Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,4,Mod(1,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, 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("2400.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.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: | \(141.604584014\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 480) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2400.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −32.0000 | −1.72784 | −0.863919 | − | 0.503631i | \(-0.831997\pi\) | ||||
−0.863919 | + | 0.503631i | \(0.831997\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 64.0000 | 1.75425 | 0.877124 | − | 0.480264i | \(-0.159459\pi\) | ||||
0.877124 | + | 0.480264i | \(0.159459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 0.128008 | 0.0640039 | − | 0.997950i | \(-0.479613\pi\) | ||||
0.0640039 | + | 0.997950i | \(0.479613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −38.0000 | −0.542138 | −0.271069 | − | 0.962560i | \(-0.587377\pi\) | ||||
−0.271069 | + | 0.962560i | \(0.587377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −116.000 | −1.40064 | −0.700322 | − | 0.713827i | \(-0.746960\pi\) | ||||
−0.700322 | + | 0.713827i | \(0.746960\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 96.0000 | 0.997567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000 | 1.08790 | 0.543951 | − | 0.839117i | \(-0.316928\pi\) | ||||
0.543951 | + | 0.839117i | \(0.316928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −122.000 | −0.781201 | −0.390601 | − | 0.920560i | \(-0.627733\pi\) | ||||
−0.390601 | + | 0.920560i | \(0.627733\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 164.000 | 0.950170 | 0.475085 | − | 0.879940i | \(-0.342417\pi\) | ||||
0.475085 | + | 0.879940i | \(0.342417\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −192.000 | −1.01282 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −146.000 | −0.648710 | −0.324355 | − | 0.945936i | \(-0.605147\pi\) | ||||
−0.324355 | + | 0.945936i | \(0.605147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18.0000 | −0.0739053 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −238.000 | −0.906570 | −0.453285 | − | 0.891366i | \(-0.649748\pi\) | ||||
−0.453285 | + | 0.891366i | \(0.649748\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 148.000 | 0.524879 | 0.262439 | − | 0.964948i | \(-0.415473\pi\) | ||||
0.262439 | + | 0.964948i | \(0.415473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 184.000 | 0.571046 | 0.285523 | − | 0.958372i | \(-0.407833\pi\) | ||||
0.285523 | + | 0.958372i | \(0.407833\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 114.000 | 0.313004 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −470.000 | −1.21810 | −0.609052 | − | 0.793131i | \(-0.708450\pi\) | ||||
−0.609052 | + | 0.793131i | \(0.708450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 348.000 | 0.808662 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −216.000 | −0.476624 | −0.238312 | − | 0.971189i | \(-0.576594\pi\) | ||||
−0.238312 | + | 0.971189i | \(0.576594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 806.000 | 1.69177 | 0.845883 | − | 0.533369i | \(-0.179074\pi\) | ||||
0.845883 | + | 0.533369i | \(0.179074\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −288.000 | −0.575946 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 732.000 | 1.33475 | 0.667373 | − | 0.744723i | \(-0.267419\pi\) | ||||
0.667373 | + | 0.744723i | \(0.267419\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −360.000 | −0.628100 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 264.000 | 0.441282 | 0.220641 | − | 0.975355i | \(-0.429185\pi\) | ||||
0.220641 | + | 0.975355i | \(0.429185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 638.000 | 1.02291 | 0.511454 | − | 0.859311i | \(-0.329107\pi\) | ||||
0.511454 | + | 0.859311i | \(0.329107\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2048.00 | −3.03106 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 596.000 | 0.848800 | 0.424400 | − | 0.905475i | \(-0.360485\pi\) | ||||
0.424400 | + | 0.905475i | \(0.360485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 884.000 | 1.16906 | 0.584528 | − | 0.811374i | \(-0.301280\pi\) | ||||
0.584528 | + | 0.811374i | \(0.301280\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 366.000 | 0.451027 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 930.000 | 1.10764 | 0.553819 | − | 0.832637i | \(-0.313170\pi\) | ||||
0.553819 | + | 0.832637i | \(0.313170\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −192.000 | −0.221177 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −492.000 | −0.548581 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −322.000 | −0.337053 | −0.168527 | − | 0.985697i | \(-0.553901\pi\) | ||||
−0.168527 | + | 0.985697i | \(0.553901\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 576.000 | 0.584749 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −946.000 | −0.931985 | −0.465993 | − | 0.884789i | \(-0.654303\pi\) | ||||
−0.465993 | + | 0.884789i | \(0.654303\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −424.000 | −0.405611 | −0.202806 | − | 0.979219i | \(-0.565006\pi\) | ||||
−0.202806 | + | 0.979219i | \(0.565006\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1668.00 | 1.50702 | 0.753512 | − | 0.657434i | \(-0.228358\pi\) | ||||
0.753512 | + | 0.657434i | \(0.228358\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1634.00 | −1.43586 | −0.717930 | − | 0.696115i | \(-0.754910\pi\) | ||||
−0.717930 | + | 0.696115i | \(0.754910\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 438.000 | 0.374533 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1686.00 | −1.40359 | −0.701794 | − | 0.712380i | \(-0.747617\pi\) | ||||
−0.701794 | + | 0.712380i | \(0.747617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 54.0000 | 0.0426692 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1216.00 | 0.936727 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2765.00 | 2.07739 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 714.000 | 0.523408 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2640.00 | −1.84458 | −0.922292 | − | 0.386494i | \(-0.873686\pi\) | ||||
−0.922292 | + | 0.386494i | \(0.873686\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −444.000 | −0.303039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2536.00 | −1.69138 | −0.845692 | − | 0.533671i | \(-0.820812\pi\) | ||||
−0.845692 | + | 0.533671i | \(0.820812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3712.00 | 2.42008 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 634.000 | 0.395374 | 0.197687 | − | 0.980265i | \(-0.436657\pi\) | ||||
0.197687 | + | 0.980265i | \(0.436657\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2980.00 | 1.81842 | 0.909210 | − | 0.416338i | \(-0.136687\pi\) | ||||
0.909210 | + | 0.416338i | \(0.136687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −552.000 | −0.329694 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 384.000 | 0.224557 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2043.00 | −1.14628 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −338.000 | −0.185839 | −0.0929196 | − | 0.995674i | \(-0.529620\pi\) | ||||
−0.0929196 | + | 0.995674i | \(0.529620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −428.000 | −0.230663 | −0.115332 | − | 0.993327i | \(-0.536793\pi\) | ||||
−0.115332 | + | 0.993327i | \(0.536793\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −342.000 | −0.180713 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3010.00 | −1.53009 | −0.765045 | − | 0.643977i | \(-0.777283\pi\) | ||||
−0.765045 | + | 0.643977i | \(0.777283\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1410.00 | 0.703272 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3840.00 | −1.87972 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 132.000 | 0.0634297 | 0.0317148 | − | 0.999497i | \(-0.489903\pi\) | ||||
0.0317148 | + | 0.999497i | \(0.489903\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2176.00 | −1.00829 | −0.504144 | − | 0.863620i | \(-0.668192\pi\) | ||||
−0.504144 | + | 0.863620i | \(0.668192\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2161.00 | −0.983614 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1044.00 | −0.466881 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2778.00 | 1.22085 | 0.610426 | − | 0.792073i | \(-0.290998\pi\) | ||||
0.610426 | + | 0.792073i | \(0.290998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 648.000 | 0.275179 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3888.00 | −1.62348 | −0.811740 | − | 0.584020i | \(-0.801479\pi\) | ||||
−0.811740 | + | 0.584020i | \(0.801479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1350.00 | 0.554391 | 0.277195 | − | 0.960814i | \(-0.410595\pi\) | ||||
0.277195 | + | 0.960814i | \(0.410595\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2418.00 | −0.976742 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2432.00 | −0.951045 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 864.000 | 0.332522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4760.00 | −1.80325 | −0.901627 | − | 0.432514i | \(-0.857626\pi\) | ||||
−0.901627 | + | 0.432514i | \(0.857626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1034.00 | −0.385642 | −0.192821 | − | 0.981234i | \(-0.561764\pi\) | ||||
−0.192821 | + | 0.981234i | \(0.561764\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1354.00 | 0.489688 | 0.244844 | − | 0.969563i | \(-0.421263\pi\) | ||||
0.244844 | + | 0.969563i | \(0.421263\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2324.00 | −0.827859 | −0.413930 | − | 0.910309i | \(-0.635844\pi\) | ||||
−0.413930 | + | 0.910309i | \(0.635844\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2196.00 | −0.770616 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3904.00 | 1.34979 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1080.00 | 0.362634 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7424.00 | −2.45708 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3220.00 | −1.05059 | −0.525294 | − | 0.850921i | \(-0.676045\pi\) | ||||
−0.525294 | + | 0.850921i | \(0.676045\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −792.000 | −0.254774 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5248.00 | −1.64174 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1914.00 | −0.590576 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −228.000 | −0.0693979 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 32.0000 | 0.00960932 | 0.00480466 | − | 0.999988i | \(-0.498471\pi\) | ||||
0.00480466 | + | 0.999988i | \(0.498471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3996.00 | 1.16839 | 0.584193 | − | 0.811614i | \(-0.301411\pi\) | ||||
0.584193 | + | 0.811614i | \(0.301411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3010.00 | −0.868587 | −0.434293 | − | 0.900771i | \(-0.643002\pi\) | ||||
−0.434293 | + | 0.900771i | \(0.643002\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6144.00 | 1.74998 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2698.00 | 0.758592 | 0.379296 | − | 0.925275i | \(-0.376166\pi\) | ||||
0.379296 | + | 0.925275i | \(0.376166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1788.00 | −0.490055 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2200.00 | −0.595423 | −0.297712 | − | 0.954656i | \(-0.596223\pi\) | ||||
−0.297712 | + | 0.954656i | \(0.596223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6174.00 | −1.65022 | −0.825109 | − | 0.564974i | \(-0.808886\pi\) | ||||
−0.825109 | + | 0.564974i | \(0.808886\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −696.000 | −0.179293 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2652.00 | −0.674955 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4808.00 | 1.20908 | 0.604538 | − | 0.796576i | \(-0.293358\pi\) | ||||
0.604538 | + | 0.796576i | \(0.293358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7680.00 | 1.90845 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3974.00 | −0.964558 | −0.482279 | − | 0.876018i | \(-0.660191\pi\) | ||||
−0.482279 | + | 0.876018i | \(0.660191\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4672.00 | 1.12086 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1098.00 | −0.260400 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1408.00 | −0.330118 | −0.165059 | − | 0.986284i | \(-0.552781\pi\) | ||||
−0.165059 | + | 0.986284i | \(0.552781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2790.00 | −0.639495 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3258.00 | −0.738453 | −0.369226 | − | 0.929340i | \(-0.620377\pi\) | ||||
−0.369226 | + | 0.929340i | \(0.620377\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8612.00 | 1.93041 | 0.965206 | − | 0.261490i | \(-0.0842139\pi\) | ||||
0.965206 | + | 0.261490i | \(0.0842139\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 576.000 | 0.127696 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4006.00 | 0.868943 | 0.434472 | − | 0.900686i | \(-0.356935\pi\) | ||||
0.434472 | + | 0.900686i | \(0.356935\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1476.00 | 0.316723 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6194.00 | 1.31496 | 0.657479 | − | 0.753473i | \(-0.271623\pi\) | ||||
0.657479 | + | 0.753473i | \(0.271623\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1724.00 | −0.362124 | −0.181062 | − | 0.983472i | \(-0.557954\pi\) | ||||
−0.181062 | + | 0.983472i | \(0.557954\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7616.00 | 1.56641 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3469.00 | −0.706086 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 966.000 | 0.194598 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2502.00 | −0.498868 | −0.249434 | − | 0.968392i | \(-0.580245\pi\) | ||||
−0.249434 | + | 0.968392i | \(0.580245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1728.00 | −0.337605 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 720.000 | 0.139260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4736.00 | −0.906905 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2838.00 | 0.538082 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6404.00 | 1.19054 | 0.595270 | − | 0.803526i | \(-0.297045\pi\) | ||||
0.595270 | + | 0.803526i | \(0.297045\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1272.00 | 0.234180 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 896.000 | 0.163368 | 0.0816841 | − | 0.996658i | \(-0.473970\pi\) | ||||
0.0816841 | + | 0.996658i | \(0.473970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4110.00 | 0.742207 | 0.371104 | − | 0.928591i | \(-0.378979\pi\) | ||||
0.371104 | + | 0.928591i | \(0.378979\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6926.00 | −1.22714 | −0.613569 | − | 0.789641i | \(-0.710267\pi\) | ||||
−0.613569 | + | 0.789641i | \(0.710267\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7808.00 | −1.37042 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5004.00 | −0.870081 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4408.00 | 0.759343 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4902.00 | 0.828995 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5888.00 | −0.986675 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2692.00 | −0.447026 | −0.223513 | − | 0.974701i | \(-0.571753\pi\) | ||||
−0.223513 | + | 0.974701i | \(0.571753\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1314.00 | −0.216237 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11914.0 | −1.92581 | −0.962903 | − | 0.269846i | \(-0.913027\pi\) | ||||
−0.962903 | + | 0.269846i | \(0.913027\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5058.00 | 0.810362 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10496.0 | 1.66683 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10816.0 | −1.70265 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6660.00 | 1.03034 | 0.515169 | − | 0.857088i | \(-0.327729\pi\) | ||||
0.515169 | + | 0.857088i | \(0.327729\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3046.00 | 0.467188 | 0.233594 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233594 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −162.000 | −0.0246351 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3522.00 | 0.531040 | 0.265520 | − | 0.964105i | \(-0.414456\pi\) | ||||
0.265520 | + | 0.964105i | \(0.414456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3648.00 | −0.540820 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8656.00 | −1.27255 | −0.636276 | − | 0.771461i | \(-0.719526\pi\) | ||||
−0.636276 | + | 0.771461i | \(0.719526\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6597.00 | 0.961802 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8295.00 | −1.19938 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −936.000 | −0.133130 | −0.0665651 | − | 0.997782i | \(-0.521204\pi\) | ||||
−0.0665651 | + | 0.997782i | \(0.521204\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2142.00 | −0.302190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15040.0 | 2.10468 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11578.0 | −1.60720 | −0.803601 | − | 0.595169i | \(-0.797085\pi\) | ||||
−0.803601 | + | 0.595169i | \(0.797085\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −732.000 | −0.0999998 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9948.00 | 1.34827 | 0.674135 | − | 0.738608i | \(-0.264517\pi\) | ||||
0.674135 | + | 0.738608i | \(0.264517\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7920.00 | 1.06497 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8336.00 | −1.11214 | −0.556070 | − | 0.831135i | \(-0.687691\pi\) | ||||
−0.556070 | + | 0.831135i | \(0.687691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1332.00 | 0.174960 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6370.00 | −0.830262 | −0.415131 | − | 0.909762i | \(-0.636264\pi\) | ||||
−0.415131 | + | 0.909762i | \(0.636264\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4560.00 | −0.589793 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7608.00 | 0.976521 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10394.0 | −1.31400 | −0.657002 | − | 0.753888i | \(-0.728176\pi\) | ||||
−0.657002 | + | 0.753888i | \(0.728176\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11136.0 | −1.39724 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7470.00 | −0.930259 | −0.465130 | − | 0.885243i | \(-0.653992\pi\) | ||||
−0.465130 | + | 0.885243i | \(0.653992\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 984.000 | 0.121629 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9344.00 | −1.13800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2810.00 | 0.339720 | 0.169860 | − | 0.985468i | \(-0.445668\pi\) | ||||
0.169860 | + | 0.985468i | \(0.445668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1902.00 | −0.228269 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6912.00 | 0.823529 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8940.00 | −1.04986 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4320.00 | −0.503689 | −0.251845 | − | 0.967768i | \(-0.581037\pi\) | ||||
−0.251845 | + | 0.967768i | \(0.581037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15122.0 | −1.75060 | −0.875298 | − | 0.483583i | \(-0.839335\pi\) | ||||
−0.875298 | + | 0.483583i | \(0.839335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1656.00 | 0.190349 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25792.0 | −2.92310 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1152.00 | −0.129648 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12616.0 | −1.40996 | −0.704978 | − | 0.709229i | \(-0.749043\pi\) | ||||
−0.704978 | + | 0.709229i | \(0.749043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15098.0 | −1.67567 | −0.837833 | − | 0.545926i | \(-0.816178\pi\) | ||||
−0.837833 | + | 0.545926i | \(0.816178\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13920.0 | −1.52376 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2372.00 | −0.257880 | −0.128940 | − | 0.991652i | \(-0.541157\pi\) | ||||
−0.128940 | + | 0.991652i | \(0.541157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.0000 | 0.00386097 | 0.00193049 | − | 0.999998i | \(-0.499386\pi\) | ||||
0.00193049 | + | 0.999998i | \(0.499386\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1014.00 | 0.107294 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7330.00 | 0.770432 | 0.385216 | − | 0.922826i | \(-0.374127\pi\) | ||||
0.385216 | + | 0.922826i | \(0.374127\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15232.0 | −1.59035 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1284.00 | 0.133173 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9642.00 | −0.986945 | −0.493472 | − | 0.869761i | \(-0.664273\pi\) | ||||
−0.493472 | + | 0.869761i | \(0.664273\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1026.00 | 0.104335 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9654.00 | 0.975340 | 0.487670 | − | 0.873028i | \(-0.337847\pi\) | ||||
0.487670 | + | 0.873028i | \(0.337847\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13960.0 | 1.40124 | 0.700622 | − | 0.713532i | \(-0.252906\pi\) | ||||
0.700622 | + | 0.713532i | \(0.252906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9996.00 | −0.990492 | −0.495246 | − | 0.868753i | \(-0.664922\pi\) | ||||
−0.495246 | + | 0.868753i | \(0.664922\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23424.0 | −2.30623 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9030.00 | 0.883398 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9472.00 | 0.920767 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4230.00 | −0.406034 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8736.00 | −0.833315 | −0.416658 | − | 0.909063i | \(-0.636799\pi\) | ||||
−0.416658 | + | 0.909063i | \(0.636799\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −876.000 | −0.0830398 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11520.0 | 1.08525 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6712.00 | −0.624537 | −0.312269 | − | 0.949994i | \(-0.601089\pi\) | ||||
−0.312269 | + | 0.949994i | \(0.601089\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −396.000 | −0.0366211 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2512.00 | −0.230886 | −0.115443 | − | 0.993314i | \(-0.536829\pi\) | ||||
−0.115443 | + | 0.993314i | \(0.536829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4636.00 | 0.423519 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8448.00 | −0.762464 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5708.00 | −0.512074 | −0.256037 | − | 0.966667i | \(-0.582417\pi\) | ||||
−0.256037 | + | 0.966667i | \(0.582417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6528.00 | 0.582135 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5440.00 | 0.482222 | 0.241111 | − | 0.970498i | \(-0.422488\pi\) | ||||
0.241111 | + | 0.970498i | \(0.422488\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6483.00 | 0.567890 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3942.00 | 0.343273 | 0.171637 | − | 0.985160i | \(-0.445095\pi\) | ||||
0.171637 | + | 0.985160i | \(0.445095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20416.0 | −1.76742 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3132.00 | 0.269554 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11776.0 | 1.00176 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8334.00 | −0.704859 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2310.00 | −0.194247 | −0.0971237 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971237 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2956.00 | 0.247145 | 0.123573 | − | 0.992336i | \(-0.460565\pi\) | ||||
0.123573 | + | 0.992336i | \(0.460565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6232.00 | −0.515124 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1944.00 | −0.158875 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1428.00 | −0.116048 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11664.0 | 0.937316 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 43584.0 | 3.48292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2078.00 | 0.165139 | 0.0825695 | − | 0.996585i | \(-0.473687\pi\) | ||||
0.0825695 | + | 0.996585i | \(0.473687\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4050.00 | −0.320078 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6164.00 | −0.481816 | −0.240908 | − | 0.970548i | \(-0.577445\pi\) | ||||
−0.240908 | + | 0.970548i | \(0.577445\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7254.00 | 0.563922 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14152.0 | 1.09418 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19072.0 | −1.46659 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13526.0 | −1.02893 | −0.514466 | − | 0.857511i | \(-0.672010\pi\) | ||||
−0.514466 | + | 0.857511i | \(0.672010\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 888.000 | 0.0671885 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7296.00 | 0.549086 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −276.000 | −0.0206608 | −0.0103304 | − | 0.999947i | \(-0.503288\pi\) | ||||
−0.0103304 | + | 0.999947i | \(0.503288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2592.00 | −0.191982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −774.000 | −0.0570260 | −0.0285130 | − | 0.999593i | \(-0.509077\pi\) | ||||
−0.0285130 | + | 0.999593i | \(0.509077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6676.00 | −0.489285 | −0.244643 | − | 0.969613i | \(-0.578671\pi\) | ||||
−0.244643 | + | 0.969613i | \(0.578671\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14280.0 | 1.04111 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11774.0 | 0.849494 | 0.424747 | − | 0.905312i | \(-0.360363\pi\) | ||||
0.424747 | + | 0.905312i | \(0.360363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3102.00 | 0.222651 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28288.0 | −2.01994 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30080.0 | −2.13685 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12292.0 | 0.864302 | 0.432151 | − | 0.901801i | \(-0.357755\pi\) | ||||
0.432151 | + | 0.901801i | \(0.357755\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19024.0 | −1.33085 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4062.00 | −0.282721 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7110.00 | −0.492365 | −0.246183 | − | 0.969223i | \(-0.579176\pi\) | ||||
−0.246183 | + | 0.969223i | \(0.579176\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6972.00 | 0.477965 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4416.00 | 0.301223 | 0.150612 | − | 0.988593i | \(-0.451876\pi\) | ||||
0.150612 | + | 0.988593i | \(0.451876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3850.00 | 0.261306 | 0.130653 | − | 0.991428i | \(-0.458293\pi\) | ||||
0.130653 | + | 0.991428i | \(0.458293\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6588.00 | 0.444916 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21880.0 | 1.46307 | 0.731534 | − | 0.681805i | \(-0.238805\pi\) | ||||
0.731534 | + | 0.681805i | \(0.238805\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11712.0 | −0.779301 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1104.00 | 0.0730983 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2786.00 | −0.183565 | −0.0917826 | − | 0.995779i | \(-0.529256\pi\) | ||||
−0.0917826 | + | 0.995779i | \(0.529256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1014.00 | −0.0661622 | −0.0330811 | − | 0.999453i | \(-0.510532\pi\) | ||||
−0.0330811 | + | 0.999453i | \(0.510532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10708.0 | 0.695300 | 0.347650 | − | 0.937624i | \(-0.386980\pi\) | ||||
0.347650 | + | 0.937624i | \(0.386980\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3240.00 | −0.209367 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29760.0 | −1.91382 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22272.0 | 1.41859 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5548.00 | 0.351690 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6660.00 | −0.420175 | −0.210087 | − | 0.977683i | \(-0.567375\pi\) | ||||
−0.210087 | + | 0.977683i | \(0.567375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9660.00 | 0.606557 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4086.00 | 0.254149 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2376.00 | 0.147094 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 90.0000 | 0.00554569 | 0.00277284 | − | 0.999996i | \(-0.499117\pi\) | ||||
0.00277284 | + | 0.999996i | \(0.499117\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21684.0 | 1.32991 | 0.664956 | − | 0.746882i | \(-0.268450\pi\) | ||||
0.664956 | + | 0.746882i | \(0.268450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1344.00 | 0.0816663 | 0.0408331 | − | 0.999166i | \(-0.486999\pi\) | ||||
0.0408331 | + | 0.999166i | \(0.486999\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13824.0 | −0.836116 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15744.0 | 0.947859 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9210.00 | 0.551937 | 0.275969 | − | 0.961167i | \(-0.411001\pi\) | ||||
0.275969 | + | 0.961167i | \(0.411001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5742.00 | 0.340969 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 184.000 | 0.0108765 | 0.00543826 | − | 0.999985i | \(-0.498269\pi\) | ||||
0.00543826 | + | 0.999985i | \(0.498269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12866.0 | −0.757079 | −0.378540 | − | 0.925585i | \(-0.623574\pi\) | ||||
−0.378540 | + | 0.925585i | \(0.623574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 684.000 | 0.0400669 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14640.0 | −0.849870 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −96.0000 | −0.00554794 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51584.0 | 2.96778 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26534.0 | 1.51978 | 0.759889 | − | 0.650053i | \(-0.225253\pi\) | ||||
0.759889 | + | 0.650053i | \(0.225253\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30062.0 | −1.70661 | −0.853306 | − | 0.521410i | \(-0.825406\pi\) | ||||
−0.853306 | + | 0.521410i | \(0.825406\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10304.0 | 0.582373 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11988.0 | −0.674569 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12724.0 | −0.712841 | −0.356420 | − | 0.934326i | \(-0.616003\pi\) | ||||
−0.356420 | + | 0.934326i | \(0.616003\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9030.00 | 0.501479 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2820.00 | −0.155927 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21972.0 | −1.20963 | −0.604815 | − | 0.796366i | \(-0.706753\pi\) | ||||
−0.604815 | + | 0.796366i | \(0.706753\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18432.0 | −1.01035 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9044.00 | 0.491486 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8094.00 | −0.437973 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15642.0 | −0.842782 | −0.421391 | − | 0.906879i | \(-0.638458\pi\) | ||||
−0.421391 | + | 0.906879i | \(0.638458\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16936.0 | 0.908611 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30272.0 | 1.61032 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36398.0 | 1.92801 | 0.964003 | − | 0.265893i | \(-0.0856668\pi\) | ||||
0.964003 | + | 0.265893i | \(0.0856668\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5364.00 | 0.282933 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19680.0 | 1.03369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6600.00 | 0.343768 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36248.0 | −1.88014 | −0.940071 | − | 0.340978i | \(-0.889242\pi\) | ||||
−0.940071 | + | 0.340978i | \(0.889242\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13568.0 | 0.700830 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18522.0 | 0.952753 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4936.00 | 0.251810 | 0.125905 | − | 0.992042i | \(-0.459816\pi\) | ||||
0.125905 | + | 0.992042i | \(0.459816\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5624.00 | −0.284557 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23838.0 | 1.20120 | 0.600598 | − | 0.799551i | \(-0.294929\pi\) | ||||
0.600598 | + | 0.799551i | \(0.294929\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46848.0 | 2.34148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31700.0 | 1.57795 | 0.788974 | − | 0.614427i | \(-0.210613\pi\) | ||||
0.788974 | + | 0.614427i | \(0.210613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2088.00 | 0.103515 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13128.0 | 0.648209 | 0.324105 | − | 0.946021i | \(-0.394937\pi\) | ||||
0.324105 | + | 0.946021i | \(0.394937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7956.00 | 0.389685 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −53376.0 | −2.60389 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15676.0 | −0.761685 | −0.380842 | − | 0.924640i | \(-0.624366\pi\) | ||||
−0.380842 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14424.0 | −0.698061 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13238.0 | 0.635592 | 0.317796 | − | 0.948159i | \(-0.397057\pi\) | ||||
0.317796 | + | 0.948159i | \(0.397057\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23040.0 | −1.10184 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5270.00 | −0.251035 | −0.125517 | − | 0.992091i | \(-0.540059\pi\) | ||||
−0.125517 | + | 0.992091i | \(0.540059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52288.0 | 2.48093 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1296.00 | −0.0610115 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8526.00 | −0.399812 | −0.199906 | − | 0.979815i | \(-0.564064\pi\) | ||||
−0.199906 | + | 0.979815i | \(0.564064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11922.0 | 0.556888 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13606.0 | −0.633084 | −0.316542 | − | 0.948579i | \(-0.602522\pi\) | ||||
−0.316542 | + | 0.948579i | \(0.602522\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14016.0 | −0.647132 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27608.0 | 1.26978 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16896.0 | 0.774118 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3294.00 | 0.150342 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8836.00 | 0.400215 | 0.200108 | − | 0.979774i | \(-0.435871\pi\) | ||||
0.200108 | + | 0.979774i | \(0.435871\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4224.00 | 0.190594 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53952.0 | 2.42517 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4836.00 | 0.216559 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29082.0 | 1.29252 | 0.646259 | − | 0.763118i | \(-0.276332\pi\) | ||||
0.646259 | + | 0.763118i | \(0.276332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6992.00 | −0.309586 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8370.00 | 0.369213 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40832.0 | 1.79443 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9774.00 | 0.426346 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26994.0 | 1.17313 | 0.586563 | − | 0.809904i | \(-0.300481\pi\) | ||||
0.586563 | + | 0.809904i | \(0.300481\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9268.00 | −0.401287 | −0.200643 | − | 0.979664i | \(-0.564303\pi\) | ||||
−0.200643 | + | 0.979664i | \(0.564303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25836.0 | −1.11452 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17168.0 | −0.735168 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1728.00 | −0.0737255 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6286.00 | 0.267214 | 0.133607 | − | 0.991034i | \(-0.457344\pi\) | ||||
0.133607 | + | 0.991034i | \(0.457344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44088.0 | −1.86733 | −0.933664 | − | 0.358150i | \(-0.883408\pi\) | ||||
−0.933664 | + | 0.358150i | \(0.883408\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30100.0 | −1.26563 | −0.632817 | − | 0.774301i | \(-0.718102\pi\) | ||||
−0.632817 | + | 0.774301i | \(0.718102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18254.0 | 0.764762 | 0.382381 | − | 0.924005i | \(-0.375104\pi\) | ||||
0.382381 | + | 0.924005i | \(0.375104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12018.0 | −0.501684 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25878.0 | −1.07637 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4428.00 | −0.182860 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13008.0 | 0.535263 | 0.267632 | − | 0.963521i | \(-0.413759\pi\) | ||||
0.267632 | + | 0.963521i | \(0.413759\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9505.00 | −0.389725 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18582.0 | −0.759191 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −88480.0 | −3.58938 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5172.00 | 0.209073 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17520.0 | −0.705732 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16094.0 | 0.646012 | 0.323006 | − | 0.946397i | \(-0.395307\pi\) | ||||
0.323006 | + | 0.946397i | \(0.395307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25938.0 | 1.03387 | 0.516934 | − | 0.856025i | \(-0.327073\pi\) | ||||
0.516934 | + | 0.856025i | \(0.327073\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38564.0 | −1.53177 | −0.765883 | − | 0.642980i | \(-0.777698\pi\) | ||||
−0.765883 | + | 0.642980i | \(0.777698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22848.0 | −0.904364 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10216.0 | −0.402963 | −0.201481 | − | 0.979492i | \(-0.564576\pi\) | ||||
−0.201481 | + | 0.979492i | \(0.564576\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10407.0 | 0.407659 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38144.0 | 1.48901 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4392.00 | 0.170858 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2898.00 | −0.112351 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17006.0 | 0.654791 | 0.327396 | − | 0.944887i | \(-0.393829\pi\) | ||||
0.327396 | + | 0.944887i | \(0.393829\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7506.00 | 0.288022 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43898.0 | 1.67873 | 0.839365 | − | 0.543568i | \(-0.182927\pi\) | ||||
0.839365 | + | 0.543568i | \(0.182927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29180.0 | −1.11210 | −0.556051 | − | 0.831149i | \(-0.687684\pi\) | ||||
−0.556051 | + | 0.831149i | \(0.687684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14752.0 | 0.558426 | 0.279213 | − | 0.960229i | \(-0.409926\pi\) | ||||
0.279213 | + | 0.960229i | \(0.409926\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 84480.0 | 3.18714 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5184.00 | 0.194916 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21344.0 | −0.799832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2160.00 | −0.0804017 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20008.0 | −0.742274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17860.0 | 0.660381 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14208.0 | 0.523602 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12020.0 | 0.440041 | 0.220021 | − | 0.975495i | \(-0.429388\pi\) | ||||
0.220021 | + | 0.975495i | \(0.429388\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8514.00 | −0.310662 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18560.0 | −0.674995 | −0.337497 | − | 0.941326i | \(-0.609580\pi\) | ||||
−0.337497 | + | 0.941326i | \(0.609580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56576.0 | 2.05081 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 81152.0 | 2.92244 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10244.0 | −0.367702 | −0.183851 | − | 0.982954i | \(-0.558856\pi\) | ||||
−0.183851 | + | 0.982954i | \(0.558856\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19212.0 | −0.687358 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1584.00 | 0.0564875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3816.00 | −0.135204 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1266.00 | 0.0447106 | 0.0223553 | − | 0.999750i | \(-0.492884\pi\) | ||||
0.0223553 | + | 0.999750i | \(0.492884\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −78996.0 | −2.78087 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2688.00 | −0.0943207 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47626.0 | −1.66048 | −0.830242 | − | 0.557403i | \(-0.811798\pi\) | ||||
−0.830242 | + | 0.557403i | \(0.811798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12330.0 | −0.428514 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31958.0 | 1.10712 | 0.553561 | − | 0.832809i | \(-0.313269\pi\) | ||||
0.553561 | + | 0.832809i | \(0.313269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28560.0 | −0.986258 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25196.0 | −0.864583 | −0.432291 | − | 0.901734i | \(-0.642295\pi\) | ||||
−0.432291 | + | 0.901734i | \(0.642295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3828.00 | 0.130940 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20778.0 | 0.708489 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51574.0 | −1.75304 | −0.876519 | − | 0.481367i | \(-0.840141\pi\) | ||||
−0.876519 | + | 0.481367i | \(0.840141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23424.0 | 0.791213 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20288.0 | −0.683143 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2895.00 | −0.0971770 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15012.0 | 0.502342 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48296.0 | −1.60610 | −0.803048 | − | 0.595914i | \(-0.796790\pi\) | ||||
−0.803048 | + | 0.595914i | \(0.796790\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13224.0 | −0.438407 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27288.0 | −0.901868 | −0.450934 | − | 0.892557i | \(-0.648909\pi\) | ||||
−0.450934 | + | 0.892557i | \(0.648909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −95360.0 | −3.14193 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14406.0 | −0.471739 | −0.235869 | − | 0.971785i | \(-0.575794\pi\) | ||||
−0.235869 | + | 0.971785i | \(0.575794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 59520.0 | 1.94307 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14706.0 | −0.478620 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18952.0 | −0.614929 | −0.307464 | − | 0.951560i | \(-0.599480\pi\) | ||||
−0.307464 | + | 0.951560i | \(0.599480\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17664.0 | 0.569657 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17760.0 | 0.571016 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44308.0 | −1.42027 | −0.710136 | − | 0.704064i | \(-0.751367\pi\) | ||||
−0.710136 | + | 0.704064i | \(0.751367\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8076.00 | 0.258091 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −954.000 | −0.0303044 | −0.0151522 | − | 0.999885i | \(-0.504823\pi\) | ||||
−0.0151522 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3942.00 | 0.124844 |
(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 | 2400.4.a.a.1.1 | 1 | ||
4.3 | odd | 2 | 2400.4.a.v.1.1 | 1 | |||
5.4 | even | 2 | 480.4.a.l.1.1 | yes | 1 | ||
15.14 | odd | 2 | 1440.4.a.j.1.1 | 1 | |||
20.19 | odd | 2 | 480.4.a.c.1.1 | ✓ | 1 | ||
40.19 | odd | 2 | 960.4.a.t.1.1 | 1 | |||
40.29 | even | 2 | 960.4.a.i.1.1 | 1 | |||
60.59 | even | 2 | 1440.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.c.1.1 | ✓ | 1 | 20.19 | odd | 2 | ||
480.4.a.l.1.1 | yes | 1 | 5.4 | even | 2 | ||
960.4.a.i.1.1 | 1 | 40.29 | even | 2 | |||
960.4.a.t.1.1 | 1 | 40.19 | odd | 2 | |||
1440.4.a.a.1.1 | 1 | 60.59 | even | 2 | |||
1440.4.a.j.1.1 | 1 | 15.14 | odd | 2 | |||
2400.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2400.4.a.v.1.1 | 1 | 4.3 | odd | 2 |