Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} + 102x^{6} - 202x^{4} + 133x^{2} - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 585) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.635993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.794363 | 0.561699 | 0.280850 | − | 0.959752i | \(-0.409384\pi\) | ||||
0.280850 | + | 0.959752i | \(0.409384\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.36899 | −0.684494 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.59800 | 1.35992 | 0.679958 | − | 0.733251i | \(-0.261998\pi\) | ||||
0.679958 | + | 0.733251i | \(0.261998\pi\) | |||||||
\(8\) | −2.67620 | −0.946179 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.794363 | −0.251200 | ||||||||
\(11\) | 3.69958 | 1.11546 | 0.557732 | − | 0.830021i | \(-0.311672\pi\) | ||||
0.557732 | + | 0.830021i | \(0.311672\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.85812 | 0.763863 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.612105 | 0.153026 | ||||||||
\(17\) | 7.56145 | 1.83392 | 0.916961 | − | 0.398977i | \(-0.130635\pi\) | ||||
0.916961 | + | 0.398977i | \(0.130635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.09683 | 1.39871 | 0.699354 | − | 0.714776i | \(-0.253471\pi\) | ||||
0.699354 | + | 0.714776i | \(0.253471\pi\) | |||||||
\(20\) | 1.36899 | 0.306115 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.93881 | 0.626556 | ||||||||
\(23\) | 4.84309 | 1.00985 | 0.504927 | − | 0.863162i | \(-0.331519\pi\) | ||||
0.504927 | + | 0.863162i | \(0.331519\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.92562 | −0.930854 | ||||||||
\(29\) | −3.06590 | −0.569322 | −0.284661 | − | 0.958628i | \(-0.591881\pi\) | ||||
−0.284661 | + | 0.958628i | \(0.591881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.25369 | 0.943591 | 0.471796 | − | 0.881708i | \(-0.343606\pi\) | ||||
0.471796 | + | 0.881708i | \(0.343606\pi\) | |||||||
\(32\) | 5.83863 | 1.03213 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00654 | 1.03011 | ||||||||
\(35\) | −3.59800 | −0.608173 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.14524 | −0.681473 | −0.340737 | − | 0.940159i | \(-0.610676\pi\) | ||||
−0.340737 | + | 0.940159i | \(0.610676\pi\) | |||||||
\(38\) | 4.84309 | 0.785653 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.67620 | 0.423144 | ||||||||
\(41\) | −3.38988 | −0.529410 | −0.264705 | − | 0.964329i | \(-0.585275\pi\) | ||||
−0.264705 | + | 0.964329i | \(0.585275\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.62852 | −0.400845 | −0.200423 | − | 0.979710i | \(-0.564232\pi\) | ||||
−0.200423 | + | 0.979710i | \(0.564232\pi\) | |||||||
\(44\) | −5.06468 | −0.763529 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.84717 | 0.567234 | ||||||||
\(47\) | −8.99327 | −1.31180 | −0.655902 | − | 0.754846i | \(-0.727711\pi\) | ||||
−0.655902 | + | 0.754846i | \(0.727711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.94559 | 0.849370 | ||||||||
\(50\) | 0.794363 | 0.112340 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.92401 | 0.813725 | 0.406863 | − | 0.913489i | \(-0.366623\pi\) | ||||
0.406863 | + | 0.913489i | \(0.366623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.69958 | −0.498851 | ||||||||
\(56\) | −9.62896 | −1.28672 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.43543 | −0.319788 | ||||||||
\(59\) | 7.80115 | 1.01562 | 0.507812 | − | 0.861468i | \(-0.330455\pi\) | ||||
0.507812 | + | 0.861468i | \(0.330455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.4449 | −1.72145 | −0.860723 | − | 0.509073i | \(-0.829988\pi\) | ||||
−0.860723 | + | 0.509073i | \(0.829988\pi\) | |||||||
\(62\) | 4.17334 | 0.530014 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.41378 | 0.426722 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.88824 | −0.597193 | −0.298597 | − | 0.954379i | \(-0.596518\pi\) | ||||
−0.298597 | + | 0.954379i | \(0.596518\pi\) | |||||||
\(68\) | −10.3515 | −1.25531 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.85812 | −0.341610 | ||||||||
\(71\) | −15.1420 | −1.79703 | −0.898513 | − | 0.438947i | \(-0.855352\pi\) | ||||
−0.898513 | + | 0.438947i | \(0.855352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.6568 | −1.48137 | −0.740685 | − | 0.671852i | \(-0.765499\pi\) | ||||
−0.740685 | + | 0.671852i | \(0.765499\pi\) | |||||||
\(74\) | −3.29282 | −0.382783 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.34648 | −0.957407 | ||||||||
\(77\) | 13.3111 | 1.51694 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.207617 | 0.0233588 | 0.0116794 | − | 0.999932i | \(-0.496282\pi\) | ||||
0.0116794 | + | 0.999932i | \(0.496282\pi\) | |||||||
\(80\) | −0.612105 | −0.0684354 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.69279 | −0.297369 | ||||||||
\(83\) | 8.67620 | 0.952336 | 0.476168 | − | 0.879354i | \(-0.342025\pi\) | ||||
0.476168 | + | 0.879354i | \(0.342025\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.56145 | −0.820155 | ||||||||
\(86\) | −2.08800 | −0.225155 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.90080 | −1.05543 | ||||||||
\(89\) | 13.2508 | 1.40458 | 0.702292 | − | 0.711889i | \(-0.252160\pi\) | ||||
0.702292 | + | 0.711889i | \(0.252160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.63013 | −0.691239 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.14392 | −0.736839 | ||||||||
\(95\) | −6.09683 | −0.625521 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3969 | 1.15718 | 0.578588 | − | 0.815620i | \(-0.303604\pi\) | ||||
0.578588 | + | 0.815620i | \(0.303604\pi\) | |||||||
\(98\) | 4.72296 | 0.477091 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.36899 | −0.136899 | ||||||||
\(101\) | 18.6380 | 1.85455 | 0.927276 | − | 0.374379i | \(-0.122144\pi\) | ||||
0.927276 | + | 0.374379i | \(0.122144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6811 | 1.24950 | 0.624752 | − | 0.780823i | \(-0.285200\pi\) | ||||
0.624752 | + | 0.780823i | \(0.285200\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.70581 | 0.457069 | ||||||||
\(107\) | 5.89062 | 0.569468 | 0.284734 | − | 0.958607i | \(-0.408095\pi\) | ||||
0.284734 | + | 0.958607i | \(0.408095\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.00497 | −0.287824 | −0.143912 | − | 0.989590i | \(-0.545968\pi\) | ||||
−0.143912 | + | 0.989590i | \(0.545968\pi\) | |||||||
\(110\) | −2.93881 | −0.280204 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.20235 | 0.208103 | ||||||||
\(113\) | 0.261568 | 0.0246062 | 0.0123031 | − | 0.999924i | \(-0.496084\pi\) | ||||
0.0123031 | + | 0.999924i | \(0.496084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.84309 | −0.451621 | ||||||||
\(116\) | 4.19717 | 0.389698 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.19694 | 0.570475 | ||||||||
\(119\) | 27.2061 | 2.49398 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.68687 | 0.244261 | ||||||||
\(122\) | −10.6801 | −0.966935 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.19224 | −0.645883 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.51732 | −0.578319 | −0.289159 | − | 0.957281i | \(-0.593376\pi\) | ||||
−0.289159 | + | 0.957281i | \(0.593376\pi\) | |||||||
\(128\) | −8.96548 | −0.792444 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.04369 | −0.790151 | −0.395076 | − | 0.918649i | \(-0.629282\pi\) | ||||
−0.395076 | + | 0.918649i | \(0.629282\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.9364 | 1.90212 | ||||||||
\(134\) | −3.88303 | −0.335443 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.2360 | −1.73522 | ||||||||
\(137\) | −6.45844 | −0.551782 | −0.275891 | − | 0.961189i | \(-0.588973\pi\) | ||||
−0.275891 | + | 0.961189i | \(0.588973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.8139 | 1.59578 | 0.797888 | − | 0.602806i | \(-0.205951\pi\) | ||||
0.797888 | + | 0.602806i | \(0.205951\pi\) | |||||||
\(140\) | 4.92562 | 0.416291 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0282 | −1.00939 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.06590 | 0.254609 | ||||||||
\(146\) | −10.0541 | −0.832084 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.67478 | 0.466464 | ||||||||
\(149\) | 9.08017 | 0.743877 | 0.371938 | − | 0.928257i | \(-0.378693\pi\) | ||||
0.371938 | + | 0.928257i | \(0.378693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.40002 | −0.602205 | −0.301103 | − | 0.953592i | \(-0.597355\pi\) | ||||
−0.301103 | + | 0.953592i | \(0.597355\pi\) | |||||||
\(152\) | −16.3163 | −1.32343 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.5738 | 0.852063 | ||||||||
\(155\) | −5.25369 | −0.421987 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3117 | −0.902775 | −0.451388 | − | 0.892328i | \(-0.649071\pi\) | ||||
−0.451388 | + | 0.892328i | \(0.649071\pi\) | |||||||
\(158\) | 0.164923 | 0.0131206 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.83863 | −0.461584 | ||||||||
\(161\) | 17.4254 | 1.37332 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.44658 | −0.191631 | −0.0958154 | − | 0.995399i | \(-0.530546\pi\) | ||||
−0.0958154 | + | 0.995399i | \(0.530546\pi\) | |||||||
\(164\) | 4.64070 | 0.362378 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.89205 | 0.534927 | ||||||||
\(167\) | 6.18957 | 0.478963 | 0.239482 | − | 0.970901i | \(-0.423023\pi\) | ||||
0.239482 | + | 0.970901i | \(0.423023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.00654 | −0.460680 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.59841 | 0.274376 | ||||||||
\(173\) | −5.46204 | −0.415271 | −0.207635 | − | 0.978206i | \(-0.566577\pi\) | ||||
−0.207635 | + | 0.978206i | \(0.566577\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.59800 | 0.271983 | ||||||||
\(176\) | 2.26453 | 0.170695 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.5260 | 0.788954 | ||||||||
\(179\) | −1.88699 | −0.141040 | −0.0705200 | − | 0.997510i | \(-0.522466\pi\) | ||||
−0.0705200 | + | 0.997510i | \(0.522466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5109 | 1.07859 | 0.539295 | − | 0.842117i | \(-0.318691\pi\) | ||||
0.539295 | + | 0.842117i | \(0.318691\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.9611 | −0.955503 | ||||||||
\(185\) | 4.14524 | 0.304764 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.9742 | 2.04568 | ||||||||
\(188\) | 12.3117 | 0.897922 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.84309 | −0.351355 | ||||||||
\(191\) | −13.2359 | −0.957718 | −0.478859 | − | 0.877892i | \(-0.658949\pi\) | ||||
−0.478859 | + | 0.877892i | \(0.658949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48680 | 0.610893 | 0.305447 | − | 0.952209i | \(-0.401194\pi\) | ||||
0.305447 | + | 0.952209i | \(0.401194\pi\) | |||||||
\(194\) | 9.05325 | 0.649985 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.13945 | −0.581389 | ||||||||
\(197\) | 11.5659 | 0.824038 | 0.412019 | − | 0.911175i | \(-0.364824\pi\) | ||||
0.412019 | + | 0.911175i | \(0.364824\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.57661 | −0.395315 | −0.197658 | − | 0.980271i | \(-0.563333\pi\) | ||||
−0.197658 | + | 0.980271i | \(0.563333\pi\) | |||||||
\(200\) | −2.67620 | −0.189236 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.8053 | 1.04170 | ||||||||
\(203\) | −11.0311 | −0.774230 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.38988 | 0.236759 | ||||||||
\(206\) | 10.0734 | 0.701845 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.5557 | 1.56021 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0454 | −0.691555 | −0.345778 | − | 0.938316i | \(-0.612385\pi\) | ||||
−0.345778 | + | 0.938316i | \(0.612385\pi\) | |||||||
\(212\) | −8.10990 | −0.556990 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.67929 | 0.319870 | ||||||||
\(215\) | 2.62852 | 0.179264 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9028 | 1.28320 | ||||||||
\(218\) | −2.38704 | −0.161671 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.06468 | 0.341460 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.01943 | 0.470056 | 0.235028 | − | 0.971989i | \(-0.424482\pi\) | ||||
0.235028 | + | 0.971989i | \(0.424482\pi\) | |||||||
\(224\) | 21.0074 | 1.40361 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.207780 | 0.0138213 | ||||||||
\(227\) | 21.3200 | 1.41506 | 0.707528 | − | 0.706685i | \(-0.249810\pi\) | ||||
0.707528 | + | 0.706685i | \(0.249810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.8980 | 1.31490 | 0.657448 | − | 0.753500i | \(-0.271636\pi\) | ||||
0.657448 | + | 0.753500i | \(0.271636\pi\) | |||||||
\(230\) | −3.84717 | −0.253675 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.20494 | 0.538681 | ||||||||
\(233\) | 2.37696 | 0.155720 | 0.0778598 | − | 0.996964i | \(-0.475191\pi\) | ||||
0.0778598 | + | 0.996964i | \(0.475191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.99327 | 0.586656 | ||||||||
\(236\) | −10.6797 | −0.695188 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 21.6115 | 1.40087 | ||||||||
\(239\) | 24.1120 | 1.55968 | 0.779838 | − | 0.625981i | \(-0.215301\pi\) | ||||
0.779838 | + | 0.625981i | \(0.215301\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3520 | −1.18215 | −0.591077 | − | 0.806615i | \(-0.701297\pi\) | ||||
−0.591077 | + | 0.806615i | \(0.701297\pi\) | |||||||
\(242\) | 2.13435 | 0.137201 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.4059 | 1.17832 | ||||||||
\(245\) | −5.94559 | −0.379850 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −14.0599 | −0.892806 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.794363 | −0.0502399 | ||||||||
\(251\) | 0.624848 | 0.0394401 | 0.0197200 | − | 0.999806i | \(-0.493723\pi\) | ||||
0.0197200 | + | 0.999806i | \(0.493723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.9174 | 1.12646 | ||||||||
\(254\) | −5.17711 | −0.324841 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.9494 | −0.871838 | ||||||||
\(257\) | 22.7480 | 1.41898 | 0.709491 | − | 0.704715i | \(-0.248925\pi\) | ||||
0.709491 | + | 0.704715i | \(0.248925\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.9146 | −0.926746 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.18397 | −0.443827 | ||||||||
\(263\) | −21.0388 | −1.29731 | −0.648654 | − | 0.761083i | \(-0.724668\pi\) | ||||
−0.648654 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.92401 | −0.363909 | ||||||||
\(266\) | 17.4254 | 1.06842 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.69194 | 0.408775 | ||||||||
\(269\) | −19.0059 | −1.15881 | −0.579406 | − | 0.815039i | \(-0.696716\pi\) | ||||
−0.579406 | + | 0.815039i | \(0.696716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.520078 | 0.0315925 | 0.0157963 | − | 0.999875i | \(-0.494972\pi\) | ||||
0.0157963 | + | 0.999875i | \(0.494972\pi\) | |||||||
\(272\) | 4.62840 | 0.280638 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.13034 | −0.309935 | ||||||||
\(275\) | 3.69958 | 0.223093 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.5333 | −1.47406 | −0.737032 | − | 0.675857i | \(-0.763774\pi\) | ||||
−0.737032 | + | 0.675857i | \(0.763774\pi\) | |||||||
\(278\) | 14.9451 | 0.896346 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.62896 | 0.575440 | ||||||||
\(281\) | −9.57446 | −0.571164 | −0.285582 | − | 0.958354i | \(-0.592187\pi\) | ||||
−0.285582 | + | 0.958354i | \(0.592187\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.40705 | −0.202528 | −0.101264 | − | 0.994860i | \(-0.532289\pi\) | ||||
−0.101264 | + | 0.994860i | \(0.532289\pi\) | |||||||
\(284\) | 20.7292 | 1.23005 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.1968 | −0.719952 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.1756 | 2.36327 | ||||||||
\(290\) | 2.43543 | 0.143014 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.3271 | 1.01399 | ||||||||
\(293\) | −17.1722 | −1.00321 | −0.501605 | − | 0.865097i | \(-0.667257\pi\) | ||||
−0.501605 | + | 0.865097i | \(0.667257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.80115 | −0.454201 | ||||||||
\(296\) | 11.0935 | 0.644796 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.21295 | 0.417835 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.45741 | −0.545116 | ||||||||
\(302\) | −5.87830 | −0.338258 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.73190 | 0.214039 | ||||||||
\(305\) | 13.4449 | 0.769854 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.06057 | 0.0605298 | 0.0302649 | − | 0.999542i | \(-0.490365\pi\) | ||||
0.0302649 | + | 0.999542i | \(0.490365\pi\) | |||||||
\(308\) | −18.2227 | −1.03833 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.17334 | −0.237030 | ||||||||
\(311\) | −23.8274 | −1.35113 | −0.675563 | − | 0.737302i | \(-0.736099\pi\) | ||||
−0.675563 | + | 0.737302i | \(0.736099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.82935 | −0.386018 | −0.193009 | − | 0.981197i | \(-0.561825\pi\) | ||||
−0.193009 | + | 0.981197i | \(0.561825\pi\) | |||||||
\(314\) | −8.98562 | −0.507088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.284225 | −0.0159889 | ||||||||
\(317\) | 20.6430 | 1.15943 | 0.579714 | − | 0.814820i | \(-0.303164\pi\) | ||||
0.579714 | + | 0.814820i | \(0.303164\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.3425 | −0.635059 | ||||||||
\(320\) | −3.41378 | −0.190836 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.8421 | 0.771391 | ||||||||
\(323\) | 46.1009 | 2.56512 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.94347 | −0.107639 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.07198 | 0.500916 | ||||||||
\(329\) | −32.3578 | −1.78394 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.4206 | −1.61710 | −0.808552 | − | 0.588425i | \(-0.799748\pi\) | ||||
−0.808552 | + | 0.588425i | \(0.799748\pi\) | |||||||
\(332\) | −11.8776 | −0.651869 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.91676 | 0.269033 | ||||||||
\(335\) | 4.88824 | 0.267073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.899872 | −0.0490191 | −0.0245096 | − | 0.999700i | \(-0.507802\pi\) | ||||
−0.0245096 | + | 0.999700i | \(0.507802\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.3515 | 0.561391 | ||||||||
\(341\) | 19.4364 | 1.05254 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.79375 | −0.204843 | ||||||||
\(344\) | 7.03444 | 0.379272 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.33884 | −0.233257 | ||||||||
\(347\) | 2.46613 | 0.132389 | 0.0661945 | − | 0.997807i | \(-0.478914\pi\) | ||||
0.0661945 | + | 0.997807i | \(0.478914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.19745 | −0.117627 | −0.0588135 | − | 0.998269i | \(-0.518732\pi\) | ||||
−0.0588135 | + | 0.998269i | \(0.518732\pi\) | |||||||
\(350\) | 2.85812 | 0.152773 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.6005 | 1.15131 | ||||||||
\(353\) | −1.67765 | −0.0892925 | −0.0446462 | − | 0.999003i | \(-0.514216\pi\) | ||||
−0.0446462 | + | 0.999003i | \(0.514216\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.1420 | 0.803654 | ||||||||
\(356\) | −18.1402 | −0.961430 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.49895 | −0.0792221 | ||||||||
\(359\) | 4.19387 | 0.221344 | 0.110672 | − | 0.993857i | \(-0.464700\pi\) | ||||
0.110672 | + | 0.993857i | \(0.464700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.1713 | 0.956384 | ||||||||
\(362\) | 11.5269 | 0.605843 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.6568 | 0.662489 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5414 | −1.22885 | −0.614427 | − | 0.788974i | \(-0.710613\pi\) | ||||
−0.614427 | + | 0.788974i | \(0.710613\pi\) | |||||||
\(368\) | 2.96448 | 0.154534 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.29282 | 0.171186 | ||||||||
\(371\) | 21.3146 | 1.10660 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.07537 | −0.366349 | −0.183174 | − | 0.983080i | \(-0.558637\pi\) | ||||
−0.183174 | + | 0.983080i | \(0.558637\pi\) | |||||||
\(374\) | 22.2216 | 1.14905 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.0678 | 1.24120 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.92966 | 0.0991199 | 0.0495600 | − | 0.998771i | \(-0.484218\pi\) | ||||
0.0495600 | + | 0.998771i | \(0.484218\pi\) | |||||||
\(380\) | 8.34648 | 0.428166 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.5141 | −0.537949 | ||||||||
\(383\) | −19.6962 | −1.00643 | −0.503215 | − | 0.864161i | \(-0.667850\pi\) | ||||
−0.503215 | + | 0.864161i | \(0.667850\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.3111 | −0.678395 | ||||||||
\(386\) | 6.74159 | 0.343138 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.6022 | −0.792081 | ||||||||
\(389\) | 1.29947 | 0.0658859 | 0.0329430 | − | 0.999457i | \(-0.489512\pi\) | ||||
0.0329430 | + | 0.999457i | \(0.489512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.6208 | 1.85199 | ||||||||
\(392\) | −15.9116 | −0.803656 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.18754 | 0.462862 | ||||||||
\(395\) | −0.207617 | −0.0104464 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.72956 | 0.0868040 | 0.0434020 | − | 0.999058i | \(-0.486180\pi\) | ||||
0.0434020 | + | 0.999058i | \(0.486180\pi\) | |||||||
\(398\) | −4.42985 | −0.222048 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.612105 | 0.0306052 | ||||||||
\(401\) | −1.10645 | −0.0552536 | −0.0276268 | − | 0.999618i | \(-0.508795\pi\) | ||||
−0.0276268 | + | 0.999618i | \(0.508795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −25.5152 | −1.26943 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.76268 | −0.434885 | ||||||||
\(407\) | −15.3356 | −0.760159 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.3878 | −1.65092 | −0.825459 | − | 0.564462i | \(-0.809084\pi\) | ||||
−0.825459 | + | 0.564462i | \(0.809084\pi\) | |||||||
\(410\) | 2.69279 | 0.132987 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.3602 | −0.855278 | ||||||||
\(413\) | 28.0685 | 1.38116 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.67620 | −0.425898 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17.9174 | 0.876368 | ||||||||
\(419\) | −18.2033 | −0.889290 | −0.444645 | − | 0.895707i | \(-0.646670\pi\) | ||||
−0.444645 | + | 0.895707i | \(0.646670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.47202 | 0.0717419 | 0.0358709 | − | 0.999356i | \(-0.488579\pi\) | ||||
0.0358709 | + | 0.999356i | \(0.488579\pi\) | |||||||
\(422\) | −7.97971 | −0.388446 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.8538 | −0.769930 | ||||||||
\(425\) | 7.56145 | 0.366784 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.3748 | −2.34102 | ||||||||
\(428\) | −8.06419 | −0.389797 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.08800 | 0.100692 | ||||||||
\(431\) | 25.9078 | 1.24794 | 0.623968 | − | 0.781450i | \(-0.285520\pi\) | ||||
0.623968 | + | 0.781450i | \(0.285520\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.8732 | 1.14727 | 0.573636 | − | 0.819110i | \(-0.305532\pi\) | ||||
0.573636 | + | 0.819110i | \(0.305532\pi\) | |||||||
\(434\) | 15.0157 | 0.720775 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.11377 | 0.197014 | ||||||||
\(437\) | 29.5275 | 1.41249 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.3754 | −1.35428 | −0.677142 | − | 0.735853i | \(-0.736782\pi\) | ||||
−0.677142 | + | 0.735853i | \(0.736782\pi\) | |||||||
\(440\) | 9.90080 | 0.472002 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.5716 | −0.597293 | −0.298646 | − | 0.954364i | \(-0.596535\pi\) | ||||
−0.298646 | + | 0.954364i | \(0.596535\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.2508 | −0.628149 | ||||||||
\(446\) | 5.57597 | 0.264030 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.2828 | 0.580306 | ||||||||
\(449\) | 36.8053 | 1.73695 | 0.868474 | − | 0.495734i | \(-0.165101\pi\) | ||||
0.868474 | + | 0.495734i | \(0.165101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5411 | −0.590538 | ||||||||
\(452\) | −0.358083 | −0.0168428 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.9358 | 0.794836 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.73250 | 0.314933 | 0.157467 | − | 0.987524i | \(-0.449667\pi\) | ||||
0.157467 | + | 0.987524i | \(0.449667\pi\) | |||||||
\(458\) | 15.8062 | 0.738575 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.63013 | 0.309132 | ||||||||
\(461\) | 30.0493 | 1.39953 | 0.699767 | − | 0.714372i | \(-0.253287\pi\) | ||||
0.699767 | + | 0.714372i | \(0.253287\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0496 | 0.838835 | 0.419418 | − | 0.907793i | \(-0.362234\pi\) | ||||
0.419418 | + | 0.907793i | \(0.362234\pi\) | |||||||
\(464\) | −1.87665 | −0.0871212 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.88816 | 0.0874676 | ||||||||
\(467\) | 26.2888 | 1.21650 | 0.608251 | − | 0.793745i | \(-0.291872\pi\) | ||||
0.608251 | + | 0.793745i | \(0.291872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5879 | −0.812132 | ||||||||
\(470\) | 7.14392 | 0.329524 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.8774 | −0.960961 | ||||||||
\(473\) | −9.72441 | −0.447129 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.09683 | 0.279742 | ||||||||
\(476\) | −37.2448 | −1.70711 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.1537 | 0.876069 | ||||||||
\(479\) | −3.11197 | −0.142190 | −0.0710948 | − | 0.997470i | \(-0.522649\pi\) | ||||
−0.0710948 | + | 0.997470i | \(0.522649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −14.5781 | −0.664015 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.67830 | −0.167195 | ||||||||
\(485\) | −11.3969 | −0.517505 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.23540 | 0.237238 | 0.118619 | − | 0.992940i | \(-0.462153\pi\) | ||||
0.118619 | + | 0.992940i | \(0.462153\pi\) | |||||||
\(488\) | 35.9813 | 1.62880 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.72296 | −0.213361 | ||||||||
\(491\) | 6.17499 | 0.278673 | 0.139337 | − | 0.990245i | \(-0.455503\pi\) | ||||
0.139337 | + | 0.990245i | \(0.455503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.1826 | −1.04409 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.21581 | 0.144394 | ||||||||
\(497\) | −54.4809 | −2.44380 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.5068 | 0.470348 | 0.235174 | − | 0.971953i | \(-0.424434\pi\) | ||||
0.235174 | + | 0.971953i | \(0.424434\pi\) | |||||||
\(500\) | 1.36899 | 0.0612230 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.496356 | 0.0221535 | ||||||||
\(503\) | 22.4351 | 1.00033 | 0.500166 | − | 0.865929i | \(-0.333272\pi\) | ||||
0.500166 | + | 0.865929i | \(0.333272\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.6380 | −0.829381 | ||||||||
\(506\) | 14.2329 | 0.632730 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.92213 | 0.395856 | ||||||||
\(509\) | −7.07738 | −0.313699 | −0.156850 | − | 0.987622i | \(-0.550134\pi\) | ||||
−0.156850 | + | 0.987622i | \(0.550134\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −45.5393 | −2.01454 | ||||||||
\(512\) | 6.85008 | 0.302734 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0702 | 0.797041 | ||||||||
\(515\) | −12.6811 | −0.558795 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.2713 | −1.46327 | ||||||||
\(518\) | −11.8476 | −0.520552 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.7073 | 1.65199 | 0.825993 | − | 0.563680i | \(-0.190615\pi\) | ||||
0.825993 | + | 0.563680i | \(0.190615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.1143 | −1.18563 | −0.592814 | − | 0.805340i | \(-0.701983\pi\) | ||||
−0.592814 | + | 0.805340i | \(0.701983\pi\) | |||||||
\(524\) | 12.3807 | 0.540854 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.7124 | −0.728697 | ||||||||
\(527\) | 39.7256 | 1.73047 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.455529 | 0.0198056 | ||||||||
\(530\) | −4.70581 | −0.204407 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −30.0306 | −1.30199 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.89062 | −0.254674 | ||||||||
\(536\) | 13.0819 | 0.565051 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.0976 | −0.650904 | ||||||||
\(539\) | 21.9962 | 0.947443 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.60518 | 0.412959 | 0.206479 | − | 0.978451i | \(-0.433799\pi\) | ||||
0.206479 | + | 0.978451i | \(0.433799\pi\) | |||||||
\(542\) | 0.413131 | 0.0177455 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 44.1485 | 1.89285 | ||||||||
\(545\) | 3.00497 | 0.128719 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.74709 | −0.373999 | −0.186999 | − | 0.982360i | \(-0.559876\pi\) | ||||
−0.186999 | + | 0.982360i | \(0.559876\pi\) | |||||||
\(548\) | 8.84153 | 0.377691 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.93881 | 0.125311 | ||||||||
\(551\) | −18.6922 | −0.796316 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.747006 | 0.0317659 | ||||||||
\(554\) | −19.4884 | −0.827981 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.7560 | −1.09230 | ||||||||
\(557\) | 34.4692 | 1.46051 | 0.730254 | − | 0.683176i | \(-0.239402\pi\) | ||||
0.730254 | + | 0.683176i | \(0.239402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.20235 | −0.0930663 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.60559 | −0.320823 | ||||||||
\(563\) | 1.03521 | 0.0436289 | 0.0218145 | − | 0.999762i | \(-0.493056\pi\) | ||||
0.0218145 | + | 0.999762i | \(0.493056\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.261568 | −0.0110042 | ||||||||
\(566\) | −2.70643 | −0.113760 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 40.5230 | 1.70031 | ||||||||
\(569\) | 8.23150 | 0.345083 | 0.172541 | − | 0.985002i | \(-0.444802\pi\) | ||||
0.172541 | + | 0.985002i | \(0.444802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.6948 | −1.74487 | −0.872436 | − | 0.488728i | \(-0.837461\pi\) | ||||
−0.872436 | + | 0.488728i | \(0.837461\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.68865 | −0.404397 | ||||||||
\(575\) | 4.84309 | 0.201971 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.80474 | 0.200024 | 0.100012 | − | 0.994986i | \(-0.468112\pi\) | ||||
0.100012 | + | 0.994986i | \(0.468112\pi\) | |||||||
\(578\) | 31.9140 | 1.32745 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.19717 | −0.174278 | ||||||||
\(581\) | 31.2169 | 1.29510 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.9163 | 0.907682 | ||||||||
\(584\) | 33.8722 | 1.40164 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.6409 | −0.563502 | ||||||||
\(587\) | 29.6737 | 1.22476 | 0.612382 | − | 0.790562i | \(-0.290211\pi\) | ||||
0.612382 | + | 0.790562i | \(0.290211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0309 | 1.31981 | ||||||||
\(590\) | −6.19694 | −0.255124 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.53732 | −0.104283 | ||||||||
\(593\) | 24.7381 | 1.01587 | 0.507936 | − | 0.861395i | \(-0.330409\pi\) | ||||
0.507936 | + | 0.861395i | \(0.330409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.2061 | −1.11534 | ||||||||
\(596\) | −12.4306 | −0.509179 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.6358 | −1.21088 | −0.605442 | − | 0.795889i | \(-0.707004\pi\) | ||||
−0.605442 | + | 0.795889i | \(0.707004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.69070 | −0.313710 | −0.156855 | − | 0.987622i | \(-0.550136\pi\) | ||||
−0.156855 | + | 0.987622i | \(0.550136\pi\) | |||||||
\(602\) | −7.51261 | −0.306191 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.1305 | 0.412206 | ||||||||
\(605\) | −2.68687 | −0.109237 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.0449 | −0.935364 | −0.467682 | − | 0.883897i | \(-0.654911\pi\) | ||||
−0.467682 | + | 0.883897i | \(0.654911\pi\) | |||||||
\(608\) | 35.5971 | 1.44365 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.6801 | 0.432426 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.61531 | 0.146021 | 0.0730106 | − | 0.997331i | \(-0.476739\pi\) | ||||
0.0730106 | + | 0.997331i | \(0.476739\pi\) | |||||||
\(614\) | 0.842475 | 0.0339995 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −35.6231 | −1.43529 | ||||||||
\(617\) | −25.2725 | −1.01743 | −0.508717 | − | 0.860934i | \(-0.669880\pi\) | ||||
−0.508717 | + | 0.860934i | \(0.669880\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.67627 | 0.228149 | 0.114074 | − | 0.993472i | \(-0.463610\pi\) | ||||
0.114074 | + | 0.993472i | \(0.463610\pi\) | |||||||
\(620\) | 7.19224 | 0.288847 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.9276 | −0.758927 | ||||||||
\(623\) | 47.6764 | 1.91012 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.42498 | −0.216826 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.4856 | 0.617944 | ||||||||
\(629\) | −31.3440 | −1.24977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.05103 | −0.280697 | −0.140349 | − | 0.990102i | \(-0.544822\pi\) | ||||
−0.140349 | + | 0.990102i | \(0.544822\pi\) | |||||||
\(632\) | −0.555625 | −0.0221016 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.3980 | 0.651249 | ||||||||
\(635\) | 6.51732 | 0.258632 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.01007 | −0.356712 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.96548 | 0.354392 | ||||||||
\(641\) | −21.9797 | −0.868145 | −0.434073 | − | 0.900878i | \(-0.642924\pi\) | ||||
−0.434073 | + | 0.900878i | \(0.642924\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.6748 | 0.815334 | 0.407667 | − | 0.913131i | \(-0.366343\pi\) | ||||
0.407667 | + | 0.913131i | \(0.366343\pi\) | |||||||
\(644\) | −23.8552 | −0.940027 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.6208 | 1.44083 | ||||||||
\(647\) | −13.2573 | −0.521198 | −0.260599 | − | 0.965447i | \(-0.583920\pi\) | ||||
−0.260599 | + | 0.965447i | \(0.583920\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.8610 | 1.13289 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.34934 | 0.131170 | ||||||||
\(653\) | 20.9720 | 0.820699 | 0.410349 | − | 0.911928i | \(-0.365407\pi\) | ||||
0.410349 | + | 0.911928i | \(0.365407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.04369 | 0.353366 | ||||||||
\(656\) | −2.07496 | −0.0810135 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −25.7038 | −1.00204 | ||||||||
\(659\) | 18.4646 | 0.719278 | 0.359639 | − | 0.933092i | \(-0.382900\pi\) | ||||
0.359639 | + | 0.933092i | \(0.382900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0221 | 1.47889 | 0.739444 | − | 0.673218i | \(-0.235088\pi\) | ||||
0.739444 | + | 0.673218i | \(0.235088\pi\) | |||||||
\(662\) | −23.3706 | −0.908326 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.2192 | −0.901081 | ||||||||
\(665\) | −21.9364 | −0.850656 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.8484 | −0.574933 | ||||||||
\(668\) | −8.47345 | −0.327848 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.88303 | 0.150015 | ||||||||
\(671\) | −49.7405 | −1.92021 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.0828 | 1.04396 | 0.521982 | − | 0.852956i | \(-0.325193\pi\) | ||||
0.521982 | + | 0.852956i | \(0.325193\pi\) | |||||||
\(674\) | −0.714824 | −0.0275340 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.5804 | 1.36747 | 0.683733 | − | 0.729732i | \(-0.260355\pi\) | ||||
0.683733 | + | 0.729732i | \(0.260355\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.0059 | 1.57366 | ||||||||
\(680\) | 20.2360 | 0.776013 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.4396 | 0.591212 | ||||||||
\(683\) | −16.2500 | −0.621790 | −0.310895 | − | 0.950444i | \(-0.600629\pi\) | ||||
−0.310895 | + | 0.950444i | \(0.600629\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.45844 | 0.246764 | ||||||||
\(686\) | −3.01362 | −0.115060 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.60893 | −0.0613398 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.65243 | 0.138945 | 0.0694724 | − | 0.997584i | \(-0.477868\pi\) | ||||
0.0694724 | + | 0.997584i | \(0.477868\pi\) | |||||||
\(692\) | 7.47746 | 0.284251 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.95901 | 0.0743628 | ||||||||
\(695\) | −18.8139 | −0.713652 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.6324 | −0.970896 | ||||||||
\(698\) | −1.74557 | −0.0660710 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.92562 | −0.186171 | ||||||||
\(701\) | −7.49092 | −0.282928 | −0.141464 | − | 0.989943i | \(-0.545181\pi\) | ||||
−0.141464 | + | 0.989943i | \(0.545181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.2728 | −0.953182 | ||||||||
\(704\) | 12.6295 | 0.475994 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.33266 | −0.0501555 | ||||||||
\(707\) | 67.0595 | 2.52203 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.7402 | −0.591137 | −0.295568 | − | 0.955322i | \(-0.595509\pi\) | ||||
−0.295568 | + | 0.955322i | \(0.595509\pi\) | |||||||
\(710\) | 12.0282 | 0.451412 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −35.4618 | −1.32899 | ||||||||
\(713\) | 25.4441 | 0.952890 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.58326 | 0.0965411 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.33145 | 0.124329 | ||||||||
\(719\) | 22.5451 | 0.840790 | 0.420395 | − | 0.907341i | \(-0.361892\pi\) | ||||
0.420395 | + | 0.907341i | \(0.361892\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.6265 | 1.69922 | ||||||||
\(722\) | 14.4346 | 0.537200 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.8653 | −0.738288 | ||||||||
\(725\) | −3.06590 | −0.113864 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.6723 | −1.02631 | −0.513155 | − | 0.858296i | \(-0.671523\pi\) | ||||
−0.513155 | + | 0.858296i | \(0.671523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0541 | 0.372119 | ||||||||
\(731\) | −19.8754 | −0.735119 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.5438 | −1.23897 | −0.619483 | − | 0.785010i | \(-0.712658\pi\) | ||||
−0.619483 | + | 0.785010i | \(0.712658\pi\) | |||||||
\(734\) | −18.7004 | −0.690246 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.2770 | 1.04230 | ||||||||
\(737\) | −18.0844 | −0.666148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.5719 | 1.86032 | 0.930158 | − | 0.367160i | \(-0.119670\pi\) | ||||
0.930158 | + | 0.367160i | \(0.119670\pi\) | |||||||
\(740\) | −5.67478 | −0.208609 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.9315 | 0.621575 | ||||||||
\(743\) | 1.69152 | 0.0620557 | 0.0310279 | − | 0.999519i | \(-0.490122\pi\) | ||||
0.0310279 | + | 0.999519i | \(0.490122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.08017 | −0.332672 | ||||||||
\(746\) | −5.62041 | −0.205778 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −38.2963 | −1.40025 | ||||||||
\(749\) | 21.1944 | 0.774428 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.6681 | 1.22857 | 0.614283 | − | 0.789086i | \(-0.289445\pi\) | ||||
0.614283 | + | 0.789086i | \(0.289445\pi\) | |||||||
\(752\) | −5.50482 | −0.200740 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.40002 | 0.269314 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.8344 | −1.81126 | −0.905631 | − | 0.424067i | \(-0.860602\pi\) | ||||
−0.905631 | + | 0.424067i | \(0.860602\pi\) | |||||||
\(758\) | 1.53285 | 0.0556756 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.3163 | 0.591855 | ||||||||
\(761\) | 21.3347 | 0.773383 | 0.386691 | − | 0.922209i | \(-0.373618\pi\) | ||||
0.386691 | + | 0.922209i | \(0.373618\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8119 | −0.391417 | ||||||||
\(764\) | 18.1198 | 0.655552 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.6459 | −0.565311 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8212 | 0.390223 | 0.195111 | − | 0.980781i | \(-0.437493\pi\) | ||||
0.195111 | + | 0.980781i | \(0.437493\pi\) | |||||||
\(770\) | −10.5738 | −0.381054 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.6183 | −0.418153 | ||||||||
\(773\) | −9.05930 | −0.325840 | −0.162920 | − | 0.986639i | \(-0.552091\pi\) | ||||
−0.162920 | + | 0.986639i | \(0.552091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.25369 | 0.188718 | ||||||||
\(776\) | −30.5003 | −1.09490 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.03225 | 0.0370081 | ||||||||
\(779\) | −20.6675 | −0.740489 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −56.0190 | −2.00452 | ||||||||
\(782\) | 29.0902 | 1.04026 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.63932 | 0.129976 | ||||||||
\(785\) | 11.3117 | 0.403733 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.4800 | 1.87071 | 0.935355 | − | 0.353712i | \(-0.115081\pi\) | ||||
0.935355 | + | 0.353712i | \(0.115081\pi\) | |||||||
\(788\) | −15.8336 | −0.564049 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.164923 | −0.00586771 | ||||||||
\(791\) | 0.941121 | 0.0334624 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.37390 | 0.0487577 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.63431 | 0.270591 | ||||||||
\(797\) | 18.6687 | 0.661279 | 0.330640 | − | 0.943757i | \(-0.392736\pi\) | ||||
0.330640 | + | 0.943757i | \(0.392736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −68.0022 | −2.40575 | ||||||||
\(800\) | 5.83863 | 0.206427 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.878924 | −0.0310359 | ||||||||
\(803\) | −46.8249 | −1.65242 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.4254 | −0.614166 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −49.8790 | −1.75474 | ||||||||
\(809\) | −40.1781 | −1.41259 | −0.706293 | − | 0.707920i | \(-0.749634\pi\) | ||||
−0.706293 | + | 0.707920i | \(0.749634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.8571 | 0.732390 | 0.366195 | − | 0.930538i | \(-0.380660\pi\) | ||||
0.366195 | + | 0.930538i | \(0.380660\pi\) | |||||||
\(812\) | 15.1014 | 0.529956 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.1821 | −0.426981 | ||||||||
\(815\) | 2.44658 | 0.0856999 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0256 | −0.560666 | ||||||||
\(818\) | −26.5220 | −0.927319 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.64070 | −0.162060 | ||||||||
\(821\) | −38.5261 | −1.34457 | −0.672286 | − | 0.740292i | \(-0.734687\pi\) | ||||
−0.672286 | + | 0.740292i | \(0.734687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.5502 | −0.995196 | −0.497598 | − | 0.867408i | \(-0.665785\pi\) | ||||
−0.497598 | + | 0.867408i | \(0.665785\pi\) | |||||||
\(824\) | −33.9371 | −1.18225 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.2966 | 0.775797 | ||||||||
\(827\) | 21.5230 | 0.748428 | 0.374214 | − | 0.927342i | \(-0.377913\pi\) | ||||
0.374214 | + | 0.927342i | \(0.377913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0960 | −0.836889 | −0.418445 | − | 0.908242i | \(-0.637425\pi\) | ||||
−0.418445 | + | 0.908242i | \(0.637425\pi\) | |||||||
\(830\) | −6.89205 | −0.239226 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44.9573 | 1.55768 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.18957 | −0.214199 | ||||||||
\(836\) | −30.8785 | −1.06795 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.4600 | −0.499513 | ||||||||
\(839\) | −42.0604 | −1.45209 | −0.726043 | − | 0.687649i | \(-0.758643\pi\) | ||||
−0.726043 | + | 0.687649i | \(0.758643\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.6003 | −0.675872 | ||||||||
\(842\) | 1.16932 | 0.0402974 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.7521 | 0.473366 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.66737 | 0.332175 | ||||||||
\(848\) | 3.62611 | 0.124521 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.00654 | 0.206023 | ||||||||
\(851\) | −20.0758 | −0.688189 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5814 | 0.636214 | 0.318107 | − | 0.948055i | \(-0.396953\pi\) | ||||
0.318107 | + | 0.948055i | \(0.396953\pi\) | |||||||
\(854\) | −38.4271 | −1.31495 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.7645 | −0.538819 | ||||||||
\(857\) | 20.5905 | 0.703359 | 0.351679 | − | 0.936120i | \(-0.385611\pi\) | ||||
0.351679 | + | 0.936120i | \(0.385611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.4044 | −1.13974 | −0.569872 | − | 0.821733i | \(-0.693007\pi\) | ||||
−0.569872 | + | 0.821733i | \(0.693007\pi\) | |||||||
\(860\) | −3.59841 | −0.122705 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.5802 | 0.700965 | ||||||||
\(863\) | −7.73166 | −0.263189 | −0.131594 | − | 0.991304i | \(-0.542010\pi\) | ||||
−0.131594 | + | 0.991304i | \(0.542010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.46204 | 0.185715 | ||||||||
\(866\) | 18.9640 | 0.644422 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −25.8777 | −0.878346 | ||||||||
\(869\) | 0.768096 | 0.0260559 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.04190 | 0.272333 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.4555 | 0.793395 | ||||||||
\(875\) | −3.59800 | −0.121635 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.5450 | −0.626221 | −0.313111 | − | 0.949717i | \(-0.601371\pi\) | ||||
−0.313111 | + | 0.949717i | \(0.601371\pi\) | |||||||
\(878\) | −22.5403 | −0.760700 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.26453 | −0.0763372 | ||||||||
\(881\) | 14.7031 | 0.495362 | 0.247681 | − | 0.968842i | \(-0.420332\pi\) | ||||
0.247681 | + | 0.968842i | \(0.420332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.7770 | 1.10303 | 0.551517 | − | 0.834163i | \(-0.314049\pi\) | ||||
0.551517 | + | 0.834163i | \(0.314049\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.98638 | −0.335499 | ||||||||
\(887\) | 11.6346 | 0.390653 | 0.195326 | − | 0.980738i | \(-0.437423\pi\) | ||||
0.195326 | + | 0.980738i | \(0.437423\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.4493 | −0.786464 | ||||||||
\(890\) | −10.5260 | −0.352831 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.60951 | −0.321750 | ||||||||
\(893\) | −54.8304 | −1.83483 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.88699 | 0.0630750 | ||||||||
\(896\) | −32.2578 | −1.07766 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.2367 | 0.975642 | ||||||||
\(899\) | −16.1073 | −0.537208 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7941 | 1.49231 | ||||||||
\(902\) | −9.96219 | −0.331704 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.700008 | −0.0232819 | ||||||||
\(905\) | −14.5109 | −0.482360 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.2083 | 1.70034 | 0.850171 | − | 0.526506i | \(-0.176498\pi\) | ||||
0.850171 | + | 0.526506i | \(0.176498\pi\) | |||||||
\(908\) | −29.1868 | −0.968598 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.9806 | −1.15896 | −0.579480 | − | 0.814986i | \(-0.696744\pi\) | ||||
−0.579480 | + | 0.814986i | \(0.696744\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0983 | 1.06230 | ||||||||
\(914\) | 5.34805 | 0.176898 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.2401 | −0.900038 | ||||||||
\(917\) | −32.5392 | −1.07454 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.5092 | −0.874458 | −0.437229 | − | 0.899350i | \(-0.644040\pi\) | ||||
−0.437229 | + | 0.899350i | \(0.644040\pi\) | |||||||
\(920\) | 12.9611 | 0.427314 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.8700 | 0.786117 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.14524 | −0.136295 | ||||||||
\(926\) | 14.3379 | 0.471173 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.9006 | −0.587617 | ||||||||
\(929\) | −11.6119 | −0.380975 | −0.190487 | − | 0.981690i | \(-0.561007\pi\) | ||||
−0.190487 | + | 0.981690i | \(0.561007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.2493 | 1.18802 | ||||||||
\(932\) | −3.25402 | −0.106589 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.8829 | 0.683308 | ||||||||
\(935\) | −27.9742 | −0.914854 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.0400 | 1.73274 | 0.866370 | − | 0.499403i | \(-0.166447\pi\) | ||||
0.866370 | + | 0.499403i | \(0.166447\pi\) | |||||||
\(938\) | −13.9711 | −0.456174 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.3117 | −0.401563 | ||||||||
\(941\) | 28.2633 | 0.921356 | 0.460678 | − | 0.887567i | \(-0.347606\pi\) | ||||
0.460678 | + | 0.887567i | \(0.347606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.4175 | −0.534627 | ||||||||
\(944\) | 4.77512 | 0.155417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.72471 | −0.251152 | ||||||||
\(947\) | 14.7748 | 0.480115 | 0.240057 | − | 0.970759i | \(-0.422834\pi\) | ||||
0.240057 | + | 0.970759i | \(0.422834\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.84309 | 0.157131 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −72.8089 | −2.35975 | ||||||||
\(953\) | −30.5951 | −0.991072 | −0.495536 | − | 0.868587i | \(-0.665028\pi\) | ||||
−0.495536 | + | 0.868587i | \(0.665028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.2359 | 0.428304 | ||||||||
\(956\) | −33.0091 | −1.06759 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.47203 | −0.0798678 | ||||||||
\(959\) | −23.2375 | −0.750377 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.39870 | −0.109636 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.1236 | 0.809177 | ||||||||
\(965\) | −8.48680 | −0.273200 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.3381 | −0.943451 | −0.471726 | − | 0.881745i | \(-0.656369\pi\) | ||||
−0.471726 | + | 0.881745i | \(0.656369\pi\) | |||||||
\(968\) | −7.19061 | −0.231115 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.05325 | −0.290682 | ||||||||
\(971\) | −35.0961 | −1.12629 | −0.563143 | − | 0.826359i | \(-0.690408\pi\) | ||||
−0.563143 | + | 0.826359i | \(0.690408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 67.6924 | 2.17012 | ||||||||
\(974\) | 4.15880 | 0.133257 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.22970 | −0.263426 | ||||||||
\(977\) | −23.4663 | −0.750754 | −0.375377 | − | 0.926872i | \(-0.622487\pi\) | ||||
−0.375377 | + | 0.926872i | \(0.622487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.0224 | 1.56676 | ||||||||
\(980\) | 8.13945 | 0.260005 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.90518 | 0.156531 | ||||||||
\(983\) | 19.0785 | 0.608511 | 0.304255 | − | 0.952591i | \(-0.401592\pi\) | ||||
0.304255 | + | 0.952591i | \(0.401592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.5659 | −0.368521 | ||||||||
\(986\) | −18.4154 | −0.586466 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.7302 | −0.404796 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7934 | 0.755822 | 0.377911 | − | 0.925842i | \(-0.376643\pi\) | ||||
0.377911 | + | 0.925842i | \(0.376643\pi\) | |||||||
\(992\) | 30.6744 | 0.973912 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −43.2776 | −1.37268 | ||||||||
\(995\) | 5.57661 | 0.176790 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.0849 | −1.71289 | −0.856444 | − | 0.516241i | \(-0.827331\pi\) | ||||
−0.856444 | + | 0.516241i | \(0.827331\pi\) | |||||||
\(998\) | 8.34620 | 0.264194 | ||||||||
\(999\) | 0 | 0 |
(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 | 7605.2.a.cu.1.6 | 10 | ||
3.2 | odd | 2 | 7605.2.a.ct.1.6 | 10 | |||
13.6 | odd | 12 | 585.2.bu.e.361.5 | yes | 20 | ||
13.11 | odd | 12 | 585.2.bu.e.316.5 | ✓ | 20 | ||
13.12 | even | 2 | 7605.2.a.ct.1.5 | 10 | |||
39.11 | even | 12 | 585.2.bu.e.316.6 | yes | 20 | ||
39.32 | even | 12 | 585.2.bu.e.361.6 | yes | 20 | ||
39.38 | odd | 2 | inner | 7605.2.a.cu.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bu.e.316.5 | ✓ | 20 | 13.11 | odd | 12 | ||
585.2.bu.e.316.6 | yes | 20 | 39.11 | even | 12 | ||
585.2.bu.e.361.5 | yes | 20 | 13.6 | odd | 12 | ||
585.2.bu.e.361.6 | yes | 20 | 39.32 | even | 12 | ||
7605.2.a.ct.1.5 | 10 | 13.12 | even | 2 | |||
7605.2.a.ct.1.6 | 10 | 3.2 | odd | 2 | |||
7605.2.a.cu.1.5 | 10 | 39.38 | odd | 2 | inner | ||
7605.2.a.cu.1.6 | 10 | 1.1 | even | 1 | trivial |