Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 19x^{5} + 19x^{4} - 35x^{3} - 10x^{2} + 18x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.411238\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.71910 | 0.768807 | 0.384403 | − | 0.923165i | \(-0.374407\pi\) | ||||
0.384403 | + | 0.923165i | \(0.374407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.210007 | 0.0793752 | 0.0396876 | − | 0.999212i | \(-0.487364\pi\) | ||||
0.0396876 | + | 0.999212i | \(0.487364\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.37289 | −0.715453 | −0.357726 | − | 0.933826i | \(-0.616448\pi\) | ||||
−0.357726 | + | 0.933826i | \(0.616448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.22411 | −0.894207 | −0.447104 | − | 0.894482i | \(-0.647545\pi\) | ||||
−0.447104 | + | 0.894482i | \(0.647545\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.71910 | 0.443871 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.22874 | −0.298013 | −0.149007 | − | 0.988836i | \(-0.547608\pi\) | ||||
−0.149007 | + | 0.988836i | \(0.547608\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.29204 | −1.67291 | −0.836454 | − | 0.548037i | \(-0.815375\pi\) | ||||
−0.836454 | + | 0.548037i | \(0.815375\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.210007 | 0.0458273 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.04468 | −0.408937 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.68744 | 0.662283 | 0.331142 | − | 0.943581i | \(-0.392566\pi\) | ||||
0.331142 | + | 0.943581i | \(0.392566\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.37289 | −0.413067 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.361024 | 0.0610241 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.65306 | 1.25816 | 0.629078 | − | 0.777342i | \(-0.283433\pi\) | ||||
0.629078 | + | 0.777342i | \(0.283433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.22411 | −0.516271 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82840 | 0.441722 | 0.220861 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220861 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.02791 | 1.37674 | 0.688372 | − | 0.725358i | \(-0.258326\pi\) | ||||
0.688372 | + | 0.725358i | \(0.258326\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.71910 | 0.256269 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.43500 | −0.792776 | −0.396388 | − | 0.918083i | \(-0.629736\pi\) | ||||
−0.396388 | + | 0.918083i | \(0.629736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95590 | −0.993700 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.22874 | −0.172058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.49073 | −0.342128 | −0.171064 | − | 0.985260i | \(-0.554720\pi\) | ||||
−0.171064 | + | 0.985260i | \(0.554720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.07924 | −0.550045 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.29204 | −0.965854 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.55638 | −0.463002 | −0.231501 | − | 0.972835i | \(-0.574364\pi\) | ||||
−0.231501 | + | 0.972835i | \(0.574364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.27294 | −0.931205 | −0.465602 | − | 0.884994i | \(-0.654162\pi\) | ||||
−0.465602 | + | 0.884994i | \(0.654162\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.210007 | 0.0264584 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.54258 | −0.687472 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.41000 | 1.14961 | 0.574807 | − | 0.818289i | \(-0.305077\pi\) | ||||
0.574807 | + | 0.818289i | \(0.305077\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.53494 | −0.894233 | −0.447117 | − | 0.894476i | \(-0.647549\pi\) | ||||
−0.447117 | + | 0.894476i | \(0.647549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.75783 | 0.439820 | 0.219910 | − | 0.975520i | \(-0.429424\pi\) | ||||
0.219910 | + | 0.975520i | \(0.429424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.04468 | −0.236100 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.498323 | −0.0567892 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.807221 | 0.0908194 | 0.0454097 | − | 0.998968i | \(-0.485541\pi\) | ||||
0.0454097 | + | 0.998968i | \(0.485541\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.58455 | 0.612984 | 0.306492 | − | 0.951873i | \(-0.400845\pi\) | ||||
0.306492 | + | 0.951873i | \(0.400845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.11233 | −0.229114 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.2438 | −1.19184 | −0.595919 | − | 0.803044i | \(-0.703212\pi\) | ||||
−0.595919 | + | 0.803044i | \(0.703212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.677086 | −0.0709779 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.68744 | 0.382370 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.5358 | −1.28614 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.5915 | −1.17694 | −0.588471 | − | 0.808519i | \(-0.700270\pi\) | ||||
−0.588471 | + | 0.808519i | \(0.700270\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.37289 | −0.238484 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.54449 | −0.153683 | −0.0768413 | − | 0.997043i | \(-0.524483\pi\) | ||||
−0.0768413 | + | 0.997043i | \(0.524483\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.7680 | −1.45513 | −0.727567 | − | 0.686037i | \(-0.759349\pi\) | ||||
−0.727567 | + | 0.686037i | \(0.759349\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.361024 | 0.0352323 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0255 | −1.16255 | −0.581273 | − | 0.813708i | \(-0.697445\pi\) | ||||
−0.581273 | + | 0.813708i | \(0.697445\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.79224 | −0.363230 | −0.181615 | − | 0.983370i | \(-0.558133\pi\) | ||||
−0.181615 | + | 0.983370i | \(0.558133\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.65306 | 0.726396 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.1915 | −1.42909 | −0.714546 | − | 0.699588i | \(-0.753367\pi\) | ||||
−0.714546 | + | 0.699588i | \(0.753367\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.71910 | 0.160307 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.22411 | −0.298069 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.258044 | −0.0236548 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.36940 | −0.488128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.82840 | 0.255029 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1105 | −1.08320 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6613 | −1.21225 | −0.606123 | − | 0.795371i | \(-0.707276\pi\) | ||||
−0.606123 | + | 0.795371i | \(0.707276\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.02791 | 0.794863 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.920826 | 0.0804530 | 0.0402265 | − | 0.999191i | \(-0.487192\pi\) | ||||
0.0402265 | + | 0.999191i | \(0.487192\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.53138 | −0.132787 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.71910 | 0.147957 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.57814 | −0.134830 | −0.0674148 | − | 0.997725i | \(-0.521475\pi\) | ||||
−0.0674148 | + | 0.997725i | \(0.521475\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.64986 | 0.648852 | 0.324426 | − | 0.945911i | \(-0.394829\pi\) | ||||
0.324426 | + | 0.945911i | \(0.394829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.43500 | −0.457709 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.65045 | 0.639763 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.71910 | 0.142764 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.95590 | −0.573713 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.562591 | 0.0460893 | 0.0230446 | − | 0.999734i | \(-0.492664\pi\) | ||||
0.0230446 | + | 0.999734i | \(0.492664\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.59101 | −0.373611 | −0.186806 | − | 0.982397i | \(-0.559813\pi\) | ||||
−0.186806 | + | 0.982397i | \(0.559813\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.22874 | −0.0993377 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.33909 | 0.509168 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6359 | −1.40750 | −0.703750 | − | 0.710448i | \(-0.748492\pi\) | ||||
−0.703750 | + | 0.710448i | \(0.748492\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.49073 | −0.197528 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.210007 | 0.0165509 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.54677 | −0.747761 | −0.373880 | − | 0.927477i | \(-0.621973\pi\) | ||||
−0.373880 | + | 0.927477i | \(0.621973\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.07924 | −0.317568 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.8167 | −1.45608 | −0.728042 | − | 0.685533i | \(-0.759569\pi\) | ||||
−0.728042 | + | 0.685533i | \(0.759569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.60511 | −0.200393 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.29204 | −0.557636 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0827733 | 0.00629314 | 0.00314657 | − | 0.999995i | \(-0.498998\pi\) | ||||
0.00314657 | + | 0.999995i | \(0.498998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.429398 | −0.0324594 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.55638 | −0.267314 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.20992 | 0.688382 | 0.344191 | − | 0.938900i | \(-0.388153\pi\) | ||||
0.344191 | + | 0.938900i | \(0.388153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.17306 | −0.681828 | −0.340914 | − | 0.940094i | \(-0.610736\pi\) | ||||
−0.340914 | + | 0.940094i | \(0.610736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.27294 | −0.537631 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.1564 | 0.967278 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.91566 | 0.213214 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.210007 | 0.0152758 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.71415 | −0.124031 | −0.0620156 | − | 0.998075i | \(-0.519753\pi\) | ||||
−0.0620156 | + | 0.998075i | \(0.519753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.98986 | 0.287196 | 0.143598 | − | 0.989636i | \(-0.454133\pi\) | ||||
0.143598 | + | 0.989636i | \(0.454133\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.54258 | −0.396912 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.34272 | −0.238159 | −0.119080 | − | 0.992885i | \(-0.537994\pi\) | ||||
−0.119080 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4507 | 1.30793 | 0.653967 | − | 0.756523i | \(-0.273104\pi\) | ||||
0.653967 | + | 0.756523i | \(0.273104\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.41000 | 0.663730 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.210007 | 0.0147396 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.86232 | 0.339599 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.3032 | 1.19689 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7086 | 1.42564 | 0.712818 | − | 0.701349i | \(-0.247418\pi\) | ||||
0.712818 | + | 0.701349i | \(0.247418\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.53494 | −0.516286 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.5199 | 1.05845 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.774388 | 0.0525689 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.75783 | 0.253930 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.96159 | 0.266486 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1547 | −0.813936 | −0.406968 | − | 0.913442i | \(-0.633414\pi\) | ||||
−0.406968 | + | 0.913442i | \(0.633414\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.04468 | −0.136312 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9879 | 0.862035 | 0.431017 | − | 0.902344i | \(-0.358155\pi\) | ||||
0.431017 | + | 0.902344i | \(0.358155\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.91961 | 0.655506 | 0.327753 | − | 0.944763i | \(-0.393709\pi\) | ||||
0.327753 | + | 0.944763i | \(0.393709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.498323 | −0.0327872 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0401 | 0.854285 | 0.427143 | − | 0.904184i | \(-0.359520\pi\) | ||||
0.427143 | + | 0.904184i | \(0.359520\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.34332 | −0.609491 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.807221 | 0.0524346 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.25253 | −0.275073 | −0.137537 | − | 0.990497i | \(-0.543918\pi\) | ||||
−0.137537 | + | 0.990497i | \(0.543918\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.22996 | −0.0792289 | −0.0396144 | − | 0.999215i | \(-0.512613\pi\) | ||||
−0.0396144 | + | 0.999215i | \(0.512613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.9579 | −0.763963 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.5103 | 1.49593 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.58455 | 0.353907 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.4225 | 0.784100 | 0.392050 | − | 0.919944i | \(-0.371766\pi\) | ||||
0.392050 | + | 0.919944i | \(0.371766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.37289 | −0.149182 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.11233 | −0.132279 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.16912 | 0.197684 | 0.0988422 | − | 0.995103i | \(-0.468486\pi\) | ||||
0.0988422 | + | 0.995103i | \(0.468486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.60720 | 0.0998663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.4038 | −0.703190 | −0.351595 | − | 0.936152i | \(-0.614361\pi\) | ||||
−0.351595 | + | 0.936152i | \(0.614361\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.28182 | −0.263030 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.2438 | −0.688108 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.50827 | 0.213903 | 0.106952 | − | 0.994264i | \(-0.465891\pi\) | ||||
0.106952 | + | 0.994264i | \(0.465891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.74651 | 0.166839 | 0.0834193 | − | 0.996515i | \(-0.473416\pi\) | ||||
0.0834193 | + | 0.996515i | \(0.473416\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.677086 | −0.0409791 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.85180 | 0.292575 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.2225 | −1.57556 | −0.787780 | − | 0.615957i | \(-0.788769\pi\) | ||||
−0.787780 | + | 0.615957i | \(0.788769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.68744 | 0.220761 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9533 | 0.832382 | 0.416191 | − | 0.909277i | \(-0.363365\pi\) | ||||
0.416191 | + | 0.909277i | \(0.363365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0948723 | 0.00563957 | 0.00281979 | − | 0.999996i | \(-0.499102\pi\) | ||||
0.00281979 | + | 0.999996i | \(0.499102\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.5358 | −0.742555 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.593984 | 0.0350618 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4902 | −0.911188 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.5915 | −0.679507 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.3283 | −1.12917 | −0.564586 | − | 0.825374i | \(-0.690964\pi\) | ||||
−0.564586 | + | 0.825374i | \(0.690964\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.11379 | −0.355959 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.37289 | −0.137689 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.22411 | −0.186455 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.89592 | 0.109279 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.54449 | −0.0887287 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.5029 | −0.715916 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.8115 | −1.58729 | −0.793644 | − | 0.608382i | \(-0.791819\pi\) | ||||
−0.793644 | + | 0.608382i | \(0.791819\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.7680 | −0.840122 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.91082 | 0.278467 | 0.139234 | − | 0.990260i | \(-0.455536\pi\) | ||||
0.139234 | + | 0.990260i | \(0.455536\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.32210 | 0.187776 | 0.0938881 | − | 0.995583i | \(-0.470070\pi\) | ||||
0.0938881 | + | 0.995583i | \(0.470070\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.361024 | 0.0203414 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0295 | 0.619477 | 0.309738 | − | 0.950822i | \(-0.399759\pi\) | ||||
0.309738 | + | 0.950822i | \(0.399759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.37289 | −0.132856 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0255 | −0.671197 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.96002 | 0.498549 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.59228 | 0.365674 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.79224 | −0.209711 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.14139 | −0.0629267 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1235 | −0.776295 | −0.388148 | − | 0.921597i | \(-0.626885\pi\) | ||||
−0.388148 | + | 0.921597i | \(0.626885\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.65306 | 0.419385 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.1768 | 0.883831 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.3246 | −1.48846 | −0.744232 | − | 0.667921i | \(-0.767184\pi\) | ||||
−0.744232 | + | 0.667921i | \(0.767184\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.1915 | −0.825087 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.74988 | −0.473832 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.93084 | −0.158250 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.71910 | 0.0925534 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.1666 | −0.599456 | −0.299728 | − | 0.954025i | \(-0.596896\pi\) | ||||
−0.299728 | + | 0.954025i | \(0.596896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7330 | 0.895697 | 0.447849 | − | 0.894109i | \(-0.352190\pi\) | ||||
0.447849 | + | 0.894109i | \(0.352190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.22411 | −0.172090 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.3617 | 1.50954 | 0.754771 | − | 0.655988i | \(-0.227748\pi\) | ||||
0.754771 | + | 0.655988i | \(0.227748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.9533 | −0.687492 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.258044 | −0.0136571 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.6653 | 1.40734 | 0.703670 | − | 0.710527i | \(-0.251543\pi\) | ||||
0.703670 | + | 0.710527i | \(0.251543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.1738 | 1.79862 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.36940 | −0.281821 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.46009 | 0.338137 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.0394 | 1.20265 | 0.601323 | − | 0.799006i | \(-0.294641\pi\) | ||||
0.601323 | + | 0.799006i | \(0.294641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.82840 | 0.147241 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.523070 | −0.0271565 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.9479 | 1.03286 | 0.516432 | − | 0.856328i | \(-0.327260\pi\) | ||||
0.516432 | + | 0.856328i | \(0.327260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1105 | −0.625386 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.22411 | −0.166050 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.94273 | −0.305257 | −0.152629 | − | 0.988284i | \(-0.548774\pi\) | ||||
−0.152629 | + | 0.988284i | \(0.548774\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.6613 | −0.699891 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.1706 | 0.877377 | 0.438688 | − | 0.898639i | \(-0.355443\pi\) | ||||
0.438688 | + | 0.898639i | \(0.355443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.856669 | −0.0436599 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.02791 | 0.458914 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.89922 | −0.501910 | −0.250955 | − | 0.967999i | \(-0.580745\pi\) | ||||
−0.250955 | + | 0.967999i | \(0.580745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.22874 | −0.0621400 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.920826 | 0.0464496 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.38770 | 0.0698226 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.53349 | −0.327906 | −0.163953 | − | 0.986468i | \(-0.552425\pi\) | ||||
−0.163953 | + | 0.986468i | \(0.552425\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.53138 | −0.0766648 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.3783 | −1.41715 | −0.708573 | − | 0.705638i | \(-0.750661\pi\) | ||||
−0.708573 | + | 0.705638i | \(0.750661\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.8887 | −0.592219 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.71910 | 0.0854229 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.1599 | −0.900151 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.9632 | −0.591543 | −0.295771 | − | 0.955259i | \(-0.595577\pi\) | ||||
−0.295771 | + | 0.955259i | \(0.595577\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.57814 | −0.0778439 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.746865 | −0.0367508 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.60042 | 0.471266 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.64986 | 0.374615 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4630 | 1.24395 | 0.621974 | − | 0.783038i | \(-0.286331\pi\) | ||||
0.621974 | + | 0.783038i | \(0.286331\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.3023 | −1.28190 | −0.640949 | − | 0.767584i | \(-0.721459\pi\) | ||||
−0.640949 | + | 0.767584i | \(0.721459\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.43500 | −0.264259 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.51238 | 0.121868 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.52737 | −0.0739145 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.65045 | 0.369367 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.9906 | 1.01108 | 0.505540 | − | 0.862803i | \(-0.331293\pi\) | ||||
0.505540 | + | 0.862803i | \(0.331293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.3754 | 0.594722 | 0.297361 | − | 0.954765i | \(-0.403894\pi\) | ||||
0.297361 | + | 0.954765i | \(0.403894\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.71910 | 0.0824247 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.29204 | −0.348825 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0738 | 1.14898 | 0.574490 | − | 0.818512i | \(-0.305200\pi\) | ||||
0.574490 | + | 0.818512i | \(0.305200\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.95590 | −0.331233 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.14360 | 0.244380 | 0.122190 | − | 0.992507i | \(-0.461008\pi\) | ||||
0.122190 | + | 0.992507i | \(0.461008\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.3292 | −0.916293 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.562591 | 0.0266097 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0027 | 0.849601 | 0.424800 | − | 0.905287i | \(-0.360344\pi\) | ||||
0.424800 | + | 0.905287i | \(0.360344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.71148 | −0.316031 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.59101 | −0.215705 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.16398 | −0.0545682 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.1329 | 1.59667 | 0.798334 | − | 0.602215i | \(-0.205715\pi\) | ||||
0.798334 | + | 0.602215i | \(0.205715\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.22874 | −0.0573527 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0677 | 0.468899 | 0.234449 | − | 0.972128i | \(-0.424671\pi\) | ||||
0.234449 | + | 0.972128i | \(0.424671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.9720 | −0.556387 | −0.278194 | − | 0.960525i | \(-0.589736\pi\) | ||||
−0.278194 | + | 0.960525i | \(0.589736\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.33909 | 0.293968 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.8685 | −0.780582 | −0.390291 | − | 0.920692i | \(-0.627626\pi\) | ||||
−0.390291 | + | 0.920692i | \(0.627626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.97617 | 0.0912508 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.6359 | −0.812620 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.4222 | −0.984995 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.9099 | 0.684113 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.49073 | −0.114043 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.7594 | 1.77096 | 0.885480 | − | 0.464677i | \(-0.153830\pi\) | ||||
0.885480 | + | 0.464677i | \(0.153830\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.6743 | −1.12505 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.210007 | 0.00955565 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.9270 | −0.904840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.17969 | −0.144085 | −0.0720427 | − | 0.997402i | \(-0.522952\pi\) | ||||
−0.0720427 | + | 0.997402i | \(0.522952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.54677 | −0.431720 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.43125 | 0.0645914 | 0.0322957 | − | 0.999478i | \(-0.489718\pi\) | ||||
0.0322957 | + | 0.999478i | \(0.489718\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.22874 | −0.0553397 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.07924 | −0.183348 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.58239 | −0.0709799 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.9140 | 1.29437 | 0.647184 | − | 0.762334i | \(-0.275946\pi\) | ||||
0.647184 | + | 0.762334i | \(0.275946\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.8167 | −0.840670 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.83555 | 0.304782 | 0.152391 | − | 0.988320i | \(-0.451303\pi\) | ||||
0.152391 | + | 0.988320i | \(0.451303\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.65514 | −0.118152 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.60511 | −0.115697 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.3988 | −0.726862 | −0.363431 | − | 0.931621i | \(-0.618395\pi\) | ||||
−0.363431 | + | 0.931621i | \(0.618395\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.789170 | 0.0349108 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.29204 | −0.321951 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.3877 | −1.11872 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.8966 | 0.567193 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0827733 | 0.00363334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 45.1845 | 1.97957 | 0.989784 | − | 0.142575i | \(-0.0455382\pi\) | ||||
0.989784 | + | 0.142575i | \(0.0455382\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.82991 | −0.386105 | −0.193052 | − | 0.981188i | \(-0.561839\pi\) | ||||
−0.193052 | + | 0.981188i | \(0.561839\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.429398 | −0.0187404 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.53090 | −0.197369 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.55638 | −0.154334 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.11909 | −0.394991 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.6730 | −0.893774 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.20992 | 0.397437 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5056 | 0.710945 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9832 | −0.687173 | −0.343586 | − | 0.939121i | \(-0.611642\pi\) | ||||
−0.343586 | + | 0.939121i | \(0.611642\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.17306 | −0.393654 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.51925 | −0.279254 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.8308 | 1.14720 | 0.573601 | − | 0.819135i | \(-0.305546\pi\) | ||||
0.573601 | + | 0.819135i | \(0.305546\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.27294 | −0.310402 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.29204 | −0.310651 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.169522 | 0.00720881 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.1564 | 0.558458 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.96427 | −0.167971 | −0.0839857 | − | 0.996467i | \(-0.526765\pi\) | ||||
−0.0839857 | + | 0.996467i | \(0.526765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.1070 | −1.23109 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.91566 | 0.123099 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.13810 | −0.0479653 | −0.0239827 | − | 0.999712i | \(-0.507635\pi\) | ||||
−0.0239827 | + | 0.999712i | \(0.507635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.1157 | −1.09870 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.210007 | 0.00881946 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.6531 | −0.823900 | −0.411950 | − | 0.911206i | \(-0.635152\pi\) | ||||
−0.411950 | + | 0.911206i | \(0.635152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0484 | −0.420511 | −0.210256 | − | 0.977646i | \(-0.567430\pi\) | ||||
−0.210256 | + | 0.977646i | \(0.567430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.71415 | −0.0716095 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.04468 | −0.0852692 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.9270 | 0.996093 | 0.498046 | − | 0.867150i | \(-0.334051\pi\) | ||||
0.498046 | + | 0.867150i | \(0.334051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.98986 | 0.165813 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.17279 | 0.0486557 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.91022 | 0.244776 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.54258 | −0.229157 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.4351 | −1.87531 | −0.937654 | − | 0.347571i | \(-0.887007\pi\) | ||||
−0.937654 | + | 0.347571i | \(0.887007\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.8889 | −1.10794 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.34272 | −0.137501 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.5765 | 1.37882 | 0.689411 | − | 0.724370i | \(-0.257869\pi\) | ||||
0.689411 | + | 0.724370i | \(0.257869\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.443604 | −0.0181860 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.4507 | 0.755136 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.5064 | −0.429278 | −0.214639 | − | 0.976693i | \(-0.568858\pi\) | ||||
−0.214639 | + | 0.976693i | \(0.568858\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.26956 | −0.378113 | −0.189057 | − | 0.981966i | \(-0.560543\pi\) | ||||
−0.189057 | + | 0.981966i | \(0.560543\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.41000 | 0.383205 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.23056 | −0.375276 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.7857 | 1.69603 | 0.848014 | − | 0.529973i | \(-0.177798\pi\) | ||||
0.848014 | + | 0.529973i | \(0.177798\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.210007 | 0.00850991 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.5230 | 0.708906 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.8443 | −0.559168 | −0.279584 | − | 0.960121i | \(-0.590197\pi\) | ||||
−0.279584 | + | 0.960121i | \(0.590197\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.86232 | 0.196068 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.6630 | −1.27470 | −0.637352 | − | 0.770573i | \(-0.719970\pi\) | ||||
−0.637352 | + | 0.770573i | \(0.719970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.1516 | −1.77460 | −0.887301 | − | 0.461191i | \(-0.847422\pi\) | ||||
−0.887301 | + | 0.461191i | \(0.847422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.36127 | −0.0946024 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.5959 | −0.423834 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.3032 | 0.691023 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.40362 | −0.374947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.420214 | 0.0167284 | 0.00836422 | − | 0.999965i | \(-0.497338\pi\) | ||||
0.00836422 | + | 0.999965i | \(0.497338\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.7086 | 0.823092 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.4852 | −0.931983 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.4266 | 0.888574 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.53494 | −0.298078 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.31380 | −0.367873 | −0.183937 | − | 0.982938i | \(-0.558884\pi\) | ||||
−0.183937 | + | 0.982938i | \(0.558884\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.1468 | 1.70154 | 0.850772 | − | 0.525535i | \(-0.176135\pi\) | ||||
0.850772 | + | 0.525535i | \(0.176135\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.5199 | 0.611096 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.0052 | 0.511287 | 0.255644 | − | 0.966771i | \(-0.417713\pi\) | ||||
0.255644 | + | 0.966771i | \(0.417713\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.43890 | 0.331256 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.774388 | 0.0303506 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.4920 | 0.958444 | 0.479222 | − | 0.877694i | \(-0.340919\pi\) | ||||
0.479222 | + | 0.877694i | \(0.340919\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.58300 | 0.0618528 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.75783 | 0.146607 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.15236 | 0.200707 | 0.100354 | − | 0.994952i | \(-0.468003\pi\) | ||||
0.100354 | + | 0.994952i | \(0.468003\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.5643 | −0.488693 | −0.244347 | − | 0.969688i | \(-0.578574\pi\) | ||||
−0.244347 | + | 0.969688i | \(0.578574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.96159 | 0.153856 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.63260 | −0.102088 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.1547 | −0.469926 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.2579 | 0.666233 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.9920 | −0.770633 | −0.385317 | − | 0.922784i | \(-0.625908\pi\) | ||||
−0.385317 | + | 0.922784i | \(0.625908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.04468 | −0.0786999 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.2945 | 1.39491 | 0.697456 | − | 0.716627i | \(-0.254315\pi\) | ||||
0.697456 | + | 0.716627i | \(0.254315\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.43430 | −0.0934199 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.9879 | 0.497696 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.0186 | −0.995573 | −0.497787 | − | 0.867300i | \(-0.665854\pi\) | ||||
−0.497787 | + | 0.867300i | \(0.665854\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.71299 | −0.103658 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.91961 | 0.378457 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.03038 | 0.305933 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.8459 | −0.488679 | −0.244340 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244340 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.498323 | −0.0189297 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.1509 | 0.498842 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.47537 | −0.131639 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.0401 | 0.493222 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.7174 | −0.895792 | −0.447896 | − | 0.894086i | \(-0.647827\pi\) | ||||
−0.447896 | + | 0.894086i | \(0.647827\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −55.8064 | −2.10478 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.34332 | −0.351890 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.324354 | −0.0121986 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.4256 | −0.541765 | −0.270883 | − | 0.962612i | \(-0.587316\pi\) | ||||
−0.270883 | + | 0.962612i | \(0.587316\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.807221 | 0.0302731 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.68744 | 0.138096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.1519 | 0.491854 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.25253 | −0.158814 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.6876 | −0.659636 | −0.329818 | − | 0.944044i | \(-0.606987\pi\) | ||||
−0.329818 | + | 0.944044i | \(0.606987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.10138 | −0.115501 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.22996 | −0.0457428 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.04468 | −0.0759376 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.0547 | 1.30011 | 0.650053 | − | 0.759889i | \(-0.274747\pi\) | ||||
0.650053 | + | 0.759889i | \(0.274747\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0930 | −0.410288 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.31412 | −0.0485383 | −0.0242691 | − | 0.999705i | \(-0.507726\pi\) | ||||
−0.0242691 | + | 0.999705i | \(0.507726\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.9579 | −0.441074 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.3289 | −0.822495 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.56395 | −0.351816 | −0.175908 | − | 0.984407i | \(-0.556286\pi\) | ||||
−0.175908 | + | 0.984407i | \(0.556286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.5103 | 0.863674 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.5554 | −0.570673 | −0.285336 | − | 0.958427i | \(-0.592105\pi\) | ||||
−0.285336 | + | 0.958427i | \(0.592105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.967153 | 0.0354337 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.58455 | 0.204328 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.52543 | −0.0922773 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.3525 | 0.998106 | 0.499053 | − | 0.866572i | \(-0.333681\pi\) | ||||
0.499053 | + | 0.866572i | \(0.333681\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.4225 | 0.452700 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.89243 | −0.287235 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.2917 | 0.628479 | 0.314240 | − | 0.949344i | \(-0.398250\pi\) | ||||
0.314240 | + | 0.949344i | \(0.398250\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.37289 | −0.0861304 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.3174 | 1.17150 | 0.585752 | − | 0.810490i | \(-0.300799\pi\) | ||||
0.585752 | + | 0.810490i | \(0.300799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.796396 | −0.0288315 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.11233 | −0.0763715 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.4662 | 0.414020 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.88519 | −0.212225 | −0.106113 | − | 0.994354i | \(-0.533840\pi\) | ||||
−0.106113 | + | 0.994354i | \(0.533840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.16912 | 0.114133 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.0255 | 0.684298 | 0.342149 | − | 0.939646i | \(-0.388845\pi\) | ||||
0.342149 | + | 0.939646i | \(0.388845\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.53964 | −0.270832 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.60720 | 0.0576578 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.6248 | −0.738961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.8796 | 0.639781 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.3180 | −1.08209 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.6197 | 0.663720 | 0.331860 | − | 0.943329i | \(-0.392324\pi\) | ||||
0.331860 | + | 0.943329i | \(0.392324\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.4038 | −0.405987 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.19031 | −0.113434 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.4488 | 0.832690 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.28182 | −0.151860 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.6132 | 0.730158 | 0.365079 | − | 0.930977i | \(-0.381042\pi\) | ||||
0.365079 | + | 0.930977i | \(0.381042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.67819 | 0.236258 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.2438 | −0.397280 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.91690 | −0.314671 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.361024 | 0.0127244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.50827 | 0.123497 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.9018 | −0.805184 | −0.402592 | − | 0.915379i | \(-0.631891\pi\) | ||||
−0.402592 | + | 0.915379i | \(0.631891\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.5774 | −0.757685 | −0.378843 | − | 0.925461i | \(-0.623678\pi\) | ||||
−0.378843 | + | 0.925461i | \(0.623678\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.74651 | 0.0963243 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.4119 | −0.574883 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −65.8319 | −2.30317 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.677086 | −0.0236593 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.3416 | 0.395824 | 0.197912 | − | 0.980220i | \(-0.436584\pi\) | ||||
0.197912 | + | 0.980220i | \(0.436584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.53006 | 0.157908 | 0.0789540 | − | 0.996878i | \(-0.474842\pi\) | ||||
0.0789540 | + | 0.996878i | \(0.474842\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.85180 | 0.168918 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.90044 | 0.100858 | 0.0504290 | − | 0.998728i | \(-0.483941\pi\) | ||||
0.0504290 | + | 0.998728i | \(0.483941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.31154 | −0.184477 | −0.0922387 | − | 0.995737i | \(-0.529402\pi\) | ||||
−0.0922387 | + | 0.995737i | \(0.529402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.2225 | −0.909650 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.54699 | 0.296136 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.3479 | −1.11945 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.68744 | 0.127457 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.2724 | 1.80464 | 0.902322 | − | 0.431063i | \(-0.141861\pi\) | ||||
0.902322 | + | 0.431063i | \(0.141861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.9533 | 0.480576 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.47845 | −0.154063 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.12761 | −0.0387452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.0948723 | 0.00325601 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.65306 | 0.262344 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2670 | 0.488492 | 0.244246 | − | 0.969713i | \(-0.421460\pi\) | ||||
0.244246 | + | 0.969713i | \(0.421460\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.5358 | −0.428714 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.13021 | 0.311882 | 0.155941 | − | 0.987766i | \(-0.450159\pi\) | ||||
0.155941 | + | 0.987766i | \(0.450159\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4652 | 0.561785 | 0.280892 | − | 0.959739i | \(-0.409370\pi\) | ||||
0.280892 | + | 0.959739i | \(0.409370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.593984 | 0.0202429 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.6882 | 0.534032 | 0.267016 | − | 0.963692i | \(-0.413962\pi\) | ||||
0.267016 | + | 0.963692i | \(0.413962\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.142296 | 0.00483820 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.4902 | −0.526075 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.91544 | −0.0649770 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.3389 | −1.02799 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.5915 | −0.392314 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.54330 | −0.0859791 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.6806 | −1.54252 | −0.771262 | − | 0.636518i | \(-0.780374\pi\) | ||||
−0.771262 | + | 0.636518i | \(0.780374\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.3283 | −0.651928 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 58.8054 | 1.98120 | 0.990602 | − | 0.136777i | \(-0.0436744\pi\) | ||||
0.990602 | + | 0.136777i | \(0.0436744\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.5660 | −0.692099 | −0.346050 | − | 0.938216i | \(-0.612477\pi\) | ||||
−0.346050 | + | 0.938216i | \(0.612477\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.11379 | −0.205513 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0199 | 0.403587 | 0.201794 | − | 0.979428i | \(-0.435323\pi\) | ||||
0.201794 | + | 0.979428i | \(0.435323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.86897 | −0.0962222 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.37289 | −0.0794947 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.6322 | 1.32624 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.8328 | 0.529232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.22411 | −0.107650 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.68744 | 0.122983 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.06046 | 0.101959 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.89592 | 0.0630924 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.7694 | −0.524194 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.278333 | 0.00924189 | 0.00462094 | − | 0.999989i | \(-0.498529\pi\) | ||||
0.00462094 | + | 0.999989i | \(0.498529\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.54449 | −0.0512275 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.1668 | 1.33079 | 0.665393 | − | 0.746493i | \(-0.268264\pi\) | ||||
0.665393 | + | 0.746493i | \(0.268264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.2515 | −0.438561 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.5029 | −0.413334 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.193380 | 0.00638597 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.1451 | 0.367644 | 0.183822 | − | 0.982960i | \(-0.441153\pi\) | ||||
0.183822 | + | 0.982960i | \(0.441153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.8115 | −0.916421 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.2935 | 0.799630 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.6481 | −0.514506 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.7680 | −0.485045 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.1350 | 0.726227 | 0.363113 | − | 0.931745i | \(-0.381714\pi\) | ||||
0.363113 | + | 0.931745i | \(0.381714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.7227 | 1.66237 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.91082 | 0.160773 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.01232 | 0.163921 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.8017 | −0.940909 | −0.470454 | − | 0.882424i | \(-0.655910\pi\) | ||||
−0.470454 | + | 0.882424i | \(0.655910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.32210 | 0.108413 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.8130 | −0.385092 | −0.192546 | − | 0.981288i | \(-0.561675\pi\) | ||||
−0.192546 | + | 0.981288i | \(0.561675\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.82840 | 0.0921055 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.361024 | 0.0117441 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.7370 | −0.836340 | −0.418170 | − | 0.908369i | \(-0.637328\pi\) | ||||
−0.418170 | + | 0.908369i | \(0.637328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.1157 | −0.393291 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.0295 | 0.357655 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.0227 | −1.39364 | −0.696821 | − | 0.717245i | \(-0.745403\pi\) | ||||
−0.696821 | + | 0.717245i | \(0.745403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.94679 | −0.0953560 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.37289 | −0.0767046 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.331420 | −0.0107021 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.4028 | −0.561381 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0255 | −0.387516 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.85898 | 0.220798 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.1451 | −1.45177 | −0.725884 | − | 0.687817i | \(-0.758569\pi\) | ||||
−0.725884 | + | 0.687817i | \(0.758569\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.96002 | 0.287837 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2567 | −0.425426 | −0.212713 | − | 0.977115i | \(-0.568230\pi\) | ||||
−0.212713 | + | 0.977115i | \(0.568230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.60652 | 0.0515028 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.59228 | 0.211122 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.0117 | 0.800197 | 0.400098 | − | 0.916472i | \(-0.368976\pi\) | ||||
0.400098 | + | 0.916472i | \(0.368976\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.6802 | 0.852704 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.79224 | −0.121077 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.4337 | 1.13016 | 0.565080 | − | 0.825036i | \(-0.308845\pi\) | ||||
0.565080 | + | 0.825036i | \(0.308845\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.74649 | −0.183098 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.14139 | −0.0363307 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.02791 | 0.287071 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.0130 | −1.46165 | −0.730825 | − | 0.682565i | \(-0.760865\pi\) | ||||
−0.730825 | + | 0.682565i | \(0.760865\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.1235 | −0.448194 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.7186 | 1.00555 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.7346 | −1.10006 | −0.550028 | − | 0.835146i | \(-0.685383\pi\) | ||||
−0.550028 | + | 0.835146i | \(0.685383\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.65306 | 0.242132 |
(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 | 8004.2.a.d.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.d.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial |