Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(1,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 624.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −20.0000 | −1.78885 | −0.894427 | − | 0.447214i | \(-0.852416\pi\) | ||||
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 32.0000 | 1.72784 | 0.863919 | − | 0.503631i | \(-0.168003\pi\) | ||||
0.863919 | + | 0.503631i | \(0.168003\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −50.0000 | −1.37051 | −0.685253 | − | 0.728305i | \(-0.740308\pi\) | ||||
−0.685253 | + | 0.728305i | \(0.740308\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −60.0000 | −1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.0000 | −0.428004 | −0.214002 | − | 0.976833i | \(-0.568650\pi\) | ||||
−0.214002 | + | 0.976833i | \(0.568650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 120.000 | 1.44894 | 0.724471 | − | 0.689306i | \(-0.242084\pi\) | ||||
0.724471 | + | 0.689306i | \(0.242084\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 96.0000 | 0.997567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.0000 | 0.181317 | 0.0906584 | − | 0.995882i | \(-0.471103\pi\) | ||||
0.0906584 | + | 0.995882i | \(0.471103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 275.000 | 2.20000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 82.0000 | 0.525070 | 0.262535 | − | 0.964923i | \(-0.415442\pi\) | ||||
0.262535 | + | 0.964923i | \(0.415442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.0000 | 0.254924 | 0.127462 | − | 0.991843i | \(-0.459317\pi\) | ||||
0.127462 | + | 0.991843i | \(0.459317\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −150.000 | −0.791262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −640.000 | −3.09085 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −306.000 | −1.35962 | −0.679812 | − | 0.733386i | \(-0.737939\pi\) | ||||
−0.679812 | + | 0.733386i | \(0.737939\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 108.000 | 0.411385 | 0.205692 | − | 0.978617i | \(-0.434055\pi\) | ||||
0.205692 | + | 0.978617i | \(0.434055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 356.000 | 1.26255 | 0.631273 | − | 0.775561i | \(-0.282533\pi\) | ||||
0.631273 | + | 0.775561i | \(0.282533\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −180.000 | −0.596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 178.000 | 0.552425 | 0.276212 | − | 0.961097i | \(-0.410921\pi\) | ||||
0.276212 | + | 0.961097i | \(0.410921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −90.0000 | −0.247108 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 198.000 | 0.513158 | 0.256579 | − | 0.966523i | \(-0.417405\pi\) | ||||
0.256579 | + | 0.966523i | \(0.417405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1000.00 | 2.45164 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 360.000 | 0.836547 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −94.0000 | −0.207420 | −0.103710 | − | 0.994608i | \(-0.533071\pi\) | ||||
−0.103710 | + | 0.994608i | \(0.533071\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −62.0000 | −0.130136 | −0.0650679 | − | 0.997881i | \(-0.520726\pi\) | ||||
−0.0650679 | + | 0.997881i | \(0.520726\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 288.000 | 0.575946 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 260.000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 140.000 | 0.255279 | 0.127640 | − | 0.991821i | \(-0.459260\pi\) | ||||
0.127640 | + | 0.991821i | \(0.459260\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 60.0000 | 0.104683 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 778.000 | 1.30045 | 0.650223 | − | 0.759744i | \(-0.274676\pi\) | ||||
0.650223 | + | 0.759744i | \(0.274676\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 62.0000 | 0.0994048 | 0.0497024 | − | 0.998764i | \(-0.484173\pi\) | ||||
0.0497024 | + | 0.998764i | \(0.484173\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 825.000 | 1.27017 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1600.00 | −2.36801 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1096.00 | 1.56088 | 0.780441 | − | 0.625230i | \(-0.214995\pi\) | ||||
0.780441 | + | 0.625230i | \(0.214995\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 462.000 | 0.610977 | 0.305488 | − | 0.952196i | \(-0.401180\pi\) | ||||
0.305488 | + | 0.952196i | \(0.401180\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 600.000 | 0.765637 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 246.000 | 0.303149 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1224.00 | 1.45779 | 0.728897 | − | 0.684623i | \(-0.240033\pi\) | ||||
0.728897 | + | 0.684623i | \(0.240033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −416.000 | −0.479216 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 132.000 | 0.147180 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2400.00 | −2.59195 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 614.000 | 0.642704 | 0.321352 | − | 0.946960i | \(-0.395863\pi\) | ||||
0.321352 | + | 0.946960i | \(0.395863\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −450.000 | −0.456835 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1058.00 | 1.04233 | 0.521163 | − | 0.853457i | \(-0.325498\pi\) | ||||
0.521163 | + | 0.853457i | \(0.325498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1768.00 | −1.69132 | −0.845661 | − | 0.533720i | \(-0.820794\pi\) | ||||
−0.845661 | + | 0.533720i | \(0.820794\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1920.00 | −1.78450 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1808.00 | 1.63351 | 0.816757 | − | 0.576982i | \(-0.195770\pi\) | ||||
0.816757 | + | 0.576982i | \(0.195770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1886.00 | −1.65730 | −0.828652 | − | 0.559765i | \(-0.810891\pi\) | ||||
−0.828652 | + | 0.559765i | \(0.810891\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −918.000 | −0.784979 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1246.00 | 1.03729 | 0.518645 | − | 0.854990i | \(-0.326437\pi\) | ||||
0.518645 | + | 0.854990i | \(0.326437\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −400.000 | −0.324349 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −960.000 | −0.739521 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1169.00 | 0.878287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 324.000 | 0.237513 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3000.00 | −2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1624.00 | −1.13470 | −0.567349 | − | 0.823477i | \(-0.692031\pi\) | ||||
−0.567349 | + | 0.823477i | \(0.692031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1068.00 | 0.728931 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2072.00 | 1.38192 | 0.690960 | − | 0.722893i | \(-0.257188\pi\) | ||||
0.690960 | + | 0.722893i | \(0.257188\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3840.00 | 2.50354 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −540.000 | −0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −756.000 | −0.471456 | −0.235728 | − | 0.971819i | \(-0.575747\pi\) | ||||
−0.235728 | + | 0.971819i | \(0.575747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −172.000 | −0.104956 | −0.0524779 | − | 0.998622i | \(-0.516712\pi\) | ||||
−0.0524779 | + | 0.998622i | \(0.516712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 534.000 | 0.318943 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 650.000 | 0.380110 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1640.00 | −0.939273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2043.00 | 1.14628 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1272.00 | 0.699371 | 0.349686 | − | 0.936867i | \(-0.386288\pi\) | ||||
0.349686 | + | 0.936867i | \(0.386288\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1404.00 | −0.756662 | −0.378331 | − | 0.925670i | \(-0.623502\pi\) | ||||
−0.378331 | + | 0.925670i | \(0.623502\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −270.000 | −0.142668 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −880.000 | −0.456021 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2170.00 | −1.10309 | −0.551544 | − | 0.834146i | \(-0.685961\pi\) | ||||
−0.551544 | + | 0.834146i | \(0.685961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 594.000 | 0.296272 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 640.000 | 0.313286 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −248.000 | −0.119171 | −0.0595855 | − | 0.998223i | \(-0.518978\pi\) | ||||
−0.0595855 | + | 0.998223i | \(0.518978\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3000.00 | 1.41545 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −102.000 | −0.0472635 | −0.0236317 | − | 0.999721i | \(-0.507523\pi\) | ||||
−0.0236317 | + | 0.999721i | \(0.507523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1080.00 | 0.482980 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 682.000 | 0.299720 | 0.149860 | − | 0.988707i | \(-0.452118\pi\) | ||||
0.149860 | + | 0.988707i | \(0.452118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8800.00 | 3.80124 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −282.000 | −0.119754 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 612.000 | 0.255548 | 0.127774 | − | 0.991803i | \(-0.459217\pi\) | ||||
0.127774 | + | 0.991803i | \(0.459217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −66.0000 | −0.0271035 | −0.0135518 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135518 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −186.000 | −0.0751340 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6120.00 | 2.43217 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1500.00 | 0.586582 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 864.000 | 0.332522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −608.000 | −0.230332 | −0.115166 | − | 0.993346i | \(-0.536740\pi\) | ||||
−0.115166 | + | 0.993346i | \(0.536740\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1370.00 | 0.510957 | 0.255479 | − | 0.966815i | \(-0.417767\pi\) | ||||
0.255479 | + | 0.966815i | \(0.417767\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 780.000 | 0.286446 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4908.00 | −1.77503 | −0.887514 | − | 0.460781i | \(-0.847569\pi\) | ||||
−0.887514 | + | 0.460781i | \(0.847569\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 328.000 | 0.116841 | 0.0584204 | − | 0.998292i | \(-0.481394\pi\) | ||||
0.0584204 | + | 0.998292i | \(0.481394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 420.000 | 0.147386 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2624.00 | 0.907235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2160.00 | −0.735907 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 180.000 | 0.0604390 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6000.00 | −1.98578 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1316.00 | −0.429371 | −0.214685 | − | 0.976683i | \(-0.568873\pi\) | ||||
−0.214685 | + | 0.976683i | \(0.568873\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2334.00 | 0.750812 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7120.00 | −2.25851 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1408.00 | 0.440467 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 186.000 | 0.0573914 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 390.000 | 0.118707 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1932.00 | 0.580163 | 0.290081 | − | 0.957002i | \(-0.406318\pi\) | ||||
0.290081 | + | 0.957002i | \(0.406318\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2475.00 | 0.733333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4998.00 | −1.46136 | −0.730680 | − | 0.682720i | \(-0.760797\pi\) | ||||
−0.730680 | + | 0.682720i | \(0.760797\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −78.0000 | −0.0225082 | −0.0112541 | − | 0.999937i | \(-0.503582\pi\) | ||||
−0.0112541 | + | 0.999937i | \(0.503582\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4800.00 | −1.36717 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1282.00 | −0.360458 | −0.180229 | − | 0.983625i | \(-0.557684\pi\) | ||||
−0.180229 | + | 0.983625i | \(0.557684\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3560.00 | −0.988208 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3288.00 | 0.901175 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −294.000 | −0.0795702 | −0.0397851 | − | 0.999208i | \(-0.512667\pi\) | ||||
−0.0397851 | + | 0.999208i | \(0.512667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4962.00 | −1.32627 | −0.663134 | − | 0.748501i | \(-0.730774\pi\) | ||||
−0.663134 | + | 0.748501i | \(0.730774\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13620.0 | −3.55163 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1560.00 | −0.401864 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1386.00 | 0.352748 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −744.000 | −0.187095 | −0.0935475 | − | 0.995615i | \(-0.529821\pi\) | ||||
−0.0935475 | + | 0.995615i | \(0.529821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1000.00 | −0.248496 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1800.00 | 0.442041 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1026.00 | −0.249028 | −0.124514 | − | 0.992218i | \(-0.539737\pi\) | ||||
−0.124514 | + | 0.992218i | \(0.539737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9792.00 | −2.34921 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 738.000 | 0.175023 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5532.00 | 1.29703 | 0.648513 | − | 0.761204i | \(-0.275391\pi\) | ||||
0.648513 | + | 0.761204i | \(0.275391\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3960.00 | −0.917966 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3672.00 | 0.841658 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3534.00 | −0.801010 | −0.400505 | − | 0.916294i | \(-0.631165\pi\) | ||||
−0.400505 | + | 0.916294i | \(0.631165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2392.00 | −0.536176 | −0.268088 | − | 0.963394i | \(-0.586392\pi\) | ||||
−0.268088 | + | 0.963394i | \(0.586392\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1248.00 | −0.276675 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13750.0 | −3.01511 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6102.00 | 1.32359 | 0.661794 | − | 0.749686i | \(-0.269796\pi\) | ||||
0.661794 | + | 0.749686i | \(0.269796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 396.000 | 0.0849746 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7540.00 | −1.60071 | −0.800354 | − | 0.599528i | \(-0.795355\pi\) | ||||
−0.800354 | + | 0.599528i | \(0.795355\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2756.00 | 0.578895 | 0.289447 | − | 0.957194i | \(-0.406528\pi\) | ||||
0.289447 | + | 0.957194i | \(0.406528\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7200.00 | −1.49646 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3456.00 | 0.710806 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4013.00 | −0.816813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1842.00 | 0.371065 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 968.000 | 0.193007 | 0.0965037 | − | 0.995333i | \(-0.469234\pi\) | ||||
0.0965037 | + | 0.995333i | \(0.469234\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1880.00 | 0.371043 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1350.00 | −0.263754 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −260.000 | −0.0502883 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11392.0 | 2.18147 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3174.00 | 0.601787 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1240.00 | 0.232794 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6436.00 | 1.19649 | 0.598244 | − | 0.801314i | \(-0.295865\pi\) | ||||
0.598244 | + | 0.801314i | \(0.295865\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5304.00 | −0.976485 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7932.00 | −1.44625 | −0.723123 | − | 0.690719i | \(-0.757294\pi\) | ||||
−0.723123 | + | 0.690719i | \(0.757294\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10358.0 | 1.87051 | 0.935254 | − | 0.353978i | \(-0.115171\pi\) | ||||
0.935254 | + | 0.353978i | \(0.115171\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5760.00 | −1.03028 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2820.00 | −0.499643 | −0.249822 | − | 0.968292i | \(-0.580372\pi\) | ||||
−0.249822 | + | 0.968292i | \(0.580372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4100.00 | −0.719611 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5424.00 | 0.943110 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3600.00 | −0.620153 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3575.00 | −0.610170 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5658.00 | −0.956844 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5696.00 | 0.954500 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4180.00 | 0.694120 | 0.347060 | − | 0.937843i | \(-0.387180\pi\) | ||||
0.347060 | + | 0.937843i | \(0.387180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2754.00 | −0.453208 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2800.00 | −0.456658 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5026.00 | −0.812414 | −0.406207 | − | 0.913781i | \(-0.633149\pi\) | ||||
−0.406207 | + | 0.913781i | \(0.633149\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3738.00 | 0.598880 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2200.00 | −0.349374 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10816.0 | 1.70265 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1200.00 | −0.187263 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7332.00 | 1.13430 | 0.567150 | − | 0.823614i | \(-0.308046\pi\) | ||||
0.567150 | + | 0.823614i | \(0.308046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8162.00 | −1.25187 | −0.625934 | − | 0.779876i | \(-0.715282\pi\) | ||||
−0.625934 | + | 0.779876i | \(0.715282\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1244.00 | 0.187568 | 0.0937839 | − | 0.995593i | \(-0.470104\pi\) | ||||
0.0937839 | + | 0.995593i | \(0.470104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15560.0 | −2.32631 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2880.00 | −0.426963 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9558.00 | −1.40516 | −0.702579 | − | 0.711605i | \(-0.747968\pi\) | ||||
−0.702579 | + | 0.711605i | \(0.747968\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7541.00 | 1.09943 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3507.00 | 0.507079 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1240.00 | −0.177821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11032.0 | 1.56912 | 0.784558 | − | 0.620055i | \(-0.212890\pi\) | ||||
0.784558 | + | 0.620055i | \(0.212890\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 972.000 | 0.137128 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6336.00 | 0.886654 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5474.00 | 0.759874 | 0.379937 | − | 0.925012i | \(-0.375946\pi\) | ||||
0.379937 | + | 0.925012i | \(0.375946\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9000.00 | −1.23935 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1066.00 | −0.145628 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7040.00 | 0.954144 | 0.477072 | − | 0.878864i | \(-0.341698\pi\) | ||||
0.477072 | + | 0.878864i | \(0.341698\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4872.00 | −0.655118 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1830.00 | 0.244148 | 0.122074 | − | 0.992521i | \(-0.461045\pi\) | ||||
0.122074 | + | 0.992521i | \(0.461045\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32000.0 | 4.23603 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3204.00 | 0.420849 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10158.0 | 1.32399 | 0.661994 | − | 0.749509i | \(-0.269711\pi\) | ||||
0.661994 | + | 0.749509i | \(0.269711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −600.000 | −0.0776044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6216.00 | 0.797852 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21920.0 | −2.79219 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12658.0 | −1.60022 | −0.800109 | − | 0.599854i | \(-0.795225\pi\) | ||||
−0.800109 | + | 0.599854i | \(0.795225\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11520.0 | 1.44542 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15720.0 | 1.95765 | 0.978827 | − | 0.204689i | \(-0.0656182\pi\) | ||||
0.978827 | + | 0.204689i | \(0.0656182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −572.000 | −0.0707031 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1620.00 | −0.198762 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15300.0 | 1.86337 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7654.00 | 0.925345 | 0.462672 | − | 0.886529i | \(-0.346891\pi\) | ||||
0.462672 | + | 0.886529i | \(0.346891\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2268.00 | −0.272195 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3008.00 | −0.358387 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9240.00 | −1.09295 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −516.000 | −0.0605962 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1848.00 | 0.215467 | 0.107734 | − | 0.994180i | \(-0.465641\pi\) | ||||
0.107734 | + | 0.994180i | \(0.465641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12542.0 | −1.45192 | −0.725962 | − | 0.687735i | \(-0.758605\pi\) | ||||
−0.725962 | + | 0.687735i | \(0.758605\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1602.00 | 0.184142 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8250.00 | −0.941609 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1984.00 | −0.224854 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1950.00 | 0.219457 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5238.00 | 0.585396 | 0.292698 | − | 0.956205i | \(-0.405447\pi\) | ||||
0.292698 | + | 0.956205i | \(0.405447\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8258.00 | −0.916522 | −0.458261 | − | 0.888818i | \(-0.651528\pi\) | ||||
−0.458261 | + | 0.888818i | \(0.651528\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4920.00 | −0.542290 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2400.00 | 0.262718 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6304.00 | 0.685361 | 0.342681 | − | 0.939452i | \(-0.388665\pi\) | ||||
0.342681 | + | 0.939452i | \(0.388665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12744.0 | −1.36678 | −0.683392 | − | 0.730051i | \(-0.739496\pi\) | ||||
−0.683392 | + | 0.730051i | \(0.739496\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24480.0 | −2.60778 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3816.00 | 0.403782 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11776.0 | −1.23774 | −0.618868 | − | 0.785495i | \(-0.712409\pi\) | ||||
−0.618868 | + | 0.785495i | \(0.712409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5400.00 | −0.563805 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4212.00 | −0.436859 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8320.00 | 0.857248 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2134.00 | 0.218434 | 0.109217 | − | 0.994018i | \(-0.465166\pi\) | ||||
0.109217 | + | 0.994018i | \(0.465166\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −810.000 | −0.0823694 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2724.00 | 0.275205 | 0.137602 | − | 0.990488i | \(-0.456060\pi\) | ||||
0.137602 | + | 0.990488i | \(0.456060\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5648.00 | 0.566922 | 0.283461 | − | 0.958984i | \(-0.408517\pi\) | ||||
0.283461 | + | 0.958984i | \(0.408517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2640.00 | −0.263284 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18224.0 | 1.80579 | 0.902897 | − | 0.429856i | \(-0.141436\pi\) | ||||
0.902897 | + | 0.429856i | \(0.141436\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4480.00 | 0.441081 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6510.00 | −0.636868 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17800.0 | −1.73033 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33000.0 | 3.18767 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1782.00 | 0.171053 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9066.00 | −0.864794 | −0.432397 | − | 0.901683i | \(-0.642332\pi\) | ||||
−0.432397 | + | 0.901683i | \(0.642332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3978.00 | 0.377092 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1920.00 | 0.180876 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12280.0 | −1.14970 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8948.00 | −0.832593 | −0.416296 | − | 0.909229i | \(-0.636672\pi\) | ||||
−0.416296 | + | 0.909229i | \(0.636672\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −744.000 | −0.0688034 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8720.00 | −0.801483 | −0.400741 | − | 0.916191i | \(-0.631247\pi\) | ||||
−0.400741 | + | 0.916191i | \(0.631247\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2460.00 | −0.224732 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9000.00 | 0.817212 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24896.0 | 2.24696 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6604.00 | −0.592456 | −0.296228 | − | 0.955117i | \(-0.595729\pi\) | ||||
−0.296228 | + | 0.955117i | \(0.595729\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −306.000 | −0.0272876 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3404.00 | −0.301743 | −0.150872 | − | 0.988553i | \(-0.548208\pi\) | ||||
−0.150872 | + | 0.988553i | \(0.548208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21160.0 | −1.86457 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −76.0000 | −0.00661815 | −0.00330908 | − | 0.999995i | \(-0.501053\pi\) | ||||
−0.00330908 | + | 0.999995i | \(0.501053\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1984.00 | 0.171755 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3240.00 | 0.278849 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35360.0 | 3.02553 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8900.00 | −0.757102 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2046.00 | 0.173043 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12054.0 | 1.01362 | 0.506809 | − | 0.862058i | \(-0.330825\pi\) | ||||
0.506809 | + | 0.862058i | \(0.330825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −276.000 | −0.0230758 | −0.0115379 | − | 0.999933i | \(-0.503673\pi\) | ||||
−0.0115379 | + | 0.999933i | \(0.503673\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26400.0 | 2.19465 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1320.00 | −0.109108 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11767.0 | −0.967124 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −846.000 | −0.0691399 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1404.00 | −0.114098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36160.0 | −2.92212 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1836.00 | 0.147540 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34050.0 | −2.72103 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13778.0 | 1.09494 | 0.547470 | − | 0.836825i | \(-0.315591\pi\) | ||||
0.547470 | + | 0.836825i | \(0.315591\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −198.000 | −0.0156482 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37720.0 | 2.96467 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10844.0 | 0.847634 | 0.423817 | − | 0.905748i | \(-0.360690\pi\) | ||||
0.423817 | + | 0.905748i | \(0.360690\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −558.000 | −0.0433786 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9840.00 | 0.760795 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35072.0 | 2.69695 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18360.0 | 1.40421 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20544.0 | 1.56280 | 0.781398 | − | 0.624033i | \(-0.214507\pi\) | ||||
0.781398 | + | 0.624033i | \(0.214507\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4628.00 | −0.350167 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4500.00 | 0.338663 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6988.00 | −0.523107 | −0.261553 | − | 0.965189i | \(-0.584235\pi\) | ||||
−0.261553 | + | 0.965189i | \(0.584235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24920.0 | −1.85556 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2592.00 | 0.191982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −706.000 | −0.0520159 | −0.0260080 | − | 0.999662i | \(-0.508280\pi\) | ||||
−0.0260080 | + | 0.999662i | \(0.508280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17532.0 | 1.28492 | 0.642462 | − | 0.766318i | \(-0.277913\pi\) | ||||
0.642462 | + | 0.766318i | \(0.277913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1824.00 | −0.132982 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5500.00 | 0.398897 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14814.0 | −1.06883 | −0.534415 | − | 0.845222i | \(-0.679468\pi\) | ||||
−0.534415 | + | 0.845222i | \(0.679468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4110.00 | 0.295001 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14784.0 | 1.05567 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9900.00 | −0.703287 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2340.00 | 0.165380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14170.0 | −0.996352 | −0.498176 | − | 0.867076i | \(-0.665997\pi\) | ||||
−0.498176 | + | 0.867076i | \(0.665997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5280.00 | 0.369369 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14724.0 | −1.02481 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11744.0 | −0.813269 | −0.406634 | − | 0.913591i | \(-0.633298\pi\) | ||||
−0.406634 | + | 0.913591i | \(0.633298\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19200.0 | 1.32290 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 984.000 | 0.0674580 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15076.0 | 1.02836 | 0.514181 | − | 0.857682i | \(-0.328096\pi\) | ||||
0.514181 | + | 0.857682i | \(0.328096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20230.0 | 1.37304 | 0.686522 | − | 0.727109i | \(-0.259137\pi\) | ||||
0.686522 | + | 0.727109i | \(0.259137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1260.00 | 0.0850931 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23380.0 | −1.57113 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28056.0 | 1.87604 | 0.938021 | − | 0.346577i | \(-0.112656\pi\) | ||||
0.938021 | + | 0.346577i | \(0.112656\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7872.00 | 0.523792 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2314.00 | −0.153215 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27446.0 | 1.80837 | 0.904187 | − | 0.427136i | \(-0.140478\pi\) | ||||
0.904187 | + | 0.427136i | \(0.140478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6480.00 | −0.424876 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8804.00 | 0.574450 | 0.287225 | − | 0.957863i | \(-0.407267\pi\) | ||||
0.287225 | + | 0.957863i | \(0.407267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3508.00 | −0.227784 | −0.113892 | − | 0.993493i | \(-0.536332\pi\) | ||||
−0.113892 | + | 0.993493i | \(0.536332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 540.000 | 0.0348945 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39168.0 | 2.51883 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25625.0 | 1.64000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18000.0 | −1.14649 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9180.00 | 0.581925 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22084.0 | −1.39326 | −0.696632 | − | 0.717428i | \(-0.745319\pi\) | ||||
−0.696632 | + | 0.717428i | \(0.745319\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3948.00 | −0.247897 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32480.0 | 2.02981 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8853.00 | −0.550657 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7002.00 | 0.433482 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7342.00 | −0.452405 | −0.226202 | − | 0.974080i | \(-0.572631\pi\) | ||||
−0.226202 | + | 0.974080i | \(0.572631\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2996.00 | −0.183749 | −0.0918746 | − | 0.995771i | \(-0.529286\pi\) | ||||
−0.0918746 | + | 0.995771i | \(0.529286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21360.0 | −1.30395 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9344.00 | −0.567775 | −0.283888 | − | 0.958858i | \(-0.591624\pi\) | ||||
−0.283888 | + | 0.958858i | \(0.591624\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4700.00 | 0.284270 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4224.00 | 0.254304 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16686.0 | −0.999960 | −0.499980 | − | 0.866037i | \(-0.666659\pi\) | ||||
−0.499980 | + | 0.866037i | \(0.666659\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41440.0 | −2.47205 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 558.000 | 0.0331349 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31356.0 | −1.85350 | −0.926750 | − | 0.375679i | \(-0.877410\pi\) | ||||
−0.926750 | + | 0.375679i | \(0.877410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 590.000 | 0.0347176 | 0.0173588 | − | 0.999849i | \(-0.494474\pi\) | ||||
0.0173588 | + | 0.999849i | \(0.494474\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1170.00 | 0.0685355 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −76800.0 | −4.47846 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1640.00 | 0.0952040 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5796.00 | 0.334957 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3100.00 | 0.178352 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5938.00 | 0.340109 | 0.170054 | − | 0.985435i | \(-0.445606\pi\) | ||||
0.170054 | + | 0.985435i | \(0.445606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7425.00 | 0.423390 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9486.00 | 0.538518 | 0.269259 | − | 0.963068i | \(-0.413221\pi\) | ||||
0.269259 | + | 0.963068i | \(0.413221\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19648.0 | 1.11049 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14994.0 | −0.843717 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26162.0 | −1.46568 | −0.732841 | − | 0.680400i | \(-0.761806\pi\) | ||||
−0.732841 | + | 0.680400i | \(0.761806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15120.0 | 0.843366 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −234.000 | −0.0129951 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2574.00 | −0.142325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17348.0 | 0.955064 | 0.477532 | − | 0.878614i | \(-0.341532\pi\) | ||||
0.477532 | + | 0.878614i | \(0.341532\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14400.0 | −0.789337 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3440.00 | 0.187751 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3240.00 | −0.176074 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3846.00 | −0.208110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 0.00161638 | 0.000808191 | − | 1.00000i | \(-0.499743\pi\) | ||||
0.000808191 | 1.00000i | \(0.499743\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36720.0 | −1.97002 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10680.0 | −0.570542 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33856.0 | 1.80097 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31466.0 | 1.66676 | 0.833378 | − | 0.552703i | \(-0.186404\pi\) | ||||
0.833378 | + | 0.552703i | \(0.186404\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9864.00 | 0.520294 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 880.000 | 0.0462220 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13000.0 | −0.679961 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −882.000 | −0.0459399 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28892.0 | 1.49859 | 0.749297 | − | 0.662234i | \(-0.230391\pi\) | ||||
0.749297 | + | 0.662234i | \(0.230391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56576.0 | −2.92233 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14886.0 | −0.765721 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22550.0 | 1.15515 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13384.0 | −0.682786 | −0.341393 | − | 0.939921i | \(-0.610899\pi\) | ||||
−0.341393 | + | 0.939921i | \(0.610899\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10680.0 | −0.540375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7130.00 | 0.359280 | 0.179640 | − | 0.983732i | \(-0.442507\pi\) | ||||
0.179640 | + | 0.983732i | \(0.442507\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −40860.0 | −2.05054 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7000.00 | −0.349862 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29268.0 | 1.45689 | 0.728444 | − | 0.685105i | \(-0.240244\pi\) | ||||
0.728444 | + | 0.685105i | \(0.240244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4680.00 | −0.232016 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9898.00 | 0.488725 | 0.244362 | − | 0.969684i | \(-0.421421\pi\) | ||||
0.244362 | + | 0.969684i | \(0.421421\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25440.0 | −1.25107 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4158.00 | 0.203659 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 57856.0 | 2.82245 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15120.0 | 0.734669 | 0.367335 | − | 0.930089i | \(-0.380270\pi\) | ||||
0.367335 | + | 0.930089i | \(0.380270\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2232.00 | −0.108019 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28080.0 | 1.35356 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5454.00 | −0.261861 | −0.130931 | − | 0.991392i | \(-0.541797\pi\) | ||||
−0.130931 | + | 0.991392i | \(0.541797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3000.00 | −0.143469 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11988.0 | −0.571044 | −0.285522 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285522 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −60352.0 | −2.86355 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5400.00 | 0.255212 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1222.00 | 0.0575279 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1338.00 | 0.0627432 | 0.0313716 | − | 0.999508i | \(-0.490012\pi\) | ||||
0.0313716 | + | 0.999508i | \(0.490012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3078.00 | −0.143776 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14408.0 | −0.670401 | −0.335200 | − | 0.942147i | \(-0.608804\pi\) | ||||
−0.335200 | + | 0.942147i | \(0.608804\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12100.0 | 0.560832 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −29376.0 | −1.35632 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12960.0 | 0.596072 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38900.0 | −1.78227 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2214.00 | 0.101050 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43400.0 | 1.97326 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10660.0 | 0.482831 | 0.241415 | − | 0.970422i | \(-0.422388\pi\) | ||||
0.241415 | + | 0.970422i | \(0.422388\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16596.0 | 0.748838 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39872.0 | 1.79227 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 806.000 | 0.0360932 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11880.0 | −0.529988 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1974.00 | 0.0877323 | 0.0438662 | − | 0.999037i | \(-0.486032\pi\) | ||||
0.0438662 | + | 0.999037i | \(0.486032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5340.00 | −0.236440 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11016.0 | 0.485932 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3100.00 | −0.136235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12800.0 | −0.560423 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10602.0 | −0.462464 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31734.0 | 1.37912 | 0.689560 | − | 0.724229i | \(-0.257804\pi\) | ||||
0.689560 | + | 0.724229i | \(0.257804\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38824.0 | 1.68100 | 0.840502 | − | 0.541808i | \(-0.182260\pi\) | ||||
0.840502 | + | 0.541808i | \(0.182260\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7176.00 | −0.309561 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4960.00 | 0.213179 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42720.0 | 1.82936 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3744.00 | −0.159739 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16736.0 | −0.711438 | −0.355719 | − | 0.934593i | \(-0.615764\pi\) | ||||
−0.355719 | + | 0.934593i | \(0.615764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42096.0 | −1.78296 | −0.891479 | − | 0.453062i | \(-0.850332\pi\) | ||||
−0.891479 | + | 0.453062i | \(0.850332\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −41250.0 | −1.74078 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24858.0 | −1.04522 | −0.522610 | − | 0.852572i | \(-0.675042\pi\) | ||||
−0.522610 | + | 0.852572i | \(0.675042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 922.000 | 0.0386277 | 0.0193139 | − | 0.999813i | \(-0.493852\pi\) | ||||
0.0193139 | + | 0.999813i | \(0.493852\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18306.0 | 0.764173 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20430.0 | −0.849769 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2040.00 | 0.0845474 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1188.00 | 0.0490601 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14294.0 | 0.588181 | 0.294090 | − | 0.955778i | \(-0.404983\pi\) | ||||
0.294090 | + | 0.955778i | \(0.404983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17665.0 | −0.724302 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22620.0 | −0.924169 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3380.00 | −0.137604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37408.0 | 1.51754 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8268.00 | 0.334225 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6120.00 | −0.246523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37966.0 | 1.52395 | 0.761976 | − | 0.647605i | \(-0.224229\pi\) | ||||
0.761976 | + | 0.647605i | \(0.224229\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21600.0 | −0.863982 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39038.0 | 1.55602 | 0.778012 | − | 0.628249i | \(-0.216228\pi\) | ||||
0.778012 | + | 0.628249i | \(0.216228\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20564.0 | −0.816804 | −0.408402 | − | 0.912802i | \(-0.633914\pi\) | ||||
−0.408402 | + | 0.912802i | \(0.633914\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10368.0 | 0.410384 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39866.0 | −1.57248 | −0.786242 | − | 0.617918i | \(-0.787976\pi\) | ||||
−0.786242 | + | 0.617918i | \(0.787976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13640.0 | −0.536155 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12039.0 | −0.471587 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −54800.0 | −2.13920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1820.00 | −0.0708018 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5526.00 | 0.214235 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −96000.0 | −3.70902 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30990.0 | 1.19322 | 0.596612 | − | 0.802530i | \(-0.296513\pi\) | ||||
0.596612 | + | 0.802530i | \(0.296513\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2904.00 | 0.111433 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4458.00 | −0.170481 | −0.0852405 | − | 0.996360i | \(-0.527166\pi\) | ||||
−0.0852405 | + | 0.996360i | \(0.527166\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3164.00 | 0.120586 | 0.0602928 | − | 0.998181i | \(-0.480797\pi\) | ||||
0.0602928 | + | 0.998181i | \(0.480797\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5640.00 | 0.214222 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32512.0 | 1.23072 | 0.615359 | − | 0.788247i | \(-0.289011\pi\) | ||||
0.615359 | + | 0.788247i | \(0.289011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −51968.0 | −1.96057 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4050.00 | −0.152278 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21360.0 | 0.800431 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12240.0 | −0.457138 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −780.000 | −0.0290339 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3608.00 | 0.133853 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5940.00 | −0.219634 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34176.0 | 1.25948 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1320.00 | 0.0484843 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10500.0 | −0.384396 | −0.192198 | − | 0.981356i | \(-0.561562\pi\) | ||||
−0.192198 | + | 0.981356i | \(0.561562\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9522.00 | 0.347442 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9840.00 | −0.357864 | −0.178932 | − | 0.983861i | \(-0.557264\pi\) | ||||
−0.178932 | + | 0.983861i | \(0.557264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23100.0 | −0.837348 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3720.00 | 0.134404 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 66304.0 | 2.38773 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35040.0 | 1.25774 | 0.628870 | − | 0.777511i | \(-0.283518\pi\) | ||||
0.628870 | + | 0.777511i | \(0.283518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19308.0 | 0.690793 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10114.0 | −0.360679 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −84150.0 | −2.99117 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15912.0 | −0.563774 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44172.0 | 1.56000 | 0.779998 | − | 0.625782i | \(-0.215220\pi\) | ||||
0.779998 | + | 0.625782i | \(0.215220\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 81720.0 | 2.87676 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23796.0 | −0.834990 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30000.0 | −1.04931 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54018.0 | −1.88334 | −0.941671 | − | 0.336535i | \(-0.890745\pi\) | ||||
−0.941671 | + | 0.336535i | \(0.890745\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31074.0 | 1.07994 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1672.00 | −0.0579231 | −0.0289616 | − | 0.999581i | \(-0.509220\pi\) | ||||
−0.0289616 | + | 0.999581i | \(0.509220\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2160.00 | 0.0745910 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17280.0 | −0.594834 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5238.00 | −0.179738 | −0.0898691 | − | 0.995954i | \(-0.528645\pi\) | ||||
−0.0898691 | + | 0.995954i | \(0.528645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −806.000 | −0.0275699 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8460.00 | −0.288469 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50042.0 | −1.70096 | −0.850482 | − | 0.526004i | \(-0.823690\pi\) | ||||
−0.850482 | + | 0.526004i | \(0.823690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12160.0 | 0.412030 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12300.0 | −0.415468 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24192.0 | −0.814599 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27855.0 | −0.935014 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16272.0 | 0.544505 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27400.0 | −0.914028 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37676.0 | −1.25293 | −0.626463 | − | 0.779452i | \(-0.715498\pi\) | ||||
−0.626463 | + | 0.779452i | \(0.715498\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10800.0 | −0.358045 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17364.0 | 0.573880 | 0.286940 | − | 0.957949i | \(-0.407362\pi\) | ||||
0.286940 | + | 0.957949i | \(0.407362\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5504.00 | −0.181346 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10725.0 | −0.352282 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14904.0 | −0.488046 | −0.244023 | − | 0.969769i | \(-0.578467\pi\) | ||||
−0.244023 | + | 0.969769i | \(0.578467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61200.0 | −1.99792 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16974.0 | −0.552434 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18038.0 | 0.585272 | 0.292636 | − | 0.956224i | \(-0.405467\pi\) | ||||
0.292636 | + | 0.956224i | \(0.405467\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 98160.0 | 3.17527 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17088.0 | 0.551081 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7120.00 | 0.228921 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46176.0 | −1.48015 | −0.740075 | − | 0.672524i | \(-0.765210\pi\) | ||||
−0.740075 | + | 0.672524i | \(0.765210\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12540.0 | 0.400750 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6560.00 | −0.209011 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55838.0 | 1.77373 | 0.886864 | − | 0.462030i | \(-0.152879\pi\) | ||||
0.886864 | + | 0.462030i | \(0.152879\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8262.00 | −0.261660 |
(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 | 624.4.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 1872.4.a.r.1.1 | 1 | |||
4.3 | odd | 2 | 78.4.a.d.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 2496.4.a.r.1.1 | 1 | |||
8.5 | even | 2 | 2496.4.a.i.1.1 | 1 | |||
12.11 | even | 2 | 234.4.a.f.1.1 | 1 | |||
20.19 | odd | 2 | 1950.4.a.h.1.1 | 1 | |||
52.31 | even | 4 | 1014.4.b.e.337.1 | 2 | |||
52.47 | even | 4 | 1014.4.b.e.337.2 | 2 | |||
52.51 | odd | 2 | 1014.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.4.a.d.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
234.4.a.f.1.1 | 1 | 12.11 | even | 2 | |||
624.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1014.4.a.d.1.1 | 1 | 52.51 | odd | 2 | |||
1014.4.b.e.337.1 | 2 | 52.31 | even | 4 | |||
1014.4.b.e.337.2 | 2 | 52.47 | even | 4 | |||
1872.4.a.r.1.1 | 1 | 3.2 | odd | 2 | |||
1950.4.a.h.1.1 | 1 | 20.19 | odd | 2 | |||
2496.4.a.i.1.1 | 1 | 8.5 | even | 2 | |||
2496.4.a.r.1.1 | 1 | 8.3 | odd | 2 |