Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6384,2,Mod(1,6384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6384.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6384.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: | \(50.9764966504\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.135076.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 3192) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.26848\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6384.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.53696 | 1.13456 | 0.567281 | − | 0.823524i | \(-0.307995\pi\) | ||||
0.567281 | + | 0.823524i | \(0.307995\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.91239 | −1.48114 | −0.740570 | − | 0.671979i | \(-0.765444\pi\) | ||||
−0.740570 | + | 0.671979i | \(0.765444\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.165497 | −0.0459005 | −0.0229502 | − | 0.999737i | \(-0.507306\pi\) | ||||
−0.0229502 | + | 0.999737i | \(0.507306\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.53696 | 0.655040 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.84768 | 1.66081 | 0.830404 | − | 0.557162i | \(-0.188110\pi\) | ||||
0.830404 | + | 0.557162i | \(0.188110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.16550 | −0.451537 | −0.225769 | − | 0.974181i | \(-0.572489\pi\) | ||||
−0.225769 | + | 0.974181i | \(0.572489\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.43617 | 0.287233 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.70246 | 0.873224 | 0.436612 | − | 0.899650i | \(-0.356178\pi\) | ||||
0.436612 | + | 0.899650i | \(0.356178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.07788 | 1.27123 | 0.635613 | − | 0.772008i | \(-0.280748\pi\) | ||||
0.635613 | + | 0.772008i | \(0.280748\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.91239 | −0.855137 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.53696 | −0.428824 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.746889 | −0.122788 | −0.0613939 | − | 0.998114i | \(-0.519555\pi\) | ||||
−0.0613939 | + | 0.998114i | \(0.519555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.165497 | −0.0265007 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.07392 | 0.480066 | 0.240033 | − | 0.970765i | \(-0.422842\pi\) | ||||
0.240033 | + | 0.970765i | \(0.422842\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.53696 | 0.378188 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.88551 | −0.566760 | −0.283380 | − | 0.959008i | \(-0.591456\pi\) | ||||
−0.283380 | + | 0.959008i | \(0.591456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.84768 | 0.958867 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.702457 | −0.0964898 | −0.0482449 | − | 0.998836i | \(-0.515363\pi\) | ||||
−0.0482449 | + | 0.998836i | \(0.515363\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.4625 | −1.68045 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.3349 | 1.73605 | 0.868025 | − | 0.496520i | \(-0.165389\pi\) | ||||
0.868025 | + | 0.496520i | \(0.165389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.419858 | −0.0520770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0439 | 1.59357 | 0.796784 | − | 0.604264i | \(-0.206533\pi\) | ||||
0.796784 | + | 0.604264i | \(0.206533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.16550 | −0.260695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.26629 | 0.981028 | 0.490514 | − | 0.871433i | \(-0.336809\pi\) | ||||
0.490514 | + | 0.871433i | \(0.336809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.05761 | −0.591949 | −0.295974 | − | 0.955196i | \(-0.595644\pi\) | ||||
−0.295974 | + | 0.955196i | \(0.595644\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.43617 | 0.165834 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.91239 | 0.559818 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.22311 | −1.03768 | −0.518840 | − | 0.854871i | \(-0.673636\pi\) | ||||
−0.518840 | + | 0.854871i | \(0.673636\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.19623 | −0.899654 | −0.449827 | − | 0.893116i | \(-0.648514\pi\) | ||||
−0.449827 | + | 0.893116i | \(0.648514\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.3723 | 1.88429 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.70246 | 0.504156 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.38861 | −0.995190 | −0.497595 | − | 0.867409i | \(-0.665783\pi\) | ||||
−0.497595 | + | 0.867409i | \(0.665783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.165497 | 0.0173488 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.07788 | 0.733942 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.53696 | −0.260287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.65531 | −0.371141 | −0.185570 | − | 0.982631i | \(-0.559413\pi\) | ||||
−0.185570 | + | 0.982631i | \(0.559413\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.91239 | −0.493713 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.389120 | 0.0387189 | 0.0193595 | − | 0.999813i | \(-0.493837\pi\) | ||||
0.0193595 | + | 0.999813i | \(0.493837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.440128 | 0.0433671 | 0.0216835 | − | 0.999765i | \(-0.493097\pi\) | ||||
0.0216835 | + | 0.999765i | \(0.493097\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.53696 | −0.247582 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.46962 | 0.528768 | 0.264384 | − | 0.964418i | \(-0.414831\pi\) | ||||
0.264384 | + | 0.964418i | \(0.414831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00396 | 0.766641 | 0.383320 | − | 0.923615i | \(-0.374781\pi\) | ||||
0.383320 | + | 0.923615i | \(0.374781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.746889 | −0.0708916 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0210 | 1.50713 | 0.753565 | − | 0.657374i | \(-0.228333\pi\) | ||||
0.753565 | + | 0.657374i | \(0.228333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.49378 | −0.512297 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.165497 | −0.0153002 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.84768 | −0.627726 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.1315 | 1.19378 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.07392 | 0.277166 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.04130 | −0.808679 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.9660 | 1.23929 | 0.619643 | − | 0.784884i | \(-0.287278\pi\) | ||||
0.619643 | + | 0.784884i | \(0.287278\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0210 | 1.57450 | 0.787251 | − | 0.616632i | \(-0.211503\pi\) | ||||
0.787251 | + | 0.616632i | \(0.211503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.53696 | 0.218347 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.66901 | 0.484336 | 0.242168 | − | 0.970234i | \(-0.422141\pi\) | ||||
0.242168 | + | 0.970234i | \(0.422141\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0700563 | −0.00594210 | −0.00297105 | − | 0.999996i | \(-0.500946\pi\) | ||||
−0.00297105 | + | 0.999996i | \(0.500946\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.88551 | −0.327219 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.812983 | 0.0679851 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.9299 | 0.990728 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.8208 | 1.13224 | 0.566122 | − | 0.824321i | \(-0.308443\pi\) | ||||
0.566122 | + | 0.824321i | \(0.308443\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.81820 | −0.310720 | −0.155360 | − | 0.987858i | \(-0.549654\pi\) | ||||
−0.155360 | + | 0.987858i | \(0.549654\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.84768 | 0.553602 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.9563 | 1.44228 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.97261 | −0.476666 | −0.238333 | − | 0.971183i | \(-0.576601\pi\) | ||||
−0.238333 | + | 0.971183i | \(0.576601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.702457 | −0.0557084 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.16550 | 0.170665 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.95630 | 0.779838 | 0.389919 | − | 0.920849i | \(-0.372503\pi\) | ||||
0.389919 | + | 0.920849i | \(0.372503\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.4625 | −0.970206 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.56383 | −0.121013 | −0.0605066 | − | 0.998168i | \(-0.519272\pi\) | ||||
−0.0605066 | + | 0.998168i | \(0.519272\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9726 | −0.997893 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.5444 | 1.79005 | 0.895023 | − | 0.446021i | \(-0.147159\pi\) | ||||
0.895023 | + | 0.446021i | \(0.147159\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.43617 | −0.108564 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.3349 | 1.00231 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.7639 | −1.70146 | −0.850728 | − | 0.525606i | \(-0.823839\pi\) | ||||
−0.850728 | + | 0.525606i | \(0.823839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.42643 | 0.626332 | 0.313166 | − | 0.949698i | \(-0.398610\pi\) | ||||
0.313166 | + | 0.949698i | \(0.398610\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.89483 | −0.139310 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −33.6385 | −2.45989 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9497 | 0.864652 | 0.432326 | − | 0.901717i | \(-0.357693\pi\) | ||||
0.432326 | + | 0.901717i | \(0.357693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.6214 | 1.34040 | 0.670201 | − | 0.742180i | \(-0.266208\pi\) | ||||
0.670201 | + | 0.742180i | \(0.266208\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.419858 | −0.0300667 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.7195 | −1.47620 | −0.738102 | − | 0.674690i | \(-0.764278\pi\) | ||||
−0.738102 | + | 0.674690i | \(0.764278\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.05761 | 0.500301 | 0.250150 | − | 0.968207i | \(-0.419520\pi\) | ||||
0.250150 | + | 0.968207i | \(0.419520\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.0439 | 0.920047 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.70246 | −0.330048 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.79841 | 0.544665 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.16550 | −0.150512 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.91239 | 0.339797 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.84233 | −0.608731 | −0.304366 | − | 0.952555i | \(-0.598444\pi\) | ||||
−0.304366 | + | 0.952555i | \(0.598444\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.26629 | 0.566397 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.07788 | −0.480478 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.05761 | −0.341762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.13327 | −0.0762319 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.28121 | −0.554551 | −0.277275 | − | 0.960791i | \(-0.589431\pi\) | ||||
−0.277275 | + | 0.960791i | \(0.589431\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.43617 | 0.0957444 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.09815 | −0.205632 | −0.102816 | − | 0.994700i | \(-0.532785\pi\) | ||||
−0.102816 | + | 0.994700i | \(0.532785\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.24915 | 0.346874 | 0.173437 | − | 0.984845i | \(-0.444513\pi\) | ||||
0.173437 | + | 0.984845i | \(0.444513\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.91239 | 0.323211 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.08184 | −0.201898 | −0.100949 | − | 0.994892i | \(-0.532188\pi\) | ||||
−0.100949 | + | 0.994892i | \(0.532188\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.85739 | −0.643025 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.22311 | −0.599105 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6055 | 0.880068 | 0.440034 | − | 0.897981i | \(-0.354966\pi\) | ||||
0.440034 | + | 0.897981i | \(0.354966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4450 | 1.25256 | 0.626280 | − | 0.779598i | \(-0.284577\pi\) | ||||
0.626280 | + | 0.779598i | \(0.284577\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.53696 | 0.162080 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.165497 | 0.0105303 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.19623 | −0.519415 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.90578 | 0.246531 | 0.123265 | − | 0.992374i | \(-0.460663\pi\) | ||||
0.123265 | + | 0.992374i | \(0.460663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.6378 | 0.668790 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.3723 | 1.08790 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.9563 | −1.49435 | −0.747177 | − | 0.664626i | \(-0.768591\pi\) | ||||
−0.747177 | + | 0.664626i | \(0.768591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.746889 | 0.0464094 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.70246 | 0.291075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.3671 | −1.37921 | −0.689607 | − | 0.724184i | \(-0.742217\pi\) | ||||
−0.689607 | + | 0.724184i | \(0.742217\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.78210 | −0.109474 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.38861 | −0.574573 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.98369 | 0.242890 | 0.121445 | − | 0.992598i | \(-0.461247\pi\) | ||||
0.121445 | + | 0.992598i | \(0.461247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.53432 | 0.336186 | 0.168093 | − | 0.985771i | \(-0.446239\pi\) | ||||
0.168093 | + | 0.985771i | \(0.446239\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.165497 | 0.0100163 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.05500 | −0.425432 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2408 | 0.675392 | 0.337696 | − | 0.941255i | \(-0.390352\pi\) | ||||
0.337696 | + | 0.941255i | \(0.390352\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.07788 | 0.423742 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.7764 | −0.821830 | −0.410915 | − | 0.911674i | \(-0.634791\pi\) | ||||
−0.410915 | + | 0.911674i | \(0.634791\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.3533 | −1.38821 | −0.694105 | − | 0.719874i | \(-0.744199\pi\) | ||||
−0.694105 | + | 0.719874i | \(0.744199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.53696 | −0.150277 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.07392 | −0.181448 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.8908 | 1.75828 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.65531 | −0.214278 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.726619 | 0.0424495 | 0.0212248 | − | 0.999775i | \(-0.493243\pi\) | ||||
0.0212248 | + | 0.999775i | \(0.493243\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.8300 | 1.96966 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.91239 | −0.285046 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.358382 | 0.0207258 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.389120 | 0.0223544 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.2218 | 0.871595 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.3349 | −0.989353 | −0.494676 | − | 0.869077i | \(-0.664713\pi\) | ||||
−0.494676 | + | 0.869077i | \(0.664713\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.440128 | 0.0250380 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.56244 | −0.202008 | −0.101004 | − | 0.994886i | \(-0.532205\pi\) | ||||
−0.101004 | + | 0.994886i | \(0.532205\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4827 | −0.988180 | −0.494090 | − | 0.869411i | \(-0.664499\pi\) | ||||
−0.494090 | + | 0.869411i | \(0.664499\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.53696 | −0.142941 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.02416 | 0.113688 | 0.0568442 | − | 0.998383i | \(-0.481896\pi\) | ||||
0.0568442 | + | 0.998383i | \(0.481896\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.1003 | −1.29337 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.46962 | 0.305284 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.84768 | −0.381015 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.237681 | −0.0131841 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.00396 | 0.442620 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.88551 | 0.214215 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.39438 | −0.0766418 | −0.0383209 | − | 0.999265i | \(-0.512201\pi\) | ||||
−0.0383209 | + | 0.999265i | \(0.512201\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.746889 | −0.0409293 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.0919 | 1.80800 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.54753 | −0.302193 | −0.151097 | − | 0.988519i | \(-0.548280\pi\) | ||||
−0.151097 | + | 0.988519i | \(0.548280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0210 | 0.870142 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.7693 | −1.88286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.49378 | −0.295775 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0268 | −0.753000 | −0.376500 | − | 0.926417i | \(-0.622873\pi\) | ||||
−0.376500 | + | 0.926417i | \(0.622873\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3591 | −0.929211 | −0.464605 | − | 0.885518i | \(-0.653804\pi\) | ||||
−0.464605 | + | 0.885518i | \(0.653804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.165497 | −0.00883355 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0694 | −0.748841 | −0.374420 | − | 0.927259i | \(-0.622158\pi\) | ||||
−0.374420 | + | 0.927259i | \(0.622158\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.9712 | 1.11304 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.84768 | −0.362418 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.1381 | −0.746181 | −0.373090 | − | 0.927795i | \(-0.621702\pi\) | ||||
−0.373090 | + | 0.927795i | \(0.621702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.1315 | 0.689227 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.8310 | −0.671603 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3925 | −0.855680 | −0.427840 | − | 0.903855i | \(-0.640725\pi\) | ||||
−0.427840 | + | 0.903855i | \(0.640725\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.07392 | 0.160022 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.702457 | 0.0364697 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.0779 | 1.29848 | 0.649242 | − | 0.760582i | \(-0.275086\pi\) | ||||
0.649242 | + | 0.760582i | \(0.275086\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.04130 | −0.466891 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.778240 | −0.0400814 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.73329 | 0.499966 | 0.249983 | − | 0.968250i | \(-0.419575\pi\) | ||||
0.249983 | + | 0.968250i | \(0.419575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.9660 | 0.715502 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.0420 | −1.84166 | −0.920830 | − | 0.389963i | \(-0.872488\pi\) | ||||
−0.920830 | + | 0.389963i | \(0.872488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.4625 | 0.635149 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.9915 | 0.557292 | 0.278646 | − | 0.960394i | \(-0.410114\pi\) | ||||
0.278646 | + | 0.960394i | \(0.410114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8286 | −0.749916 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0210 | 0.909039 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.3987 | −1.17731 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3185 | 0.668439 | 0.334219 | − | 0.942495i | \(-0.391527\pi\) | ||||
0.334219 | + | 0.942495i | \(0.391527\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.00000 | 0.0500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.27422 | 0.313319 | 0.156660 | − | 0.987653i | \(-0.449927\pi\) | ||||
0.156660 | + | 0.987653i | \(0.449927\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.17137 | −0.0583499 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.53696 | 0.126063 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.66901 | 0.181866 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.0315 | −1.88054 | −0.940268 | − | 0.340436i | \(-0.889425\pi\) | ||||
−0.940268 | + | 0.340436i | \(0.889425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.66901 | 0.279631 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.3349 | −0.656165 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.7935 | −1.02071 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0700563 | −0.00343067 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.0598 | 1.41966 | 0.709832 | − | 0.704371i | \(-0.248771\pi\) | ||||
0.709832 | + | 0.704371i | \(0.248771\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.1042 | −1.32098 | −0.660490 | − | 0.750835i | \(-0.729651\pi\) | ||||
−0.660490 | + | 0.750835i | \(0.729651\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.88551 | −0.188920 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.83441 | 0.477039 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.00000 | −0.290360 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.812983 | 0.0392512 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0092 | −0.626632 | −0.313316 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313316 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.4651 | −0.695150 | −0.347575 | − | 0.937652i | \(-0.612995\pi\) | ||||
−0.347575 | + | 0.937652i | \(0.612995\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.9299 | 0.571997 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.16550 | 0.103590 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.8753 | 1.37814 | 0.689071 | − | 0.724694i | \(-0.258019\pi\) | ||||
0.689071 | + | 0.724694i | \(0.258019\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.7556 | 0.796082 | 0.398041 | − | 0.917368i | \(-0.369690\pi\) | ||||
0.398041 | + | 0.917368i | \(0.369690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.8185 | −1.12911 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.8208 | 0.653702 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2468 | 0.483578 | 0.241789 | − | 0.970329i | \(-0.422266\pi\) | ||||
0.241789 | + | 0.970329i | \(0.422266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.1003 | −0.711044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.81820 | −0.179394 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.419858 | 0.0196833 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.5403 | 1.52217 | 0.761086 | − | 0.648651i | \(-0.224667\pi\) | ||||
0.761086 | + | 0.648651i | \(0.224667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.84768 | 0.319622 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.2199 | −1.64035 | −0.820177 | − | 0.572110i | \(-0.806125\pi\) | ||||
−0.820177 | + | 0.572110i | \(0.806125\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.2755 | 1.36055 | 0.680274 | − | 0.732958i | \(-0.261861\pi\) | ||||
0.680274 | + | 0.732958i | \(0.261861\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.9563 | 0.832704 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.6196 | 1.83338 | 0.916688 | − | 0.399604i | \(-0.130852\pi\) | ||||
0.916688 | + | 0.399604i | \(0.130852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.0439 | −0.602312 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.97261 | −0.275203 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.43617 | −0.0658958 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.702457 | −0.0321633 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.1760 | 0.739099 | 0.369549 | − | 0.929211i | \(-0.379512\pi\) | ||||
0.369549 | + | 0.929211i | \(0.379512\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.123608 | 0.00563602 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.16550 | 0.0985335 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.27338 | −0.421083 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.41851 | −0.290850 | −0.145425 | − | 0.989369i | \(-0.546455\pi\) | ||||
−0.145425 | + | 0.989369i | \(0.546455\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.95630 | 0.450240 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.1217 | −1.58502 | −0.792510 | − | 0.609859i | \(-0.791226\pi\) | ||||
−0.792510 | + | 0.609859i | \(0.791226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.2009 | 1.45026 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.4625 | −0.560149 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.26629 | −0.370794 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.9712 | −0.580673 | −0.290336 | − | 0.956925i | \(-0.593767\pi\) | ||||
−0.290336 | + | 0.956925i | \(0.593767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.56383 | −0.0698670 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.2225 | 1.30297 | 0.651483 | − | 0.758663i | \(-0.274147\pi\) | ||||
0.651483 | + | 0.758663i | \(0.274147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.987182 | 0.0439290 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9726 | −0.576134 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.9414 | −1.63740 | −0.818698 | − | 0.574224i | \(-0.805304\pi\) | ||||
−0.818698 | + | 0.574224i | \(0.805304\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.05761 | 0.223736 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.11659 | 0.0492027 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.0871 | 0.839451 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.5444 | 1.03348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.6298 | −0.553323 | −0.276661 | − | 0.960967i | \(-0.589228\pi\) | ||||
−0.276661 | + | 0.960967i | \(0.589228\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.5778 | −1.16216 | −0.581082 | − | 0.813845i | \(-0.697370\pi\) | ||||
−0.581082 | + | 0.813845i | \(0.697370\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.43617 | −0.0626794 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 48.4671 | 2.11126 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3106 | −0.796114 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.3349 | 0.578683 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.508723 | −0.0220352 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.8762 | 0.599920 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.7639 | −0.982336 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.91239 | −0.211591 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.4757 | 1.65420 | 0.827099 | − | 0.562056i | \(-0.189989\pi\) | ||||
0.827099 | + | 0.562056i | \(0.189989\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.42643 | 0.361613 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.3057 | 0.869802 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.7993 | 0.974827 | 0.487414 | − | 0.873171i | \(-0.337940\pi\) | ||||
0.487414 | + | 0.873171i | \(0.337940\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.70246 | −0.200331 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.22311 | 0.392206 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.89483 | −0.0804309 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.45470 | −0.315866 | −0.157933 | − | 0.987450i | \(-0.550483\pi\) | ||||
−0.157933 | + | 0.987450i | \(0.550483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.6385 | −1.42022 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.0576 | 1.14034 | 0.570171 | − | 0.821526i | \(-0.306877\pi\) | ||||
0.570171 | + | 0.821526i | \(0.306877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.6446 | 1.70993 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.3256 | −1.10363 | −0.551814 | − | 0.833967i | \(-0.686064\pi\) | ||||
−0.551814 | + | 0.833967i | \(0.686064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.96875 | 0.124238 | 0.0621191 | − | 0.998069i | \(-0.480214\pi\) | ||||
0.0621191 | + | 0.998069i | \(0.480214\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.9497 | 0.499207 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.11001 | −0.129696 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.1637 | −1.00595 | −0.502974 | − | 0.864302i | \(-0.667761\pi\) | ||||
−0.502974 | + | 0.864302i | \(0.667761\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.6214 | 0.773881 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.19623 | 0.340037 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.45074 | 0.142915 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.419858 | −0.0173590 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.2226 | −0.917225 | −0.458612 | − | 0.888636i | \(-0.651653\pi\) | ||||
−0.458612 | + | 0.888636i | \(0.651653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.07788 | −0.291639 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.7195 | −0.852286 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.9576 | 0.942757 | 0.471378 | − | 0.881931i | \(-0.343757\pi\) | ||||
0.471378 | + | 0.881931i | \(0.343757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.3723 | −0.712195 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.05761 | 0.288849 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.2847 | 1.07396 | 0.536982 | − | 0.843593i | \(-0.319564\pi\) | ||||
0.536982 | + | 0.843593i | \(0.319564\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9229 | −0.527136 | −0.263568 | − | 0.964641i | \(-0.584899\pi\) | ||||
−0.263568 | + | 0.964641i | \(0.584899\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.0439 | 0.531189 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.3142 | 1.35441 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.4127 | 1.47795 | 0.738974 | − | 0.673734i | \(-0.235311\pi\) | ||||
0.738974 | + | 0.673734i | \(0.235311\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.70246 | −0.190553 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.643039 | 0.0260146 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.5444 | 1.43562 | 0.717812 | − | 0.696237i | \(-0.245144\pi\) | ||||
0.717812 | + | 0.696237i | \(0.245144\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.79841 | 0.314462 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.3231 | −0.576625 | −0.288313 | − | 0.957536i | \(-0.593094\pi\) | ||||
−0.288313 | + | 0.957536i | \(0.593094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.83934 | −0.114123 | −0.0570614 | − | 0.998371i | \(-0.518173\pi\) | ||||
−0.0570614 | + | 0.998371i | \(0.518173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.16550 | −0.0868984 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.38861 | 0.376147 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1183 | −1.20473 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.91239 | 0.196182 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.11446 | −0.203927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4827 | 0.616356 | 0.308178 | − | 0.951329i | \(-0.400281\pi\) | ||||
0.308178 | + | 0.951329i | \(0.400281\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.84233 | −0.351451 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.4313 | 1.40605 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.165497 | −0.00655721 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.26629 | 0.327009 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.0321 | −0.554234 | −0.277117 | − | 0.960836i | \(-0.589379\pi\) | ||||
−0.277117 | + | 0.960836i | \(0.589379\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.02636 | 0.0799118 | 0.0399559 | − | 0.999201i | \(-0.487278\pi\) | ||||
0.0399559 | + | 0.999201i | \(0.487278\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.9250 | 1.49099 | 0.745493 | − | 0.666513i | \(-0.232214\pi\) | ||||
0.745493 | + | 0.666513i | \(0.232214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −65.5060 | −2.57133 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.07788 | −0.277404 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.0100 | −1.60484 | −0.802422 | − | 0.596757i | \(-0.796455\pi\) | ||||
−0.802422 | + | 0.596757i | \(0.796455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.7186 | 1.78637 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.05761 | −0.197316 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.389898 | −0.0151883 | −0.00759414 | − | 0.999971i | \(-0.502417\pi\) | ||||
−0.00759414 | + | 0.999971i | \(0.502417\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.1734 | 0.940237 | 0.470119 | − | 0.882603i | \(-0.344211\pi\) | ||||
0.470119 | + | 0.882603i | \(0.344211\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.13327 | −0.0440125 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.53696 | 0.0983791 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.1832 | −0.394293 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.28121 | −0.320170 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.4743 | −1.13784 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3387 | 0.629811 | 0.314906 | − | 0.949123i | \(-0.398027\pi\) | ||||
0.314906 | + | 0.949123i | \(0.398027\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.43617 | 0.0552780 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.6932 | −0.449408 | −0.224704 | − | 0.974427i | \(-0.572141\pi\) | ||||
−0.224704 | + | 0.974427i | \(0.572141\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.65531 | 0.140278 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.09815 | −0.118721 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.3115 | 0.547613 | 0.273806 | − | 0.961785i | \(-0.411717\pi\) | ||||
0.273806 | + | 0.961785i | \(0.411717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.3820 | 0.549510 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.24915 | 0.200268 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.116254 | 0.00442893 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.4109 | 1.76555 | 0.882777 | − | 0.469792i | \(-0.155671\pi\) | ||||
0.882777 | + | 0.469792i | \(0.155671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.91239 | 0.186606 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.177730 | −0.00674169 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.0492 | 0.797296 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.08184 | −0.116566 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.8825 | −0.902029 | −0.451014 | − | 0.892517i | \(-0.648938\pi\) | ||||
−0.451014 | + | 0.892517i | \(0.648938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.746889 | 0.0281695 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.85739 | −0.371251 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.389120 | −0.0146344 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.8362 | 1.60875 | 0.804373 | − | 0.594124i | \(-0.202501\pi\) | ||||
0.804373 | + | 0.594124i | \(0.202501\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.22311 | −0.345894 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.3271 | −0.574006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.06251 | 0.0771333 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.6055 | 0.508108 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.07918 | −0.152128 | −0.0760638 | − | 0.997103i | \(-0.524235\pi\) | ||||
−0.0760638 | + | 0.997103i | \(0.524235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.440128 | −0.0163912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.4450 | 0.723166 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.75351 | 0.250819 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.0525 | 1.85635 | 0.928173 | − | 0.372150i | \(-0.121379\pi\) | ||||
0.928173 | + | 0.372150i | \(0.121379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5879 | 0.723494 | 0.361747 | − | 0.932276i | \(-0.382180\pi\) | ||||
0.361747 | + | 0.932276i | \(0.382180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.53696 | 0.0935772 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −64.0768 | −2.36030 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.530454 | 0.0195131 | 0.00975653 | − | 0.999952i | \(-0.496894\pi\) | ||||
0.00975653 | + | 0.999952i | \(0.496894\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.165497 | 0.00607967 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.3402 | −1.51663 | −0.758313 | − | 0.651891i | \(-0.773976\pi\) | ||||
−0.758313 | + | 0.651891i | \(0.773976\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.0628 | 1.28460 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.19623 | −0.299885 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.46962 | −0.199855 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.7555 | 1.74262 | 0.871311 | − | 0.490731i | \(-0.163270\pi\) | ||||
0.871311 | + | 0.490731i | \(0.163270\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.90578 | 0.142335 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.68661 | −0.352532 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.75259 | −0.281773 | −0.140886 | − | 0.990026i | \(-0.544995\pi\) | ||||
−0.140886 | + | 0.990026i | \(0.544995\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.6378 | 0.386126 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.3618 | −0.629366 | −0.314683 | − | 0.949197i | \(-0.601898\pi\) | ||||
−0.314683 | + | 0.949197i | \(0.601898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.00396 | −0.289763 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.3723 | 0.628097 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.20687 | −0.0796856 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.6026 | −0.670828 | −0.335414 | − | 0.942071i | \(-0.608876\pi\) | ||||
−0.335414 | + | 0.942071i | \(0.608876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.9563 | −0.862765 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.59122 | 0.129167 | 0.0645837 | − | 0.997912i | \(-0.479428\pi\) | ||||
0.0645837 | + | 0.997912i | \(0.479428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.1650 | 0.365138 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.746889 | 0.0267945 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.07392 | −0.110135 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40.6072 | −1.45304 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.70246 | 0.168052 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.1523 | −0.540808 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.4157 | −1.44066 | −0.720332 | − | 0.693630i | \(-0.756010\pi\) | ||||
−0.720332 | + | 0.693630i | \(0.756010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.3671 | −0.796289 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.0210 | −0.569641 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.992979 | −0.0352617 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.78210 | −0.0632047 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.7124 | 0.591983 | 0.295991 | − | 0.955191i | \(-0.404350\pi\) | ||||
0.295991 | + | 0.955191i | \(0.404350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.6067 | −0.941279 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.38861 | −0.331730 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.8449 | 0.876759 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.49378 | 0.193630 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.98369 | 0.140233 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.0324 | −1.16136 | −0.580678 | − | 0.814133i | \(-0.697212\pi\) | ||||
−0.580678 | + | 0.814133i | \(0.697212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.55804 | −0.335628 | −0.167814 | − | 0.985819i | \(-0.553671\pi\) | ||||
−0.167814 | + | 0.985819i | \(0.553671\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.53432 | 0.194097 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.2587 | 0.884775 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.165497 | 0.00578292 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.8489 | 1.14643 | 0.573217 | − | 0.819403i | \(-0.305695\pi\) | ||||
0.573217 | + | 0.819403i | \(0.305695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2716 | −0.427763 | −0.213881 | − | 0.976860i | \(-0.568611\pi\) | ||||
−0.213881 | + | 0.976860i | \(0.568611\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.05500 | −0.245624 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.9302 | −1.21464 | −0.607321 | − | 0.794456i | \(-0.707756\pi\) | ||||
−0.607321 | + | 0.794456i | \(0.707756\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.7099 | −0.476163 | −0.238082 | − | 0.971245i | \(-0.576519\pi\) | ||||
−0.238082 | + | 0.971245i | \(0.576519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2408 | 0.389938 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.84768 | 0.237258 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.96739 | −0.137297 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.07788 | 0.244647 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.2116 | −1.66445 | −0.832225 | − | 0.554438i | \(-0.812933\pi\) | ||||
−0.832225 | + | 0.554438i | \(0.812933\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.88690 | −0.237479 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.7764 | −0.474484 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.9110 | −1.13217 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.1315 | −0.451205 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.3533 | −0.801483 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.61739 | 0.0554433 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.38648 | 0.0474721 | 0.0237360 | − | 0.999718i | \(-0.492444\pi\) | ||||
0.0237360 | + | 0.999718i | \(0.492444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.53696 | −0.0867622 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.1984 | −0.416690 | −0.208345 | − | 0.978055i | \(-0.566808\pi\) | ||||
−0.208345 | + | 0.978055i | \(0.566808\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.7293 | −0.707273 | −0.353637 | − | 0.935383i | \(-0.615055\pi\) | ||||
−0.353637 | + | 0.935383i | \(0.615055\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.07392 | −0.104759 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.1843 | −1.57213 | −0.786066 | − | 0.618142i | \(-0.787886\pi\) | ||||
−0.786066 | + | 0.618142i | \(0.787886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 59.7311 | 2.03092 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.8908 | 1.01514 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.3075 | 1.53695 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.15872 | −0.0731456 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.65531 | −0.123714 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.04130 | 0.305652 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.232940 | 0.00786582 | 0.00393291 | − | 0.999992i | \(-0.498748\pi\) | ||||
0.00393291 | + | 0.999992i | \(0.498748\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.726619 | 0.0245083 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −57.8591 | −1.94932 | −0.974661 | − | 0.223686i | \(-0.928191\pi\) | ||||
−0.974661 | + | 0.223686i | \(0.928191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.6825 | −1.57099 | −0.785496 | − | 0.618866i | \(-0.787592\pi\) | ||||
−0.785496 | + | 0.618866i | \(0.787592\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.8300 | 1.13718 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.0508 | −1.78127 | −0.890636 | − | 0.454718i | \(-0.849740\pi\) | ||||
−0.890636 | + | 0.454718i | \(0.849740\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.9660 | −0.468406 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.91239 | −0.164571 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.88551 | 0.130024 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −57.7512 | −1.93041 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.358382 | 0.0119660 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.2834 | 1.11006 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.81020 | −0.160251 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.3775 | 0.710613 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.33361 | −0.143895 | −0.0719475 | − | 0.997408i | \(-0.522921\pi\) | ||||
−0.0719475 | + | 0.997408i | \(0.522921\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.389120 | 0.0129063 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.7959 | −1.94799 | −0.973997 | − | 0.226559i | \(-0.927252\pi\) | ||||
−0.973997 | + | 0.226559i | \(0.927252\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.2631 | 1.33251 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.2218 | 0.503216 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.0210 | −0.595106 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.31153 | −0.142224 | −0.0711121 | − | 0.997468i | \(-0.522655\pi\) | ||||
−0.0711121 | + | 0.997468i | \(0.522655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.3349 | −0.571203 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.36804 | −0.0450297 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.07266 | −0.0352687 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.440128 | 0.0144557 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.2454 | −1.68131 | −0.840653 | − | 0.541574i | \(-0.817829\pi\) | ||||
−0.840653 | + | 0.541574i | \(0.817829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.56244 | −0.116629 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −85.3394 | −2.79090 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.97577 | −0.260557 | −0.130278 | − | 0.991477i | \(-0.541587\pi\) | ||||
−0.130278 | + | 0.991477i | \(0.541587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.4827 | −0.570526 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.9087 | 1.20319 | 0.601595 | − | 0.798801i | \(-0.294532\pi\) | ||||
0.601595 | + | 0.798801i | \(0.294532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.65656 | −0.216768 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.53696 | −0.0825273 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.3586 | −1.27898 | −0.639491 | − | 0.768798i | \(-0.720855\pi\) | ||||
−0.639491 | + | 0.768798i | \(0.720855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.837018 | 0.0271707 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.02416 | 0.0656380 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.4075 | −1.27653 | −0.638267 | − | 0.769815i | \(-0.720348\pi\) | ||||
−0.638267 | + | 0.769815i | \(0.720348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.3160 | 0.981002 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.1003 | −0.746726 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.66901 | −0.183062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0964 | 0.616013 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.46962 | 0.176256 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47.2419 | 1.52077 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0636 | 1.54562 | 0.772811 | − | 0.634637i | \(-0.218850\pi\) | ||||
0.772811 | + | 0.634637i | \(0.218850\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.84768 | −0.219979 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.1041 | −0.773539 | −0.386769 | − | 0.922176i | \(-0.626409\pi\) | ||||
−0.386769 | + | 0.922176i | \(0.626409\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0700563 | 0.00224590 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.237681 | −0.00761187 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.0840 | 1.05845 | 0.529226 | − | 0.848481i | \(-0.322482\pi\) | ||||
0.529226 | + | 0.848481i | \(0.322482\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.1205 | 1.47402 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.00396 | 0.255547 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.2724 | 0.487112 | 0.243556 | − | 0.969887i | \(-0.421686\pi\) | ||||
0.243556 | + | 0.969887i | \(0.421686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.5645 | −1.67485 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.88551 | 0.123677 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.5946 | 0.431848 | 0.215924 | − | 0.976410i | \(-0.430724\pi\) | ||||
0.215924 | + | 0.976410i | \(0.430724\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.39438 | −0.0442492 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.9049 | 0.567623 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.15506 | 0.163262 | 0.0816312 | − | 0.996663i | \(-0.473987\pi\) | ||||
0.0816312 | + | 0.996663i | \(0.473987\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.746889 | −0.0236305 |
(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 | 6384.2.a.ce.1.4 | 5 | ||
4.3 | odd | 2 | 3192.2.a.ba.1.4 | ✓ | 5 | ||
12.11 | even | 2 | 9576.2.a.co.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3192.2.a.ba.1.4 | ✓ | 5 | 4.3 | odd | 2 | ||
6384.2.a.ce.1.4 | 5 | 1.1 | even | 1 | trivial | ||
9576.2.a.co.1.2 | 5 | 12.11 | even | 2 |