Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,4,Mod(1,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, 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("672.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.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: | \(39.6492835239\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 672.1 |
$q$-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 | ||||||||
\(5\) | −18.0000 | −1.60997 | −0.804984 | − | 0.593296i | \(-0.797826\pi\) | ||||
−0.804984 | + | 0.593296i | \(0.797826\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.0000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 58.0000 | 1.23741 | 0.618704 | − | 0.785624i | \(-0.287658\pi\) | ||||
0.618704 | + | 0.785624i | \(0.287658\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −54.0000 | −0.929516 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −130.000 | −1.85468 | −0.927342 | − | 0.374215i | \(-0.877912\pi\) | ||||
−0.927342 | + | 0.374215i | \(0.877912\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 92.0000 | 1.11086 | 0.555428 | − | 0.831565i | \(-0.312555\pi\) | ||||
0.555428 | + | 0.831565i | \(0.312555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 84.0000 | 0.761531 | 0.380765 | − | 0.924672i | \(-0.375661\pi\) | ||||
0.380765 | + | 0.924672i | \(0.375661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 199.000 | 1.59200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −250.000 | −1.60082 | −0.800411 | − | 0.599452i | \(-0.795385\pi\) | ||||
−0.800411 | + | 0.599452i | \(0.795385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −72.0000 | −0.417148 | −0.208574 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208574 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 132.000 | 0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 126.000 | 0.608511 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −354.000 | −1.57290 | −0.786449 | − | 0.617655i | \(-0.788083\pi\) | ||||
−0.786449 | + | 0.617655i | \(0.788083\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 174.000 | 0.714418 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 334.000 | 1.27224 | 0.636122 | − | 0.771588i | \(-0.280537\pi\) | ||||
0.636122 | + | 0.771588i | \(0.280537\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −416.000 | −1.47534 | −0.737668 | − | 0.675164i | \(-0.764073\pi\) | ||||
−0.737668 | + | 0.675164i | \(0.764073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −162.000 | −0.536656 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −464.000 | −1.44003 | −0.720014 | − | 0.693959i | \(-0.755865\pi\) | ||||
−0.720014 | + | 0.693959i | \(0.755865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −390.000 | −1.07080 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −450.000 | −1.16627 | −0.583134 | − | 0.812376i | \(-0.698174\pi\) | ||||
−0.583134 | + | 0.812376i | \(0.698174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −792.000 | −1.94170 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 276.000 | 0.641353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −516.000 | −1.13860 | −0.569301 | − | 0.822129i | \(-0.692786\pi\) | ||||
−0.569301 | + | 0.822129i | \(0.692786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 58.0000 | 0.121740 | 0.0608700 | − | 0.998146i | \(-0.480612\pi\) | ||||
0.0608700 | + | 0.998146i | \(0.480612\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1044.00 | −1.99219 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −656.000 | −1.19617 | −0.598083 | − | 0.801434i | \(-0.704071\pi\) | ||||
−0.598083 | + | 0.801434i | \(0.704071\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 252.000 | 0.439670 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −940.000 | −1.57123 | −0.785616 | − | 0.618714i | \(-0.787654\pi\) | ||||
−0.785616 | + | 0.618714i | \(0.787654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 178.000 | 0.285388 | 0.142694 | − | 0.989767i | \(-0.454424\pi\) | ||||
0.142694 | + | 0.989767i | \(0.454424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 597.000 | 0.919142 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −308.000 | −0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1072.00 | 1.52670 | 0.763351 | − | 0.645984i | \(-0.223553\pi\) | ||||
0.763351 | + | 0.645984i | \(0.223553\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 660.000 | 0.872824 | 0.436412 | − | 0.899747i | \(-0.356249\pi\) | ||||
0.436412 | + | 0.899747i | \(0.356249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2340.00 | 2.98598 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −750.000 | −0.924235 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1254.00 | 1.49353 | 0.746763 | − | 0.665091i | \(-0.231607\pi\) | ||||
0.746763 | + | 0.665091i | \(0.231607\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −406.000 | −0.467696 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −216.000 | −0.240840 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1656.00 | −1.78844 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 210.000 | 0.219817 | 0.109909 | − | 0.993942i | \(-0.464944\pi\) | ||||
0.109909 | + | 0.993942i | \(0.464944\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 396.000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −186.000 | −0.183244 | −0.0916222 | − | 0.995794i | \(-0.529205\pi\) | ||||
−0.0916222 | + | 0.995794i | \(0.529205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 472.000 | 0.451530 | 0.225765 | − | 0.974182i | \(-0.427512\pi\) | ||||
0.225765 | + | 0.974182i | \(0.427512\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 378.000 | 0.351324 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1212.00 | −1.09503 | −0.547516 | − | 0.836795i | \(-0.684427\pi\) | ||||
−0.547516 | + | 0.836795i | \(0.684427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1386.00 | −1.21793 | −0.608967 | − | 0.793196i | \(-0.708416\pi\) | ||||
−0.608967 | + | 0.793196i | \(0.708416\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1062.00 | −0.908113 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 114.000 | 0.0949046 | 0.0474523 | − | 0.998874i | \(-0.484890\pi\) | ||||
0.0474523 | + | 0.998874i | \(0.484890\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1512.00 | −1.22604 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 522.000 | 0.412469 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 910.000 | 0.701005 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 605.000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1002.00 | 0.734531 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1332.00 | −0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 792.000 | 0.553375 | 0.276688 | − | 0.960960i | \(-0.410763\pi\) | ||||
0.276688 | + | 0.960960i | \(0.410763\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1248.00 | −0.851785 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −428.000 | −0.285454 | −0.142727 | − | 0.989762i | \(-0.545587\pi\) | ||||
−0.142727 | + | 0.989762i | \(0.545587\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −644.000 | −0.419864 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −486.000 | −0.309839 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2238.00 | −1.39566 | −0.697829 | − | 0.716264i | \(-0.745851\pi\) | ||||
−0.697829 | + | 0.716264i | \(0.745851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 300.000 | 0.183062 | 0.0915312 | − | 0.995802i | \(-0.470824\pi\) | ||||
0.0915312 | + | 0.995802i | \(0.470824\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1392.00 | −0.831401 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2552.00 | 1.49237 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4500.00 | 2.57727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1646.00 | 0.905004 | 0.452502 | − | 0.891763i | \(-0.350532\pi\) | ||||
0.452502 | + | 0.891763i | \(0.350532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1184.00 | −0.638096 | −0.319048 | − | 0.947738i | \(-0.603363\pi\) | ||||
−0.319048 | + | 0.947738i | \(0.603363\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1170.00 | −0.618228 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1296.00 | 0.671595 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1150.00 | −0.584586 | −0.292293 | − | 0.956329i | \(-0.594418\pi\) | ||||
−0.292293 | + | 0.956329i | \(0.594418\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1350.00 | −0.673346 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −588.000 | −0.287832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −344.000 | −0.165302 | −0.0826508 | − | 0.996579i | \(-0.526339\pi\) | ||||
−0.0826508 | + | 0.996579i | \(0.526339\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2376.00 | −1.12104 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2304.00 | −1.06760 | −0.533799 | − | 0.845611i | \(-0.679236\pi\) | ||||
−0.533799 | + | 0.845611i | \(0.679236\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1167.00 | 0.531179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 828.000 | 0.370285 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2742.00 | 1.20503 | 0.602516 | − | 0.798107i | \(-0.294165\pi\) | ||||
0.602516 | + | 0.798107i | \(0.294165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1393.00 | −0.601719 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1548.00 | −0.657372 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3940.00 | −1.64519 | −0.822596 | − | 0.568626i | \(-0.807475\pi\) | ||||
−0.822596 | + | 0.568626i | \(0.807475\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1970.00 | 0.809000 | 0.404500 | − | 0.914538i | \(-0.367446\pi\) | ||||
0.404500 | + | 0.914538i | \(0.367446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 174.000 | 0.0702866 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6372.00 | 2.53232 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5720.00 | −2.23683 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −476.000 | −0.180325 | −0.0901627 | − | 0.995927i | \(-0.528739\pi\) | ||||
−0.0901627 | + | 0.995927i | \(0.528739\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −782.000 | −0.291656 | −0.145828 | − | 0.989310i | \(-0.546585\pi\) | ||||
−0.145828 | + | 0.989310i | \(0.546585\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3132.00 | −1.15019 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2066.00 | −0.747190 | −0.373595 | − | 0.927592i | \(-0.621875\pi\) | ||||
−0.373595 | + | 0.927592i | \(0.621875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 768.000 | 0.273578 | 0.136789 | − | 0.990600i | \(-0.456322\pi\) | ||||
0.136789 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1968.00 | −0.690607 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1750.00 | 0.605054 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6012.00 | −2.04827 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 756.000 | 0.253844 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4048.00 | 1.33974 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4248.00 | 1.38599 | 0.692996 | − | 0.720941i | \(-0.256290\pi\) | ||||
0.692996 | + | 0.720941i | \(0.256290\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2820.00 | −0.907151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7488.00 | 2.37524 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 504.000 | 0.157667 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 534.000 | 0.164769 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7540.00 | −2.29500 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3496.00 | −1.04982 | −0.524909 | − | 0.851158i | \(-0.675901\pi\) | ||||
−0.524909 | + | 0.851158i | \(0.675901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1791.00 | 0.530667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5620.00 | −1.64323 | −0.821613 | − | 0.570045i | \(-0.806926\pi\) | ||||
−0.821613 | + | 0.570045i | \(0.806926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1982.00 | −0.571940 | −0.285970 | − | 0.958239i | \(-0.592316\pi\) | ||||
−0.285970 | + | 0.958239i | \(0.592316\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −924.000 | −0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1342.00 | −0.377328 | −0.188664 | − | 0.982042i | \(-0.560416\pi\) | ||||
−0.188664 | + | 0.982042i | \(0.560416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8352.00 | 2.31840 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3216.00 | 0.881442 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2828.00 | −0.765390 | −0.382695 | − | 0.923875i | \(-0.625004\pi\) | ||||
−0.382695 | + | 0.923875i | \(0.625004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2002.00 | 0.535104 | 0.267552 | − | 0.963543i | \(-0.413785\pi\) | ||||
0.267552 | + | 0.963543i | \(0.413785\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −882.000 | −0.229996 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5336.00 | 1.37458 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1980.00 | 0.503925 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1188.00 | 0.298749 | 0.149374 | − | 0.988781i | \(-0.452274\pi\) | ||||
0.149374 | + | 0.988781i | \(0.452274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3696.00 | 0.918441 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7020.00 | 1.72396 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5506.00 | −1.33640 | −0.668200 | − | 0.743982i | \(-0.732935\pi\) | ||||
−0.668200 | + | 0.743982i | \(0.732935\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2478.00 | 0.594500 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2250.00 | −0.533607 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4076.00 | 0.955654 | 0.477827 | − | 0.878454i | \(-0.341425\pi\) | ||||
0.477827 | + | 0.878454i | \(0.341425\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8100.00 | 1.87766 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3762.00 | 0.862287 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5938.00 | −1.34590 | −0.672948 | − | 0.739689i | \(-0.734972\pi\) | ||||
−0.672948 | + | 0.739689i | \(0.734972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 592.000 | 0.132699 | 0.0663495 | − | 0.997796i | \(-0.478865\pi\) | ||||
0.0663495 | + | 0.997796i | \(0.478865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1218.00 | −0.270025 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8756.00 | 1.92002 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5254.00 | 1.13965 | 0.569824 | − | 0.821767i | \(-0.307012\pi\) | ||||
0.569824 | + | 0.821767i | \(0.307012\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −648.000 | −0.139049 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3410.00 | 0.723927 | 0.361964 | − | 0.932192i | \(-0.382106\pi\) | ||||
0.361964 | + | 0.932192i | \(0.382106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2212.00 | −0.464628 | −0.232314 | − | 0.972641i | \(-0.574630\pi\) | ||||
−0.232314 | + | 0.972641i | \(0.574630\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4968.00 | −1.03256 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2338.00 | −0.480863 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11987.0 | 2.43985 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 630.000 | 0.126912 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2122.00 | −0.423101 | −0.211550 | − | 0.977367i | \(-0.567851\pi\) | ||||
−0.211550 | + | 0.977367i | \(0.567851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9288.00 | 1.83311 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1188.00 | 0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4872.00 | 0.942325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2912.00 | 0.557624 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −558.000 | −0.105796 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1044.00 | −0.195998 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2588.00 | 0.481124 | 0.240562 | − | 0.970634i | \(-0.422668\pi\) | ||||
0.240562 | + | 0.970634i | \(0.422668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1416.00 | 0.260691 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2728.00 | 0.497398 | 0.248699 | − | 0.968581i | \(-0.419997\pi\) | ||||
0.248699 | + | 0.968581i | \(0.419997\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6446.00 | −1.16406 | −0.582028 | − | 0.813169i | \(-0.697741\pi\) | ||||
−0.582028 | + | 0.813169i | \(0.697741\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1134.00 | 0.202837 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4234.00 | −0.750174 | −0.375087 | − | 0.926990i | \(-0.622387\pi\) | ||||
−0.375087 | + | 0.926990i | \(0.622387\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11000.0 | −1.93066 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3636.00 | −0.632217 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11960.0 | −2.06029 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11542.0 | 1.96995 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4158.00 | −0.703174 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3248.00 | 0.544280 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4592.00 | −0.762535 | −0.381268 | − | 0.924465i | \(-0.624512\pi\) | ||||
−0.381268 | + | 0.924465i | \(0.624512\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3186.00 | −0.524299 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11808.0 | 1.92579 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1006.00 | −0.162612 | −0.0813061 | − | 0.996689i | \(-0.525909\pi\) | ||||
−0.0813061 | + | 0.996689i | \(0.525909\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 342.000 | 0.0547932 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3168.00 | −0.503099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4536.00 | −0.707855 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4644.00 | 0.718452 | 0.359226 | − | 0.933251i | \(-0.383041\pi\) | ||||
0.359226 | + | 0.933251i | \(0.383041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4786.00 | 0.734065 | 0.367033 | − | 0.930208i | \(-0.380374\pi\) | ||||
0.367033 | + | 0.930208i | \(0.380374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1566.00 | 0.238139 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1302.00 | 0.196313 | 0.0981565 | − | 0.995171i | \(-0.468705\pi\) | ||||
0.0981565 | + | 0.995171i | \(0.468705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16920.0 | 2.52963 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2730.00 | 0.404725 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11260.0 | 1.65538 | 0.827688 | − | 0.561188i | \(-0.189656\pi\) | ||||
0.827688 | + | 0.561188i | \(0.189656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1815.00 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3204.00 | −0.459466 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2792.00 | 0.397115 | 0.198558 | − | 0.980089i | \(-0.436374\pi\) | ||||
0.198558 | + | 0.980089i | \(0.436374\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3006.00 | 0.424082 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3150.00 | 0.440808 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4118.00 | 0.571641 | 0.285820 | − | 0.958283i | \(-0.407734\pi\) | ||||
0.285820 | + | 0.958283i | \(0.407734\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3996.00 | −0.550273 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14500.0 | −1.98087 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8624.00 | 1.16883 | 0.584413 | − | 0.811456i | \(-0.301325\pi\) | ||||
0.584413 | + | 0.811456i | \(0.301325\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2376.00 | 0.319491 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6488.00 | 0.865591 | 0.432795 | − | 0.901492i | \(-0.357527\pi\) | ||||
0.432795 | + | 0.901492i | \(0.357527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5544.00 | 0.733892 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3744.00 | −0.491778 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1406.00 | 0.183257 | 0.0916286 | − | 0.995793i | \(-0.470793\pi\) | ||||
0.0916286 | + | 0.995793i | \(0.470793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10920.0 | −1.41240 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1284.00 | −0.164807 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19296.0 | −2.45794 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9378.00 | 1.18556 | 0.592781 | − | 0.805363i | \(-0.298030\pi\) | ||||
0.592781 | + | 0.805363i | \(0.298030\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1932.00 | −0.242408 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2890.00 | 0.359900 | 0.179950 | − | 0.983676i | \(-0.442406\pi\) | ||||
0.179950 | + | 0.983676i | \(0.442406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4176.00 | −0.516182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1458.00 | −0.178885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15576.0 | −1.89699 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10582.0 | −1.27933 | −0.639665 | − | 0.768654i | \(-0.720927\pi\) | ||||
−0.639665 | + | 0.768654i | \(0.720927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6714.00 | −0.805784 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3612.00 | 0.430351 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11880.0 | −1.40522 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 900.000 | 0.105691 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9500.00 | −1.10765 | −0.553825 | − | 0.832633i | \(-0.686832\pi\) | ||||
−0.553825 | + | 0.832633i | \(0.686832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 598.000 | 0.0692274 | 0.0346137 | − | 0.999401i | \(-0.488980\pi\) | ||||
0.0346137 | + | 0.999401i | \(0.488980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4176.00 | −0.480010 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25870.0 | −2.95266 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −406.000 | −0.0460134 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7656.00 | 0.861620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3708.00 | 0.414404 | 0.207202 | − | 0.978298i | \(-0.433564\pi\) | ||||
0.207202 | + | 0.978298i | \(0.433564\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13706.0 | 1.52117 | 0.760587 | − | 0.649236i | \(-0.224911\pi\) | ||||
0.760587 | + | 0.649236i | \(0.224911\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13500.0 | 1.48799 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7728.00 | 0.845951 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8232.00 | −0.894970 | −0.447485 | − | 0.894291i | \(-0.647680\pi\) | ||||
−0.447485 | + | 0.894291i | \(0.647680\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2524.00 | 0.270697 | 0.135349 | − | 0.990798i | \(-0.456785\pi\) | ||||
0.135349 | + | 0.990798i | \(0.456785\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22572.0 | −2.40453 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4938.00 | 0.522504 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3630.00 | −0.381537 | −0.190769 | − | 0.981635i | \(-0.561098\pi\) | ||||
−0.190769 | + | 0.981635i | \(0.561098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14696.0 | 1.53438 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3552.00 | −0.368405 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7308.00 | 0.752977 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5386.00 | 0.551305 | 0.275653 | − | 0.961257i | \(-0.411106\pi\) | ||||
0.275653 | + | 0.961257i | \(0.411106\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3510.00 | −0.356934 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11766.0 | 1.18871 | 0.594357 | − | 0.804201i | \(-0.297407\pi\) | ||||
0.594357 | + | 0.804201i | \(0.297407\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10240.0 | −1.02785 | −0.513923 | − | 0.857836i | \(-0.671808\pi\) | ||||
−0.513923 | + | 0.857836i | \(0.671808\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3888.00 | 0.387746 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6076.00 | 0.602064 | 0.301032 | − | 0.953614i | \(-0.402669\pi\) | ||||
0.301032 | + | 0.953614i | \(0.402669\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4592.00 | 0.452108 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3450.00 | −0.337511 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18304.0 | −1.77932 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18308.0 | 1.76848 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4050.00 | −0.388756 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6480.00 | 0.618118 | 0.309059 | − | 0.951043i | \(-0.399986\pi\) | ||||
0.309059 | + | 0.951043i | \(0.399986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20532.0 | −1.94632 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1764.00 | −0.166180 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3780.00 | −0.353899 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4240.00 | 0.394523 | 0.197262 | − | 0.980351i | \(-0.436795\pi\) | ||||
0.197262 | + | 0.980351i | \(0.436795\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1032.00 | −0.0954369 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17892.0 | −1.64451 | −0.822255 | − | 0.569119i | \(-0.807284\pi\) | ||||
−0.822255 | + | 0.569119i | \(0.807284\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32500.0 | 2.96902 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7128.00 | −0.647232 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6580.00 | 0.593870 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4616.00 | −0.414109 | −0.207055 | − | 0.978329i | \(-0.566388\pi\) | ||||
−0.207055 | + | 0.978329i | \(0.566388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6912.00 | −0.616378 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3696.00 | 0.327627 | 0.163814 | − | 0.986491i | \(-0.447620\pi\) | ||||
0.163814 | + | 0.986491i | \(0.447620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3348.00 | 0.295018 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3501.00 | 0.306676 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16738.0 | −1.45756 | −0.728781 | − | 0.684747i | \(-0.759913\pi\) | ||||
−0.728781 | + | 0.684747i | \(0.759913\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1246.00 | −0.107867 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2484.00 | 0.213784 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8496.00 | −0.726949 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20416.0 | −1.73674 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8226.00 | 0.695725 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19062.0 | 1.60292 | 0.801460 | − | 0.598048i | \(-0.204057\pi\) | ||||
0.801460 | + | 0.598048i | \(0.204057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12268.0 | −1.02570 | −0.512851 | − | 0.858478i | \(-0.671411\pi\) | ||||
−0.512851 | + | 0.858478i | \(0.671411\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4179.00 | −0.347403 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9360.00 | 0.773677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5111.00 | −0.420071 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4644.00 | −0.379534 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19372.0 | 1.57429 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21816.0 | 1.76297 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11820.0 | −0.949852 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2156.00 | 0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17042.0 | −1.35433 | −0.677165 | − | 0.735831i | \(-0.736792\pi\) | ||||
−0.677165 | + | 0.735831i | \(0.736792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5910.00 | 0.467076 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24948.0 | 1.96083 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3656.00 | −0.285776 | −0.142888 | − | 0.989739i | \(-0.545639\pi\) | ||||
−0.142888 | + | 0.989739i | \(0.545639\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 522.000 | 0.0405800 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23000.0 | −1.77828 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7504.00 | −0.577039 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19116.0 | 1.46203 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14038.0 | 1.06788 | 0.533940 | − | 0.845522i | \(-0.320711\pi\) | ||||
0.533940 | + | 0.845522i | \(0.320711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24128.0 | −1.82559 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17160.0 | −1.29144 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18332.0 | −1.37229 | −0.686147 | − | 0.727463i | \(-0.740699\pi\) | ||||
−0.686147 | + | 0.727463i | \(0.740699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2052.00 | −0.152793 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10046.0 | −0.740159 | −0.370079 | − | 0.929000i | \(-0.620669\pi\) | ||||
−0.370079 | + | 0.929000i | \(0.620669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5704.00 | −0.418047 | −0.209024 | − | 0.977911i | \(-0.567029\pi\) | ||||
−0.209024 | + | 0.977911i | \(0.567029\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1428.00 | −0.104111 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16716.0 | 1.21236 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24610.0 | 1.77561 | 0.887806 | − | 0.460219i | \(-0.152229\pi\) | ||||
0.887806 | + | 0.460219i | \(0.152229\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2346.00 | −0.168388 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4620.00 | −0.329897 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19800.0 | −1.40657 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9396.00 | −0.664063 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18516.0 | 1.30194 | 0.650969 | − | 0.759105i | \(-0.274363\pi\) | ||||
0.650969 | + | 0.759105i | \(0.274363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6624.00 | −0.463391 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6198.00 | −0.431390 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20038.0 | 1.38763 | 0.693813 | − | 0.720155i | \(-0.255929\pi\) | ||||
0.693813 | + | 0.720155i | \(0.255929\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16380.0 | −1.12860 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2304.00 | 0.157950 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2596.00 | 0.177078 | 0.0885390 | − | 0.996073i | \(-0.471780\pi\) | ||||
0.0885390 | + | 0.996073i | \(0.471780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5190.00 | −0.352254 | −0.176127 | − | 0.984367i | \(-0.556357\pi\) | ||||
−0.176127 | + | 0.984367i | \(0.556357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5904.00 | −0.398722 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10890.0 | −0.731804 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6536.00 | 0.437048 | 0.218524 | − | 0.975832i | \(-0.429876\pi\) | ||||
0.218524 | + | 0.975832i | \(0.429876\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5250.00 | 0.349328 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26912.0 | −1.78190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4702.00 | 0.309807 | 0.154904 | − | 0.987930i | \(-0.450493\pi\) | ||||
0.154904 | + | 0.987930i | \(0.450493\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18036.0 | −1.18257 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8638.00 | −0.563619 | −0.281809 | − | 0.959470i | \(-0.590935\pi\) | ||||
−0.281809 | + | 0.959470i | \(0.590935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19676.0 | −1.27762 | −0.638809 | − | 0.769366i | \(-0.720572\pi\) | ||||
−0.638809 | + | 0.769366i | \(0.720572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2268.00 | 0.146557 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8778.00 | −0.564499 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −899.000 | −0.0575360 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12144.0 | 0.773500 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 46020.0 | 2.91723 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26720.0 | 1.68575 | 0.842874 | − | 0.538112i | \(-0.180862\pi\) | ||||
0.842874 | + | 0.538112i | \(0.180862\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12744.0 | 0.800203 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14256.0 | −0.890917 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2842.00 | 0.176773 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8460.00 | −0.523744 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1990.00 | −0.122621 | −0.0613107 | − | 0.998119i | \(-0.519528\pi\) | ||||
−0.0613107 | + | 0.998119i | \(0.519528\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6956.00 | −0.426622 | −0.213311 | − | 0.976984i | \(-0.568425\pi\) | ||||
−0.213311 | + | 0.976984i | \(0.568425\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22464.0 | 1.37135 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15984.0 | −0.971246 | −0.485623 | − | 0.874168i | \(-0.661407\pi\) | ||||
−0.485623 | + | 0.874168i | \(0.661407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22704.0 | −1.37320 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1512.00 | 0.0910291 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6614.00 | 0.396364 | 0.198182 | − | 0.980165i | \(-0.436496\pi\) | ||||
0.198182 | + | 0.980165i | \(0.436496\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7704.00 | 0.459573 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1602.00 | 0.0951293 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29364.0 | −1.73575 | −0.867875 | − | 0.496783i | \(-0.834515\pi\) | ||||
−0.867875 | + | 0.496783i | \(0.834515\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3150.00 | −0.185357 | −0.0926784 | − | 0.995696i | \(-0.529543\pi\) | ||||
−0.0926784 | + | 0.995696i | \(0.529543\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22620.0 | −1.32502 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11592.0 | 0.675968 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21000.0 | −1.21908 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10488.0 | −0.606113 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2552.00 | 0.146824 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8402.00 | 0.481238 | 0.240619 | − | 0.970620i | \(-0.422650\pi\) | ||||
0.240619 | + | 0.970620i | \(0.422650\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5373.00 | 0.306381 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7854.00 | 0.445870 | 0.222935 | − | 0.974833i | \(-0.428436\pi\) | ||||
0.222935 | + | 0.974833i | \(0.428436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1470.00 | −0.0830831 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16860.0 | −0.948717 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14244.0 | −0.797996 | −0.398998 | − | 0.916952i | \(-0.630642\pi\) | ||||
−0.398998 | + | 0.916952i | \(0.630642\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40284.0 | 2.24697 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5946.00 | −0.330210 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26100.0 | −1.44315 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22420.0 | 1.23429 | 0.617147 | − | 0.786848i | \(-0.288288\pi\) | ||||
0.617147 | + | 0.786848i | \(0.288288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2772.00 | −0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5400.00 | −0.294725 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43420.0 | −2.35961 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4026.00 | −0.217850 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19814.0 | 1.06757 | 0.533783 | − | 0.845621i | \(-0.320770\pi\) | ||||
0.533783 | + | 0.845621i | \(0.320770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32568.0 | −1.74726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25056.0 | 1.33853 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1302.00 | 0.0692599 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15986.0 | −0.846780 | −0.423390 | − | 0.905948i | \(-0.639160\pi\) | ||||
−0.423390 | + | 0.905948i | \(0.639160\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9648.00 | 0.508901 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6048.00 | −0.317671 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45936.0 | −2.40267 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8484.00 | −0.441898 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22440.0 | 1.16394 | 0.581969 | − | 0.813211i | \(-0.302283\pi\) | ||||
0.581969 | + | 0.813211i | \(0.302283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3304.00 | −0.170662 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6006.00 | 0.308943 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −49750.0 | −2.54851 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10264.0 | 0.523619 | 0.261809 | − | 0.965120i | \(-0.415681\pi\) | ||||
0.261809 | + | 0.965120i | \(0.415681\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54080.0 | 2.73628 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9282.00 | 0.467720 | 0.233860 | − | 0.972270i | \(-0.424864\pi\) | ||||
0.233860 | + | 0.972270i | \(0.424864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2646.00 | −0.132788 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28864.0 | −1.44263 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12792.0 | 0.636754 | 0.318377 | − | 0.947964i | \(-0.396862\pi\) | ||||
0.318377 | + | 0.947964i | \(0.396862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16008.0 | 0.793615 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25644.0 | 1.26620 | 0.633100 | − | 0.774070i | \(-0.281782\pi\) | ||||
0.633100 | + | 0.774070i | \(0.281782\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29628.0 | −1.45703 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5940.00 | 0.290941 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8484.00 | 0.413883 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4528.00 | −0.220012 | −0.110006 | − | 0.993931i | \(-0.535087\pi\) | ||||
−0.110006 | + | 0.993931i | \(0.535087\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3564.00 | 0.172483 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21312.0 | 1.02732 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31310.0 | 1.50328 | 0.751639 | − | 0.659575i | \(-0.229264\pi\) | ||||
0.751639 | + | 0.659575i | \(0.229264\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11088.0 | 0.530262 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16622.0 | 0.791783 | 0.395892 | − | 0.918297i | \(-0.370436\pi\) | ||||
0.395892 | + | 0.918297i | \(0.370436\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9702.00 | 0.460335 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21060.0 | 0.995328 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29928.0 | −1.40891 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9814.00 | −0.460211 | −0.230105 | − | 0.973166i | \(-0.573907\pi\) | ||||
−0.230105 | + | 0.973166i | \(0.573907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16518.0 | −0.771571 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7686.00 | 0.357628 | 0.178814 | − | 0.983883i | \(-0.442774\pi\) | ||||
0.178814 | + | 0.983883i | \(0.442774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14328.0 | −0.664099 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7434.00 | 0.343235 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30728.0 | 1.41328 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41360.0 | −1.89498 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6750.00 | −0.308078 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20700.0 | 0.941165 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5860.00 | 0.265421 | 0.132711 | − | 0.991155i | \(-0.457632\pi\) | ||||
0.132711 | + | 0.991155i | \(0.457632\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12228.0 | 0.551747 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −798.000 | −0.0358706 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3364.00 | 0.150642 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24300.0 | 1.08407 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15450.0 | −0.686659 | −0.343329 | − | 0.939215i | \(-0.611555\pi\) | ||||
−0.343329 | + | 0.939215i | \(0.611555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60320.0 | 2.67080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11286.0 | 0.497842 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7832.00 | 0.344191 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10584.0 | 0.463400 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17814.0 | −0.777054 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26726.0 | −1.16148 | −0.580739 | − | 0.814090i | \(-0.697236\pi\) | ||||
−0.580739 | + | 0.814090i | \(0.697236\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3052.00 | −0.132146 | −0.0660729 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660729 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1776.00 | 0.0766138 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6192.00 | 0.266130 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38272.0 | −1.63888 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3654.00 | −0.155899 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23838.0 | 1.01334 | 0.506670 | − | 0.862140i | \(-0.330876\pi\) | ||||
0.506670 | + | 0.862140i | \(0.330876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19136.0 | 0.810497 | 0.405248 | − | 0.914207i | \(-0.367185\pi\) | ||||
0.405248 | + | 0.914207i | \(0.367185\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26268.0 | 1.10853 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32556.0 | −1.36890 | −0.684452 | − | 0.729058i | \(-0.739958\pi\) | ||||
−0.684452 | + | 0.729058i | \(0.739958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33086.0 | −1.38616 | −0.693079 | − | 0.720862i | \(-0.743746\pi\) | ||||
−0.693079 | + | 0.720862i | \(0.743746\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15762.0 | 0.657976 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6370.00 | −0.264955 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41472.0 | 1.71880 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1944.00 | −0.0802801 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35248.0 | 1.45041 | 0.725206 | − | 0.688532i | \(-0.241744\pi\) | ||||
0.725206 | + | 0.688532i | \(0.241744\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38111.0 | 1.56263 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10230.0 | 0.417960 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21006.0 | −0.855182 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4235.00 | −0.171802 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6636.00 | −0.268253 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29736.0 | −1.19781 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8922.00 | 0.358128 | 0.179064 | − | 0.983837i | \(-0.442693\pi\) | ||||
0.179064 | + | 0.983837i | \(0.442693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14904.0 | −0.596147 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28126.0 | 1.12108 | 0.560540 | − | 0.828127i | \(-0.310594\pi\) | ||||
0.560540 | + | 0.828127i | \(0.310594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28916.0 | 1.14855 | 0.574273 | − | 0.818664i | \(-0.305285\pi\) | ||||
0.574273 | + | 0.818664i | \(0.305285\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7014.00 | −0.277627 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22308.0 | −0.879923 | −0.439961 | − | 0.898017i | \(-0.645008\pi\) | ||||
−0.439961 | + | 0.898017i | \(0.645008\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49356.0 | −1.94006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35961.0 | 1.40865 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47168.0 | 1.84127 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38048.0 | −1.48015 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1890.00 | 0.0732724 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9324.00 | 0.360239 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34970.0 | −1.34647 | −0.673234 | − | 0.739429i | \(-0.735095\pi\) | ||||
−0.673234 | + | 0.739429i | \(0.735095\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6366.00 | −0.244277 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −858.000 | −0.0328113 | −0.0164056 | − | 0.999865i | \(-0.505222\pi\) | ||||
−0.0164056 | + | 0.999865i | \(0.505222\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24088.0 | 0.918036 | 0.459018 | − | 0.888427i | \(-0.348201\pi\) | ||||
0.459018 | + | 0.888427i | \(0.348201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27864.0 | 1.05835 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30960.0 | −1.17197 | −0.585984 | − | 0.810323i | \(-0.699292\pi\) | ||||
−0.585984 | + | 0.810323i | \(0.699292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5544.00 | −0.209156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3564.00 | 0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42688.0 | −1.59966 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 70920.0 | 2.64871 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14616.0 | 0.544051 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18000.0 | 0.667779 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58500.0 | 2.16306 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8736.00 | 0.321944 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35460.0 | −1.30246 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37048.0 | −1.35629 | −0.678147 | − | 0.734926i | \(-0.737217\pi\) | ||||
−0.678147 | + | 0.734926i | \(0.737217\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1674.00 | −0.0610815 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25228.0 | 0.917498 | 0.458749 | − | 0.888566i | \(-0.348298\pi\) | ||||
0.458749 | + | 0.888566i | \(0.348298\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29040.0 | 1.05267 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3132.00 | −0.113159 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2996.00 | 0.107892 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19336.0 | −0.694054 | −0.347027 | − | 0.937855i | \(-0.612809\pi\) | ||||
−0.347027 | + | 0.937855i | \(0.612809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7764.00 | 0.277777 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54520.0 | −1.94426 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −70446.0 | −2.50405 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4248.00 | 0.150510 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11926.0 | 0.421183 | 0.210592 | − | 0.977574i | \(-0.432461\pi\) | ||||
0.210592 | + | 0.977574i | \(0.432461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4508.00 | 0.158694 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8184.00 | 0.287173 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 102960. | 3.60123 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4698.00 | 0.163796 | 0.0818981 | − | 0.996641i | \(-0.473902\pi\) | ||||
0.0818981 | + | 0.996641i | \(0.473902\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19338.0 | −0.672068 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12986.0 | −0.449874 | −0.224937 | − | 0.974373i | \(-0.572218\pi\) | ||||
−0.224937 | + | 0.974373i | \(0.572218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28056.0 | 0.968854 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3402.00 | 0.117108 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17972.0 | −0.616696 | −0.308348 | − | 0.951274i | \(-0.599776\pi\) | ||||
−0.308348 | + | 0.951274i | \(0.599776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10324.0 | 0.353141 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12702.0 | −0.433113 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5414.00 | −0.184026 | −0.0920129 | − | 0.995758i | \(-0.529330\pi\) | ||||
−0.0920129 | + | 0.995758i | \(0.529330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8568.00 | 0.290318 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −33000.0 | −1.11467 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15666.0 | 0.527509 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24607.0 | −0.825988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10908.0 | −0.365011 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14076.0 | 0.469557 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57496.0 | −1.91204 | −0.956022 | − | 0.293295i | \(-0.905248\pi\) | ||||
−0.956022 | + | 0.293295i | \(0.905248\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35880.0 | −1.18951 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36812.0 | −1.21664 | −0.608318 | − | 0.793693i | \(-0.708155\pi\) | ||||
−0.608318 | + | 0.793693i | \(0.708155\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2100.00 | −0.0691911 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 34626.0 | 1.13735 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26442.0 | 0.865870 | 0.432935 | − | 0.901425i | \(-0.357478\pi\) | ||||
0.432935 | + | 0.901425i | \(0.357478\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 55176.0 | 1.80126 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12474.0 | −0.405978 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35240.0 | 1.14342 | 0.571710 | − | 0.820456i | \(-0.306280\pi\) | ||||
0.571710 | + | 0.820456i | \(0.306280\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37188.0 | 1.20295 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9744.00 | 0.314240 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34944.0 | −1.12351 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36472.0 | −1.16909 | −0.584547 | − | 0.811360i | \(-0.698728\pi\) | ||||
−0.584547 | + | 0.811360i | \(0.698728\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13776.0 | −0.440250 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13824.0 | −0.440453 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25090.0 | 0.796999 | 0.398500 | − | 0.917168i | \(-0.369531\pi\) | ||||
0.398500 | + | 0.917168i | \(0.369531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9558.00 | −0.302704 |
(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 | 672.4.a.c.1.1 | yes | 1 | |
3.2 | odd | 2 | 2016.4.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 672.4.a.a.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 1344.4.a.bb.1.1 | 1 | |||
8.5 | even | 2 | 1344.4.a.m.1.1 | 1 | |||
12.11 | even | 2 | 2016.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
672.4.a.c.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
1344.4.a.m.1.1 | 1 | 8.5 | even | 2 | |||
1344.4.a.bb.1.1 | 1 | 8.3 | odd | 2 | |||
2016.4.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
2016.4.a.f.1.1 | 1 | 12.11 | even | 2 |