Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(70.8022920069\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.0539949 | −0.0269975 | − | 0.999636i | \(-0.508595\pi\) | ||||
−0.0269975 | + | 0.999636i | \(0.508595\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −42.0000 | −1.15123 | −0.575613 | − | 0.817723i | \(-0.695236\pi\) | ||||
−0.575613 | + | 0.817723i | \(0.695236\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 67.0000 | 1.42942 | 0.714710 | − | 0.699421i | \(-0.246559\pi\) | ||||
0.714710 | + | 0.699421i | \(0.246559\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −54.0000 | −0.770407 | −0.385204 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385204 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 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 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −162.000 | −1.46867 | −0.734333 | − | 0.678789i | \(-0.762505\pi\) | ||||
−0.734333 | + | 0.678789i | \(0.762505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −210.000 | −1.34469 | −0.672345 | − | 0.740238i | \(-0.734713\pi\) | ||||
−0.672345 | + | 0.740238i | \(0.734713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 193.000 | 1.11819 | 0.559094 | − | 0.829104i | \(-0.311149\pi\) | ||||
0.559094 | + | 0.829104i | \(0.311149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 126.000 | 0.664660 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 286.000 | 1.27076 | 0.635380 | − | 0.772200i | \(-0.280844\pi\) | ||||
0.635380 | + | 0.772200i | \(0.280844\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −201.000 | −0.825276 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.0000 | 0.0457094 | 0.0228547 | − | 0.999739i | \(-0.492724\pi\) | ||||
0.0228547 | + | 0.999739i | \(0.492724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 263.000 | 0.932724 | 0.466362 | − | 0.884594i | \(-0.345564\pi\) | ||||
0.466362 | + | 0.884594i | \(0.345564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 414.000 | 1.28485 | 0.642427 | − | 0.766347i | \(-0.277928\pi\) | ||||
0.642427 | + | 0.766347i | \(0.277928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.000 | −0.997085 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 162.000 | 0.444795 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 192.000 | 0.497608 | 0.248804 | − | 0.968554i | \(-0.419962\pi\) | ||||
0.248804 | + | 0.968554i | \(0.419962\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −345.000 | −0.801691 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −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 | \(0.779380\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.00000 | −0.0179983 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 299.000 | 0.545204 | 0.272602 | − | 0.962127i | \(-0.412116\pi\) | ||||
0.272602 | + | 0.962127i | \(0.412116\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 486.000 | 0.847935 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 228.000 | 0.381107 | 0.190554 | − | 0.981677i | \(-0.438972\pi\) | ||||
0.190554 | + | 0.981677i | \(0.438972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −938.000 | −1.50390 | −0.751949 | − | 0.659221i | \(-0.770886\pi\) | ||||
−0.751949 | + | 0.659221i | \(0.770886\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 42.0000 | 0.0621603 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 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 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −462.000 | −0.610977 | −0.305488 | − | 0.952196i | \(-0.598820\pi\) | ||||
−0.305488 | + | 0.952196i | \(0.598820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 630.000 | 0.776357 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −240.000 | −0.285842 | −0.142921 | − | 0.989734i | \(-0.545650\pi\) | ||||
−0.142921 | + | 0.989734i | \(0.545650\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −67.0000 | −0.0771814 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −579.000 | −0.645586 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 511.000 | 0.534889 | 0.267444 | − | 0.963573i | \(-0.413821\pi\) | ||||
0.267444 | + | 0.963573i | \(0.413821\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −378.000 | −0.383742 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 912.000 | 0.898489 | 0.449245 | − | 0.893409i | \(-0.351693\pi\) | ||||
0.449245 | + | 0.893409i | \(0.351693\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 668.000 | 0.639029 | 0.319515 | − | 0.947581i | \(-0.396480\pi\) | ||||
0.319515 | + | 0.947581i | \(0.396480\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1296.00 | −1.17093 | −0.585463 | − | 0.810699i | \(-0.699087\pi\) | ||||
−0.585463 | + | 0.810699i | \(0.699087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1735.00 | −1.52461 | −0.762307 | − | 0.647216i | \(-0.775933\pi\) | ||||
−0.762307 | + | 0.647216i | \(0.775933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −858.000 | −0.733673 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1092.00 | 0.909086 | 0.454543 | − | 0.890725i | \(-0.349803\pi\) | ||||
0.454543 | + | 0.890725i | \(0.349803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 603.000 | 0.476473 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 54.0000 | 0.0415981 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 433.000 | 0.325319 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −36.0000 | −0.0263903 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −0.0111793 | −0.00558965 | − | 0.999984i | \(-0.501779\pi\) | ||||
−0.00558965 | + | 0.999984i | \(0.501779\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −789.000 | −0.538508 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1992.00 | −1.32856 | −0.664282 | − | 0.747482i | \(-0.731263\pi\) | ||||
−0.664282 | + | 0.747482i | \(0.731263\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −115.000 | −0.0749757 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2346.00 | 1.46301 | 0.731505 | − | 0.681836i | \(-0.238818\pi\) | ||||
0.731505 | + | 0.681836i | \(0.238818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −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 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2814.00 | −1.64558 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1026.00 | 0.575667 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2070.00 | −1.13813 | −0.569064 | − | 0.822293i | \(-0.692694\pi\) | ||||
−0.569064 | + | 0.822293i | \(0.692694\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2237.00 | −1.20559 | −0.602796 | − | 0.797895i | \(-0.705947\pi\) | ||||
−0.602796 | + | 0.797895i | \(0.705947\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −486.000 | −0.256802 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 241.000 | 0.122509 | 0.0612544 | − | 0.998122i | \(-0.480490\pi\) | ||||
0.0612544 | + | 0.998122i | \(0.480490\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −576.000 | −0.287294 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 162.000 | 0.0793006 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3547.00 | −1.70443 | −0.852216 | − | 0.523190i | \(-0.824742\pi\) | ||||
−0.852216 | + | 0.523190i | \(0.824742\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 984.000 | 0.455953 | 0.227977 | − | 0.973667i | \(-0.426789\pi\) | ||||
0.227977 | + | 0.973667i | \(0.426789\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2292.00 | 1.04324 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1035.00 | 0.462856 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3618.00 | −1.59001 | −0.795004 | − | 0.606604i | \(-0.792531\pi\) | ||||
−0.795004 | + | 0.606604i | \(0.792531\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2070.00 | 0.879044 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.487121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2199.00 | 0.888277 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2268.00 | 0.886912 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.0000 | 0.0103913 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1302.00 | −0.493243 | −0.246622 | − | 0.969112i | \(-0.579320\pi\) | ||||
−0.246622 | + | 0.969112i | \(0.579320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4163.00 | −1.55264 | −0.776319 | − | 0.630340i | \(-0.782916\pi\) | ||||
−0.776319 | + | 0.630340i | \(0.782916\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3054.00 | −1.10451 | −0.552255 | − | 0.833675i | \(-0.686233\pi\) | ||||
−0.552255 | + | 0.833675i | \(0.686233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −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 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 210.000 | 0.0726065 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1458.00 | −0.489556 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4830.00 | −1.59856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2443.00 | 0.797076 | 0.398538 | − | 0.917152i | \(-0.369518\pi\) | ||||
0.398538 | + | 0.917152i | \(0.369518\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −684.000 | −0.220032 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −193.000 | −0.0603765 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2814.00 | 0.868276 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3618.00 | −1.10124 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.0000 | 0.00690670 | 0.00345335 | − | 0.999994i | \(-0.498901\pi\) | ||||
0.00345335 | + | 0.999994i | \(0.498901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1956.00 | −0.571913 | −0.285957 | − | 0.958243i | \(-0.592311\pi\) | ||||
−0.285957 | + | 0.958243i | \(0.592311\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1805.00 | 0.520864 | 0.260432 | − | 0.965492i | \(-0.416135\pi\) | ||||
0.260432 | + | 0.965492i | \(0.416135\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −126.000 | −0.0358883 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3468.00 | −0.975091 | −0.487546 | − | 0.873098i | \(-0.662108\pi\) | ||||
−0.487546 | + | 0.873098i | \(0.662108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −480.000 | −0.131558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(0.755582\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7705.00 | 1.98485 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1386.00 | 0.352748 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5028.00 | 1.26440 | 0.632200 | − | 0.774805i | \(-0.282152\pi\) | ||||
0.632200 | + | 0.774805i | \(0.282152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6804.00 | 1.69077 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −564.000 | −0.136892 | −0.0684462 | − | 0.997655i | \(-0.521804\pi\) | ||||
−0.0684462 | + | 0.997655i | \(0.521804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −286.000 | −0.0686146 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1890.00 | −0.448230 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1812.00 | −0.424839 | −0.212420 | − | 0.977179i | \(-0.568134\pi\) | ||||
−0.212420 | + | 0.977179i | \(0.568134\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 720.000 | 0.165031 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5190.00 | −1.17636 | −0.588178 | − | 0.808731i | \(-0.700155\pi\) | ||||
−0.588178 | + | 0.808731i | \(0.700155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4592.00 | −1.02931 | −0.514657 | − | 0.857396i | \(-0.672081\pi\) | ||||
−0.514657 | + | 0.857396i | \(0.672081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 201.000 | 0.0445607 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2191.00 | 0.475251 | 0.237625 | − | 0.971357i | \(-0.423631\pi\) | ||||
0.237625 | + | 0.971357i | \(0.423631\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1737.00 | 0.372729 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7842.00 | 1.66482 | 0.832410 | − | 0.554160i | \(-0.186960\pi\) | ||||
0.832410 | + | 0.554160i | \(0.186960\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −247.000 | −0.0518821 | −0.0259410 | − | 0.999663i | \(-0.508258\pi\) | ||||
−0.0259410 | + | 0.999663i | \(0.508258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.00246808 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1533.00 | −0.308818 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5442.00 | 1.08507 | 0.542534 | − | 0.840034i | \(-0.317465\pi\) | ||||
0.542534 | + | 0.840034i | \(0.317465\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1134.00 | 0.221553 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10854.0 | −2.09934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −263.000 | −0.0503624 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2736.00 | −0.518743 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3871.00 | −0.719641 | −0.359820 | − | 0.933022i | \(-0.617162\pi\) | ||||
−0.359820 | + | 0.933022i | \(0.617162\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2004.00 | −0.368944 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5718.00 | 1.04257 | 0.521283 | − | 0.853384i | \(-0.325454\pi\) | ||||
0.521283 | + | 0.853384i | \(0.325454\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3637.00 | 0.656790 | 0.328395 | − | 0.944540i | \(-0.393492\pi\) | ||||
0.328395 | + | 0.944540i | \(0.393492\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1296.00 | 0.229623 | 0.114812 | − | 0.993387i | \(-0.463374\pi\) | ||||
0.114812 | + | 0.993387i | \(0.463374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8820.00 | 1.54804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3888.00 | 0.676034 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6210.00 | −1.06976 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5205.00 | 0.880236 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −414.000 | −0.0693756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5132.00 | −0.852206 | −0.426103 | − | 0.904675i | \(-0.640114\pi\) | ||||
−0.426103 | + | 0.904675i | \(0.640114\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2574.00 | 0.423587 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6751.00 | 1.09125 | 0.545624 | − | 0.838030i | \(-0.316293\pi\) | ||||
0.545624 | + | 0.838030i | \(0.316293\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3276.00 | −0.524861 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8106.00 | −1.28729 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 685.000 | 0.107832 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5226.00 | −0.808491 | −0.404246 | − | 0.914651i | \(-0.632466\pi\) | ||||
−0.404246 | + | 0.914651i | \(0.632466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6190.00 | −0.949407 | −0.474704 | − | 0.880146i | \(-0.657445\pi\) | ||||
−0.474704 | + | 0.880146i | \(0.657445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1809.00 | −0.275092 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6618.00 | −0.997849 | −0.498924 | − | 0.866646i | \(-0.666271\pi\) | ||||
−0.498924 | + | 0.866646i | \(0.666271\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −162.000 | −0.0240167 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1299.00 | −0.187823 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −871.000 | −0.123885 | −0.0619425 | − | 0.998080i | \(-0.519730\pi\) | ||||
−0.0619425 | + | 0.998080i | \(0.519730\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 108.000 | 0.0152365 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −192.000 | −0.0268683 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6383.00 | −0.886057 | −0.443028 | − | 0.896508i | \(-0.646096\pi\) | ||||
−0.443028 | + | 0.896508i | \(0.646096\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14070.0 | −1.92213 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 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 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9828.00 | 1.31119 | 0.655597 | − | 0.755111i | \(-0.272417\pi\) | ||||
0.655597 | + | 0.755111i | \(0.272417\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2367.00 | 0.310908 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12540.0 | 1.63446 | 0.817228 | − | 0.576315i | \(-0.195510\pi\) | ||||
0.817228 | + | 0.576315i | \(0.195510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8748.00 | 1.13147 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5976.00 | 0.767047 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1381.00 | 0.174585 | 0.0872927 | − | 0.996183i | \(-0.472178\pi\) | ||||
0.0872927 | + | 0.996183i | \(0.472178\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 345.000 | 0.0432872 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14232.0 | 1.77235 | 0.886175 | − | 0.463351i | \(-0.153353\pi\) | ||||
0.886175 | + | 0.463351i | \(0.153353\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12931.0 | 1.59836 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12012.0 | −1.46293 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2645.00 | 0.319772 | 0.159886 | − | 0.987135i | \(-0.448887\pi\) | ||||
0.159886 | + | 0.987135i | \(0.448887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7038.00 | −0.844669 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 690.000 | 0.0822099 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8700.00 | 1.02168 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −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 | \(0.727867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3726.00 | 0.428284 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 733.000 | 0.0830734 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8442.00 | 0.950078 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3258.00 | 0.364112 | 0.182056 | − | 0.983288i | \(-0.441725\pi\) | ||||
0.182056 | + | 0.983288i | \(0.441725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1163.00 | −0.129077 | −0.0645384 | − | 0.997915i | \(-0.520557\pi\) | ||||
−0.0645384 | + | 0.997915i | \(0.520557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18630.0 | −2.03934 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −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 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16368.0 | 1.75546 | 0.877728 | − | 0.479159i | \(-0.159058\pi\) | ||||
0.877728 | + | 0.479159i | \(0.159058\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6210.00 | 0.657098 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16380.0 | 1.72165 | 0.860824 | − | 0.508903i | \(-0.169949\pi\) | ||||
0.860824 | + | 0.508903i | \(0.169949\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −504.000 | −0.0526218 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6711.00 | 0.696049 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13786.0 | 1.41112 | 0.705560 | − | 0.708650i | \(-0.250696\pi\) | ||||
0.705560 | + | 0.708650i | \(0.250696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1458.00 | 0.148265 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11832.0 | 1.19538 | 0.597691 | − | 0.801726i | \(-0.296085\pi\) | ||||
0.597691 | + | 0.801726i | \(0.296085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3008.00 | 0.301930 | 0.150965 | − | 0.988539i | \(-0.451762\pi\) | ||||
0.150965 | + | 0.988539i | \(0.451762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4434.00 | 0.439360 | 0.219680 | − | 0.975572i | \(-0.429499\pi\) | ||||
0.219680 | + | 0.975572i | \(0.429499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −299.000 | −0.0294382 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −723.000 | −0.0707305 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11046.0 | −1.07378 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1728.00 | 0.165869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −486.000 | −0.0457842 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8671.00 | −0.806818 | −0.403409 | − | 0.915020i | \(-0.632175\pi\) | ||||
−0.403409 | + | 0.915020i | \(0.632175\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10641.0 | 0.984055 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19368.0 | 1.78017 | 0.890087 | − | 0.455790i | \(-0.150643\pi\) | ||||
0.890087 | + | 0.455790i | \(0.150643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11340.0 | 1.03596 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −228.000 | −0.0205779 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10452.0 | −0.926504 | −0.463252 | − | 0.886227i | \(-0.653318\pi\) | ||||
−0.463252 | + | 0.886227i | \(0.653318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6876.00 | −0.602315 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19770.0 | −1.72159 | −0.860796 | − | 0.508951i | \(-0.830033\pi\) | ||||
−0.860796 | + | 0.508951i | \(0.830033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 938.000 | 0.0812029 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3105.00 | −0.267230 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17388.0 | −1.47916 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10854.0 | 0.917992 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11238.0 | −0.945001 | −0.472501 | − | 0.881330i | \(-0.656649\pi\) | ||||
−0.472501 | + | 0.881330i | \(0.656649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7447.00 | −0.622628 | −0.311314 | − | 0.950307i | \(-0.600769\pi\) | ||||
−0.311314 | + | 0.950307i | \(0.600769\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10422.0 | −0.861460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14077.0 | 1.15698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6210.00 | −0.507516 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 804.000 | 0.0653379 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −450.000 | −0.0361619 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14364.0 | 1.14787 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17623.0 | −1.40050 | −0.700251 | − | 0.713896i | \(-0.746929\pi\) | ||||
−0.700251 | + | 0.713896i | \(0.746929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −591.000 | −0.0467076 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10096.0 | −0.789166 | −0.394583 | − | 0.918860i | \(-0.629111\pi\) | ||||
−0.394583 | + | 0.918860i | \(0.629111\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6597.00 | −0.512847 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24150.0 | −1.86720 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −160.000 | −0.0123036 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14514.0 | −1.10409 | −0.552045 | − | 0.833814i | \(-0.686152\pi\) | ||||
−0.552045 | + | 0.833814i | \(0.686152\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17621.0 | 1.33325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6804.00 | −0.512059 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10242.0 | −0.766694 | −0.383347 | − | 0.923604i | \(-0.625229\pi\) | ||||
−0.383347 | + | 0.923604i | \(0.625229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −81.0000 | −0.00599944 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6750.00 | −0.497319 | −0.248660 | − | 0.968591i | \(-0.579990\pi\) | ||||
−0.248660 | + | 0.968591i | \(0.579990\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17117.0 | −1.25451 | −0.627254 | − | 0.778815i | \(-0.715821\pi\) | ||||
−0.627254 | + | 0.778815i | \(0.715821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3906.00 | 0.284774 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 301.000 | 0.0217171 | 0.0108586 | − | 0.999941i | \(-0.496544\pi\) | ||||
0.0108586 | + | 0.999941i | \(0.496544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12489.0 | 0.896416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 462.000 | 0.0329897 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8064.00 | −0.572859 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15456.0 | −1.08678 | −0.543388 | − | 0.839482i | \(-0.682859\pi\) | ||||
−0.543388 | + | 0.839482i | \(0.682859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22195.0 | 1.55268 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9162.00 | 0.637689 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9492.00 | 0.657318 | 0.328659 | − | 0.944449i | \(-0.393403\pi\) | ||||
0.328659 | + | 0.944449i | \(0.393403\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10275.0 | 0.704402 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | \(0.334663\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2691.00 | 0.181735 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16184.0 | 1.08219 | 0.541094 | − | 0.840962i | \(-0.318010\pi\) | ||||
0.541094 | + | 0.840962i | \(0.318010\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −630.000 | −0.0419194 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27738.0 | 1.83659 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18502.0 | 1.21907 | 0.609534 | − | 0.792760i | \(-0.291357\pi\) | ||||
0.609534 | + | 0.792760i | \(0.291357\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13896.0 | 0.906697 | 0.453348 | − | 0.891333i | \(-0.350229\pi\) | ||||
0.453348 | + | 0.891333i | \(0.350229\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 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 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 240.000 | 0.0154340 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14490.0 | 0.922926 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15444.0 | −0.979003 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −467.000 | −0.0294627 | −0.0147314 | − | 0.999891i | \(-0.504689\pi\) | ||||
−0.0147314 | + | 0.999891i | \(0.504689\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7329.00 | −0.460192 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22914.0 | −1.42525 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2052.00 | 0.127036 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30612.0 | 1.88627 | 0.943137 | − | 0.332405i | \(-0.107860\pi\) | ||||
0.943137 | + | 0.332405i | \(0.107860\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1852.00 | −0.113586 | −0.0567930 | − | 0.998386i | \(-0.518087\pi\) | ||||
−0.0567930 | + | 0.998386i | \(0.518087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21156.0 | −1.28551 | −0.642757 | − | 0.766070i | \(-0.722210\pi\) | ||||
−0.642757 | + | 0.766070i | \(0.722210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28980.0 | 1.75280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 579.000 | 0.0348584 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9702.00 | 0.581422 | 0.290711 | − | 0.956811i | \(-0.406108\pi\) | ||||
0.290711 | + | 0.956811i | \(0.406108\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8442.00 | −0.501300 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | \(0.702089\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10854.0 | 0.635799 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34020.0 | 1.97490 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −69.0000 | −0.00398758 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30786.0 | 1.77121 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16882.0 | 0.966944 | 0.483472 | − | 0.875360i | \(-0.339376\pi\) | ||||
0.483472 | + | 0.875360i | \(0.339376\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20934.0 | −1.18842 | −0.594209 | − | 0.804311i | \(-0.702535\pi\) | ||||
−0.594209 | + | 0.804311i | \(0.702535\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −511.000 | −0.0288813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5868.00 | 0.330194 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8712.00 | −0.488075 | −0.244038 | − | 0.969766i | \(-0.578472\pi\) | ||||
−0.244038 | + | 0.969766i | \(0.578472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5415.00 | −0.300721 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12864.0 | 0.711291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14128.0 | 0.777792 | 0.388896 | − | 0.921282i | \(-0.372856\pi\) | ||||
0.388896 | + | 0.921282i | \(0.372856\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 378.000 | 0.0207201 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −648.000 | −0.0352148 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10404.0 | 0.562969 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28278.0 | −1.52360 | −0.761801 | − | 0.647811i | \(-0.775685\pi\) | ||||
−0.761801 | + | 0.647811i | \(0.775685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32890.0 | 1.76454 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −912.000 | −0.0485138 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8885.00 | 0.470639 | 0.235320 | − | 0.971918i | \(-0.424386\pi\) | ||||
0.235320 | + | 0.971918i | \(0.424386\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1440.00 | 0.0759553 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31266.0 | −1.64225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7920.00 | 0.412521 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16149.0 | 0.830688 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1801.00 | −0.0918781 | −0.0459391 | − | 0.998944i | \(-0.514628\pi\) | ||||
−0.0459391 | + | 0.998944i | \(0.514628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14202.0 | −0.718577 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7882.00 | 0.397174 | 0.198587 | − | 0.980083i | \(-0.436365\pi\) | ||||
0.198587 | + | 0.980083i | \(0.436365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12558.0 | −0.627652 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −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 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20652.0 | −1.01972 | −0.509858 | − | 0.860259i | \(-0.670302\pi\) | ||||
−0.509858 | + | 0.860259i | \(0.670302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4158.00 | −0.203659 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1296.00 | 0.0632240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7472.00 | −0.363059 | −0.181529 | − | 0.983386i | \(-0.558105\pi\) | ||||
−0.181529 | + | 0.983386i | \(0.558105\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15084.0 | −0.730002 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32251.0 | 1.54846 | 0.774229 | − | 0.632906i | \(-0.218138\pi\) | ||||
0.774229 | + | 0.632906i | \(0.218138\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20412.0 | −0.976164 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16812.0 | 0.800834 | 0.400417 | − | 0.916333i | \(-0.368865\pi\) | ||||
0.400417 | + | 0.916333i | \(0.368865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1735.00 | 0.0823214 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −46230.0 | −2.17636 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34645.0 | −1.62462 | −0.812309 | − | 0.583228i | \(-0.801789\pi\) | ||||
−0.812309 | + | 0.583228i | \(0.801789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1692.00 | 0.0790349 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8412.00 | 0.391408 | 0.195704 | − | 0.980663i | \(-0.437301\pi\) | ||||
0.195704 | + | 0.980663i | \(0.437301\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 858.000 | 0.0396146 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1380.00 | 0.0634706 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9576.00 | −0.438740 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5670.00 | 0.258786 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18329.0 | 0.830188 | 0.415094 | − | 0.909778i | \(-0.363749\pi\) | ||||
0.415094 | + | 0.909778i | \(0.363749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5436.00 | 0.245281 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1092.00 | −0.0490860 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49111.0 | −2.19922 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16044.0 | −0.713059 | −0.356529 | − | 0.934284i | \(-0.616040\pi\) | ||||
−0.356529 | + | 0.934284i | \(0.616040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22356.0 | −0.989860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2160.00 | −0.0952807 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39396.0 | 1.73133 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15570.0 | 0.679170 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24000.0 | −1.04301 | −0.521505 | − | 0.853248i | \(-0.674629\pi\) | ||||
−0.521505 | + | 0.853248i | \(0.674629\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5117.00 | −0.221556 | −0.110778 | − | 0.993845i | \(-0.535334\pi\) | ||||
−0.110778 | + | 0.993845i | \(0.535334\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13776.0 | 0.594275 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30245.0 | 1.29515 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −603.000 | −0.0257271 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13542.0 | 0.575663 | 0.287831 | − | 0.957681i | \(-0.407066\pi\) | ||||
0.287831 | + | 0.957681i | \(0.407066\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1283.00 | 0.0543409 | 0.0271705 | − | 0.999631i | \(-0.491350\pi\) | ||||
0.0271705 | + | 0.999631i | \(0.491350\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16344.0 | 0.687227 | 0.343613 | − | 0.939111i | \(-0.388349\pi\) | ||||
0.343613 | + | 0.939111i | \(0.388349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −790.000 | −0.0330975 | −0.0165488 | − | 0.999863i | \(-0.505268\pi\) | ||||
−0.0165488 | + | 0.999863i | \(0.505268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6573.00 | −0.274386 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18468.0 | 0.768161 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5211.00 | −0.215195 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23526.0 | −0.961184 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −433.000 | −0.0175656 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 741.000 | 0.0299541 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46332.0 | −1.86632 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24743.0 | −0.993182 | −0.496591 | − | 0.867985i | \(-0.665415\pi\) | ||||
−0.496591 | + | 0.867985i | \(0.665415\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23556.0 | 0.938924 | 0.469462 | − | 0.882953i | \(-0.344448\pi\) | ||||
0.469462 | + | 0.882953i | \(0.344448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 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 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37032.0 | −1.46070 | −0.730350 | − | 0.683073i | \(-0.760643\pi\) | ||||
−0.730350 | + | 0.683073i | \(0.760643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5991.00 | 0.234677 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6720.00 | −0.262325 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20033.0 | 0.779325 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4599.00 | 0.178296 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2519.00 | −0.0969904 | −0.0484952 | − | 0.998823i | \(-0.515443\pi\) | ||||
−0.0484952 | + | 0.998823i | \(0.515443\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16326.0 | −0.626465 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43992.0 | 1.68232 | 0.841162 | − | 0.540783i | \(-0.181872\pi\) | ||||
0.841162 | + | 0.540783i | \(0.181872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19177.0 | −0.730869 | −0.365435 | − | 0.930837i | \(-0.619080\pi\) | ||||
−0.365435 | + | 0.930837i | \(0.619080\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44994.0 | 1.70321 | 0.851607 | − | 0.524181i | \(-0.175628\pi\) | ||||
0.851607 | + | 0.524181i | \(0.175628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | 0.000603625 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3402.00 | −0.127914 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 47610.0 | 1.78411 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32562.0 | 1.21206 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40530.0 | −1.50362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10368.0 | −0.383361 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 789.000 | 0.0290767 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52396.0 | −1.91817 | −0.959085 | − | 0.283117i | \(-0.908631\pi\) | ||||
−0.959085 | + | 0.283117i | \(0.908631\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8208.00 | 0.299496 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7242.00 | −0.263379 | −0.131689 | − | 0.991291i | \(-0.542040\pi\) | ||||
−0.131689 | + | 0.991291i | \(0.542040\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19404.0 | 0.703372 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1992.00 | 0.0717357 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −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 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15276.0 | 0.544762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6012.00 | 0.213010 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3030.00 | −0.107009 | −0.0535043 | − | 0.998568i | \(-0.517039\pi\) | ||||
−0.0535043 | + | 0.998568i | \(0.517039\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39330.0 | −1.38452 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17154.0 | −0.601926 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5759.00 | −0.200788 | −0.100394 | − | 0.994948i | \(-0.532010\pi\) | ||||
−0.100394 | + | 0.994948i | \(0.532010\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10911.0 | −0.379198 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −258.000 | −0.00893790 | −0.00446895 | − | 0.999990i | \(-0.501423\pi\) | ||||
−0.00446895 | + | 0.999990i | \(0.501423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1944.00 | −0.0671319 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1374.00 | 0.0471478 | 0.0235739 | − | 0.999722i | \(-0.492495\pi\) | ||||
0.0235739 | + | 0.999722i | \(0.492495\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62846.0 | −2.14970 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3888.00 | −0.132573 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9288.00 | −0.315706 | −0.157853 | − | 0.987463i | \(-0.550457\pi\) | ||||
−0.157853 | + | 0.987463i | \(0.550457\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −26460.0 | −0.893762 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2346.00 | −0.0789951 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7458.00 | 0.250344 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11664.0 | −0.390309 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21616.0 | −0.718846 | −0.359423 | − | 0.933175i | \(-0.617026\pi\) | ||||
−0.359423 | + | 0.933175i | \(0.617026\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18630.0 | 0.617628 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19098.0 | 0.631188 | 0.315594 | − | 0.948894i | \(-0.397796\pi\) | ||||
0.315594 | + | 0.948894i | \(0.397796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2900.00 | 0.0955496 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18246.0 | 0.597483 | 0.298742 | − | 0.954334i | \(-0.403433\pi\) | ||||
0.298742 | + | 0.954334i | \(0.403433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10080.0 | 0.329069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15615.0 | −0.508204 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38772.0 | −1.25802 | −0.629011 | − | 0.777397i | \(-0.716540\pi\) | ||||
−0.629011 | + | 0.777397i | \(0.716540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1242.00 | 0.0400540 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42606.0 | −1.36986 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23053.0 | 0.738953 | 0.369477 | − | 0.929240i | \(-0.379537\pi\) | ||||
0.369477 | + | 0.929240i | \(0.379537\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15396.0 | 0.492021 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10366.0 | 0.329282 | 0.164641 | − | 0.986354i | \(-0.447353\pi\) | ||||
0.164641 | + | 0.986354i | \(0.447353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 | 1200.4.a.i.1.1 | 1 | ||
4.3 | odd | 2 | 150.4.a.h.1.1 | yes | 1 | ||
5.2 | odd | 4 | 1200.4.f.c.49.2 | 2 | |||
5.3 | odd | 4 | 1200.4.f.c.49.1 | 2 | |||
5.4 | even | 2 | 1200.4.a.bb.1.1 | 1 | |||
12.11 | even | 2 | 450.4.a.f.1.1 | 1 | |||
20.3 | even | 4 | 150.4.c.e.49.1 | 2 | |||
20.7 | even | 4 | 150.4.c.e.49.2 | 2 | |||
20.19 | odd | 2 | 150.4.a.a.1.1 | ✓ | 1 | ||
60.23 | odd | 4 | 450.4.c.a.199.2 | 2 | |||
60.47 | odd | 4 | 450.4.c.a.199.1 | 2 | |||
60.59 | even | 2 | 450.4.a.o.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.4.a.a.1.1 | ✓ | 1 | 20.19 | odd | 2 | ||
150.4.a.h.1.1 | yes | 1 | 4.3 | odd | 2 | ||
150.4.c.e.49.1 | 2 | 20.3 | even | 4 | |||
150.4.c.e.49.2 | 2 | 20.7 | even | 4 | |||
450.4.a.f.1.1 | 1 | 12.11 | even | 2 | |||
450.4.a.o.1.1 | 1 | 60.59 | even | 2 | |||
450.4.c.a.199.1 | 2 | 60.47 | odd | 4 | |||
450.4.c.a.199.2 | 2 | 60.23 | odd | 4 | |||
1200.4.a.i.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1200.4.a.bb.1.1 | 1 | 5.4 | even | 2 | |||
1200.4.f.c.49.1 | 2 | 5.3 | odd | 4 | |||
1200.4.f.c.49.2 | 2 | 5.2 | odd | 4 |