Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,4,Mod(49,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, 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("150.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(8.85028650086\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.49 |
Dual form | 150.4.c.e.49.1 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 1.00000i | 0.0539949i | 0.999636 | + | 0.0269975i | \(0.00859460\pi\) | ||||
−0.999636 | + | 0.0269975i | \(0.991405\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.0000 | 1.15123 | 0.575613 | − | 0.817723i | \(-0.304764\pi\) | ||||
0.575613 | + | 0.817723i | \(0.304764\pi\) | |||||||
\(12\) | 12.0000i | 0.288675i | ||||||||
\(13\) | − 67.0000i | − 1.42942i | −0.699421 | − | 0.714710i | \(-0.746559\pi\) | ||||
0.699421 | − | 0.714710i | \(-0.253441\pi\) | |||||||
\(14\) | −2.00000 | −0.0381802 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − 54.0000i | − 0.770407i | −0.922832 | − | 0.385204i | \(-0.874131\pi\) | ||||
0.922832 | − | 0.385204i | \(-0.125869\pi\) | |||||||
\(18\) | − 18.0000i | − 0.235702i | ||||||||
\(19\) | 115.000 | 1.38857 | 0.694284 | − | 0.719701i | \(-0.255721\pi\) | ||||
0.694284 | + | 0.719701i | \(0.255721\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | 0.0311740 | ||||||||
\(22\) | 84.0000i | 0.814039i | ||||||||
\(23\) | − 162.000i | − 1.46867i | −0.678789 | − | 0.734333i | \(-0.737495\pi\) | ||||
0.678789 | − | 0.734333i | \(-0.262505\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 134.000 | 1.01075 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − 4.00000i | − 0.0269975i | ||||||||
\(29\) | 210.000 | 1.34469 | 0.672345 | − | 0.740238i | \(-0.265287\pi\) | ||||
0.672345 | + | 0.740238i | \(0.265287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −193.000 | −1.11819 | −0.559094 | − | 0.829104i | \(-0.688851\pi\) | ||||
−0.559094 | + | 0.829104i | \(0.688851\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | − 126.000i | − 0.664660i | ||||||||
\(34\) | 108.000 | 0.544760 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 286.000i | 1.27076i | 0.772200 | + | 0.635380i | \(0.219156\pi\) | ||||
−0.772200 | + | 0.635380i | \(0.780844\pi\) | |||||||
\(38\) | 230.000i | 0.981866i | ||||||||
\(39\) | −201.000 | −0.825276 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.0000 | 0.0457094 | 0.0228547 | − | 0.999739i | \(-0.492724\pi\) | ||||
0.0228547 | + | 0.999739i | \(0.492724\pi\) | |||||||
\(42\) | 6.00000i | 0.0220433i | ||||||||
\(43\) | 263.000i | 0.932724i | 0.884594 | + | 0.466362i | \(0.154436\pi\) | ||||
−0.884594 | + | 0.466362i | \(0.845564\pi\) | |||||||
\(44\) | −168.000 | −0.575613 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 324.000 | 1.03850 | ||||||||
\(47\) | − 414.000i | − 1.28485i | −0.766347 | − | 0.642427i | \(-0.777928\pi\) | ||||
0.766347 | − | 0.642427i | \(-0.222072\pi\) | |||||||
\(48\) | − 48.0000i | − 0.144338i | ||||||||
\(49\) | 342.000 | 0.997085 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −162.000 | −0.444795 | ||||||||
\(52\) | 268.000i | 0.714710i | ||||||||
\(53\) | − 192.000i | − 0.497608i | −0.968554 | − | 0.248804i | \(-0.919962\pi\) | ||||
0.968554 | − | 0.248804i | \(-0.0800375\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.00000 | 0.0190901 | ||||||||
\(57\) | − 345.000i | − 0.801691i | ||||||||
\(58\) | 420.000i | 0.950840i | ||||||||
\(59\) | −690.000 | −1.52255 | −0.761274 | − | 0.648430i | \(-0.775426\pi\) | ||||
−0.761274 | + | 0.648430i | \(0.775426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −733.000 | −1.53854 | −0.769271 | − | 0.638923i | \(-0.779380\pi\) | ||||
−0.769271 | + | 0.638923i | \(0.779380\pi\) | |||||||
\(62\) | − 386.000i | − 0.790678i | ||||||||
\(63\) | − 9.00000i | − 0.0179983i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 252.000 | 0.469986 | ||||||||
\(67\) | − 299.000i | − 0.545204i | −0.962127 | − | 0.272602i | \(-0.912116\pi\) | ||||
0.962127 | − | 0.272602i | \(-0.0878842\pi\) | |||||||
\(68\) | 216.000i | 0.385204i | ||||||||
\(69\) | −486.000 | −0.847935 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −228.000 | −0.381107 | −0.190554 | − | 0.981677i | \(-0.561028\pi\) | ||||
−0.190554 | + | 0.981677i | \(0.561028\pi\) | |||||||
\(72\) | 72.0000i | 0.117851i | ||||||||
\(73\) | 938.000i | 1.50390i | 0.659221 | + | 0.751949i | \(0.270886\pi\) | ||||
−0.659221 | + | 0.751949i | \(0.729114\pi\) | |||||||
\(74\) | −572.000 | −0.898563 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −460.000 | −0.694284 | ||||||||
\(77\) | 42.0000i | 0.0621603i | ||||||||
\(78\) | − 402.000i | − 0.583558i | ||||||||
\(79\) | 160.000 | 0.227866 | 0.113933 | − | 0.993488i | \(-0.463655\pi\) | ||||
0.113933 | + | 0.993488i | \(0.463655\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 24.0000i | 0.0323214i | ||||||||
\(83\) | − 462.000i | − 0.610977i | −0.952196 | − | 0.305488i | \(-0.901180\pi\) | ||||
0.952196 | − | 0.305488i | \(-0.0988197\pi\) | |||||||
\(84\) | −12.0000 | −0.0155870 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −526.000 | −0.659535 | ||||||||
\(87\) | − 630.000i | − 0.776357i | ||||||||
\(88\) | − 336.000i | − 0.407020i | ||||||||
\(89\) | 240.000 | 0.285842 | 0.142921 | − | 0.989734i | \(-0.454350\pi\) | ||||
0.142921 | + | 0.989734i | \(0.454350\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 67.0000 | 0.0771814 | ||||||||
\(92\) | 648.000i | 0.734333i | ||||||||
\(93\) | 579.000i | 0.645586i | ||||||||
\(94\) | 828.000 | 0.908529 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 511.000i | 0.534889i | 0.963573 | + | 0.267444i | \(0.0861791\pi\) | ||||
−0.963573 | + | 0.267444i | \(0.913821\pi\) | |||||||
\(98\) | 684.000i | 0.705045i | ||||||||
\(99\) | −378.000 | −0.383742 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 912.000 | 0.898489 | 0.449245 | − | 0.893409i | \(-0.351693\pi\) | ||||
0.449245 | + | 0.893409i | \(0.351693\pi\) | |||||||
\(102\) | − 324.000i | − 0.314517i | ||||||||
\(103\) | 668.000i | 0.639029i | 0.947581 | + | 0.319515i | \(0.103520\pi\) | ||||
−0.947581 | + | 0.319515i | \(0.896480\pi\) | |||||||
\(104\) | −536.000 | −0.505376 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 384.000 | 0.351862 | ||||||||
\(107\) | 1296.00i | 1.17093i | 0.810699 | + | 0.585463i | \(0.199087\pi\) | ||||
−0.810699 | + | 0.585463i | \(0.800913\pi\) | |||||||
\(108\) | − 108.000i | − 0.0962250i | ||||||||
\(109\) | 1735.00 | 1.52461 | 0.762307 | − | 0.647216i | \(-0.224067\pi\) | ||||
0.762307 | + | 0.647216i | \(0.224067\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 858.000 | 0.733673 | ||||||||
\(112\) | 16.0000i | 0.0134987i | ||||||||
\(113\) | − 1092.00i | − 0.909086i | −0.890725 | − | 0.454543i | \(-0.849803\pi\) | ||||
0.890725 | − | 0.454543i | \(-0.150197\pi\) | |||||||
\(114\) | 690.000 | 0.566881 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −840.000 | −0.672345 | ||||||||
\(117\) | 603.000i | 0.476473i | ||||||||
\(118\) | − 1380.00i | − 1.07660i | ||||||||
\(119\) | 54.0000 | 0.0415981 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 433.000 | 0.325319 | ||||||||
\(122\) | − 1466.00i | − 1.08791i | ||||||||
\(123\) | − 36.0000i | − 0.0263903i | ||||||||
\(124\) | 772.000 | 0.559094 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.0000 | 0.0127267 | ||||||||
\(127\) | 16.0000i | 0.0111793i | 0.999984 | + | 0.00558965i | \(0.00177925\pi\) | ||||
−0.999984 | + | 0.00558965i | \(0.998221\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | 789.000 | 0.538508 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1992.00 | 1.32856 | 0.664282 | − | 0.747482i | \(-0.268737\pi\) | ||||
0.664282 | + | 0.747482i | \(0.268737\pi\) | |||||||
\(132\) | 504.000i | 0.332330i | ||||||||
\(133\) | 115.000i | 0.0749757i | ||||||||
\(134\) | 598.000 | 0.385517 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −432.000 | −0.272380 | ||||||||
\(137\) | 2346.00i | 1.46301i | 0.681836 | + | 0.731505i | \(0.261182\pi\) | ||||
−0.681836 | + | 0.731505i | \(0.738818\pi\) | |||||||
\(138\) | − 972.000i | − 0.599581i | ||||||||
\(139\) | −2900.00 | −1.76960 | −0.884801 | − | 0.465968i | \(-0.845706\pi\) | ||||
−0.884801 | + | 0.465968i | \(0.845706\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1242.00 | −0.741810 | ||||||||
\(142\) | − 456.000i | − 0.269484i | ||||||||
\(143\) | − 2814.00i | − 1.64558i | ||||||||
\(144\) | −144.000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1876.00 | −1.06342 | ||||||||
\(147\) | − 1026.00i | − 0.575667i | ||||||||
\(148\) | − 1144.00i | − 0.635380i | ||||||||
\(149\) | 2070.00 | 1.13813 | 0.569064 | − | 0.822293i | \(-0.307306\pi\) | ||||
0.569064 | + | 0.822293i | \(0.307306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2237.00 | 1.20559 | 0.602796 | − | 0.797895i | \(-0.294053\pi\) | ||||
0.602796 | + | 0.797895i | \(0.294053\pi\) | |||||||
\(152\) | − 920.000i | − 0.490933i | ||||||||
\(153\) | 486.000i | 0.256802i | ||||||||
\(154\) | −84.0000 | −0.0439540 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 804.000 | 0.412638 | ||||||||
\(157\) | 241.000i | 0.122509i | 0.998122 | + | 0.0612544i | \(0.0195101\pi\) | ||||
−0.998122 | + | 0.0612544i | \(0.980490\pi\) | |||||||
\(158\) | 320.000i | 0.161126i | ||||||||
\(159\) | −576.000 | −0.287294 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 162.000 | 0.0793006 | ||||||||
\(162\) | 162.000i | 0.0785674i | ||||||||
\(163\) | − 3547.00i | − 1.70443i | −0.523190 | − | 0.852216i | \(-0.675258\pi\) | ||||
0.523190 | − | 0.852216i | \(-0.324742\pi\) | |||||||
\(164\) | −48.0000 | −0.0228547 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 924.000 | 0.432026 | ||||||||
\(167\) | − 984.000i | − 0.455953i | −0.973667 | − | 0.227977i | \(-0.926789\pi\) | ||||
0.973667 | − | 0.227977i | \(-0.0732110\pi\) | |||||||
\(168\) | − 24.0000i | − 0.0110217i | ||||||||
\(169\) | −2292.00 | −1.04324 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1035.00 | −0.462856 | ||||||||
\(172\) | − 1052.00i | − 0.466362i | ||||||||
\(173\) | 3618.00i | 1.59001i | 0.606604 | + | 0.795004i | \(0.292531\pi\) | ||||
−0.606604 | + | 0.795004i | \(0.707469\pi\) | |||||||
\(174\) | 1260.00 | 0.548968 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 672.000 | 0.287806 | ||||||||
\(177\) | 2070.00i | 0.879044i | ||||||||
\(178\) | 480.000i | 0.202121i | ||||||||
\(179\) | 150.000 | 0.0626342 | 0.0313171 | − | 0.999509i | \(-0.490030\pi\) | ||||
0.0313171 | + | 0.999509i | \(0.490030\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 197.000 | 0.0809000 | 0.0404500 | − | 0.999182i | \(-0.487121\pi\) | ||||
0.0404500 | + | 0.999182i | \(0.487121\pi\) | |||||||
\(182\) | 134.000i | 0.0545755i | ||||||||
\(183\) | 2199.00i | 0.888277i | ||||||||
\(184\) | −1296.00 | −0.519252 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1158.00 | −0.456498 | ||||||||
\(187\) | − 2268.00i | − 0.886912i | ||||||||
\(188\) | 1656.00i | 0.642427i | ||||||||
\(189\) | −27.0000 | −0.0103913 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1302.00 | 0.493243 | 0.246622 | − | 0.969112i | \(-0.420680\pi\) | ||||
0.246622 | + | 0.969112i | \(0.420680\pi\) | |||||||
\(192\) | 192.000i | 0.0721688i | ||||||||
\(193\) | 4163.00i | 1.55264i | 0.630340 | + | 0.776319i | \(0.282916\pi\) | ||||
−0.630340 | + | 0.776319i | \(0.717084\pi\) | |||||||
\(194\) | −1022.00 | −0.378223 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1368.00 | −0.498542 | ||||||||
\(197\) | − 3054.00i | − 1.10451i | −0.833675 | − | 0.552255i | \(-0.813767\pi\) | ||||
0.833675 | − | 0.552255i | \(-0.186233\pi\) | |||||||
\(198\) | − 756.000i | − 0.271346i | ||||||||
\(199\) | −3425.00 | −1.22006 | −0.610030 | − | 0.792379i | \(-0.708842\pi\) | ||||
−0.610030 | + | 0.792379i | \(0.708842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −897.000 | −0.314774 | ||||||||
\(202\) | 1824.00i | 0.635328i | ||||||||
\(203\) | 210.000i | 0.0726065i | ||||||||
\(204\) | 648.000 | 0.222397 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1336.00 | −0.451862 | ||||||||
\(207\) | 1458.00i | 0.489556i | ||||||||
\(208\) | − 1072.00i | − 0.357355i | ||||||||
\(209\) | 4830.00 | 1.59856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2443.00 | −0.797076 | −0.398538 | − | 0.917152i | \(-0.630482\pi\) | ||||
−0.398538 | + | 0.917152i | \(0.630482\pi\) | |||||||
\(212\) | 768.000i | 0.248804i | ||||||||
\(213\) | 684.000i | 0.220032i | ||||||||
\(214\) | −2592.00 | −0.827969 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | − 193.000i | − 0.0603765i | ||||||||
\(218\) | 3470.00i | 1.07806i | ||||||||
\(219\) | 2814.00 | 0.868276 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3618.00 | −1.10124 | ||||||||
\(222\) | 1716.00i | 0.518785i | ||||||||
\(223\) | 23.0000i | 0.00690670i | 0.999994 | + | 0.00345335i | \(0.00109924\pi\) | ||||
−0.999994 | + | 0.00345335i | \(0.998901\pi\) | |||||||
\(224\) | −32.0000 | −0.00954504 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2184.00 | 0.642821 | ||||||||
\(227\) | 1956.00i | 0.571913i | 0.958243 | + | 0.285957i | \(0.0923113\pi\) | ||||
−0.958243 | + | 0.285957i | \(0.907689\pi\) | |||||||
\(228\) | 1380.00i | 0.400845i | ||||||||
\(229\) | −1805.00 | −0.520864 | −0.260432 | − | 0.965492i | \(-0.583865\pi\) | ||||
−0.260432 | + | 0.965492i | \(0.583865\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 126.000 | 0.0358883 | ||||||||
\(232\) | − 1680.00i | − 0.475420i | ||||||||
\(233\) | 3468.00i | 0.975091i | 0.873098 | + | 0.487546i | \(0.162108\pi\) | ||||
−0.873098 | + | 0.487546i | \(0.837892\pi\) | |||||||
\(234\) | −1206.00 | −0.336917 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2760.00 | 0.761274 | ||||||||
\(237\) | − 480.000i | − 0.131558i | ||||||||
\(238\) | 108.000i | 0.0294143i | ||||||||
\(239\) | −2640.00 | −0.714508 | −0.357254 | − | 0.934007i | \(-0.616287\pi\) | ||||
−0.357254 | + | 0.934007i | \(0.616287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5383.00 | −1.43879 | −0.719397 | − | 0.694599i | \(-0.755582\pi\) | ||||
−0.719397 | + | 0.694599i | \(0.755582\pi\) | |||||||
\(242\) | 866.000i | 0.230035i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 2932.00 | 0.769271 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 72.0000 | 0.0186608 | ||||||||
\(247\) | − 7705.00i | − 1.98485i | ||||||||
\(248\) | 1544.00i | 0.395339i | ||||||||
\(249\) | −1386.00 | −0.352748 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5028.00 | −1.26440 | −0.632200 | − | 0.774805i | \(-0.717848\pi\) | ||||
−0.632200 | + | 0.774805i | \(0.717848\pi\) | |||||||
\(252\) | 36.0000i | 0.00899915i | ||||||||
\(253\) | − 6804.00i | − 1.69077i | ||||||||
\(254\) | −32.0000 | −0.00790496 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 564.000i | − 0.136892i | −0.997655 | − | 0.0684462i | \(-0.978196\pi\) | ||||
0.997655 | − | 0.0684462i | \(-0.0218042\pi\) | |||||||
\(258\) | 1578.00i | 0.380783i | ||||||||
\(259\) | −286.000 | −0.0686146 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1890.00 | −0.448230 | ||||||||
\(262\) | 3984.00i | 0.939436i | ||||||||
\(263\) | − 1812.00i | − 0.424839i | −0.977179 | − | 0.212420i | \(-0.931866\pi\) | ||||
0.977179 | − | 0.212420i | \(-0.0681344\pi\) | |||||||
\(264\) | −1008.00 | −0.234993 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −230.000 | −0.0530158 | ||||||||
\(267\) | − 720.000i | − 0.165031i | ||||||||
\(268\) | 1196.00i | 0.272602i | ||||||||
\(269\) | 5190.00 | 1.17636 | 0.588178 | − | 0.808731i | \(-0.299845\pi\) | ||||
0.588178 | + | 0.808731i | \(0.299845\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4592.00 | 1.02931 | 0.514657 | − | 0.857396i | \(-0.327919\pi\) | ||||
0.514657 | + | 0.857396i | \(0.327919\pi\) | |||||||
\(272\) | − 864.000i | − 0.192602i | ||||||||
\(273\) | − 201.000i | − 0.0445607i | ||||||||
\(274\) | −4692.00 | −1.03450 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1944.00 | 0.423968 | ||||||||
\(277\) | 2191.00i | 0.475251i | 0.971357 | + | 0.237625i | \(0.0763690\pi\) | ||||
−0.971357 | + | 0.237625i | \(0.923631\pi\) | |||||||
\(278\) | − 5800.00i | − 1.25130i | ||||||||
\(279\) | 1737.00 | 0.372729 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7842.00 | 1.66482 | 0.832410 | − | 0.554160i | \(-0.186960\pi\) | ||||
0.832410 | + | 0.554160i | \(0.186960\pi\) | |||||||
\(282\) | − 2484.00i | − 0.524539i | ||||||||
\(283\) | − 247.000i | − 0.0518821i | −0.999663 | − | 0.0259410i | \(-0.991742\pi\) | ||||
0.999663 | − | 0.0259410i | \(-0.00825821\pi\) | |||||||
\(284\) | 912.000 | 0.190554 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5628.00 | 1.16360 | ||||||||
\(287\) | 12.0000i | 0.00246808i | ||||||||
\(288\) | − 288.000i | − 0.0589256i | ||||||||
\(289\) | 1997.00 | 0.406473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1533.00 | 0.308818 | ||||||||
\(292\) | − 3752.00i | − 0.751949i | ||||||||
\(293\) | − 5442.00i | − 1.08507i | −0.840034 | − | 0.542534i | \(-0.817465\pi\) | ||||
0.840034 | − | 0.542534i | \(-0.182535\pi\) | |||||||
\(294\) | 2052.00 | 0.407058 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2288.00 | 0.449281 | ||||||||
\(297\) | 1134.00i | 0.221553i | ||||||||
\(298\) | 4140.00i | 0.804778i | ||||||||
\(299\) | −10854.0 | −2.09934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −263.000 | −0.0503624 | ||||||||
\(302\) | 4474.00i | 0.852483i | ||||||||
\(303\) | − 2736.00i | − 0.518743i | ||||||||
\(304\) | 1840.00 | 0.347142 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −972.000 | −0.181587 | ||||||||
\(307\) | 3871.00i | 0.719641i | 0.933022 | + | 0.359820i | \(0.117162\pi\) | ||||
−0.933022 | + | 0.359820i | \(0.882838\pi\) | |||||||
\(308\) | − 168.000i | − 0.0310802i | ||||||||
\(309\) | 2004.00 | 0.368944 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5718.00 | −1.04257 | −0.521283 | − | 0.853384i | \(-0.674546\pi\) | ||||
−0.521283 | + | 0.853384i | \(0.674546\pi\) | |||||||
\(312\) | 1608.00i | 0.291779i | ||||||||
\(313\) | − 3637.00i | − 0.656790i | −0.944540 | − | 0.328395i | \(-0.893492\pi\) | ||||
0.944540 | − | 0.328395i | \(-0.106508\pi\) | |||||||
\(314\) | −482.000 | −0.0866269 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −640.000 | −0.113933 | ||||||||
\(317\) | 1296.00i | 0.229623i | 0.993387 | + | 0.114812i | \(0.0366265\pi\) | ||||
−0.993387 | + | 0.114812i | \(0.963374\pi\) | |||||||
\(318\) | − 1152.00i | − 0.203148i | ||||||||
\(319\) | 8820.00 | 1.54804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3888.00 | 0.676034 | ||||||||
\(322\) | 324.000i | 0.0560740i | ||||||||
\(323\) | − 6210.00i | − 1.06976i | ||||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7094.00 | 1.20522 | ||||||||
\(327\) | − 5205.00i | − 0.880236i | ||||||||
\(328\) | − 96.0000i | − 0.0161607i | ||||||||
\(329\) | 414.000 | 0.0693756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5132.00 | 0.852206 | 0.426103 | − | 0.904675i | \(-0.359886\pi\) | ||||
0.426103 | + | 0.904675i | \(0.359886\pi\) | |||||||
\(332\) | 1848.00i | 0.305488i | ||||||||
\(333\) | − 2574.00i | − 0.423587i | ||||||||
\(334\) | 1968.00 | 0.322408 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 48.0000 | 0.00779350 | ||||||||
\(337\) | 6751.00i | 1.09125i | 0.838030 | + | 0.545624i | \(0.183707\pi\) | ||||
−0.838030 | + | 0.545624i | \(0.816293\pi\) | |||||||
\(338\) | − 4584.00i | − 0.737683i | ||||||||
\(339\) | −3276.00 | −0.524861 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8106.00 | −1.28729 | ||||||||
\(342\) | − 2070.00i | − 0.327289i | ||||||||
\(343\) | 685.000i | 0.107832i | ||||||||
\(344\) | 2104.00 | 0.329768 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7236.00 | −1.12431 | ||||||||
\(347\) | 5226.00i | 0.808491i | 0.914651 | + | 0.404246i | \(0.132466\pi\) | ||||
−0.914651 | + | 0.404246i | \(0.867534\pi\) | |||||||
\(348\) | 2520.00i | 0.388179i | ||||||||
\(349\) | 6190.00 | 0.949407 | 0.474704 | − | 0.880146i | \(-0.342555\pi\) | ||||
0.474704 | + | 0.880146i | \(0.342555\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1809.00 | 0.275092 | ||||||||
\(352\) | 1344.00i | 0.203510i | ||||||||
\(353\) | 6618.00i | 0.997849i | 0.866646 | + | 0.498924i | \(0.166271\pi\) | ||||
−0.866646 | + | 0.498924i | \(0.833729\pi\) | |||||||
\(354\) | −4140.00 | −0.621578 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −960.000 | −0.142921 | ||||||||
\(357\) | − 162.000i | − 0.0240167i | ||||||||
\(358\) | 300.000i | 0.0442891i | ||||||||
\(359\) | 3420.00 | 0.502787 | 0.251394 | − | 0.967885i | \(-0.419111\pi\) | ||||
0.251394 | + | 0.967885i | \(0.419111\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6366.00 | 0.928124 | ||||||||
\(362\) | 394.000i | 0.0572049i | ||||||||
\(363\) | − 1299.00i | − 0.187823i | ||||||||
\(364\) | −268.000 | −0.0385907 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4398.00 | −0.628107 | ||||||||
\(367\) | 871.000i | 0.123885i | 0.998080 | + | 0.0619425i | \(0.0197296\pi\) | ||||
−0.998080 | + | 0.0619425i | \(0.980270\pi\) | |||||||
\(368\) | − 2592.00i | − 0.367167i | ||||||||
\(369\) | −108.000 | −0.0152365 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 192.000 | 0.0268683 | ||||||||
\(372\) | − 2316.00i | − 0.322793i | ||||||||
\(373\) | 6383.00i | 0.886057i | 0.896508 | + | 0.443028i | \(0.146096\pi\) | ||||
−0.896508 | + | 0.443028i | \(0.853904\pi\) | |||||||
\(374\) | 4536.00 | 0.627142 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3312.00 | −0.454264 | ||||||||
\(377\) | − 14070.0i | − 1.92213i | ||||||||
\(378\) | − 54.0000i | − 0.00734778i | ||||||||
\(379\) | 9865.00 | 1.33702 | 0.668511 | − | 0.743703i | \(-0.266932\pi\) | ||||
0.668511 | + | 0.743703i | \(0.266932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 48.0000 | 0.00645437 | ||||||||
\(382\) | 2604.00i | 0.348775i | ||||||||
\(383\) | 9828.00i | 1.31119i | 0.755111 | + | 0.655597i | \(0.227583\pi\) | ||||
−0.755111 | + | 0.655597i | \(0.772417\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8326.00 | −1.09788 | ||||||||
\(387\) | − 2367.00i | − 0.310908i | ||||||||
\(388\) | − 2044.00i | − 0.267444i | ||||||||
\(389\) | −12540.0 | −1.63446 | −0.817228 | − | 0.576315i | \(-0.804490\pi\) | ||||
−0.817228 | + | 0.576315i | \(0.804490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8748.00 | −1.13147 | ||||||||
\(392\) | − 2736.00i | − 0.352523i | ||||||||
\(393\) | − 5976.00i | − 0.767047i | ||||||||
\(394\) | 6108.00 | 0.781007 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1512.00 | 0.191871 | ||||||||
\(397\) | 1381.00i | 0.174585i | 0.996183 | + | 0.0872927i | \(0.0278215\pi\) | ||||
−0.996183 | + | 0.0872927i | \(0.972178\pi\) | |||||||
\(398\) | − 6850.00i | − 0.862712i | ||||||||
\(399\) | 345.000 | 0.0432872 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14232.0 | 1.77235 | 0.886175 | − | 0.463351i | \(-0.153353\pi\) | ||||
0.886175 | + | 0.463351i | \(0.153353\pi\) | |||||||
\(402\) | − 1794.00i | − 0.222579i | ||||||||
\(403\) | 12931.0i | 1.59836i | ||||||||
\(404\) | −3648.00 | −0.449245 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −420.000 | −0.0513405 | ||||||||
\(407\) | 12012.0i | 1.46293i | ||||||||
\(408\) | 1296.00i | 0.157259i | ||||||||
\(409\) | −2645.00 | −0.319772 | −0.159886 | − | 0.987135i | \(-0.551113\pi\) | ||||
−0.159886 | + | 0.987135i | \(0.551113\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7038.00 | 0.844669 | ||||||||
\(412\) | − 2672.00i | − 0.319515i | ||||||||
\(413\) | − 690.000i | − 0.0822099i | ||||||||
\(414\) | −2916.00 | −0.346168 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2144.00 | 0.252688 | ||||||||
\(417\) | 8700.00i | 1.02168i | ||||||||
\(418\) | 9660.00i | 1.13035i | ||||||||
\(419\) | −3000.00 | −0.349784 | −0.174892 | − | 0.984588i | \(-0.555958\pi\) | ||||
−0.174892 | + | 0.984588i | \(0.555958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11338.0 | −1.31254 | −0.656271 | − | 0.754525i | \(-0.727867\pi\) | ||||
−0.656271 | + | 0.754525i | \(0.727867\pi\) | |||||||
\(422\) | − 4886.00i | − 0.563618i | ||||||||
\(423\) | 3726.00i | 0.428284i | ||||||||
\(424\) | −1536.00 | −0.175931 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1368.00 | −0.155586 | ||||||||
\(427\) | − 733.000i | − 0.0830734i | ||||||||
\(428\) | − 5184.00i | − 0.585463i | ||||||||
\(429\) | −8442.00 | −0.950078 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3258.00 | −0.364112 | −0.182056 | − | 0.983288i | \(-0.558275\pi\) | ||||
−0.182056 | + | 0.983288i | \(0.558275\pi\) | |||||||
\(432\) | 432.000i | 0.0481125i | ||||||||
\(433\) | 1163.00i | 0.129077i | 0.997915 | + | 0.0645384i | \(0.0205575\pi\) | ||||
−0.997915 | + | 0.0645384i | \(0.979443\pi\) | |||||||
\(434\) | 386.000 | 0.0426926 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6940.00 | −0.762307 | ||||||||
\(437\) | − 18630.0i | − 2.03934i | ||||||||
\(438\) | 5628.00i | 0.613964i | ||||||||
\(439\) | −6695.00 | −0.727870 | −0.363935 | − | 0.931424i | \(-0.618567\pi\) | ||||
−0.363935 | + | 0.931424i | \(0.618567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3078.00 | −0.332362 | ||||||||
\(442\) | − 7236.00i | − 0.778691i | ||||||||
\(443\) | 16368.0i | 1.75546i | 0.479159 | + | 0.877728i | \(0.340942\pi\) | ||||
−0.479159 | + | 0.877728i | \(0.659058\pi\) | |||||||
\(444\) | −3432.00 | −0.366837 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −46.0000 | −0.00488377 | ||||||||
\(447\) | − 6210.00i | − 0.657098i | ||||||||
\(448\) | − 64.0000i | − 0.00674937i | ||||||||
\(449\) | −16380.0 | −1.72165 | −0.860824 | − | 0.508903i | \(-0.830051\pi\) | ||||
−0.860824 | + | 0.508903i | \(0.830051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 504.000 | 0.0526218 | ||||||||
\(452\) | 4368.00i | 0.454543i | ||||||||
\(453\) | − 6711.00i | − 0.696049i | ||||||||
\(454\) | −3912.00 | −0.404404 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2760.00 | −0.283440 | ||||||||
\(457\) | 13786.0i | 1.41112i | 0.708650 | + | 0.705560i | \(0.249304\pi\) | ||||
−0.708650 | + | 0.705560i | \(0.750696\pi\) | |||||||
\(458\) | − 3610.00i | − 0.368306i | ||||||||
\(459\) | 1458.00 | 0.148265 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11832.0 | 1.19538 | 0.597691 | − | 0.801726i | \(-0.296085\pi\) | ||||
0.597691 | + | 0.801726i | \(0.296085\pi\) | |||||||
\(462\) | 252.000i | 0.0253768i | ||||||||
\(463\) | 3008.00i | 0.301930i | 0.988539 | + | 0.150965i | \(0.0482381\pi\) | ||||
−0.988539 | + | 0.150965i | \(0.951762\pi\) | |||||||
\(464\) | 3360.00 | 0.336173 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6936.00 | −0.689494 | ||||||||
\(467\) | − 4434.00i | − 0.439360i | −0.975572 | − | 0.219680i | \(-0.929499\pi\) | ||||
0.975572 | − | 0.219680i | \(-0.0705013\pi\) | |||||||
\(468\) | − 2412.00i | − 0.238237i | ||||||||
\(469\) | 299.000 | 0.0294382 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 723.000 | 0.0707305 | ||||||||
\(472\) | 5520.00i | 0.538302i | ||||||||
\(473\) | 11046.0i | 1.07378i | ||||||||
\(474\) | 960.000 | 0.0930259 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −216.000 | −0.0207990 | ||||||||
\(477\) | 1728.00i | 0.165869i | ||||||||
\(478\) | − 5280.00i | − 0.505233i | ||||||||
\(479\) | −7410.00 | −0.706830 | −0.353415 | − | 0.935467i | \(-0.614980\pi\) | ||||
−0.353415 | + | 0.935467i | \(0.614980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19162.0 | 1.81645 | ||||||||
\(482\) | − 10766.0i | − 1.01738i | ||||||||
\(483\) | − 486.000i | − 0.0457842i | ||||||||
\(484\) | −1732.00 | −0.162660 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 8671.00i | 0.806818i | 0.915020 | + | 0.403409i | \(0.132175\pi\) | ||||
−0.915020 | + | 0.403409i | \(0.867825\pi\) | |||||||
\(488\) | 5864.00i | 0.543957i | ||||||||
\(489\) | −10641.0 | −0.984055 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19368.0 | −1.78017 | −0.890087 | − | 0.455790i | \(-0.849357\pi\) | ||||
−0.890087 | + | 0.455790i | \(0.849357\pi\) | |||||||
\(492\) | 144.000i | 0.0131952i | ||||||||
\(493\) | − 11340.0i | − 1.03596i | ||||||||
\(494\) | 15410.0 | 1.40350 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3088.00 | −0.279547 | ||||||||
\(497\) | − 228.000i | − 0.0205779i | ||||||||
\(498\) | − 2772.00i | − 0.249430i | ||||||||
\(499\) | 8875.00 | 0.796192 | 0.398096 | − | 0.917344i | \(-0.369671\pi\) | ||||
0.398096 | + | 0.917344i | \(0.369671\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2952.00 | −0.263245 | ||||||||
\(502\) | − 10056.0i | − 0.894066i | ||||||||
\(503\) | − 10452.0i | − 0.926504i | −0.886227 | − | 0.463252i | \(-0.846682\pi\) | ||||
0.886227 | − | 0.463252i | \(-0.153318\pi\) | |||||||
\(504\) | −72.0000 | −0.00636336 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13608.0 | 1.19555 | ||||||||
\(507\) | 6876.00i | 0.602315i | ||||||||
\(508\) | − 64.0000i | − 0.00558965i | ||||||||
\(509\) | 19770.0 | 1.72159 | 0.860796 | − | 0.508951i | \(-0.169967\pi\) | ||||
0.860796 | + | 0.508951i | \(0.169967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −938.000 | −0.0812029 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 3105.00i | 0.267230i | ||||||||
\(514\) | 1128.00 | 0.0967976 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3156.00 | −0.269254 | ||||||||
\(517\) | − 17388.0i | − 1.47916i | ||||||||
\(518\) | − 572.000i | − 0.0485178i | ||||||||
\(519\) | 10854.0 | 0.917992 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11238.0 | −0.945001 | −0.472501 | − | 0.881330i | \(-0.656649\pi\) | ||||
−0.472501 | + | 0.881330i | \(0.656649\pi\) | |||||||
\(522\) | − 3780.00i | − 0.316947i | ||||||||
\(523\) | − 7447.00i | − 0.622628i | −0.950307 | − | 0.311314i | \(-0.899231\pi\) | ||||
0.950307 | − | 0.311314i | \(-0.100769\pi\) | |||||||
\(524\) | −7968.00 | −0.664282 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3624.00 | 0.300407 | ||||||||
\(527\) | 10422.0i | 0.861460i | ||||||||
\(528\) | − 2016.00i | − 0.166165i | ||||||||
\(529\) | −14077.0 | −1.15698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6210.00 | 0.507516 | ||||||||
\(532\) | − 460.000i | − 0.0374878i | ||||||||
\(533\) | − 804.000i | − 0.0653379i | ||||||||
\(534\) | 1440.00 | 0.116695 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2392.00 | −0.192759 | ||||||||
\(537\) | − 450.000i | − 0.0361619i | ||||||||
\(538\) | 10380.0i | 0.831810i | ||||||||
\(539\) | 14364.0 | 1.14787 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17623.0 | −1.40050 | −0.700251 | − | 0.713896i | \(-0.746929\pi\) | ||||
−0.700251 | + | 0.713896i | \(0.746929\pi\) | |||||||
\(542\) | 9184.00i | 0.727835i | ||||||||
\(543\) | − 591.000i | − 0.0467076i | ||||||||
\(544\) | 1728.00 | 0.136190 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 402.000 | 0.0315092 | ||||||||
\(547\) | 10096.0i | 0.789166i | 0.918860 | + | 0.394583i | \(0.129111\pi\) | ||||
−0.918860 | + | 0.394583i | \(0.870889\pi\) | |||||||
\(548\) | − 9384.00i | − 0.731505i | ||||||||
\(549\) | 6597.00 | 0.512847 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24150.0 | 1.86720 | ||||||||
\(552\) | 3888.00i | 0.299790i | ||||||||
\(553\) | 160.000i | 0.0123036i | ||||||||
\(554\) | −4382.00 | −0.336053 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11600.0 | 0.884801 | ||||||||
\(557\) | − 14514.0i | − 1.10409i | −0.833814 | − | 0.552045i | \(-0.813848\pi\) | ||||
0.833814 | − | 0.552045i | \(-0.186152\pi\) | |||||||
\(558\) | 3474.00i | 0.263559i | ||||||||
\(559\) | 17621.0 | 1.33325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6804.00 | −0.512059 | ||||||||
\(562\) | 15684.0i | 1.17721i | ||||||||
\(563\) | − 10242.0i | − 0.766694i | −0.923604 | − | 0.383347i | \(-0.874771\pi\) | ||||
0.923604 | − | 0.383347i | \(-0.125229\pi\) | |||||||
\(564\) | 4968.00 | 0.370905 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 494.000 | 0.0366862 | ||||||||
\(567\) | 81.0000i | 0.00599944i | ||||||||
\(568\) | 1824.00i | 0.134742i | ||||||||
\(569\) | 6750.00 | 0.497319 | 0.248660 | − | 0.968591i | \(-0.420010\pi\) | ||||
0.248660 | + | 0.968591i | \(0.420010\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17117.0 | 1.25451 | 0.627254 | − | 0.778815i | \(-0.284179\pi\) | ||||
0.627254 | + | 0.778815i | \(0.284179\pi\) | |||||||
\(572\) | 11256.0i | 0.822792i | ||||||||
\(573\) | − 3906.00i | − 0.284774i | ||||||||
\(574\) | −24.0000 | −0.00174519 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 301.000i | 0.0217171i | 0.999941 | + | 0.0108586i | \(0.00345646\pi\) | ||||
−0.999941 | + | 0.0108586i | \(0.996544\pi\) | |||||||
\(578\) | 3994.00i | 0.287420i | ||||||||
\(579\) | 12489.0 | 0.896416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 462.000 | 0.0329897 | ||||||||
\(582\) | 3066.00i | 0.218367i | ||||||||
\(583\) | − 8064.00i | − 0.572859i | ||||||||
\(584\) | 7504.00 | 0.531708 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10884.0 | 0.767259 | ||||||||
\(587\) | 15456.0i | 1.08678i | 0.839482 | + | 0.543388i | \(0.182859\pi\) | ||||
−0.839482 | + | 0.543388i | \(0.817141\pi\) | |||||||
\(588\) | 4104.00i | 0.287834i | ||||||||
\(589\) | −22195.0 | −1.55268 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9162.00 | −0.637689 | ||||||||
\(592\) | 4576.00i | 0.317690i | ||||||||
\(593\) | − 9492.00i | − 0.657318i | −0.944449 | − | 0.328659i | \(-0.893403\pi\) | ||||
0.944449 | − | 0.328659i | \(-0.106597\pi\) | |||||||
\(594\) | −2268.00 | −0.156662 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8280.00 | −0.569064 | ||||||||
\(597\) | 10275.0i | 0.704402i | ||||||||
\(598\) | − 21708.0i | − 1.48446i | ||||||||
\(599\) | −1500.00 | −0.102318 | −0.0511589 | − | 0.998691i | \(-0.516291\pi\) | ||||
−0.0511589 | + | 0.998691i | \(0.516291\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14627.0 | 0.992758 | 0.496379 | − | 0.868106i | \(-0.334663\pi\) | ||||
0.496379 | + | 0.868106i | \(0.334663\pi\) | |||||||
\(602\) | − 526.000i | − 0.0356116i | ||||||||
\(603\) | 2691.00i | 0.181735i | ||||||||
\(604\) | −8948.00 | −0.602796 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5472.00 | 0.366807 | ||||||||
\(607\) | − 16184.0i | − 1.08219i | −0.840962 | − | 0.541094i | \(-0.818010\pi\) | ||||
0.840962 | − | 0.541094i | \(-0.181990\pi\) | |||||||
\(608\) | 3680.00i | 0.245467i | ||||||||
\(609\) | 630.000 | 0.0419194 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27738.0 | −1.83659 | ||||||||
\(612\) | − 1944.00i | − 0.128401i | ||||||||
\(613\) | − 18502.0i | − 1.21907i | −0.792760 | − | 0.609534i | \(-0.791357\pi\) | ||||
0.792760 | − | 0.609534i | \(-0.208643\pi\) | |||||||
\(614\) | −7742.00 | −0.508863 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 336.000 | 0.0219770 | ||||||||
\(617\) | 13896.0i | 0.906697i | 0.891333 | + | 0.453348i | \(0.149771\pi\) | ||||
−0.891333 | + | 0.453348i | \(0.850229\pi\) | |||||||
\(618\) | 4008.00i | 0.260883i | ||||||||
\(619\) | 9895.00 | 0.642510 | 0.321255 | − | 0.946993i | \(-0.395895\pi\) | ||||
0.321255 | + | 0.946993i | \(0.395895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4374.00 | 0.282645 | ||||||||
\(622\) | − 11436.0i | − 0.737206i | ||||||||
\(623\) | 240.000i | 0.0154340i | ||||||||
\(624\) | −3216.00 | −0.206319 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7274.00 | 0.464421 | ||||||||
\(627\) | − 14490.0i | − 0.922926i | ||||||||
\(628\) | − 964.000i | − 0.0612544i | ||||||||
\(629\) | 15444.0 | 0.979003 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 467.000 | 0.0294627 | 0.0147314 | − | 0.999891i | \(-0.495311\pi\) | ||||
0.0147314 | + | 0.999891i | \(0.495311\pi\) | |||||||
\(632\) | − 1280.00i | − 0.0805628i | ||||||||
\(633\) | 7329.00i | 0.460192i | ||||||||
\(634\) | −2592.00 | −0.162368 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2304.00 | 0.143647 | ||||||||
\(637\) | − 22914.0i | − 1.42525i | ||||||||
\(638\) | 17640.0i | 1.09463i | ||||||||
\(639\) | 2052.00 | 0.127036 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30612.0 | 1.88627 | 0.943137 | − | 0.332405i | \(-0.107860\pi\) | ||||
0.943137 | + | 0.332405i | \(0.107860\pi\) | |||||||
\(642\) | 7776.00i | 0.478028i | ||||||||
\(643\) | − 1852.00i | − 0.113586i | −0.998386 | − | 0.0567930i | \(-0.981913\pi\) | ||||
0.998386 | − | 0.0567930i | \(-0.0180875\pi\) | |||||||
\(644\) | −648.000 | −0.0396503 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12420.0 | 0.756437 | ||||||||
\(647\) | 21156.0i | 1.28551i | 0.766070 | + | 0.642757i | \(0.222210\pi\) | ||||
−0.766070 | + | 0.642757i | \(0.777790\pi\) | |||||||
\(648\) | − 648.000i | − 0.0392837i | ||||||||
\(649\) | −28980.0 | −1.75280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −579.000 | −0.0348584 | ||||||||
\(652\) | 14188.0i | 0.852216i | ||||||||
\(653\) | − 9702.00i | − 0.581422i | −0.956811 | − | 0.290711i | \(-0.906108\pi\) | ||||
0.956811 | − | 0.290711i | \(-0.0938918\pi\) | |||||||
\(654\) | 10410.0 | 0.622421 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 192.000 | 0.0114273 | ||||||||
\(657\) | − 8442.00i | − 0.501300i | ||||||||
\(658\) | 828.000i | 0.0490559i | ||||||||
\(659\) | −1980.00 | −0.117041 | −0.0585204 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585204 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20158.0 | −1.18617 | −0.593083 | − | 0.805142i | \(-0.702089\pi\) | ||||
−0.593083 | + | 0.805142i | \(0.702089\pi\) | |||||||
\(662\) | 10264.0i | 0.602601i | ||||||||
\(663\) | 10854.0i | 0.635799i | ||||||||
\(664\) | −3696.00 | −0.216013 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5148.00 | 0.299521 | ||||||||
\(667\) | − 34020.0i | − 1.97490i | ||||||||
\(668\) | 3936.00i | 0.227977i | ||||||||
\(669\) | 69.0000 | 0.00398758 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30786.0 | −1.77121 | ||||||||
\(672\) | 96.0000i | 0.00551083i | ||||||||
\(673\) | − 16882.0i | − 0.966944i | −0.875360 | − | 0.483472i | \(-0.839376\pi\) | ||||
0.875360 | − | 0.483472i | \(-0.160624\pi\) | |||||||
\(674\) | −13502.0 | −0.771628 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9168.00 | 0.521620 | ||||||||
\(677\) | − 20934.0i | − 1.18842i | −0.804311 | − | 0.594209i | \(-0.797465\pi\) | ||||
0.804311 | − | 0.594209i | \(-0.202535\pi\) | |||||||
\(678\) | − 6552.00i | − 0.371133i | ||||||||
\(679\) | −511.000 | −0.0288813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5868.00 | 0.330194 | ||||||||
\(682\) | − 16212.0i | − 0.910249i | ||||||||
\(683\) | − 8712.00i | − 0.488075i | −0.969766 | − | 0.244038i | \(-0.921528\pi\) | ||||
0.969766 | − | 0.244038i | \(-0.0784720\pi\) | |||||||
\(684\) | 4140.00 | 0.231428 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1370.00 | −0.0762490 | ||||||||
\(687\) | 5415.00i | 0.300721i | ||||||||
\(688\) | 4208.00i | 0.233181i | ||||||||
\(689\) | −12864.0 | −0.711291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14128.0 | −0.777792 | −0.388896 | − | 0.921282i | \(-0.627144\pi\) | ||||
−0.388896 | + | 0.921282i | \(0.627144\pi\) | |||||||
\(692\) | − 14472.0i | − 0.795004i | ||||||||
\(693\) | − 378.000i | − 0.0207201i | ||||||||
\(694\) | −10452.0 | −0.571689 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5040.00 | −0.274484 | ||||||||
\(697\) | − 648.000i | − 0.0352148i | ||||||||
\(698\) | 12380.0i | 0.671332i | ||||||||
\(699\) | 10404.0 | 0.562969 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28278.0 | −1.52360 | −0.761801 | − | 0.647811i | \(-0.775685\pi\) | ||||
−0.761801 | + | 0.647811i | \(0.775685\pi\) | |||||||
\(702\) | 3618.00i | 0.194519i | ||||||||
\(703\) | 32890.0i | 1.76454i | ||||||||
\(704\) | −2688.00 | −0.143903 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13236.0 | −0.705586 | ||||||||
\(707\) | 912.000i | 0.0485138i | ||||||||
\(708\) | − 8280.00i | − 0.439522i | ||||||||
\(709\) | −8885.00 | −0.470639 | −0.235320 | − | 0.971918i | \(-0.575614\pi\) | ||||
−0.235320 | + | 0.971918i | \(0.575614\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1440.00 | −0.0759553 | ||||||||
\(712\) | − 1920.00i | − 0.101060i | ||||||||
\(713\) | 31266.0i | 1.64225i | ||||||||
\(714\) | 324.000 | 0.0169823 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −600.000 | −0.0313171 | ||||||||
\(717\) | 7920.00i | 0.412521i | ||||||||
\(718\) | 6840.00i | 0.355524i | ||||||||
\(719\) | 7530.00 | 0.390572 | 0.195286 | − | 0.980746i | \(-0.437436\pi\) | ||||
0.195286 | + | 0.980746i | \(0.437436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −668.000 | −0.0345043 | ||||||||
\(722\) | 12732.0i | 0.656283i | ||||||||
\(723\) | 16149.0i | 0.830688i | ||||||||
\(724\) | −788.000 | −0.0404500 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2598.00 | 0.132811 | ||||||||
\(727\) | 1801.00i | 0.0918781i | 0.998944 | + | 0.0459391i | \(0.0146280\pi\) | ||||
−0.998944 | + | 0.0459391i | \(0.985372\pi\) | |||||||
\(728\) | − 536.000i | − 0.0272877i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14202.0 | 0.718577 | ||||||||
\(732\) | − 8796.00i | − 0.444139i | ||||||||
\(733\) | − 7882.00i | − 0.397174i | −0.980083 | − | 0.198587i | \(-0.936365\pi\) | ||||
0.980083 | − | 0.198587i | \(-0.0636352\pi\) | |||||||
\(734\) | −1742.00 | −0.0876000 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5184.00 | 0.259626 | ||||||||
\(737\) | − 12558.0i | − 0.627652i | ||||||||
\(738\) | − 216.000i | − 0.0107738i | ||||||||
\(739\) | −33860.0 | −1.68547 | −0.842734 | − | 0.538331i | \(-0.819055\pi\) | ||||
−0.842734 | + | 0.538331i | \(0.819055\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23115.0 | −1.14595 | ||||||||
\(742\) | 384.000i | 0.0189988i | ||||||||
\(743\) | − 20652.0i | − 1.01972i | −0.860259 | − | 0.509858i | \(-0.829698\pi\) | ||||
0.860259 | − | 0.509858i | \(-0.170302\pi\) | |||||||
\(744\) | 4632.00 | 0.228249 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12766.0 | −0.626537 | ||||||||
\(747\) | 4158.00i | 0.203659i | ||||||||
\(748\) | 9072.00i | 0.443456i | ||||||||
\(749\) | −1296.00 | −0.0632240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7472.00 | 0.363059 | 0.181529 | − | 0.983386i | \(-0.441895\pi\) | ||||
0.181529 | + | 0.983386i | \(0.441895\pi\) | |||||||
\(752\) | − 6624.00i | − 0.321213i | ||||||||
\(753\) | 15084.0i | 0.730002i | ||||||||
\(754\) | 28140.0 | 1.35915 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 108.000 | 0.00519566 | ||||||||
\(757\) | 32251.0i | 1.54846i | 0.632906 | + | 0.774229i | \(0.281862\pi\) | ||||
−0.632906 | + | 0.774229i | \(0.718138\pi\) | |||||||
\(758\) | 19730.0i | 0.945417i | ||||||||
\(759\) | −20412.0 | −0.976164 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16812.0 | 0.800834 | 0.400417 | − | 0.916333i | \(-0.368865\pi\) | ||||
0.400417 | + | 0.916333i | \(0.368865\pi\) | |||||||
\(762\) | 96.0000i | 0.00456393i | ||||||||
\(763\) | 1735.00i | 0.0823214i | ||||||||
\(764\) | −5208.00 | −0.246622 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19656.0 | −0.927154 | ||||||||
\(767\) | 46230.0i | 2.17636i | ||||||||
\(768\) | − 768.000i | − 0.0360844i | ||||||||
\(769\) | 34645.0 | 1.62462 | 0.812309 | − | 0.583228i | \(-0.198211\pi\) | ||||
0.812309 | + | 0.583228i | \(0.198211\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1692.00 | −0.0790349 | ||||||||
\(772\) | − 16652.0i | − 0.776319i | ||||||||
\(773\) | − 8412.00i | − 0.391408i | −0.980663 | − | 0.195704i | \(-0.937301\pi\) | ||||
0.980663 | − | 0.195704i | \(-0.0626992\pi\) | |||||||
\(774\) | 4734.00 | 0.219845 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4088.00 | 0.189112 | ||||||||
\(777\) | 858.000i | 0.0396146i | ||||||||
\(778\) | − 25080.0i | − 1.15573i | ||||||||
\(779\) | 1380.00 | 0.0634706 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9576.00 | −0.438740 | ||||||||
\(782\) | − 17496.0i | − 0.800071i | ||||||||
\(783\) | 5670.00i | 0.258786i | ||||||||
\(784\) | 5472.00 | 0.249271 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 11952.0 | 0.542384 | ||||||||
\(787\) | − 18329.0i | − 0.830188i | −0.909778 | − | 0.415094i | \(-0.863749\pi\) | ||||
0.909778 | − | 0.415094i | \(-0.136251\pi\) | |||||||
\(788\) | 12216.0i | 0.552255i | ||||||||
\(789\) | −5436.00 | −0.245281 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1092.00 | 0.0490860 | ||||||||
\(792\) | 3024.00i | 0.135673i | ||||||||
\(793\) | 49111.0i | 2.19922i | ||||||||
\(794\) | −2762.00 | −0.123451 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13700.0 | 0.610030 | ||||||||
\(797\) | − 16044.0i | − 0.713059i | −0.934284 | − | 0.356529i | \(-0.883960\pi\) | ||||
0.934284 | − | 0.356529i | \(-0.116040\pi\) | |||||||
\(798\) | 690.000i | 0.0306087i | ||||||||
\(799\) | −22356.0 | −0.989860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2160.00 | −0.0952807 | ||||||||
\(802\) | 28464.0i | 1.25324i | ||||||||
\(803\) | 39396.0i | 1.73133i | ||||||||
\(804\) | 3588.00 | 0.157387 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25862.0 | −1.13021 | ||||||||
\(807\) | − 15570.0i | − 0.679170i | ||||||||
\(808\) | − 7296.00i | − 0.317664i | ||||||||
\(809\) | 24000.0 | 1.04301 | 0.521505 | − | 0.853248i | \(-0.325371\pi\) | ||||
0.521505 | + | 0.853248i | \(0.325371\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5117.00 | 0.221556 | 0.110778 | − | 0.993845i | \(-0.464666\pi\) | ||||
0.110778 | + | 0.993845i | \(0.464666\pi\) | |||||||
\(812\) | − 840.000i | − 0.0363032i | ||||||||
\(813\) | − 13776.0i | − 0.594275i | ||||||||
\(814\) | −24024.0 | −1.03445 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2592.00 | −0.111199 | ||||||||
\(817\) | 30245.0i | 1.29515i | ||||||||
\(818\) | − 5290.00i | − 0.226113i | ||||||||
\(819\) | −603.000 | −0.0257271 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13542.0 | 0.575663 | 0.287831 | − | 0.957681i | \(-0.407066\pi\) | ||||
0.287831 | + | 0.957681i | \(0.407066\pi\) | |||||||
\(822\) | 14076.0i | 0.597271i | ||||||||
\(823\) | 1283.00i | 0.0543409i | 0.999631 | + | 0.0271705i | \(0.00864969\pi\) | ||||
−0.999631 | + | 0.0271705i | \(0.991350\pi\) | |||||||
\(824\) | 5344.00 | 0.225931 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1380.00 | 0.0581312 | ||||||||
\(827\) | − 16344.0i | − 0.687227i | −0.939111 | − | 0.343613i | \(-0.888349\pi\) | ||||
0.939111 | − | 0.343613i | \(-0.111651\pi\) | |||||||
\(828\) | − 5832.00i | − 0.244778i | ||||||||
\(829\) | 790.000 | 0.0330975 | 0.0165488 | − | 0.999863i | \(-0.494732\pi\) | ||||
0.0165488 | + | 0.999863i | \(0.494732\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6573.00 | 0.274386 | ||||||||
\(832\) | 4288.00i | 0.178677i | ||||||||
\(833\) | − 18468.0i | − 0.768161i | ||||||||
\(834\) | −17400.0 | −0.722437 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −19320.0 | −0.799278 | ||||||||
\(837\) | − 5211.00i | − 0.215195i | ||||||||
\(838\) | − 6000.00i | − 0.247335i | ||||||||
\(839\) | 9990.00 | 0.411076 | 0.205538 | − | 0.978649i | \(-0.434106\pi\) | ||||
0.205538 | + | 0.978649i | \(0.434106\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19711.0 | 0.808192 | ||||||||
\(842\) | − 22676.0i | − 0.928108i | ||||||||
\(843\) | − 23526.0i | − 0.961184i | ||||||||
\(844\) | 9772.00 | 0.398538 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7452.00 | −0.302843 | ||||||||
\(847\) | 433.000i | 0.0175656i | ||||||||
\(848\) | − 3072.00i | − 0.124402i | ||||||||
\(849\) | −741.000 | −0.0299541 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46332.0 | 1.86632 | ||||||||
\(852\) | − 2736.00i | − 0.110016i | ||||||||
\(853\) | 24743.0i | 0.993182i | 0.867985 | + | 0.496591i | \(0.165415\pi\) | ||||
−0.867985 | + | 0.496591i | \(0.834585\pi\) | |||||||
\(854\) | 1466.00 | 0.0587418 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10368.0 | 0.413985 | ||||||||
\(857\) | 23556.0i | 0.938924i | 0.882953 | + | 0.469462i | \(0.155552\pi\) | ||||
−0.882953 | + | 0.469462i | \(0.844448\pi\) | |||||||
\(858\) | − 16884.0i | − 0.671807i | ||||||||
\(859\) | 34000.0 | 1.35048 | 0.675242 | − | 0.737597i | \(-0.264039\pi\) | ||||
0.675242 | + | 0.737597i | \(0.264039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.0000 | 0.00142494 | ||||||||
\(862\) | − 6516.00i | − 0.257466i | ||||||||
\(863\) | − 37032.0i | − 1.46070i | −0.683073 | − | 0.730350i | \(-0.739357\pi\) | ||||
0.683073 | − | 0.730350i | \(-0.260643\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2326.00 | −0.0912710 | ||||||||
\(867\) | − 5991.00i | − 0.234677i | ||||||||
\(868\) | 772.000i | 0.0301882i | ||||||||
\(869\) | 6720.00 | 0.262325 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20033.0 | −0.779325 | ||||||||
\(872\) | − 13880.0i | − 0.539032i | ||||||||
\(873\) | − 4599.00i | − 0.178296i | ||||||||
\(874\) | 37260.0 | 1.44203 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11256.0 | −0.434138 | ||||||||
\(877\) | − 2519.00i | − 0.0969904i | −0.998823 | − | 0.0484952i | \(-0.984557\pi\) | ||||
0.998823 | − | 0.0484952i | \(-0.0154426\pi\) | |||||||
\(878\) | − 13390.0i | − 0.514682i | ||||||||
\(879\) | −16326.0 | −0.626465 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43992.0 | 1.68232 | 0.841162 | − | 0.540783i | \(-0.181872\pi\) | ||||
0.841162 | + | 0.540783i | \(0.181872\pi\) | |||||||
\(882\) | − 6156.00i | − 0.235015i | ||||||||
\(883\) | − 19177.0i | − 0.730869i | −0.930837 | − | 0.365435i | \(-0.880920\pi\) | ||||
0.930837 | − | 0.365435i | \(-0.119080\pi\) | |||||||
\(884\) | 14472.0 | 0.550618 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32736.0 | −1.24130 | ||||||||
\(887\) | − 44994.0i | − 1.70321i | −0.524181 | − | 0.851607i | \(-0.675628\pi\) | ||||
0.524181 | − | 0.851607i | \(-0.324372\pi\) | |||||||
\(888\) | − 6864.00i | − 0.259393i | ||||||||
\(889\) | −16.0000 | −0.000603625 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3402.00 | 0.127914 | ||||||||
\(892\) | − 92.0000i | − 0.00345335i | ||||||||
\(893\) | − 47610.0i | − 1.78411i | ||||||||
\(894\) | 12420.0 | 0.464639 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 128.000 | 0.00477252 | ||||||||
\(897\) | 32562.0i | 1.21206i | ||||||||
\(898\) | − 32760.0i | − 1.21739i | ||||||||
\(899\) | −40530.0 | −1.50362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10368.0 | −0.383361 | ||||||||
\(902\) | 1008.00i | 0.0372092i | ||||||||
\(903\) | 789.000i | 0.0290767i | ||||||||
\(904\) | −8736.00 | −0.321410 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13422.0 | 0.492181 | ||||||||
\(907\) | 52396.0i | 1.91817i | 0.283117 | + | 0.959085i | \(0.408631\pi\) | ||||
−0.283117 | + | 0.959085i | \(0.591369\pi\) | |||||||
\(908\) | − 7824.00i | − 0.285957i | ||||||||
\(909\) | −8208.00 | −0.299496 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7242.00 | 0.263379 | 0.131689 | − | 0.991291i | \(-0.457960\pi\) | ||||
0.131689 | + | 0.991291i | \(0.457960\pi\) | |||||||
\(912\) | − 5520.00i | − 0.200423i | ||||||||
\(913\) | − 19404.0i | − 0.703372i | ||||||||
\(914\) | −27572.0 | −0.997813 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7220.00 | 0.260432 | ||||||||
\(917\) | 1992.00i | 0.0717357i | ||||||||
\(918\) | 2916.00i | 0.104839i | ||||||||
\(919\) | −4085.00 | −0.146629 | −0.0733143 | − | 0.997309i | \(-0.523358\pi\) | ||||
−0.0733143 | + | 0.997309i | \(0.523358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11613.0 | 0.415485 | ||||||||
\(922\) | 23664.0i | 0.845263i | ||||||||
\(923\) | 15276.0i | 0.544762i | ||||||||
\(924\) | −504.000 | −0.0179441 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6016.00 | −0.213497 | ||||||||
\(927\) | − 6012.00i | − 0.213010i | ||||||||
\(928\) | 6720.00i | 0.237710i | ||||||||
\(929\) | 3030.00 | 0.107009 | 0.0535043 | − | 0.998568i | \(-0.482961\pi\) | ||||
0.0535043 | + | 0.998568i | \(0.482961\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39330.0 | 1.38452 | ||||||||
\(932\) | − 13872.0i | − 0.487546i | ||||||||
\(933\) | 17154.0i | 0.601926i | ||||||||
\(934\) | 8868.00 | 0.310674 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4824.00 | 0.168459 | ||||||||
\(937\) | − 5759.00i | − 0.200788i | −0.994948 | − | 0.100394i | \(-0.967990\pi\) | ||||
0.994948 | − | 0.100394i | \(-0.0320103\pi\) | |||||||
\(938\) | 598.000i | 0.0208160i | ||||||||
\(939\) | −10911.0 | −0.379198 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −258.000 | −0.00893790 | −0.00446895 | − | 0.999990i | \(-0.501423\pi\) | ||||
−0.00446895 | + | 0.999990i | \(0.501423\pi\) | |||||||
\(942\) | 1446.00i | 0.0500140i | ||||||||
\(943\) | − 1944.00i | − 0.0671319i | ||||||||
\(944\) | −11040.0 | −0.380637 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22092.0 | −0.759274 | ||||||||
\(947\) | − 1374.00i | − 0.0471478i | −0.999722 | − | 0.0235739i | \(-0.992495\pi\) | ||||
0.999722 | − | 0.0235739i | \(-0.00750451\pi\) | |||||||
\(948\) | 1920.00i | 0.0657792i | ||||||||
\(949\) | 62846.0 | 2.14970 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3888.00 | 0.132573 | ||||||||
\(952\) | − 432.000i | − 0.0147071i | ||||||||
\(953\) | 9288.00i | 0.315706i | 0.987463 | + | 0.157853i | \(0.0504572\pi\) | ||||
−0.987463 | + | 0.157853i | \(0.949543\pi\) | |||||||
\(954\) | −3456.00 | −0.117287 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10560.0 | 0.357254 | ||||||||
\(957\) | − 26460.0i | − 0.893762i | ||||||||
\(958\) | − 14820.0i | − 0.499804i | ||||||||
\(959\) | −2346.00 | −0.0789951 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7458.00 | 0.250344 | ||||||||
\(962\) | 38324.0i | 1.28442i | ||||||||
\(963\) | − 11664.0i | − 0.390309i | ||||||||
\(964\) | 21532.0 | 0.719397 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 972.000 | 0.0323743 | ||||||||
\(967\) | 21616.0i | 0.718846i | 0.933175 | + | 0.359423i | \(0.117026\pi\) | ||||
−0.933175 | + | 0.359423i | \(0.882974\pi\) | |||||||
\(968\) | − 3464.00i | − 0.115018i | ||||||||
\(969\) | −18630.0 | −0.617628 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19098.0 | −0.631188 | −0.315594 | − | 0.948894i | \(-0.602204\pi\) | ||||
−0.315594 | + | 0.948894i | \(0.602204\pi\) | |||||||
\(972\) | 972.000i | 0.0320750i | ||||||||
\(973\) | − 2900.00i | − 0.0955496i | ||||||||
\(974\) | −17342.0 | −0.570507 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11728.0 | −0.384635 | ||||||||
\(977\) | 18246.0i | 0.597483i | 0.954334 | + | 0.298742i | \(0.0965669\pi\) | ||||
−0.954334 | + | 0.298742i | \(0.903433\pi\) | |||||||
\(978\) | − 21282.0i | − 0.695832i | ||||||||
\(979\) | 10080.0 | 0.329069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15615.0 | −0.508204 | ||||||||
\(982\) | − 38736.0i | − 1.25877i | ||||||||
\(983\) | − 38772.0i | − 1.25802i | −0.777397 | − | 0.629011i | \(-0.783460\pi\) | ||||
0.777397 | − | 0.629011i | \(-0.216540\pi\) | |||||||
\(984\) | −288.000 | −0.00933039 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22680.0 | 0.732534 | ||||||||
\(987\) | − 1242.00i | − 0.0400540i | ||||||||
\(988\) | 30820.0i | 0.992424i | ||||||||
\(989\) | 42606.0 | 1.36986 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23053.0 | −0.738953 | −0.369477 | − | 0.929240i | \(-0.620463\pi\) | ||||
−0.369477 | + | 0.929240i | \(0.620463\pi\) | |||||||
\(992\) | − 6176.00i | − 0.197670i | ||||||||
\(993\) | − 15396.0i | − 0.492021i | ||||||||
\(994\) | 456.000 | 0.0145507 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5544.00 | 0.176374 | ||||||||
\(997\) | 10366.0i | 0.329282i | 0.986354 | + | 0.164641i | \(0.0526466\pi\) | ||||
−0.986354 | + | 0.164641i | \(0.947353\pi\) | |||||||
\(998\) | 17750.0i | 0.562992i | ||||||||
\(999\) | −7722.00 | −0.244558 |
(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 | 150.4.c.e.49.2 | 2 | ||
3.2 | odd | 2 | 450.4.c.a.199.1 | 2 | |||
4.3 | odd | 2 | 1200.4.f.c.49.2 | 2 | |||
5.2 | odd | 4 | 150.4.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 150.4.a.h.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 150.4.c.e.49.1 | 2 | ||
15.2 | even | 4 | 450.4.a.o.1.1 | 1 | |||
15.8 | even | 4 | 450.4.a.f.1.1 | 1 | |||
15.14 | odd | 2 | 450.4.c.a.199.2 | 2 | |||
20.3 | even | 4 | 1200.4.a.i.1.1 | 1 | |||
20.7 | even | 4 | 1200.4.a.bb.1.1 | 1 | |||
20.19 | odd | 2 | 1200.4.f.c.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.4.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
150.4.a.h.1.1 | yes | 1 | 5.3 | odd | 4 | ||
150.4.c.e.49.1 | 2 | 5.4 | even | 2 | inner | ||
150.4.c.e.49.2 | 2 | 1.1 | even | 1 | trivial | ||
450.4.a.f.1.1 | 1 | 15.8 | even | 4 | |||
450.4.a.o.1.1 | 1 | 15.2 | even | 4 | |||
450.4.c.a.199.1 | 2 | 3.2 | odd | 2 | |||
450.4.c.a.199.2 | 2 | 15.14 | odd | 2 | |||
1200.4.a.i.1.1 | 1 | 20.3 | even | 4 | |||
1200.4.a.bb.1.1 | 1 | 20.7 | even | 4 | |||
1200.4.f.c.49.1 | 2 | 20.19 | odd | 2 | |||
1200.4.f.c.49.2 | 2 | 4.3 | odd | 2 |