Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2028,4,Mod(1,2028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2028.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2028.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: | \(119.655873492\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 156) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2028.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.00000 | 0.536656 | 0.268328 | − | 0.963328i | \(-0.413529\pi\) | ||||
0.268328 | + | 0.963328i | \(0.413529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000 | 0.215980 | 0.107990 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107990 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −36.0000 | −0.986764 | −0.493382 | − | 0.869813i | \(-0.664240\pi\) | ||||
−0.493382 | + | 0.869813i | \(0.664240\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.0000 | −0.309839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 66.0000 | 0.941609 | 0.470804 | − | 0.882238i | \(-0.343964\pi\) | ||||
0.470804 | + | 0.882238i | \(0.343964\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −56.0000 | −0.676173 | −0.338086 | − | 0.941115i | \(-0.609780\pi\) | ||||
−0.338086 | + | 0.941115i | \(0.609780\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.0000 | −0.124696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 96.0000 | 0.870321 | 0.435161 | − | 0.900353i | \(-0.356692\pi\) | ||||
0.435161 | + | 0.900353i | \(0.356692\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 222.000 | 1.42153 | 0.710765 | − | 0.703430i | \(-0.248349\pi\) | ||||
0.710765 | + | 0.703430i | \(0.248349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −260.000 | −1.50637 | −0.753184 | − | 0.657810i | \(-0.771483\pi\) | ||||
−0.753184 | + | 0.657810i | \(0.771483\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 108.000 | 0.569709 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.0000 | 0.115907 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 106.000 | 0.470981 | 0.235490 | − | 0.971877i | \(-0.424330\pi\) | ||||
0.235490 | + | 0.971877i | \(0.424330\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 90.0000 | 0.342820 | 0.171410 | − | 0.985200i | \(-0.445168\pi\) | ||||
0.171410 | + | 0.985200i | \(0.445168\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 44.0000 | 0.156045 | 0.0780225 | − | 0.996952i | \(-0.475139\pi\) | ||||
0.0780225 | + | 0.996952i | \(0.475139\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 54.0000 | 0.178885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −168.000 | −0.521390 | −0.260695 | − | 0.965421i | \(-0.583952\pi\) | ||||
−0.260695 | + | 0.965421i | \(0.583952\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −327.000 | −0.953353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −198.000 | −0.543638 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 30.0000 | 0.0777513 | 0.0388756 | − | 0.999244i | \(-0.487622\pi\) | ||||
0.0388756 | + | 0.999244i | \(0.487622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −216.000 | −0.529553 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 168.000 | 0.390388 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −348.000 | −0.767894 | −0.383947 | − | 0.923355i | \(-0.625435\pi\) | ||||
−0.383947 | + | 0.923355i | \(0.625435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −346.000 | −0.726242 | −0.363121 | − | 0.931742i | \(-0.618289\pi\) | ||||
−0.363121 | + | 0.931742i | \(0.618289\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 36.0000 | 0.0719932 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 256.000 | 0.466797 | 0.233398 | − | 0.972381i | \(-0.425015\pi\) | ||||
0.233398 | + | 0.972381i | \(0.425015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −288.000 | −0.502480 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 168.000 | 0.280816 | 0.140408 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140408 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 814.000 | 1.30509 | 0.652544 | − | 0.757750i | \(-0.273702\pi\) | ||||
0.652544 | + | 0.757750i | \(0.273702\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 267.000 | 0.411073 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −144.000 | −0.213121 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 200.000 | 0.284832 | 0.142416 | − | 0.989807i | \(-0.454513\pi\) | ||||
0.142416 | + | 0.989807i | \(0.454513\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1236.00 | −1.63456 | −0.817281 | − | 0.576240i | \(-0.804520\pi\) | ||||
−0.817281 | + | 0.576240i | \(0.804520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 396.000 | 0.505320 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −666.000 | −0.820721 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −318.000 | −0.378741 | −0.189370 | − | 0.981906i | \(-0.560645\pi\) | ||||
−0.189370 | + | 0.981906i | \(0.560645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 780.000 | 0.869701 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −336.000 | −0.362872 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 502.000 | 0.525468 | 0.262734 | − | 0.964868i | \(-0.415376\pi\) | ||||
0.262734 | + | 0.964868i | \(0.415376\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −324.000 | −0.328921 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1062.00 | 1.04627 | 0.523133 | − | 0.852251i | \(-0.324763\pi\) | ||||
0.523133 | + | 0.852251i | \(0.324763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −64.0000 | −0.0612243 | −0.0306122 | − | 0.999531i | \(-0.509746\pi\) | ||||
−0.0306122 | + | 0.999531i | \(0.509746\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −72.0000 | −0.0669189 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −444.000 | −0.401150 | −0.200575 | − | 0.979678i | \(-0.564281\pi\) | ||||
−0.200575 | + | 0.979678i | \(0.564281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1382.00 | −1.21442 | −0.607209 | − | 0.794542i | \(-0.707711\pi\) | ||||
−0.607209 | + | 0.794542i | \(0.707711\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −318.000 | −0.271921 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −870.000 | −0.724272 | −0.362136 | − | 0.932125i | \(-0.617952\pi\) | ||||
−0.362136 | + | 0.932125i | \(0.617952\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 576.000 | 0.467063 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 264.000 | 0.203368 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −270.000 | −0.197927 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1284.00 | −0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 464.000 | 0.324200 | 0.162100 | − | 0.986774i | \(-0.448173\pi\) | ||||
0.162100 | + | 0.986774i | \(0.448173\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −132.000 | −0.0900927 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1548.00 | 1.03244 | 0.516219 | − | 0.856457i | \(-0.327339\pi\) | ||||
0.516219 | + | 0.856457i | \(0.327339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −224.000 | −0.146040 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −162.000 | −0.103280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −294.000 | −0.183344 | −0.0916720 | − | 0.995789i | \(-0.529221\pi\) | ||||
−0.0916720 | + | 0.995789i | \(0.529221\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2564.00 | 1.56457 | 0.782286 | − | 0.622919i | \(-0.214053\pi\) | ||||
0.782286 | + | 0.622919i | \(0.214053\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 504.000 | 0.301025 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1332.00 | 0.762873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 981.000 | 0.550418 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −114.000 | −0.0626795 | −0.0313397 | − | 0.999509i | \(-0.509977\pi\) | ||||
−0.0313397 | + | 0.999509i | \(0.509977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2036.00 | −1.09727 | −0.548634 | − | 0.836063i | \(-0.684852\pi\) | ||||
−0.548634 | + | 0.836063i | \(0.684852\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 594.000 | 0.313870 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1560.00 | −0.808401 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2870.00 | 1.45892 | 0.729462 | − | 0.684022i | \(-0.239771\pi\) | ||||
0.729462 | + | 0.684022i | \(0.239771\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −90.0000 | −0.0448897 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 384.000 | 0.187972 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1472.00 | −0.707337 | −0.353669 | − | 0.935371i | \(-0.615066\pi\) | ||||
−0.353669 | + | 0.935371i | \(0.615066\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 648.000 | 0.305738 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 240.000 | 0.111208 | 0.0556041 | − | 0.998453i | \(-0.482292\pi\) | ||||
0.0556041 | + | 0.998453i | \(0.482292\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −504.000 | −0.225391 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −306.000 | −0.134478 | −0.0672392 | − | 0.997737i | \(-0.521419\pi\) | ||||
−0.0672392 | + | 0.997737i | \(0.521419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −356.000 | −0.153778 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1044.00 | 0.443344 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2052.00 | −0.856836 | −0.428418 | − | 0.903581i | \(-0.640929\pi\) | ||||
−0.428418 | + | 0.903581i | \(0.640929\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4498.00 | −1.84715 | −0.923574 | − | 0.383421i | \(-0.874746\pi\) | ||||
−0.923574 | + | 0.383421i | \(0.874746\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1038.00 | 0.419296 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 636.000 | 0.252755 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2376.00 | −0.929146 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −108.000 | −0.0415653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4056.00 | −1.53655 | −0.768277 | − | 0.640117i | \(-0.778886\pi\) | ||||
−0.768277 | + | 0.640117i | \(0.778886\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2062.00 | 0.769047 | 0.384523 | − | 0.923115i | \(-0.374366\pi\) | ||||
0.384523 | + | 0.923115i | \(0.374366\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4374.00 | 1.58190 | 0.790951 | − | 0.611880i | \(-0.209586\pi\) | ||||
0.790951 | + | 0.611880i | \(0.209586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2536.00 | −0.903378 | −0.451689 | − | 0.892175i | \(-0.649178\pi\) | ||||
−0.451689 | + | 0.892175i | \(0.649178\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −768.000 | −0.269505 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 888.000 | 0.307022 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 540.000 | 0.183977 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 864.000 | 0.290107 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2016.00 | 0.667223 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4444.00 | −1.44994 | −0.724971 | − | 0.688780i | \(-0.758147\pi\) | ||||
−0.724971 | + | 0.688780i | \(0.758147\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −504.000 | −0.162129 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 264.000 | 0.0837426 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1040.00 | −0.325345 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2442.00 | −0.753493 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2716.00 | 0.815591 | 0.407796 | − | 0.913073i | \(-0.366298\pi\) | ||||
0.407796 | + | 0.913073i | \(0.366298\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −801.000 | −0.237333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4692.00 | 1.37189 | 0.685945 | − | 0.727653i | \(-0.259389\pi\) | ||||
0.685945 | + | 0.727653i | \(0.259389\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6446.00 | −1.86010 | −0.930052 | − | 0.367429i | \(-0.880238\pi\) | ||||
−0.930052 | + | 0.367429i | \(0.880238\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 432.000 | 0.123046 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3102.00 | −0.872184 | −0.436092 | − | 0.899902i | \(-0.643638\pi\) | ||||
−0.436092 | + | 0.899902i | \(0.643638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1008.00 | −0.279807 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −600.000 | −0.164448 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −816.000 | −0.220848 | −0.110424 | − | 0.993885i | \(-0.535221\pi\) | ||||
−0.110424 | + | 0.993885i | \(0.535221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3818.00 | −1.02049 | −0.510247 | − | 0.860028i | \(-0.670446\pi\) | ||||
−0.510247 | + | 0.860028i | \(0.670446\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1962.00 | −0.511623 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3708.00 | 0.943715 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6612.00 | −1.66273 | −0.831366 | − | 0.555725i | \(-0.812441\pi\) | ||||
−0.831366 | + | 0.555725i | \(0.812441\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3456.00 | −0.858802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1188.00 | −0.291747 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4806.00 | −1.16650 | −0.583249 | − | 0.812293i | \(-0.698219\pi\) | ||||
−0.583249 | + | 0.812293i | \(0.698219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 424.000 | 0.101722 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1998.00 | 0.473843 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4584.00 | −1.07476 | −0.537379 | − | 0.843341i | \(-0.680586\pi\) | ||||
−0.537379 | + | 0.843341i | \(0.680586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 180.000 | 0.0417257 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 954.000 | 0.218666 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7134.00 | 1.61698 | 0.808490 | − | 0.588510i | \(-0.200285\pi\) | ||||
0.808490 | + | 0.588510i | \(0.200285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3140.00 | −0.703843 | −0.351921 | − | 0.936030i | \(-0.614472\pi\) | ||||
−0.351921 | + | 0.936030i | \(0.614472\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3204.00 | 0.702576 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4786.00 | −1.03813 | −0.519067 | − | 0.854734i | \(-0.673720\pi\) | ||||
−0.519067 | + | 0.854734i | \(0.673720\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2340.00 | −0.502122 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3798.00 | −0.806298 | −0.403149 | − | 0.915134i | \(-0.632084\pi\) | ||||
−0.403149 | + | 0.915134i | \(0.632084\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3572.00 | 0.750295 | 0.375147 | − | 0.926965i | \(-0.377592\pi\) | ||||
0.375147 | + | 0.926965i | \(0.377592\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1008.00 | 0.209504 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 360.000 | 0.0740423 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −557.000 | −0.113373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1506.00 | −0.303379 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7122.00 | −1.42004 | −0.710020 | − | 0.704182i | \(-0.751314\pi\) | ||||
−0.710020 | + | 0.704182i | \(0.751314\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2088.00 | −0.412095 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 972.000 | 0.189903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 176.000 | 0.0337026 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3186.00 | −0.604062 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2076.00 | −0.389742 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6856.00 | 1.27457 | 0.637284 | − | 0.770629i | \(-0.280058\pi\) | ||||
0.637284 | + | 0.770629i | \(0.280058\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 192.000 | 0.0353479 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8832.00 | −1.61034 | −0.805172 | − | 0.593042i | \(-0.797927\pi\) | ||||
−0.805172 | + | 0.593042i | \(0.797927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3626.00 | 0.654804 | 0.327402 | − | 0.944885i | \(-0.393827\pi\) | ||||
0.327402 | + | 0.944885i | \(0.393827\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 216.000 | 0.0386356 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10146.0 | −1.79765 | −0.898827 | − | 0.438304i | \(-0.855579\pi\) | ||||
−0.898827 | + | 0.438304i | \(0.855579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7992.00 | −1.40272 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1332.00 | 0.231604 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3696.00 | −0.636690 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4146.00 | 0.701145 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −672.000 | −0.112610 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6536.00 | −1.08535 | −0.542675 | − | 0.839943i | \(-0.682589\pi\) | ||||
−0.542675 | + | 0.839943i | \(0.682589\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 954.000 | 0.156994 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1536.00 | 0.250509 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6094.00 | −0.985048 | −0.492524 | − | 0.870299i | \(-0.663926\pi\) | ||||
−0.492524 | + | 0.870299i | \(0.663926\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2610.00 | 0.418159 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9360.00 | 1.48643 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2680.00 | −0.421885 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1728.00 | −0.269659 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2724.00 | −0.421418 | −0.210709 | − | 0.977549i | \(-0.567577\pi\) | ||||
−0.210709 | + | 0.977549i | \(0.567577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1522.00 | 0.233441 | 0.116720 | − | 0.993165i | \(-0.462762\pi\) | ||||
0.116720 | + | 0.993165i | \(0.462762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1362.00 | 0.205360 | 0.102680 | − | 0.994714i | \(-0.467258\pi\) | ||||
0.102680 | + | 0.994714i | \(0.467258\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1008.00 | 0.150702 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −792.000 | −0.117415 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8880.00 | −1.30548 | −0.652742 | − | 0.757581i | \(-0.726381\pi\) | ||||
−0.652742 | + | 0.757581i | \(0.726381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3723.00 | −0.542790 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 105.000 | 0.0151820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4884.00 | 0.700384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3712.00 | −0.527970 | −0.263985 | − | 0.964527i | \(-0.585037\pi\) | ||||
−0.263985 | + | 0.964527i | \(0.585037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 810.000 | 0.114273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 120.000 | 0.0167927 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5726.00 | 0.794855 | 0.397428 | − | 0.917634i | \(-0.369903\pi\) | ||||
0.397428 | + | 0.917634i | \(0.369903\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3852.00 | 0.530444 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13168.0 | 1.78468 | 0.892341 | − | 0.451361i | \(-0.149061\pi\) | ||||
0.892341 | + | 0.451361i | \(0.149061\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1392.00 | −0.187177 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4872.00 | −0.649994 | −0.324997 | − | 0.945715i | \(-0.605363\pi\) | ||||
−0.324997 | + | 0.945715i | \(0.605363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −864.000 | −0.114373 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 396.000 | 0.0520150 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1266.00 | −0.165010 | −0.0825048 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825048 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6336.00 | 0.819502 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4644.00 | −0.596078 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1200.00 | 0.152857 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4882.00 | 0.617180 | 0.308590 | − | 0.951195i | \(-0.400143\pi\) | ||||
0.308590 | + | 0.951195i | \(0.400143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 672.000 | 0.0843160 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 90.0000 | 0.0112079 | 0.00560397 | − | 0.999984i | \(-0.498216\pi\) | ||||
0.00560397 | + | 0.999984i | \(0.498216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 486.000 | 0.0596285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3816.00 | −0.464747 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2354.00 | −0.284591 | −0.142296 | − | 0.989824i | \(-0.545448\pi\) | ||||
−0.142296 | + | 0.989824i | \(0.545448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 882.000 | 0.105854 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1392.00 | −0.165849 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7416.00 | −0.877198 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7692.00 | −0.903307 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7020.00 | 0.818495 | 0.409248 | − | 0.912423i | \(-0.365791\pi\) | ||||
0.409248 | + | 0.912423i | \(0.365791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −302.000 | −0.0349610 | −0.0174805 | − | 0.999847i | \(-0.505564\pi\) | ||||
−0.0174805 | + | 0.999847i | \(0.505564\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1512.00 | −0.173797 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5874.00 | −0.670426 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1384.00 | −0.156854 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9816.00 | −1.09703 | −0.548515 | − | 0.836141i | \(-0.684807\pi\) | ||||
−0.548515 | + | 0.836141i | \(0.684807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14782.0 | −1.64059 | −0.820297 | − | 0.571937i | \(-0.806192\pi\) | ||||
−0.820297 | + | 0.571937i | \(0.806192\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3996.00 | −0.440445 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5376.00 | −0.588487 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3584.00 | 0.389647 | 0.194823 | − | 0.980838i | \(-0.437587\pi\) | ||||
0.194823 | + | 0.980838i | \(0.437587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2943.00 | −0.317784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 180.000 | 0.0193049 | 0.00965244 | − | 0.999953i | \(-0.496927\pi\) | ||||
0.00965244 | + | 0.999953i | \(0.496927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1908.00 | −0.203254 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 342.000 | 0.0361880 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3450.00 | 0.362618 | 0.181309 | − | 0.983426i | \(-0.441967\pi\) | ||||
0.181309 | + | 0.983426i | \(0.441967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3240.00 | −0.338283 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6108.00 | 0.633507 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16654.0 | 1.70469 | 0.852343 | − | 0.522984i | \(-0.175181\pi\) | ||||
0.852343 | + | 0.522984i | \(0.175181\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1782.00 | −0.181213 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14046.0 | 1.41906 | 0.709531 | − | 0.704674i | \(-0.248907\pi\) | ||||
0.709531 | + | 0.704674i | \(0.248907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4588.00 | 0.460524 | 0.230262 | − | 0.973129i | \(-0.426042\pi\) | ||||
0.230262 | + | 0.973129i | \(0.426042\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4680.00 | 0.466731 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15372.0 | −1.52319 | −0.761597 | − | 0.648051i | \(-0.775584\pi\) | ||||
−0.761597 | + | 0.648051i | \(0.775584\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1024.00 | 0.100819 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8610.00 | −0.842310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1584.00 | −0.153980 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4984.00 | 0.481435 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 270.000 | 0.0259171 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12864.0 | −1.22708 | −0.613540 | − | 0.789664i | \(-0.710255\pi\) | ||||
−0.613540 | + | 0.789664i | \(0.710255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1152.00 | −0.108525 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3012.00 | 0.281996 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10276.0 | 0.956160 | 0.478080 | − | 0.878316i | \(-0.341333\pi\) | ||||
0.478080 | + | 0.878316i | \(0.341333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4416.00 | 0.408381 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11220.0 | −1.03127 | −0.515633 | − | 0.856810i | \(-0.672443\pi\) | ||||
−0.515633 | + | 0.856810i | \(0.672443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14652.0 | 1.33853 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1944.00 | −0.176518 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 672.000 | 0.0606505 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17264.0 | −1.54878 | −0.774392 | − | 0.632707i | \(-0.781944\pi\) | ||||
−0.774392 | + | 0.632707i | \(0.781944\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −720.000 | −0.0642060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1896.00 | −0.168069 | −0.0840343 | − | 0.996463i | \(-0.526781\pi\) | ||||
−0.0840343 | + | 0.996463i | \(0.526781\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6372.00 | 0.561486 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5010.00 | −0.436276 | −0.218138 | − | 0.975918i | \(-0.569998\pi\) | ||||
−0.218138 | + | 0.975918i | \(0.569998\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3256.00 | 0.281873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1512.00 | 0.130129 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −384.000 | −0.0328564 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6048.00 | 0.514489 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 918.000 | 0.0776411 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8610.00 | 0.724013 | 0.362007 | − | 0.932176i | \(-0.382092\pi\) | ||||
0.362007 | + | 0.932176i | \(0.382092\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5308.00 | −0.443791 | −0.221895 | − | 0.975070i | \(-0.571224\pi\) | ||||
−0.221895 | + | 0.975070i | \(0.571224\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1068.00 | 0.0887835 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17160.0 | −1.41841 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2951.00 | −0.242541 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3132.00 | −0.255965 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2664.00 | −0.215280 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6156.00 | 0.494695 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11772.0 | 0.940735 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6182.00 | −0.491285 | −0.245642 | − | 0.969361i | \(-0.578999\pi\) | ||||
−0.245642 | + | 0.969361i | \(0.578999\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13494.0 | 1.06645 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8292.00 | −0.651725 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1292.00 | 0.100991 | 0.0504954 | − | 0.998724i | \(-0.483920\pi\) | ||||
0.0504954 | + | 0.998724i | \(0.483920\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3114.00 | −0.242081 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12432.0 | −0.961200 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 800.000 | 0.0615180 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1908.00 | −0.145928 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12774.0 | 0.971727 | 0.485863 | − | 0.874035i | \(-0.338505\pi\) | ||||
0.485863 | + | 0.874035i | \(0.338505\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7128.00 | 0.536443 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16908.0 | 1.26570 | 0.632848 | − | 0.774276i | \(-0.281886\pi\) | ||||
0.632848 | + | 0.774276i | \(0.281886\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5220.00 | −0.388685 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 324.000 | 0.0239977 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11214.0 | −0.826213 | −0.413107 | − | 0.910683i | \(-0.635556\pi\) | ||||
−0.413107 | + | 0.910683i | \(0.635556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25220.0 | 1.84838 | 0.924189 | − | 0.381935i | \(-0.124742\pi\) | ||||
0.924189 | + | 0.381935i | \(0.124742\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12168.0 | 0.887130 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8544.00 | −0.619669 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17710.0 | 1.27778 | 0.638888 | − | 0.769300i | \(-0.279395\pi\) | ||||
0.638888 | + | 0.769300i | \(0.279395\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6186.00 | −0.444009 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4944.00 | −0.353032 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1080.00 | −0.0767222 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20028.0 | −1.40825 | −0.704126 | − | 0.710075i | \(-0.748661\pi\) | ||||
−0.704126 | + | 0.710075i | \(0.748661\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14560.0 | 1.01856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13122.0 | −0.913311 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19926.0 | −1.37987 | −0.689935 | − | 0.723871i | \(-0.742361\pi\) | ||||
−0.689935 | + | 0.723871i | \(0.742361\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1584.00 | 0.109139 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7608.00 | 0.521566 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1704.00 | −0.116233 | −0.0581165 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581165 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11018.0 | 0.747810 | 0.373905 | − | 0.927467i | \(-0.378019\pi\) | ||||
0.373905 | + | 0.927467i | \(0.378019\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2304.00 | 0.155599 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −210.000 | −0.0141119 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −448.000 | −0.0299568 | −0.0149784 | − | 0.999888i | \(-0.504768\pi\) | ||||
−0.0149784 | + | 0.999888i | \(0.504768\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2664.00 | −0.177259 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12586.0 | 0.829272 | 0.414636 | − | 0.909987i | \(-0.363909\pi\) | ||||
0.414636 | + | 0.909987i | \(0.363909\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1620.00 | −0.106219 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29610.0 | 1.93202 | 0.966008 | − | 0.258513i | \(-0.0832324\pi\) | ||||
0.966008 | + | 0.258513i | \(0.0832324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7120.00 | 0.462321 | 0.231161 | − | 0.972916i | \(-0.425748\pi\) | ||||
0.231161 | + | 0.972916i | \(0.425748\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2592.00 | −0.167493 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1272.00 | −0.0818003 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6048.00 | −0.385221 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6996.00 | 0.443480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15580.0 | 0.982932 | 0.491466 | − | 0.870897i | \(-0.336461\pi\) | ||||
0.491466 | + | 0.870897i | \(0.336461\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13332.0 | 0.837124 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2784.00 | 0.173984 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1512.00 | 0.0936053 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19806.0 | −1.22042 | −0.610211 | − | 0.792239i | \(-0.708915\pi\) | ||||
−0.610211 | + | 0.792239i | \(0.708915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24032.0 | −1.47392 | −0.736959 | − | 0.675937i | \(-0.763739\pi\) | ||||
−0.736959 | + | 0.675937i | \(0.763739\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −792.000 | −0.0483488 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2808.00 | −0.170624 | −0.0853121 | − | 0.996354i | \(-0.527189\pi\) | ||||
−0.0853121 | + | 0.996354i | \(0.527189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12528.0 | 0.757730 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3120.00 | 0.187838 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23886.0 | 1.43144 | 0.715721 | − | 0.698386i | \(-0.246098\pi\) | ||||
0.715721 | + | 0.698386i | \(0.246098\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9288.00 | 0.554064 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7326.00 | 0.435030 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3948.00 | −0.233372 | −0.116686 | − | 0.993169i | \(-0.537227\pi\) | ||||
−0.116686 | + | 0.993169i | \(0.537227\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5750.00 | −0.338350 | −0.169175 | − | 0.985586i | \(-0.554110\pi\) | ||||
−0.169175 | + | 0.985586i | \(0.554110\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1344.00 | −0.0783731 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21312.0 | 1.23719 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8148.00 | −0.470882 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12456.0 | 0.716630 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28082.0 | 1.60844 | 0.804221 | − | 0.594330i | \(-0.202583\pi\) | ||||
0.804221 | + | 0.594330i | \(0.202583\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2403.00 | 0.137024 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27954.0 | −1.58694 | −0.793471 | − | 0.608608i | \(-0.791728\pi\) | ||||
−0.793471 | + | 0.608608i | \(0.791728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2008.00 | 0.113490 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14076.0 | −0.792061 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28428.0 | 1.59263 | 0.796316 | − | 0.604881i | \(-0.206779\pi\) | ||||
0.796316 | + | 0.604881i | \(0.206779\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1764.00 | −0.0983927 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19338.0 | 1.07393 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21680.0 | −1.19355 | −0.596777 | − | 0.802407i | \(-0.703552\pi\) | ||||
−0.596777 | + | 0.802407i | \(0.703552\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1296.00 | −0.0710404 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15384.0 | 0.839638 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5940.00 | 0.322803 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9306.00 | 0.503555 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7482.00 | −0.403126 | −0.201563 | − | 0.979476i | \(-0.564602\pi\) | ||||
−0.201563 | + | 0.979476i | \(0.564602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5936.00 | −0.318464 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3024.00 | 0.161547 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4248.00 | 0.225972 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2270.00 | −0.120242 | −0.0601210 | − | 0.998191i | \(-0.519149\pi\) | ||||
−0.0601210 | + | 0.998191i | \(0.519149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1800.00 | 0.0949441 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24960.0 | −1.31102 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2448.00 | 0.127507 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36024.0 | 1.86852 | 0.934262 | − | 0.356588i | \(-0.116060\pi\) | ||||
0.934262 | + | 0.356588i | \(0.116060\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −256.000 | −0.0132232 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11454.0 | 0.589182 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19758.0 | −1.01213 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21544.0 | −1.09907 | −0.549534 | − | 0.835471i | \(-0.685195\pi\) | ||||
−0.549534 | + | 0.835471i | \(0.685195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2904.00 | 0.146933 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1018.00 | 0.0512970 | 0.0256485 | − | 0.999671i | \(-0.491835\pi\) | ||||
0.0256485 | + | 0.999671i | \(0.491835\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5886.00 | 0.295386 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9216.00 | −0.460618 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24568.0 | 1.22293 | 0.611467 | − | 0.791270i | \(-0.290580\pi\) | ||||
0.611467 | + | 0.791270i | \(0.290580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16968.0 | −0.837814 | −0.418907 | − | 0.908029i | \(-0.637587\pi\) | ||||
−0.418907 | + | 0.908029i | \(0.637587\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −684.000 | −0.0336373 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11124.0 | −0.544854 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1776.00 | −0.0866404 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3224.00 | 0.156652 | 0.0783259 | − | 0.996928i | \(-0.475043\pi\) | ||||
0.0783259 | + | 0.996928i | \(0.475043\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19836.0 | 0.959979 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12216.0 | −0.588855 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31570.0 | −1.51576 | −0.757881 | − | 0.652393i | \(-0.773765\pi\) | ||||
−0.757881 | + | 0.652393i | \(0.773765\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10368.0 | 0.495829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34890.0 | 1.66197 | 0.830987 | − | 0.556293i | \(-0.187777\pi\) | ||||
0.830987 | + | 0.556293i | \(0.187777\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5528.00 | −0.262290 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3564.00 | 0.168440 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11522.0 | −0.540304 | −0.270152 | − | 0.962818i | \(-0.587074\pi\) | ||||
−0.270152 | + | 0.962818i | \(0.587074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14418.0 | 0.673478 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28158.0 | 1.31018 | 0.655092 | − | 0.755549i | \(-0.272630\pi\) | ||||
0.655092 | + | 0.755549i | \(0.272630\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23140.0 | 1.07253 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1272.00 | −0.0587294 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5040.00 | −0.231806 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6048.00 | −0.277099 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5994.00 | −0.273574 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17220.0 | 0.782940 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14504.0 | −0.656940 | −0.328470 | − | 0.944514i | \(-0.606533\pi\) | ||||
−0.328470 | + | 0.944514i | \(0.606533\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13752.0 | 0.620512 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3480.00 | −0.156428 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −540.000 | −0.0240903 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18090.0 | −0.803991 | −0.401995 | − | 0.915642i | \(-0.631683\pi\) | ||||
−0.401995 | + | 0.915642i | \(0.631683\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11088.0 | −0.490945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2862.00 | −0.126247 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29304.0 | −1.28782 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2304.00 | 0.100876 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21402.0 | −0.933564 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36402.0 | 1.58199 | 0.790993 | − | 0.611826i | \(-0.209565\pi\) | ||||
0.790993 | + | 0.611826i | \(0.209565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32368.0 | 1.40147 | 0.700736 | − | 0.713420i | \(-0.252855\pi\) | ||||
0.700736 | + | 0.713420i | \(0.252855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9420.00 | 0.406364 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8832.00 | −0.379597 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2464.00 | −0.105513 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35778.0 | −1.52090 | −0.760451 | − | 0.649395i | \(-0.775022\pi\) | ||||
−0.760451 | + | 0.649395i | \(0.775022\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10240.0 | −0.433711 | −0.216855 | − | 0.976204i | \(-0.569580\pi\) | ||||
−0.216855 | + | 0.976204i | \(0.569580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9612.00 | −0.405633 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16284.0 | 0.684704 | 0.342352 | − | 0.939572i | \(-0.388776\pi\) | ||||
0.342352 | + | 0.939572i | \(0.388776\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14150.0 | 0.592822 | 0.296411 | − | 0.955060i | \(-0.404210\pi\) | ||||
0.296411 | + | 0.955060i | \(0.404210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14358.0 | 0.599366 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21582.0 | −0.897685 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1440.00 | 0.0596805 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7020.00 | 0.289900 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39576.0 | −1.62850 | −0.814252 | − | 0.580511i | \(-0.802853\pi\) | ||||
−0.814252 | + | 0.580511i | \(0.802853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24895.0 | 1.02075 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11394.0 | 0.465516 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −140.000 | −0.00567941 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10716.0 | −0.433183 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10176.0 | 0.409905 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6922.00 | 0.277848 | 0.138924 | − | 0.990303i | \(-0.455636\pi\) | ||||
0.138924 | + | 0.990303i | \(0.455636\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3024.00 | −0.120957 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48162.0 | 1.91970 | 0.959850 | − | 0.280514i | \(-0.0905050\pi\) | ||||
0.959850 | + | 0.280514i | \(0.0905050\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27652.0 | −1.09834 | −0.549170 | − | 0.835711i | \(-0.685056\pi\) | ||||
−0.549170 | + | 0.835711i | \(0.685056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1080.00 | −0.0427483 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −648.000 | −0.0255599 | −0.0127799 | − | 0.999918i | \(-0.504068\pi\) | ||||
−0.0127799 | + | 0.999918i | \(0.504068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1836.00 | −0.0721686 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1671.00 | 0.0654558 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7200.00 | −0.281062 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4518.00 | 0.175156 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5136.00 | −0.198433 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7166.00 | −0.275916 | −0.137958 | − | 0.990438i | \(-0.544054\pi\) | ||||
−0.137958 | + | 0.990438i | \(0.544054\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21366.0 | 0.819860 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37062.0 | −1.41731 | −0.708655 | − | 0.705555i | \(-0.750698\pi\) | ||||
−0.708655 | + | 0.705555i | \(0.750698\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24716.0 | 0.941970 | 0.470985 | − | 0.882141i | \(-0.343899\pi\) | ||||
0.470985 | + | 0.882141i | \(0.343899\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6264.00 | 0.237923 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48672.0 | 1.84244 | 0.921221 | − | 0.389040i | \(-0.127193\pi\) | ||||
0.921221 | + | 0.389040i | \(0.127193\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1856.00 | 0.0700205 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2916.00 | −0.109640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9408.00 | 0.352550 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12312.0 | −0.459827 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57720.0 | −2.14135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1980.00 | 0.0732113 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −528.000 | −0.0194582 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26988.0 | −0.991283 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9484.00 | −0.347201 | −0.173600 | − | 0.984816i | \(-0.555540\pi\) | ||||
−0.173600 | + | 0.984816i | \(0.555540\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9558.00 | 0.348756 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12792.0 | 0.465223 | 0.232611 | − | 0.972570i | \(-0.425273\pi\) | ||||
0.232611 | + | 0.972570i | \(0.425273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44496.0 | 1.61293 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6228.00 | 0.225018 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6192.00 | 0.222986 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18592.0 | −0.667349 | −0.333674 | − | 0.942688i | \(-0.608289\pi\) | ||||
−0.333674 | + | 0.942688i | \(0.608289\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20568.0 | −0.735873 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9434.00 | −0.335338 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −576.000 | −0.0204081 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15378.0 | 0.543096 | 0.271548 | − | 0.962425i | \(-0.412464\pi\) | ||||
0.271548 | + | 0.962425i | \(0.412464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18312.0 | 0.644631 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26496.0 | 0.929732 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14256.0 | −0.498632 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37078.0 | −1.29273 | −0.646364 | − | 0.763030i | \(-0.723711\pi\) | ||||
−0.646364 | + | 0.763030i | \(0.723711\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10878.0 | −0.378051 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10842.0 | −0.375599 | −0.187800 | − | 0.982207i | \(-0.560136\pi\) | ||||
−0.187800 | + | 0.982207i | \(0.560136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8640.00 | 0.298364 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −648.000 | −0.0223063 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41508.0 | −1.42432 | −0.712159 | − | 0.702018i | \(-0.752282\pi\) | ||||
−0.712159 | + | 0.702018i | \(0.752282\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30438.0 | 1.03788 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38706.0 | 1.31565 | 0.657823 | − | 0.753173i | \(-0.271478\pi\) | ||||
0.657823 | + | 0.753173i | \(0.271478\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24336.0 | −0.824602 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23976.0 | 0.809858 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1176.00 | −0.0395986 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37809.0 | 1.26914 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3996.00 | −0.133717 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12372.0 | 0.412714 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24388.0 | 0.811029 | 0.405515 | − | 0.914089i | \(-0.367092\pi\) | ||||
0.405515 | + | 0.914089i | \(0.367092\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11088.0 | 0.367593 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14100.0 | −0.466005 | −0.233002 | − | 0.972476i | \(-0.574855\pi\) | ||||
−0.233002 | + | 0.972476i | \(0.574855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10256.0 | 0.337916 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44838.0 | −1.46826 | −0.734132 | − | 0.679006i | \(-0.762411\pi\) | ||||
−0.734132 | + | 0.679006i | \(0.762411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11448.0 | 0.373728 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12438.0 | −0.404806 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13176.0 | −0.427517 | −0.213758 | − | 0.976887i | \(-0.568571\pi\) | ||||
−0.213758 | + | 0.976887i | \(0.568571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26244.0 | 0.848937 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2016.00 | 0.0650152 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4224.00 | 0.135809 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43648.0 | −1.39912 | −0.699558 | − | 0.714576i | \(-0.746620\pi\) | ||||
−0.699558 | + | 0.714576i | \(0.746620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19608.0 | 0.626627 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15216.0 | −0.484804 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 62750.0 | 1.99329 | 0.996646 | − | 0.0818317i | \(-0.0260770\pi\) | ||||
0.996646 | + | 0.0818317i | \(0.0260770\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2862.00 | −0.0906403 |
(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 | 2028.4.a.a.1.1 | 1 | ||
13.5 | odd | 4 | 2028.4.b.a.337.1 | 2 | |||
13.8 | odd | 4 | 2028.4.b.a.337.2 | 2 | |||
13.12 | even | 2 | 156.4.a.a.1.1 | ✓ | 1 | ||
39.38 | odd | 2 | 468.4.a.b.1.1 | 1 | |||
52.51 | odd | 2 | 624.4.a.h.1.1 | 1 | |||
104.51 | odd | 2 | 2496.4.a.e.1.1 | 1 | |||
104.77 | even | 2 | 2496.4.a.n.1.1 | 1 | |||
156.155 | even | 2 | 1872.4.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.4.a.a.1.1 | ✓ | 1 | 13.12 | even | 2 | ||
468.4.a.b.1.1 | 1 | 39.38 | odd | 2 | |||
624.4.a.h.1.1 | 1 | 52.51 | odd | 2 | |||
1872.4.a.j.1.1 | 1 | 156.155 | even | 2 | |||
2028.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2028.4.b.a.337.1 | 2 | 13.5 | odd | 4 | |||
2028.4.b.a.337.2 | 2 | 13.8 | odd | 4 | |||
2496.4.a.e.1.1 | 1 | 104.51 | odd | 2 | |||
2496.4.a.n.1.1 | 1 | 104.77 | even | 2 |