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 | \(-0.168003\pi\) | ||||
0.863919 | + | 0.503631i | \(0.168003\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −64.0000 | −1.75425 | −0.877124 | − | 0.480264i | \(-0.840541\pi\) | ||||
−0.877124 | + | 0.480264i | \(0.840541\pi\) | |||||||
\(12\) | 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 | \(-0.253040\pi\) | ||||
0.700322 | + | 0.713827i | \(0.253040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 96.0000 | 0.997567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −120.000 | −1.08790 | −0.543951 | − | 0.839117i | \(-0.683072\pi\) | ||||
−0.543951 | + | 0.839117i | \(0.683072\pi\) | |||||||
\(24\) | 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 | \(-0.657583\pi\) | ||||
−0.475085 | + | 0.879940i | \(0.657583\pi\) | |||||||
\(32\) | 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 | \(-0.584527\pi\) | ||||
−0.262439 | + | 0.964948i | \(0.584527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −184.000 | −0.571046 | −0.285523 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285523 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(48\) | 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 | \(-0.423406\pi\) | ||||
0.238312 | + | 0.971189i | \(0.423406\pi\) | |||||||
\(60\) | 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 | \(-0.732581\pi\) | ||||
−0.667373 | + | 0.744723i | \(0.732581\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −360.000 | −0.628100 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −264.000 | −0.441282 | −0.220641 | − | 0.975355i | \(-0.570815\pi\) | ||||
−0.220641 | + | 0.975355i | \(0.570815\pi\) | |||||||
\(72\) | 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 | \(-0.639515\pi\) | ||||
−0.424400 | + | 0.905475i | \(0.639515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −884.000 | −1.16906 | −0.584528 | − | 0.811374i | \(-0.698720\pi\) | ||||
−0.584528 | + | 0.811374i | \(0.698720\pi\) | |||||||
\(84\) | 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 | \(-0.434994\pi\) | ||||
0.202806 | + | 0.979219i | \(0.434994\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1668.00 | −1.50702 | −0.753512 | − | 0.657434i | \(-0.771642\pi\) | ||||
−0.753512 | + | 0.657434i | \(0.771642\pi\) | |||||||
\(108\) | 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 | \(-0.126314\pi\) | ||||
0.922292 | + | 0.386494i | \(0.126314\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −444.000 | −0.303039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2536.00 | 1.69138 | 0.845692 | − | 0.533671i | \(-0.179188\pi\) | ||||
0.845692 | + | 0.533671i | \(0.179188\pi\) | |||||||
\(132\) | 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 | \(-0.863313\pi\) | ||||
−0.909210 | + | 0.416338i | \(0.863313\pi\) | |||||||
\(140\) | 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 | \(-0.463207\pi\) | ||||
0.115332 | + | 0.993327i | \(0.463207\pi\) | |||||||
\(152\) | 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 | \(-0.510097\pi\) | ||||
−0.0317148 | + | 0.999497i | \(0.510097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2176.00 | 1.00829 | 0.504144 | − | 0.863620i | \(-0.331808\pi\) | ||||
0.504144 | + | 0.863620i | \(0.331808\pi\) | |||||||
\(168\) | 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 | \(-0.198521\pi\) | ||||
0.811740 | + | 0.584020i | \(0.198521\pi\) | |||||||
\(180\) | 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 | \(-0.142374\pi\) | ||||
0.901627 | + | 0.432514i | \(0.142374\pi\) | |||||||
\(192\) | 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 | \(-0.364156\pi\) | ||||
0.413930 | + | 0.910309i | \(0.364156\pi\) | |||||||
\(200\) | 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 | \(-0.323955\pi\) | ||||
0.525294 | + | 0.850921i | \(0.323955\pi\) | |||||||
\(212\) | 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 | \(-0.501529\pi\) | ||||
−0.00480466 | + | 0.999988i | \(0.501529\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3996.00 | −1.16839 | −0.584193 | − | 0.811614i | \(-0.698589\pi\) | ||||
−0.584193 | + | 0.811614i | \(0.698589\pi\) | |||||||
\(228\) | 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 | \(-0.403777\pi\) | ||||
0.297712 | + | 0.954656i | \(0.403777\pi\) | |||||||
\(240\) | 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 | \(-0.706642\pi\) | ||||
−0.604538 | + | 0.796576i | \(0.706642\pi\) | |||||||
\(252\) | 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 | \(-0.447219\pi\) | ||||
0.165059 | + | 0.986284i | \(0.447219\pi\) | |||||||
\(264\) | 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 | \(-0.915786\pi\) | ||||
−0.965206 | + | 0.261490i | \(0.915786\pi\) | |||||||
\(272\) | 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 | \(-0.442046\pi\) | ||||
0.181062 | + | 0.983472i | \(0.442046\pi\) | |||||||
\(284\) | 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 | \(-0.702955\pi\) | ||||
−0.595270 | + | 0.803526i | \(0.702955\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1272.00 | 0.234180 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −896.000 | −0.163368 | −0.0816841 | − | 0.996658i | \(-0.526030\pi\) | ||||
−0.0816841 | + | 0.996658i | \(0.526030\pi\) | |||||||
\(312\) | 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 | \(-0.428247\pi\) | ||||
0.223513 | + | 0.974701i | \(0.428247\pi\) | |||||||
\(332\) | 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 | \(-0.672271\pi\) | ||||
−0.515169 | + | 0.857088i | \(0.672271\pi\) | |||||||
\(348\) | 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 | \(-0.280474\pi\) | ||||
0.636276 | + | 0.771461i | \(0.280474\pi\) | |||||||
\(360\) | 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 | \(-0.478796\pi\) | ||||
0.0665651 | + | 0.997782i | \(0.478796\pi\) | |||||||
\(368\) | 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 | \(-0.735483\pi\) | ||||
−0.674135 | + | 0.738608i | \(0.735483\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7920.00 | 1.06497 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8336.00 | 1.11214 | 0.556070 | − | 0.831135i | \(-0.312309\pi\) | ||||
0.556070 | + | 0.831135i | \(0.312309\pi\) | |||||||
\(384\) | 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 | \(-0.418963\pi\) | ||||
0.251845 | + | 0.967768i | \(0.418963\pi\) | |||||||
\(420\) | 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 | \(-0.250957\pi\) | ||||
0.704978 | + | 0.709229i | \(0.250957\pi\) | |||||||
\(432\) | 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 | \(-0.458843\pi\) | ||||
0.128940 | + | 0.991652i | \(0.458843\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.0000 | −0.00386097 | −0.00193049 | − | 0.999998i | \(-0.500614\pi\) | ||||
−0.00193049 | + | 0.999998i | \(0.500614\pi\) | |||||||
\(444\) | 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 | \(-0.747094\pi\) | ||||
−0.700622 | + | 0.713532i | \(0.747094\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9996.00 | 0.990492 | 0.495246 | − | 0.868753i | \(-0.335078\pi\) | ||||
0.495246 | + | 0.868753i | \(0.335078\pi\) | |||||||
\(468\) | 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 | \(-0.363201\pi\) | ||||
0.416658 | + | 0.909063i | \(0.363201\pi\) | |||||||
\(480\) | 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 | \(-0.398911\pi\) | ||||
0.312269 | + | 0.949994i | \(0.398911\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −396.000 | −0.0366211 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2512.00 | 0.230886 | 0.115443 | − | 0.993314i | \(-0.463171\pi\) | ||||
0.115443 | + | 0.993314i | \(0.463171\pi\) | |||||||
\(492\) | 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 | \(-0.417583\pi\) | ||||
0.256037 | + | 0.966667i | \(0.417583\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6528.00 | 0.582135 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5440.00 | −0.482222 | −0.241111 | − | 0.970498i | \(-0.577512\pi\) | ||||
−0.241111 | + | 0.970498i | \(0.577512\pi\) | |||||||
\(504\) | 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 | \(-0.539435\pi\) | ||||
−0.123573 | + | 0.992336i | \(0.539435\pi\) | |||||||
\(524\) | 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 | \(-0.422555\pi\) | ||||
0.240908 | + | 0.970548i | \(0.422555\pi\) | |||||||
\(548\) | 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 | \(-0.496712\pi\) | ||||
0.0103304 | + | 0.999947i | \(0.496712\pi\) | |||||||
\(564\) | 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 | \(-0.421329\pi\) | ||||
0.244643 | + | 0.969613i | \(0.421329\pi\) | |||||||
\(572\) | 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 | \(-0.642245\pi\) | ||||
−0.432151 | + | 0.901801i | \(0.642245\pi\) | |||||||
\(588\) | 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 | \(-0.548124\pi\) | ||||
−0.150612 | + | 0.988593i | \(0.548124\pi\) | |||||||
\(600\) | 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 | \(-0.761195\pi\) | ||||
−0.731534 | + | 0.681805i | \(0.761195\pi\) | |||||||
\(608\) | 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 | \(-0.613020\pi\) | ||||
−0.347650 | + | 0.937624i | \(0.613020\pi\) | |||||||
\(620\) | 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 | \(-0.432625\pi\) | ||||
0.210087 | + | 0.977683i | \(0.432625\pi\) | |||||||
\(632\) | 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 | \(-0.731550\pi\) | ||||
−0.664956 | + | 0.746882i | \(0.731550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1344.00 | −0.0816663 | −0.0408331 | − | 0.999166i | \(-0.513001\pi\) | ||||
−0.0408331 | + | 0.999166i | \(0.513001\pi\) | |||||||
\(648\) | 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 | \(-0.501731\pi\) | ||||
−0.00543826 | + | 0.999985i | \(0.501731\pi\) | |||||||
\(660\) | 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 | \(-0.383997\pi\) | ||||
0.356420 | + | 0.934326i | \(0.383997\pi\) | |||||||
\(684\) | 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 | \(-0.293247\pi\) | ||||
0.604815 | + | 0.796366i | \(0.293247\pi\) | |||||||
\(692\) | 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 | \(-0.110758\pi\) | ||||
0.940071 | + | 0.340978i | \(0.110758\pi\) | |||||||
\(720\) | 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 | \(-0.540184\pi\) | ||||
−0.125905 | + | 0.992042i | \(0.540184\pi\) | |||||||
\(728\) | 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 | \(-0.789387\pi\) | ||||
−0.788974 | + | 0.614427i | \(0.789387\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2088.00 | 0.103515 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13128.0 | −0.648209 | −0.324105 | − | 0.946021i | \(-0.605063\pi\) | ||||
−0.324105 | + | 0.946021i | \(0.605063\pi\) | |||||||
\(744\) | 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 | \(-0.375634\pi\) | ||||
0.380842 | + | 0.924640i | \(0.375634\pi\) | |||||||
\(752\) | 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 | \(-0.564129\pi\) | ||||
−0.200108 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(788\) | 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 | \(-0.435697\pi\) | ||||
0.200643 | + | 0.979664i | \(0.435697\pi\) | |||||||
\(812\) | 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 | \(-0.116592\pi\) | ||||
0.933664 | + | 0.358150i | \(0.116592\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30100.0 | 1.26563 | 0.632817 | − | 0.774301i | \(-0.281898\pi\) | ||||
0.632817 | + | 0.774301i | \(0.281898\pi\) | |||||||
\(828\) | 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 | \(-0.586241\pi\) | ||||
−0.267632 | + | 0.963521i | \(0.586241\pi\) | |||||||
\(840\) | 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 | \(-0.222302\pi\) | ||||
0.765883 | + | 0.642980i | \(0.222302\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22848.0 | −0.904364 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10216.0 | 0.402963 | 0.201481 | − | 0.979492i | \(-0.435424\pi\) | ||||
0.201481 | + | 0.979492i | \(0.435424\pi\) | |||||||
\(864\) | 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 | \(-0.312316\pi\) | ||||
0.556051 | + | 0.831149i | \(0.312316\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14752.0 | −0.558426 | −0.279213 | − | 0.960229i | \(-0.590074\pi\) | ||||
−0.279213 | + | 0.960229i | \(0.590074\pi\) | |||||||
\(888\) | 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 | \(-0.570612\pi\) | ||||
−0.220021 | + | 0.975495i | \(0.570612\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8514.00 | −0.310662 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18560.0 | 0.674995 | 0.337497 | − | 0.941326i | \(-0.390420\pi\) | ||||
0.337497 | + | 0.941326i | \(0.390420\pi\) | |||||||
\(912\) | 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 | \(-0.441144\pi\) | ||||
0.183851 | + | 0.982954i | \(0.441144\pi\) | |||||||
\(920\) | 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 | \(-0.357705\pi\) | ||||
0.432291 | + | 0.901734i | \(0.357705\pi\) | |||||||
\(948\) | 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 | \(-0.203210\pi\) | ||||
0.803048 | + | 0.595914i | \(0.203210\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13224.0 | −0.438407 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27288.0 | 0.901868 | 0.450934 | − | 0.892557i | \(-0.351091\pi\) | ||||
0.450934 | + | 0.892557i | \(0.351091\pi\) | |||||||
\(972\) | 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 | \(-0.400520\pi\) | ||||
0.307464 | + | 0.951560i | \(0.400520\pi\) | |||||||
\(984\) | 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 | \(-0.248633\pi\) | ||||
0.710136 | + | 0.704064i | \(0.248633\pi\) | |||||||
\(992\) | 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.v.1.1 | 1 | ||
4.3 | odd | 2 | 2400.4.a.a.1.1 | 1 | |||
5.4 | even | 2 | 480.4.a.c.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 1440.4.a.a.1.1 | 1 | |||
20.19 | odd | 2 | 480.4.a.l.1.1 | yes | 1 | ||
40.19 | odd | 2 | 960.4.a.i.1.1 | 1 | |||
40.29 | even | 2 | 960.4.a.t.1.1 | 1 | |||
60.59 | even | 2 | 1440.4.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.c.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
480.4.a.l.1.1 | yes | 1 | 20.19 | odd | 2 | ||
960.4.a.i.1.1 | 1 | 40.19 | odd | 2 | |||
960.4.a.t.1.1 | 1 | 40.29 | even | 2 | |||
1440.4.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
1440.4.a.j.1.1 | 1 | 60.59 | even | 2 | |||
2400.4.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
2400.4.a.v.1.1 | 1 | 1.1 | even | 1 | trivial |