Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [42,6,Mod(1,42)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42, 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("42.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.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: | \(6.73612043215\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 42.1 |
$q$-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 | ||||||||
\(5\) | 76.0000 | 1.35953 | 0.679765 | − | 0.733430i | \(-0.262082\pi\) | ||||
0.679765 | + | 0.733430i | \(0.262082\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 304.000 | 0.961332 | ||||||||
\(11\) | 650.000 | 1.61969 | 0.809845 | − | 0.586645i | \(-0.199551\pi\) | ||||
0.809845 | + | 0.586645i | \(0.199551\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 762.000 | 1.25054 | 0.625269 | − | 0.780410i | \(-0.284989\pi\) | ||||
0.625269 | + | 0.780410i | \(0.284989\pi\) | |||||||
\(14\) | −196.000 | −0.267261 | ||||||||
\(15\) | −684.000 | −0.784925 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −556.000 | −0.466608 | −0.233304 | − | 0.972404i | \(-0.574954\pi\) | ||||
−0.233304 | + | 0.972404i | \(0.574954\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | −2452.00 | −1.55825 | −0.779124 | − | 0.626870i | \(-0.784336\pi\) | ||||
−0.779124 | + | 0.626870i | \(0.784336\pi\) | |||||||
\(20\) | 1216.00 | 0.679765 | ||||||||
\(21\) | 441.000 | 0.218218 | ||||||||
\(22\) | 2600.00 | 1.14529 | ||||||||
\(23\) | −2950.00 | −1.16279 | −0.581397 | − | 0.813620i | \(-0.697493\pi\) | ||||
−0.581397 | + | 0.813620i | \(0.697493\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 2651.00 | 0.848320 | ||||||||
\(26\) | 3048.00 | 0.884263 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −784.000 | −0.188982 | ||||||||
\(29\) | −674.000 | −0.148821 | −0.0744106 | − | 0.997228i | \(-0.523708\pi\) | ||||
−0.0744106 | + | 0.997228i | \(0.523708\pi\) | |||||||
\(30\) | −2736.00 | −0.555026 | ||||||||
\(31\) | −3024.00 | −0.565168 | −0.282584 | − | 0.959243i | \(-0.591192\pi\) | ||||
−0.282584 | + | 0.959243i | \(0.591192\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −5850.00 | −0.935128 | ||||||||
\(34\) | −2224.00 | −0.329942 | ||||||||
\(35\) | −3724.00 | −0.513854 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 7730.00 | 0.928272 | 0.464136 | − | 0.885764i | \(-0.346365\pi\) | ||||
0.464136 | + | 0.885764i | \(0.346365\pi\) | |||||||
\(38\) | −9808.00 | −1.10185 | ||||||||
\(39\) | −6858.00 | −0.721998 | ||||||||
\(40\) | 4864.00 | 0.480666 | ||||||||
\(41\) | −17016.0 | −1.58088 | −0.790438 | − | 0.612542i | \(-0.790147\pi\) | ||||
−0.790438 | + | 0.612542i | \(0.790147\pi\) | |||||||
\(42\) | 1764.00 | 0.154303 | ||||||||
\(43\) | 21836.0 | 1.80095 | 0.900476 | − | 0.434907i | \(-0.143219\pi\) | ||||
0.900476 | + | 0.434907i | \(0.143219\pi\) | |||||||
\(44\) | 10400.0 | 0.809845 | ||||||||
\(45\) | 6156.00 | 0.453176 | ||||||||
\(46\) | −11800.0 | −0.822219 | ||||||||
\(47\) | −23940.0 | −1.58081 | −0.790405 | − | 0.612585i | \(-0.790130\pi\) | ||||
−0.790405 | + | 0.612585i | \(0.790130\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 10604.0 | 0.599853 | ||||||||
\(51\) | 5004.00 | 0.269396 | ||||||||
\(52\) | 12192.0 | 0.625269 | ||||||||
\(53\) | 15594.0 | 0.762549 | 0.381275 | − | 0.924462i | \(-0.375485\pi\) | ||||
0.381275 | + | 0.924462i | \(0.375485\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 49400.0 | 2.20201 | ||||||||
\(56\) | −3136.00 | −0.133631 | ||||||||
\(57\) | 22068.0 | 0.899655 | ||||||||
\(58\) | −2696.00 | −0.105233 | ||||||||
\(59\) | 5608.00 | 0.209738 | 0.104869 | − | 0.994486i | \(-0.466558\pi\) | ||||
0.104869 | + | 0.994486i | \(0.466558\pi\) | |||||||
\(60\) | −10944.0 | −0.392462 | ||||||||
\(61\) | 150.000 | 0.00516139 | 0.00258069 | − | 0.999997i | \(-0.499179\pi\) | ||||
0.00258069 | + | 0.999997i | \(0.499179\pi\) | |||||||
\(62\) | −12096.0 | −0.399634 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 57912.0 | 1.70014 | ||||||||
\(66\) | −23400.0 | −0.661235 | ||||||||
\(67\) | −43784.0 | −1.19159 | −0.595797 | − | 0.803135i | \(-0.703164\pi\) | ||||
−0.595797 | + | 0.803135i | \(0.703164\pi\) | |||||||
\(68\) | −8896.00 | −0.233304 | ||||||||
\(69\) | 26550.0 | 0.671339 | ||||||||
\(70\) | −14896.0 | −0.363349 | ||||||||
\(71\) | −39178.0 | −0.922351 | −0.461176 | − | 0.887309i | \(-0.652572\pi\) | ||||
−0.461176 | + | 0.887309i | \(0.652572\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | −23570.0 | −0.517669 | −0.258835 | − | 0.965922i | \(-0.583338\pi\) | ||||
−0.258835 | + | 0.965922i | \(0.583338\pi\) | |||||||
\(74\) | 30920.0 | 0.656387 | ||||||||
\(75\) | −23859.0 | −0.489778 | ||||||||
\(76\) | −39232.0 | −0.779124 | ||||||||
\(77\) | −31850.0 | −0.612185 | ||||||||
\(78\) | −27432.0 | −0.510530 | ||||||||
\(79\) | −17892.0 | −0.322546 | −0.161273 | − | 0.986910i | \(-0.551560\pi\) | ||||
−0.161273 | + | 0.986910i | \(0.551560\pi\) | |||||||
\(80\) | 19456.0 | 0.339882 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −68064.0 | −1.11785 | ||||||||
\(83\) | 38972.0 | 0.620951 | 0.310476 | − | 0.950581i | \(-0.399512\pi\) | ||||
0.310476 | + | 0.950581i | \(0.399512\pi\) | |||||||
\(84\) | 7056.00 | 0.109109 | ||||||||
\(85\) | −42256.0 | −0.634368 | ||||||||
\(86\) | 87344.0 | 1.27346 | ||||||||
\(87\) | 6066.00 | 0.0859220 | ||||||||
\(88\) | 41600.0 | 0.572647 | ||||||||
\(89\) | 6024.00 | 0.0806139 | 0.0403070 | − | 0.999187i | \(-0.487166\pi\) | ||||
0.0403070 | + | 0.999187i | \(0.487166\pi\) | |||||||
\(90\) | 24624.0 | 0.320444 | ||||||||
\(91\) | −37338.0 | −0.472659 | ||||||||
\(92\) | −47200.0 | −0.581397 | ||||||||
\(93\) | 27216.0 | 0.326300 | ||||||||
\(94\) | −95760.0 | −1.11780 | ||||||||
\(95\) | −186352. | −2.11848 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | 108430. | 1.17009 | 0.585046 | − | 0.811000i | \(-0.301076\pi\) | ||||
0.585046 | + | 0.811000i | \(0.301076\pi\) | |||||||
\(98\) | 9604.00 | 0.101015 | ||||||||
\(99\) | 52650.0 | 0.539896 | ||||||||
\(100\) | 42416.0 | 0.424160 | ||||||||
\(101\) | −70424.0 | −0.686938 | −0.343469 | − | 0.939164i | \(-0.611602\pi\) | ||||
−0.343469 | + | 0.939164i | \(0.611602\pi\) | |||||||
\(102\) | 20016.0 | 0.190492 | ||||||||
\(103\) | −31552.0 | −0.293045 | −0.146522 | − | 0.989207i | \(-0.546808\pi\) | ||||
−0.146522 | + | 0.989207i | \(0.546808\pi\) | |||||||
\(104\) | 48768.0 | 0.442132 | ||||||||
\(105\) | 33516.0 | 0.296674 | ||||||||
\(106\) | 62376.0 | 0.539204 | ||||||||
\(107\) | 108282. | 0.914317 | 0.457159 | − | 0.889385i | \(-0.348867\pi\) | ||||
0.457159 | + | 0.889385i | \(0.348867\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | −72146.0 | −0.581629 | −0.290814 | − | 0.956779i | \(-0.593926\pi\) | ||||
−0.290814 | + | 0.956779i | \(0.593926\pi\) | |||||||
\(110\) | 197600. | 1.55706 | ||||||||
\(111\) | −69570.0 | −0.535938 | ||||||||
\(112\) | −12544.0 | −0.0944911 | ||||||||
\(113\) | 220906. | 1.62746 | 0.813732 | − | 0.581240i | \(-0.197432\pi\) | ||||
0.813732 | + | 0.581240i | \(0.197432\pi\) | |||||||
\(114\) | 88272.0 | 0.636152 | ||||||||
\(115\) | −224200. | −1.58085 | ||||||||
\(116\) | −10784.0 | −0.0744106 | ||||||||
\(117\) | 61722.0 | 0.416846 | ||||||||
\(118\) | 22432.0 | 0.148307 | ||||||||
\(119\) | 27244.0 | 0.176361 | ||||||||
\(120\) | −43776.0 | −0.277513 | ||||||||
\(121\) | 261449. | 1.62339 | ||||||||
\(122\) | 600.000 | 0.00364965 | ||||||||
\(123\) | 153144. | 0.912719 | ||||||||
\(124\) | −48384.0 | −0.282584 | ||||||||
\(125\) | −36024.0 | −0.206213 | ||||||||
\(126\) | −15876.0 | −0.0890871 | ||||||||
\(127\) | −239652. | −1.31847 | −0.659237 | − | 0.751935i | \(-0.729121\pi\) | ||||
−0.659237 | + | 0.751935i | \(0.729121\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −196524. | −1.03978 | ||||||||
\(130\) | 231648. | 1.20218 | ||||||||
\(131\) | −274172. | −1.39587 | −0.697935 | − | 0.716161i | \(-0.745897\pi\) | ||||
−0.697935 | + | 0.716161i | \(0.745897\pi\) | |||||||
\(132\) | −93600.0 | −0.467564 | ||||||||
\(133\) | 120148. | 0.588962 | ||||||||
\(134\) | −175136. | −0.842584 | ||||||||
\(135\) | −55404.0 | −0.261642 | ||||||||
\(136\) | −35584.0 | −0.164971 | ||||||||
\(137\) | −391154. | −1.78052 | −0.890259 | − | 0.455455i | \(-0.849477\pi\) | ||||
−0.890259 | + | 0.455455i | \(0.849477\pi\) | |||||||
\(138\) | 106200. | 0.474708 | ||||||||
\(139\) | 339364. | 1.48980 | 0.744901 | − | 0.667175i | \(-0.232497\pi\) | ||||
0.744901 | + | 0.667175i | \(0.232497\pi\) | |||||||
\(140\) | −59584.0 | −0.256927 | ||||||||
\(141\) | 215460. | 0.912681 | ||||||||
\(142\) | −156712. | −0.652201 | ||||||||
\(143\) | 495300. | 2.02548 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −51224.0 | −0.202327 | ||||||||
\(146\) | −94280.0 | −0.366047 | ||||||||
\(147\) | −21609.0 | −0.0824786 | ||||||||
\(148\) | 123680. | 0.464136 | ||||||||
\(149\) | −29334.0 | −0.108244 | −0.0541222 | − | 0.998534i | \(-0.517236\pi\) | ||||
−0.0541222 | + | 0.998534i | \(0.517236\pi\) | |||||||
\(150\) | −95436.0 | −0.346325 | ||||||||
\(151\) | 71608.0 | 0.255575 | 0.127788 | − | 0.991802i | \(-0.459212\pi\) | ||||
0.127788 | + | 0.991802i | \(0.459212\pi\) | |||||||
\(152\) | −156928. | −0.550924 | ||||||||
\(153\) | −45036.0 | −0.155536 | ||||||||
\(154\) | −127400. | −0.432880 | ||||||||
\(155\) | −229824. | −0.768362 | ||||||||
\(156\) | −109728. | −0.360999 | ||||||||
\(157\) | 296318. | 0.959420 | 0.479710 | − | 0.877427i | \(-0.340742\pi\) | ||||
0.479710 | + | 0.877427i | \(0.340742\pi\) | |||||||
\(158\) | −71568.0 | −0.228074 | ||||||||
\(159\) | −140346. | −0.440258 | ||||||||
\(160\) | 77824.0 | 0.240333 | ||||||||
\(161\) | 144550. | 0.439494 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −480400. | −1.41623 | −0.708115 | − | 0.706097i | \(-0.750454\pi\) | ||||
−0.708115 | + | 0.706097i | \(0.750454\pi\) | |||||||
\(164\) | −272256. | −0.790438 | ||||||||
\(165\) | −444600. | −1.27133 | ||||||||
\(166\) | 155888. | 0.439079 | ||||||||
\(167\) | 160180. | 0.444444 | 0.222222 | − | 0.974996i | \(-0.428669\pi\) | ||||
0.222222 | + | 0.974996i | \(0.428669\pi\) | |||||||
\(168\) | 28224.0 | 0.0771517 | ||||||||
\(169\) | 209351. | 0.563843 | ||||||||
\(170\) | −169024. | −0.448566 | ||||||||
\(171\) | −198612. | −0.519416 | ||||||||
\(172\) | 349376. | 0.900476 | ||||||||
\(173\) | −8984.00 | −0.0228220 | −0.0114110 | − | 0.999935i | \(-0.503632\pi\) | ||||
−0.0114110 | + | 0.999935i | \(0.503632\pi\) | |||||||
\(174\) | 24264.0 | 0.0607560 | ||||||||
\(175\) | −129899. | −0.320635 | ||||||||
\(176\) | 166400. | 0.404922 | ||||||||
\(177\) | −50472.0 | −0.121093 | ||||||||
\(178\) | 24096.0 | 0.0570026 | ||||||||
\(179\) | 182886. | 0.426627 | 0.213313 | − | 0.976984i | \(-0.431575\pi\) | ||||
0.213313 | + | 0.976984i | \(0.431575\pi\) | |||||||
\(180\) | 98496.0 | 0.226588 | ||||||||
\(181\) | 138330. | 0.313848 | 0.156924 | − | 0.987611i | \(-0.449842\pi\) | ||||
0.156924 | + | 0.987611i | \(0.449842\pi\) | |||||||
\(182\) | −149352. | −0.334220 | ||||||||
\(183\) | −1350.00 | −0.00297993 | ||||||||
\(184\) | −188800. | −0.411109 | ||||||||
\(185\) | 587480. | 1.26201 | ||||||||
\(186\) | 108864. | 0.230729 | ||||||||
\(187\) | −361400. | −0.755760 | ||||||||
\(188\) | −383040. | −0.790405 | ||||||||
\(189\) | 35721.0 | 0.0727393 | ||||||||
\(190\) | −745408. | −1.49799 | ||||||||
\(191\) | 327222. | 0.649021 | 0.324511 | − | 0.945882i | \(-0.394800\pi\) | ||||
0.324511 | + | 0.945882i | \(0.394800\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 786902. | 1.52064 | 0.760322 | − | 0.649547i | \(-0.225041\pi\) | ||||
0.760322 | + | 0.649547i | \(0.225041\pi\) | |||||||
\(194\) | 433720. | 0.827380 | ||||||||
\(195\) | −521208. | −0.981577 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | 423098. | 0.776740 | 0.388370 | − | 0.921504i | \(-0.373038\pi\) | ||||
0.388370 | + | 0.921504i | \(0.373038\pi\) | |||||||
\(198\) | 210600. | 0.381764 | ||||||||
\(199\) | 1.02392e6 | 1.83288 | 0.916439 | − | 0.400175i | \(-0.131051\pi\) | ||||
0.916439 | + | 0.400175i | \(0.131051\pi\) | |||||||
\(200\) | 169664. | 0.299926 | ||||||||
\(201\) | 394056. | 0.687967 | ||||||||
\(202\) | −281696. | −0.485738 | ||||||||
\(203\) | 33026.0 | 0.0562491 | ||||||||
\(204\) | 80064.0 | 0.134698 | ||||||||
\(205\) | −1.29322e6 | −2.14925 | ||||||||
\(206\) | −126208. | −0.207214 | ||||||||
\(207\) | −238950. | −0.387598 | ||||||||
\(208\) | 195072. | 0.312634 | ||||||||
\(209\) | −1.59380e6 | −2.52388 | ||||||||
\(210\) | 134064. | 0.209780 | ||||||||
\(211\) | 461516. | 0.713642 | 0.356821 | − | 0.934173i | \(-0.383861\pi\) | ||||
0.356821 | + | 0.934173i | \(0.383861\pi\) | |||||||
\(212\) | 249504. | 0.381275 | ||||||||
\(213\) | 352602. | 0.532520 | ||||||||
\(214\) | 433128. | 0.646520 | ||||||||
\(215\) | 1.65954e6 | 2.44845 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 148176. | 0.213613 | ||||||||
\(218\) | −288584. | −0.411274 | ||||||||
\(219\) | 212130. | 0.298877 | ||||||||
\(220\) | 790400. | 1.10101 | ||||||||
\(221\) | −423672. | −0.583511 | ||||||||
\(222\) | −278280. | −0.378965 | ||||||||
\(223\) | 995048. | 1.33993 | 0.669965 | − | 0.742393i | \(-0.266309\pi\) | ||||
0.669965 | + | 0.742393i | \(0.266309\pi\) | |||||||
\(224\) | −50176.0 | −0.0668153 | ||||||||
\(225\) | 214731. | 0.282773 | ||||||||
\(226\) | 883624. | 1.15079 | ||||||||
\(227\) | −95568.0 | −0.123097 | −0.0615486 | − | 0.998104i | \(-0.519604\pi\) | ||||
−0.0615486 | + | 0.998104i | \(0.519604\pi\) | |||||||
\(228\) | 353088. | 0.449827 | ||||||||
\(229\) | −1.04409e6 | −1.31567 | −0.657836 | − | 0.753161i | \(-0.728528\pi\) | ||||
−0.657836 | + | 0.753161i | \(0.728528\pi\) | |||||||
\(230\) | −896800. | −1.11783 | ||||||||
\(231\) | 286650. | 0.353445 | ||||||||
\(232\) | −43136.0 | −0.0526163 | ||||||||
\(233\) | −1.16941e6 | −1.41116 | −0.705581 | − | 0.708629i | \(-0.749314\pi\) | ||||
−0.705581 | + | 0.708629i | \(0.749314\pi\) | |||||||
\(234\) | 246888. | 0.294754 | ||||||||
\(235\) | −1.81944e6 | −2.14916 | ||||||||
\(236\) | 89728.0 | 0.104869 | ||||||||
\(237\) | 161028. | 0.186222 | ||||||||
\(238\) | 108976. | 0.124706 | ||||||||
\(239\) | −27342.0 | −0.0309625 | −0.0154812 | − | 0.999880i | \(-0.504928\pi\) | ||||
−0.0154812 | + | 0.999880i | \(0.504928\pi\) | |||||||
\(240\) | −175104. | −0.196231 | ||||||||
\(241\) | −907714. | −1.00671 | −0.503357 | − | 0.864078i | \(-0.667902\pi\) | ||||
−0.503357 | + | 0.864078i | \(0.667902\pi\) | |||||||
\(242\) | 1.04580e6 | 1.14791 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 2400.00 | 0.00258069 | ||||||||
\(245\) | 182476. | 0.194218 | ||||||||
\(246\) | 612576. | 0.645390 | ||||||||
\(247\) | −1.86842e6 | −1.94865 | ||||||||
\(248\) | −193536. | −0.199817 | ||||||||
\(249\) | −350748. | −0.358506 | ||||||||
\(250\) | −144096. | −0.145815 | ||||||||
\(251\) | 44088.0 | 0.0441709 | 0.0220854 | − | 0.999756i | \(-0.492969\pi\) | ||||
0.0220854 | + | 0.999756i | \(0.492969\pi\) | |||||||
\(252\) | −63504.0 | −0.0629941 | ||||||||
\(253\) | −1.91750e6 | −1.88336 | ||||||||
\(254\) | −958608. | −0.932302 | ||||||||
\(255\) | 380304. | 0.366252 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −829200. | −0.783117 | −0.391558 | − | 0.920153i | \(-0.628064\pi\) | ||||
−0.391558 | + | 0.920153i | \(0.628064\pi\) | |||||||
\(258\) | −786096. | −0.735235 | ||||||||
\(259\) | −378770. | −0.350854 | ||||||||
\(260\) | 926592. | 0.850071 | ||||||||
\(261\) | −54594.0 | −0.0496071 | ||||||||
\(262\) | −1.09669e6 | −0.987029 | ||||||||
\(263\) | 1.31947e6 | 1.17627 | 0.588137 | − | 0.808761i | \(-0.299861\pi\) | ||||
0.588137 | + | 0.808761i | \(0.299861\pi\) | |||||||
\(264\) | −374400. | −0.330618 | ||||||||
\(265\) | 1.18514e6 | 1.03671 | ||||||||
\(266\) | 480592. | 0.416459 | ||||||||
\(267\) | −54216.0 | −0.0465425 | ||||||||
\(268\) | −700544. | −0.595797 | ||||||||
\(269\) | −783788. | −0.660416 | −0.330208 | − | 0.943908i | \(-0.607119\pi\) | ||||
−0.330208 | + | 0.943908i | \(0.607119\pi\) | |||||||
\(270\) | −221616. | −0.185009 | ||||||||
\(271\) | 955080. | 0.789981 | 0.394990 | − | 0.918685i | \(-0.370748\pi\) | ||||
0.394990 | + | 0.918685i | \(0.370748\pi\) | |||||||
\(272\) | −142336. | −0.116652 | ||||||||
\(273\) | 336042. | 0.272890 | ||||||||
\(274\) | −1.56462e6 | −1.25902 | ||||||||
\(275\) | 1.72315e6 | 1.37401 | ||||||||
\(276\) | 424800. | 0.335669 | ||||||||
\(277\) | 1.91273e6 | 1.49780 | 0.748901 | − | 0.662682i | \(-0.230582\pi\) | ||||
0.748901 | + | 0.662682i | \(0.230582\pi\) | |||||||
\(278\) | 1.35746e6 | 1.05345 | ||||||||
\(279\) | −244944. | −0.188389 | ||||||||
\(280\) | −238336. | −0.181675 | ||||||||
\(281\) | −1.02620e6 | −0.775295 | −0.387648 | − | 0.921808i | \(-0.626712\pi\) | ||||
−0.387648 | + | 0.921808i | \(0.626712\pi\) | |||||||
\(282\) | 861840. | 0.645363 | ||||||||
\(283\) | 1.74668e6 | 1.29642 | 0.648211 | − | 0.761461i | \(-0.275518\pi\) | ||||
0.648211 | + | 0.761461i | \(0.275518\pi\) | |||||||
\(284\) | −626848. | −0.461176 | ||||||||
\(285\) | 1.67717e6 | 1.22311 | ||||||||
\(286\) | 1.98120e6 | 1.43223 | ||||||||
\(287\) | 833784. | 0.597515 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | −1.11072e6 | −0.782277 | ||||||||
\(290\) | −204896. | −0.143067 | ||||||||
\(291\) | −975870. | −0.675553 | ||||||||
\(292\) | −377120. | −0.258835 | ||||||||
\(293\) | 2.23212e6 | 1.51897 | 0.759484 | − | 0.650526i | \(-0.225452\pi\) | ||||
0.759484 | + | 0.650526i | \(0.225452\pi\) | |||||||
\(294\) | −86436.0 | −0.0583212 | ||||||||
\(295\) | 426208. | 0.285146 | ||||||||
\(296\) | 494720. | 0.328194 | ||||||||
\(297\) | −473850. | −0.311709 | ||||||||
\(298\) | −117336. | −0.0765404 | ||||||||
\(299\) | −2.24790e6 | −1.45412 | ||||||||
\(300\) | −381744. | −0.244889 | ||||||||
\(301\) | −1.06996e6 | −0.680696 | ||||||||
\(302\) | 286432. | 0.180719 | ||||||||
\(303\) | 633816. | 0.396604 | ||||||||
\(304\) | −627712. | −0.389562 | ||||||||
\(305\) | 11400.0 | 0.00701706 | ||||||||
\(306\) | −180144. | −0.109981 | ||||||||
\(307\) | 1.85324e6 | 1.12224 | 0.561119 | − | 0.827735i | \(-0.310371\pi\) | ||||
0.561119 | + | 0.827735i | \(0.310371\pi\) | |||||||
\(308\) | −509600. | −0.306092 | ||||||||
\(309\) | 283968. | 0.169189 | ||||||||
\(310\) | −919296. | −0.543314 | ||||||||
\(311\) | −450956. | −0.264383 | −0.132191 | − | 0.991224i | \(-0.542201\pi\) | ||||
−0.132191 | + | 0.991224i | \(0.542201\pi\) | |||||||
\(312\) | −438912. | −0.255265 | ||||||||
\(313\) | 1.60263e6 | 0.924642 | 0.462321 | − | 0.886713i | \(-0.347017\pi\) | ||||
0.462321 | + | 0.886713i | \(0.347017\pi\) | |||||||
\(314\) | 1.18527e6 | 0.678413 | ||||||||
\(315\) | −301644. | −0.171285 | ||||||||
\(316\) | −286272. | −0.161273 | ||||||||
\(317\) | −20862.0 | −0.0116602 | −0.00583012 | − | 0.999983i | \(-0.501856\pi\) | ||||
−0.00583012 | + | 0.999983i | \(0.501856\pi\) | |||||||
\(318\) | −561384. | −0.311309 | ||||||||
\(319\) | −438100. | −0.241044 | ||||||||
\(320\) | 311296. | 0.169941 | ||||||||
\(321\) | −974538. | −0.527881 | ||||||||
\(322\) | 578200. | 0.310770 | ||||||||
\(323\) | 1.36331e6 | 0.727091 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 2.02006e6 | 1.06086 | ||||||||
\(326\) | −1.92160e6 | −1.00143 | ||||||||
\(327\) | 649314. | 0.335804 | ||||||||
\(328\) | −1.08902e6 | −0.558924 | ||||||||
\(329\) | 1.17306e6 | 0.597490 | ||||||||
\(330\) | −1.77840e6 | −0.898969 | ||||||||
\(331\) | 2.07621e6 | 1.04160 | 0.520801 | − | 0.853678i | \(-0.325633\pi\) | ||||
0.520801 | + | 0.853678i | \(0.325633\pi\) | |||||||
\(332\) | 623552. | 0.310476 | ||||||||
\(333\) | 626130. | 0.309424 | ||||||||
\(334\) | 640720. | 0.314269 | ||||||||
\(335\) | −3.32758e6 | −1.62001 | ||||||||
\(336\) | 112896. | 0.0545545 | ||||||||
\(337\) | 1.20508e6 | 0.578019 | 0.289009 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289009 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(338\) | 837404. | 0.398697 | ||||||||
\(339\) | −1.98815e6 | −0.939617 | ||||||||
\(340\) | −676096. | −0.317184 | ||||||||
\(341\) | −1.96560e6 | −0.915396 | ||||||||
\(342\) | −794448. | −0.367282 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 1.39750e6 | 0.636732 | ||||||||
\(345\) | 2.01780e6 | 0.912705 | ||||||||
\(346\) | −35936.0 | −0.0161376 | ||||||||
\(347\) | −876642. | −0.390840 | −0.195420 | − | 0.980720i | \(-0.562607\pi\) | ||||
−0.195420 | + | 0.980720i | \(0.562607\pi\) | |||||||
\(348\) | 97056.0 | 0.0429610 | ||||||||
\(349\) | −1.29593e6 | −0.569532 | −0.284766 | − | 0.958597i | \(-0.591916\pi\) | ||||
−0.284766 | + | 0.958597i | \(0.591916\pi\) | |||||||
\(350\) | −519596. | −0.226723 | ||||||||
\(351\) | −555498. | −0.240666 | ||||||||
\(352\) | 665600. | 0.286323 | ||||||||
\(353\) | −3.99040e6 | −1.70443 | −0.852215 | − | 0.523192i | \(-0.824741\pi\) | ||||
−0.852215 | + | 0.523192i | \(0.824741\pi\) | |||||||
\(354\) | −201888. | −0.0856253 | ||||||||
\(355\) | −2.97753e6 | −1.25396 | ||||||||
\(356\) | 96384.0 | 0.0403070 | ||||||||
\(357\) | −245196. | −0.101822 | ||||||||
\(358\) | 731544. | 0.301671 | ||||||||
\(359\) | 4.06452e6 | 1.66446 | 0.832229 | − | 0.554432i | \(-0.187064\pi\) | ||||
0.832229 | + | 0.554432i | \(0.187064\pi\) | |||||||
\(360\) | 393984. | 0.160222 | ||||||||
\(361\) | 3.53620e6 | 1.42814 | ||||||||
\(362\) | 553320. | 0.221924 | ||||||||
\(363\) | −2.35304e6 | −0.937266 | ||||||||
\(364\) | −597408. | −0.236329 | ||||||||
\(365\) | −1.79132e6 | −0.703787 | ||||||||
\(366\) | −5400.00 | −0.00210713 | ||||||||
\(367\) | −1.67243e6 | −0.648162 | −0.324081 | − | 0.946029i | \(-0.605055\pi\) | ||||
−0.324081 | + | 0.946029i | \(0.605055\pi\) | |||||||
\(368\) | −755200. | −0.290698 | ||||||||
\(369\) | −1.37830e6 | −0.526959 | ||||||||
\(370\) | 2.34992e6 | 0.892378 | ||||||||
\(371\) | −764106. | −0.288216 | ||||||||
\(372\) | 435456. | 0.163150 | ||||||||
\(373\) | 3.16769e6 | 1.17888 | 0.589441 | − | 0.807812i | \(-0.299348\pi\) | ||||
0.589441 | + | 0.807812i | \(0.299348\pi\) | |||||||
\(374\) | −1.44560e6 | −0.534403 | ||||||||
\(375\) | 324216. | 0.119057 | ||||||||
\(376\) | −1.53216e6 | −0.558901 | ||||||||
\(377\) | −513588. | −0.186106 | ||||||||
\(378\) | 142884. | 0.0514344 | ||||||||
\(379\) | −4.20388e6 | −1.50332 | −0.751662 | − | 0.659548i | \(-0.770748\pi\) | ||||
−0.751662 | + | 0.659548i | \(0.770748\pi\) | |||||||
\(380\) | −2.98163e6 | −1.05924 | ||||||||
\(381\) | 2.15687e6 | 0.761222 | ||||||||
\(382\) | 1.30889e6 | 0.458927 | ||||||||
\(383\) | −342616. | −0.119347 | −0.0596734 | − | 0.998218i | \(-0.519006\pi\) | ||||
−0.0596734 | + | 0.998218i | \(0.519006\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | −2.42060e6 | −0.832283 | ||||||||
\(386\) | 3.14761e6 | 1.07526 | ||||||||
\(387\) | 1.76872e6 | 0.600317 | ||||||||
\(388\) | 1.73488e6 | 0.585046 | ||||||||
\(389\) | −3.83959e6 | −1.28650 | −0.643252 | − | 0.765654i | \(-0.722415\pi\) | ||||
−0.643252 | + | 0.765654i | \(0.722415\pi\) | |||||||
\(390\) | −2.08483e6 | −0.694080 | ||||||||
\(391\) | 1.64020e6 | 0.542569 | ||||||||
\(392\) | 153664. | 0.0505076 | ||||||||
\(393\) | 2.46755e6 | 0.805906 | ||||||||
\(394\) | 1.69239e6 | 0.549238 | ||||||||
\(395\) | −1.35979e6 | −0.438510 | ||||||||
\(396\) | 842400. | 0.269948 | ||||||||
\(397\) | 3.43894e6 | 1.09509 | 0.547543 | − | 0.836777i | \(-0.315563\pi\) | ||||
0.547543 | + | 0.836777i | \(0.315563\pi\) | |||||||
\(398\) | 4.09568e6 | 1.29604 | ||||||||
\(399\) | −1.08133e6 | −0.340038 | ||||||||
\(400\) | 678656. | 0.212080 | ||||||||
\(401\) | −3.89421e6 | −1.20937 | −0.604684 | − | 0.796466i | \(-0.706701\pi\) | ||||
−0.604684 | + | 0.796466i | \(0.706701\pi\) | |||||||
\(402\) | 1.57622e6 | 0.486466 | ||||||||
\(403\) | −2.30429e6 | −0.706764 | ||||||||
\(404\) | −1.12678e6 | −0.343469 | ||||||||
\(405\) | 498636. | 0.151059 | ||||||||
\(406\) | 132104. | 0.0397741 | ||||||||
\(407\) | 5.02450e6 | 1.50351 | ||||||||
\(408\) | 320256. | 0.0952460 | ||||||||
\(409\) | −1.64679e6 | −0.486778 | −0.243389 | − | 0.969929i | \(-0.578259\pi\) | ||||
−0.243389 | + | 0.969929i | \(0.578259\pi\) | |||||||
\(410\) | −5.17286e6 | −1.51975 | ||||||||
\(411\) | 3.52039e6 | 1.02798 | ||||||||
\(412\) | −504832. | −0.146522 | ||||||||
\(413\) | −274792. | −0.0792737 | ||||||||
\(414\) | −955800. | −0.274073 | ||||||||
\(415\) | 2.96187e6 | 0.844201 | ||||||||
\(416\) | 780288. | 0.221066 | ||||||||
\(417\) | −3.05428e6 | −0.860138 | ||||||||
\(418\) | −6.37520e6 | −1.78465 | ||||||||
\(419\) | −1.67659e6 | −0.466544 | −0.233272 | − | 0.972412i | \(-0.574943\pi\) | ||||
−0.233272 | + | 0.972412i | \(0.574943\pi\) | |||||||
\(420\) | 536256. | 0.148337 | ||||||||
\(421\) | −566742. | −0.155840 | −0.0779202 | − | 0.996960i | \(-0.524828\pi\) | ||||
−0.0779202 | + | 0.996960i | \(0.524828\pi\) | |||||||
\(422\) | 1.84606e6 | 0.504621 | ||||||||
\(423\) | −1.93914e6 | −0.526936 | ||||||||
\(424\) | 998016. | 0.269602 | ||||||||
\(425\) | −1.47396e6 | −0.395833 | ||||||||
\(426\) | 1.41041e6 | 0.376548 | ||||||||
\(427\) | −7350.00 | −0.00195082 | ||||||||
\(428\) | 1.73251e6 | 0.457159 | ||||||||
\(429\) | −4.45770e6 | −1.16941 | ||||||||
\(430\) | 6.63814e6 | 1.73131 | ||||||||
\(431\) | 6.68468e6 | 1.73335 | 0.866677 | − | 0.498870i | \(-0.166251\pi\) | ||||
0.866677 | + | 0.498870i | \(0.166251\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 6.91337e6 | 1.77203 | 0.886013 | − | 0.463661i | \(-0.153464\pi\) | ||||
0.886013 | + | 0.463661i | \(0.153464\pi\) | |||||||
\(434\) | 592704. | 0.151047 | ||||||||
\(435\) | 461016. | 0.116813 | ||||||||
\(436\) | −1.15434e6 | −0.290814 | ||||||||
\(437\) | 7.23340e6 | 1.81192 | ||||||||
\(438\) | 848520. | 0.211338 | ||||||||
\(439\) | −4.56281e6 | −1.12998 | −0.564990 | − | 0.825098i | \(-0.691120\pi\) | ||||
−0.564990 | + | 0.825098i | \(0.691120\pi\) | |||||||
\(440\) | 3.16160e6 | 0.778530 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | −1.69469e6 | −0.412605 | ||||||||
\(443\) | 4.59760e6 | 1.11307 | 0.556534 | − | 0.830825i | \(-0.312131\pi\) | ||||
0.556534 | + | 0.830825i | \(0.312131\pi\) | |||||||
\(444\) | −1.11312e6 | −0.267969 | ||||||||
\(445\) | 457824. | 0.109597 | ||||||||
\(446\) | 3.98019e6 | 0.947473 | ||||||||
\(447\) | 264006. | 0.0624950 | ||||||||
\(448\) | −200704. | −0.0472456 | ||||||||
\(449\) | 1.70658e6 | 0.399494 | 0.199747 | − | 0.979848i | \(-0.435988\pi\) | ||||
0.199747 | + | 0.979848i | \(0.435988\pi\) | |||||||
\(450\) | 858924. | 0.199951 | ||||||||
\(451\) | −1.10604e7 | −2.56053 | ||||||||
\(452\) | 3.53450e6 | 0.813732 | ||||||||
\(453\) | −644472. | −0.147557 | ||||||||
\(454\) | −382272. | −0.0870428 | ||||||||
\(455\) | −2.83769e6 | −0.642593 | ||||||||
\(456\) | 1.41235e6 | 0.318076 | ||||||||
\(457\) | −6.93916e6 | −1.55423 | −0.777117 | − | 0.629356i | \(-0.783319\pi\) | ||||
−0.777117 | + | 0.629356i | \(0.783319\pi\) | |||||||
\(458\) | −4.17634e6 | −0.930320 | ||||||||
\(459\) | 405324. | 0.0897988 | ||||||||
\(460\) | −3.58720e6 | −0.790426 | ||||||||
\(461\) | −2.61805e6 | −0.573753 | −0.286877 | − | 0.957968i | \(-0.592617\pi\) | ||||
−0.286877 | + | 0.957968i | \(0.592617\pi\) | |||||||
\(462\) | 1.14660e6 | 0.249923 | ||||||||
\(463\) | 7.13602e6 | 1.54705 | 0.773524 | − | 0.633767i | \(-0.218492\pi\) | ||||
0.773524 | + | 0.633767i | \(0.218492\pi\) | |||||||
\(464\) | −172544. | −0.0372053 | ||||||||
\(465\) | 2.06842e6 | 0.443614 | ||||||||
\(466\) | −4.67764e6 | −0.997843 | ||||||||
\(467\) | −2.17398e6 | −0.461278 | −0.230639 | − | 0.973039i | \(-0.574082\pi\) | ||||
−0.230639 | + | 0.973039i | \(0.574082\pi\) | |||||||
\(468\) | 987552. | 0.208423 | ||||||||
\(469\) | 2.14542e6 | 0.450380 | ||||||||
\(470\) | −7.27776e6 | −1.51968 | ||||||||
\(471\) | −2.66686e6 | −0.553922 | ||||||||
\(472\) | 358912. | 0.0741537 | ||||||||
\(473\) | 1.41934e7 | 2.91698 | ||||||||
\(474\) | 644112. | 0.131679 | ||||||||
\(475\) | −6.50025e6 | −1.32189 | ||||||||
\(476\) | 435904. | 0.0881807 | ||||||||
\(477\) | 1.26311e6 | 0.254183 | ||||||||
\(478\) | −109368. | −0.0218938 | ||||||||
\(479\) | −4.63294e6 | −0.922609 | −0.461305 | − | 0.887242i | \(-0.652619\pi\) | ||||
−0.461305 | + | 0.887242i | \(0.652619\pi\) | |||||||
\(480\) | −700416. | −0.138756 | ||||||||
\(481\) | 5.89026e6 | 1.16084 | ||||||||
\(482\) | −3.63086e6 | −0.711855 | ||||||||
\(483\) | −1.30095e6 | −0.253742 | ||||||||
\(484\) | 4.18318e6 | 0.811696 | ||||||||
\(485\) | 8.24068e6 | 1.59077 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −4.56645e6 | −0.872481 | −0.436241 | − | 0.899830i | \(-0.643690\pi\) | ||||
−0.436241 | + | 0.899830i | \(0.643690\pi\) | |||||||
\(488\) | 9600.00 | 0.00182483 | ||||||||
\(489\) | 4.32360e6 | 0.817661 | ||||||||
\(490\) | 729904. | 0.137333 | ||||||||
\(491\) | −5.31429e6 | −0.994813 | −0.497407 | − | 0.867518i | \(-0.665714\pi\) | ||||
−0.497407 | + | 0.867518i | \(0.665714\pi\) | |||||||
\(492\) | 2.45030e6 | 0.456360 | ||||||||
\(493\) | 374744. | 0.0694412 | ||||||||
\(494\) | −7.47370e6 | −1.37790 | ||||||||
\(495\) | 4.00140e6 | 0.734005 | ||||||||
\(496\) | −774144. | −0.141292 | ||||||||
\(497\) | 1.91972e6 | 0.348616 | ||||||||
\(498\) | −1.40299e6 | −0.253502 | ||||||||
\(499\) | −2.46314e6 | −0.442831 | −0.221415 | − | 0.975180i | \(-0.571068\pi\) | ||||
−0.221415 | + | 0.975180i | \(0.571068\pi\) | |||||||
\(500\) | −576384. | −0.103107 | ||||||||
\(501\) | −1.44162e6 | −0.256600 | ||||||||
\(502\) | 176352. | 0.0312335 | ||||||||
\(503\) | 2.79924e6 | 0.493310 | 0.246655 | − | 0.969103i | \(-0.420669\pi\) | ||||
0.246655 | + | 0.969103i | \(0.420669\pi\) | |||||||
\(504\) | −254016. | −0.0445435 | ||||||||
\(505\) | −5.35222e6 | −0.933912 | ||||||||
\(506\) | −7.67000e6 | −1.33174 | ||||||||
\(507\) | −1.88416e6 | −0.325535 | ||||||||
\(508\) | −3.83443e6 | −0.659237 | ||||||||
\(509\) | 1.99914e6 | 0.342018 | 0.171009 | − | 0.985269i | \(-0.445297\pi\) | ||||
0.171009 | + | 0.985269i | \(0.445297\pi\) | |||||||
\(510\) | 1.52122e6 | 0.258980 | ||||||||
\(511\) | 1.15493e6 | 0.195661 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 1.78751e6 | 0.299885 | ||||||||
\(514\) | −3.31680e6 | −0.553747 | ||||||||
\(515\) | −2.39795e6 | −0.398403 | ||||||||
\(516\) | −3.14438e6 | −0.519890 | ||||||||
\(517\) | −1.55610e7 | −2.56042 | ||||||||
\(518\) | −1.51508e6 | −0.248091 | ||||||||
\(519\) | 80856.0 | 0.0131763 | ||||||||
\(520\) | 3.70637e6 | 0.601091 | ||||||||
\(521\) | 3.52160e6 | 0.568390 | 0.284195 | − | 0.958767i | \(-0.408274\pi\) | ||||
0.284195 | + | 0.958767i | \(0.408274\pi\) | |||||||
\(522\) | −218376. | −0.0350775 | ||||||||
\(523\) | 2.60685e6 | 0.416737 | 0.208369 | − | 0.978050i | \(-0.433185\pi\) | ||||
0.208369 | + | 0.978050i | \(0.433185\pi\) | |||||||
\(524\) | −4.38675e6 | −0.697935 | ||||||||
\(525\) | 1.16909e6 | 0.185119 | ||||||||
\(526\) | 5.27786e6 | 0.831752 | ||||||||
\(527\) | 1.68134e6 | 0.263712 | ||||||||
\(528\) | −1.49760e6 | −0.233782 | ||||||||
\(529\) | 2.26616e6 | 0.352088 | ||||||||
\(530\) | 4.74058e6 | 0.733063 | ||||||||
\(531\) | 454248. | 0.0699128 | ||||||||
\(532\) | 1.92237e6 | 0.294481 | ||||||||
\(533\) | −1.29662e7 | −1.97694 | ||||||||
\(534\) | −216864. | −0.0329105 | ||||||||
\(535\) | 8.22943e6 | 1.24304 | ||||||||
\(536\) | −2.80218e6 | −0.421292 | ||||||||
\(537\) | −1.64597e6 | −0.246313 | ||||||||
\(538\) | −3.13515e6 | −0.466985 | ||||||||
\(539\) | 1.56065e6 | 0.231384 | ||||||||
\(540\) | −886464. | −0.130821 | ||||||||
\(541\) | −1.37441e6 | −0.201894 | −0.100947 | − | 0.994892i | \(-0.532187\pi\) | ||||
−0.100947 | + | 0.994892i | \(0.532187\pi\) | |||||||
\(542\) | 3.82032e6 | 0.558601 | ||||||||
\(543\) | −1.24497e6 | −0.181200 | ||||||||
\(544\) | −569344. | −0.0824855 | ||||||||
\(545\) | −5.48310e6 | −0.790742 | ||||||||
\(546\) | 1.34417e6 | 0.192962 | ||||||||
\(547\) | −8.78398e6 | −1.25523 | −0.627614 | − | 0.778524i | \(-0.715968\pi\) | ||||
−0.627614 | + | 0.778524i | \(0.715968\pi\) | |||||||
\(548\) | −6.25846e6 | −0.890259 | ||||||||
\(549\) | 12150.0 | 0.00172046 | ||||||||
\(550\) | 6.89260e6 | 0.971575 | ||||||||
\(551\) | 1.65265e6 | 0.231900 | ||||||||
\(552\) | 1.69920e6 | 0.237354 | ||||||||
\(553\) | 876708. | 0.121911 | ||||||||
\(554\) | 7.65092e6 | 1.05911 | ||||||||
\(555\) | −5.28732e6 | −0.728623 | ||||||||
\(556\) | 5.42982e6 | 0.744901 | ||||||||
\(557\) | 6.29262e6 | 0.859396 | 0.429698 | − | 0.902973i | \(-0.358620\pi\) | ||||
0.429698 | + | 0.902973i | \(0.358620\pi\) | |||||||
\(558\) | −979776. | −0.133211 | ||||||||
\(559\) | 1.66390e7 | 2.25216 | ||||||||
\(560\) | −953344. | −0.128463 | ||||||||
\(561\) | 3.25260e6 | 0.436338 | ||||||||
\(562\) | −4.10481e6 | −0.548216 | ||||||||
\(563\) | 4.86582e6 | 0.646971 | 0.323485 | − | 0.946233i | \(-0.395145\pi\) | ||||
0.323485 | + | 0.946233i | \(0.395145\pi\) | |||||||
\(564\) | 3.44736e6 | 0.456340 | ||||||||
\(565\) | 1.67889e7 | 2.21259 | ||||||||
\(566\) | 6.98670e6 | 0.916709 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | −2.50739e6 | −0.326100 | ||||||||
\(569\) | −4.46383e6 | −0.577998 | −0.288999 | − | 0.957329i | \(-0.593322\pi\) | ||||
−0.288999 | + | 0.957329i | \(0.593322\pi\) | |||||||
\(570\) | 6.70867e6 | 0.864867 | ||||||||
\(571\) | 8.17054e6 | 1.04872 | 0.524361 | − | 0.851496i | \(-0.324304\pi\) | ||||
0.524361 | + | 0.851496i | \(0.324304\pi\) | |||||||
\(572\) | 7.92480e6 | 1.01274 | ||||||||
\(573\) | −2.94500e6 | −0.374713 | ||||||||
\(574\) | 3.33514e6 | 0.422507 | ||||||||
\(575\) | −7.82045e6 | −0.986421 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −5.50343e6 | −0.688167 | −0.344084 | − | 0.938939i | \(-0.611810\pi\) | ||||
−0.344084 | + | 0.938939i | \(0.611810\pi\) | |||||||
\(578\) | −4.44288e6 | −0.553153 | ||||||||
\(579\) | −7.08212e6 | −0.877944 | ||||||||
\(580\) | −819584. | −0.101163 | ||||||||
\(581\) | −1.90963e6 | −0.234697 | ||||||||
\(582\) | −3.90348e6 | −0.477688 | ||||||||
\(583\) | 1.01361e7 | 1.23509 | ||||||||
\(584\) | −1.50848e6 | −0.183024 | ||||||||
\(585\) | 4.69087e6 | 0.566714 | ||||||||
\(586\) | 8.92848e6 | 1.07407 | ||||||||
\(587\) | 8.14251e6 | 0.975356 | 0.487678 | − | 0.873024i | \(-0.337844\pi\) | ||||
0.487678 | + | 0.873024i | \(0.337844\pi\) | |||||||
\(588\) | −345744. | −0.0412393 | ||||||||
\(589\) | 7.41485e6 | 0.880672 | ||||||||
\(590\) | 1.70483e6 | 0.201628 | ||||||||
\(591\) | −3.80788e6 | −0.448451 | ||||||||
\(592\) | 1.97888e6 | 0.232068 | ||||||||
\(593\) | −2.73136e6 | −0.318964 | −0.159482 | − | 0.987201i | \(-0.550982\pi\) | ||||
−0.159482 | + | 0.987201i | \(0.550982\pi\) | |||||||
\(594\) | −1.89540e6 | −0.220412 | ||||||||
\(595\) | 2.07054e6 | 0.239768 | ||||||||
\(596\) | −469344. | −0.0541222 | ||||||||
\(597\) | −9.21528e6 | −1.05821 | ||||||||
\(598\) | −8.99160e6 | −1.02822 | ||||||||
\(599\) | 1.23733e6 | 0.140902 | 0.0704510 | − | 0.997515i | \(-0.477556\pi\) | ||||
0.0704510 | + | 0.997515i | \(0.477556\pi\) | |||||||
\(600\) | −1.52698e6 | −0.173163 | ||||||||
\(601\) | −1.59756e7 | −1.80414 | −0.902071 | − | 0.431587i | \(-0.857954\pi\) | ||||
−0.902071 | + | 0.431587i | \(0.857954\pi\) | |||||||
\(602\) | −4.27986e6 | −0.481324 | ||||||||
\(603\) | −3.54650e6 | −0.397198 | ||||||||
\(604\) | 1.14573e6 | 0.127788 | ||||||||
\(605\) | 1.98701e7 | 2.20705 | ||||||||
\(606\) | 2.53526e6 | 0.280441 | ||||||||
\(607\) | −1.88275e6 | −0.207406 | −0.103703 | − | 0.994608i | \(-0.533069\pi\) | ||||
−0.103703 | + | 0.994608i | \(0.533069\pi\) | |||||||
\(608\) | −2.51085e6 | −0.275462 | ||||||||
\(609\) | −297234. | −0.0324755 | ||||||||
\(610\) | 45600.0 | 0.00496181 | ||||||||
\(611\) | −1.82423e7 | −1.97686 | ||||||||
\(612\) | −720576. | −0.0777681 | ||||||||
\(613\) | −9.82804e6 | −1.05637 | −0.528185 | − | 0.849130i | \(-0.677127\pi\) | ||||
−0.528185 | + | 0.849130i | \(0.677127\pi\) | |||||||
\(614\) | 7.41294e6 | 0.793542 | ||||||||
\(615\) | 1.16389e7 | 1.24087 | ||||||||
\(616\) | −2.03840e6 | −0.216440 | ||||||||
\(617\) | −8.21262e6 | −0.868498 | −0.434249 | − | 0.900793i | \(-0.642986\pi\) | ||||
−0.434249 | + | 0.900793i | \(0.642986\pi\) | |||||||
\(618\) | 1.13587e6 | 0.119635 | ||||||||
\(619\) | 6.98465e6 | 0.732686 | 0.366343 | − | 0.930480i | \(-0.380610\pi\) | ||||
0.366343 | + | 0.930480i | \(0.380610\pi\) | |||||||
\(620\) | −3.67718e6 | −0.384181 | ||||||||
\(621\) | 2.15055e6 | 0.223780 | ||||||||
\(622\) | −1.80382e6 | −0.186947 | ||||||||
\(623\) | −295176. | −0.0304692 | ||||||||
\(624\) | −1.75565e6 | −0.180499 | ||||||||
\(625\) | −1.10222e7 | −1.12867 | ||||||||
\(626\) | 6.41054e6 | 0.653820 | ||||||||
\(627\) | 1.43442e7 | 1.45716 | ||||||||
\(628\) | 4.74109e6 | 0.479710 | ||||||||
\(629\) | −4.29788e6 | −0.433139 | ||||||||
\(630\) | −1.20658e6 | −0.121116 | ||||||||
\(631\) | 1.26789e7 | 1.26767 | 0.633837 | − | 0.773467i | \(-0.281479\pi\) | ||||
0.633837 | + | 0.773467i | \(0.281479\pi\) | |||||||
\(632\) | −1.14509e6 | −0.114037 | ||||||||
\(633\) | −4.15364e6 | −0.412022 | ||||||||
\(634\) | −83448.0 | −0.00824504 | ||||||||
\(635\) | −1.82136e7 | −1.79250 | ||||||||
\(636\) | −2.24554e6 | −0.220129 | ||||||||
\(637\) | 1.82956e6 | 0.178648 | ||||||||
\(638\) | −1.75240e6 | −0.170444 | ||||||||
\(639\) | −3.17342e6 | −0.307450 | ||||||||
\(640\) | 1.24518e6 | 0.120167 | ||||||||
\(641\) | −1.40324e7 | −1.34892 | −0.674460 | − | 0.738311i | \(-0.735624\pi\) | ||||
−0.674460 | + | 0.738311i | \(0.735624\pi\) | |||||||
\(642\) | −3.89815e6 | −0.373268 | ||||||||
\(643\) | 1.30368e6 | 0.124349 | 0.0621745 | − | 0.998065i | \(-0.480196\pi\) | ||||
0.0621745 | + | 0.998065i | \(0.480196\pi\) | |||||||
\(644\) | 2.31280e6 | 0.219747 | ||||||||
\(645\) | −1.49358e7 | −1.41361 | ||||||||
\(646\) | 5.45325e6 | 0.514131 | ||||||||
\(647\) | 1.57110e6 | 0.147551 | 0.0737757 | − | 0.997275i | \(-0.476495\pi\) | ||||
0.0737757 | + | 0.997275i | \(0.476495\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 3.64520e6 | 0.339711 | ||||||||
\(650\) | 8.08025e6 | 0.750138 | ||||||||
\(651\) | −1.33358e6 | −0.123330 | ||||||||
\(652\) | −7.68640e6 | −0.708115 | ||||||||
\(653\) | −8.34115e6 | −0.765496 | −0.382748 | − | 0.923853i | \(-0.625022\pi\) | ||||
−0.382748 | + | 0.923853i | \(0.625022\pi\) | |||||||
\(654\) | 2.59726e6 | 0.237449 | ||||||||
\(655\) | −2.08371e7 | −1.89773 | ||||||||
\(656\) | −4.35610e6 | −0.395219 | ||||||||
\(657\) | −1.90917e6 | −0.172556 | ||||||||
\(658\) | 4.69224e6 | 0.422489 | ||||||||
\(659\) | 6.18334e6 | 0.554638 | 0.277319 | − | 0.960778i | \(-0.410554\pi\) | ||||
0.277319 | + | 0.960778i | \(0.410554\pi\) | |||||||
\(660\) | −7.11360e6 | −0.635667 | ||||||||
\(661\) | 928966. | 0.0826982 | 0.0413491 | − | 0.999145i | \(-0.486834\pi\) | ||||
0.0413491 | + | 0.999145i | \(0.486834\pi\) | |||||||
\(662\) | 8.30485e6 | 0.736524 | ||||||||
\(663\) | 3.81305e6 | 0.336890 | ||||||||
\(664\) | 2.49421e6 | 0.219539 | ||||||||
\(665\) | 9.13125e6 | 0.800711 | ||||||||
\(666\) | 2.50452e6 | 0.218796 | ||||||||
\(667\) | 1.98830e6 | 0.173048 | ||||||||
\(668\) | 2.56288e6 | 0.222222 | ||||||||
\(669\) | −8.95543e6 | −0.773609 | ||||||||
\(670\) | −1.33103e7 | −1.14552 | ||||||||
\(671\) | 97500.0 | 0.00835985 | ||||||||
\(672\) | 451584. | 0.0385758 | ||||||||
\(673\) | 1.79131e7 | 1.52452 | 0.762259 | − | 0.647272i | \(-0.224090\pi\) | ||||
0.762259 | + | 0.647272i | \(0.224090\pi\) | |||||||
\(674\) | 4.82033e6 | 0.408721 | ||||||||
\(675\) | −1.93258e6 | −0.163259 | ||||||||
\(676\) | 3.34962e6 | 0.281922 | ||||||||
\(677\) | −4.96397e6 | −0.416253 | −0.208126 | − | 0.978102i | \(-0.566737\pi\) | ||||
−0.208126 | + | 0.978102i | \(0.566737\pi\) | |||||||
\(678\) | −7.95262e6 | −0.664409 | ||||||||
\(679\) | −5.31307e6 | −0.442253 | ||||||||
\(680\) | −2.70438e6 | −0.224283 | ||||||||
\(681\) | 860112. | 0.0710701 | ||||||||
\(682\) | −7.86240e6 | −0.647283 | ||||||||
\(683\) | 89526.0 | 0.00734340 | 0.00367170 | − | 0.999993i | \(-0.498831\pi\) | ||||
0.00367170 | + | 0.999993i | \(0.498831\pi\) | |||||||
\(684\) | −3.17779e6 | −0.259708 | ||||||||
\(685\) | −2.97277e7 | −2.42067 | ||||||||
\(686\) | −470596. | −0.0381802 | ||||||||
\(687\) | 9.39677e6 | 0.759603 | ||||||||
\(688\) | 5.59002e6 | 0.450238 | ||||||||
\(689\) | 1.18826e7 | 0.953596 | ||||||||
\(690\) | 8.07120e6 | 0.645380 | ||||||||
\(691\) | −142396. | −0.0113450 | −0.00567248 | − | 0.999984i | \(-0.501806\pi\) | ||||
−0.00567248 | + | 0.999984i | \(0.501806\pi\) | |||||||
\(692\) | −143744. | −0.0114110 | ||||||||
\(693\) | −2.57985e6 | −0.204062 | ||||||||
\(694\) | −3.50657e6 | −0.276365 | ||||||||
\(695\) | 2.57917e7 | 2.02543 | ||||||||
\(696\) | 388224. | 0.0303780 | ||||||||
\(697\) | 9.46090e6 | 0.737650 | ||||||||
\(698\) | −5.18372e6 | −0.402720 | ||||||||
\(699\) | 1.05247e7 | 0.814735 | ||||||||
\(700\) | −2.07838e6 | −0.160317 | ||||||||
\(701\) | 1.03935e7 | 0.798852 | 0.399426 | − | 0.916765i | \(-0.369209\pi\) | ||||
0.399426 | + | 0.916765i | \(0.369209\pi\) | |||||||
\(702\) | −2.22199e6 | −0.170177 | ||||||||
\(703\) | −1.89540e7 | −1.44648 | ||||||||
\(704\) | 2.66240e6 | 0.202461 | ||||||||
\(705\) | 1.63750e7 | 1.24082 | ||||||||
\(706\) | −1.59616e7 | −1.20521 | ||||||||
\(707\) | 3.45078e6 | 0.259638 | ||||||||
\(708\) | −807552. | −0.0605463 | ||||||||
\(709\) | 4.65503e6 | 0.347782 | 0.173891 | − | 0.984765i | \(-0.444366\pi\) | ||||
0.173891 | + | 0.984765i | \(0.444366\pi\) | |||||||
\(710\) | −1.19101e7 | −0.886686 | ||||||||
\(711\) | −1.44925e6 | −0.107515 | ||||||||
\(712\) | 385536. | 0.0285013 | ||||||||
\(713\) | 8.92080e6 | 0.657173 | ||||||||
\(714\) | −980784. | −0.0719992 | ||||||||
\(715\) | 3.76428e7 | 2.75370 | ||||||||
\(716\) | 2.92618e6 | 0.213313 | ||||||||
\(717\) | 246078. | 0.0178762 | ||||||||
\(718\) | 1.62581e7 | 1.17695 | ||||||||
\(719\) | −6.72134e6 | −0.484880 | −0.242440 | − | 0.970166i | \(-0.577948\pi\) | ||||
−0.242440 | + | 0.970166i | \(0.577948\pi\) | |||||||
\(720\) | 1.57594e6 | 0.113294 | ||||||||
\(721\) | 1.54605e6 | 0.110760 | ||||||||
\(722\) | 1.41448e7 | 1.00984 | ||||||||
\(723\) | 8.16943e6 | 0.581227 | ||||||||
\(724\) | 2.21328e6 | 0.156924 | ||||||||
\(725\) | −1.78677e6 | −0.126248 | ||||||||
\(726\) | −9.41216e6 | −0.662747 | ||||||||
\(727\) | −1.24076e7 | −0.870670 | −0.435335 | − | 0.900269i | \(-0.643370\pi\) | ||||
−0.435335 | + | 0.900269i | \(0.643370\pi\) | |||||||
\(728\) | −2.38963e6 | −0.167110 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −7.16528e6 | −0.497652 | ||||||||
\(731\) | −1.21408e7 | −0.840339 | ||||||||
\(732\) | −21600.0 | −0.00148996 | ||||||||
\(733\) | 1.35958e7 | 0.934641 | 0.467321 | − | 0.884088i | \(-0.345219\pi\) | ||||
0.467321 | + | 0.884088i | \(0.345219\pi\) | |||||||
\(734\) | −6.68973e6 | −0.458319 | ||||||||
\(735\) | −1.64228e6 | −0.112132 | ||||||||
\(736\) | −3.02080e6 | −0.205555 | ||||||||
\(737\) | −2.84596e7 | −1.93001 | ||||||||
\(738\) | −5.51318e6 | −0.372616 | ||||||||
\(739\) | 2.56819e6 | 0.172988 | 0.0864941 | − | 0.996252i | \(-0.472434\pi\) | ||||
0.0864941 | + | 0.996252i | \(0.472434\pi\) | |||||||
\(740\) | 9.39968e6 | 0.631006 | ||||||||
\(741\) | 1.68158e7 | 1.12505 | ||||||||
\(742\) | −3.05642e6 | −0.203800 | ||||||||
\(743\) | −2.02133e7 | −1.34327 | −0.671637 | − | 0.740880i | \(-0.734409\pi\) | ||||
−0.671637 | + | 0.740880i | \(0.734409\pi\) | |||||||
\(744\) | 1.74182e6 | 0.115364 | ||||||||
\(745\) | −2.22938e6 | −0.147161 | ||||||||
\(746\) | 1.26707e7 | 0.833595 | ||||||||
\(747\) | 3.15673e6 | 0.206984 | ||||||||
\(748\) | −5.78240e6 | −0.377880 | ||||||||
\(749\) | −5.30582e6 | −0.345579 | ||||||||
\(750\) | 1.29686e6 | 0.0841863 | ||||||||
\(751\) | 7.04813e6 | 0.456010 | 0.228005 | − | 0.973660i | \(-0.426780\pi\) | ||||
0.228005 | + | 0.973660i | \(0.426780\pi\) | |||||||
\(752\) | −6.12864e6 | −0.395202 | ||||||||
\(753\) | −396792. | −0.0255021 | ||||||||
\(754\) | −2.05435e6 | −0.131597 | ||||||||
\(755\) | 5.44221e6 | 0.347462 | ||||||||
\(756\) | 571536. | 0.0363696 | ||||||||
\(757\) | −2.04120e7 | −1.29463 | −0.647315 | − | 0.762223i | \(-0.724108\pi\) | ||||
−0.647315 | + | 0.762223i | \(0.724108\pi\) | |||||||
\(758\) | −1.68155e7 | −1.06301 | ||||||||
\(759\) | 1.72575e7 | 1.08736 | ||||||||
\(760\) | −1.19265e7 | −0.748997 | ||||||||
\(761\) | −5.07974e6 | −0.317965 | −0.158983 | − | 0.987281i | \(-0.550821\pi\) | ||||
−0.158983 | + | 0.987281i | \(0.550821\pi\) | |||||||
\(762\) | 8.62747e6 | 0.538265 | ||||||||
\(763\) | 3.53515e6 | 0.219835 | ||||||||
\(764\) | 5.23555e6 | 0.324511 | ||||||||
\(765\) | −3.42274e6 | −0.211456 | ||||||||
\(766\) | −1.37046e6 | −0.0843909 | ||||||||
\(767\) | 4.27330e6 | 0.262286 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 2.33898e7 | 1.42630 | 0.713149 | − | 0.701012i | \(-0.247268\pi\) | ||||
0.713149 | + | 0.701012i | \(0.247268\pi\) | |||||||
\(770\) | −9.68240e6 | −0.588513 | ||||||||
\(771\) | 7.46280e6 | 0.452133 | ||||||||
\(772\) | 1.25904e7 | 0.760322 | ||||||||
\(773\) | −1.11253e6 | −0.0669672 | −0.0334836 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334836 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(774\) | 7.07486e6 | 0.424488 | ||||||||
\(775\) | −8.01662e6 | −0.479443 | ||||||||
\(776\) | 6.93952e6 | 0.413690 | ||||||||
\(777\) | 3.40893e6 | 0.202566 | ||||||||
\(778\) | −1.53584e7 | −0.909696 | ||||||||
\(779\) | 4.17232e7 | 2.46340 | ||||||||
\(780\) | −8.33933e6 | −0.490789 | ||||||||
\(781\) | −2.54657e7 | −1.49392 | ||||||||
\(782\) | 6.56080e6 | 0.383654 | ||||||||
\(783\) | 491346. | 0.0286407 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | 2.25202e7 | 1.30436 | ||||||||
\(786\) | 9.87019e6 | 0.569861 | ||||||||
\(787\) | 2.00812e6 | 0.115572 | 0.0577859 | − | 0.998329i | \(-0.481596\pi\) | ||||
0.0577859 | + | 0.998329i | \(0.481596\pi\) | |||||||
\(788\) | 6.76957e6 | 0.388370 | ||||||||
\(789\) | −1.18752e7 | −0.679123 | ||||||||
\(790\) | −5.43917e6 | −0.310074 | ||||||||
\(791\) | −1.08244e7 | −0.615124 | ||||||||
\(792\) | 3.36960e6 | 0.190882 | ||||||||
\(793\) | 114300. | 0.00645451 | ||||||||
\(794\) | 1.37558e7 | 0.774343 | ||||||||
\(795\) | −1.06663e7 | −0.598544 | ||||||||
\(796\) | 1.63827e7 | 0.916439 | ||||||||
\(797\) | 3.00897e7 | 1.67792 | 0.838961 | − | 0.544191i | \(-0.183163\pi\) | ||||
0.838961 | + | 0.544191i | \(0.183163\pi\) | |||||||
\(798\) | −4.32533e6 | −0.240443 | ||||||||
\(799\) | 1.33106e7 | 0.737619 | ||||||||
\(800\) | 2.71462e6 | 0.149963 | ||||||||
\(801\) | 487944. | 0.0268713 | ||||||||
\(802\) | −1.55768e7 | −0.855152 | ||||||||
\(803\) | −1.53205e7 | −0.838463 | ||||||||
\(804\) | 6.30490e6 | 0.343984 | ||||||||
\(805\) | 1.09858e7 | 0.597506 | ||||||||
\(806\) | −9.21715e6 | −0.499757 | ||||||||
\(807\) | 7.05409e6 | 0.381292 | ||||||||
\(808\) | −4.50714e6 | −0.242869 | ||||||||
\(809\) | −1.88207e6 | −0.101103 | −0.0505515 | − | 0.998721i | \(-0.516098\pi\) | ||||
−0.0505515 | + | 0.998721i | \(0.516098\pi\) | |||||||
\(810\) | 1.99454e6 | 0.106815 | ||||||||
\(811\) | 4.88220e6 | 0.260654 | 0.130327 | − | 0.991471i | \(-0.458397\pi\) | ||||
0.130327 | + | 0.991471i | \(0.458397\pi\) | |||||||
\(812\) | 528416. | 0.0281246 | ||||||||
\(813\) | −8.59572e6 | −0.456096 | ||||||||
\(814\) | 2.00980e7 | 1.06314 | ||||||||
\(815\) | −3.65104e7 | −1.92541 | ||||||||
\(816\) | 1.28102e6 | 0.0673491 | ||||||||
\(817\) | −5.35419e7 | −2.80633 | ||||||||
\(818\) | −6.58718e6 | −0.344204 | ||||||||
\(819\) | −3.02438e6 | −0.157553 | ||||||||
\(820\) | −2.06915e7 | −1.07462 | ||||||||
\(821\) | 8.37096e6 | 0.433429 | 0.216714 | − | 0.976235i | \(-0.430466\pi\) | ||||
0.216714 | + | 0.976235i | \(0.430466\pi\) | |||||||
\(822\) | 1.40815e7 | 0.726893 | ||||||||
\(823\) | −2.02090e7 | −1.04003 | −0.520015 | − | 0.854157i | \(-0.674074\pi\) | ||||
−0.520015 | + | 0.854157i | \(0.674074\pi\) | |||||||
\(824\) | −2.01933e6 | −0.103607 | ||||||||
\(825\) | −1.55084e7 | −0.793288 | ||||||||
\(826\) | −1.09917e6 | −0.0560549 | ||||||||
\(827\) | −1.31059e7 | −0.666352 | −0.333176 | − | 0.942865i | \(-0.608120\pi\) | ||||
−0.333176 | + | 0.942865i | \(0.608120\pi\) | |||||||
\(828\) | −3.82320e6 | −0.193799 | ||||||||
\(829\) | 3.18667e7 | 1.61046 | 0.805232 | − | 0.592960i | \(-0.202041\pi\) | ||||
0.805232 | + | 0.592960i | \(0.202041\pi\) | |||||||
\(830\) | 1.18475e7 | 0.596941 | ||||||||
\(831\) | −1.72146e7 | −0.864756 | ||||||||
\(832\) | 3.12115e6 | 0.156317 | ||||||||
\(833\) | −1.33496e6 | −0.0666583 | ||||||||
\(834\) | −1.22171e7 | −0.608209 | ||||||||
\(835\) | 1.21737e7 | 0.604235 | ||||||||
\(836\) | −2.55008e7 | −1.26194 | ||||||||
\(837\) | 2.20450e6 | 0.108767 | ||||||||
\(838\) | −6.70637e6 | −0.329896 | ||||||||
\(839\) | 9.94742e6 | 0.487872 | 0.243936 | − | 0.969791i | \(-0.421561\pi\) | ||||
0.243936 | + | 0.969791i | \(0.421561\pi\) | |||||||
\(840\) | 2.14502e6 | 0.104890 | ||||||||
\(841\) | −2.00569e7 | −0.977852 | ||||||||
\(842\) | −2.26697e6 | −0.110196 | ||||||||
\(843\) | 9.23582e6 | 0.447617 | ||||||||
\(844\) | 7.38426e6 | 0.356821 | ||||||||
\(845\) | 1.59107e7 | 0.766561 | ||||||||
\(846\) | −7.75656e6 | −0.372600 | ||||||||
\(847\) | −1.28110e7 | −0.613585 | ||||||||
\(848\) | 3.99206e6 | 0.190637 | ||||||||
\(849\) | −1.57201e7 | −0.748489 | ||||||||
\(850\) | −5.89582e6 | −0.279896 | ||||||||
\(851\) | −2.28035e7 | −1.07939 | ||||||||
\(852\) | 5.64163e6 | 0.266260 | ||||||||
\(853\) | −6.52611e6 | −0.307102 | −0.153551 | − | 0.988141i | \(-0.549071\pi\) | ||||
−0.153551 | + | 0.988141i | \(0.549071\pi\) | |||||||
\(854\) | −29400.0 | −0.00137944 | ||||||||
\(855\) | −1.50945e7 | −0.706161 | ||||||||
\(856\) | 6.93005e6 | 0.323260 | ||||||||
\(857\) | −8.76238e6 | −0.407540 | −0.203770 | − | 0.979019i | \(-0.565319\pi\) | ||||
−0.203770 | + | 0.979019i | \(0.565319\pi\) | |||||||
\(858\) | −1.78308e7 | −0.826899 | ||||||||
\(859\) | 6.47942e6 | 0.299608 | 0.149804 | − | 0.988716i | \(-0.452136\pi\) | ||||
0.149804 | + | 0.988716i | \(0.452136\pi\) | |||||||
\(860\) | 2.65526e7 | 1.22422 | ||||||||
\(861\) | −7.50406e6 | −0.344975 | ||||||||
\(862\) | 2.67387e7 | 1.22567 | ||||||||
\(863\) | −1.83417e7 | −0.838323 | −0.419162 | − | 0.907912i | \(-0.637676\pi\) | ||||
−0.419162 | + | 0.907912i | \(0.637676\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | −682784. | −0.0310272 | ||||||||
\(866\) | 2.76535e7 | 1.25301 | ||||||||
\(867\) | 9.99649e6 | 0.451648 | ||||||||
\(868\) | 2.37082e6 | 0.106807 | ||||||||
\(869\) | −1.16298e7 | −0.522424 | ||||||||
\(870\) | 1.84406e6 | 0.0825996 | ||||||||
\(871\) | −3.33634e7 | −1.49013 | ||||||||
\(872\) | −4.61734e6 | −0.205637 | ||||||||
\(873\) | 8.78283e6 | 0.390031 | ||||||||
\(874\) | 2.89336e7 | 1.28122 | ||||||||
\(875\) | 1.76518e6 | 0.0779413 | ||||||||
\(876\) | 3.39408e6 | 0.149438 | ||||||||
\(877\) | 2.69065e7 | 1.18129 | 0.590647 | − | 0.806930i | \(-0.298873\pi\) | ||||
0.590647 | + | 0.806930i | \(0.298873\pi\) | |||||||
\(878\) | −1.82512e7 | −0.799017 | ||||||||
\(879\) | −2.00891e7 | −0.876976 | ||||||||
\(880\) | 1.26464e7 | 0.550504 | ||||||||
\(881\) | −1.52174e7 | −0.660542 | −0.330271 | − | 0.943886i | \(-0.607140\pi\) | ||||
−0.330271 | + | 0.943886i | \(0.607140\pi\) | |||||||
\(882\) | 777924. | 0.0336718 | ||||||||
\(883\) | −2.61520e7 | −1.12877 | −0.564383 | − | 0.825513i | \(-0.690886\pi\) | ||||
−0.564383 | + | 0.825513i | \(0.690886\pi\) | |||||||
\(884\) | −6.77875e6 | −0.291756 | ||||||||
\(885\) | −3.83587e6 | −0.164629 | ||||||||
\(886\) | 1.83904e7 | 0.787058 | ||||||||
\(887\) | −1.08021e7 | −0.460997 | −0.230499 | − | 0.973073i | \(-0.574036\pi\) | ||||
−0.230499 | + | 0.973073i | \(0.574036\pi\) | |||||||
\(888\) | −4.45248e6 | −0.189483 | ||||||||
\(889\) | 1.17429e7 | 0.498337 | ||||||||
\(890\) | 1.83130e6 | 0.0774968 | ||||||||
\(891\) | 4.26465e6 | 0.179965 | ||||||||
\(892\) | 1.59208e7 | 0.669965 | ||||||||
\(893\) | 5.87009e7 | 2.46329 | ||||||||
\(894\) | 1.05602e6 | 0.0441906 | ||||||||
\(895\) | 1.38993e7 | 0.580011 | ||||||||
\(896\) | −802816. | −0.0334077 | ||||||||
\(897\) | 2.02311e7 | 0.839534 | ||||||||
\(898\) | 6.82631e6 | 0.282485 | ||||||||
\(899\) | 2.03818e6 | 0.0841090 | ||||||||
\(900\) | 3.43570e6 | 0.141387 | ||||||||
\(901\) | −8.67026e6 | −0.355812 | ||||||||
\(902\) | −4.42416e7 | −1.81057 | ||||||||
\(903\) | 9.62968e6 | 0.393000 | ||||||||
\(904\) | 1.41380e7 | 0.575395 | ||||||||
\(905\) | 1.05131e7 | 0.426686 | ||||||||
\(906\) | −2.57789e6 | −0.104338 | ||||||||
\(907\) | −9.84167e6 | −0.397238 | −0.198619 | − | 0.980077i | \(-0.563646\pi\) | ||||
−0.198619 | + | 0.980077i | \(0.563646\pi\) | |||||||
\(908\) | −1.52909e6 | −0.0615486 | ||||||||
\(909\) | −5.70434e6 | −0.228979 | ||||||||
\(910\) | −1.13508e7 | −0.454382 | ||||||||
\(911\) | 2.72509e7 | 1.08789 | 0.543945 | − | 0.839121i | \(-0.316930\pi\) | ||||
0.543945 | + | 0.839121i | \(0.316930\pi\) | |||||||
\(912\) | 5.64941e6 | 0.224914 | ||||||||
\(913\) | 2.53318e7 | 1.00575 | ||||||||
\(914\) | −2.77566e7 | −1.09901 | ||||||||
\(915\) | −102600. | −0.00405130 | ||||||||
\(916\) | −1.67054e7 | −0.657836 | ||||||||
\(917\) | 1.34344e7 | 0.527589 | ||||||||
\(918\) | 1.62130e6 | 0.0634974 | ||||||||
\(919\) | 2.86432e7 | 1.11875 | 0.559374 | − | 0.828916i | \(-0.311042\pi\) | ||||
0.559374 | + | 0.828916i | \(0.311042\pi\) | |||||||
\(920\) | −1.43488e7 | −0.558915 | ||||||||
\(921\) | −1.66791e7 | −0.647924 | ||||||||
\(922\) | −1.04722e7 | −0.405705 | ||||||||
\(923\) | −2.98536e7 | −1.15343 | ||||||||
\(924\) | 4.58640e6 | 0.176723 | ||||||||
\(925\) | 2.04922e7 | 0.787472 | ||||||||
\(926\) | 2.85441e7 | 1.09393 | ||||||||
\(927\) | −2.55571e6 | −0.0976816 | ||||||||
\(928\) | −690176. | −0.0263081 | ||||||||
\(929\) | 6.78492e6 | 0.257932 | 0.128966 | − | 0.991649i | \(-0.458834\pi\) | ||||
0.128966 | + | 0.991649i | \(0.458834\pi\) | |||||||
\(930\) | 8.27366e6 | 0.313683 | ||||||||
\(931\) | −5.88725e6 | −0.222607 | ||||||||
\(932\) | −1.87106e7 | −0.705581 | ||||||||
\(933\) | 4.05860e6 | 0.152641 | ||||||||
\(934\) | −8.69590e6 | −0.326173 | ||||||||
\(935\) | −2.74664e7 | −1.02748 | ||||||||
\(936\) | 3.95021e6 | 0.147377 | ||||||||
\(937\) | 3.00308e7 | 1.11742 | 0.558712 | − | 0.829362i | \(-0.311296\pi\) | ||||
0.558712 | + | 0.829362i | \(0.311296\pi\) | |||||||
\(938\) | 8.58166e6 | 0.318467 | ||||||||
\(939\) | −1.44237e7 | −0.533842 | ||||||||
\(940\) | −2.91110e7 | −1.07458 | ||||||||
\(941\) | 2.30725e7 | 0.849415 | 0.424707 | − | 0.905331i | \(-0.360377\pi\) | ||||
0.424707 | + | 0.905331i | \(0.360377\pi\) | |||||||
\(942\) | −1.06674e7 | −0.391682 | ||||||||
\(943\) | 5.01972e7 | 1.83823 | ||||||||
\(944\) | 1.43565e6 | 0.0524346 | ||||||||
\(945\) | 2.71480e6 | 0.0988912 | ||||||||
\(946\) | 5.67736e7 | 2.06262 | ||||||||
\(947\) | 2.71433e7 | 0.983531 | 0.491765 | − | 0.870728i | \(-0.336352\pi\) | ||||
0.491765 | + | 0.870728i | \(0.336352\pi\) | |||||||
\(948\) | 2.57645e6 | 0.0931109 | ||||||||
\(949\) | −1.79603e7 | −0.647365 | ||||||||
\(950\) | −2.60010e7 | −0.934719 | ||||||||
\(951\) | 187758. | 0.00673205 | ||||||||
\(952\) | 1.74362e6 | 0.0623532 | ||||||||
\(953\) | −1.61552e7 | −0.576209 | −0.288104 | − | 0.957599i | \(-0.593025\pi\) | ||||
−0.288104 | + | 0.957599i | \(0.593025\pi\) | |||||||
\(954\) | 5.05246e6 | 0.179735 | ||||||||
\(955\) | 2.48689e7 | 0.882364 | ||||||||
\(956\) | −437472. | −0.0154812 | ||||||||
\(957\) | 3.94290e6 | 0.139167 | ||||||||
\(958\) | −1.85318e7 | −0.652383 | ||||||||
\(959\) | 1.91665e7 | 0.672973 | ||||||||
\(960\) | −2.80166e6 | −0.0981156 | ||||||||
\(961\) | −1.94846e7 | −0.680585 | ||||||||
\(962\) | 2.35610e7 | 0.820837 | ||||||||
\(963\) | 8.77084e6 | 0.304772 | ||||||||
\(964\) | −1.45234e7 | −0.503357 | ||||||||
\(965\) | 5.98046e7 | 2.06736 | ||||||||
\(966\) | −5.20380e6 | −0.179423 | ||||||||
\(967\) | −3.80323e7 | −1.30793 | −0.653967 | − | 0.756523i | \(-0.726897\pi\) | ||||
−0.653967 | + | 0.756523i | \(0.726897\pi\) | |||||||
\(968\) | 1.67327e7 | 0.573956 | ||||||||
\(969\) | −1.22698e7 | −0.419786 | ||||||||
\(970\) | 3.29627e7 | 1.12485 | ||||||||
\(971\) | −2.23104e7 | −0.759379 | −0.379689 | − | 0.925114i | \(-0.623969\pi\) | ||||
−0.379689 | + | 0.925114i | \(0.623969\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −1.66288e7 | −0.563093 | ||||||||
\(974\) | −1.82658e7 | −0.616937 | ||||||||
\(975\) | −1.81806e7 | −0.612485 | ||||||||
\(976\) | 38400.0 | 0.00129035 | ||||||||
\(977\) | 3.06930e7 | 1.02873 | 0.514367 | − | 0.857570i | \(-0.328027\pi\) | ||||
0.514367 | + | 0.857570i | \(0.328027\pi\) | |||||||
\(978\) | 1.72944e7 | 0.578174 | ||||||||
\(979\) | 3.91560e6 | 0.130569 | ||||||||
\(980\) | 2.91962e6 | 0.0971092 | ||||||||
\(981\) | −5.84383e6 | −0.193876 | ||||||||
\(982\) | −2.12572e7 | −0.703439 | ||||||||
\(983\) | −1.52706e7 | −0.504048 | −0.252024 | − | 0.967721i | \(-0.581096\pi\) | ||||
−0.252024 | + | 0.967721i | \(0.581096\pi\) | |||||||
\(984\) | 9.80122e6 | 0.322695 | ||||||||
\(985\) | 3.21554e7 | 1.05600 | ||||||||
\(986\) | 1.49898e6 | 0.0491024 | ||||||||
\(987\) | −1.05575e7 | −0.344961 | ||||||||
\(988\) | −2.98948e7 | −0.974323 | ||||||||
\(989\) | −6.44162e7 | −2.09413 | ||||||||
\(990\) | 1.60056e7 | 0.519020 | ||||||||
\(991\) | 3.16279e7 | 1.02303 | 0.511513 | − | 0.859276i | \(-0.329085\pi\) | ||||
0.511513 | + | 0.859276i | \(0.329085\pi\) | |||||||
\(992\) | −3.09658e6 | −0.0999085 | ||||||||
\(993\) | −1.86859e7 | −0.601369 | ||||||||
\(994\) | 7.67889e6 | 0.246509 | ||||||||
\(995\) | 7.78179e7 | 2.49185 | ||||||||
\(996\) | −5.61197e6 | −0.179253 | ||||||||
\(997\) | −3.55842e7 | −1.13376 | −0.566878 | − | 0.823802i | \(-0.691849\pi\) | ||||
−0.566878 | + | 0.823802i | \(0.691849\pi\) | |||||||
\(998\) | −9.85256e6 | −0.313129 | ||||||||
\(999\) | −5.63517e6 | −0.178646 |
(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 | 42.6.a.e.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 126.6.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 336.6.a.q.1.1 | 1 | |||
5.2 | odd | 4 | 1050.6.g.h.799.2 | 2 | |||
5.3 | odd | 4 | 1050.6.g.h.799.1 | 2 | |||
5.4 | even | 2 | 1050.6.a.f.1.1 | 1 | |||
7.2 | even | 3 | 294.6.e.d.67.1 | 2 | |||
7.3 | odd | 6 | 294.6.e.c.79.1 | 2 | |||
7.4 | even | 3 | 294.6.e.d.79.1 | 2 | |||
7.5 | odd | 6 | 294.6.e.c.67.1 | 2 | |||
7.6 | odd | 2 | 294.6.a.k.1.1 | 1 | |||
12.11 | even | 2 | 1008.6.a.d.1.1 | 1 | |||
21.20 | even | 2 | 882.6.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.a.e.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
126.6.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
294.6.a.k.1.1 | 1 | 7.6 | odd | 2 | |||
294.6.e.c.67.1 | 2 | 7.5 | odd | 6 | |||
294.6.e.c.79.1 | 2 | 7.3 | odd | 6 | |||
294.6.e.d.67.1 | 2 | 7.2 | even | 3 | |||
294.6.e.d.79.1 | 2 | 7.4 | even | 3 | |||
336.6.a.q.1.1 | 1 | 4.3 | odd | 2 | |||
882.6.a.j.1.1 | 1 | 21.20 | even | 2 | |||
1008.6.a.d.1.1 | 1 | 12.11 | even | 2 | |||
1050.6.a.f.1.1 | 1 | 5.4 | even | 2 | |||
1050.6.g.h.799.1 | 2 | 5.3 | odd | 4 | |||
1050.6.g.h.799.2 | 2 | 5.2 | odd | 4 |