Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.21 | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.d.223.22 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.15485 | 0.282178 | 0.141089 | − | 0.989997i | \(-0.454940\pi\) | ||||
0.141089 | + | 0.989997i | \(0.454940\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.11026 | + | 17.4833i | −0.329923 | + | 0.944008i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.9479 | 1.67059 | 0.835294 | − | 0.549803i | \(-0.185297\pi\) | ||||
0.835294 | + | 0.549803i | \(0.185297\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 59.6460 | 1.27253 | 0.636263 | − | 0.771472i | \(-0.280479\pi\) | ||||
0.636263 | + | 0.771472i | \(0.280479\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 9.46455i | − | 0.162916i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.4250i | 0.305667i | 0.988252 | + | 0.152833i | \(0.0488398\pi\) | ||||
−0.988252 | + | 0.152833i | \(0.951160\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 95.5205i | 1.15336i | 0.816969 | + | 0.576682i | \(0.195653\pi\) | ||||
−0.816969 | + | 0.576682i | \(0.804347\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 52.4498 | + | 18.3308i | 0.545023 | + | 0.190481i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 46.3236i | − | 0.419963i | −0.977705 | − | 0.209981i | \(-0.932660\pi\) | ||
0.977705 | − | 0.209981i | \(-0.0673403\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −115.047 | −0.920375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 107.590i | 0.688932i | 0.938799 | + | 0.344466i | \(0.111940\pi\) | ||||
−0.938799 | + | 0.344466i | \(0.888060\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 94.2549 | 0.546086 | 0.273043 | − | 0.962002i | \(-0.411970\pi\) | ||||
0.273043 | + | 0.962002i | \(0.411970\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 182.844i | − | 0.964515i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −19.2770 | + | 55.1571i | −0.0930971 | + | 0.266379i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 131.650i | − | 0.584949i | −0.956273 | − | 0.292475i | \(-0.905521\pi\) | ||
0.956273 | − | 0.292475i | \(-0.0944787\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 178.938i | − | 0.734693i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 283.782i | 1.08096i | 0.841358 | + | 0.540479i | \(0.181757\pi\) | ||||
−0.841358 | + | 0.540479i | \(0.818243\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −373.255 | −1.32374 | −0.661871 | − | 0.749618i | \(-0.730237\pi\) | ||||
−0.661871 | + | 0.749618i | \(0.730237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −28.3937 | −0.0940595 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 136.224 | 0.422773 | 0.211387 | − | 0.977403i | \(-0.432202\pi\) | ||||
0.211387 | + | 0.977403i | \(0.432202\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −268.330 | − | 213.655i | −0.782302 | − | 0.622900i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 64.2751 | 0.176477 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 298.133i | 0.772674i | 0.922358 | + | 0.386337i | \(0.126260\pi\) | ||||
−0.922358 | + | 0.386337i | \(0.873740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 192.281 | 0.471404 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 286.561 | 0.665895 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 468.435i | − | 1.03365i | −0.856092 | − | 0.516823i | \(-0.827115\pi\) | ||
0.856092 | − | 0.516823i | \(-0.172885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −563.070 | −1.18186 | −0.590932 | − | 0.806721i | \(-0.701240\pi\) | ||||
−0.590932 | + | 0.806721i | \(0.701240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 54.9923 | − | 157.349i | 0.109974 | − | 0.314669i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 188.174 | 0.359079 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 160.990 | 0.293553 | 0.146777 | − | 0.989170i | \(-0.453110\pi\) | ||||
0.146777 | + | 0.989170i | \(0.453110\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −138.971 | −0.242466 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 409.730i | − | 0.684873i | −0.939541 | − | 0.342437i | \(-0.888748\pi\) | ||
0.939541 | − | 0.342437i | \(-0.111252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 930.545i | 1.49195i | 0.665976 | + | 0.745973i | \(0.268015\pi\) | ||||
−0.665976 | + | 0.745973i | \(0.731985\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 345.141i | 0.531379i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −372.407 | + | 1065.57i | −0.551165 | + | 1.57705i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 442.826i | 0.630656i | 0.948983 | + | 0.315328i | \(0.102115\pi\) | ||||
−0.948983 | + | 0.315328i | \(0.897885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 190.709i | 0.252205i | 0.992017 | + | 0.126102i | \(0.0402468\pi\) | ||||
−0.992017 | + | 0.126102i | \(0.959753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 67.5928i | 0.0862526i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 322.771 | 0.397755 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 829.404i | 0.987828i | 0.869511 | + | 0.493914i | \(0.164434\pi\) | ||||
−0.869511 | + | 0.493914i | \(0.835566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −364.453 | + | 1042.81i | −0.419835 | + | 1.20127i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 282.765i | − | 0.315283i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 301.353i | 0.325454i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1030.40i | 1.07857i | 0.842123 | + | 0.539285i | \(0.181306\pi\) | ||||
−0.842123 | + | 0.539285i | \(0.818694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −548.531 | −0.556863 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1784.29 | 1.75785 | 0.878926 | − | 0.476958i | \(-0.158261\pi\) | ||||
0.878926 | + | 0.476958i | \(0.158261\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 288.271 | 0.275769 | 0.137885 | − | 0.990448i | \(-0.455970\pi\) | ||||
0.137885 | + | 0.990448i | \(0.455970\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 165.471 | + | 57.8309i | 0.153794 | + | 0.0537497i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 292.479 | 0.264252 | 0.132126 | − | 0.991233i | \(-0.457820\pi\) | ||||
0.132126 | + | 0.991233i | \(0.457820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 518.765i | 0.455860i | 0.973678 | + | 0.227930i | \(0.0731957\pi\) | ||||
−0.973678 | + | 0.227930i | \(0.926804\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −394.950 | −0.337721 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1101.69 | −0.917156 | −0.458578 | − | 0.888654i | \(-0.651641\pi\) | ||||
−0.458578 | + | 0.888654i | \(0.651641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 146.144i | − | 0.118504i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −536.814 | −0.424175 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −374.580 | − | 130.913i | −0.288552 | − | 0.100847i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2383.64 | 1.79087 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 851.345 | 0.624091 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −757.312 | −0.541889 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1739.50i | − | 1.21540i | −0.794168 | − | 0.607698i | \(-0.792093\pi\) | ||
0.794168 | − | 0.607698i | \(-0.207907\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1119.77i | 0.764263i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2546.59i | 1.69845i | 0.528033 | + | 0.849224i | \(0.322930\pi\) | ||||
−0.528033 | + | 0.849224i | \(0.677070\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1670.01 | − | 583.655i | −1.08878 | − | 0.380521i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 85.1810i | 0.0543053i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −197.078 | −0.122902 | −0.0614509 | − | 0.998110i | \(-0.519573\pi\) | ||||
−0.0614509 | + | 0.998110i | \(0.519573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 810.877i | − | 0.494803i | −0.968913 | − | 0.247402i | \(-0.920423\pi\) | ||
0.968913 | − | 0.247402i | \(-0.0795767\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 408.673i | − | 0.244088i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3635.30 | 2.12587 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 339.432i | 0.194402i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −640.964 | + | 804.989i | −0.359631 | + | 0.451662i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1838.58i | − | 1.01089i | −0.862860 | − | 0.505443i | \(-0.831329\pi\) | ||
0.862860 | − | 0.505443i | \(-0.168671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 43.6496i | − | 0.0235242i | −0.999931 | − | 0.0117621i | \(-0.996256\pi\) | ||
0.999931 | − | 0.0117621i | \(-0.00374408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 192.825i | − | 0.101889i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 297.360 | 0.154094 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −193.518 | −0.0983721 | −0.0491860 | − | 0.998790i | \(-0.515663\pi\) | ||||
−0.0491860 | + | 0.998790i | \(0.515663\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 894.399 | 0.446103 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 809.888 | + | 283.049i | 0.396448 | + | 0.138555i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1656.29 | 0.795893 | 0.397946 | − | 0.917409i | \(-0.369723\pi\) | ||||
0.397946 | + | 0.917409i | \(0.369723\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 576.844i | − | 0.272165i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4172.57 | 1.93343 | 0.966716 | − | 0.255851i | \(-0.0823555\pi\) | ||||
0.966716 | + | 0.255851i | \(0.0823555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1360.65 | 0.619322 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 859.684i | − | 0.384454i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3172.52 | −1.39423 | −0.697116 | − | 0.716958i | \(-0.745534\pi\) | ||||
−0.697116 | + | 0.716958i | \(0.745534\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 702.966 | − | 2011.40i | 0.303653 | − | 0.868842i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1405.31 | −0.596776 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −137.757 | −0.0575221 | −0.0287611 | − | 0.999586i | \(-0.509156\pi\) | ||||
−0.0287611 | + | 0.999586i | \(0.509156\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −978.118 | −0.401674 | −0.200837 | − | 0.979625i | \(-0.564366\pi\) | ||||
−0.200837 | + | 0.979625i | \(0.564366\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1689.21i | 0.682350i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 415.336i | − | 0.165060i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1305.81i | 0.510644i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −472.048 | − | 164.977i | −0.181674 | − | 0.0634937i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4051.60i | − | 1.53489i | −0.641116 | − | 0.767444i | \(-0.721528\pi\) | ||
0.641116 | − | 0.767444i | \(-0.278472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1175.58 | 0.438444 | 0.219222 | − | 0.975675i | \(-0.429648\pi\) | ||||
0.219222 | + | 0.975675i | \(0.429648\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 564.523i | − | 0.207315i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3303.51i | 1.19475i | 0.801963 | + | 0.597374i | \(0.203789\pi\) | ||||
−0.801963 | + | 0.597374i | \(0.796211\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4452.76 | 1.58617 | 0.793086 | − | 0.609110i | \(-0.208473\pi\) | ||||
0.793086 | + | 0.609110i | \(0.208473\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 482.970i | − | 0.169483i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1881.03 | − | 657.405i | −0.650358 | − | 0.227295i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 895.289i | 0.305023i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 416.912i | 0.139988i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5821.77i | 1.92680i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5875.61 | 1.91703 | 0.958516 | − | 0.285038i | \(-0.0920061\pi\) | ||||
0.958516 | + | 0.285038i | \(0.0920061\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1229.19 | −0.395412 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1177.57 | −0.373532 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −575.921 | + | 1647.88i | −0.180166 | + | 0.515510i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2791.63 | 0.861375 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1277.92i | 0.388969i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1909.89 | −0.573524 | −0.286762 | − | 0.958002i | \(-0.592579\pi\) | ||||
−0.286762 | + | 0.958002i | \(0.592579\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1035.42 | 0.306792 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4211.95i | 1.23153i | 0.787931 | + | 0.615764i | \(0.211152\pi\) | ||||
−0.787931 | + | 0.615764i | \(0.788848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 135.681 | 0.0391532 | 0.0195766 | − | 0.999808i | \(-0.493768\pi\) | ||||
0.0195766 | + | 0.999808i | \(0.493768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3196.70 | + | 1117.22i | 0.910509 | + | 0.318215i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −613.936 | −0.172619 | −0.0863096 | − | 0.996268i | \(-0.527507\pi\) | ||||
−0.0863096 | + | 0.996268i | \(0.527507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 429.767 | 0.119298 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1328.48 | 0.364109 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4611.45i | 1.24807i | 0.781395 | + | 0.624037i | \(0.214508\pi\) | ||||
−0.781395 | + | 0.624037i | \(0.785492\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4934.31i | 1.31887i | 0.751763 | + | 0.659433i | \(0.229204\pi\) | ||||
−0.751763 | + | 0.659433i | \(0.770796\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −846.540 | − | 674.048i | −0.220749 | − | 0.175769i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5697.42i | 1.46768i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 572.126 | 0.145611 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3655.89i | 0.919353i | 0.888086 | + | 0.459676i | \(0.152035\pi\) | ||||
−0.888086 | + | 0.459676i | \(0.847965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2823.32i | − | 0.701585i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 202.779 | 0.0497980 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4419.08i | 1.07259i | 0.844032 | + | 0.536294i | \(0.180176\pi\) | ||||
−0.844032 | + | 0.536294i | \(0.819824\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2301.67 | + | 804.415i | 0.552197 | + | 0.192988i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 968.314i | − | 0.229644i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5949.45i | − | 1.39490i | −0.716633 | − | 0.697450i | \(-0.754318\pi\) | ||
0.716633 | − | 0.697450i | \(-0.245682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 940.565i | 0.218032i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2488.21 | 0.570323 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −735.471 | −0.166701 | −0.0833503 | − | 0.996520i | \(-0.526562\pi\) | ||||
−0.0833503 | + | 0.996520i | \(0.526562\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8337.62 | 1.86891 | 0.934454 | − | 0.356084i | \(-0.115888\pi\) | ||||
0.934454 | + | 0.356084i | \(0.115888\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3128.42 | + | 1093.36i | 0.693556 | + | 0.242392i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7011.86 | −1.53757 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3922.04i | 0.850731i | 0.905022 | + | 0.425366i | \(0.139855\pi\) | ||||
−0.905022 | + | 0.425366i | \(0.860145\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −848.294 | −0.182029 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6465.12 | 1.37251 | 0.686257 | − | 0.727359i | \(-0.259253\pi\) | ||||
0.686257 | + | 0.727359i | \(0.259253\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 868.108i | − | 0.182345i | −0.995835 | − | 0.0911726i | \(-0.970939\pi\) | ||
0.995835 | − | 0.0911726i | \(-0.0290615\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 904.059 | 0.187901 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4961.43 | − | 1733.98i | −1.02043 | − | 0.356633i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4453.97 | 0.906568 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3091.20 | 0.622713 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4595.00 | −0.916186 | −0.458093 | − | 0.888904i | \(-0.651467\pi\) | ||||
−0.458093 | + | 0.888904i | \(0.651467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1477.84i | − | 0.291673i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1645.59i | 0.321505i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 2763.02i | − | 0.534413i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2280.69 | − | 6525.73i | 0.436733 | − | 1.24962i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5352.86i | − | 1.01490i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1776.40 | −0.333497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3217.92i | 0.598230i | 0.954217 | + | 0.299115i | \(0.0966914\pi\) | ||||
−0.954217 | + | 0.299115i | \(0.903309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 864.814i | − | 0.159215i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7883.65 | −1.43743 | −0.718715 | − | 0.695305i | \(-0.755269\pi\) | ||||
−0.718715 | + | 0.695305i | \(0.755269\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2670.55i | − | 0.482263i | −0.970492 | − | 0.241131i | \(-0.922482\pi\) | ||
0.970492 | − | 0.241131i | \(-0.0775185\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 173.493 | − | 496.414i | 0.0310324 | − | 0.0887929i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5005.09i | 0.886794i | 0.896325 | + | 0.443397i | \(0.146227\pi\) | ||||
−0.896325 | + | 0.443397i | \(0.853773\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6557.41i | 1.15092i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 877.436i | − | 0.152566i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2046.53 | −0.352545 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6862.09 | −1.17120 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1556.30 | 0.263191 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −832.365 | + | 2381.65i | −0.139483 | + | 0.399101i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10962.6 | −1.82042 | −0.910210 | − | 0.414148i | \(-0.864080\pi\) | ||||
−0.910210 | + | 0.414148i | \(0.864080\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1184.85i | 0.194983i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 507.900 | 0.0828344 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10584.5 | −1.71090 | −0.855448 | − | 0.517888i | \(-0.826718\pi\) | ||||
−0.855448 | + | 0.517888i | \(0.826718\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3305.08i | 0.529520i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5744.63 | 0.912285 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5374.94 | − | 3385.79i | 0.846121 | − | 0.532990i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −438.432 | −0.0684185 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3267.07 | −0.505434 | −0.252717 | − | 0.967540i | \(-0.581324\pi\) | ||||
−0.252717 | + | 0.967540i | \(0.581324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5781.37 | −0.886732 | −0.443366 | − | 0.896341i | \(-0.646216\pi\) | ||||
−0.443366 | + | 0.896341i | \(0.646216\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1610.44i | 0.244898i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10650.3i | − | 1.60583i | −0.596093 | − | 0.802915i | \(-0.703281\pi\) | ||
0.596093 | − | 0.802915i | \(-0.296719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1292.64i | − | 0.193256i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −392.738 | + | 1123.74i | −0.0582238 | + | 0.166596i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9179.33i | − | 1.34949i | −0.738051 | − | 0.674745i | \(-0.764254\pi\) | ||
0.738051 | − | 0.674745i | \(-0.235746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2265.16 | −0.330247 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7150.93i | − | 1.03396i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2935.73i | 0.420995i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2199.66 | −0.312865 | −0.156433 | − | 0.987689i | \(-0.549999\pi\) | ||||
−0.156433 | + | 0.987689i | \(0.549999\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2554.03i | − | 0.360319i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5212.34 | − | 1821.67i | −0.729410 | − | 0.254923i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1961.66i | 0.272309i | 0.990688 | + | 0.136154i | \(0.0434743\pi\) | ||||
−0.990688 | + | 0.136154i | \(0.956526\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2271.94i | 0.312859i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6417.34i | 0.876684i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4839.03 | 0.655842 | 0.327921 | − | 0.944705i | \(-0.393652\pi\) | ||||
0.327921 | + | 0.944705i | \(0.393652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5218.49 | −0.701709 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14701.3 | 1.96136 | 0.980678 | − | 0.195628i | \(-0.0626744\pi\) | ||||
0.980678 | + | 0.195628i | \(0.0626744\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1174.89 | + | 3361.71i | −0.155527 | + | 0.445009i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3359.30 | 0.441248 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15110.1i | 1.96945i | 0.174126 | + | 0.984723i | \(0.444290\pi\) | ||||
−0.174126 | + | 0.984723i | \(0.555710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 992.486 | 0.128369 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7639.77 | 0.980599 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1397.05i | 0.177958i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11309.2 | 1.42971 | 0.714854 | − | 0.699274i | \(-0.246493\pi\) | ||||
0.714854 | + | 0.699274i | \(0.246493\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1750.96 | + | 5010.03i | −0.219694 | + | 0.628610i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12823.1 | −1.59690 | −0.798450 | − | 0.602061i | \(-0.794346\pi\) | ||||
−0.798450 | + | 0.602061i | \(0.794346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5621.93 | 0.694909 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 255.543 | 0.0313532 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8023.79i | − | 0.977210i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3805.30i | − | 0.460049i | −0.973185 | − | 0.230025i | \(-0.926119\pi\) | ||
0.973185 | − | 0.230025i | \(-0.0738807\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 591.235i | 0.0709574i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8189.78 | + | 2862.26i | 0.975770 | + | 0.341023i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 601.658i | 0.0711668i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2432.63 | −0.285675 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8027.30i | 0.935941i | 0.883744 | + | 0.467970i | \(0.155015\pi\) | ||||
−0.883744 | + | 0.467970i | \(0.844985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 16646.2i | − | 1.92705i | −0.267622 | − | 0.963524i | \(-0.586238\pi\) | ||
0.267622 | − | 0.963524i | \(-0.413762\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1226.02 | −0.140924 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2464.89i | − | 0.281328i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3440.50 | − | 9844.30i | 0.389924 | − | 1.11569i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 10905.9i | − | 1.22737i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 602.051i | 0.0672849i | 0.999434 | + | 0.0336425i | \(0.0107107\pi\) | ||||
−0.999434 | + | 0.0336425i | \(0.989289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9231.81i | − | 1.02460i | −0.858806 | − | 0.512301i | \(-0.828793\pi\) | ||
0.858806 | − | 0.512301i | \(-0.171207\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1018.30 | 0.112238 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4424.85 | 0.484369 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11079.3 | −1.20452 | −0.602262 | − | 0.798298i | \(-0.705734\pi\) | ||||
−0.602262 | + | 0.798298i | \(0.705734\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2414.97 | + | 1922.89i | 0.260767 | + | 0.207633i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3757.07 | −0.402943 | −0.201471 | − | 0.979494i | \(-0.564572\pi\) | ||||
−0.201471 | + | 0.979494i | \(0.564572\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2616.65i | 0.278744i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5515.73 | −0.583635 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5309.74 | −0.558090 | −0.279045 | − | 0.960278i | \(-0.590018\pi\) | ||||
−0.279045 | + | 0.960278i | \(0.590018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17295.9i | 1.80583i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −130.949 | −0.0135817 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1149.79 | + | 3289.90i | −0.118469 | + | 0.338974i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17826.5 | 1.82470 | 0.912350 | − | 0.409412i | \(-0.134266\pi\) | ||||
0.912350 | + | 0.409412i | \(0.134266\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −578.476 | −0.0588256 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7613.64 | 0.769203 | 0.384601 | − | 0.923083i | \(-0.374339\pi\) | ||||
0.384601 | + | 0.923083i | \(0.374339\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 831.086i | − | 0.0834208i | −0.999130 | − | 0.0417104i | \(-0.986719\pi\) | ||
0.999130 | − | 0.0417104i | \(-0.0132807\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 892.080i | − | 0.0889661i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11189.4i | 1.10875i | 0.832267 | + | 0.554374i | \(0.187042\pi\) | ||||
−0.832267 | + | 0.554374i | \(0.812958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −983.691 | + | 2814.63i | −0.0968500 | + | 0.277117i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 580.554i | 0.0567951i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22749.1 | −2.21143 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 10989.3i | − | 1.06153i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2683.20i | − | 0.257558i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8503.67 | −0.811154 | −0.405577 | − | 0.914061i | \(-0.632929\pi\) | ||||
−0.405577 | + | 0.914061i | \(0.632929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7852.40i | − | 0.744363i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 849.147 | − | 2429.66i | 0.0799949 | − | 0.228889i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3250.76i | 0.304349i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1829.08i | 0.170192i | 0.996373 | + | 0.0850962i | \(0.0271198\pi\) | ||||
−0.996373 | + | 0.0850962i | \(0.972880\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 4968.87i | − | 0.459509i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15970.1 | −1.46786 | −0.733931 | − | 0.679224i | \(-0.762316\pi\) | ||||
−0.733931 | + | 0.679224i | \(0.762316\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2305.13 | −0.210584 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1730.53 | −0.157135 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7163.42 | + | 2503.55i | 0.646526 | + | 0.225955i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1903.84 | −0.170796 | −0.0853982 | − | 0.996347i | \(-0.527216\pi\) | ||||
−0.0853982 | + | 0.996347i | \(0.527216\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 12517.7i | − | 1.11627i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5674.20 | −0.502982 | −0.251491 | − | 0.967860i | \(-0.580921\pi\) | ||||
−0.251491 | + | 0.967860i | \(0.580921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5629.16 | 0.496028 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4081.95i | − | 0.357566i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10624.8 | 0.925219 | 0.462609 | − | 0.886562i | \(-0.346913\pi\) | ||||
0.462609 | + | 0.886562i | \(0.346913\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16269.0 | − | 5685.87i | −1.40841 | − | 0.492227i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2579.05 | −0.221965 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 909.453 | 0.0778161 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8302.58 | 0.706280 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9517.56i | 0.804961i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 695.563i | − | 0.0584898i | −0.999572 | − | 0.0292449i | \(-0.990690\pi\) | ||
0.999572 | − | 0.0292449i | \(-0.00931026\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 11831.5i | − | 0.989211i | −0.869118 | − | 0.494605i | \(-0.835313\pi\) | ||
0.869118 | − | 0.494605i | \(-0.164687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6034.19 | − | 2108.90i | −0.501626 | − | 0.175314i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2019.42i | 0.166921i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10021.1 | 0.823631 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4215.92i | 0.344549i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16926.5i | 1.37555i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 922.726 | 0.0745662 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 413.272i | 0.0332104i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16354.1 | − | 13021.8i | −1.30690 | − | 1.04061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10553.5i | − | 0.838687i | −0.907828 | − | 0.419343i | \(-0.862260\pi\) | ||
0.907828 | − | 0.419343i | \(-0.137740\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2934.36i | 0.231907i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1636.63i | 0.128634i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1001.89 | 0.0783136 | 0.0391568 | − | 0.999233i | \(-0.487533\pi\) | ||||
0.0391568 | + | 0.999233i | \(0.487533\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5067.63 | 0.393955 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10277.1 | −0.794589 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7742.05 | − | 2705.78i | −0.595344 | − | 0.208068i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1246.01 | −0.0952975 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12853.2i | 0.977752i | 0.872353 | + | 0.488876i | \(0.162593\pi\) | ||||
−0.872353 | + | 0.488876i | \(0.837407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22263.2 | −1.68450 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3917.43 | 0.294820 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 10159.5i | − | 0.760518i | −0.924880 | − | 0.380259i | \(-0.875835\pi\) | ||
0.924880 | − | 0.380259i | \(-0.124165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3475.68 | −0.258802 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −494.931 | + | 1416.14i | −0.0366581 | + | 0.104890i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9104.92 | −0.670823 | −0.335411 | − | 0.942072i | \(-0.608875\pi\) | ||||
−0.335411 | + | 0.942072i | \(0.608875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21714.0 | 1.59143 | 0.795713 | − | 0.605674i | \(-0.207097\pi\) | ||||
0.795713 | + | 0.605674i | \(0.207097\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12154.8 | −0.886168 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5329.39i | 0.386523i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 12878.6i | − | 0.929191i | −0.885523 | − | 0.464595i | \(-0.846200\pi\) | ||
0.885523 | − | 0.464595i | \(-0.153800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 3526.73i | − | 0.253136i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3334.21 | − | 1165.28i | −0.238083 | − | 0.0832081i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18170.6i | 1.29082i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1693.57 | −0.119693 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19024.7i | − | 1.33771i | −0.743394 | − | 0.668854i | \(-0.766785\pi\) | ||
0.743394 | − | 0.668854i | \(-0.233215\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9003.27i | 0.629836i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9910.53 | 0.689788 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25477.9i | − | 1.76434i | −0.470934 | − | 0.882169i | \(-0.656083\pi\) | ||
0.470934 | − | 0.882169i | \(-0.343917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1181.74 | − | 413.010i | −0.0814232 | − | 0.0284567i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 13358.3i | − | 0.915776i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12475.5i | 0.850976i | 0.904964 | + | 0.425488i | \(0.139898\pi\) | ||||
−0.904964 | + | 0.425488i | \(0.860102\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 947.642i | 0.0643180i | 0.999483 | + | 0.0321590i | \(0.0102383\pi\) | ||||
−0.999483 | + | 0.0321590i | \(0.989762\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1448.91 | −0.0978511 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7520.04 | 0.505344 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17586.1 | 1.17594 | 0.587971 | − | 0.808882i | \(-0.299927\pi\) | ||||
0.587971 | + | 0.808882i | \(0.299927\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1972.22 | + | 5643.10i | −0.131229 | + | 0.375484i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8125.24 | 0.537990 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9936.44i | − | 0.654697i | −0.944904 | − | 0.327348i | \(-0.893845\pi\) | ||
0.944904 | − | 0.327348i | \(-0.106155\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2685.87 | 0.176105 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23950.9 | −1.56277 | −0.781383 | − | 0.624051i | \(-0.785486\pi\) | ||||
−0.781383 | + | 0.624051i | \(0.785486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26145.1i | − | 1.69767i | −0.528654 | − | 0.848837i | \(-0.677303\pi\) | ||
0.528654 | − | 0.848837i | \(-0.322697\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1250.74 | 0.0808218 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14500.7 | − | 5067.87i | −0.932517 | − | 0.325907i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11991.7 | 0.767466 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17465.3 | 1.11244 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2820.61 | 0.178800 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6978.35i | 0.440260i | 0.975471 | + | 0.220130i | \(0.0706481\pi\) | ||||
−0.975471 | + | 0.220130i | \(0.929352\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 17626.8i | − | 1.10680i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 5487.85i | − | 0.342958i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16004.8 | − | 12743.6i | −0.995499 | − | 0.792656i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3687.57i | 0.228291i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9353.09 | 0.576326 | 0.288163 | − | 0.957581i | \(-0.406956\pi\) | ||||
0.288163 | + | 0.957581i | \(0.406956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11216.2i | − | 0.687906i | −0.938987 | − | 0.343953i | \(-0.888234\pi\) | ||
0.938987 | − | 0.343953i | \(-0.111766\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3532.70i | 0.215659i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8875.46 | −0.539305 | −0.269653 | − | 0.962958i | \(-0.586909\pi\) | ||||
−0.269653 | + | 0.962958i | \(0.586909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28550.1i | − | 1.72680i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4943.65 | + | 1727.76i | 0.297630 | + | 0.104019i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 12.5387i | − | 0.000751419i | −1.00000 | 0.000375710i | \(-0.999880\pi\) | |||
1.00000 | 0.000375710i | \(-0.000119592\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8034.11i | 0.479265i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8374.90i | − | 0.497315i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −127.456 | −0.00753414 | −0.00376707 | − | 0.999993i | \(-0.501199\pi\) | ||||
−0.00376707 | + | 0.999993i | \(0.501199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18113.0 | 1.06583 | 0.532916 | − | 0.846168i | \(-0.321096\pi\) | ||||
0.532916 | + | 0.846168i | \(0.321096\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3833.76 | 0.224571 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5268.63 | − | 1841.34i | −0.307231 | − | 0.107375i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4983.98 | 0.289326 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5729.67i | 0.331124i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34317.9 | −1.97441 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11689.6 | −0.669540 | −0.334770 | − | 0.942300i | \(-0.608659\pi\) | ||||
−0.334770 | + | 0.942300i | \(0.608659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 3106.27i | − | 0.177126i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16101.4 | 0.914070 | 0.457035 | − | 0.889449i | \(-0.348911\pi\) | ||||
0.457035 | + | 0.889449i | \(0.348911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18014.8 | − | 6296.02i | −1.01818 | − | 0.355845i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12635.8 | 0.711023 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23914.0 | −1.33974 | −0.669870 | − | 0.742478i | \(-0.733650\pi\) | ||||
−0.669870 | + | 0.742478i | \(0.733650\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −621.753 | −0.0346802 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 407.044i | − | 0.0226051i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17782.4i | 0.983247i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27330.4i | 1.50463i | 0.658805 | + | 0.752314i | \(0.271062\pi\) | ||||
−0.658805 | + | 0.752314i | \(0.728938\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3351.66 | − | 9590.11i | 0.183722 | − | 0.525683i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2558.20i | − | 0.139623i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6080.04 | −0.330413 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1841.81i | 0.0996617i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13641.6i | 0.735002i | 0.930023 | + | 0.367501i | \(0.119787\pi\) | ||||
−0.930023 | + | 0.367501i | \(0.880213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12575.3 | 0.674659 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 1289.30i | − | 0.0688765i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10902.4 | + | 31195.1i | −0.579956 | + | 1.65943i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 25345.6i | − | 1.34256i | −0.741205 | − | 0.671278i | \(-0.765746\pi\) | ||
0.741205 | − | 0.671278i | \(-0.234254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3985.43i | − | 0.210219i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4366.23i | − | 0.229336i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11468.8 | 0.599874 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13834.3 | 0.720576 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13143.0 | 0.681715 | 0.340857 | − | 0.940115i | \(-0.389283\pi\) | ||||
0.340857 | + | 0.940115i | \(0.389283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1761.41 | + | 5039.93i | −0.0909826 | + | 0.260328i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14802.9 | 0.761447 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 12377.9i | − | 0.634076i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7313.19 | 0.373083 | 0.186541 | − | 0.982447i | \(-0.440272\pi\) | ||||
0.186541 | + | 0.982447i | \(0.440272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7997.02i | − | 0.404624i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2577.28 | 0.129869 | 0.0649344 | − | 0.997890i | \(-0.479316\pi\) | ||||
0.0649344 | + | 0.997890i | \(0.479316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2022.15 | + | 2539.62i | −0.101480 | + | 0.127449i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9812.00 | 0.490407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5495.97 | −0.273576 | −0.136788 | − | 0.990600i | \(-0.543678\pi\) | ||||
−0.136788 | + | 0.990600i | \(0.543678\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17092.3 | 0.847368 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16818.0i | − | 0.830409i | −0.909728 | − | 0.415204i | \(-0.863710\pi\) | ||
0.909728 | − | 0.415204i | \(-0.136290\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5800.43i | − | 0.285250i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1716.38i | − | 0.0840683i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1787.12 | + | 5113.48i | −0.0871828 | + | 0.249456i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10217.3i | 0.496450i | 0.968702 | + | 0.248225i | \(0.0798472\pi\) | ||||
−0.968702 | + | 0.248225i | \(0.920153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10967.7 | 0.530789 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 137.708i | − | 0.00663802i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2257.96i | − | 0.108411i | −0.998530 | − | 0.0542055i | \(-0.982737\pi\) | ||
0.998530 | − | 0.0542055i | \(-0.0172626\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8469.97 | −0.405060 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 27933.8i | − | 1.33061i | −0.746570 | − | 0.665307i | \(-0.768301\pi\) | ||
0.746570 | − | 0.665307i | \(-0.231699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9069.71 | − | 3169.79i | −0.430335 | − | 0.150399i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 608.336i | − | 0.0287509i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 27940.3i | − | 1.31534i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33790.5i | 1.58455i | 0.610166 | + | 0.792274i | \(0.291103\pi\) | ||||
−0.610166 | + | 0.792274i | \(0.708897\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13257.3 | 0.619259 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18955.5 | 0.881996 | 0.440998 | − | 0.897508i | \(-0.354625\pi\) | ||||
0.440998 | + | 0.897508i | \(0.354625\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10843.7 | −0.502604 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2413.25 | − | 6905.02i | 0.111422 | − | 0.318811i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27107.0 | −1.24674 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 24972.2i | − | 1.14414i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2904.94 | −0.132585 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −610.520 | −0.0277585 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3001.54i | 0.135951i | 0.997687 | + | 0.0679754i | \(0.0216539\pi\) | ||||
−0.997687 | + | 0.0679754i | \(0.978346\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17848.3 | −0.805346 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6731.63 | − | 19261.2i | 0.302591 | − | 0.865803i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33584.9 | −1.50395 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2821.69 | 0.125881 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14068.6 | −0.625265 | −0.312633 | − | 0.949874i | \(-0.601211\pi\) | ||||
−0.312633 | + | 0.949874i | \(0.601211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2918.61i | 0.129228i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7464.64i | − | 0.329276i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56714.7i | 2.49243i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2555.08 | + | 892.978i | 0.111869 | + | 0.0390973i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2206.41i | 0.0962446i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4579.59 | −0.199023 | −0.0995117 | − | 0.995036i | \(-0.531728\pi\) | ||||
−0.0995117 | + | 0.995036i | \(0.531728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28588.1i | − | 1.23781i | −0.785465 | − | 0.618906i | \(-0.787576\pi\) | ||
0.785465 | − | 0.618906i | \(-0.212424\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 25012.8i | − | 1.07901i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5225.34 | 0.224584 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 35653.5i | − | 1.52676i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3280.07 | − | 9385.27i | 0.139945 | − | 0.400425i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13834.8i | 0.588107i | 0.955789 | + | 0.294054i | \(0.0950045\pi\) | ||||
−0.955789 | + | 0.294054i | \(0.904996\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33259.1i | 1.40867i | 0.709866 | + | 0.704337i | \(0.248756\pi\) | ||||
−0.709866 | + | 0.704337i | \(0.751244\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21035.6i | 0.887716i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17593.0 | −0.739744 | −0.369872 | − | 0.929083i | \(-0.620598\pi\) | ||||
−0.369872 | + | 0.929083i | \(0.620598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10912.0 | 0.457164 | 0.228582 | − | 0.973525i | \(-0.426591\pi\) | ||||
0.228582 | + | 0.973525i | \(0.426591\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11766.1 | 0.491170 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4577.56 | − | 5748.97i | 0.190400 | − | 0.239124i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13163.8 | 0.545573 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2544.88i | 0.105094i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24129.6 | −0.992905 | −0.496452 | − | 0.868064i | \(-0.665364\pi\) | ||||
−0.496452 | + | 0.868064i | \(0.665364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12813.3 | 0.525372 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 19395.3i | − | 0.792421i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4292.65 | 0.174759 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14564.7 | + | 41673.9i | −0.590848 | + | 1.69059i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2604.32 | −0.105277 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6098.50 | −0.245657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15204.6 | −0.610310 | −0.305155 | − | 0.952303i | \(-0.598708\pi\) | ||||
−0.305155 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2712.18i | − | 0.108485i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13467.4i | 0.536799i | 0.963308 | + | 0.268400i | \(0.0864948\pi\) | ||||
−0.963308 | + | 0.268400i | \(0.913505\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 796.377i | − | 0.0316322i | −0.999875 | − | 0.0158161i | \(-0.994965\pi\) | ||
0.999875 | − | 0.0158161i | \(-0.00503463\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5201.94 | + | 14884.3i | −0.205902 | + | 0.589147i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 33680.2i | − | 1.32849i | −0.747514 | − | 0.664246i | \(-0.768753\pi\) | ||
0.747514 | − | 0.664246i | \(-0.231247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10008.8 | −0.393422 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 13361.9i | − | 0.523407i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26989.3i | 1.05357i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9602.42 | 0.373554 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9273.61i | − | 0.359524i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4627.37 | − | 13240.3i | 0.178781 | − | 0.511547i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11140.6i | 0.428954i | 0.976729 | + | 0.214477i | \(0.0688047\pi\) | ||||
−0.976729 | + | 0.214477i | \(0.931195\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13785.0i | 0.528960i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2372.73i | 0.0907370i | 0.998970 | + | 0.0453685i | \(0.0144462\pi\) | ||||
−0.998970 | + | 0.0453685i | \(0.985554\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17403.2 | −0.663267 | −0.331634 | − | 0.943408i | \(-0.607600\pi\) | ||||
−0.331634 | + | 0.943408i | \(0.607600\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4433.53 | −0.168397 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31804.3 | 1.20393 | 0.601965 | − | 0.798523i | \(-0.294385\pi\) | ||||
0.601965 | + | 0.798523i | \(0.294385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30412.1 | + | 10628.8i | 1.14734 | + | 0.400987i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4936.78 | 0.185621 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13012.2i | 0.487611i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −434.603 | −0.0162315 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8289.06 | −0.308544 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10140.9i | 0.376217i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6387.51 | −0.236181 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19577.2 | − | 6842.06i | −0.721470 | − | 0.252148i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3085.82 | −0.113344 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1321.37 | −0.0483741 | −0.0241871 | − | 0.999707i | \(-0.507700\pi\) | ||||
−0.0241871 | + | 0.999707i | \(0.507700\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16058.6 | −0.585951 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15070.8i | 0.548098i | 0.961716 | + | 0.274049i | \(0.0883631\pi\) | ||||
−0.961716 | + | 0.274049i | \(0.911637\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11623.3i | 0.421330i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5329.20i | 0.192544i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44522.7 | − | 15560.3i | −1.60335 | − | 0.560357i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 42833.7i | − | 1.53749i | −0.639556 | − | 0.768744i | \(-0.720882\pi\) | ||
0.639556 | − | 0.768744i | \(-0.279118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9653.77 | 0.345388 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 24438.8i | − | 0.871519i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15145.9i | 0.538373i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2594.44 | −0.0919231 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19434.7i | − | 0.686362i | −0.939269 | − | 0.343181i | \(-0.888496\pi\) | ||
0.939269 | − | 0.343181i | \(-0.111504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20408.4 | − | 25631.0i | 0.718429 | − | 0.902278i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23651.0i | 0.829901i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4119.64i | 0.144093i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42125.9i | 1.46872i | 0.678759 | + | 0.734361i | \(0.262518\pi\) | ||||
−0.678759 | + | 0.734361i | \(0.737482\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8011.64 | −0.278435 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1325.03 | 0.0459030 | 0.0229515 | − | 0.999737i | \(-0.492694\pi\) | ||||
0.0229515 | + | 0.999737i | \(0.492694\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13145.8 | 0.453962 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1489.24 | − | 520.478i | −0.0512646 | − | 0.0179166i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42522.6 | −1.45913 | −0.729566 | − | 0.683910i | \(-0.760278\pi\) | ||||
−0.729566 | + | 0.683910i | \(0.760278\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55503.3i | 1.89854i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15015.3 | 0.511991 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30507.0 | −1.03696 | −0.518478 | − | 0.855091i | \(-0.673501\pi\) | ||||
−0.518478 | + | 0.855091i | \(0.673501\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 12782.2i | − | 0.433112i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19672.2 | 0.664486 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1204.20 | − | 3445.57i | 0.0405481 | − | 0.116020i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20907.0 | −0.701790 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2632.31 | −0.0880840 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3708.77 | 0.123720 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15544.9i | − | 0.516950i | −0.966018 | − | 0.258475i | \(-0.916780\pi\) | ||
0.966018 | − | 0.258475i | \(-0.0832199\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6139.59i | 0.203542i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 939.518i | − | 0.0310510i | −0.999879 | − | 0.0155255i | \(-0.995058\pi\) | ||
0.999879 | − | 0.0155255i | \(-0.00494213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14176.8 | + | 4954.67i | 0.467098 | + | 0.163247i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20586.3i | 0.676193i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7969.39 | 0.260966 | 0.130483 | − | 0.991451i | \(-0.458347\pi\) | ||||
0.130483 | + | 0.991451i | \(0.458347\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50550.4i | 1.65025i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4668.89i | − | 0.151953i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35911.0 | 1.16519 | 0.582595 | − | 0.812762i | \(-0.302037\pi\) | ||||
0.582595 | + | 0.812762i | \(0.302037\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10422.1i | 0.337132i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7144.94 | + | 2497.10i | 0.230421 | + | 0.0805303i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17290.5i | 0.555922i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 29077.2i | − | 0.932055i | −0.884770 | − | 0.466027i | \(-0.845685\pi\) | ||
0.884770 | − | 0.466027i | \(-0.154315\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32887.8i | 1.05102i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14047.8 | 0.447583 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18798.3 | −0.597141 | −0.298570 | − | 0.954388i | \(-0.596510\pi\) | ||||
−0.298570 | + | 0.954388i | \(0.596510\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3554.55 | 0.112574 |
(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 | 1344.4.p.d.223.21 | yes | 32 | |
4.3 | odd | 2 | inner | 1344.4.p.d.223.4 | yes | 32 | |
7.6 | odd | 2 | 1344.4.p.c.223.20 | yes | 32 | ||
8.3 | odd | 2 | 1344.4.p.c.223.19 | ✓ | 32 | ||
8.5 | even | 2 | 1344.4.p.c.223.32 | yes | 32 | ||
28.27 | even | 2 | 1344.4.p.c.223.31 | yes | 32 | ||
56.13 | odd | 2 | inner | 1344.4.p.d.223.3 | yes | 32 | |
56.27 | even | 2 | inner | 1344.4.p.d.223.22 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.c.223.19 | ✓ | 32 | 8.3 | odd | 2 | ||
1344.4.p.c.223.20 | yes | 32 | 7.6 | odd | 2 | ||
1344.4.p.c.223.31 | yes | 32 | 28.27 | even | 2 | ||
1344.4.p.c.223.32 | yes | 32 | 8.5 | even | 2 | ||
1344.4.p.d.223.3 | yes | 32 | 56.13 | odd | 2 | inner | |
1344.4.p.d.223.4 | yes | 32 | 4.3 | odd | 2 | inner | |
1344.4.p.d.223.21 | yes | 32 | 1.1 | even | 1 | trivial | |
1344.4.p.d.223.22 | yes | 32 | 56.27 | even | 2 | inner |