Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(2591,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.b (of order \(2\), degree \(1\), 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.5 | ||
Root | \(-1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2591 |
Dual form | 2880.2.b.a.2591.4 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.16228i | 1.19523i | 0.801784 | + | 0.597614i | \(0.203885\pi\) | ||||
−0.801784 | + | 0.597614i | \(0.796115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.16228i | 0.350440i | 0.984529 | + | 0.175220i | \(0.0560637\pi\) | ||||
−0.984529 | + | 0.175220i | \(0.943936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.88635i | − 1.63258i | −0.577643 | − | 0.816290i | \(-0.696027\pi\) | ||||
0.577643 | − | 0.816290i | \(-0.303973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.64371i | − 0.398658i | −0.979933 | − | 0.199329i | \(-0.936124\pi\) | ||||
0.979933 | − | 0.199329i | \(-0.0638762\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.64371 | −0.377093 | −0.188546 | − | 0.982064i | \(-0.560378\pi\) | ||||
−0.188546 | + | 0.982064i | \(0.560378\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.32456 | −1.54583 | −0.772916 | − | 0.634509i | \(-0.781202\pi\) | ||||
−0.772916 | + | 0.634509i | \(0.781202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 4.32456i | − 0.776713i | −0.921509 | − | 0.388357i | \(-0.873043\pi\) | ||||
0.921509 | − | 0.388357i | \(-0.126957\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.16228i | − 0.534522i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.59893i | − 0.427262i | −0.976914 | − | 0.213631i | \(-0.931471\pi\) | ||||
0.976914 | − | 0.213631i | \(-0.0685290\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.53006i | 1.17600i | 0.808862 | + | 0.587999i | \(0.200084\pi\) | ||||
−0.808862 | + | 0.587999i | \(0.799916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48528 | 1.29399 | 0.646997 | − | 0.762493i | \(-0.276025\pi\) | ||||
0.646997 | + | 0.762493i | \(0.276025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.1290 | −1.47747 | −0.738733 | − | 0.673999i | \(-0.764575\pi\) | ||||
−0.738733 | + | 0.673999i | \(0.764575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.32456 | 0.319302 | 0.159651 | − | 0.987174i | \(-0.448963\pi\) | ||||
0.159651 | + | 0.987174i | \(0.448963\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.16228i | − 0.156721i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 13.1623i | − 1.71358i | −0.515663 | − | 0.856791i | \(-0.672454\pi\) | ||||
0.515663 | − | 0.856791i | \(-0.327546\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 8.48528i | − 1.08643i | −0.839594 | − | 0.543214i | \(-0.817207\pi\) | ||||
0.839594 | − | 0.543214i | \(-0.182793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.88635i | 0.730112i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7727 | 1.43826 | 0.719132 | − | 0.694873i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694873i | \(0.244540\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.7727 | 1.39716 | 0.698581 | − | 0.715531i | \(-0.253815\pi\) | ||||
0.698581 | + | 0.715531i | \(0.253815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.67544 | −0.418856 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.324555i | 0.0365153i | 0.999833 | + | 0.0182577i | \(0.00581192\pi\) | ||||
−0.999833 | + | 0.0182577i | \(0.994188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.32456i | 0.255153i | 0.991829 | + | 0.127577i | \(0.0407198\pi\) | ||||
−0.991829 | + | 0.127577i | \(0.959280\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.64371i | 0.178285i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 16.0153i | − 1.69762i | −0.528696 | − | 0.848811i | \(-0.677319\pi\) | ||||
0.528696 | − | 0.848811i | \(-0.322681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.6143 | 1.95131 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.64371 | 0.168641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.324555 | −0.0329536 | −0.0164768 | − | 0.999864i | \(-0.505245\pi\) | ||||
−0.0164768 | + | 0.999864i | \(0.505245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 0.837722i | − 0.0825432i | −0.999148 | − | 0.0412716i | \(-0.986859\pi\) | ||||
0.999148 | − | 0.0412716i | \(-0.0131409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 14.3246i | − 1.38481i | −0.721510 | − | 0.692404i | \(-0.756552\pi\) | ||||
0.721510 | − | 0.692404i | \(-0.243448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.48528i | − 0.812743i | −0.913708 | − | 0.406371i | \(-0.866794\pi\) | ||||
0.913708 | − | 0.406371i | \(-0.133206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 10.1290i | − 0.952855i | −0.879214 | − | 0.476428i | \(-0.841931\pi\) | ||||
0.879214 | − | 0.476428i | \(-0.158069\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.19786 | 0.476487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.64911 | 0.877192 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1623i | 1.34543i | 0.739900 | + | 0.672717i | \(0.234873\pi\) | ||||
−0.739900 | + | 0.672717i | \(0.765127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 15.4868i | − 1.35309i | −0.736401 | − | 0.676545i | \(-0.763476\pi\) | ||||
0.736401 | − | 0.676545i | \(-0.236524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 5.19786i | − 0.450712i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.84157i | 0.584515i | 0.956340 | + | 0.292257i | \(0.0944064\pi\) | ||||
−0.956340 | + | 0.292257i | \(0.905594\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9706 | 1.43942 | 0.719712 | − | 0.694273i | \(-0.244274\pi\) | ||||
0.719712 | + | 0.694273i | \(0.244274\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.84157 | 0.572121 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.32456 | 0.691317 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.67544 | −0.301104 | −0.150552 | − | 0.988602i | \(-0.548105\pi\) | ||||
−0.150552 | + | 0.988602i | \(0.548105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 10.0000i | − 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.32456i | 0.347357i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 14.3716i | − 1.14698i | −0.819212 | − | 0.573491i | \(-0.805589\pi\) | ||||
0.819212 | − | 0.573491i | \(-0.194411\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.2580 | −1.56761 | −0.783805 | − | 0.621007i | \(-0.786724\pi\) | ||||
−0.783805 | + | 0.621007i | \(0.786724\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.6491 | −1.66532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9737 | −1.44254 | −0.721271 | − | 0.692653i | \(-0.756442\pi\) | ||||
−0.721271 | + | 0.692653i | \(0.756442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.16228i | 0.239046i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.4868i | 1.15754i | 0.815491 | + | 0.578770i | \(0.196467\pi\) | ||||
−0.815491 | + | 0.578770i | \(0.803533\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 11.7727i | − 0.875058i | −0.899204 | − | 0.437529i | \(-0.855854\pi\) | ||||
0.899204 | − | 0.437529i | \(-0.144146\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.59893i | 0.191077i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.91045 | 0.139706 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.28742 | 0.237869 | 0.118935 | − | 0.992902i | \(-0.462052\pi\) | ||||
0.118935 | + | 0.992902i | \(0.462052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3246 | −0.887141 | −0.443570 | − | 0.896240i | \(-0.646288\pi\) | ||||
−0.443570 | + | 0.896240i | \(0.646288\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.6491 | −0.758718 | −0.379359 | − | 0.925250i | \(-0.623855\pi\) | ||||
−0.379359 | + | 0.925250i | \(0.623855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 18.6491i | − 1.32200i | −0.750386 | − | 0.661000i | \(-0.770132\pi\) | ||||
0.750386 | − | 0.661000i | \(-0.229868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 26.3246i | − 1.84762i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 7.53006i | − 0.525922i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 1.91045i | − 0.132148i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.5454 | −1.62093 | −0.810466 | − | 0.585786i | \(-0.800786\pi\) | ||||
−0.810466 | + | 0.585786i | \(0.800786\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.48528 | −0.578691 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.6754 | 0.928350 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.67544 | −0.650841 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 13.4868i | − 0.903145i | −0.892234 | − | 0.451573i | \(-0.850863\pi\) | ||||
0.892234 | − | 0.451573i | \(-0.149137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.6491i | 1.10504i | 0.833500 | + | 0.552520i | \(0.186334\pi\) | ||||
−0.833500 | + | 0.552520i | \(0.813666\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 20.2580i | − 1.33869i | −0.742954 | − | 0.669343i | \(-0.766576\pi\) | ||||
0.742954 | − | 0.669343i | \(-0.233424\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.93113i | 0.323049i | 0.986869 | + | 0.161524i | \(0.0516411\pi\) | ||||
−0.986869 | + | 0.161524i | \(0.948359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.1290 | 0.660742 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.2580 | 1.31038 | 0.655190 | − | 0.755464i | \(-0.272589\pi\) | ||||
0.655190 | + | 0.755464i | \(0.272589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.67544i | 0.615634i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.48683i | 0.220087i | 0.993927 | + | 0.110043i | \(0.0350990\pi\) | ||||
−0.993927 | + | 0.110043i | \(0.964901\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.0996i | 1.69042i | 0.534431 | + | 0.845212i | \(0.320526\pi\) | ||||
−0.534431 | + | 0.845212i | \(0.679474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.21854 | 0.510675 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.28742 | 0.202711 | 0.101355 | − | 0.994850i | \(-0.467682\pi\) | ||||
0.101355 | + | 0.994850i | \(0.467682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.32456 | −0.142796 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.9737 | 1.52267 | 0.761336 | − | 0.648358i | \(-0.224544\pi\) | ||||
0.761336 | + | 0.648358i | \(0.224544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.6491i | 1.13285i | 0.824112 | + | 0.566426i | \(0.191674\pi\) | ||||
−0.824112 | + | 0.566426i | \(0.808326\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.16228i | 0.0700880i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 0.688486i | − 0.0413671i | −0.999786 | − | 0.0206836i | \(-0.993416\pi\) | ||||
0.999786 | − | 0.0206836i | \(-0.00658425\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 7.53006i | − 0.449206i | −0.974450 | − | 0.224603i | \(-0.927892\pi\) | ||||
0.974450 | − | 0.224603i | \(-0.0721085\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.8121 | −1.40559 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.2982 | 0.841072 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.1623i | 0.766337i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8328i | 1.54662i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.48528i | 0.485866i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2580 | −1.15618 | −0.578092 | − | 0.815972i | \(-0.696203\pi\) | ||||
−0.578092 | + | 0.815972i | \(0.696203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.57484 | −0.372825 | −0.186412 | − | 0.982472i | \(-0.559686\pi\) | ||||
−0.186412 | + | 0.982472i | \(0.559686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9737 | 0.959408 | 0.479704 | − | 0.877430i | \(-0.340744\pi\) | ||||
0.479704 | + | 0.877430i | \(0.340744\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 9.67544i | − 0.541721i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.70178i | 0.150331i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 5.88635i | − 0.326516i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 32.0307i | − 1.76591i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.9017 | 1.20383 | 0.601913 | − | 0.798562i | \(-0.294405\pi\) | ||||
0.601913 | + | 0.798562i | \(0.294405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.7727 | −0.643211 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.6491 | 1.66956 | 0.834782 | − | 0.550581i | \(-0.185594\pi\) | ||||
0.834782 | + | 0.550581i | \(0.185594\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.02633 | 0.272191 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6491i | 0.682988i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 24.0000i | − 1.28839i | −0.764862 | − | 0.644194i | \(-0.777193\pi\) | ||||
0.764862 | − | 0.644194i | \(-0.222807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.0601i | 0.806150i | 0.915167 | + | 0.403075i | \(0.132059\pi\) | ||||
−0.915167 | + | 0.403075i | \(0.867941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 25.1891i | − 1.34068i | −0.742054 | − | 0.670340i | \(-0.766148\pi\) | ||||
0.742054 | − | 0.670340i | \(-0.233852\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.7727 | −0.624830 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.7433 | 1.51701 | 0.758506 | − | 0.651666i | \(-0.225930\pi\) | ||||
0.758506 | + | 0.651666i | \(0.225930\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2982 | −0.857801 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.51317i | 0.339985i | 0.985445 | + | 0.169992i | \(0.0543743\pi\) | ||||
−0.985445 | + | 0.169992i | \(0.945626\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.35089i | 0.381639i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.3716i | 0.744135i | 0.928206 | + | 0.372067i | \(0.121351\pi\) | ||||
−0.928206 | + | 0.372067i | \(0.878649\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 49.0012i | 2.52369i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.8121 | 1.21674 | 0.608372 | − | 0.793652i | \(-0.291823\pi\) | ||||
0.608372 | + | 0.793652i | \(0.291823\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.67544 | 0.187318 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 0.324555i | − 0.0163302i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.1443i | 1.31215i | 0.754697 | + | 0.656073i | \(0.227784\pi\) | ||||
−0.754697 | + | 0.656073i | \(0.772216\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 27.7880i | − 1.38767i | −0.720135 | − | 0.693834i | \(-0.755920\pi\) | ||||
0.720135 | − | 0.693834i | \(-0.244080\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.4558 | −1.26805 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.02068 | 0.149730 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.6491 | −1.51550 | −0.757750 | − | 0.652544i | \(-0.773702\pi\) | ||||
−0.757750 | + | 0.652544i | \(0.773702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 41.6228 | 2.04812 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 2.32456i | − 0.114108i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 3.48683i | − 0.170343i | −0.996366 | − | 0.0851715i | \(-0.972856\pi\) | ||||
0.996366 | − | 0.0851715i | \(-0.0271438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 3.28742i | − 0.160219i | −0.996786 | − | 0.0801095i | \(-0.974473\pi\) | ||||
0.996786 | − | 0.0801095i | \(-0.0255270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 1.64371i | − 0.0797316i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.8328 | 1.29853 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.6055 | −1.85956 | −0.929781 | − | 0.368113i | \(-0.880004\pi\) | ||||
−0.929781 | + | 0.368113i | \(0.880004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.2982 | −1.69632 | −0.848162 | − | 0.529737i | \(-0.822291\pi\) | ||||
−0.848162 | + | 0.529737i | \(0.822291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 9.35089i | − 0.446294i | −0.974785 | − | 0.223147i | \(-0.928367\pi\) | ||||
0.974785 | − | 0.223147i | \(-0.0716329\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.6491i | 0.791023i | 0.918461 | + | 0.395512i | \(0.129433\pi\) | ||||
−0.918461 | + | 0.395512i | \(0.870567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.0153i | 0.759200i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.33219i | 0.110063i | 0.998485 | + | 0.0550315i | \(0.0175259\pi\) | ||||
−0.998485 | + | 0.0550315i | \(0.982474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.75202 | −0.412116 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.6143 | −0.872651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.6228 | 1.57281 | 0.786404 | − | 0.617713i | \(-0.211941\pi\) | ||||
0.786404 | + | 0.617713i | \(0.211941\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.3246 | 0.946609 | 0.473304 | − | 0.880899i | \(-0.343061\pi\) | ||||
0.473304 | + | 0.880899i | \(0.343061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 35.1623i | − 1.63413i | −0.576546 | − | 0.817065i | \(-0.695600\pi\) | ||||
0.576546 | − | 0.817065i | \(-0.304400\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.3246i | 1.77345i | 0.462298 | + | 0.886724i | \(0.347025\pi\) | ||||
−0.462298 | + | 0.886724i | \(0.652975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37.2285i | 1.71905i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.86225i | 0.453467i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.64371 | −0.0754185 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.1684 | 1.01290 | 0.506451 | − | 0.862269i | \(-0.330957\pi\) | ||||
0.506451 | + | 0.862269i | \(0.330957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.2982 | −0.697539 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.324555 | 0.0147373 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.1623i | 0.687068i | 0.939140 | + | 0.343534i | \(0.111624\pi\) | ||||
−0.939140 | + | 0.343534i | \(0.888376\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 8.51317i | − 0.384194i | −0.981376 | − | 0.192097i | \(-0.938471\pi\) | ||||
0.981376 | − | 0.192097i | \(-0.0615288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.6831i | 0.616258i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.2285i | 1.66993i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.8723 | −1.74016 | −0.870080 | − | 0.492910i | \(-0.835933\pi\) | ||||
−0.870080 | + | 0.492910i | \(0.835933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.1290 | −0.451629 | −0.225815 | − | 0.974170i | \(-0.572504\pi\) | ||||
−0.225815 | + | 0.974170i | \(0.572504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.2982 | −1.74186 | −0.870932 | − | 0.491404i | \(-0.836484\pi\) | ||||
−0.870932 | + | 0.491404i | \(0.836484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 6.32456i | − 0.279782i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.837722i | 0.0369145i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 11.7727i | − 0.517763i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 12.7279i | − 0.557620i | −0.960346 | − | 0.278810i | \(-0.910060\pi\) | ||||
0.960346 | − | 0.278810i | \(-0.0899400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.28742 | −0.143749 | −0.0718744 | − | 0.997414i | \(-0.522898\pi\) | ||||
−0.0718744 | + | 0.997414i | \(0.522898\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.10831 | −0.309643 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.3246 | 1.91991 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.3246i | 0.619305i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3.48683i | − 0.150189i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 18.3475i | − 0.788822i | −0.918934 | − | 0.394411i | \(-0.870949\pi\) | ||||
0.918934 | − | 0.394411i | \(-0.129051\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.48528i | 0.363470i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.7138 | −1.95458 | −0.977291 | − | 0.211902i | \(-0.932034\pi\) | ||||
−0.977291 | + | 0.211902i | \(0.932034\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.6831 | 0.582922 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.02633 | −0.0436442 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.6754 | 0.918418 | 0.459209 | − | 0.888328i | \(-0.348133\pi\) | ||||
0.459209 | + | 0.888328i | \(0.348133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 49.9473i | − 2.11255i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.9473i | 1.59929i | 0.600473 | + | 0.799645i | \(0.294979\pi\) | ||||
−0.600473 | + | 0.799645i | \(0.705021\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.1290i | 0.426130i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 38.1838i | − 1.60075i | −0.599502 | − | 0.800373i | \(-0.704635\pi\) | ||||
0.599502 | − | 0.800373i | \(-0.295365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.1891 | −1.05413 | −0.527066 | − | 0.849825i | \(-0.676708\pi\) | ||||
−0.527066 | + | 0.849825i | \(0.676708\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.3246 | 1.01264 | 0.506322 | − | 0.862344i | \(-0.331005\pi\) | ||||
0.506322 | + | 0.862344i | \(0.331005\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.35089 | −0.304966 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.70178i | 0.111896i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.02633i | 0.207459i | 0.994606 | + | 0.103730i | \(0.0330776\pi\) | ||||
−0.994606 | + | 0.103730i | \(0.966922\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.10831i | 0.292893i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 30.3870i | − 1.24784i | −0.781487 | − | 0.623922i | \(-0.785538\pi\) | ||||
0.781487 | − | 0.623922i | \(-0.214462\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.19786 | −0.213092 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0307 | 1.30874 | 0.654369 | − | 0.756175i | \(-0.272934\pi\) | ||||
0.654369 | + | 0.756175i | \(0.272934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3509 | −0.463012 | −0.231506 | − | 0.972833i | \(-0.574365\pi\) | ||||
−0.231506 | + | 0.972833i | \(0.574365\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.64911 | −0.392292 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.1623i | 1.10248i | 0.834346 | + | 0.551241i | \(0.185846\pi\) | ||||
−0.834346 | + | 0.551241i | \(0.814154\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 59.6228i | 2.41208i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 9.17377i | − 0.370525i | −0.982689 | − | 0.185262i | \(-0.940686\pi\) | ||||
0.982689 | − | 0.185262i | \(-0.0593135\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.3269i | 0.617036i | 0.951219 | + | 0.308518i | \(0.0998330\pi\) | ||||
−0.951219 | + | 0.308518i | \(0.900167\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.1202 | −1.21063 | −0.605317 | − | 0.795984i | \(-0.706954\pi\) | ||||
−0.605317 | + | 0.795984i | \(0.706954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 50.6450 | 2.02905 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.27189 | −0.170331 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.97367i | 0.357236i | 0.983918 | + | 0.178618i | \(0.0571626\pi\) | ||||
−0.983918 | + | 0.178618i | \(0.942837\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 15.1623i | − 0.601697i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.6590i | 0.699677i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 7.53006i | − 0.297419i | −0.988881 | − | 0.148710i | \(-0.952488\pi\) | ||||
0.988881 | − | 0.148710i | \(-0.0475120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.6831 | −0.539611 | −0.269805 | − | 0.962915i | \(-0.586959\pi\) | ||||
−0.269805 | + | 0.962915i | \(0.586959\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.6744 | −1.32388 | −0.661938 | − | 0.749558i | \(-0.730266\pi\) | ||||
−0.661938 | + | 0.749558i | \(0.730266\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2982 | 0.600508 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.2982 | −1.06826 | −0.534131 | − | 0.845402i | \(-0.679361\pi\) | ||||
−0.534131 | + | 0.845402i | \(0.679361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.4868i | 0.605121i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.51317i | 0.331626i | 0.986157 | + | 0.165813i | \(0.0530248\pi\) | ||||
−0.986157 | + | 0.165813i | \(0.946975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.7138i | 1.77806i | 0.457847 | + | 0.889031i | \(0.348621\pi\) | ||||
−0.457847 | + | 0.889031i | \(0.651379\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.19786i | 0.201565i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.86225 | 0.380728 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.6491 | 1.02725 | 0.513624 | − | 0.858015i | \(-0.328303\pi\) | ||||
0.513624 | + | 0.858015i | \(0.328303\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.9473 | 1.22784 | 0.613918 | − | 0.789370i | \(-0.289593\pi\) | ||||
0.613918 | + | 0.789370i | \(0.289593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1.02633i | − 0.0393871i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.3246i | 1.00728i | 0.863913 | + | 0.503641i | \(0.168006\pi\) | ||||
−0.863913 | + | 0.503641i | \(0.831994\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 6.84157i | − 0.261403i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 13.6831i | − 0.521286i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6143 | −0.708120 | −0.354060 | − | 0.935223i | \(-0.615199\pi\) | ||||
−0.354060 | + | 0.935223i | \(0.615199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.9706 | −0.643730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.3772 | 0.468821 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.27189i | 0.161117i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 18.9737i | − 0.713578i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.28742i | 0.123462i | 0.998093 | + | 0.0617308i | \(0.0196620\pi\) | ||||
−0.998093 | + | 0.0617308i | \(0.980338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.84157 | −0.255860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.4558 | 0.949343 | 0.474671 | − | 0.880163i | \(-0.342567\pi\) | ||||
0.474671 | + | 0.880163i | \(0.342567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.64911 | 0.0986580 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.32456 | −0.309166 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 3.81139i | − 0.141357i | −0.997499 | − | 0.0706783i | \(-0.977484\pi\) | ||||
0.997499 | − | 0.0706783i | \(-0.0225164\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 13.9473i | − 0.515861i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 17.6590i | − 0.652252i | −0.945326 | − | 0.326126i | \(-0.894257\pi\) | ||||
0.945326 | − | 0.326126i | \(-0.105743\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.6831i | 0.504025i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.1597 | −1.55087 | −0.775434 | − | 0.631428i | \(-0.782469\pi\) | ||||
−0.775434 | + | 0.631428i | \(0.782469\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.6744 | −1.23539 | −0.617697 | − | 0.786416i | \(-0.711934\pi\) | ||||
−0.617697 | + | 0.786416i | \(0.711934\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.67544 | 0.134658 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.2982 | 1.65516 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.9737i | 1.05726i | 0.848851 | + | 0.528632i | \(0.177295\pi\) | ||||
−0.848851 | + | 0.528632i | \(0.822705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0000i | 0.363937i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.4023i | 1.68652i | 0.537505 | + | 0.843260i | \(0.319367\pi\) | ||||
−0.537505 | + | 0.843260i | \(0.680633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7279i | 0.461387i | 0.973026 | + | 0.230693i | \(0.0740994\pi\) | ||||
−0.973026 | + | 0.230693i | \(0.925901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.8328 | 0.971413 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −77.4778 | −2.79756 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.6491 | −0.744626 | −0.372313 | − | 0.928107i | \(-0.621435\pi\) | ||||
−0.372313 | + | 0.928107i | \(0.621435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.2982 | −0.550239 | −0.275119 | − | 0.961410i | \(-0.588717\pi\) | ||||
−0.275119 | + | 0.961410i | \(0.588717\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 4.32456i | − 0.155343i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 12.3772i | − 0.443460i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6831i | 0.489621i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.3716i | 0.512946i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.3957 | −0.370568 | −0.185284 | − | 0.982685i | \(-0.559320\pi\) | ||||
−0.185284 | + | 0.982685i | \(0.559320\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.0307 | 1.13888 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.9473 | −1.77368 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.3246 | −1.35753 | −0.678763 | − | 0.734358i | \(-0.737484\pi\) | ||||
−0.678763 | + | 0.734358i | \(0.737484\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.6491i | 0.589003i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.32456i | − 0.0820318i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 16.0153i | − 0.563069i | −0.959551 | − | 0.281535i | \(-0.909157\pi\) | ||||
0.959551 | − | 0.281535i | \(-0.0908434\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.57484 | −0.230874 | −0.115437 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115437 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.9473 | −0.487955 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.6228 | 1.45264 | 0.726322 | − | 0.687354i | \(-0.241228\pi\) | ||||
0.726322 | + | 0.687354i | \(0.241228\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 22.7851i | − 0.794237i | −0.917767 | − | 0.397119i | \(-0.870010\pi\) | ||||
0.917767 | − | 0.397119i | \(-0.129990\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.9473i | 1.73684i | 0.495830 | + | 0.868419i | \(0.334864\pi\) | ||||
−0.495830 | + | 0.868419i | \(0.665136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.19786i | 0.180529i | 0.995918 | + | 0.0902646i | \(0.0287713\pi\) | ||||
−0.995918 | + | 0.0902646i | \(0.971229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.93113i | 0.170853i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.2580 | 0.701056 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.19786 | 0.179450 | 0.0897251 | − | 0.995967i | \(-0.471401\pi\) | ||||
0.0897251 | + | 0.995967i | \(0.471401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40.2982 | 1.38959 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.6491 | 0.744752 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.5132i | 1.04844i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.3422i | 1.07314i | 0.843857 | + | 0.536568i | \(0.180280\pi\) | ||||
−0.843857 | + | 0.536568i | \(0.819720\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.5848i | 1.21555i | 0.794107 | + | 0.607777i | \(0.207939\pi\) | ||||
−0.794107 | + | 0.607777i | \(0.792061\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.6656 | 1.83105 | 0.915524 | − | 0.402264i | \(-0.131776\pi\) | ||||
0.915524 | + | 0.402264i | \(0.131776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.2285 | 1.26727 | 0.633637 | − | 0.773630i | \(-0.281561\pi\) | ||||
0.633637 | + | 0.773630i | \(0.281561\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.9737 | 0.645124 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.377223 | −0.0127964 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 69.2982i | − 2.34808i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.16228i | − 0.106904i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 9.17377i | − 0.309776i | −0.987932 | − | 0.154888i | \(-0.950498\pi\) | ||||
0.987932 | − | 0.154888i | \(-0.0495017\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0153i | 0.539571i | 0.962921 | + | 0.269785i | \(0.0869527\pi\) | ||||
−0.962921 | + | 0.269785i | \(0.913047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.9706 | −0.571105 | −0.285552 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285552 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.2580 | −0.680196 | −0.340098 | − | 0.940390i | \(-0.610460\pi\) | ||||
−0.340098 | + | 0.940390i | \(0.610460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.9473 | −1.60810 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6491 | 0.557141 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 15.4868i | − 0.517668i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.0000i | 1.20067i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.82089i | − 0.127292i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.7727i | 0.391338i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0601 | 0.500063 | 0.250031 | − | 0.968238i | \(-0.419559\pi\) | ||||
0.250031 | + | 0.968238i | \(0.419559\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.6537 | −1.01560 | −0.507801 | − | 0.861474i | \(-0.669542\pi\) | ||||
−0.507801 | + | 0.861474i | \(0.669542\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.70178 | −0.0894158 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.9737 | 1.61725 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 40.9737i | − 1.35160i | −0.737087 | − | 0.675798i | \(-0.763799\pi\) | ||||
0.737087 | − | 0.675798i | \(-0.236201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 69.2982i | − 2.28098i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2.59893i | − 0.0854524i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 27.7880i | − 0.911696i | −0.890058 | − | 0.455848i | \(-0.849336\pi\) | ||||
0.890058 | − | 0.455848i | \(-0.150664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.93113 | 0.161611 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.91045 | −0.0624783 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.9473 | −1.82383 | −0.911915 | − | 0.410378i | \(-0.865397\pi\) | ||||
−0.911915 | + | 0.410378i | \(0.865397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 54.5964i | − 1.77415i | −0.461629 | − | 0.887073i | \(-0.652735\pi\) | ||||
0.461629 | − | 0.887073i | \(-0.347265\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.7727i | 0.382158i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 36.9618i | − 1.19731i | −0.801007 | − | 0.598655i | \(-0.795702\pi\) | ||||
0.801007 | − | 0.598655i | \(-0.204298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.28742 | −0.106378 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.6350 | −0.698629 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2982 | 0.396717 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.3246 | 0.396741 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.1359i | 1.35500i | 0.735522 | + | 0.677500i | \(0.236937\pi\) | ||||
−0.735522 | + | 0.677500i | \(0.763063\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 32.1359i | − 1.03129i | −0.856802 | − | 0.515646i | \(-0.827552\pi\) | ||||
0.856802 | − | 0.515646i | \(-0.172448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 53.6656i | 1.72044i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.3269i | 0.490349i | 0.969479 | + | 0.245175i | \(0.0788453\pi\) | ||||
−0.969479 | + | 0.245175i | \(0.921155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.6143 | 0.594915 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.3870 | −0.969194 | −0.484597 | − | 0.874738i | \(-0.661034\pi\) | ||||
−0.484597 | + | 0.874738i | \(0.661034\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6491 | 0.339309 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.701779i | 0.0222927i | 0.999938 | + | 0.0111464i | \(0.00354807\pi\) | ||||
−0.999938 | + | 0.0111464i | \(0.996452\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.6491i | 0.591217i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 7.79680i | − 0.246927i | −0.992349 | − | 0.123463i | \(-0.960600\pi\) | ||||
0.992349 | − | 0.123463i | \(-0.0394002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2880.2.b.a.2591.5 | yes | 8 | |
3.2 | odd | 2 | 2880.2.b.d.2591.7 | yes | 8 | ||
4.3 | odd | 2 | inner | 2880.2.b.a.2591.3 | ✓ | 8 | |
8.3 | odd | 2 | 2880.2.b.d.2591.2 | yes | 8 | ||
8.5 | even | 2 | 2880.2.b.d.2591.8 | yes | 8 | ||
12.11 | even | 2 | 2880.2.b.d.2591.1 | yes | 8 | ||
24.5 | odd | 2 | inner | 2880.2.b.a.2591.6 | yes | 8 | |
24.11 | even | 2 | inner | 2880.2.b.a.2591.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2880.2.b.a.2591.3 | ✓ | 8 | 4.3 | odd | 2 | inner | |
2880.2.b.a.2591.4 | yes | 8 | 24.11 | even | 2 | inner | |
2880.2.b.a.2591.5 | yes | 8 | 1.1 | even | 1 | trivial | |
2880.2.b.a.2591.6 | yes | 8 | 24.5 | odd | 2 | inner | |
2880.2.b.d.2591.1 | yes | 8 | 12.11 | even | 2 | ||
2880.2.b.d.2591.2 | yes | 8 | 8.3 | odd | 2 | ||
2880.2.b.d.2591.7 | yes | 8 | 3.2 | odd | 2 | ||
2880.2.b.d.2591.8 | yes | 8 | 8.5 | even | 2 |