Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, 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("784.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −10.0000 | −1.92450 | −0.962250 | − | 0.272166i | \(-0.912260\pi\) | ||||
−0.962250 | + | 0.272166i | \(0.912260\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.00000 | 0.715542 | 0.357771 | − | 0.933809i | \(-0.383537\pi\) | ||||
0.357771 | + | 0.933809i | \(0.383537\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 73.0000 | 2.70370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 40.0000 | 1.09640 | 0.548202 | − | 0.836346i | \(-0.315312\pi\) | ||||
0.548202 | + | 0.836346i | \(0.315312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.0000 | 0.256015 | 0.128008 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128008 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −80.0000 | −1.37706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 58.0000 | 0.827474 | 0.413737 | − | 0.910396i | \(-0.364223\pi\) | ||||
0.413737 | + | 0.910396i | \(0.364223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.0000 | 0.313937 | 0.156969 | − | 0.987604i | \(-0.449828\pi\) | ||||
0.156969 | + | 0.987604i | \(0.449828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 64.0000 | 0.580214 | 0.290107 | − | 0.956994i | \(-0.406309\pi\) | ||||
0.290107 | + | 0.956994i | \(0.406309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −61.0000 | −0.488000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −460.000 | −3.27878 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −62.0000 | −0.397004 | −0.198502 | − | 0.980101i | \(-0.563608\pi\) | ||||
−0.198502 | + | 0.980101i | \(0.563608\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 252.000 | 1.46002 | 0.730009 | − | 0.683438i | \(-0.239516\pi\) | ||||
0.730009 | + | 0.683438i | \(0.239516\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −400.000 | −2.11003 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.0000 | 0.115524 | 0.0577618 | − | 0.998330i | \(-0.481604\pi\) | ||||
0.0577618 | + | 0.998330i | \(0.481604\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −120.000 | −0.492702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.0228547 | −0.0114273 | − | 0.999935i | \(-0.503638\pi\) | ||||
−0.0114273 | + | 0.999935i | \(0.503638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −416.000 | −1.47534 | −0.737668 | − | 0.675164i | \(-0.764073\pi\) | ||||
−0.737668 | + | 0.675164i | \(0.764073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 584.000 | 1.93461 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −396.000 | −1.22899 | −0.614495 | − | 0.788921i | \(-0.710640\pi\) | ||||
−0.614495 | + | 0.788921i | \(0.710640\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −580.000 | −1.59248 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −450.000 | −1.16627 | −0.583134 | − | 0.812376i | \(-0.698174\pi\) | ||||
−0.583134 | + | 0.812376i | \(0.698174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 320.000 | 0.784523 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −260.000 | −0.604173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 274.000 | 0.604606 | 0.302303 | − | 0.953212i | \(-0.402245\pi\) | ||||
0.302303 | + | 0.953212i | \(0.402245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 576.000 | 1.20900 | 0.604502 | − | 0.796604i | \(-0.293372\pi\) | ||||
0.604502 | + | 0.796604i | \(0.293372\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 96.0000 | 0.183190 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 476.000 | 0.867950 | 0.433975 | − | 0.900925i | \(-0.357111\pi\) | ||||
0.433975 | + | 0.900925i | \(0.357111\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −640.000 | −1.11662 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 448.000 | 0.748843 | 0.374421 | − | 0.927259i | \(-0.377841\pi\) | ||||
0.374421 | + | 0.927259i | \(0.377841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 158.000 | 0.253322 | 0.126661 | − | 0.991946i | \(-0.459574\pi\) | ||||
0.126661 | + | 0.991946i | \(0.459574\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 610.000 | 0.939156 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 936.000 | 1.33302 | 0.666508 | − | 0.745498i | \(-0.267788\pi\) | ||||
0.666508 | + | 0.745498i | \(0.267788\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2629.00 | 3.60631 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 530.000 | 0.700904 | 0.350452 | − | 0.936581i | \(-0.386028\pi\) | ||||
0.350452 | + | 0.936581i | \(0.386028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 464.000 | 0.592093 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 620.000 | 0.764034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 390.000 | 0.464493 | 0.232247 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232247 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2520.00 | −2.80980 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 208.000 | 0.224635 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −214.000 | −0.224004 | −0.112002 | − | 0.993708i | \(-0.535726\pi\) | ||||
−0.112002 | + | 0.993708i | \(0.535726\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2920.00 | 2.96435 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1432.00 | −1.41079 | −0.705393 | − | 0.708817i | \(-0.749229\pi\) | ||||
−0.705393 | + | 0.708817i | \(0.749229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 764.000 | 0.730866 | 0.365433 | − | 0.930838i | \(-0.380921\pi\) | ||||
0.365433 | + | 0.930838i | \(0.380921\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −324.000 | −0.292731 | −0.146366 | − | 0.989231i | \(-0.546758\pi\) | ||||
−0.146366 | + | 0.989231i | \(0.546758\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1334.00 | −1.17224 | −0.586119 | − | 0.810225i | \(-0.699345\pi\) | ||||
−0.586119 | + | 0.810225i | \(0.699345\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −260.000 | −0.222325 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1798.00 | 1.49683 | 0.748414 | − | 0.663232i | \(-0.230816\pi\) | ||||
0.748414 | + | 0.663232i | \(0.230816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 512.000 | 0.415167 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 876.000 | 0.692190 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 269.000 | 0.202104 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 60.0000 | 0.0439839 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1488.00 | −1.06473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 384.000 | 0.268303 | 0.134152 | − | 0.990961i | \(-0.457169\pi\) | ||||
0.134152 | + | 0.990961i | \(0.457169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4160.00 | 2.83928 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1814.00 | −1.20985 | −0.604923 | − | 0.796284i | \(-0.706796\pi\) | ||||
−0.604923 | + | 0.796284i | \(0.706796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3680.00 | −2.34610 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1666.00 | 1.03895 | 0.519474 | − | 0.854486i | \(-0.326128\pi\) | ||||
0.519474 | + | 0.854486i | \(0.326128\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1126.00 | 0.687094 | 0.343547 | − | 0.939135i | \(-0.388372\pi\) | ||||
0.343547 | + | 0.939135i | \(0.388372\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3960.00 | 2.36519 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 480.000 | 0.280697 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −496.000 | −0.284073 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2694.00 | 1.48122 | 0.740608 | − | 0.671938i | \(-0.234538\pi\) | ||||
0.740608 | + | 0.671938i | \(0.234538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2648.00 | 1.42709 | 0.713547 | − | 0.700607i | \(-0.247088\pi\) | ||||
0.713547 | + | 0.700607i | \(0.247088\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4234.00 | 2.23725 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2016.00 | 1.04470 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 556.000 | 0.282635 | 0.141317 | − | 0.989964i | \(-0.454866\pi\) | ||||
0.141317 | + | 0.989964i | \(0.454866\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4500.00 | 2.24449 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 328.000 | 0.157613 | 0.0788066 | − | 0.996890i | \(-0.474889\pi\) | ||||
0.0788066 | + | 0.996890i | \(0.474889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3200.00 | −1.50982 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4268.00 | −1.97765 | −0.988826 | − | 0.149077i | \(-0.952370\pi\) | ||||
−0.988826 | + | 0.149077i | \(0.952370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2053.00 | −0.934456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1898.00 | 0.848793 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3476.00 | 1.52760 | 0.763802 | − | 0.645451i | \(-0.223331\pi\) | ||||
0.763802 | + | 0.645451i | \(0.223331\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2740.00 | −1.16357 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2268.00 | −0.947029 | −0.473515 | − | 0.880786i | \(-0.657015\pi\) | ||||
−0.473515 | + | 0.880786i | \(0.657015\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 276.000 | 0.113342 | 0.0566710 | − | 0.998393i | \(-0.481951\pi\) | ||||
0.0566710 | + | 0.998393i | \(0.481951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5760.00 | −2.32673 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 208.000 | 0.0826620 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2320.00 | 0.907247 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3000.00 | 1.13650 | 0.568252 | − | 0.822854i | \(-0.307620\pi\) | ||||
0.568252 | + | 0.822854i | \(0.307620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3278.00 | 1.22257 | 0.611284 | − | 0.791411i | \(-0.290653\pi\) | ||||
0.611284 | + | 0.791411i | \(0.290653\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −960.000 | −0.352549 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2362.00 | −0.854241 | −0.427121 | − | 0.904195i | \(-0.640472\pi\) | ||||
−0.427121 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1036.00 | −0.369046 | −0.184523 | − | 0.982828i | \(-0.559074\pi\) | ||||
−0.184523 | + | 0.982828i | \(0.559074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4760.00 | −1.67037 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −48.0000 | −0.0163535 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4672.00 | 1.56873 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1040.00 | 0.344202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3524.00 | −1.14977 | −0.574887 | − | 0.818233i | \(-0.694954\pi\) | ||||
−0.574887 | + | 0.818233i | \(0.694954\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4480.00 | −1.44115 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3328.00 | −1.05566 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1580.00 | −0.487518 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 696.000 | 0.211846 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1336.00 | −0.401189 | −0.200595 | − | 0.979674i | \(-0.564287\pi\) | ||||
−0.200595 | + | 0.979674i | \(0.564287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4453.00 | −1.31941 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1290.00 | 0.377182 | 0.188591 | − | 0.982056i | \(-0.439608\pi\) | ||||
0.188591 | + | 0.982056i | \(0.439608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5524.00 | −1.59404 | −0.797022 | − | 0.603950i | \(-0.793593\pi\) | ||||
−0.797022 | + | 0.603950i | \(0.793593\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6314.00 | 1.77530 | 0.887648 | − | 0.460523i | \(-0.152338\pi\) | ||||
0.887648 | + | 0.460523i | \(0.152338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3168.00 | −0.879394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9360.00 | −2.56539 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3960.00 | 1.07176 | 0.535881 | − | 0.844294i | \(-0.319980\pi\) | ||||
0.535881 | + | 0.844294i | \(0.319980\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7018.00 | 1.87581 | 0.937903 | − | 0.346898i | \(-0.112765\pi\) | ||||
0.937903 | + | 0.346898i | \(0.112765\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13870.0 | −3.66157 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 312.000 | 0.0803728 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5300.00 | −1.34889 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2394.00 | −0.602024 | −0.301012 | − | 0.953620i | \(-0.597324\pi\) | ||||
−0.301012 | + | 0.953620i | \(0.597324\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2560.00 | 0.636149 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4640.00 | −1.13948 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2766.00 | 0.671355 | 0.335678 | − | 0.941977i | \(-0.391035\pi\) | ||||
0.335678 | + | 0.941977i | \(0.391035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4526.00 | −1.07338 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7968.00 | −1.86817 | −0.934084 | − | 0.357055i | \(-0.883781\pi\) | ||||
−0.934084 | + | 0.357055i | \(0.883781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3600.00 | −0.834514 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3900.00 | −0.893918 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2900.00 | 0.657309 | 0.328654 | − | 0.944450i | \(-0.393405\pi\) | ||||
0.328654 | + | 0.944450i | \(0.393405\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2640.00 | 0.591766 | 0.295883 | − | 0.955224i | \(-0.404386\pi\) | ||||
0.295883 | + | 0.955224i | \(0.404386\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2440.00 | −0.535046 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1522.00 | −0.330138 | −0.165069 | − | 0.986282i | \(-0.552785\pi\) | ||||
−0.165069 | + | 0.986282i | \(0.552785\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18396.0 | 3.94745 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4534.00 | −0.962547 | −0.481274 | − | 0.876570i | \(-0.659826\pi\) | ||||
−0.481274 | + | 0.876570i | \(0.659826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4834.00 | 1.01538 | 0.507688 | − | 0.861541i | \(-0.330500\pi\) | ||||
0.507688 | + | 0.861541i | \(0.330500\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2080.00 | −0.432311 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1549.00 | −0.315286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2140.00 | 0.431096 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4656.00 | 0.928350 | 0.464175 | − | 0.885744i | \(-0.346351\pi\) | ||||
0.464175 | + | 0.885744i | \(0.346351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2192.00 | 0.432621 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18400.0 | −3.59487 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 768.000 | 0.148544 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14320.0 | 2.71506 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4608.00 | 0.865093 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7238.00 | −1.34558 | −0.672792 | − | 0.739831i | \(-0.734905\pi\) | ||||
−0.672792 | + | 0.739831i | \(0.734905\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7640.00 | −1.40655 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1096.00 | 0.199834 | 0.0999171 | − | 0.994996i | \(-0.468142\pi\) | ||||
0.0999171 | + | 0.994996i | \(0.468142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3818.00 | 0.689476 | 0.344738 | − | 0.938699i | \(-0.387968\pi\) | ||||
0.344738 | + | 0.938699i | \(0.387968\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1998.00 | 0.354003 | 0.177001 | − | 0.984211i | \(-0.443360\pi\) | ||||
0.177001 | + | 0.984211i | \(0.443360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2480.00 | −0.435277 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3240.00 | 0.563362 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1508.00 | 0.259775 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −732.000 | −0.124936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13340.0 | 2.25597 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7936.00 | 1.31783 | 0.658915 | − | 0.752217i | \(-0.271016\pi\) | ||||
0.658915 | + | 0.752217i | \(0.271016\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1898.00 | 0.312342 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3808.00 | 0.621055 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2766.00 | 0.447103 | 0.223551 | − | 0.974692i | \(-0.428235\pi\) | ||||
0.223551 | + | 0.974692i | \(0.428235\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17980.0 | −2.88065 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10080.0 | 1.60077 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5120.00 | −0.798990 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8352.00 | −1.29210 | −0.646050 | − | 0.763295i | \(-0.723580\pi\) | ||||
−0.646050 | + | 0.763295i | \(0.723580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5924.00 | 0.908609 | 0.454304 | − | 0.890847i | \(-0.349888\pi\) | ||||
0.454304 | + | 0.890847i | \(0.349888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5520.00 | −0.839418 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2226.00 | −0.335632 | −0.167816 | − | 0.985818i | \(-0.553671\pi\) | ||||
−0.167816 | + | 0.985818i | \(0.553671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3584.00 | 0.535828 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3880.00 | −0.570414 | −0.285207 | − | 0.958466i | \(-0.592062\pi\) | ||||
−0.285207 | + | 0.958466i | \(0.592062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6183.00 | −0.901443 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2690.00 | −0.388949 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1264.00 | 0.181262 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2584.00 | −0.367531 | −0.183765 | − | 0.982970i | \(-0.558829\pi\) | ||||
−0.183765 | + | 0.982970i | \(0.558829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −438.000 | −0.0617923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10534.0 | 1.46228 | 0.731139 | − | 0.682228i | \(-0.238989\pi\) | ||||
0.731139 | + | 0.682228i | \(0.238989\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14880.0 | 2.04907 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −744.000 | −0.101639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4472.00 | 0.606098 | 0.303049 | − | 0.952975i | \(-0.401995\pi\) | ||||
0.303049 | + | 0.952975i | \(0.401995\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3840.00 | −0.516350 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2468.00 | 0.329266 | 0.164633 | − | 0.986355i | \(-0.447356\pi\) | ||||
0.164633 | + | 0.986355i | \(0.447356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30368.0 | −3.98887 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1046.00 | −0.136335 | −0.0681675 | − | 0.997674i | \(-0.521715\pi\) | ||||
−0.0681675 | + | 0.997674i | \(0.521715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3712.00 | 0.480112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18140.0 | 2.32835 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7488.00 | 0.953828 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2124.00 | −0.268515 | −0.134258 | − | 0.990946i | \(-0.542865\pi\) | ||||
−0.134258 | + | 0.990946i | \(0.542865\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11598.0 | 1.44433 | 0.722165 | − | 0.691721i | \(-0.243147\pi\) | ||||
0.722165 | + | 0.691721i | \(0.243147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3024.00 | 0.373787 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21032.0 | 2.58047 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1040.00 | 0.126661 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2770.00 | 0.334884 | 0.167442 | − | 0.985882i | \(-0.446449\pi\) | ||||
0.167442 | + | 0.985882i | \(0.446449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16660.0 | −1.99946 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4240.00 | 0.501526 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11260.0 | −1.32231 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9438.00 | 1.10042 | 0.550211 | − | 0.835026i | \(-0.314547\pi\) | ||||
0.550211 | + | 0.835026i | \(0.314547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5550.00 | 0.642495 | 0.321248 | − | 0.946995i | \(-0.395898\pi\) | ||||
0.321248 | + | 0.946995i | \(0.395898\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28908.0 | −3.32283 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3538.00 | −0.403808 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4800.00 | −0.540201 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3000.00 | 0.335278 | 0.167639 | − | 0.985848i | \(-0.446386\pi\) | ||||
0.167639 | + | 0.985848i | \(0.446386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12926.0 | −1.43460 | −0.717302 | − | 0.696762i | \(-0.754623\pi\) | ||||
−0.717302 | + | 0.696762i | \(0.754623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4960.00 | 0.546698 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1664.00 | 0.182151 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −408.000 | −0.0443571 | −0.0221786 | − | 0.999754i | \(-0.507060\pi\) | ||||
−0.0221786 | + | 0.999754i | \(0.507060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14452.0 | 1.54997 | 0.774983 | − | 0.631982i | \(-0.217758\pi\) | ||||
0.774983 | + | 0.631982i | \(0.217758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3120.00 | 0.332364 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26940.0 | −2.85060 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10258.0 | 1.07818 | 0.539092 | − | 0.842247i | \(-0.318767\pi\) | ||||
0.539092 | + | 0.842247i | \(0.318767\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −240.000 | −0.0250580 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −26480.0 | −2.74644 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5498.00 | −0.562769 | −0.281385 | − | 0.959595i | \(-0.590794\pi\) | ||||
−0.281385 | + | 0.959595i | \(0.590794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26680.0 | −2.71311 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16316.0 | 1.64840 | 0.824199 | − | 0.566300i | \(-0.191625\pi\) | ||||
0.824199 | + | 0.566300i | \(0.191625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8944.00 | −0.897760 | −0.448880 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448880 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20160.0 | −2.01053 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9422.00 | −0.933615 | −0.466807 | − | 0.884359i | \(-0.654596\pi\) | ||||
−0.466807 | + | 0.884359i | \(0.654596\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5560.00 | −0.543931 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16640.0 | −1.61756 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1586.00 | −0.153201 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32850.0 | −3.15325 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13820.0 | 1.31827 | 0.659136 | − | 0.752024i | \(-0.270922\pi\) | ||||
0.659136 | + | 0.752024i | \(0.270922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 312.000 | 0.0295758 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1712.00 | −0.160284 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13264.0 | 1.23419 | 0.617094 | − | 0.786890i | \(-0.288310\pi\) | ||||
0.617094 | + | 0.786890i | \(0.288310\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3280.00 | −0.303327 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5940.00 | 0.545964 | 0.272982 | − | 0.962019i | \(-0.411990\pi\) | ||||
0.272982 | + | 0.962019i | \(0.411990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3596.00 | −0.328511 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23360.0 | 2.12112 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8252.00 | 0.740301 | 0.370151 | − | 0.928972i | \(-0.379306\pi\) | ||||
0.370151 | + | 0.928972i | \(0.379306\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42680.0 | 3.80599 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4704.00 | 0.416980 | 0.208490 | − | 0.978024i | \(-0.433145\pi\) | ||||
0.208490 | + | 0.978024i | \(0.433145\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11456.0 | −1.00948 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20530.0 | 1.79836 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10788.0 | 0.939430 | 0.469715 | − | 0.882818i | \(-0.344357\pi\) | ||||
0.469715 | + | 0.882818i | \(0.344357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11960.0 | −1.02933 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6112.00 | 0.522965 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15840.0 | −1.34747 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34760.0 | −2.93987 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14586.0 | 1.22653 | 0.613267 | − | 0.789876i | \(-0.289855\pi\) | ||||
0.613267 | + | 0.789876i | \(0.289855\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0000 | 0.00217381 | 0.00108690 | − | 0.999999i | \(-0.499654\pi\) | ||||
0.00108690 | + | 0.999999i | \(0.499654\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14616.0 | 1.20813 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8071.00 | −0.663352 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20002.0 | 1.63468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −72.0000 | −0.00585116 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2592.00 | −0.209462 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22680.0 | 1.82256 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11214.0 | 0.891178 | 0.445589 | − | 0.895238i | \(-0.352994\pi\) | ||||
0.445589 | + | 0.895238i | \(0.352994\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2760.00 | −0.218127 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10672.0 | −0.838786 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5424.00 | 0.423973 | 0.211987 | − | 0.977273i | \(-0.432007\pi\) | ||||
0.211987 | + | 0.977273i | \(0.432007\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 42048.0 | 3.26879 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1612.00 | −0.124634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2080.00 | −0.159083 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17618.0 | −1.34021 | −0.670106 | − | 0.742265i | \(-0.733752\pi\) | ||||
−0.670106 | + | 0.742265i | \(0.733752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4992.00 | −0.377709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23200.0 | −1.74600 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3562.00 | −0.266644 | −0.133322 | − | 0.991073i | \(-0.542564\pi\) | ||||
−0.133322 | + | 0.991073i | \(0.542564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14384.0 | 1.07104 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2838.00 | 0.209095 | 0.104548 | − | 0.994520i | \(-0.466661\pi\) | ||||
0.104548 | + | 0.994520i | \(0.466661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 360.000 | 0.0263845 | 0.0131922 | − | 0.999913i | \(-0.495801\pi\) | ||||
0.0131922 | + | 0.999913i | \(0.495801\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30000.0 | −2.18720 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3904.00 | −0.283144 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22018.0 | −1.58860 | −0.794299 | − | 0.607527i | \(-0.792162\pi\) | ||||
−0.794299 | + | 0.607527i | \(0.792162\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32780.0 | −2.35283 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18000.0 | −1.27870 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7008.00 | 0.495291 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1454.00 | 0.102237 | 0.0511184 | − | 0.998693i | \(-0.483721\pi\) | ||||
0.0511184 | + | 0.998693i | \(0.483721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6552.00 | 0.458354 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23620.0 | 1.64399 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13818.0 | −0.956892 | −0.478446 | − | 0.878117i | \(-0.658800\pi\) | ||||
−0.478446 | + | 0.878117i | \(0.658800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10360.0 | 0.710229 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6696.00 | −0.456746 | −0.228373 | − | 0.973574i | \(-0.573341\pi\) | ||||
−0.228373 | + | 0.973574i | \(0.573341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10010.0 | −0.679395 | −0.339698 | − | 0.940535i | \(-0.610325\pi\) | ||||
−0.339698 | + | 0.940535i | \(0.610325\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 34748.0 | 2.34668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2152.00 | 0.144614 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2880.00 | 0.192579 | 0.0962896 | − | 0.995353i | \(-0.469303\pi\) | ||||
0.0962896 | + | 0.995353i | \(0.469303\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4752.00 | −0.314640 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6522.00 | 0.429724 | 0.214862 | − | 0.976644i | \(-0.431070\pi\) | ||||
0.214862 | + | 0.976644i | \(0.431070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 480.000 | 0.0314723 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6614.00 | 0.431555 | 0.215778 | − | 0.976443i | \(-0.430771\pi\) | ||||
0.215778 | + | 0.976443i | \(0.430771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5266.00 | 0.341936 | 0.170968 | − | 0.985277i | \(-0.445311\pi\) | ||||
0.170968 | + | 0.985277i | \(0.445311\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29440.0 | −1.90239 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4279.00 | −0.273856 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10400.0 | −0.662418 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1508.00 | 0.0955928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3344.00 | −0.210971 | −0.105485 | − | 0.994421i | \(-0.533640\pi\) | ||||
−0.105485 | + | 0.994421i | \(0.533640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 35240.0 | 2.21274 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3072.00 | 0.191982 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32704.0 | 2.02465 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4882.00 | −0.300823 | −0.150411 | − | 0.988623i | \(-0.548060\pi\) | ||||
−0.150411 | + | 0.988623i | \(0.548060\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15898.0 | −0.975048 | −0.487524 | − | 0.873110i | \(-0.662100\pi\) | ||||
−0.487524 | + | 0.873110i | \(0.662100\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33280.0 | 2.03163 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6132.00 | 0.372602 | 0.186301 | − | 0.982493i | \(-0.440350\pi\) | ||||
0.186301 | + | 0.982493i | \(0.440350\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10960.0 | 0.662893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24198.0 | −1.45014 | −0.725070 | − | 0.688676i | \(-0.758192\pi\) | ||||
−0.725070 | + | 0.688676i | \(0.758192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14512.0 | −0.865696 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11534.0 | 0.684907 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17456.0 | −1.03185 | −0.515925 | − | 0.856634i | \(-0.672552\pi\) | ||||
−0.515925 | + | 0.856634i | \(0.672552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 656.000 | 0.0386013 | 0.0193006 | − | 0.999814i | \(-0.493856\pi\) | ||||
0.0193006 | + | 0.999814i | \(0.493856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6960.00 | −0.407698 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3968.00 | −0.230347 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13360.0 | 0.772089 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23040.0 | 1.32556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18214.0 | −1.04324 | −0.521618 | − | 0.853179i | \(-0.674671\pi\) | ||||
−0.521618 | + | 0.853179i | \(0.674671\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 28060.0 | 1.60004 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30252.0 | −1.71740 | −0.858699 | − | 0.512480i | \(-0.828727\pi\) | ||||
−0.858699 | + | 0.512480i | \(0.828727\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12900.0 | −0.725887 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10836.0 | 0.607069 | 0.303534 | − | 0.952820i | \(-0.401833\pi\) | ||||
0.303534 | + | 0.952820i | \(0.401833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13328.0 | 0.743411 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 55240.0 | 3.06774 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5400.00 | −0.298583 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9578.00 | 0.527300 | 0.263650 | − | 0.964618i | \(-0.415074\pi\) | ||||
0.263650 | + | 0.964618i | \(0.415074\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9008.00 | 0.491644 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −348.000 | −0.0189117 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −63140.0 | −3.41656 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12442.0 | 0.670368 | 0.335184 | − | 0.942153i | \(-0.391202\pi\) | ||||
0.335184 | + | 0.942153i | \(0.391202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 676.000 | 0.0362672 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31680.0 | 1.69239 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25174.0 | −1.33347 | −0.666734 | − | 0.745295i | \(-0.732308\pi\) | ||||
−0.666734 | + | 0.745295i | \(0.732308\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 68328.0 | 3.60408 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16128.0 | 0.847123 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3840.00 | 0.200850 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39600.0 | −2.06261 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34188.0 | 1.77329 | 0.886646 | − | 0.462448i | \(-0.153029\pi\) | ||||
0.886646 | + | 0.462448i | \(0.153029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −70180.0 | −3.60999 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3782.00 | 0.193738 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5204.00 | −0.265482 | −0.132741 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132741 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 67717.0 | 3.44038 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24128.0 | −1.22080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32880.0 | 1.65682 | 0.828411 | − | 0.560121i | \(-0.189245\pi\) | ||||
0.828411 | + | 0.560121i | \(0.189245\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19040.0 | 0.951625 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3912.00 | 0.194730 | 0.0973648 | − | 0.995249i | \(-0.468959\pi\) | ||||
0.0973648 | + | 0.995249i | \(0.468959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3120.00 | −0.154678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16008.0 | 0.790413 | 0.395206 | − | 0.918592i | \(-0.370673\pi\) | ||||
0.395206 | + | 0.918592i | \(0.370673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21552.0 | 1.05987 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 38690.0 | 1.89504 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9960.00 | −0.483949 | −0.241974 | − | 0.970283i | \(-0.577795\pi\) | ||||
−0.241974 | + | 0.970283i | \(0.577795\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23940.0 | 1.15860 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21184.0 | 1.02115 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12378.0 | 0.594301 | 0.297151 | − | 0.954831i | \(-0.403964\pi\) | ||||
0.297151 | + | 0.954831i | \(0.403964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25600.0 | −1.22427 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34670.0 | −1.65149 | −0.825747 | − | 0.564041i | \(-0.809246\pi\) | ||||
−0.825747 | + | 0.564041i | \(0.809246\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33872.0 | 1.60084 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3288.00 | 0.154789 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10898.0 | 0.511043 | 0.255521 | − | 0.966803i | \(-0.417753\pi\) | ||||
0.255521 | + | 0.966803i | \(0.417753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27660.0 | −1.29202 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25808.0 | 1.20084 | 0.600420 | − | 0.799685i | \(-0.295000\pi\) | ||||
0.600420 | + | 0.799685i | \(0.295000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15372.0 | −0.712488 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −156.000 | −0.00717494 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17920.0 | 0.821035 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28520.0 | 1.30169 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4448.00 | 0.202237 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21054.0 | −0.953614 | −0.476807 | − | 0.879008i | \(-0.658206\pi\) | ||||
−0.476807 | + | 0.879008i | \(0.658206\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 79680.0 | 3.59529 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6912.00 | 0.309524 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36000.0 | 1.60602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24276.0 | 1.07892 | 0.539461 | − | 0.842011i | \(-0.318628\pi\) | ||||
0.539461 | + | 0.842011i | \(0.318628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22968.0 | −1.01696 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28470.0 | 1.25585 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6320.00 | 0.277743 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29000.0 | −1.26499 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21526.0 | 0.935493 | 0.467747 | − | 0.883863i | \(-0.345066\pi\) | ||||
0.467747 | + | 0.883863i | \(0.345066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12806.0 | −0.554475 | −0.277238 | − | 0.960801i | \(-0.589419\pi\) | ||||
−0.277238 | + | 0.960801i | \(0.589419\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26400.0 | −1.13885 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2624.00 | 0.112779 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10816.0 | −0.463163 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13214.0 | 0.561720 | 0.280860 | − | 0.959749i | \(-0.409380\pi\) | ||||
0.280860 | + | 0.959749i | \(0.409380\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32248.0 | −1.36585 | −0.682925 | − | 0.730488i | \(-0.739292\pi\) | ||||
−0.682925 | + | 0.730488i | \(0.739292\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24400.0 | 1.02970 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14316.0 | 0.601954 | 0.300977 | − | 0.953631i | \(-0.402687\pi\) | ||||
0.300977 | + | 0.953631i | \(0.402687\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25168.0 | −1.05443 | −0.527214 | − | 0.849733i | \(-0.676763\pi\) | ||||
−0.527214 | + | 0.849733i | \(0.676763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15220.0 | 0.635350 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34144.0 | −1.41509 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −115920. | −4.78707 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9356.00 | 0.384988 | 0.192494 | − | 0.981298i | \(-0.438342\pi\) | ||||
0.192494 | + | 0.981298i | \(0.438342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20545.0 | −0.842388 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 45340.0 | 1.85242 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16424.0 | −0.668642 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48340.0 | −1.95409 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1664.00 | 0.0670284 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2372.00 | −0.0952119 | −0.0476059 | − | 0.998866i | \(-0.515159\pi\) | ||||
−0.0476059 | + | 0.998866i | \(0.515159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15184.0 | 0.607347 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11694.0 | −0.466114 | −0.233057 | − | 0.972463i | \(-0.574873\pi\) | ||||
−0.233057 | + | 0.972463i | \(0.574873\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20506.0 | −0.814500 | −0.407250 | − | 0.913317i | \(-0.633512\pi\) | ||||
−0.407250 | + | 0.913317i | \(0.633512\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28136.0 | 1.10980 | 0.554902 | − | 0.831916i | \(-0.312756\pi\) | ||||
0.554902 | + | 0.831916i | \(0.312756\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27808.0 | 1.09306 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15490.0 | 0.606768 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37440.0 | 1.46152 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5712.00 | 0.222209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15622.0 | −0.605641 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37070.0 | −1.42733 | −0.713663 | − | 0.700489i | \(-0.752965\pi\) | ||||
−0.713663 | + | 0.700489i | \(0.752965\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −46560.0 | −1.78661 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6198.00 | 0.237021 | 0.118511 | − | 0.992953i | \(-0.462188\pi\) | ||||
0.118511 | + | 0.992953i | \(0.462188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31876.0 | 1.21485 | 0.607425 | − | 0.794377i | \(-0.292202\pi\) | ||||
0.607425 | + | 0.794377i | \(0.292202\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21920.0 | −0.832579 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −132.000 | −0.00499676 | −0.00249838 | − | 0.999997i | \(-0.500795\pi\) | ||||
−0.00249838 | + | 0.999997i | \(0.500795\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 105160. | 3.95398 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10296.0 | −0.385826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18144.0 | −0.677639 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7680.00 | −0.285873 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15624.0 | −0.579632 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26100.0 | −0.965058 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2208.00 | 0.0811010 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38244.0 | −1.40008 | −0.700039 | − | 0.714104i | \(-0.746834\pi\) | ||||
−0.700039 | + | 0.714104i | \(0.746834\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −104536. | −3.81435 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7008.00 | 0.254869 | 0.127434 | − | 0.991847i | \(-0.459326\pi\) | ||||
0.127434 | + | 0.991847i | \(0.459326\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21200.0 | 0.768475 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46080.0 | −1.66487 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36664.0 | −1.31603 | −0.658016 | − | 0.753004i | \(-0.728604\pi\) | ||||
−0.658016 | + | 0.753004i | \(0.728604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 72380.0 | 2.58958 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5376.00 | 0.191715 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1586.00 | −0.0563755 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 55772.0 | 1.97604 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45510.0 | −1.60725 | −0.803625 | − | 0.595136i | \(-0.797098\pi\) | ||||
−0.803625 | + | 0.595136i | \(0.797098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10960.0 | −0.384581 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18560.0 | 0.649173 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3838.00 | 0.133812 | 0.0669061 | − | 0.997759i | \(-0.478687\pi\) | ||||
0.0669061 | + | 0.997759i | \(0.478687\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38180.0 | −1.32690 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16832.0 | 0.583111 | 0.291556 | − | 0.956554i | \(-0.405827\pi\) | ||||
0.291556 | + | 0.956554i | \(0.405827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −384.000 | −0.0132606 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40928.0 | 1.40442 | 0.702208 | − | 0.711972i | \(-0.252198\pi\) | ||||
0.702208 | + | 0.711972i | \(0.252198\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1896.00 | 0.0648543 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19980.0 | −0.681279 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24070.0 | −0.818157 | −0.409079 | − | 0.912499i | \(-0.634150\pi\) | ||||
−0.409079 | + | 0.912499i | \(0.634150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24000.0 | 0.813217 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24800.0 | 0.837691 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33713.0 | 1.13165 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23652.0 | −0.791459 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26224.0 | 0.874798 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17152.0 | 0.570394 | 0.285197 | − | 0.958469i | \(-0.407941\pi\) | ||||
0.285197 | + | 0.958469i | \(0.407941\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15080.0 | −0.499937 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32910.0 | −1.08767 | −0.543837 | − | 0.839191i | \(-0.683029\pi\) | ||||
−0.543837 | + | 0.839191i | \(0.683029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7320.00 | 0.240439 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6822.00 | −0.223393 | −0.111697 | − | 0.993742i | \(-0.535628\pi\) | ||||
−0.111697 | + | 0.993742i | \(0.535628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15600.0 | 0.509273 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −97382.0 | −3.16939 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48420.0 | −1.57107 | −0.785533 | − | 0.618820i | \(-0.787611\pi\) | ||||
−0.785533 | + | 0.618820i | \(0.787611\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18896.0 | −0.611245 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26624.0 | −0.856010 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49216.0 | 1.57760 | 0.788798 | − | 0.614652i | \(-0.210704\pi\) | ||||
0.788798 | + | 0.614652i | \(0.210704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −79360.0 | −2.53617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8288.00 | −0.264068 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35264.0 | −1.12018 | −0.560091 | − | 0.828431i | \(-0.689234\pi\) | ||||
−0.560091 | + | 0.828431i | \(0.689234\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11960.0 | −0.378776 |
(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 | 784.4.a.a.1.1 | 1 | ||
4.3 | odd | 2 | 196.4.a.d.1.1 | 1 | |||
7.6 | odd | 2 | 112.4.a.g.1.1 | 1 | |||
12.11 | even | 2 | 1764.4.a.c.1.1 | 1 | |||
21.20 | even | 2 | 1008.4.a.o.1.1 | 1 | |||
28.3 | even | 6 | 196.4.e.f.177.1 | 2 | |||
28.11 | odd | 6 | 196.4.e.a.177.1 | 2 | |||
28.19 | even | 6 | 196.4.e.f.165.1 | 2 | |||
28.23 | odd | 6 | 196.4.e.a.165.1 | 2 | |||
28.27 | even | 2 | 28.4.a.a.1.1 | ✓ | 1 | ||
56.13 | odd | 2 | 448.4.a.a.1.1 | 1 | |||
56.27 | even | 2 | 448.4.a.p.1.1 | 1 | |||
84.11 | even | 6 | 1764.4.k.m.1549.1 | 2 | |||
84.23 | even | 6 | 1764.4.k.m.361.1 | 2 | |||
84.47 | odd | 6 | 1764.4.k.d.361.1 | 2 | |||
84.59 | odd | 6 | 1764.4.k.d.1549.1 | 2 | |||
84.83 | odd | 2 | 252.4.a.d.1.1 | 1 | |||
140.27 | odd | 4 | 700.4.e.a.449.2 | 2 | |||
140.83 | odd | 4 | 700.4.e.a.449.1 | 2 | |||
140.139 | even | 2 | 700.4.a.n.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.a.a.1.1 | ✓ | 1 | 28.27 | even | 2 | ||
112.4.a.g.1.1 | 1 | 7.6 | odd | 2 | |||
196.4.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
196.4.e.a.165.1 | 2 | 28.23 | odd | 6 | |||
196.4.e.a.177.1 | 2 | 28.11 | odd | 6 | |||
196.4.e.f.165.1 | 2 | 28.19 | even | 6 | |||
196.4.e.f.177.1 | 2 | 28.3 | even | 6 | |||
252.4.a.d.1.1 | 1 | 84.83 | odd | 2 | |||
448.4.a.a.1.1 | 1 | 56.13 | odd | 2 | |||
448.4.a.p.1.1 | 1 | 56.27 | even | 2 | |||
700.4.a.n.1.1 | 1 | 140.139 | even | 2 | |||
700.4.e.a.449.1 | 2 | 140.83 | odd | 4 | |||
700.4.e.a.449.2 | 2 | 140.27 | odd | 4 | |||
784.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1008.4.a.o.1.1 | 1 | 21.20 | even | 2 | |||
1764.4.a.c.1.1 | 1 | 12.11 | even | 2 | |||
1764.4.k.d.361.1 | 2 | 84.47 | odd | 6 | |||
1764.4.k.d.1549.1 | 2 | 84.59 | odd | 6 | |||
1764.4.k.m.361.1 | 2 | 84.23 | even | 6 | |||
1764.4.k.m.1549.1 | 2 | 84.11 | even | 6 |