Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.353553 | 0.176777 | − | 0.984251i | \(-0.443433\pi\) | ||||
0.176777 | + | 0.984251i | \(0.443433\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | −12.0000 | −1.07331 | −0.536656 | − | 0.843801i | \(-0.680313\pi\) | ||||
−0.536656 | + | 0.843801i | \(0.680313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −15.0000 | −0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −12.0000 | −0.379473 | ||||||||
\(11\) | −20.0000 | −0.548202 | −0.274101 | − | 0.961701i | \(-0.588380\pi\) | ||||
−0.274101 | + | 0.961701i | \(0.588380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −84.0000 | −1.79211 | −0.896054 | − | 0.443945i | \(-0.853579\pi\) | ||||
−0.896054 | + | 0.443945i | \(0.853579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | 96.0000 | 1.36961 | 0.684806 | − | 0.728725i | \(-0.259887\pi\) | ||||
0.684806 | + | 0.728725i | \(0.259887\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.0000 | 0.144894 | 0.0724471 | − | 0.997372i | \(-0.476919\pi\) | ||||
0.0724471 | + | 0.997372i | \(0.476919\pi\) | |||||||
\(20\) | 84.0000 | 0.939149 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −20.0000 | −0.193819 | ||||||||
\(23\) | 176.000 | 1.59559 | 0.797794 | − | 0.602930i | \(-0.206000\pi\) | ||||
0.797794 | + | 0.602930i | \(0.206000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | −84.0000 | −0.633606 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −58.0000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −264.000 | −1.52954 | −0.764771 | − | 0.644302i | \(-0.777148\pi\) | ||||
−0.764771 | + | 0.644302i | \(0.777148\pi\) | |||||||
\(32\) | 161.000 | 0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 96.0000 | 0.484231 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 258.000 | 1.14635 | 0.573175 | − | 0.819433i | \(-0.305712\pi\) | ||||
0.573175 | + | 0.819433i | \(0.305712\pi\) | |||||||
\(38\) | 12.0000 | 0.0512278 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 180.000 | 0.711512 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 156.000 | 0.553251 | 0.276625 | − | 0.960978i | \(-0.410784\pi\) | ||||
0.276625 | + | 0.960978i | \(0.410784\pi\) | |||||||
\(44\) | 140.000 | 0.479677 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 176.000 | 0.564126 | ||||||||
\(47\) | 408.000 | 1.26623 | 0.633116 | − | 0.774057i | \(-0.281776\pi\) | ||||
0.633116 | + | 0.774057i | \(0.281776\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 19.0000 | 0.0537401 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 588.000 | 1.56809 | ||||||||
\(53\) | 722.000 | 1.87121 | 0.935607 | − | 0.353044i | \(-0.114853\pi\) | ||||
0.935607 | + | 0.353044i | \(0.114853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 240.000 | 0.588393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −58.0000 | −0.131306 | ||||||||
\(59\) | −492.000 | −1.08564 | −0.542822 | − | 0.839848i | \(-0.682644\pi\) | ||||
−0.542822 | + | 0.839848i | \(0.682644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −492.000 | −1.03269 | −0.516345 | − | 0.856380i | \(-0.672708\pi\) | ||||
−0.516345 | + | 0.856380i | \(0.672708\pi\) | |||||||
\(62\) | −264.000 | −0.540775 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 1008.00 | 1.92349 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 412.000 | 0.751251 | 0.375625 | − | 0.926772i | \(-0.377428\pi\) | ||||
0.375625 | + | 0.926772i | \(0.377428\pi\) | |||||||
\(68\) | −672.000 | −1.19841 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −296.000 | −0.494771 | −0.247385 | − | 0.968917i | \(-0.579571\pi\) | ||||
−0.247385 | + | 0.968917i | \(0.579571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 240.000 | 0.384793 | 0.192396 | − | 0.981317i | \(-0.438374\pi\) | ||||
0.192396 | + | 0.981317i | \(0.438374\pi\) | |||||||
\(74\) | 258.000 | 0.405296 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −84.0000 | −0.126782 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 776.000 | 1.10515 | 0.552575 | − | 0.833463i | \(-0.313645\pi\) | ||||
0.552575 | + | 0.833463i | \(0.313645\pi\) | |||||||
\(80\) | −492.000 | −0.687591 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −924.000 | −1.22195 | −0.610977 | − | 0.791648i | \(-0.709223\pi\) | ||||
−0.610977 | + | 0.791648i | \(0.709223\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1152.00 | −1.47002 | ||||||||
\(86\) | 156.000 | 0.195604 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 300.000 | 0.363410 | ||||||||
\(89\) | 744.000 | 0.886111 | 0.443055 | − | 0.896494i | \(-0.353895\pi\) | ||||
0.443055 | + | 0.896494i | \(0.353895\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1232.00 | −1.39614 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 408.000 | 0.447681 | ||||||||
\(95\) | −144.000 | −0.155517 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −168.000 | −0.175854 | −0.0879269 | − | 0.996127i | \(-0.528024\pi\) | ||||
−0.0879269 | + | 0.996127i | \(0.528024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −133.000 | −0.133000 | ||||||||
\(101\) | 1524.00 | 1.50142 | 0.750711 | − | 0.660630i | \(-0.229711\pi\) | ||||
0.750711 | + | 0.660630i | \(0.229711\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −408.000 | −0.390305 | −0.195153 | − | 0.980773i | \(-0.562520\pi\) | ||||
−0.195153 | + | 0.980773i | \(0.562520\pi\) | |||||||
\(104\) | 1260.00 | 1.18801 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 722.000 | 0.661574 | ||||||||
\(107\) | 820.000 | 0.740863 | 0.370432 | − | 0.928860i | \(-0.379210\pi\) | ||||
0.370432 | + | 0.928860i | \(0.379210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −918.000 | −0.806683 | −0.403342 | − | 0.915050i | \(-0.632151\pi\) | ||||
−0.403342 | + | 0.915050i | \(0.632151\pi\) | |||||||
\(110\) | 240.000 | 0.208028 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 110.000 | 0.0915746 | 0.0457873 | − | 0.998951i | \(-0.485420\pi\) | ||||
0.0457873 | + | 0.998951i | \(0.485420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2112.00 | −1.71257 | ||||||||
\(116\) | 406.000 | 0.324967 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −492.000 | −0.383833 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | −492.000 | −0.365111 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1848.00 | 1.33835 | ||||||||
\(125\) | 1272.00 | 0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 0.0111793 | 0.00558965 | − | 0.999984i | \(-0.498221\pi\) | ||||
0.00558965 | + | 0.999984i | \(0.498221\pi\) | |||||||
\(128\) | −1455.00 | −1.00473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1008.00 | 0.680057 | ||||||||
\(131\) | −1692.00 | −1.12848 | −0.564239 | − | 0.825611i | \(-0.690831\pi\) | ||||
−0.564239 | + | 0.825611i | \(0.690831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 412.000 | 0.265607 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1440.00 | −0.907934 | ||||||||
\(137\) | −1126.00 | −0.702195 | −0.351097 | − | 0.936339i | \(-0.614191\pi\) | ||||
−0.351097 | + | 0.936339i | \(0.614191\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1092.00 | 0.666347 | 0.333173 | − | 0.942866i | \(-0.391881\pi\) | ||||
0.333173 | + | 0.942866i | \(0.391881\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −296.000 | −0.174928 | ||||||||
\(143\) | 1680.00 | 0.982438 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 696.000 | 0.398618 | ||||||||
\(146\) | 240.000 | 0.136045 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1806.00 | −1.00306 | ||||||||
\(149\) | −1070.00 | −0.588307 | −0.294154 | − | 0.955758i | \(-0.595038\pi\) | ||||
−0.294154 | + | 0.955758i | \(0.595038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −120.000 | −0.0646719 | −0.0323360 | − | 0.999477i | \(-0.510295\pi\) | ||||
−0.0323360 | + | 0.999477i | \(0.510295\pi\) | |||||||
\(152\) | −180.000 | −0.0960522 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3168.00 | 1.64168 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1836.00 | 0.933304 | 0.466652 | − | 0.884441i | \(-0.345460\pi\) | ||||
0.466652 | + | 0.884441i | \(0.345460\pi\) | |||||||
\(158\) | 776.000 | 0.390729 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1932.00 | −0.954613 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 916.000 | 0.440164 | 0.220082 | − | 0.975481i | \(-0.429368\pi\) | ||||
0.220082 | + | 0.975481i | \(0.429368\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −924.000 | −0.432026 | ||||||||
\(167\) | −504.000 | −0.233537 | −0.116769 | − | 0.993159i | \(-0.537254\pi\) | ||||
−0.116769 | + | 0.993159i | \(0.537254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4859.00 | 2.21165 | ||||||||
\(170\) | −1152.00 | −0.519732 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1092.00 | −0.484094 | ||||||||
\(173\) | 1836.00 | 0.806870 | 0.403435 | − | 0.915008i | \(-0.367816\pi\) | ||||
0.403435 | + | 0.915008i | \(0.367816\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −820.000 | −0.351192 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 744.000 | 0.313287 | ||||||||
\(179\) | −2372.00 | −0.990456 | −0.495228 | − | 0.868763i | \(-0.664915\pi\) | ||||
−0.495228 | + | 0.868763i | \(0.664915\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1092.00 | −0.448440 | −0.224220 | − | 0.974539i | \(-0.571983\pi\) | ||||
−0.224220 | + | 0.974539i | \(0.571983\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2640.00 | −1.05774 | ||||||||
\(185\) | −3096.00 | −1.23039 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1920.00 | −0.750825 | ||||||||
\(188\) | −2856.00 | −1.10795 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −144.000 | −0.0549835 | ||||||||
\(191\) | −2512.00 | −0.951633 | −0.475817 | − | 0.879545i | \(-0.657847\pi\) | ||||
−0.475817 | + | 0.879545i | \(0.657847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2430.00 | −0.906297 | −0.453148 | − | 0.891435i | \(-0.649699\pi\) | ||||
−0.453148 | + | 0.891435i | \(0.649699\pi\) | |||||||
\(194\) | −168.000 | −0.0621737 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1762.00 | 0.637245 | 0.318623 | − | 0.947882i | \(-0.396780\pi\) | ||||
0.318623 | + | 0.947882i | \(0.396780\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3096.00 | 1.10286 | 0.551431 | − | 0.834220i | \(-0.314082\pi\) | ||||
0.551431 | + | 0.834220i | \(0.314082\pi\) | |||||||
\(200\) | −285.000 | −0.100763 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1524.00 | 0.530833 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −408.000 | −0.137994 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3444.00 | −1.14807 | ||||||||
\(209\) | −240.000 | −0.0794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 156.000 | 0.0508980 | 0.0254490 | − | 0.999676i | \(-0.491898\pi\) | ||||
0.0254490 | + | 0.999676i | \(0.491898\pi\) | |||||||
\(212\) | −5054.00 | −1.63731 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 820.000 | 0.261935 | ||||||||
\(215\) | −1872.00 | −0.593811 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −918.000 | −0.285206 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1680.00 | −0.514844 | ||||||||
\(221\) | −8064.00 | −2.45449 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5040.00 | 1.51347 | 0.756734 | − | 0.653723i | \(-0.226794\pi\) | ||||
0.756734 | + | 0.653723i | \(0.226794\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 110.000 | 0.0323765 | ||||||||
\(227\) | −2172.00 | −0.635069 | −0.317535 | − | 0.948247i | \(-0.602855\pi\) | ||||
−0.317535 | + | 0.948247i | \(0.602855\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2700.00 | 0.779131 | 0.389566 | − | 0.920999i | \(-0.372625\pi\) | ||||
0.389566 | + | 0.920999i | \(0.372625\pi\) | |||||||
\(230\) | −2112.00 | −0.605483 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 870.000 | 0.246200 | ||||||||
\(233\) | 3802.00 | 1.06900 | 0.534501 | − | 0.845168i | \(-0.320500\pi\) | ||||
0.534501 | + | 0.845168i | \(0.320500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4896.00 | −1.35906 | ||||||||
\(236\) | 3444.00 | 0.949938 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4408.00 | 1.19301 | 0.596506 | − | 0.802609i | \(-0.296555\pi\) | ||||
0.596506 | + | 0.802609i | \(0.296555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3096.00 | 0.827514 | 0.413757 | − | 0.910387i | \(-0.364216\pi\) | ||||
0.413757 | + | 0.910387i | \(0.364216\pi\) | |||||||
\(242\) | −931.000 | −0.247301 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3444.00 | 0.903605 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1008.00 | −0.259666 | ||||||||
\(248\) | 3960.00 | 1.01395 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1272.00 | 0.321793 | ||||||||
\(251\) | 924.000 | 0.232360 | 0.116180 | − | 0.993228i | \(-0.462935\pi\) | ||||
0.116180 | + | 0.993228i | \(0.462935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3520.00 | −0.874706 | ||||||||
\(254\) | 16.0000 | 0.00395248 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | 2760.00 | 0.669899 | 0.334950 | − | 0.942236i | \(-0.391281\pi\) | ||||
0.334950 | + | 0.942236i | \(0.391281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7056.00 | −1.68306 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1692.00 | −0.398978 | ||||||||
\(263\) | 2360.00 | 0.553323 | 0.276661 | − | 0.960967i | \(-0.410772\pi\) | ||||
0.276661 | + | 0.960967i | \(0.410772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8664.00 | −2.00840 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2884.00 | −0.657345 | ||||||||
\(269\) | −4020.00 | −0.911166 | −0.455583 | − | 0.890193i | \(-0.650569\pi\) | ||||
−0.455583 | + | 0.890193i | \(0.650569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4800.00 | 1.07594 | 0.537969 | − | 0.842965i | \(-0.319192\pi\) | ||||
0.537969 | + | 0.842965i | \(0.319192\pi\) | |||||||
\(272\) | 3936.00 | 0.877408 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1126.00 | −0.248263 | ||||||||
\(275\) | −380.000 | −0.0833268 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6446.00 | 1.39820 | 0.699102 | − | 0.715022i | \(-0.253583\pi\) | ||||
0.699102 | + | 0.715022i | \(0.253583\pi\) | |||||||
\(278\) | 1092.00 | 0.235589 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2602.00 | 0.552393 | 0.276196 | − | 0.961101i | \(-0.410926\pi\) | ||||
0.276196 | + | 0.961101i | \(0.410926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6900.00 | −1.44934 | −0.724669 | − | 0.689098i | \(-0.758007\pi\) | ||||
−0.724669 | + | 0.689098i | \(0.758007\pi\) | |||||||
\(284\) | 2072.00 | 0.432925 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1680.00 | 0.347344 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4303.00 | 0.875840 | ||||||||
\(290\) | 696.000 | 0.140933 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1680.00 | −0.336694 | ||||||||
\(293\) | 4452.00 | 0.887674 | 0.443837 | − | 0.896107i | \(-0.353617\pi\) | ||||
0.443837 | + | 0.896107i | \(0.353617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5904.00 | 1.16523 | ||||||||
\(296\) | −3870.00 | −0.759930 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1070.00 | −0.207998 | ||||||||
\(299\) | −14784.0 | −2.85947 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −120.000 | −0.0228650 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 492.000 | 0.0928228 | ||||||||
\(305\) | 5904.00 | 1.10840 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2436.00 | −0.452866 | −0.226433 | − | 0.974027i | \(-0.572706\pi\) | ||||
−0.226433 | + | 0.974027i | \(0.572706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3168.00 | 0.580420 | ||||||||
\(311\) | 7488.00 | 1.36529 | 0.682646 | − | 0.730750i | \(-0.260829\pi\) | ||||
0.682646 | + | 0.730750i | \(0.260829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1752.00 | −0.316386 | −0.158193 | − | 0.987408i | \(-0.550567\pi\) | ||||
−0.158193 | + | 0.987408i | \(0.550567\pi\) | |||||||
\(314\) | 1836.00 | 0.329973 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5432.00 | −0.967006 | ||||||||
\(317\) | 1562.00 | 0.276753 | 0.138376 | − | 0.990380i | \(-0.455812\pi\) | ||||
0.138376 | + | 0.990380i | \(0.455812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1160.00 | 0.203597 | ||||||||
\(320\) | 2004.00 | 0.350084 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1152.00 | 0.198449 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1596.00 | −0.272400 | ||||||||
\(326\) | 916.000 | 0.155621 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7092.00 | −1.17768 | −0.588839 | − | 0.808250i | \(-0.700415\pi\) | ||||
−0.588839 | + | 0.808250i | \(0.700415\pi\) | |||||||
\(332\) | 6468.00 | 1.06921 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −504.000 | −0.0825678 | ||||||||
\(335\) | −4944.00 | −0.806327 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 366.000 | 0.0591611 | 0.0295805 | − | 0.999562i | \(-0.490583\pi\) | ||||
0.0295805 | + | 0.999562i | \(0.490583\pi\) | |||||||
\(338\) | 4859.00 | 0.781937 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8064.00 | 1.28627 | ||||||||
\(341\) | 5280.00 | 0.838499 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2340.00 | −0.366757 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1836.00 | 0.285272 | ||||||||
\(347\) | 6364.00 | 0.984546 | 0.492273 | − | 0.870441i | \(-0.336166\pi\) | ||||
0.492273 | + | 0.870441i | \(0.336166\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10500.0 | −1.61046 | −0.805232 | − | 0.592960i | \(-0.797959\pi\) | ||||
−0.805232 | + | 0.592960i | \(0.797959\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3220.00 | −0.487576 | ||||||||
\(353\) | −408.000 | −0.0615174 | −0.0307587 | − | 0.999527i | \(-0.509792\pi\) | ||||
−0.0307587 | + | 0.999527i | \(0.509792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3552.00 | 0.531044 | ||||||||
\(356\) | −5208.00 | −0.775347 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2372.00 | −0.350179 | ||||||||
\(359\) | 11936.0 | 1.75476 | 0.877379 | − | 0.479798i | \(-0.159290\pi\) | ||||
0.877379 | + | 0.479798i | \(0.159290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6715.00 | −0.979006 | ||||||||
\(362\) | −1092.00 | −0.158548 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2880.00 | −0.413003 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2448.00 | −0.348187 | −0.174093 | − | 0.984729i | \(-0.555699\pi\) | ||||
−0.174093 | + | 0.984729i | \(0.555699\pi\) | |||||||
\(368\) | 7216.00 | 1.02217 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3096.00 | −0.435009 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11374.0 | 1.57888 | 0.789442 | − | 0.613826i | \(-0.210370\pi\) | ||||
0.789442 | + | 0.613826i | \(0.210370\pi\) | |||||||
\(374\) | −1920.00 | −0.265457 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6120.00 | −0.839401 | ||||||||
\(377\) | 4872.00 | 0.665572 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5892.00 | −0.798553 | −0.399277 | − | 0.916830i | \(-0.630739\pi\) | ||||
−0.399277 | + | 0.916830i | \(0.630739\pi\) | |||||||
\(380\) | 1008.00 | 0.136077 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2512.00 | −0.336453 | ||||||||
\(383\) | 10488.0 | 1.39925 | 0.699624 | − | 0.714511i | \(-0.253351\pi\) | ||||
0.699624 | + | 0.714511i | \(0.253351\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2430.00 | −0.320424 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1176.00 | 0.153872 | ||||||||
\(389\) | −4514.00 | −0.588352 | −0.294176 | − | 0.955751i | \(-0.595045\pi\) | ||||
−0.294176 | + | 0.955751i | \(0.595045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16896.0 | 2.18534 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1762.00 | 0.225300 | ||||||||
\(395\) | −9312.00 | −1.18617 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6036.00 | −0.763068 | −0.381534 | − | 0.924355i | \(-0.624604\pi\) | ||||
−0.381534 | + | 0.924355i | \(0.624604\pi\) | |||||||
\(398\) | 3096.00 | 0.389921 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 779.000 | 0.0973750 | ||||||||
\(401\) | 6770.00 | 0.843086 | 0.421543 | − | 0.906808i | \(-0.361489\pi\) | ||||
0.421543 | + | 0.906808i | \(0.361489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22176.0 | 2.74110 | ||||||||
\(404\) | −10668.0 | −1.31374 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5160.00 | −0.628432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12504.0 | 1.51169 | 0.755847 | − | 0.654748i | \(-0.227225\pi\) | ||||
0.755847 | + | 0.654748i | \(0.227225\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2856.00 | 0.341517 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11088.0 | 1.31154 | ||||||||
\(416\) | −13524.0 | −1.59392 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −240.000 | −0.0280832 | ||||||||
\(419\) | −9492.00 | −1.10672 | −0.553359 | − | 0.832943i | \(-0.686654\pi\) | ||||
−0.553359 | + | 0.832943i | \(0.686654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5182.00 | 0.599894 | 0.299947 | − | 0.953956i | \(-0.403031\pi\) | ||||
0.299947 | + | 0.953956i | \(0.403031\pi\) | |||||||
\(422\) | 156.000 | 0.0179952 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10830.0 | −1.24045 | ||||||||
\(425\) | 1824.00 | 0.208181 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5740.00 | −0.648256 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1872.00 | −0.209944 | ||||||||
\(431\) | 5720.00 | 0.639264 | 0.319632 | − | 0.947542i | \(-0.396441\pi\) | ||||
0.319632 | + | 0.947542i | \(0.396441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13608.0 | 1.51030 | 0.755149 | − | 0.655554i | \(-0.227565\pi\) | ||||
0.755149 | + | 0.655554i | \(0.227565\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6426.00 | 0.705848 | ||||||||
\(437\) | 2112.00 | 0.231191 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12864.0 | 1.39855 | 0.699277 | − | 0.714851i | \(-0.253505\pi\) | ||||
0.699277 | + | 0.714851i | \(0.253505\pi\) | |||||||
\(440\) | −3600.00 | −0.390053 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8064.00 | −0.867795 | ||||||||
\(443\) | 13252.0 | 1.42127 | 0.710634 | − | 0.703562i | \(-0.248408\pi\) | ||||
0.710634 | + | 0.703562i | \(0.248408\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8928.00 | −0.951074 | ||||||||
\(446\) | 5040.00 | 0.535092 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −226.000 | −0.0237541 | −0.0118771 | − | 0.999929i | \(-0.503781\pi\) | ||||
−0.0118771 | + | 0.999929i | \(0.503781\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −770.000 | −0.0801278 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2172.00 | −0.224531 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11334.0 | −1.16014 | −0.580068 | − | 0.814568i | \(-0.696974\pi\) | ||||
−0.580068 | + | 0.814568i | \(0.696974\pi\) | |||||||
\(458\) | 2700.00 | 0.275464 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14784.0 | 1.49849 | ||||||||
\(461\) | 1596.00 | 0.161243 | 0.0806216 | − | 0.996745i | \(-0.474309\pi\) | ||||
0.0806216 | + | 0.996745i | \(0.474309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12728.0 | 1.27758 | 0.638791 | − | 0.769380i | \(-0.279435\pi\) | ||||
0.638791 | + | 0.769380i | \(0.279435\pi\) | |||||||
\(464\) | −2378.00 | −0.237922 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3802.00 | 0.377949 | ||||||||
\(467\) | 3012.00 | 0.298456 | 0.149228 | − | 0.988803i | \(-0.452321\pi\) | ||||
0.149228 | + | 0.988803i | \(0.452321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4896.00 | −0.480501 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7380.00 | 0.719687 | ||||||||
\(473\) | −3120.00 | −0.303293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 228.000 | 0.0220239 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4408.00 | 0.421793 | ||||||||
\(479\) | 4296.00 | 0.409790 | 0.204895 | − | 0.978784i | \(-0.434315\pi\) | ||||
0.204895 | + | 0.978784i | \(0.434315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21672.0 | −2.05438 | ||||||||
\(482\) | 3096.00 | 0.292570 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6517.00 | 0.612040 | ||||||||
\(485\) | 2016.00 | 0.188746 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8184.00 | −0.761504 | −0.380752 | − | 0.924677i | \(-0.624335\pi\) | ||||
−0.380752 | + | 0.924677i | \(0.624335\pi\) | |||||||
\(488\) | 7380.00 | 0.684584 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12164.0 | 1.11803 | 0.559016 | − | 0.829157i | \(-0.311179\pi\) | ||||
0.559016 | + | 0.829157i | \(0.311179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5568.00 | −0.508661 | ||||||||
\(494\) | −1008.00 | −0.0918058 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10824.0 | −0.979863 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 972.000 | 0.0871998 | 0.0435999 | − | 0.999049i | \(-0.486117\pi\) | ||||
0.0435999 | + | 0.999049i | \(0.486117\pi\) | |||||||
\(500\) | −8904.00 | −0.796398 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 924.000 | 0.0821517 | ||||||||
\(503\) | −7728.00 | −0.685039 | −0.342519 | − | 0.939511i | \(-0.611280\pi\) | ||||
−0.342519 | + | 0.939511i | \(0.611280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18288.0 | −1.61150 | ||||||||
\(506\) | −3520.00 | −0.309255 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −112.000 | −0.00978188 | ||||||||
\(509\) | −11604.0 | −1.01049 | −0.505244 | − | 0.862977i | \(-0.668597\pi\) | ||||
−0.505244 | + | 0.862977i | \(0.668597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11521.0 | 0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2760.00 | 0.236845 | ||||||||
\(515\) | 4896.00 | 0.418919 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8160.00 | −0.694152 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15120.0 | −1.27511 | ||||||||
\(521\) | 10848.0 | 0.912206 | 0.456103 | − | 0.889927i | \(-0.349245\pi\) | ||||
0.456103 | + | 0.889927i | \(0.349245\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18132.0 | −1.51598 | −0.757989 | − | 0.652267i | \(-0.773818\pi\) | ||||
−0.757989 | + | 0.652267i | \(0.773818\pi\) | |||||||
\(524\) | 11844.0 | 0.987419 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2360.00 | 0.195629 | ||||||||
\(527\) | −25344.0 | −2.09488 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18809.0 | 1.54590 | ||||||||
\(530\) | −8664.00 | −0.710076 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9840.00 | −0.795178 | ||||||||
\(536\) | −6180.00 | −0.498014 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4020.00 | −0.322146 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6950.00 | 0.552318 | 0.276159 | − | 0.961112i | \(-0.410938\pi\) | ||||
0.276159 | + | 0.961112i | \(0.410938\pi\) | |||||||
\(542\) | 4800.00 | 0.380402 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15456.0 | 1.21814 | ||||||||
\(545\) | 11016.0 | 0.865823 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17012.0 | 1.32976 | 0.664882 | − | 0.746949i | \(-0.268482\pi\) | ||||
0.664882 | + | 0.746949i | \(0.268482\pi\) | |||||||
\(548\) | 7882.00 | 0.614420 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −380.000 | −0.0294605 | ||||||||
\(551\) | −696.000 | −0.0538123 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6446.00 | 0.494340 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7644.00 | −0.583054 | ||||||||
\(557\) | −3926.00 | −0.298653 | −0.149327 | − | 0.988788i | \(-0.547711\pi\) | ||||
−0.149327 | + | 0.988788i | \(0.547711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13104.0 | −0.991485 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2602.00 | 0.195300 | ||||||||
\(563\) | 18828.0 | 1.40942 | 0.704712 | − | 0.709494i | \(-0.251076\pi\) | ||||
0.704712 | + | 0.709494i | \(0.251076\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1320.00 | −0.0982882 | ||||||||
\(566\) | −6900.00 | −0.512418 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4440.00 | 0.327990 | ||||||||
\(569\) | −11990.0 | −0.883387 | −0.441693 | − | 0.897166i | \(-0.645622\pi\) | ||||
−0.441693 | + | 0.897166i | \(0.645622\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15716.0 | −1.15183 | −0.575914 | − | 0.817510i | \(-0.695354\pi\) | ||||
−0.575914 | + | 0.817510i | \(0.695354\pi\) | |||||||
\(572\) | −11760.0 | −0.859633 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3344.00 | 0.242529 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13872.0 | −1.00086 | −0.500432 | − | 0.865776i | \(-0.666826\pi\) | ||||
−0.500432 | + | 0.865776i | \(0.666826\pi\) | |||||||
\(578\) | 4303.00 | 0.309656 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4872.00 | −0.348791 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14440.0 | −1.02580 | ||||||||
\(584\) | −3600.00 | −0.255084 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4452.00 | 0.313840 | ||||||||
\(587\) | −8820.00 | −0.620171 | −0.310085 | − | 0.950709i | \(-0.600358\pi\) | ||||
−0.310085 | + | 0.950709i | \(0.600358\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3168.00 | −0.221622 | ||||||||
\(590\) | 5904.00 | 0.411973 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10578.0 | 0.734380 | ||||||||
\(593\) | 16872.0 | 1.16838 | 0.584191 | − | 0.811617i | \(-0.301412\pi\) | ||||
0.584191 | + | 0.811617i | \(0.301412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7490.00 | 0.514769 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14784.0 | −1.01097 | ||||||||
\(599\) | 6056.00 | 0.413091 | 0.206545 | − | 0.978437i | \(-0.433778\pi\) | ||||
0.206545 | + | 0.978437i | \(0.433778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10752.0 | 0.729756 | 0.364878 | − | 0.931055i | \(-0.381111\pi\) | ||||
0.364878 | + | 0.931055i | \(0.381111\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 840.000 | 0.0565879 | ||||||||
\(605\) | 11172.0 | 0.750754 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20256.0 | 1.35447 | 0.677237 | − | 0.735765i | \(-0.263177\pi\) | ||||
0.677237 | + | 0.735765i | \(0.263177\pi\) | |||||||
\(608\) | 1932.00 | 0.128870 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5904.00 | 0.391879 | ||||||||
\(611\) | −34272.0 | −2.26923 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28190.0 | −1.85740 | −0.928698 | − | 0.370838i | \(-0.879071\pi\) | ||||
−0.928698 | + | 0.370838i | \(0.879071\pi\) | |||||||
\(614\) | −2436.00 | −0.160112 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29318.0 | −1.91296 | −0.956482 | − | 0.291793i | \(-0.905748\pi\) | ||||
−0.956482 | + | 0.291793i | \(0.905748\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24348.0 | 1.58098 | 0.790492 | − | 0.612473i | \(-0.209825\pi\) | ||||
0.790492 | + | 0.612473i | \(0.209825\pi\) | |||||||
\(620\) | −22176.0 | −1.43647 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7488.00 | 0.482703 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | −1752.00 | −0.111859 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12852.0 | −0.816641 | ||||||||
\(629\) | 24768.0 | 1.57006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25184.0 | −1.58884 | −0.794421 | − | 0.607368i | \(-0.792226\pi\) | ||||
−0.794421 | + | 0.607368i | \(0.792226\pi\) | |||||||
\(632\) | −11640.0 | −0.732618 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1562.00 | 0.0978469 | ||||||||
\(635\) | −192.000 | −0.0119989 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1160.00 | 0.0719825 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17460.0 | 1.07839 | ||||||||
\(641\) | −32318.0 | −1.99140 | −0.995698 | − | 0.0926628i | \(-0.970462\pi\) | ||||
−0.995698 | + | 0.0926628i | \(0.970462\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3948.00 | −0.242137 | −0.121068 | − | 0.992644i | \(-0.538632\pi\) | ||||
−0.121068 | + | 0.992644i | \(0.538632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1152.00 | 0.0701623 | ||||||||
\(647\) | −13848.0 | −0.841454 | −0.420727 | − | 0.907187i | \(-0.638225\pi\) | ||||
−0.420727 | + | 0.907187i | \(0.638225\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9840.00 | 0.595152 | ||||||||
\(650\) | −1596.00 | −0.0963081 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6412.00 | −0.385143 | ||||||||
\(653\) | 3158.00 | 0.189253 | 0.0946264 | − | 0.995513i | \(-0.469834\pi\) | ||||
0.0946264 | + | 0.995513i | \(0.469834\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20304.0 | 1.21121 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24596.0 | 1.45391 | 0.726953 | − | 0.686687i | \(-0.240936\pi\) | ||||
0.726953 | + | 0.686687i | \(0.240936\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15468.0 | −0.910190 | −0.455095 | − | 0.890443i | \(-0.650395\pi\) | ||||
−0.455095 | + | 0.890443i | \(0.650395\pi\) | |||||||
\(662\) | −7092.00 | −0.416372 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13860.0 | 0.810049 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10208.0 | −0.592587 | ||||||||
\(668\) | 3528.00 | 0.204345 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4944.00 | −0.285080 | ||||||||
\(671\) | 9840.00 | 0.566124 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13470.0 | 0.771516 | 0.385758 | − | 0.922600i | \(-0.373940\pi\) | ||||
0.385758 | + | 0.922600i | \(0.373940\pi\) | |||||||
\(674\) | 366.000 | 0.0209166 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34013.0 | −1.93520 | ||||||||
\(677\) | 9564.00 | 0.542946 | 0.271473 | − | 0.962446i | \(-0.412489\pi\) | ||||
0.271473 | + | 0.962446i | \(0.412489\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17280.0 | 0.974497 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5280.00 | 0.296454 | ||||||||
\(683\) | −13852.0 | −0.776035 | −0.388018 | − | 0.921652i | \(-0.626840\pi\) | ||||
−0.388018 | + | 0.921652i | \(0.626840\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13512.0 | 0.753674 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6396.00 | 0.354426 | ||||||||
\(689\) | −60648.0 | −3.35342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −324.000 | −0.0178373 | −0.00891863 | − | 0.999960i | \(-0.502839\pi\) | ||||
−0.00891863 | + | 0.999960i | \(0.502839\pi\) | |||||||
\(692\) | −12852.0 | −0.706011 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6364.00 | 0.348090 | ||||||||
\(695\) | −13104.0 | −0.715199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −10500.0 | −0.569385 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24922.0 | −1.34278 | −0.671392 | − | 0.741103i | \(-0.734303\pi\) | ||||
−0.671392 | + | 0.741103i | \(0.734303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3096.00 | 0.166099 | ||||||||
\(704\) | 3340.00 | 0.178808 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −408.000 | −0.0217497 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17886.0 | −0.947423 | −0.473711 | − | 0.880680i | \(-0.657086\pi\) | ||||
−0.473711 | + | 0.880680i | \(0.657086\pi\) | |||||||
\(710\) | 3552.00 | 0.187752 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11160.0 | −0.587414 | ||||||||
\(713\) | −46464.0 | −2.44052 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20160.0 | −1.05446 | ||||||||
\(716\) | 16604.0 | 0.866649 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11936.0 | 0.620401 | ||||||||
\(719\) | 6792.00 | 0.352293 | 0.176147 | − | 0.984364i | \(-0.443637\pi\) | ||||
0.176147 | + | 0.984364i | \(0.443637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6715.00 | −0.346131 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7644.00 | 0.392385 | ||||||||
\(725\) | −1102.00 | −0.0564514 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1512.00 | 0.0771348 | 0.0385674 | − | 0.999256i | \(-0.487721\pi\) | ||||
0.0385674 | + | 0.999256i | \(0.487721\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2880.00 | −0.146019 | ||||||||
\(731\) | 14976.0 | 0.757739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11244.0 | −0.566585 | −0.283292 | − | 0.959034i | \(-0.591427\pi\) | ||||
−0.283292 | + | 0.959034i | \(0.591427\pi\) | |||||||
\(734\) | −2448.00 | −0.123103 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28336.0 | 1.41913 | ||||||||
\(737\) | −8240.00 | −0.411838 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1996.00 | −0.0993559 | −0.0496780 | − | 0.998765i | \(-0.515820\pi\) | ||||
−0.0496780 | + | 0.998765i | \(0.515820\pi\) | |||||||
\(740\) | 21672.0 | 1.07659 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 656.000 | 0.0323907 | 0.0161954 | − | 0.999869i | \(-0.494845\pi\) | ||||
0.0161954 | + | 0.999869i | \(0.494845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12840.0 | 0.631438 | ||||||||
\(746\) | 11374.0 | 0.558219 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13440.0 | 0.656972 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1056.00 | 0.0513102 | 0.0256551 | − | 0.999671i | \(-0.491833\pi\) | ||||
0.0256551 | + | 0.999671i | \(0.491833\pi\) | |||||||
\(752\) | 16728.0 | 0.811180 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4872.00 | 0.235315 | ||||||||
\(755\) | 1440.00 | 0.0694132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18702.0 | −0.897934 | −0.448967 | − | 0.893548i | \(-0.648208\pi\) | ||||
−0.448967 | + | 0.893548i | \(0.648208\pi\) | |||||||
\(758\) | −5892.00 | −0.282331 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2160.00 | 0.103094 | ||||||||
\(761\) | −17904.0 | −0.852851 | −0.426425 | − | 0.904523i | \(-0.640227\pi\) | ||||
−0.426425 | + | 0.904523i | \(0.640227\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17584.0 | 0.832679 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10488.0 | 0.494709 | ||||||||
\(767\) | 41328.0 | 1.94559 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7560.00 | −0.354513 | −0.177257 | − | 0.984165i | \(-0.556722\pi\) | ||||
−0.177257 | + | 0.984165i | \(0.556722\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17010.0 | 0.793009 | ||||||||
\(773\) | 14292.0 | 0.665003 | 0.332502 | − | 0.943103i | \(-0.392107\pi\) | ||||
0.332502 | + | 0.943103i | \(0.392107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5016.00 | −0.232490 | ||||||||
\(776\) | 2520.00 | 0.116576 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4514.00 | −0.208014 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5920.00 | 0.271235 | ||||||||
\(782\) | 16896.0 | 0.772634 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22032.0 | −1.00173 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26364.0 | 1.19412 | 0.597062 | − | 0.802195i | \(-0.296335\pi\) | ||||
0.597062 | + | 0.802195i | \(0.296335\pi\) | |||||||
\(788\) | −12334.0 | −0.557590 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9312.00 | −0.419375 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41328.0 | 1.85069 | ||||||||
\(794\) | −6036.00 | −0.269785 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21672.0 | −0.965005 | ||||||||
\(797\) | −17220.0 | −0.765325 | −0.382662 | − | 0.923888i | \(-0.624993\pi\) | ||||
−0.382662 | + | 0.923888i | \(0.624993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39168.0 | 1.73425 | ||||||||
\(800\) | 3059.00 | 0.135190 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6770.00 | 0.298076 | ||||||||
\(803\) | −4800.00 | −0.210944 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22176.0 | 0.969127 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22860.0 | −0.995312 | ||||||||
\(809\) | −16442.0 | −0.714549 | −0.357274 | − | 0.933999i | \(-0.616294\pi\) | ||||
−0.357274 | + | 0.933999i | \(0.616294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31332.0 | −1.35662 | −0.678308 | − | 0.734778i | \(-0.737286\pi\) | ||||
−0.678308 | + | 0.734778i | \(0.737286\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5160.00 | −0.222184 | ||||||||
\(815\) | −10992.0 | −0.472433 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1872.00 | 0.0801628 | ||||||||
\(818\) | 12504.0 | 0.534465 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25810.0 | 1.09717 | 0.548584 | − | 0.836095i | \(-0.315167\pi\) | ||||
0.548584 | + | 0.836095i | \(0.315167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12368.0 | 0.523841 | 0.261921 | − | 0.965089i | \(-0.415644\pi\) | ||||
0.261921 | + | 0.965089i | \(0.415644\pi\) | |||||||
\(824\) | 6120.00 | 0.258738 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6316.00 | −0.265573 | −0.132786 | − | 0.991145i | \(-0.542392\pi\) | ||||
−0.132786 | + | 0.991145i | \(0.542392\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23868.0 | −0.999964 | −0.499982 | − | 0.866036i | \(-0.666660\pi\) | ||||
−0.499982 | + | 0.866036i | \(0.666660\pi\) | |||||||
\(830\) | 11088.0 | 0.463699 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14028.0 | 0.584535 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6048.00 | 0.250658 | ||||||||
\(836\) | 1680.00 | 0.0695024 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9492.00 | −0.391284 | ||||||||
\(839\) | 48216.0 | 1.98403 | 0.992015 | − | 0.126120i | \(-0.0402524\pi\) | ||||
0.992015 | + | 0.126120i | \(0.0402524\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | 5182.00 | 0.212094 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1092.00 | −0.0445358 | ||||||||
\(845\) | −58308.0 | −2.37379 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 29602.0 | 1.19875 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1824.00 | 0.0736032 | ||||||||
\(851\) | 45408.0 | 1.82910 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27300.0 | −1.09582 | −0.547910 | − | 0.836537i | \(-0.684576\pi\) | ||||
−0.547910 | + | 0.836537i | \(0.684576\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12300.0 | −0.491128 | ||||||||
\(857\) | −8640.00 | −0.344384 | −0.172192 | − | 0.985063i | \(-0.555085\pi\) | ||||
−0.172192 | + | 0.985063i | \(0.555085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24372.0 | 0.968058 | 0.484029 | − | 0.875052i | \(-0.339173\pi\) | ||||
0.484029 | + | 0.875052i | \(0.339173\pi\) | |||||||
\(860\) | 13104.0 | 0.519585 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5720.00 | 0.226014 | ||||||||
\(863\) | −2176.00 | −0.0858307 | −0.0429154 | − | 0.999079i | \(-0.513665\pi\) | ||||
−0.0429154 | + | 0.999079i | \(0.513665\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22032.0 | −0.866024 | ||||||||
\(866\) | 13608.0 | 0.533971 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15520.0 | −0.605846 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34608.0 | −1.34632 | ||||||||
\(872\) | 13770.0 | 0.534760 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2112.00 | 0.0817385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27574.0 | −1.06170 | −0.530848 | − | 0.847467i | \(-0.678127\pi\) | ||||
−0.530848 | + | 0.847467i | \(0.678127\pi\) | |||||||
\(878\) | 12864.0 | 0.494464 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9840.00 | 0.376939 | ||||||||
\(881\) | −16968.0 | −0.648884 | −0.324442 | − | 0.945906i | \(-0.605176\pi\) | ||||
−0.324442 | + | 0.945906i | \(0.605176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1860.00 | −0.0708879 | −0.0354439 | − | 0.999372i | \(-0.511285\pi\) | ||||
−0.0354439 | + | 0.999372i | \(0.511285\pi\) | |||||||
\(884\) | 56448.0 | 2.14768 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13252.0 | 0.502494 | ||||||||
\(887\) | −2280.00 | −0.0863077 | −0.0431538 | − | 0.999068i | \(-0.513741\pi\) | ||||
−0.0431538 | + | 0.999068i | \(0.513741\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8928.00 | −0.336255 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −35280.0 | −1.32428 | ||||||||
\(893\) | 4896.00 | 0.183470 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28464.0 | 1.06307 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −226.000 | −0.00839835 | ||||||||
\(899\) | 15312.0 | 0.568058 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 69312.0 | 2.56284 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1650.00 | −0.0607060 | ||||||||
\(905\) | 13104.0 | 0.481317 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36084.0 | 1.32100 | 0.660501 | − | 0.750825i | \(-0.270344\pi\) | ||||
0.660501 | + | 0.750825i | \(0.270344\pi\) | |||||||
\(908\) | 15204.0 | 0.555686 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24152.0 | −0.878366 | −0.439183 | − | 0.898398i | \(-0.644732\pi\) | ||||
−0.439183 | + | 0.898398i | \(0.644732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18480.0 | 0.669878 | ||||||||
\(914\) | −11334.0 | −0.410170 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18900.0 | −0.681740 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36336.0 | 1.30426 | 0.652130 | − | 0.758108i | \(-0.273876\pi\) | ||||
0.652130 | + | 0.758108i | \(0.273876\pi\) | |||||||
\(920\) | 31680.0 | 1.13528 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1596.00 | 0.0570081 | ||||||||
\(923\) | 24864.0 | 0.886683 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4902.00 | 0.174245 | ||||||||
\(926\) | 12728.0 | 0.451693 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9338.00 | −0.330318 | ||||||||
\(929\) | −432.000 | −0.0152567 | −0.00762834 | − | 0.999971i | \(-0.502428\pi\) | ||||
−0.00762834 | + | 0.999971i | \(0.502428\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −26614.0 | −0.935376 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3012.00 | 0.105520 | ||||||||
\(935\) | 23040.0 | 0.805870 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22176.0 | 0.773168 | 0.386584 | − | 0.922254i | \(-0.373655\pi\) | ||||
0.386584 | + | 0.922254i | \(0.373655\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 34272.0 | 1.18918 | ||||||||
\(941\) | 43524.0 | 1.50780 | 0.753901 | − | 0.656988i | \(-0.228170\pi\) | ||||
0.753901 | + | 0.656988i | \(0.228170\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −20172.0 | −0.695490 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3120.00 | −0.107230 | ||||||||
\(947\) | −1868.00 | −0.0640991 | −0.0320495 | − | 0.999486i | \(-0.510203\pi\) | ||||
−0.0320495 | + | 0.999486i | \(0.510203\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20160.0 | −0.689590 | ||||||||
\(950\) | 228.000 | 0.00778663 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9238.00 | 0.314006 | 0.157003 | − | 0.987598i | \(-0.449817\pi\) | ||||
0.157003 | + | 0.987598i | \(0.449817\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30144.0 | 1.02140 | ||||||||
\(956\) | −30856.0 | −1.04389 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4296.00 | 0.144883 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39905.0 | 1.33950 | ||||||||
\(962\) | −21672.0 | −0.726334 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21672.0 | −0.724075 | ||||||||
\(965\) | 29160.0 | 0.972739 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30616.0 | −1.01814 | −0.509071 | − | 0.860724i | \(-0.670011\pi\) | ||||
−0.509071 | + | 0.860724i | \(0.670011\pi\) | |||||||
\(968\) | 13965.0 | 0.463690 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2016.00 | 0.0667318 | ||||||||
\(971\) | 27540.0 | 0.910196 | 0.455098 | − | 0.890441i | \(-0.349604\pi\) | ||||
0.455098 | + | 0.890441i | \(0.349604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8184.00 | −0.269232 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20172.0 | −0.661568 | ||||||||
\(977\) | 16402.0 | 0.537100 | 0.268550 | − | 0.963266i | \(-0.413456\pi\) | ||||
0.268550 | + | 0.963266i | \(0.413456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14880.0 | −0.485768 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12164.0 | 0.395284 | ||||||||
\(983\) | −55176.0 | −1.79028 | −0.895138 | − | 0.445789i | \(-0.852923\pi\) | ||||
−0.895138 | + | 0.445789i | \(0.852923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21144.0 | −0.683963 | ||||||||
\(986\) | −5568.00 | −0.179839 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7056.00 | 0.227208 | ||||||||
\(989\) | 27456.0 | 0.882760 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27096.0 | 0.868550 | 0.434275 | − | 0.900780i | \(-0.357005\pi\) | ||||
0.434275 | + | 0.900780i | \(0.357005\pi\) | |||||||
\(992\) | −42504.0 | −1.36039 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −37152.0 | −1.18372 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16812.0 | −0.534044 | −0.267022 | − | 0.963691i | \(-0.586040\pi\) | ||||
−0.267022 | + | 0.963691i | \(0.586040\pi\) | |||||||
\(998\) | 972.000 | 0.0308298 | ||||||||
\(999\) | 0 | 0 |
(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 | 441.4.a.g.1.1 | 1 | ||
3.2 | odd | 2 | 147.4.a.d.1.1 | ✓ | 1 | ||
7.2 | even | 3 | 441.4.e.g.361.1 | 2 | |||
7.3 | odd | 6 | 441.4.e.f.226.1 | 2 | |||
7.4 | even | 3 | 441.4.e.g.226.1 | 2 | |||
7.5 | odd | 6 | 441.4.e.f.361.1 | 2 | |||
7.6 | odd | 2 | 441.4.a.h.1.1 | 1 | |||
12.11 | even | 2 | 2352.4.a.bi.1.1 | 1 | |||
21.2 | odd | 6 | 147.4.e.f.67.1 | 2 | |||
21.5 | even | 6 | 147.4.e.e.67.1 | 2 | |||
21.11 | odd | 6 | 147.4.e.f.79.1 | 2 | |||
21.17 | even | 6 | 147.4.e.e.79.1 | 2 | |||
21.20 | even | 2 | 147.4.a.e.1.1 | yes | 1 | ||
84.83 | odd | 2 | 2352.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.d.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
147.4.a.e.1.1 | yes | 1 | 21.20 | even | 2 | ||
147.4.e.e.67.1 | 2 | 21.5 | even | 6 | |||
147.4.e.e.79.1 | 2 | 21.17 | even | 6 | |||
147.4.e.f.67.1 | 2 | 21.2 | odd | 6 | |||
147.4.e.f.79.1 | 2 | 21.11 | odd | 6 | |||
441.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
441.4.a.h.1.1 | 1 | 7.6 | odd | 2 | |||
441.4.e.f.226.1 | 2 | 7.3 | odd | 6 | |||
441.4.e.f.361.1 | 2 | 7.5 | odd | 6 | |||
441.4.e.g.226.1 | 2 | 7.4 | even | 3 | |||
441.4.e.g.361.1 | 2 | 7.2 | even | 3 | |||
2352.4.a.b.1.1 | 1 | 84.83 | odd | 2 | |||
2352.4.a.bi.1.1 | 1 | 12.11 | even | 2 |