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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 31 x^{10} + 80 x^{9} + 347 x^{8} - 697 x^{7} - 1714 x^{6} + 2146 x^{5} + 3304 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.06377\) 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 | ||||||||
\(5\) | −3.06377 | −1.37016 | −0.685079 | − | 0.728469i | \(-0.740232\pi\) | ||||
−0.685079 | + | 0.728469i | \(0.740232\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.59303 | 1.35804 | 0.679018 | − | 0.734121i | \(-0.262406\pi\) | ||||
0.679018 | + | 0.734121i | \(0.262406\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.57105 | 1.07671 | 0.538355 | − | 0.842718i | \(-0.319046\pi\) | ||||
0.538355 | + | 0.842718i | \(0.319046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.11209 | 0.308440 | 0.154220 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154220 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.06377 | 0.791061 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.35191 | −1.29803 | −0.649014 | − | 0.760776i | \(-0.724818\pi\) | ||||
−0.649014 | + | 0.760776i | \(0.724818\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.67014 | −0.383157 | −0.191579 | − | 0.981477i | \(-0.561361\pi\) | ||||
−0.191579 | + | 0.981477i | \(0.561361\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.59303 | −0.784063 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.38666 | 0.877332 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.98746 | 1.07538 | 0.537690 | − | 0.843143i | \(-0.319297\pi\) | ||||
0.537690 | + | 0.843143i | \(0.319297\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.57105 | −0.621639 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.0082 | −1.86072 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.76622 | −0.783562 | −0.391781 | − | 0.920059i | \(-0.628141\pi\) | ||||
−0.391781 | + | 0.920059i | \(0.628141\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.11209 | −0.178078 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.76801 | 0.588464 | 0.294232 | − | 0.955734i | \(-0.404936\pi\) | ||||
0.294232 | + | 0.955734i | \(0.404936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7805 | −1.79651 | −0.898256 | − | 0.439473i | \(-0.855165\pi\) | ||||
−0.898256 | + | 0.439473i | \(0.855165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.06377 | −0.456719 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.41650 | −0.935943 | −0.467971 | − | 0.883744i | \(-0.655015\pi\) | ||||
−0.467971 | + | 0.883744i | \(0.655015\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.90985 | 0.844264 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.35191 | 0.749417 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.261608 | −0.0359346 | −0.0179673 | − | 0.999839i | \(-0.505719\pi\) | ||||
−0.0179673 | + | 0.999839i | \(0.505719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.9408 | −1.47526 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.67014 | 0.221216 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.33982 | −0.955563 | −0.477781 | − | 0.878479i | \(-0.658559\pi\) | ||||
−0.477781 | + | 0.878479i | \(0.658559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.81452 | −0.488399 | −0.244199 | − | 0.969725i | \(-0.578525\pi\) | ||||
−0.244199 | + | 0.969725i | \(0.578525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.59303 | 0.452679 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.40720 | −0.422611 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.212601 | −0.0259734 | −0.0129867 | − | 0.999916i | \(-0.504134\pi\) | ||||
−0.0129867 | + | 0.999916i | \(0.504134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.4656 | −1.83542 | −0.917712 | − | 0.397245i | \(-0.869966\pi\) | ||||
−0.917712 | + | 0.397245i | \(0.869966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.2479 | 1.78464 | 0.892318 | − | 0.451408i | \(-0.149078\pi\) | ||||
0.892318 | + | 0.451408i | \(0.149078\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.38666 | −0.506528 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.8309 | 1.46221 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1479 | 1.59176 | 0.795879 | − | 0.605455i | \(-0.207009\pi\) | ||||
0.795879 | + | 0.605455i | \(0.207009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.48671 | 0.492481 | 0.246240 | − | 0.969209i | \(-0.420805\pi\) | ||||
0.246240 | + | 0.969209i | \(0.420805\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.3970 | 1.77850 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.32038 | 0.775958 | 0.387979 | − | 0.921668i | \(-0.373173\pi\) | ||||
0.387979 | + | 0.921668i | \(0.373173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.99579 | 0.418872 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.98746 | −0.620871 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.11693 | 0.524986 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.66075 | 0.574762 | 0.287381 | − | 0.957816i | \(-0.407215\pi\) | ||||
0.287381 | + | 0.957816i | \(0.407215\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.57105 | 0.358904 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.0231709 | −0.00230559 | −0.00115279 | − | 0.999999i | \(-0.500367\pi\) | ||||
−0.00115279 | + | 0.999999i | \(0.500367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.51046 | −0.542962 | −0.271481 | − | 0.962444i | \(-0.587513\pi\) | ||||
−0.271481 | + | 0.962444i | \(0.587513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.0082 | 1.07429 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.17665 | 0.307099 | 0.153549 | − | 0.988141i | \(-0.450930\pi\) | ||||
0.153549 | + | 0.988141i | \(0.450930\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5216 | −1.10357 | −0.551783 | − | 0.833987i | \(-0.686053\pi\) | ||||
−0.551783 | + | 0.833987i | \(0.686053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.76622 | 0.452390 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0994853 | −0.00935879 | −0.00467940 | − | 0.999989i | \(-0.501490\pi\) | ||||
−0.00467940 | + | 0.999989i | \(0.501490\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.06377 | −0.285698 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.11209 | 0.102813 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.2296 | −1.76277 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.75237 | 0.159306 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.76801 | −0.339750 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.87914 | 0.168075 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.69936 | 0.417001 | 0.208500 | − | 0.978022i | \(-0.433142\pi\) | ||||
0.208500 | + | 0.978022i | \(0.433142\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.7805 | 1.03722 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.2208 | −1.32985 | −0.664924 | − | 0.746911i | \(-0.731536\pi\) | ||||
−0.664924 | + | 0.746911i | \(0.731536\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00087 | −0.520342 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.06377 | 0.263687 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.8868 | −1.35730 | −0.678651 | − | 0.734461i | \(-0.737435\pi\) | ||||
−0.678651 | + | 0.734461i | \(0.737435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.61451 | −0.391397 | −0.195699 | − | 0.980664i | \(-0.562697\pi\) | ||||
−0.195699 | + | 0.980664i | \(0.562697\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.41650 | 0.540367 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.97134 | 0.332100 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.06377 | 0.254432 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.90985 | −0.487436 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.38885 | 0.523395 | 0.261697 | − | 0.965150i | \(-0.415718\pi\) | ||||
0.261697 | + | 0.965150i | \(0.415718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.13056 | −0.580276 | −0.290138 | − | 0.956985i | \(-0.593701\pi\) | ||||
−0.290138 | + | 0.956985i | \(0.593701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.35191 | −0.432676 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.3442 | −1.47344 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.2868 | 1.53926 | 0.769628 | − | 0.638492i | \(-0.220442\pi\) | ||||
0.769628 | + | 0.638492i | \(0.220442\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.261608 | 0.0207468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.59303 | 0.283170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3483 | 1.12384 | 0.561922 | − | 0.827190i | \(-0.310062\pi\) | ||||
0.561922 | + | 0.827190i | \(0.310062\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.9408 | 0.851744 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.56450 | −0.430594 | −0.215297 | − | 0.976549i | \(-0.569072\pi\) | ||||
−0.215297 | + | 0.976549i | \(0.569072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7632 | −0.904865 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.67014 | −0.127719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.66312 | 0.202473 | 0.101236 | − | 0.994862i | \(-0.467720\pi\) | ||||
0.101236 | + | 0.994862i | \(0.467720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.7614 | 1.19145 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.33982 | 0.551694 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.69011 | −0.425299 | −0.212649 | − | 0.977129i | \(-0.568209\pi\) | ||||
−0.212649 | + | 0.977129i | \(0.568209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.03851 | −0.523168 | −0.261584 | − | 0.965181i | \(-0.584245\pi\) | ||||
−0.261584 | + | 0.965181i | \(0.584245\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.81452 | 0.281977 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.6026 | 1.07360 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.1119 | −1.39760 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.59303 | −0.261354 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7486 | −1.57367 | −0.786836 | − | 0.617162i | \(-0.788282\pi\) | ||||
−0.786836 | + | 0.617162i | \(0.788282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.55878 | 0.328148 | 0.164074 | − | 0.986448i | \(-0.447536\pi\) | ||||
0.164074 | + | 0.986448i | \(0.447536\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.40720 | 0.243994 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.74978 | 0.195914 | 0.0979569 | − | 0.995191i | \(-0.468769\pi\) | ||||
0.0979569 | + | 0.995191i | \(0.468769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.3927 | 1.72915 | 0.864575 | − | 0.502503i | \(-0.167587\pi\) | ||||
0.864575 | + | 0.502503i | \(0.167587\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.212601 | 0.0149957 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.59303 | −0.252181 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.5443 | −0.806289 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.96416 | −0.412550 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.28159 | −0.638971 | −0.319485 | − | 0.947591i | \(-0.603510\pi\) | ||||
−0.319485 | + | 0.947591i | \(0.603510\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.4656 | 1.05968 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 36.0927 | 2.46150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.5131 | 1.46041 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.2479 | −1.03036 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.95183 | −0.400363 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.8162 | 1.32699 | 0.663497 | − | 0.748179i | \(-0.269072\pi\) | ||||
0.663497 | + | 0.748179i | \(0.269072\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.38666 | 0.292444 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.50724 | 0.498273 | 0.249136 | − | 0.968468i | \(-0.419853\pi\) | ||||
0.249136 | + | 0.968468i | \(0.419853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.32203 | −0.549935 | −0.274968 | − | 0.961453i | \(-0.588667\pi\) | ||||
−0.274968 | + | 0.961453i | \(0.588667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.8309 | −0.844209 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5592 | 0.888293 | 0.444146 | − | 0.895954i | \(-0.353507\pi\) | ||||
0.444146 | + | 0.895954i | \(0.353507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.6586 | 1.28239 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.1479 | −0.919002 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.02517 | −0.325051 | −0.162526 | − | 0.986704i | \(-0.551964\pi\) | ||||
−0.162526 | + | 0.986704i | \(0.551964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.24679 | −0.144729 | −0.0723644 | − | 0.997378i | \(-0.523054\pi\) | ||||
−0.0723644 | + | 0.997378i | \(0.523054\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.1064 | −1.15677 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.85736 | −0.118181 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.48671 | −0.284334 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.86119 | 0.243716 | 0.121858 | − | 0.992548i | \(-0.461115\pi\) | ||||
0.121858 | + | 0.992548i | \(0.461115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.57105 | 0.224510 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.3970 | −1.02682 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.1469 | −1.25673 | −0.628365 | − | 0.777919i | \(-0.716275\pi\) | ||||
−0.628365 | + | 0.777919i | \(0.716275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.1252 | −1.06411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −32.1602 | −1.98308 | −0.991542 | − | 0.129788i | \(-0.958570\pi\) | ||||
−0.991542 | + | 0.129788i | \(0.958570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.801505 | 0.0492360 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.32038 | −0.448000 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.6391 | −0.648678 | −0.324339 | − | 0.945941i | \(-0.605142\pi\) | ||||
−0.324339 | + | 0.945941i | \(0.605142\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.40339 | −0.328233 | −0.164116 | − | 0.986441i | \(-0.552477\pi\) | ||||
−0.164116 | + | 0.986441i | \(0.552477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.99579 | −0.241836 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.6650 | 0.944633 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.0246 | −1.02291 | −0.511454 | − | 0.859311i | \(-0.670893\pi\) | ||||
−0.511454 | + | 0.859311i | \(0.670893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.98746 | 0.358460 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.47389 | 0.147580 | 0.0737898 | − | 0.997274i | \(-0.476491\pi\) | ||||
0.0737898 | + | 0.997274i | \(0.476491\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.6982 | 1.11150 | 0.555748 | − | 0.831351i | \(-0.312432\pi\) | ||||
0.555748 | + | 0.831351i | \(0.312432\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.11693 | −0.303101 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.5386 | 0.799156 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.6429 | 0.684878 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.66075 | −0.331839 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.6458 | −1.14772 | −0.573861 | − | 0.818953i | \(-0.694555\pi\) | ||||
−0.573861 | + | 0.818953i | \(0.694555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.4875 | 1.30927 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.57105 | −0.207213 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.11209 | 0.0643141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.3277 | −2.43973 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.0231709 | 0.00133113 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.6868 | 0.669183 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.5654 | −0.717144 | −0.358572 | − | 0.933502i | \(-0.616736\pi\) | ||||
−0.358572 | + | 0.933502i | \(0.616736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.51046 | 0.313479 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0036 | −0.623954 | −0.311977 | − | 0.950090i | \(-0.600991\pi\) | ||||
−0.311977 | + | 0.950090i | \(0.600991\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4938 | 0.875762 | 0.437881 | − | 0.899033i | \(-0.355729\pi\) | ||||
0.437881 | + | 0.899033i | \(0.355729\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.0082 | −0.620241 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.06492 | 0.228309 | 0.114154 | − | 0.993463i | \(-0.463584\pi\) | ||||
0.114154 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.57105 | −0.199940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.17665 | −0.177304 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.93846 | 0.497349 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.87838 | 0.270604 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.5216 | 0.637145 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.0547 | −1.27104 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.8554 | −0.816524 | −0.408262 | − | 0.912865i | \(-0.633865\pi\) | ||||
−0.408262 | + | 0.912865i | \(0.633865\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.76622 | −0.261187 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.651360 | 0.0355876 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.2412 | −0.830242 | −0.415121 | − | 0.909766i | \(-0.636261\pi\) | ||||
−0.415121 | + | 0.909766i | \(0.636261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0994853 | 0.00540330 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.3815 | 1.15787 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.91694 | −0.211495 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.06377 | 0.164948 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.98566 | −0.213962 | −0.106981 | − | 0.994261i | \(-0.534118\pi\) | ||||
−0.106981 | + | 0.994261i | \(0.534118\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3660 | −1.14370 | −0.571848 | − | 0.820360i | \(-0.693773\pi\) | ||||
−0.571848 | + | 0.820360i | \(0.693773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.11209 | −0.0593592 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.96364 | 0.104514 | 0.0522569 | − | 0.998634i | \(-0.483359\pi\) | ||||
0.0522569 | + | 0.998634i | \(0.483359\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 47.3829 | 2.51482 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.2296 | 1.01774 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.1743 | −0.853646 | −0.426823 | − | 0.904335i | \(-0.640367\pi\) | ||||
−0.426823 | + | 0.904335i | \(0.640367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2106 | −0.853191 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.75237 | −0.0919756 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −46.7161 | −2.44523 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.17933 | 0.426957 | 0.213479 | − | 0.976948i | \(-0.431521\pi\) | ||||
0.213479 | + | 0.976948i | \(0.431521\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.76801 | 0.196155 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.939964 | −0.0488005 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.4633 | −0.955994 | −0.477997 | − | 0.878361i | \(-0.658637\pi\) | ||||
−0.477997 | + | 0.878361i | \(0.658637\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.87914 | −0.0970381 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.11209 | −0.0572758 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.89915 | −0.508485 | −0.254243 | − | 0.967140i | \(-0.581826\pi\) | ||||
−0.254243 | + | 0.967140i | \(0.581826\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.69936 | −0.240755 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.58947 | −0.438901 | −0.219451 | − | 0.975624i | \(-0.570426\pi\) | ||||
−0.219451 | + | 0.975624i | \(0.570426\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −39.3108 | −2.00346 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.7805 | −0.598837 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.3169 | −0.523088 | −0.261544 | − | 0.965191i | \(-0.584232\pi\) | ||||
−0.261544 | + | 0.965191i | \(0.584232\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.35191 | −0.270658 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.2208 | 0.767788 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −43.3457 | −2.18096 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.68400 | −0.285272 | −0.142636 | − | 0.989775i | \(-0.545558\pi\) | ||||
−0.142636 | + | 0.989775i | \(0.545558\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.00087 | 0.300419 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.02992 | 0.301120 | 0.150560 | − | 0.988601i | \(-0.451892\pi\) | ||||
0.150560 | + | 0.988601i | \(0.451892\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.65863 | 0.331690 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.06377 | −0.152240 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.0204 | −0.843669 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.16164 | 0.403567 | 0.201784 | − | 0.979430i | \(-0.435326\pi\) | ||||
0.201784 | + | 0.979430i | \(0.435326\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.8868 | 0.783638 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.3722 | −1.29769 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7462 | −0.674776 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.61451 | 0.225973 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.6677 | −0.570007 | −0.285003 | − | 0.958527i | \(-0.591995\pi\) | ||||
−0.285003 | + | 0.958527i | \(0.591995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.91906 | −0.0935293 | −0.0467647 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467647 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.41650 | −0.311981 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.4770 | −1.13880 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.7057 | −0.663264 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.97134 | −0.191738 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5396 | 0.796684 | 0.398342 | − | 0.917237i | \(-0.369586\pi\) | ||||
0.398342 | + | 0.917237i | \(0.369586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.1753 | 1.20985 | 0.604923 | − | 0.796284i | \(-0.293204\pi\) | ||||
0.604923 | + | 0.796284i | \(0.293204\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.06377 | −0.146896 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.67014 | −0.0798938 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.53610 | 0.121042 | 0.0605208 | − | 0.998167i | \(-0.480724\pi\) | ||||
0.0605208 | + | 0.998167i | \(0.480724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.90985 | 0.281421 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.1892 | −0.959219 | −0.479610 | − | 0.877482i | \(-0.659222\pi\) | ||||
−0.479610 | + | 0.877482i | \(0.659222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.4279 | −1.06319 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.38885 | −0.302182 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.7302 | −0.553584 | −0.276792 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.4557 | 0.633606 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.13056 | 0.335023 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.2422 | −0.573921 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.00150 | −0.421072 | −0.210536 | − | 0.977586i | \(-0.567521\pi\) | ||||
−0.210536 | + | 0.977586i | \(0.567521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.35191 | 0.249806 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.8985 | −0.926764 | −0.463382 | − | 0.886159i | \(-0.653364\pi\) | ||||
−0.463382 | + | 0.886159i | \(0.653364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.02956 | −0.140796 | −0.0703978 | − | 0.997519i | \(-0.522427\pi\) | ||||
−0.0703978 | + | 0.997519i | \(0.522427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.3442 | 0.850691 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.74598 | −0.265892 | −0.132946 | − | 0.991123i | \(-0.542444\pi\) | ||||
−0.132946 | + | 0.991123i | \(0.542444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.763882 | −0.0352728 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.2868 | −0.888690 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −42.0688 | −1.93432 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.32635 | −0.336156 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.261608 | −0.0119782 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.9178 | 0.681614 | 0.340807 | − | 0.940133i | \(-0.389300\pi\) | ||||
0.340807 | + | 0.940133i | \(0.389300\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.30049 | −0.241681 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.59303 | −0.163488 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.3432 | −0.787514 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.1042 | −1.31884 | −0.659418 | − | 0.751776i | \(-0.729197\pi\) | ||||
−0.659418 | + | 0.751776i | \(0.729197\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.3483 | −0.648851 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.5168 | −1.73824 | −0.869120 | − | 0.494602i | \(-0.835314\pi\) | ||||
−0.869120 | + | 0.494602i | \(0.835314\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.35191 | 0.241038 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.9408 | −0.491755 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −55.5682 | −2.49257 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.15238 | −0.320185 | −0.160092 | − | 0.987102i | \(-0.551179\pi\) | ||||
−0.160092 | + | 0.987102i | \(0.551179\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.56450 | 0.248604 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.5510 | −1.67432 | −0.837158 | − | 0.546961i | \(-0.815785\pi\) | ||||
−0.837158 | + | 0.546961i | \(0.815785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0709901 | 0.00315902 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.7632 | 0.522424 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.74755 | −0.121783 | −0.0608914 | − | 0.998144i | \(-0.519394\pi\) | ||||
−0.0608914 | + | 0.998144i | \(0.519394\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.7862 | 2.42360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.67014 | 0.0737386 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.8828 | 0.743943 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.9136 | −1.00774 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.66312 | −0.116898 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.5716 | −1.12031 | −0.560156 | − | 0.828387i | \(-0.689259\pi\) | ||||
−0.560156 | + | 0.828387i | \(0.689259\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5183 | 0.766024 | 0.383012 | − | 0.923743i | \(-0.374887\pi\) | ||||
0.383012 | + | 0.923743i | \(0.374887\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.7614 | −0.687883 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.0444 | −1.39587 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.33982 | −0.318521 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.19039 | 0.181506 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.73252 | −0.420774 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.69011 | 0.245546 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.1043 | 0.909029 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.9368 | −1.33008 | −0.665039 | − | 0.746809i | \(-0.731585\pi\) | ||||
−0.665039 | + | 0.746809i | \(0.731585\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.03851 | 0.302051 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.2994 | 1.51206 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.4338 | 1.17299 | 0.586493 | − | 0.809955i | \(-0.300508\pi\) | ||||
0.586493 | + | 0.809955i | \(0.300508\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.81452 | −0.162800 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.67014 | 0.0711505 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.8337 | 2.16167 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.6026 | −0.619845 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.3290 | 0.776627 | 0.388313 | − | 0.921527i | \(-0.373058\pi\) | ||||
0.388313 | + | 0.921527i | \(0.373058\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.1010 | −0.554115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.1119 | 0.806906 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.98199 | 0.294256 | 0.147128 | − | 0.989117i | \(-0.452997\pi\) | ||||
0.147128 | + | 0.989117i | \(0.452997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.304800 | 0.0128230 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.59303 | 0.150893 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.0041 | 1.63514 | 0.817569 | − | 0.575831i | \(-0.195321\pi\) | ||||
0.817569 | + | 0.575831i | \(0.195321\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1398 | 0.591730 | 0.295865 | − | 0.955230i | \(-0.404392\pi\) | ||||
0.295865 | + | 0.955230i | \(0.404392\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.7486 | 0.908560 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.38666 | 0.182936 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.1894 | −1.71474 | −0.857369 | − | 0.514702i | \(-0.827903\pi\) | ||||
−0.857369 | + | 0.514702i | \(0.827903\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.55878 | −0.189456 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.1209 | 0.668807 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.934213 | −0.0386912 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.40720 | −0.140870 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.7763 | 1.14645 | 0.573225 | − | 0.819398i | \(-0.305692\pi\) | ||||
0.573225 | + | 0.819398i | \(0.305692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.99992 | −0.412040 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.74978 | −0.113111 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.43304 | 0.223108 | 0.111554 | − | 0.993758i | \(-0.464417\pi\) | ||||
0.111554 | + | 0.993758i | \(0.464417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 58.9149 | 2.41527 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.3927 | −0.998326 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.30603 | −0.0533631 | −0.0266816 | − | 0.999644i | \(-0.508494\pi\) | ||||
−0.0266816 | + | 0.999644i | \(0.508494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.8724 | −1.42248 | −0.711238 | − | 0.702951i | \(-0.751865\pi\) | ||||
−0.711238 | + | 0.702951i | \(0.751865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.212601 | −0.00865779 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.36885 | −0.218275 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.4139 | 1.72153 | 0.860764 | − | 0.509004i | \(-0.169986\pi\) | ||||
0.860764 | + | 0.509004i | \(0.169986\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.59303 | 0.145597 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.13576 | −0.288682 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.94979 | −0.361479 | −0.180739 | − | 0.983531i | \(-0.557849\pi\) | ||||
−0.180739 | + | 0.983531i | \(0.557849\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.5443 | 0.465511 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.1866 | 1.01397 | 0.506986 | − | 0.861954i | \(-0.330759\pi\) | ||||
0.506986 | + | 0.861954i | \(0.330759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.2846 | −0.775112 | −0.387556 | − | 0.921846i | \(-0.626681\pi\) | ||||
−0.387556 | + | 0.921846i | \(0.626681\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.3023 | 1.05378 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.6905 | −1.10762 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.96416 | 0.238186 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.5084 | 1.01709 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.6072 | 1.69616 | 0.848082 | − | 0.529865i | \(-0.177757\pi\) | ||||
0.848082 | + | 0.529865i | \(0.177757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.28159 | 0.368910 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.3977 | −0.571356 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.57231 | 0.260405 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.4656 | −0.611808 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.7436 | −1.29329 | −0.646647 | − | 0.762789i | \(-0.723829\pi\) | ||||
−0.646647 | + | 0.762789i | \(0.723829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.2307 | −0.797821 | −0.398911 | − | 0.916990i | \(-0.630612\pi\) | ||||
−0.398911 | + | 0.916990i | \(0.630612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −36.0927 | −1.42115 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.7182 | 0.775201 | 0.387601 | − | 0.921827i | \(-0.373304\pi\) | ||||
0.387601 | + | 0.921827i | \(0.373304\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.2108 | −1.02886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.5131 | −0.843166 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.4049 | 1.46377 | 0.731884 | − | 0.681430i | \(-0.238641\pi\) | ||||
0.731884 | + | 0.681430i | \(0.238641\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.6330 | 1.82210 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.2479 | 0.594878 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.1613 | −1.33074 | −0.665368 | − | 0.746516i | \(-0.731725\pi\) | ||||
−0.665368 | + | 0.746516i | \(0.731725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.1100 | 1.17114 | 0.585572 | − | 0.810620i | \(-0.300870\pi\) | ||||
0.585572 | + | 0.810620i | \(0.300870\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.95183 | 0.231150 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.3853 | 0.712950 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.8162 | −0.766140 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.6218 | −0.525864 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.3930 | −0.554811 | −0.277405 | − | 0.960753i | \(-0.589475\pi\) | ||||
−0.277405 | + | 0.960753i | \(0.589475\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.38666 | −0.168843 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.90351 | 0.380623 | 0.190311 | − | 0.981724i | \(-0.439050\pi\) | ||||
0.190311 | + | 0.981724i | \(0.439050\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.3392 | 0.780548 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.50724 | −0.287678 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.6562 | 0.943442 | 0.471721 | − | 0.881748i | \(-0.343633\pi\) | ||||
0.471721 | + | 0.881748i | \(0.343633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.6735 | 1.85972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.32203 | 0.317505 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.290933 | −0.0110836 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.2353 | −0.503496 | −0.251748 | − | 0.967793i | \(-0.581005\pi\) | ||||
−0.251748 | + | 0.967793i | \(0.581005\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.8309 | 0.487404 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1378 | 0.536276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.1661 | −0.763844 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.5592 | −0.512856 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.304707 | 0.0115086 | 0.00575432 | − | 0.999983i | \(-0.498168\pi\) | ||||
0.00575432 | + | 0.999983i | \(0.498168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.96027 | 0.300227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.6586 | −0.740388 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0832536 | −0.00313107 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.7708 | 1.41851 | 0.709256 | − | 0.704951i | \(-0.249031\pi\) | ||||
0.709256 | + | 0.704951i | \(0.249031\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.1479 | 0.530586 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.98746 | 0.224232 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.1673 | −0.455030 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.02517 | 0.187668 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.6927 | 0.398769 | 0.199385 | − | 0.979921i | \(-0.436106\pi\) | ||||
0.199385 | + | 0.979921i | \(0.436106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.7992 | −0.737362 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.24679 | 0.0835592 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.38666 | −0.162916 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.2928 | −0.826795 | −0.413397 | − | 0.910551i | \(-0.635658\pi\) | ||||
−0.413397 | + | 0.910551i | \(0.635658\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 63.0482 | 2.33192 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.1613 | −1.40952 | −0.704759 | − | 0.709447i | \(-0.748945\pi\) | ||||
−0.704759 | + | 0.709447i | \(0.748945\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.1064 | 0.667864 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.759209 | −0.0279658 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.0827 | −1.65839 | −0.829197 | − | 0.558957i | \(-0.811202\pi\) | ||||
−0.829197 | + | 0.558957i | \(0.811202\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.85736 | 0.0682318 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.4523 | 1.19056 | 0.595280 | − | 0.803518i | \(-0.297041\pi\) | ||||
0.595280 | + | 0.803518i | \(0.297041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.5739 | −0.717133 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.48671 | 0.164160 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.4138 | 0.417051 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.5238 | −1.88013 | −0.940065 | − | 0.340994i | \(-0.889236\pi\) | ||||
−0.940065 | + | 0.340994i | \(0.889236\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.86119 | −0.140709 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.8464 | 0.795070 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0031 | 0.872409 | 0.436205 | − | 0.899848i | \(-0.356322\pi\) | ||||
0.436205 | + | 0.899848i | \(0.356322\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.57105 | −0.129621 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.1063 | −0.402605 | −0.201302 | − | 0.979529i | \(-0.564517\pi\) | ||||
−0.201302 | + | 0.979529i | \(0.564517\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.3973 | −1.49868 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.3970 | 0.592835 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.16257 | −0.294733 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.5474 | 1.10157 | 0.550784 | − | 0.834648i | \(-0.314329\pi\) | ||||
0.550784 | + | 0.834648i | \(0.314329\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.1469 | 0.725573 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.2240 | −1.26692 | −0.633460 | − | 0.773775i | \(-0.718366\pi\) | ||||
−0.633460 | + | 0.773775i | \(0.718366\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.2650 | 0.943465 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.1252 | 0.614362 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.29312 | −0.225474 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.2282 | −1.97622 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −59.0903 | −2.10902 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.36305 | −0.298111 | −0.149055 | − | 0.988829i | \(-0.547623\pi\) | ||||
−0.149055 | + | 0.988829i | \(0.547623\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.1602 | 1.14493 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.357454 | −0.0127096 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.24210 | −0.150642 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.801505 | −0.0284264 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.6446 | −1.40429 | −0.702143 | − | 0.712036i | \(-0.747773\pi\) | ||||
−0.702143 | + | 0.712036i | \(0.747773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.3405 | 1.21488 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.32038 | 0.258653 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.4511 | 1.92154 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.0082 | −0.387988 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.6391 | 0.374514 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.856343 | 0.0301074 | 0.0150537 | − | 0.999887i | \(-0.495208\pi\) | ||||
0.0150537 | + | 0.999887i | \(0.495208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.9984 | −1.22896 | −0.614480 | − | 0.788932i | \(-0.710634\pi\) | ||||
−0.614480 | + | 0.788932i | \(0.710634\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.40339 | 0.189505 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −43.9597 | −1.53984 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.6752 | 0.688346 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.99579 | 0.139624 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.38652 | −0.222891 | −0.111445 | − | 0.993771i | \(-0.535548\pi\) | ||||
−0.111445 | + | 0.993771i | \(0.535548\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.71924 | −0.199360 | −0.0996802 | − | 0.995020i | \(-0.531782\pi\) | ||||
−0.0996802 | + | 0.995020i | \(0.531782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.6650 | −0.545384 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.17831 | 0.284388 | 0.142194 | − | 0.989839i | \(-0.454584\pi\) | ||||
0.142194 | + | 0.989839i | \(0.454584\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.1778 | 1.15231 | 0.576156 | − | 0.817340i | \(-0.304552\pi\) | ||||
0.576156 | + | 0.817340i | \(0.304552\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.0246 | 0.590576 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.6290 | −1.09588 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.0483 | 0.589982 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.98746 | −0.206957 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5616 | 0.778914 | 0.389457 | − | 0.921045i | \(-0.372663\pi\) | ||||
0.389457 | + | 0.921045i | \(0.372663\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.47389 | −0.0852052 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.0398 | 1.23981 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.29632 | 0.216344 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.6982 | −0.641722 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.76622 | −0.163384 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.1924 | 0.520177 | 0.260088 | − | 0.965585i | \(-0.416248\pi\) | ||||
0.260088 | + | 0.965585i | \(0.416248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.11693 | 0.174995 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.28683 | 0.214754 | 0.107377 | − | 0.994218i | \(-0.465755\pi\) | ||||
0.107377 | + | 0.994218i | \(0.465755\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.15460 | 0.312351 | 0.156175 | − | 0.987729i | \(-0.450083\pi\) | ||||
0.156175 | + | 0.987729i | \(0.450083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.5386 | −0.461393 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.4016 | −1.20508 | −0.602542 | − | 0.798087i | \(-0.705845\pi\) | ||||
−0.602542 | + | 0.798087i | \(0.705845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.15916 | −0.277420 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.6429 | −0.395415 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.5227 | 1.71386 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.236433 | −0.00801122 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.66075 | 0.191587 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.75179 | 0.228252 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.5745 | −1.53894 | −0.769471 | − | 0.638682i | \(-0.779480\pi\) | ||||
−0.769471 | + | 0.638682i | \(0.779480\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.6458 | 0.662638 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.80769 | −0.128284 | −0.0641422 | − | 0.997941i | \(-0.520431\pi\) | ||||
−0.0641422 | + | 0.997941i | \(0.520431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.1228 | −1.68677 | −0.843384 | − | 0.537312i | \(-0.819440\pi\) | ||||
−0.843384 | + | 0.537312i | \(0.819440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.4875 | −0.755908 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.2728 | 0.982884 | 0.491442 | − | 0.870910i | \(-0.336470\pi\) | ||||
0.491442 | + | 0.870910i | \(0.336470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8849 | 0.566302 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.57105 | 0.119635 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.7165 | 0.358613 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.4332 | 0.582727 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.11209 | −0.0371318 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.98746 | −0.199693 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.40010 | 0.0466441 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42.3277 | 1.40858 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.5643 | 0.716823 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0482385 | 0.00160173 | 0.000800866 | − | 1.00000i | \(-0.499745\pi\) | ||||
0.000800866 | 1.00000i | \(0.499745\pi\) | ||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0231709 | −0.000768529 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −59.2456 | −1.96289 | −0.981447 | − | 0.191734i | \(-0.938589\pi\) | ||||
−0.981447 | + | 0.191734i | \(0.938589\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0223 | 0.530259 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.6868 | −0.386353 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −54.6888 | −1.80598 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.5343 | 1.07321 | 0.536604 | − | 0.843834i | \(-0.319707\pi\) | ||||
0.536604 | + | 0.843834i | \(0.319707\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.5654 | 0.414043 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.1992 | −0.566118 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.9078 | −0.687443 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.51046 | −0.180987 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.1472 | 1.21876 | 0.609380 | − | 0.792878i | \(-0.291418\pi\) | ||||
0.609380 | + | 0.792878i | \(0.291418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.87030 | −0.323486 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.0036 | 0.360240 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 58.5544 | 1.91493 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.3829 | −0.437199 | −0.218599 | − | 0.975815i | \(-0.570149\pi\) | ||||
−0.218599 | + | 0.975815i | \(0.570149\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.4938 | −0.505622 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.67507 | 0.119804 | 0.0599019 | − | 0.998204i | \(-0.480921\pi\) | ||||
0.0599019 | + | 0.998204i | \(0.480921\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.76801 | 0.122703 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.0082 | 0.358097 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.2302 | 0.494916 | 0.247458 | − | 0.968899i | \(-0.420405\pi\) | ||||
0.247458 | + | 0.968899i | \(0.420405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.9571 | 0.550452 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.06492 | −0.131814 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.3029 | 0.754855 | 0.377428 | − | 0.926039i | \(-0.376809\pi\) | ||||
0.377428 | + | 0.926039i | \(0.376809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 66.6326 | 2.15618 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.57105 | 0.115436 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −57.0817 | −1.84327 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.84972 | 0.156442 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.17665 | 0.102366 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.9670 | −0.449614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.5543 | −1.23982 | −0.619911 | − | 0.784672i | \(-0.712831\pi\) | ||||
−0.619911 | + | 0.784672i | \(0.712831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.93846 | −0.287145 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.9412 | 1.50642 | 0.753208 | − | 0.657782i | \(-0.228505\pi\) | ||||
0.753208 | + | 0.657782i | \(0.228505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.5800 | −0.531532 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.87838 | −0.156233 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.4403 | −0.525973 | −0.262986 | − | 0.964800i | \(-0.584707\pi\) | ||||
−0.262986 | + | 0.964800i | \(0.584707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.1414 | 0.835483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.5216 | −0.367856 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.4253 | 0.460095 | 0.230048 | − | 0.973179i | \(-0.426112\pi\) | ||||
0.230048 | + | 0.973179i | \(0.426112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.42468 | −0.268433 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.0547 | 0.733838 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.7805 | −0.374599 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.6353 | 0.973162 | 0.486581 | − | 0.873635i | \(-0.338244\pi\) | ||||
0.486581 | + | 0.873635i | \(0.338244\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.8554 | 0.471420 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −74.7334 | −2.36921 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.4323 | 1.28051 | 0.640253 | − | 0.768164i | \(-0.278830\pi\) | ||||
0.640253 | + | 0.768164i | \(0.278830\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.76622 | 0.150797 |
(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.g.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.g.1.3 | ✓ | 12 | 1.1 | even | 1 | trivial |