Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,4,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("400.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\), degree \(1\), not 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: | \(23.6007640023\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.4.c.f.49.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 6.00000i | 1.15470i | 0.816497 | + | 0.577350i | \(0.195913\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 34.0000i | − 1.83583i | −0.396780 | − | 0.917914i | \(-0.629872\pi\) | ||||
0.396780 | − | 0.917914i | \(-0.370128\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.0000 | −0.438562 | −0.219281 | − | 0.975662i | \(-0.570371\pi\) | ||||
−0.219281 | + | 0.975662i | \(0.570371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 58.0000i | 1.23741i | 0.785624 | + | 0.618704i | \(0.212342\pi\) | ||||
−0.785624 | + | 0.618704i | \(0.787658\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 70.0000i | 0.998676i | 0.866407 | + | 0.499338i | \(0.166423\pi\) | ||||
−0.866407 | + | 0.499338i | \(0.833577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.0482980 | 0.0241490 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241490 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 204.000 | 2.11983 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 134.000i | 1.21482i | 0.794387 | + | 0.607412i | \(0.207792\pi\) | ||||
−0.794387 | + | 0.607412i | \(0.792208\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 108.000i | 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 242.000 | 1.54960 | 0.774798 | − | 0.632209i | \(-0.217852\pi\) | ||||
0.774798 | + | 0.632209i | \(0.217852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −100.000 | −0.579372 | −0.289686 | − | 0.957122i | \(-0.593551\pi\) | ||||
−0.289686 | + | 0.957122i | \(0.593551\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 96.0000i | − 0.506408i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 438.000i | 1.94613i | 0.230534 | + | 0.973064i | \(0.425953\pi\) | ||||
−0.230534 | + | 0.973064i | \(0.574047\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −348.000 | −1.42884 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −138.000 | −0.525658 | −0.262829 | − | 0.964842i | \(-0.584656\pi\) | ||||
−0.262829 | + | 0.964842i | \(0.584656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 178.000i | − 0.631273i | −0.948880 | − | 0.315637i | \(-0.897782\pi\) | ||||
0.948880 | − | 0.315637i | \(-0.102218\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22.0000i | 0.0682772i | 0.999417 | + | 0.0341386i | \(0.0108688\pi\) | ||||
−0.999417 | + | 0.0341386i | \(0.989131\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −813.000 | −2.37026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −420.000 | −1.15317 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 162.000i | 0.419857i | 0.977717 | + | 0.209928i | \(0.0673231\pi\) | ||||
−0.977717 | + | 0.209928i | \(0.932677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24.0000i | 0.0557698i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −268.000 | −0.591367 | −0.295683 | − | 0.955286i | \(-0.595547\pi\) | ||||
−0.295683 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 250.000 | 0.524741 | 0.262371 | − | 0.964967i | \(-0.415496\pi\) | ||||
0.262371 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 306.000i | 0.611942i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 422.000i | 0.769485i | 0.923024 | + | 0.384743i | \(0.125710\pi\) | ||||
−0.923024 | + | 0.384743i | \(0.874290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −804.000 | −1.40276 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 852.000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 306.000i | 0.490611i | 0.969446 | + | 0.245305i | \(0.0788882\pi\) | ||||
−0.969446 | + | 0.245305i | \(0.921112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 544.000i | 0.805124i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −456.000 | −0.649418 | −0.324709 | − | 0.945814i | \(-0.605266\pi\) | ||||
−0.324709 | + | 0.945814i | \(0.605266\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −891.000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 434.000i | − 0.573948i | −0.957938 | − | 0.286974i | \(-0.907351\pi\) | ||||
0.957938 | − | 0.286974i | \(-0.0926493\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1452.00i | 1.78932i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 726.000 | 0.864672 | 0.432336 | − | 0.901712i | \(-0.357689\pi\) | ||||
0.432336 | + | 0.901712i | \(0.357689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1972.00 | 2.27167 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 600.000i | − 0.669001i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1378.00i | − 1.44242i | −0.692717 | − | 0.721210i | \(-0.743586\pi\) | ||||
0.692717 | − | 0.721210i | \(-0.256414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 144.000 | 0.146187 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 126.000 | 0.124133 | 0.0620667 | − | 0.998072i | \(-0.480231\pi\) | ||||
0.0620667 | + | 0.998072i | \(0.480231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1262.00i | 1.20727i | 0.797262 | + | 0.603634i | \(0.206281\pi\) | ||||
−0.797262 | + | 0.603634i | \(0.793719\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 510.000i | 0.460781i | 0.973098 | + | 0.230390i | \(0.0740003\pi\) | ||||
−0.973098 | + | 0.230390i | \(0.926000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −26.0000 | −0.0228472 | −0.0114236 | − | 0.999935i | \(-0.503636\pi\) | ||||
−0.0114236 | + | 0.999935i | \(0.503636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2628.00 | −2.24720 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1242.00i | 1.03396i | 0.855997 | + | 0.516980i | \(0.172944\pi\) | ||||
−0.855997 | + | 0.516980i | \(0.827056\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 522.000i | − 0.412469i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2380.00 | 1.83340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1075.00 | −0.807663 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 828.000i | − 0.606978i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 978.000i | − 0.683334i | −0.939821 | − | 0.341667i | \(-0.889008\pi\) | ||||
0.939821 | − | 0.341667i | \(-0.110992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1068.00 | 0.728931 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 912.000 | 0.608258 | 0.304129 | − | 0.952631i | \(-0.401635\pi\) | ||||
0.304129 | + | 0.952631i | \(0.401635\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 136.000i | − 0.0886669i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 926.000i | 0.577471i | 0.957409 | + | 0.288735i | \(0.0932348\pi\) | ||||
−0.957409 | + | 0.288735i | \(0.906765\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 516.000 | 0.314867 | 0.157434 | − | 0.987530i | \(-0.449678\pi\) | ||||
0.157434 | + | 0.987530i | \(0.449678\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −132.000 | −0.0788398 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 928.000i | − 0.542680i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 4878.00i | − 2.73694i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 958.000 | 0.526728 | 0.263364 | − | 0.964697i | \(-0.415168\pi\) | ||||
0.263364 | + | 0.964697i | \(0.415168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −332.000 | −0.178926 | −0.0894628 | − | 0.995990i | \(-0.528515\pi\) | ||||
−0.0894628 | + | 0.995990i | \(0.528515\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 630.000i | − 0.332892i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1022.00i | 0.519519i | 0.965673 | + | 0.259759i | \(0.0836433\pi\) | ||||
−0.965673 | + | 0.259759i | \(0.916357\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −972.000 | −0.484809 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4556.00 | 2.23021 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 926.000i | 0.444969i | 0.974936 | + | 0.222484i | \(0.0714166\pi\) | ||||
−0.974936 | + | 0.222484i | \(0.928583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 654.000i | 0.303042i | 0.988454 | + | 0.151521i | \(0.0484171\pi\) | ||||
−0.988454 | + | 0.151521i | \(0.951583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1167.00 | −0.531179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −36.0000 | −0.0160993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1294.00i | − 0.568676i | −0.958724 | − | 0.284338i | \(-0.908226\pi\) | ||||
0.958724 | − | 0.284338i | \(-0.0917738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1608.00i | − 0.682851i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2836.00 | −1.18420 | −0.592102 | − | 0.805863i | \(-0.701702\pi\) | ||||
−0.592102 | + | 0.805863i | \(0.701702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1742.00 | 0.715369 | 0.357685 | − | 0.933842i | \(-0.383566\pi\) | ||||
0.357685 | + | 0.933842i | \(0.383566\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1500.00i | 0.605919i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1120.00i | − 0.437981i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3672.00 | 1.41322 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4460.00 | −1.68960 | −0.844802 | − | 0.535079i | \(-0.820282\pi\) | ||||
−0.844802 | + | 0.535079i | \(0.820282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 3782.00i | − 1.41054i | −0.708939 | − | 0.705270i | \(-0.750826\pi\) | ||||
0.708939 | − | 0.705270i | \(-0.249174\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4474.00i | − 1.61807i | −0.587762 | − | 0.809034i | \(-0.699991\pi\) | ||||
0.587762 | − | 0.809034i | \(-0.300009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3608.00 | 1.28525 | 0.642624 | − | 0.766182i | \(-0.277846\pi\) | ||||
0.642624 | + | 0.766182i | \(0.277846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2532.00 | −0.888525 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8228.00i | − 2.84479i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1206.00i | − 0.404941i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −64.0000 | −0.0211817 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 256.000 | 0.0835250 | 0.0417625 | − | 0.999128i | \(-0.486703\pi\) | ||||
0.0417625 | + | 0.999128i | \(0.486703\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5112.00i | 1.64445i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3400.00i | 1.06363i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1836.00 | −0.566509 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4060.00 | −1.23577 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5158.00i | 1.54890i | 0.632634 | + | 0.774451i | \(0.281974\pi\) | ||||
−0.632634 | + | 0.774451i | \(0.718026\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2226.00i | − 0.650858i | −0.945566 | − | 0.325429i | \(-0.894491\pi\) | ||||
0.945566 | − | 0.325429i | \(-0.105509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2086.00 | −0.601951 | −0.300975 | − | 0.953632i | \(-0.597312\pi\) | ||||
−0.300975 | + | 0.953632i | \(0.597312\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3264.00 | −0.929677 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 5718.00i | − 1.60772i | −0.594819 | − | 0.803860i | \(-0.702776\pi\) | ||||
0.594819 | − | 0.803860i | \(-0.297224\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2736.00i | − 0.749883i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3624.00 | −0.980825 | −0.490412 | − | 0.871491i | \(-0.663154\pi\) | ||||
−0.490412 | + | 0.871491i | \(0.663154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −82.0000 | −0.0219174 | −0.0109587 | − | 0.999940i | \(-0.503488\pi\) | ||||
−0.0109587 | + | 0.999940i | \(0.503488\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2430.00i | − 0.641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 232.000i | 0.0597644i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2604.00 | 0.662738 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5040.00 | 1.26742 | 0.633709 | − | 0.773571i | \(-0.281532\pi\) | ||||
0.633709 | + | 0.773571i | \(0.281532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2144.00i | − 0.532775i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2310.00i | 0.560676i | 0.959901 | + | 0.280338i | \(0.0904466\pi\) | ||||
−0.959901 | + | 0.280338i | \(0.909553\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14892.0 | 3.57276 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2178.00 | −0.516532 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4110.00i | 0.963625i | 0.876274 | + | 0.481813i | \(0.160021\pi\) | ||||
−0.876274 | + | 0.481813i | \(0.839979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4356.00i | 0.998438i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −746.000 | −0.169087 | −0.0845435 | − | 0.996420i | \(-0.526943\pi\) | ||||
−0.0845435 | + | 0.996420i | \(0.526943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4596.00 | 1.03021 | 0.515105 | − | 0.857127i | \(-0.327753\pi\) | ||||
0.515105 | + | 0.857127i | \(0.327753\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11832.0i | 2.62310i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2206.00i | 0.478504i | 0.970957 | + | 0.239252i | \(0.0769023\pi\) | ||||
−0.970957 | + | 0.239252i | \(0.923098\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 900.000 | 0.193124 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8278.00 | 1.75738 | 0.878691 | − | 0.477392i | \(-0.158418\pi\) | ||||
0.878691 | + | 0.477392i | \(0.158418\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1178.00i | − 0.247438i | −0.992317 | − | 0.123719i | \(-0.960518\pi\) | ||||
0.992317 | − | 0.123719i | \(-0.0394821\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4692.00i | 0.965017i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.00264604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8268.00 | 1.66556 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 106.000i | 0.0211351i | 0.999944 | + | 0.0105676i | \(0.00336382\pi\) | ||||
−0.999944 | + | 0.0105676i | \(0.996636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1728.00i | − 0.337605i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7772.00 | −1.50323 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6052.00 | −1.15891 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 756.000i | 0.143337i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8134.00i | 1.51216i | 0.654482 | + | 0.756078i | \(0.272887\pi\) | ||||
−0.654482 | + | 0.756078i | \(0.727113\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7572.00 | −1.39403 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4396.00 | 0.801525 | 0.400763 | − | 0.916182i | \(-0.368745\pi\) | ||||
0.400763 | + | 0.916182i | \(0.368745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4826.00i | 0.871507i | 0.900066 | + | 0.435753i | \(0.143518\pi\) | ||||
−0.900066 | + | 0.435753i | \(0.856482\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7026.00i | − 1.24486i | −0.782677 | − | 0.622428i | \(-0.786146\pi\) | ||||
0.782677 | − | 0.622428i | \(-0.213854\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3872.00 | −0.679594 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3060.00 | −0.532064 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 280.000i | 0.0482341i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 156.000i | − 0.0263817i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 748.000 | 0.125345 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8808.00 | −1.46263 | −0.731316 | − | 0.682038i | \(-0.761094\pi\) | ||||
−0.731316 | + | 0.682038i | \(0.761094\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3942.00i | − 0.648710i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 5602.00i | − 0.905520i | −0.891632 | − | 0.452760i | \(-0.850439\pi\) | ||||
0.891632 | − | 0.452760i | \(-0.149561\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7452.00 | −1.19391 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1600.00 | 0.254090 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15980.0i | 2.51557i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6634.00i | − 1.02632i | −0.858294 | − | 0.513158i | \(-0.828475\pi\) | ||||
0.858294 | − | 0.513158i | \(-0.171525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3198.00 | −0.490501 | −0.245251 | − | 0.969460i | \(-0.578870\pi\) | ||||
−0.245251 | + | 0.969460i | \(0.578870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6264.00 | −0.952557 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 5230.00i | − 0.788569i | −0.918988 | − | 0.394284i | \(-0.870992\pi\) | ||||
0.918988 | − | 0.394284i | \(-0.129008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14280.0i | 2.11702i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −312.000 | −0.0458683 | −0.0229342 | − | 0.999737i | \(-0.507301\pi\) | ||||
−0.0229342 | + | 0.999737i | \(0.507301\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6843.00 | −0.997667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 6450.00i | − 0.932609i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10790.0i | 1.53470i | 0.641231 | + | 0.767348i | \(0.278424\pi\) | ||||
−0.641231 | + | 0.767348i | \(0.721576\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1242.00 | 0.175219 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5508.00 | 0.770785 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4190.00i | − 0.581635i | −0.956778 | − | 0.290818i | \(-0.906073\pi\) | ||||
0.956778 | − | 0.290818i | \(-0.0939273\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14036.0i | 1.91748i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6980.00 | −0.946012 | −0.473006 | − | 0.881059i | \(-0.656831\pi\) | ||||
−0.473006 | + | 0.881059i | \(0.656831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5868.00 | 0.789047 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 13962.0i | − 1.86273i | −0.364089 | − | 0.931364i | \(-0.618620\pi\) | ||||
0.364089 | − | 0.931364i | \(-0.381380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1602.00i | 0.210424i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3810.00 | −0.496593 | −0.248296 | − | 0.968684i | \(-0.579871\pi\) | ||||
−0.248296 | + | 0.968684i | \(0.579871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9380.00 | −1.21321 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5472.00i | 0.702356i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9158.00i | 1.15775i | 0.815416 | + | 0.578875i | \(0.196508\pi\) | ||||
−0.815416 | + | 0.578875i | \(0.803492\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 816.000 | 0.102384 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4866.00 | 0.605976 | 0.302988 | − | 0.952994i | \(-0.402016\pi\) | ||||
0.302988 | + | 0.952994i | \(0.402016\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5800.00i | − 0.716920i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 7008.00i | − 0.853498i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13486.0 | −1.63042 | −0.815208 | − | 0.579169i | \(-0.803377\pi\) | ||||
−0.815208 | + | 0.579169i | \(0.803377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5556.00 | −0.666806 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9112.00i | 1.08565i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3096.00i | 0.363577i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5628.00 | 0.656195 | 0.328098 | − | 0.944644i | \(-0.393593\pi\) | ||||
0.328098 | + | 0.944644i | \(0.393593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7938.00 | 0.918942 | 0.459471 | − | 0.888193i | \(-0.348039\pi\) | ||||
0.459471 | + | 0.888193i | \(0.348039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 198.000i | − 0.0227591i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 8500.00i | − 0.963334i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5568.00 | 0.626633 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1916.00 | −0.214131 | −0.107066 | − | 0.994252i | \(-0.534145\pi\) | ||||
−0.107066 | + | 0.994252i | \(0.534145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 16510.0i | − 1.83238i | −0.400746 | − | 0.916189i | \(-0.631249\pi\) | ||||
0.400746 | − | 0.916189i | \(-0.368751\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 536.000i | 0.0586736i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1256.00 | −0.136550 | −0.0682752 | − | 0.997667i | \(-0.521750\pi\) | ||||
−0.0682752 | + | 0.997667i | \(0.521750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7317.00 | 0.790087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12222.0i | 1.31080i | 0.755282 | + | 0.655400i | \(0.227500\pi\) | ||||
−0.755282 | + | 0.655400i | \(0.772500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5748.00i | 0.608213i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5946.00 | 0.624965 | 0.312482 | − | 0.949924i | \(-0.398840\pi\) | ||||
0.312482 | + | 0.949924i | \(0.398840\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2208.00 | 0.230534 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1992.00i | − 0.206606i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1258.00i | − 0.128768i | −0.997925 | − | 0.0643838i | \(-0.979492\pi\) | ||||
0.997925 | − | 0.0643838i | \(-0.0205082\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7560.00 | −0.768781 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16422.0 | 1.65911 | 0.829554 | − | 0.558426i | \(-0.188595\pi\) | ||||
0.829554 | + | 0.558426i | \(0.188595\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2658.00i | − 0.266799i | −0.991062 | − | 0.133399i | \(-0.957411\pi\) | ||||
0.991062 | − | 0.133399i | \(-0.0425893\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3686.00i | 0.365241i | 0.983183 | + | 0.182621i | \(0.0584580\pi\) | ||||
−0.983183 | + | 0.182621i | \(0.941542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14348.0 | 1.41264 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6132.00 | −0.599889 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2848.00i | 0.276852i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1458.00i | − 0.139952i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 88.0000 | 0.00839420 | 0.00419710 | − | 0.999991i | \(-0.498664\pi\) | ||||
0.00419710 | + | 0.999991i | \(0.498664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25404.0 | −2.40816 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27336.0i | 2.57522i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 14714.0i | − 1.36911i | −0.728963 | − | 0.684553i | \(-0.759997\pi\) | ||||
0.728963 | − | 0.684553i | \(-0.240003\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5556.00 | −0.513806 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7344.00 | 0.675010 | 0.337505 | − | 0.941324i | \(-0.390417\pi\) | ||||
0.337505 | + | 0.941324i | \(0.390417\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16940.0i | 1.54754i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 28968.0i | − 2.61447i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1604.00 | 0.143898 | 0.0719488 | − | 0.997408i | \(-0.477078\pi\) | ||||
0.0719488 | + | 0.997408i | \(0.477078\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3924.00 | −0.349923 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 14802.0i | − 1.31210i | −0.754715 | − | 0.656052i | \(-0.772225\pi\) | ||||
0.754715 | − | 0.656052i | \(-0.227775\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 7002.00i | − 0.613353i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22514.0 | 1.96054 | 0.980271 | − | 0.197660i | \(-0.0633342\pi\) | ||||
0.980271 | + | 0.197660i | \(0.0633342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10404.0 | 0.900677 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 432.000i | 0.0371799i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 352.000i | − 0.0299438i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7764.00 | 0.656651 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6710.00 | −0.564243 | −0.282121 | − | 0.959379i | \(-0.591038\pi\) | ||||
−0.282121 | + | 0.959379i | \(0.591038\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7930.00i | − 0.663011i | −0.943453 | − | 0.331505i | \(-0.892443\pi\) | ||||
0.943453 | − | 0.331505i | \(-0.107557\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 7000.00i | − 0.578605i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5789.00 | −0.475795 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2412.00 | 0.197122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 8004.00i | − 0.650454i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 17016.0i | − 1.36740i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13008.0 | 1.03951 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4918.00 | 0.390834 | 0.195417 | − | 0.980720i | \(-0.437394\pi\) | ||||
0.195417 | + | 0.980720i | \(0.437394\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10452.0i | 0.826037i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3922.00i | − 0.306568i | −0.988182 | − | 0.153284i | \(-0.951015\pi\) | ||||
0.988182 | − | 0.153284i | \(-0.0489849\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2250.00 | −0.174914 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 968.000 | 0.0748424 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15504.0i | 1.19222i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 17786.0i | − 1.35299i | −0.736446 | − | 0.676496i | \(-0.763497\pi\) | ||||
0.736446 | − | 0.676496i | \(-0.236503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10324.0 | 0.781143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6720.00 | 0.505737 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 20266.0i | − 1.51707i | −0.651633 | − | 0.758535i | \(-0.725916\pi\) | ||||
0.651633 | − | 0.758535i | \(-0.274084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30294.0i | 2.24379i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13358.0 | −0.984177 | −0.492088 | − | 0.870545i | \(-0.663766\pi\) | ||||
−0.492088 | + | 0.870545i | \(0.663766\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16360.0 | −1.19903 | −0.599514 | − | 0.800364i | \(-0.704639\pi\) | ||||
−0.599514 | + | 0.800364i | \(0.704639\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 26760.0i | − 1.95099i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15574.0i | 1.12366i | 0.827251 | + | 0.561832i | \(0.189903\pi\) | ||||
−0.827251 | + | 0.561832i | \(0.810097\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22692.0 | 1.62875 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14756.0 | −1.05367 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2592.00i | − 0.184133i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6654.00i | 0.467870i | 0.972252 | + | 0.233935i | \(0.0751604\pi\) | ||||
−0.972252 | + | 0.233935i | \(0.924840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −400.000 | −0.0279825 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26844.0 | 1.86838 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 17742.0i | − 1.22863i | −0.789062 | − | 0.614314i | \(-0.789433\pi\) | ||||
0.789062 | − | 0.614314i | \(-0.210567\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21648.0i | 1.48408i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15840.0 | 1.08048 | 0.540238 | − | 0.841512i | \(-0.318334\pi\) | ||||
0.540238 | + | 0.841512i | \(0.318334\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3002.00 | −0.203751 | −0.101875 | − | 0.994797i | \(-0.532484\pi\) | ||||
−0.101875 | + | 0.994797i | \(0.532484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3798.00i | − 0.256495i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 23610.0i | − 1.57875i | −0.613912 | − | 0.789374i | \(-0.710405\pi\) | ||||
0.613912 | − | 0.789374i | \(-0.289595\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 49368.0 | 3.28488 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1276.00 | −0.0844868 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23850.0i | 1.57144i | 0.618583 | + | 0.785720i | \(0.287707\pi\) | ||||
−0.618583 | + | 0.785720i | \(0.712293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5334.00i | 0.348037i | 0.984742 | + | 0.174018i | \(0.0556752\pi\) | ||||
−0.984742 | + | 0.174018i | \(0.944325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2164.00 | −0.140515 | −0.0702573 | − | 0.997529i | \(-0.522382\pi\) | ||||
−0.0702573 | + | 0.997529i | \(0.522382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14472.0 | −0.935171 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 24684.0i | − 1.58739i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 384.000i | − 0.0244585i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30660.0 | −1.94355 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25220.0 | 1.59111 | 0.795557 | − | 0.605879i | \(-0.207179\pi\) | ||||
0.795557 | + | 0.605879i | \(0.207179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1536.00i | 0.0964463i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 47154.0i | − 2.93298i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7668.00 | −0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12306.0 | −0.758280 | −0.379140 | − | 0.925339i | \(-0.623780\pi\) | ||||
−0.379140 | + | 0.925339i | \(0.623780\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27414.0i | 1.68134i | 0.541547 | + | 0.840671i | \(0.317839\pi\) | ||||
−0.541547 | + | 0.840671i | \(0.682161\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 21834.0i | − 1.32671i | −0.748304 | − | 0.663356i | \(-0.769131\pi\) | ||||
0.748304 | − | 0.663356i | \(-0.230869\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4288.00 | 0.259351 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20400.0 | −1.22817 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 23998.0i | − 1.43815i | −0.694931 | − | 0.719077i | \(-0.744565\pi\) | ||||
0.694931 | − | 0.719077i | \(-0.255435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 2754.00i | − 0.163537i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32004.0 | −1.89180 | −0.945902 | − | 0.324452i | \(-0.894820\pi\) | ||||
−0.945902 | + | 0.324452i | \(0.894820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8526.00 | −0.501699 | −0.250849 | − | 0.968026i | \(-0.580710\pi\) | ||||
−0.250849 | + | 0.968026i | \(0.580710\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 24360.0i | − 1.42694i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32428.0i | 1.88248i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30948.0 | −1.78852 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4000.00 | −0.230132 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8178.00i | 0.468408i | 0.972187 | + | 0.234204i | \(0.0752484\pi\) | ||||
−0.972187 | + | 0.234204i | \(0.924752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16646.0i | 0.944989i | 0.881334 | + | 0.472495i | \(0.156646\pi\) | ||||
−0.881334 | + | 0.472495i | \(0.843354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −46852.0 | −2.64803 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13356.0 | 0.751546 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22446.0i | 1.25750i | 0.777608 | + | 0.628750i | \(0.216433\pi\) | ||||
−0.777608 | + | 0.628750i | \(0.783567\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 12516.0i | − 0.695073i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9396.00 | −0.519534 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35336.0 | −1.94536 | −0.972681 | − | 0.232147i | \(-0.925425\pi\) | ||||
−0.972681 | + | 0.232147i | \(0.925425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 4896.00i | − 0.268375i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 9660.00i | − 0.524962i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34308.0 | 1.85643 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3482.00 | 0.187608 | 0.0938041 | − | 0.995591i | \(-0.470097\pi\) | ||||
0.0938041 | + | 0.995591i | \(0.470097\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1752.00i | 0.0939942i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4284.00i | − 0.227887i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19402.0 | 1.02773 | 0.513863 | − | 0.857872i | \(-0.328214\pi\) | ||||
0.513863 | + | 0.857872i | \(0.328214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4104.00 | 0.216473 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 13400.0i | − 0.703834i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 21744.0i | − 1.13256i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9896.00 | −0.513294 | −0.256647 | − | 0.966505i | \(-0.582618\pi\) | ||||
−0.256647 | + | 0.966505i | \(0.582618\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42908.0 | 2.21633 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 492.000i | − 0.0253080i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 494.000i | 0.0252014i | 0.999921 | + | 0.0126007i | \(0.00401104\pi\) | ||||
−0.999921 | + | 0.0126007i | \(0.995989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9477.00 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12460.0 | 0.630437 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9282.00i | 0.467720i | 0.972270 | + | 0.233860i | \(0.0751357\pi\) | ||||
−0.972270 | + | 0.233860i | \(0.924864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 6752.00i | − 0.337467i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3252.00 | −0.161877 | −0.0809383 | − | 0.996719i | \(-0.525792\pi\) | ||||
−0.0809383 | + | 0.996719i | \(0.525792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1392.00 | −0.0690100 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4710.00i | 0.232561i | 0.993216 | + | 0.116281i | \(0.0370972\pi\) | ||||
−0.993216 | + | 0.116281i | \(0.962903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3906.00i | 0.191316i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17340.0 | 0.845914 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25764.0 | −1.25185 | −0.625927 | − | 0.779882i | \(-0.715279\pi\) | ||||
−0.625927 | + | 0.779882i | \(0.715279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30240.0i | 1.46349i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30094.0i | 1.44489i | 0.691426 | + | 0.722447i | \(0.256983\pi\) | ||||
−0.691426 | + | 0.722447i | \(0.743017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12864.0 | 0.615196 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22362.0 | 1.06521 | 0.532603 | − | 0.846365i | \(-0.321214\pi\) | ||||
0.532603 | + | 0.846365i | \(0.321214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 884.000i | 0.0419436i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 15544.0i | − 0.731762i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30398.0 | 1.42546 | 0.712731 | − | 0.701438i | \(-0.247458\pi\) | ||||
0.712731 | + | 0.701438i | \(0.247458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13860.0 | −0.647413 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1290.00i | 0.0600234i | 0.999550 | + | 0.0300117i | \(0.00955445\pi\) | ||||
−0.999550 | + | 0.0300117i | \(0.990446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 89352.0i | 4.12546i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −552.000 | −0.0253883 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13632.0 | −0.624573 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26136.0i | 1.19288i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0000i | 0 0.000634112i | 1.00000 | 0.000317056i | \(0.000100922\pi\) | |||||
−1.00000 | 0.000317056i | \(0.999899\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24660.0 | −1.11270 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42228.0 | 1.89817 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14500.0i | 0.649319i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38814.0i | 1.72505i | 0.506017 | + | 0.862523i | \(0.331117\pi\) | ||||
−0.506017 | + | 0.862523i | \(0.668883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1540.00 | −0.0681868 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6534.00 | −0.288224 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4896.00i | − 0.215163i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 4476.00i | − 0.195245i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27402.0 | −1.19086 | −0.595428 | − | 0.803408i | \(-0.703018\pi\) | ||||
−0.595428 | + | 0.803408i | \(0.703018\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28576.0 | 1.23729 | 0.618643 | − | 0.785672i | \(-0.287683\pi\) | ||||
0.618643 | + | 0.785672i | \(0.287683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27576.0i | 1.18958i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 712.000i | − 0.0304893i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17748.0 | −0.757223 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31762.0 | 1.35018 | 0.675092 | − | 0.737733i | \(-0.264104\pi\) | ||||
0.675092 | + | 0.737733i | \(0.264104\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 20506.0i | − 0.868523i | −0.900787 | − | 0.434261i | \(-0.857009\pi\) | ||||
0.900787 | − | 0.434261i | \(-0.142991\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13014.0i | 0.547208i | 0.961842 | + | 0.273604i | \(0.0882158\pi\) | ||||
−0.961842 | + | 0.273604i | \(0.911784\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22790.0 | 0.954800 | 0.477400 | − | 0.878686i | \(-0.341579\pi\) | ||||
0.477400 | + | 0.878686i | \(0.341579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13236.0 | −0.552529 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 56910.0i | − 2.36712i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 10800.0i | − 0.446001i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23696.0 | 0.975062 | 0.487531 | − | 0.873106i | \(-0.337898\pi\) | ||||
0.487531 | + | 0.873106i | \(0.337898\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34175.0 | 1.40125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 49668.0i | 2.02925i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36550.0i | 1.48273i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7068.00 | 0.285716 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58692.0 | −2.36420 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5306.00i | 0.212982i | 0.994314 | + | 0.106491i | \(0.0339616\pi\) | ||||
−0.994314 | + | 0.106491i | \(0.966038\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21054.0i | 0.839196i | 0.907710 | + | 0.419598i | \(0.137829\pi\) | ||||
−0.907710 | + | 0.419598i | \(0.862171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7364.00 | 0.292499 | 0.146249 | − | 0.989248i | \(-0.453280\pi\) | ||||
0.146249 | + | 0.989248i | \(0.453280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28152.0 | −1.11431 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 17226.0i | − 0.679467i | −0.940522 | − | 0.339733i | \(-0.889663\pi\) | ||||
0.940522 | − | 0.339733i | \(-0.110337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 78.0000i | 0.00305539i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7296.00 | 0.284810 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24476.0 | −0.952167 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12402.0i | 0.480807i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 21202.0i | − 0.816352i | −0.912903 | − | 0.408176i | \(-0.866165\pi\) | ||||
0.912903 | − | 0.408176i | \(-0.133835\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −636.000 | −0.0244047 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29490.0 | −1.12774 | −0.563872 | − | 0.825862i | \(-0.690689\pi\) | ||||
−0.563872 | + | 0.825862i | \(0.690689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2570.00i | − 0.0979472i | −0.998800 | − | 0.0489736i | \(-0.984405\pi\) | ||||
0.998800 | − | 0.0489736i | \(-0.0155950\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36334.0i | 1.37540i | 0.725997 | + | 0.687698i | \(0.241379\pi\) | ||||
−0.725997 | + | 0.687698i | \(0.758621\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33252.0 | −1.25448 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14256.0 | 0.536020 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 88.0000i | 0.00329766i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 46632.0i | − 1.73578i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24200.0 | −0.897792 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11340.0 | −0.419301 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 36312.0i | − 1.33819i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 12474.0i | − 0.456662i | −0.973584 | − | 0.228331i | \(-0.926673\pi\) | ||||
0.973584 | − | 0.228331i | \(-0.0733268\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1134.00 | −0.0413778 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41132.0 | 1.49590 | 0.747949 | − | 0.663756i | \(-0.231039\pi\) | ||||
0.747949 | + | 0.663756i | \(0.231039\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6944.00i | 0.251712i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 31008.0i | − 1.11666i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38416.0 | −1.37892 | −0.689460 | − | 0.724324i | \(-0.742152\pi\) | ||||
−0.689460 | + | 0.724324i | \(0.742152\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48804.0 | −1.74609 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49416.0i | 1.76224i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 11358.0i | − 0.402423i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41302.0 | −1.45864 | −0.729319 | − | 0.684174i | \(-0.760163\pi\) | ||||
−0.729319 | + | 0.684174i | \(0.760163\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3252.00 | −0.114479 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26376.0i | 0.925521i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26150.0i | 0.911722i | 0.890051 | + | 0.455861i | \(0.150669\pi\) | ||||
−0.890051 | + | 0.455861i | \(0.849331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28956.0 | −1.00633 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35254.0 | 1.22130 | 0.610652 | − | 0.791899i | \(-0.290907\pi\) | ||||
0.610652 | + | 0.791899i | \(0.290907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 18492.0i | − 0.638582i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18550.0i | 0.636530i | 0.948002 | + | 0.318265i | \(0.103100\pi\) | ||||
−0.948002 | + | 0.318265i | \(0.896900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17748.0 | −0.607086 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42156.0 | 1.43744 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17322.0i | 0.588788i | 0.955684 | + | 0.294394i | \(0.0951177\pi\) | ||||
−0.955684 | + | 0.294394i | \(0.904882\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 23232.0i | − 0.784727i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31484.0 | 1.06014 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19791.0 | −0.664328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 4590.00i | − 0.153594i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35190.0i | 1.17025i | 0.810942 | + | 0.585126i | \(0.198955\pi\) | ||||
−0.810942 | + | 0.585126i | \(0.801045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1680.00 | −0.0556960 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40696.0 | 1.34500 | 0.672501 | − | 0.740096i | \(-0.265220\pi\) | ||||
0.672501 | + | 0.740096i | \(0.265220\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 17544.0i | − 0.578042i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 44306.0i | − 1.45084i | −0.688304 | − | 0.725422i | \(-0.741645\pi\) | ||||
0.688304 | − | 0.725422i | \(-0.258355\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11616.0 | −0.379212 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 234.000 | 0.00761574 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18798.0i | 0.609932i | 0.952363 | + | 0.304966i | \(0.0986451\pi\) | ||||
−0.952363 | + | 0.304966i | \(0.901355\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4488.00i | 0.144736i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23852.0 | 0.766885 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2468.00 | −0.0791106 | −0.0395553 | − | 0.999217i | \(-0.512594\pi\) | ||||
−0.0395553 | + | 0.999217i | \(0.512594\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 52848.0i | − 1.68890i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61086.0i | 1.94043i | 0.242237 | + | 0.970217i | \(0.422119\pi\) | ||||
−0.242237 | + | 0.970217i | \(0.577881\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −47304.0 | −1.49813 |
(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 | 400.4.c.f.49.2 | 2 | ||
4.3 | odd | 2 | 200.4.c.c.49.1 | 2 | |||
5.2 | odd | 4 | 80.4.a.e.1.1 | 1 | |||
5.3 | odd | 4 | 400.4.a.e.1.1 | 1 | |||
5.4 | even | 2 | inner | 400.4.c.f.49.1 | 2 | ||
12.11 | even | 2 | 1800.4.f.j.649.2 | 2 | |||
15.2 | even | 4 | 720.4.a.bd.1.1 | 1 | |||
20.3 | even | 4 | 200.4.a.i.1.1 | 1 | |||
20.7 | even | 4 | 40.4.a.a.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 200.4.c.c.49.2 | 2 | |||
40.3 | even | 4 | 1600.4.a.j.1.1 | 1 | |||
40.13 | odd | 4 | 1600.4.a.br.1.1 | 1 | |||
40.27 | even | 4 | 320.4.a.l.1.1 | 1 | |||
40.37 | odd | 4 | 320.4.a.c.1.1 | 1 | |||
60.23 | odd | 4 | 1800.4.a.bi.1.1 | 1 | |||
60.47 | odd | 4 | 360.4.a.h.1.1 | 1 | |||
60.59 | even | 2 | 1800.4.f.j.649.1 | 2 | |||
80.27 | even | 4 | 1280.4.d.p.641.2 | 2 | |||
80.37 | odd | 4 | 1280.4.d.a.641.1 | 2 | |||
80.67 | even | 4 | 1280.4.d.p.641.1 | 2 | |||
80.77 | odd | 4 | 1280.4.d.a.641.2 | 2 | |||
140.27 | odd | 4 | 1960.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.a.a.1.1 | ✓ | 1 | 20.7 | even | 4 | ||
80.4.a.e.1.1 | 1 | 5.2 | odd | 4 | |||
200.4.a.i.1.1 | 1 | 20.3 | even | 4 | |||
200.4.c.c.49.1 | 2 | 4.3 | odd | 2 | |||
200.4.c.c.49.2 | 2 | 20.19 | odd | 2 | |||
320.4.a.c.1.1 | 1 | 40.37 | odd | 4 | |||
320.4.a.l.1.1 | 1 | 40.27 | even | 4 | |||
360.4.a.h.1.1 | 1 | 60.47 | odd | 4 | |||
400.4.a.e.1.1 | 1 | 5.3 | odd | 4 | |||
400.4.c.f.49.1 | 2 | 5.4 | even | 2 | inner | ||
400.4.c.f.49.2 | 2 | 1.1 | even | 1 | trivial | ||
720.4.a.bd.1.1 | 1 | 15.2 | even | 4 | |||
1280.4.d.a.641.1 | 2 | 80.37 | odd | 4 | |||
1280.4.d.a.641.2 | 2 | 80.77 | odd | 4 | |||
1280.4.d.p.641.1 | 2 | 80.67 | even | 4 | |||
1280.4.d.p.641.2 | 2 | 80.27 | even | 4 | |||
1600.4.a.j.1.1 | 1 | 40.3 | even | 4 | |||
1600.4.a.br.1.1 | 1 | 40.13 | odd | 4 | |||
1800.4.a.bi.1.1 | 1 | 60.23 | odd | 4 | |||
1800.4.f.j.649.1 | 2 | 60.59 | even | 2 | |||
1800.4.f.j.649.2 | 2 | 12.11 | even | 2 | |||
1960.4.a.h.1.1 | 1 | 140.27 | odd | 4 |