Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,4,Mod(1,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, 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("1800.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.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: | \(106.203438010\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 200) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1800.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.00000 | −0.323970 | −0.161985 | − | 0.986793i | \(-0.551790\pi\) | ||||
−0.161985 | + | 0.986793i | \(0.551790\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.0000 | 0.520792 | 0.260396 | − | 0.965502i | \(-0.416147\pi\) | ||||
0.260396 | + | 0.965502i | \(0.416147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.0000 | 0.256015 | 0.128008 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128008 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 75.0000 | 1.07001 | 0.535005 | − | 0.844849i | \(-0.320310\pi\) | ||||
0.535005 | + | 0.844849i | \(0.320310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −91.0000 | −1.09878 | −0.549390 | − | 0.835566i | \(-0.685140\pi\) | ||||
−0.549390 | + | 0.835566i | \(0.685140\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −174.000 | −1.57746 | −0.788728 | − | 0.614742i | \(-0.789260\pi\) | ||||
−0.788728 | + | 0.614742i | \(0.789260\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 272.000 | 1.74169 | 0.870847 | − | 0.491554i | \(-0.163571\pi\) | ||||
0.870847 | + | 0.491554i | \(0.163571\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −230.000 | −1.33256 | −0.666278 | − | 0.745704i | \(-0.732113\pi\) | ||||
−0.666278 | + | 0.745704i | \(0.732113\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −182.000 | −0.808665 | −0.404333 | − | 0.914612i | \(-0.632496\pi\) | ||||
−0.404333 | + | 0.914612i | \(0.632496\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −117.000 | −0.445667 | −0.222833 | − | 0.974857i | \(-0.571531\pi\) | ||||
−0.222833 | + | 0.974857i | \(0.571531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 372.000 | 1.31929 | 0.659645 | − | 0.751577i | \(-0.270707\pi\) | ||||
0.659645 | + | 0.751577i | \(0.270707\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 52.0000 | 0.161383 | 0.0806913 | − | 0.996739i | \(-0.474287\pi\) | ||||
0.0806913 | + | 0.996739i | \(0.474287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −307.000 | −0.895044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 402.000 | 1.04187 | 0.520933 | − | 0.853597i | \(-0.325584\pi\) | ||||
0.520933 | + | 0.853597i | \(0.325584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −312.000 | −0.688457 | −0.344228 | − | 0.938886i | \(-0.611859\pi\) | ||||
−0.344228 | + | 0.938886i | \(0.611859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 170.000 | 0.356824 | 0.178412 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178412 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 763.000 | 1.39127 | 0.695636 | − | 0.718394i | \(-0.255122\pi\) | ||||
0.695636 | + | 0.718394i | \(0.255122\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52.0000 | 0.0869192 | 0.0434596 | − | 0.999055i | \(-0.486162\pi\) | ||||
0.0434596 | + | 0.999055i | \(0.486162\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −981.000 | −1.57284 | −0.786420 | − | 0.617692i | \(-0.788068\pi\) | ||||
−0.786420 | + | 0.617692i | \(0.788068\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −114.000 | −0.168721 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1054.00 | 1.50107 | 0.750533 | − | 0.660833i | \(-0.229797\pi\) | ||||
0.750533 | + | 0.660833i | \(0.229797\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −351.000 | −0.464184 | −0.232092 | − | 0.972694i | \(-0.574557\pi\) | ||||
−0.232092 | + | 0.972694i | \(0.574557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −799.000 | −0.951616 | −0.475808 | − | 0.879549i | \(-0.657844\pi\) | ||||
−0.475808 | + | 0.879549i | \(0.657844\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −72.0000 | −0.0829412 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 962.000 | 1.00697 | 0.503486 | − | 0.864003i | \(-0.332051\pi\) | ||||
0.503486 | + | 0.864003i | \(0.332051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −486.000 | −0.478800 | −0.239400 | − | 0.970921i | \(-0.576951\pi\) | ||||
−0.239400 | + | 0.970921i | \(0.576951\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1188.00 | −1.13648 | −0.568238 | − | 0.822864i | \(-0.692375\pi\) | ||||
−0.568238 | + | 0.822864i | \(0.692375\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1325.00 | −1.19713 | −0.598563 | − | 0.801075i | \(-0.704262\pi\) | ||||
−0.598563 | + | 0.801075i | \(0.704262\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 126.000 | 0.110721 | 0.0553606 | − | 0.998466i | \(-0.482369\pi\) | ||||
0.0553606 | + | 0.998466i | \(0.482369\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −183.000 | −0.152347 | −0.0761734 | − | 0.997095i | \(-0.524270\pi\) | ||||
−0.0761734 | + | 0.997095i | \(0.524270\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −450.000 | −0.346651 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −970.000 | −0.728775 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −902.000 | −0.630233 | −0.315116 | − | 0.949053i | \(-0.602044\pi\) | ||||
−0.315116 | + | 0.949053i | \(0.602044\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2068.00 | −1.37925 | −0.689626 | − | 0.724166i | \(-0.742225\pi\) | ||||
−0.689626 | + | 0.724166i | \(0.742225\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 546.000 | 0.355971 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1339.00 | 0.835025 | 0.417513 | − | 0.908671i | \(-0.362902\pi\) | ||||
0.417513 | + | 0.908671i | \(0.362902\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2939.00 | −1.79340 | −0.896700 | − | 0.442638i | \(-0.854043\pi\) | ||||
−0.896700 | + | 0.442638i | \(0.854043\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 228.000 | 0.133331 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 208.000 | 0.114363 | 0.0571813 | − | 0.998364i | \(-0.481789\pi\) | ||||
0.0571813 | + | 0.998364i | \(0.481789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2678.00 | −1.44326 | −0.721631 | − | 0.692278i | \(-0.756607\pi\) | ||||
−0.721631 | + | 0.692278i | \(0.756607\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1482.00 | 0.753353 | 0.376677 | − | 0.926345i | \(-0.377067\pi\) | ||||
0.376677 | + | 0.926345i | \(0.377067\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1044.00 | 0.511048 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1469.00 | −0.705895 | −0.352948 | − | 0.935643i | \(-0.614821\pi\) | ||||
−0.352948 | + | 0.935643i | \(0.614821\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4004.00 | 1.85532 | 0.927661 | − | 0.373423i | \(-0.121816\pi\) | ||||
0.927661 | + | 0.373423i | \(0.121816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2053.00 | −0.934456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3224.00 | −1.41686 | −0.708428 | − | 0.705783i | \(-0.750595\pi\) | ||||
−0.708428 | + | 0.705783i | \(0.750595\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4191.00 | 1.75000 | 0.875000 | − | 0.484123i | \(-0.160861\pi\) | ||||
0.875000 | + | 0.484123i | \(0.160861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3718.00 | −1.52683 | −0.763416 | − | 0.645907i | \(-0.776480\pi\) | ||||
−0.763416 | + | 0.645907i | \(0.776480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1425.00 | 0.557253 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −870.000 | −0.329586 | −0.164793 | − | 0.986328i | \(-0.552696\pi\) | ||||
−0.164793 | + | 0.986328i | \(0.552696\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2197.00 | 0.819396 | 0.409698 | − | 0.912221i | \(-0.365634\pi\) | ||||
0.409698 | + | 0.912221i | \(0.365634\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2314.00 | 0.836882 | 0.418441 | − | 0.908244i | \(-0.362577\pi\) | ||||
0.418441 | + | 0.908244i | \(0.362577\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −252.000 | −0.0897679 | −0.0448839 | − | 0.998992i | \(-0.514292\pi\) | ||||
−0.0448839 | + | 0.998992i | \(0.514292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1632.00 | −0.564256 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1729.00 | −0.572237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −741.000 | −0.241766 | −0.120883 | − | 0.992667i | \(-0.538573\pi\) | ||||
−0.120883 | + | 0.992667i | \(0.538573\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1380.00 | 0.431707 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 900.000 | 0.273939 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5092.00 | −1.52908 | −0.764542 | − | 0.644574i | \(-0.777035\pi\) | ||||
−0.764542 | + | 0.644574i | \(0.777035\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5876.00 | −1.71808 | −0.859039 | − | 0.511910i | \(-0.828938\pi\) | ||||
−0.859039 | + | 0.511910i | \(0.828938\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −604.000 | −0.174295 | −0.0871473 | − | 0.996195i | \(-0.527775\pi\) | ||||
−0.0871473 | + | 0.996195i | \(0.527775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −278.000 | −0.0781647 | −0.0390824 | − | 0.999236i | \(-0.512443\pi\) | ||||
−0.0390824 | + | 0.999236i | \(0.512443\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2496.00 | −0.675535 | −0.337767 | − | 0.941230i | \(-0.609672\pi\) | ||||
−0.337767 | + | 0.941230i | \(0.609672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2567.00 | −0.686120 | −0.343060 | − | 0.939313i | \(-0.611463\pi\) | ||||
−0.343060 | + | 0.939313i | \(0.611463\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1092.00 | −0.281305 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5395.00 | −1.35669 | −0.678345 | − | 0.734743i | \(-0.737303\pi\) | ||||
−0.678345 | + | 0.734743i | \(0.737303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3306.00 | −0.821527 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1490.00 | 0.361648 | 0.180824 | − | 0.983515i | \(-0.442123\pi\) | ||||
0.180824 | + | 0.983515i | \(0.442123\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1092.00 | 0.261983 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3330.00 | 0.780748 | 0.390374 | − | 0.920656i | \(-0.372346\pi\) | ||||
0.390374 | + | 0.920656i | \(0.372346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6096.00 | −1.38171 | −0.690854 | − | 0.722994i | \(-0.742765\pi\) | ||||
−0.690854 | + | 0.722994i | \(0.742765\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6006.00 | −1.34627 | −0.673134 | − | 0.739521i | \(-0.735052\pi\) | ||||
−0.673134 | + | 0.739521i | \(0.735052\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6976.00 | 1.51317 | 0.756583 | − | 0.653897i | \(-0.226867\pi\) | ||||
0.756583 | + | 0.653897i | \(0.226867\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3998.00 | −0.848757 | −0.424378 | − | 0.905485i | \(-0.639507\pi\) | ||||
−0.424378 | + | 0.905485i | \(0.639507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0000 | −0.00273064 | −0.00136532 | − | 0.999999i | \(-0.500435\pi\) | ||||
−0.00136532 | + | 0.999999i | \(0.500435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 702.000 | 0.144382 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 712.000 | 0.144922 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4466.00 | 0.890466 | 0.445233 | − | 0.895415i | \(-0.353121\pi\) | ||||
0.445233 | + | 0.895415i | \(0.353121\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2088.00 | −0.403853 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2232.00 | −0.427410 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9041.00 | 1.68077 | 0.840386 | − | 0.541988i | \(-0.182328\pi\) | ||||
0.840386 | + | 0.541988i | \(0.182328\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 346.000 | 0.0630864 | 0.0315432 | − | 0.999502i | \(-0.489958\pi\) | ||||
0.0315432 | + | 0.999502i | \(0.489958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10646.0 | −1.92252 | −0.961258 | − | 0.275650i | \(-0.911107\pi\) | ||||
−0.961258 | + | 0.275650i | \(0.911107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8116.00 | 1.43798 | 0.718990 | − | 0.695020i | \(-0.244604\pi\) | ||||
0.718990 | + | 0.695020i | \(0.244604\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5168.00 | 0.907061 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6825.00 | −1.17571 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −312.000 | −0.0522830 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3007.00 | −0.499334 | −0.249667 | − | 0.968332i | \(-0.580321\pi\) | ||||
−0.249667 | + | 0.968332i | \(0.580321\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 83.0000 | 0.0134163 | 0.00670816 | − | 0.999978i | \(-0.497865\pi\) | ||||
0.00670816 | + | 0.999978i | \(0.497865\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4370.00 | −0.693985 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3900.00 | 0.613936 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6189.00 | −0.957472 | −0.478736 | − | 0.877959i | \(-0.658905\pi\) | ||||
−0.478736 | + | 0.877959i | \(0.658905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5362.00 | −0.822411 | −0.411205 | − | 0.911543i | \(-0.634892\pi\) | ||||
−0.411205 | + | 0.911543i | \(0.634892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1690.00 | 0.254815 | 0.127407 | − | 0.991850i | \(-0.459334\pi\) | ||||
0.127407 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1638.00 | −0.240809 | −0.120404 | − | 0.992725i | \(-0.538419\pi\) | ||||
−0.120404 | + | 0.992725i | \(0.538419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1422.00 | 0.207319 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7580.00 | −1.07813 | −0.539064 | − | 0.842265i | \(-0.681222\pi\) | ||||
−0.539064 | + | 0.842265i | \(0.681222\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2412.00 | −0.337533 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5630.00 | −0.781529 | −0.390765 | − | 0.920491i | \(-0.627789\pi\) | ||||
−0.390765 | + | 0.920491i | \(0.627789\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3264.00 | 0.445901 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4385.00 | −0.594307 | −0.297153 | − | 0.954830i | \(-0.596037\pi\) | ||||
−0.297153 | + | 0.954830i | \(0.596037\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12558.0 | −1.67541 | −0.837707 | − | 0.546119i | \(-0.816104\pi\) | ||||
−0.837707 | + | 0.546119i | \(0.816104\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6570.00 | 0.856330 | 0.428165 | − | 0.903701i | \(-0.359160\pi\) | ||||
0.428165 | + | 0.903701i | \(0.359160\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13050.0 | −1.68789 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1268.00 | 0.160300 | 0.0801500 | − | 0.996783i | \(-0.474460\pi\) | ||||
0.0801500 | + | 0.996783i | \(0.474460\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6299.00 | 0.784432 | 0.392216 | − | 0.919873i | \(-0.371709\pi\) | ||||
0.392216 | + | 0.919873i | \(0.371709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2760.00 | −0.341155 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3458.00 | −0.421147 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13459.0 | −1.62715 | −0.813575 | − | 0.581459i | \(-0.802482\pi\) | ||||
−0.813575 | + | 0.581459i | \(0.802482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1872.00 | 0.223039 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9567.00 | 1.11546 | 0.557731 | − | 0.830022i | \(-0.311672\pi\) | ||||
0.557731 | + | 0.830022i | \(0.311672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2708.00 | 0.313491 | 0.156746 | − | 0.987639i | \(-0.449900\pi\) | ||||
0.156746 | + | 0.987639i | \(0.449900\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1020.00 | −0.115600 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5126.00 | −0.572879 | −0.286439 | − | 0.958098i | \(-0.592472\pi\) | ||||
−0.286439 | + | 0.958098i | \(0.592472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11445.0 | 1.27023 | 0.635117 | − | 0.772416i | \(-0.280952\pi\) | ||||
0.635117 | + | 0.772416i | \(0.280952\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15834.0 | 1.73328 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5096.00 | −0.554029 | −0.277015 | − | 0.960866i | \(-0.589345\pi\) | ||||
−0.277015 | + | 0.960866i | \(0.589345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13247.0 | −1.42073 | −0.710366 | − | 0.703833i | \(-0.751470\pi\) | ||||
−0.710366 | + | 0.703833i | \(0.751470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7449.00 | −0.782940 | −0.391470 | − | 0.920191i | \(-0.628033\pi\) | ||||
−0.391470 | + | 0.920191i | \(0.628033\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2223.00 | −0.232100 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3497.00 | 0.357949 | 0.178975 | − | 0.983854i | \(-0.442722\pi\) | ||||
0.178975 | + | 0.983854i | \(0.442722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13108.0 | 1.32430 | 0.662148 | − | 0.749373i | \(-0.269645\pi\) | ||||
0.662148 | + | 0.749373i | \(0.269645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5428.00 | −0.544839 | −0.272420 | − | 0.962179i | \(-0.587824\pi\) | ||||
−0.272420 | + | 0.962179i | \(0.587824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1516.00 | 0.150219 | 0.0751093 | − | 0.997175i | \(-0.476069\pi\) | ||||
0.0751093 | + | 0.997175i | \(0.476069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4578.00 | −0.450730 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7068.00 | 0.687076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14762.0 | 1.40813 | 0.704064 | − | 0.710137i | \(-0.251367\pi\) | ||||
0.704064 | + | 0.710137i | \(0.251367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2184.00 | −0.207031 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3926.00 | −0.365306 | −0.182653 | − | 0.983177i | \(-0.558468\pi\) | ||||
−0.182653 | + | 0.983177i | \(0.558468\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −996.000 | −0.0915455 | −0.0457728 | − | 0.998952i | \(-0.514575\pi\) | ||||
−0.0457728 | + | 0.998952i | \(0.514575\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20400.0 | 1.86363 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −312.000 | −0.0281592 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7804.00 | 0.700110 | 0.350055 | − | 0.936729i | \(-0.386163\pi\) | ||||
0.350055 | + | 0.936729i | \(0.386163\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16732.0 | 1.48319 | 0.741593 | − | 0.670850i | \(-0.234070\pi\) | ||||
0.741593 | + | 0.670850i | \(0.234070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10426.0 | −0.907906 | −0.453953 | − | 0.891026i | \(-0.649987\pi\) | ||||
−0.453953 | + | 0.891026i | \(0.649987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5886.00 | 0.509552 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 988.000 | 0.0840468 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2235.00 | 0.187941 | 0.0939704 | − | 0.995575i | \(-0.470044\pi\) | ||||
0.0939704 | + | 0.995575i | \(0.470044\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10855.0 | −0.907564 | −0.453782 | − | 0.891113i | \(-0.649926\pi\) | ||||
−0.453782 | + | 0.891113i | \(0.649926\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17250.0 | −1.42585 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18109.0 | 1.48837 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1404.00 | −0.114098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5833.00 | −0.466132 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10608.0 | 0.843019 | 0.421510 | − | 0.906824i | \(-0.361500\pi\) | ||||
0.421510 | + | 0.906824i | \(0.361500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11583.0 | −0.905399 | −0.452700 | − | 0.891663i | \(-0.649539\pi\) | ||||
−0.452700 | + | 0.891663i | \(0.649539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24752.0 | −1.91374 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6324.00 | −0.486300 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17244.0 | −1.31176 | −0.655881 | − | 0.754864i | \(-0.727703\pi\) | ||||
−0.655881 | + | 0.754864i | \(0.727703\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4464.00 | 0.337759 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18416.0 | 1.37858 | 0.689291 | − | 0.724484i | \(-0.257922\pi\) | ||||
0.689291 | + | 0.724484i | \(0.257922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11913.0 | −0.877713 | −0.438857 | − | 0.898557i | \(-0.644616\pi\) | ||||
−0.438857 | + | 0.898557i | \(0.644616\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3900.00 | 0.285832 | 0.142916 | − | 0.989735i | \(-0.454352\pi\) | ||||
0.142916 | + | 0.989735i | \(0.454352\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24899.0 | 1.79646 | 0.898231 | − | 0.439523i | \(-0.144853\pi\) | ||||
0.898231 | + | 0.439523i | \(0.144853\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2106.00 | 0.150381 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7638.00 | 0.542596 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1751.00 | −0.123120 | −0.0615601 | − | 0.998103i | \(-0.519608\pi\) | ||||
−0.0615601 | + | 0.998103i | \(0.519608\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20930.0 | 1.46419 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10887.0 | −0.753922 | −0.376961 | − | 0.926229i | \(-0.623031\pi\) | ||||
−0.376961 | + | 0.926229i | \(0.623031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14650.0 | 0.999303 | 0.499652 | − | 0.866226i | \(-0.333461\pi\) | ||||
0.499652 | + | 0.866226i | \(0.333461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4237.00 | −0.287572 | −0.143786 | − | 0.989609i | \(-0.545928\pi\) | ||||
−0.143786 | + | 0.989609i | \(0.545928\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11440.0 | 0.764968 | 0.382484 | − | 0.923962i | \(-0.375069\pi\) | ||||
0.382484 | + | 0.923962i | \(0.375069\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 624.000 | 0.0413164 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19370.0 | −1.27626 | −0.638130 | − | 0.769929i | \(-0.720292\pi\) | ||||
−0.638130 | + | 0.769929i | \(0.720292\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21346.0 | 1.39280 | 0.696400 | − | 0.717654i | \(-0.254784\pi\) | ||||
0.696400 | + | 0.717654i | \(0.254784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7436.00 | 0.482840 | 0.241420 | − | 0.970421i | \(-0.422387\pi\) | ||||
0.241420 | + | 0.970421i | \(0.422387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4794.00 | 0.308295 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13650.0 | −0.865280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22490.0 | 1.41888 | 0.709440 | − | 0.704766i | \(-0.248948\pi\) | ||||
0.709440 | + | 0.704766i | \(0.248948\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3684.00 | −0.229145 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16086.0 | 0.991199 | 0.495600 | − | 0.868551i | \(-0.334948\pi\) | ||||
0.495600 | + | 0.868551i | \(0.334948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2396.00 | −0.146950 | −0.0734751 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734751 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23244.0 | −1.41239 | −0.706195 | − | 0.708018i | \(-0.749590\pi\) | ||||
−0.706195 | + | 0.708018i | \(0.749590\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5928.00 | −0.358543 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13598.0 | −0.814902 | −0.407451 | − | 0.913227i | \(-0.633582\pi\) | ||||
−0.407451 | + | 0.913227i | \(0.633582\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9751.00 | −0.576396 | −0.288198 | − | 0.957571i | \(-0.593056\pi\) | ||||
−0.288198 | + | 0.957571i | \(0.593056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19104.0 | 1.12414 | 0.562072 | − | 0.827088i | \(-0.310004\pi\) | ||||
0.562072 | + | 0.827088i | \(0.310004\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −47328.0 | −2.74745 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3230.00 | 0.185831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25402.0 | 1.45494 | 0.727470 | − | 0.686139i | \(-0.240696\pi\) | ||||
0.727470 | + | 0.686139i | \(0.240696\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2224.00 | 0.126256 | 0.0631280 | − | 0.998005i | \(-0.479892\pi\) | ||||
0.0631280 | + | 0.998005i | \(0.479892\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5772.00 | −0.326228 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8281.00 | −0.463929 | −0.231965 | − | 0.972724i | \(-0.574515\pi\) | ||||
−0.231965 | + | 0.972724i | \(0.574515\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4824.00 | 0.266734 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 481.000 | 0.0264806 | 0.0132403 | − | 0.999912i | \(-0.495785\pi\) | ||||
0.0132403 | + | 0.999912i | \(0.495785\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8775.00 | −0.476868 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16788.0 | 0.904528 | 0.452264 | − | 0.891884i | \(-0.350617\pi\) | ||||
0.452264 | + | 0.891884i | \(0.350617\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16562.0 | 0.888546 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2916.00 | 0.155117 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23452.0 | −1.24225 | −0.621127 | − | 0.783710i | \(-0.713325\pi\) | ||||
−0.621127 | + | 0.783710i | \(0.713325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40020.0 | 2.10205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20886.0 | 1.08333 | 0.541666 | − | 0.840594i | \(-0.317794\pi\) | ||||
0.541666 | + | 0.840594i | \(0.317794\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7128.00 | 0.368184 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22576.0 | 1.15172 | 0.575858 | − | 0.817550i | \(-0.304668\pi\) | ||||
0.575858 | + | 0.817550i | \(0.304668\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27900.0 | 1.41165 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35308.0 | 1.77917 | 0.889584 | − | 0.456771i | \(-0.150994\pi\) | ||||
0.889584 | + | 0.456771i | \(0.150994\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14497.0 | 0.724564 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 188.000 | 0.00935818 | 0.00467909 | − | 0.999989i | \(-0.498511\pi\) | ||||
0.00467909 | + | 0.999989i | \(0.498511\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29870.0 | −1.47486 | −0.737432 | − | 0.675421i | \(-0.763962\pi\) | ||||
−0.737432 | + | 0.675421i | \(0.763962\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7950.00 | 0.387833 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22784.0 | 1.10706 | 0.553529 | − | 0.832830i | \(-0.313281\pi\) | ||||
0.553529 | + | 0.832830i | \(0.313281\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28496.0 | −1.36817 | −0.684085 | − | 0.729402i | \(-0.739798\pi\) | ||||
−0.684085 | + | 0.729402i | \(0.739798\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7397.00 | −0.352354 | −0.176177 | − | 0.984359i | \(-0.556373\pi\) | ||||
−0.176177 | + | 0.984359i | \(0.556373\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −756.000 | −0.0358703 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3744.00 | −0.176256 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8883.00 | −0.416553 | −0.208276 | − | 0.978070i | \(-0.566785\pi\) | ||||
−0.208276 | + | 0.978070i | \(0.566785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33960.0 | 1.58015 | 0.790075 | − | 0.613010i | \(-0.210041\pi\) | ||||
0.790075 | + | 0.613010i | \(0.210041\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10647.0 | 0.489690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 988.000 | 0.0452669 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32084.0 | −1.45320 | −0.726602 | − | 0.687059i | \(-0.758901\pi\) | ||||
−0.726602 | + | 0.687059i | \(0.758901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1098.00 | 0.0493557 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2040.00 | 0.0913525 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4766.00 | 0.211820 | 0.105910 | − | 0.994376i | \(-0.466224\pi\) | ||||
0.105910 | + | 0.994376i | \(0.466224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3900.00 | 0.172681 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18639.0 | −0.819123 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31278.0 | 1.35930 | 0.679651 | − | 0.733535i | \(-0.262131\pi\) | ||||
0.679651 | + | 0.733535i | \(0.262131\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29956.0 | −1.29704 | −0.648519 | − | 0.761199i | \(-0.724611\pi\) | ||||
−0.648519 | + | 0.761199i | \(0.724611\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33852.0 | −1.44961 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14642.0 | −0.622423 | −0.311212 | − | 0.950341i | \(-0.600735\pi\) | ||||
−0.311212 | + | 0.950341i | \(0.600735\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20844.0 | 0.882839 | 0.441419 | − | 0.897301i | \(-0.354475\pi\) | ||||
0.441419 | + | 0.897301i | \(0.354475\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23751.0 | −0.998674 | −0.499337 | − | 0.866408i | \(-0.666423\pi\) | ||||
−0.499337 | + | 0.866408i | \(0.666423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11380.0 | 0.476772 | 0.238386 | − | 0.971171i | \(-0.423382\pi\) | ||||
0.238386 | + | 0.971171i | \(0.423382\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23025.0 | −0.957706 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29744.0 | 1.22393 | 0.611965 | − | 0.790885i | \(-0.290379\pi\) | ||||
0.611965 | + | 0.790885i | \(0.290379\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49595.0 | 2.03350 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5820.00 | 0.236101 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31668.0 | 1.27563 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37726.0 | −1.51432 | −0.757159 | − | 0.653230i | \(-0.773413\pi\) | ||||
−0.757159 | + | 0.653230i | \(0.773413\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5429.00 | −0.216396 | −0.108198 | − | 0.994129i | \(-0.534508\pi\) | ||||
−0.108198 | + | 0.994129i | \(0.534508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32149.0 | 1.27696 | 0.638481 | − | 0.769638i | \(-0.279563\pi\) | ||||
0.638481 | + | 0.769638i | \(0.279563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29176.0 | 1.15083 | 0.575413 | − | 0.817863i | \(-0.304841\pi\) | ||||
0.575413 | + | 0.817863i | \(0.304841\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20026.0 | 0.781744 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9156.00 | 0.356187 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20068.0 | 0.772689 | 0.386344 | − | 0.922355i | \(-0.373738\pi\) | ||||
0.386344 | + | 0.922355i | \(0.373738\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36850.0 | 1.40920 | 0.704602 | − | 0.709603i | \(-0.251126\pi\) | ||||
0.704602 | + | 0.709603i | \(0.251126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30025.0 | 1.14431 | 0.572153 | − | 0.820147i | \(-0.306108\pi\) | ||||
0.572153 | + | 0.820147i | \(0.306108\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −156.000 | −0.00590526 | −0.00295263 | − | 0.999996i | \(-0.500940\pi\) | ||||
−0.00295263 | + | 0.999996i | \(0.500940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5412.00 | 0.204176 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4732.00 | −0.177324 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −62560.0 | −2.32090 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30150.0 | 1.11481 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −356.000 | −0.0130328 | −0.00651642 | − | 0.999979i | \(-0.502074\pi\) | ||||
−0.00651642 | + | 0.999979i | \(0.502074\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8748.00 | −0.318149 | −0.159075 | − | 0.987267i | \(-0.550851\pi\) | ||||
−0.159075 | + | 0.987267i | \(0.550851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6669.00 | −0.241743 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12408.0 | 0.446836 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36974.0 | 1.32716 | 0.663580 | − | 0.748105i | \(-0.269036\pi\) | ||||
0.663580 | + | 0.748105i | \(0.269036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 624.000 | 0.0222527 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44382.0 | −1.56741 | −0.783706 | − | 0.621132i | \(-0.786673\pi\) | ||||
−0.783706 | + | 0.621132i | \(0.786673\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27937.0 | 0.983457 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2445.00 | −0.0852451 | −0.0426226 | − | 0.999091i | \(-0.513571\pi\) | ||||
−0.0426226 | + | 0.999091i | \(0.513571\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7076.00 | 0.245134 | 0.122567 | − | 0.992460i | \(-0.460887\pi\) | ||||
0.122567 | + | 0.992460i | \(0.460887\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20358.0 | 0.703020 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1560.00 | −0.0535303 | −0.0267651 | − | 0.999642i | \(-0.508521\pi\) | ||||
−0.0267651 | + | 0.999642i | \(0.508521\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11772.0 | −0.402672 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35087.0 | 1.19263 | 0.596317 | − | 0.802749i | \(-0.296630\pi\) | ||||
0.596317 | + | 0.802749i | \(0.296630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8034.00 | −0.270523 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23109.0 | 0.775704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9360.00 | −0.311269 | −0.155635 | − | 0.987815i | \(-0.549742\pi\) | ||||
−0.155635 | + | 0.987815i | \(0.549742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22269.0 | −0.735990 | −0.367995 | − | 0.929828i | \(-0.619956\pi\) | ||||
−0.367995 | + | 0.929828i | \(0.619956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17634.0 | 0.581007 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37249.0 | −1.21976 | −0.609878 | − | 0.792496i | \(-0.708781\pi\) | ||||
−0.609878 | + | 0.792496i | \(0.708781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15181.0 | −0.495594 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17602.0 | 0.571126 | 0.285563 | − | 0.958360i | \(-0.407819\pi\) | ||||
0.285563 | + | 0.958360i | \(0.407819\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −64728.0 | −2.08112 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26402.0 | −0.846304 | −0.423152 | − | 0.906059i | \(-0.639076\pi\) | ||||
−0.423152 | + | 0.906059i | \(0.639076\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16836.0 | 0.534806 | 0.267403 | − | 0.963585i | \(-0.413835\pi\) | ||||
0.267403 | + | 0.963585i | \(0.413835\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1800.4.a.l.1.1 | 1 | ||
3.2 | odd | 2 | 200.4.a.f.1.1 | yes | 1 | ||
5.2 | odd | 4 | 1800.4.f.p.649.1 | 2 | |||
5.3 | odd | 4 | 1800.4.f.p.649.2 | 2 | |||
5.4 | even | 2 | 1800.4.a.w.1.1 | 1 | |||
12.11 | even | 2 | 400.4.a.j.1.1 | 1 | |||
15.2 | even | 4 | 200.4.c.g.49.1 | 2 | |||
15.8 | even | 4 | 200.4.c.g.49.2 | 2 | |||
15.14 | odd | 2 | 200.4.a.e.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 1600.4.a.w.1.1 | 1 | |||
24.11 | even | 2 | 1600.4.a.be.1.1 | 1 | |||
60.23 | odd | 4 | 400.4.c.m.49.1 | 2 | |||
60.47 | odd | 4 | 400.4.c.m.49.2 | 2 | |||
60.59 | even | 2 | 400.4.a.k.1.1 | 1 | |||
120.29 | odd | 2 | 1600.4.a.bf.1.1 | 1 | |||
120.59 | even | 2 | 1600.4.a.v.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.4.a.e.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
200.4.a.f.1.1 | yes | 1 | 3.2 | odd | 2 | ||
200.4.c.g.49.1 | 2 | 15.2 | even | 4 | |||
200.4.c.g.49.2 | 2 | 15.8 | even | 4 | |||
400.4.a.j.1.1 | 1 | 12.11 | even | 2 | |||
400.4.a.k.1.1 | 1 | 60.59 | even | 2 | |||
400.4.c.m.49.1 | 2 | 60.23 | odd | 4 | |||
400.4.c.m.49.2 | 2 | 60.47 | odd | 4 | |||
1600.4.a.v.1.1 | 1 | 120.59 | even | 2 | |||
1600.4.a.w.1.1 | 1 | 24.5 | odd | 2 | |||
1600.4.a.be.1.1 | 1 | 24.11 | even | 2 | |||
1600.4.a.bf.1.1 | 1 | 120.29 | odd | 2 | |||
1800.4.a.l.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1800.4.a.w.1.1 | 1 | 5.4 | even | 2 | |||
1800.4.f.p.649.1 | 2 | 5.2 | odd | 4 | |||
1800.4.f.p.649.2 | 2 | 5.3 | odd | 4 |