Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,4,Mod(1,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.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: | \(11.8003820011\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 200.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.192450 | −0.0962250 | − | 0.995360i | \(-0.530677\pi\) | ||||
−0.0962250 | + | 0.995360i | \(0.530677\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000 | 0.323970 | 0.161985 | − | 0.986793i | \(-0.448210\pi\) | ||||
0.161985 | + | 0.986793i | \(0.448210\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.0000 | −0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.0000 | −0.520792 | −0.260396 | − | 0.965502i | \(-0.583853\pi\) | ||||
−0.260396 | + | 0.965502i | \(0.583853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.0000 | −0.256015 | −0.128008 | − | 0.991773i | \(-0.540858\pi\) | ||||
−0.128008 | + | 0.991773i | \(0.540858\pi\) | |||||||
\(14\) | 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 | ||||||||
\(21\) | −6.00000 | −0.0623480 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 53.0000 | 0.377772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −272.000 | −1.74169 | −0.870847 | − | 0.491554i | \(-0.836429\pi\) | ||||
−0.870847 | + | 0.491554i | \(0.836429\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −230.000 | −1.33256 | −0.666278 | − | 0.745704i | \(-0.732113\pi\) | ||||
−0.666278 | + | 0.745704i | \(0.732113\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 19.0000 | 0.100227 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 182.000 | 0.808665 | 0.404333 | − | 0.914612i | \(-0.367504\pi\) | ||||
0.404333 | + | 0.914612i | \(0.367504\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.0000 | 0.0492702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 117.000 | 0.445667 | 0.222833 | − | 0.974857i | \(-0.428469\pi\) | ||||
0.222833 | + | 0.974857i | \(0.428469\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −372.000 | −1.31929 | −0.659645 | − | 0.751577i | \(-0.729293\pi\) | ||||
−0.659645 | + | 0.751577i | \(0.729293\pi\) | |||||||
\(44\) | 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 | ||||||||
\(51\) | −75.0000 | −0.205924 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 91.0000 | 0.211460 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 312.000 | 0.688457 | 0.344228 | − | 0.938886i | \(-0.388141\pi\) | ||||
0.344228 | + | 0.938886i | \(0.388141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 170.000 | 0.356824 | 0.178412 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178412 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −156.000 | −0.311971 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −763.000 | −1.39127 | −0.695636 | − | 0.718394i | \(-0.744878\pi\) | ||||
−0.695636 | + | 0.718394i | \(0.744878\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 174.000 | 0.303582 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −52.0000 | −0.0869192 | −0.0434596 | − | 0.999055i | \(-0.513838\pi\) | ||||
−0.0434596 | + | 0.999055i | \(0.513838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 981.000 | 1.57284 | 0.786420 | − | 0.617692i | \(-0.211932\pi\) | ||||
0.786420 | + | 0.617692i | \(0.211932\pi\) | |||||||
\(74\) | 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 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 272.000 | 0.335189 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 799.000 | 0.951616 | 0.475808 | − | 0.879549i | \(-0.342156\pi\) | ||||
0.475808 | + | 0.879549i | \(0.342156\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −72.0000 | −0.0829412 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 230.000 | 0.256450 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −962.000 | −1.00697 | −0.503486 | − | 0.864003i | \(-0.667949\pi\) | ||||
−0.503486 | + | 0.864003i | \(0.667949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 494.000 | 0.501504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 486.000 | 0.478800 | 0.239400 | − | 0.970921i | \(-0.423049\pi\) | ||||
0.239400 | + | 0.970921i | \(0.423049\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1188.00 | 1.13648 | 0.568238 | − | 0.822864i | \(-0.307625\pi\) | ||||
0.568238 | + | 0.822864i | \(0.307625\pi\) | |||||||
\(104\) | 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 | ||||||||
\(111\) | −182.000 | −0.155628 | ||||||||
\(112\) | 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 | ||||||||
\(117\) | 312.000 | 0.246533 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 450.000 | 0.346651 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −970.000 | −0.728775 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −117.000 | −0.0857686 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 902.000 | 0.630233 | 0.315116 | − | 0.949053i | \(-0.397956\pi\) | ||||
0.315116 | + | 0.949053i | \(0.397956\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 372.000 | 0.253897 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2068.00 | 1.37925 | 0.689626 | − | 0.724166i | \(-0.257775\pi\) | ||||
0.689626 | + | 0.724166i | \(0.257775\pi\) | |||||||
\(132\) | 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 | ||||||||
\(141\) | −52.0000 | −0.0310581 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 228.000 | 0.133331 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 307.000 | 0.172251 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −208.000 | −0.114363 | −0.0571813 | − | 0.998364i | \(-0.518211\pi\) | ||||
−0.0571813 | + | 0.998364i | \(0.518211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2678.00 | −1.44326 | −0.721631 | − | 0.692278i | \(-0.756607\pi\) | ||||
−0.721631 | + | 0.692278i | \(0.756607\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1950.00 | −1.03038 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1482.00 | −0.753353 | −0.376677 | − | 0.926345i | \(-0.622933\pi\) | ||||
−0.376677 | + | 0.926345i | \(0.622933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −402.000 | −0.200507 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1044.00 | −0.511048 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1469.00 | 0.705895 | 0.352948 | − | 0.935643i | \(-0.385179\pi\) | ||||
0.352948 | + | 0.935643i | \(0.385179\pi\) | |||||||
\(164\) | 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 | ||||||||
\(171\) | 2366.00 | 1.05809 | ||||||||
\(172\) | 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 | ||||||||
\(177\) | −312.000 | −0.132494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4191.00 | −1.75000 | −0.875000 | − | 0.484123i | \(-0.839139\pi\) | ||||
−0.875000 | + | 0.484123i | \(0.839139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3718.00 | −1.52683 | −0.763416 | − | 0.645907i | \(-0.776480\pi\) | ||||
−0.763416 | + | 0.645907i | \(0.776480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −170.000 | −0.0686708 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1425.00 | −0.557253 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 318.000 | 0.122387 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 870.000 | 0.329586 | 0.164793 | − | 0.986328i | \(-0.447304\pi\) | ||||
0.164793 | + | 0.986328i | \(0.447304\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2197.00 | −0.819396 | −0.409698 | − | 0.912221i | \(-0.634366\pi\) | ||||
−0.409698 | + | 0.912221i | \(0.634366\pi\) | |||||||
\(194\) | 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 | ||||||||
\(201\) | 763.000 | 0.267751 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1632.00 | −0.564256 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4524.00 | 1.51903 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 52.0000 | 0.0167276 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1380.00 | −0.431707 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −981.000 | −0.302693 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −900.000 | −0.273939 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5092.00 | 1.52908 | 0.764542 | − | 0.644574i | \(-0.222965\pi\) | ||||
0.764542 | + | 0.644574i | \(0.222965\pi\) | |||||||
\(224\) | 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 | ||||||||
\(231\) | 114.000 | 0.0324703 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | −1054.00 | −0.288880 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2496.00 | 0.675535 | 0.337767 | − | 0.941230i | \(-0.390328\pi\) | ||||
0.337767 | + | 0.941230i | \(0.390328\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2567.00 | −0.686120 | −0.343060 | − | 0.939313i | \(-0.611463\pi\) | ||||
−0.343060 | + | 0.939313i | \(0.611463\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2080.00 | −0.549103 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1092.00 | 0.281305 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 351.000 | 0.0893322 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5395.00 | 1.35669 | 0.678345 | − | 0.734743i | \(-0.262697\pi\) | ||||
0.678345 | + | 0.734743i | \(0.262697\pi\) | |||||||
\(252\) | 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 | ||||||||
\(261\) | 7072.00 | 1.67719 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | −799.000 | −0.183139 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6096.00 | 1.38171 | 0.690854 | − | 0.722994i | \(-0.257235\pi\) | ||||
0.690854 | + | 0.722994i | \(0.257235\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6006.00 | −1.34627 | −0.673134 | − | 0.739521i | \(-0.735052\pi\) | ||||
−0.673134 | + | 0.739521i | \(0.735052\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 72.0000 | 0.0159620 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6976.00 | −1.51317 | −0.756583 | − | 0.653897i | \(-0.773133\pi\) | ||||
−0.756583 | + | 0.653897i | \(0.773133\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5980.00 | 1.28320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3998.00 | 0.848757 | 0.424378 | − | 0.905485i | \(-0.360493\pi\) | ||||
0.424378 | + | 0.905485i | \(0.360493\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0000 | 0.00273064 | 0.00136532 | − | 0.999999i | \(-0.499565\pi\) | ||||
0.00136532 | + | 0.999999i | \(0.499565\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 702.000 | 0.144382 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 712.000 | 0.144922 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 962.000 | 0.193792 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | −1007.00 | −0.196741 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2088.00 | 0.403853 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2232.00 | −0.427410 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −486.000 | −0.0921451 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9041.00 | −1.68077 | −0.840386 | − | 0.541988i | \(-0.817672\pi\) | ||||
−0.840386 | + | 0.541988i | \(0.817672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1188.00 | −0.218715 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −346.000 | −0.0630864 | −0.0315432 | − | 0.999502i | \(-0.510042\pi\) | ||||
−0.0315432 | + | 0.999502i | \(0.510042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10646.0 | 1.92252 | 0.961258 | − | 0.275650i | \(-0.0888932\pi\) | ||||
0.961258 | + | 0.275650i | \(0.0888932\pi\) | |||||||
\(314\) | 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 | ||||||||
\(321\) | 1325.00 | 0.230387 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6825.00 | −1.17571 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −126.000 | −0.0213083 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | −4732.00 | −0.778715 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −83.0000 | −0.0134163 | −0.00670816 | − | 0.999978i | \(-0.502135\pi\) | ||||
−0.00670816 | + | 0.999978i | \(0.502135\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 183.000 | 0.0293192 | ||||||||
\(340\) | 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 | ||||||||
\(351\) | −636.000 | −0.0967156 | ||||||||
\(352\) | 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 | ||||||||
\(357\) | −450.000 | −0.0667130 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1638.00 | 0.240809 | 0.120404 | − | 0.992725i | \(-0.461581\pi\) | ||||
0.120404 | + | 0.992725i | \(0.461581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1422.00 | 0.207319 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 970.000 | 0.140253 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7580.00 | 1.07813 | 0.539064 | − | 0.842265i | \(-0.318778\pi\) | ||||
0.539064 | + | 0.842265i | \(0.318778\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3042.00 | −0.429160 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2412.00 | 0.337533 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5630.00 | 0.781529 | 0.390765 | − | 0.920491i | \(-0.372211\pi\) | ||||
0.390765 | + | 0.920491i | \(0.372211\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | −902.000 | −0.121288 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 9672.00 | 1.27043 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6570.00 | −0.856330 | −0.428165 | − | 0.903701i | \(-0.640840\pi\) | ||||
−0.428165 | + | 0.903701i | \(0.640840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13050.0 | −1.68789 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2068.00 | −0.265437 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1268.00 | −0.160300 | −0.0801500 | − | 0.996783i | \(-0.525540\pi\) | ||||
−0.0801500 | + | 0.996783i | \(0.525540\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 546.000 | 0.0685067 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6299.00 | −0.784432 | −0.392216 | − | 0.919873i | \(-0.628291\pi\) | ||||
−0.392216 | + | 0.919873i | \(0.628291\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | −1339.00 | −0.160701 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1872.00 | 0.223039 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2939.00 | 0.345140 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9567.00 | −1.11546 | −0.557731 | − | 0.830022i | \(-0.688328\pi\) | ||||
−0.557731 | + | 0.830022i | \(0.688328\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2708.00 | 0.313491 | 0.156746 | − | 0.987639i | \(-0.449900\pi\) | ||||
0.156746 | + | 0.987639i | \(0.449900\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1352.00 | −0.155405 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1020.00 | 0.115600 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −228.000 | −0.0256595 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5126.00 | 0.572879 | 0.286439 | − | 0.958098i | \(-0.407528\pi\) | ||||
0.286439 | + | 0.958098i | \(0.407528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11445.0 | −1.27023 | −0.635117 | − | 0.772416i | \(-0.719048\pi\) | ||||
−0.635117 | + | 0.772416i | \(0.719048\pi\) | |||||||
\(434\) | 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 | ||||||||
\(441\) | 7982.00 | 0.861894 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 208.000 | 0.0220091 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7449.00 | 0.782940 | 0.391470 | − | 0.920191i | \(-0.371967\pi\) | ||||
0.391470 | + | 0.920191i | \(0.371967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2223.00 | −0.232100 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2678.00 | 0.277756 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3497.00 | −0.357949 | −0.178975 | − | 0.983854i | \(-0.557278\pi\) | ||||
−0.178975 | + | 0.983854i | \(0.557278\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3975.00 | 0.404220 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13108.0 | −1.32430 | −0.662148 | − | 0.749373i | \(-0.730355\pi\) | ||||
−0.662148 | + | 0.749373i | \(0.730355\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5428.00 | 0.544839 | 0.272420 | − | 0.962179i | \(-0.412176\pi\) | ||||
0.272420 | + | 0.962179i | \(0.412176\pi\) | |||||||
\(464\) | 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 | ||||||||
\(471\) | 1482.00 | 0.144983 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7068.00 | 0.687076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10452.0 | −1.00328 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14762.0 | −1.40813 | −0.704064 | − | 0.710137i | \(-0.748633\pi\) | ||||
−0.704064 | + | 0.710137i | \(0.748633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2184.00 | −0.207031 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1044.00 | 0.0983512 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3926.00 | 0.365306 | 0.182653 | − | 0.983177i | \(-0.441532\pi\) | ||||
0.182653 | + | 0.983177i | \(0.441532\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1469.00 | −0.135850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 996.000 | 0.0915455 | 0.0457728 | − | 0.998952i | \(-0.485425\pi\) | ||||
0.0457728 | + | 0.998952i | \(0.485425\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | −4004.00 | −0.357057 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 2053.00 | 0.179836 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10426.0 | 0.907906 | 0.453953 | − | 0.891026i | \(-0.350013\pi\) | ||||
0.453953 | + | 0.891026i | \(0.350013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5886.00 | 0.509552 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4823.00 | −0.415089 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −988.000 | −0.0840468 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3224.00 | 0.272674 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2235.00 | −0.187941 | −0.0939704 | − | 0.995575i | \(-0.529956\pi\) | ||||
−0.0939704 | + | 0.995575i | \(0.529956\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10855.0 | 0.907564 | 0.453782 | − | 0.891113i | \(-0.350074\pi\) | ||||
0.453782 | + | 0.891113i | \(0.350074\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17250.0 | −1.42585 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18109.0 | 1.48837 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8112.00 | −0.662958 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1404.00 | −0.114098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4191.00 | 0.336788 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 3718.00 | 0.293839 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11583.0 | 0.905399 | 0.452700 | − | 0.891663i | \(-0.350461\pi\) | ||||
0.452700 | + | 0.891663i | \(0.350461\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4420.00 | −0.343608 | ||||||||
\(550\) | 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 | ||||||||
\(561\) | 1425.00 | 0.107243 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 3894.00 | 0.288417 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11913.0 | 0.877713 | 0.438857 | − | 0.898557i | \(-0.355384\pi\) | ||||
0.438857 | + | 0.898557i | \(0.355384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3900.00 | 0.285832 | 0.142916 | − | 0.989735i | \(-0.454352\pi\) | ||||
0.142916 | + | 0.989735i | \(0.454352\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −870.000 | −0.0634289 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24899.0 | −1.79646 | −0.898231 | − | 0.439523i | \(-0.855147\pi\) | ||||
−0.898231 | + | 0.439523i | \(0.855147\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2197.00 | 0.157693 | ||||||||
\(580\) | 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 | ||||||||
\(591\) | −2314.00 | −0.161058 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 252.000 | 0.0172758 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14650.0 | −0.999303 | −0.499652 | − | 0.866226i | \(-0.666539\pi\) | ||||
−0.499652 | + | 0.866226i | \(0.666539\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4237.00 | −0.287572 | −0.143786 | − | 0.989609i | \(-0.545928\pi\) | ||||
−0.143786 | + | 0.989609i | \(0.545928\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19838.0 | 1.33974 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11440.0 | −0.764968 | −0.382484 | − | 0.923962i | \(-0.624931\pi\) | ||||
−0.382484 | + | 0.923962i | \(0.624931\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1632.00 | 0.108591 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −624.000 | −0.0413164 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19370.0 | 1.27626 | 0.638130 | − | 0.769929i | \(-0.279708\pi\) | ||||
0.638130 | + | 0.769929i | \(0.279708\pi\) | |||||||
\(614\) | 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 | ||||||||
\(621\) | −9222.00 | −0.595920 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4794.00 | 0.308295 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1729.00 | −0.110127 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 741.000 | 0.0465278 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3684.00 | 0.229145 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1352.00 | 0.0837000 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16086.0 | −0.991199 | −0.495600 | − | 0.868551i | \(-0.665052\pi\) | ||||
−0.495600 | + | 0.868551i | \(0.665052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2396.00 | 0.146950 | 0.0734751 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734751 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | 1380.00 | 0.0830821 | ||||||||
\(652\) | 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 | ||||||||
\(657\) | −25506.0 | −1.51459 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9751.00 | 0.576396 | 0.288198 | − | 0.957571i | \(-0.406944\pi\) | ||||
0.288198 | + | 0.957571i | \(0.406944\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19104.0 | 1.12414 | 0.562072 | − | 0.827088i | \(-0.310004\pi\) | ||||
0.562072 | + | 0.827088i | \(0.310004\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 900.000 | 0.0527196 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 47328.0 | 2.74745 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5092.00 | −0.294272 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3230.00 | −0.185831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25402.0 | −1.45494 | −0.727470 | − | 0.686139i | \(-0.759304\pi\) | ||||
−0.727470 | + | 0.686139i | \(0.759304\pi\) | |||||||
\(674\) | 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 | ||||||||
\(681\) | 5876.00 | 0.330644 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 604.000 | 0.0335430 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 2964.00 | 0.162472 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8775.00 | 0.476868 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 278.000 | 0.0150428 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16788.0 | −0.904528 | −0.452264 | − | 0.891884i | \(-0.649383\pi\) | ||||
−0.452264 | + | 0.891884i | \(0.649383\pi\) | |||||||
\(702\) | 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 | ||||||||
\(711\) | −27404.0 | −1.44547 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40020.0 | 2.10205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2496.00 | −0.130007 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20886.0 | −1.08333 | −0.541666 | − | 0.840594i | \(-0.682206\pi\) | ||||
−0.541666 | + | 0.840594i | \(0.682206\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7128.00 | 0.368184 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2567.00 | 0.132044 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22576.0 | −1.15172 | −0.575858 | − | 0.817550i | \(-0.695332\pi\) | ||||
−0.575858 | + | 0.817550i | \(0.695332\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27900.0 | −1.41165 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35308.0 | −1.77917 | −0.889584 | − | 0.456771i | \(-0.849006\pi\) | ||||
−0.889584 | + | 0.456771i | \(0.849006\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | −1092.00 | −0.0541371 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 9126.00 | 0.446992 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | −5395.00 | −0.261095 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28496.0 | 1.36817 | 0.684085 | − | 0.729402i | \(-0.260202\pi\) | ||||
0.684085 | + | 0.729402i | \(0.260202\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3306.00 | −0.158103 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7397.00 | 0.352354 | 0.176177 | − | 0.984359i | \(-0.443627\pi\) | ||||
0.176177 | + | 0.984359i | \(0.443627\pi\) | |||||||
\(762\) | 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 | ||||||||
\(771\) | −1490.00 | −0.0695993 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | −1092.00 | −0.0504186 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10647.0 | −0.489690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 988.000 | 0.0452669 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14416.0 | −0.657964 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32084.0 | 1.45320 | 0.726602 | − | 0.687059i | \(-0.241099\pi\) | ||||
0.726602 | + | 0.687059i | \(0.241099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3330.00 | −0.150255 | ||||||||
\(790\) | 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 | ||||||||
\(801\) | −20774.0 | −0.916371 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18639.0 | −0.819123 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6096.00 | −0.265910 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31278.0 | −1.35930 | −0.679651 | − | 0.733535i | \(-0.737869\pi\) | ||||
−0.679651 | + | 0.733535i | \(0.737869\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29956.0 | −1.29704 | −0.648519 | − | 0.761199i | \(-0.724611\pi\) | ||||
−0.648519 | + | 0.761199i | \(0.724611\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6006.00 | 0.259089 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33852.0 | 1.44961 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1872.00 | 0.0798693 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14642.0 | 0.622423 | 0.311212 | − | 0.950341i | \(-0.399265\pi\) | ||||
0.311212 | + | 0.950341i | \(0.399265\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20844.0 | −0.882839 | −0.441419 | − | 0.897301i | \(-0.645525\pi\) | ||||
−0.441419 | + | 0.897301i | \(0.645525\pi\) | |||||||
\(824\) | 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 | ||||||||
\(831\) | 6976.00 | 0.291209 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23025.0 | −0.957706 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12190.0 | −0.503403 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29744.0 | −1.22393 | −0.611965 | − | 0.790885i | \(-0.709621\pi\) | ||||
−0.611965 | + | 0.790885i | \(0.709621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49595.0 | 2.03350 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3998.00 | −0.163343 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5820.00 | −0.236101 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0000 | −0.000525511 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31668.0 | −1.27563 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37726.0 | 1.51432 | 0.757159 | − | 0.653230i | \(-0.226587\pi\) | ||||
0.757159 | + | 0.653230i | \(0.226587\pi\) | |||||||
\(854\) | 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 | ||||||||
\(861\) | −702.000 | −0.0277864 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | −712.000 | −0.0278902 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20026.0 | −0.781744 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9156.00 | 0.356187 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25012.0 | 0.969677 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20068.0 | −0.772689 | −0.386344 | − | 0.922355i | \(-0.626262\pi\) | ||||
−0.386344 | + | 0.922355i | \(0.626262\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4466.00 | −0.171370 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36850.0 | −1.40920 | −0.704602 | − | 0.709603i | \(-0.748874\pi\) | ||||
−0.704602 | + | 0.709603i | \(0.748874\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30025.0 | −1.14431 | −0.572153 | − | 0.820147i | \(-0.693892\pi\) | ||||
−0.572153 | + | 0.820147i | \(0.693892\pi\) | |||||||
\(884\) | 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 | ||||||||
\(891\) | −12331.0 | −0.463641 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4732.00 | −0.177324 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2088.00 | −0.0777216 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 62560.0 | 2.32090 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30150.0 | 1.11481 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2232.00 | 0.0822550 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 356.000 | 0.0130328 | 0.00651642 | − | 0.999979i | \(-0.497926\pi\) | ||||
0.00651642 | + | 0.999979i | \(0.497926\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12636.0 | −0.461067 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8748.00 | 0.318149 | 0.159075 | − | 0.987267i | \(-0.449149\pi\) | ||||
0.159075 | + | 0.987267i | \(0.449149\pi\) | |||||||
\(912\) | 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 | ||||||||
\(921\) | 9041.00 | 0.323465 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 624.000 | 0.0222527 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30888.0 | −1.09439 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44382.0 | 1.56741 | 0.783706 | − | 0.621132i | \(-0.213327\pi\) | ||||
0.783706 | + | 0.621132i | \(0.213327\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27937.0 | 0.983457 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 346.000 | 0.0121410 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2445.00 | 0.0852451 | 0.0426226 | − | 0.999091i | \(-0.486429\pi\) | ||||
0.0426226 | + | 0.999091i | \(0.486429\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10646.0 | −0.369988 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7076.00 | −0.245134 | −0.122567 | − | 0.992460i | \(-0.539113\pi\) | ||||
−0.122567 | + | 0.992460i | \(0.539113\pi\) | |||||||
\(942\) | 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 | ||||||||
\(951\) | −8116.00 | −0.276740 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | −5168.00 | −0.174564 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8034.00 | 0.270523 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23109.0 | 0.775704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34450.0 | 1.15279 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9360.00 | 0.311269 | 0.155635 | − | 0.987815i | \(-0.450258\pi\) | ||||
0.155635 | + | 0.987815i | \(0.450258\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6825.00 | 0.226265 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22269.0 | 0.735990 | 0.367995 | − | 0.929828i | \(-0.380044\pi\) | ||||
0.367995 | + | 0.929828i | \(0.380044\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | −3276.00 | −0.106620 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | −312.000 | −0.0100619 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 3007.00 | 0.0960969 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16836.0 | −0.534806 | −0.267403 | − | 0.963585i | \(-0.586165\pi\) | ||||
−0.267403 | + | 0.963585i | \(0.586165\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9646.00 | 0.305491 |
(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 | 200.4.a.e.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 1800.4.a.w.1.1 | 1 | |||
4.3 | odd | 2 | 400.4.a.k.1.1 | 1 | |||
5.2 | odd | 4 | 200.4.c.g.49.2 | 2 | |||
5.3 | odd | 4 | 200.4.c.g.49.1 | 2 | |||
5.4 | even | 2 | 200.4.a.f.1.1 | yes | 1 | ||
8.3 | odd | 2 | 1600.4.a.v.1.1 | 1 | |||
8.5 | even | 2 | 1600.4.a.bf.1.1 | 1 | |||
15.2 | even | 4 | 1800.4.f.p.649.2 | 2 | |||
15.8 | even | 4 | 1800.4.f.p.649.1 | 2 | |||
15.14 | odd | 2 | 1800.4.a.l.1.1 | 1 | |||
20.3 | even | 4 | 400.4.c.m.49.2 | 2 | |||
20.7 | even | 4 | 400.4.c.m.49.1 | 2 | |||
20.19 | odd | 2 | 400.4.a.j.1.1 | 1 | |||
40.19 | odd | 2 | 1600.4.a.be.1.1 | 1 | |||
40.29 | even | 2 | 1600.4.a.w.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.4.a.e.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
200.4.a.f.1.1 | yes | 1 | 5.4 | even | 2 | ||
200.4.c.g.49.1 | 2 | 5.3 | odd | 4 | |||
200.4.c.g.49.2 | 2 | 5.2 | odd | 4 | |||
400.4.a.j.1.1 | 1 | 20.19 | odd | 2 | |||
400.4.a.k.1.1 | 1 | 4.3 | odd | 2 | |||
400.4.c.m.49.1 | 2 | 20.7 | even | 4 | |||
400.4.c.m.49.2 | 2 | 20.3 | even | 4 | |||
1600.4.a.v.1.1 | 1 | 8.3 | odd | 2 | |||
1600.4.a.w.1.1 | 1 | 40.29 | even | 2 | |||
1600.4.a.be.1.1 | 1 | 40.19 | odd | 2 | |||
1600.4.a.bf.1.1 | 1 | 8.5 | even | 2 | |||
1800.4.a.l.1.1 | 1 | 15.14 | odd | 2 | |||
1800.4.a.w.1.1 | 1 | 3.2 | odd | 2 | |||
1800.4.f.p.649.1 | 2 | 15.8 | even | 4 | |||
1800.4.f.p.649.2 | 2 | 15.2 | even | 4 |