Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [116,4,Mod(1,116)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(116, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("116.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 116 = 2^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 116.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: | \(6.84422156067\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 116.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.60555 | −0.693889 | −0.346944 | − | 0.937886i | \(-0.612781\pi\) | ||||
−0.346944 | + | 0.937886i | \(0.612781\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.21110 | 0.197767 | 0.0988835 | − | 0.995099i | \(-0.468473\pi\) | ||||
0.0988835 | + | 0.995099i | \(0.468473\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.42221 | 0.238777 | 0.119388 | − | 0.992848i | \(-0.461907\pi\) | ||||
0.119388 | + | 0.992848i | \(0.461907\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.0000 | −0.518519 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.3944 | −0.339733 | −0.169867 | − | 0.985467i | \(-0.554334\pi\) | ||||
−0.169867 | + | 0.985467i | \(0.554334\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48.6333 | −1.03757 | −0.518787 | − | 0.854904i | \(-0.673616\pi\) | ||||
−0.518787 | + | 0.854904i | \(0.673616\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.97224 | −0.137228 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −101.322 | −1.44554 | −0.722771 | − | 0.691087i | \(-0.757132\pi\) | ||||
−0.722771 | + | 0.691087i | \(0.757132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −59.2666 | −0.715615 | −0.357808 | − | 0.933795i | \(-0.616476\pi\) | ||||
−0.357808 | + | 0.933795i | \(0.616476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −15.9445 | −0.165684 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.0555 | 0.163688 | 0.0818442 | − | 0.996645i | \(-0.473919\pi\) | ||||
0.0818442 | + | 0.996645i | \(0.473919\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −120.111 | −0.960888 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 147.828 | 1.05368 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.8167 | 0.120606 | 0.0603029 | − | 0.998180i | \(-0.480793\pi\) | ||||
0.0603029 | + | 0.998180i | \(0.480793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 44.6888 | 0.235737 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.77795 | 0.0472221 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 101.066 | 0.449060 | 0.224530 | − | 0.974467i | \(-0.427915\pi\) | ||||
0.224530 | + | 0.974467i | \(0.427915\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 175.350 | 0.719960 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.7889 | 0.155370 | 0.0776848 | − | 0.996978i | \(-0.475247\pi\) | ||||
0.0776848 | + | 0.996978i | \(0.475247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 152.450 | 0.540660 | 0.270330 | − | 0.962768i | \(-0.412867\pi\) | ||||
0.270330 | + | 0.962768i | \(0.412867\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −30.9554 | −0.102546 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 121.328 | 0.376543 | 0.188271 | − | 0.982117i | \(-0.439712\pi\) | ||||
0.188271 | + | 0.982117i | \(0.439712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −323.444 | −0.942986 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 365.322 | 1.00305 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 177.700 | 0.460546 | 0.230273 | − | 0.973126i | \(-0.426038\pi\) | ||||
0.230273 | + | 0.973126i | \(0.426038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −27.4054 | −0.0671881 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 213.689 | 0.496557 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 109.611 | 0.241868 | 0.120934 | − | 0.992661i | \(-0.461411\pi\) | ||||
0.120934 | + | 0.992661i | \(0.461411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 61.7662 | 0.129645 | 0.0648226 | − | 0.997897i | \(-0.479352\pi\) | ||||
0.0648226 | + | 0.997897i | \(0.479352\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −61.9109 | −0.123810 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −107.533 | −0.205198 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −471.532 | −0.859804 | −0.429902 | − | 0.902876i | \(-0.641452\pi\) | ||||
−0.429902 | + | 0.902876i | \(0.641452\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −65.1001 | −0.113582 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 546.522 | 0.913524 | 0.456762 | − | 0.889589i | \(-0.349009\pi\) | ||||
0.456762 | + | 0.889589i | \(0.349009\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 169.733 | 0.272133 | 0.136066 | − | 0.990700i | \(-0.456554\pi\) | ||||
0.136066 | + | 0.990700i | \(0.456554\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 433.066 | 0.666749 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −54.8108 | −0.0811204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 184.916 | 0.263350 | 0.131675 | − | 0.991293i | \(-0.457964\pi\) | ||||
0.131675 | + | 0.991293i | \(0.457964\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −155.000 | −0.212620 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 210.500 | 0.278378 | 0.139189 | − | 0.990266i | \(-0.455551\pi\) | ||||
0.139189 | + | 0.990266i | \(0.455551\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −224.034 | −0.285881 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 104.561 | 0.128852 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1393.32 | −1.65946 | −0.829729 | − | 0.558167i | \(-0.811505\pi\) | ||||
−0.829729 | + | 0.558167i | \(0.811505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −215.066 | −0.247748 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −75.0555 | −0.0836870 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −131.045 | −0.141525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1099.43 | −1.15083 | −0.575415 | − | 0.817862i | \(-0.695159\pi\) | ||||
−0.575415 | + | 0.817862i | \(0.695159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 173.522 | 0.176158 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 322.799 | 0.318017 | 0.159008 | − | 0.987277i | \(-0.449170\pi\) | ||||
0.159008 | + | 0.987277i | \(0.449170\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1741.61 | −1.66608 | −0.833038 | − | 0.553215i | \(-0.813401\pi\) | ||||
−0.833038 | + | 0.553215i | \(0.813401\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −35.2549 | −0.0327669 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 560.244 | 0.506176 | 0.253088 | − | 0.967443i | \(-0.418554\pi\) | ||||
0.253088 | + | 0.967443i | \(0.418554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −987.700 | −0.867931 | −0.433966 | − | 0.900929i | \(-0.642886\pi\) | ||||
−0.433966 | + | 0.900929i | \(0.642886\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −364.400 | −0.311598 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 493.532 | 0.410864 | 0.205432 | − | 0.978671i | \(-0.434140\pi\) | ||||
0.205432 | + | 0.978671i | \(0.434140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39.9226 | 0.0323722 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 680.866 | 0.538001 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −448.067 | −0.345162 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1177.38 | −0.884581 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −147.066 | −0.107809 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −541.966 | −0.387799 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −663.822 | −0.463816 | −0.231908 | − | 0.972738i | \(-0.574497\pi\) | ||||
−0.231908 | + | 0.972738i | \(0.574497\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −549.666 | −0.375158 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1456.67 | 0.971523 | 0.485761 | − | 0.874091i | \(-0.338542\pi\) | ||||
0.485761 | + | 0.874091i | \(0.338542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −262.089 | −0.170872 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 326.862 | 0.208384 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2670.15 | 1.66516 | 0.832579 | − | 0.553907i | \(-0.186864\pi\) | ||||
0.832579 | + | 0.553907i | \(0.186864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 958.476 | 0.584870 | 0.292435 | − | 0.956285i | \(-0.405535\pi\) | ||||
0.292435 | + | 0.956285i | \(0.405535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −437.454 | −0.261279 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 602.783 | 0.352498 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −64.1220 | −0.0367244 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1166.19 | 0.654327 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 490.435 | 0.269651 | 0.134825 | − | 0.990869i | \(-0.456953\pi\) | ||||
0.134825 | + | 0.990869i | \(0.456953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1999.24 | −1.07746 | −0.538728 | − | 0.842480i | \(-0.681095\pi\) | ||||
−0.538728 | + | 0.842480i | \(0.681095\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1418.51 | 0.749541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 46.0278 | 0.0238519 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1830.68 | 0.930598 | 0.465299 | − | 0.885154i | \(-0.345947\pi\) | ||||
0.465299 | + | 0.885154i | \(0.345947\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −640.706 | −0.319568 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 79.8452 | 0.0390850 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2884.29 | 1.38598 | 0.692991 | − | 0.720946i | \(-0.256292\pi\) | ||||
0.692991 | + | 0.720946i | \(0.256292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 98.8116 | 0.0466210 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1658.79 | 0.768628 | 0.384314 | − | 0.923203i | \(-0.374438\pi\) | ||||
0.384314 | + | 0.923203i | \(0.374438\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.199 | 0.0765583 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 829.733 | 0.371060 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2925.53 | 1.28569 | 0.642844 | − | 0.765997i | \(-0.277754\pi\) | ||||
0.642844 | + | 0.765997i | \(0.277754\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −531.156 | −0.229438 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −395.210 | −0.167829 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4190.23 | −1.74968 | −0.874839 | − | 0.484413i | \(-0.839033\pi\) | ||||
−0.874839 | + | 0.484413i | \(0.839033\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −321.969 | −0.132220 | −0.0661098 | − | 0.997812i | \(-0.521059\pi\) | ||||
−0.0661098 | + | 0.997812i | \(0.521059\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −222.701 | −0.0899593 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 223.468 | 0.0888093 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1255.83 | 0.491099 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 653.724 | 0.251595 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −914.466 | −0.346432 | −0.173216 | − | 0.984884i | \(-0.555416\pi\) | ||||
−0.173216 | + | 0.984884i | \(0.555416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1055.21 | −0.393552 | −0.196776 | − | 0.980448i | \(-0.563047\pi\) | ||||
−0.196776 | + | 0.980448i | \(0.563047\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 387.717 | 0.142384 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 549.869 | 0.198866 | 0.0994328 | − | 0.995044i | \(-0.468297\pi\) | ||||
0.0994328 | + | 0.995044i | \(0.468297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4225.60 | −1.50525 | −0.752625 | − | 0.658449i | \(-0.771213\pi\) | ||||
−0.752625 | + | 0.658449i | \(0.771213\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1700.13 | 0.596608 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −128.244 | −0.0443397 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 90.1884 | 0.0307270 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −252.777 | −0.0848755 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 734.577 | 0.243118 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −692.728 | −0.226016 | −0.113008 | − | 0.993594i | \(-0.536049\pi\) | ||||
−0.113008 | + | 0.993594i | \(0.536049\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1970.51 | −0.633884 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 337.082 | 0.106925 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 92.0555 | 0.0287979 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −611.980 | −0.188830 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4927.63 | 1.49986 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3864.52 | −1.16048 | −0.580241 | − | 0.814445i | \(-0.697042\pi\) | ||||
−0.580241 | + | 0.814445i | \(0.697042\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1681.55 | 0.498238 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3410.81 | −0.997283 | −0.498642 | − | 0.866808i | \(-0.666168\pi\) | ||||
−0.498642 | + | 0.866808i | \(0.666168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2695.50 | −0.777833 | −0.388916 | − | 0.921273i | \(-0.627150\pi\) | ||||
−0.388916 | + | 0.921273i | \(0.627150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 197.623 | 0.0562885 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4829.82 | 1.35799 | 0.678995 | − | 0.734143i | \(-0.262416\pi\) | ||||
0.678995 | + | 0.734143i | \(0.262416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 268.269 | 0.0744677 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −666.724 | −0.182736 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4869.12 | −1.31781 | −0.658906 | − | 0.752225i | \(-0.728981\pi\) | ||||
−0.658906 | + | 0.752225i | \(0.728981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3096.69 | −0.827698 | −0.413849 | − | 0.910345i | \(-0.635816\pi\) | ||||
−0.413849 | + | 0.910345i | \(0.635816\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3432.48 | −0.906148 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −715.168 | −0.186491 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2882.33 | 0.742503 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −758.967 | −0.193163 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2208.84 | 0.555461 | 0.277730 | − | 0.960659i | \(-0.410418\pi\) | ||||
0.277730 | + | 0.960659i | \(0.410418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −223.788 | −0.0556104 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 807.765 | 0.198369 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 526.955 | 0.127901 | 0.0639504 | − | 0.997953i | \(-0.479630\pi\) | ||||
0.0639504 | + | 0.997953i | \(0.479630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 446.937 | 0.107225 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 406.000 | 0.0962865 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4892.69 | −1.14713 | −0.573567 | − | 0.819158i | \(-0.694441\pi\) | ||||
−0.573567 | + | 0.819158i | \(0.694441\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 392.912 | 0.0910808 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5023.69 | 1.15148 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4744.74 | −1.07543 | −0.537717 | − | 0.843125i | \(-0.680713\pi\) | ||||
−0.537717 | + | 0.843125i | \(0.680713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8187.57 | −1.83527 | −0.917637 | − | 0.397420i | \(-0.869906\pi\) | ||||
−0.917637 | + | 0.397420i | \(0.869906\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 775.433 | 0.171910 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1488.71 | 0.326446 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4966.39 | −1.07726 | −0.538631 | − | 0.842542i | \(-0.681058\pi\) | ||||
−0.538631 | + | 0.842542i | \(0.681058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −291.433 | −0.0625364 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 81.1971 | 0.0172378 | 0.00861888 | − | 0.999963i | \(-0.497256\pi\) | ||||
0.00861888 | + | 0.999963i | \(0.497256\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 213.170 | 0.0447762 | 0.0223881 | − | 0.999749i | \(-0.492873\pi\) | ||||
0.0223881 | + | 0.999749i | \(0.492873\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 472.488 | 0.0982027 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 180.377 | 0.0370986 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5353.17 | 1.08959 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3964.06 | 0.798548 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6346.40 | −1.26539 | −0.632697 | − | 0.774399i | \(-0.718052\pi\) | ||||
−0.632697 | + | 0.774399i | \(0.718052\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 242.362 | 0.0478334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1832.24 | −0.357971 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −878.099 | −0.169839 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 674.165 | 0.129097 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1163.87 | −0.220668 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 136.571 | 0.0256395 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5636.38 | 1.04784 | 0.523918 | − | 0.851769i | \(-0.324470\pi\) | ||||
0.523918 | + | 0.851769i | \(0.324470\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6279.46 | 1.15607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −586.998 | −0.107028 | −0.0535138 | − | 0.998567i | \(-0.517042\pi\) | ||||
−0.0535138 | + | 0.998567i | \(0.517042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1249.95 | −0.225723 | −0.112862 | − | 0.993611i | \(-0.536002\pi\) | ||||
−0.112862 | + | 0.993611i | \(0.536002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −136.891 | −0.0244856 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4821.77 | 0.854314 | 0.427157 | − | 0.904177i | \(-0.359515\pi\) | ||||
0.427157 | + | 0.904177i | \(0.359515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 359.439 | 0.0630869 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2019.99 | −0.351230 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6005.02 | 1.03445 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5841.40 | 0.996992 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3561.20 | 0.602247 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 536.537 | 0.0899096 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8287.49 | 1.37620 | 0.688100 | − | 0.725616i | \(-0.258445\pi\) | ||||
0.688100 | + | 0.725616i | \(0.258445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1414.93 | −0.232846 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1042.61 | −0.170041 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9910.59 | 1.60197 | 0.800985 | − | 0.598684i | \(-0.204309\pi\) | ||||
0.800985 | + | 0.598684i | \(0.204309\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1779.46 | −0.285094 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −258.011 | −0.0409738 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2947.15 | −0.463940 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −143.943 | −0.0224627 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9826.54 | 1.52022 | 0.760110 | − | 0.649794i | \(-0.225145\pi\) | ||||
0.760110 | + | 0.649794i | \(0.225145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7438.96 | −1.14097 | −0.570485 | − | 0.821308i | \(-0.693245\pi\) | ||||
−0.570485 | + | 0.821308i | \(0.693245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7189.35 | −1.09327 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9385.04 | −1.41506 | −0.707529 | − | 0.706684i | \(-0.750190\pi\) | ||||
−0.707529 | + | 0.706684i | \(0.750190\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1208.42 | 0.180665 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1615.53 | 0.239504 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6673.24 | 0.981059 | 0.490529 | − | 0.871425i | \(-0.336803\pi\) | ||||
0.490529 | + | 0.871425i | \(0.336803\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3346.47 | −0.487894 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4245.10 | 0.613801 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 375.296 | 0.0538189 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12384.4 | 1.76147 | 0.880733 | − | 0.473613i | \(-0.157051\pi\) | ||||
0.880733 | + | 0.473613i | \(0.157051\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −571.045 | −0.0805620 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 785.825 | 0.109968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5167.77 | −0.717364 | −0.358682 | − | 0.933460i | \(-0.616774\pi\) | ||||
−0.358682 | + | 0.933460i | \(0.616774\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1954.08 | 0.269089 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1410.37 | 0.192673 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7398.92 | 1.00279 | 0.501395 | − | 0.865219i | \(-0.332820\pi\) | ||||
0.501395 | + | 0.865219i | \(0.332820\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2393.44 | 0.321837 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3262.55 | −0.435270 | −0.217635 | − | 0.976030i | \(-0.569834\pi\) | ||||
−0.217635 | + | 0.976030i | \(0.569834\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −121.192 | −0.0160429 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2134.30 | −0.280342 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5819.82 | −0.758552 | −0.379276 | − | 0.925284i | \(-0.623827\pi\) | ||||
−0.379276 | + | 0.925284i | \(0.623827\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1829.42 | −0.236619 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5252.08 | −0.674129 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 408.868 | 0.0520820 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7678.61 | −0.970726 | −0.485363 | − | 0.874313i | \(-0.661313\pi\) | ||||
−0.485363 | + | 0.874313i | \(0.661313\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 944.976 | 0.118566 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1125.32 | −0.140139 | −0.0700693 | − | 0.997542i | \(-0.522322\pi\) | ||||
−0.0700693 | + | 0.997542i | \(0.522322\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1012.38 | −0.125137 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −342.721 | −0.0420492 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1252.66 | −0.152561 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11937.5 | −1.44321 | −0.721605 | − | 0.692305i | \(-0.756595\pi\) | ||||
−0.721605 | + | 0.692305i | \(0.756595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9627.37 | −1.15543 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 484.724 | 0.0577523 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 465.436 | 0.0550539 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3455.84 | −0.405834 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16082.3 | −1.87511 | −0.937554 | − | 0.347840i | \(-0.886915\pi\) | ||||
−0.937554 | + | 0.347840i | \(0.886915\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6896.09 | 0.798326 | 0.399163 | − | 0.916880i | \(-0.369301\pi\) | ||||
0.399163 | + | 0.916880i | \(0.369301\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1698.59 | −0.195244 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12169.9 | 1.38900 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 273.143 | 0.0309562 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2173.37 | −0.244595 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9632.03 | −1.07647 | −0.538235 | − | 0.842795i | \(-0.680909\pi\) | ||||
−0.538235 | + | 0.842795i | \(0.680909\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6657.14 | 0.738850 | 0.369425 | − | 0.929261i | \(-0.379555\pi\) | ||||
0.369425 | + | 0.929261i | \(0.379555\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 231.195 | 0.0254827 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1070.09 | −0.117138 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16147.8 | 1.75556 | 0.877781 | − | 0.479061i | \(-0.159023\pi\) | ||||
0.877781 | + | 0.479061i | \(0.159023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4528.22 | 0.488956 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6307.18 | −0.676440 | −0.338220 | − | 0.941067i | \(-0.609825\pi\) | ||||
−0.338220 | + | 0.941067i | \(0.609825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3080.77 | −0.328186 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1768.29 | −0.187108 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11001.7 | −1.15636 | −0.578178 | − | 0.815911i | \(-0.696236\pi\) | ||||
−0.578178 | + | 0.815911i | \(0.696236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −505.556 | −0.0527843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7208.37 | 0.747635 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −475.534 | −0.0489964 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1258.34 | 0.128802 | 0.0644011 | − | 0.997924i | \(-0.479486\pi\) | ||||
0.0644011 | + | 0.997924i | \(0.479486\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14978.2 | −1.52314 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7461.56 | −0.753838 | −0.376919 | − | 0.926246i | \(-0.623016\pi\) | ||||
−0.376919 | + | 0.926246i | \(0.623016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7744.02 | 0.777311 | 0.388655 | − | 0.921383i | \(-0.372940\pi\) | ||||
0.388655 | + | 0.921383i | \(0.372940\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −165.955 | −0.0165505 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −244.138 | −0.0241913 | −0.0120957 | − | 0.999927i | \(-0.503850\pi\) | ||||
−0.0120957 | + | 0.999927i | \(0.503850\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2085.21 | −0.205301 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6600.60 | −0.645731 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1889.53 | −0.183680 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7118.57 | 0.687626 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2487.80 | −0.238802 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4381.25 | −0.417922 | −0.208961 | − | 0.977924i | \(-0.567008\pi\) | ||||
−0.208961 | + | 0.977924i | \(0.567008\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4915.20 | −0.465933 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −287.886 | −0.0271206 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2430.96 | −0.227596 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15726.4 | 1.46331 | 0.731654 | − | 0.681676i | \(-0.238749\pi\) | ||||
0.731654 | + | 0.681676i | \(0.238749\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10399.5 | −0.961718 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17159.0 | 1.57714 | 0.788568 | − | 0.614947i | \(-0.210823\pi\) | ||||
0.788568 | + | 0.614947i | \(0.210823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2938.34 | 0.268431 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 383.676 | 0.0348383 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2416.83 | 0.218128 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21508.3 | 1.92955 | 0.964774 | − | 0.263081i | \(-0.0847386\pi\) | ||||
0.964774 | + | 0.263081i | \(0.0847386\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5980.84 | −0.533342 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22195.2 | −1.96746 | −0.983731 | − | 0.179648i | \(-0.942504\pi\) | ||||
−0.983731 | + | 0.179648i | \(0.942504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 713.742 | 0.0628933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −606.449 | −0.0531229 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11767.9 | 1.02476 | 0.512381 | − | 0.858758i | \(-0.328763\pi\) | ||||
0.512381 | + | 0.858758i | \(0.328763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 750.592 | 0.0649790 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8761.24 | −0.754032 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3850.88 | −0.329495 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1503.79 | −0.127924 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10548.2 | −0.892125 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8418.16 | 0.707881 | 0.353941 | − | 0.935268i | \(-0.384842\pi\) | ||||
0.353941 | + | 0.935268i | \(0.384842\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3414.16 | 0.285451 | 0.142726 | − | 0.989762i | \(-0.454413\pi\) | ||||
0.142726 | + | 0.989762i | \(0.454413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1915.11 | 0.159204 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2109.19 | −0.174341 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11841.0 | −0.973206 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1534.56 | −0.125413 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1983.70 | −0.161207 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1238.76 | 0.100105 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15108.1 | 1.21408 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4008.91 | 0.320364 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15393.9 | 1.22335 | 0.611677 | − | 0.791108i | \(-0.290495\pi\) | ||||
0.611677 | + | 0.791108i | \(0.290495\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1160.87 | 0.0917457 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2183.91 | −0.171648 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9547.99 | 0.746330 | 0.373165 | − | 0.927765i | \(-0.378273\pi\) | ||||
0.373165 | + | 0.927765i | \(0.378273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −864.727 | −0.0672234 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1718.73 | 0.132886 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 817.736 | 0.0628819 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −805.726 | −0.0616238 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19667.1 | 1.49609 | 0.748044 | − | 0.663649i | \(-0.230993\pi\) | ||||
0.748044 | + | 0.663649i | \(0.230993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7414.15 | −0.560975 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4527.97 | −0.340768 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13151.8 | 0.984517 | 0.492258 | − | 0.870449i | \(-0.336172\pi\) | ||||
0.492258 | + | 0.870449i | \(0.336172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1091.25 | 0.0812553 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −685.442 | −0.0507687 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17071.3 | 1.25776 | 0.628880 | − | 0.777502i | \(-0.283514\pi\) | ||||
0.628880 | + | 0.777502i | \(0.283514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10724.9 | −0.786033 | −0.393017 | − | 0.919531i | \(-0.628568\pi\) | ||||
−0.393017 | + | 0.919531i | \(0.628568\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3297.15 | 0.240385 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2168.67 | −0.157286 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10700.0 | −0.772008 | −0.386004 | − | 0.922497i | \(-0.626145\pi\) | ||||
−0.386004 | + | 0.922497i | \(0.626145\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3804.61 | 0.273081 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 930.872 | 0.0664700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2202.49 | −0.156463 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1505.47 | 0.106399 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10143.6 | −0.713237 | −0.356618 | − | 0.934250i | \(-0.616070\pi\) | ||||
−0.356618 | + | 0.934250i | \(0.616070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1233.73 | −0.0863074 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1982.58 | −0.137991 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4547.22 | −0.314894 | −0.157447 | − | 0.987527i | \(-0.550326\pi\) | ||||
−0.157447 | + | 0.987527i | \(0.550326\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −990.723 | −0.0682616 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15235.6 | 1.04448 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26519.1 | 1.80892 | 0.904458 | − | 0.426563i | \(-0.140276\pi\) | ||||
0.904458 | + | 0.426563i | \(0.140276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4927.20 | 0.334417 | 0.167209 | − | 0.985922i | \(-0.446525\pi\) | ||||
0.167209 | + | 0.985922i | \(0.446525\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6601.45 | 0.445824 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2603.30 | −0.174941 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16406.6 | 1.09707 | 0.548535 | − | 0.836127i | \(-0.315186\pi\) | ||||
0.548535 | + | 0.836127i | \(0.315186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 462.390 | 0.0307668 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5900.58 | −0.390691 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4914.16 | −0.323786 | −0.161893 | − | 0.986808i | \(-0.551760\pi\) | ||||
−0.161893 | + | 0.986808i | \(0.551760\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −325.179 | −0.0213211 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −186.272 | −0.0121540 | −0.00607702 | − | 0.999982i | \(-0.501934\pi\) | ||||
−0.00607702 | + | 0.999982i | \(0.501934\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 408.125 | 0.0265007 | 0.0132503 | − | 0.999912i | \(-0.495782\pi\) | ||||
0.0132503 | + | 0.999912i | \(0.495782\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2669.10 | 0.172476 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6161.55 | −0.396240 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13815.5 | 0.884194 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2648.56 | −0.168697 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10240.3 | −0.649136 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16001.4 | 1.00952 | 0.504760 | − | 0.863260i | \(-0.331581\pi\) | ||||
0.504760 | + | 0.863260i | \(0.331581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2497.66 | 0.156830 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1467.78 | −0.0917275 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15730.2 | 0.978417 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7651.30 | −0.473679 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16188.4 | −0.997510 | −0.498755 | − | 0.866743i | \(-0.666209\pi\) | ||||
−0.498755 | + | 0.866743i | \(0.666209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24550.3 | −1.50571 | −0.752854 | − | 0.658187i | \(-0.771323\pi\) | ||||
−0.752854 | + | 0.658187i | \(0.771323\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1215.37 | −0.0741939 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4566.00 | 0.277447 | 0.138723 | − | 0.990331i | \(-0.455700\pi\) | ||||
0.138723 | + | 0.990331i | \(0.455700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1358.57 | −0.0821705 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −331.911 | −0.0199825 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12985.7 | 0.778209 | 0.389105 | − | 0.921194i | \(-0.372784\pi\) | ||||
0.389105 | + | 0.921194i | \(0.372784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3220.84 | 0.192135 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2376.26 | −0.141106 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22004.9 | −1.30074 | −0.650370 | − | 0.759618i | \(-0.725386\pi\) | ||||
−0.650370 | + | 0.759618i | \(0.725386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10592.0 | −0.623267 | −0.311634 | − | 0.950202i | \(-0.600876\pi\) | ||||
−0.311634 | + | 0.950202i | \(0.600876\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17766.8 | −1.04073 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −579.506 | −0.0337929 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −523.610 | −0.0303962 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13933.7 | 0.805246 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −765.558 | −0.0440448 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −131.859 | −0.00755242 | −0.00377621 | − | 0.999993i | \(-0.501202\pi\) | ||||
−0.00377621 | + | 0.999993i | \(0.501202\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17755.7 | −1.01247 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15415.4 | −0.875130 | −0.437565 | − | 0.899187i | \(-0.644159\pi\) | ||||
−0.437565 | + | 0.899187i | \(0.644159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4861.92 | −0.274791 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12297.8 | 0.692003 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26452.5 | −1.48196 | −0.740978 | − | 0.671530i | \(-0.765638\pi\) | ||||
−0.740978 | + | 0.671530i | \(0.765638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5903.98 | 0.329313 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9718.76 | 0.539729 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8642.13 | −0.477850 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20331.6 | −1.11932 | −0.559661 | − | 0.828721i | \(-0.689069\pi\) | ||||
−0.559661 | + | 0.828721i | \(0.689069\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 767.351 | 0.0420624 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2119.29 | 0.115668 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4132.82 | −0.224593 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17414.2 | −0.942294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13325.5 | −0.717973 | −0.358987 | − | 0.933343i | \(-0.616878\pi\) | ||||
−0.358987 | + | 0.933343i | \(0.616878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5989.87 | −0.321354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −967.256 | −0.0516723 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1427.48 | 0.0759350 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33177.3 | −1.75741 | −0.878703 | − | 0.477370i | \(-0.841590\pi\) | ||||
−0.878703 | + | 0.477370i | \(0.841590\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2588.82 | −0.136552 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 375.855 | 0.0197418 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1332.82 | 0.0697125 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17555.9 | 0.914415 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12840.3 | 0.666013 | 0.333007 | − | 0.942924i | \(-0.391937\pi\) | ||||
0.333007 | + | 0.942924i | \(0.391937\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7701.76 | −0.397820 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11165.3 | 0.574330 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3483.22 | 0.178432 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23615.7 | −1.20475 | −0.602377 | − | 0.798212i | \(-0.705780\pi\) | ||||
−0.602377 | + | 0.798212i | \(0.705780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16561.0 | 0.841386 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15446.6 | −0.781548 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23648.0 | 1.19162 | 0.595812 | − | 0.803124i | \(-0.296830\pi\) | ||||
0.595812 | + | 0.803124i | \(0.296830\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2578.58 | 0.129404 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5844.38 | 0.292104 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18418.8 | −0.916841 | −0.458420 | − | 0.888735i | \(-0.651585\pi\) | ||||
−0.458420 | + | 0.888735i | \(0.651585\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10392.4 | −0.515215 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19005.1 | 0.938396 | 0.469198 | − | 0.883093i | \(-0.344543\pi\) | ||||
0.469198 | + | 0.883093i | \(0.344543\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1084.40 | 0.0533280 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2946.99 | −0.144344 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2477.51 | 0.120863 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26136.1 | 1.26993 | 0.634967 | − | 0.772540i | \(-0.281014\pi\) | ||||
0.634967 | + | 0.772540i | \(0.281014\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7964.08 | −0.385428 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4420.53 | −0.213085 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19642.3 | −0.943081 | −0.471540 | − | 0.881844i | \(-0.656302\pi\) | ||||
−0.471540 | + | 0.881844i | \(0.656302\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 806.880 | 0.0385874 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36349.8 | 1.73151 | 0.865754 | − | 0.500469i | \(-0.166839\pi\) | ||||
0.865754 | + | 0.500469i | \(0.166839\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4367.81 | −0.207242 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3136.47 | 0.148234 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5330.77 | −0.250955 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4940.72 | −0.231686 | −0.115843 | − | 0.993268i | \(-0.536957\pi\) | ||||
−0.115843 | + | 0.993268i | \(0.536957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1899.96 | −0.0887490 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4543.81 | −0.211422 | −0.105711 | − | 0.994397i | \(-0.533712\pi\) | ||||
−0.105711 | + | 0.994397i | \(0.533712\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2500.31 | −0.115889 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1611.45 | −0.0744023 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2417.42 | −0.111185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6773.83 | −0.310354 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4287.00 | −0.195664 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4047.81 | 0.184042 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18523.9 | 0.839016 | 0.419508 | − | 0.907752i | \(-0.362203\pi\) | ||||
0.419508 | + | 0.907752i | \(0.362203\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17640.9 | 0.795984 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2182.50 | 0.0981047 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3003.90 | −0.134516 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1416.67 | −0.0631999 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9666.66 | 0.429624 | 0.214812 | − | 0.976655i | \(-0.431086\pi\) | ||||
0.214812 | + | 0.976655i | \(0.431086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12293.2 | −0.544309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19506.5 | 0.860459 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2103.74 | −0.0924526 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 176.546 | 0.00772972 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17107.4 | 0.746232 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8733.19 | 0.379533 | 0.189767 | − | 0.981829i | \(-0.439227\pi\) | ||||
0.189767 | + | 0.981829i | \(0.439227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14082.6 | 0.609750 | 0.304875 | − | 0.952392i | \(-0.401385\pi\) | ||||
0.304875 | + | 0.952392i | \(0.401385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29520.7 | 1.27348 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6377.47 | 0.274102 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9035.19 | −0.386905 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3010.93 | 0.128462 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15741.2 | −0.669149 | −0.334574 | − | 0.942369i | \(-0.608593\pi\) | ||||
−0.334574 | + | 0.942369i | \(0.608593\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2136.76 | −0.0905014 | −0.0452507 | − | 0.998976i | \(-0.514409\pi\) | ||||
−0.0452507 | + | 0.998976i | \(0.514409\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5367.62 | −0.226517 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2966.17 | 0.124721 | 0.0623603 | − | 0.998054i | \(-0.480137\pi\) | ||||
0.0623603 | + | 0.998054i | \(0.480137\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28562.2 | −1.19663 | −0.598316 | − | 0.801260i | \(-0.704163\pi\) | ||||
−0.598316 | + | 0.801260i | \(0.704163\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17906.6 | 0.747500 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32772.0 | 1.36313 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3667.75 | 0.152009 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3077.28 | 0.127080 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9658.72 | −0.397445 | −0.198722 | − | 0.980056i | \(-0.563679\pi\) | ||||
−0.198722 | + | 0.980056i | \(0.563679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −292.760 | −0.0119611 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 371.904 | 0.0151407 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5206.61 | −0.211217 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −768.597 | −0.0310697 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1824.81 | 0.0735060 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5702.59 | −0.228901 | −0.114451 | − | 0.993429i | \(-0.536511\pi\) | ||||
−0.114451 | + | 0.993429i | \(0.536511\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1834.62 | 0.0733834 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11141.0 | −0.444071 | −0.222035 | − | 0.975039i | \(-0.571270\pi\) | ||||
−0.222035 | + | 0.975039i | \(0.571270\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15527.7 | −0.616763 | −0.308382 | − | 0.951263i | \(-0.599787\pi\) | ||||
−0.308382 | + | 0.951263i | \(0.599787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −650.358 | −0.0257423 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19168.3 | 0.756080 | 0.378040 | − | 0.925789i | \(-0.376598\pi\) | ||||
0.378040 | + | 0.925789i | \(0.376598\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6468.65 | 0.254267 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19301.1 | −0.756057 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2291.93 | −0.0894689 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22932.2 | 0.892110 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15392.1 | 0.596727 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2396.68 | −0.0925973 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33530.4 | −1.29104 | −0.645519 | − | 0.763744i | \(-0.723359\pi\) | ||||
−0.645519 | + | 0.763744i | \(0.723359\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22882.3 | 0.878043 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1779.67 | −0.0680574 | −0.0340287 | − | 0.999421i | \(-0.510834\pi\) | ||||
−0.0340287 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47347.6 | 1.80450 | 0.902250 | − | 0.431212i | \(-0.141914\pi\) | ||||
0.902250 | + | 0.431212i | \(0.141914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −873.849 | −0.0331911 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33076.7 | 1.25210 | 0.626048 | − | 0.779785i | \(-0.284672\pi\) | ||||
0.626048 | + | 0.779785i | \(0.284672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2935.56 | −0.110748 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1921.14 | 0.0722341 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7190.70 | −0.269460 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9265.03 | −0.346029 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3166.03 | 0.117849 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −603.683 | −0.0223959 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18004.9 | −0.665739 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2430.74 | −0.0895790 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −711.906 | −0.0261487 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2824.54 | 0.103404 | 0.0517019 | − | 0.998663i | \(-0.483535\pi\) | ||||
0.0517019 | + | 0.998663i | \(0.483535\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4519.19 | −0.164898 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41606.9 | 1.51317 | 0.756586 | − | 0.653895i | \(-0.226866\pi\) | ||||
0.756586 | + | 0.653895i | \(0.226866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2609.03 | −0.0945741 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −492.415 | −0.0177910 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6441.68 | 0.231977 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 618.058 | 0.0221848 | 0.0110924 | − | 0.999938i | \(-0.496469\pi\) | ||||
0.0110924 | + | 0.999938i | \(0.496469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20322.3 | −0.727081 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26579.1 | −0.947848 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12139.2 | −0.431497 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24382.5 | 0.863892 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8931.48 | −0.315428 | −0.157714 | − | 0.987485i | \(-0.550412\pi\) | ||||
−0.157714 | + | 0.987485i | \(0.550412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19169.4 | 0.674815 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2116.45 | 0.0742652 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2776.77 | 0.0971232 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37657.4 | −1.31293 | −0.656464 | − | 0.754357i | \(-0.727949\pi\) | ||||
−0.656464 | + | 0.754357i | \(0.727949\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4506.76 | 0.156627 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43174.4 | 1.49569 | 0.747846 | − | 0.663872i | \(-0.231088\pi\) | ||||
0.747846 | + | 0.663872i | \(0.231088\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 736.464 | 0.0254322 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1445.45 | 0.0497572 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36963.1 | −1.26836 | −0.634181 | − | 0.773185i | \(-0.718663\pi\) | ||||
−0.634181 | + | 0.773185i | \(0.718663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8254.66 | −0.282358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17385.1 | −0.592799 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32697.1 | 1.11140 | 0.555699 | − | 0.831384i | \(-0.312451\pi\) | ||||
0.555699 | + | 0.831384i | \(0.312451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2021.98 | −0.0685127 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1295.98 | −0.0437753 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11808.0 | 0.397601 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29357.7 | −0.985454 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7843.42 | −0.262462 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2333.17 | −0.0778316 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4649.77 | 0.154629 | 0.0773146 | − | 0.997007i | \(-0.475365\pi\) | ||||
0.0773146 | + | 0.997007i | \(0.475365\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21651.4 | −0.717795 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27533.7 | 0.909987 | 0.454994 | − | 0.890495i | \(-0.349642\pi\) | ||||
0.454994 | + | 0.890495i | \(0.349642\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4238.58 | 0.139653 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21061.5 | −0.691801 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16474.7 | −0.539482 | −0.269741 | − | 0.962933i | \(-0.586938\pi\) | ||||
−0.269741 | + | 0.962933i | \(0.586938\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17269.4 | 0.563773 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13827.8 | 0.450038 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26969.9 | 0.875084 | 0.437542 | − | 0.899198i | \(-0.355849\pi\) | ||||
0.437542 | + | 0.899198i | \(0.355849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1215.82 | 0.0393291 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1934.51 | −0.0623872 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2752.56 | 0.0884999 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6331.81 | 0.202963 | 0.101482 | − | 0.994837i | \(-0.467642\pi\) | ||||
0.101482 | + | 0.994837i | \(0.467642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29881.0 | −0.954929 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9343.23 | −0.297689 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53115.7 | −1.68725 | −0.843626 | − | 0.536932i | \(-0.819583\pi\) | ||||
−0.843626 | + | 0.536932i | \(0.819583\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14940.4 | 0.473167 |
(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 | 116.4.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1044.4.a.d.1.1 | 2 | |||
4.3 | odd | 2 | 464.4.a.d.1.2 | 2 | |||
8.3 | odd | 2 | 1856.4.a.k.1.1 | 2 | |||
8.5 | even | 2 | 1856.4.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
116.4.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
464.4.a.d.1.2 | 2 | 4.3 | odd | 2 | |||
1044.4.a.d.1.1 | 2 | 3.2 | odd | 2 | |||
1856.4.a.j.1.2 | 2 | 8.5 | even | 2 | |||
1856.4.a.k.1.1 | 2 | 8.3 | odd | 2 |