Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,4,Mod(1,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, 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("720.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.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: | \(42.4813752041\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 360) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 720.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.0000 | 0.971909 | 0.485954 | − | 0.873984i | \(-0.338472\pi\) | ||||
0.485954 | + | 0.873984i | \(0.338472\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 34.0000 | 0.931944 | 0.465972 | − | 0.884799i | \(-0.345705\pi\) | ||||
0.465972 | + | 0.884799i | \(0.345705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.0000 | 0.256015 | 0.128008 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128008 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 102.000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −164.000 | −1.98022 | −0.990110 | − | 0.140293i | \(-0.955195\pi\) | ||||
−0.990110 | + | 0.140293i | \(0.955195\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 48.0000 | 0.435161 | 0.217580 | − | 0.976042i | \(-0.430184\pi\) | ||||
0.217580 | + | 0.976042i | \(0.430184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −146.000 | −0.934880 | −0.467440 | − | 0.884025i | \(-0.654824\pi\) | ||||
−0.467440 | + | 0.884025i | \(0.654824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −100.000 | −0.579372 | −0.289686 | − | 0.957122i | \(-0.593551\pi\) | ||||
−0.289686 | + | 0.957122i | \(0.593551\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −90.0000 | −0.434651 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 328.000 | 1.45737 | 0.728687 | − | 0.684846i | \(-0.240131\pi\) | ||||
0.728687 | + | 0.684846i | \(0.240131\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 288.000 | 1.09703 | 0.548513 | − | 0.836142i | \(-0.315194\pi\) | ||||
0.548513 | + | 0.836142i | \(0.315194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −120.000 | −0.425577 | −0.212789 | − | 0.977098i | \(-0.568255\pi\) | ||||
−0.212789 | + | 0.977098i | \(0.568255\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16.0000 | 0.0496562 | 0.0248281 | − | 0.999692i | \(-0.492096\pi\) | ||||
0.0248281 | + | 0.999692i | \(0.492096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.0000 | −0.0553936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 126.000 | 0.326555 | 0.163278 | − | 0.986580i | \(-0.447793\pi\) | ||||
0.163278 | + | 0.986580i | \(0.447793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −170.000 | −0.416778 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 642.000 | 1.41663 | 0.708316 | − | 0.705896i | \(-0.249455\pi\) | ||||
0.708316 | + | 0.705896i | \(0.249455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 602.000 | 1.26358 | 0.631789 | − | 0.775141i | \(-0.282321\pi\) | ||||
0.631789 | + | 0.775141i | \(0.282321\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −60.0000 | −0.114494 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −436.000 | −0.795013 | −0.397507 | − | 0.917599i | \(-0.630124\pi\) | ||||
−0.397507 | + | 0.917599i | \(0.630124\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 652.000 | 1.08983 | 0.544917 | − | 0.838490i | \(-0.316561\pi\) | ||||
0.544917 | + | 0.838490i | \(0.316561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1062.00 | 1.70271 | 0.851354 | − | 0.524591i | \(-0.175782\pi\) | ||||
0.851354 | + | 0.524591i | \(0.175782\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 612.000 | 0.905765 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −388.000 | −0.552575 | −0.276287 | − | 0.961075i | \(-0.589104\pi\) | ||||
−0.276287 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −444.000 | −0.587173 | −0.293586 | − | 0.955933i | \(-0.594849\pi\) | ||||
−0.293586 | + | 0.955933i | \(0.594849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −510.000 | −0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 820.000 | 0.976627 | 0.488314 | − | 0.872668i | \(-0.337612\pi\) | ||||
0.488314 | + | 0.872668i | \(0.337612\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 216.000 | 0.248824 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 820.000 | 0.885581 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −766.000 | −0.801809 | −0.400905 | − | 0.916120i | \(-0.631304\pi\) | ||||
−0.400905 | + | 0.916120i | \(0.631304\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 798.000 | 0.786178 | 0.393089 | − | 0.919500i | \(-0.371406\pi\) | ||||
0.393089 | + | 0.919500i | \(0.371406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 402.000 | 0.384565 | 0.192283 | − | 0.981340i | \(-0.438411\pi\) | ||||
0.192283 | + | 0.981340i | \(0.438411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1444.00 | 1.30464 | 0.652321 | − | 0.757943i | \(-0.273795\pi\) | ||||
0.652321 | + | 0.757943i | \(0.273795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −198.000 | −0.173990 | −0.0869952 | − | 0.996209i | \(-0.527726\pi\) | ||||
−0.0869952 | + | 0.996209i | \(0.527726\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2010.00 | 1.67332 | 0.836659 | − | 0.547724i | \(-0.184506\pi\) | ||||
0.836659 | + | 0.547724i | \(0.184506\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −240.000 | −0.194610 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1836.00 | 1.41433 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −175.000 | −0.131480 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 866.000 | 0.605079 | 0.302540 | − | 0.953137i | \(-0.402166\pi\) | ||||
0.302540 | + | 0.953137i | \(0.402166\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2098.00 | −1.39926 | −0.699630 | − | 0.714505i | \(-0.746652\pi\) | ||||
−0.699630 | + | 0.714505i | \(0.746652\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2952.00 | −1.92459 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −886.000 | −0.552526 | −0.276263 | − | 0.961082i | \(-0.589096\pi\) | ||||
−0.276263 | + | 0.961082i | \(0.589096\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 500.000 | 0.305104 | 0.152552 | − | 0.988295i | \(-0.451251\pi\) | ||||
0.152552 | + | 0.988295i | \(0.451251\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 408.000 | 0.238592 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 730.000 | 0.418091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2302.00 | −1.26569 | −0.632843 | − | 0.774280i | \(-0.718112\pi\) | ||||
−0.632843 | + | 0.774280i | \(0.718112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2384.00 | 1.28482 | 0.642408 | − | 0.766363i | \(-0.277936\pi\) | ||||
0.642408 | + | 0.766363i | \(0.277936\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 500.000 | 0.259103 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1452.00 | 0.738103 | 0.369052 | − | 0.929409i | \(-0.379683\pi\) | ||||
0.369052 | + | 0.929409i | \(0.379683\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 864.000 | 0.422936 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −604.000 | −0.290239 | −0.145119 | − | 0.989414i | \(-0.546357\pi\) | ||||
−0.145119 | + | 0.989414i | \(0.546357\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −664.000 | −0.307676 | −0.153838 | − | 0.988096i | \(-0.549163\pi\) | ||||
−0.153838 | + | 0.988096i | \(0.549163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2053.00 | −0.934456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4118.00 | 1.80974 | 0.904872 | − | 0.425684i | \(-0.139966\pi\) | ||||
0.904872 | + | 0.425684i | \(0.139966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 450.000 | 0.194382 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1746.00 | 0.729062 | 0.364531 | − | 0.931191i | \(-0.381229\pi\) | ||||
0.364531 | + | 0.931191i | \(0.381229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1270.00 | −0.521538 | −0.260769 | − | 0.965401i | \(-0.583976\pi\) | ||||
−0.260769 | + | 0.965401i | \(0.583976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1640.00 | −0.651758 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3468.00 | 1.35618 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2676.00 | 1.01376 | 0.506881 | − | 0.862016i | \(-0.330798\pi\) | ||||
0.506881 | + | 0.862016i | \(0.330798\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3146.00 | −1.17334 | −0.586668 | − | 0.809827i | \(-0.699561\pi\) | ||||
−0.586668 | + | 0.809827i | \(0.699561\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3674.00 | 1.32874 | 0.664370 | − | 0.747404i | \(-0.268700\pi\) | ||||
0.664370 | + | 0.747404i | \(0.268700\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1392.00 | 0.495861 | 0.247930 | − | 0.968778i | \(-0.420250\pi\) | ||||
0.247930 | + | 0.968778i | \(0.420250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2628.00 | −0.908618 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1440.00 | −0.490605 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5576.00 | −1.84545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 540.000 | 0.176185 | 0.0880927 | − | 0.996112i | \(-0.471923\pi\) | ||||
0.0880927 | + | 0.996112i | \(0.471923\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 600.000 | 0.190324 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1800.00 | −0.563097 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1224.00 | 0.372557 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4166.00 | −1.25101 | −0.625507 | − | 0.780219i | \(-0.715108\pi\) | ||||
−0.625507 | + | 0.780219i | \(0.715108\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5024.00 | −1.46896 | −0.734481 | − | 0.678629i | \(-0.762575\pi\) | ||||
−0.734481 | + | 0.678629i | \(0.762575\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4454.00 | 1.28528 | 0.642639 | − | 0.766169i | \(-0.277840\pi\) | ||||
0.642639 | + | 0.766169i | \(0.277840\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1526.00 | 0.429063 | 0.214531 | − | 0.976717i | \(-0.431178\pi\) | ||||
0.214531 | + | 0.976717i | \(0.431178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −80.0000 | −0.0222069 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6828.00 | 1.84798 | 0.923989 | − | 0.382420i | \(-0.124909\pi\) | ||||
0.923989 | + | 0.382420i | \(0.124909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5782.00 | 1.54544 | 0.772721 | − | 0.634746i | \(-0.218895\pi\) | ||||
0.772721 | + | 0.634746i | \(0.218895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 95.0000 | 0.0247728 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1968.00 | −0.506967 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6394.00 | −1.60791 | −0.803956 | − | 0.594689i | \(-0.797275\pi\) | ||||
−0.803956 | + | 0.594689i | \(0.797275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1632.00 | 0.405545 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1862.00 | −0.451939 | −0.225970 | − | 0.974134i | \(-0.572555\pi\) | ||||
−0.225970 | + | 0.974134i | \(0.572555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5904.00 | 1.41644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6504.00 | −1.52492 | −0.762460 | − | 0.647036i | \(-0.776008\pi\) | ||||
−0.762460 | + | 0.647036i | \(0.776008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −630.000 | −0.146040 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8298.00 | −1.88081 | −0.940405 | − | 0.340056i | \(-0.889554\pi\) | ||||
−0.940405 | + | 0.340056i | \(0.889554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1848.00 | −0.414236 | −0.207118 | − | 0.978316i | \(-0.566408\pi\) | ||||
−0.207118 | + | 0.978316i | \(0.566408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 850.000 | 0.186389 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2824.00 | 0.612555 | 0.306277 | − | 0.951942i | \(-0.400916\pi\) | ||||
0.306277 | + | 0.951942i | \(0.400916\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1940.00 | 0.411853 | 0.205927 | − | 0.978567i | \(-0.433979\pi\) | ||||
0.205927 | + | 0.978567i | \(0.433979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6548.00 | −1.37540 | −0.687700 | − | 0.725995i | \(-0.741380\pi\) | ||||
−0.687700 | + | 0.725995i | \(0.741380\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5184.00 | 1.06621 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5491.00 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6566.00 | −1.30918 | −0.654590 | − | 0.755984i | \(-0.727159\pi\) | ||||
−0.654590 | + | 0.755984i | \(0.727159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3210.00 | −0.633537 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 576.000 | 0.111408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2160.00 | −0.413622 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3010.00 | −0.565089 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8432.00 | −1.56756 | −0.783778 | − | 0.621041i | \(-0.786710\pi\) | ||||
−0.783778 | + | 0.621041i | \(0.786710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4916.00 | −0.896337 | −0.448168 | − | 0.893949i | \(-0.647924\pi\) | ||||
−0.448168 | + | 0.893949i | \(0.647924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10106.0 | −1.82500 | −0.912500 | − | 0.409077i | \(-0.865851\pi\) | ||||
−0.912500 | + | 0.409077i | \(0.865851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3382.00 | −0.599218 | −0.299609 | − | 0.954062i | \(-0.596856\pi\) | ||||
−0.299609 | + | 0.954062i | \(0.596856\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4964.00 | −0.871256 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16728.0 | −2.88164 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 300.000 | 0.0512031 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 288.000 | 0.0482613 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6460.00 | 1.07273 | 0.536365 | − | 0.843986i | \(-0.319797\pi\) | ||||
0.536365 | + | 0.843986i | \(0.319797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2180.00 | 0.355541 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5294.00 | 0.855735 | 0.427867 | − | 0.903842i | \(-0.359265\pi\) | ||||
0.427867 | + | 0.903842i | \(0.359265\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3400.00 | −0.539942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6516.00 | −1.02575 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12096.0 | −1.87132 | −0.935659 | − | 0.352906i | \(-0.885194\pi\) | ||||
−0.935659 | + | 0.352906i | \(0.885194\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −862.000 | −0.132211 | −0.0661057 | − | 0.997813i | \(-0.521057\pi\) | ||||
−0.0661057 | + | 0.997813i | \(0.521057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6878.00 | 1.03705 | 0.518525 | − | 0.855062i | \(-0.326481\pi\) | ||||
0.518525 | + | 0.855062i | \(0.326481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3260.00 | −0.487388 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6216.00 | 0.913838 | 0.456919 | − | 0.889508i | \(-0.348953\pi\) | ||||
0.456919 | + | 0.889508i | \(0.348953\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20037.0 | 2.92127 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5310.00 | −0.761474 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13274.0 | 1.88800 | 0.944002 | − | 0.329941i | \(-0.107029\pi\) | ||||
0.944002 | + | 0.329941i | \(0.107029\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2268.00 | 0.317382 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1300.00 | 0.180460 | 0.0902298 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902298 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1752.00 | −0.239344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13324.0 | −1.80583 | −0.902913 | − | 0.429824i | \(-0.858576\pi\) | ||||
−0.902913 | + | 0.429824i | \(0.858576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6192.00 | 0.826100 | 0.413050 | − | 0.910708i | \(-0.364463\pi\) | ||||
0.413050 | + | 0.910708i | \(0.364463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3060.00 | −0.405070 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2022.00 | −0.263546 | −0.131773 | − | 0.991280i | \(-0.542067\pi\) | ||||
−0.131773 | + | 0.991280i | \(0.542067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4896.00 | 0.633252 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1940.00 | 0.247119 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7856.00 | 0.993152 | 0.496576 | − | 0.867993i | \(-0.334590\pi\) | ||||
0.496576 | + | 0.867993i | \(0.334590\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1148.00 | −0.142964 | −0.0714818 | − | 0.997442i | \(-0.522773\pi\) | ||||
−0.0714818 | + | 0.997442i | \(0.522773\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1200.00 | −0.148328 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11152.0 | 1.35819 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6310.00 | −0.762859 | −0.381430 | − | 0.924398i | \(-0.624568\pi\) | ||||
−0.381430 | + | 0.924398i | \(0.624568\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11556.0 | 1.37684 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2220.00 | 0.262592 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13362.0 | −1.55794 | −0.778969 | − | 0.627062i | \(-0.784257\pi\) | ||||
−0.778969 | + | 0.627062i | \(0.784257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5146.00 | −0.595726 | −0.297863 | − | 0.954609i | \(-0.596274\pi\) | ||||
−0.297863 | + | 0.954609i | \(0.596274\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2550.00 | 0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10836.0 | 1.22808 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6368.00 | −0.711684 | −0.355842 | − | 0.934546i | \(-0.615806\pi\) | ||||
−0.355842 | + | 0.934546i | \(0.615806\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6138.00 | −0.681232 | −0.340616 | − | 0.940202i | \(-0.610636\pi\) | ||||
−0.340616 | + | 0.940202i | \(0.610636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7872.00 | −0.861714 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4424.00 | 0.480970 | 0.240485 | − | 0.970653i | \(-0.422693\pi\) | ||||
0.240485 | + | 0.970653i | \(0.422693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −488.000 | −0.0523377 | −0.0261688 | − | 0.999658i | \(-0.508331\pi\) | ||||
−0.0261688 | + | 0.999658i | \(0.508331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4100.00 | −0.436761 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16884.0 | −1.77462 | −0.887311 | − | 0.461172i | \(-0.847429\pi\) | ||||
−0.887311 | + | 0.461172i | \(0.847429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9792.00 | 1.02237 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1080.00 | −0.111277 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5398.00 | −0.552533 | −0.276267 | − | 0.961081i | \(-0.589097\pi\) | ||||
−0.276267 | + | 0.961081i | \(0.589097\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6122.00 | 0.618503 | 0.309252 | − | 0.950980i | \(-0.399921\pi\) | ||||
0.309252 | + | 0.950980i | \(0.399921\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8162.00 | −0.819266 | −0.409633 | − | 0.912250i | \(-0.634343\pi\) | ||||
−0.409633 | + | 0.912250i | \(0.634343\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2660.00 | −0.263576 | −0.131788 | − | 0.991278i | \(-0.542072\pi\) | ||||
−0.131788 | + | 0.991278i | \(0.542072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7848.00 | −0.772680 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4080.00 | −0.396614 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4100.00 | −0.396044 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9788.00 | 0.933664 | 0.466832 | − | 0.884346i | \(-0.345395\pi\) | ||||
0.466832 | + | 0.884346i | \(0.345395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3936.00 | 0.373111 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3830.00 | 0.358580 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4714.00 | −0.438628 | −0.219314 | − | 0.975654i | \(-0.570382\pi\) | ||||
−0.219314 | + | 0.975654i | \(0.570382\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6690.00 | −0.614899 | −0.307450 | − | 0.951564i | \(-0.599476\pi\) | ||||
−0.307450 | + | 0.951564i | \(0.599476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14892.0 | −1.36045 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11736.0 | 1.05922 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20636.0 | 1.85129 | 0.925646 | − | 0.378392i | \(-0.123523\pi\) | ||||
0.925646 | + | 0.378392i | \(0.123523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15952.0 | 1.41404 | 0.707022 | − | 0.707191i | \(-0.250038\pi\) | ||||
0.707022 | + | 0.707191i | \(0.250038\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3990.00 | −0.351589 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2230.00 | 0.194191 | 0.0970953 | − | 0.995275i | \(-0.469045\pi\) | ||||
0.0970953 | + | 0.995275i | \(0.469045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19116.0 | 1.65488 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2010.00 | −0.171983 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 544.000 | 0.0462768 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1260.00 | −0.105953 | −0.0529766 | − | 0.998596i | \(-0.516871\pi\) | ||||
−0.0529766 | + | 0.998596i | \(0.516871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2900.00 | −0.242463 | −0.121231 | − | 0.992624i | \(-0.538684\pi\) | ||||
−0.121231 | + | 0.992624i | \(0.538684\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10200.0 | −0.843110 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3456.00 | 0.280855 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7220.00 | −0.583454 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −646.000 | −0.0516237 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19554.0 | 1.55396 | 0.776980 | − | 0.629526i | \(-0.216751\pi\) | ||||
0.776980 | + | 0.629526i | \(0.216751\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 990.000 | 0.0778109 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2664.00 | −0.208235 | −0.104117 | − | 0.994565i | \(-0.533202\pi\) | ||||
−0.104117 | + | 0.994565i | \(0.533202\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23944.0 | 1.85127 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6984.00 | −0.537052 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11358.0 | 0.864011 | 0.432005 | − | 0.901871i | \(-0.357806\pi\) | ||||
0.432005 | + | 0.901871i | \(0.357806\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1440.00 | −0.108954 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2440.00 | −0.182653 | −0.0913266 | − | 0.995821i | \(-0.529111\pi\) | ||||
−0.0913266 | + | 0.995821i | \(0.529111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10050.0 | −0.748330 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24156.0 | 1.77974 | 0.889870 | − | 0.456214i | \(-0.150795\pi\) | ||||
0.889870 | + | 0.456214i | \(0.150795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2220.00 | 0.162704 | 0.0813521 | − | 0.996685i | \(-0.474076\pi\) | ||||
0.0813521 | + | 0.996685i | \(0.474076\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1200.00 | 0.0870321 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5782.00 | −0.417171 | −0.208586 | − | 0.978004i | \(-0.566886\pi\) | ||||
−0.208586 | + | 0.978004i | \(0.566886\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7992.00 | −0.570678 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4284.00 | 0.304331 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1684.00 | 0.118409 | 0.0592045 | − | 0.998246i | \(-0.481144\pi\) | ||||
0.0592045 | + | 0.998246i | \(0.481144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16400.0 | 1.14728 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15246.0 | −1.05578 | −0.527891 | − | 0.849312i | \(-0.677017\pi\) | ||||
−0.527891 | + | 0.849312i | \(0.677017\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9180.00 | −0.632510 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9016.00 | 0.614998 | 0.307499 | − | 0.951548i | \(-0.400508\pi\) | ||||
0.307499 | + | 0.951548i | \(0.400508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18682.0 | −1.26798 | −0.633989 | − | 0.773342i | \(-0.718584\pi\) | ||||
−0.633989 | + | 0.773342i | \(0.718584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 875.000 | 0.0587997 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22022.0 | 1.47256 | 0.736281 | − | 0.676676i | \(-0.236580\pi\) | ||||
0.736281 | + | 0.676676i | \(0.236580\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 192.000 | 0.0127127 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22808.0 | −1.50278 | −0.751392 | − | 0.659856i | \(-0.770617\pi\) | ||||
−0.751392 | + | 0.659856i | \(0.770617\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9422.00 | 0.614774 | 0.307387 | − | 0.951585i | \(-0.400545\pi\) | ||||
0.307387 | + | 0.951585i | \(0.400545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4172.00 | −0.270900 | −0.135450 | − | 0.990784i | \(-0.543248\pi\) | ||||
−0.135450 | + | 0.990784i | \(0.543248\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14760.0 | 0.949192 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33456.0 | 2.12079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11572.0 | 0.730070 | 0.365035 | − | 0.930994i | \(-0.381057\pi\) | ||||
0.365035 | + | 0.930994i | \(0.381057\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4330.00 | −0.270600 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −228.000 | −0.0141816 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 936.000 | 0.0576752 | 0.0288376 | − | 0.999584i | \(-0.490819\pi\) | ||||
0.0288376 | + | 0.999584i | \(0.490819\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15892.0 | −0.974680 | −0.487340 | − | 0.873212i | \(-0.662033\pi\) | ||||
−0.487340 | + | 0.873212i | \(0.662033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25056.0 | 1.52249 | 0.761247 | − | 0.648463i | \(-0.224588\pi\) | ||||
0.761247 | + | 0.648463i | \(0.224588\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21828.0 | 1.32022 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4054.00 | −0.242948 | −0.121474 | − | 0.992595i | \(-0.538762\pi\) | ||||
−0.121474 | + | 0.992595i | \(0.538762\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10490.0 | 0.625768 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6758.00 | 0.399475 | 0.199738 | − | 0.979849i | \(-0.435991\pi\) | ||||
0.199738 | + | 0.979849i | \(0.435991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25098.0 | 1.47685 | 0.738426 | − | 0.674335i | \(-0.235569\pi\) | ||||
0.738426 | + | 0.674335i | \(0.235569\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14760.0 | 0.860704 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7008.00 | −0.406823 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20468.0 | 1.17758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2830.00 | 0.162093 | 0.0810464 | − | 0.996710i | \(-0.474174\pi\) | ||||
0.0810464 | + | 0.996710i | \(0.474174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10654.0 | −0.604825 | −0.302412 | − | 0.953177i | \(-0.597792\pi\) | ||||
−0.302412 | + | 0.953177i | \(0.597792\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13788.0 | −0.779286 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17156.0 | 0.961136 | 0.480568 | − | 0.876957i | \(-0.340430\pi\) | ||||
0.480568 | + | 0.876957i | \(0.340430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4430.00 | 0.247097 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1512.00 | 0.0836032 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 812.000 | 0.0447032 | 0.0223516 | − | 0.999750i | \(-0.492885\pi\) | ||||
0.0223516 | + | 0.999750i | \(0.492885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2500.00 | −0.136447 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29376.0 | 1.59641 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30270.0 | 1.63093 | 0.815465 | − | 0.578806i | \(-0.196481\pi\) | ||||
0.815465 | + | 0.578806i | \(0.196481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53792.0 | −2.88592 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14364.0 | 0.764093 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −394.000 | −0.0208702 | −0.0104351 | − | 0.999946i | \(-0.503322\pi\) | ||||
−0.0104351 | + | 0.999946i | \(0.503322\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4800.00 | −0.252120 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2040.00 | −0.106702 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37224.0 | −1.93077 | −0.965383 | − | 0.260836i | \(-0.916002\pi\) | ||||
−0.965383 | + | 0.260836i | \(0.916002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7236.00 | 0.373762 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3650.00 | −0.186976 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12614.0 | 0.643504 | 0.321752 | − | 0.946824i | \(-0.395728\pi\) | ||||
0.321752 | + | 0.946824i | \(0.395728\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12240.0 | −0.619306 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25664.0 | −1.29321 | −0.646604 | − | 0.762826i | \(-0.723811\pi\) | ||||
−0.646604 | + | 0.762826i | \(0.723811\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14824.0 | −0.740908 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18772.0 | 0.934424 | 0.467212 | − | 0.884145i | \(-0.345259\pi\) | ||||
0.467212 | + | 0.884145i | \(0.345259\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19376.0 | −0.956711 | −0.478356 | − | 0.878166i | \(-0.658767\pi\) | ||||
−0.478356 | + | 0.878166i | \(0.658767\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11510.0 | 0.566032 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25992.0 | 1.26799 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30092.0 | −1.46215 | −0.731074 | − | 0.682299i | \(-0.760980\pi\) | ||||
−0.731074 | + | 0.682299i | \(0.760980\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11920.0 | −0.574587 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18136.0 | 0.870758 | 0.435379 | − | 0.900247i | \(-0.356614\pi\) | ||||
0.435379 | + | 0.900247i | \(0.356614\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10948.0 | −0.521504 | −0.260752 | − | 0.965406i | \(-0.583971\pi\) | ||||
−0.260752 | + | 0.965406i | \(0.583971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3564.00 | −0.169103 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7704.00 | 0.362680 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1422.00 | 0.0666822 | 0.0333411 | − | 0.999444i | \(-0.489385\pi\) | ||||
0.0333411 | + | 0.999444i | \(0.489385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26142.0 | −1.21638 | −0.608190 | − | 0.793791i | \(-0.708104\pi\) | ||||
−0.608190 | + | 0.793791i | \(0.708104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2500.00 | −0.115874 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47232.0 | −2.17235 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22168.0 | 1.01566 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7260.00 | −0.330090 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23404.0 | −1.06005 | −0.530027 | − | 0.847981i | \(-0.677818\pi\) | ||||
−0.530027 | + | 0.847981i | \(0.677818\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36180.0 | 1.62631 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7224.00 | 0.323495 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1418.00 | −0.0630215 | −0.0315108 | − | 0.999503i | \(-0.510032\pi\) | ||||
−0.0315108 | + | 0.999503i | \(0.510032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1632.00 | 0.0722603 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36108.0 | 1.58683 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4320.00 | −0.189143 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17304.0 | 0.752010 | 0.376005 | − | 0.926618i | \(-0.377298\pi\) | ||||
0.376005 | + | 0.926618i | \(0.377298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28012.0 | 1.21287 | 0.606433 | − | 0.795135i | \(-0.292600\pi\) | ||||
0.606433 | + | 0.795135i | \(0.292600\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3020.00 | 0.129799 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19680.0 | 0.842737 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32266.0 | −1.37161 | −0.685805 | − | 0.727786i | \(-0.740550\pi\) | ||||
−0.685805 | + | 0.727786i | \(0.740550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4962.00 | −0.210163 | −0.105082 | − | 0.994464i | \(-0.533510\pi\) | ||||
−0.105082 | + | 0.994464i | \(0.533510\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5064.00 | 0.212929 | 0.106465 | − | 0.994316i | \(-0.466047\pi\) | ||||
0.106465 | + | 0.994316i | \(0.466047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8174.00 | −0.342454 | −0.171227 | − | 0.985232i | \(-0.554773\pi\) | ||||
−0.171227 | + | 0.985232i | \(0.554773\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1938.00 | −0.0806095 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3320.00 | 0.137597 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28240.0 | −1.16204 | −0.581021 | − | 0.813889i | \(-0.697347\pi\) | ||||
−0.581021 | + | 0.813889i | \(0.697347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3073.00 | −0.125999 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10265.0 | 0.417901 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3150.00 | −0.127787 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15744.0 | 0.634192 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10472.0 | 0.420345 | 0.210173 | − | 0.977664i | \(-0.432597\pi\) | ||||
0.210173 | + | 0.977664i | \(0.432597\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32102.0 | 1.27956 | 0.639780 | − | 0.768558i | \(-0.279025\pi\) | ||||
0.639780 | + | 0.768558i | \(0.279025\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11060.0 | 0.439304 | 0.219652 | − | 0.975578i | \(-0.429508\pi\) | ||||
0.219652 | + | 0.975578i | \(0.429508\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36088.0 | 1.42346 | 0.711732 | − | 0.702451i | \(-0.247911\pi\) | ||||
0.711732 | + | 0.702451i | \(0.247911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20590.0 | −0.809342 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13192.0 | −0.514969 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5232.00 | −0.203536 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2250.00 | −0.0869302 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34508.0 | −1.32868 | −0.664340 | − | 0.747431i | \(-0.731287\pi\) | ||||
−0.664340 | + | 0.747431i | \(0.731287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6596.00 | 0.252242 | 0.126121 | − | 0.992015i | \(-0.459747\pi\) | ||||
0.126121 | + | 0.992015i | \(0.459747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17620.0 | −0.671529 | −0.335765 | − | 0.941946i | \(-0.608995\pi\) | ||||
−0.335765 | + | 0.941946i | \(0.608995\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50784.0 | −1.92239 | −0.961195 | − | 0.275870i | \(-0.911034\pi\) | ||||
−0.961195 | + | 0.275870i | \(0.911034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15588.0 | 0.588082 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2624.00 | −0.0983301 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8730.00 | −0.326047 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14600.0 | 0.541643 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12852.0 | 0.475208 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6350.00 | 0.233239 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16072.0 | −0.588381 | −0.294191 | − | 0.955747i | \(-0.595050\pi\) | ||||
−0.294191 | + | 0.955747i | \(0.595050\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41760.0 | −1.51874 | −0.759369 | − | 0.650660i | \(-0.774492\pi\) | ||||
−0.759369 | + | 0.650660i | \(0.774492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15096.0 | −0.547212 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37764.0 | −1.35995 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34100.0 | −1.22400 | −0.612000 | − | 0.790858i | \(-0.709635\pi\) | ||||
−0.612000 | + | 0.790858i | \(0.709635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7824.00 | 0.279014 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8200.00 | 0.291475 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22812.0 | 0.805638 | 0.402819 | − | 0.915280i | \(-0.368030\pi\) | ||||
0.402819 | + | 0.915280i | \(0.368030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3116.00 | 0.109691 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17340.0 | −0.606501 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38982.0 | −1.35911 | −0.679555 | − | 0.733624i | \(-0.737827\pi\) | ||||
−0.679555 | + | 0.733624i | \(0.737827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52766.0 | −1.82797 | −0.913986 | − | 0.405745i | \(-0.867012\pi\) | ||||
−0.913986 | + | 0.405745i | \(0.867012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13824.0 | 0.477382 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13608.0 | 0.466949 | 0.233474 | − | 0.972363i | \(-0.424990\pi\) | ||||
0.233474 | + | 0.972363i | \(0.424990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12744.0 | 0.435920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6446.00 | −0.219104 | −0.109552 | − | 0.993981i | \(-0.534942\pi\) | ||||
−0.109552 | + | 0.993981i | \(0.534942\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13380.0 | −0.453368 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15948.0 | −0.537005 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19791.0 | −0.664328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15730.0 | 0.524732 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42642.0 | 1.41807 | 0.709035 | − | 0.705173i | \(-0.249131\pi\) | ||||
0.709035 | + | 0.705173i | \(0.249131\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19938.0 | −0.658950 | −0.329475 | − | 0.944164i | \(-0.606872\pi\) | ||||
−0.329475 | + | 0.944164i | \(0.606872\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9000.00 | 0.296533 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49754.0 | −1.62924 | −0.814622 | − | 0.579992i | \(-0.803056\pi\) | ||||
−0.814622 | + | 0.579992i | \(0.803056\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27880.0 | 0.910162 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7936.00 | 0.257497 | 0.128748 | − | 0.991677i | \(-0.458904\pi\) | ||||
0.128748 | + | 0.991677i | \(0.458904\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18370.0 | −0.594230 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5760.00 | −0.185194 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33248.0 | 1.06575 | 0.532875 | − | 0.846194i | \(-0.321112\pi\) | ||||
0.532875 | + | 0.846194i | \(0.321112\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6960.00 | −0.221756 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20196.0 | −0.641538 | −0.320769 | − | 0.947157i | \(-0.603941\pi\) | ||||
−0.320769 | + | 0.947157i | \(0.603941\pi\) | |||||||
\(998\) | 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 | 720.4.a.m.1.1 | 1 | ||
3.2 | odd | 2 | 720.4.a.z.1.1 | 1 | |||
4.3 | odd | 2 | 360.4.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 360.4.a.j.1.1 | yes | 1 | ||
20.3 | even | 4 | 1800.4.f.e.649.2 | 2 | |||
20.7 | even | 4 | 1800.4.f.e.649.1 | 2 | |||
20.19 | odd | 2 | 1800.4.a.bc.1.1 | 1 | |||
60.23 | odd | 4 | 1800.4.f.s.649.2 | 2 | |||
60.47 | odd | 4 | 1800.4.f.s.649.1 | 2 | |||
60.59 | even | 2 | 1800.4.a.be.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.4.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
360.4.a.j.1.1 | yes | 1 | 12.11 | even | 2 | ||
720.4.a.m.1.1 | 1 | 1.1 | even | 1 | trivial | ||
720.4.a.z.1.1 | 1 | 3.2 | odd | 2 | |||
1800.4.a.bc.1.1 | 1 | 20.19 | odd | 2 | |||
1800.4.a.be.1.1 | 1 | 60.59 | even | 2 | |||
1800.4.f.e.649.1 | 2 | 20.7 | even | 4 | |||
1800.4.f.e.649.2 | 2 | 20.3 | even | 4 | |||
1800.4.f.s.649.1 | 2 | 60.47 | odd | 4 | |||
1800.4.f.s.649.2 | 2 | 60.23 | odd | 4 |