Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 109x^{4} + 41x^{3} + 2208x^{2} - 3204x + 560 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.22733\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.22733 | −1.27762 | −0.638812 | − | 0.769363i | \(-0.720574\pi\) | ||||
−0.638812 | + | 0.769363i | \(0.720574\pi\) | |||||||
\(3\) | 15.9209 | 1.02133 | 0.510664 | − | 0.859780i | \(-0.329400\pi\) | ||||
0.510664 | + | 0.859780i | \(0.329400\pi\) | |||||||
\(4\) | 20.2343 | 0.632321 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −115.066 | −1.30487 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 85.0347 | 0.469755 | ||||||||
\(9\) | 10.4759 | 0.0431108 | ||||||||
\(10\) | −180.683 | −0.571371 | ||||||||
\(11\) | −387.066 | −0.964504 | −0.482252 | − | 0.876033i | \(-0.660181\pi\) | ||||
−0.482252 | + | 0.876033i | \(0.660181\pi\) | |||||||
\(12\) | 322.149 | 0.645808 | ||||||||
\(13\) | 920.823 | 1.51118 | 0.755592 | − | 0.655042i | \(-0.227349\pi\) | ||||
0.755592 | + | 0.655042i | \(0.227349\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 398.023 | 0.456752 | ||||||||
\(16\) | −1262.07 | −1.23249 | ||||||||
\(17\) | −678.473 | −0.569390 | −0.284695 | − | 0.958618i | \(-0.591892\pi\) | ||||
−0.284695 | + | 0.958618i | \(0.591892\pi\) | |||||||
\(18\) | −75.7130 | −0.0550794 | ||||||||
\(19\) | −2764.19 | −1.75664 | −0.878322 | − | 0.478070i | \(-0.841337\pi\) | ||||
−0.878322 | + | 0.478070i | \(0.841337\pi\) | |||||||
\(20\) | 505.857 | 0.282783 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2797.46 | 1.23227 | ||||||||
\(23\) | 2065.73 | 0.814241 | 0.407121 | − | 0.913374i | \(-0.366533\pi\) | ||||
0.407121 | + | 0.913374i | \(0.366533\pi\) | |||||||
\(24\) | 1353.83 | 0.479774 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −6655.09 | −1.93073 | ||||||||
\(27\) | −3702.00 | −0.977298 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2921.75 | −0.645131 | −0.322565 | − | 0.946547i | \(-0.604545\pi\) | ||||
−0.322565 | + | 0.946547i | \(0.604545\pi\) | |||||||
\(30\) | −2876.64 | −0.583557 | ||||||||
\(31\) | −4255.06 | −0.795246 | −0.397623 | − | 0.917549i | \(-0.630165\pi\) | ||||
−0.397623 | + | 0.917549i | \(0.630165\pi\) | |||||||
\(32\) | 6400.29 | 1.10490 | ||||||||
\(33\) | −6162.46 | −0.985074 | ||||||||
\(34\) | 4903.55 | 0.727467 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 211.973 | 0.0272599 | ||||||||
\(37\) | −154.621 | −0.0185680 | −0.00928399 | − | 0.999957i | \(-0.502955\pi\) | ||||
−0.00928399 | + | 0.999957i | \(0.502955\pi\) | |||||||
\(38\) | 19977.7 | 2.24433 | ||||||||
\(39\) | 14660.4 | 1.54342 | ||||||||
\(40\) | 2125.87 | 0.210081 | ||||||||
\(41\) | 7600.35 | 0.706112 | 0.353056 | − | 0.935602i | \(-0.385142\pi\) | ||||
0.353056 | + | 0.935602i | \(0.385142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13533.2 | 1.11616 | 0.558082 | − | 0.829786i | \(-0.311537\pi\) | ||||
0.558082 | + | 0.829786i | \(0.311537\pi\) | |||||||
\(44\) | −7832.01 | −0.609876 | ||||||||
\(45\) | 261.898 | 0.0192797 | ||||||||
\(46\) | −14929.7 | −1.04029 | ||||||||
\(47\) | −15002.5 | −0.990650 | −0.495325 | − | 0.868708i | \(-0.664951\pi\) | ||||
−0.495325 | + | 0.868708i | \(0.664951\pi\) | |||||||
\(48\) | −20093.3 | −1.25878 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4517.08 | −0.255525 | ||||||||
\(51\) | −10801.9 | −0.581534 | ||||||||
\(52\) | 18632.2 | 0.955555 | ||||||||
\(53\) | 18078.9 | 0.884060 | 0.442030 | − | 0.897000i | \(-0.354259\pi\) | ||||
0.442030 | + | 0.897000i | \(0.354259\pi\) | |||||||
\(54\) | 26755.6 | 1.24862 | ||||||||
\(55\) | −9676.66 | −0.431339 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −44008.4 | −1.79411 | ||||||||
\(58\) | 21116.4 | 0.824234 | ||||||||
\(59\) | −6479.69 | −0.242339 | −0.121170 | − | 0.992632i | \(-0.538665\pi\) | ||||
−0.121170 | + | 0.992632i | \(0.538665\pi\) | |||||||
\(60\) | 8053.71 | 0.288814 | ||||||||
\(61\) | −4006.33 | −0.137855 | −0.0689274 | − | 0.997622i | \(-0.521958\pi\) | ||||
−0.0689274 | + | 0.997622i | \(0.521958\pi\) | |||||||
\(62\) | 30752.7 | 1.01602 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5870.74 | −0.179161 | ||||||||
\(65\) | 23020.6 | 0.675822 | ||||||||
\(66\) | 44538.1 | 1.25855 | ||||||||
\(67\) | −33620.3 | −0.914986 | −0.457493 | − | 0.889213i | \(-0.651252\pi\) | ||||
−0.457493 | + | 0.889213i | \(0.651252\pi\) | |||||||
\(68\) | −13728.4 | −0.360038 | ||||||||
\(69\) | 32888.3 | 0.831608 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61404.3 | −1.44562 | −0.722808 | − | 0.691049i | \(-0.757149\pi\) | ||||
−0.722808 | + | 0.691049i | \(0.757149\pi\) | |||||||
\(72\) | 890.817 | 0.0202515 | ||||||||
\(73\) | 42664.3 | 0.937039 | 0.468520 | − | 0.883453i | \(-0.344788\pi\) | ||||
0.468520 | + | 0.883453i | \(0.344788\pi\) | |||||||
\(74\) | 1117.50 | 0.0237229 | ||||||||
\(75\) | 9950.58 | 0.204266 | ||||||||
\(76\) | −55931.4 | −1.11076 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −105955. | −1.97190 | ||||||||
\(79\) | −107893. | −1.94502 | −0.972510 | − | 0.232862i | \(-0.925191\pi\) | ||||
−0.972510 | + | 0.232862i | \(0.925191\pi\) | |||||||
\(80\) | −31551.8 | −0.551187 | ||||||||
\(81\) | −61484.9 | −1.04125 | ||||||||
\(82\) | −54930.2 | −0.902145 | ||||||||
\(83\) | −99024.8 | −1.57779 | −0.788894 | − | 0.614529i | \(-0.789346\pi\) | ||||
−0.788894 | + | 0.614529i | \(0.789346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16961.8 | −0.254639 | ||||||||
\(86\) | −97808.7 | −1.42604 | ||||||||
\(87\) | −46516.9 | −0.658890 | ||||||||
\(88\) | −32914.1 | −0.453080 | ||||||||
\(89\) | −7661.84 | −0.102532 | −0.0512659 | − | 0.998685i | \(-0.516326\pi\) | ||||
−0.0512659 | + | 0.998685i | \(0.516326\pi\) | |||||||
\(90\) | −1892.82 | −0.0246323 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 41798.5 | 0.514862 | ||||||||
\(93\) | −67744.5 | −0.812207 | ||||||||
\(94\) | 108428. | 1.26568 | ||||||||
\(95\) | −69104.7 | −0.785595 | ||||||||
\(96\) | 101899. | 1.12847 | ||||||||
\(97\) | −87087.4 | −0.939779 | −0.469890 | − | 0.882725i | \(-0.655706\pi\) | ||||
−0.469890 | + | 0.882725i | \(0.655706\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4054.88 | −0.0415805 | ||||||||
\(100\) | 12646.4 | 0.126464 | ||||||||
\(101\) | −72757.1 | −0.709695 | −0.354848 | − | 0.934924i | \(-0.615467\pi\) | ||||
−0.354848 | + | 0.934924i | \(0.615467\pi\) | |||||||
\(102\) | 78069.0 | 0.742982 | ||||||||
\(103\) | −49822.1 | −0.462732 | −0.231366 | − | 0.972867i | \(-0.574319\pi\) | ||||
−0.231366 | + | 0.972867i | \(0.574319\pi\) | |||||||
\(104\) | 78301.9 | 0.709886 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −130662. | −1.12950 | ||||||||
\(107\) | −79308.8 | −0.669672 | −0.334836 | − | 0.942276i | \(-0.608681\pi\) | ||||
−0.334836 | + | 0.942276i | \(0.608681\pi\) | |||||||
\(108\) | −74907.3 | −0.617966 | ||||||||
\(109\) | −183107. | −1.47618 | −0.738089 | − | 0.674703i | \(-0.764272\pi\) | ||||
−0.738089 | + | 0.674703i | \(0.764272\pi\) | |||||||
\(110\) | 69936.4 | 0.551089 | ||||||||
\(111\) | −2461.71 | −0.0189640 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 137042. | 1.00962 | 0.504809 | − | 0.863231i | \(-0.331563\pi\) | ||||
0.504809 | + | 0.863231i | \(0.331563\pi\) | |||||||
\(114\) | 318064. | 2.29220 | ||||||||
\(115\) | 51643.2 | 0.364140 | ||||||||
\(116\) | −59119.5 | −0.407930 | ||||||||
\(117\) | 9646.47 | 0.0651484 | ||||||||
\(118\) | 46830.8 | 0.309618 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 33845.8 | 0.214561 | ||||||||
\(121\) | −11230.6 | −0.0697329 | ||||||||
\(122\) | 28955.0 | 0.176126 | ||||||||
\(123\) | 121005. | 0.721172 | ||||||||
\(124\) | −86098.1 | −0.502851 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −43001.7 | −0.236579 | −0.118290 | − | 0.992979i | \(-0.537741\pi\) | ||||
−0.118290 | + | 0.992979i | \(0.537741\pi\) | |||||||
\(128\) | −162380. | −0.876005 | ||||||||
\(129\) | 215461. | 1.13997 | ||||||||
\(130\) | −166377. | −0.863447 | ||||||||
\(131\) | 21205.7 | 0.107963 | 0.0539815 | − | 0.998542i | \(-0.482809\pi\) | ||||
0.0539815 | + | 0.998542i | \(0.482809\pi\) | |||||||
\(132\) | −124693. | −0.622884 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 242985. | 1.16901 | ||||||||
\(135\) | −92550.0 | −0.437061 | ||||||||
\(136\) | −57693.7 | −0.267474 | ||||||||
\(137\) | 285197. | 1.29820 | 0.649102 | − | 0.760701i | \(-0.275145\pi\) | ||||
0.649102 | + | 0.760701i | \(0.275145\pi\) | |||||||
\(138\) | −237694. | −1.06248 | ||||||||
\(139\) | 282350. | 1.23951 | 0.619756 | − | 0.784794i | \(-0.287231\pi\) | ||||
0.619756 | + | 0.784794i | \(0.287231\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −238855. | −1.01178 | ||||||||
\(142\) | 443789. | 1.84695 | ||||||||
\(143\) | −356420. | −1.45754 | ||||||||
\(144\) | −13221.4 | −0.0531337 | ||||||||
\(145\) | −73043.7 | −0.288511 | ||||||||
\(146\) | −308349. | −1.19718 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3128.65 | −0.0117409 | ||||||||
\(149\) | 69436.1 | 0.256224 | 0.128112 | − | 0.991760i | \(-0.459108\pi\) | ||||
0.128112 | + | 0.991760i | \(0.459108\pi\) | |||||||
\(150\) | −71916.1 | −0.260974 | ||||||||
\(151\) | 258978. | 0.924315 | 0.462157 | − | 0.886798i | \(-0.347075\pi\) | ||||
0.462157 | + | 0.886798i | \(0.347075\pi\) | |||||||
\(152\) | −235052. | −0.825192 | ||||||||
\(153\) | −7107.63 | −0.0245469 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −106376. | −0.355645 | ||||||||
\(156\) | 296642. | 0.975935 | ||||||||
\(157\) | 102995. | 0.333477 | 0.166738 | − | 0.986001i | \(-0.446676\pi\) | ||||
0.166738 | + | 0.986001i | \(0.446676\pi\) | |||||||
\(158\) | 779775. | 2.48500 | ||||||||
\(159\) | 287832. | 0.902915 | ||||||||
\(160\) | 160007. | 0.494128 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 444372. | 1.33033 | ||||||||
\(163\) | −581424. | −1.71405 | −0.857026 | − | 0.515272i | \(-0.827691\pi\) | ||||
−0.857026 | + | 0.515272i | \(0.827691\pi\) | |||||||
\(164\) | 153788. | 0.446490 | ||||||||
\(165\) | −154061. | −0.440539 | ||||||||
\(166\) | 715685. | 2.01582 | ||||||||
\(167\) | 475920. | 1.32051 | 0.660257 | − | 0.751040i | \(-0.270447\pi\) | ||||
0.660257 | + | 0.751040i | \(0.270447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 476621. | 1.28368 | ||||||||
\(170\) | 122589. | 0.325333 | ||||||||
\(171\) | −28957.4 | −0.0757304 | ||||||||
\(172\) | 273834. | 0.705775 | ||||||||
\(173\) | −285658. | −0.725657 | −0.362828 | − | 0.931856i | \(-0.618189\pi\) | ||||
−0.362828 | + | 0.931856i | \(0.618189\pi\) | |||||||
\(174\) | 336193. | 0.841813 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 488505. | 1.18874 | ||||||||
\(177\) | −103163. | −0.247508 | ||||||||
\(178\) | 55374.7 | 0.130997 | ||||||||
\(179\) | −450892. | −1.05182 | −0.525909 | − | 0.850541i | \(-0.676275\pi\) | ||||
−0.525909 | + | 0.850541i | \(0.676275\pi\) | |||||||
\(180\) | 5299.32 | 0.0121910 | ||||||||
\(181\) | −151606. | −0.343969 | −0.171985 | − | 0.985100i | \(-0.555018\pi\) | ||||
−0.171985 | + | 0.985100i | \(0.555018\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −63784.4 | −0.140795 | ||||||||
\(184\) | 175658. | 0.382494 | ||||||||
\(185\) | −3865.53 | −0.00830385 | ||||||||
\(186\) | 489612. | 1.03769 | ||||||||
\(187\) | 262614. | 0.549179 | ||||||||
\(188\) | −303566. | −0.626409 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 499443. | 1.00369 | ||||||||
\(191\) | 514986. | 1.02144 | 0.510719 | − | 0.859748i | \(-0.329379\pi\) | ||||
0.510719 | + | 0.859748i | \(0.329379\pi\) | |||||||
\(192\) | −93467.7 | −0.182982 | ||||||||
\(193\) | −769968. | −1.48792 | −0.743959 | − | 0.668225i | \(-0.767054\pi\) | ||||
−0.743959 | + | 0.668225i | \(0.767054\pi\) | |||||||
\(194\) | 629409. | 1.20068 | ||||||||
\(195\) | 366509. | 0.690236 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −246901. | −0.453269 | −0.226635 | − | 0.973980i | \(-0.572772\pi\) | ||||
−0.226635 | + | 0.973980i | \(0.572772\pi\) | |||||||
\(198\) | 29306.0 | 0.0531243 | ||||||||
\(199\) | −890639. | −1.59430 | −0.797148 | − | 0.603783i | \(-0.793659\pi\) | ||||
−0.797148 | + | 0.603783i | \(0.793659\pi\) | |||||||
\(200\) | 53146.7 | 0.0939509 | ||||||||
\(201\) | −535266. | −0.934501 | ||||||||
\(202\) | 525839. | 0.906723 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −218569. | −0.367717 | ||||||||
\(205\) | 190009. | 0.315783 | ||||||||
\(206\) | 360081. | 0.591197 | ||||||||
\(207\) | 21640.4 | 0.0351026 | ||||||||
\(208\) | −1.16214e6 | −1.86252 | ||||||||
\(209\) | 1.06992e6 | 1.69429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −538746. | −0.833063 | −0.416531 | − | 0.909121i | \(-0.636754\pi\) | ||||
−0.416531 | + | 0.909121i | \(0.636754\pi\) | |||||||
\(212\) | 365813. | 0.559010 | ||||||||
\(213\) | −977614. | −1.47645 | ||||||||
\(214\) | 573191. | 0.855588 | ||||||||
\(215\) | 338329. | 0.499164 | ||||||||
\(216\) | −314798. | −0.459090 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.32338e6 | 1.88600 | ||||||||
\(219\) | 679256. | 0.957025 | ||||||||
\(220\) | −195800. | −0.272745 | ||||||||
\(221\) | −624753. | −0.860454 | ||||||||
\(222\) | 17791.6 | 0.0242288 | ||||||||
\(223\) | −1.34117e6 | −1.80602 | −0.903011 | − | 0.429618i | \(-0.858648\pi\) | ||||
−0.903011 | + | 0.429618i | \(0.858648\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6547.46 | 0.00862216 | ||||||||
\(226\) | −990447. | −1.28991 | ||||||||
\(227\) | 581025. | 0.748394 | 0.374197 | − | 0.927349i | \(-0.377918\pi\) | ||||
0.374197 | + | 0.927349i | \(0.377918\pi\) | |||||||
\(228\) | −890479. | −1.13445 | ||||||||
\(229\) | 998618. | 1.25838 | 0.629188 | − | 0.777253i | \(-0.283387\pi\) | ||||
0.629188 | + | 0.777253i | \(0.283387\pi\) | |||||||
\(230\) | −373242. | −0.465234 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −248450. | −0.303053 | ||||||||
\(233\) | 1.37979e6 | 1.66503 | 0.832517 | − | 0.553999i | \(-0.186899\pi\) | ||||
0.832517 | + | 0.553999i | \(0.186899\pi\) | |||||||
\(234\) | −69718.2 | −0.0832351 | ||||||||
\(235\) | −375064. | −0.443032 | ||||||||
\(236\) | −131112. | −0.153236 | ||||||||
\(237\) | −1.71775e6 | −1.98650 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 508394. | 0.575713 | 0.287856 | − | 0.957674i | \(-0.407057\pi\) | ||||
0.287856 | + | 0.957674i | \(0.407057\pi\) | |||||||
\(240\) | −502333. | −0.562942 | ||||||||
\(241\) | −185871. | −0.206143 | −0.103072 | − | 0.994674i | \(-0.532867\pi\) | ||||
−0.103072 | + | 0.994674i | \(0.532867\pi\) | |||||||
\(242\) | 81166.9 | 0.0890924 | ||||||||
\(243\) | −79311.0 | −0.0861624 | ||||||||
\(244\) | −81065.1 | −0.0871685 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −874540. | −0.921386 | ||||||||
\(247\) | −2.54533e6 | −2.65461 | ||||||||
\(248\) | −361828. | −0.373570 | ||||||||
\(249\) | −1.57657e6 | −1.61144 | ||||||||
\(250\) | −112927. | −0.114274 | ||||||||
\(251\) | 421837. | 0.422630 | 0.211315 | − | 0.977418i | \(-0.432225\pi\) | ||||
0.211315 | + | 0.977418i | \(0.432225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −799573. | −0.785339 | ||||||||
\(254\) | 310788. | 0.302259 | ||||||||
\(255\) | −270048. | −0.260070 | ||||||||
\(256\) | 1.36143e6 | 1.29836 | ||||||||
\(257\) | 1.94672e6 | 1.83853 | 0.919265 | − | 0.393639i | \(-0.128784\pi\) | ||||
0.919265 | + | 0.393639i | \(0.128784\pi\) | |||||||
\(258\) | −1.55720e6 | −1.45645 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 465805. | 0.427337 | ||||||||
\(261\) | −30608.0 | −0.0278121 | ||||||||
\(262\) | −153261. | −0.137936 | ||||||||
\(263\) | 1.63031e6 | 1.45339 | 0.726693 | − | 0.686962i | \(-0.241056\pi\) | ||||
0.726693 | + | 0.686962i | \(0.241056\pi\) | |||||||
\(264\) | −524023. | −0.462743 | ||||||||
\(265\) | 451972. | 0.395363 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −121984. | −0.104719 | ||||||||
\(268\) | −680282. | −0.578565 | ||||||||
\(269\) | −1.37145e6 | −1.15558 | −0.577788 | − | 0.816187i | \(-0.696084\pi\) | ||||
−0.577788 | + | 0.816187i | \(0.696084\pi\) | |||||||
\(270\) | 668889. | 0.558399 | ||||||||
\(271\) | 761737. | 0.630060 | 0.315030 | − | 0.949082i | \(-0.397985\pi\) | ||||
0.315030 | + | 0.949082i | \(0.397985\pi\) | |||||||
\(272\) | 856281. | 0.701769 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.06121e6 | −1.65862 | ||||||||
\(275\) | −241917. | −0.192901 | ||||||||
\(276\) | 665471. | 0.525843 | ||||||||
\(277\) | −2.06875e6 | −1.61997 | −0.809987 | − | 0.586448i | \(-0.800526\pi\) | ||||
−0.809987 | + | 0.586448i | \(0.800526\pi\) | |||||||
\(278\) | −2.04064e6 | −1.58363 | ||||||||
\(279\) | −44575.7 | −0.0342837 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 431842. | 0.326257 | 0.163128 | − | 0.986605i | \(-0.447842\pi\) | ||||
0.163128 | + | 0.986605i | \(0.447842\pi\) | |||||||
\(282\) | 1.72628e6 | 1.29267 | ||||||||
\(283\) | 1.43347e6 | 1.06395 | 0.531977 | − | 0.846759i | \(-0.321449\pi\) | ||||
0.531977 | + | 0.846759i | \(0.321449\pi\) | |||||||
\(284\) | −1.24247e6 | −0.914094 | ||||||||
\(285\) | −1.10021e6 | −0.802350 | ||||||||
\(286\) | 2.57596e6 | 1.86219 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 67049.0 | 0.0476333 | ||||||||
\(289\) | −959531. | −0.675794 | ||||||||
\(290\) | 527911. | 0.368609 | ||||||||
\(291\) | −1.38651e6 | −0.959823 | ||||||||
\(292\) | 863282. | 0.592510 | ||||||||
\(293\) | 138921. | 0.0945363 | 0.0472682 | − | 0.998882i | \(-0.484948\pi\) | ||||
0.0472682 | + | 0.998882i | \(0.484948\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −161992. | −0.108377 | ||||||||
\(296\) | −13148.2 | −0.00872240 | ||||||||
\(297\) | 1.43292e6 | 0.942607 | ||||||||
\(298\) | −501838. | −0.327358 | ||||||||
\(299\) | 1.90217e6 | 1.23047 | ||||||||
\(300\) | 201343. | 0.129162 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.87172e6 | −1.18093 | ||||||||
\(303\) | −1.15836e6 | −0.724832 | ||||||||
\(304\) | 3.48860e6 | 2.16505 | ||||||||
\(305\) | −100158. | −0.0616505 | ||||||||
\(306\) | 51369.2 | 0.0313617 | ||||||||
\(307\) | 631297. | 0.382285 | 0.191143 | − | 0.981562i | \(-0.438781\pi\) | ||||
0.191143 | + | 0.981562i | \(0.438781\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −793215. | −0.472601 | ||||||||
\(310\) | 768818. | 0.454380 | ||||||||
\(311\) | 2.20444e6 | 1.29240 | 0.646199 | − | 0.763169i | \(-0.276358\pi\) | ||||
0.646199 | + | 0.763169i | \(0.276358\pi\) | |||||||
\(312\) | 1.24664e6 | 0.725027 | ||||||||
\(313\) | −441934. | −0.254974 | −0.127487 | − | 0.991840i | \(-0.540691\pi\) | ||||
−0.127487 | + | 0.991840i | \(0.540691\pi\) | |||||||
\(314\) | −744376. | −0.426058 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.18313e6 | −1.22988 | ||||||||
\(317\) | 1.33132e6 | 0.744103 | 0.372052 | − | 0.928212i | \(-0.378654\pi\) | ||||
0.372052 | + | 0.928212i | \(0.378654\pi\) | |||||||
\(318\) | −2.08026e6 | −1.15359 | ||||||||
\(319\) | 1.13091e6 | 0.622231 | ||||||||
\(320\) | −146769. | −0.0801232 | ||||||||
\(321\) | −1.26267e6 | −0.683954 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.87543e6 | 1.00022 | ||||||||
\(324\) | −1.24410e6 | −0.658406 | ||||||||
\(325\) | 575514. | 0.302237 | ||||||||
\(326\) | 4.20215e6 | 2.18991 | ||||||||
\(327\) | −2.91523e6 | −1.50766 | ||||||||
\(328\) | 646293. | 0.331700 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.11345e6 | 0.562843 | ||||||||
\(331\) | 1.50280e6 | 0.753931 | 0.376966 | − | 0.926227i | \(-0.376967\pi\) | ||||
0.376966 | + | 0.926227i | \(0.376967\pi\) | |||||||
\(332\) | −2.00370e6 | −0.997670 | ||||||||
\(333\) | −1619.80 | −0.000800481 0 | ||||||||
\(334\) | −3.43963e6 | −1.68712 | ||||||||
\(335\) | −840507. | −0.409194 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.34434e6 | −1.12447 | −0.562233 | − | 0.826979i | \(-0.690058\pi\) | ||||
−0.562233 | + | 0.826979i | \(0.690058\pi\) | |||||||
\(338\) | −3.44470e6 | −1.64006 | ||||||||
\(339\) | 2.18183e6 | 1.03115 | ||||||||
\(340\) | −343210. | −0.161014 | ||||||||
\(341\) | 1.64699e6 | 0.767017 | ||||||||
\(342\) | 209285. | 0.0967549 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.15079e6 | 0.524324 | ||||||||
\(345\) | 822207. | 0.371906 | ||||||||
\(346\) | 2.06454e6 | 0.927116 | ||||||||
\(347\) | 279935. | 0.124805 | 0.0624026 | − | 0.998051i | \(-0.480124\pi\) | ||||
0.0624026 | + | 0.998051i | \(0.480124\pi\) | |||||||
\(348\) | −941237. | −0.416630 | ||||||||
\(349\) | −1.16659e6 | −0.512691 | −0.256346 | − | 0.966585i | \(-0.582519\pi\) | ||||
−0.256346 | + | 0.966585i | \(0.582519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.40888e6 | −1.47688 | ||||||||
\(352\) | −2.47734e6 | −1.06568 | ||||||||
\(353\) | −1.55443e6 | −0.663949 | −0.331975 | − | 0.943288i | \(-0.607715\pi\) | ||||
−0.331975 | + | 0.943288i | \(0.607715\pi\) | |||||||
\(354\) | 745590. | 0.316222 | ||||||||
\(355\) | −1.53511e6 | −0.646499 | ||||||||
\(356\) | −155032. | −0.0648330 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.25875e6 | 1.34383 | ||||||||
\(359\) | 856494. | 0.350742 | 0.175371 | − | 0.984502i | \(-0.443887\pi\) | ||||
0.175371 | + | 0.984502i | \(0.443887\pi\) | |||||||
\(360\) | 22270.4 | 0.00905675 | ||||||||
\(361\) | 5.16464e6 | 2.08580 | ||||||||
\(362\) | 1.09571e6 | 0.439463 | ||||||||
\(363\) | −178801. | −0.0712202 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.06661e6 | 0.419057 | ||||||||
\(366\) | 460991. | 0.179883 | ||||||||
\(367\) | 909272. | 0.352394 | 0.176197 | − | 0.984355i | \(-0.443620\pi\) | ||||
0.176197 | + | 0.984355i | \(0.443620\pi\) | |||||||
\(368\) | −2.60709e6 | −1.00355 | ||||||||
\(369\) | 79620.7 | 0.0304411 | ||||||||
\(370\) | 27937.5 | 0.0106092 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.37076e6 | −0.513576 | ||||||||
\(373\) | −133835. | −0.0498080 | −0.0249040 | − | 0.999690i | \(-0.507928\pi\) | ||||
−0.0249040 | + | 0.999690i | \(0.507928\pi\) | |||||||
\(374\) | −1.89800e6 | −0.701644 | ||||||||
\(375\) | 248764. | 0.0913504 | ||||||||
\(376\) | −1.27574e6 | −0.465363 | ||||||||
\(377\) | −2.69041e6 | −0.974912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.07715e6 | 0.385192 | 0.192596 | − | 0.981278i | \(-0.438309\pi\) | ||||
0.192596 | + | 0.981278i | \(0.438309\pi\) | |||||||
\(380\) | −1.39828e6 | −0.496749 | ||||||||
\(381\) | −684627. | −0.241625 | ||||||||
\(382\) | −3.72198e6 | −1.30501 | ||||||||
\(383\) | −461084. | −0.160614 | −0.0803069 | − | 0.996770i | \(-0.525590\pi\) | ||||
−0.0803069 | + | 0.996770i | \(0.525590\pi\) | |||||||
\(384\) | −2.58523e6 | −0.894688 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.56481e6 | 1.90100 | ||||||||
\(387\) | 141773. | 0.0481188 | ||||||||
\(388\) | −1.76215e6 | −0.594243 | ||||||||
\(389\) | 235175. | 0.0787983 | 0.0393992 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393992 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(390\) | −2.64888e6 | −0.881862 | ||||||||
\(391\) | −1.40154e6 | −0.463621 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 337615. | 0.110266 | ||||||||
\(394\) | 1.78443e6 | 0.579108 | ||||||||
\(395\) | −2.69732e6 | −0.869839 | ||||||||
\(396\) | −82047.6 | −0.0262923 | ||||||||
\(397\) | 3.60978e6 | 1.14949 | 0.574744 | − | 0.818334i | \(-0.305102\pi\) | ||||
0.574744 | + | 0.818334i | \(0.305102\pi\) | |||||||
\(398\) | 6.43694e6 | 2.03691 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −788794. | −0.246498 | ||||||||
\(401\) | 4.78064e6 | 1.48465 | 0.742327 | − | 0.670038i | \(-0.233722\pi\) | ||||
0.742327 | + | 0.670038i | \(0.233722\pi\) | |||||||
\(402\) | 3.86854e6 | 1.19394 | ||||||||
\(403\) | −3.91815e6 | −1.20176 | ||||||||
\(404\) | −1.47219e6 | −0.448756 | ||||||||
\(405\) | −1.53712e6 | −0.465662 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 59848.7 | 0.0179089 | ||||||||
\(408\) | −918538. | −0.273179 | ||||||||
\(409\) | −332478. | −0.0982778 | −0.0491389 | − | 0.998792i | \(-0.515648\pi\) | ||||
−0.0491389 | + | 0.998792i | \(0.515648\pi\) | |||||||
\(410\) | −1.37325e6 | −0.403452 | ||||||||
\(411\) | 4.54060e6 | 1.32589 | ||||||||
\(412\) | −1.00812e6 | −0.292595 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −156402. | −0.0448479 | ||||||||
\(415\) | −2.47562e6 | −0.705609 | ||||||||
\(416\) | 5.89353e6 | 1.66972 | ||||||||
\(417\) | 4.49528e6 | 1.26595 | ||||||||
\(418\) | −7.73270e6 | −2.16466 | ||||||||
\(419\) | 3.01019e6 | 0.837643 | 0.418822 | − | 0.908068i | \(-0.362443\pi\) | ||||
0.418822 | + | 0.908068i | \(0.362443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.57143e6 | −0.707083 | −0.353541 | − | 0.935419i | \(-0.615023\pi\) | ||||
−0.353541 | + | 0.935419i | \(0.615023\pi\) | |||||||
\(422\) | 3.89369e6 | 1.06434 | ||||||||
\(423\) | −157166. | −0.0427078 | ||||||||
\(424\) | 1.53733e6 | 0.415291 | ||||||||
\(425\) | −424046. | −0.113878 | ||||||||
\(426\) | 7.06554e6 | 1.88634 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.60476e6 | −0.423448 | ||||||||
\(429\) | −5.67453e6 | −1.48863 | ||||||||
\(430\) | −2.44522e6 | −0.637744 | ||||||||
\(431\) | −5.76915e6 | −1.49596 | −0.747978 | − | 0.663723i | \(-0.768975\pi\) | ||||
−0.747978 | + | 0.663723i | \(0.768975\pi\) | |||||||
\(432\) | 4.67218e6 | 1.20451 | ||||||||
\(433\) | 1.93748e6 | 0.496611 | 0.248306 | − | 0.968682i | \(-0.420126\pi\) | ||||
0.248306 | + | 0.968682i | \(0.420126\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.16292e6 | −0.294665 | ||||||||
\(436\) | −3.70504e6 | −0.933419 | ||||||||
\(437\) | −5.71006e6 | −1.43033 | ||||||||
\(438\) | −4.90921e6 | −1.22272 | ||||||||
\(439\) | −4.48026e6 | −1.10954 | −0.554769 | − | 0.832004i | \(-0.687193\pi\) | ||||
−0.554769 | + | 0.832004i | \(0.687193\pi\) | |||||||
\(440\) | −822852. | −0.202624 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.51530e6 | 1.09934 | ||||||||
\(443\) | 2.62761e6 | 0.636139 | 0.318069 | − | 0.948067i | \(-0.396965\pi\) | ||||
0.318069 | + | 0.948067i | \(0.396965\pi\) | |||||||
\(444\) | −49811.0 | −0.0119913 | ||||||||
\(445\) | −191546. | −0.0458536 | ||||||||
\(446\) | 9.69310e6 | 2.30742 | ||||||||
\(447\) | 1.10549e6 | 0.261689 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.11083e6 | −1.43049 | −0.715244 | − | 0.698875i | \(-0.753684\pi\) | ||||
−0.715244 | + | 0.698875i | \(0.753684\pi\) | |||||||
\(450\) | −47320.6 | −0.0110159 | ||||||||
\(451\) | −2.94184e6 | −0.681048 | ||||||||
\(452\) | 2.77294e6 | 0.638403 | ||||||||
\(453\) | 4.12316e6 | 0.944029 | ||||||||
\(454\) | −4.19926e6 | −0.956166 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.74224e6 | −0.842791 | ||||||||
\(457\) | 3.93604e6 | 0.881595 | 0.440797 | − | 0.897607i | \(-0.354696\pi\) | ||||
0.440797 | + | 0.897607i | \(0.354696\pi\) | |||||||
\(458\) | −7.21734e6 | −1.60773 | ||||||||
\(459\) | 2.51171e6 | 0.556464 | ||||||||
\(460\) | 1.04496e6 | 0.230253 | ||||||||
\(461\) | −3.61769e6 | −0.792827 | −0.396414 | − | 0.918072i | \(-0.629745\pi\) | ||||
−0.396414 | + | 0.918072i | \(0.629745\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.68308e6 | 1.44885 | 0.724426 | − | 0.689352i | \(-0.242105\pi\) | ||||
0.724426 | + | 0.689352i | \(0.242105\pi\) | |||||||
\(464\) | 3.68745e6 | 0.795118 | ||||||||
\(465\) | −1.69361e6 | −0.363230 | ||||||||
\(466\) | −9.97219e6 | −2.12729 | ||||||||
\(467\) | 2.36830e6 | 0.502510 | 0.251255 | − | 0.967921i | \(-0.419157\pi\) | ||||
0.251255 | + | 0.967921i | \(0.419157\pi\) | |||||||
\(468\) | 195189. | 0.0411947 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.71071e6 | 0.566028 | ||||||||
\(471\) | 1.63977e6 | 0.340589 | ||||||||
\(472\) | −550998. | −0.113840 | ||||||||
\(473\) | −5.23824e6 | −1.07654 | ||||||||
\(474\) | 1.24147e7 | 2.53800 | ||||||||
\(475\) | −1.72762e6 | −0.351329 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 189393. | 0.0381125 | ||||||||
\(478\) | −3.67433e6 | −0.735544 | ||||||||
\(479\) | 2.26976e6 | 0.452004 | 0.226002 | − | 0.974127i | \(-0.427434\pi\) | ||||
0.226002 | + | 0.974127i | \(0.427434\pi\) | |||||||
\(480\) | 2.54746e6 | 0.504667 | ||||||||
\(481\) | −142379. | −0.0280597 | ||||||||
\(482\) | 1.34335e6 | 0.263373 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −227242. | −0.0440936 | ||||||||
\(485\) | −2.17718e6 | −0.420282 | ||||||||
\(486\) | 573207. | 0.110083 | ||||||||
\(487\) | −1.69003e6 | −0.322904 | −0.161452 | − | 0.986881i | \(-0.551618\pi\) | ||||
−0.161452 | + | 0.986881i | \(0.551618\pi\) | |||||||
\(488\) | −340677. | −0.0647579 | ||||||||
\(489\) | −9.25681e6 | −1.75061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.12583e6 | 0.585143 | 0.292572 | − | 0.956244i | \(-0.405489\pi\) | ||||
0.292572 | + | 0.956244i | \(0.405489\pi\) | |||||||
\(492\) | 2.44844e6 | 0.456013 | ||||||||
\(493\) | 1.98233e6 | 0.367331 | ||||||||
\(494\) | 1.83959e7 | 3.39160 | ||||||||
\(495\) | −101372. | −0.0185954 | ||||||||
\(496\) | 5.37018e6 | 0.980133 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.13944e7 | 2.05881 | ||||||||
\(499\) | −9.40680e6 | −1.69118 | −0.845591 | − | 0.533831i | \(-0.820752\pi\) | ||||
−0.845591 | + | 0.533831i | \(0.820752\pi\) | |||||||
\(500\) | 316161. | 0.0565565 | ||||||||
\(501\) | 7.57709e6 | 1.34868 | ||||||||
\(502\) | −3.04875e6 | −0.539961 | ||||||||
\(503\) | −7.23245e6 | −1.27458 | −0.637288 | − | 0.770626i | \(-0.719944\pi\) | ||||
−0.637288 | + | 0.770626i | \(0.719944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.81893e6 | −0.317385 | ||||||||
\(506\) | 5.77878e6 | 1.00337 | ||||||||
\(507\) | 7.58825e6 | 1.31106 | ||||||||
\(508\) | −870109. | −0.149594 | ||||||||
\(509\) | −4.10701e6 | −0.702638 | −0.351319 | − | 0.936256i | \(-0.614267\pi\) | ||||
−0.351319 | + | 0.936256i | \(0.614267\pi\) | |||||||
\(510\) | 1.95173e6 | 0.332272 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4.64339e6 | −0.782816 | ||||||||
\(513\) | 1.02330e7 | 1.71676 | ||||||||
\(514\) | −1.40696e7 | −2.34895 | ||||||||
\(515\) | −1.24555e6 | −0.206940 | ||||||||
\(516\) | 4.35969e6 | 0.720828 | ||||||||
\(517\) | 5.80698e6 | 0.955486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.54794e6 | −0.741134 | ||||||||
\(520\) | 1.95755e6 | 0.317471 | ||||||||
\(521\) | −6.80125e6 | −1.09773 | −0.548863 | − | 0.835912i | \(-0.684939\pi\) | ||||
−0.548863 | + | 0.835912i | \(0.684939\pi\) | |||||||
\(522\) | 221214. | 0.0355334 | ||||||||
\(523\) | 3.31515e6 | 0.529968 | 0.264984 | − | 0.964253i | \(-0.414633\pi\) | ||||
0.264984 | + | 0.964253i | \(0.414633\pi\) | |||||||
\(524\) | 429083. | 0.0682674 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.17828e7 | −1.85688 | ||||||||
\(527\) | 2.88694e6 | 0.452805 | ||||||||
\(528\) | 7.77746e6 | 1.21410 | ||||||||
\(529\) | −2.16912e6 | −0.337011 | ||||||||
\(530\) | −3.26655e6 | −0.505126 | ||||||||
\(531\) | −67880.7 | −0.0104475 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.99857e6 | 1.06707 | ||||||||
\(534\) | 881616. | 0.133791 | ||||||||
\(535\) | −1.98272e6 | −0.299486 | ||||||||
\(536\) | −2.85889e6 | −0.429819 | ||||||||
\(537\) | −7.17863e6 | −1.07425 | ||||||||
\(538\) | 9.91190e6 | 1.47639 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.87268e6 | −0.276363 | ||||||||
\(541\) | 3.47955e6 | 0.511129 | 0.255564 | − | 0.966792i | \(-0.417739\pi\) | ||||
0.255564 | + | 0.966792i | \(0.417739\pi\) | |||||||
\(542\) | −5.50532e6 | −0.804979 | ||||||||
\(543\) | −2.41371e6 | −0.351305 | ||||||||
\(544\) | −4.34242e6 | −0.629122 | ||||||||
\(545\) | −4.57768e6 | −0.660167 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.55022e6 | 0.364426 | 0.182213 | − | 0.983259i | \(-0.441674\pi\) | ||||
0.182213 | + | 0.983259i | \(0.441674\pi\) | |||||||
\(548\) | 5.77075e6 | 0.820882 | ||||||||
\(549\) | −41970.0 | −0.00594303 | ||||||||
\(550\) | 1.74841e6 | 0.246454 | ||||||||
\(551\) | 8.07626e6 | 1.13326 | ||||||||
\(552\) | 2.79664e6 | 0.390652 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.49515e7 | 2.06972 | ||||||||
\(555\) | −61542.8 | −0.00848096 | ||||||||
\(556\) | 5.71315e6 | 0.783771 | ||||||||
\(557\) | 3.34227e6 | 0.456461 | 0.228230 | − | 0.973607i | \(-0.426706\pi\) | ||||
0.228230 | + | 0.973607i | \(0.426706\pi\) | |||||||
\(558\) | 322163. | 0.0438016 | ||||||||
\(559\) | 1.24616e7 | 1.68673 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.18106e6 | 0.560892 | ||||||||
\(562\) | −3.12107e6 | −0.416833 | ||||||||
\(563\) | 6.30412e6 | 0.838212 | 0.419106 | − | 0.907937i | \(-0.362344\pi\) | ||||
0.419106 | + | 0.907937i | \(0.362344\pi\) | |||||||
\(564\) | −4.83305e6 | −0.639770 | ||||||||
\(565\) | 3.42605e6 | 0.451515 | ||||||||
\(566\) | −1.03602e7 | −1.35933 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.22150e6 | −0.679085 | ||||||||
\(569\) | 3.52056e6 | 0.455860 | 0.227930 | − | 0.973678i | \(-0.426804\pi\) | ||||
0.227930 | + | 0.973678i | \(0.426804\pi\) | |||||||
\(570\) | 7.95159e6 | 1.02510 | ||||||||
\(571\) | −7.51318e6 | −0.964348 | −0.482174 | − | 0.876076i | \(-0.660153\pi\) | ||||
−0.482174 | + | 0.876076i | \(0.660153\pi\) | |||||||
\(572\) | −7.21190e6 | −0.921636 | ||||||||
\(573\) | 8.19906e6 | 1.04322 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.29108e6 | 0.162848 | ||||||||
\(576\) | −61501.5 | −0.00772377 | ||||||||
\(577\) | 6.67495e6 | 0.834658 | 0.417329 | − | 0.908756i | \(-0.362966\pi\) | ||||
0.417329 | + | 0.908756i | \(0.362966\pi\) | |||||||
\(578\) | 6.93485e6 | 0.863411 | ||||||||
\(579\) | −1.22586e7 | −1.51965 | ||||||||
\(580\) | −1.47799e6 | −0.182432 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.00208e7 | 1.22629 | ||||||||
\(583\) | −6.99772e6 | −0.852679 | ||||||||
\(584\) | 3.62795e6 | 0.440179 | ||||||||
\(585\) | 241162. | 0.0291353 | ||||||||
\(586\) | −1.00403e6 | −0.120782 | ||||||||
\(587\) | 1.44246e7 | 1.72785 | 0.863927 | − | 0.503617i | \(-0.167998\pi\) | ||||
0.863927 | + | 0.503617i | \(0.167998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.17618e7 | 1.39696 | ||||||||
\(590\) | 1.17077e6 | 0.138466 | ||||||||
\(591\) | −3.93089e6 | −0.462937 | ||||||||
\(592\) | 195143. | 0.0228849 | ||||||||
\(593\) | −8.63292e6 | −1.00814 | −0.504070 | − | 0.863663i | \(-0.668165\pi\) | ||||
−0.504070 | + | 0.863663i | \(0.668165\pi\) | |||||||
\(594\) | −1.03562e7 | −1.20430 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.40499e6 | 0.162016 | ||||||||
\(597\) | −1.41798e7 | −1.62830 | ||||||||
\(598\) | −1.37476e7 | −1.57208 | ||||||||
\(599\) | 5.75996e6 | 0.655922 | 0.327961 | − | 0.944691i | \(-0.393638\pi\) | ||||
0.327961 | + | 0.944691i | \(0.393638\pi\) | |||||||
\(600\) | 846144. | 0.0959547 | ||||||||
\(601\) | 6.23001e6 | 0.703562 | 0.351781 | − | 0.936082i | \(-0.385576\pi\) | ||||
0.351781 | + | 0.936082i | \(0.385576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −352204. | −0.0394458 | ||||||||
\(604\) | 5.24023e6 | 0.584464 | ||||||||
\(605\) | −280764. | −0.0311855 | ||||||||
\(606\) | 8.37185e6 | 0.926062 | ||||||||
\(607\) | −2.79863e6 | −0.308301 | −0.154150 | − | 0.988047i | \(-0.549264\pi\) | ||||
−0.154150 | + | 0.988047i | \(0.549264\pi\) | |||||||
\(608\) | −1.76916e7 | −1.94092 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 723876. | 0.0787661 | ||||||||
\(611\) | −1.38147e7 | −1.49706 | ||||||||
\(612\) | −143818. | −0.0155215 | ||||||||
\(613\) | 1.24192e7 | 1.33488 | 0.667438 | − | 0.744665i | \(-0.267391\pi\) | ||||
0.667438 | + | 0.744665i | \(0.267391\pi\) | |||||||
\(614\) | −4.56259e6 | −0.488417 | ||||||||
\(615\) | 3.02511e6 | 0.322518 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.63980e6 | 0.596418 | 0.298209 | − | 0.954501i | \(-0.403611\pi\) | ||||
0.298209 | + | 0.954501i | \(0.403611\pi\) | |||||||
\(618\) | 5.73282e6 | 0.603806 | ||||||||
\(619\) | −5.79714e6 | −0.608117 | −0.304059 | − | 0.952653i | \(-0.598342\pi\) | ||||
−0.304059 | + | 0.952653i | \(0.598342\pi\) | |||||||
\(620\) | −2.15245e6 | −0.224882 | ||||||||
\(621\) | −7.64732e6 | −0.795756 | ||||||||
\(622\) | −1.59322e7 | −1.65120 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.85024e7 | −1.90225 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 3.19400e6 | 0.325761 | ||||||||
\(627\) | 1.70342e7 | 1.73042 | ||||||||
\(628\) | 2.08402e6 | 0.210864 | ||||||||
\(629\) | 104906. | 0.0105724 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.41197e6 | −0.341140 | −0.170570 | − | 0.985346i | \(-0.554561\pi\) | ||||
−0.170570 | + | 0.985346i | \(0.554561\pi\) | |||||||
\(632\) | −9.17461e6 | −0.913682 | ||||||||
\(633\) | −8.57733e6 | −0.850830 | ||||||||
\(634\) | −9.62186e6 | −0.950684 | ||||||||
\(635\) | −1.07504e6 | −0.105801 | ||||||||
\(636\) | 5.82408e6 | 0.570932 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.17346e6 | −0.794977 | ||||||||
\(639\) | −643267. | −0.0623217 | ||||||||
\(640\) | −4.05949e6 | −0.391761 | ||||||||
\(641\) | −1.18486e7 | −1.13900 | −0.569499 | − | 0.821992i | \(-0.692863\pi\) | ||||
−0.569499 | + | 0.821992i | \(0.692863\pi\) | |||||||
\(642\) | 9.12573e6 | 0.873836 | ||||||||
\(643\) | 6.05156e6 | 0.577218 | 0.288609 | − | 0.957447i | \(-0.406807\pi\) | ||||
0.288609 | + | 0.957447i | \(0.406807\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.38651e6 | 0.509810 | ||||||||
\(646\) | −1.35543e7 | −1.27790 | ||||||||
\(647\) | 9.82251e6 | 0.922490 | 0.461245 | − | 0.887273i | \(-0.347403\pi\) | ||||
0.461245 | + | 0.887273i | \(0.347403\pi\) | |||||||
\(648\) | −5.22835e6 | −0.489133 | ||||||||
\(649\) | 2.50807e6 | 0.233737 | ||||||||
\(650\) | −4.15943e6 | −0.386145 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.17647e7 | −1.08383 | ||||||||
\(653\) | −957185. | −0.0878442 | −0.0439221 | − | 0.999035i | \(-0.513985\pi\) | ||||
−0.0439221 | + | 0.999035i | \(0.513985\pi\) | |||||||
\(654\) | 2.10694e7 | 1.92622 | ||||||||
\(655\) | 530144. | 0.0482826 | ||||||||
\(656\) | −9.59217e6 | −0.870277 | ||||||||
\(657\) | 446949. | 0.0403965 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.54679e7 | −1.38745 | −0.693725 | − | 0.720240i | \(-0.744032\pi\) | ||||
−0.693725 | + | 0.720240i | \(0.744032\pi\) | |||||||
\(660\) | −3.11732e6 | −0.278562 | ||||||||
\(661\) | 3.95036e6 | 0.351668 | 0.175834 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175834 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(662\) | −1.08612e7 | −0.963240 | ||||||||
\(663\) | −9.94665e6 | −0.878806 | ||||||||
\(664\) | −8.42055e6 | −0.741174 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11706.8 | 0.00102271 | ||||||||
\(667\) | −6.03553e6 | −0.525292 | ||||||||
\(668\) | 9.62990e6 | 0.834989 | ||||||||
\(669\) | −2.13527e7 | −1.84454 | ||||||||
\(670\) | 6.07462e6 | 0.522796 | ||||||||
\(671\) | 1.55071e6 | 0.132961 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.64772e7 | −1.40231 | −0.701157 | − | 0.713007i | \(-0.747333\pi\) | ||||
−0.701157 | + | 0.713007i | \(0.747333\pi\) | |||||||
\(674\) | 1.69433e7 | 1.43664 | ||||||||
\(675\) | −2.31375e6 | −0.195460 | ||||||||
\(676\) | 9.64409e6 | 0.811698 | ||||||||
\(677\) | 9.00324e6 | 0.754966 | 0.377483 | − | 0.926017i | \(-0.376790\pi\) | ||||
0.377483 | + | 0.926017i | \(0.376790\pi\) | |||||||
\(678\) | −1.57688e7 | −1.31742 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.44234e6 | −0.119618 | ||||||||
\(681\) | 9.25046e6 | 0.764356 | ||||||||
\(682\) | −1.19033e7 | −0.979959 | ||||||||
\(683\) | 9.38382e6 | 0.769711 | 0.384856 | − | 0.922977i | \(-0.374251\pi\) | ||||
0.384856 | + | 0.922977i | \(0.374251\pi\) | |||||||
\(684\) | −585933. | −0.0478859 | ||||||||
\(685\) | 7.12992e6 | 0.580575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.58989e7 | 1.28522 | ||||||||
\(688\) | −1.70798e7 | −1.37566 | ||||||||
\(689\) | 1.66474e7 | 1.33598 | ||||||||
\(690\) | −5.94236e6 | −0.475156 | ||||||||
\(691\) | 5.05803e6 | 0.402983 | 0.201491 | − | 0.979490i | \(-0.435421\pi\) | ||||
0.201491 | + | 0.979490i | \(0.435421\pi\) | |||||||
\(692\) | −5.78009e6 | −0.458848 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.02318e6 | −0.159454 | ||||||||
\(695\) | 7.05875e6 | 0.554327 | ||||||||
\(696\) | −3.95555e6 | −0.309517 | ||||||||
\(697\) | −5.15663e6 | −0.402054 | ||||||||
\(698\) | 8.43135e6 | 0.655026 | ||||||||
\(699\) | 2.19675e7 | 1.70055 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.25374e7 | −1.73224 | −0.866121 | − | 0.499835i | \(-0.833394\pi\) | ||||
−0.866121 | + | 0.499835i | \(0.833394\pi\) | |||||||
\(702\) | 2.46371e7 | 1.88689 | ||||||||
\(703\) | 427402. | 0.0326173 | ||||||||
\(704\) | 2.27237e6 | 0.172801 | ||||||||
\(705\) | −5.97136e6 | −0.452481 | ||||||||
\(706\) | 1.12344e7 | 0.848277 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.08742e6 | −0.156505 | ||||||||
\(709\) | −2.37037e6 | −0.177093 | −0.0885463 | − | 0.996072i | \(-0.528222\pi\) | ||||
−0.0885463 | + | 0.996072i | \(0.528222\pi\) | |||||||
\(710\) | 1.10947e7 | 0.825982 | ||||||||
\(711\) | −1.13028e6 | −0.0838514 | ||||||||
\(712\) | −651523. | −0.0481648 | ||||||||
\(713\) | −8.78979e6 | −0.647522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.91049e6 | −0.651833 | ||||||||
\(716\) | −9.12349e6 | −0.665087 | ||||||||
\(717\) | 8.09411e6 | 0.587992 | ||||||||
\(718\) | −6.19016e6 | −0.448117 | ||||||||
\(719\) | 1.25461e7 | 0.905077 | 0.452539 | − | 0.891745i | \(-0.350518\pi\) | ||||
0.452539 | + | 0.891745i | \(0.350518\pi\) | |||||||
\(720\) | −330534. | −0.0237621 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.73266e7 | −2.66486 | ||||||||
\(723\) | −2.95924e6 | −0.210540 | ||||||||
\(724\) | −3.06764e6 | −0.217499 | ||||||||
\(725\) | −1.82609e6 | −0.129026 | ||||||||
\(726\) | 1.29225e6 | 0.0909926 | ||||||||
\(727\) | −5.18009e6 | −0.363498 | −0.181749 | − | 0.983345i | \(-0.558176\pi\) | ||||
−0.181749 | + | 0.983345i | \(0.558176\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.36781e7 | 0.953252 | ||||||||
\(730\) | −7.70873e6 | −0.535397 | ||||||||
\(731\) | −9.18189e6 | −0.635534 | ||||||||
\(732\) | −1.29063e6 | −0.0890276 | ||||||||
\(733\) | 1.54379e7 | 1.06127 | 0.530637 | − | 0.847599i | \(-0.321953\pi\) | ||||
0.530637 | + | 0.847599i | \(0.321953\pi\) | |||||||
\(734\) | −6.57161e6 | −0.450227 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.32213e7 | 0.899659 | ||||||||
\(737\) | 1.30133e7 | 0.882507 | ||||||||
\(738\) | −575445. | −0.0388922 | ||||||||
\(739\) | −1.64732e7 | −1.10960 | −0.554801 | − | 0.831983i | \(-0.687206\pi\) | ||||
−0.554801 | + | 0.831983i | \(0.687206\pi\) | |||||||
\(740\) | −78216.2 | −0.00525070 | ||||||||
\(741\) | −4.05240e7 | −2.71123 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.59403e7 | −1.72386 | −0.861931 | − | 0.507026i | \(-0.830745\pi\) | ||||
−0.861931 | + | 0.507026i | \(0.830745\pi\) | |||||||
\(744\) | −5.76063e6 | −0.381538 | ||||||||
\(745\) | 1.73590e6 | 0.114587 | ||||||||
\(746\) | 967273. | 0.0636358 | ||||||||
\(747\) | −1.03738e6 | −0.0680198 | ||||||||
\(748\) | 5.31381e6 | 0.347258 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.79790e6 | −0.116711 | ||||||||
\(751\) | 1.18608e7 | 0.767386 | 0.383693 | − | 0.923461i | \(-0.374652\pi\) | ||||
0.383693 | + | 0.923461i | \(0.374652\pi\) | |||||||
\(752\) | 1.89343e7 | 1.22097 | ||||||||
\(753\) | 6.71603e6 | 0.431643 | ||||||||
\(754\) | 1.94445e7 | 1.24557 | ||||||||
\(755\) | 6.47444e6 | 0.413366 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.25104e6 | −0.396472 | −0.198236 | − | 0.980154i | \(-0.563521\pi\) | ||||
−0.198236 | + | 0.980154i | \(0.563521\pi\) | |||||||
\(758\) | −7.78491e6 | −0.492131 | ||||||||
\(759\) | −1.27300e7 | −0.802088 | ||||||||
\(760\) | −5.87630e6 | −0.369037 | ||||||||
\(761\) | −2.20531e7 | −1.38041 | −0.690206 | − | 0.723613i | \(-0.742480\pi\) | ||||
−0.690206 | + | 0.723613i | \(0.742480\pi\) | |||||||
\(762\) | 4.94803e6 | 0.308706 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.04204e7 | 0.645877 | ||||||||
\(765\) | −177691. | −0.0109777 | ||||||||
\(766\) | 3.33240e6 | 0.205204 | ||||||||
\(767\) | −5.96664e6 | −0.366220 | ||||||||
\(768\) | 2.16753e7 | 1.32606 | ||||||||
\(769\) | 1.37289e7 | 0.837181 | 0.418591 | − | 0.908175i | \(-0.362524\pi\) | ||||
0.418591 | + | 0.908175i | \(0.362524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.09936e7 | 1.87774 | ||||||||
\(772\) | −1.55797e7 | −0.940843 | ||||||||
\(773\) | 1.50716e7 | 0.907213 | 0.453606 | − | 0.891202i | \(-0.350137\pi\) | ||||
0.453606 | + | 0.891202i | \(0.350137\pi\) | |||||||
\(774\) | −1.02464e6 | −0.0614777 | ||||||||
\(775\) | −2.65941e6 | −0.159049 | ||||||||
\(776\) | −7.40545e6 | −0.441466 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.69969e6 | −0.100675 | ||||||||
\(779\) | −2.10088e7 | −1.24039 | ||||||||
\(780\) | 7.41604e6 | 0.436451 | ||||||||
\(781\) | 2.37675e7 | 1.39430 | ||||||||
\(782\) | 1.01294e7 | 0.592333 | ||||||||
\(783\) | 1.08163e7 | 0.630485 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.57487e6 | 0.149135 | ||||||||
\(786\) | −2.44006e6 | −0.140878 | ||||||||
\(787\) | −1.93056e7 | −1.11108 | −0.555541 | − | 0.831489i | \(-0.687489\pi\) | ||||
−0.555541 | + | 0.831489i | \(0.687489\pi\) | |||||||
\(788\) | −4.99586e6 | −0.286612 | ||||||||
\(789\) | 2.59561e7 | 1.48438 | ||||||||
\(790\) | 1.94944e7 | 1.11133 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −344806. | −0.0195327 | ||||||||
\(793\) | −3.68911e6 | −0.208324 | ||||||||
\(794\) | −2.60891e7 | −1.46861 | ||||||||
\(795\) | 7.19581e6 | 0.403796 | ||||||||
\(796\) | −1.80215e7 | −1.00811 | ||||||||
\(797\) | −2.05347e7 | −1.14510 | −0.572549 | − | 0.819871i | \(-0.694045\pi\) | ||||
−0.572549 | + | 0.819871i | \(0.694045\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.01788e7 | 0.564067 | ||||||||
\(800\) | 4.00018e6 | 0.220981 | ||||||||
\(801\) | −80264.9 | −0.00442023 | ||||||||
\(802\) | −3.45513e7 | −1.89683 | ||||||||
\(803\) | −1.65139e7 | −0.903778 | ||||||||
\(804\) | −1.08307e7 | −0.590905 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.83178e7 | 1.53540 | ||||||||
\(807\) | −2.18347e7 | −1.18022 | ||||||||
\(808\) | −6.18688e6 | −0.333383 | ||||||||
\(809\) | 7.34708e6 | 0.394678 | 0.197339 | − | 0.980335i | \(-0.436770\pi\) | ||||
0.197339 | + | 0.980335i | \(0.436770\pi\) | |||||||
\(810\) | 1.11093e7 | 0.594941 | ||||||||
\(811\) | −2.36201e7 | −1.26104 | −0.630522 | − | 0.776171i | \(-0.717159\pi\) | ||||
−0.630522 | + | 0.776171i | \(0.717159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.21276e7 | 0.643498 | ||||||||
\(814\) | −432546. | −0.0228808 | ||||||||
\(815\) | −1.45356e7 | −0.766548 | ||||||||
\(816\) | 1.36328e7 | 0.716736 | ||||||||
\(817\) | −3.74082e7 | −1.96070 | ||||||||
\(818\) | 2.40293e6 | 0.125562 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.84469e6 | 0.199676 | ||||||||
\(821\) | 1.84495e7 | 0.955272 | 0.477636 | − | 0.878558i | \(-0.341494\pi\) | ||||
0.477636 | + | 0.878558i | \(0.341494\pi\) | |||||||
\(822\) | −3.28164e7 | −1.69399 | ||||||||
\(823\) | −1.01309e7 | −0.521374 | −0.260687 | − | 0.965423i | \(-0.583949\pi\) | ||||
−0.260687 | + | 0.965423i | \(0.583949\pi\) | |||||||
\(824\) | −4.23661e6 | −0.217370 | ||||||||
\(825\) | −3.85154e6 | −0.197015 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.10559e6 | −0.462961 | −0.231480 | − | 0.972840i | \(-0.574357\pi\) | ||||
−0.231480 | + | 0.972840i | \(0.574357\pi\) | |||||||
\(828\) | 437878. | 0.0221961 | ||||||||
\(829\) | 2.40432e7 | 1.21508 | 0.607540 | − | 0.794289i | \(-0.292156\pi\) | ||||
0.607540 | + | 0.794289i | \(0.292156\pi\) | |||||||
\(830\) | 1.78921e7 | 0.901502 | ||||||||
\(831\) | −3.29364e7 | −1.65452 | ||||||||
\(832\) | −5.40591e6 | −0.270745 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.24888e7 | −1.61741 | ||||||||
\(835\) | 1.18980e7 | 0.590552 | ||||||||
\(836\) | 2.16492e7 | 1.07134 | ||||||||
\(837\) | 1.57522e7 | 0.777192 | ||||||||
\(838\) | −2.17557e7 | −1.07019 | ||||||||
\(839\) | 3.70147e7 | 1.81539 | 0.907694 | − | 0.419633i | \(-0.137841\pi\) | ||||
0.907694 | + | 0.419633i | \(0.137841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.19745e7 | −0.583806 | ||||||||
\(842\) | 1.85846e7 | 0.903385 | ||||||||
\(843\) | 6.87533e6 | 0.333215 | ||||||||
\(844\) | −1.09011e7 | −0.526763 | ||||||||
\(845\) | 1.19155e7 | 0.574079 | ||||||||
\(846\) | 1.13589e6 | 0.0545644 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.28168e7 | −1.08960 | ||||||||
\(849\) | 2.28222e7 | 1.08665 | ||||||||
\(850\) | 3.06472e6 | 0.145493 | ||||||||
\(851\) | −319405. | −0.0151188 | ||||||||
\(852\) | −1.97813e7 | −0.933590 | ||||||||
\(853\) | 79427.6 | 0.00373765 | 0.00186883 | − | 0.999998i | \(-0.499405\pi\) | ||||
0.00186883 | + | 0.999998i | \(0.499405\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −723936. | −0.0338676 | ||||||||
\(856\) | −6.74400e6 | −0.314581 | ||||||||
\(857\) | −1.28759e7 | −0.598859 | −0.299430 | − | 0.954118i | \(-0.596796\pi\) | ||||
−0.299430 | + | 0.954118i | \(0.596796\pi\) | |||||||
\(858\) | 4.10117e7 | 1.90191 | ||||||||
\(859\) | −3.82897e6 | −0.177051 | −0.0885256 | − | 0.996074i | \(-0.528216\pi\) | ||||
−0.0885256 | + | 0.996074i | \(0.528216\pi\) | |||||||
\(860\) | 6.84585e6 | 0.315632 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.16956e7 | 1.91127 | ||||||||
\(863\) | −1.27055e7 | −0.580718 | −0.290359 | − | 0.956918i | \(-0.593775\pi\) | ||||
−0.290359 | + | 0.956918i | \(0.593775\pi\) | |||||||
\(864\) | −2.36939e7 | −1.07982 | ||||||||
\(865\) | −7.14145e6 | −0.324524 | ||||||||
\(866\) | −1.40028e7 | −0.634482 | ||||||||
\(867\) | −1.52766e7 | −0.690208 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.17616e7 | 1.87598 | ||||||||
\(870\) | 8.40483e6 | 0.376470 | ||||||||
\(871\) | −3.09583e7 | −1.38271 | ||||||||
\(872\) | −1.55705e7 | −0.693442 | ||||||||
\(873\) | −912321. | −0.0405147 | ||||||||
\(874\) | 4.12685e7 | 1.82743 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.37443e7 | 0.605147 | ||||||||
\(877\) | −1.88584e7 | −0.827953 | −0.413977 | − | 0.910288i | \(-0.635860\pi\) | ||||
−0.413977 | + | 0.910288i | \(0.635860\pi\) | |||||||
\(878\) | 3.23803e7 | 1.41757 | ||||||||
\(879\) | 2.21175e6 | 0.0965526 | ||||||||
\(880\) | 1.22126e7 | 0.531622 | ||||||||
\(881\) | 3.82921e7 | 1.66215 | 0.831073 | − | 0.556163i | \(-0.187727\pi\) | ||||
0.831073 | + | 0.556163i | \(0.187727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.02825e7 | 1.30704 | 0.653521 | − | 0.756909i | \(-0.273291\pi\) | ||||
0.653521 | + | 0.756909i | \(0.273291\pi\) | |||||||
\(884\) | −1.26414e7 | −0.544084 | ||||||||
\(885\) | −2.57907e6 | −0.110689 | ||||||||
\(886\) | −1.89906e7 | −0.812746 | ||||||||
\(887\) | 2.80881e7 | 1.19871 | 0.599354 | − | 0.800484i | \(-0.295424\pi\) | ||||
0.599354 | + | 0.800484i | \(0.295424\pi\) | |||||||
\(888\) | −209331. | −0.00890843 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.38437e6 | 0.0585836 | ||||||||
\(891\) | 2.37987e7 | 1.00429 | ||||||||
\(892\) | −2.71377e7 | −1.14199 | ||||||||
\(893\) | 4.14699e7 | 1.74022 | ||||||||
\(894\) | −7.98972e6 | −0.334340 | ||||||||
\(895\) | −1.12723e7 | −0.470387 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.02843e7 | 1.25671 | ||||||||
\(898\) | 4.41650e7 | 1.82762 | ||||||||
\(899\) | 1.24322e7 | 0.513037 | ||||||||
\(900\) | 132483. | 0.00545198 | ||||||||
\(901\) | −1.22660e7 | −0.503375 | ||||||||
\(902\) | 2.12616e7 | 0.870122 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.16533e7 | 0.474273 | ||||||||
\(905\) | −3.79015e6 | −0.153828 | ||||||||
\(906\) | −2.97995e7 | −1.20611 | ||||||||
\(907\) | 1.50416e7 | 0.607121 | 0.303561 | − | 0.952812i | \(-0.401824\pi\) | ||||
0.303561 | + | 0.952812i | \(0.401824\pi\) | |||||||
\(908\) | 1.17566e7 | 0.473226 | ||||||||
\(909\) | −762198. | −0.0305955 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.53071e7 | 0.611078 | 0.305539 | − | 0.952179i | \(-0.401163\pi\) | ||||
0.305539 | + | 0.952179i | \(0.401163\pi\) | |||||||
\(912\) | 5.55418e7 | 2.21122 | ||||||||
\(913\) | 3.83292e7 | 1.52178 | ||||||||
\(914\) | −2.84471e7 | −1.12635 | ||||||||
\(915\) | −1.59461e6 | −0.0629654 | ||||||||
\(916\) | 2.02063e7 | 0.795698 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.81529e7 | −0.710951 | ||||||||
\(919\) | 2.42413e7 | 0.946820 | 0.473410 | − | 0.880842i | \(-0.343023\pi\) | ||||
0.473410 | + | 0.880842i | \(0.343023\pi\) | |||||||
\(920\) | 4.39146e6 | 0.171056 | ||||||||
\(921\) | 1.00508e7 | 0.390439 | ||||||||
\(922\) | 2.61462e7 | 1.01293 | ||||||||
\(923\) | −5.65425e7 | −2.18459 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −96638.2 | −0.00371360 | ||||||||
\(926\) | −4.83008e7 | −1.85109 | ||||||||
\(927\) | −521933. | −0.0199488 | ||||||||
\(928\) | −1.87000e7 | −0.712808 | ||||||||
\(929\) | 2.10562e7 | 0.800461 | 0.400231 | − | 0.916414i | \(-0.368930\pi\) | ||||
0.400231 | + | 0.916414i | \(0.368930\pi\) | |||||||
\(930\) | 1.22403e7 | 0.464071 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.79191e7 | 1.05284 | ||||||||
\(933\) | 3.50967e7 | 1.31996 | ||||||||
\(934\) | −1.71165e7 | −0.642019 | ||||||||
\(935\) | 6.56535e6 | 0.245600 | ||||||||
\(936\) | 820285. | 0.0306038 | ||||||||
\(937\) | 1.43242e7 | 0.532993 | 0.266497 | − | 0.963836i | \(-0.414134\pi\) | ||||
0.266497 | + | 0.963836i | \(0.414134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.03600e6 | −0.260413 | ||||||||
\(940\) | −7.58915e6 | −0.280139 | ||||||||
\(941\) | 1.12722e7 | 0.414988 | 0.207494 | − | 0.978236i | \(-0.433469\pi\) | ||||
0.207494 | + | 0.978236i | \(0.433469\pi\) | |||||||
\(942\) | −1.18512e7 | −0.435145 | ||||||||
\(943\) | 1.57002e7 | 0.574946 | ||||||||
\(944\) | 8.17782e6 | 0.298681 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.78584e7 | 1.37542 | ||||||||
\(947\) | −2.86149e7 | −1.03685 | −0.518427 | − | 0.855122i | \(-0.673482\pi\) | ||||
−0.518427 | + | 0.855122i | \(0.673482\pi\) | |||||||
\(948\) | −3.47574e7 | −1.25611 | ||||||||
\(949\) | 3.92863e7 | 1.41604 | ||||||||
\(950\) | 1.24861e7 | 0.448866 | ||||||||
\(951\) | 2.11958e7 | 0.759974 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.67535e7 | −0.954219 | −0.477109 | − | 0.878844i | \(-0.658315\pi\) | ||||
−0.477109 | + | 0.878844i | \(0.658315\pi\) | |||||||
\(954\) | −1.36881e6 | −0.0486935 | ||||||||
\(955\) | 1.28747e7 | 0.456801 | ||||||||
\(956\) | 1.02870e7 | 0.364036 | ||||||||
\(957\) | 1.80051e7 | 0.635502 | ||||||||
\(958\) | −1.64043e7 | −0.577490 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.33669e6 | −0.0818320 | ||||||||
\(961\) | −1.05236e7 | −0.367585 | ||||||||
\(962\) | 1.02902e6 | 0.0358497 | ||||||||
\(963\) | −830833. | −0.0288701 | ||||||||
\(964\) | −3.76096e6 | −0.130349 | ||||||||
\(965\) | −1.92492e7 | −0.665417 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.79212e7 | −0.616311 | −0.308155 | − | 0.951336i | \(-0.599712\pi\) | ||||
−0.308155 | + | 0.951336i | \(0.599712\pi\) | |||||||
\(968\) | −954987. | −0.0327574 | ||||||||
\(969\) | 2.98585e7 | 1.02155 | ||||||||
\(970\) | 1.57352e7 | 0.536962 | ||||||||
\(971\) | −3.38258e7 | −1.15133 | −0.575666 | − | 0.817685i | \(-0.695257\pi\) | ||||
−0.575666 | + | 0.817685i | \(0.695257\pi\) | |||||||
\(972\) | −1.60480e6 | −0.0544823 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.22144e7 | 0.412549 | ||||||||
\(975\) | 9.16272e6 | 0.308683 | ||||||||
\(976\) | 5.05627e6 | 0.169905 | ||||||||
\(977\) | 3.62165e7 | 1.21386 | 0.606931 | − | 0.794754i | \(-0.292400\pi\) | ||||
0.606931 | + | 0.794754i | \(0.292400\pi\) | |||||||
\(978\) | 6.69020e7 | 2.23662 | ||||||||
\(979\) | 2.96564e6 | 0.0988922 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.91822e6 | −0.0636393 | ||||||||
\(982\) | −2.25914e7 | −0.747593 | ||||||||
\(983\) | −1.07386e7 | −0.354456 | −0.177228 | − | 0.984170i | \(-0.556713\pi\) | ||||
−0.177228 | + | 0.984170i | \(0.556713\pi\) | |||||||
\(984\) | 1.02896e7 | 0.338774 | ||||||||
\(985\) | −6.17251e6 | −0.202708 | ||||||||
\(986\) | −1.43269e7 | −0.469311 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.15029e7 | −1.67857 | ||||||||
\(989\) | 2.79558e7 | 0.908828 | ||||||||
\(990\) | 732649. | 0.0237579 | ||||||||
\(991\) | 5.29006e6 | 0.171110 | 0.0855552 | − | 0.996333i | \(-0.472734\pi\) | ||||
0.0855552 | + | 0.996333i | \(0.472734\pi\) | |||||||
\(992\) | −2.72336e7 | −0.878670 | ||||||||
\(993\) | 2.39260e7 | 0.770011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.22660e7 | −0.712991 | ||||||||
\(996\) | −3.19007e7 | −1.01895 | ||||||||
\(997\) | 1.70145e7 | 0.542103 | 0.271051 | − | 0.962565i | \(-0.412629\pi\) | ||||
0.271051 | + | 0.962565i | \(0.412629\pi\) | |||||||
\(998\) | 6.79860e7 | 2.16069 | ||||||||
\(999\) | 572407. | 0.0181464 |
(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 | 245.6.a.h.1.2 | 6 | ||
7.3 | odd | 6 | 35.6.e.a.16.5 | yes | 12 | ||
7.5 | odd | 6 | 35.6.e.a.11.5 | ✓ | 12 | ||
7.6 | odd | 2 | 245.6.a.i.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.e.a.11.5 | ✓ | 12 | 7.5 | odd | 6 | ||
35.6.e.a.16.5 | yes | 12 | 7.3 | odd | 6 | ||
245.6.a.h.1.2 | 6 | 1.1 | even | 1 | trivial | ||
245.6.a.i.1.2 | 6 | 7.6 | odd | 2 |