Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.6525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.c.649.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 34.0000i | 1.83583i | 0.396780 | + | 0.917914i | \(0.370128\pi\) | ||||
−0.396780 | + | 0.917914i | \(0.629872\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −48.0000 | −1.31569 | −0.657843 | − | 0.753155i | \(-0.728531\pi\) | ||||
−0.657843 | + | 0.753155i | \(0.728531\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 70.0000i | − 1.49342i | −0.665148 | − | 0.746712i | \(-0.731631\pi\) | ||||
0.665148 | − | 0.746712i | \(-0.268369\pi\) | |||||||
\(14\) | 68.0000 | 1.29813 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 27.0000i | 0.385204i | 0.981277 | + | 0.192602i | \(0.0616926\pi\) | ||||
−0.981277 | + | 0.192602i | \(0.938307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −119.000 | −1.43687 | −0.718433 | − | 0.695596i | \(-0.755141\pi\) | ||||
−0.718433 | + | 0.695596i | \(0.755141\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 96.0000i | 0.930330i | ||||||||
\(23\) | − 51.0000i | − 0.462358i | −0.972911 | − | 0.231179i | \(-0.925742\pi\) | ||||
0.972911 | − | 0.231179i | \(-0.0742583\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −140.000 | −1.05601 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 136.000i | − 0.917914i | ||||||||
\(29\) | 30.0000 | 0.192099 | 0.0960493 | − | 0.995377i | \(-0.469379\pi\) | ||||
0.0960493 | + | 0.995377i | \(0.469379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −133.000 | −0.770565 | −0.385282 | − | 0.922799i | \(-0.625896\pi\) | ||||
−0.385282 | + | 0.922799i | \(0.625896\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 54.0000 | 0.272380 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 218.000i | − 0.968621i | −0.874896 | − | 0.484311i | \(-0.839070\pi\) | ||||
0.874896 | − | 0.484311i | \(-0.160930\pi\) | |||||||
\(38\) | 238.000i | 1.01602i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 156.000 | 0.594222 | 0.297111 | − | 0.954843i | \(-0.403977\pi\) | ||||
0.297111 | + | 0.954843i | \(0.403977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 88.0000i | − 0.312090i | −0.987750 | − | 0.156045i | \(-0.950125\pi\) | ||||
0.987750 | − | 0.156045i | \(-0.0498745\pi\) | |||||||
\(44\) | 192.000 | 0.657843 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −102.000 | −0.326937 | ||||||||
\(47\) | 516.000i | 1.60141i | 0.599058 | + | 0.800706i | \(0.295542\pi\) | ||||
−0.599058 | + | 0.800706i | \(0.704458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −813.000 | −2.37026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 280.000i | 0.746712i | ||||||||
\(53\) | − 639.000i | − 1.65610i | −0.560653 | − | 0.828051i | \(-0.689450\pi\) | ||||
0.560653 | − | 0.828051i | \(-0.310550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −272.000 | −0.649063 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 60.0000i | − 0.135834i | ||||||||
\(59\) | 654.000 | 1.44311 | 0.721555 | − | 0.692357i | \(-0.243427\pi\) | ||||
0.721555 | + | 0.692357i | \(0.243427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 461.000 | 0.967623 | 0.483811 | − | 0.875172i | \(-0.339252\pi\) | ||||
0.483811 | + | 0.875172i | \(0.339252\pi\) | |||||||
\(62\) | 266.000i | 0.544872i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 182.000i | − 0.331863i | −0.986137 | − | 0.165932i | \(-0.946937\pi\) | ||||
0.986137 | − | 0.165932i | \(-0.0530631\pi\) | |||||||
\(68\) | − 108.000i | − 0.192602i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 900.000 | 1.50437 | 0.752186 | − | 0.658951i | \(-0.229000\pi\) | ||||
0.752186 | + | 0.658951i | \(0.229000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 704.000i | 1.12873i | 0.825527 | + | 0.564363i | \(0.190878\pi\) | ||||
−0.825527 | + | 0.564363i | \(0.809122\pi\) | |||||||
\(74\) | −436.000 | −0.684919 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 476.000 | 0.718433 | ||||||||
\(77\) | − 1632.00i | − 2.41537i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1375.00 | 1.95822 | 0.979111 | − | 0.203325i | \(-0.0651748\pi\) | ||||
0.979111 | + | 0.203325i | \(0.0651748\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 312.000i | − 0.420178i | ||||||||
\(83\) | 915.000i | 1.21005i | 0.796206 | + | 0.605026i | \(0.206837\pi\) | ||||
−0.796206 | + | 0.605026i | \(0.793163\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −176.000 | −0.220681 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 384.000i | − 0.465165i | ||||||||
\(89\) | 1116.00 | 1.32917 | 0.664583 | − | 0.747215i | \(-0.268609\pi\) | ||||
0.664583 | + | 0.747215i | \(0.268609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2380.00 | 2.74167 | ||||||||
\(92\) | 204.000i | 0.231179i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1032.00 | 1.13237 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0000i | 0.0167480i | 0.999965 | + | 0.00837399i | \(0.00266555\pi\) | ||||
−0.999965 | + | 0.00837399i | \(0.997334\pi\) | |||||||
\(98\) | 1626.00i | 1.67603i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 348.000 | 0.342844 | 0.171422 | − | 0.985198i | \(-0.445164\pi\) | ||||
0.171422 | + | 0.985198i | \(0.445164\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 412.000i | − 0.394132i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) | ||||
0.980390 | − | 0.197066i | \(-0.0631413\pi\) | |||||||
\(104\) | 560.000 | 0.528005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1278.00 | −1.17104 | ||||||||
\(107\) | 900.000i | 0.813143i | 0.913619 | + | 0.406571i | \(0.133276\pi\) | ||||
−0.913619 | + | 0.406571i | \(0.866724\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 115.000 | 0.101055 | 0.0505275 | − | 0.998723i | \(-0.483910\pi\) | ||||
0.0505275 | + | 0.998723i | \(0.483910\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 544.000i | 0.458957i | ||||||||
\(113\) | 966.000i | 0.804191i | 0.915598 | + | 0.402096i | \(0.131718\pi\) | ||||
−0.915598 | + | 0.402096i | \(0.868282\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −120.000 | −0.0960493 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 1308.00i | − 1.02043i | ||||||||
\(119\) | −918.000 | −0.707167 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 973.000 | 0.731029 | ||||||||
\(122\) | − 922.000i | − 0.684213i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 532.000 | 0.385282 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1406.00i | − 0.982381i | −0.871052 | − | 0.491190i | \(-0.836562\pi\) | ||||
0.871052 | − | 0.491190i | \(-0.163438\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 246.000 | 0.164070 | 0.0820348 | − | 0.996629i | \(-0.473858\pi\) | ||||
0.0820348 | + | 0.996629i | \(0.473858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4046.00i | − 2.63784i | ||||||||
\(134\) | −364.000 | −0.234663 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −216.000 | −0.136190 | ||||||||
\(137\) | − 519.000i | − 0.323658i | −0.986819 | − | 0.161829i | \(-0.948261\pi\) | ||||
0.986819 | − | 0.161829i | \(-0.0517393\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1316.00 | −0.803034 | −0.401517 | − | 0.915852i | \(-0.631517\pi\) | ||||
−0.401517 | + | 0.915852i | \(0.631517\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 1800.00i | − 1.06375i | ||||||||
\(143\) | 3360.00i | 1.96488i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1408.00 | 0.798130 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 872.000i | 0.484311i | ||||||||
\(149\) | −372.000 | −0.204533 | −0.102267 | − | 0.994757i | \(-0.532609\pi\) | ||||
−0.102267 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1456.00 | −0.784686 | −0.392343 | − | 0.919819i | \(-0.628335\pi\) | ||||
−0.392343 | + | 0.919819i | \(0.628335\pi\) | |||||||
\(152\) | − 952.000i | − 0.508009i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3264.00 | −1.70793 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 956.000i | − 0.485969i | −0.970030 | − | 0.242984i | \(-0.921874\pi\) | ||||
0.970030 | − | 0.242984i | \(-0.0781264\pi\) | |||||||
\(158\) | − 2750.00i | − 1.38467i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1734.00 | 0.848810 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2446.00i | − 1.17537i | −0.809089 | − | 0.587686i | \(-0.800039\pi\) | ||||
0.809089 | − | 0.587686i | \(-0.199961\pi\) | |||||||
\(164\) | −624.000 | −0.297111 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1830.00 | 0.855636 | ||||||||
\(167\) | 3111.00i | 1.44154i | 0.693177 | + | 0.720768i | \(0.256211\pi\) | ||||
−0.693177 | + | 0.720768i | \(0.743789\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2703.00 | −1.23031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 352.000i | 0.156045i | ||||||||
\(173\) | − 2397.00i | − 1.05341i | −0.850047 | − | 0.526707i | \(-0.823427\pi\) | ||||
0.850047 | − | 0.526707i | \(-0.176573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −768.000 | −0.328921 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 2232.00i | − 0.939862i | ||||||||
\(179\) | 540.000 | 0.225483 | 0.112742 | − | 0.993624i | \(-0.464037\pi\) | ||||
0.112742 | + | 0.993624i | \(0.464037\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2333.00 | 0.958069 | 0.479035 | − | 0.877796i | \(-0.340987\pi\) | ||||
0.479035 | + | 0.877796i | \(0.340987\pi\) | |||||||
\(182\) | − 4760.00i | − 1.93865i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 408.000 | 0.163468 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1296.00i | − 0.506807i | ||||||||
\(188\) | − 2064.00i | − 0.800706i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2730.00 | −1.03422 | −0.517110 | − | 0.855919i | \(-0.672992\pi\) | ||||
−0.517110 | + | 0.855919i | \(0.672992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4570.00i | − 1.70443i | −0.523188 | − | 0.852217i | \(-0.675258\pi\) | ||||
0.523188 | − | 0.852217i | \(-0.324742\pi\) | |||||||
\(194\) | 32.0000 | 0.0118426 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3252.00 | 1.18513 | ||||||||
\(197\) | − 675.000i | − 0.244121i | −0.992523 | − | 0.122060i | \(-0.961050\pi\) | ||||
0.992523 | − | 0.122060i | \(-0.0389501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3112.00 | 1.10856 | 0.554281 | − | 0.832330i | \(-0.312993\pi\) | ||||
0.554281 | + | 0.832330i | \(0.312993\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 696.000i | − 0.242428i | ||||||||
\(203\) | 1020.00i | 0.352660i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −824.000 | −0.278693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 1120.00i | − 0.373356i | ||||||||
\(209\) | 5712.00 | 1.89047 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2441.00 | 0.796424 | 0.398212 | − | 0.917294i | \(-0.369631\pi\) | ||||
0.398212 | + | 0.917294i | \(0.369631\pi\) | |||||||
\(212\) | 2556.00i | 0.828051i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1800.00 | 0.574979 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 4522.00i | − 1.41462i | ||||||||
\(218\) | − 230.000i | − 0.0714567i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1890.00 | 0.575272 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3418.00i | − 1.02640i | −0.858270 | − | 0.513198i | \(-0.828461\pi\) | ||||
0.858270 | − | 0.513198i | \(-0.171539\pi\) | |||||||
\(224\) | 1088.00 | 0.324532 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1932.00 | 0.568649 | ||||||||
\(227\) | 4377.00i | 1.27979i | 0.768464 | + | 0.639894i | \(0.221022\pi\) | ||||
−0.768464 | + | 0.639894i | \(0.778978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4187.00 | −1.20823 | −0.604115 | − | 0.796897i | \(-0.706473\pi\) | ||||
−0.604115 | + | 0.796897i | \(0.706473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 240.000i | 0.0679171i | ||||||||
\(233\) | − 1098.00i | − 0.308723i | −0.988014 | − | 0.154361i | \(-0.950668\pi\) | ||||
0.988014 | − | 0.154361i | \(-0.0493320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2616.00 | −0.721555 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1836.00i | 0.500043i | ||||||||
\(239\) | −6474.00 | −1.75217 | −0.876084 | − | 0.482158i | \(-0.839853\pi\) | ||||
−0.876084 | + | 0.482158i | \(0.839853\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3251.00 | 0.868943 | 0.434472 | − | 0.900686i | \(-0.356935\pi\) | ||||
0.434472 | + | 0.900686i | \(0.356935\pi\) | |||||||
\(242\) | − 1946.00i | − 0.516916i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1844.00 | −0.483811 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8330.00i | 2.14585i | ||||||||
\(248\) | − 1064.00i | − 0.272436i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1728.00 | 0.434543 | 0.217272 | − | 0.976111i | \(-0.430284\pi\) | ||||
0.217272 | + | 0.976111i | \(0.430284\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2448.00i | 0.608318i | ||||||||
\(254\) | −2812.00 | −0.694648 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5469.00i | 1.32742i | 0.747990 | + | 0.663710i | \(0.231019\pi\) | ||||
−0.747990 | + | 0.663710i | \(0.768981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7412.00 | 1.77822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 492.000i | − 0.116015i | ||||||||
\(263\) | − 3216.00i | − 0.754019i | −0.926209 | − | 0.377010i | \(-0.876952\pi\) | ||||
0.926209 | − | 0.377010i | \(-0.123048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8092.00 | −1.86523 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 728.000i | 0.165932i | ||||||||
\(269\) | 8010.00 | 1.81553 | 0.907766 | − | 0.419476i | \(-0.137786\pi\) | ||||
0.907766 | + | 0.419476i | \(0.137786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3805.00 | −0.852905 | −0.426453 | − | 0.904510i | \(-0.640237\pi\) | ||||
−0.426453 | + | 0.904510i | \(0.640237\pi\) | |||||||
\(272\) | 432.000i | 0.0963009i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1038.00 | −0.228861 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3224.00i | − 0.699319i | −0.936877 | − | 0.349660i | \(-0.886297\pi\) | ||||
0.936877 | − | 0.349660i | \(-0.113703\pi\) | |||||||
\(278\) | 2632.00i | 0.567830i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4530.00 | −0.961698 | −0.480849 | − | 0.876803i | \(-0.659671\pi\) | ||||
−0.480849 | + | 0.876803i | \(0.659671\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3292.00i | − 0.691481i | −0.938330 | − | 0.345740i | \(-0.887628\pi\) | ||||
0.938330 | − | 0.345740i | \(-0.112372\pi\) | |||||||
\(284\) | −3600.00 | −0.752186 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6720.00 | 1.38938 | ||||||||
\(287\) | 5304.00i | 1.09089i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4184.00 | 0.851618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 2816.00i | − 0.564363i | ||||||||
\(293\) | − 7953.00i | − 1.58573i | −0.609397 | − | 0.792866i | \(-0.708588\pi\) | ||||
0.609397 | − | 0.792866i | \(-0.291412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1744.00 | 0.342459 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 744.000i | 0.144627i | ||||||||
\(299\) | −3570.00 | −0.690496 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2992.00 | 0.572944 | ||||||||
\(302\) | 2912.00i | 0.554857i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1904.00 | −0.359217 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5290.00i | 0.983441i | 0.870753 | + | 0.491720i | \(0.163632\pi\) | ||||
−0.870753 | + | 0.491720i | \(0.836368\pi\) | |||||||
\(308\) | 6528.00i | 1.20769i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5358.00 | 0.976927 | 0.488464 | − | 0.872584i | \(-0.337558\pi\) | ||||
0.488464 | + | 0.872584i | \(0.337558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5600.00i | 1.01128i | 0.862744 | + | 0.505640i | \(0.168744\pi\) | ||||
−0.862744 | + | 0.505640i | \(0.831256\pi\) | |||||||
\(314\) | −1912.00 | −0.343632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5500.00 | −0.979111 | ||||||||
\(317\) | − 7341.00i | − 1.30067i | −0.759649 | − | 0.650334i | \(-0.774629\pi\) | ||||
0.759649 | − | 0.650334i | \(-0.225371\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1440.00 | −0.252741 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 3468.00i | − 0.600199i | ||||||||
\(323\) | − 3213.00i | − 0.553486i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4892.00 | −0.831113 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1248.00i | 0.210089i | ||||||||
\(329\) | −17544.0 | −2.93991 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 380.000 | 0.0631018 | 0.0315509 | − | 0.999502i | \(-0.489955\pi\) | ||||
0.0315509 | + | 0.999502i | \(0.489955\pi\) | |||||||
\(332\) | − 3660.00i | − 0.605026i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6222.00 | 1.01932 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 434.000i | − 0.0701528i | −0.999385 | − | 0.0350764i | \(-0.988833\pi\) | ||||
0.999385 | − | 0.0350764i | \(-0.0111675\pi\) | |||||||
\(338\) | 5406.00i | 0.869963i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6384.00 | 1.01382 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 15980.0i | − 2.51557i | ||||||||
\(344\) | 704.000 | 0.110341 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4794.00 | −0.744876 | ||||||||
\(347\) | − 8004.00i | − 1.23826i | −0.785287 | − | 0.619131i | \(-0.787485\pi\) | ||||
0.785287 | − | 0.619131i | \(-0.212515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1109.00 | −0.170096 | −0.0850479 | − | 0.996377i | \(-0.527104\pi\) | ||||
−0.0850479 | + | 0.996377i | \(0.527104\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1536.00i | 0.232583i | ||||||||
\(353\) | − 7662.00i | − 1.15526i | −0.816298 | − | 0.577630i | \(-0.803977\pi\) | ||||
0.816298 | − | 0.577630i | \(-0.196023\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4464.00 | −0.664583 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 1080.00i | − 0.159441i | ||||||||
\(359\) | 8478.00 | 1.24638 | 0.623192 | − | 0.782069i | \(-0.285836\pi\) | ||||
0.623192 | + | 0.782069i | \(0.285836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7302.00 | 1.06459 | ||||||||
\(362\) | − 4666.00i | − 0.677457i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9520.00 | −1.37083 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 13286.0i | − 1.88971i | −0.327489 | − | 0.944855i | \(-0.606202\pi\) | ||||
0.327489 | − | 0.944855i | \(-0.393798\pi\) | |||||||
\(368\) | − 816.000i | − 0.115590i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21726.0 | 3.04032 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3080.00i | 0.427551i | 0.976883 | + | 0.213775i | \(0.0685760\pi\) | ||||
−0.976883 | + | 0.213775i | \(0.931424\pi\) | |||||||
\(374\) | −2592.00 | −0.358367 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4128.00 | −0.566184 | ||||||||
\(377\) | − 2100.00i | − 0.286885i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10109.0 | −1.37009 | −0.685045 | − | 0.728500i | \(-0.740218\pi\) | ||||
−0.685045 | + | 0.728500i | \(0.740218\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5460.00i | 0.731303i | ||||||||
\(383\) | − 8727.00i | − 1.16431i | −0.813080 | − | 0.582153i | \(-0.802211\pi\) | ||||
0.813080 | − | 0.582153i | \(-0.197789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9140.00 | −1.20522 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 64.0000i | − 0.00837399i | ||||||||
\(389\) | 2712.00 | 0.353480 | 0.176740 | − | 0.984258i | \(-0.443445\pi\) | ||||
0.176740 | + | 0.984258i | \(0.443445\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1377.00 | 0.178102 | ||||||||
\(392\) | − 6504.00i | − 0.838014i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1350.00 | −0.172619 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8818.00i | 1.11477i | 0.830255 | + | 0.557384i | \(0.188195\pi\) | ||||
−0.830255 | + | 0.557384i | \(0.811805\pi\) | |||||||
\(398\) | − 6224.00i | − 0.783872i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3306.00 | 0.411705 | 0.205853 | − | 0.978583i | \(-0.434003\pi\) | ||||
0.205853 | + | 0.978583i | \(0.434003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9310.00i | 1.15078i | ||||||||
\(404\) | −1392.00 | −0.171422 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2040.00 | 0.249368 | ||||||||
\(407\) | 10464.0i | 1.27440i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6401.00 | −0.773861 | −0.386930 | − | 0.922109i | \(-0.626465\pi\) | ||||
−0.386930 | + | 0.922109i | \(0.626465\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1648.00i | 0.197066i | ||||||||
\(413\) | 22236.0i | 2.64930i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2240.00 | −0.264002 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 11424.0i | − 1.33676i | ||||||||
\(419\) | 2256.00 | 0.263038 | 0.131519 | − | 0.991314i | \(-0.458015\pi\) | ||||
0.131519 | + | 0.991314i | \(0.458015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1811.00 | 0.209650 | 0.104825 | − | 0.994491i | \(-0.466572\pi\) | ||||
0.104825 | + | 0.994491i | \(0.466572\pi\) | |||||||
\(422\) | − 4882.00i | − 0.563156i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5112.00 | 0.585520 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15674.0i | 1.77639i | ||||||||
\(428\) | − 3600.00i | − 0.406571i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5454.00 | −0.609536 | −0.304768 | − | 0.952427i | \(-0.598579\pi\) | ||||
−0.304768 | + | 0.952427i | \(0.598579\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2990.00i | 0.331848i | 0.986139 | + | 0.165924i | \(0.0530607\pi\) | ||||
−0.986139 | + | 0.165924i | \(0.946939\pi\) | |||||||
\(434\) | −9044.00 | −1.00029 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −460.000 | −0.0505275 | ||||||||
\(437\) | 6069.00i | 0.664347i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9371.00 | −1.01880 | −0.509400 | − | 0.860530i | \(-0.670133\pi\) | ||||
−0.509400 | + | 0.860530i | \(0.670133\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 3780.00i | − 0.406779i | ||||||||
\(443\) | 6171.00i | 0.661835i | 0.943660 | + | 0.330918i | \(0.107358\pi\) | ||||
−0.943660 | + | 0.330918i | \(0.892642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6836.00 | −0.725771 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 2176.00i | − 0.229478i | ||||||||
\(449\) | −4122.00 | −0.433250 | −0.216625 | − | 0.976255i | \(-0.569505\pi\) | ||||
−0.216625 | + | 0.976255i | \(0.569505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7488.00 | −0.781810 | ||||||||
\(452\) | − 3864.00i | − 0.402096i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8754.00 | 0.904946 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 7076.00i | − 0.724292i | −0.932121 | − | 0.362146i | \(-0.882044\pi\) | ||||
0.932121 | − | 0.362146i | \(-0.117956\pi\) | |||||||
\(458\) | 8374.00i | 0.854348i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 762.000 | 0.0769846 | 0.0384923 | − | 0.999259i | \(-0.487745\pi\) | ||||
0.0384923 | + | 0.999259i | \(0.487745\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8822.00i | 0.885514i | 0.896642 | + | 0.442757i | \(0.146000\pi\) | ||||
−0.896642 | + | 0.442757i | \(0.854000\pi\) | |||||||
\(464\) | 480.000 | 0.0480247 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2196.00 | −0.218300 | ||||||||
\(467\) | 4977.00i | 0.493165i | 0.969122 | + | 0.246583i | \(0.0793076\pi\) | ||||
−0.969122 | + | 0.246583i | \(0.920692\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6188.00 | 0.609244 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5232.00i | 0.510217i | ||||||||
\(473\) | 4224.00i | 0.410613i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3672.00 | 0.353584 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12948.0i | 1.23897i | ||||||||
\(479\) | −10104.0 | −0.963807 | −0.481903 | − | 0.876224i | \(-0.660054\pi\) | ||||
−0.481903 | + | 0.876224i | \(0.660054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15260.0 | −1.44656 | ||||||||
\(482\) | − 6502.00i | − 0.614436i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3892.00 | −0.365515 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 14924.0i | − 1.38865i | −0.719663 | − | 0.694323i | \(-0.755704\pi\) | ||||
0.719663 | − | 0.694323i | \(-0.244296\pi\) | |||||||
\(488\) | 3688.00i | 0.342106i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1146.00 | 0.105332 | 0.0526662 | − | 0.998612i | \(-0.483228\pi\) | ||||
0.0526662 | + | 0.998612i | \(0.483228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 810.000i | 0.0739971i | ||||||||
\(494\) | 16660.0 | 1.51735 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2128.00 | −0.192641 | ||||||||
\(497\) | 30600.0i | 2.76177i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14965.0 | 1.34254 | 0.671268 | − | 0.741215i | \(-0.265750\pi\) | ||||
0.671268 | + | 0.741215i | \(0.265750\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 3456.00i | − 0.307269i | ||||||||
\(503\) | 15525.0i | 1.37619i | 0.725619 | + | 0.688097i | \(0.241554\pi\) | ||||
−0.725619 | + | 0.688097i | \(0.758446\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4896.00 | 0.430146 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5624.00i | 0.491190i | ||||||||
\(509\) | 8196.00 | 0.713716 | 0.356858 | − | 0.934159i | \(-0.383848\pi\) | ||||
0.356858 | + | 0.934159i | \(0.383848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23936.0 | −2.07215 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10938.0 | 0.938627 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 24768.0i | − 2.10695i | ||||||||
\(518\) | − 14824.0i | − 1.25739i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4932.00 | 0.414731 | 0.207365 | − | 0.978264i | \(-0.433511\pi\) | ||||
0.207365 | + | 0.978264i | \(0.433511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5938.00i | − 0.496464i | −0.968701 | − | 0.248232i | \(-0.920150\pi\) | ||||
0.968701 | − | 0.248232i | \(-0.0798495\pi\) | |||||||
\(524\) | −984.000 | −0.0820348 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6432.00 | −0.533172 | ||||||||
\(527\) | − 3591.00i | − 0.296824i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9566.00 | 0.786225 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16184.0i | 1.31892i | ||||||||
\(533\) | − 10920.0i | − 0.887425i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1456.00 | 0.117331 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 16020.0i | − 1.28378i | ||||||||
\(539\) | 39024.0 | 3.11852 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6730.00 | −0.534834 | −0.267417 | − | 0.963581i | \(-0.586170\pi\) | ||||
−0.267417 | + | 0.963581i | \(0.586170\pi\) | |||||||
\(542\) | 7610.00i | 0.603095i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 864.000 | 0.0680950 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17656.0i | 1.38010i | 0.723761 | + | 0.690051i | \(0.242412\pi\) | ||||
−0.723761 | + | 0.690051i | \(0.757588\pi\) | |||||||
\(548\) | 2076.00i | 0.161829i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3570.00 | −0.276020 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46750.0i | 3.59496i | ||||||||
\(554\) | −6448.00 | −0.494493 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5264.00 | 0.401517 | ||||||||
\(557\) | − 7974.00i | − 0.606587i | −0.952897 | − | 0.303294i | \(-0.901914\pi\) | ||||
0.952897 | − | 0.303294i | \(-0.0980863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6160.00 | −0.466083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9060.00i | 0.680023i | ||||||||
\(563\) | − 25332.0i | − 1.89630i | −0.317824 | − | 0.948150i | \(-0.602952\pi\) | ||||
0.317824 | − | 0.948150i | \(-0.397048\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6584.00 | −0.488951 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7200.00i | 0.531876i | ||||||||
\(569\) | 1038.00 | 0.0764767 | 0.0382383 | − | 0.999269i | \(-0.487825\pi\) | ||||
0.0382383 | + | 0.999269i | \(0.487825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15671.0 | 1.14853 | 0.574265 | − | 0.818669i | \(-0.305288\pi\) | ||||
0.574265 | + | 0.818669i | \(0.305288\pi\) | |||||||
\(572\) | − 13440.0i | − 0.982438i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10608.0 | 0.771375 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 916.000i | 0.0660894i | 0.999454 | + | 0.0330447i | \(0.0105204\pi\) | ||||
−0.999454 | + | 0.0330447i | \(0.989480\pi\) | |||||||
\(578\) | − 8368.00i | − 0.602185i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31110.0 | −2.22145 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30672.0i | 2.17891i | ||||||||
\(584\) | −5632.00 | −0.399065 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15906.0 | −1.12128 | ||||||||
\(587\) | − 9141.00i | − 0.642742i | −0.946953 | − | 0.321371i | \(-0.895856\pi\) | ||||
0.946953 | − | 0.321371i | \(-0.104144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15827.0 | 1.10720 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 3488.00i | − 0.242155i | ||||||||
\(593\) | 5247.00i | 0.363353i | 0.983358 | + | 0.181677i | \(0.0581524\pi\) | ||||
−0.983358 | + | 0.181677i | \(0.941848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1488.00 | 0.102267 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7140.00i | 0.488255i | ||||||||
\(599\) | 24162.0 | 1.64813 | 0.824067 | − | 0.566492i | \(-0.191700\pi\) | ||||
0.824067 | + | 0.566492i | \(0.191700\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14357.0 | 0.974433 | 0.487217 | − | 0.873281i | \(-0.338012\pi\) | ||||
0.487217 | + | 0.873281i | \(0.338012\pi\) | |||||||
\(602\) | − 5984.00i | − 0.405132i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5824.00 | 0.392343 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 3152.00i | − 0.210767i | −0.994432 | − | 0.105384i | \(-0.966393\pi\) | ||||
0.994432 | − | 0.105384i | \(-0.0336071\pi\) | |||||||
\(608\) | 3808.00i | 0.254005i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36120.0 | 2.39159 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4592.00i | 0.302560i | 0.988491 | + | 0.151280i | \(0.0483395\pi\) | ||||
−0.988491 | + | 0.151280i | \(0.951661\pi\) | |||||||
\(614\) | 10580.0 | 0.695397 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13056.0 | 0.853963 | ||||||||
\(617\) | 7359.00i | 0.480166i | 0.970752 | + | 0.240083i | \(0.0771746\pi\) | ||||
−0.970752 | + | 0.240083i | \(0.922825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15712.0 | 1.02022 | 0.510112 | − | 0.860108i | \(-0.329604\pi\) | ||||
0.510112 | + | 0.860108i | \(0.329604\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 10716.0i | − 0.690792i | ||||||||
\(623\) | 37944.0i | 2.44012i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11200.0 | 0.715083 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3824.00i | 0.242984i | ||||||||
\(629\) | 5886.00 | 0.373116 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3175.00 | −0.200309 | −0.100154 | − | 0.994972i | \(-0.531934\pi\) | ||||
−0.100154 | + | 0.994972i | \(0.531934\pi\) | |||||||
\(632\) | 11000.0i | 0.692336i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14682.0 | −0.919711 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 56910.0i | 3.53981i | ||||||||
\(638\) | 2880.00i | 0.178715i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 96.0000 | 0.00591540 | 0.00295770 | − | 0.999996i | \(-0.499059\pi\) | ||||
0.00295770 | + | 0.999996i | \(0.499059\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 18070.0i | − 1.10826i | −0.832430 | − | 0.554130i | \(-0.813051\pi\) | ||||
0.832430 | − | 0.554130i | \(-0.186949\pi\) | |||||||
\(644\) | −6936.00 | −0.424405 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6426.00 | −0.391374 | ||||||||
\(647\) | − 1341.00i | − 0.0814840i | −0.999170 | − | 0.0407420i | \(-0.987028\pi\) | ||||
0.999170 | − | 0.0407420i | \(-0.0129722\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31392.0 | −1.89868 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9784.00i | 0.587686i | ||||||||
\(653\) | − 24495.0i | − 1.46794i | −0.679183 | − | 0.733969i | \(-0.737666\pi\) | ||||
0.679183 | − | 0.733969i | \(-0.262334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2496.00 | 0.148556 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 35088.0i | 2.07883i | ||||||||
\(659\) | 12378.0 | 0.731682 | 0.365841 | − | 0.930677i | \(-0.380781\pi\) | ||||
0.365841 | + | 0.930677i | \(0.380781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24442.0 | −1.43825 | −0.719125 | − | 0.694880i | \(-0.755457\pi\) | ||||
−0.719125 | + | 0.694880i | \(0.755457\pi\) | |||||||
\(662\) | − 760.000i | − 0.0446197i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7320.00 | −0.427818 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1530.00i | − 0.0888183i | ||||||||
\(668\) | − 12444.0i | − 0.720768i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22128.0 | −1.27309 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2378.00i | 0.136204i | 0.997678 | + | 0.0681019i | \(0.0216943\pi\) | ||||
−0.997678 | + | 0.0681019i | \(0.978306\pi\) | |||||||
\(674\) | −868.000 | −0.0496055 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10812.0 | 0.615157 | ||||||||
\(677\) | − 5478.00i | − 0.310985i | −0.987837 | − | 0.155492i | \(-0.950304\pi\) | ||||
0.987837 | − | 0.155492i | \(-0.0496964\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −544.000 | −0.0307464 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 12768.0i | − 0.716880i | ||||||||
\(683\) | 8595.00i | 0.481521i | 0.970585 | + | 0.240760i | \(0.0773968\pi\) | ||||
−0.970585 | + | 0.240760i | \(0.922603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −31960.0 | −1.77877 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 1408.00i | − 0.0780225i | ||||||||
\(689\) | −44730.0 | −2.47326 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31615.0 | −1.74051 | −0.870254 | − | 0.492603i | \(-0.836046\pi\) | ||||
−0.870254 | + | 0.492603i | \(0.836046\pi\) | |||||||
\(692\) | 9588.00i | 0.526707i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16008.0 | −0.875584 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4212.00i | 0.228897i | ||||||||
\(698\) | 2218.00i | 0.120276i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29790.0 | 1.60507 | 0.802534 | − | 0.596606i | \(-0.203485\pi\) | ||||
0.802534 | + | 0.596606i | \(0.203485\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25942.0i | 1.39178i | ||||||||
\(704\) | 3072.00 | 0.164461 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15324.0 | −0.816893 | ||||||||
\(707\) | 11832.0i | 0.629403i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3818.00 | −0.202240 | −0.101120 | − | 0.994874i | \(-0.532243\pi\) | ||||
−0.101120 | + | 0.994874i | \(0.532243\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8928.00i | 0.469931i | ||||||||
\(713\) | 6783.00i | 0.356277i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2160.00 | −0.112742 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 16956.0i | − 0.881326i | ||||||||
\(719\) | 28314.0 | 1.46861 | 0.734307 | − | 0.678817i | \(-0.237507\pi\) | ||||
0.734307 | + | 0.678817i | \(0.237507\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14008.0 | 0.723558 | ||||||||
\(722\) | − 14604.0i | − 0.752776i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9332.00 | −0.479035 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 56.0000i | − 0.00285684i | −0.999999 | − | 0.00142842i | \(-0.999545\pi\) | ||||
0.999999 | − | 0.00142842i | \(-0.000454681\pi\) | |||||||
\(728\) | 19040.0i | 0.969326i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2376.00 | 0.120218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 34432.0i | − 1.73503i | −0.497413 | − | 0.867514i | \(-0.665717\pi\) | ||||
0.497413 | − | 0.867514i | \(-0.334283\pi\) | |||||||
\(734\) | −26572.0 | −1.33623 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1632.00 | −0.0817341 | ||||||||
\(737\) | 8736.00i | 0.436628i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1051.00 | 0.0523162 | 0.0261581 | − | 0.999658i | \(-0.491673\pi\) | ||||
0.0261581 | + | 0.999658i | \(0.491673\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 43452.0i | − 2.14983i | ||||||||
\(743\) | 39144.0i | 1.93278i | 0.257084 | + | 0.966389i | \(0.417238\pi\) | ||||
−0.257084 | + | 0.966389i | \(0.582762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6160.00 | 0.302324 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5184.00i | 0.253403i | ||||||||
\(749\) | −30600.0 | −1.49279 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1735.00 | −0.0843023 | −0.0421512 | − | 0.999111i | \(-0.513421\pi\) | ||||
−0.0421512 | + | 0.999111i | \(0.513421\pi\) | |||||||
\(752\) | 8256.00i | 0.400353i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4200.00 | −0.202858 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 6698.00i | − 0.321589i | −0.986988 | − | 0.160795i | \(-0.948594\pi\) | ||||
0.986988 | − | 0.160795i | \(-0.0514057\pi\) | |||||||
\(758\) | 20218.0i | 0.968801i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38766.0 | 1.84660 | 0.923302 | − | 0.384074i | \(-0.125479\pi\) | ||||
0.923302 | + | 0.384074i | \(0.125479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3910.00i | 0.185520i | ||||||||
\(764\) | 10920.0 | 0.517110 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17454.0 | −0.823288 | ||||||||
\(767\) | − 45780.0i | − 2.15518i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23501.0 | −1.10204 | −0.551019 | − | 0.834492i | \(-0.685761\pi\) | ||||
−0.551019 | + | 0.834492i | \(0.685761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18280.0i | 0.852217i | ||||||||
\(773\) | − 3591.00i | − 0.167088i | −0.996504 | − | 0.0835442i | \(-0.973376\pi\) | ||||
0.996504 | − | 0.0835442i | \(-0.0266240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −128.000 | −0.00592130 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 5424.00i | − 0.249948i | ||||||||
\(779\) | −18564.0 | −0.853818 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43200.0 | −1.97928 | ||||||||
\(782\) | − 2754.00i | − 0.125937i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13008.0 | −0.592566 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20716.0i | 0.938305i | 0.883117 | + | 0.469152i | \(0.155440\pi\) | ||||
−0.883117 | + | 0.469152i | \(0.844560\pi\) | |||||||
\(788\) | 2700.00i | 0.122060i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32844.0 | −1.47636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 32270.0i | − 1.44507i | ||||||||
\(794\) | 17636.0 | 0.788260 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12448.0 | −0.554281 | ||||||||
\(797\) | 42981.0i | 1.91024i | 0.296211 | + | 0.955122i | \(0.404277\pi\) | ||||
−0.296211 | + | 0.955122i | \(0.595723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13932.0 | −0.616869 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 6612.00i | − 0.291119i | ||||||||
\(803\) | − 33792.0i | − 1.48505i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18620.0 | 0.813724 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2784.00i | 0.121214i | ||||||||
\(809\) | 2268.00 | 0.0985644 | 0.0492822 | − | 0.998785i | \(-0.484307\pi\) | ||||
0.0492822 | + | 0.998785i | \(0.484307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11756.0 | 0.509012 | 0.254506 | − | 0.967071i | \(-0.418087\pi\) | ||||
0.254506 | + | 0.967071i | \(0.418087\pi\) | |||||||
\(812\) | − 4080.00i | − 0.176330i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20928.0 | 0.901138 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10472.0i | 0.448432i | ||||||||
\(818\) | 12802.0i | 0.547202i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8646.00 | 0.367537 | 0.183768 | − | 0.982970i | \(-0.441170\pi\) | ||||
0.183768 | + | 0.982970i | \(0.441170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10784.0i | 0.456752i | 0.973573 | + | 0.228376i | \(0.0733415\pi\) | ||||
−0.973573 | + | 0.228376i | \(0.926659\pi\) | |||||||
\(824\) | 3296.00 | 0.139347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 44472.0 | 1.87334 | ||||||||
\(827\) | − 42597.0i | − 1.79110i | −0.444957 | − | 0.895552i | \(-0.646781\pi\) | ||||
0.444957 | − | 0.895552i | \(-0.353219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26458.0 | 1.10847 | 0.554237 | − | 0.832359i | \(-0.313010\pi\) | ||||
0.554237 | + | 0.832359i | \(0.313010\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4480.00i | 0.186678i | ||||||||
\(833\) | − 21951.0i | − 0.913034i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22848.0 | −0.945233 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 4512.00i | − 0.185996i | ||||||||
\(839\) | 11496.0 | 0.473046 | 0.236523 | − | 0.971626i | \(-0.423992\pi\) | ||||
0.236523 | + | 0.971626i | \(0.423992\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23489.0 | −0.963098 | ||||||||
\(842\) | − 3622.00i | − 0.148245i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9764.00 | −0.398212 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33082.0i | 1.34204i | ||||||||
\(848\) | − 10224.0i | − 0.414025i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11118.0 | −0.447850 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21548.0i | 0.864935i | 0.901650 | + | 0.432467i | \(0.142357\pi\) | ||||
−0.901650 | + | 0.432467i | \(0.857643\pi\) | |||||||
\(854\) | 31348.0 | 1.25610 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7200.00 | −0.287489 | ||||||||
\(857\) | − 6261.00i | − 0.249559i | −0.992185 | − | 0.124779i | \(-0.960178\pi\) | ||||
0.992185 | − | 0.124779i | \(-0.0398223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3355.00 | 0.133261 | 0.0666305 | − | 0.997778i | \(-0.478775\pi\) | ||||
0.0666305 | + | 0.997778i | \(0.478775\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10908.0i | 0.431007i | ||||||||
\(863\) | 19701.0i | 0.777091i | 0.921429 | + | 0.388546i | \(0.127022\pi\) | ||||
−0.921429 | + | 0.388546i | \(0.872978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5980.00 | 0.234652 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18088.0i | 0.707312i | ||||||||
\(869\) | −66000.0 | −2.57641 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12740.0 | −0.495612 | ||||||||
\(872\) | 920.000i | 0.0357284i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12138.0 | 0.469764 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 16292.0i | − 0.627300i | −0.949539 | − | 0.313650i | \(-0.898448\pi\) | ||||
0.949539 | − | 0.313650i | \(-0.101552\pi\) | |||||||
\(878\) | 18742.0i | 0.720401i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9270.00 | 0.354500 | 0.177250 | − | 0.984166i | \(-0.443280\pi\) | ||||
0.177250 | + | 0.984166i | \(0.443280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38486.0i | 1.46677i | 0.679814 | + | 0.733384i | \(0.262060\pi\) | ||||
−0.679814 | + | 0.733384i | \(0.737940\pi\) | |||||||
\(884\) | −7560.00 | −0.287636 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12342.0 | 0.467988 | ||||||||
\(887\) | − 1893.00i | − 0.0716581i | −0.999358 | − | 0.0358290i | \(-0.988593\pi\) | ||||
0.999358 | − | 0.0358290i | \(-0.0114072\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47804.0 | 1.80348 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13672.0i | 0.513198i | ||||||||
\(893\) | − 61404.0i | − 2.30102i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4352.00 | −0.162266 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8244.00i | 0.306354i | ||||||||
\(899\) | −3990.00 | −0.148024 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17253.0 | 0.637936 | ||||||||
\(902\) | 14976.0i | 0.552823i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7728.00 | −0.284325 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 44876.0i | − 1.64287i | −0.570302 | − | 0.821435i | \(-0.693174\pi\) | ||||
0.570302 | − | 0.821435i | \(-0.306826\pi\) | |||||||
\(908\) | − 17508.0i | − 0.639894i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23802.0 | 0.865637 | 0.432819 | − | 0.901481i | \(-0.357519\pi\) | ||||
0.432819 | + | 0.901481i | \(0.357519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 43920.0i | − 1.59205i | ||||||||
\(914\) | −14152.0 | −0.512152 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16748.0 | 0.604115 | ||||||||
\(917\) | 8364.00i | 0.301204i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24784.0 | 0.889607 | 0.444803 | − | 0.895628i | \(-0.353274\pi\) | ||||
0.444803 | + | 0.895628i | \(0.353274\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 1524.00i | − 0.0544363i | ||||||||
\(923\) | − 63000.0i | − 2.24666i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17644.0 | 0.626153 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 960.000i | − 0.0339586i | ||||||||
\(929\) | −9060.00 | −0.319967 | −0.159983 | − | 0.987120i | \(-0.551144\pi\) | ||||
−0.159983 | + | 0.987120i | \(0.551144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 96747.0 | 3.40575 | ||||||||
\(932\) | 4392.00i | 0.154361i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9954.00 | 0.348720 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 6176.00i | − 0.215327i | −0.994187 | − | 0.107663i | \(-0.965663\pi\) | ||||
0.994187 | − | 0.107663i | \(-0.0343369\pi\) | |||||||
\(938\) | − 12376.0i | − 0.430800i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4182.00 | −0.144877 | −0.0724385 | − | 0.997373i | \(-0.523078\pi\) | ||||
−0.0724385 | + | 0.997373i | \(0.523078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 7956.00i | − 0.274743i | ||||||||
\(944\) | 10464.0 | 0.360778 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8448.00 | 0.290347 | ||||||||
\(947\) | − 44079.0i | − 1.51254i | −0.654260 | − | 0.756270i | \(-0.727020\pi\) | ||||
0.654260 | − | 0.756270i | \(-0.272980\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49280.0 | 1.68567 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 7344.00i | − 0.250021i | ||||||||
\(953\) | 12726.0i | 0.432566i | 0.976331 | + | 0.216283i | \(0.0693934\pi\) | ||||
−0.976331 | + | 0.216283i | \(0.930607\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 25896.0 | 0.876084 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20208.0i | 0.681514i | ||||||||
\(959\) | 17646.0 | 0.594180 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12102.0 | −0.406230 | ||||||||
\(962\) | 30520.0i | 1.02287i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13004.0 | −0.434472 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 45218.0i | − 1.50374i | −0.659314 | − | 0.751868i | \(-0.729153\pi\) | ||||
0.659314 | − | 0.751868i | \(-0.270847\pi\) | |||||||
\(968\) | 7784.00i | 0.258458i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3978.00 | −0.131473 | −0.0657364 | − | 0.997837i | \(-0.520940\pi\) | ||||
−0.0657364 | + | 0.997837i | \(0.520940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 44744.0i | − 1.47423i | ||||||||
\(974\) | −29848.0 | −0.981922 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7376.00 | 0.241906 | ||||||||
\(977\) | − 23466.0i | − 0.768417i | −0.923246 | − | 0.384209i | \(-0.874474\pi\) | ||||
0.923246 | − | 0.384209i | \(-0.125526\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53568.0 | −1.74876 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 2292.00i | − 0.0744813i | ||||||||
\(983\) | 47913.0i | 1.55462i | 0.629120 | + | 0.777308i | \(0.283415\pi\) | ||||
−0.629120 | + | 0.777308i | \(0.716585\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1620.00 | 0.0523238 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 33320.0i | − 1.07293i | ||||||||
\(989\) | −4488.00 | −0.144297 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31997.0 | 1.02565 | 0.512825 | − | 0.858493i | \(-0.328599\pi\) | ||||
0.512825 | + | 0.858493i | \(0.328599\pi\) | |||||||
\(992\) | 4256.00i | 0.136218i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 61200.0 | 1.95286 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45628.0i | 1.44940i | 0.689064 | + | 0.724701i | \(0.258022\pi\) | ||||
−0.689064 | + | 0.724701i | \(0.741978\pi\) | |||||||
\(998\) | − 29930.0i | − 0.949316i | ||||||||
\(999\) | 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 | 1350.4.c.c.649.1 | 2 | ||
3.2 | odd | 2 | 1350.4.c.r.649.2 | 2 | |||
5.2 | odd | 4 | 270.4.a.k.1.1 | yes | 1 | ||
5.3 | odd | 4 | 1350.4.a.n.1.1 | 1 | |||
5.4 | even | 2 | inner | 1350.4.c.c.649.2 | 2 | ||
15.2 | even | 4 | 270.4.a.a.1.1 | ✓ | 1 | ||
15.8 | even | 4 | 1350.4.a.bb.1.1 | 1 | |||
15.14 | odd | 2 | 1350.4.c.r.649.1 | 2 | |||
20.7 | even | 4 | 2160.4.a.t.1.1 | 1 | |||
45.2 | even | 12 | 810.4.e.x.271.1 | 2 | |||
45.7 | odd | 12 | 810.4.e.d.271.1 | 2 | |||
45.22 | odd | 12 | 810.4.e.d.541.1 | 2 | |||
45.32 | even | 12 | 810.4.e.x.541.1 | 2 | |||
60.47 | odd | 4 | 2160.4.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.a.1.1 | ✓ | 1 | 15.2 | even | 4 | ||
270.4.a.k.1.1 | yes | 1 | 5.2 | odd | 4 | ||
810.4.e.d.271.1 | 2 | 45.7 | odd | 12 | |||
810.4.e.d.541.1 | 2 | 45.22 | odd | 12 | |||
810.4.e.x.271.1 | 2 | 45.2 | even | 12 | |||
810.4.e.x.541.1 | 2 | 45.32 | even | 12 | |||
1350.4.a.n.1.1 | 1 | 5.3 | odd | 4 | |||
1350.4.a.bb.1.1 | 1 | 15.8 | even | 4 | |||
1350.4.c.c.649.1 | 2 | 1.1 | even | 1 | trivial | ||
1350.4.c.c.649.2 | 2 | 5.4 | even | 2 | inner | ||
1350.4.c.r.649.1 | 2 | 15.14 | odd | 2 | |||
1350.4.c.r.649.2 | 2 | 3.2 | odd | 2 | |||
2160.4.a.j.1.1 | 1 | 60.47 | odd | 4 | |||
2160.4.a.t.1.1 | 1 | 20.7 | even | 4 |