Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7360,2,Mod(1,7360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7360 = 2^{6} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7360.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: | \(58.7698958877\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13955077.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 14x^{3} - x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.30649\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7360.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.30649 | −1.90900 | −0.954501 | − | 0.298206i | \(-0.903612\pi\) | ||||
−0.954501 | + | 0.298206i | \(0.903612\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.55040 | −0.963960 | −0.481980 | − | 0.876182i | \(-0.660082\pi\) | ||||
−0.481980 | + | 0.876182i | \(0.660082\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.93288 | 2.64429 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.72314 | 0.821056 | 0.410528 | − | 0.911848i | \(-0.365344\pi\) | ||||
0.410528 | + | 0.911848i | \(0.365344\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.12637 | −1.97650 | −0.988250 | − | 0.152845i | \(-0.951156\pi\) | ||||
−0.988250 | + | 0.152845i | \(0.951156\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.30649 | −0.853732 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.924010 | 0.224105 | 0.112053 | − | 0.993702i | \(-0.464257\pi\) | ||||
0.112053 | + | 0.993702i | \(0.464257\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.51623 | −1.72434 | −0.862171 | − | 0.506617i | \(-0.830896\pi\) | ||||
−0.862171 | + | 0.506617i | \(0.830896\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.43286 | 1.84020 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.3105 | −3.13896 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.38248 | 0.442415 | 0.221208 | − | 0.975227i | \(-0.429000\pi\) | ||||
0.221208 | + | 0.975227i | \(0.429000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.866248 | 0.155583 | 0.0777913 | − | 0.996970i | \(-0.475213\pi\) | ||||
0.0777913 | + | 0.996970i | \(0.475213\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.00402 | −1.56740 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.55040 | −0.431096 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.352855 | −0.0580089 | −0.0290045 | − | 0.999579i | \(-0.509234\pi\) | ||||
−0.0290045 | + | 0.999579i | \(0.509234\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 23.5633 | 3.77315 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.34066 | 0.677896 | 0.338948 | − | 0.940805i | \(-0.389929\pi\) | ||||
0.338948 | + | 0.940805i | \(0.389929\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.93288 | 1.18256 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.3239 | −1.94349 | −0.971746 | − | 0.236027i | \(-0.924155\pi\) | ||||
−0.971746 | + | 0.236027i | \(0.924155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.495474 | −0.0707819 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.05523 | −0.427818 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.99262 | −0.548429 | −0.274214 | − | 0.961669i | \(-0.588418\pi\) | ||||
−0.274214 | + | 0.961669i | \(0.588418\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.72314 | 0.367187 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24.8523 | 3.29177 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.84064 | 0.500009 | 0.250004 | − | 0.968245i | \(-0.419568\pi\) | ||||
0.250004 | + | 0.968245i | \(0.419568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.14262 | 1.17059 | 0.585296 | − | 0.810820i | \(-0.300978\pi\) | ||||
0.585296 | + | 0.810820i | \(0.300978\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −20.2320 | −2.54899 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.12637 | −0.883918 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.15933 | 0.385974 | 0.192987 | − | 0.981201i | \(-0.438183\pi\) | ||||
0.192987 | + | 0.981201i | \(0.438183\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.30649 | 0.398055 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.07883 | −0.721424 | −0.360712 | − | 0.932677i | \(-0.617466\pi\) | ||||
−0.360712 | + | 0.932677i | \(0.617466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3239 | −1.32536 | −0.662682 | − | 0.748901i | \(-0.730582\pi\) | ||||
−0.662682 | + | 0.748901i | \(0.730582\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.30649 | −0.381801 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.94508 | −0.791465 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0593 | −1.35677 | −0.678386 | − | 0.734706i | \(-0.737320\pi\) | ||||
−0.678386 | + | 0.734706i | \(0.737320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.1319 | 3.34799 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.35285 | 0.697316 | 0.348658 | − | 0.937250i | \(-0.386637\pi\) | ||||
0.348658 | + | 0.937250i | \(0.386637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.924010 | 0.100223 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.87765 | −0.844572 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.71377 | −1.02966 | −0.514829 | − | 0.857293i | \(-0.672145\pi\) | ||||
−0.514829 | + | 0.857293i | \(0.672145\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.1751 | 1.90527 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.86424 | −0.297008 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.51623 | −0.771149 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.76465 | 0.889916 | 0.444958 | − | 0.895552i | \(-0.353219\pi\) | ||||
0.444958 | + | 0.895552i | \(0.353219\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21.6023 | 2.17111 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.74794 | −0.472438 | −0.236219 | − | 0.971700i | \(-0.575908\pi\) | ||||
−0.236219 | + | 0.971700i | \(0.575908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6304 | 1.24451 | 0.622255 | − | 0.782814i | \(-0.286217\pi\) | ||||
0.622255 | + | 0.782814i | \(0.286217\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.43286 | 0.822963 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.9658 | 1.25345 | 0.626727 | − | 0.779239i | \(-0.284394\pi\) | ||||
0.626727 | + | 0.779239i | \(0.284394\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0040 | 1.43712 | 0.718562 | − | 0.695463i | \(-0.244801\pi\) | ||||
0.718562 | + | 0.695463i | \(0.244801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.16671 | 0.110739 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.13496 | 0.200840 | 0.100420 | − | 0.994945i | \(-0.467981\pi\) | ||||
0.100420 | + | 0.994945i | \(0.467981\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −56.5326 | −5.22644 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.35659 | −0.216029 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.58454 | −0.325867 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.3523 | −1.29411 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.54181 | −0.314285 | −0.157142 | − | 0.987576i | \(-0.550228\pi\) | ||||
−0.157142 | + | 0.987576i | \(0.550228\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.5499 | −1.70808 | −0.854042 | − | 0.520205i | \(-0.825856\pi\) | ||||
−0.854042 | + | 0.520205i | \(0.825856\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.1694 | 1.66220 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.3105 | −1.40379 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.41544 | 0.377236 | 0.188618 | − | 0.982051i | \(-0.439599\pi\) | ||||
0.188618 | + | 0.982051i | \(0.439599\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.9954 | −1.86563 | −0.932814 | − | 0.360358i | \(-0.882655\pi\) | ||||
−0.932814 | + | 0.360358i | \(0.882655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 44.0554 | 3.71013 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.4061 | −1.62282 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.38248 | 0.197854 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.63828 | 0.135123 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.0780 | −1.56293 | −0.781466 | − | 0.623947i | \(-0.785528\pi\) | ||||
−0.781466 | + | 0.623947i | \(0.785528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.75273 | −0.630908 | −0.315454 | − | 0.948941i | \(-0.602157\pi\) | ||||
−0.315454 | + | 0.948941i | \(0.602157\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.33006 | 0.592600 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.866248 | 0.0695787 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.5129 | −1.39768 | −0.698841 | − | 0.715277i | \(-0.746300\pi\) | ||||
−0.698841 | + | 0.715277i | \(0.746300\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.2016 | 1.04695 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.55040 | 0.200999 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.55491 | 0.200116 | 0.100058 | − | 0.994982i | \(-0.468097\pi\) | ||||
0.100058 | + | 0.994982i | \(0.468097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.00402 | −0.700962 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.61301 | −0.279583 | −0.139791 | − | 0.990181i | \(-0.544643\pi\) | ||||
−0.139791 | + | 0.990181i | \(0.544643\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.7852 | 2.90655 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −59.6253 | −4.55966 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.7824 | −0.971827 | −0.485913 | − | 0.874007i | \(-0.661513\pi\) | ||||
−0.485913 | + | 0.874007i | \(0.661513\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.55040 | −0.192792 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.6990 | −0.954519 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0149 | −0.748546 | −0.374273 | − | 0.927318i | \(-0.622108\pi\) | ||||
−0.374273 | + | 0.927318i | \(0.622108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.96248 | −0.740505 | −0.370252 | − | 0.928931i | \(-0.620729\pi\) | ||||
−0.370252 | + | 0.928931i | \(0.620729\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.2300 | −2.23466 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.352855 | −0.0259424 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.51621 | 0.184003 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 41.5983 | 3.02583 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.61298 | −0.478498 | −0.239249 | − | 0.970958i | \(-0.576901\pi\) | ||||
−0.239249 | + | 0.970958i | \(0.576901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0540 | −1.37154 | −0.685768 | − | 0.727820i | \(-0.740534\pi\) | ||||
−0.685768 | + | 0.727820i | \(0.740534\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.5633 | 1.68740 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0886 | 0.790030 | 0.395015 | − | 0.918675i | \(-0.370739\pi\) | ||||
0.395015 | + | 0.918675i | \(0.370739\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.71377 | 0.263263 | 0.131631 | − | 0.991299i | \(-0.457979\pi\) | ||||
0.131631 | + | 0.991299i | \(0.457979\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.4463 | −0.736825 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.07627 | −0.426471 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.34066 | 0.303165 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.93288 | −0.551373 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.4677 | −1.41578 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.7656 | 1.49841 | 0.749204 | − | 0.662339i | \(-0.230436\pi\) | ||||
0.749204 | + | 0.662339i | \(0.230436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.0996 | 1.37720 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.20928 | −0.149975 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 37.4424 | 2.53012 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.58484 | −0.442944 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.90730 | 0.462547 | 0.231273 | − | 0.972889i | \(-0.425711\pi\) | ||||
0.231273 | + | 0.972889i | \(0.425711\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.93288 | 0.528858 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.0325 | 1.52872 | 0.764359 | − | 0.644791i | \(-0.223055\pi\) | ||||
0.764359 | + | 0.644791i | \(0.223055\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9665 | −0.856854 | −0.428427 | − | 0.903576i | \(-0.640932\pi\) | ||||
−0.428427 | + | 0.903576i | \(0.640932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.9638 | 1.51091 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.80934 | −0.315071 | −0.157535 | − | 0.987513i | \(-0.550355\pi\) | ||||
−0.157535 | + | 0.987513i | \(0.550355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.3239 | −0.869156 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 39.8738 | 2.59008 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.4661 | −1.32384 | −0.661922 | − | 0.749573i | \(-0.730259\pi\) | ||||
−0.661922 | + | 0.749573i | \(0.730259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.8657 | 1.73057 | 0.865287 | − | 0.501277i | \(-0.167136\pi\) | ||||
0.865287 | + | 0.501277i | \(0.167136\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −50.6993 | −3.25236 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.495474 | −0.0316546 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 53.5635 | 3.40816 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.0057 | −1.33118 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.9625 | 1.00754 | 0.503771 | − | 0.863837i | \(-0.331945\pi\) | ||||
0.503771 | + | 0.863837i | \(0.331945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.72314 | −0.171202 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.05523 | −0.191326 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.33867 | 0.208261 | 0.104130 | − | 0.994564i | \(-0.466794\pi\) | ||||
0.104130 | + | 0.994564i | \(0.466794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.899919 | 0.0559183 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.8999 | 1.16988 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.3880 | −1.44217 | −0.721083 | − | 0.692849i | \(-0.756355\pi\) | ||||
−0.721083 | + | 0.692849i | \(0.756355\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.99262 | −0.245265 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.1185 | 1.96562 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.1378 | −0.861995 | −0.430998 | − | 0.902353i | \(-0.641838\pi\) | ||||
−0.430998 | + | 0.902353i | \(0.641838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9283 | 1.57503 | 0.787517 | − | 0.616293i | \(-0.211366\pi\) | ||||
0.787517 | + | 0.616293i | \(0.211366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −60.0957 | −3.63716 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.72314 | 0.164211 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.07117 | −0.0643603 | −0.0321802 | − | 0.999482i | \(-0.510245\pi\) | ||||
−0.0321802 | + | 0.999482i | \(0.510245\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.87184 | 0.411406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2260 | 0.729341 | 0.364671 | − | 0.931137i | \(-0.381182\pi\) | ||||
0.364671 | + | 0.931137i | \(0.381182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.5454 | 1.81573 | 0.907867 | − | 0.419259i | \(-0.137710\pi\) | ||||
0.907867 | + | 0.419259i | \(0.137710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.8523 | 1.47213 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.0704 | −0.653465 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1462 | −0.949777 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.9802 | −1.69885 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.46838 | 0.494728 | 0.247364 | − | 0.968923i | \(-0.420436\pi\) | ||||
0.247364 | + | 0.968923i | \(0.420436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.84064 | 0.223611 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −44.4157 | −2.57726 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.12637 | 0.412129 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6990 | 0.901885 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.14262 | 0.523505 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.32802 | 0.0757942 | 0.0378971 | − | 0.999282i | \(-0.487934\pi\) | ||||
0.0378971 | + | 0.999282i | \(0.487934\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −41.7623 | −2.37578 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.2971 | 1.37776 | 0.688882 | − | 0.724874i | \(-0.258102\pi\) | ||||
0.688882 | + | 0.724874i | \(0.258102\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.3478 | 1.15013 | 0.575063 | − | 0.818109i | \(-0.304977\pi\) | ||||
0.575063 | + | 0.818109i | \(0.304977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.2320 | −1.13994 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.57309 | 0.481513 | 0.240756 | − | 0.970586i | \(-0.422604\pi\) | ||||
0.240756 | + | 0.970586i | \(0.422604\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.48781 | 0.363248 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.8714 | −2.39285 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.94508 | −0.386434 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.12637 | −0.395300 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −49.6106 | −2.74347 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.9813 | 1.87345 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.9767 | 1.15299 | 0.576493 | − | 0.817102i | \(-0.304421\pi\) | ||||
0.576493 | + | 0.817102i | \(0.304421\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.79915 | −0.153393 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.15933 | 0.172613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.17314 | −0.118379 | −0.0591894 | − | 0.998247i | \(-0.518852\pi\) | ||||
−0.0591894 | + | 0.998247i | \(0.518852\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.05922 | −0.383404 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.35891 | 0.127742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1164 | 1.03219 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.30649 | 0.178015 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.1335 | 1.72502 | 0.862509 | − | 0.506042i | \(-0.168892\pi\) | ||||
0.862509 | + | 0.506042i | \(0.168892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.5157 | −0.723479 | −0.361740 | − | 0.932279i | \(-0.617817\pi\) | ||||
−0.361740 | + | 0.932279i | \(0.617817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 116.235 | 6.20415 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.0645 | −1.49372 | −0.746861 | − | 0.664981i | \(-0.768440\pi\) | ||||
−0.746861 | + | 0.664981i | \(0.768440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.07883 | −0.322631 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.79205 | 0.412399 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.2340 | 1.06791 | 0.533956 | − | 0.845513i | \(-0.320705\pi\) | ||||
0.533956 | + | 0.845513i | \(0.320705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.4937 | 1.97336 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.8522 | 0.622081 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.3239 | −0.592721 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.76666 | 0.248818 | 0.124409 | − | 0.992231i | \(-0.460297\pi\) | ||||
0.124409 | + | 0.992231i | \(0.460297\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 34.4339 | 1.79256 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1828 | 0.528663 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.1510 | 1.50938 | 0.754690 | − | 0.656082i | \(-0.227787\pi\) | ||||
0.754690 | + | 0.656082i | \(0.227787\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.30649 | −0.170746 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.9784 | −0.874434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.20856 | −0.216179 | −0.108090 | − | 0.994141i | \(-0.534473\pi\) | ||||
−0.108090 | + | 0.994141i | \(0.534473\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7110 | 0.599971 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.55206 | 0.181502 | 0.0907508 | − | 0.995874i | \(-0.471073\pi\) | ||||
0.0907508 | + | 0.995874i | \(0.471073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.94508 | −0.353954 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.2515 | 1.48311 | 0.741554 | − | 0.670893i | \(-0.234089\pi\) | ||||
0.741554 | + | 0.670893i | \(0.234089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.924010 | −0.0467292 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 64.6416 | 3.26074 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0593 | −0.606767 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.8000 | 0.893356 | 0.446678 | − | 0.894695i | \(-0.352607\pi\) | ||||
0.446678 | + | 0.894695i | \(0.352607\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −63.3834 | −3.17314 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.6210 | −0.580327 | −0.290164 | − | 0.956977i | \(-0.593710\pi\) | ||||
−0.290164 | + | 0.956977i | \(0.593710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.17320 | −0.307509 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.1319 | 1.49727 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.960871 | −0.0476286 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5710 | −0.671041 | −0.335521 | − | 0.942033i | \(-0.608912\pi\) | ||||
−0.335521 | + | 0.942033i | \(0.608912\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.5996 | −0.720145 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.79516 | −0.481988 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.35285 | 0.311849 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 72.7277 | 3.56149 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4959 | −0.659317 | −0.329658 | − | 0.944100i | \(-0.606934\pi\) | ||||
−0.329658 | + | 0.944100i | \(0.606934\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.6495 | −1.83492 | −0.917462 | − | 0.397824i | \(-0.869766\pi\) | ||||
−0.917462 | + | 0.397824i | \(0.869766\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −105.697 | −5.13916 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.924010 | 0.0448211 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.3173 | −1.12840 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 64.1660 | 3.09796 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0568 | 0.484421 | 0.242210 | − | 0.970224i | \(-0.422128\pi\) | ||||
0.242210 | + | 0.970224i | \(0.422128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.30001 | 0.110531 | 0.0552657 | − | 0.998472i | \(-0.482399\pi\) | ||||
0.0552657 | + | 0.998472i | \(0.482399\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.87765 | −0.377704 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.51623 | 0.359550 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.4273 | 0.593124 | 0.296562 | − | 0.955014i | \(-0.404160\pi\) | ||||
0.296562 | + | 0.955014i | \(0.404160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.93053 | −0.187168 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.18268 | −0.103702 | −0.0518510 | − | 0.998655i | \(-0.516512\pi\) | ||||
−0.0518510 | + | 0.998655i | \(0.516512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.71377 | −0.460477 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 63.0813 | 2.98364 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.09603 | 0.146111 | 0.0730554 | − | 0.997328i | \(-0.476725\pi\) | ||||
0.0730554 | + | 0.997328i | \(0.476725\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8202 | 0.556591 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.6343 | 1.20441 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.1751 | 0.852061 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.320363 | −0.0149860 | −0.00749298 | − | 0.999972i | \(-0.502385\pi\) | ||||
−0.00749298 | + | 0.999972i | \(0.502385\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.0711 | −0.703458 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.3239 | 0.713706 | 0.356853 | − | 0.934161i | \(-0.383850\pi\) | ||||
0.356853 | + | 0.934161i | \(0.383850\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.81556 | 0.316746 | 0.158373 | − | 0.987379i | \(-0.449375\pi\) | ||||
0.158373 | + | 0.987379i | \(0.449375\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.86424 | −0.132826 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.2444 | −1.26072 | −0.630360 | − | 0.776303i | \(-0.717093\pi\) | ||||
−0.630360 | + | 0.776303i | \(0.717093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.05755 | −0.372063 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 57.9062 | 2.66818 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.51623 | −0.344868 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.6730 | −1.45021 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.5031 | 1.07388 | 0.536942 | − | 0.843619i | \(-0.319579\pi\) | ||||
0.536942 | + | 0.843619i | \(0.319579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.51457 | 0.114655 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.43286 | −0.383709 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.76465 | 0.397982 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.63058 | 0.345774 | 0.172887 | − | 0.984942i | \(-0.444690\pi\) | ||||
0.172887 | + | 0.984942i | \(0.444690\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.44779 | −0.382022 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.1206 | 0.862902 | 0.431451 | − | 0.902136i | \(-0.358002\pi\) | ||||
0.431451 | + | 0.902136i | \(0.358002\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.20144 | 0.0991477 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.6023 | 0.970951 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.5034 | 0.695424 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6581 | 1.14861 | 0.574306 | − | 0.818641i | \(-0.305272\pi\) | ||||
0.574306 | + | 0.818641i | \(0.305272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.9464 | 0.533725 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.42282 | −0.375555 | −0.187777 | − | 0.982212i | \(-0.560128\pi\) | ||||
−0.187777 | + | 0.982212i | \(0.560128\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.74794 | −0.211281 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −124.936 | −5.54862 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.2328 | −0.808153 | −0.404076 | − | 0.914725i | \(-0.632407\pi\) | ||||
−0.404076 | + | 0.914725i | \(0.632407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.8805 | 1.27760 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 122.594 | 5.41264 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.6304 | 0.556562 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.2828 | −1.59572 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.2648 | 1.85522 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.8738 | 0.870689 | 0.435345 | − | 0.900264i | \(-0.356627\pi\) | ||||
0.435345 | + | 0.900264i | \(0.356627\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7228 | 0.862418 | 0.431209 | − | 0.902252i | \(-0.358087\pi\) | ||||
0.431209 | + | 0.902252i | \(0.358087\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.43286 | 0.368040 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.800422 | 0.0348669 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.4673 | 1.32217 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.9331 | −1.33986 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.9658 | 0.560562 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.1141 | 1.42898 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.34924 | −0.0581160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.4662 | 0.707938 | 0.353969 | − | 0.935257i | \(-0.384832\pi\) | ||||
0.353969 | + | 0.935257i | \(0.384832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.9408 | 1.41363 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.0040 | 0.642702 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.3286 | 1.63881 | 0.819405 | − | 0.573215i | \(-0.194304\pi\) | ||||
0.819405 | + | 0.573215i | \(0.194304\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 72.5273 | 3.09539 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.9073 | −0.762875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.7559 | 1.30787 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.16671 | 0.0495241 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.3973 | 0.864263 | 0.432132 | − | 0.901811i | \(-0.357762\pi\) | ||||
0.432132 | + | 0.901811i | \(0.357762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.31981 | −0.351263 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.72270 | 0.0726032 | 0.0363016 | − | 0.999341i | \(-0.488442\pi\) | ||||
0.0363016 | + | 0.999341i | \(0.488442\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.13496 | 0.0898184 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −76.8483 | −3.22733 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.3283 | 1.06182 | 0.530909 | − | 0.847429i | \(-0.321850\pi\) | ||||
0.530909 | + | 0.847429i | \(0.321850\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.68968 | 0.238106 | 0.119053 | − | 0.992888i | \(-0.462014\pi\) | ||||
0.119053 | + | 0.992888i | \(0.462014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.8658 | 0.913455 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0377 | −0.750918 | −0.375459 | − | 0.926839i | \(-0.622515\pi\) | ||||
−0.375459 | + | 0.926839i | \(0.622515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 63.0019 | 2.61827 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.2023 | −0.672185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.8724 | −0.450291 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −56.5326 | −2.33734 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.1894 | −0.544383 | −0.272192 | − | 0.962243i | \(-0.587748\pi\) | ||||
−0.272192 | + | 0.962243i | \(0.587748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.51092 | −0.268278 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.6643 | −1.50817 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.326755 | −0.0134182 | −0.00670911 | − | 0.999977i | \(-0.502136\pi\) | ||||
−0.00670911 | + | 0.999977i | \(0.502136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.35659 | −0.0966109 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.2796 | −0.502569 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.49619 | −0.306286 | −0.153143 | − | 0.988204i | \(-0.548939\pi\) | ||||
−0.153143 | + | 0.988204i | \(0.548939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.121724 | 0.00496523 | 0.00248262 | − | 0.999997i | \(-0.499210\pi\) | ||||
0.00248262 | + | 0.999997i | \(0.499210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.0626 | 1.02063 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.58454 | −0.145732 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.52992 | 0.0620975 | 0.0310488 | − | 0.999518i | \(-0.490115\pi\) | ||||
0.0310488 | + | 0.999518i | \(0.490115\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.0911 | 0.814134 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 94.9512 | 3.84131 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3927 | −0.985211 | −0.492605 | − | 0.870253i | \(-0.663955\pi\) | ||||
−0.492605 | + | 0.870253i | \(0.663955\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.3523 | −0.578742 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.8906 | 1.12283 | 0.561416 | − | 0.827534i | \(-0.310257\pi\) | ||||
0.561416 | + | 0.827534i | \(0.310257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8617 | −0.516957 | −0.258478 | − | 0.966017i | \(-0.583221\pi\) | ||||
−0.258478 | + | 0.966017i | \(0.583221\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.3105 | 0.654518 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.7740 | 0.992549 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 67.6763 | 2.70273 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.326041 | −0.0130001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.9518 | −0.475794 | −0.237897 | − | 0.971290i | \(-0.576458\pi\) | ||||
−0.237897 | + | 0.971290i | \(0.576458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −71.9679 | −2.86047 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.54181 | −0.140552 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.53093 | 0.139901 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −48.2226 | −1.90766 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.9139 | −0.944544 | −0.472272 | − | 0.881453i | \(-0.656566\pi\) | ||||
−0.472272 | + | 0.881453i | \(0.656566\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.87313 | −0.152741 | −0.0763707 | − | 0.997079i | \(-0.524333\pi\) | ||||
−0.0763707 | + | 0.997079i | \(0.524333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.3330 | −0.406231 | −0.203115 | − | 0.979155i | \(-0.565107\pi\) | ||||
−0.203115 | + | 0.979155i | \(0.565107\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.4586 | 0.410535 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.30495 | 0.286303 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.6319 | −0.846522 | −0.423261 | − | 0.906008i | \(-0.639115\pi\) | ||||
−0.423261 | + | 0.906008i | \(0.639115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.5499 | −0.763878 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −89.8312 | −3.50465 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.7168 | −0.612238 | −0.306119 | − | 0.951993i | \(-0.599030\pi\) | ||||
−0.306119 | + | 0.951993i | \(0.599030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.3002 | 1.56750 | 0.783749 | − | 0.621078i | \(-0.213305\pi\) | ||||
0.783749 | + | 0.621078i | \(0.213305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.7727 | 0.845582 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.1694 | 0.743357 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.38248 | −0.0922500 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.8389 | −0.883003 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.8966 | 0.961122 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.69888 | −0.258223 | −0.129111 | − | 0.991630i | \(-0.541212\pi\) | ||||
−0.129111 | + | 0.991630i | \(0.541212\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.3105 | −0.627792 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.5812 | 0.867866 | 0.433933 | − | 0.900945i | \(-0.357125\pi\) | ||||
0.433933 | + | 0.900945i | \(0.357125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.3533 | −0.857843 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −76.1566 | −2.91833 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.42797 | 0.0546398 | 0.0273199 | − | 0.999627i | \(-0.491303\pi\) | ||||
0.0273199 | + | 0.999627i | \(0.491303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.41544 | 0.168705 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.8738 | 1.63574 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.4529 | 1.08397 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.50255 | 0.0571595 | 0.0285798 | − | 0.999592i | \(-0.490902\pi\) | ||||
0.0285798 | + | 0.999592i | \(0.490902\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −55.0944 | −2.09286 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.9954 | −0.834334 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.01081 | 0.151920 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.9020 | 0.601471 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.7341 | −0.707577 | −0.353789 | − | 0.935325i | \(-0.615107\pi\) | ||||
−0.353789 | + | 0.935325i | \(0.615107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.65214 | 0.100027 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 44.0554 | 1.65922 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.1091 | 0.455411 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5052 | 0.507199 | 0.253599 | − | 0.967309i | \(-0.418385\pi\) | ||||
0.253599 | + | 0.967309i | \(0.418385\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −95.6646 | −3.58770 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.866248 | −0.0324412 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.4061 | −0.725746 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 67.6711 | 2.52722 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.7496 | 1.18406 | 0.592030 | − | 0.805916i | \(-0.298327\pi\) | ||||
0.592030 | + | 0.805916i | \(0.298327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.2126 | −1.19966 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −88.8313 | −3.30367 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.38248 | 0.0884831 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6531 | 0.803070 | 0.401535 | − | 0.915844i | \(-0.368477\pi\) | ||||
0.401535 | + | 0.915844i | \(0.368477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 77.2411 | 2.86078 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.640507 | −0.0236577 | −0.0118288 | − | 0.999930i | \(-0.503765\pi\) | ||||
−0.0118288 | + | 0.999930i | \(0.503765\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.63828 | 0.0604288 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.60329 | 0.316906 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.8191 | −0.618700 | −0.309350 | − | 0.950948i | \(-0.600111\pi\) | ||||
−0.309350 | + | 0.950948i | \(0.600111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −177.107 | −6.50619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.9691 | −0.585851 | −0.292925 | − | 0.956135i | \(-0.594629\pi\) | ||||
−0.292925 | + | 0.956135i | \(0.594629\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.0780 | −0.698965 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 50.3964 | 1.84391 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.0680 | −1.20828 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.09841 | −0.295515 | −0.147758 | − | 0.989024i | \(-0.547206\pi\) | ||||
−0.147758 | + | 0.989024i | \(0.547206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −52.7798 | −1.92340 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.75273 | −0.282151 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.5691 | −0.747598 | −0.373799 | − | 0.927510i | \(-0.621945\pi\) | ||||
−0.373799 | + | 0.927510i | \(0.621945\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.00402 | 0.326825 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.1840 | −0.622919 | −0.311459 | − | 0.950259i | \(-0.600818\pi\) | ||||
−0.311459 | + | 0.950259i | \(0.600818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.2662 | −1.38533 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.33006 | 0.265019 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.3698 | −0.988268 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.8648 | 1.50968 | 0.754841 | − | 0.655908i | \(-0.227714\pi\) | ||||
0.754841 | + | 0.655908i | \(0.227714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0393 | −0.397570 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.7639 | 1.28634 | 0.643170 | − | 0.765724i | \(-0.277619\pi\) | ||||
0.643170 | + | 0.765724i | \(0.277619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.866248 | 0.0311165 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.97557 | −0.106748 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.6254 | −1.16893 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.5535 | −0.592330 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.8595 | −1.38872 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.5129 | −0.625062 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.9835 | −0.961858 | −0.480929 | − | 0.876759i | \(-0.659701\pi\) | ||||
−0.480929 | + | 0.876759i | \(0.659701\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 77.3321 | 2.75310 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.44500 | −0.193602 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −65.1537 | −2.31368 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.2016 | 0.468211 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.7226 | −0.946561 | −0.473281 | − | 0.880912i | \(-0.656930\pi\) | ||||
−0.473281 | + | 0.880912i | \(0.656930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.3114 | −0.435547 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −77.0582 | −2.72272 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.8366 | −1.08820 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.55040 | 0.0898897 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.7464 | 1.64555 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.0319 | 1.75903 | 0.879513 | − | 0.475874i | \(-0.157868\pi\) | ||||
0.879513 | + | 0.475874i | \(0.157868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.5774 | −1.17906 | −0.589531 | − | 0.807746i | \(-0.700687\pi\) | ||||
−0.589531 | + | 0.807746i | \(0.700687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −85.7318 | −3.00675 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.55491 | 0.0894946 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 144.181 | 5.03808 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.1429 | −0.947295 | −0.473647 | − | 0.880715i | \(-0.657063\pi\) | ||||
−0.473647 | + | 0.880715i | \(0.657063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.6392 | 1.13773 | 0.568866 | − | 0.822431i | \(-0.307382\pi\) | ||||
0.568866 | + | 0.822431i | \(0.307382\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.00402 | −0.313480 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.0828 | 1.28949 | 0.644747 | − | 0.764396i | \(-0.276963\pi\) | ||||
0.644747 | + | 0.764396i | \(0.276963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.9405 | −1.17880 | −0.589401 | − | 0.807841i | \(-0.700636\pi\) | ||||
−0.589401 | + | 0.807841i | \(0.700636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.54181 | 0.122864 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.457823 | −0.0158626 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.61301 | −0.125033 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.1289 | −0.488368 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.36929 | −0.0472730 | −0.0236365 | − | 0.999721i | \(-0.507524\pi\) | ||||
−0.0236365 | + | 0.999721i | \(0.507524\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3238 | −0.804269 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −40.4251 | −1.39231 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.7852 | 1.29985 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.14199 | 0.314122 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −100.998 | −3.46624 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.352855 | 0.0120957 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.21382 | −0.315475 | −0.157738 | − | 0.987481i | \(-0.550420\pi\) | ||||
−0.157738 | + | 0.987481i | \(0.550420\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −59.6253 | −2.03914 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.3564 | 0.490405 | 0.245202 | − | 0.969472i | \(-0.421146\pi\) | ||||
0.245202 | + | 0.969472i | \(0.421146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.3758 | −1.07053 | −0.535264 | − | 0.844685i | \(-0.679788\pi\) | ||||
−0.535264 | + | 0.844685i | \(0.679788\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.6042 | 1.24747 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.1214 | 0.889182 | 0.444591 | − | 0.895734i | \(-0.353349\pi\) | ||||
0.444591 | + | 0.895734i | \(0.353349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.7824 | −0.434614 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 53.3873 | 1.81313 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.8390 | −1.11399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.5146 | −0.762877 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 69.5289 | 2.35320 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.55040 | −0.0862192 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5530 | 0.390118 | 0.195059 | − | 0.980792i | \(-0.437510\pi\) | ||||
0.195059 | + | 0.980792i | \(0.437510\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.0006 | −0.944437 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.3559 | −1.15748 | −0.578740 | − | 0.815512i | \(-0.696456\pi\) | ||||
−0.578740 | + | 0.815512i | \(0.696456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.8316 | −0.431818 | −0.215909 | − | 0.976414i | \(-0.569271\pi\) | ||||
−0.215909 | + | 0.976414i | \(0.569271\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.6990 | −0.426874 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.46724 | −0.0492652 | −0.0246326 | − | 0.999697i | \(-0.507842\pi\) | ||||
−0.0246326 | + | 0.999697i | \(0.507842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.03303 | 0.302958 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 82.0533 | 2.74889 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 100.146 | 3.35125 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0149 | −0.334760 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.5633 | −0.786755 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.06382 | 0.0688322 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.68922 | −0.122906 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.96248 | −0.331164 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.44558 | −0.147613 | −0.0738066 | − | 0.997273i | \(-0.523515\pi\) | ||||
−0.0738066 | + | 0.997273i | \(0.523515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.6648 | −1.24926 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.1697 | 1.33088 | 0.665440 | − | 0.746451i | \(-0.268244\pi\) | ||||
0.665440 | + | 0.746451i | \(0.268244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.2997 | 0.572536 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −30.2300 | −0.999372 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49.8600 | 1.64652 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.8063 | 1.54400 | 0.771999 | − | 0.635624i | \(-0.219257\pi\) | ||||
0.771999 | + | 0.635624i | \(0.219257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.39109 | −0.144691 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43.3200 | 1.42590 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.352855 | −0.0116018 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 100.195 | 3.29085 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.92145 | 0.292703 | 0.146352 | − | 0.989233i | \(-0.453247\pi\) | ||||
0.146352 | + | 0.989233i | \(0.453247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.72409 | 0.122052 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −80.3382 | −2.63016 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.51621 | 0.0822887 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.70070 | 0.251571 | 0.125785 | − | 0.992057i | \(-0.459855\pi\) | ||||
0.125785 | + | 0.992057i | \(0.459855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −67.2799 | −2.19560 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.8979 | 0.550856 | 0.275428 | − | 0.961322i | \(-0.411180\pi\) | ||||
0.275428 | + | 0.961322i | \(0.411180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.34066 | −0.141351 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.5983 | 1.35319 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.7150 | 1.42055 | 0.710273 | − | 0.703927i | \(-0.248572\pi\) | ||||
0.710273 | + | 0.703927i | \(0.248572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 80.6985 | 2.61958 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.3469 | −0.919210 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.2353 | 0.979418 | 0.489709 | − | 0.871886i | \(-0.337103\pi\) | ||||
0.489709 | + | 0.871886i | \(0.337103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.61298 | −0.213991 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.4519 | −0.693441 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.2611 | −0.363641 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2496 | −0.975794 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 102.856 | 3.31450 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.0540 | −0.613370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.2727 | 0.523296 | 0.261648 | − | 0.965163i | \(-0.415734\pi\) | ||||
0.261648 | + | 0.965163i | \(0.415734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.9638 | 0.737704 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.21424 | −0.199424 | −0.0997122 | − | 0.995016i | \(-0.531792\pi\) | ||||
−0.0997122 | + | 0.995016i | \(0.531792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56.0971 | 1.79839 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.5633 | 0.754629 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.6705 | 0.821271 | 0.410636 | − | 0.911800i | \(-0.365307\pi\) | ||||
0.410636 | + | 0.911800i | \(0.365307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.4519 | −0.845407 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 119.025 | 3.80018 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.7124 | −0.979574 | −0.489787 | − | 0.871842i | \(-0.662925\pi\) | ||||
−0.489787 | + | 0.871842i | \(0.662925\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.0886 | 0.353312 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −112.359 | −3.57642 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4052 | 0.934086 | 0.467043 | − | 0.884235i | \(-0.345319\pi\) | ||||
0.467043 | + | 0.884235i | \(0.345319\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −69.3594 | −2.20105 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.71377 | 0.117735 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.59825 | −0.177298 | −0.0886492 | − | 0.996063i | \(-0.528255\pi\) | ||||
−0.0886492 | + | 0.996063i | \(0.528255\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.75524 | 0.182088 |
(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 | 7360.2.a.co.1.1 | 5 | ||
4.3 | odd | 2 | 7360.2.a.cp.1.5 | 5 | |||
8.3 | odd | 2 | 1840.2.a.v.1.1 | 5 | |||
8.5 | even | 2 | 920.2.a.j.1.5 | ✓ | 5 | ||
24.5 | odd | 2 | 8280.2.a.bs.1.2 | 5 | |||
40.13 | odd | 4 | 4600.2.e.u.4049.9 | 10 | |||
40.19 | odd | 2 | 9200.2.a.cu.1.5 | 5 | |||
40.29 | even | 2 | 4600.2.a.be.1.1 | 5 | |||
40.37 | odd | 4 | 4600.2.e.u.4049.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.j.1.5 | ✓ | 5 | 8.5 | even | 2 | ||
1840.2.a.v.1.1 | 5 | 8.3 | odd | 2 | |||
4600.2.a.be.1.1 | 5 | 40.29 | even | 2 | |||
4600.2.e.u.4049.2 | 10 | 40.37 | odd | 4 | |||
4600.2.e.u.4049.9 | 10 | 40.13 | odd | 4 | |||
7360.2.a.co.1.1 | 5 | 1.1 | even | 1 | trivial | ||
7360.2.a.cp.1.5 | 5 | 4.3 | odd | 2 | |||
8280.2.a.bs.1.2 | 5 | 24.5 | odd | 2 | |||
9200.2.a.cu.1.5 | 5 | 40.19 | odd | 2 |