Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −2.90959 | −1.67985 | −0.839926 | − | 0.542701i | \(-0.817402\pi\) | ||||
−0.839926 | + | 0.542701i | \(0.817402\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.15278 | −1.85718 | −0.928590 | − | 0.371107i | \(-0.878978\pi\) | ||||
−0.928590 | + | 0.371107i | \(0.878978\pi\) | |||||||
\(6\) | −2.90959 | −1.18783 | ||||||||
\(7\) | 3.02073 | 1.14173 | 0.570864 | − | 0.821044i | \(-0.306608\pi\) | ||||
0.570864 | + | 0.821044i | \(0.306608\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.46571 | 1.82190 | ||||||||
\(10\) | −4.15278 | −1.31322 | ||||||||
\(11\) | 1.94973 | 0.587866 | 0.293933 | − | 0.955826i | \(-0.405036\pi\) | ||||
0.293933 | + | 0.955826i | \(0.405036\pi\) | |||||||
\(12\) | −2.90959 | −0.839926 | ||||||||
\(13\) | 7.15763 | 1.98517 | 0.992584 | − | 0.121560i | \(-0.0387895\pi\) | ||||
0.992584 | + | 0.121560i | \(0.0387895\pi\) | |||||||
\(14\) | 3.02073 | 0.807324 | ||||||||
\(15\) | 12.0829 | 3.11979 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.01914 | 0.247178 | 0.123589 | − | 0.992334i | \(-0.460560\pi\) | ||||
0.123589 | + | 0.992334i | \(0.460560\pi\) | |||||||
\(18\) | 5.46571 | 1.28828 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −4.15278 | −0.928590 | ||||||||
\(21\) | −8.78908 | −1.91793 | ||||||||
\(22\) | 1.94973 | 0.415684 | ||||||||
\(23\) | 3.81312 | 0.795091 | 0.397545 | − | 0.917583i | \(-0.369862\pi\) | ||||
0.397545 | + | 0.917583i | \(0.369862\pi\) | |||||||
\(24\) | −2.90959 | −0.593917 | ||||||||
\(25\) | 12.2456 | 2.44912 | ||||||||
\(26\) | 7.15763 | 1.40373 | ||||||||
\(27\) | −7.17419 | −1.38067 | ||||||||
\(28\) | 3.02073 | 0.570864 | ||||||||
\(29\) | 10.1658 | 1.88775 | 0.943875 | − | 0.330302i | \(-0.107151\pi\) | ||||
0.943875 | + | 0.330302i | \(0.107151\pi\) | |||||||
\(30\) | 12.0829 | 2.20602 | ||||||||
\(31\) | 4.20950 | 0.756049 | 0.378024 | − | 0.925796i | \(-0.376604\pi\) | ||||
0.378024 | + | 0.925796i | \(0.376604\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.67292 | −0.987528 | ||||||||
\(34\) | 1.01914 | 0.174781 | ||||||||
\(35\) | −12.5444 | −2.12040 | ||||||||
\(36\) | 5.46571 | 0.910951 | ||||||||
\(37\) | 9.42107 | 1.54881 | 0.774407 | − | 0.632688i | \(-0.218048\pi\) | ||||
0.774407 | + | 0.632688i | \(0.218048\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −20.8257 | −3.33479 | ||||||||
\(40\) | −4.15278 | −0.656612 | ||||||||
\(41\) | 0.697666 | 0.108957 | 0.0544786 | − | 0.998515i | \(-0.482650\pi\) | ||||
0.0544786 | + | 0.998515i | \(0.482650\pi\) | |||||||
\(42\) | −8.78908 | −1.35618 | ||||||||
\(43\) | 7.53762 | 1.14948 | 0.574738 | − | 0.818338i | \(-0.305104\pi\) | ||||
0.574738 | + | 0.818338i | \(0.305104\pi\) | |||||||
\(44\) | 1.94973 | 0.293933 | ||||||||
\(45\) | −22.6979 | −3.38360 | ||||||||
\(46\) | 3.81312 | 0.562214 | ||||||||
\(47\) | −5.51721 | −0.804768 | −0.402384 | − | 0.915471i | \(-0.631818\pi\) | ||||
−0.402384 | + | 0.915471i | \(0.631818\pi\) | |||||||
\(48\) | −2.90959 | −0.419963 | ||||||||
\(49\) | 2.12481 | 0.303544 | ||||||||
\(50\) | 12.2456 | 1.73179 | ||||||||
\(51\) | −2.96528 | −0.415222 | ||||||||
\(52\) | 7.15763 | 0.992584 | ||||||||
\(53\) | −3.63798 | −0.499715 | −0.249857 | − | 0.968283i | \(-0.580384\pi\) | ||||
−0.249857 | + | 0.968283i | \(0.580384\pi\) | |||||||
\(54\) | −7.17419 | −0.976283 | ||||||||
\(55\) | −8.09681 | −1.09177 | ||||||||
\(56\) | 3.02073 | 0.403662 | ||||||||
\(57\) | 2.90959 | 0.385384 | ||||||||
\(58\) | 10.1658 | 1.33484 | ||||||||
\(59\) | 7.99315 | 1.04062 | 0.520309 | − | 0.853978i | \(-0.325817\pi\) | ||||
0.520309 | + | 0.853978i | \(0.325817\pi\) | |||||||
\(60\) | 12.0829 | 1.55989 | ||||||||
\(61\) | −1.55823 | −0.199511 | −0.0997557 | − | 0.995012i | \(-0.531806\pi\) | ||||
−0.0997557 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(62\) | 4.20950 | 0.534607 | ||||||||
\(63\) | 16.5104 | 2.08012 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −29.7241 | −3.68682 | ||||||||
\(66\) | −5.67292 | −0.698288 | ||||||||
\(67\) | 1.68379 | 0.205708 | 0.102854 | − | 0.994696i | \(-0.467203\pi\) | ||||
0.102854 | + | 0.994696i | \(0.467203\pi\) | |||||||
\(68\) | 1.01914 | 0.123589 | ||||||||
\(69\) | −11.0946 | −1.33563 | ||||||||
\(70\) | −12.5444 | −1.49935 | ||||||||
\(71\) | −11.8559 | −1.40704 | −0.703518 | − | 0.710678i | \(-0.748388\pi\) | ||||
−0.703518 | + | 0.710678i | \(0.748388\pi\) | |||||||
\(72\) | 5.46571 | 0.644140 | ||||||||
\(73\) | 3.13570 | 0.367006 | 0.183503 | − | 0.983019i | \(-0.441256\pi\) | ||||
0.183503 | + | 0.983019i | \(0.441256\pi\) | |||||||
\(74\) | 9.42107 | 1.09518 | ||||||||
\(75\) | −35.6296 | −4.11415 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 5.88961 | 0.671183 | ||||||||
\(78\) | −20.8257 | −2.35805 | ||||||||
\(79\) | −1.68328 | −0.189384 | −0.0946918 | − | 0.995507i | \(-0.530187\pi\) | ||||
−0.0946918 | + | 0.995507i | \(0.530187\pi\) | |||||||
\(80\) | −4.15278 | −0.464295 | ||||||||
\(81\) | 4.47682 | 0.497424 | ||||||||
\(82\) | 0.697666 | 0.0770443 | ||||||||
\(83\) | −5.75209 | −0.631374 | −0.315687 | − | 0.948863i | \(-0.602235\pi\) | ||||
−0.315687 | + | 0.948863i | \(0.602235\pi\) | |||||||
\(84\) | −8.78908 | −0.958967 | ||||||||
\(85\) | −4.23226 | −0.459053 | ||||||||
\(86\) | 7.53762 | 0.812802 | ||||||||
\(87\) | −29.5784 | −3.17114 | ||||||||
\(88\) | 1.94973 | 0.207842 | ||||||||
\(89\) | −8.16873 | −0.865884 | −0.432942 | − | 0.901422i | \(-0.642524\pi\) | ||||
−0.432942 | + | 0.901422i | \(0.642524\pi\) | |||||||
\(90\) | −22.6979 | −2.39257 | ||||||||
\(91\) | 21.6213 | 2.26652 | ||||||||
\(92\) | 3.81312 | 0.397545 | ||||||||
\(93\) | −12.2479 | −1.27005 | ||||||||
\(94\) | −5.51721 | −0.569057 | ||||||||
\(95\) | 4.15278 | 0.426066 | ||||||||
\(96\) | −2.90959 | −0.296959 | ||||||||
\(97\) | 11.4176 | 1.15928 | 0.579642 | − | 0.814871i | \(-0.303193\pi\) | ||||
0.579642 | + | 0.814871i | \(0.303193\pi\) | |||||||
\(98\) | 2.12481 | 0.214638 | ||||||||
\(99\) | 10.6567 | 1.07103 | ||||||||
\(100\) | 12.2456 | 1.22456 | ||||||||
\(101\) | 17.1859 | 1.71006 | 0.855031 | − | 0.518577i | \(-0.173538\pi\) | ||||
0.855031 | + | 0.518577i | \(0.173538\pi\) | |||||||
\(102\) | −2.96528 | −0.293606 | ||||||||
\(103\) | −0.905175 | −0.0891896 | −0.0445948 | − | 0.999005i | \(-0.514200\pi\) | ||||
−0.0445948 | + | 0.999005i | \(0.514200\pi\) | |||||||
\(104\) | 7.15763 | 0.701863 | ||||||||
\(105\) | 36.4991 | 3.56195 | ||||||||
\(106\) | −3.63798 | −0.353352 | ||||||||
\(107\) | −6.25612 | −0.604802 | −0.302401 | − | 0.953181i | \(-0.597788\pi\) | ||||
−0.302401 | + | 0.953181i | \(0.597788\pi\) | |||||||
\(108\) | −7.17419 | −0.690337 | ||||||||
\(109\) | 6.87919 | 0.658907 | 0.329453 | − | 0.944172i | \(-0.393136\pi\) | ||||
0.329453 | + | 0.944172i | \(0.393136\pi\) | |||||||
\(110\) | −8.09681 | −0.772000 | ||||||||
\(111\) | −27.4114 | −2.60178 | ||||||||
\(112\) | 3.02073 | 0.285432 | ||||||||
\(113\) | −15.0441 | −1.41523 | −0.707616 | − | 0.706598i | \(-0.750229\pi\) | ||||
−0.707616 | + | 0.706598i | \(0.750229\pi\) | |||||||
\(114\) | 2.90959 | 0.272508 | ||||||||
\(115\) | −15.8351 | −1.47663 | ||||||||
\(116\) | 10.1658 | 0.943875 | ||||||||
\(117\) | 39.1215 | 3.61678 | ||||||||
\(118\) | 7.99315 | 0.735829 | ||||||||
\(119\) | 3.07854 | 0.282210 | ||||||||
\(120\) | 12.0829 | 1.10301 | ||||||||
\(121\) | −7.19855 | −0.654413 | ||||||||
\(122\) | −1.55823 | −0.141076 | ||||||||
\(123\) | −2.02992 | −0.183032 | ||||||||
\(124\) | 4.20950 | 0.378024 | ||||||||
\(125\) | −30.0893 | −2.69127 | ||||||||
\(126\) | 16.5104 | 1.47086 | ||||||||
\(127\) | −15.5694 | −1.38156 | −0.690779 | − | 0.723066i | \(-0.742732\pi\) | ||||
−0.690779 | + | 0.723066i | \(0.742732\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −21.9314 | −1.93095 | ||||||||
\(130\) | −29.7241 | −2.60697 | ||||||||
\(131\) | −15.0676 | −1.31646 | −0.658229 | − | 0.752818i | \(-0.728694\pi\) | ||||
−0.658229 | + | 0.752818i | \(0.728694\pi\) | |||||||
\(132\) | −5.67292 | −0.493764 | ||||||||
\(133\) | −3.02073 | −0.261930 | ||||||||
\(134\) | 1.68379 | 0.145457 | ||||||||
\(135\) | 29.7928 | 2.56416 | ||||||||
\(136\) | 1.01914 | 0.0873905 | ||||||||
\(137\) | 3.33949 | 0.285312 | 0.142656 | − | 0.989772i | \(-0.454436\pi\) | ||||
0.142656 | + | 0.989772i | \(0.454436\pi\) | |||||||
\(138\) | −11.0946 | −0.944436 | ||||||||
\(139\) | 19.3076 | 1.63765 | 0.818826 | − | 0.574042i | \(-0.194625\pi\) | ||||
0.818826 | + | 0.574042i | \(0.194625\pi\) | |||||||
\(140\) | −12.5444 | −1.06020 | ||||||||
\(141\) | 16.0528 | 1.35189 | ||||||||
\(142\) | −11.8559 | −0.994924 | ||||||||
\(143\) | 13.9554 | 1.16701 | ||||||||
\(144\) | 5.46571 | 0.455475 | ||||||||
\(145\) | −42.2165 | −3.50589 | ||||||||
\(146\) | 3.13570 | 0.259513 | ||||||||
\(147\) | −6.18231 | −0.509909 | ||||||||
\(148\) | 9.42107 | 0.774407 | ||||||||
\(149\) | 5.10176 | 0.417953 | 0.208976 | − | 0.977921i | \(-0.432987\pi\) | ||||
0.208976 | + | 0.977921i | \(0.432987\pi\) | |||||||
\(150\) | −35.6296 | −2.90915 | ||||||||
\(151\) | 12.0241 | 0.978505 | 0.489252 | − | 0.872142i | \(-0.337270\pi\) | ||||
0.489252 | + | 0.872142i | \(0.337270\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 5.57031 | 0.450333 | ||||||||
\(154\) | 5.88961 | 0.474598 | ||||||||
\(155\) | −17.4811 | −1.40412 | ||||||||
\(156\) | −20.8257 | −1.66739 | ||||||||
\(157\) | −2.70273 | −0.215701 | −0.107851 | − | 0.994167i | \(-0.534397\pi\) | ||||
−0.107851 | + | 0.994167i | \(0.534397\pi\) | |||||||
\(158\) | −1.68328 | −0.133914 | ||||||||
\(159\) | 10.5850 | 0.839447 | ||||||||
\(160\) | −4.15278 | −0.328306 | ||||||||
\(161\) | 11.5184 | 0.907778 | ||||||||
\(162\) | 4.47682 | 0.351732 | ||||||||
\(163\) | 13.4310 | 1.05200 | 0.525999 | − | 0.850485i | \(-0.323692\pi\) | ||||
0.525999 | + | 0.850485i | \(0.323692\pi\) | |||||||
\(164\) | 0.697666 | 0.0544786 | ||||||||
\(165\) | 23.5584 | 1.83402 | ||||||||
\(166\) | −5.75209 | −0.446449 | ||||||||
\(167\) | −9.30505 | −0.720046 | −0.360023 | − | 0.932943i | \(-0.617231\pi\) | ||||
−0.360023 | + | 0.932943i | \(0.617231\pi\) | |||||||
\(168\) | −8.78908 | −0.678092 | ||||||||
\(169\) | 38.2316 | 2.94089 | ||||||||
\(170\) | −4.23226 | −0.324600 | ||||||||
\(171\) | −5.46571 | −0.417973 | ||||||||
\(172\) | 7.53762 | 0.574738 | ||||||||
\(173\) | −5.62614 | −0.427747 | −0.213874 | − | 0.976861i | \(-0.568608\pi\) | ||||
−0.213874 | + | 0.976861i | \(0.568608\pi\) | |||||||
\(174\) | −29.5784 | −2.24234 | ||||||||
\(175\) | 36.9906 | 2.79623 | ||||||||
\(176\) | 1.94973 | 0.146967 | ||||||||
\(177\) | −23.2568 | −1.74809 | ||||||||
\(178\) | −8.16873 | −0.612272 | ||||||||
\(179\) | 6.67942 | 0.499243 | 0.249622 | − | 0.968343i | \(-0.419694\pi\) | ||||
0.249622 | + | 0.968343i | \(0.419694\pi\) | |||||||
\(180\) | −22.6979 | −1.69180 | ||||||||
\(181\) | −16.2828 | −1.21029 | −0.605145 | − | 0.796116i | \(-0.706885\pi\) | ||||
−0.605145 | + | 0.796116i | \(0.706885\pi\) | |||||||
\(182\) | 21.6213 | 1.60267 | ||||||||
\(183\) | 4.53382 | 0.335149 | ||||||||
\(184\) | 3.81312 | 0.281107 | ||||||||
\(185\) | −39.1236 | −2.87643 | ||||||||
\(186\) | −12.2479 | −0.898061 | ||||||||
\(187\) | 1.98705 | 0.145307 | ||||||||
\(188\) | −5.51721 | −0.402384 | ||||||||
\(189\) | −21.6713 | −1.57635 | ||||||||
\(190\) | 4.15278 | 0.301274 | ||||||||
\(191\) | 16.0005 | 1.15775 | 0.578877 | − | 0.815415i | \(-0.303491\pi\) | ||||
0.578877 | + | 0.815415i | \(0.303491\pi\) | |||||||
\(192\) | −2.90959 | −0.209981 | ||||||||
\(193\) | −12.4466 | −0.895926 | −0.447963 | − | 0.894052i | \(-0.647850\pi\) | ||||
−0.447963 | + | 0.894052i | \(0.647850\pi\) | |||||||
\(194\) | 11.4176 | 0.819737 | ||||||||
\(195\) | 86.4848 | 6.19330 | ||||||||
\(196\) | 2.12481 | 0.151772 | ||||||||
\(197\) | 14.3766 | 1.02429 | 0.512144 | − | 0.858899i | \(-0.328851\pi\) | ||||
0.512144 | + | 0.858899i | \(0.328851\pi\) | |||||||
\(198\) | 10.6567 | 0.757336 | ||||||||
\(199\) | 19.1040 | 1.35425 | 0.677125 | − | 0.735868i | \(-0.263226\pi\) | ||||
0.677125 | + | 0.735868i | \(0.263226\pi\) | |||||||
\(200\) | 12.2456 | 0.865894 | ||||||||
\(201\) | −4.89914 | −0.345558 | ||||||||
\(202\) | 17.1859 | 1.20920 | ||||||||
\(203\) | 30.7083 | 2.15530 | ||||||||
\(204\) | −2.96528 | −0.207611 | ||||||||
\(205\) | −2.89725 | −0.202353 | ||||||||
\(206\) | −0.905175 | −0.0630665 | ||||||||
\(207\) | 20.8414 | 1.44858 | ||||||||
\(208\) | 7.15763 | 0.496292 | ||||||||
\(209\) | −1.94973 | −0.134866 | ||||||||
\(210\) | 36.4991 | 2.51868 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −3.63798 | −0.249857 | ||||||||
\(213\) | 34.4958 | 2.36361 | ||||||||
\(214\) | −6.25612 | −0.427660 | ||||||||
\(215\) | −31.3021 | −2.13478 | ||||||||
\(216\) | −7.17419 | −0.488142 | ||||||||
\(217\) | 12.7158 | 0.863203 | ||||||||
\(218\) | 6.87919 | 0.465917 | ||||||||
\(219\) | −9.12361 | −0.616516 | ||||||||
\(220\) | −8.09681 | −0.545887 | ||||||||
\(221\) | 7.29462 | 0.490689 | ||||||||
\(222\) | −27.4114 | −1.83974 | ||||||||
\(223\) | −17.1649 | −1.14945 | −0.574724 | − | 0.818347i | \(-0.694891\pi\) | ||||
−0.574724 | + | 0.818347i | \(0.694891\pi\) | |||||||
\(224\) | 3.02073 | 0.201831 | ||||||||
\(225\) | 66.9308 | 4.46205 | ||||||||
\(226\) | −15.0441 | −1.00072 | ||||||||
\(227\) | −14.3527 | −0.952622 | −0.476311 | − | 0.879277i | \(-0.658026\pi\) | ||||
−0.476311 | + | 0.879277i | \(0.658026\pi\) | |||||||
\(228\) | 2.90959 | 0.192692 | ||||||||
\(229\) | 6.65984 | 0.440095 | 0.220047 | − | 0.975489i | \(-0.429379\pi\) | ||||
0.220047 | + | 0.975489i | \(0.429379\pi\) | |||||||
\(230\) | −15.8351 | −1.04413 | ||||||||
\(231\) | −17.1363 | −1.12749 | ||||||||
\(232\) | 10.1658 | 0.667421 | ||||||||
\(233\) | 9.07581 | 0.594576 | 0.297288 | − | 0.954788i | \(-0.403918\pi\) | ||||
0.297288 | + | 0.954788i | \(0.403918\pi\) | |||||||
\(234\) | 39.1215 | 2.55745 | ||||||||
\(235\) | 22.9118 | 1.49460 | ||||||||
\(236\) | 7.99315 | 0.520309 | ||||||||
\(237\) | 4.89764 | 0.318136 | ||||||||
\(238\) | 3.07854 | 0.199552 | ||||||||
\(239\) | −14.6906 | −0.950257 | −0.475128 | − | 0.879916i | \(-0.657598\pi\) | ||||
−0.475128 | + | 0.879916i | \(0.657598\pi\) | |||||||
\(240\) | 12.0829 | 0.779947 | ||||||||
\(241\) | −23.1588 | −1.49179 | −0.745894 | − | 0.666065i | \(-0.767977\pi\) | ||||
−0.745894 | + | 0.666065i | \(0.767977\pi\) | |||||||
\(242\) | −7.19855 | −0.462740 | ||||||||
\(243\) | 8.49686 | 0.545074 | ||||||||
\(244\) | −1.55823 | −0.0997557 | ||||||||
\(245\) | −8.82386 | −0.563736 | ||||||||
\(246\) | −2.02992 | −0.129423 | ||||||||
\(247\) | −7.15763 | −0.455429 | ||||||||
\(248\) | 4.20950 | 0.267304 | ||||||||
\(249\) | 16.7362 | 1.06061 | ||||||||
\(250\) | −30.0893 | −1.90302 | ||||||||
\(251\) | −12.5886 | −0.794588 | −0.397294 | − | 0.917691i | \(-0.630051\pi\) | ||||
−0.397294 | + | 0.917691i | \(0.630051\pi\) | |||||||
\(252\) | 16.5104 | 1.04006 | ||||||||
\(253\) | 7.43456 | 0.467407 | ||||||||
\(254\) | −15.5694 | −0.976909 | ||||||||
\(255\) | 12.3141 | 0.771141 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.4693 | −1.46397 | −0.731986 | − | 0.681319i | \(-0.761406\pi\) | ||||
−0.731986 | + | 0.681319i | \(0.761406\pi\) | |||||||
\(258\) | −21.9314 | −1.36539 | ||||||||
\(259\) | 28.4585 | 1.76833 | ||||||||
\(260\) | −29.7241 | −1.84341 | ||||||||
\(261\) | 55.5635 | 3.43930 | ||||||||
\(262\) | −15.0676 | −0.930877 | ||||||||
\(263\) | 6.34196 | 0.391062 | 0.195531 | − | 0.980698i | \(-0.437357\pi\) | ||||
0.195531 | + | 0.980698i | \(0.437357\pi\) | |||||||
\(264\) | −5.67292 | −0.349144 | ||||||||
\(265\) | 15.1077 | 0.928060 | ||||||||
\(266\) | −3.02073 | −0.185213 | ||||||||
\(267\) | 23.7676 | 1.45456 | ||||||||
\(268\) | 1.68379 | 0.102854 | ||||||||
\(269\) | 19.2182 | 1.17176 | 0.585878 | − | 0.810400i | \(-0.300750\pi\) | ||||
0.585878 | + | 0.810400i | \(0.300750\pi\) | |||||||
\(270\) | 29.7928 | 1.81313 | ||||||||
\(271\) | −27.7948 | −1.68842 | −0.844208 | − | 0.536015i | \(-0.819929\pi\) | ||||
−0.844208 | + | 0.536015i | \(0.819929\pi\) | |||||||
\(272\) | 1.01914 | 0.0617944 | ||||||||
\(273\) | −62.9089 | −3.80742 | ||||||||
\(274\) | 3.33949 | 0.201746 | ||||||||
\(275\) | 23.8756 | 1.43975 | ||||||||
\(276\) | −11.0946 | −0.667817 | ||||||||
\(277\) | −8.51136 | −0.511398 | −0.255699 | − | 0.966756i | \(-0.582306\pi\) | ||||
−0.255699 | + | 0.966756i | \(0.582306\pi\) | |||||||
\(278\) | 19.3076 | 1.15799 | ||||||||
\(279\) | 23.0079 | 1.37745 | ||||||||
\(280\) | −12.5444 | −0.749673 | ||||||||
\(281\) | 29.3230 | 1.74926 | 0.874632 | − | 0.484787i | \(-0.161103\pi\) | ||||
0.874632 | + | 0.484787i | \(0.161103\pi\) | |||||||
\(282\) | 16.0528 | 0.955931 | ||||||||
\(283\) | 1.05656 | 0.0628062 | 0.0314031 | − | 0.999507i | \(-0.490002\pi\) | ||||
0.0314031 | + | 0.999507i | \(0.490002\pi\) | |||||||
\(284\) | −11.8559 | −0.703518 | ||||||||
\(285\) | −12.0829 | −0.715728 | ||||||||
\(286\) | 13.9554 | 0.825203 | ||||||||
\(287\) | 2.10746 | 0.124399 | ||||||||
\(288\) | 5.46571 | 0.322070 | ||||||||
\(289\) | −15.9614 | −0.938903 | ||||||||
\(290\) | −42.2165 | −2.47904 | ||||||||
\(291\) | −33.2206 | −1.94742 | ||||||||
\(292\) | 3.13570 | 0.183503 | ||||||||
\(293\) | −12.4399 | −0.726745 | −0.363373 | − | 0.931644i | \(-0.618375\pi\) | ||||
−0.363373 | + | 0.931644i | \(0.618375\pi\) | |||||||
\(294\) | −6.18231 | −0.360560 | ||||||||
\(295\) | −33.1938 | −1.93262 | ||||||||
\(296\) | 9.42107 | 0.547589 | ||||||||
\(297\) | −13.9877 | −0.811651 | ||||||||
\(298\) | 5.10176 | 0.295537 | ||||||||
\(299\) | 27.2929 | 1.57839 | ||||||||
\(300\) | −35.6296 | −2.05708 | ||||||||
\(301\) | 22.7691 | 1.31239 | ||||||||
\(302\) | 12.0241 | 0.691907 | ||||||||
\(303\) | −50.0039 | −2.87265 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 6.47100 | 0.370528 | ||||||||
\(306\) | 5.57031 | 0.318434 | ||||||||
\(307\) | −17.3312 | −0.989141 | −0.494571 | − | 0.869137i | \(-0.664675\pi\) | ||||
−0.494571 | + | 0.869137i | \(0.664675\pi\) | |||||||
\(308\) | 5.88961 | 0.335592 | ||||||||
\(309\) | 2.63369 | 0.149825 | ||||||||
\(310\) | −17.4811 | −0.992862 | ||||||||
\(311\) | −2.20615 | −0.125099 | −0.0625496 | − | 0.998042i | \(-0.519923\pi\) | ||||
−0.0625496 | + | 0.998042i | \(0.519923\pi\) | |||||||
\(312\) | −20.8257 | −1.17903 | ||||||||
\(313\) | 18.6570 | 1.05456 | 0.527278 | − | 0.849693i | \(-0.323213\pi\) | ||||
0.527278 | + | 0.849693i | \(0.323213\pi\) | |||||||
\(314\) | −2.70273 | −0.152524 | ||||||||
\(315\) | −68.5641 | −3.86315 | ||||||||
\(316\) | −1.68328 | −0.0946918 | ||||||||
\(317\) | 4.76007 | 0.267352 | 0.133676 | − | 0.991025i | \(-0.457322\pi\) | ||||
0.133676 | + | 0.991025i | \(0.457322\pi\) | |||||||
\(318\) | 10.5850 | 0.593578 | ||||||||
\(319\) | 19.8207 | 1.10974 | ||||||||
\(320\) | −4.15278 | −0.232148 | ||||||||
\(321\) | 18.2027 | 1.01598 | ||||||||
\(322\) | 11.5184 | 0.641896 | ||||||||
\(323\) | −1.01914 | −0.0567064 | ||||||||
\(324\) | 4.47682 | 0.248712 | ||||||||
\(325\) | 87.6494 | 4.86191 | ||||||||
\(326\) | 13.4310 | 0.743875 | ||||||||
\(327\) | −20.0156 | −1.10687 | ||||||||
\(328\) | 0.697666 | 0.0385222 | ||||||||
\(329\) | −16.6660 | −0.918826 | ||||||||
\(330\) | 23.5584 | 1.29685 | ||||||||
\(331\) | 11.8428 | 0.650938 | 0.325469 | − | 0.945553i | \(-0.394478\pi\) | ||||
0.325469 | + | 0.945553i | \(0.394478\pi\) | |||||||
\(332\) | −5.75209 | −0.315687 | ||||||||
\(333\) | 51.4928 | 2.82179 | ||||||||
\(334\) | −9.30505 | −0.509150 | ||||||||
\(335\) | −6.99241 | −0.382036 | ||||||||
\(336\) | −8.78908 | −0.479484 | ||||||||
\(337\) | −23.8124 | −1.29714 | −0.648572 | − | 0.761153i | \(-0.724634\pi\) | ||||
−0.648572 | + | 0.761153i | \(0.724634\pi\) | |||||||
\(338\) | 38.2316 | 2.07953 | ||||||||
\(339\) | 43.7722 | 2.37738 | ||||||||
\(340\) | −4.23226 | −0.229527 | ||||||||
\(341\) | 8.20740 | 0.444455 | ||||||||
\(342\) | −5.46571 | −0.295551 | ||||||||
\(343\) | −14.7266 | −0.795164 | ||||||||
\(344\) | 7.53762 | 0.406401 | ||||||||
\(345\) | 46.0735 | 2.48051 | ||||||||
\(346\) | −5.62614 | −0.302463 | ||||||||
\(347\) | 34.6997 | 1.86278 | 0.931388 | − | 0.364027i | \(-0.118599\pi\) | ||||
0.931388 | + | 0.364027i | \(0.118599\pi\) | |||||||
\(348\) | −29.5784 | −1.58557 | ||||||||
\(349\) | −29.2926 | −1.56800 | −0.784000 | − | 0.620761i | \(-0.786824\pi\) | ||||
−0.784000 | + | 0.620761i | \(0.786824\pi\) | |||||||
\(350\) | 36.9906 | 1.97723 | ||||||||
\(351\) | −51.3502 | −2.74087 | ||||||||
\(352\) | 1.94973 | 0.103921 | ||||||||
\(353\) | −5.86582 | −0.312206 | −0.156103 | − | 0.987741i | \(-0.549893\pi\) | ||||
−0.156103 | + | 0.987741i | \(0.549893\pi\) | |||||||
\(354\) | −23.2568 | −1.23608 | ||||||||
\(355\) | 49.2349 | 2.61312 | ||||||||
\(356\) | −8.16873 | −0.432942 | ||||||||
\(357\) | −8.95730 | −0.474070 | ||||||||
\(358\) | 6.67942 | 0.353018 | ||||||||
\(359\) | −0.441918 | −0.0233235 | −0.0116618 | − | 0.999932i | \(-0.503712\pi\) | ||||
−0.0116618 | + | 0.999932i | \(0.503712\pi\) | |||||||
\(360\) | −22.6979 | −1.19628 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −16.2828 | −0.855804 | ||||||||
\(363\) | 20.9448 | 1.09932 | ||||||||
\(364\) | 21.6213 | 1.13326 | ||||||||
\(365\) | −13.0219 | −0.681597 | ||||||||
\(366\) | 4.53382 | 0.236986 | ||||||||
\(367\) | 17.2015 | 0.897911 | 0.448955 | − | 0.893554i | \(-0.351796\pi\) | ||||
0.448955 | + | 0.893554i | \(0.351796\pi\) | |||||||
\(368\) | 3.81312 | 0.198773 | ||||||||
\(369\) | 3.81324 | 0.198509 | ||||||||
\(370\) | −39.1236 | −2.03394 | ||||||||
\(371\) | −10.9893 | −0.570539 | ||||||||
\(372\) | −12.2479 | −0.635025 | ||||||||
\(373\) | 10.6175 | 0.549755 | 0.274877 | − | 0.961479i | \(-0.411363\pi\) | ||||
0.274877 | + | 0.961479i | \(0.411363\pi\) | |||||||
\(374\) | 1.98705 | 0.102748 | ||||||||
\(375\) | 87.5476 | 4.52094 | ||||||||
\(376\) | −5.51721 | −0.284528 | ||||||||
\(377\) | 72.7633 | 3.74750 | ||||||||
\(378\) | −21.6713 | −1.11465 | ||||||||
\(379\) | −17.9307 | −0.921037 | −0.460519 | − | 0.887650i | \(-0.652337\pi\) | ||||
−0.460519 | + | 0.887650i | \(0.652337\pi\) | |||||||
\(380\) | 4.15278 | 0.213033 | ||||||||
\(381\) | 45.3004 | 2.32081 | ||||||||
\(382\) | 16.0005 | 0.818655 | ||||||||
\(383\) | 17.9992 | 0.919716 | 0.459858 | − | 0.887992i | \(-0.347900\pi\) | ||||
0.459858 | + | 0.887992i | \(0.347900\pi\) | |||||||
\(384\) | −2.90959 | −0.148479 | ||||||||
\(385\) | −24.4583 | −1.24651 | ||||||||
\(386\) | −12.4466 | −0.633515 | ||||||||
\(387\) | 41.1984 | 2.09423 | ||||||||
\(388\) | 11.4176 | 0.579642 | ||||||||
\(389\) | −31.9610 | −1.62049 | −0.810243 | − | 0.586094i | \(-0.800665\pi\) | ||||
−0.810243 | + | 0.586094i | \(0.800665\pi\) | |||||||
\(390\) | 86.4848 | 4.37933 | ||||||||
\(391\) | 3.88610 | 0.196529 | ||||||||
\(392\) | 2.12481 | 0.107319 | ||||||||
\(393\) | 43.8404 | 2.21145 | ||||||||
\(394\) | 14.3766 | 0.724281 | ||||||||
\(395\) | 6.99028 | 0.351719 | ||||||||
\(396\) | 10.6567 | 0.535517 | ||||||||
\(397\) | 7.68750 | 0.385825 | 0.192912 | − | 0.981216i | \(-0.438207\pi\) | ||||
0.192912 | + | 0.981216i | \(0.438207\pi\) | |||||||
\(398\) | 19.1040 | 0.957599 | ||||||||
\(399\) | 8.78908 | 0.440004 | ||||||||
\(400\) | 12.2456 | 0.612279 | ||||||||
\(401\) | 31.2202 | 1.55906 | 0.779532 | − | 0.626362i | \(-0.215457\pi\) | ||||
0.779532 | + | 0.626362i | \(0.215457\pi\) | |||||||
\(402\) | −4.89914 | −0.244347 | ||||||||
\(403\) | 30.1300 | 1.50088 | ||||||||
\(404\) | 17.1859 | 0.855031 | ||||||||
\(405\) | −18.5912 | −0.923807 | ||||||||
\(406\) | 30.7083 | 1.52403 | ||||||||
\(407\) | 18.3686 | 0.910495 | ||||||||
\(408\) | −2.96528 | −0.146803 | ||||||||
\(409\) | 33.3660 | 1.64984 | 0.824921 | − | 0.565249i | \(-0.191220\pi\) | ||||
0.824921 | + | 0.565249i | \(0.191220\pi\) | |||||||
\(410\) | −2.89725 | −0.143085 | ||||||||
\(411\) | −9.71653 | −0.479281 | ||||||||
\(412\) | −0.905175 | −0.0445948 | ||||||||
\(413\) | 24.1451 | 1.18810 | ||||||||
\(414\) | 20.8414 | 1.02430 | ||||||||
\(415\) | 23.8872 | 1.17258 | ||||||||
\(416\) | 7.15763 | 0.350931 | ||||||||
\(417\) | −56.1773 | −2.75101 | ||||||||
\(418\) | −1.94973 | −0.0953645 | ||||||||
\(419\) | −13.8340 | −0.675837 | −0.337919 | − | 0.941175i | \(-0.609723\pi\) | ||||
−0.337919 | + | 0.941175i | \(0.609723\pi\) | |||||||
\(420\) | 36.4991 | 1.78097 | ||||||||
\(421\) | 17.9771 | 0.876152 | 0.438076 | − | 0.898938i | \(-0.355660\pi\) | ||||
0.438076 | + | 0.898938i | \(0.355660\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −30.1554 | −1.46621 | ||||||||
\(424\) | −3.63798 | −0.176676 | ||||||||
\(425\) | 12.4800 | 0.605367 | ||||||||
\(426\) | 34.4958 | 1.67132 | ||||||||
\(427\) | −4.70700 | −0.227788 | ||||||||
\(428\) | −6.25612 | −0.302401 | ||||||||
\(429\) | −40.6046 | −1.96041 | ||||||||
\(430\) | −31.3021 | −1.50952 | ||||||||
\(431\) | 34.4107 | 1.65750 | 0.828752 | − | 0.559616i | \(-0.189052\pi\) | ||||
0.828752 | + | 0.559616i | \(0.189052\pi\) | |||||||
\(432\) | −7.17419 | −0.345168 | ||||||||
\(433\) | −32.8764 | −1.57994 | −0.789969 | − | 0.613147i | \(-0.789903\pi\) | ||||
−0.789969 | + | 0.613147i | \(0.789903\pi\) | |||||||
\(434\) | 12.7158 | 0.610376 | ||||||||
\(435\) | 122.833 | 5.88938 | ||||||||
\(436\) | 6.87919 | 0.329453 | ||||||||
\(437\) | −3.81312 | −0.182406 | ||||||||
\(438\) | −9.12361 | −0.435943 | ||||||||
\(439\) | 12.5408 | 0.598539 | 0.299270 | − | 0.954169i | \(-0.403257\pi\) | ||||
0.299270 | + | 0.954169i | \(0.403257\pi\) | |||||||
\(440\) | −8.09681 | −0.386000 | ||||||||
\(441\) | 11.6136 | 0.553027 | ||||||||
\(442\) | 7.29462 | 0.346970 | ||||||||
\(443\) | −7.63728 | −0.362858 | −0.181429 | − | 0.983404i | \(-0.558072\pi\) | ||||
−0.181429 | + | 0.983404i | \(0.558072\pi\) | |||||||
\(444\) | −27.4114 | −1.30089 | ||||||||
\(445\) | 33.9229 | 1.60810 | ||||||||
\(446\) | −17.1649 | −0.812783 | ||||||||
\(447\) | −14.8440 | −0.702098 | ||||||||
\(448\) | 3.02073 | 0.142716 | ||||||||
\(449\) | −16.9124 | −0.798148 | −0.399074 | − | 0.916919i | \(-0.630668\pi\) | ||||
−0.399074 | + | 0.916919i | \(0.630668\pi\) | |||||||
\(450\) | 66.9308 | 3.15515 | ||||||||
\(451\) | 1.36026 | 0.0640522 | ||||||||
\(452\) | −15.0441 | −0.707616 | ||||||||
\(453\) | −34.9851 | −1.64374 | ||||||||
\(454\) | −14.3527 | −0.673606 | ||||||||
\(455\) | −89.7883 | −4.20934 | ||||||||
\(456\) | 2.90959 | 0.136254 | ||||||||
\(457\) | −17.7455 | −0.830102 | −0.415051 | − | 0.909798i | \(-0.636236\pi\) | ||||
−0.415051 | + | 0.909798i | \(0.636236\pi\) | |||||||
\(458\) | 6.65984 | 0.311194 | ||||||||
\(459\) | −7.31150 | −0.341271 | ||||||||
\(460\) | −15.8351 | −0.738313 | ||||||||
\(461\) | −28.6682 | −1.33521 | −0.667606 | − | 0.744515i | \(-0.732681\pi\) | ||||
−0.667606 | + | 0.744515i | \(0.732681\pi\) | |||||||
\(462\) | −17.1363 | −0.797255 | ||||||||
\(463\) | 2.56062 | 0.119002 | 0.0595011 | − | 0.998228i | \(-0.481049\pi\) | ||||
0.0595011 | + | 0.998228i | \(0.481049\pi\) | |||||||
\(464\) | 10.1658 | 0.471938 | ||||||||
\(465\) | 50.8629 | 2.35871 | ||||||||
\(466\) | 9.07581 | 0.420429 | ||||||||
\(467\) | −20.0042 | −0.925682 | −0.462841 | − | 0.886441i | \(-0.653170\pi\) | ||||
−0.462841 | + | 0.886441i | \(0.653170\pi\) | |||||||
\(468\) | 39.1215 | 1.80839 | ||||||||
\(469\) | 5.08627 | 0.234862 | ||||||||
\(470\) | 22.9118 | 1.05684 | ||||||||
\(471\) | 7.86384 | 0.362346 | ||||||||
\(472\) | 7.99315 | 0.367914 | ||||||||
\(473\) | 14.6963 | 0.675738 | ||||||||
\(474\) | 4.89764 | 0.224956 | ||||||||
\(475\) | −12.2456 | −0.561866 | ||||||||
\(476\) | 3.07854 | 0.141105 | ||||||||
\(477\) | −19.8841 | −0.910431 | ||||||||
\(478\) | −14.6906 | −0.671933 | ||||||||
\(479\) | 5.04331 | 0.230435 | 0.115217 | − | 0.993340i | \(-0.463244\pi\) | ||||
0.115217 | + | 0.993340i | \(0.463244\pi\) | |||||||
\(480\) | 12.0829 | 0.551506 | ||||||||
\(481\) | 67.4325 | 3.07466 | ||||||||
\(482\) | −23.1588 | −1.05485 | ||||||||
\(483\) | −33.5138 | −1.52493 | ||||||||
\(484\) | −7.19855 | −0.327207 | ||||||||
\(485\) | −47.4149 | −2.15300 | ||||||||
\(486\) | 8.49686 | 0.385426 | ||||||||
\(487\) | 11.0808 | 0.502118 | 0.251059 | − | 0.967972i | \(-0.419221\pi\) | ||||
0.251059 | + | 0.967972i | \(0.419221\pi\) | |||||||
\(488\) | −1.55823 | −0.0705379 | ||||||||
\(489\) | −39.0787 | −1.76720 | ||||||||
\(490\) | −8.82386 | −0.398621 | ||||||||
\(491\) | 9.19476 | 0.414954 | 0.207477 | − | 0.978240i | \(-0.433475\pi\) | ||||
0.207477 | + | 0.978240i | \(0.433475\pi\) | |||||||
\(492\) | −2.02992 | −0.0915159 | ||||||||
\(493\) | 10.3604 | 0.466610 | ||||||||
\(494\) | −7.15763 | −0.322037 | ||||||||
\(495\) | −44.2548 | −1.98910 | ||||||||
\(496\) | 4.20950 | 0.189012 | ||||||||
\(497\) | −35.8134 | −1.60645 | ||||||||
\(498\) | 16.7362 | 0.749968 | ||||||||
\(499\) | −29.6428 | −1.32699 | −0.663496 | − | 0.748180i | \(-0.730928\pi\) | ||||
−0.663496 | + | 0.748180i | \(0.730928\pi\) | |||||||
\(500\) | −30.0893 | −1.34564 | ||||||||
\(501\) | 27.0739 | 1.20957 | ||||||||
\(502\) | −12.5886 | −0.561859 | ||||||||
\(503\) | 3.40931 | 0.152013 | 0.0760067 | − | 0.997107i | \(-0.475783\pi\) | ||||
0.0760067 | + | 0.997107i | \(0.475783\pi\) | |||||||
\(504\) | 16.5104 | 0.735432 | ||||||||
\(505\) | −71.3693 | −3.17589 | ||||||||
\(506\) | 7.43456 | 0.330507 | ||||||||
\(507\) | −111.238 | −4.94026 | ||||||||
\(508\) | −15.5694 | −0.690779 | ||||||||
\(509\) | 32.1399 | 1.42458 | 0.712289 | − | 0.701886i | \(-0.247659\pi\) | ||||
0.712289 | + | 0.701886i | \(0.247659\pi\) | |||||||
\(510\) | 12.3141 | 0.545279 | ||||||||
\(511\) | 9.47211 | 0.419022 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.17419 | 0.316748 | ||||||||
\(514\) | −23.4693 | −1.03518 | ||||||||
\(515\) | 3.75899 | 0.165641 | ||||||||
\(516\) | −21.9314 | −0.965474 | ||||||||
\(517\) | −10.7571 | −0.473096 | ||||||||
\(518\) | 28.4585 | 1.25039 | ||||||||
\(519\) | 16.3697 | 0.718552 | ||||||||
\(520\) | −29.7241 | −1.30349 | ||||||||
\(521\) | −3.70118 | −0.162152 | −0.0810759 | − | 0.996708i | \(-0.525836\pi\) | ||||
−0.0810759 | + | 0.996708i | \(0.525836\pi\) | |||||||
\(522\) | 55.5635 | 2.43195 | ||||||||
\(523\) | −16.1140 | −0.704614 | −0.352307 | − | 0.935884i | \(-0.614603\pi\) | ||||
−0.352307 | + | 0.935884i | \(0.614603\pi\) | |||||||
\(524\) | −15.0676 | −0.658229 | ||||||||
\(525\) | −107.627 | −4.69725 | ||||||||
\(526\) | 6.34196 | 0.276522 | ||||||||
\(527\) | 4.29007 | 0.186878 | ||||||||
\(528\) | −5.67292 | −0.246882 | ||||||||
\(529\) | −8.46011 | −0.367831 | ||||||||
\(530\) | 15.1077 | 0.656238 | ||||||||
\(531\) | 43.6882 | 1.89591 | ||||||||
\(532\) | −3.02073 | −0.130965 | ||||||||
\(533\) | 4.99363 | 0.216298 | ||||||||
\(534\) | 23.7676 | 1.02853 | ||||||||
\(535\) | 25.9803 | 1.12323 | ||||||||
\(536\) | 1.68379 | 0.0727287 | ||||||||
\(537\) | −19.4344 | −0.838655 | ||||||||
\(538\) | 19.2182 | 0.828556 | ||||||||
\(539\) | 4.14280 | 0.178443 | ||||||||
\(540\) | 29.7928 | 1.28208 | ||||||||
\(541\) | −26.9278 | −1.15772 | −0.578859 | − | 0.815428i | \(-0.696502\pi\) | ||||
−0.578859 | + | 0.815428i | \(0.696502\pi\) | |||||||
\(542\) | −27.7948 | −1.19389 | ||||||||
\(543\) | 47.3762 | 2.03311 | ||||||||
\(544\) | 1.01914 | 0.0436952 | ||||||||
\(545\) | −28.5678 | −1.22371 | ||||||||
\(546\) | −62.9089 | −2.69225 | ||||||||
\(547\) | −3.90587 | −0.167003 | −0.0835016 | − | 0.996508i | \(-0.526610\pi\) | ||||
−0.0835016 | + | 0.996508i | \(0.526610\pi\) | |||||||
\(548\) | 3.33949 | 0.142656 | ||||||||
\(549\) | −8.51684 | −0.363490 | ||||||||
\(550\) | 23.8756 | 1.01806 | ||||||||
\(551\) | −10.1658 | −0.433080 | ||||||||
\(552\) | −11.0946 | −0.472218 | ||||||||
\(553\) | −5.08473 | −0.216225 | ||||||||
\(554\) | −8.51136 | −0.361613 | ||||||||
\(555\) | 113.834 | 4.83197 | ||||||||
\(556\) | 19.3076 | 0.818826 | ||||||||
\(557\) | 38.7742 | 1.64292 | 0.821458 | − | 0.570269i | \(-0.193161\pi\) | ||||
0.821458 | + | 0.570269i | \(0.193161\pi\) | |||||||
\(558\) | 23.0079 | 0.974002 | ||||||||
\(559\) | 53.9514 | 2.28190 | ||||||||
\(560\) | −12.5444 | −0.530099 | ||||||||
\(561\) | −5.78149 | −0.244095 | ||||||||
\(562\) | 29.3230 | 1.23692 | ||||||||
\(563\) | 34.8720 | 1.46968 | 0.734840 | − | 0.678240i | \(-0.237257\pi\) | ||||
0.734840 | + | 0.678240i | \(0.237257\pi\) | |||||||
\(564\) | 16.0528 | 0.675945 | ||||||||
\(565\) | 62.4749 | 2.62834 | ||||||||
\(566\) | 1.05656 | 0.0444107 | ||||||||
\(567\) | 13.5233 | 0.567924 | ||||||||
\(568\) | −11.8559 | −0.497462 | ||||||||
\(569\) | −14.2554 | −0.597616 | −0.298808 | − | 0.954313i | \(-0.596589\pi\) | ||||
−0.298808 | + | 0.954313i | \(0.596589\pi\) | |||||||
\(570\) | −12.0829 | −0.506096 | ||||||||
\(571\) | 5.78533 | 0.242109 | 0.121054 | − | 0.992646i | \(-0.461372\pi\) | ||||
0.121054 | + | 0.992646i | \(0.461372\pi\) | |||||||
\(572\) | 13.9554 | 0.583507 | ||||||||
\(573\) | −46.5548 | −1.94485 | ||||||||
\(574\) | 2.10746 | 0.0879637 | ||||||||
\(575\) | 46.6939 | 1.94727 | ||||||||
\(576\) | 5.46571 | 0.227738 | ||||||||
\(577\) | −28.9710 | −1.20608 | −0.603038 | − | 0.797712i | \(-0.706043\pi\) | ||||
−0.603038 | + | 0.797712i | \(0.706043\pi\) | |||||||
\(578\) | −15.9614 | −0.663905 | ||||||||
\(579\) | 36.2145 | 1.50502 | ||||||||
\(580\) | −42.2165 | −1.75295 | ||||||||
\(581\) | −17.3755 | −0.720858 | ||||||||
\(582\) | −33.2206 | −1.37704 | ||||||||
\(583\) | −7.09308 | −0.293765 | ||||||||
\(584\) | 3.13570 | 0.129756 | ||||||||
\(585\) | −162.463 | −6.71701 | ||||||||
\(586\) | −12.4399 | −0.513886 | ||||||||
\(587\) | −45.7854 | −1.88976 | −0.944882 | − | 0.327410i | \(-0.893824\pi\) | ||||
−0.944882 | + | 0.327410i | \(0.893824\pi\) | |||||||
\(588\) | −6.18231 | −0.254954 | ||||||||
\(589\) | −4.20950 | −0.173450 | ||||||||
\(590\) | −33.1938 | −1.36657 | ||||||||
\(591\) | −41.8299 | −1.72065 | ||||||||
\(592\) | 9.42107 | 0.387204 | ||||||||
\(593\) | 10.5318 | 0.432489 | 0.216244 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216244 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(594\) | −13.9877 | −0.573924 | ||||||||
\(595\) | −12.7845 | −0.524114 | ||||||||
\(596\) | 5.10176 | 0.208976 | ||||||||
\(597\) | −55.5849 | −2.27494 | ||||||||
\(598\) | 27.2929 | 1.11609 | ||||||||
\(599\) | −35.3648 | −1.44497 | −0.722483 | − | 0.691389i | \(-0.756999\pi\) | ||||
−0.722483 | + | 0.691389i | \(0.756999\pi\) | |||||||
\(600\) | −35.6296 | −1.45457 | ||||||||
\(601\) | −21.9281 | −0.894464 | −0.447232 | − | 0.894418i | \(-0.647590\pi\) | ||||
−0.447232 | + | 0.894418i | \(0.647590\pi\) | |||||||
\(602\) | 22.7691 | 0.927999 | ||||||||
\(603\) | 9.20310 | 0.374779 | ||||||||
\(604\) | 12.0241 | 0.489252 | ||||||||
\(605\) | 29.8940 | 1.21536 | ||||||||
\(606\) | −50.0039 | −2.03127 | ||||||||
\(607\) | 19.6293 | 0.796728 | 0.398364 | − | 0.917228i | \(-0.369578\pi\) | ||||
0.398364 | + | 0.917228i | \(0.369578\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −89.3485 | −3.62058 | ||||||||
\(610\) | 6.47100 | 0.262003 | ||||||||
\(611\) | −39.4901 | −1.59760 | ||||||||
\(612\) | 5.57031 | 0.225167 | ||||||||
\(613\) | −33.3190 | −1.34574 | −0.672870 | − | 0.739760i | \(-0.734939\pi\) | ||||
−0.672870 | + | 0.739760i | \(0.734939\pi\) | |||||||
\(614\) | −17.3312 | −0.699429 | ||||||||
\(615\) | 8.42982 | 0.339923 | ||||||||
\(616\) | 5.88961 | 0.237299 | ||||||||
\(617\) | −2.01887 | −0.0812767 | −0.0406384 | − | 0.999174i | \(-0.512939\pi\) | ||||
−0.0406384 | + | 0.999174i | \(0.512939\pi\) | |||||||
\(618\) | 2.63369 | 0.105942 | ||||||||
\(619\) | 15.6910 | 0.630676 | 0.315338 | − | 0.948979i | \(-0.397882\pi\) | ||||
0.315338 | + | 0.948979i | \(0.397882\pi\) | |||||||
\(620\) | −17.4811 | −0.702059 | ||||||||
\(621\) | −27.3560 | −1.09776 | ||||||||
\(622\) | −2.20615 | −0.0884584 | ||||||||
\(623\) | −24.6755 | −0.988604 | ||||||||
\(624\) | −20.8257 | −0.833697 | ||||||||
\(625\) | 63.7265 | 2.54906 | ||||||||
\(626\) | 18.6570 | 0.745683 | ||||||||
\(627\) | 5.67292 | 0.226554 | ||||||||
\(628\) | −2.70273 | −0.107851 | ||||||||
\(629\) | 9.60138 | 0.382832 | ||||||||
\(630\) | −68.5641 | −2.73166 | ||||||||
\(631\) | −20.2060 | −0.804390 | −0.402195 | − | 0.915554i | \(-0.631753\pi\) | ||||
−0.402195 | + | 0.915554i | \(0.631753\pi\) | |||||||
\(632\) | −1.68328 | −0.0669572 | ||||||||
\(633\) | 2.90959 | 0.115646 | ||||||||
\(634\) | 4.76007 | 0.189047 | ||||||||
\(635\) | 64.6561 | 2.56580 | ||||||||
\(636\) | 10.5850 | 0.419723 | ||||||||
\(637\) | 15.2086 | 0.602586 | ||||||||
\(638\) | 19.8207 | 0.784708 | ||||||||
\(639\) | −64.8008 | −2.56348 | ||||||||
\(640\) | −4.15278 | −0.164153 | ||||||||
\(641\) | 7.16583 | 0.283033 | 0.141517 | − | 0.989936i | \(-0.454802\pi\) | ||||
0.141517 | + | 0.989936i | \(0.454802\pi\) | |||||||
\(642\) | 18.2027 | 0.718405 | ||||||||
\(643\) | −28.5747 | −1.12687 | −0.563437 | − | 0.826159i | \(-0.690521\pi\) | ||||
−0.563437 | + | 0.826159i | \(0.690521\pi\) | |||||||
\(644\) | 11.5184 | 0.453889 | ||||||||
\(645\) | 91.0761 | 3.58612 | ||||||||
\(646\) | −1.01914 | −0.0400975 | ||||||||
\(647\) | −19.5375 | −0.768099 | −0.384049 | − | 0.923313i | \(-0.625471\pi\) | ||||
−0.384049 | + | 0.923313i | \(0.625471\pi\) | |||||||
\(648\) | 4.47682 | 0.175866 | ||||||||
\(649\) | 15.5845 | 0.611745 | ||||||||
\(650\) | 87.6494 | 3.43789 | ||||||||
\(651\) | −36.9976 | −1.45005 | ||||||||
\(652\) | 13.4310 | 0.525999 | ||||||||
\(653\) | 31.5416 | 1.23432 | 0.617160 | − | 0.786838i | \(-0.288283\pi\) | ||||
0.617160 | + | 0.786838i | \(0.288283\pi\) | |||||||
\(654\) | −20.0156 | −0.782672 | ||||||||
\(655\) | 62.5723 | 2.44490 | ||||||||
\(656\) | 0.697666 | 0.0272393 | ||||||||
\(657\) | 17.1388 | 0.668650 | ||||||||
\(658\) | −16.6660 | −0.649708 | ||||||||
\(659\) | −21.0459 | −0.819831 | −0.409916 | − | 0.912123i | \(-0.634442\pi\) | ||||
−0.409916 | + | 0.912123i | \(0.634442\pi\) | |||||||
\(660\) | 23.5584 | 0.917009 | ||||||||
\(661\) | 1.86235 | 0.0724369 | 0.0362184 | − | 0.999344i | \(-0.488469\pi\) | ||||
0.0362184 | + | 0.999344i | \(0.488469\pi\) | |||||||
\(662\) | 11.8428 | 0.460283 | ||||||||
\(663\) | −21.2243 | −0.824285 | ||||||||
\(664\) | −5.75209 | −0.223224 | ||||||||
\(665\) | 12.5444 | 0.486452 | ||||||||
\(666\) | 51.4928 | 1.99531 | ||||||||
\(667\) | 38.7636 | 1.50093 | ||||||||
\(668\) | −9.30505 | −0.360023 | ||||||||
\(669\) | 49.9429 | 1.93090 | ||||||||
\(670\) | −6.99241 | −0.270140 | ||||||||
\(671\) | −3.03814 | −0.117286 | ||||||||
\(672\) | −8.78908 | −0.339046 | ||||||||
\(673\) | 20.7209 | 0.798734 | 0.399367 | − | 0.916791i | \(-0.369230\pi\) | ||||
0.399367 | + | 0.916791i | \(0.369230\pi\) | |||||||
\(674\) | −23.8124 | −0.917220 | ||||||||
\(675\) | −87.8522 | −3.38143 | ||||||||
\(676\) | 38.2316 | 1.47045 | ||||||||
\(677\) | 38.2054 | 1.46835 | 0.734177 | − | 0.678958i | \(-0.237568\pi\) | ||||
0.734177 | + | 0.678958i | \(0.237568\pi\) | |||||||
\(678\) | 43.7722 | 1.68106 | ||||||||
\(679\) | 34.4895 | 1.32359 | ||||||||
\(680\) | −4.23226 | −0.162300 | ||||||||
\(681\) | 41.7605 | 1.60026 | ||||||||
\(682\) | 8.20740 | 0.314277 | ||||||||
\(683\) | −24.4622 | −0.936022 | −0.468011 | − | 0.883723i | \(-0.655029\pi\) | ||||
−0.468011 | + | 0.883723i | \(0.655029\pi\) | |||||||
\(684\) | −5.46571 | −0.208986 | ||||||||
\(685\) | −13.8682 | −0.529875 | ||||||||
\(686\) | −14.7266 | −0.562266 | ||||||||
\(687\) | −19.3774 | −0.739294 | ||||||||
\(688\) | 7.53762 | 0.287369 | ||||||||
\(689\) | −26.0393 | −0.992018 | ||||||||
\(690\) | 46.0735 | 1.75399 | ||||||||
\(691\) | −36.0523 | −1.37149 | −0.685746 | − | 0.727841i | \(-0.740524\pi\) | ||||
−0.685746 | + | 0.727841i | \(0.740524\pi\) | |||||||
\(692\) | −5.62614 | −0.213874 | ||||||||
\(693\) | 32.1909 | 1.22283 | ||||||||
\(694\) | 34.6997 | 1.31718 | ||||||||
\(695\) | −80.1804 | −3.04141 | ||||||||
\(696\) | −29.5784 | −1.12117 | ||||||||
\(697\) | 0.711019 | 0.0269318 | ||||||||
\(698\) | −29.2926 | −1.10874 | ||||||||
\(699\) | −26.4069 | −0.998800 | ||||||||
\(700\) | 36.9906 | 1.39811 | ||||||||
\(701\) | −28.0614 | −1.05986 | −0.529932 | − | 0.848040i | \(-0.677782\pi\) | ||||
−0.529932 | + | 0.848040i | \(0.677782\pi\) | |||||||
\(702\) | −51.3502 | −1.93809 | ||||||||
\(703\) | −9.42107 | −0.355322 | ||||||||
\(704\) | 1.94973 | 0.0734833 | ||||||||
\(705\) | −66.6638 | −2.51070 | ||||||||
\(706\) | −5.86582 | −0.220763 | ||||||||
\(707\) | 51.9140 | 1.95243 | ||||||||
\(708\) | −23.2568 | −0.874043 | ||||||||
\(709\) | −13.5688 | −0.509586 | −0.254793 | − | 0.966996i | \(-0.582007\pi\) | ||||
−0.254793 | + | 0.966996i | \(0.582007\pi\) | |||||||
\(710\) | 49.2349 | 1.84775 | ||||||||
\(711\) | −9.20030 | −0.345038 | ||||||||
\(712\) | −8.16873 | −0.306136 | ||||||||
\(713\) | 16.0513 | 0.601127 | ||||||||
\(714\) | −8.95730 | −0.335218 | ||||||||
\(715\) | −57.9539 | −2.16735 | ||||||||
\(716\) | 6.67942 | 0.249622 | ||||||||
\(717\) | 42.7436 | 1.59629 | ||||||||
\(718\) | −0.441918 | −0.0164922 | ||||||||
\(719\) | −45.3428 | −1.69100 | −0.845500 | − | 0.533975i | \(-0.820698\pi\) | ||||
−0.845500 | + | 0.533975i | \(0.820698\pi\) | |||||||
\(720\) | −22.6979 | −0.845900 | ||||||||
\(721\) | −2.73429 | −0.101830 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 67.3825 | 2.50598 | ||||||||
\(724\) | −16.2828 | −0.605145 | ||||||||
\(725\) | 124.487 | 4.62332 | ||||||||
\(726\) | 20.9448 | 0.777335 | ||||||||
\(727\) | 2.59966 | 0.0964162 | 0.0482081 | − | 0.998837i | \(-0.484649\pi\) | ||||
0.0482081 | + | 0.998837i | \(0.484649\pi\) | |||||||
\(728\) | 21.6213 | 0.801337 | ||||||||
\(729\) | −38.1528 | −1.41307 | ||||||||
\(730\) | −13.0219 | −0.481962 | ||||||||
\(731\) | 7.68188 | 0.284125 | ||||||||
\(732\) | 4.53382 | 0.167575 | ||||||||
\(733\) | 50.3954 | 1.86140 | 0.930698 | − | 0.365788i | \(-0.119201\pi\) | ||||
0.930698 | + | 0.365788i | \(0.119201\pi\) | |||||||
\(734\) | 17.2015 | 0.634919 | ||||||||
\(735\) | 25.6738 | 0.946992 | ||||||||
\(736\) | 3.81312 | 0.140553 | ||||||||
\(737\) | 3.28294 | 0.120929 | ||||||||
\(738\) | 3.81324 | 0.140367 | ||||||||
\(739\) | −51.5853 | −1.89759 | −0.948797 | − | 0.315885i | \(-0.897699\pi\) | ||||
−0.948797 | + | 0.315885i | \(0.897699\pi\) | |||||||
\(740\) | −39.1236 | −1.43821 | ||||||||
\(741\) | 20.8257 | 0.765053 | ||||||||
\(742\) | −10.9893 | −0.403432 | ||||||||
\(743\) | 12.8723 | 0.472240 | 0.236120 | − | 0.971724i | \(-0.424124\pi\) | ||||
0.236120 | + | 0.971724i | \(0.424124\pi\) | |||||||
\(744\) | −12.2479 | −0.449030 | ||||||||
\(745\) | −21.1865 | −0.776213 | ||||||||
\(746\) | 10.6175 | 0.388735 | ||||||||
\(747\) | −31.4392 | −1.15030 | ||||||||
\(748\) | 1.98705 | 0.0726536 | ||||||||
\(749\) | −18.8981 | −0.690520 | ||||||||
\(750\) | 87.5476 | 3.19679 | ||||||||
\(751\) | −40.4289 | −1.47527 | −0.737635 | − | 0.675199i | \(-0.764058\pi\) | ||||
−0.737635 | + | 0.675199i | \(0.764058\pi\) | |||||||
\(752\) | −5.51721 | −0.201192 | ||||||||
\(753\) | 36.6278 | 1.33479 | ||||||||
\(754\) | 72.7633 | 2.64988 | ||||||||
\(755\) | −49.9333 | −1.81726 | ||||||||
\(756\) | −21.6713 | −0.788177 | ||||||||
\(757\) | 24.2399 | 0.881014 | 0.440507 | − | 0.897749i | \(-0.354799\pi\) | ||||
0.440507 | + | 0.897749i | \(0.354799\pi\) | |||||||
\(758\) | −17.9307 | −0.651272 | ||||||||
\(759\) | −21.6315 | −0.785174 | ||||||||
\(760\) | 4.15278 | 0.150637 | ||||||||
\(761\) | −9.40814 | −0.341045 | −0.170522 | − | 0.985354i | \(-0.554546\pi\) | ||||
−0.170522 | + | 0.985354i | \(0.554546\pi\) | |||||||
\(762\) | 45.3004 | 1.64106 | ||||||||
\(763\) | 20.7802 | 0.752293 | ||||||||
\(764\) | 16.0005 | 0.578877 | ||||||||
\(765\) | −23.1323 | −0.836350 | ||||||||
\(766\) | 17.9992 | 0.650338 | ||||||||
\(767\) | 57.2119 | 2.06580 | ||||||||
\(768\) | −2.90959 | −0.104991 | ||||||||
\(769\) | −46.7257 | −1.68497 | −0.842485 | − | 0.538720i | \(-0.818908\pi\) | ||||
−0.842485 | + | 0.538720i | \(0.818908\pi\) | |||||||
\(770\) | −24.4583 | −0.881415 | ||||||||
\(771\) | 68.2859 | 2.45926 | ||||||||
\(772\) | −12.4466 | −0.447963 | ||||||||
\(773\) | −23.5066 | −0.845473 | −0.422736 | − | 0.906253i | \(-0.638930\pi\) | ||||
−0.422736 | + | 0.906253i | \(0.638930\pi\) | |||||||
\(774\) | 41.1984 | 1.48085 | ||||||||
\(775\) | 51.5478 | 1.85165 | ||||||||
\(776\) | 11.4176 | 0.409869 | ||||||||
\(777\) | −82.8025 | −2.97052 | ||||||||
\(778\) | −31.9610 | −1.14586 | ||||||||
\(779\) | −0.697666 | −0.0249965 | ||||||||
\(780\) | 86.4848 | 3.09665 | ||||||||
\(781\) | −23.1158 | −0.827148 | ||||||||
\(782\) | 3.88610 | 0.138967 | ||||||||
\(783\) | −72.9317 | −2.60637 | ||||||||
\(784\) | 2.12481 | 0.0758860 | ||||||||
\(785\) | 11.2239 | 0.400596 | ||||||||
\(786\) | 43.8404 | 1.56373 | ||||||||
\(787\) | −6.72057 | −0.239563 | −0.119781 | − | 0.992800i | \(-0.538219\pi\) | ||||
−0.119781 | + | 0.992800i | \(0.538219\pi\) | |||||||
\(788\) | 14.3766 | 0.512144 | ||||||||
\(789\) | −18.4525 | −0.656926 | ||||||||
\(790\) | 6.99028 | 0.248703 | ||||||||
\(791\) | −45.4442 | −1.61581 | ||||||||
\(792\) | 10.6567 | 0.378668 | ||||||||
\(793\) | −11.1533 | −0.396064 | ||||||||
\(794\) | 7.68750 | 0.272819 | ||||||||
\(795\) | −43.9573 | −1.55900 | ||||||||
\(796\) | 19.1040 | 0.677125 | ||||||||
\(797\) | 28.2983 | 1.00238 | 0.501189 | − | 0.865338i | \(-0.332896\pi\) | ||||
0.501189 | + | 0.865338i | \(0.332896\pi\) | |||||||
\(798\) | 8.78908 | 0.311130 | ||||||||
\(799\) | −5.62280 | −0.198920 | ||||||||
\(800\) | 12.2456 | 0.432947 | ||||||||
\(801\) | −44.6479 | −1.57756 | ||||||||
\(802\) | 31.2202 | 1.10243 | ||||||||
\(803\) | 6.11378 | 0.215751 | ||||||||
\(804\) | −4.89914 | −0.172779 | ||||||||
\(805\) | −47.8334 | −1.68591 | ||||||||
\(806\) | 30.1300 | 1.06129 | ||||||||
\(807\) | −55.9171 | −1.96837 | ||||||||
\(808\) | 17.1859 | 0.604598 | ||||||||
\(809\) | 1.85205 | 0.0651146 | 0.0325573 | − | 0.999470i | \(-0.489635\pi\) | ||||
0.0325573 | + | 0.999470i | \(0.489635\pi\) | |||||||
\(810\) | −18.5912 | −0.653230 | ||||||||
\(811\) | 45.4507 | 1.59599 | 0.797995 | − | 0.602664i | \(-0.205894\pi\) | ||||
0.797995 | + | 0.602664i | \(0.205894\pi\) | |||||||
\(812\) | 30.7083 | 1.07765 | ||||||||
\(813\) | 80.8716 | 2.83629 | ||||||||
\(814\) | 18.3686 | 0.643817 | ||||||||
\(815\) | −55.7760 | −1.95375 | ||||||||
\(816\) | −2.96528 | −0.103805 | ||||||||
\(817\) | −7.53762 | −0.263708 | ||||||||
\(818\) | 33.3660 | 1.16661 | ||||||||
\(819\) | 118.175 | 4.12938 | ||||||||
\(820\) | −2.89725 | −0.101177 | ||||||||
\(821\) | −5.32174 | −0.185730 | −0.0928651 | − | 0.995679i | \(-0.529603\pi\) | ||||
−0.0928651 | + | 0.995679i | \(0.529603\pi\) | |||||||
\(822\) | −9.71653 | −0.338903 | ||||||||
\(823\) | −13.8074 | −0.481294 | −0.240647 | − | 0.970613i | \(-0.577360\pi\) | ||||
−0.240647 | + | 0.970613i | \(0.577360\pi\) | |||||||
\(824\) | −0.905175 | −0.0315333 | ||||||||
\(825\) | −69.4682 | −2.41857 | ||||||||
\(826\) | 24.1451 | 0.840117 | ||||||||
\(827\) | −35.4391 | −1.23234 | −0.616170 | − | 0.787614i | \(-0.711316\pi\) | ||||
−0.616170 | + | 0.787614i | \(0.711316\pi\) | |||||||
\(828\) | 20.8414 | 0.724289 | ||||||||
\(829\) | 26.9862 | 0.937271 | 0.468636 | − | 0.883392i | \(-0.344746\pi\) | ||||
0.468636 | + | 0.883392i | \(0.344746\pi\) | |||||||
\(830\) | 23.8872 | 0.829136 | ||||||||
\(831\) | 24.7646 | 0.859073 | ||||||||
\(832\) | 7.15763 | 0.248146 | ||||||||
\(833\) | 2.16547 | 0.0750292 | ||||||||
\(834\) | −56.1773 | −1.94526 | ||||||||
\(835\) | 38.6418 | 1.33726 | ||||||||
\(836\) | −1.94973 | −0.0674329 | ||||||||
\(837\) | −30.1998 | −1.04386 | ||||||||
\(838\) | −13.8340 | −0.477889 | ||||||||
\(839\) | 5.72977 | 0.197814 | 0.0989068 | − | 0.995097i | \(-0.468465\pi\) | ||||
0.0989068 | + | 0.995097i | \(0.468465\pi\) | |||||||
\(840\) | 36.4991 | 1.25934 | ||||||||
\(841\) | 74.3445 | 2.56360 | ||||||||
\(842\) | 17.9771 | 0.619533 | ||||||||
\(843\) | −85.3179 | −2.93851 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −158.768 | −5.46177 | ||||||||
\(846\) | −30.1554 | −1.03677 | ||||||||
\(847\) | −21.7449 | −0.747162 | ||||||||
\(848\) | −3.63798 | −0.124929 | ||||||||
\(849\) | −3.07417 | −0.105505 | ||||||||
\(850\) | 12.4800 | 0.428059 | ||||||||
\(851\) | 35.9237 | 1.23145 | ||||||||
\(852\) | 34.4958 | 1.18181 | ||||||||
\(853\) | 9.82818 | 0.336510 | 0.168255 | − | 0.985743i | \(-0.446187\pi\) | ||||
0.168255 | + | 0.985743i | \(0.446187\pi\) | |||||||
\(854\) | −4.70700 | −0.161070 | ||||||||
\(855\) | 22.6979 | 0.776251 | ||||||||
\(856\) | −6.25612 | −0.213830 | ||||||||
\(857\) | 25.3796 | 0.866950 | 0.433475 | − | 0.901166i | \(-0.357287\pi\) | ||||
0.433475 | + | 0.901166i | \(0.357287\pi\) | |||||||
\(858\) | −40.6046 | −1.38622 | ||||||||
\(859\) | −9.13659 | −0.311736 | −0.155868 | − | 0.987778i | \(-0.549817\pi\) | ||||
−0.155868 | + | 0.987778i | \(0.549817\pi\) | |||||||
\(860\) | −31.3021 | −1.06739 | ||||||||
\(861\) | −6.13184 | −0.208973 | ||||||||
\(862\) | 34.4107 | 1.17203 | ||||||||
\(863\) | −22.9804 | −0.782263 | −0.391131 | − | 0.920335i | \(-0.627916\pi\) | ||||
−0.391131 | + | 0.920335i | \(0.627916\pi\) | |||||||
\(864\) | −7.17419 | −0.244071 | ||||||||
\(865\) | 23.3641 | 0.794404 | ||||||||
\(866\) | −32.8764 | −1.11719 | ||||||||
\(867\) | 46.4410 | 1.57722 | ||||||||
\(868\) | 12.7158 | 0.431601 | ||||||||
\(869\) | −3.28194 | −0.111332 | ||||||||
\(870\) | 122.833 | 4.16442 | ||||||||
\(871\) | 12.0519 | 0.408364 | ||||||||
\(872\) | 6.87919 | 0.232959 | ||||||||
\(873\) | 62.4053 | 2.11210 | ||||||||
\(874\) | −3.81312 | −0.128981 | ||||||||
\(875\) | −90.8918 | −3.07270 | ||||||||
\(876\) | −9.12361 | −0.308258 | ||||||||
\(877\) | −38.9306 | −1.31459 | −0.657296 | − | 0.753632i | \(-0.728300\pi\) | ||||
−0.657296 | + | 0.753632i | \(0.728300\pi\) | |||||||
\(878\) | 12.5408 | 0.423231 | ||||||||
\(879\) | 36.1949 | 1.22082 | ||||||||
\(880\) | −8.09681 | −0.272943 | ||||||||
\(881\) | −23.5053 | −0.791912 | −0.395956 | − | 0.918269i | \(-0.629587\pi\) | ||||
−0.395956 | + | 0.918269i | \(0.629587\pi\) | |||||||
\(882\) | 11.6136 | 0.391049 | ||||||||
\(883\) | −13.9825 | −0.470548 | −0.235274 | − | 0.971929i | \(-0.575599\pi\) | ||||
−0.235274 | + | 0.971929i | \(0.575599\pi\) | |||||||
\(884\) | 7.29462 | 0.245345 | ||||||||
\(885\) | 96.5803 | 3.24651 | ||||||||
\(886\) | −7.63728 | −0.256580 | ||||||||
\(887\) | −19.4188 | −0.652021 | −0.326010 | − | 0.945366i | \(-0.605704\pi\) | ||||
−0.326010 | + | 0.945366i | \(0.605704\pi\) | |||||||
\(888\) | −27.4114 | −0.919868 | ||||||||
\(889\) | −47.0308 | −1.57736 | ||||||||
\(890\) | 33.9229 | 1.13710 | ||||||||
\(891\) | 8.72859 | 0.292419 | ||||||||
\(892\) | −17.1649 | −0.574724 | ||||||||
\(893\) | 5.51721 | 0.184626 | ||||||||
\(894\) | −14.8440 | −0.496459 | ||||||||
\(895\) | −27.7382 | −0.927185 | ||||||||
\(896\) | 3.02073 | 0.100915 | ||||||||
\(897\) | −79.4111 | −2.65146 | ||||||||
\(898\) | −16.9124 | −0.564376 | ||||||||
\(899\) | 42.7932 | 1.42723 | ||||||||
\(900\) | 66.9308 | 2.23103 | ||||||||
\(901\) | −3.70761 | −0.123518 | ||||||||
\(902\) | 1.36026 | 0.0452917 | ||||||||
\(903\) | −66.2487 | −2.20462 | ||||||||
\(904\) | −15.0441 | −0.500360 | ||||||||
\(905\) | 67.6188 | 2.24772 | ||||||||
\(906\) | −34.9851 | −1.16230 | ||||||||
\(907\) | 28.6747 | 0.952126 | 0.476063 | − | 0.879411i | \(-0.342063\pi\) | ||||
0.476063 | + | 0.879411i | \(0.342063\pi\) | |||||||
\(908\) | −14.3527 | −0.476311 | ||||||||
\(909\) | 93.9331 | 3.11556 | ||||||||
\(910\) | −89.7883 | −2.97645 | ||||||||
\(911\) | −30.8665 | −1.02265 | −0.511327 | − | 0.859386i | \(-0.670846\pi\) | ||||
−0.511327 | + | 0.859386i | \(0.670846\pi\) | |||||||
\(912\) | 2.90959 | 0.0963461 | ||||||||
\(913\) | −11.2150 | −0.371163 | ||||||||
\(914\) | −17.7455 | −0.586970 | ||||||||
\(915\) | −18.8280 | −0.622433 | ||||||||
\(916\) | 6.65984 | 0.220047 | ||||||||
\(917\) | −45.5150 | −1.50304 | ||||||||
\(918\) | −7.31150 | −0.241315 | ||||||||
\(919\) | −25.9388 | −0.855643 | −0.427821 | − | 0.903863i | \(-0.640719\pi\) | ||||
−0.427821 | + | 0.903863i | \(0.640719\pi\) | |||||||
\(920\) | −15.8351 | −0.522066 | ||||||||
\(921\) | 50.4265 | 1.66161 | ||||||||
\(922\) | −28.6682 | −0.944137 | ||||||||
\(923\) | −84.8600 | −2.79320 | ||||||||
\(924\) | −17.1363 | −0.563744 | ||||||||
\(925\) | 115.367 | 3.79323 | ||||||||
\(926\) | 2.56062 | 0.0841473 | ||||||||
\(927\) | −4.94742 | −0.162495 | ||||||||
\(928\) | 10.1658 | 0.333710 | ||||||||
\(929\) | −32.5571 | −1.06816 | −0.534082 | − | 0.845433i | \(-0.679343\pi\) | ||||
−0.534082 | + | 0.845433i | \(0.679343\pi\) | |||||||
\(930\) | 50.8629 | 1.66786 | ||||||||
\(931\) | −2.12481 | −0.0696377 | ||||||||
\(932\) | 9.07581 | 0.297288 | ||||||||
\(933\) | 6.41898 | 0.210148 | ||||||||
\(934\) | −20.0042 | −0.654556 | ||||||||
\(935\) | −8.25177 | −0.269862 | ||||||||
\(936\) | 39.1215 | 1.27873 | ||||||||
\(937\) | 20.4620 | 0.668464 | 0.334232 | − | 0.942491i | \(-0.391523\pi\) | ||||
0.334232 | + | 0.942491i | \(0.391523\pi\) | |||||||
\(938\) | 5.08627 | 0.166073 | ||||||||
\(939\) | −54.2842 | −1.77150 | ||||||||
\(940\) | 22.9118 | 0.747299 | ||||||||
\(941\) | 33.0659 | 1.07792 | 0.538958 | − | 0.842333i | \(-0.318818\pi\) | ||||
0.538958 | + | 0.842333i | \(0.318818\pi\) | |||||||
\(942\) | 7.86384 | 0.256218 | ||||||||
\(943\) | 2.66029 | 0.0866308 | ||||||||
\(944\) | 7.99315 | 0.260155 | ||||||||
\(945\) | 89.9961 | 2.92757 | ||||||||
\(946\) | 14.6963 | 0.477819 | ||||||||
\(947\) | −7.41391 | −0.240920 | −0.120460 | − | 0.992718i | \(-0.538437\pi\) | ||||
−0.120460 | + | 0.992718i | \(0.538437\pi\) | |||||||
\(948\) | 4.89764 | 0.159068 | ||||||||
\(949\) | 22.4442 | 0.728569 | ||||||||
\(950\) | −12.2456 | −0.397299 | ||||||||
\(951\) | −13.8499 | −0.449112 | ||||||||
\(952\) | 3.07854 | 0.0997762 | ||||||||
\(953\) | −15.8671 | −0.513987 | −0.256994 | − | 0.966413i | \(-0.582732\pi\) | ||||
−0.256994 | + | 0.966413i | \(0.582732\pi\) | |||||||
\(954\) | −19.8841 | −0.643772 | ||||||||
\(955\) | −66.4465 | −2.15016 | ||||||||
\(956\) | −14.6906 | −0.475128 | ||||||||
\(957\) | −57.6700 | −1.86421 | ||||||||
\(958\) | 5.04331 | 0.162942 | ||||||||
\(959\) | 10.0877 | 0.325748 | ||||||||
\(960\) | 12.0829 | 0.389973 | ||||||||
\(961\) | −13.2801 | −0.428390 | ||||||||
\(962\) | 67.4325 | 2.17411 | ||||||||
\(963\) | −34.1941 | −1.10189 | ||||||||
\(964\) | −23.1588 | −0.745894 | ||||||||
\(965\) | 51.6880 | 1.66390 | ||||||||
\(966\) | −33.5138 | −1.07829 | ||||||||
\(967\) | 9.86280 | 0.317166 | 0.158583 | − | 0.987346i | \(-0.449307\pi\) | ||||
0.158583 | + | 0.987346i | \(0.449307\pi\) | |||||||
\(968\) | −7.19855 | −0.231370 | ||||||||
\(969\) | 2.96528 | 0.0952584 | ||||||||
\(970\) | −47.4149 | −1.52240 | ||||||||
\(971\) | 0.323688 | 0.0103876 | 0.00519382 | − | 0.999987i | \(-0.498347\pi\) | ||||
0.00519382 | + | 0.999987i | \(0.498347\pi\) | |||||||
\(972\) | 8.49686 | 0.272537 | ||||||||
\(973\) | 58.3231 | 1.86975 | ||||||||
\(974\) | 11.0808 | 0.355051 | ||||||||
\(975\) | −255.024 | −8.16729 | ||||||||
\(976\) | −1.55823 | −0.0498778 | ||||||||
\(977\) | 22.5466 | 0.721331 | 0.360665 | − | 0.932695i | \(-0.382550\pi\) | ||||
0.360665 | + | 0.932695i | \(0.382550\pi\) | |||||||
\(978\) | −39.0787 | −1.24960 | ||||||||
\(979\) | −15.9268 | −0.509024 | ||||||||
\(980\) | −8.82386 | −0.281868 | ||||||||
\(981\) | 37.5996 | 1.20046 | ||||||||
\(982\) | 9.19476 | 0.293417 | ||||||||
\(983\) | 15.5583 | 0.496233 | 0.248116 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248116 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(984\) | −2.02992 | −0.0647115 | ||||||||
\(985\) | −59.7028 | −1.90229 | ||||||||
\(986\) | 10.3604 | 0.329943 | ||||||||
\(987\) | 48.4912 | 1.54349 | ||||||||
\(988\) | −7.15763 | −0.227714 | ||||||||
\(989\) | 28.7418 | 0.913937 | ||||||||
\(990\) | −44.2548 | −1.40651 | ||||||||
\(991\) | −5.67356 | −0.180227 | −0.0901133 | − | 0.995932i | \(-0.528723\pi\) | ||||
−0.0901133 | + | 0.995932i | \(0.528723\pi\) | |||||||
\(992\) | 4.20950 | 0.133652 | ||||||||
\(993\) | −34.4576 | −1.09348 | ||||||||
\(994\) | −35.8134 | −1.13593 | ||||||||
\(995\) | −79.3349 | −2.51509 | ||||||||
\(996\) | 16.7362 | 0.530307 | ||||||||
\(997\) | 24.7691 | 0.784445 | 0.392223 | − | 0.919870i | \(-0.371706\pi\) | ||||
0.392223 | + | 0.919870i | \(0.371706\pi\) | |||||||
\(998\) | −29.6428 | −0.938325 | ||||||||
\(999\) | −67.5885 | −2.13841 |
(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 | 8018.2.a.j.1.4 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.4 | ✓ | 47 | 1.1 | even | 1 | trivial |