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22464.4 | 0.0445565 | 0.0222783 | − | 0.999752i | \(-0.492908\pi\) | ||||
0.0222783 | + | 0.999752i | \(0.492908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 830124. | 1.60417 | 0.802083 | − | 0.597212i | \(-0.203725\pi\) | ||||
0.802083 | + | 0.597212i | \(0.203725\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 547015. | 1.03018 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 802058. | 1.47245 | 0.736224 | − | 0.676738i | \(-0.236607\pi\) | ||||
0.736224 | + | 0.676738i | \(0.236607\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 187945. | 0.336432 | 0.168216 | − | 0.985750i | \(-0.446199\pi\) | ||||
0.168216 | + | 0.985750i | \(0.446199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −407180. | −0.710879 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 144897. | 0.246785 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −306788. | −0.509864 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 952164. | 1.54449 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 238642. | 0.377904 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −327613. | −0.506589 | −0.253294 | − | 0.967389i | \(-0.581514\pi\) | ||||
−0.253294 | + | 0.967389i | \(0.581514\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 246251. | 0.371902 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −160579. | −0.236915 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 58200.0 | 0.0839022 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −966970. | −1.36239 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −310751. | −0.427988 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 166692. | 0.224467 | 0.112234 | − | 0.993682i | \(-0.464199\pi\) | ||||
0.112234 | + | 0.993682i | \(0.464199\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.26602e6 | 2.98406 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 155259. | 0.199982 | 0.0999912 | − | 0.994988i | \(-0.468119\pi\) | ||||
0.0999912 | + | 0.994988i | \(0.468119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.01590e6 | −1.28016 | −0.640079 | − | 0.768309i | \(-0.721098\pi\) | ||||
−0.640079 | + | 0.768309i | \(0.721098\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −46508.7 | −0.0573462 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23299.8 | 0.0281166 | 0.0140583 | − | 0.999901i | \(-0.495525\pi\) | ||||
0.0140583 | + | 0.999901i | \(0.495525\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 613633. | 0.724835 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −364686. | −0.421743 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4871.64 | −0.00551671 | −0.00275836 | − | 0.999996i | \(-0.500878\pi\) | ||||
−0.00275836 | + | 0.999996i | \(0.500878\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 918873. | 1.01909 | 0.509545 | − | 0.860444i | \(-0.329814\pi\) | ||||
0.509545 | + | 0.860444i | \(0.329814\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −380672. | −0.413557 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.42553e6 | −1.51727 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −640362. | −0.667856 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −269796. | −0.275764 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.47118e6 | −1.47395 | −0.736973 | − | 0.675922i | \(-0.763746\pi\) | ||||
−0.736973 | + | 0.675922i | \(0.763746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 158458. | 0.155637 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.23916e6 | −3.11948 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −813506. | −0.768295 | −0.384147 | − | 0.923272i | \(-0.625505\pi\) | ||||
−0.384147 | + | 0.923272i | \(0.625505\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 51067.0 | 0.0473033 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.75147e6 | 3.40879 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −691865. | −0.616782 | −0.308391 | − | 0.951260i | \(-0.599791\pi\) | ||||
−0.308391 | + | 0.951260i | \(0.599791\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −334587. | −0.292681 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.39552e6 | 2.05647 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −759828. | −0.640228 | −0.320114 | − | 0.947379i | \(-0.603721\pi\) | ||||
−0.320114 | + | 0.947379i | \(0.603721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −954020. | −0.789104 | −0.394552 | − | 0.918874i | \(-0.629100\pi\) | ||||
−0.394552 | + | 0.918874i | \(0.629100\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 124799. | 0.101346 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 377110. | 0.300702 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.03398e6 | 0.809680 | 0.404840 | − | 0.914387i | \(-0.367327\pi\) | ||||
0.404840 | + | 0.914387i | \(0.367327\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.50683e6 | 1.15892 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.05117e6 | 1.54966 | 0.774829 | − | 0.632171i | \(-0.217836\pi\) | ||||
0.774829 | + | 0.632171i | \(0.217836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.37044e6 | 1.75940 | 0.879698 | − | 0.475533i | \(-0.157745\pi\) | ||||
0.879698 | + | 0.475533i | \(0.157745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.67491e6 | −4.86780 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −69992.7 | −0.0501589 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 420259. | 0.295987 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.30912e6 | −1.59850 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.48623e6 | 1.01138 | 0.505692 | − | 0.862714i | \(-0.331237\pi\) | ||||
0.505692 | + | 0.862714i | \(0.331237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.43136e6 | −1.62665 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −633746. | −0.416892 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −425200. | −0.275052 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36635.5 | −0.0233070 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.05597e6 | −1.28650 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.40824e6 | −2.09788 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.62571e6 | 0.984456 | 0.492228 | − | 0.870466i | \(-0.336183\pi\) | ||||
0.492228 | + | 0.870466i | \(0.336183\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 808378. | 0.481636 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.07269e6 | −1.21516 | −0.607581 | − | 0.794258i | \(-0.707860\pi\) | ||||
−0.607581 | + | 0.794258i | \(0.707860\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −345918. | −0.199578 | −0.0997889 | − | 0.995009i | \(-0.531817\pi\) | ||||
−0.0997889 | + | 0.995009i | \(0.531817\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 882725. | 0.501244 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 574435. | 0.321065 | 0.160532 | − | 0.987031i | \(-0.448679\pi\) | ||||
0.160532 | + | 0.987031i | \(0.448679\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 624316. | 0.343501 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.49417e6 | −2.97604 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.79191e6 | 2.02233 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.01192e6 | −0.531419 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.08512e6 | 0.561187 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 139998. | 0.0713072 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.12898e6 | 0.566393 | 0.283196 | − | 0.959062i | \(-0.408605\pi\) | ||||
0.283196 | + | 0.959062i | \(0.408605\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.32216e6 | 0.653390 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.28612e6 | 0.626135 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −370207. | −0.177570 | −0.0887850 | − | 0.996051i | \(-0.528298\pi\) | ||||
−0.0887850 | + | 0.996051i | \(0.528298\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.14072e6 | −0.539112 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 250766. | 0.116784 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −658239. | −0.302098 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.43214e6 | −2.00477 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −372676. | −0.166153 | −0.0830764 | − | 0.996543i | \(-0.526475\pi\) | ||||
−0.0830764 | + | 0.996543i | \(0.526475\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.14587e6 | −0.943060 | −0.471530 | − | 0.881850i | \(-0.656298\pi\) | ||||
−0.471530 | + | 0.881850i | \(0.656298\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.70056e6 | 0.736759 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.87740e6 | −1.22903 | −0.614517 | − | 0.788904i | \(-0.710649\pi\) | ||||
−0.614517 | + | 0.788904i | \(0.710649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −777807. | −0.327568 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −739003. | −0.306885 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −647359. | −0.265100 | −0.132550 | − | 0.991176i | \(-0.542316\pi\) | ||||
−0.132550 | + | 0.991176i | \(0.542316\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.33787e6 | 2.15576 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.22775e6 | 1.68400 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.05427e6 | 1.19998 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.06021e6 | −1.18600 | −0.593001 | − | 0.805202i | \(-0.702057\pi\) | ||||
−0.593001 | + | 0.805202i | \(0.702057\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.81215e6 | −0.692834 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −76335.0 | −0.0287931 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.54156e6 | 1.31802 | 0.659010 | − | 0.752134i | \(-0.270975\pi\) | ||||
0.659010 | + | 0.752134i | \(0.270975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.08582e6 | −1.13316 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.67526e6 | −0.607057 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.92757e6 | 1.40451 | 0.702257 | − | 0.711923i | \(-0.252176\pi\) | ||||
0.702257 | + | 0.711923i | \(0.252176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.83696e6 | 3.47175 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.29688e6 | 0.451754 | 0.225877 | − | 0.974156i | \(-0.427475\pi\) | ||||
0.225877 | + | 0.974156i | \(0.427475\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 146902. | 0.0505099 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −948517. | −0.321934 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −100541. | −0.0336874 | −0.0168437 | − | 0.999858i | \(-0.505362\pi\) | ||||
−0.0168437 | + | 0.999858i | \(0.505362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.51783e6 | 0.832884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.68293e6 | −0.549647 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.15190e6 | 0.371467 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.36979e6 | 1.07307 | 0.536533 | − | 0.843879i | \(-0.319734\pi\) | ||||
0.536533 | + | 0.843879i | \(0.319734\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.52286e6 | −0.478880 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.73407e6 | 1.47019 | 0.735095 | − | 0.677964i | \(-0.237138\pi\) | ||||
0.735095 | + | 0.677964i | \(0.237138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −672894. | −0.206388 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.90015e6 | 2.09036 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 220032. | 0.0658416 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −84169.8 | −0.0248799 | −0.0124399 | − | 0.999923i | \(-0.503960\pi\) | ||||
−0.0124399 | + | 0.999923i | \(0.503960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.51740e6 | 2.48715 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −554705. | −0.160025 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 852178. | 0.242890 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.32694e6 | −1.50016 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.45191e6 | 0.404022 | 0.202011 | − | 0.979383i | \(-0.435252\pi\) | ||||
0.202011 | + | 0.979383i | \(0.435252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.69910e6 | 1.29214 | 0.646070 | − | 0.763278i | \(-0.276411\pi\) | ||||
0.646070 | + | 0.763278i | \(0.276411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.62464e6 | 0.984950 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.99210e6 | 1.60919 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −777577. | −0.206383 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 537723. | 0.141064 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.34282e6 | −0.866803 | −0.433401 | − | 0.901201i | \(-0.642687\pi\) | ||||
−0.433401 | + | 0.901201i | \(0.642687\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 629642. | 0.161389 | 0.0806945 | − | 0.996739i | \(-0.474286\pi\) | ||||
0.0806945 | + | 0.996739i | \(0.474286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.74623e7 | −4.42465 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.18847e6 | 1.29968 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.24963e6 | −1.54772 | −0.773861 | − | 0.633355i | \(-0.781677\pi\) | ||||
−0.773861 | + | 0.633355i | \(0.781677\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.42041e6 | −2.06175 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.58305e6 | −1.59374 | −0.796871 | − | 0.604149i | \(-0.793513\pi\) | ||||
−0.796871 | + | 0.604149i | \(0.793513\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.56648e6 | −1.81131 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.25108e7 | 2.96153 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.62106e6 | 0.379476 | 0.189738 | − | 0.981835i | \(-0.439236\pi\) | ||||
0.189738 | + | 0.981835i | \(0.439236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −301577. | −0.0698163 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.39090e7 | −3.18456 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −394191. | −0.0892644 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.01194e6 | −1.34656 | −0.673278 | − | 0.739390i | \(-0.735114\pi\) | ||||
−0.673278 | + | 0.739390i | \(0.735114\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00699e7 | −2.23097 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.97072e6 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 925538. | 0.200651 | 0.100326 | − | 0.994955i | \(-0.468012\pi\) | ||||
0.100326 | + | 0.994955i | \(0.468012\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.01401e6 | −1.50430 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.87994e6 | −0.398890 | −0.199445 | − | 0.979909i | \(-0.563914\pi\) | ||||
−0.199445 | + | 0.979909i | \(0.563914\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 293423. | 0.0615973 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.58195e6 | −1.99022 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −157851. | −0.0324411 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.23479e7 | 2.51107 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.97636e6 | −0.397713 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.18229e6 | −1.62943 | −0.814716 | − | 0.579860i | \(-0.803107\pi\) | ||||
−0.814716 | + | 0.579860i | \(0.803107\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −590425. | −0.116360 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.01118e6 | −0.197224 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.29356e6 | 1.40794 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.84424e6 | 0.352367 | 0.176184 | − | 0.984357i | \(-0.443625\pi\) | ||||
0.176184 | + | 0.984357i | \(0.443625\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.88465e6 | 0.545534 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.29014e6 | 0.803096 | 0.401548 | − | 0.915838i | \(-0.368472\pi\) | ||||
0.401548 | + | 0.915838i | \(0.368472\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.92009e6 | 1.83822 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.80339e6 | 0.697683 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −177454. | −0.0322252 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.80338e6 | 1.40291 | 0.701457 | − | 0.712711i | \(-0.252533\pi\) | ||||
0.701457 | + | 0.712711i | \(0.252533\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.14111e6 | 0.915087 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −673490. | −0.118689 | −0.0593446 | − | 0.998238i | \(-0.518901\pi\) | ||||
−0.0593446 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.49397e6 | 1.13314 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.76589e6 | 1.51452 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.44081e6 | 1.61516 | 0.807579 | − | 0.589760i | \(-0.200778\pi\) | ||||
0.807579 | + | 0.589760i | \(0.200778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 696821. | 0.118051 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.07510e7 | −3.48134 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.55334e6 | −0.424220 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 603210. | 0.0992527 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.35199e7 | −2.20321 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.01037e7 | −1.63074 | −0.815369 | − | 0.578941i | \(-0.803466\pi\) | ||||
−0.815369 | + | 0.578941i | \(0.803466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.22441e6 | −0.195737 | −0.0978687 | − | 0.995199i | \(-0.531203\pi\) | ||||
−0.0978687 | + | 0.995199i | \(0.531203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.40647e6 | −0.381049 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.98455e6 | 0.624961 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.99120e6 | −0.464735 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.43617e7 | −2.21039 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 809239. | 0.123384 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.73539e7 | 2.62127 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.02972e7 | 1.54093 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.40132e6 | −0.207761 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.66077e6 | −0.390853 | −0.195426 | − | 0.980718i | \(-0.562609\pi\) | ||||
−0.195426 | + | 0.980718i | \(0.562609\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.26696e7 | −1.84402 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.42745e6 | −0.494288 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.44368e6 | −1.06370 | −0.531850 | − | 0.846839i | \(-0.678503\pi\) | ||||
−0.531850 | + | 0.846839i | \(0.678503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.01320e7 | −2.85072 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.04423e7 | 2.86847 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 262801. | 0.0365438 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.15438e6 | −0.848110 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.55246e6 | 0.758311 | 0.379155 | − | 0.925333i | \(-0.376215\pi\) | ||||
0.379155 | + | 0.925333i | \(0.376215\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 423571. | 0.0573320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.18414e6 | −0.427154 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.05400e6 | 0.273105 | 0.136552 | − | 0.990633i | \(-0.456398\pi\) | ||||
0.136552 | + | 0.990633i | \(0.456398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.60307e6 | 0.474845 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.57424e6 | 0.205643 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.13151e6 | 0.664453 | 0.332227 | − | 0.943200i | \(-0.392200\pi\) | ||||
0.332227 | + | 0.943200i | \(0.392200\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.13394e7 | 1.45546 | 0.727730 | − | 0.685863i | \(-0.240575\pi\) | ||||
0.727730 | + | 0.685863i | \(0.240575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −617664. | −0.0785898 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.19899e6 | 1.03417 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.19195e6 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.28245e7 | −2.82946 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 194421. | 0.0238948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −328904. | −0.0400772 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.02058e7 | −1.23299 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.32138e6 | −0.876997 | −0.438498 | − | 0.898732i | \(-0.644490\pi\) | ||||
−0.438498 | + | 0.898732i | \(0.644490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.21094e6 | 0.975225 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.20528e7 | −2.59714 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.89330e6 | 1.03855 | 0.519274 | − | 0.854608i | \(-0.326203\pi\) | ||||
0.519274 | + | 0.854608i | \(0.326203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.33421e6 | 0.270301 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.16758e6 | −0.593406 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.52622e6 | −0.857057 | −0.428529 | − | 0.903528i | \(-0.640968\pi\) | ||||
−0.428529 | + | 0.903528i | \(0.640968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.53849e7 | 1.73743 | 0.868716 | − | 0.495311i | \(-0.164946\pi\) | ||||
0.868716 | + | 0.495311i | \(0.164946\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.59690e6 | 0.850830 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.33537e7 | −1.48325 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.10155e7 | 1.21348 | 0.606740 | − | 0.794900i | \(-0.292477\pi\) | ||||
0.606740 | + | 0.794900i | \(0.292477\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.98397e6 | −0.435285 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.61863e6 | −0.175406 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.89814e6 | −0.956419 | −0.478209 | − | 0.878246i | \(-0.658714\pi\) | ||||
−0.478209 | + | 0.878246i | \(0.658714\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.43522e6 | 0.899309 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.40581e6 | 0.783177 | 0.391588 | − | 0.920140i | \(-0.371926\pi\) | ||||
0.391588 | + | 0.920140i | \(0.371926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.41475e7 | −1.48406 | −0.742032 | − | 0.670364i | \(-0.766138\pi\) | ||||
−0.742032 | + | 0.670364i | \(0.766138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.37787e7 | −1.43377 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.72627e6 | −0.178192 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.05719e6 | −0.415456 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.56153e6 | −0.666555 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.49621e6 | 0.352347 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.57148e6 | −0.956986 | −0.478493 | − | 0.878091i | \(-0.658817\pi\) | ||||
−0.478493 | + | 0.878091i | \(0.658817\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.00781e6 | 0.893532 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.10710e7 | −3.05788 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.76023e6 | 0.367169 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.59440e6 | −0.445119 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −637566. | −0.0612887 | −0.0306443 | − | 0.999530i | \(-0.509756\pi\) | ||||
−0.0306443 | + | 0.999530i | \(0.509756\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.89702e7 | 1.80944 | 0.904718 | − | 0.426010i | \(-0.140081\pi\) | ||||
0.904718 | + | 0.426010i | \(0.140081\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.41516e6 | 0.417876 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.02807e7 | −1.90468 | −0.952338 | − | 0.305044i | \(-0.901329\pi\) | ||||
−0.952338 | + | 0.305044i | \(0.901329\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.39006e6 | −0.222739 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.60022e6 | −0.147989 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.76628e6 | −0.345645 | −0.172822 | − | 0.984953i | \(-0.555289\pi\) | ||||
−0.172822 | + | 0.984953i | \(0.555289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.31568e6 | 0.484123 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.80411e7 | 1.63061 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.70994e7 | 1.53379 | 0.766897 | − | 0.641770i | \(-0.221800\pi\) | ||||
0.766897 | + | 0.641770i | \(0.221800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 875240. | 0.0779154 | 0.0389577 | − | 0.999241i | \(-0.487596\pi\) | ||||
0.0389577 | + | 0.999241i | \(0.487596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.54417e6 | 0.754894 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.81009e6 | 0.421793 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.35737e7 | 1.18136 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.58324e6 | −0.395920 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.35034e6 | −0.287265 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.59835e7 | −1.36030 | −0.680149 | − | 0.733074i | \(-0.738085\pi\) | ||||
−0.680149 | + | 0.733074i | \(0.738085\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.27914e7 | −2.77013 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.27744e7 | −1.90974 | −0.954871 | − | 0.297020i | \(-0.904007\pi\) | ||||
−0.954871 | + | 0.297020i | \(0.904007\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.66400e6 | 0.138509 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.26888e6 | −0.352733 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.16349e7 | 0.954354 | 0.477177 | − | 0.878807i | \(-0.341660\pi\) | ||||
0.477177 | + | 0.878807i | \(0.341660\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.69030e7 | −2.19066 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.79325e7 | 2.25797 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 882566. | 0.0708271 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.50626e6 | 0.438694 | 0.219347 | − | 0.975647i | \(-0.429607\pi\) | ||||
0.219347 | + | 0.975647i | \(0.429607\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 867731. | 0.0686360 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.68257e7 | 1.32133 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.79192e6 | −0.373618 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −640633. | −0.0495926 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.26842e7 | −0.974916 | −0.487458 | − | 0.873146i | \(-0.662076\pi\) | ||||
−0.487458 | + | 0.873146i | \(0.662076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.20462e6 | 0.549823 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.68720e7 | −1.27848 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.48158e6 | 0.111475 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 919145. | 0.0686702 | 0.0343351 | − | 0.999410i | \(-0.489069\pi\) | ||||
0.0343351 | + | 0.999410i | \(0.489069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.80408e6 | 0.504772 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.45207e6 | 0.401640 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.69845e6 | −0.124247 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 133947. | 0.00973049 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.21135e6 | −0.520228 | −0.260114 | − | 0.965578i | \(-0.583760\pi\) | ||||
−0.260114 | + | 0.965578i | \(0.583760\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −582536. | −0.0417335 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.52646e7 | −1.79749 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.23035e7 | 2.28247 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.15671e6 | 0.291685 | 0.145842 | − | 0.989308i | \(-0.453411\pi\) | ||||
0.145842 | + | 0.989308i | \(0.453411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.84023e6 | −0.616091 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.50818e6 | −0.173607 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.05351e6 | 0.278658 | 0.139329 | − | 0.990246i | \(-0.455505\pi\) | ||||
0.139329 | + | 0.990246i | \(0.455505\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.91954e7 | 2.67619 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.26427e6 | 0.0857375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.27176e7 | −0.856629 | −0.428315 | − | 0.903630i | \(-0.640892\pi\) | ||||
−0.428315 | + | 0.903630i | \(0.640892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.76069e7 | 1.17798 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.86660e6 | 0.124045 | 0.0620224 | − | 0.998075i | \(-0.480245\pi\) | ||||
0.0620224 | + | 0.998075i | \(0.480245\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.95165e7 | −2.60848 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.03369e6 | 0.330054 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.95922e6 | 0.257873 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.61334e7 | −1.69081 | −0.845407 | − | 0.534122i | \(-0.820642\pi\) | ||||
−0.845407 | + | 0.534122i | \(0.820642\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.04505e7 | 2.59978 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.39328e7 | 2.80492 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.20591e6 | 0.0764846 | 0.0382423 | − | 0.999268i | \(-0.487824\pi\) | ||||
0.0382423 | + | 0.999268i | \(0.487824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.35685e6 | −0.274516 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.63050e6 | −0.102061 | −0.0510303 | − | 0.998697i | \(-0.516251\pi\) | ||||
−0.0510303 | + | 0.998697i | \(0.516251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −781961. | −0.0486266 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.04341e7 | 3.73361 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.41337e6 | 0.393639 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.03077e6 | −0.184815 | −0.0924074 | − | 0.995721i | \(-0.529456\pi\) | ||||
−0.0924074 | + | 0.995721i | \(0.529456\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.23676e7 | 1.35513 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.56440e7 | 0.941669 | 0.470834 | − | 0.882222i | \(-0.343953\pi\) | ||||
0.470834 | + | 0.882222i | \(0.343953\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.29752e7 | 0.775995 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.40410e6 | −0.0834346 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.87468e6 | −0.583015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −764595. | −0.0448543 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.42871e7 | −3.16441 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.02655e7 | 1.75297 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.77750e7 | −1.59852 | −0.799260 | − | 0.600986i | \(-0.794775\pi\) | ||||
−0.799260 | + | 0.600986i | \(0.794775\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.90230e7 | 1.08789 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 822028. | 0.0467138 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.99016e6 | 0.507673 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.19957e6 | 0.516237 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −646020. | −0.0360247 | −0.0180123 | − | 0.999838i | \(-0.505734\pi\) | ||||
−0.0180123 | + | 0.999838i | \(0.505734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.58473e6 | 0.531145 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.46941e7 | −2.46132 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.00239e6 | 0.164315 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.19390e6 | 0.173713 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.08917e7 | 1.12925 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.67691e6 | −0.0900823 | −0.0450412 | − | 0.998985i | \(-0.514342\pi\) | ||||
−0.0450412 | + | 0.998985i | \(0.514342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.09231e7 | −0.583169 | −0.291585 | − | 0.956545i | \(-0.594183\pi\) | ||||
−0.291585 | + | 0.956545i | \(0.594183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.62310e7 | 1.39184 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.11145e6 | −0.480500 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.16860e6 | −0.270905 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.32843e6 | −0.121298 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.94364e7 | 1.00637 | 0.503186 | − | 0.864178i | \(-0.332161\pi\) | ||||
0.503186 | + | 0.864178i | \(0.332161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.08462e7 | 1.58746 | 0.793730 | − | 0.608271i | \(-0.208136\pi\) | ||||
0.793730 | + | 0.608271i | \(0.208136\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.03687e7 | −0.530384 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.97925e7 | 1.00632 | 0.503161 | − | 0.864193i | \(-0.332170\pi\) | ||||
0.503161 | + | 0.864193i | \(0.332170\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.75755e7 | −0.888223 | −0.444111 | − | 0.895972i | \(-0.646481\pi\) | ||||
−0.444111 | + | 0.895972i | \(0.646481\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.84296e7 | −1.42813 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.22663e7 | −1.11182 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.62387e7 | −0.805999 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.18052e7 | −1.07584 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.50238e7 | 0.736842 | 0.368421 | − | 0.929659i | \(-0.379899\pi\) | ||||
0.368421 | + | 0.929659i | \(0.379899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.29682e7 | 1.60733 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.63974e7 | −2.73332 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.76879e7 | −1.33398 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.04661e6 | −0.145918 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.51759e7 | −3.10326 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.78387e6 | 0.226441 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.88390e7 | 1.82766 | 0.913829 | − | 0.406099i | \(-0.133111\pi\) | ||||
0.913829 | + | 0.406099i | \(0.133111\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.24536e8 | 5.82613 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.57330e6 | −0.166195 | −0.0830975 | − | 0.996541i | \(-0.526481\pi\) | ||||
−0.0830975 | + | 0.996541i | \(0.526481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.27850e6 | −0.151598 | −0.0757988 | − | 0.997123i | \(-0.524151\pi\) | ||||
−0.0757988 | + | 0.997123i | \(0.524151\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.92447e6 | 0.0884713 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.93441e7 | −0.884139 | −0.442070 | − | 0.896981i | \(-0.645756\pi\) | ||||
−0.442070 | + | 0.896981i | \(0.645756\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.27039e7 | 1.94056 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.15551e7 | −0.522068 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.13233e6 | 0.0508655 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.39248e6 | −0.151521 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.30820e7 | 1.91320 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.22371e6 | 0.0981880 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.57531e7 | −1.13066 | −0.565329 | − | 0.824866i | \(-0.691251\pi\) | ||||
−0.565329 | + | 0.824866i | \(0.691251\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.08642e7 | −1.78390 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.39384e6 | 0.190724 | 0.0953618 | − | 0.995443i | \(-0.469599\pi\) | ||||
0.0953618 | + | 0.995443i | \(0.469599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.21529e7 | −0.956156 | −0.478078 | − | 0.878317i | \(-0.658666\pi\) | ||||
−0.478078 | + | 0.878317i | \(0.658666\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.68507e7 | 2.86912 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.36187e7 | 1.86150 | 0.930750 | − | 0.365655i | \(-0.119155\pi\) | ||||
0.930750 | + | 0.365655i | \(0.119155\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.08874e6 | −0.300825 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.78294e6 | 0.286236 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.97512e7 | 0.828828 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.25247e7 | −1.35724 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.16910e7 | 0.485143 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.14808e7 | 0.886443 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.22613e6 | −0.214471 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.00730e6 | 0.0411094 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.00183e7 | 1.62419 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.38621e7 | −0.559515 | −0.279758 | − | 0.960071i | \(-0.590254\pi\) | ||||
−0.279758 | + | 0.960071i | \(0.590254\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.83589e7 | 1.53977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.31037e7 | 0.922329 | 0.461164 | − | 0.887315i | \(-0.347432\pi\) | ||||
0.461164 | + | 0.887315i | \(0.347432\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 837702. | 0.0332593 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.37103e7 | 3.70028 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.21275e6 | 0.0476266 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.27313e7 | 0.887842 | 0.443921 | − | 0.896066i | \(-0.353587\pi\) | ||||
0.443921 | + | 0.896066i | \(0.353587\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.46992e7 | −1.73640 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.05168e6 | 0.0792694 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.13850e7 | 0.437499 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.50822e7 | −0.576455 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.32467e7 | −1.26389 | −0.631945 | − | 0.775013i | \(-0.717743\pi\) | ||||
−0.631945 | + | 0.775013i | \(0.717743\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.58840e7 | −1.73495 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.69892e7 | 2.14333 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.00574e7 | 0.376233 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.72533e7 | 0.641981 | 0.320991 | − | 0.947082i | \(-0.395984\pi\) | ||||
0.320991 | + | 0.947082i | \(0.395984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.51110e6 | 0.352019 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.12167e6 | 0.0412945 | 0.0206473 | − | 0.999787i | \(-0.493427\pi\) | ||||
0.0206473 | + | 0.999787i | \(0.493427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.55679e6 | −0.240111 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.27738e7 | −0.465309 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.89113e7 | −1.40994 | −0.704970 | − | 0.709237i | \(-0.749040\pi\) | ||||
−0.704970 | + | 0.709237i | \(0.749040\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.05647e6 | −0.290388 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.57942e7 | −0.566301 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.79943e7 | −0.641803 | −0.320902 | − | 0.947113i | \(-0.603986\pi\) | ||||
−0.320902 | + | 0.947113i | \(0.603986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.95095e6 | 0.0692210 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.71657e7 | −0.605874 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.13783e6 | −0.215510 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00011e7 | −0.698626 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.02507e8 | 3.56194 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.20932e7 | 2.49216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.31110e7 | −0.794791 | −0.397395 | − | 0.917648i | \(-0.630086\pi\) | ||||
−0.397395 | + | 0.917648i | \(0.630086\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.04260e8 | −3.56703 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.50927e7 | 1.19445 | 0.597226 | − | 0.802073i | \(-0.296270\pi\) | ||||
0.597226 | + | 0.802073i | \(0.296270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.83871e6 | 0.129988 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.78230e7 | 0.937329 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.20029e6 | 0.241331 | 0.120666 | − | 0.992693i | \(-0.461497\pi\) | ||||
0.120666 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.43795e6 | −0.248026 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.02455e7 | −0.671669 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.28324e7 | 1.08373 | 0.541863 | − | 0.840467i | \(-0.317719\pi\) | ||||
0.541863 | + | 0.840467i | \(0.317719\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.96558e7 | 2.28753 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.84929e6 | −0.125773 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.43195e6 | −0.111571 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.19670e7 | −1.68090 | −0.840452 | − | 0.541885i | \(-0.817711\pi\) | ||||
−0.840452 | + | 0.541885i | \(0.817711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.10417e7 | −0.999015 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.63223e7 | 0.522665 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.30582e6 | −0.169050 | −0.0845249 | − | 0.996421i | \(-0.526937\pi\) | ||||
−0.0845249 | + | 0.996421i | \(0.526937\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.91328e7 | −0.606548 |
(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 | 688.6.a.h.1.1 | 10 | ||
4.3 | odd | 2 | 43.6.a.b.1.1 | ✓ | 10 | ||
12.11 | even | 2 | 387.6.a.e.1.10 | 10 | |||
20.19 | odd | 2 | 1075.6.a.b.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.b.1.1 | ✓ | 10 | 4.3 | odd | 2 | ||
387.6.a.e.1.10 | 10 | 12.11 | even | 2 | |||
688.6.a.h.1.1 | 10 | 1.1 | even | 1 | trivial | ||
1075.6.a.b.1.10 | 10 | 20.19 | odd | 2 |