Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,4,Mod(1,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("450.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.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: | \(26.5508595026\) |
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 | \(\chi\) | \(=\) | 450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.0539949 | 0.0269975 | − | 0.999636i | \(-0.491405\pi\) | ||||
0.0269975 | + | 0.999636i | \(0.491405\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(0.246559\pi\) | |||||||
\(14\) | −2.00000 | −0.0381802 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 54.0000 | 0.770407 | 0.385204 | − | 0.922832i | \(-0.374131\pi\) | ||||
0.385204 | + | 0.922832i | \(0.374131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −115.000 | −1.38857 | −0.694284 | − | 0.719701i | \(-0.744279\pi\) | ||||
−0.694284 | + | 0.719701i | \(0.744279\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 84.0000 | 0.814039 | ||||||||
\(23\) | −162.000 | −1.46867 | −0.734333 | − | 0.678789i | \(-0.762505\pi\) | ||||
−0.734333 | + | 0.678789i | \(0.762505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −134.000 | −1.01075 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000 | 0.0269975 | ||||||||
\(29\) | 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 | \(0.688851\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −108.000 | −0.544760 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 286.000 | 1.27076 | 0.635380 | − | 0.772200i | \(-0.280844\pi\) | ||||
0.635380 | + | 0.772200i | \(0.280844\pi\) | |||||||
\(38\) | 230.000 | 0.981866 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.0000 | −0.0457094 | −0.0228547 | − | 0.999739i | \(-0.507276\pi\) | ||||
−0.0228547 | + | 0.999739i | \(0.507276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −263.000 | −0.932724 | −0.466362 | − | 0.884594i | \(-0.654436\pi\) | ||||
−0.466362 | + | 0.884594i | \(0.654436\pi\) | |||||||
\(44\) | −168.000 | −0.575613 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 324.000 | 1.03850 | ||||||||
\(47\) | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 268.000 | 0.714710 | ||||||||
\(53\) | −192.000 | −0.497608 | −0.248804 | − | 0.968554i | \(-0.580038\pi\) | ||||
−0.248804 | + | 0.968554i | \(0.580038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.00000 | −0.0190901 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −420.000 | −0.950840 | ||||||||
\(59\) | −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 | \(0.779380\pi\) | |||||||
\(62\) | 386.000 | 0.790678 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −299.000 | −0.545204 | −0.272602 | − | 0.962127i | \(-0.587884\pi\) | ||||
−0.272602 | + | 0.962127i | \(0.587884\pi\) | |||||||
\(68\) | 216.000 | 0.385204 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(0.770886\pi\) | |||||||
\(74\) | −572.000 | −0.898563 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −460.000 | −0.694284 | ||||||||
\(77\) | −42.0000 | −0.0621603 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −160.000 | −0.227866 | −0.113933 | − | 0.993488i | \(-0.536345\pi\) | ||||
−0.113933 | + | 0.993488i | \(0.536345\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 24.0000 | 0.0323214 | ||||||||
\(83\) | −462.000 | −0.610977 | −0.305488 | − | 0.952196i | \(-0.598820\pi\) | ||||
−0.305488 | + | 0.952196i | \(0.598820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 526.000 | 0.659535 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 336.000 | 0.407020 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | −648.000 | −0.734333 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −828.000 | −0.908529 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 511.000 | 0.534889 | 0.267444 | − | 0.963573i | \(-0.413821\pi\) | ||||
0.267444 | + | 0.963573i | \(0.413821\pi\) | |||||||
\(98\) | 684.000 | 0.705045 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −912.000 | −0.898489 | −0.449245 | − | 0.893409i | \(-0.648307\pi\) | ||||
−0.449245 | + | 0.893409i | \(0.648307\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −668.000 | −0.639029 | −0.319515 | − | 0.947581i | \(-0.603520\pi\) | ||||
−0.319515 | + | 0.947581i | \(0.603520\pi\) | |||||||
\(104\) | −536.000 | −0.505376 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 384.000 | 0.351862 | ||||||||
\(107\) | −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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.0000 | 0.0134987 | ||||||||
\(113\) | −1092.00 | −0.909086 | −0.454543 | − | 0.890725i | \(-0.650197\pi\) | ||||
−0.454543 | + | 0.890725i | \(0.650197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 840.000 | 0.672345 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1380.00 | 1.07660 | ||||||||
\(119\) | 54.0000 | 0.0415981 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 433.000 | 0.325319 | ||||||||
\(122\) | 1466.00 | 1.08791 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −772.000 | −0.559094 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 0.0111793 | 0.00558965 | − | 0.999984i | \(-0.498221\pi\) | ||||
0.00558965 | + | 0.999984i | \(0.498221\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | 598.000 | 0.385517 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −432.000 | −0.272380 | ||||||||
\(137\) | −2346.00 | −1.46301 | −0.731505 | − | 0.681836i | \(-0.761182\pi\) | ||||
−0.731505 | + | 0.681836i | \(0.761182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2900.00 | 1.76960 | 0.884801 | − | 0.465968i | \(-0.154294\pi\) | ||||
0.884801 | + | 0.465968i | \(0.154294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −456.000 | −0.269484 | ||||||||
\(143\) | −2814.00 | −1.64558 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1876.00 | 1.06342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1144.00 | 0.635380 | ||||||||
\(149\) | 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 | \(0.294053\pi\) | |||||||
\(152\) | 920.000 | 0.490933 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 84.0000 | 0.0439540 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 241.000 | 0.122509 | 0.0612544 | − | 0.998122i | \(-0.480490\pi\) | ||||
0.0612544 | + | 0.998122i | \(0.480490\pi\) | |||||||
\(158\) | 320.000 | 0.161126 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −162.000 | −0.0793006 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3547.00 | 1.70443 | 0.852216 | − | 0.523190i | \(-0.175258\pi\) | ||||
0.852216 | + | 0.523190i | \(0.175258\pi\) | |||||||
\(164\) | −48.0000 | −0.0228547 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 924.000 | 0.432026 | ||||||||
\(167\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1052.00 | −0.466362 | ||||||||
\(173\) | 3618.00 | 1.59001 | 0.795004 | − | 0.606604i | \(-0.207469\pi\) | ||||
0.795004 | + | 0.606604i | \(0.207469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −672.000 | −0.287806 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −480.000 | −0.202121 | ||||||||
\(179\) | 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 | \(0.487121\pi\) | |||||||
\(182\) | −134.000 | −0.0545755 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1296.00 | 0.519252 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2268.00 | −0.886912 | ||||||||
\(188\) | 1656.00 | 0.642427 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(0.782916\pi\) | |||||||
\(194\) | −1022.00 | −0.378223 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1368.00 | −0.498542 | ||||||||
\(197\) | 3054.00 | 1.10451 | 0.552255 | − | 0.833675i | \(-0.313767\pi\) | ||||
0.552255 | + | 0.833675i | \(0.313767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3425.00 | 1.22006 | 0.610030 | − | 0.792379i | \(-0.291158\pi\) | ||||
0.610030 | + | 0.792379i | \(0.291158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1824.00 | 0.635328 | ||||||||
\(203\) | 210.000 | 0.0726065 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1336.00 | 0.451862 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1072.00 | 0.357355 | ||||||||
\(209\) | 4830.00 | 1.59856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2443.00 | −0.797076 | −0.398538 | − | 0.917152i | \(-0.630482\pi\) | ||||
−0.398538 | + | 0.917152i | \(0.630482\pi\) | |||||||
\(212\) | −768.000 | −0.248804 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2592.00 | 0.827969 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −193.000 | −0.0603765 | ||||||||
\(218\) | 3470.00 | 1.07806 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3618.00 | 1.10124 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.0000 | −0.00690670 | −0.00345335 | − | 0.999994i | \(-0.501099\pi\) | ||||
−0.00345335 | + | 0.999994i | \(0.501099\pi\) | |||||||
\(224\) | −32.0000 | −0.00954504 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2184.00 | 0.642821 | ||||||||
\(227\) | −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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1680.00 | −0.475420 | ||||||||
\(233\) | 3468.00 | 0.975091 | 0.487546 | − | 0.873098i | \(-0.337892\pi\) | ||||
0.487546 | + | 0.873098i | \(0.337892\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2760.00 | −0.761274 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −108.000 | −0.0294143 | ||||||||
\(239\) | −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 | \(0.755582\pi\) | |||||||
\(242\) | −866.000 | −0.230035 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2932.00 | −0.769271 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7705.00 | −1.98485 | ||||||||
\(248\) | 1544.00 | 0.395339 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(254\) | −32.0000 | −0.00790496 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 564.000 | 0.136892 | 0.0684462 | − | 0.997655i | \(-0.478196\pi\) | ||||
0.0684462 | + | 0.997655i | \(0.478196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 286.000 | 0.0686146 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3984.00 | 0.939436 | ||||||||
\(263\) | −1812.00 | −0.424839 | −0.212420 | − | 0.977179i | \(-0.568134\pi\) | ||||
−0.212420 | + | 0.977179i | \(0.568134\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 230.000 | 0.0530158 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1196.00 | −0.272602 | ||||||||
\(269\) | 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 | \(0.327919\pi\) | |||||||
\(272\) | 864.000 | 0.192602 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4692.00 | 1.03450 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2191.00 | 0.475251 | 0.237625 | − | 0.971357i | \(-0.423631\pi\) | ||||
0.237625 | + | 0.971357i | \(0.423631\pi\) | |||||||
\(278\) | −5800.00 | −1.25130 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7842.00 | −1.66482 | −0.832410 | − | 0.554160i | \(-0.813040\pi\) | ||||
−0.832410 | + | 0.554160i | \(0.813040\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 247.000 | 0.0518821 | 0.0259410 | − | 0.999663i | \(-0.491742\pi\) | ||||
0.0259410 | + | 0.999663i | \(0.491742\pi\) | |||||||
\(284\) | 912.000 | 0.190554 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5628.00 | 1.16360 | ||||||||
\(287\) | −12.0000 | −0.00246808 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3752.00 | −0.751949 | ||||||||
\(293\) | −5442.00 | −1.08507 | −0.542534 | − | 0.840034i | \(-0.682535\pi\) | ||||
−0.542534 | + | 0.840034i | \(0.682535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2288.00 | −0.449281 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4140.00 | −0.804778 | ||||||||
\(299\) | −10854.0 | −2.09934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −263.000 | −0.0503624 | ||||||||
\(302\) | −4474.00 | −0.852483 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1840.00 | −0.347142 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3871.00 | 0.719641 | 0.359820 | − | 0.933022i | \(-0.382838\pi\) | ||||
0.359820 | + | 0.933022i | \(0.382838\pi\) | |||||||
\(308\) | −168.000 | −0.0310802 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(0.393492\pi\) | |||||||
\(314\) | −482.000 | −0.0866269 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −640.000 | −0.113933 | ||||||||
\(317\) | −1296.00 | −0.229623 | −0.114812 | − | 0.993387i | \(-0.536626\pi\) | ||||
−0.114812 | + | 0.993387i | \(0.536626\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8820.00 | −1.54804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 324.000 | 0.0560740 | ||||||||
\(323\) | −6210.00 | −1.06976 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7094.00 | −1.20522 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 96.0000 | 0.0161607 | ||||||||
\(329\) | 414.000 | 0.0693756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5132.00 | 0.852206 | 0.426103 | − | 0.904675i | \(-0.359886\pi\) | ||||
0.426103 | + | 0.904675i | \(0.359886\pi\) | |||||||
\(332\) | −1848.00 | −0.305488 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1968.00 | −0.322408 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6751.00 | 1.09125 | 0.545624 | − | 0.838030i | \(-0.316293\pi\) | ||||
0.545624 | + | 0.838030i | \(0.316293\pi\) | |||||||
\(338\) | −4584.00 | −0.737683 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8106.00 | 1.28729 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −685.000 | −0.107832 | ||||||||
\(344\) | 2104.00 | 0.329768 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7236.00 | −1.12431 | ||||||||
\(347\) | −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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1344.00 | 0.203510 | ||||||||
\(353\) | 6618.00 | 0.997849 | 0.498924 | − | 0.866646i | \(-0.333729\pi\) | ||||
0.498924 | + | 0.866646i | \(0.333729\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 960.000 | 0.142921 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −300.000 | −0.0442891 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | −394.000 | −0.0572049 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 268.000 | 0.0385907 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 871.000 | 0.123885 | 0.0619425 | − | 0.998080i | \(-0.480270\pi\) | ||||
0.0619425 | + | 0.998080i | \(0.480270\pi\) | |||||||
\(368\) | −2592.00 | −0.367167 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | \(0.646096\pi\) | |||||||
\(374\) | 4536.00 | 0.627142 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3312.00 | −0.454264 | ||||||||
\(377\) | 14070.0 | 1.92213 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9865.00 | −1.33702 | −0.668511 | − | 0.743703i | \(-0.733068\pi\) | ||||
−0.668511 | + | 0.743703i | \(0.733068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2604.00 | 0.348775 | ||||||||
\(383\) | 9828.00 | 1.31119 | 0.655597 | − | 0.755111i | \(-0.272417\pi\) | ||||
0.655597 | + | 0.755111i | \(0.272417\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8326.00 | 1.09788 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2044.00 | 0.267444 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | 2736.00 | 0.352523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6108.00 | −0.781007 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1381.00 | 0.174585 | 0.0872927 | − | 0.996183i | \(-0.472178\pi\) | ||||
0.0872927 | + | 0.996183i | \(0.472178\pi\) | |||||||
\(398\) | −6850.00 | −0.862712 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14232.0 | −1.77235 | −0.886175 | − | 0.463351i | \(-0.846647\pi\) | ||||
−0.886175 | + | 0.463351i | \(0.846647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12931.0 | −1.59836 | ||||||||
\(404\) | −3648.00 | −0.449245 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −420.000 | −0.0513405 | ||||||||
\(407\) | −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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2672.00 | −0.319515 | ||||||||
\(413\) | −690.000 | −0.0822099 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2144.00 | −0.252688 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9660.00 | −1.13035 | ||||||||
\(419\) | −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 | \(0.727867\pi\) | |||||||
\(422\) | 4886.00 | 0.563618 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1536.00 | 0.175931 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −733.000 | −0.0830734 | ||||||||
\(428\) | −5184.00 | −0.585463 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(0.520557\pi\) | |||||||
\(434\) | 386.000 | 0.0426926 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6940.00 | −0.762307 | ||||||||
\(437\) | 18630.0 | 2.03934 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6695.00 | 0.727870 | 0.363935 | − | 0.931424i | \(-0.381433\pi\) | ||||
0.363935 | + | 0.931424i | \(0.381433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7236.00 | −0.778691 | ||||||||
\(443\) | 16368.0 | 1.75546 | 0.877728 | − | 0.479159i | \(-0.159058\pi\) | ||||
0.877728 | + | 0.479159i | \(0.159058\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 46.0000 | 0.00488377 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 64.0000 | 0.00674937 | ||||||||
\(449\) | −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 | ||||||||
\(452\) | −4368.00 | −0.454543 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3912.00 | 0.404404 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13786.0 | 1.41112 | 0.705560 | − | 0.708650i | \(-0.250696\pi\) | ||||
0.705560 | + | 0.708650i | \(0.250696\pi\) | |||||||
\(458\) | −3610.00 | −0.368306 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11832.0 | −1.19538 | −0.597691 | − | 0.801726i | \(-0.703915\pi\) | ||||
−0.597691 | + | 0.801726i | \(0.703915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3008.00 | −0.301930 | −0.150965 | − | 0.988539i | \(-0.548238\pi\) | ||||
−0.150965 | + | 0.988539i | \(0.548238\pi\) | |||||||
\(464\) | 3360.00 | 0.336173 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6936.00 | −0.689494 | ||||||||
\(467\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5520.00 | 0.538302 | ||||||||
\(473\) | 11046.0 | 1.07378 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 216.000 | 0.0207990 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5280.00 | 0.505233 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 10766.0 | 1.01738 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1732.00 | 0.162660 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8671.00 | 0.806818 | 0.403409 | − | 0.915020i | \(-0.367825\pi\) | ||||
0.403409 | + | 0.915020i | \(0.367825\pi\) | |||||||
\(488\) | 5864.00 | 0.543957 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(494\) | 15410.0 | 1.40350 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3088.00 | −0.279547 | ||||||||
\(497\) | 228.000 | 0.0205779 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8875.00 | −0.796192 | −0.398096 | − | 0.917344i | \(-0.630329\pi\) | ||||
−0.398096 | + | 0.917344i | \(0.630329\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10056.0 | −0.894066 | ||||||||
\(503\) | −10452.0 | −0.926504 | −0.463252 | − | 0.886227i | \(-0.653318\pi\) | ||||
−0.463252 | + | 0.886227i | \(0.653318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −13608.0 | −1.19555 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 64.0000 | 0.00558965 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1128.00 | −0.0967976 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17388.0 | −1.47916 | ||||||||
\(518\) | −572.000 | −0.0485178 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11238.0 | 0.945001 | 0.472501 | − | 0.881330i | \(-0.343351\pi\) | ||||
0.472501 | + | 0.881330i | \(0.343351\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7447.00 | 0.622628 | 0.311314 | − | 0.950307i | \(-0.399231\pi\) | ||||
0.311314 | + | 0.950307i | \(0.399231\pi\) | |||||||
\(524\) | −7968.00 | −0.664282 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3624.00 | 0.300407 | ||||||||
\(527\) | −10422.0 | −0.861460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14077.0 | 1.15698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −460.000 | −0.0374878 | ||||||||
\(533\) | −804.000 | −0.0653379 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2392.00 | 0.192759 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10380.0 | −0.831810 | ||||||||
\(539\) | 14364.0 | 1.14787 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17623.0 | −1.40050 | −0.700251 | − | 0.713896i | \(-0.746929\pi\) | ||||
−0.700251 | + | 0.713896i | \(0.746929\pi\) | |||||||
\(542\) | −9184.00 | −0.727835 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1728.00 | −0.136190 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10096.0 | 0.789166 | 0.394583 | − | 0.918860i | \(-0.370889\pi\) | ||||
0.394583 | + | 0.918860i | \(0.370889\pi\) | |||||||
\(548\) | −9384.00 | −0.731505 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24150.0 | −1.86720 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −160.000 | −0.0123036 | ||||||||
\(554\) | −4382.00 | −0.336053 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11600.0 | 0.884801 | ||||||||
\(557\) | 14514.0 | 1.10409 | 0.552045 | − | 0.833814i | \(-0.313848\pi\) | ||||
0.552045 | + | 0.833814i | \(0.313848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17621.0 | −1.33325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15684.0 | 1.17721 | ||||||||
\(563\) | −10242.0 | −0.766694 | −0.383347 | − | 0.923604i | \(-0.625229\pi\) | ||||
−0.383347 | + | 0.923604i | \(0.625229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −494.000 | −0.0366862 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1824.00 | −0.134742 | ||||||||
\(569\) | 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 | \(0.284179\pi\) | |||||||
\(572\) | −11256.0 | −0.822792 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.0000 | 0.00174519 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 301.000 | 0.0217171 | 0.0108586 | − | 0.999941i | \(-0.496544\pi\) | ||||
0.0108586 | + | 0.999941i | \(0.496544\pi\) | |||||||
\(578\) | 3994.00 | 0.287420 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −462.000 | −0.0329897 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8064.00 | 0.572859 | ||||||||
\(584\) | 7504.00 | 0.531708 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10884.0 | 0.767259 | ||||||||
\(587\) | −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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4576.00 | 0.317690 | ||||||||
\(593\) | −9492.00 | −0.657318 | −0.328659 | − | 0.944449i | \(-0.606597\pi\) | ||||
−0.328659 | + | 0.944449i | \(0.606597\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8280.00 | 0.569064 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21708.0 | 1.48446 | ||||||||
\(599\) | −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 | \(0.334663\pi\) | |||||||
\(602\) | 526.000 | 0.0356116 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8948.00 | 0.602796 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16184.0 | −1.08219 | −0.541094 | − | 0.840962i | \(-0.681990\pi\) | ||||
−0.541094 | + | 0.840962i | \(0.681990\pi\) | |||||||
\(608\) | 3680.00 | 0.245467 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | \(0.291357\pi\) | |||||||
\(614\) | −7742.00 | −0.508863 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 336.000 | 0.0219770 | ||||||||
\(617\) | −13896.0 | −0.906697 | −0.453348 | − | 0.891333i | \(-0.649771\pi\) | ||||
−0.453348 | + | 0.891333i | \(0.649771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9895.00 | −0.642510 | −0.321255 | − | 0.946993i | \(-0.604105\pi\) | ||||
−0.321255 | + | 0.946993i | \(0.604105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11436.0 | −0.737206 | ||||||||
\(623\) | 240.000 | 0.0154340 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7274.00 | −0.464421 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 964.000 | 0.0612544 | ||||||||
\(629\) | 15444.0 | 0.979003 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 467.000 | 0.0294627 | 0.0147314 | − | 0.999891i | \(-0.495311\pi\) | ||||
0.0147314 | + | 0.999891i | \(0.495311\pi\) | |||||||
\(632\) | 1280.00 | 0.0805628 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2592.00 | 0.162368 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22914.0 | −1.42525 | ||||||||
\(638\) | 17640.0 | 1.09463 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30612.0 | −1.88627 | −0.943137 | − | 0.332405i | \(-0.892140\pi\) | ||||
−0.943137 | + | 0.332405i | \(0.892140\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1852.00 | 0.113586 | 0.0567930 | − | 0.998386i | \(-0.481913\pi\) | ||||
0.0567930 | + | 0.998386i | \(0.481913\pi\) | |||||||
\(644\) | −648.000 | −0.0396503 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12420.0 | 0.756437 | ||||||||
\(647\) | −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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14188.0 | 0.852216 | ||||||||
\(653\) | −9702.00 | −0.581422 | −0.290711 | − | 0.956811i | \(-0.593892\pi\) | ||||
−0.290711 | + | 0.956811i | \(0.593892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −192.000 | −0.0114273 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −828.000 | −0.0490559 | ||||||||
\(659\) | −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 | \(0.702089\pi\) | |||||||
\(662\) | −10264.0 | −0.602601 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3696.00 | 0.216013 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34020.0 | −1.97490 | ||||||||
\(668\) | 3936.00 | 0.227977 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | \(0.339376\pi\) | |||||||
\(674\) | −13502.0 | −0.771628 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9168.00 | 0.521620 | ||||||||
\(677\) | 20934.0 | 1.18842 | 0.594209 | − | 0.804311i | \(-0.297465\pi\) | ||||
0.594209 | + | 0.804311i | \(0.297465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 511.000 | 0.0288813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16212.0 | −0.910249 | ||||||||
\(683\) | −8712.00 | −0.488075 | −0.244038 | − | 0.969766i | \(-0.578472\pi\) | ||||
−0.244038 | + | 0.969766i | \(0.578472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1370.00 | 0.0762490 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4208.00 | −0.233181 | ||||||||
\(689\) | −12864.0 | −0.711291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14128.0 | −0.777792 | −0.388896 | − | 0.921282i | \(-0.627144\pi\) | ||||
−0.388896 | + | 0.921282i | \(0.627144\pi\) | |||||||
\(692\) | 14472.0 | 0.795004 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10452.0 | 0.571689 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −648.000 | −0.0352148 | ||||||||
\(698\) | 12380.0 | 0.671332 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28278.0 | 1.52360 | 0.761801 | − | 0.647811i | \(-0.224315\pi\) | ||||
0.761801 | + | 0.647811i | \(0.224315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32890.0 | −1.76454 | ||||||||
\(704\) | −2688.00 | −0.143903 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13236.0 | −0.705586 | ||||||||
\(707\) | −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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1920.00 | −0.101060 | ||||||||
\(713\) | 31266.0 | 1.64225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 600.000 | 0.0313171 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6840.00 | −0.355524 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | −12732.0 | −0.656283 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 788.000 | 0.0404500 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1801.00 | 0.0918781 | 0.0459391 | − | 0.998944i | \(-0.485372\pi\) | ||||
0.0459391 | + | 0.998944i | \(0.485372\pi\) | |||||||
\(728\) | −536.000 | −0.0272877 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | \(0.436365\pi\) | |||||||
\(734\) | −1742.00 | −0.0876000 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5184.00 | 0.259626 | ||||||||
\(737\) | 12558.0 | 0.627652 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33860.0 | 1.68547 | 0.842734 | − | 0.538331i | \(-0.180945\pi\) | ||||
0.842734 | + | 0.538331i | \(0.180945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 384.000 | 0.0189988 | ||||||||
\(743\) | −20652.0 | −1.01972 | −0.509858 | − | 0.860259i | \(-0.670302\pi\) | ||||
−0.509858 | + | 0.860259i | \(0.670302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12766.0 | 0.626537 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9072.00 | −0.443456 | ||||||||
\(749\) | −1296.00 | −0.0632240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7472.00 | 0.363059 | 0.181529 | − | 0.983386i | \(-0.441895\pi\) | ||||
0.181529 | + | 0.983386i | \(0.441895\pi\) | |||||||
\(752\) | 6624.00 | 0.321213 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −28140.0 | −1.35915 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32251.0 | 1.54846 | 0.774229 | − | 0.632906i | \(-0.218138\pi\) | ||||
0.774229 | + | 0.632906i | \(0.218138\pi\) | |||||||
\(758\) | 19730.0 | 0.945417 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16812.0 | −0.800834 | −0.400417 | − | 0.916333i | \(-0.631135\pi\) | ||||
−0.400417 | + | 0.916333i | \(0.631135\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1735.00 | −0.0823214 | ||||||||
\(764\) | −5208.00 | −0.246622 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19656.0 | −0.927154 | ||||||||
\(767\) | −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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16652.0 | −0.776319 | ||||||||
\(773\) | −8412.00 | −0.391408 | −0.195704 | − | 0.980663i | \(-0.562699\pi\) | ||||
−0.195704 | + | 0.980663i | \(0.562699\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4088.00 | −0.189112 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25080.0 | 1.15573 | ||||||||
\(779\) | 1380.00 | 0.0634706 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9576.00 | −0.438740 | ||||||||
\(782\) | 17496.0 | 0.800071 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5472.00 | −0.249271 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18329.0 | −0.830188 | −0.415094 | − | 0.909778i | \(-0.636251\pi\) | ||||
−0.415094 | + | 0.909778i | \(0.636251\pi\) | |||||||
\(788\) | 12216.0 | 0.552255 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1092.00 | −0.0490860 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49111.0 | −2.19922 | ||||||||
\(794\) | −2762.00 | −0.123451 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13700.0 | 0.610030 | ||||||||
\(797\) | 16044.0 | 0.713059 | 0.356529 | − | 0.934284i | \(-0.383960\pi\) | ||||
0.356529 | + | 0.934284i | \(0.383960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22356.0 | 0.989860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28464.0 | 1.25324 | ||||||||
\(803\) | 39396.0 | 1.73133 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25862.0 | 1.13021 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7296.00 | 0.317664 | ||||||||
\(809\) | 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 | \(0.464666\pi\) | |||||||
\(812\) | 840.000 | 0.0363032 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24024.0 | 1.03445 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30245.0 | 1.29515 | ||||||||
\(818\) | −5290.00 | −0.226113 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13542.0 | −0.575663 | −0.287831 | − | 0.957681i | \(-0.592934\pi\) | ||||
−0.287831 | + | 0.957681i | \(0.592934\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1283.00 | −0.0543409 | −0.0271705 | − | 0.999631i | \(-0.508650\pi\) | ||||
−0.0271705 | + | 0.999631i | \(0.508650\pi\) | |||||||
\(824\) | 5344.00 | 0.225931 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1380.00 | 0.0581312 | ||||||||
\(827\) | 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 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4288.00 | 0.178677 | ||||||||
\(833\) | −18468.0 | −0.768161 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 19320.0 | 0.799278 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6000.00 | 0.247335 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 22676.0 | 0.928108 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9772.00 | −0.398538 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 433.000 | 0.0175656 | ||||||||
\(848\) | −3072.00 | −0.124402 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | \(0.665415\pi\) | |||||||
\(854\) | 1466.00 | 0.0587418 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10368.0 | 0.413985 | ||||||||
\(857\) | −23556.0 | −0.938924 | −0.469462 | − | 0.882953i | \(-0.655552\pi\) | ||||
−0.469462 | + | 0.882953i | \(0.655552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34000.0 | −1.35048 | −0.675242 | − | 0.737597i | \(-0.735961\pi\) | ||||
−0.675242 | + | 0.737597i | \(0.735961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6516.00 | −0.257466 | ||||||||
\(863\) | −37032.0 | −1.46070 | −0.730350 | − | 0.683073i | \(-0.760643\pi\) | ||||
−0.730350 | + | 0.683073i | \(0.760643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2326.00 | 0.0912710 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −772.000 | −0.0301882 | ||||||||
\(869\) | 6720.00 | 0.262325 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20033.0 | −0.779325 | ||||||||
\(872\) | 13880.0 | 0.539032 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −37260.0 | −1.44203 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2519.00 | −0.0969904 | −0.0484952 | − | 0.998823i | \(-0.515443\pi\) | ||||
−0.0484952 | + | 0.998823i | \(0.515443\pi\) | |||||||
\(878\) | −13390.0 | −0.514682 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43992.0 | −1.68232 | −0.841162 | − | 0.540783i | \(-0.818128\pi\) | ||||
−0.841162 | + | 0.540783i | \(0.818128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19177.0 | 0.730869 | 0.365435 | − | 0.930837i | \(-0.380920\pi\) | ||||
0.365435 | + | 0.930837i | \(0.380920\pi\) | |||||||
\(884\) | 14472.0 | 0.550618 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32736.0 | −1.24130 | ||||||||
\(887\) | 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 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −92.0000 | −0.00345335 | ||||||||
\(893\) | −47610.0 | −1.78411 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −128.000 | −0.00477252 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32760.0 | 1.21739 | ||||||||
\(899\) | −40530.0 | −1.50362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10368.0 | −0.383361 | ||||||||
\(902\) | −1008.00 | −0.0372092 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8736.00 | 0.321410 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52396.0 | 1.91817 | 0.959085 | − | 0.283117i | \(-0.0913686\pi\) | ||||
0.959085 | + | 0.283117i | \(0.0913686\pi\) | |||||||
\(908\) | −7824.00 | −0.285957 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | −27572.0 | −0.997813 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7220.00 | 0.260432 | ||||||||
\(917\) | −1992.00 | −0.0717357 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4085.00 | 0.146629 | 0.0733143 | − | 0.997309i | \(-0.476642\pi\) | ||||
0.0733143 | + | 0.997309i | \(0.476642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23664.0 | 0.845263 | ||||||||
\(923\) | 15276.0 | 0.544762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6016.00 | 0.213497 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6720.00 | −0.237710 | ||||||||
\(929\) | 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 | ||||||||
\(932\) | 13872.0 | 0.487546 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8868.00 | −0.310674 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5759.00 | −0.200788 | −0.100394 | − | 0.994948i | \(-0.532010\pi\) | ||||
−0.100394 | + | 0.994948i | \(0.532010\pi\) | |||||||
\(938\) | 598.000 | 0.0208160 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 258.000 | 0.00893790 | 0.00446895 | − | 0.999990i | \(-0.498577\pi\) | ||||
0.00446895 | + | 0.999990i | \(0.498577\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1944.00 | 0.0671319 | ||||||||
\(944\) | −11040.0 | −0.380637 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22092.0 | −0.759274 | ||||||||
\(947\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −432.000 | −0.0147071 | ||||||||
\(953\) | 9288.00 | 0.315706 | 0.157853 | − | 0.987463i | \(-0.449543\pi\) | ||||
0.157853 | + | 0.987463i | \(0.449543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10560.0 | −0.357254 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14820.0 | 0.499804 | ||||||||
\(959\) | −2346.00 | −0.0789951 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7458.00 | 0.250344 | ||||||||
\(962\) | −38324.0 | −1.28442 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21532.0 | −0.719397 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21616.0 | 0.718846 | 0.359423 | − | 0.933175i | \(-0.382974\pi\) | ||||
0.359423 | + | 0.933175i | \(0.382974\pi\) | |||||||
\(968\) | −3464.00 | −0.115018 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(974\) | −17342.0 | −0.570507 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11728.0 | −0.384635 | ||||||||
\(977\) | −18246.0 | −0.597483 | −0.298742 | − | 0.954334i | \(-0.596567\pi\) | ||||
−0.298742 | + | 0.954334i | \(0.596567\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10080.0 | −0.329069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −38736.0 | −1.25877 | ||||||||
\(983\) | −38772.0 | −1.25802 | −0.629011 | − | 0.777397i | \(-0.716540\pi\) | ||||
−0.629011 | + | 0.777397i | \(0.716540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −22680.0 | −0.732534 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30820.0 | −0.992424 | ||||||||
\(989\) | 42606.0 | 1.36986 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23053.0 | −0.738953 | −0.369477 | − | 0.929240i | \(-0.620463\pi\) | ||||
−0.369477 | + | 0.929240i | \(0.620463\pi\) | |||||||
\(992\) | 6176.00 | 0.197670 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −456.000 | −0.0145507 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10366.0 | 0.329282 | 0.164641 | − | 0.986354i | \(-0.447353\pi\) | ||||
0.164641 | + | 0.986354i | \(0.447353\pi\) | |||||||
\(998\) | 17750.0 | 0.562992 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.4.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 150.4.a.h.1.1 | yes | 1 | ||
5.2 | odd | 4 | 450.4.c.a.199.1 | 2 | |||
5.3 | odd | 4 | 450.4.c.a.199.2 | 2 | |||
5.4 | even | 2 | 450.4.a.o.1.1 | 1 | |||
12.11 | even | 2 | 1200.4.a.i.1.1 | 1 | |||
15.2 | even | 4 | 150.4.c.e.49.2 | 2 | |||
15.8 | even | 4 | 150.4.c.e.49.1 | 2 | |||
15.14 | odd | 2 | 150.4.a.a.1.1 | ✓ | 1 | ||
60.23 | odd | 4 | 1200.4.f.c.49.1 | 2 | |||
60.47 | odd | 4 | 1200.4.f.c.49.2 | 2 | |||
60.59 | even | 2 | 1200.4.a.bb.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.4.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
150.4.a.h.1.1 | yes | 1 | 3.2 | odd | 2 | ||
150.4.c.e.49.1 | 2 | 15.8 | even | 4 | |||
150.4.c.e.49.2 | 2 | 15.2 | even | 4 | |||
450.4.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
450.4.a.o.1.1 | 1 | 5.4 | even | 2 | |||
450.4.c.a.199.1 | 2 | 5.2 | odd | 4 | |||
450.4.c.a.199.2 | 2 | 5.3 | odd | 4 | |||
1200.4.a.i.1.1 | 1 | 12.11 | even | 2 | |||
1200.4.a.bb.1.1 | 1 | 60.59 | even | 2 | |||
1200.4.f.c.49.1 | 2 | 60.23 | odd | 4 | |||
1200.4.f.c.49.2 | 2 | 60.47 | odd | 4 |