Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 22x^{6} + 60x^{5} + 87x^{4} - 176x^{3} - 40x^{2} + 64x + 16 \) |
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 | \(-3.71976\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.63704 | −1.17932 | −0.589659 | − | 0.807652i | \(-0.700738\pi\) | ||||
−0.589659 | + | 0.807652i | \(0.700738\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.63704 | −0.833904 | ||||||||
\(11\) | −3.26053 | −0.983087 | −0.491543 | − | 0.870853i | \(-0.663567\pi\) | ||||
−0.491543 | + | 0.870853i | \(0.663567\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.44345 | −1.23239 | −0.616196 | − | 0.787593i | \(-0.711327\pi\) | ||||
−0.616196 | + | 0.787593i | \(0.711327\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.63704 | 0.680880 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.36962 | 0.574718 | 0.287359 | − | 0.957823i | \(-0.407223\pi\) | ||||
0.287359 | + | 0.957823i | \(0.407223\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.63704 | −0.589659 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.26053 | −0.695147 | ||||||||
\(23\) | −1.98320 | −0.413526 | −0.206763 | − | 0.978391i | \(-0.566293\pi\) | ||||
−0.206763 | + | 0.978391i | \(0.566293\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.95397 | 0.390793 | ||||||||
\(26\) | −4.44345 | −0.871432 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0962338 | 0.0178702 | 0.00893508 | − | 0.999960i | \(-0.497156\pi\) | ||||
0.00893508 | + | 0.999960i | \(0.497156\pi\) | |||||||
\(30\) | 2.63704 | 0.481455 | ||||||||
\(31\) | 2.43285 | 0.436953 | 0.218477 | − | 0.975842i | \(-0.429891\pi\) | ||||
0.218477 | + | 0.975842i | \(0.429891\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.26053 | 0.567586 | ||||||||
\(34\) | 2.36962 | 0.406387 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.452007 | −0.0743094 | −0.0371547 | − | 0.999310i | \(-0.511829\pi\) | ||||
−0.0371547 | + | 0.999310i | \(0.511829\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 4.44345 | 0.711522 | ||||||||
\(40\) | −2.63704 | −0.416952 | ||||||||
\(41\) | −9.53392 | −1.48895 | −0.744474 | − | 0.667651i | \(-0.767300\pi\) | ||||
−0.744474 | + | 0.667651i | \(0.767300\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.1761 | 1.85684 | 0.928422 | − | 0.371528i | \(-0.121166\pi\) | ||||
0.928422 | + | 0.371528i | \(0.121166\pi\) | |||||||
\(44\) | −3.26053 | −0.491543 | ||||||||
\(45\) | −2.63704 | −0.393106 | ||||||||
\(46\) | −1.98320 | −0.292407 | ||||||||
\(47\) | −13.3321 | −1.94469 | −0.972343 | − | 0.233558i | \(-0.924963\pi\) | ||||
−0.972343 | + | 0.233558i | \(0.924963\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.95397 | 0.276333 | ||||||||
\(51\) | −2.36962 | −0.331814 | ||||||||
\(52\) | −4.44345 | −0.616196 | ||||||||
\(53\) | 7.24699 | 0.995450 | 0.497725 | − | 0.867335i | \(-0.334169\pi\) | ||||
0.497725 | + | 0.867335i | \(0.334169\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 8.59814 | 1.15937 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0.0962338 | 0.0126361 | ||||||||
\(59\) | 1.31981 | 0.171824 | 0.0859121 | − | 0.996303i | \(-0.472620\pi\) | ||||
0.0859121 | + | 0.996303i | \(0.472620\pi\) | |||||||
\(60\) | 2.63704 | 0.340440 | ||||||||
\(61\) | 5.52115 | 0.706910 | 0.353455 | − | 0.935451i | \(-0.385007\pi\) | ||||
0.353455 | + | 0.935451i | \(0.385007\pi\) | |||||||
\(62\) | 2.43285 | 0.308973 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.7175 | 1.45338 | ||||||||
\(66\) | 3.26053 | 0.401344 | ||||||||
\(67\) | 5.74748 | 0.702166 | 0.351083 | − | 0.936344i | \(-0.385813\pi\) | ||||
0.351083 | + | 0.936344i | \(0.385813\pi\) | |||||||
\(68\) | 2.36962 | 0.287359 | ||||||||
\(69\) | 1.98320 | 0.238750 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1849 | 1.32740 | 0.663701 | − | 0.747998i | \(-0.268985\pi\) | ||||
0.663701 | + | 0.747998i | \(0.268985\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −4.16583 | −0.487573 | −0.243787 | − | 0.969829i | \(-0.578390\pi\) | ||||
−0.243787 | + | 0.969829i | \(0.578390\pi\) | |||||||
\(74\) | −0.452007 | −0.0525447 | ||||||||
\(75\) | −1.95397 | −0.225625 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.44345 | 0.503122 | ||||||||
\(79\) | −12.9020 | −1.45159 | −0.725796 | − | 0.687910i | \(-0.758528\pi\) | ||||
−0.725796 | + | 0.687910i | \(0.758528\pi\) | |||||||
\(80\) | −2.63704 | −0.294830 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.53392 | −1.05285 | ||||||||
\(83\) | −2.69233 | −0.295522 | −0.147761 | − | 0.989023i | \(-0.547207\pi\) | ||||
−0.147761 | + | 0.989023i | \(0.547207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.24879 | −0.677776 | ||||||||
\(86\) | 12.1761 | 1.31299 | ||||||||
\(87\) | −0.0962338 | −0.0103173 | ||||||||
\(88\) | −3.26053 | −0.347574 | ||||||||
\(89\) | −0.282443 | −0.0299388 | −0.0149694 | − | 0.999888i | \(-0.504765\pi\) | ||||
−0.0149694 | + | 0.999888i | \(0.504765\pi\) | |||||||
\(90\) | −2.63704 | −0.277968 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.98320 | −0.206763 | ||||||||
\(93\) | −2.43285 | −0.252275 | ||||||||
\(94\) | −13.3321 | −1.37510 | ||||||||
\(95\) | 2.63704 | 0.270554 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 3.67729 | 0.373372 | 0.186686 | − | 0.982420i | \(-0.440225\pi\) | ||||
0.186686 | + | 0.982420i | \(0.440225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.26053 | −0.327696 | ||||||||
\(100\) | 1.95397 | 0.195397 | ||||||||
\(101\) | 13.0331 | 1.29685 | 0.648423 | − | 0.761280i | \(-0.275429\pi\) | ||||
0.648423 | + | 0.761280i | \(0.275429\pi\) | |||||||
\(102\) | −2.36962 | −0.234628 | ||||||||
\(103\) | 11.7777 | 1.16050 | 0.580248 | − | 0.814440i | \(-0.302956\pi\) | ||||
0.580248 | + | 0.814440i | \(0.302956\pi\) | |||||||
\(104\) | −4.44345 | −0.435716 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.24699 | 0.703890 | ||||||||
\(107\) | −2.34941 | −0.227126 | −0.113563 | − | 0.993531i | \(-0.536226\pi\) | ||||
−0.113563 | + | 0.993531i | \(0.536226\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 8.67251 | 0.830676 | 0.415338 | − | 0.909667i | \(-0.363663\pi\) | ||||
0.415338 | + | 0.909667i | \(0.363663\pi\) | |||||||
\(110\) | 8.59814 | 0.819801 | ||||||||
\(111\) | 0.452007 | 0.0429026 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1344 | 1.04744 | 0.523718 | − | 0.851892i | \(-0.324545\pi\) | ||||
0.523718 | + | 0.851892i | \(0.324545\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 5.22978 | 0.487680 | ||||||||
\(116\) | 0.0962338 | 0.00893508 | ||||||||
\(117\) | −4.44345 | −0.410797 | ||||||||
\(118\) | 1.31981 | 0.121498 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.63704 | 0.240727 | ||||||||
\(121\) | −0.368940 | −0.0335400 | ||||||||
\(122\) | 5.52115 | 0.499861 | ||||||||
\(123\) | 9.53392 | 0.859645 | ||||||||
\(124\) | 2.43285 | 0.218477 | ||||||||
\(125\) | 8.03251 | 0.718449 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6003 | −1.02936 | −0.514678 | − | 0.857383i | \(-0.672089\pi\) | ||||
−0.514678 | + | 0.857383i | \(0.672089\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.1761 | −1.07205 | ||||||||
\(130\) | 11.7175 | 1.02770 | ||||||||
\(131\) | 10.3929 | 0.908032 | 0.454016 | − | 0.890994i | \(-0.349991\pi\) | ||||
0.454016 | + | 0.890994i | \(0.349991\pi\) | |||||||
\(132\) | 3.26053 | 0.283793 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.74748 | 0.496506 | ||||||||
\(135\) | 2.63704 | 0.226960 | ||||||||
\(136\) | 2.36962 | 0.203194 | ||||||||
\(137\) | −7.75165 | −0.662268 | −0.331134 | − | 0.943584i | \(-0.607431\pi\) | ||||
−0.331134 | + | 0.943584i | \(0.607431\pi\) | |||||||
\(138\) | 1.98320 | 0.168821 | ||||||||
\(139\) | 11.7319 | 0.995083 | 0.497542 | − | 0.867440i | \(-0.334236\pi\) | ||||
0.497542 | + | 0.867440i | \(0.334236\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.3321 | 1.12276 | ||||||||
\(142\) | 11.1849 | 0.938616 | ||||||||
\(143\) | 14.4880 | 1.21155 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.253772 | −0.0210746 | ||||||||
\(146\) | −4.16583 | −0.344766 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.452007 | −0.0371547 | ||||||||
\(149\) | 0.858768 | 0.0703530 | 0.0351765 | − | 0.999381i | \(-0.488801\pi\) | ||||
0.0351765 | + | 0.999381i | \(0.488801\pi\) | |||||||
\(150\) | −1.95397 | −0.159541 | ||||||||
\(151\) | 8.05804 | 0.655754 | 0.327877 | − | 0.944720i | \(-0.393667\pi\) | ||||
0.327877 | + | 0.944720i | \(0.393667\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 2.36962 | 0.191573 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.41552 | −0.515307 | ||||||||
\(156\) | 4.44345 | 0.355761 | ||||||||
\(157\) | 9.13601 | 0.729133 | 0.364566 | − | 0.931177i | \(-0.381217\pi\) | ||||
0.364566 | + | 0.931177i | \(0.381217\pi\) | |||||||
\(158\) | −12.9020 | −1.02643 | ||||||||
\(159\) | −7.24699 | −0.574723 | ||||||||
\(160\) | −2.63704 | −0.208476 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.30168 | 0.650238 | 0.325119 | − | 0.945673i | \(-0.394596\pi\) | ||||
0.325119 | + | 0.945673i | \(0.394596\pi\) | |||||||
\(164\) | −9.53392 | −0.744474 | ||||||||
\(165\) | −8.59814 | −0.669364 | ||||||||
\(166\) | −2.69233 | −0.208965 | ||||||||
\(167\) | 1.27909 | 0.0989787 | 0.0494893 | − | 0.998775i | \(-0.484241\pi\) | ||||
0.0494893 | + | 0.998775i | \(0.484241\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.74426 | 0.518789 | ||||||||
\(170\) | −6.24879 | −0.479260 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 12.1761 | 0.928422 | ||||||||
\(173\) | −22.0420 | −1.67583 | −0.837913 | − | 0.545804i | \(-0.816224\pi\) | ||||
−0.837913 | + | 0.545804i | \(0.816224\pi\) | |||||||
\(174\) | −0.0962338 | −0.00729547 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.26053 | −0.245772 | ||||||||
\(177\) | −1.31981 | −0.0992027 | ||||||||
\(178\) | −0.282443 | −0.0211700 | ||||||||
\(179\) | −0.655972 | −0.0490297 | −0.0245148 | − | 0.999699i | \(-0.507804\pi\) | ||||
−0.0245148 | + | 0.999699i | \(0.507804\pi\) | |||||||
\(180\) | −2.63704 | −0.196553 | ||||||||
\(181\) | 0.349942 | 0.0260110 | 0.0130055 | − | 0.999915i | \(-0.495860\pi\) | ||||
0.0130055 | + | 0.999915i | \(0.495860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.52115 | −0.408135 | ||||||||
\(184\) | −1.98320 | −0.146204 | ||||||||
\(185\) | 1.19196 | 0.0876345 | ||||||||
\(186\) | −2.43285 | −0.178385 | ||||||||
\(187\) | −7.72623 | −0.564998 | ||||||||
\(188\) | −13.3321 | −0.972343 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.63704 | 0.191311 | ||||||||
\(191\) | −5.30321 | −0.383727 | −0.191863 | − | 0.981422i | \(-0.561453\pi\) | ||||
−0.191863 | + | 0.981422i | \(0.561453\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −0.418560 | −0.0301286 | −0.0150643 | − | 0.999887i | \(-0.504795\pi\) | ||||
−0.0150643 | + | 0.999887i | \(0.504795\pi\) | |||||||
\(194\) | 3.67729 | 0.264014 | ||||||||
\(195\) | −11.7175 | −0.839111 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.6356 | 1.82646 | 0.913230 | − | 0.407445i | \(-0.133580\pi\) | ||||
0.913230 | + | 0.407445i | \(0.133580\pi\) | |||||||
\(198\) | −3.26053 | −0.231716 | ||||||||
\(199\) | 27.6516 | 1.96017 | 0.980084 | − | 0.198583i | \(-0.0636341\pi\) | ||||
0.980084 | + | 0.198583i | \(0.0636341\pi\) | |||||||
\(200\) | 1.95397 | 0.138166 | ||||||||
\(201\) | −5.74748 | −0.405396 | ||||||||
\(202\) | 13.0331 | 0.917009 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.36962 | −0.165907 | ||||||||
\(205\) | 25.1413 | 1.75594 | ||||||||
\(206\) | 11.7777 | 0.820594 | ||||||||
\(207\) | −1.98320 | −0.137842 | ||||||||
\(208\) | −4.44345 | −0.308098 | ||||||||
\(209\) | 3.26053 | 0.225536 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.66873 | −0.665623 | −0.332811 | − | 0.942993i | \(-0.607997\pi\) | ||||
−0.332811 | + | 0.942993i | \(0.607997\pi\) | |||||||
\(212\) | 7.24699 | 0.497725 | ||||||||
\(213\) | −11.1849 | −0.766376 | ||||||||
\(214\) | −2.34941 | −0.160603 | ||||||||
\(215\) | −32.1089 | −2.18981 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.67251 | 0.587376 | ||||||||
\(219\) | 4.16583 | 0.281501 | ||||||||
\(220\) | 8.59814 | 0.579687 | ||||||||
\(221\) | −10.5293 | −0.708278 | ||||||||
\(222\) | 0.452007 | 0.0303367 | ||||||||
\(223\) | −0.367428 | −0.0246048 | −0.0123024 | − | 0.999924i | \(-0.503916\pi\) | ||||
−0.0123024 | + | 0.999924i | \(0.503916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.95397 | 0.130264 | ||||||||
\(226\) | 11.1344 | 0.740649 | ||||||||
\(227\) | 15.9079 | 1.05584 | 0.527921 | − | 0.849294i | \(-0.322972\pi\) | ||||
0.527921 | + | 0.849294i | \(0.322972\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −11.3895 | −0.752640 | −0.376320 | − | 0.926490i | \(-0.622811\pi\) | ||||
−0.376320 | + | 0.926490i | \(0.622811\pi\) | |||||||
\(230\) | 5.22978 | 0.344842 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0962338 | 0.00631806 | ||||||||
\(233\) | −3.01687 | −0.197642 | −0.0988210 | − | 0.995105i | \(-0.531507\pi\) | ||||
−0.0988210 | + | 0.995105i | \(0.531507\pi\) | |||||||
\(234\) | −4.44345 | −0.290477 | ||||||||
\(235\) | 35.1572 | 2.29340 | ||||||||
\(236\) | 1.31981 | 0.0859121 | ||||||||
\(237\) | 12.9020 | 0.838077 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.2992 | −1.83052 | −0.915261 | − | 0.402861i | \(-0.868016\pi\) | ||||
−0.915261 | + | 0.402861i | \(0.868016\pi\) | |||||||
\(240\) | 2.63704 | 0.170220 | ||||||||
\(241\) | 21.4909 | 1.38435 | 0.692174 | − | 0.721731i | \(-0.256653\pi\) | ||||
0.692174 | + | 0.721731i | \(0.256653\pi\) | |||||||
\(242\) | −0.368940 | −0.0237163 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.52115 | 0.353455 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.53392 | 0.607861 | ||||||||
\(247\) | 4.44345 | 0.282730 | ||||||||
\(248\) | 2.43285 | 0.154486 | ||||||||
\(249\) | 2.69233 | 0.170620 | ||||||||
\(250\) | 8.03251 | 0.508020 | ||||||||
\(251\) | 17.1974 | 1.08549 | 0.542744 | − | 0.839898i | \(-0.317385\pi\) | ||||
0.542744 | + | 0.839898i | \(0.317385\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.46630 | 0.406533 | ||||||||
\(254\) | −11.6003 | −0.727865 | ||||||||
\(255\) | 6.24879 | 0.391314 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.5578 | 0.783335 | 0.391667 | − | 0.920107i | \(-0.371898\pi\) | ||||
0.391667 | + | 0.920107i | \(0.371898\pi\) | |||||||
\(258\) | −12.1761 | −0.758053 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 11.7175 | 0.726691 | ||||||||
\(261\) | 0.0962338 | 0.00595672 | ||||||||
\(262\) | 10.3929 | 0.642076 | ||||||||
\(263\) | −10.6077 | −0.654098 | −0.327049 | − | 0.945007i | \(-0.606054\pi\) | ||||
−0.327049 | + | 0.945007i | \(0.606054\pi\) | |||||||
\(264\) | 3.26053 | 0.200672 | ||||||||
\(265\) | −19.1106 | −1.17395 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.282443 | 0.0172852 | ||||||||
\(268\) | 5.74748 | 0.351083 | ||||||||
\(269\) | 26.0968 | 1.59115 | 0.795576 | − | 0.605854i | \(-0.207168\pi\) | ||||
0.795576 | + | 0.605854i | \(0.207168\pi\) | |||||||
\(270\) | 2.63704 | 0.160485 | ||||||||
\(271\) | −12.2869 | −0.746377 | −0.373189 | − | 0.927755i | \(-0.621736\pi\) | ||||
−0.373189 | + | 0.927755i | \(0.621736\pi\) | |||||||
\(272\) | 2.36962 | 0.143680 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.75165 | −0.468294 | ||||||||
\(275\) | −6.37097 | −0.384184 | ||||||||
\(276\) | 1.98320 | 0.119375 | ||||||||
\(277\) | 19.7258 | 1.18521 | 0.592603 | − | 0.805495i | \(-0.298100\pi\) | ||||
0.592603 | + | 0.805495i | \(0.298100\pi\) | |||||||
\(278\) | 11.7319 | 0.703630 | ||||||||
\(279\) | 2.43285 | 0.145651 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.56281 | 0.0932292 | 0.0466146 | − | 0.998913i | \(-0.485157\pi\) | ||||
0.0466146 | + | 0.998913i | \(0.485157\pi\) | |||||||
\(282\) | 13.3321 | 0.793915 | ||||||||
\(283\) | 26.3439 | 1.56598 | 0.782990 | − | 0.622034i | \(-0.213694\pi\) | ||||
0.782990 | + | 0.622034i | \(0.213694\pi\) | |||||||
\(284\) | 11.1849 | 0.663701 | ||||||||
\(285\) | −2.63704 | −0.156205 | ||||||||
\(286\) | 14.4880 | 0.856694 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −11.3849 | −0.669699 | ||||||||
\(290\) | −0.253772 | −0.0149020 | ||||||||
\(291\) | −3.67729 | −0.215567 | ||||||||
\(292\) | −4.16583 | −0.243787 | ||||||||
\(293\) | −10.6076 | −0.619700 | −0.309850 | − | 0.950785i | \(-0.600279\pi\) | ||||
−0.309850 | + | 0.950785i | \(0.600279\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.48038 | −0.202636 | ||||||||
\(296\) | −0.452007 | −0.0262723 | ||||||||
\(297\) | 3.26053 | 0.189195 | ||||||||
\(298\) | 0.858768 | 0.0497471 | ||||||||
\(299\) | 8.81227 | 0.509627 | ||||||||
\(300\) | −1.95397 | −0.112812 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.05804 | 0.463688 | ||||||||
\(303\) | −13.0331 | −0.748734 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −14.5595 | −0.833673 | ||||||||
\(306\) | 2.36962 | 0.135462 | ||||||||
\(307\) | 16.2375 | 0.926723 | 0.463362 | − | 0.886169i | \(-0.346643\pi\) | ||||
0.463362 | + | 0.886169i | \(0.346643\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.7777 | −0.670012 | ||||||||
\(310\) | −6.41552 | −0.364377 | ||||||||
\(311\) | −23.0812 | −1.30881 | −0.654406 | − | 0.756143i | \(-0.727081\pi\) | ||||
−0.654406 | + | 0.756143i | \(0.727081\pi\) | |||||||
\(312\) | 4.44345 | 0.251561 | ||||||||
\(313\) | −13.2774 | −0.750485 | −0.375243 | − | 0.926927i | \(-0.622441\pi\) | ||||
−0.375243 | + | 0.926927i | \(0.622441\pi\) | |||||||
\(314\) | 9.13601 | 0.515575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.9020 | −0.725796 | ||||||||
\(317\) | −13.3284 | −0.748597 | −0.374298 | − | 0.927308i | \(-0.622116\pi\) | ||||
−0.374298 | + | 0.927308i | \(0.622116\pi\) | |||||||
\(318\) | −7.24699 | −0.406391 | ||||||||
\(319\) | −0.313773 | −0.0175679 | ||||||||
\(320\) | −2.63704 | −0.147415 | ||||||||
\(321\) | 2.34941 | 0.131131 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.36962 | −0.131849 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −8.68235 | −0.481610 | ||||||||
\(326\) | 8.30168 | 0.459787 | ||||||||
\(327\) | −8.67251 | −0.479591 | ||||||||
\(328\) | −9.53392 | −0.526423 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.59814 | −0.473312 | ||||||||
\(331\) | −28.1155 | −1.54537 | −0.772685 | − | 0.634790i | \(-0.781087\pi\) | ||||
−0.772685 | + | 0.634790i | \(0.781087\pi\) | |||||||
\(332\) | −2.69233 | −0.147761 | ||||||||
\(333\) | −0.452007 | −0.0247698 | ||||||||
\(334\) | 1.27909 | 0.0699885 | ||||||||
\(335\) | −15.1563 | −0.828078 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.5947 | 1.66660 | 0.833301 | − | 0.552820i | \(-0.186448\pi\) | ||||
0.833301 | + | 0.552820i | \(0.186448\pi\) | |||||||
\(338\) | 6.74426 | 0.366839 | ||||||||
\(339\) | −11.1344 | −0.604737 | ||||||||
\(340\) | −6.24879 | −0.338888 | ||||||||
\(341\) | −7.93239 | −0.429563 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.1761 | 0.656493 | ||||||||
\(345\) | −5.22978 | −0.281562 | ||||||||
\(346\) | −22.0420 | −1.18499 | ||||||||
\(347\) | −31.0492 | −1.66681 | −0.833403 | − | 0.552666i | \(-0.813611\pi\) | ||||
−0.833403 | + | 0.552666i | \(0.813611\pi\) | |||||||
\(348\) | −0.0962338 | −0.00515867 | ||||||||
\(349\) | 14.0808 | 0.753727 | 0.376863 | − | 0.926269i | \(-0.377003\pi\) | ||||
0.376863 | + | 0.926269i | \(0.377003\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.44345 | 0.237174 | ||||||||
\(352\) | −3.26053 | −0.173787 | ||||||||
\(353\) | −1.99562 | −0.106216 | −0.0531082 | − | 0.998589i | \(-0.516913\pi\) | ||||
−0.0531082 | + | 0.998589i | \(0.516913\pi\) | |||||||
\(354\) | −1.31981 | −0.0701469 | ||||||||
\(355\) | −29.4950 | −1.56543 | ||||||||
\(356\) | −0.282443 | −0.0149694 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.655972 | −0.0346692 | ||||||||
\(359\) | 18.6935 | 0.986603 | 0.493301 | − | 0.869858i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869858i | \(0.335790\pi\) | |||||||
\(360\) | −2.63704 | −0.138984 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0.349942 | 0.0183926 | ||||||||
\(363\) | 0.368940 | 0.0193643 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.9854 | 0.575004 | ||||||||
\(366\) | −5.52115 | −0.288595 | ||||||||
\(367\) | 10.8045 | 0.563989 | 0.281994 | − | 0.959416i | \(-0.409004\pi\) | ||||
0.281994 | + | 0.959416i | \(0.409004\pi\) | |||||||
\(368\) | −1.98320 | −0.103382 | ||||||||
\(369\) | −9.53392 | −0.496316 | ||||||||
\(370\) | 1.19196 | 0.0619670 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.43285 | −0.126138 | ||||||||
\(373\) | 6.33223 | 0.327870 | 0.163935 | − | 0.986471i | \(-0.447581\pi\) | ||||
0.163935 | + | 0.986471i | \(0.447581\pi\) | |||||||
\(374\) | −7.72623 | −0.399514 | ||||||||
\(375\) | −8.03251 | −0.414797 | ||||||||
\(376\) | −13.3321 | −0.687550 | ||||||||
\(377\) | −0.427610 | −0.0220230 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.1117 | 0.776237 | 0.388119 | − | 0.921609i | \(-0.373125\pi\) | ||||
0.388119 | + | 0.921609i | \(0.373125\pi\) | |||||||
\(380\) | 2.63704 | 0.135277 | ||||||||
\(381\) | 11.6003 | 0.594299 | ||||||||
\(382\) | −5.30321 | −0.271336 | ||||||||
\(383\) | −7.15839 | −0.365777 | −0.182888 | − | 0.983134i | \(-0.558545\pi\) | ||||
−0.182888 | + | 0.983134i | \(0.558545\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.418560 | −0.0213041 | ||||||||
\(387\) | 12.1761 | 0.618948 | ||||||||
\(388\) | 3.67729 | 0.186686 | ||||||||
\(389\) | −19.6296 | −0.995261 | −0.497631 | − | 0.867389i | \(-0.665796\pi\) | ||||
−0.497631 | + | 0.867389i | \(0.665796\pi\) | |||||||
\(390\) | −11.7175 | −0.593341 | ||||||||
\(391\) | −4.69945 | −0.237661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.3929 | −0.524252 | ||||||||
\(394\) | 25.6356 | 1.29150 | ||||||||
\(395\) | 34.0231 | 1.71189 | ||||||||
\(396\) | −3.26053 | −0.163848 | ||||||||
\(397\) | 3.05488 | 0.153320 | 0.0766599 | − | 0.997057i | \(-0.475574\pi\) | ||||
0.0766599 | + | 0.997057i | \(0.475574\pi\) | |||||||
\(398\) | 27.6516 | 1.38605 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.95397 | 0.0976983 | ||||||||
\(401\) | 27.6978 | 1.38316 | 0.691581 | − | 0.722299i | \(-0.256915\pi\) | ||||
0.691581 | + | 0.722299i | \(0.256915\pi\) | |||||||
\(402\) | −5.74748 | −0.286658 | ||||||||
\(403\) | −10.8103 | −0.538497 | ||||||||
\(404\) | 13.0331 | 0.648423 | ||||||||
\(405\) | −2.63704 | −0.131035 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.47378 | 0.0730526 | ||||||||
\(408\) | −2.36962 | −0.117314 | ||||||||
\(409\) | 19.5395 | 0.966166 | 0.483083 | − | 0.875575i | \(-0.339517\pi\) | ||||
0.483083 | + | 0.875575i | \(0.339517\pi\) | |||||||
\(410\) | 25.1413 | 1.24164 | ||||||||
\(411\) | 7.75165 | 0.382361 | ||||||||
\(412\) | 11.7777 | 0.580248 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.98320 | −0.0974691 | ||||||||
\(415\) | 7.09978 | 0.348514 | ||||||||
\(416\) | −4.44345 | −0.217858 | ||||||||
\(417\) | −11.7319 | −0.574512 | ||||||||
\(418\) | 3.26053 | 0.159478 | ||||||||
\(419\) | 19.3022 | 0.942972 | 0.471486 | − | 0.881874i | \(-0.343718\pi\) | ||||
0.471486 | + | 0.881874i | \(0.343718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.33795 | 0.260156 | 0.130078 | − | 0.991504i | \(-0.458477\pi\) | ||||
0.130078 | + | 0.991504i | \(0.458477\pi\) | |||||||
\(422\) | −9.66873 | −0.470667 | ||||||||
\(423\) | −13.3321 | −0.648229 | ||||||||
\(424\) | 7.24699 | 0.351945 | ||||||||
\(425\) | 4.63016 | 0.224596 | ||||||||
\(426\) | −11.1849 | −0.541910 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.34941 | −0.113563 | ||||||||
\(429\) | −14.4880 | −0.699488 | ||||||||
\(430\) | −32.1089 | −1.54843 | ||||||||
\(431\) | 8.06973 | 0.388705 | 0.194353 | − | 0.980932i | \(-0.437739\pi\) | ||||
0.194353 | + | 0.980932i | \(0.437739\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −0.207726 | −0.00998266 | −0.00499133 | − | 0.999988i | \(-0.501589\pi\) | ||||
−0.00499133 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.253772 | 0.0121674 | ||||||||
\(436\) | 8.67251 | 0.415338 | ||||||||
\(437\) | 1.98320 | 0.0948695 | ||||||||
\(438\) | 4.16583 | 0.199051 | ||||||||
\(439\) | 28.9616 | 1.38226 | 0.691131 | − | 0.722729i | \(-0.257113\pi\) | ||||
0.691131 | + | 0.722729i | \(0.257113\pi\) | |||||||
\(440\) | 8.59814 | 0.409900 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.5293 | −0.500828 | ||||||||
\(443\) | −5.50387 | −0.261497 | −0.130748 | − | 0.991416i | \(-0.541738\pi\) | ||||
−0.130748 | + | 0.991416i | \(0.541738\pi\) | |||||||
\(444\) | 0.452007 | 0.0214513 | ||||||||
\(445\) | 0.744811 | 0.0353074 | ||||||||
\(446\) | −0.367428 | −0.0173982 | ||||||||
\(447\) | −0.858768 | −0.0406183 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.546522 | 0.0257920 | 0.0128960 | − | 0.999917i | \(-0.495895\pi\) | ||||
0.0128960 | + | 0.999917i | \(0.495895\pi\) | |||||||
\(450\) | 1.95397 | 0.0921108 | ||||||||
\(451\) | 31.0856 | 1.46377 | ||||||||
\(452\) | 11.1344 | 0.523718 | ||||||||
\(453\) | −8.05804 | −0.378600 | ||||||||
\(454\) | 15.9079 | 0.746593 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 38.6840 | 1.80956 | 0.904781 | − | 0.425878i | \(-0.140035\pi\) | ||||
0.904781 | + | 0.425878i | \(0.140035\pi\) | |||||||
\(458\) | −11.3895 | −0.532197 | ||||||||
\(459\) | −2.36962 | −0.110605 | ||||||||
\(460\) | 5.22978 | 0.243840 | ||||||||
\(461\) | −29.2112 | −1.36050 | −0.680250 | − | 0.732980i | \(-0.738129\pi\) | ||||
−0.680250 | + | 0.732980i | \(0.738129\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1418 | −0.982544 | −0.491272 | − | 0.871006i | \(-0.663468\pi\) | ||||
−0.491272 | + | 0.871006i | \(0.663468\pi\) | |||||||
\(464\) | 0.0962338 | 0.00446754 | ||||||||
\(465\) | 6.41552 | 0.297513 | ||||||||
\(466\) | −3.01687 | −0.139754 | ||||||||
\(467\) | 20.4481 | 0.946224 | 0.473112 | − | 0.881002i | \(-0.343131\pi\) | ||||
0.473112 | + | 0.881002i | \(0.343131\pi\) | |||||||
\(468\) | −4.44345 | −0.205399 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 35.1572 | 1.62168 | ||||||||
\(471\) | −9.13601 | −0.420965 | ||||||||
\(472\) | 1.31981 | 0.0607490 | ||||||||
\(473\) | −39.7007 | −1.82544 | ||||||||
\(474\) | 12.9020 | 0.592610 | ||||||||
\(475\) | −1.95397 | −0.0896541 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.24699 | 0.331817 | ||||||||
\(478\) | −28.2992 | −1.29437 | ||||||||
\(479\) | −23.9563 | −1.09459 | −0.547296 | − | 0.836939i | \(-0.684343\pi\) | ||||
−0.547296 | + | 0.836939i | \(0.684343\pi\) | |||||||
\(480\) | 2.63704 | 0.120364 | ||||||||
\(481\) | 2.00847 | 0.0915783 | ||||||||
\(482\) | 21.4909 | 0.978882 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.368940 | −0.0167700 | ||||||||
\(485\) | −9.69716 | −0.440325 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 14.0906 | 0.638507 | 0.319253 | − | 0.947669i | \(-0.396568\pi\) | ||||
0.319253 | + | 0.947669i | \(0.396568\pi\) | |||||||
\(488\) | 5.52115 | 0.249931 | ||||||||
\(489\) | −8.30168 | −0.375415 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.3018 | 0.555174 | 0.277587 | − | 0.960700i | \(-0.410465\pi\) | ||||
0.277587 | + | 0.960700i | \(0.410465\pi\) | |||||||
\(492\) | 9.53392 | 0.429822 | ||||||||
\(493\) | 0.228038 | 0.0102703 | ||||||||
\(494\) | 4.44345 | 0.199920 | ||||||||
\(495\) | 8.59814 | 0.386458 | ||||||||
\(496\) | 2.43285 | 0.109238 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.69233 | 0.120646 | ||||||||
\(499\) | 5.60115 | 0.250742 | 0.125371 | − | 0.992110i | \(-0.459988\pi\) | ||||
0.125371 | + | 0.992110i | \(0.459988\pi\) | |||||||
\(500\) | 8.03251 | 0.359225 | ||||||||
\(501\) | −1.27909 | −0.0571454 | ||||||||
\(502\) | 17.1974 | 0.767556 | ||||||||
\(503\) | 2.52742 | 0.112692 | 0.0563461 | − | 0.998411i | \(-0.482055\pi\) | ||||
0.0563461 | + | 0.998411i | \(0.482055\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.3689 | −1.52939 | ||||||||
\(506\) | 6.46630 | 0.287462 | ||||||||
\(507\) | −6.74426 | −0.299523 | ||||||||
\(508\) | −11.6003 | −0.514678 | ||||||||
\(509\) | −18.1208 | −0.803190 | −0.401595 | − | 0.915817i | \(-0.631544\pi\) | ||||
−0.401595 | + | 0.915817i | \(0.631544\pi\) | |||||||
\(510\) | 6.24879 | 0.276701 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 12.5578 | 0.553901 | ||||||||
\(515\) | −31.0583 | −1.36859 | ||||||||
\(516\) | −12.1761 | −0.536025 | ||||||||
\(517\) | 43.4697 | 1.91180 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0420 | 0.967538 | ||||||||
\(520\) | 11.7175 | 0.513848 | ||||||||
\(521\) | −23.0907 | −1.01162 | −0.505812 | − | 0.862644i | \(-0.668807\pi\) | ||||
−0.505812 | + | 0.862644i | \(0.668807\pi\) | |||||||
\(522\) | 0.0962338 | 0.00421204 | ||||||||
\(523\) | 21.0628 | 0.921011 | 0.460505 | − | 0.887657i | \(-0.347668\pi\) | ||||
0.460505 | + | 0.887657i | \(0.347668\pi\) | |||||||
\(524\) | 10.3929 | 0.454016 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.6077 | −0.462517 | ||||||||
\(527\) | 5.76495 | 0.251125 | ||||||||
\(528\) | 3.26053 | 0.141896 | ||||||||
\(529\) | −19.0669 | −0.828996 | ||||||||
\(530\) | −19.1106 | −0.830110 | ||||||||
\(531\) | 1.31981 | 0.0572747 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.3635 | 1.83497 | ||||||||
\(534\) | 0.282443 | 0.0122225 | ||||||||
\(535\) | 6.19549 | 0.267854 | ||||||||
\(536\) | 5.74748 | 0.248253 | ||||||||
\(537\) | 0.655972 | 0.0283073 | ||||||||
\(538\) | 26.0968 | 1.12511 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.63704 | 0.113480 | ||||||||
\(541\) | 34.2111 | 1.47085 | 0.735425 | − | 0.677606i | \(-0.236983\pi\) | ||||
0.735425 | + | 0.677606i | \(0.236983\pi\) | |||||||
\(542\) | −12.2869 | −0.527769 | ||||||||
\(543\) | −0.349942 | −0.0150175 | ||||||||
\(544\) | 2.36962 | 0.101597 | ||||||||
\(545\) | −22.8697 | −0.979632 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.99258 | −0.427252 | −0.213626 | − | 0.976916i | \(-0.568527\pi\) | ||||
−0.213626 | + | 0.976916i | \(0.568527\pi\) | |||||||
\(548\) | −7.75165 | −0.331134 | ||||||||
\(549\) | 5.52115 | 0.235637 | ||||||||
\(550\) | −6.37097 | −0.271659 | ||||||||
\(551\) | −0.0962338 | −0.00409970 | ||||||||
\(552\) | 1.98320 | 0.0844107 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19.7258 | 0.838067 | ||||||||
\(555\) | −1.19196 | −0.0505958 | ||||||||
\(556\) | 11.7319 | 0.497542 | ||||||||
\(557\) | −36.7882 | −1.55877 | −0.779384 | − | 0.626546i | \(-0.784468\pi\) | ||||
−0.779384 | + | 0.626546i | \(0.784468\pi\) | |||||||
\(558\) | 2.43285 | 0.102991 | ||||||||
\(559\) | −54.1041 | −2.28836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.72623 | 0.326202 | ||||||||
\(562\) | 1.56281 | 0.0659230 | ||||||||
\(563\) | −26.7311 | −1.12658 | −0.563291 | − | 0.826259i | \(-0.690465\pi\) | ||||
−0.563291 | + | 0.826259i | \(0.690465\pi\) | |||||||
\(564\) | 13.3321 | 0.561382 | ||||||||
\(565\) | −29.3618 | −1.23526 | ||||||||
\(566\) | 26.3439 | 1.10732 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1849 | 0.469308 | ||||||||
\(569\) | −5.65805 | −0.237198 | −0.118599 | − | 0.992942i | \(-0.537840\pi\) | ||||
−0.118599 | + | 0.992942i | \(0.537840\pi\) | |||||||
\(570\) | −2.63704 | −0.110453 | ||||||||
\(571\) | −13.8124 | −0.578030 | −0.289015 | − | 0.957325i | \(-0.593328\pi\) | ||||
−0.289015 | + | 0.957325i | \(0.593328\pi\) | |||||||
\(572\) | 14.4880 | 0.605774 | ||||||||
\(573\) | 5.30321 | 0.221545 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.87511 | −0.161603 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −21.2759 | −0.885727 | −0.442864 | − | 0.896589i | \(-0.646037\pi\) | ||||
−0.442864 | + | 0.896589i | \(0.646037\pi\) | |||||||
\(578\) | −11.3849 | −0.473549 | ||||||||
\(579\) | 0.418560 | 0.0173947 | ||||||||
\(580\) | −0.253772 | −0.0105373 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.67729 | −0.152429 | ||||||||
\(583\) | −23.6290 | −0.978614 | ||||||||
\(584\) | −4.16583 | −0.172383 | ||||||||
\(585\) | 11.7175 | 0.484461 | ||||||||
\(586\) | −10.6076 | −0.438194 | ||||||||
\(587\) | −2.14686 | −0.0886103 | −0.0443052 | − | 0.999018i | \(-0.514107\pi\) | ||||
−0.0443052 | + | 0.999018i | \(0.514107\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.43285 | −0.100244 | ||||||||
\(590\) | −3.48038 | −0.143285 | ||||||||
\(591\) | −25.6356 | −1.05451 | ||||||||
\(592\) | −0.452007 | −0.0185774 | ||||||||
\(593\) | −29.3692 | −1.20605 | −0.603025 | − | 0.797723i | \(-0.706038\pi\) | ||||
−0.603025 | + | 0.797723i | \(0.706038\pi\) | |||||||
\(594\) | 3.26053 | 0.133781 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.858768 | 0.0351765 | ||||||||
\(597\) | −27.6516 | −1.13170 | ||||||||
\(598\) | 8.81227 | 0.360360 | ||||||||
\(599\) | 10.9089 | 0.445725 | 0.222863 | − | 0.974850i | \(-0.428460\pi\) | ||||
0.222863 | + | 0.974850i | \(0.428460\pi\) | |||||||
\(600\) | −1.95397 | −0.0797703 | ||||||||
\(601\) | 6.34523 | 0.258827 | 0.129414 | − | 0.991591i | \(-0.458690\pi\) | ||||
0.129414 | + | 0.991591i | \(0.458690\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.74748 | 0.234055 | ||||||||
\(604\) | 8.05804 | 0.327877 | ||||||||
\(605\) | 0.972907 | 0.0395543 | ||||||||
\(606\) | −13.0331 | −0.529435 | ||||||||
\(607\) | −43.4796 | −1.76478 | −0.882392 | − | 0.470516i | \(-0.844068\pi\) | ||||
−0.882392 | + | 0.470516i | \(0.844068\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.5595 | −0.589496 | ||||||||
\(611\) | 59.2405 | 2.39661 | ||||||||
\(612\) | 2.36962 | 0.0957864 | ||||||||
\(613\) | 5.58771 | 0.225685 | 0.112843 | − | 0.993613i | \(-0.464004\pi\) | ||||
0.112843 | + | 0.993613i | \(0.464004\pi\) | |||||||
\(614\) | 16.2375 | 0.655292 | ||||||||
\(615\) | −25.1413 | −1.01380 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.4172 | 0.701190 | 0.350595 | − | 0.936527i | \(-0.385979\pi\) | ||||
0.350595 | + | 0.936527i | \(0.385979\pi\) | |||||||
\(618\) | −11.7777 | −0.473770 | ||||||||
\(619\) | 16.0433 | 0.644834 | 0.322417 | − | 0.946598i | \(-0.395505\pi\) | ||||
0.322417 | + | 0.946598i | \(0.395505\pi\) | |||||||
\(620\) | −6.41552 | −0.257654 | ||||||||
\(621\) | 1.98320 | 0.0795832 | ||||||||
\(622\) | −23.0812 | −0.925470 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.44345 | 0.177880 | ||||||||
\(625\) | −30.9518 | −1.23807 | ||||||||
\(626\) | −13.2774 | −0.530673 | ||||||||
\(627\) | −3.26053 | −0.130213 | ||||||||
\(628\) | 9.13601 | 0.364566 | ||||||||
\(629\) | −1.07109 | −0.0427070 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0407 | −0.479332 | −0.239666 | − | 0.970855i | \(-0.577038\pi\) | ||||
−0.239666 | + | 0.970855i | \(0.577038\pi\) | |||||||
\(632\) | −12.9020 | −0.513215 | ||||||||
\(633\) | 9.66873 | 0.384298 | ||||||||
\(634\) | −13.3284 | −0.529338 | ||||||||
\(635\) | 30.5903 | 1.21394 | ||||||||
\(636\) | −7.24699 | −0.287362 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.313773 | −0.0124224 | ||||||||
\(639\) | 11.1849 | 0.442468 | ||||||||
\(640\) | −2.63704 | −0.104238 | ||||||||
\(641\) | 18.7444 | 0.740358 | 0.370179 | − | 0.928961i | \(-0.379296\pi\) | ||||
0.370179 | + | 0.928961i | \(0.379296\pi\) | |||||||
\(642\) | 2.34941 | 0.0927240 | ||||||||
\(643\) | −1.01673 | −0.0400960 | −0.0200480 | − | 0.999799i | \(-0.506382\pi\) | ||||
−0.0200480 | + | 0.999799i | \(0.506382\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.1089 | 1.26429 | ||||||||
\(646\) | −2.36962 | −0.0932316 | ||||||||
\(647\) | −47.7699 | −1.87803 | −0.939014 | − | 0.343880i | \(-0.888259\pi\) | ||||
−0.939014 | + | 0.343880i | \(0.888259\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −4.30327 | −0.168918 | ||||||||
\(650\) | −8.68235 | −0.340550 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.30168 | 0.325119 | ||||||||
\(653\) | 35.2589 | 1.37979 | 0.689893 | − | 0.723911i | \(-0.257658\pi\) | ||||
0.689893 | + | 0.723911i | \(0.257658\pi\) | |||||||
\(654\) | −8.67251 | −0.339122 | ||||||||
\(655\) | −27.4065 | −1.07086 | ||||||||
\(656\) | −9.53392 | −0.372237 | ||||||||
\(657\) | −4.16583 | −0.162524 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.3855 | −1.76797 | −0.883985 | − | 0.467516i | \(-0.845149\pi\) | ||||
−0.883985 | + | 0.467516i | \(0.845149\pi\) | |||||||
\(660\) | −8.59814 | −0.334682 | ||||||||
\(661\) | −10.1740 | −0.395723 | −0.197862 | − | 0.980230i | \(-0.563400\pi\) | ||||
−0.197862 | + | 0.980230i | \(0.563400\pi\) | |||||||
\(662\) | −28.1155 | −1.09274 | ||||||||
\(663\) | 10.5293 | 0.408924 | ||||||||
\(664\) | −2.69233 | −0.104483 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.452007 | −0.0175149 | ||||||||
\(667\) | −0.190851 | −0.00738979 | ||||||||
\(668\) | 1.27909 | 0.0494893 | ||||||||
\(669\) | 0.367428 | 0.0142056 | ||||||||
\(670\) | −15.1563 | −0.585539 | ||||||||
\(671\) | −18.0019 | −0.694955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.3657 | −1.13196 | −0.565982 | − | 0.824417i | \(-0.691503\pi\) | ||||
−0.565982 | + | 0.824417i | \(0.691503\pi\) | |||||||
\(674\) | 30.5947 | 1.17846 | ||||||||
\(675\) | −1.95397 | −0.0752082 | ||||||||
\(676\) | 6.74426 | 0.259395 | ||||||||
\(677\) | 5.24950 | 0.201755 | 0.100877 | − | 0.994899i | \(-0.467835\pi\) | ||||
0.100877 | + | 0.994899i | \(0.467835\pi\) | |||||||
\(678\) | −11.1344 | −0.427614 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.24879 | −0.239630 | ||||||||
\(681\) | −15.9079 | −0.609590 | ||||||||
\(682\) | −7.93239 | −0.303747 | ||||||||
\(683\) | 10.8055 | 0.413462 | 0.206731 | − | 0.978398i | \(-0.433718\pi\) | ||||
0.206731 | + | 0.978398i | \(0.433718\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 20.4414 | 0.781025 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.3895 | 0.434537 | ||||||||
\(688\) | 12.1761 | 0.464211 | ||||||||
\(689\) | −32.2016 | −1.22678 | ||||||||
\(690\) | −5.22978 | −0.199094 | ||||||||
\(691\) | −34.2368 | −1.30243 | −0.651215 | − | 0.758893i | \(-0.725740\pi\) | ||||
−0.651215 | + | 0.758893i | \(0.725740\pi\) | |||||||
\(692\) | −22.0420 | −0.837913 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.0492 | −1.17861 | ||||||||
\(695\) | −30.9374 | −1.17352 | ||||||||
\(696\) | −0.0962338 | −0.00364773 | ||||||||
\(697\) | −22.5918 | −0.855726 | ||||||||
\(698\) | 14.0808 | 0.532965 | ||||||||
\(699\) | 3.01687 | 0.114109 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0826 | 1.36282 | 0.681411 | − | 0.731901i | \(-0.261367\pi\) | ||||
0.681411 | + | 0.731901i | \(0.261367\pi\) | |||||||
\(702\) | 4.44345 | 0.167707 | ||||||||
\(703\) | 0.452007 | 0.0170478 | ||||||||
\(704\) | −3.26053 | −0.122886 | ||||||||
\(705\) | −35.1572 | −1.32410 | ||||||||
\(706\) | −1.99562 | −0.0751063 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.31981 | −0.0496014 | ||||||||
\(709\) | −28.6794 | −1.07708 | −0.538539 | − | 0.842601i | \(-0.681024\pi\) | ||||
−0.538539 | + | 0.842601i | \(0.681024\pi\) | |||||||
\(710\) | −29.4950 | −1.10693 | ||||||||
\(711\) | −12.9020 | −0.483864 | ||||||||
\(712\) | −0.282443 | −0.0105850 | ||||||||
\(713\) | −4.82484 | −0.180692 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.2054 | −1.42880 | ||||||||
\(716\) | −0.655972 | −0.0245148 | ||||||||
\(717\) | 28.2992 | 1.05685 | ||||||||
\(718\) | 18.6935 | 0.697634 | ||||||||
\(719\) | 3.74972 | 0.139841 | 0.0699205 | − | 0.997553i | \(-0.477725\pi\) | ||||
0.0699205 | + | 0.997553i | \(0.477725\pi\) | |||||||
\(720\) | −2.63704 | −0.0982766 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −21.4909 | −0.799254 | ||||||||
\(724\) | 0.349942 | 0.0130055 | ||||||||
\(725\) | 0.188038 | 0.00698354 | ||||||||
\(726\) | 0.368940 | 0.0136926 | ||||||||
\(727\) | 52.4402 | 1.94490 | 0.972450 | − | 0.233111i | \(-0.0748904\pi\) | ||||
0.972450 | + | 0.233111i | \(0.0748904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.9854 | 0.406589 | ||||||||
\(731\) | 28.8529 | 1.06716 | ||||||||
\(732\) | −5.52115 | −0.204067 | ||||||||
\(733\) | 33.4542 | 1.23566 | 0.617830 | − | 0.786312i | \(-0.288012\pi\) | ||||
0.617830 | + | 0.786312i | \(0.288012\pi\) | |||||||
\(734\) | 10.8045 | 0.398800 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.98320 | −0.0731018 | ||||||||
\(737\) | −18.7398 | −0.690290 | ||||||||
\(738\) | −9.53392 | −0.350948 | ||||||||
\(739\) | 45.5330 | 1.67496 | 0.837479 | − | 0.546469i | \(-0.184028\pi\) | ||||
0.837479 | + | 0.546469i | \(0.184028\pi\) | |||||||
\(740\) | 1.19196 | 0.0438173 | ||||||||
\(741\) | −4.44345 | −0.163234 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.9381 | −1.02495 | −0.512474 | − | 0.858703i | \(-0.671271\pi\) | ||||
−0.512474 | + | 0.858703i | \(0.671271\pi\) | |||||||
\(744\) | −2.43285 | −0.0891927 | ||||||||
\(745\) | −2.26460 | −0.0829686 | ||||||||
\(746\) | 6.33223 | 0.231839 | ||||||||
\(747\) | −2.69233 | −0.0985073 | ||||||||
\(748\) | −7.72623 | −0.282499 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.03251 | −0.293306 | ||||||||
\(751\) | −34.3955 | −1.25511 | −0.627554 | − | 0.778573i | \(-0.715944\pi\) | ||||
−0.627554 | + | 0.778573i | \(0.715944\pi\) | |||||||
\(752\) | −13.3321 | −0.486171 | ||||||||
\(753\) | −17.1974 | −0.626707 | ||||||||
\(754\) | −0.427610 | −0.0155726 | ||||||||
\(755\) | −21.2493 | −0.773343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.4913 | −0.781113 | −0.390557 | − | 0.920579i | \(-0.627717\pi\) | ||||
−0.390557 | + | 0.920579i | \(0.627717\pi\) | |||||||
\(758\) | 15.1117 | 0.548882 | ||||||||
\(759\) | −6.46630 | −0.234712 | ||||||||
\(760\) | 2.63704 | 0.0956554 | ||||||||
\(761\) | 17.5599 | 0.636545 | 0.318272 | − | 0.947999i | \(-0.396897\pi\) | ||||
0.318272 | + | 0.947999i | \(0.396897\pi\) | |||||||
\(762\) | 11.6003 | 0.420233 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.30321 | −0.191863 | ||||||||
\(765\) | −6.24879 | −0.225925 | ||||||||
\(766\) | −7.15839 | −0.258643 | ||||||||
\(767\) | −5.86450 | −0.211755 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 44.6752 | 1.61103 | 0.805515 | − | 0.592575i | \(-0.201889\pi\) | ||||
0.805515 | + | 0.592575i | \(0.201889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.5578 | −0.452258 | ||||||||
\(772\) | −0.418560 | −0.0150643 | ||||||||
\(773\) | −30.7531 | −1.10611 | −0.553057 | − | 0.833143i | \(-0.686539\pi\) | ||||
−0.553057 | + | 0.833143i | \(0.686539\pi\) | |||||||
\(774\) | 12.1761 | 0.437662 | ||||||||
\(775\) | 4.75371 | 0.170758 | ||||||||
\(776\) | 3.67729 | 0.132007 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.6296 | −0.703756 | ||||||||
\(779\) | 9.53392 | 0.341588 | ||||||||
\(780\) | −11.7175 | −0.419555 | ||||||||
\(781\) | −36.4687 | −1.30495 | ||||||||
\(782\) | −4.69945 | −0.168052 | ||||||||
\(783\) | −0.0962338 | −0.00343912 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.0920 | −0.859880 | ||||||||
\(786\) | −10.3929 | −0.370702 | ||||||||
\(787\) | −24.3598 | −0.868333 | −0.434167 | − | 0.900833i | \(-0.642957\pi\) | ||||
−0.434167 | + | 0.900833i | \(0.642957\pi\) | |||||||
\(788\) | 25.6356 | 0.913230 | ||||||||
\(789\) | 10.6077 | 0.377643 | ||||||||
\(790\) | 34.0231 | 1.21049 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.26053 | −0.115858 | ||||||||
\(793\) | −24.5329 | −0.871191 | ||||||||
\(794\) | 3.05488 | 0.108414 | ||||||||
\(795\) | 19.1106 | 0.677782 | ||||||||
\(796\) | 27.6516 | 0.980084 | ||||||||
\(797\) | −14.4957 | −0.513465 | −0.256732 | − | 0.966483i | \(-0.582646\pi\) | ||||
−0.256732 | + | 0.966483i | \(0.582646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.5920 | −1.11765 | ||||||||
\(800\) | 1.95397 | 0.0690831 | ||||||||
\(801\) | −0.282443 | −0.00997962 | ||||||||
\(802\) | 27.6978 | 0.978043 | ||||||||
\(803\) | 13.5828 | 0.479327 | ||||||||
\(804\) | −5.74748 | −0.202698 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.8103 | −0.380775 | ||||||||
\(807\) | −26.0968 | −0.918652 | ||||||||
\(808\) | 13.0331 | 0.458504 | ||||||||
\(809\) | 7.30039 | 0.256668 | 0.128334 | − | 0.991731i | \(-0.459037\pi\) | ||||
0.128334 | + | 0.991731i | \(0.459037\pi\) | |||||||
\(810\) | −2.63704 | −0.0926560 | ||||||||
\(811\) | −48.0207 | −1.68624 | −0.843118 | − | 0.537729i | \(-0.819283\pi\) | ||||
−0.843118 | + | 0.537729i | \(0.819283\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2869 | 0.430921 | ||||||||
\(814\) | 1.47378 | 0.0516560 | ||||||||
\(815\) | −21.8918 | −0.766838 | ||||||||
\(816\) | −2.36962 | −0.0829534 | ||||||||
\(817\) | −12.1761 | −0.425989 | ||||||||
\(818\) | 19.5395 | 0.683183 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.1413 | 0.877972 | ||||||||
\(821\) | −55.0416 | −1.92096 | −0.960482 | − | 0.278342i | \(-0.910215\pi\) | ||||
−0.960482 | + | 0.278342i | \(0.910215\pi\) | |||||||
\(822\) | 7.75165 | 0.270370 | ||||||||
\(823\) | −4.50808 | −0.157142 | −0.0785709 | − | 0.996909i | \(-0.525036\pi\) | ||||
−0.0785709 | + | 0.996909i | \(0.525036\pi\) | |||||||
\(824\) | 11.7777 | 0.410297 | ||||||||
\(825\) | 6.37097 | 0.221809 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.7492 | −0.373786 | −0.186893 | − | 0.982380i | \(-0.559842\pi\) | ||||
−0.186893 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(828\) | −1.98320 | −0.0689211 | ||||||||
\(829\) | 23.9667 | 0.832399 | 0.416199 | − | 0.909273i | \(-0.363362\pi\) | ||||
0.416199 | + | 0.909273i | \(0.363362\pi\) | |||||||
\(830\) | 7.09978 | 0.246437 | ||||||||
\(831\) | −19.7258 | −0.684279 | ||||||||
\(832\) | −4.44345 | −0.154049 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −11.7319 | −0.406241 | ||||||||
\(835\) | −3.37300 | −0.116727 | ||||||||
\(836\) | 3.26053 | 0.112768 | ||||||||
\(837\) | −2.43285 | −0.0840917 | ||||||||
\(838\) | 19.3022 | 0.666782 | ||||||||
\(839\) | 13.5218 | 0.466826 | 0.233413 | − | 0.972378i | \(-0.425011\pi\) | ||||
0.233413 | + | 0.972378i | \(0.425011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9907 | −0.999681 | ||||||||
\(842\) | 5.33795 | 0.183958 | ||||||||
\(843\) | −1.56281 | −0.0538259 | ||||||||
\(844\) | −9.66873 | −0.332811 | ||||||||
\(845\) | −17.7849 | −0.611818 | ||||||||
\(846\) | −13.3321 | −0.458367 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.24699 | 0.248863 | ||||||||
\(849\) | −26.3439 | −0.904119 | ||||||||
\(850\) | 4.63016 | 0.158813 | ||||||||
\(851\) | 0.896421 | 0.0307289 | ||||||||
\(852\) | −11.1849 | −0.383188 | ||||||||
\(853\) | −44.1133 | −1.51041 | −0.755206 | − | 0.655487i | \(-0.772463\pi\) | ||||
−0.755206 | + | 0.655487i | \(0.772463\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.63704 | 0.0901848 | ||||||||
\(856\) | −2.34941 | −0.0803013 | ||||||||
\(857\) | 24.3784 | 0.832750 | 0.416375 | − | 0.909193i | \(-0.363300\pi\) | ||||
0.416375 | + | 0.909193i | \(0.363300\pi\) | |||||||
\(858\) | −14.4880 | −0.494612 | ||||||||
\(859\) | 42.2602 | 1.44190 | 0.720950 | − | 0.692987i | \(-0.243706\pi\) | ||||
0.720950 | + | 0.692987i | \(0.243706\pi\) | |||||||
\(860\) | −32.1089 | −1.09491 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.06973 | 0.274856 | ||||||||
\(863\) | 11.1263 | 0.378743 | 0.189372 | − | 0.981905i | \(-0.439355\pi\) | ||||
0.189372 | + | 0.981905i | \(0.439355\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 58.1257 | 1.97633 | ||||||||
\(866\) | −0.207726 | −0.00705881 | ||||||||
\(867\) | 11.3849 | 0.386651 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.0675 | 1.42704 | ||||||||
\(870\) | 0.253772 | 0.00860368 | ||||||||
\(871\) | −25.5386 | −0.865344 | ||||||||
\(872\) | 8.67251 | 0.293688 | ||||||||
\(873\) | 3.67729 | 0.124457 | ||||||||
\(874\) | 1.98320 | 0.0670829 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.16583 | 0.140750 | ||||||||
\(877\) | 22.5809 | 0.762502 | 0.381251 | − | 0.924471i | \(-0.375493\pi\) | ||||
0.381251 | + | 0.924471i | \(0.375493\pi\) | |||||||
\(878\) | 28.9616 | 0.977407 | ||||||||
\(879\) | 10.6076 | 0.357784 | ||||||||
\(880\) | 8.59814 | 0.289843 | ||||||||
\(881\) | 22.5436 | 0.759513 | 0.379756 | − | 0.925086i | \(-0.376008\pi\) | ||||
0.379756 | + | 0.925086i | \(0.376008\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.41767 | −0.316930 | −0.158465 | − | 0.987365i | \(-0.550655\pi\) | ||||
−0.158465 | + | 0.987365i | \(0.550655\pi\) | |||||||
\(884\) | −10.5293 | −0.354139 | ||||||||
\(885\) | 3.48038 | 0.116992 | ||||||||
\(886\) | −5.50387 | −0.184906 | ||||||||
\(887\) | −3.88840 | −0.130560 | −0.0652798 | − | 0.997867i | \(-0.520794\pi\) | ||||
−0.0652798 | + | 0.997867i | \(0.520794\pi\) | |||||||
\(888\) | 0.452007 | 0.0151683 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.744811 | 0.0249661 | ||||||||
\(891\) | −3.26053 | −0.109232 | ||||||||
\(892\) | −0.367428 | −0.0123024 | ||||||||
\(893\) | 13.3321 | 0.446141 | ||||||||
\(894\) | −0.858768 | −0.0287215 | ||||||||
\(895\) | 1.72982 | 0.0578216 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.81227 | −0.294233 | ||||||||
\(898\) | 0.546522 | 0.0182377 | ||||||||
\(899\) | 0.234123 | 0.00780843 | ||||||||
\(900\) | 1.95397 | 0.0651322 | ||||||||
\(901\) | 17.1726 | 0.572103 | ||||||||
\(902\) | 31.0856 | 1.03504 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.1344 | 0.370324 | ||||||||
\(905\) | −0.922811 | −0.0306753 | ||||||||
\(906\) | −8.05804 | −0.267710 | ||||||||
\(907\) | −8.38922 | −0.278560 | −0.139280 | − | 0.990253i | \(-0.544479\pi\) | ||||
−0.139280 | + | 0.990253i | \(0.544479\pi\) | |||||||
\(908\) | 15.9079 | 0.527921 | ||||||||
\(909\) | 13.0331 | 0.432282 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.5150 | 0.348377 | 0.174188 | − | 0.984712i | \(-0.444270\pi\) | ||||
0.174188 | + | 0.984712i | \(0.444270\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 8.77843 | 0.290524 | ||||||||
\(914\) | 38.6840 | 1.27955 | ||||||||
\(915\) | 14.5595 | 0.481321 | ||||||||
\(916\) | −11.3895 | −0.376320 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.36962 | −0.0782092 | ||||||||
\(919\) | −27.1316 | −0.894990 | −0.447495 | − | 0.894287i | \(-0.647684\pi\) | ||||
−0.447495 | + | 0.894287i | \(0.647684\pi\) | |||||||
\(920\) | 5.22978 | 0.172421 | ||||||||
\(921\) | −16.2375 | −0.535044 | ||||||||
\(922\) | −29.2112 | −0.962019 | ||||||||
\(923\) | −49.6995 | −1.63588 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.883205 | −0.0290396 | ||||||||
\(926\) | −21.1418 | −0.694764 | ||||||||
\(927\) | 11.7777 | 0.386832 | ||||||||
\(928\) | 0.0962338 | 0.00315903 | ||||||||
\(929\) | 34.9902 | 1.14799 | 0.573995 | − | 0.818859i | \(-0.305393\pi\) | ||||
0.573995 | + | 0.818859i | \(0.305393\pi\) | |||||||
\(930\) | 6.41552 | 0.210373 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.01687 | −0.0988210 | ||||||||
\(933\) | 23.0812 | 0.755643 | ||||||||
\(934\) | 20.4481 | 0.669081 | ||||||||
\(935\) | 20.3744 | 0.666313 | ||||||||
\(936\) | −4.44345 | −0.145239 | ||||||||
\(937\) | 0.164326 | 0.00536828 | 0.00268414 | − | 0.999996i | \(-0.499146\pi\) | ||||
0.00268414 | + | 0.999996i | \(0.499146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.2774 | 0.433293 | ||||||||
\(940\) | 35.1572 | 1.14670 | ||||||||
\(941\) | 21.8637 | 0.712738 | 0.356369 | − | 0.934345i | \(-0.384015\pi\) | ||||
0.356369 | + | 0.934345i | \(0.384015\pi\) | |||||||
\(942\) | −9.13601 | −0.297667 | ||||||||
\(943\) | 18.9077 | 0.615720 | ||||||||
\(944\) | 1.31981 | 0.0429560 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.7007 | −1.29078 | ||||||||
\(947\) | 29.1135 | 0.946063 | 0.473031 | − | 0.881046i | \(-0.343160\pi\) | ||||
0.473031 | + | 0.881046i | \(0.343160\pi\) | |||||||
\(948\) | 12.9020 | 0.419039 | ||||||||
\(949\) | 18.5107 | 0.600881 | ||||||||
\(950\) | −1.95397 | −0.0633950 | ||||||||
\(951\) | 13.3284 | 0.432202 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.81327 | −0.123524 | −0.0617619 | − | 0.998091i | \(-0.519672\pi\) | ||||
−0.0617619 | + | 0.998091i | \(0.519672\pi\) | |||||||
\(954\) | 7.24699 | 0.234630 | ||||||||
\(955\) | 13.9848 | 0.452536 | ||||||||
\(956\) | −28.2992 | −0.915261 | ||||||||
\(957\) | 0.313773 | 0.0101428 | ||||||||
\(958\) | −23.9563 | −0.773993 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.63704 | 0.0851100 | ||||||||
\(961\) | −25.0812 | −0.809072 | ||||||||
\(962\) | 2.00847 | 0.0647556 | ||||||||
\(963\) | −2.34941 | −0.0757088 | ||||||||
\(964\) | 21.4909 | 0.692174 | ||||||||
\(965\) | 1.10376 | 0.0355312 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.4232 | −1.39639 | −0.698197 | − | 0.715905i | \(-0.746014\pi\) | ||||
−0.698197 | + | 0.715905i | \(0.746014\pi\) | |||||||
\(968\) | −0.368940 | −0.0118582 | ||||||||
\(969\) | 2.36962 | 0.0761233 | ||||||||
\(970\) | −9.69716 | −0.311357 | ||||||||
\(971\) | −10.4462 | −0.335234 | −0.167617 | − | 0.985852i | \(-0.553607\pi\) | ||||
−0.167617 | + | 0.985852i | \(0.553607\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14.0906 | 0.451492 | ||||||||
\(975\) | 8.68235 | 0.278058 | ||||||||
\(976\) | 5.52115 | 0.176728 | ||||||||
\(977\) | −3.59658 | −0.115065 | −0.0575324 | − | 0.998344i | \(-0.518323\pi\) | ||||
−0.0575324 | + | 0.998344i | \(0.518323\pi\) | |||||||
\(978\) | −8.30168 | −0.265458 | ||||||||
\(979\) | 0.920912 | 0.0294325 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.67251 | 0.276892 | ||||||||
\(982\) | 12.3018 | 0.392567 | ||||||||
\(983\) | −47.5539 | −1.51673 | −0.758367 | − | 0.651828i | \(-0.774002\pi\) | ||||
−0.758367 | + | 0.651828i | \(0.774002\pi\) | |||||||
\(984\) | 9.53392 | 0.303930 | ||||||||
\(985\) | −67.6020 | −2.15398 | ||||||||
\(986\) | 0.228038 | 0.00726221 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.44345 | 0.141365 | ||||||||
\(989\) | −24.1478 | −0.767854 | ||||||||
\(990\) | 8.59814 | 0.273267 | ||||||||
\(991\) | 9.75973 | 0.310028 | 0.155014 | − | 0.987912i | \(-0.450458\pi\) | ||||
0.155014 | + | 0.987912i | \(0.450458\pi\) | |||||||
\(992\) | 2.43285 | 0.0772431 | ||||||||
\(993\) | 28.1155 | 0.892220 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −72.9182 | −2.31166 | ||||||||
\(996\) | 2.69233 | 0.0853098 | ||||||||
\(997\) | 8.52971 | 0.270139 | 0.135069 | − | 0.990836i | \(-0.456874\pi\) | ||||
0.135069 | + | 0.990836i | \(0.456874\pi\) | |||||||
\(998\) | 5.60115 | 0.177301 | ||||||||
\(999\) | 0.452007 | 0.0143009 |
(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 | 5586.2.a.ce.1.3 | ✓ | 8 | |
7.6 | odd | 2 | 5586.2.a.cf.1.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5586.2.a.ce.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5586.2.a.cf.1.6 | yes | 8 | 7.6 | odd | 2 |