Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(49,1200)]
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, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.f (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(70.8022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.49 |
Dual form | 1200.4.f.m.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.0000i | 1.07990i | 0.841698 | + | 0.539949i | \(0.181557\pi\) | ||||
−0.841698 | + | 0.539949i | \(0.818443\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.0000 | 0.657843 | 0.328921 | − | 0.944357i | \(-0.393315\pi\) | ||||
0.328921 | + | 0.944357i | \(0.393315\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 74.0000i | 1.57876i | 0.613904 | + | 0.789381i | \(0.289598\pi\) | ||||
−0.613904 | + | 0.789381i | \(0.710402\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 54.0000i | − 0.770407i | −0.922832 | − | 0.385204i | \(-0.874131\pi\) | ||||
0.922832 | − | 0.385204i | \(-0.125869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −124.000 | −1.49724 | −0.748620 | − | 0.663000i | \(-0.769283\pi\) | ||||
−0.748620 | + | 0.663000i | \(0.769283\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −60.0000 | −0.623480 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000i | 1.08790i | 0.839117 | + | 0.543951i | \(0.183072\pi\) | ||||
−0.839117 | + | 0.543951i | \(0.816928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 78.0000 | 0.499456 | 0.249728 | − | 0.968316i | \(-0.419659\pi\) | ||||
0.249728 | + | 0.968316i | \(0.419659\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −200.000 | −1.15874 | −0.579372 | − | 0.815063i | \(-0.696702\pi\) | ||||
−0.579372 | + | 0.815063i | \(0.696702\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 72.0000i | 0.379806i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 70.0000i | 0.311025i | 0.987834 | + | 0.155513i | \(0.0497029\pi\) | ||||
−0.987834 | + | 0.155513i | \(0.950297\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −222.000 | −0.911499 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 330.000 | 1.25701 | 0.628504 | − | 0.777806i | \(-0.283668\pi\) | ||||
0.628504 | + | 0.777806i | \(0.283668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 92.0000i | − 0.326276i | −0.986603 | − | 0.163138i | \(-0.947838\pi\) | ||||
0.986603 | − | 0.163138i | \(-0.0521616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 24.0000i | − 0.0744843i | −0.999306 | − | 0.0372421i | \(-0.988143\pi\) | ||||
0.999306 | − | 0.0372421i | \(-0.0118573\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −57.0000 | −0.166181 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 162.000 | 0.444795 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 450.000i | 1.16627i | 0.812376 | + | 0.583134i | \(0.198174\pi\) | ||||
−0.812376 | + | 0.583134i | \(0.801826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 372.000i | − 0.864432i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 24.0000 | 0.0529582 | 0.0264791 | − | 0.999649i | \(-0.491570\pi\) | ||||
0.0264791 | + | 0.999649i | \(0.491570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −322.000 | −0.675867 | −0.337933 | − | 0.941170i | \(-0.609728\pi\) | ||||
−0.337933 | + | 0.941170i | \(0.609728\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 180.000i | − 0.359966i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 196.000i | − 0.357391i | −0.983904 | − | 0.178696i | \(-0.942812\pi\) | ||||
0.983904 | − | 0.178696i | \(-0.0571877\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −360.000 | −0.628100 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 288.000 | 0.481399 | 0.240699 | − | 0.970600i | \(-0.422623\pi\) | ||||
0.240699 | + | 0.970600i | \(0.422623\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 430.000i | − 0.689420i | −0.938709 | − | 0.344710i | \(-0.887977\pi\) | ||||
0.938709 | − | 0.344710i | \(-0.112023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 480.000i | 0.710404i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −520.000 | −0.740564 | −0.370282 | − | 0.928919i | \(-0.620739\pi\) | ||||
−0.370282 | + | 0.928919i | \(0.620739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 156.000i | − 0.206304i | −0.994666 | − | 0.103152i | \(-0.967107\pi\) | ||||
0.994666 | − | 0.103152i | \(-0.0328928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 234.000i | 0.288361i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1026.00 | −1.22198 | −0.610988 | − | 0.791640i | \(-0.709227\pi\) | ||||
−0.610988 | + | 0.791640i | \(0.709227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1480.00 | −1.70490 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 600.000i | − 0.669001i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 286.000i | 0.299370i | 0.988734 | + | 0.149685i | \(0.0478260\pi\) | ||||
−0.988734 | + | 0.149685i | \(0.952174\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −216.000 | −0.219281 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1734.00 | −1.70831 | −0.854156 | − | 0.520017i | \(-0.825925\pi\) | ||||
−0.854156 | + | 0.520017i | \(0.825925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 452.000i | − 0.432397i | −0.976349 | − | 0.216198i | \(-0.930634\pi\) | ||||
0.976349 | − | 0.216198i | \(-0.0693658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1404.00i | − 1.26850i | −0.773127 | − | 0.634251i | \(-0.781308\pi\) | ||||
0.773127 | − | 0.634251i | \(-0.218692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1474.00 | 1.29526 | 0.647631 | − | 0.761954i | \(-0.275760\pi\) | ||||
0.647631 | + | 0.761954i | \(0.275760\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −210.000 | −0.179570 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1086.00i | 0.904091i | 0.891995 | + | 0.452046i | \(0.149306\pi\) | ||||
−0.891995 | + | 0.452046i | \(0.850694\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 666.000i | − 0.526254i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1080.00 | 0.831962 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −755.000 | −0.567243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 990.000i | 0.725734i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1244.00i | 0.869190i | 0.900626 | + | 0.434595i | \(0.143109\pi\) | ||||
−0.900626 | + | 0.434595i | \(0.856891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 276.000 | 0.188376 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2328.00 | −1.55266 | −0.776329 | − | 0.630327i | \(-0.782921\pi\) | ||||
−0.776329 | + | 0.630327i | \(0.782921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2480.00i | − 1.61687i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2118.00i | − 1.32082i | −0.750903 | − | 0.660412i | \(-0.770382\pi\) | ||||
0.750903 | − | 0.660412i | \(-0.229618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2324.00 | 1.41812 | 0.709062 | − | 0.705147i | \(-0.249119\pi\) | ||||
0.709062 | + | 0.705147i | \(0.249119\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 72.0000 | 0.0430035 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1776.00i | 1.03858i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 171.000i | − 0.0959445i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −258.000 | −0.141854 | −0.0709268 | − | 0.997482i | \(-0.522596\pi\) | ||||
−0.0709268 | + | 0.997482i | \(0.522596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 808.000 | 0.435458 | 0.217729 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217729 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 486.000i | 0.256802i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2378.00i | − 1.20882i | −0.796673 | − | 0.604411i | \(-0.793408\pi\) | ||||
0.796673 | − | 0.604411i | \(-0.206592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1350.00 | −0.673346 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2400.00 | −1.17482 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 52.0000i | 0.0249874i | 0.999922 | + | 0.0124937i | \(0.00397698\pi\) | ||||
−0.999922 | + | 0.0124937i | \(0.996023\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3720.00i | − 1.72373i | −0.507141 | − | 0.861863i | \(-0.669298\pi\) | ||||
0.507141 | − | 0.861863i | \(-0.330702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3279.00 | −1.49249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1116.00 | 0.499080 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 426.000i | 0.187215i | 0.995609 | + | 0.0936075i | \(0.0298399\pi\) | ||||
−0.995609 | + | 0.0936075i | \(0.970160\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 72.0000i | 0.0305754i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1440.00 | −0.601289 | −0.300644 | − | 0.953736i | \(-0.597202\pi\) | ||||
−0.300644 | + | 0.953736i | \(0.597202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3130.00 | −1.28537 | −0.642683 | − | 0.766133i | \(-0.722179\pi\) | ||||
−0.642683 | + | 0.766133i | \(0.722179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 966.000i | − 0.390212i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1296.00i | − 0.506807i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 540.000 | 0.207827 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3576.00 | −1.35471 | −0.677357 | − | 0.735655i | \(-0.736875\pi\) | ||||
−0.677357 | + | 0.735655i | \(0.736875\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2666.00i | 0.994315i | 0.867660 | + | 0.497158i | \(0.165623\pi\) | ||||
−0.867660 | + | 0.497158i | \(0.834377\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2718.00i | 0.982992i | 0.870880 | + | 0.491496i | \(0.163550\pi\) | ||||
−0.870880 | + | 0.491496i | \(0.836450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3832.00 | −1.36504 | −0.682521 | − | 0.730866i | \(-0.739116\pi\) | ||||
−0.682521 | + | 0.730866i | \(0.739116\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 588.000 | 0.206340 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1560.00i | 0.539362i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1080.00i | − 0.362634i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2976.00 | −0.984948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1100.00 | −0.358896 | −0.179448 | − | 0.983767i | \(-0.557431\pi\) | ||||
−0.179448 | + | 0.983767i | \(0.557431\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 864.000i | 0.277936i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 4000.00i | − 1.25133i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1290.00 | 0.398037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3996.00 | 1.21629 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1964.00i | − 0.589772i | −0.955532 | − | 0.294886i | \(-0.904718\pi\) | ||||
0.955532 | − | 0.294886i | \(-0.0952817\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 660.000i | 0.192977i | 0.995334 | + | 0.0964884i | \(0.0307611\pi\) | ||||
−0.995334 | + | 0.0964884i | \(0.969239\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1906.00 | 0.550009 | 0.275004 | − | 0.961443i | \(-0.411321\pi\) | ||||
0.275004 | + | 0.961443i | \(0.411321\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1440.00 | −0.410152 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1458.00i | − 0.409943i | −0.978768 | − | 0.204972i | \(-0.934290\pi\) | ||||
0.978768 | − | 0.204972i | \(-0.0657102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1560.00i | − 0.427565i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1176.00 | 0.318281 | 0.159140 | − | 0.987256i | \(-0.449128\pi\) | ||||
0.159140 | + | 0.987256i | \(0.449128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 866.000 | 0.231469 | 0.115734 | − | 0.993280i | \(-0.463078\pi\) | ||||
0.115734 | + | 0.993280i | \(0.463078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 9176.00i | − 2.36379i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 468.000 | 0.119110 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −432.000 | −0.108636 | −0.0543179 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543179 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2880.00i | 0.715668i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2526.00i | − 0.613103i | −0.951854 | − | 0.306552i | \(-0.900825\pi\) | ||||
0.951854 | − | 0.306552i | \(-0.0991752\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1400.00 | −0.335876 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −702.000 | −0.166485 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 5448.00i | − 1.27733i | −0.769484 | − | 0.638666i | \(-0.779487\pi\) | ||||
0.769484 | − | 0.638666i | \(-0.220513\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3078.00i | − 0.705508i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2574.00 | 0.583418 | 0.291709 | − | 0.956507i | \(-0.405776\pi\) | ||||
0.291709 | + | 0.956507i | \(0.405776\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3184.00 | 0.713706 | 0.356853 | − | 0.934161i | \(-0.383850\pi\) | ||||
0.356853 | + | 0.934161i | \(0.383850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 4440.00i | − 0.984326i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3962.00i | − 0.859399i | −0.902972 | − | 0.429699i | \(-0.858620\pi\) | ||||
0.902972 | − | 0.429699i | \(-0.141380\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1800.00 | 0.386248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8286.00 | −1.75908 | −0.879540 | − | 0.475825i | \(-0.842149\pi\) | ||||
−0.879540 | + | 0.475825i | \(0.842149\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2716.00i | 0.570493i | 0.958454 | + | 0.285246i | \(0.0920754\pi\) | ||||
−0.958454 | + | 0.285246i | \(0.907925\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6600.00i | 1.35744i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1997.00 | 0.406473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −858.000 | −0.172841 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6018.00i | 1.19992i | 0.800032 | + | 0.599958i | \(0.204816\pi\) | ||||
−0.800032 | + | 0.599958i | \(0.795184\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 648.000i | − 0.126602i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8880.00 | −1.71754 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1840.00 | 0.352345 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 5202.00i | − 0.986294i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9236.00i | 1.71702i | 0.512793 | + | 0.858512i | \(0.328611\pi\) | ||||
−0.512793 | + | 0.858512i | \(0.671389\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1356.00 | 0.249644 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1536.00 | −0.280060 | −0.140030 | − | 0.990147i | \(-0.544720\pi\) | ||||
−0.140030 | + | 0.990147i | \(0.544720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 7342.00i | − 1.32586i | −0.748681 | − | 0.662930i | \(-0.769313\pi\) | ||||
0.748681 | − | 0.662930i | \(-0.230687\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3894.00i | 0.689933i | 0.938615 | + | 0.344967i | \(0.112110\pi\) | ||||
−0.938615 | + | 0.344967i | \(0.887890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1872.00 | 0.328564 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4212.00 | 0.732370 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6696.00i | 1.15348i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4422.00i | 0.747820i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 480.000 | 0.0804354 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3692.00 | −0.613084 | −0.306542 | − | 0.951857i | \(-0.599172\pi\) | ||||
−0.306542 | + | 0.951857i | \(0.599172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 630.000i | − 0.103675i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8998.00i | 1.45446i | 0.686395 | + | 0.727229i | \(0.259192\pi\) | ||||
−0.686395 | + | 0.727229i | \(0.740808\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3258.00 | −0.521977 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4800.00 | −0.762271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5720.00i | 0.900440i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5244.00i | 0.811276i | 0.914034 | + | 0.405638i | \(0.132951\pi\) | ||||
−0.914034 | + | 0.405638i | \(0.867049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6302.00 | −0.966585 | −0.483293 | − | 0.875459i | \(-0.660559\pi\) | ||||
−0.483293 | + | 0.875459i | \(0.660559\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1998.00 | 0.303833 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3414.00i | 0.514756i | 0.966311 | + | 0.257378i | \(0.0828586\pi\) | ||||
−0.966311 | + | 0.257378i | \(0.917141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3240.00i | 0.480333i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4824.00 | 0.709195 | 0.354597 | − | 0.935019i | \(-0.384618\pi\) | ||||
0.354597 | + | 0.935019i | \(0.384618\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8517.00 | 1.24173 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2265.00i | − 0.327498i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3508.00i | − 0.498954i | −0.968381 | − | 0.249477i | \(-0.919741\pi\) | ||||
0.968381 | − | 0.249477i | \(-0.0802587\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2970.00 | −0.419003 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9000.00 | −1.25945 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10802.0i | 1.49948i | 0.661732 | + | 0.749740i | \(0.269822\pi\) | ||||
−0.661732 | + | 0.749740i | \(0.730178\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5772.00i | 0.788523i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1460.00 | 0.197876 | 0.0989382 | − | 0.995094i | \(-0.468455\pi\) | ||||
0.0989382 | + | 0.995094i | \(0.468455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3732.00 | −0.501827 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4872.00i | 0.649994i | 0.945715 | + | 0.324997i | \(0.105363\pi\) | ||||
−0.945715 | + | 0.324997i | \(0.894637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 828.000i | 0.108759i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14046.0 | 1.83075 | 0.915373 | − | 0.402606i | \(-0.131896\pi\) | ||||
0.915373 | + | 0.402606i | \(0.131896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6480.00 | 0.838127 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 6984.00i | − 0.896428i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2734.00i | 0.345631i | 0.984954 | + | 0.172816i | \(0.0552864\pi\) | ||||
−0.984954 | + | 0.172816i | \(0.944714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7440.00 | 0.933498 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15942.0 | −1.98530 | −0.992650 | − | 0.121019i | \(-0.961384\pi\) | ||||
−0.992650 | + | 0.121019i | \(0.961384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 14800.0i | − 1.82938i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1680.00i | 0.204606i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8714.00 | −1.05350 | −0.526748 | − | 0.850022i | \(-0.676589\pi\) | ||||
−0.526748 | + | 0.850022i | \(0.676589\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6354.00 | 0.762578 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 480.000i | 0.0571895i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6972.00i | 0.818754i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11976.0 | 1.39634 | 0.698169 | − | 0.715933i | \(-0.253998\pi\) | ||||
0.698169 | + | 0.715933i | \(0.253998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11054.0 | 1.27967 | 0.639833 | − | 0.768514i | \(-0.279004\pi\) | ||||
0.639833 | + | 0.768514i | \(0.279004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 216.000i | 0.0248281i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6440.00i | − 0.729868i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5328.00 | −0.599623 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −720.000 | −0.0804668 | −0.0402334 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402334 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 15622.0i | − 1.73382i | −0.498462 | − | 0.866912i | \(-0.666102\pi\) | ||||
0.498462 | − | 0.866912i | \(-0.333898\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 14880.0i | − 1.62885i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9880.00 | −1.07414 | −0.537069 | − | 0.843538i | \(-0.680469\pi\) | ||||
−0.537069 | + | 0.843538i | \(0.680469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 513.000 | 0.0553936 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16116.0i | 1.72843i | 0.503123 | + | 0.864215i | \(0.332184\pi\) | ||||
−0.503123 | + | 0.864215i | \(0.667816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 774.000i | − 0.0818992i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9018.00 | −0.947852 | −0.473926 | − | 0.880565i | \(-0.657164\pi\) | ||||
−0.473926 | + | 0.880565i | \(0.657164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7920.00 | 0.826914 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2424.00i | 0.251412i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3670.00i | 0.375657i | 0.982202 | + | 0.187829i | \(0.0601450\pi\) | ||||
−0.982202 | + | 0.187829i | \(0.939855\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1458.00 | −0.148265 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17562.0 | 1.77428 | 0.887141 | − | 0.461499i | \(-0.152688\pi\) | ||||
0.887141 | + | 0.461499i | \(0.152688\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1172.00i | − 0.117640i | −0.998269 | − | 0.0588202i | \(-0.981266\pi\) | ||||
0.998269 | − | 0.0588202i | \(-0.0187338\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6876.00i | 0.681335i | 0.940184 | + | 0.340667i | \(0.110653\pi\) | ||||
−0.940184 | + | 0.340667i | \(0.889347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3920.00 | 0.385946 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7134.00 | 0.697914 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 2208.00i | − 0.214638i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4050.00i | − 0.388756i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2280.00 | 0.217486 | 0.108743 | − | 0.994070i | \(-0.465317\pi\) | ||||
0.108743 | + | 0.994070i | \(0.465317\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5180.00 | −0.491035 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 7200.00i | − 0.678284i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3076.00i | − 0.286215i | −0.989707 | − | 0.143108i | \(-0.954290\pi\) | ||||
0.989707 | − | 0.143108i | \(-0.0457095\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −156.000 | −0.0144265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18912.0 | 1.73826 | 0.869131 | − | 0.494582i | \(-0.164679\pi\) | ||||
0.869131 | + | 0.494582i | \(0.164679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4212.00i | − 0.384785i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5760.00i | 0.519862i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9956.00 | 0.893170 | 0.446585 | − | 0.894741i | \(-0.352640\pi\) | ||||
0.446585 | + | 0.894741i | \(0.352640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11160.0 | 0.995194 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10656.0i | 0.944588i | 0.881441 | + | 0.472294i | \(0.156574\pi\) | ||||
−0.881441 | + | 0.472294i | \(0.843426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9837.00i | − 0.861689i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2766.00 | 0.240866 | 0.120433 | − | 0.992721i | \(-0.461572\pi\) | ||||
0.120433 | + | 0.992721i | \(0.461572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8600.00 | 0.744504 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3348.00i | 0.288144i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 576.000i | − 0.0489989i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1278.00 | −0.108089 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10530.0 | 0.885466 | 0.442733 | − | 0.896654i | \(-0.354009\pi\) | ||||
0.442733 | + | 0.896654i | \(0.354009\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 12692.0i | − 1.06115i | −0.847637 | − | 0.530576i | \(-0.821976\pi\) | ||||
0.847637 | − | 0.530576i | \(-0.178024\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10800.0i | 0.892705i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2233.00 | −0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −216.000 | −0.0176527 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24420.0i | 1.98452i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 4320.00i | − 0.347154i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1368.00 | −0.109321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18110.0 | 1.43920 | 0.719602 | − | 0.694386i | \(-0.244324\pi\) | ||||
0.719602 | + | 0.694386i | \(0.244324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 9390.00i | − 0.742106i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3620.00i | 0.282962i | 0.989941 | + | 0.141481i | \(0.0451864\pi\) | ||||
−0.989941 | + | 0.141481i | \(0.954814\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2898.00 | 0.225289 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9672.00 | −0.747806 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 10400.0i | − 0.799734i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14166.0i | 1.07762i | 0.842428 | + | 0.538809i | \(0.181125\pi\) | ||||
−0.842428 | + | 0.538809i | \(0.818875\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6808.00 | 0.515112 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3888.00 | 0.292605 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13404.0i | 1.00339i | 0.865043 | + | 0.501697i | \(0.167291\pi\) | ||||
−0.865043 | + | 0.501697i | \(0.832709\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1620.00i | 0.119989i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18654.0 | 1.37437 | 0.687185 | − | 0.726483i | \(-0.258846\pi\) | ||||
0.687185 | + | 0.726483i | \(0.258846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7684.00 | 0.563162 | 0.281581 | − | 0.959537i | \(-0.409141\pi\) | ||||
0.281581 | + | 0.959537i | \(0.409141\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 10728.0i | − 0.782144i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1726.00i | 0.124531i | 0.998060 | + | 0.0622654i | \(0.0198325\pi\) | ||||
−0.998060 | + | 0.0622654i | \(0.980167\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7998.00 | −0.574068 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3120.00 | 0.222787 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10800.0i | 0.767222i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10596.0i | 0.745049i | 0.928022 | + | 0.372524i | \(0.121508\pi\) | ||||
−0.928022 | + | 0.372524i | \(0.878492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24800.0 | 1.73492 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8154.00 | −0.567531 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2862.00i | 0.198193i | 0.995078 | + | 0.0990963i | \(0.0315952\pi\) | ||||
−0.995078 | + | 0.0990963i | \(0.968405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 11496.0i | − 0.788107i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23592.0 | −1.60925 | −0.804627 | − | 0.593781i | \(-0.797635\pi\) | ||||
−0.804627 | + | 0.593781i | \(0.797635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9574.00 | −0.649803 | −0.324902 | − | 0.945748i | \(-0.605331\pi\) | ||||
−0.324902 | + | 0.945748i | \(0.605331\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1764.00i | 0.119130i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17444.0i | 1.16644i | 0.812314 | + | 0.583221i | \(0.198208\pi\) | ||||
−0.812314 | + | 0.583221i | \(0.801792\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4680.00 | −0.311401 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1776.00 | 0.117593 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2374.00i | − 0.156419i | −0.996937 | − | 0.0782096i | \(-0.975080\pi\) | ||||
0.996937 | − | 0.0782096i | \(-0.0249203\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12162.0i | 0.793555i | 0.917915 | + | 0.396778i | \(0.129872\pi\) | ||||
−0.917915 | + | 0.396778i | \(0.870128\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8804.00 | 0.571668 | 0.285834 | − | 0.958279i | \(-0.407729\pi\) | ||||
0.285834 | + | 0.958279i | \(0.407729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3240.00 | 0.209367 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 20520.0i | − 1.31961i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 8928.00i | − 0.568660i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3780.00 | 0.239616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12688.0 | 0.800478 | 0.400239 | − | 0.916411i | \(-0.368927\pi\) | ||||
0.400239 | + | 0.916411i | \(0.368927\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 3300.00i | − 0.207209i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4218.00i | − 0.262360i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2592.00 | −0.160466 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9150.00 | −0.563812 | −0.281906 | − | 0.959442i | \(-0.590967\pi\) | ||||
−0.281906 | + | 0.959442i | \(0.590967\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 25292.0i | − 1.55120i | −0.631227 | − | 0.775598i | \(-0.717448\pi\) | ||||
0.631227 | − | 0.775598i | \(-0.282552\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2736.00i | − 0.166249i | −0.996539 | − | 0.0831246i | \(-0.973510\pi\) | ||||
0.996539 | − | 0.0831246i | \(-0.0264900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 576.000 | 0.0348382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12000.0 | 0.722453 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22218.0i | 1.33148i | 0.746183 | + | 0.665741i | \(0.231884\pi\) | ||||
−0.746183 | + | 0.665741i | \(0.768116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3870.00i | 0.229807i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14520.0 | 0.858299 | 0.429149 | − | 0.903234i | \(-0.358813\pi\) | ||||
0.429149 | + | 0.903234i | \(0.358813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10618.0 | −0.624799 | −0.312400 | − | 0.949951i | \(-0.601133\pi\) | ||||
−0.312400 | + | 0.949951i | \(0.601133\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11988.0i | 0.702225i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9360.00i | 0.543359i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5892.00 | 0.340505 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7728.00 | −0.444614 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1370.00i | 0.0784690i | 0.999230 | + | 0.0392345i | \(0.0124919\pi\) | ||||
−0.999230 | + | 0.0392345i | \(0.987508\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13758.0i | 0.781038i | 0.920595 | + | 0.390519i | \(0.127704\pi\) | ||||
−0.920595 | + | 0.390519i | \(0.872296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5720.00 | −0.323289 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1980.00 | −0.111415 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 11988.0i | − 0.671608i | −0.941932 | − | 0.335804i | \(-0.890992\pi\) | ||||
0.941932 | − | 0.335804i | \(-0.109008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5718.00i | 0.317548i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33300.0 | −1.84126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32996.0 | −1.81654 | −0.908268 | − | 0.418388i | \(-0.862595\pi\) | ||||
−0.908268 | + | 0.418388i | \(0.862595\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 4320.00i | − 0.236801i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 17820.0i | − 0.968408i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4374.00 | 0.236681 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25902.0 | −1.39558 | −0.697792 | − | 0.716300i | \(-0.745834\pi\) | ||||
−0.697792 | + | 0.716300i | \(0.745834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 8680.00i | − 0.465679i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 34680.0i | − 1.84480i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27394.0 | 1.45106 | 0.725531 | − | 0.688189i | \(-0.241594\pi\) | ||||
0.725531 | + | 0.688189i | \(0.241594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4680.00 | 0.246855 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 24000.0i | − 1.26060i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3528.00i | 0.183760i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34848.0 | 1.80753 | 0.903763 | − | 0.428033i | \(-0.140793\pi\) | ||||
0.903763 | + | 0.428033i | \(0.140793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9040.00 | 0.466945 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2598.00i | 0.133639i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28028.0i | 1.42985i | 0.699201 | + | 0.714925i | \(0.253539\pi\) | ||||
−0.699201 | + | 0.714925i | \(0.746461\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4968.00 | −0.251365 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18002.0i | 0.907120i | 0.891226 | + | 0.453560i | \(0.149846\pi\) | ||||
−0.891226 | + | 0.453560i | \(0.850154\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 4704.00i | − 0.235107i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15284.0 | 0.760800 | 0.380400 | − | 0.924822i | \(-0.375786\pi\) | ||||
0.380400 | + | 0.924822i | \(0.375786\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27528.0 | 1.36473 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18768.0i | 0.926691i | 0.886178 | + | 0.463345i | \(0.153351\pi\) | ||||
−0.886178 | + | 0.463345i | \(0.846649\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1404.00i | 0.0687680i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28080.0 | 1.36985 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8696.00 | −0.422532 | −0.211266 | − | 0.977429i | \(-0.567759\pi\) | ||||
−0.211266 | + | 0.977429i | \(0.567759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 1296.00i | − 0.0627209i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38662.0i | 1.85627i | 0.372247 | + | 0.928134i | \(0.378587\pi\) | ||||
−0.372247 | + | 0.928134i | \(0.621413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8640.00 | −0.413191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23874.0 | 1.13723 | 0.568615 | − | 0.822604i | \(-0.307479\pi\) | ||||
0.568615 | + | 0.822604i | \(0.307479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29480.0i | 1.39875i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1776.00i | 0.0836084i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23618.0 | −1.10753 | −0.553763 | − | 0.832675i | \(-0.686808\pi\) | ||||
−0.553763 | + | 0.832675i | \(0.686808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7578.00 | 0.353975 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11538.0i | 0.536860i | 0.963299 | + | 0.268430i | \(0.0865049\pi\) | ||||
−0.963299 | + | 0.268430i | \(0.913495\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 4200.00i | − 0.193918i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40920.0 | −1.88204 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6912.00 | 0.316685 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2106.00i | − 0.0961204i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 14884.0i | − 0.674152i | −0.941478 | − | 0.337076i | \(-0.890562\pi\) | ||||
0.941478 | − | 0.337076i | \(-0.109438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16344.0 | 0.737467 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21720.0 | −0.976327 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 23828.0i | − 1.06703i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11334.0i | 0.503728i | 0.967763 | + | 0.251864i | \(0.0810435\pi\) | ||||
−0.967763 | + | 0.251864i | \(0.918957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1296.00 | −0.0573832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9234.00 | 0.407325 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10320.0i | − 0.453530i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7722.00i | 0.336837i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44730.0 | −1.94391 | −0.971955 | − | 0.235167i | \(-0.924436\pi\) | ||||
−0.971955 | + | 0.235167i | \(0.924436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42748.0 | 1.85091 | 0.925453 | − | 0.378862i | \(-0.123684\pi\) | ||||
0.925453 | + | 0.378862i | \(0.123684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9552.00i | 0.412058i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11408.0i | 0.488513i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13320.0 | 0.568301 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31686.0 | −1.34695 | −0.673477 | − | 0.739208i | \(-0.735200\pi\) | ||||
−0.673477 | + | 0.739208i | \(0.735200\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 11036.0i | − 0.467425i | −0.972306 | − | 0.233713i | \(-0.924913\pi\) | ||||
0.972306 | − | 0.233713i | \(-0.0750875\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25884.0i | 1.08836i | 0.838968 | + | 0.544181i | \(0.183159\pi\) | ||||
−0.838968 | + | 0.544181i | \(0.816841\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15950.0 | −0.668234 | −0.334117 | − | 0.942532i | \(-0.608438\pi\) | ||||
−0.334117 | + | 0.942532i | \(0.608438\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11886.0 | 0.496174 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3078.00i | 0.128027i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5400.00i | 0.223000i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13800.0 | 0.567853 | 0.283927 | − | 0.958846i | \(-0.408363\pi\) | ||||
0.283927 | + | 0.958846i | \(0.408363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18305.0 | −0.750543 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 24858.0i | − 1.01560i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 15100.0i | − 0.612565i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8148.00 | −0.329374 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8400.00 | −0.338365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 27862.0i | − 1.11838i | −0.829040 | − | 0.559189i | \(-0.811113\pi\) | ||||
0.829040 | − | 0.559189i | \(-0.188887\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7314.00i | 0.291530i | 0.989319 | + | 0.145765i | \(0.0465644\pi\) | ||||
−0.989319 | + | 0.145765i | \(0.953436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28780.0 | −1.14314 | −0.571572 | − | 0.820552i | \(-0.693666\pi\) | ||||
−0.571572 | + | 0.820552i | \(0.693666\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19800.0 | −0.783719 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32688.0i | 1.28935i | 0.764455 | + | 0.644677i | \(0.223008\pi\) | ||||
−0.764455 | + | 0.644677i | \(0.776992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5991.00i | 0.234677i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12480.0 | −0.487175 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14504.0 | 0.564236 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 2574.00i | − 0.0997900i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 36650.0i | − 1.41115i | −0.708633 | − | 0.705577i | \(-0.750688\pi\) | ||||
0.708633 | − | 0.705577i | \(-0.249312\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18054.0 | −0.692772 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2646.00 | −0.101187 | −0.0505936 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505936 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 10892.0i | − 0.415113i | −0.978223 | − | 0.207557i | \(-0.933449\pi\) | ||||
0.978223 | − | 0.207557i | \(-0.0665511\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 43464.0i | − 1.64530i | −0.568550 | − | 0.822648i | \(-0.692496\pi\) | ||||
0.568550 | − | 0.822648i | \(-0.307504\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24880.0 | −0.938637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1944.00 | 0.0730937 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2976.00i | 0.111521i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 26640.0i | − 0.991621i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15600.0 | −0.578742 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24300.0 | 0.898502 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5520.00i | 0.203426i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 14884.0i | − 0.544890i | −0.962171 | − | 0.272445i | \(-0.912168\pi\) | ||||
0.962171 | − | 0.272445i | \(-0.0878323\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15606.0 | 0.569437 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1248.00 | 0.0453876 | 0.0226938 | − | 0.999742i | \(-0.492776\pi\) | ||||
0.0226938 | + | 0.999742i | \(0.492776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 3744.00i | − 0.135716i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 46560.0i | − 1.67671i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6640.00 | −0.238339 | −0.119169 | − | 0.992874i | \(-0.538023\pi\) | ||||
−0.119169 | + | 0.992874i | \(0.538023\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27708.0 | −0.991324 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21312.0i | 0.760014i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4068.00i | 0.144132i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29946.0 | −1.05758 | −0.528792 | − | 0.848751i | \(-0.677355\pi\) | ||||
−0.528792 | + | 0.848751i | \(0.677355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7068.00 | 0.248812 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 4608.00i | − 0.161693i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 45002.0i | − 1.56900i | −0.620130 | − | 0.784499i | \(-0.712920\pi\) | ||||
0.620130 | − | 0.784499i | \(-0.287080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22026.0 | 0.765486 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6090.00 | 0.210976 | 0.105488 | − | 0.994421i | \(-0.466360\pi\) | ||||
0.105488 | + | 0.994421i | \(0.466360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39600.0i | 1.36750i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56388.0i | 1.93491i | 0.253035 | + | 0.967457i | \(0.418571\pi\) | ||||
−0.253035 | + | 0.967457i | \(0.581429\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31820.0 | 1.08843 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11682.0 | −0.398333 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10854.0i | 0.368936i | 0.982839 | + | 0.184468i | \(0.0590561\pi\) | ||||
−0.982839 | + | 0.184468i | \(0.940944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5616.00i | 0.189696i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42360.0 | 1.42636 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10209.0 | 0.342687 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12636.0i | 0.422834i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 42316.0i | − 1.40723i | −0.710582 | − | 0.703615i | \(-0.751568\pi\) | ||||
0.710582 | − | 0.703615i | \(-0.248432\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20088.0 | −0.665964 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24480.0 | −0.809063 | −0.404532 | − | 0.914524i | \(-0.632565\pi\) | ||||
−0.404532 | + | 0.914524i | \(0.632565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46480.0i | 1.53143i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6906.00i | 0.226144i | 0.993587 | + | 0.113072i | \(0.0360690\pi\) | ||||
−0.993587 | + | 0.113072i | \(0.963931\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24624.0 | −0.803868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13266.0 | −0.431754 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 6960.00i | − 0.225829i | −0.993605 | − | 0.112914i | \(-0.963981\pi\) | ||||
0.993605 | − | 0.112914i | \(-0.0360186\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1440.00i | 0.0464394i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11040.0 | 0.354956 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47792.0 | −1.53195 | −0.765975 | − | 0.642870i | \(-0.777744\pi\) | ||||
−0.765975 | + | 0.642870i | \(0.777744\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 11076.0i | − 0.353964i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 9938.00i | − 0.315687i | −0.987464 | − | 0.157843i | \(-0.949546\pi\) | ||||
0.987464 | − | 0.157843i | \(-0.0504541\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1890.00 | 0.0598568 |
(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.f.m.49.2 | 2 | ||
4.3 | odd | 2 | 75.4.b.a.49.1 | 2 | |||
5.2 | odd | 4 | 240.4.a.f.1.1 | 1 | |||
5.3 | odd | 4 | 1200.4.a.o.1.1 | 1 | |||
5.4 | even | 2 | inner | 1200.4.f.m.49.1 | 2 | ||
12.11 | even | 2 | 225.4.b.d.199.2 | 2 | |||
15.2 | even | 4 | 720.4.a.r.1.1 | 1 | |||
20.3 | even | 4 | 75.4.a.a.1.1 | 1 | |||
20.7 | even | 4 | 15.4.a.b.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 75.4.b.a.49.2 | 2 | |||
40.27 | even | 4 | 960.4.a.bi.1.1 | 1 | |||
40.37 | odd | 4 | 960.4.a.l.1.1 | 1 | |||
60.23 | odd | 4 | 225.4.a.g.1.1 | 1 | |||
60.47 | odd | 4 | 45.4.a.b.1.1 | 1 | |||
60.59 | even | 2 | 225.4.b.d.199.1 | 2 | |||
140.27 | odd | 4 | 735.4.a.i.1.1 | 1 | |||
180.7 | even | 12 | 405.4.e.d.271.1 | 2 | |||
180.47 | odd | 12 | 405.4.e.k.271.1 | 2 | |||
180.67 | even | 12 | 405.4.e.d.136.1 | 2 | |||
180.167 | odd | 12 | 405.4.e.k.136.1 | 2 | |||
220.87 | odd | 4 | 1815.4.a.a.1.1 | 1 | |||
420.167 | even | 4 | 2205.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.a.b.1.1 | ✓ | 1 | 20.7 | even | 4 | ||
45.4.a.b.1.1 | 1 | 60.47 | odd | 4 | |||
75.4.a.a.1.1 | 1 | 20.3 | even | 4 | |||
75.4.b.a.49.1 | 2 | 4.3 | odd | 2 | |||
75.4.b.a.49.2 | 2 | 20.19 | odd | 2 | |||
225.4.a.g.1.1 | 1 | 60.23 | odd | 4 | |||
225.4.b.d.199.1 | 2 | 60.59 | even | 2 | |||
225.4.b.d.199.2 | 2 | 12.11 | even | 2 | |||
240.4.a.f.1.1 | 1 | 5.2 | odd | 4 | |||
405.4.e.d.136.1 | 2 | 180.67 | even | 12 | |||
405.4.e.d.271.1 | 2 | 180.7 | even | 12 | |||
405.4.e.k.136.1 | 2 | 180.167 | odd | 12 | |||
405.4.e.k.271.1 | 2 | 180.47 | odd | 12 | |||
720.4.a.r.1.1 | 1 | 15.2 | even | 4 | |||
735.4.a.i.1.1 | 1 | 140.27 | odd | 4 | |||
960.4.a.l.1.1 | 1 | 40.37 | odd | 4 | |||
960.4.a.bi.1.1 | 1 | 40.27 | even | 4 | |||
1200.4.a.o.1.1 | 1 | 5.3 | odd | 4 | |||
1200.4.f.m.49.1 | 2 | 5.4 | even | 2 | inner | ||
1200.4.f.m.49.2 | 2 | 1.1 | even | 1 | trivial | ||
1815.4.a.a.1.1 | 1 | 220.87 | odd | 4 | |||
2205.4.a.c.1.1 | 1 | 420.167 | even | 4 |