Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.00000 | −0.536656 | −0.268328 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268328 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −0.109640 | −0.0548202 | − | 0.998496i | \(-0.517459\pi\) | ||||
−0.0548202 | + | 0.998496i | \(0.517459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.0000 | 0.981393 | 0.490696 | − | 0.871331i | \(-0.336742\pi\) | ||||
0.490696 | + | 0.871331i | \(0.336742\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18.0000 | 0.309839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −82.0000 | −1.16988 | −0.584939 | − | 0.811077i | \(-0.698882\pi\) | ||||
−0.584939 | + | 0.811077i | \(0.698882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 84.0000 | 1.01426 | 0.507130 | − | 0.861870i | \(-0.330707\pi\) | ||||
0.507130 | + | 0.861870i | \(0.330707\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −44.0000 | −0.398897 | −0.199449 | − | 0.979908i | \(-0.563915\pi\) | ||||
−0.199449 | + | 0.979908i | \(0.563915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −70.0000 | −0.448230 | −0.224115 | − | 0.974563i | \(-0.571949\pi\) | ||||
−0.224115 | + | 0.974563i | \(0.571949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 152.000 | 0.880645 | 0.440323 | − | 0.897840i | \(-0.354864\pi\) | ||||
0.440323 | + | 0.897840i | \(0.354864\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000 | 0.0633010 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 42.0000 | 0.202837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 146.000 | 0.648710 | 0.324355 | − | 0.945936i | \(-0.394853\pi\) | ||||
0.324355 | + | 0.945936i | \(0.394853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −138.000 | −0.566607 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 94.0000 | 0.358057 | 0.179028 | − | 0.983844i | \(-0.442705\pi\) | ||||
0.179028 | + | 0.983844i | \(0.442705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 488.000 | 1.73068 | 0.865341 | − | 0.501184i | \(-0.167102\pi\) | ||||
0.865341 | + | 0.501184i | \(0.167102\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −54.0000 | −0.178885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 32.0000 | 0.0993123 | 0.0496562 | − | 0.998766i | \(-0.484187\pi\) | ||||
0.0496562 | + | 0.998766i | \(0.484187\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 246.000 | 0.675429 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 562.000 | 1.45654 | 0.728270 | − | 0.685290i | \(-0.240325\pi\) | ||||
0.728270 | + | 0.685290i | \(0.240325\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24.0000 | 0.0588393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −252.000 | −0.585583 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −476.000 | −1.05034 | −0.525169 | − | 0.850998i | \(-0.675998\pi\) | ||||
−0.525169 | + | 0.850998i | \(0.675998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34.0000 | −0.0713648 | −0.0356824 | − | 0.999363i | \(-0.511360\pi\) | ||||
−0.0356824 | + | 0.999363i | \(0.511360\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −276.000 | −0.526671 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −520.000 | −0.948181 | −0.474090 | − | 0.880476i | \(-0.657223\pi\) | ||||
−0.474090 | + | 0.880476i | \(0.657223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 132.000 | 0.230303 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.0000 | 0.0601748 | 0.0300874 | − | 0.999547i | \(-0.490421\pi\) | ||||
0.0300874 | + | 0.999547i | \(0.490421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −654.000 | −1.04856 | −0.524280 | − | 0.851546i | \(-0.675666\pi\) | ||||
−0.524280 | + | 0.851546i | \(0.675666\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 267.000 | 0.411073 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 28.0000 | 0.0414402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 608.000 | 0.865890 | 0.432945 | − | 0.901420i | \(-0.357474\pi\) | ||||
0.432945 | + | 0.901420i | \(0.357474\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 284.000 | 0.375579 | 0.187789 | − | 0.982209i | \(-0.439868\pi\) | ||||
0.187789 | + | 0.982209i | \(0.439868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 492.000 | 0.627822 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 210.000 | 0.258786 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −954.000 | −1.13622 | −0.568111 | − | 0.822952i | \(-0.692326\pi\) | ||||
−0.568111 | + | 0.822952i | \(0.692326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −322.000 | −0.370932 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −456.000 | −0.508441 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −504.000 | −0.544309 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1694.00 | −1.77319 | −0.886596 | − | 0.462544i | \(-0.846937\pi\) | ||||
−0.886596 | + | 0.462544i | \(0.846937\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −36.0000 | −0.0365468 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −318.000 | −0.313289 | −0.156644 | − | 0.987655i | \(-0.550068\pi\) | ||||
−0.156644 | + | 0.987655i | \(0.550068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 872.000 | 0.834182 | 0.417091 | − | 0.908865i | \(-0.363050\pi\) | ||||
0.417091 | + | 0.908865i | \(0.363050\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −126.000 | −0.117108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −364.000 | −0.328871 | −0.164436 | − | 0.986388i | \(-0.552580\pi\) | ||||
−0.164436 | + | 0.986388i | \(0.552580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −838.000 | −0.736384 | −0.368192 | − | 0.929750i | \(-0.620023\pi\) | ||||
−0.368192 | + | 0.929750i | \(0.620023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −438.000 | −0.374533 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −366.000 | −0.304694 | −0.152347 | − | 0.988327i | \(-0.548683\pi\) | ||||
−0.152347 | + | 0.988327i | \(0.548683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 264.000 | 0.214071 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 414.000 | 0.327131 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 574.000 | 0.442172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1315.00 | −0.987979 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −282.000 | −0.206724 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 536.000 | 0.374506 | 0.187253 | − | 0.982312i | \(-0.440042\pi\) | ||||
0.187253 | + | 0.982312i | \(0.440042\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1464.00 | −0.999209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1980.00 | 1.32056 | 0.660280 | − | 0.751019i | \(-0.270438\pi\) | ||||
0.660280 | + | 0.751019i | \(0.270438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −588.000 | −0.383354 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 162.000 | 0.103280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2878.00 | −1.79477 | −0.897387 | − | 0.441244i | \(-0.854537\pi\) | ||||
−0.897387 | + | 0.441244i | \(0.854537\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1436.00 | −0.876258 | −0.438129 | − | 0.898912i | \(-0.644359\pi\) | ||||
−0.438129 | + | 0.898912i | \(0.644359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −96.0000 | −0.0573380 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −184.000 | −0.107600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 420.000 | 0.240546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1374.00 | −0.755453 | −0.377726 | − | 0.925917i | \(-0.623294\pi\) | ||||
−0.377726 | + | 0.925917i | \(0.623294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −688.000 | −0.370786 | −0.185393 | − | 0.982664i | \(-0.559356\pi\) | ||||
−0.185393 | + | 0.982664i | \(0.559356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −738.000 | −0.389959 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −912.000 | −0.472604 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | 0.00305001 | 0.00152501 | − | 0.999999i | \(-0.499515\pi\) | ||||
0.00152501 | + | 0.999999i | \(0.499515\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1686.00 | −0.840934 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 308.000 | 0.150769 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −0.00768845 | −0.00384422 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384422 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −72.0000 | −0.0339709 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1952.00 | −0.904493 | −0.452246 | − | 0.891893i | \(-0.649377\pi\) | ||||
−0.452246 | + | 0.891893i | \(0.649377\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −81.0000 | −0.0368685 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 756.000 | 0.338086 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 642.000 | 0.282141 | 0.141070 | − | 0.990000i | \(-0.454946\pi\) | ||||
0.141070 | + | 0.990000i | \(0.454946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 623.000 | 0.269111 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1428.00 | 0.606413 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −468.000 | −0.195419 | −0.0977094 | − | 0.995215i | \(-0.531152\pi\) | ||||
−0.0977094 | + | 0.995215i | \(0.531152\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −138.000 | −0.0566710 | −0.0283355 | − | 0.999598i | \(-0.509021\pi\) | ||||
−0.0283355 | + | 0.999598i | \(0.509021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 102.000 | 0.0412025 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −876.000 | −0.348134 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 328.000 | 0.128266 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1980.00 | −0.750093 | −0.375047 | − | 0.927006i | \(-0.622373\pi\) | ||||
−0.375047 | + | 0.927006i | \(0.622373\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1294.00 | −0.482612 | −0.241306 | − | 0.970449i | \(-0.577576\pi\) | ||||
−0.241306 | + | 0.970449i | \(0.577576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 828.000 | 0.304073 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4542.00 | −1.64266 | −0.821330 | − | 0.570453i | \(-0.806768\pi\) | ||||
−0.821330 | + | 0.570453i | \(0.806768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2992.00 | 1.06582 | 0.532908 | − | 0.846173i | \(-0.321099\pi\) | ||||
0.532908 | + | 0.846173i | \(0.321099\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1560.00 | 0.547432 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 490.000 | 0.169415 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −564.000 | −0.192154 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −396.000 | −0.132966 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −336.000 | −0.111204 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3344.00 | −1.09104 | −0.545522 | − | 0.838096i | \(-0.683669\pi\) | ||||
−0.545522 | + | 0.838096i | \(0.683669\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −108.000 | −0.0347420 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2928.00 | −0.928781 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1064.00 | −0.332853 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1962.00 | 0.605387 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3772.00 | −1.14811 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5640.00 | 1.69364 | 0.846821 | − | 0.531877i | \(-0.178513\pi\) | ||||
0.846821 | + | 0.531877i | \(0.178513\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −801.000 | −0.237333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2660.00 | 0.777755 | 0.388878 | − | 0.921289i | \(-0.372863\pi\) | ||||
0.388878 | + | 0.921289i | \(0.372863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5626.00 | −1.62348 | −0.811739 | − | 0.584020i | \(-0.801479\pi\) | ||||
−0.811739 | + | 0.584020i | \(0.801479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −84.0000 | −0.0239255 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −606.000 | −0.170388 | −0.0851939 | − | 0.996364i | \(-0.527151\pi\) | ||||
−0.0851939 | + | 0.996364i | \(0.527151\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −192.000 | −0.0532966 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1824.00 | −0.499922 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6300.00 | −1.70508 | −0.852538 | − | 0.522665i | \(-0.824938\pi\) | ||||
−0.852538 | + | 0.522665i | \(0.824938\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2210.00 | 0.590700 | 0.295350 | − | 0.955389i | \(-0.404564\pi\) | ||||
0.295350 | + | 0.955389i | \(0.404564\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −294.000 | −0.0766652 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3864.00 | 0.995386 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −852.000 | −0.216841 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5044.00 | −1.26842 | −0.634212 | − | 0.773159i | \(-0.718675\pi\) | ||||
−0.634212 | + | 0.773159i | \(0.718675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 176.000 | 0.0437353 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1476.00 | −0.362473 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −98.0000 | −0.0237863 | −0.0118931 | − | 0.999929i | \(-0.503786\pi\) | ||||
−0.0118931 | + | 0.999929i | \(0.503786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1022.00 | −0.245189 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −630.000 | −0.149410 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5732.00 | −1.34392 | −0.671959 | − | 0.740589i | \(-0.734547\pi\) | ||||
−0.671959 | + | 0.740589i | \(0.734547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3372.00 | −0.781662 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2862.00 | 0.655998 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −630.000 | −0.142795 | −0.0713974 | − | 0.997448i | \(-0.522746\pi\) | ||||
−0.0713974 | + | 0.997448i | \(0.522746\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2560.00 | −0.573834 | −0.286917 | − | 0.957955i | \(-0.592630\pi\) | ||||
−0.286917 | + | 0.957955i | \(0.592630\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 966.000 | 0.214157 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 356.000 | 0.0780640 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2266.00 | 0.491519 | 0.245759 | − | 0.969331i | \(-0.420963\pi\) | ||||
0.245759 | + | 0.969331i | \(0.420963\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1368.00 | 0.293548 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4338.00 | 0.920937 | 0.460469 | − | 0.887676i | \(-0.347681\pi\) | ||||
0.460469 | + | 0.887676i | \(0.347681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6364.00 | −1.33675 | −0.668376 | − | 0.743824i | \(-0.733010\pi\) | ||||
−0.668376 | + | 0.743824i | \(0.733010\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1512.00 | 0.314257 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −658.000 | −0.135333 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1811.00 | 0.368614 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5082.00 | 1.02375 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1778.00 | 0.354511 | 0.177256 | − | 0.984165i | \(-0.443278\pi\) | ||||
0.177256 | + | 0.984165i | \(0.443278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2856.00 | 0.563670 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 108.000 | 0.0211003 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2024.00 | −0.391475 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3416.00 | −0.654136 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 954.000 | 0.180877 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 204.000 | 0.0382984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1364.00 | 0.253575 | 0.126788 | − | 0.991930i | \(-0.459533\pi\) | ||||
0.126788 | + | 0.991930i | \(0.459533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2616.00 | −0.481615 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7512.00 | 1.36967 | 0.684834 | − | 0.728700i | \(-0.259875\pi\) | ||||
0.684834 | + | 0.728700i | \(0.259875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2914.00 | 0.526227 | 0.263113 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263113 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 378.000 | 0.0676123 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7846.00 | −1.39014 | −0.695071 | − | 0.718941i | \(-0.744627\pi\) | ||||
−0.695071 | + | 0.718941i | \(0.744627\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 280.000 | 0.0491442 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1092.00 | 0.189874 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6888.00 | −1.18656 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4094.00 | −0.698752 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2514.00 | 0.425151 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −224.000 | −0.0375365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.0000 | 0.00398538 | 0.00199269 | − | 0.999998i | \(-0.499366\pi\) | ||||
0.00199269 | + | 0.999998i | \(0.499366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1314.00 | 0.216237 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3120.00 | 0.508847 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5970.00 | 0.965005 | 0.482502 | − | 0.875895i | \(-0.339728\pi\) | ||||
0.482502 | + | 0.875895i | \(0.339728\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1098.00 | 0.175915 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −608.000 | −0.0965544 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −792.000 | −0.123594 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10212.0 | 1.57985 | 0.789926 | − | 0.613202i | \(-0.210119\pi\) | ||||
0.789926 | + | 0.613202i | \(0.210119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3914.00 | −0.600320 | −0.300160 | − | 0.953889i | \(-0.597040\pi\) | ||||
−0.300160 | + | 0.953889i | \(0.597040\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1242.00 | −0.188869 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3222.00 | 0.485807 | 0.242903 | − | 0.970050i | \(-0.421900\pi\) | ||||
0.242903 | + | 0.970050i | \(0.421900\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −216.000 | −0.0322932 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1722.00 | −0.255288 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3140.00 | −0.461624 | −0.230812 | − | 0.972998i | \(-0.574138\pi\) | ||||
−0.230812 | + | 0.972998i | \(0.574138\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 197.000 | 0.0287214 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3945.00 | 0.570410 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3924.00 | 0.562717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6680.00 | 0.950118 | 0.475059 | − | 0.879954i | \(-0.342427\pi\) | ||||
0.475059 | + | 0.879954i | \(0.342427\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 846.000 | 0.119352 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3934.00 | −0.550520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7830.00 | −1.08692 | −0.543461 | − | 0.839434i | \(-0.682886\pi\) | ||||
−0.543461 | + | 0.839434i | \(0.682886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3852.00 | −0.530444 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3220.00 | −0.439890 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11368.0 | −1.54073 | −0.770363 | − | 0.637606i | \(-0.779925\pi\) | ||||
−0.770363 | + | 0.637606i | \(0.779925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1608.00 | −0.216221 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 136.000 | 0.0181443 | 0.00907216 | − | 0.999959i | \(-0.497112\pi\) | ||||
0.00907216 | + | 0.999959i | \(0.497112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −168.000 | −0.0222392 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4392.00 | 0.576894 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13374.0 | −1.74316 | −0.871579 | − | 0.490255i | \(-0.836904\pi\) | ||||
−0.871579 | + | 0.490255i | \(0.836904\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3608.00 | 0.466661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5940.00 | −0.762426 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3648.00 | −0.464686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6406.00 | 0.809844 | 0.404922 | − | 0.914351i | \(-0.367299\pi\) | ||||
0.404922 | + | 0.914351i | \(0.367299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1764.00 | 0.221329 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3958.00 | −0.492900 | −0.246450 | − | 0.969155i | \(-0.579264\pi\) | ||||
−0.246450 | + | 0.969155i | \(0.579264\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6992.00 | 0.864259 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −486.000 | −0.0596285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −584.000 | −0.0711248 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12614.0 | −1.52499 | −0.762497 | − | 0.646992i | \(-0.776027\pi\) | ||||
−0.762497 | + | 0.646992i | \(0.776027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8634.00 | 1.03621 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3332.00 | 0.396990 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1704.00 | −0.201557 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4308.00 | 0.505908 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1404.00 | 0.163699 | 0.0818495 | − | 0.996645i | \(-0.473917\pi\) | ||||
0.0818495 | + | 0.996645i | \(0.473917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1482.00 | 0.171564 | 0.0857818 | − | 0.996314i | \(-0.472661\pi\) | ||||
0.0857818 | + | 0.996314i | \(0.472661\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 288.000 | 0.0331041 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7298.00 | 0.832953 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 238.000 | 0.0269734 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 552.000 | 0.0621231 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14228.0 | −1.59011 | −0.795056 | − | 0.606535i | \(-0.792559\pi\) | ||||
−0.795056 | + | 0.606535i | \(0.792559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11674.0 | 1.29565 | 0.647825 | − | 0.761789i | \(-0.275679\pi\) | ||||
0.647825 | + | 0.761789i | \(0.275679\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1260.00 | −0.138879 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3696.00 | −0.404585 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14712.0 | 1.59947 | 0.799733 | − | 0.600356i | \(-0.204974\pi\) | ||||
0.799733 | + | 0.600356i | \(0.204974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2940.00 | 0.315313 | 0.157656 | − | 0.987494i | \(-0.449606\pi\) | ||||
0.157656 | + | 0.987494i | \(0.449606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5724.00 | 0.609761 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4122.00 | 0.436161 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4818.00 | 0.506404 | 0.253202 | − | 0.967413i | \(-0.418516\pi\) | ||||
0.253202 | + | 0.967413i | \(0.418516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −376.000 | −0.0392575 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2064.00 | 0.214073 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1932.00 | 0.199063 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2122.00 | 0.217206 | 0.108603 | − | 0.994085i | \(-0.465362\pi\) | ||||
0.108603 | + | 0.994085i | \(0.465362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2214.00 | 0.225143 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15010.0 | 1.51645 | 0.758227 | − | 0.651991i | \(-0.226066\pi\) | ||||
0.758227 | + | 0.651991i | \(0.226066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5712.00 | 0.573346 | 0.286673 | − | 0.958029i | \(-0.407451\pi\) | ||||
0.286673 | + | 0.958029i | \(0.407451\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2736.00 | 0.272858 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10356.0 | 1.02616 | 0.513082 | − | 0.858340i | \(-0.328504\pi\) | ||||
0.513082 | + | 0.858340i | \(0.328504\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3640.00 | 0.358379 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0000 | −0.00176093 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1952.00 | −0.189753 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7476.00 | −0.722152 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5058.00 | 0.485513 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16992.0 | −1.62084 | −0.810422 | − | 0.585847i | \(-0.800762\pi\) | ||||
−0.810422 | + | 0.585847i | \(0.800762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6716.00 | 0.636639 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −924.000 | −0.0870465 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10164.0 | 0.951595 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12000.0 | −1.11657 | −0.558287 | − | 0.829648i | \(-0.688541\pi\) | ||||
−0.558287 | + | 0.829648i | \(0.688541\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 48.0000 | 0.00443893 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4804.00 | −0.441551 | −0.220775 | − | 0.975325i | \(-0.570859\pi\) | ||||
−0.220775 | + | 0.975325i | \(0.570859\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5740.00 | 0.524374 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 216.000 | 0.0196131 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −252.000 | −0.0227440 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11696.0 | 1.04927 | 0.524634 | − | 0.851328i | \(-0.324202\pi\) | ||||
0.524634 | + | 0.851328i | \(0.324202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5856.00 | 0.522209 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3328.00 | 0.295006 | 0.147503 | − | 0.989062i | \(-0.452876\pi\) | ||||
0.147503 | + | 0.989062i | \(0.452876\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1908.00 | 0.168128 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 243.000 | 0.0212860 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15290.0 | 1.33147 | 0.665734 | − | 0.746189i | \(-0.268119\pi\) | ||||
0.665734 | + | 0.746189i | \(0.268119\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4578.00 | 0.396319 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2268.00 | −0.195194 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5232.00 | −0.447669 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −128.000 | −0.0108887 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1926.00 | −0.162894 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1946.00 | −0.163639 | −0.0818194 | − | 0.996647i | \(-0.526073\pi\) | ||||
−0.0818194 | + | 0.996647i | \(0.526073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11468.0 | 0.958816 | 0.479408 | − | 0.877592i | \(-0.340851\pi\) | ||||
0.479408 | + | 0.877592i | \(0.340851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1869.00 | −0.155371 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12464.0 | −1.03025 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10231.0 | −0.840881 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4284.00 | −0.350113 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4324.00 | 0.351394 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2184.00 | 0.176491 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1404.00 | 0.112825 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −196.000 | −0.0156629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20178.0 | 1.60355 | 0.801774 | − | 0.597627i | \(-0.203890\pi\) | ||||
0.801774 | + | 0.597627i | \(0.203890\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 414.000 | 0.0327190 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5028.00 | 0.395185 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4864.00 | −0.380200 | −0.190100 | − | 0.981765i | \(-0.560881\pi\) | ||||
−0.190100 | + | 0.981765i | \(0.560881\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −306.000 | −0.0237883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5880.00 | −0.454621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4256.00 | −0.327276 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2628.00 | 0.200995 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13722.0 | 1.04384 | 0.521921 | − | 0.852994i | \(-0.325216\pi\) | ||||
0.521921 | + | 0.852994i | \(0.325216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22448.0 | 1.69848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −984.000 | −0.0740544 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26468.0 | −1.98134 | −0.990669 | − | 0.136290i | \(-0.956482\pi\) | ||||
−0.990669 | + | 0.136290i | \(0.956482\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2196.00 | 0.163516 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7518.00 | −0.553903 | −0.276952 | − | 0.960884i | \(-0.589324\pi\) | ||||
−0.276952 | + | 0.960884i | \(0.589324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16432.0 | 1.20430 | 0.602152 | − | 0.798381i | \(-0.294310\pi\) | ||||
0.602152 | + | 0.798381i | \(0.294310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5940.00 | 0.433066 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3916.00 | 0.284015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5822.00 | −0.420057 | −0.210029 | − | 0.977695i | \(-0.567356\pi\) | ||||
−0.210029 | + | 0.977695i | \(0.567356\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3882.00 | 0.278636 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1988.00 | −0.141955 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2248.00 | −0.159696 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2484.00 | −0.175557 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21540.0 | −1.51457 | −0.757284 | − | 0.653086i | \(-0.773474\pi\) | ||||
−0.757284 | + | 0.653086i | \(0.773474\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12768.0 | 0.893203 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13626.0 | 0.948390 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3066.00 | −0.212320 | −0.106160 | − | 0.994349i | \(-0.533856\pi\) | ||||
−0.106160 | + | 0.994349i | \(0.533856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3444.00 | −0.237295 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8976.00 | −0.615349 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20652.0 | −1.40871 | −0.704355 | − | 0.709847i | \(-0.748764\pi\) | ||||
−0.704355 | + | 0.709847i | \(0.748764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6074.00 | 0.412252 | 0.206126 | − | 0.978525i | \(-0.433914\pi\) | ||||
0.206126 | + | 0.978525i | \(0.433914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4680.00 | −0.316060 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7890.00 | 0.530205 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8136.00 | −0.544036 | −0.272018 | − | 0.962292i | \(-0.587691\pi\) | ||||
−0.272018 | + | 0.962292i | \(0.587691\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1470.00 | −0.0978118 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1472.00 | 0.0974644 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5102.00 | −0.336163 | −0.168081 | − | 0.985773i | \(-0.553757\pi\) | ||||
−0.168081 | + | 0.985773i | \(0.553757\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1692.00 | 0.110940 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3074.00 | 0.200575 | 0.100287 | − | 0.994959i | \(-0.468024\pi\) | ||||
0.100287 | + | 0.994959i | \(0.468024\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5156.00 | −0.334793 | −0.167397 | − | 0.985890i | \(-0.553536\pi\) | ||||
−0.167397 | + | 0.985890i | \(0.553536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1188.00 | 0.0767678 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6678.00 | 0.429452 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1008.00 | 0.0642036 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11972.0 | −0.758911 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20320.0 | −1.28198 | −0.640988 | − | 0.767551i | \(-0.721475\pi\) | ||||
−0.640988 | + | 0.767551i | \(0.721475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10032.0 | 0.629915 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3216.00 | −0.200981 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2254.00 | 0.140199 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 324.000 | 0.0200583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14842.0 | 0.914546 | 0.457273 | − | 0.889326i | \(-0.348826\pi\) | ||||
0.457273 | + | 0.889326i | \(0.348826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14516.0 | −0.890288 | −0.445144 | − | 0.895459i | \(-0.646848\pi\) | ||||
−0.445144 | + | 0.895459i | \(0.646848\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8784.00 | 0.536232 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6096.00 | −0.370415 | −0.185207 | − | 0.982699i | \(-0.559296\pi\) | ||||
−0.185207 | + | 0.982699i | \(0.559296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1904.00 | 0.115160 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3192.00 | 0.192173 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8650.00 | 0.518378 | 0.259189 | − | 0.965827i | \(-0.416545\pi\) | ||||
0.259189 | + | 0.965827i | \(0.416545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11880.0 | −0.708687 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5886.00 | −0.349520 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22260.0 | −1.31582 | −0.657911 | − | 0.753096i | \(-0.728560\pi\) | ||||
−0.657911 | + | 0.753096i | \(0.728560\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14406.0 | 0.847698 | 0.423849 | − | 0.905733i | \(-0.360679\pi\) | ||||
0.423849 | + | 0.905733i | \(0.360679\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11316.0 | 0.662861 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3528.00 | 0.205729 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3080.00 | 0.178798 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16920.0 | −0.977825 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 136.000 | 0.00782447 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8334.00 | −0.477343 | −0.238672 | − | 0.971100i | \(-0.576712\pi\) | ||||
−0.238672 | + | 0.971100i | \(0.576712\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2403.00 | 0.137024 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22314.0 | 1.26676 | 0.633380 | − | 0.773841i | \(-0.281667\pi\) | ||||
0.633380 | + | 0.773841i | \(0.281667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11858.0 | 0.670204 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7980.00 | −0.449037 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13692.0 | 0.767071 | 0.383536 | − | 0.923526i | \(-0.374706\pi\) | ||||
0.383536 | + | 0.923526i | \(0.374706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17268.0 | 0.963177 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16878.0 | 0.937316 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25852.0 | 1.42944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29020.0 | 1.59765 | 0.798823 | − | 0.601567i | \(-0.205457\pi\) | ||||
0.798823 | + | 0.601567i | \(0.205457\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 252.000 | 0.0138134 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8616.00 | 0.470250 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7708.00 | −0.418883 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1818.00 | 0.0983735 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16410.0 | 0.884161 | 0.442081 | − | 0.896975i | \(-0.354240\pi\) | ||||
0.442081 | + | 0.896975i | \(0.354240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12264.0 | 0.657959 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 576.000 | 0.0307708 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2226.00 | 0.118412 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11170.0 | 0.591676 | 0.295838 | − | 0.955238i | \(-0.404401\pi\) | ||||
0.295838 | + | 0.955238i | \(0.404401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5472.00 | 0.288630 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6688.00 | −0.351287 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1104.00 | 0.0577444 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18900.0 | 0.984426 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22728.0 | −1.17888 | −0.589438 | − | 0.807814i | \(-0.700651\pi\) | ||||
−0.589438 | + | 0.807814i | \(0.700651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6104.00 | −0.315291 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6630.00 | −0.341041 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6230.00 | 0.319140 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1288.00 | 0.0657074 | 0.0328537 | − | 0.999460i | \(-0.489540\pi\) | ||||
0.0328537 | + | 0.999460i | \(0.489540\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40016.0 | −2.02469 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −266.000 | −0.0134037 | −0.00670187 | − | 0.999978i | \(-0.502133\pi\) | ||||
−0.00670187 | + | 0.999978i | \(0.502133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 882.000 | 0.0442627 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2080.00 | 0.103959 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25280.0 | 1.25838 | 0.629188 | − | 0.777253i | \(-0.283388\pi\) | ||||
0.629188 | + | 0.777253i | \(0.283388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11592.0 | −0.574687 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6964.00 | −0.343855 | −0.171928 | − | 0.985110i | \(-0.555000\pi\) | ||||
−0.171928 | + | 0.985110i | \(0.555000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8244.00 | 0.405419 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2556.00 | 0.125193 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2548.00 | 0.124302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20208.0 | 0.981891 | 0.490946 | − | 0.871190i | \(-0.336651\pi\) | ||||
0.490946 | + | 0.871190i | \(0.336651\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15132.0 | 0.732325 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4128.00 | 0.198985 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24766.0 | −1.18908 | −0.594541 | − | 0.804065i | \(-0.702666\pi\) | ||||
−0.594541 | + | 0.804065i | \(0.702666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −528.000 | −0.0252506 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34338.0 | −1.63568 | −0.817839 | − | 0.575447i | \(-0.804828\pi\) | ||||
−0.817839 | + | 0.575447i | \(0.804828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5866.00 | 0.278327 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4428.00 | 0.209274 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21896.0 | −1.03079 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41178.0 | 1.93097 | 0.965485 | − | 0.260457i | \(-0.0838732\pi\) | ||||
0.965485 | + | 0.260457i | \(0.0838732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 294.000 | 0.0137330 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21918.0 | −1.01984 | −0.509920 | − | 0.860222i | \(-0.670325\pi\) | ||||
−0.509920 | + | 0.860222i | \(0.670325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13528.0 | −0.627019 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3066.00 | 0.141560 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7896.00 | 0.363162 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −144.000 | −0.00659760 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1890.00 | 0.0862619 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −0.00163681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17972.0 | −0.814019 | −0.407009 | − | 0.913424i | \(-0.633428\pi\) | ||||
−0.407009 | + | 0.913424i | \(0.633428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17196.0 | 0.775911 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2562.00 | 0.115163 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1564.00 | −0.0700369 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10116.0 | 0.451293 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27310.0 | −1.21376 | −0.606882 | − | 0.794792i | \(-0.707580\pi\) | ||||
−0.606882 | + | 0.794792i | \(0.707580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2624.00 | −0.116183 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8586.00 | −0.378741 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2616.00 | 0.114965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1848.00 | −0.0809111 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1890.00 | 0.0824426 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5734.00 | −0.249192 | −0.124596 | − | 0.992208i | \(-0.539764\pi\) | ||||
−0.124596 | + | 0.992208i | \(0.539764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40556.0 | 1.75600 | 0.877999 | − | 0.478663i | \(-0.158878\pi\) | ||||
0.877999 | + | 0.478663i | \(0.158878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7680.00 | 0.331303 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 96.0000 | 0.00412605 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40992.0 | 1.75536 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2898.00 | −0.123644 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28046.0 | −1.19222 | −0.596110 | − | 0.802903i | \(-0.703288\pi\) | ||||
−0.596110 | + | 0.802903i | \(0.703288\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31744.0 | −1.34450 | −0.672252 | − | 0.740323i | \(-0.734673\pi\) | ||||
−0.672252 | + | 0.740323i | \(0.734673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1068.00 | −0.0450703 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41244.0 | −1.73421 | −0.867107 | − | 0.498123i | \(-0.834023\pi\) | ||||
−0.867107 | + | 0.498123i | \(0.834023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20298.0 | −0.850396 | −0.425198 | − | 0.905100i | \(-0.639796\pi\) | ||||
−0.425198 | + | 0.905100i | \(0.639796\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6798.00 | −0.283779 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4018.00 | −0.167125 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11712.0 | 0.485402 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4104.00 | −0.169480 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40048.0 | 1.64793 | 0.823963 | − | 0.566643i | \(-0.191758\pi\) | ||||
0.823963 | + | 0.566643i | \(0.191758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19489.0 | −0.799090 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13014.0 | −0.531703 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 486.000 | 0.0197857 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9205.00 | 0.373421 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19092.0 | 0.771774 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6424.00 | −0.258768 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7758.00 | 0.311405 | 0.155703 | − | 0.987804i | \(-0.450236\pi\) | ||||
0.155703 | + | 0.987804i | \(0.450236\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4536.00 | −0.181436 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28434.0 | −1.13336 | −0.566678 | − | 0.823939i | \(-0.691772\pi\) | ||||
−0.566678 | + | 0.823939i | \(0.691772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16028.0 | 0.636634 | 0.318317 | − | 0.947984i | \(-0.396882\pi\) | ||||
0.318317 | + | 0.947984i | \(0.396882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1974.00 | 0.0781344 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40188.0 | 1.58519 | 0.792593 | − | 0.609751i | \(-0.208731\pi\) | ||||
0.792593 | + | 0.609751i | \(0.208731\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3852.00 | −0.151413 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5433.00 | −0.212819 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2432.00 | −0.0949367 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23920.0 | −0.930538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15246.0 | −0.591064 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8988.00 | −0.347257 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32810.0 | 1.26330 | 0.631651 | − | 0.775253i | \(-0.282378\pi\) | ||||
0.631651 | + | 0.775253i | \(0.282378\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5334.00 | −0.204677 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17414.0 | 0.665939 | 0.332970 | − | 0.942938i | \(-0.391949\pi\) | ||||
0.332970 | + | 0.942938i | \(0.391949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8656.00 | 0.329895 | 0.164948 | − | 0.986302i | \(-0.447254\pi\) | ||||
0.164948 | + | 0.986302i | \(0.447254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8568.00 | −0.325435 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3824.00 | 0.144755 | 0.0723773 | − | 0.997377i | \(-0.476941\pi\) | ||||
0.0723773 | + | 0.997377i | \(0.476941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3752.00 | −0.141550 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −324.000 | −0.0121823 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2688.00 | 0.100728 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2808.00 | 0.104873 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6072.00 | 0.226018 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10640.0 | −0.394732 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46084.0 | −1.70397 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10248.0 | 0.377666 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 828.000 | 0.0304129 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41008.0 | 1.50127 | 0.750633 | − | 0.660719i | \(-0.229749\pi\) | ||||
0.750633 | + | 0.660719i | \(0.229749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2862.00 | −0.104430 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51172.0 | −1.86104 | −0.930518 | − | 0.366246i | \(-0.880643\pi\) | ||||
−0.930518 | + | 0.366246i | \(0.880643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1136.00 | −0.0411787 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −612.000 | −0.0221116 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13860.0 | −0.499125 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31432.0 | −1.12823 | −0.564116 | − | 0.825695i | \(-0.690783\pi\) | ||||
−0.564116 | + | 0.825695i | \(0.690783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4092.00 | −0.146402 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1656.00 | 0.0590552 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12994.0 | −0.461881 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7848.00 | 0.278061 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38214.0 | 1.34958 | 0.674790 | − | 0.738009i | \(-0.264234\pi\) | ||||
0.674790 | + | 0.738009i | \(0.264234\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4116.00 | 0.144894 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22536.0 | −0.790778 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1968.00 | −0.0688347 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41446.0 | −1.44502 | −0.722509 | − | 0.691362i | \(-0.757011\pi\) | ||||
−0.722509 | + | 0.691362i | \(0.757011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8742.00 | −0.303817 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2590.00 | −0.0897254 | −0.0448627 | − | 0.998993i | \(-0.514285\pi\) | ||||
−0.0448627 | + | 0.998993i | \(0.514285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4136.00 | −0.142828 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1134.00 | −0.0390360 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3980.00 | 0.136571 | 0.0682854 | − | 0.997666i | \(-0.478247\pi\) | ||||
0.0682854 | + | 0.997666i | \(0.478247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30084.0 | −1.02905 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23538.0 | 0.802599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6778.00 | 0.230389 | 0.115195 | − | 0.993343i | \(-0.463251\pi\) | ||||
0.115195 | + | 0.993343i | \(0.463251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11880.0 | 0.402542 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −840.000 | −0.0283734 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20146.0 | 0.678361 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6687.00 | −0.224464 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3276.00 | −0.109624 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7764.00 | 0.258997 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −296.000 | −0.00984356 | −0.00492178 | − | 0.999988i | \(-0.501567\pi\) | ||||
−0.00492178 | + | 0.999988i | \(0.501567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20664.0 | 0.685060 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25356.0 | 0.838015 | 0.419008 | − | 0.907983i | \(-0.362378\pi\) | ||||
0.419008 | + | 0.907983i | \(0.362378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10052.0 | 0.331195 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12282.0 | 0.403424 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53290.0 | 1.74503 | 0.872517 | − | 0.488584i | \(-0.162486\pi\) | ||||
0.872517 | + | 0.488584i | \(0.162486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3816.00 | 0.124576 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7542.00 | −0.245461 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28584.0 | 0.927455 | 0.463727 | − | 0.885978i | \(-0.346512\pi\) | ||||
0.463727 | + | 0.885978i | \(0.346512\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27252.0 | 0.881544 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 672.000 | 0.0216717 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21472.0 | −0.690364 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3592.00 | −0.115140 | −0.0575699 | − | 0.998341i | \(-0.518335\pi\) | ||||
−0.0575699 | + | 0.998341i | \(0.518335\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −72.0000 | −0.00230096 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17952.0 | −0.571977 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9290.00 | −0.295103 | −0.147551 | − | 0.989054i | \(-0.547139\pi\) | ||||
−0.147551 | + | 0.989054i | \(0.547139\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3942.00 | −0.124844 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1344.4.a.c.1.1 | 1 | ||
4.3 | odd | 2 | 1344.4.a.r.1.1 | 1 | |||
8.3 | odd | 2 | 672.4.a.b.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 672.4.a.d.1.1 | yes | 1 | ||
24.5 | odd | 2 | 2016.4.a.a.1.1 | 1 | |||
24.11 | even | 2 | 2016.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.b.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
672.4.a.d.1.1 | yes | 1 | 8.5 | even | 2 | ||
1344.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1344.4.a.r.1.1 | 1 | 4.3 | odd | 2 | |||
2016.4.a.a.1.1 | 1 | 24.5 | odd | 2 | |||
2016.4.a.b.1.1 | 1 | 24.11 | even | 2 |