Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.284897.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 5x^{2} + 10x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80442\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(5\) | −3.40664 | −1.52349 | −0.761747 | − | 0.647875i | \(-0.775658\pi\) | ||||
−0.761747 | + | 0.647875i | \(0.775658\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.548479 | 0.207306 | 0.103653 | − | 0.994614i | \(-0.466947\pi\) | ||||
0.103653 | + | 0.994614i | \(0.466947\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.977163 | −0.294626 | −0.147313 | − | 0.989090i | \(-0.547062\pi\) | ||||
−0.147313 | + | 0.989090i | \(0.547062\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.94627 | −0.539797 | −0.269899 | − | 0.962889i | \(-0.586990\pi\) | ||||
−0.269899 | + | 0.962889i | \(0.586990\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.40664 | −0.879590 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.38380 | 0.335621 | 0.167810 | − | 0.985819i | \(-0.446330\pi\) | ||||
0.167810 | + | 0.985819i | \(0.446330\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.16100 | −0.266352 | −0.133176 | − | 0.991092i | \(-0.542518\pi\) | ||||
−0.133176 | + | 0.991092i | \(0.542518\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.548479 | 0.119688 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.44417 | 0.926673 | 0.463336 | − | 0.886182i | \(-0.346652\pi\) | ||||
0.463336 | + | 0.886182i | \(0.346652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.60517 | 1.32103 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.71999 | 0.690785 | 0.345393 | − | 0.938458i | \(-0.387746\pi\) | ||||
0.345393 | + | 0.938458i | \(0.387746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46700 | 0.981903 | 0.490951 | − | 0.871187i | \(-0.336649\pi\) | ||||
0.490951 | + | 0.871187i | \(0.336649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.977163 | −0.170102 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.86847 | −0.315829 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.93026 | −0.481732 | −0.240866 | − | 0.970558i | \(-0.577431\pi\) | ||||
−0.240866 | + | 0.970558i | \(0.577431\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.94627 | −0.311652 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.35002 | 0.991706 | 0.495853 | − | 0.868407i | \(-0.334856\pi\) | ||||
0.495853 | + | 0.868407i | \(0.334856\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.3309 | −1.72794 | −0.863970 | − | 0.503544i | \(-0.832029\pi\) | ||||
−0.863970 | + | 0.503544i | \(0.832029\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.40664 | −0.507831 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.2154 | 1.49008 | 0.745038 | − | 0.667022i | \(-0.232431\pi\) | ||||
0.745038 | + | 0.667022i | \(0.232431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.69917 | −0.957024 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.38380 | 0.193771 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.23512 | 0.444378 | 0.222189 | − | 0.975004i | \(-0.428680\pi\) | ||||
0.222189 | + | 0.975004i | \(0.428680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.32884 | 0.448860 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.16100 | −0.153779 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.8823 | −1.67713 | −0.838566 | − | 0.544800i | \(-0.816605\pi\) | ||||
−0.838566 | + | 0.544800i | \(0.816605\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.9043 | −1.90831 | −0.954153 | − | 0.299321i | \(-0.903240\pi\) | ||||
−0.954153 | + | 0.299321i | \(0.903240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.548479 | 0.0691019 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.63022 | 0.822378 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.2508 | −1.86318 | −0.931591 | − | 0.363508i | \(-0.881579\pi\) | ||||
−0.931591 | + | 0.363508i | \(0.881579\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.44417 | 0.535015 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4987 | −1.36464 | −0.682322 | − | 0.731052i | \(-0.739030\pi\) | ||||
−0.682322 | + | 0.731052i | \(0.739030\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.389926 | −0.0456373 | −0.0228187 | − | 0.999740i | \(-0.507264\pi\) | ||||
−0.0228187 | + | 0.999740i | \(0.507264\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.60517 | 0.762699 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.535953 | −0.0610776 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.1425 | −1.14113 | −0.570563 | − | 0.821254i | \(-0.693275\pi\) | ||||
−0.570563 | + | 0.821254i | \(0.693275\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.41931 | −0.594847 | −0.297423 | − | 0.954746i | \(-0.596127\pi\) | ||||
−0.297423 | + | 0.954746i | \(0.596127\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.71410 | −0.511316 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.71999 | 0.398825 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.1536 | −1.81828 | −0.909142 | − | 0.416487i | \(-0.863261\pi\) | ||||
−0.909142 | + | 0.416487i | \(0.863261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.06749 | −0.111903 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.46700 | 0.566902 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.95512 | 0.405786 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.62873 | −0.266907 | −0.133453 | − | 0.991055i | \(-0.542607\pi\) | ||||
−0.133453 | + | 0.991055i | \(0.542607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.977163 | −0.0982086 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7613 | 1.07079 | 0.535393 | − | 0.844603i | \(-0.320163\pi\) | ||||
0.535393 | + | 0.844603i | \(0.320163\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.545324 | 0.0537323 | 0.0268662 | − | 0.999639i | \(-0.491447\pi\) | ||||
0.0268662 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.86847 | −0.182344 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2316 | −1.18248 | −0.591239 | − | 0.806496i | \(-0.701361\pi\) | ||||
−0.591239 | + | 0.806496i | \(0.701361\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.42284 | 0.327848 | 0.163924 | − | 0.986473i | \(-0.447585\pi\) | ||||
0.163924 | + | 0.986473i | \(0.447585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.93026 | −0.278128 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.9535 | 1.12449 | 0.562243 | − | 0.826972i | \(-0.309938\pi\) | ||||
0.562243 | + | 0.826972i | \(0.309938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.1397 | −1.41178 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.94627 | −0.179932 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.758985 | 0.0695760 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0452 | −0.913196 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.35002 | 0.572562 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.46823 | −0.489093 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.62801 | −0.321934 | −0.160967 | − | 0.986960i | \(-0.551461\pi\) | ||||
−0.160967 | + | 0.986960i | \(0.551461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.3309 | −0.997626 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.01253 | 0.525317 | 0.262658 | − | 0.964889i | \(-0.415401\pi\) | ||||
0.262658 | + | 0.964889i | \(0.415401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.636786 | −0.0552163 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.40664 | −0.293197 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.87068 | −0.330695 | −0.165347 | − | 0.986235i | \(-0.552875\pi\) | ||||
−0.165347 | + | 0.986235i | \(0.552875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.82501 | 0.494071 | 0.247035 | − | 0.969006i | \(-0.420544\pi\) | ||||
0.247035 | + | 0.969006i | \(0.420544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2154 | 0.860295 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.90182 | 0.159038 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.6727 | −1.05241 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.69917 | −0.552538 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.1095 | 1.15589 | 0.577947 | − | 0.816074i | \(-0.303854\pi\) | ||||
0.577947 | + | 0.816074i | \(0.303854\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.7002 | 1.68456 | 0.842278 | − | 0.539043i | \(-0.181214\pi\) | ||||
0.842278 | + | 0.539043i | \(0.181214\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.38380 | 0.111874 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.6241 | −1.49592 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.25155 | 0.498928 | 0.249464 | − | 0.968384i | \(-0.419746\pi\) | ||||
0.249464 | + | 0.968384i | \(0.419746\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.23512 | 0.256562 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.43753 | 0.192104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3332 | 0.809360 | 0.404680 | − | 0.914458i | \(-0.367383\pi\) | ||||
0.404680 | + | 0.914458i | \(0.367383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.32884 | 0.259150 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.21205 | −0.708619 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.16100 | −0.0887841 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.48522 | −0.341005 | −0.170503 | − | 0.985357i | \(-0.554539\pi\) | ||||
−0.170503 | + | 0.985357i | \(0.554539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.62280 | 0.273858 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.8823 | −0.968292 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.1276 | 1.50441 | 0.752205 | − | 0.658929i | \(-0.228990\pi\) | ||||
0.752205 | + | 0.658929i | \(0.228990\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.5001 | −1.67242 | −0.836210 | − | 0.548409i | \(-0.815234\pi\) | ||||
−0.836210 | + | 0.548409i | \(0.815234\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.9043 | −1.10176 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.98233 | 0.733916 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.35220 | −0.0988824 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.548479 | 0.0398960 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.9408 | −0.791651 | −0.395826 | − | 0.918326i | \(-0.629542\pi\) | ||||
−0.395826 | + | 0.918326i | \(0.629542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.36096 | 0.313909 | 0.156954 | − | 0.987606i | \(-0.449832\pi\) | ||||
0.156954 | + | 0.987606i | \(0.449832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.63022 | 0.474800 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.29648 | −0.519853 | −0.259926 | − | 0.965628i | \(-0.583698\pi\) | ||||
−0.259926 | + | 0.965628i | \(0.583698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7900 | −1.61554 | −0.807770 | − | 0.589498i | \(-0.799325\pi\) | ||||
−0.807770 | + | 0.589498i | \(0.799325\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.2508 | −1.07571 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.04034 | 0.143204 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.6322 | −1.51086 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.44417 | 0.308891 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.13449 | 0.0784743 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3625 | −1.60834 | −0.804169 | − | 0.594401i | \(-0.797389\pi\) | ||||
−0.804169 | + | 0.594401i | \(0.797389\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4987 | −0.787877 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 38.6001 | 2.63251 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.99854 | 0.203554 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.389926 | −0.0263487 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.69324 | −0.181167 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.93666 | 0.196653 | 0.0983267 | − | 0.995154i | \(-0.468651\pi\) | ||||
0.0983267 | + | 0.995154i | \(0.468651\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.60517 | 0.440345 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.3110 | −1.34809 | −0.674045 | − | 0.738690i | \(-0.735445\pi\) | ||||
−0.674045 | + | 0.738690i | \(0.735445\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.90723 | 0.258197 | 0.129098 | − | 0.991632i | \(-0.458792\pi\) | ||||
0.129098 | + | 0.991632i | \(0.458792\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.535953 | −0.0352631 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.0582 | −1.70713 | −0.853564 | − | 0.520988i | \(-0.825564\pi\) | ||||
−0.853564 | + | 0.520988i | \(0.825564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.8003 | −2.27012 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.1425 | −0.658829 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.1406 | 1.43216 | 0.716080 | − | 0.698018i | \(-0.245935\pi\) | ||||
0.716080 | + | 0.698018i | \(0.245935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5932 | −1.26211 | −0.631053 | − | 0.775740i | \(-0.717377\pi\) | ||||
−0.631053 | + | 0.775740i | \(0.717377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.8216 | 1.45802 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.25962 | 0.143776 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.41931 | −0.343435 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5771 | 0.856978 | 0.428489 | − | 0.903547i | \(-0.359046\pi\) | ||||
0.428489 | + | 0.903547i | \(0.359046\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.34268 | −0.273022 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.71410 | −0.295208 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.8735 | −1.23968 | −0.619838 | − | 0.784730i | \(-0.712802\pi\) | ||||
−0.619838 | + | 0.784730i | \(0.712802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.60719 | −0.0998657 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.71999 | 0.230262 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.8907 | −1.22651 | −0.613257 | − | 0.789884i | \(-0.710141\pi\) | ||||
−0.613257 | + | 0.789884i | \(0.710141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0209 | −0.677008 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.1536 | −1.04979 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4649 | 0.820972 | 0.410486 | − | 0.911867i | \(-0.365359\pi\) | ||||
0.410486 | + | 0.911867i | \(0.365359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3536 | 1.29714 | 0.648570 | − | 0.761155i | \(-0.275368\pi\) | ||||
0.648570 | + | 0.761155i | \(0.275368\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.06749 | −0.0646072 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.45433 | −0.389211 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.62547 | 0.338002 | 0.169001 | − | 0.985616i | \(-0.445946\pi\) | ||||
0.169001 | + | 0.985616i | \(0.445946\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.46700 | 0.327301 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.1233 | −0.723216 | −0.361608 | − | 0.932330i | \(-0.617772\pi\) | ||||
−0.361608 | + | 0.932330i | \(0.617772\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.83994 | −0.168817 | −0.0844084 | − | 0.996431i | \(-0.526900\pi\) | ||||
−0.0844084 | + | 0.996431i | \(0.526900\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.95512 | 0.234281 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.48285 | 0.205586 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0851 | −0.887359 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.62873 | −0.154099 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.8412 | −1.04229 | −0.521147 | − | 0.853467i | \(-0.674496\pi\) | ||||
−0.521147 | + | 0.853467i | \(0.674496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 43.8853 | 2.55510 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.977163 | −0.0567007 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.64953 | −0.500215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.21474 | −0.358211 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.7613 | 0.618219 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 50.7737 | 2.90729 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.9879 | 1.02662 | 0.513311 | − | 0.858203i | \(-0.328419\pi\) | ||||
0.513311 | + | 0.858203i | \(0.328419\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.545324 | 0.0310224 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.91959 | −0.505783 | −0.252892 | − | 0.967495i | \(-0.581382\pi\) | ||||
−0.252892 | + | 0.967495i | \(0.581382\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.72295 | 0.210434 | 0.105217 | − | 0.994449i | \(-0.466446\pi\) | ||||
0.105217 | + | 0.994449i | \(0.466446\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.86847 | −0.105276 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.1341 | −0.962348 | −0.481174 | − | 0.876625i | \(-0.659790\pi\) | ||||
−0.481174 | + | 0.876625i | \(0.659790\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.63504 | −0.203523 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2316 | −0.682704 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.60660 | −0.0893933 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.8554 | −0.713090 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.42284 | 0.189283 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.60296 | 0.308901 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 36.3810 | 1.99968 | 0.999839 | − | 0.0179188i | \(-0.00570404\pi\) | ||||
0.999839 | + | 0.0179188i | \(0.00570404\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.93026 | −0.160577 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 51.9539 | 2.83855 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.6702 | 0.853612 | 0.426806 | − | 0.904343i | \(-0.359639\pi\) | ||||
0.426806 | + | 0.904343i | \(0.359639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.9535 | 0.649223 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.34215 | −0.289294 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.51371 | −0.405702 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.1397 | −0.815092 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.96072 | 0.212623 | 0.106311 | − | 0.994333i | \(-0.466096\pi\) | ||||
0.106311 | + | 0.994333i | \(0.466096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.7431 | −0.575066 | −0.287533 | − | 0.957771i | \(-0.592835\pi\) | ||||
−0.287533 | + | 0.957771i | \(0.592835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.94627 | −0.103884 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.7105 | 0.782961 | 0.391480 | − | 0.920186i | \(-0.371963\pi\) | ||||
0.391480 | + | 0.920186i | \(0.371963\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.1719 | 2.07903 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.758985 | 0.0401697 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.3440 | −0.651490 | −0.325745 | − | 0.945458i | \(-0.605615\pi\) | ||||
−0.325745 | + | 0.945458i | \(0.605615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6521 | −0.929056 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0452 | −0.527234 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.32833 | 0.0695282 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.3455 | 1.11422 | 0.557112 | − | 0.830437i | \(-0.311909\pi\) | ||||
0.557112 | + | 0.830437i | \(0.311909\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.35002 | 0.330569 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.77440 | 0.0921221 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.0396748 | −0.00205428 | −0.00102714 | − | 0.999999i | \(-0.500327\pi\) | ||||
−0.00102714 | + | 0.999999i | \(0.500327\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.46823 | −0.282378 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.24009 | −0.372884 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.2798 | 1.60673 | 0.803367 | − | 0.595485i | \(-0.203040\pi\) | ||||
0.803367 | + | 0.595485i | \(0.203040\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.62801 | −0.185868 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.7930 | −0.960277 | −0.480139 | − | 0.877193i | \(-0.659414\pi\) | ||||
−0.480139 | + | 0.877193i | \(0.659414\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.82580 | 0.0930513 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.3309 | −0.575980 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.3125 | −1.73971 | −0.869856 | − | 0.493306i | \(-0.835788\pi\) | ||||
−0.869856 | + | 0.493306i | \(0.835788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.14983 | 0.311011 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.01253 | 0.303292 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.5520 | 1.73850 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.8147 | −0.843903 | −0.421952 | − | 0.906618i | \(-0.638655\pi\) | ||||
−0.421952 | + | 0.906618i | \(0.638655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.636786 | −0.0318792 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.8464 | 1.88996 | 0.944980 | − | 0.327129i | \(-0.106081\pi\) | ||||
0.944980 | + | 0.327129i | \(0.106081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.6402 | −0.530028 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.40664 | −0.169277 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.86334 | 0.141931 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.8406 | −1.17884 | −0.589422 | − | 0.807825i | \(-0.700644\pi\) | ||||
−0.589422 | + | 0.807825i | \(0.700644\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.87068 | −0.190927 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.06567 | −0.347679 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.4616 | 0.906246 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.82501 | 0.285252 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.1953 | −1.27972 | −0.639862 | − | 0.768490i | \(-0.721008\pi\) | ||||
−0.639862 | + | 0.768490i | \(0.721008\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.289799 | −0.0141239 | −0.00706196 | − | 0.999975i | \(-0.502248\pi\) | ||||
−0.00706196 | + | 0.999975i | \(0.502248\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.2154 | 0.496692 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.14023 | 0.443366 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.17472 | −0.395602 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.90182 | 0.0918207 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.1155 | 0.776258 | 0.388129 | − | 0.921605i | \(-0.373122\pi\) | ||||
0.388129 | + | 0.921605i | \(0.373122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.0680 | 0.579949 | 0.289974 | − | 0.957034i | \(-0.406353\pi\) | ||||
0.289974 | + | 0.957034i | \(0.406353\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6727 | −0.607607 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.15969 | −0.246822 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5088 | −0.501560 | −0.250780 | − | 0.968044i | \(-0.580687\pi\) | ||||
−0.250780 | + | 0.968044i | \(0.580687\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.69917 | −0.319008 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.8417 | −0.942708 | −0.471354 | − | 0.881944i | \(-0.656235\pi\) | ||||
−0.471354 | + | 0.881944i | \(0.656235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 58.4362 | 2.77014 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.1095 | 0.667356 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.0031 | −0.755234 | −0.377617 | − | 0.925962i | \(-0.623256\pi\) | ||||
−0.377617 | + | 0.925962i | \(0.623256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.20500 | −0.292182 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.7002 | 0.972579 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.63654 | 0.170484 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.4461 | 1.09676 | 0.548381 | − | 0.836228i | \(-0.315244\pi\) | ||||
0.548381 | + | 0.836228i | \(0.315244\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.38380 | 0.0645902 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6649 | 1.14876 | 0.574379 | − | 0.818590i | \(-0.305244\pi\) | ||||
0.574379 | + | 0.818590i | \(0.305244\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.63528 | −0.122472 | −0.0612359 | − | 0.998123i | \(-0.519504\pi\) | ||||
−0.0612359 | + | 0.998123i | \(0.519504\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.6241 | −0.863672 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7325 | −0.542917 | −0.271459 | − | 0.962450i | \(-0.587506\pi\) | ||||
−0.271459 | + | 0.962450i | \(0.587506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.36475 | −0.386248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.25155 | 0.288056 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0721 | 0.509095 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.66862 | −0.351861 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.23512 | 0.148126 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.1101 | 1.19300 | 0.596501 | − | 0.802612i | \(-0.296557\pi\) | ||||
0.596501 | + | 0.802612i | \(0.296557\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.70307 | 0.260038 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.43753 | 0.110912 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.95512 | 0.406631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.1754 | 1.32206 | 0.661032 | − | 0.750358i | \(-0.270119\pi\) | ||||
0.661032 | + | 0.750358i | \(0.270119\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.3332 | 0.467284 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.31324 | 0.375171 | 0.187586 | − | 0.982248i | \(-0.439934\pi\) | ||||
0.187586 | + | 0.982248i | \(0.439934\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.14772 | 0.231842 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.32884 | 0.149620 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.30679 | −0.282898 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.0939 | 1.48148 | 0.740742 | − | 0.671789i | \(-0.234474\pi\) | ||||
0.740742 | + | 0.671789i | \(0.234474\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.4327 | −1.00022 | −0.500112 | − | 0.865961i | \(-0.666708\pi\) | ||||
−0.500112 | + | 0.865961i | \(0.666708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.6597 | −1.63134 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.21205 | −0.409121 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.47758 | 0.331438 | 0.165719 | − | 0.986173i | \(-0.447006\pi\) | ||||
0.165719 | + | 0.986173i | \(0.447006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.213866 | −0.00946088 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.16100 | −0.0512595 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.85772 | −0.0818609 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.98215 | −0.439014 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.48522 | −0.196879 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.51154 | −0.197654 | −0.0988271 | − | 0.995105i | \(-0.531509\pi\) | ||||
−0.0988271 | + | 0.995105i | \(0.531509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.9098 | 1.22041 | 0.610206 | − | 0.792243i | \(-0.291087\pi\) | ||||
0.610206 | + | 0.792243i | \(0.291087\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.62280 | 0.158112 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.56524 | 0.329547 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.24938 | −0.141277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8823 | −0.559044 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.3588 | −0.535320 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41.6688 | 1.80150 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.1276 | 0.868572 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.54618 | 0.281964 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.7584 | −1.23642 | −0.618211 | − | 0.786012i | \(-0.712142\pi\) | ||||
−0.618211 | + | 0.786012i | \(0.712142\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.5001 | −0.965572 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.6604 | −0.499475 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.8889 | −0.978659 | −0.489330 | − | 0.872099i | \(-0.662758\pi\) | ||||
−0.489330 | + | 0.872099i | \(0.662758\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.9043 | −0.636102 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.31892 | −0.183992 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.56298 | −0.236562 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.98233 | 0.423727 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.8344 | 1.77258 | 0.886291 | − | 0.463129i | \(-0.153273\pi\) | ||||
0.886291 | + | 0.463129i | \(0.153273\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.0529 | 0.932737 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.35220 | −0.0570898 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.9234 | 1.42970 | 0.714851 | − | 0.699277i | \(-0.246495\pi\) | ||||
0.714851 | + | 0.699277i | \(0.246495\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.7211 | −1.71315 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.548479 | 0.0230340 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.0510 | −1.09212 | −0.546058 | − | 0.837747i | \(-0.683872\pi\) | ||||
−0.546058 | + | 0.837747i | \(0.683872\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.91990 | −0.164043 | −0.0820214 | − | 0.996631i | \(-0.526138\pi\) | ||||
−0.0820214 | + | 0.996631i | \(0.526138\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.9408 | −0.457060 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.3545 | 1.22417 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.8384 | −1.28382 | −0.641910 | − | 0.766780i | \(-0.721858\pi\) | ||||
−0.641910 | + | 0.766780i | \(0.721858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.36096 | 0.181235 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.97238 | −0.123315 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.16124 | −0.130925 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.63022 | 0.274126 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.0392 | 1.36367 | 0.681837 | − | 0.731504i | \(-0.261181\pi\) | ||||
0.681837 | + | 0.731504i | \(0.261181\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.34721 | −0.261532 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.29648 | −0.300137 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.8895 | −1.63807 | −0.819033 | − | 0.573747i | \(-0.805489\pi\) | ||||
−0.819033 | + | 0.573747i | \(0.805489\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.58559 | −0.105999 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.7900 | −0.932732 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.18551 | 0.293592 | 0.146796 | − | 0.989167i | \(-0.453104\pi\) | ||||
0.146796 | + | 0.989167i | \(0.453104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6866 | −0.517499 | −0.258749 | − | 0.965944i | \(-0.583310\pi\) | ||||
−0.258749 | + | 0.965944i | \(0.583310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.2508 | −0.621061 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.2202 | 1.39125 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.5231 | −1.03595 | −0.517975 | − | 0.855396i | \(-0.673314\pi\) | ||||
−0.517975 | + | 0.855396i | \(0.673314\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.04034 | 0.0826786 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.8820 | −0.804339 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.66709 | 0.350060 | 0.175030 | − | 0.984563i | \(-0.443998\pi\) | ||||
0.175030 | + | 0.984563i | \(0.443998\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.6322 | −0.872294 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.3383 | 1.66422 | 0.832109 | − | 0.554613i | \(-0.187134\pi\) | ||||
0.832109 | + | 0.554613i | \(0.187134\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.59969 | −0.225071 | −0.112535 | − | 0.993648i | \(-0.535897\pi\) | ||||
−0.112535 | + | 0.993648i | \(0.535897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.44417 | 0.178338 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.40842 | −0.376940 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.3976 | −0.575903 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.13449 | 0.0453071 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.05489 | −0.161679 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.900479 | 0.0358475 | 0.0179237 | − | 0.999839i | \(-0.494294\pi\) | ||||
0.0179237 | + | 0.999839i | \(0.494294\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.3625 | −0.928574 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.3593 | 0.490464 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.0384 | 0.516599 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.4987 | −0.454881 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.5091 | 0.691567 | 0.345783 | − | 0.938314i | \(-0.387613\pi\) | ||||
0.345783 | + | 0.938314i | \(0.387613\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.47894 | −0.137196 | −0.0685980 | − | 0.997644i | \(-0.521853\pi\) | ||||
−0.0685980 | + | 0.997644i | \(0.521853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.6001 | 1.51988 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.60160 | 0.377478 | 0.188739 | − | 0.982027i | \(-0.439560\pi\) | ||||
0.188739 | + | 0.982027i | \(0.439560\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.5881 | 0.494126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.99854 | 0.117522 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.8659 | 0.620879 | 0.310440 | − | 0.950593i | \(-0.399524\pi\) | ||||
0.310440 | + | 0.950593i | \(0.399524\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.4825 | −0.800317 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.389926 | −0.0152124 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.2593 | −0.945008 | −0.472504 | − | 0.881328i | \(-0.656650\pi\) | ||||
−0.472504 | + | 0.881328i | \(0.656650\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.6372 | 0.919381 | 0.459690 | − | 0.888079i | \(-0.347960\pi\) | ||||
0.459690 | + | 0.888079i | \(0.347960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.69324 | −0.104597 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.16930 | 0.0841218 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.5323 | 0.640132 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.93666 | 0.113538 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.5640 | 0.562236 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.6912 | 1.45289 | 0.726445 | − | 0.687224i | \(-0.241171\pi\) | ||||
0.726445 | + | 0.687224i | \(0.241171\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.60517 | 0.254233 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.7588 | −1.45119 | −0.725594 | − | 0.688123i | \(-0.758435\pi\) | ||||
−0.725594 | + | 0.688123i | \(0.758435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.44180 | −0.0553313 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.3110 | −0.778320 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.5037 | 0.937608 | 0.468804 | − | 0.883302i | \(-0.344685\pi\) | ||||
0.468804 | + | 0.883302i | \(0.344685\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.1860 | 0.503811 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.90723 | 0.149070 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.29641 | −0.239874 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.7858 | −1.32331 | −0.661657 | − | 0.749807i | \(-0.730146\pi\) | ||||
−0.661657 | + | 0.749807i | \(0.730146\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.535953 | −0.0203592 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.8437 | −0.752714 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.78715 | 0.332837 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.0582 | −0.985611 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.1262 | −0.533540 | −0.266770 | − | 0.963760i | \(-0.585956\pi\) | ||||
−0.266770 | + | 0.963760i | \(0.585956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.40204 | 0.128310 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.8003 | −1.31065 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.90233 | 0.221980 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.3280 | −1.17655 | −0.588275 | − | 0.808661i | \(-0.700193\pi\) | ||||
−0.588275 | + | 0.808661i | \(0.700193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.1425 | −0.380375 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.2963 | 0.909903 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.47881 | −0.242294 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.1406 | 0.826858 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.1522 | 0.490494 | 0.245247 | − | 0.969461i | \(-0.421131\pi\) | ||||
0.245247 | + | 0.969461i | \(0.421131\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.299099 | 0.0111390 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.5932 | −0.728677 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.5712 | 0.912551 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.9706 | −1.63078 | −0.815390 | − | 0.578913i | \(-0.803477\pi\) | ||||
−0.815390 | + | 0.578913i | \(0.803477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.6796 | −0.579932 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.8792 | −1.10361 | −0.551806 | − | 0.833972i | \(-0.686061\pi\) | ||||
−0.551806 | + | 0.833972i | \(0.686061\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.8216 | 0.841789 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.9025 | 0.548941 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.1071 | 1.54894 | 0.774468 | − | 0.632613i | \(-0.218018\pi\) | ||||
0.774468 | + | 0.632613i | \(0.218018\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.25962 | 0.0830093 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.40968 | 0.198462 | 0.0992310 | − | 0.995064i | \(-0.468362\pi\) | ||||
0.0992310 | + | 0.995064i | \(0.468362\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.0659 | −1.76100 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.41931 | −0.198282 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.70880 | −0.245134 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2028 | 0.883173 | 0.441587 | − | 0.897219i | \(-0.354416\pi\) | ||||
0.441587 | + | 0.897219i | \(0.354416\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.5771 | 0.494776 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −70.5180 | −2.56641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1230 | 0.404273 | 0.202137 | − | 0.979357i | \(-0.435212\pi\) | ||||
0.202137 | + | 0.979357i | \(0.435212\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.34268 | −0.157629 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.2131 | 1.67522 | 0.837612 | − | 0.546266i | \(-0.183951\pi\) | ||||
0.837612 | + | 0.546266i | \(0.183951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.87736 | 0.0679648 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.71410 | −0.170439 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.0724 | 0.905311 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.85940 | −0.103113 | −0.0515563 | − | 0.998670i | \(-0.516418\pi\) | ||||
−0.0515563 | + | 0.998670i | \(0.516418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.8735 | −0.715727 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.3191 | −0.550991 | −0.275496 | − | 0.961302i | \(-0.588842\pi\) | ||||
−0.275496 | + | 0.961302i | \(0.588842\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.1105 | 1.29713 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.60719 | −0.0576575 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.37239 | −0.264143 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2361 | 0.402059 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.71999 | 0.132942 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.2968 | −0.760114 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.1474 | −0.789471 | −0.394735 | − | 0.918795i | \(-0.629164\pi\) | ||||
−0.394735 | + | 0.918795i | \(0.629164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.8907 | −0.708128 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.55622 | 0.233112 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.0078 | 1.03010 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.0209 | −0.390871 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.24008 | −0.114770 | −0.0573848 | − | 0.998352i | \(-0.518276\pi\) | ||||
−0.0573848 | + | 0.998352i | \(0.518276\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.1361 | 0.500100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.1536 | −0.606094 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.381021 | 0.0134459 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.30379 | −0.292670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.4649 | 0.473989 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.7561 | 0.378163 | 0.189081 | − | 0.981961i | \(-0.439449\pi\) | ||||
0.189081 | + | 0.981961i | \(0.439449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −56.3522 | −1.97879 | −0.989396 | − | 0.145241i | \(-0.953604\pi\) | ||||
−0.989396 | + | 0.145241i | \(0.953604\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.3536 | 0.748904 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.2015 | −1.23306 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.1552 | 0.460241 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.06749 | −0.0373010 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.76637 | −0.236148 | −0.118074 | − | 0.993005i | \(-0.537672\pi\) | ||||
−0.118074 | + | 0.993005i | \(0.537672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.4265 | 0.990886 | 0.495443 | − | 0.868640i | \(-0.335006\pi\) | ||||
0.495443 | + | 0.868640i | \(0.335006\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.45433 | −0.224711 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.3921 | 0.465689 | 0.232844 | − | 0.972514i | \(-0.425197\pi\) | ||||
0.232844 | + | 0.972514i | \(0.425197\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.5846 | 0.819126 | 0.409563 | − | 0.912282i | \(-0.365681\pi\) | ||||
0.409563 | + | 0.912282i | \(0.365681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.62547 | 0.195145 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.27031 | −0.321197 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.40664 | −0.117892 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.46700 | 0.188967 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.8349 | −0.857394 | −0.428697 | − | 0.903448i | \(-0.641027\pi\) | ||||
−0.428697 | + | 0.903448i | \(0.641027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.1617 | −0.522816 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1233 | −0.417549 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.3821 | 1.07958 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.50956 | −0.189311 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.83994 | −0.0974664 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.0226 | −0.446408 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.2493 | −0.522127 | −0.261063 | − | 0.965322i | \(-0.584073\pi\) | ||||
−0.261063 | + | 0.965322i | \(0.584073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.95512 | 0.135262 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00641 | 0.102697 | 0.0513485 | − | 0.998681i | \(-0.483648\pi\) | ||||
0.0513485 | + | 0.998681i | \(0.483648\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.7316 | 0.912070 | 0.456035 | − | 0.889962i | \(-0.349269\pi\) | ||||
0.456035 | + | 0.889962i | \(0.349269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.48285 | 0.118695 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.1526 | 0.549839 | 0.274920 | − | 0.961467i | \(-0.411349\pi\) | ||||
0.274920 | + | 0.961467i | \(0.411349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.2795 | 0.519519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.0851 | −0.512317 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.91092 | 0.336205 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.6821 | 1.00574 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.62873 | −0.0889689 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.99921 | −0.101392 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.9473 | 1.78790 | 0.893952 | − | 0.448162i | \(-0.147921\pi\) | ||||
0.893952 | + | 0.448162i | \(0.147921\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.8412 | −0.601769 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.3111 | −1.42550 | −0.712749 | − | 0.701420i | \(-0.752550\pi\) | ||||
−0.712749 | + | 0.701420i | \(0.752550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.9912 | 0.740063 | 0.370032 | − | 0.929019i | \(-0.379347\pi\) | ||||
0.370032 | + | 0.929019i | \(0.379347\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43.8853 | 1.47519 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.9683 | 1.10697 | 0.553483 | − | 0.832860i | \(-0.313298\pi\) | ||||
0.553483 | + | 0.832860i | \(0.313298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.98989 | −0.0667386 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.977163 | −0.0327362 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.8602 | −0.396885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −68.5676 | −2.29196 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.64953 | −0.288800 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.3372 | 0.678284 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.47676 | 0.149143 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.21474 | −0.206813 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 76.6497 | 2.54792 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.7799 | −0.689985 | −0.344992 | − | 0.938606i | \(-0.612118\pi\) | ||||
−0.344992 | + | 0.938606i | \(0.612118\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.7613 | 0.356929 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.6556 | −0.518694 | −0.259347 | − | 0.965784i | \(-0.583507\pi\) | ||||
−0.259347 | + | 0.965784i | \(0.583507\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.29555 | 0.175257 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 50.7737 | 1.67853 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.29774 | 0.108901 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9838 | 0.428296 | 0.214148 | − | 0.976801i | \(-0.431303\pi\) | ||||
0.214148 | + | 0.976801i | \(0.431303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.9879 | 0.592720 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.3795 | 0.736631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.3549 | −0.636384 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.545324 | 0.0179108 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.96973 | 0.0646246 | 0.0323123 | − | 0.999478i | \(-0.489713\pi\) | ||||
0.0323123 | + | 0.999478i | \(0.489713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.77776 | 0.254906 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.91959 | −0.292014 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.60644 | 0.150647 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.8351 | −1.43203 | −0.716016 | − | 0.698084i | \(-0.754036\pi\) | ||||
−0.716016 | + | 0.698084i | \(0.754036\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.72295 | 0.121494 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.35649 | −0.174617 | −0.0873083 | − | 0.996181i | \(-0.527827\pi\) | ||||
−0.0873083 | + | 0.996181i | \(0.527827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.2205 | 0.918987 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.86847 | −0.0607813 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.7424 | −1.19397 | −0.596985 | − | 0.802253i | \(-0.703635\pi\) | ||||
−0.596985 | + | 0.802253i | \(0.703635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.758899 | 0.0246349 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.1341 | −0.555612 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.0794 | 0.682828 | 0.341414 | − | 0.939913i | \(-0.389094\pi\) | ||||
0.341414 | + | 0.939913i | \(0.389094\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.2715 | 1.20608 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.63504 | −0.117504 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.12299 | −0.0685549 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.11186 | −0.0358666 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.2316 | −0.394159 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.8562 | −0.478238 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.90443 | −0.0934001 | −0.0467001 | − | 0.998909i | \(-0.514871\pi\) | ||||
−0.0467001 | + | 0.998909i | \(0.514871\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.60660 | −0.0516113 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.3856 | 1.10349 | 0.551743 | − | 0.834014i | \(-0.313963\pi\) | ||||
0.551743 | + | 0.834014i | \(0.313963\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.19490 | 0.102424 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.8554 | −0.411703 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.2981 | 0.585407 | 0.292704 | − | 0.956203i | \(-0.405445\pi\) | ||||
0.292704 | + | 0.956203i | \(0.405445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.7619 | 0.535713 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.42284 | 0.109283 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.5885 | −0.911831 | −0.455915 | − | 0.890023i | \(-0.650688\pi\) | ||||
−0.455915 | + | 0.890023i | \(0.650688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.8565 | 0.791992 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.60296 | 0.178344 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.3562 | −1.60123 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.21688 | 0.102188 | 0.0510938 | − | 0.998694i | \(-0.483729\pi\) | ||||
0.0510938 | + | 0.998694i | \(0.483729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36.3810 | 1.15452 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 77.6372 | 2.46126 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.7255 | −1.19478 | −0.597390 | − | 0.801951i | \(-0.703796\pi\) | ||||
−0.597390 | + | 0.801951i | \(0.703796\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.93026 | −0.0927094 |
(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 | 4008.2.a.f.1.1 | ✓ | 5 | |
4.3 | odd | 2 | 8016.2.a.s.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.f.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
8016.2.a.s.1.1 | 5 | 4.3 | odd | 2 |