Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, 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("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 30) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-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 | ||||||||
\(7\) | −4.00000 | −0.215980 | −0.107990 | − | 0.994152i | \(-0.534441\pi\) | ||||
−0.107990 | + | 0.994152i | \(0.534441\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.0000 | 1.31569 | 0.657843 | − | 0.753155i | \(-0.271469\pi\) | ||||
0.657843 | + | 0.753155i | \(0.271469\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.0426692 | −0.0213346 | − | 0.999772i | \(-0.506792\pi\) | ||||
−0.0213346 | + | 0.999772i | \(0.506792\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 114.000 | 1.62642 | 0.813208 | − | 0.581974i | \(-0.197719\pi\) | ||||
0.813208 | + | 0.581974i | \(0.197719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −140.000 | −1.69043 | −0.845216 | − | 0.534425i | \(-0.820528\pi\) | ||||
−0.845216 | + | 0.534425i | \(0.820528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.0000 | −0.124696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 210.000 | 1.34469 | 0.672345 | − | 0.740238i | \(-0.265287\pi\) | ||||
0.672345 | + | 0.740238i | \(0.265287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −272.000 | −1.57589 | −0.787946 | − | 0.615745i | \(-0.788855\pi\) | ||||
−0.787946 | + | 0.615745i | \(0.788855\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 144.000 | 0.759612 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 334.000 | 1.48403 | 0.742017 | − | 0.670381i | \(-0.233869\pi\) | ||||
0.742017 | + | 0.670381i | \(0.233869\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | −0.0246351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −198.000 | −0.754205 | −0.377102 | − | 0.926172i | \(-0.623080\pi\) | ||||
−0.377102 | + | 0.926172i | \(0.623080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −268.000 | −0.950456 | −0.475228 | − | 0.879863i | \(-0.657634\pi\) | ||||
−0.475228 | + | 0.879863i | \(0.657634\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 216.000 | 0.670358 | 0.335179 | − | 0.942154i | \(-0.391203\pi\) | ||||
0.335179 | + | 0.942154i | \(0.391203\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −327.000 | −0.953353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 342.000 | 0.939011 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 78.0000 | 0.202153 | 0.101077 | − | 0.994879i | \(-0.467771\pi\) | ||||
0.101077 | + | 0.994879i | \(0.467771\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −420.000 | −0.975971 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −240.000 | −0.529582 | −0.264791 | − | 0.964306i | \(-0.585303\pi\) | ||||
−0.264791 | + | 0.964306i | \(0.585303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 302.000 | 0.633888 | 0.316944 | − | 0.948444i | \(-0.397343\pi\) | ||||
0.316944 | + | 0.948444i | \(0.397343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −36.0000 | −0.0719932 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 596.000 | 1.08676 | 0.543381 | − | 0.839487i | \(-0.317144\pi\) | ||||
0.543381 | + | 0.839487i | \(0.317144\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 216.000 | 0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 768.000 | 1.28373 | 0.641865 | − | 0.766818i | \(-0.278161\pi\) | ||||
0.641865 | + | 0.766818i | \(0.278161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 478.000 | 0.766379 | 0.383190 | − | 0.923670i | \(-0.374826\pi\) | ||||
0.383190 | + | 0.923670i | \(0.374826\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −192.000 | −0.284161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 640.000 | 0.911464 | 0.455732 | − | 0.890117i | \(-0.349378\pi\) | ||||
0.455732 | + | 0.890117i | \(0.349378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −348.000 | −0.460216 | −0.230108 | − | 0.973165i | \(-0.573908\pi\) | ||||
−0.230108 | + | 0.973165i | \(0.573908\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 630.000 | 0.776357 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 210.000 | 0.250112 | 0.125056 | − | 0.992150i | \(-0.460089\pi\) | ||||
0.125056 | + | 0.992150i | \(0.460089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.00921569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −816.000 | −0.909841 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1534.00 | 1.60571 | 0.802856 | − | 0.596173i | \(-0.203313\pi\) | ||||
0.802856 | + | 0.596173i | \(0.203313\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 432.000 | 0.438562 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1722.00 | 1.69649 | 0.848245 | − | 0.529605i | \(-0.177660\pi\) | ||||
0.848245 | + | 0.529605i | \(0.177660\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1052.00 | 1.00638 | 0.503188 | − | 0.864177i | \(-0.332160\pi\) | ||||
0.503188 | + | 0.864177i | \(0.332160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −564.000 | −0.509570 | −0.254785 | − | 0.966998i | \(-0.582005\pi\) | ||||
−0.254785 | + | 0.966998i | \(0.582005\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −610.000 | −0.536031 | −0.268016 | − | 0.963415i | \(-0.586368\pi\) | ||||
−0.268016 | + | 0.963415i | \(0.586368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1002.00 | 0.856807 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1302.00 | −1.08391 | −0.541955 | − | 0.840407i | \(-0.682316\pi\) | ||||
−0.541955 | + | 0.840407i | \(0.682316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.0000 | −0.0142231 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −456.000 | −0.351273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 973.000 | 0.731029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −594.000 | −0.435440 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −124.000 | −0.0866395 | −0.0433198 | − | 0.999061i | \(-0.513793\pi\) | ||||
−0.0433198 | + | 0.999061i | \(0.513793\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −804.000 | −0.548746 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −192.000 | −0.128054 | −0.0640272 | − | 0.997948i | \(-0.520394\pi\) | ||||
−0.0640272 | + | 0.997948i | \(0.520394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 560.000 | 0.365099 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2514.00 | 1.56778 | 0.783889 | − | 0.620901i | \(-0.213233\pi\) | ||||
0.783889 | + | 0.620901i | \(0.213233\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1340.00 | −0.817679 | −0.408839 | − | 0.912606i | \(-0.634066\pi\) | ||||
−0.408839 | + | 0.912606i | \(0.634066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 648.000 | 0.387032 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −96.0000 | −0.0561393 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −981.000 | −0.550418 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1410.00 | 0.775246 | 0.387623 | − | 0.921818i | \(-0.373296\pi\) | ||||
0.387623 | + | 0.921818i | \(0.373296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2128.00 | 1.14685 | 0.573424 | − | 0.819258i | \(-0.305615\pi\) | ||||
0.573424 | + | 0.819258i | \(0.305615\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1026.00 | 0.542138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3026.00 | −1.53822 | −0.769112 | − | 0.639114i | \(-0.779301\pi\) | ||||
−0.769112 | + | 0.639114i | \(0.779301\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 234.000 | 0.116713 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −288.000 | −0.140979 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2612.00 | 1.25514 | 0.627569 | − | 0.778561i | \(-0.284050\pi\) | ||||
0.627569 | + | 0.778561i | \(0.284050\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.0000 | −0.0111208 | −0.00556041 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00556041 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2193.00 | −0.998179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1260.00 | −0.563477 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1962.00 | −0.862243 | −0.431122 | − | 0.902294i | \(-0.641882\pi\) | ||||
−0.431122 | + | 0.902294i | \(0.641882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −720.000 | −0.305754 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 120.000 | 0.0501074 | 0.0250537 | − | 0.999686i | \(-0.492024\pi\) | ||||
0.0250537 | + | 0.999686i | \(0.492024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 902.000 | 0.370415 | 0.185208 | − | 0.982699i | \(-0.440704\pi\) | ||||
0.185208 | + | 0.982699i | \(0.440704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 906.000 | 0.365975 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5472.00 | 2.13985 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −108.000 | −0.0415653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 168.000 | 0.0636443 | 0.0318221 | − | 0.999494i | \(-0.489869\pi\) | ||||
0.0318221 | + | 0.999494i | \(0.489869\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1318.00 | 0.491563 | 0.245782 | − | 0.969325i | \(-0.420955\pi\) | ||||
0.245782 | + | 0.969325i | \(0.420955\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4014.00 | 1.45170 | 0.725852 | − | 0.687851i | \(-0.241446\pi\) | ||||
0.725852 | + | 0.687851i | \(0.241446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2000.00 | −0.712443 | −0.356222 | − | 0.934401i | \(-0.615935\pi\) | ||||
−0.356222 | + | 0.934401i | \(0.615935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1788.00 | 0.627442 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −840.000 | −0.290426 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 648.000 | 0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6720.00 | −2.22408 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3868.00 | 1.26201 | 0.631005 | − | 0.775779i | \(-0.282643\pi\) | ||||
0.631005 | + | 0.775779i | \(0.282643\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2304.00 | 0.741162 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1088.00 | 0.340361 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1434.00 | 0.442469 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −228.000 | −0.0693979 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3148.00 | −0.945317 | −0.472658 | − | 0.881246i | \(-0.656706\pi\) | ||||
−0.472658 | + | 0.881246i | \(0.656706\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2556.00 | 0.747347 | 0.373673 | − | 0.927560i | \(-0.378098\pi\) | ||||
0.373673 | + | 0.927560i | \(0.378098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −610.000 | −0.176026 | −0.0880130 | − | 0.996119i | \(-0.528052\pi\) | ||||
−0.0880130 | + | 0.996119i | \(0.528052\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −576.000 | −0.164061 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2058.00 | 0.578644 | 0.289322 | − | 0.957232i | \(-0.406570\pi\) | ||||
0.289322 | + | 0.957232i | \(0.406570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1920.00 | 0.526234 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4920.00 | −1.33158 | −0.665792 | − | 0.746138i | \(-0.731906\pi\) | ||||
−0.665792 | + | 0.746138i | \(0.731906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1438.00 | −0.384356 | −0.192178 | − | 0.981360i | \(-0.561555\pi\) | ||||
−0.192178 | + | 0.981360i | \(0.561555\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 280.000 | 0.0721294 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1044.00 | −0.265706 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −792.000 | −0.199166 | −0.0995829 | − | 0.995029i | \(-0.531751\pi\) | ||||
−0.0995829 | + | 0.995029i | \(0.531751\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3456.00 | 0.858802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2166.00 | −0.525725 | −0.262863 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262863 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1336.00 | −0.320521 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1890.00 | 0.448230 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3192.00 | 0.748392 | 0.374196 | − | 0.927350i | \(-0.377919\pi\) | ||||
0.374196 | + | 0.927350i | \(0.377919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 630.000 | 0.144402 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5490.00 | 1.24435 | 0.622177 | − | 0.782877i | \(-0.286248\pi\) | ||||
0.622177 | + | 0.782877i | \(0.286248\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6328.00 | 1.41845 | 0.709223 | − | 0.704985i | \(-0.249046\pi\) | ||||
0.709223 | + | 0.704985i | \(0.249046\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 24.0000 | 0.00532068 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 574.000 | 0.124507 | 0.0622533 | − | 0.998060i | \(-0.480171\pi\) | ||||
0.0622533 | + | 0.998060i | \(0.480171\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2448.00 | −0.525297 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4242.00 | 0.900557 | 0.450278 | − | 0.892888i | \(-0.351325\pi\) | ||||
0.450278 | + | 0.892888i | \(0.351325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −628.000 | −0.131911 | −0.0659553 | − | 0.997823i | \(-0.521009\pi\) | ||||
−0.0659553 | + | 0.997823i | \(0.521009\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 792.000 | 0.162893 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8083.00 | 1.64523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4602.00 | 0.927058 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 558.000 | 0.111258 | 0.0556292 | − | 0.998451i | \(-0.482284\pi\) | ||||
0.0556292 | + | 0.998451i | \(0.482284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1296.00 | 0.253204 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −144.000 | −0.0278520 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1072.00 | 0.205279 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5166.00 | 0.979468 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6964.00 | −1.29465 | −0.647323 | − | 0.762216i | \(-0.724112\pi\) | ||||
−0.647323 | + | 0.762216i | \(0.724112\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3156.00 | 0.581031 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2832.00 | −0.516360 | −0.258180 | − | 0.966097i | \(-0.583123\pi\) | ||||
−0.258180 | + | 0.966097i | \(0.583123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8642.00 | −1.56062 | −0.780311 | − | 0.625392i | \(-0.784939\pi\) | ||||
−0.780311 | + | 0.625392i | \(0.784939\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2214.00 | 0.392273 | 0.196137 | − | 0.980577i | \(-0.437160\pi\) | ||||
0.196137 | + | 0.980577i | \(0.437160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10080.0 | 1.76919 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1692.00 | −0.294200 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15960.0 | −2.74934 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1830.00 | −0.309478 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −864.000 | −0.144784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10772.0 | −1.78877 | −0.894385 | − | 0.447299i | \(-0.852386\pi\) | ||||
−0.894385 | + | 0.447299i | \(0.852386\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3006.00 | 0.494678 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1654.00 | 0.267356 | 0.133678 | − | 0.991025i | \(-0.457321\pi\) | ||||
0.133678 | + | 0.991025i | \(0.457321\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3906.00 | −0.625796 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13056.0 | −2.07338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2680.00 | 0.421885 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2196.00 | 0.339733 | 0.169867 | − | 0.985467i | \(-0.445666\pi\) | ||||
0.169867 | + | 0.985467i | \(0.445666\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8270.00 | 1.26843 | 0.634216 | − | 0.773156i | \(-0.281323\pi\) | ||||
0.634216 | + | 0.773156i | \(0.281323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −54.0000 | −0.00821170 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10302.0 | −1.55331 | −0.776657 | − | 0.629923i | \(-0.783086\pi\) | ||||
−0.776657 | + | 0.629923i | \(0.783086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1368.00 | −0.202807 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2280.00 | 0.335192 | 0.167596 | − | 0.985856i | \(-0.446400\pi\) | ||||
0.167596 | + | 0.985856i | \(0.446400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12741.0 | 1.85756 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2919.00 | 0.422060 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8764.00 | −1.24653 | −0.623266 | − | 0.782010i | \(-0.714195\pi\) | ||||
−0.623266 | + | 0.782010i | \(0.714195\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1782.00 | −0.251402 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −312.000 | −0.0436610 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1318.00 | 0.182958 | 0.0914792 | − | 0.995807i | \(-0.470841\pi\) | ||||
0.0914792 | + | 0.995807i | \(0.470841\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −420.000 | −0.0573769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1100.00 | −0.149085 | −0.0745425 | − | 0.997218i | \(-0.523750\pi\) | ||||
−0.0745425 | + | 0.997218i | \(0.523750\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −372.000 | −0.0500214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3528.00 | −0.470685 | −0.235343 | − | 0.971912i | \(-0.575621\pi\) | ||||
−0.235343 | + | 0.971912i | \(0.575621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2412.00 | −0.316819 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9630.00 | −1.25517 | −0.627584 | − | 0.778549i | \(-0.715956\pi\) | ||||
−0.627584 | + | 0.778549i | \(0.715956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8208.00 | 1.06163 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −576.000 | −0.0739322 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3094.00 | 0.391142 | 0.195571 | − | 0.980690i | \(-0.437344\pi\) | ||||
0.195571 | + | 0.980690i | \(0.437344\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1680.00 | 0.210790 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1638.00 | −0.203985 | −0.101992 | − | 0.994785i | \(-0.532522\pi\) | ||||
−0.101992 | + | 0.994785i | \(0.532522\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 544.000 | 0.0672421 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16032.0 | 1.95252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13750.0 | −1.66233 | −0.831166 | − | 0.556024i | \(-0.812326\pi\) | ||||
−0.831166 | + | 0.556024i | \(0.812326\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7542.00 | 0.905157 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 960.000 | 0.114379 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4020.00 | −0.472087 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12480.0 | 1.45510 | 0.727551 | − | 0.686053i | \(-0.240658\pi\) | ||||
0.727551 | + | 0.686053i | \(0.240658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7262.00 | 0.840685 | 0.420342 | − | 0.907366i | \(-0.361910\pi\) | ||||
0.420342 | + | 0.907366i | \(0.361910\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1944.00 | 0.223453 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1208.00 | −0.136907 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −288.000 | −0.0324121 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9792.00 | −1.09435 | −0.547174 | − | 0.837019i | \(-0.684296\pi\) | ||||
−0.547174 | + | 0.837019i | \(0.684296\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1802.00 | −0.199997 | −0.0999984 | − | 0.994988i | \(-0.531884\pi\) | ||||
−0.0999984 | + | 0.994988i | \(0.531884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10080.0 | −1.10341 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2320.00 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2943.00 | −0.317784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11172.0 | 1.19819 | 0.599095 | − | 0.800678i | \(-0.295527\pi\) | ||||
0.599095 | + | 0.800678i | \(0.295527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4230.00 | 0.447589 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6810.00 | 0.715777 | 0.357888 | − | 0.933764i | \(-0.383497\pi\) | ||||
0.357888 | + | 0.933764i | \(0.383497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9504.00 | −0.992297 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6384.00 | 0.662134 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17066.0 | −1.74686 | −0.873429 | − | 0.486952i | \(-0.838109\pi\) | ||||
−0.873429 | + | 0.486952i | \(0.838109\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3078.00 | 0.313004 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18918.0 | −1.91128 | −0.955639 | − | 0.294541i | \(-0.904833\pi\) | ||||
−0.955639 | + | 0.294541i | \(0.904833\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1052.00 | 0.105595 | 0.0527976 | − | 0.998605i | \(-0.483186\pi\) | ||||
0.0527976 | + | 0.998605i | \(0.483186\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11076.0 | 1.09751 | 0.548754 | − | 0.835984i | \(-0.315102\pi\) | ||||
0.548754 | + | 0.835984i | \(0.315102\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2384.00 | −0.234718 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9078.00 | −0.888094 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12864.0 | −1.25050 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 702.000 | 0.0673844 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9000.00 | 0.858498 | 0.429249 | − | 0.903186i | \(-0.358778\pi\) | ||||
0.429249 | + | 0.903186i | \(0.358778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −668.000 | −0.0633226 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −864.000 | −0.0813941 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8764.00 | −0.815472 | −0.407736 | − | 0.913100i | \(-0.633682\pi\) | ||||
−0.407736 | + | 0.913100i | \(0.633682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7836.00 | 0.724655 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5592.00 | −0.513978 | −0.256989 | − | 0.966414i | \(-0.582730\pi\) | ||||
−0.256989 | + | 0.966414i | \(0.582730\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23940.0 | 2.18703 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3072.00 | −0.277260 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4700.00 | −0.421645 | −0.210823 | − | 0.977524i | \(-0.567614\pi\) | ||||
−0.210823 | + | 0.977524i | \(0.567614\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −72.0000 | −0.00642060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11808.0 | −1.04671 | −0.523353 | − | 0.852116i | \(-0.675319\pi\) | ||||
−0.523353 | + | 0.852116i | \(0.675319\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6579.00 | −0.576299 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1170.00 | 0.101885 | 0.0509424 | − | 0.998702i | \(-0.483778\pi\) | ||||
0.0509424 | + | 0.998702i | \(0.483778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1912.00 | −0.165522 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3780.00 | −0.325324 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10368.0 | 0.881981 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5886.00 | −0.497816 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16638.0 | −1.39909 | −0.699543 | − | 0.714590i | \(-0.746613\pi\) | ||||
−0.699543 | + | 0.714590i | \(0.746613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15692.0 | 1.31198 | 0.655988 | − | 0.754771i | \(-0.272252\pi\) | ||||
0.655988 | + | 0.754771i | \(0.272252\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31008.0 | −2.56305 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2160.00 | −0.176527 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 396.000 | 0.0321814 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 360.000 | 0.0289295 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15696.0 | −1.25431 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22018.0 | −1.74977 | −0.874887 | − | 0.484327i | \(-0.839064\pi\) | ||||
−0.874887 | + | 0.484327i | \(0.839064\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2706.00 | 0.213859 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4564.00 | −0.356751 | −0.178375 | − | 0.983963i | \(-0.557084\pi\) | ||||
−0.178375 | + | 0.983963i | \(0.557084\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2718.00 | 0.211296 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29400.0 | −2.27311 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2560.00 | −0.196858 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7734.00 | 0.588331 | 0.294165 | − | 0.955755i | \(-0.404958\pi\) | ||||
0.294165 | + | 0.955755i | \(0.404958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 536.000 | 0.0405552 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16416.0 | 1.23544 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20148.0 | −1.50824 | −0.754118 | − | 0.656739i | \(-0.771935\pi\) | ||||
−0.754118 | + | 0.656739i | \(0.771935\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −324.000 | −0.0239977 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24030.0 | −1.77046 | −0.885228 | − | 0.465156i | \(-0.845998\pi\) | ||||
−0.885228 | + | 0.465156i | \(0.845998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2372.00 | −0.173844 | −0.0869222 | − | 0.996215i | \(-0.527703\pi\) | ||||
−0.0869222 | + | 0.996215i | \(0.527703\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 504.000 | 0.0367450 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8546.00 | −0.616594 | −0.308297 | − | 0.951290i | \(-0.599759\pi\) | ||||
−0.308297 | + | 0.951290i | \(0.599759\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3954.00 | 0.283804 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1392.00 | 0.0993974 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3744.00 | 0.265970 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15444.0 | −1.08593 | −0.542966 | − | 0.839755i | \(-0.682699\pi\) | ||||
−0.542966 | + | 0.839755i | \(0.682699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38080.0 | 2.66394 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12042.0 | 0.838142 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18342.0 | −1.27018 | −0.635089 | − | 0.772439i | \(-0.719037\pi\) | ||||
−0.635089 | + | 0.772439i | \(0.719037\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6000.00 | −0.411329 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24600.0 | −1.67801 | −0.839006 | − | 0.544123i | \(-0.816863\pi\) | ||||
−0.839006 | + | 0.544123i | \(0.816863\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8998.00 | −0.610709 | −0.305354 | − | 0.952239i | \(-0.598775\pi\) | ||||
−0.305354 | + | 0.952239i | \(0.598775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5364.00 | 0.362254 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4076.00 | 0.272553 | 0.136277 | − | 0.990671i | \(-0.456486\pi\) | ||||
0.136277 | + | 0.990671i | \(0.456486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2520.00 | −0.167677 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −432.000 | −0.0286037 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4078.00 | 0.268693 | 0.134347 | − | 0.990934i | \(-0.457106\pi\) | ||||
0.134347 | + | 0.990934i | \(0.457106\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10086.0 | −0.658099 | −0.329049 | − | 0.944313i | \(-0.606728\pi\) | ||||
−0.329049 | + | 0.944313i | \(0.606728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8780.00 | −0.570110 | −0.285055 | − | 0.958511i | \(-0.592012\pi\) | ||||
−0.285055 | + | 0.958511i | \(0.592012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1944.00 | 0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −840.000 | −0.0540191 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20160.0 | −1.28407 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38076.0 | 2.41366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2792.00 | −0.176145 | −0.0880727 | − | 0.996114i | \(-0.528071\pi\) | ||||
−0.0880727 | + | 0.996114i | \(0.528071\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11604.0 | 0.728622 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 654.000 | 0.0406788 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6912.00 | 0.427910 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7602.00 | 0.468426 | 0.234213 | − | 0.972185i | \(-0.424749\pi\) | ||||
0.234213 | + | 0.972185i | \(0.424749\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24212.0 | 1.48496 | 0.742479 | − | 0.669869i | \(-0.233650\pi\) | ||||
0.742479 | + | 0.669869i | \(0.233650\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9456.00 | 0.574581 | 0.287290 | − | 0.957844i | \(-0.407246\pi\) | ||||
0.287290 | + | 0.957844i | \(0.407246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11520.0 | −0.696764 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3264.00 | 0.196507 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9558.00 | 0.572792 | 0.286396 | − | 0.958111i | \(-0.407543\pi\) | ||||
0.286396 | + | 0.958111i | \(0.407543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4302.00 | 0.255460 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29280.0 | 1.73078 | 0.865392 | − | 0.501095i | \(-0.167069\pi\) | ||||
0.865392 | + | 0.501095i | \(0.167069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29098.0 | −1.71223 | −0.856113 | − | 0.516789i | \(-0.827127\pi\) | ||||
−0.856113 | + | 0.516789i | \(0.827127\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −684.000 | −0.0400669 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15120.0 | 0.877734 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9444.00 | −0.545779 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14496.0 | 0.833997 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11638.0 | 0.666585 | 0.333293 | − | 0.942823i | \(-0.391840\pi\) | ||||
0.333293 | + | 0.942823i | \(0.391840\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3426.00 | −0.194493 | −0.0972466 | − | 0.995260i | \(-0.531004\pi\) | ||||
−0.0972466 | + | 0.995260i | \(0.531004\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6136.00 | −0.346801 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7668.00 | 0.431481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20148.0 | −1.12876 | −0.564379 | − | 0.825516i | \(-0.690884\pi\) | ||||
−0.564379 | + | 0.825516i | \(0.690884\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1830.00 | −0.101629 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −156.000 | −0.00862573 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29428.0 | 1.62011 | 0.810053 | − | 0.586356i | \(-0.199438\pi\) | ||||
0.810053 | + | 0.586356i | \(0.199438\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1728.00 | −0.0947205 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22572.0 | −1.22665 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6174.00 | 0.334080 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16242.0 | 0.875110 | 0.437555 | − | 0.899192i | \(-0.355845\pi\) | ||||
0.437555 | + | 0.899192i | \(0.355845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46760.0 | −2.50866 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6888.00 | −0.366407 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2030.00 | 0.107529 | 0.0537646 | − | 0.998554i | \(-0.482878\pi\) | ||||
0.0537646 | + | 0.998554i | \(0.482878\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5760.00 | 0.303821 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19584.0 | −1.02865 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14760.0 | −0.768790 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6960.00 | −0.361007 | −0.180504 | − | 0.983574i | \(-0.557773\pi\) | ||||
−0.180504 | + | 0.983574i | \(0.557773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4208.00 | −0.217357 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4314.00 | −0.221908 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18596.0 | 0.948676 | 0.474338 | − | 0.880343i | \(-0.342687\pi\) | ||||
0.474338 | + | 0.880343i | \(0.342687\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30552.0 | −1.54584 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21242.0 | −1.07038 | −0.535192 | − | 0.844731i | \(-0.679761\pi\) | ||||
−0.535192 | + | 0.844731i | \(0.679761\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28608.0 | 1.42984 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 340.000 | 0.0169244 | 0.00846218 | − | 0.999964i | \(-0.497306\pi\) | ||||
0.00846218 | + | 0.999964i | \(0.497306\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 840.000 | 0.0416440 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21888.0 | −1.08074 | −0.540372 | − | 0.841426i | \(-0.681716\pi\) | ||||
−0.540372 | + | 0.841426i | \(0.681716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3132.00 | −0.153405 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2256.00 | 0.110057 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17792.0 | −0.864500 | −0.432250 | − | 0.901754i | \(-0.642280\pi\) | ||||
−0.432250 | + | 0.901754i | \(0.642280\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2376.00 | −0.114988 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37346.0 | −1.79308 | −0.896541 | − | 0.442960i | \(-0.853928\pi\) | ||||
−0.896541 | + | 0.442960i | \(0.853928\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10368.0 | 0.495829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11358.0 | −0.541034 | −0.270517 | − | 0.962715i | \(-0.587195\pi\) | ||||
−0.270517 | + | 0.962715i | \(0.587195\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2440.00 | 0.115772 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 480.000 | 0.0225969 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34270.0 | −1.60703 | −0.803516 | − | 0.595283i | \(-0.797040\pi\) | ||||
−0.803516 | + | 0.595283i | \(0.797040\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6498.00 | −0.303528 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13278.0 | 0.617822 | 0.308911 | − | 0.951091i | \(-0.400035\pi\) | ||||
0.308911 | + | 0.951091i | \(0.400035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4008.00 | −0.185053 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27720.0 | 1.27493 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36864.0 | 1.68899 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5670.00 | 0.258786 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11164.0 | −0.505659 | −0.252829 | − | 0.967511i | \(-0.581361\pi\) | ||||
−0.252829 | + | 0.967511i | \(0.581361\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9576.00 | 0.432084 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5208.00 | 0.234103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −604.000 | −0.0270475 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5094.00 | 0.226397 | 0.113199 | − | 0.993572i | \(-0.463890\pi\) | ||||
0.113199 | + | 0.993572i | \(0.463890\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24624.0 | 1.09028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1890.00 | 0.0833706 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22944.0 | 1.00831 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16470.0 | 0.718428 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8790.00 | −0.382002 | −0.191001 | − | 0.981590i | \(-0.561173\pi\) | ||||
−0.191001 | + | 0.981590i | \(0.561173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5852.00 | −0.253380 | −0.126690 | − | 0.991942i | \(-0.540435\pi\) | ||||
−0.126690 | + | 0.991942i | \(0.540435\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18984.0 | 0.818940 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37520.0 | 1.60668 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 72.0000 | 0.00307190 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29478.0 | −1.25309 | −0.626546 | − | 0.779384i | \(-0.715532\pi\) | ||||
−0.626546 | + | 0.779384i | \(0.715532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39332.0 | 1.66589 | 0.832945 | − | 0.553356i | \(-0.186653\pi\) | ||||
0.832945 | + | 0.553356i | \(0.186653\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6756.00 | 0.284074 | 0.142037 | − | 0.989861i | \(-0.454635\pi\) | ||||
0.142037 | + | 0.989861i | \(0.454635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3950.00 | 0.165488 | 0.0827438 | − | 0.996571i | \(-0.473632\pi\) | ||||
0.0827438 | + | 0.996571i | \(0.473632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1722.00 | 0.0718839 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37278.0 | −1.55055 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7344.00 | −0.303280 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12360.0 | −0.508599 | −0.254300 | − | 0.967126i | \(-0.581845\pi\) | ||||
−0.254300 | + | 0.967126i | \(0.581845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19711.0 | 0.808192 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12726.0 | 0.519937 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3892.00 | −0.157887 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1884.00 | −0.0761587 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24048.0 | 0.968690 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35998.0 | 1.44496 | 0.722478 | − | 0.691394i | \(-0.243003\pi\) | ||||
0.722478 | + | 0.691394i | \(0.243003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21594.0 | 0.860720 | 0.430360 | − | 0.902657i | \(-0.358387\pi\) | ||||
0.430360 | + | 0.902657i | \(0.358387\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9260.00 | −0.367808 | −0.183904 | − | 0.982944i | \(-0.558874\pi\) | ||||
−0.183904 | + | 0.982944i | \(0.558874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2376.00 | 0.0940463 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31632.0 | 1.24770 | 0.623850 | − | 0.781544i | \(-0.285567\pi\) | ||||
0.623850 | + | 0.781544i | \(0.285567\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24249.0 | 0.949872 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30720.0 | 1.19920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1192.00 | −0.0463713 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13806.0 | 0.535237 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39694.0 | 1.52836 | 0.764180 | − | 0.645003i | \(-0.223144\pi\) | ||||
0.764180 | + | 0.645003i | \(0.223144\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1674.00 | 0.0642351 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1242.00 | 0.0474961 | 0.0237480 | − | 0.999718i | \(-0.492440\pi\) | ||||
0.0237480 | + | 0.999718i | \(0.492440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2668.00 | −0.101682 | −0.0508411 | − | 0.998707i | \(-0.516190\pi\) | ||||
−0.0508411 | + | 0.998707i | \(0.516190\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4344.00 | −0.164439 | −0.0822194 | − | 0.996614i | \(-0.526201\pi\) | ||||
−0.0822194 | + | 0.996614i | \(0.526201\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 496.000 | 0.0187124 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3888.00 | 0.146187 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30240.0 | −1.13319 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −432.000 | −0.0160803 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57120.0 | −2.11909 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8892.00 | 0.328785 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3216.00 | 0.118518 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4436.00 | 0.162398 | 0.0811990 | − | 0.996698i | \(-0.474125\pi\) | ||||
0.0811990 | + | 0.996698i | \(0.474125\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15498.0 | 0.565496 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22752.0 | −0.827450 | −0.413725 | − | 0.910402i | \(-0.635773\pi\) | ||||
−0.413725 | + | 0.910402i | \(0.635773\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16704.0 | −0.605500 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 768.000 | 0.0276571 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27160.0 | 0.974892 | 0.487446 | − | 0.873153i | \(-0.337929\pi\) | ||||
0.487446 | + | 0.873153i | \(0.337929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20892.0 | −0.747465 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1536.00 | −0.0547758 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9468.00 | 0.335458 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33030.0 | −1.16650 | −0.583250 | − | 0.812292i | \(-0.698219\pi\) | ||||
−0.583250 | + | 0.812292i | \(0.698219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45780.0 | 1.61158 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8496.00 | −0.298121 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29974.0 | 1.04505 | 0.522523 | − | 0.852625i | \(-0.324991\pi\) | ||||
0.522523 | + | 0.852625i | \(0.324991\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25926.0 | −0.901026 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13962.0 | 0.483686 | 0.241843 | − | 0.970315i | \(-0.422248\pi\) | ||||
0.241843 | + | 0.970315i | \(0.422248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14256.0 | −0.492300 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35196.0 | 1.20773 | 0.603863 | − | 0.797088i | \(-0.293627\pi\) | ||||
0.603863 | + | 0.797088i | \(0.293627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −956.000 | −0.0327008 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6642.00 | 0.226479 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28338.0 | 0.963230 | 0.481615 | − | 0.876383i | \(-0.340050\pi\) | ||||
0.481615 | + | 0.876383i | \(0.340050\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30240.0 | 1.02144 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10056.0 | −0.338608 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44193.0 | 1.48343 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5076.00 | −0.169857 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17524.0 | −0.582765 | −0.291383 | − | 0.956607i | \(-0.594115\pi\) | ||||
−0.291383 | + | 0.956607i | \(0.594115\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −47880.0 | −1.58733 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26808.0 | 0.886004 | 0.443002 | − | 0.896521i | \(-0.353913\pi\) | ||||
0.443002 | + | 0.896521i | \(0.353913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5360.00 | 0.176602 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10914.0 | 0.357390 | 0.178695 | − | 0.983905i | \(-0.442813\pi\) | ||||
0.178695 | + | 0.983905i | \(0.442813\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10080.0 | 0.329069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5490.00 | −0.178677 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22272.0 | 0.722652 | 0.361326 | − | 0.932440i | \(-0.382324\pi\) | ||||
0.361326 | + | 0.932440i | \(0.382324\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2592.00 | −0.0835910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19296.0 | −0.620402 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14072.0 | −0.451071 | −0.225536 | − | 0.974235i | \(-0.572413\pi\) | ||||
−0.225536 | + | 0.974235i | \(0.572413\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32316.0 | −1.03275 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4826.00 | −0.153301 | −0.0766504 | − | 0.997058i | \(-0.524423\pi\) | ||||
−0.0766504 | + | 0.997058i | \(0.524423\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9018.00 | 0.285602 |
(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 | 1200.4.a.ba.1.1 | 1 | ||
4.3 | odd | 2 | 150.4.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 1200.4.f.r.49.1 | 2 | |||
5.3 | odd | 4 | 1200.4.f.r.49.2 | 2 | |||
5.4 | even | 2 | 240.4.a.b.1.1 | 1 | |||
12.11 | even | 2 | 450.4.a.r.1.1 | 1 | |||
15.14 | odd | 2 | 720.4.a.y.1.1 | 1 | |||
20.3 | even | 4 | 150.4.c.c.49.2 | 2 | |||
20.7 | even | 4 | 150.4.c.c.49.1 | 2 | |||
20.19 | odd | 2 | 30.4.a.b.1.1 | ✓ | 1 | ||
40.19 | odd | 2 | 960.4.a.n.1.1 | 1 | |||
40.29 | even | 2 | 960.4.a.bg.1.1 | 1 | |||
60.23 | odd | 4 | 450.4.c.j.199.1 | 2 | |||
60.47 | odd | 4 | 450.4.c.j.199.2 | 2 | |||
60.59 | even | 2 | 90.4.a.c.1.1 | 1 | |||
140.139 | even | 2 | 1470.4.a.r.1.1 | 1 | |||
180.59 | even | 6 | 810.4.e.p.541.1 | 2 | |||
180.79 | odd | 6 | 810.4.e.i.271.1 | 2 | |||
180.119 | even | 6 | 810.4.e.p.271.1 | 2 | |||
180.139 | odd | 6 | 810.4.e.i.541.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.4.a.b.1.1 | ✓ | 1 | 20.19 | odd | 2 | ||
90.4.a.c.1.1 | 1 | 60.59 | even | 2 | |||
150.4.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
150.4.c.c.49.1 | 2 | 20.7 | even | 4 | |||
150.4.c.c.49.2 | 2 | 20.3 | even | 4 | |||
240.4.a.b.1.1 | 1 | 5.4 | even | 2 | |||
450.4.a.r.1.1 | 1 | 12.11 | even | 2 | |||
450.4.c.j.199.1 | 2 | 60.23 | odd | 4 | |||
450.4.c.j.199.2 | 2 | 60.47 | odd | 4 | |||
720.4.a.y.1.1 | 1 | 15.14 | odd | 2 | |||
810.4.e.i.271.1 | 2 | 180.79 | odd | 6 | |||
810.4.e.i.541.1 | 2 | 180.139 | odd | 6 | |||
810.4.e.p.271.1 | 2 | 180.119 | even | 6 | |||
810.4.e.p.541.1 | 2 | 180.59 | even | 6 | |||
960.4.a.n.1.1 | 1 | 40.19 | odd | 2 | |||
960.4.a.bg.1.1 | 1 | 40.29 | even | 2 | |||
1200.4.a.ba.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1200.4.f.r.49.1 | 2 | 5.2 | odd | 4 | |||
1200.4.f.r.49.2 | 2 | 5.3 | odd | 4 | |||
1470.4.a.r.1.1 | 1 | 140.139 | even | 2 |