Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + 4748 x^{12} - 40524 x^{11} - 220 x^{10} + 82500 x^{9} - 21992 x^{8} - 84720 x^{7} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.09326\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | −3.09326 | −1.78590 | −0.892948 | − | 0.450159i | \(-0.851367\pi\) | ||||
−0.892948 | + | 0.450159i | \(0.851367\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.53432 | −1.13338 | −0.566691 | − | 0.823930i | \(-0.691777\pi\) | ||||
−0.566691 | + | 0.823930i | \(0.691777\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.56828 | 2.18943 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41450 | 0.727999 | 0.364000 | − | 0.931399i | \(-0.381411\pi\) | ||||
0.364000 | + | 0.931399i | \(0.381411\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.891914 | −0.247372 | −0.123686 | − | 0.992321i | \(-0.539472\pi\) | ||||
−0.123686 | + | 0.992321i | \(0.539472\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.83932 | 2.02410 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.35119 | 0.327712 | 0.163856 | − | 0.986484i | \(-0.447607\pi\) | ||||
0.163856 | + | 0.986484i | \(0.447607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.44412 | −1.70780 | −0.853899 | − | 0.520439i | \(-0.825768\pi\) | ||||
−0.853899 | + | 0.520439i | \(0.825768\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.55317 | 1.57494 | 0.787472 | − | 0.616350i | \(-0.211389\pi\) | ||||
0.787472 | + | 0.616350i | \(0.211389\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.42278 | 0.284556 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.0376 | −2.12419 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.21648 | −1.71146 | −0.855729 | − | 0.517424i | \(-0.826891\pi\) | ||||
−0.855729 | + | 0.517424i | \(0.826891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.97616 | 1.43256 | 0.716280 | − | 0.697813i | \(-0.245843\pi\) | ||||
0.716280 | + | 0.697813i | \(0.245843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.46869 | −1.30013 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.88292 | −0.638348 | −0.319174 | − | 0.947696i | \(-0.603405\pi\) | ||||
−0.319174 | + | 0.947696i | \(0.603405\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.75893 | 0.441782 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1485 | −1.54763 | −0.773817 | − | 0.633409i | \(-0.781655\pi\) | ||||
−0.773817 | + | 0.633409i | \(0.781655\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −16.6461 | −2.48146 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3109 | −1.64986 | −0.824929 | − | 0.565237i | \(-0.808785\pi\) | ||||
−0.824929 | + | 0.565237i | \(0.808785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.17959 | −0.585260 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.76801 | 0.929658 | 0.464829 | − | 0.885400i | \(-0.346116\pi\) | ||||
0.464829 | + | 0.885400i | \(0.346116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.11912 | −0.825101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 23.0266 | 3.04995 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.15894 | −0.671637 | −0.335818 | − | 0.941927i | \(-0.609013\pi\) | ||||
−0.335818 | + | 0.941927i | \(0.609013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0219 | 1.53925 | 0.769626 | − | 0.638495i | \(-0.220443\pi\) | ||||
0.769626 | + | 0.638495i | \(0.220443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.26040 | 0.280368 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3013 | 1.25851 | 0.629253 | − | 0.777201i | \(-0.283361\pi\) | ||||
0.629253 | + | 0.777201i | \(0.283361\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −23.3639 | −2.81269 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.32034 | −0.275374 | −0.137687 | − | 0.990476i | \(-0.543967\pi\) | ||||
−0.137687 | + | 0.990476i | \(0.543967\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.1459 | 1.53861 | 0.769307 | − | 0.638879i | \(-0.220602\pi\) | ||||
0.769307 | + | 0.638879i | \(0.220602\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.40103 | −0.508187 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1492 | 1.14187 | 0.570936 | − | 0.820995i | \(-0.306581\pi\) | ||||
0.570936 | + | 0.820995i | \(0.306581\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.4375 | 1.60416 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.32036 | −0.583986 | −0.291993 | − | 0.956420i | \(-0.594318\pi\) | ||||
−0.291993 | + | 0.956420i | \(0.594318\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.42435 | −0.371423 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28.5090 | 3.05649 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.69894 | 0.180087 | 0.0900437 | − | 0.995938i | \(-0.471299\pi\) | ||||
0.0900437 | + | 0.995938i | \(0.471299\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.6724 | −2.55840 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.8658 | 1.93559 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.08919 | −0.719798 | −0.359899 | − | 0.932991i | \(-0.617189\pi\) | ||||
−0.359899 | + | 0.932991i | \(0.617189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.8591 | 1.59390 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7826 | 1.07291 | 0.536453 | − | 0.843930i | \(-0.319764\pi\) | ||||
0.536453 | + | 0.843930i | \(0.319764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5587 | 1.43451 | 0.717253 | − | 0.696813i | \(-0.245399\pi\) | ||||
0.717253 | + | 0.696813i | \(0.245399\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.44009 | 0.912608 | 0.456304 | − | 0.889824i | \(-0.349173\pi\) | ||||
0.456304 | + | 0.889824i | \(0.349173\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.6416 | −1.11506 | −0.557530 | − | 0.830156i | \(-0.688251\pi\) | ||||
−0.557530 | + | 0.830156i | \(0.688251\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0109 | 1.14002 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.52290 | 0.143263 | 0.0716314 | − | 0.997431i | \(-0.477179\pi\) | ||||
0.0716314 | + | 0.997431i | \(0.477179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.1421 | −1.78501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.85834 | −0.541604 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.17019 | −0.470017 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.09326 | −0.278910 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.06582 | 0.810872 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.05647 | 0.626160 | 0.313080 | − | 0.949727i | \(-0.398639\pi\) | ||||
0.313080 | + | 0.949727i | \(0.398639\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 31.3920 | 2.76391 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4188 | 0.997661 | 0.498830 | − | 0.866700i | \(-0.333763\pi\) | ||||
0.498830 | + | 0.866700i | \(0.333763\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.9729 | 2.40752 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.77920 | −0.322879 | −0.161439 | − | 0.986883i | \(-0.551614\pi\) | ||||
−0.161439 | + | 0.986883i | \(0.551614\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.31034 | 0.450418 | 0.225209 | − | 0.974311i | \(-0.427694\pi\) | ||||
0.225209 | + | 0.974311i | \(0.427694\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 34.9875 | 2.94648 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.15353 | −0.180087 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.3575 | 1.93974 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.8886 | −1.30165 | −0.650823 | − | 0.759229i | \(-0.725576\pi\) | ||||
−0.650823 | + | 0.759229i | \(0.725576\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.47462 | −0.689655 | −0.344828 | − | 0.938666i | \(-0.612063\pi\) | ||||
−0.344828 | + | 0.938666i | \(0.612063\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.87501 | 0.717502 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.2141 | −1.62364 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.38861 | −0.749292 | −0.374646 | − | 0.927168i | \(-0.622236\pi\) | ||||
−0.374646 | + | 0.927168i | \(0.622236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.9353 | −1.66027 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.69722 | 0.211263 | 0.105631 | − | 0.994405i | \(-0.466314\pi\) | ||||
0.105631 | + | 0.994405i | \(0.466314\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.9280 | 1.47355 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.40120 | 0.185811 | 0.0929054 | − | 0.995675i | \(-0.470385\pi\) | ||||
0.0929054 | + | 0.995675i | \(0.470385\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2045 | −0.938807 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −48.8951 | −3.73910 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.05489 | −0.384316 | −0.192158 | − | 0.981364i | \(-0.561549\pi\) | ||||
−0.192158 | + | 0.981364i | \(0.561549\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.9580 | 1.19947 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.5635 | 0.939040 | 0.469520 | − | 0.882922i | \(-0.344427\pi\) | ||||
0.469520 | + | 0.882922i | \(0.344427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.30529 | −0.320010 | −0.160005 | − | 0.987116i | \(-0.551151\pi\) | ||||
−0.160005 | + | 0.987116i | \(0.551151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −37.1870 | −2.74894 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.84056 | 0.723492 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.26245 | 0.238574 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.6058 | −1.27391 | −0.636956 | − | 0.770900i | \(-0.719807\pi\) | ||||
−0.636956 | + | 0.770900i | \(0.719807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.3865 | 1.46745 | 0.733727 | − | 0.679445i | \(-0.237779\pi\) | ||||
0.733727 | + | 0.679445i | \(0.237779\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.99200 | −0.500708 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6477 | 0.829867 | 0.414934 | − | 0.909852i | \(-0.363805\pi\) | ||||
0.414934 | + | 0.909852i | \(0.363805\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.84480 | 0.556103 | 0.278052 | − | 0.960566i | \(-0.410311\pi\) | ||||
0.278052 | + | 0.960566i | \(0.410311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −31.8647 | −2.24756 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.53432 | −0.177005 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 49.6113 | 3.44823 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.9738 | −1.24328 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2163 | 1.18522 | 0.592608 | − | 0.805491i | \(-0.298098\pi\) | ||||
0.592608 | + | 0.805491i | \(0.298098\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.17744 | 0.491790 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.7196 | 1.75406 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −40.6638 | −2.74781 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.20515 | −0.0810670 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.19556 | 0.280956 | 0.140478 | − | 0.990084i | \(-0.455136\pi\) | ||||
0.140478 | + | 0.990084i | \(0.455136\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.34521 | 0.623014 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.1726 | 0.675179 | 0.337590 | − | 0.941293i | \(-0.390388\pi\) | ||||
0.337590 | + | 0.941293i | \(0.390388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6246 | −1.23075 | −0.615373 | − | 0.788236i | \(-0.710995\pi\) | ||||
−0.615373 | + | 0.788236i | \(0.710995\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.28474 | −0.0841663 | −0.0420832 | − | 0.999114i | \(-0.513399\pi\) | ||||
−0.0420832 | + | 0.999114i | \(0.513399\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.6653 | 1.86992 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −31.3941 | −2.03926 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.7684 | −1.27871 | −0.639356 | − | 0.768911i | \(-0.720799\pi\) | ||||
−0.639356 | + | 0.768911i | \(0.720799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5512 | −0.744078 | −0.372039 | − | 0.928217i | \(-0.621341\pi\) | ||||
−0.372039 | + | 0.928217i | \(0.621341\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.5460 | −0.740677 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.63951 | 0.422462 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.4573 | 1.04294 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.54044 | 0.412829 | 0.206415 | − | 0.978465i | \(-0.433820\pi\) | ||||
0.206415 | + | 0.978465i | \(0.433820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.2371 | 1.14656 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.5924 | 0.663324 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.450903 | −0.0281266 | −0.0140633 | − | 0.999901i | \(-0.504477\pi\) | ||||
−0.0140633 | + | 0.999901i | \(0.504477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −60.5364 | −3.74711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.3401 | 1.13090 | 0.565451 | − | 0.824782i | \(-0.308702\pi\) | ||||
0.565451 | + | 0.824782i | \(0.308702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.1523 | −1.05366 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.25527 | −0.321618 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.51595 | −0.580198 | −0.290099 | − | 0.956997i | \(-0.593688\pi\) | ||||
−0.290099 | + | 0.956997i | \(0.593688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.2628 | 1.53460 | 0.767302 | − | 0.641286i | \(-0.221599\pi\) | ||||
0.767302 | + | 0.641286i | \(0.221599\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.43530 | 0.207156 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.3777 | −1.10421 | −0.552103 | − | 0.833776i | \(-0.686175\pi\) | ||||
−0.552103 | + | 0.833776i | \(0.686175\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 52.3896 | 3.13649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.32543 | −0.317688 | −0.158844 | − | 0.987304i | \(-0.550777\pi\) | ||||
−0.158844 | + | 0.987304i | \(0.550777\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0777 | 0.836833 | 0.418417 | − | 0.908255i | \(-0.362585\pi\) | ||||
0.418417 | + | 0.908255i | \(0.362585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −58.3568 | −3.45676 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1743 | −0.892605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.9287 | 1.28548 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.1515 | −0.826741 | −0.413370 | − | 0.910563i | \(-0.635648\pi\) | ||||
−0.413370 | + | 0.910563i | \(0.635648\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.0744 | 0.761222 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.6504 | −1.54641 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.73678 | −0.389598 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.3533 | −1.91610 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.4674 | −1.74456 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.7727 | 1.69922 | 0.849608 | − | 0.527415i | \(-0.176839\pi\) | ||||
0.849608 | + | 0.527415i | \(0.176839\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −45.0337 | −2.56188 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.4152 | −1.27105 | −0.635524 | − | 0.772081i | \(-0.719216\pi\) | ||||
−0.635524 | + | 0.772081i | \(0.719216\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.8733 | −1.46244 | −0.731222 | − | 0.682139i | \(-0.761050\pi\) | ||||
−0.731222 | + | 0.682139i | \(0.761050\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.8452 | 1.28311 | 0.641556 | − | 0.767076i | \(-0.278289\pi\) | ||||
0.641556 | + | 0.767076i | \(0.278289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.2532 | −1.24594 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.2007 | −1.62982 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.0584 | −0.559666 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.26900 | −0.0703913 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 36.0105 | 1.99138 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.55666 | −0.525281 | −0.262641 | − | 0.964894i | \(-0.584593\pi\) | ||||
−0.262641 | + | 0.964894i | \(0.584593\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.5041 | −1.39762 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.1068 | −1.42637 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.53495 | 0.247034 | 0.123517 | − | 0.992342i | \(-0.460583\pi\) | ||||
0.123517 | + | 0.992342i | \(0.460583\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.71075 | −0.255853 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.2584 | 1.04290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 59.2117 | 3.18785 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.1857 | 1.40572 | 0.702860 | − | 0.711328i | \(-0.251906\pi\) | ||||
0.702860 | + | 0.711328i | \(0.251906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.83829 | −0.151930 | −0.0759650 | − | 0.997110i | \(-0.524204\pi\) | ||||
−0.0759650 | + | 0.997110i | \(0.524204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.84462 | 0.525467 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.5144 | 1.09187 | 0.545935 | − | 0.837828i | \(-0.316175\pi\) | ||||
0.545935 | + | 0.837828i | \(0.316175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.88050 | 0.312104 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.41431 | −0.0746443 | −0.0373222 | − | 0.999303i | \(-0.511883\pi\) | ||||
−0.0373222 | + | 0.999303i | \(0.511883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.4149 | 1.91657 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.9928 | 0.839402 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.3160 | −1.74384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.3424 | −1.58386 | −0.791931 | − | 0.610610i | \(-0.790924\pi\) | ||||
−0.791931 | + | 0.610610i | \(0.790924\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.56828 | 0.341931 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.60510 | −0.445555 | −0.222778 | − | 0.974869i | \(-0.571512\pi\) | ||||
−0.222778 | + | 0.974869i | \(0.571512\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.0430 | −1.44813 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.22031 | 0.423368 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.73291 | −0.397213 | −0.198606 | − | 0.980079i | \(-0.563642\pi\) | ||||
−0.198606 | + | 0.980079i | \(0.563642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.8275 | −1.11826 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.4109 | −1.29844 | −0.649219 | − | 0.760602i | \(-0.724904\pi\) | ||||
−0.649219 | + | 0.760602i | \(0.724904\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −66.6583 | −3.38843 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.4305 | 0.579551 | 0.289775 | − | 0.957095i | \(-0.406419\pi\) | ||||
0.289775 | + | 0.957095i | \(0.406419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2058 | 0.516129 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −35.3212 | −1.78172 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.7213 | −1.29418 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.99386 | −0.401200 | −0.200600 | − | 0.979673i | \(-0.564289\pi\) | ||||
−0.200600 | + | 0.979673i | \(0.564289\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.0156 | −1.39903 | −0.699517 | − | 0.714616i | \(-0.746602\pi\) | ||||
−0.699517 | + | 0.714616i | \(0.746602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.11405 | −0.354376 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −36.5892 | −1.81813 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.37531 | −0.464717 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5813 | −1.01768 | −0.508840 | − | 0.860861i | \(-0.669925\pi\) | ||||
−0.508840 | + | 0.860861i | \(0.669925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.6901 | 0.576628 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.4835 | 0.661879 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.4263 | −0.804399 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.7420 | 1.11102 | 0.555509 | − | 0.831511i | \(-0.312523\pi\) | ||||
0.555509 | + | 0.831511i | \(0.312523\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.8504 | −0.918711 | −0.459355 | − | 0.888253i | \(-0.651920\pi\) | ||||
−0.459355 | + | 0.888253i | \(0.651920\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −74.2929 | −3.61224 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.92245 | 0.0932524 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.66143 | 0.321617 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.4089 | −0.742218 | −0.371109 | − | 0.928589i | \(-0.621022\pi\) | ||||
−0.371109 | + | 0.928589i | \(0.621022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4547 | −0.886878 | −0.443439 | − | 0.896305i | \(-0.646242\pi\) | ||||
−0.443439 | + | 0.896305i | \(0.646242\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −72.2510 | −3.46417 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −56.2267 | −2.68969 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.4328 | −1.26157 | −0.630784 | − | 0.775958i | \(-0.717267\pi\) | ||||
−0.630784 | + | 0.775958i | \(0.717267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.9044 | 1.89592 | 0.947959 | − | 0.318393i | \(-0.103143\pi\) | ||||
0.947959 | + | 0.318393i | \(0.103143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.30566 | −0.204108 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 49.1477 | 2.32461 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.80415 | 0.226722 | 0.113361 | − | 0.993554i | \(-0.463838\pi\) | ||||
0.113361 | + | 0.993554i | \(0.463838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.41450 | 0.113694 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.2142 | 1.23165 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6661 | −0.686051 | −0.343026 | − | 0.939326i | \(-0.611452\pi\) | ||||
−0.343026 | + | 0.939326i | \(0.611452\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.9140 | −0.696124 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7184 | −0.871800 | −0.435900 | − | 0.899995i | \(-0.643570\pi\) | ||||
−0.435900 | + | 0.899995i | \(0.643570\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.63278 | 0.447673 | 0.223837 | − | 0.974627i | \(-0.428142\pi\) | ||||
0.223837 | + | 0.974627i | \(0.428142\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 62.5277 | 2.89965 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.7209 | −1.37532 | −0.687659 | − | 0.726034i | \(-0.741362\pi\) | ||||
−0.687659 | + | 0.726034i | \(0.741362\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.0414 | 1.33816 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.5036 | −1.12668 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.5913 | −0.485964 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 44.4542 | 2.03542 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.3588 | 0.518996 | 0.259498 | − | 0.965744i | \(-0.416443\pi\) | ||||
0.259498 | + | 0.965744i | \(0.416443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.46323 | 0.157910 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.9663 | 0.815806 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.1923 | −1.77597 | −0.887986 | − | 0.459870i | \(-0.847896\pi\) | ||||
−0.887986 | + | 0.459870i | \(0.847896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.34321 | −0.377293 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9009 | 0.672467 | 0.336234 | − | 0.941779i | \(-0.390847\pi\) | ||||
0.336234 | + | 0.941779i | \(0.390847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.4532 | −0.560866 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −40.1921 | −1.80650 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3001 | 0.774461 | 0.387230 | − | 0.921983i | \(-0.373432\pi\) | ||||
0.387230 | + | 0.921983i | \(0.373432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.42756 | −0.331839 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.56980 | −0.337521 | −0.168760 | − | 0.985657i | \(-0.553976\pi\) | ||||
−0.168760 | + | 0.985657i | \(0.553976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.3265 | −1.21601 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.7517 | 1.67661 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.1762 | 1.60348 | 0.801741 | − | 0.597672i | \(-0.203907\pi\) | ||||
0.801741 | + | 0.597672i | \(0.203907\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 82.1655 | 3.62769 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.8963 | −1.62584 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.3101 | −1.20109 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.6361 | 0.686349 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.34941 | 0.0591188 | 0.0295594 | − | 0.999563i | \(-0.490590\pi\) | ||||
0.0295594 | + | 0.999563i | \(0.490590\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5118 | −1.11555 | −0.557776 | − | 0.829991i | \(-0.688345\pi\) | ||||
−0.557776 | + | 0.829991i | \(0.688345\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.7773 | 0.469467 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.0503 | 1.48045 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.8854 | −1.47050 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.891914 | −0.0386331 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.9242 | −1.03433 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −38.8622 | −1.67703 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.1873 | −1.12588 | −0.562939 | − | 0.826498i | \(-0.690329\pi\) | ||||
−0.562939 | + | 0.826498i | \(0.690329\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.3174 | 0.571504 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.5035 | 1.26379 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.4992 | −0.534428 | −0.267214 | − | 0.963637i | \(-0.586103\pi\) | ||||
−0.267214 | + | 0.963637i | \(0.586103\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 78.9635 | 3.37008 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 68.6086 | 2.92282 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.4394 | −1.29208 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.1455 | 0.556994 | 0.278497 | − | 0.960437i | \(-0.410164\pi\) | ||||
0.278497 | + | 0.960437i | \(0.410164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.05160 | 0.382842 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.0916 | −0.426069 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.8786 | −1.59639 | −0.798197 | − | 0.602397i | \(-0.794212\pi\) | ||||
−0.798197 | + | 0.602397i | \(0.794212\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.85953 | −0.162372 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.2804 | 1.39519 | 0.697593 | − | 0.716494i | \(-0.254254\pi\) | ||||
0.697593 | + | 0.716494i | \(0.254254\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.0184 | −1.50732 | −0.753662 | − | 0.657262i | \(-0.771714\pi\) | ||||
−0.753662 | + | 0.657262i | \(0.771714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 54.4595 | 2.27508 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.7465 | 0.448160 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.793094 | −0.0330169 | −0.0165085 | − | 0.999864i | \(-0.505255\pi\) | ||||
−0.0165085 | + | 0.999864i | \(0.505255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −63.0609 | −2.62072 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.3414 | 0.676790 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.8469 | 0.613844 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.44222 | −0.265899 | −0.132949 | − | 0.991123i | \(-0.542445\pi\) | ||||
−0.132949 | + | 0.991123i | \(0.542445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −59.3755 | −2.44652 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.0295 | −1.48206 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.73231 | 0.153268 | 0.0766338 | − | 0.997059i | \(-0.475583\pi\) | ||||
0.0766338 | + | 0.997059i | \(0.475583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.2661 | −0.993143 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.1341 | −1.55812 | −0.779059 | − | 0.626951i | \(-0.784303\pi\) | ||||
−0.779059 | + | 0.626951i | \(0.784303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.1688 | −1.67931 | −0.839655 | − | 0.543121i | \(-0.817243\pi\) | ||||
−0.839655 | + | 0.543121i | \(0.817243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 67.6619 | 2.75541 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.1029 | 0.532709 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.1125 | 1.34400 | 0.671998 | − | 0.740553i | \(-0.265436\pi\) | ||||
0.671998 | + | 0.740553i | \(0.265436\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.0883 | 0.408129 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.9028 | −0.561530 | −0.280765 | − | 0.959777i | \(-0.590588\pi\) | ||||
−0.280765 | + | 0.959777i | \(0.590588\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.83932 | 0.316112 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.8528 | −1.44338 | −0.721690 | − | 0.692216i | \(-0.756635\pi\) | ||||
−0.721690 | + | 0.692216i | \(0.756635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.1844 | 1.61515 | 0.807574 | − | 0.589766i | \(-0.200780\pi\) | ||||
0.807574 | + | 0.589766i | \(0.200780\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −83.3691 | −3.34549 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.0896 | −1.20358 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 55.5978 | 2.22036 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.24657 | −0.209194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0862 | −0.401523 | −0.200762 | − | 0.979640i | \(-0.564342\pi\) | ||||
−0.200762 | + | 0.979640i | \(0.564342\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −53.2545 | −2.11667 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.8833 | −0.709679 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.2407 | −0.602912 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.06812 | 0.160681 | 0.0803406 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803406 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.9405 | 1.06243 | 0.531215 | − | 0.847237i | \(-0.321736\pi\) | ||||
0.531215 | + | 0.847237i | \(0.321736\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −79.5575 | −3.13257 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.6010 | −0.652654 | −0.326327 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326327 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.4563 | −0.488951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.6084 | −1.11953 | −0.559767 | − | 0.828650i | \(-0.689109\pi\) | ||||
−0.559767 | + | 0.828650i | \(0.689109\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.9388 | −1.13073 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 86.3462 | 3.36868 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.2029 | 0.709083 | 0.354541 | − | 0.935040i | \(-0.384637\pi\) | ||||
0.354541 | + | 0.935040i | \(0.384637\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.933185 | 0.0362967 | 0.0181484 | − | 0.999835i | \(-0.494223\pi\) | ||||
0.0181484 | + | 0.999835i | \(0.494223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.72784 | 0.144777 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −69.6136 | −2.69545 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9780 | −0.501758 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.0270 | 1.12057 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.00774 | −0.115940 | −0.0579699 | − | 0.998318i | \(-0.518463\pi\) | ||||
−0.0579699 | + | 0.998318i | \(0.518463\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.7041 | −0.604452 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.6115 | 0.523134 | 0.261567 | − | 0.965185i | \(-0.415761\pi\) | ||||
0.261567 | + | 0.965185i | \(0.415761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.4666 | −1.20580 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.3001 | 1.12114 | 0.560570 | − | 0.828107i | \(-0.310582\pi\) | ||||
0.560570 | + | 0.828107i | \(0.310582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.57770 | 0.365945 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 57.6107 | 2.19799 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.03649 | −0.229972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.2738 | −1.79838 | −0.899190 | − | 0.437558i | \(-0.855843\pi\) | ||||
−0.899190 | + | 0.437558i | \(0.855843\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.4581 | −0.510495 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.35119 | 0.0511801 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.97405 | 0.150312 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0423 | 0.870297 | 0.435149 | − | 0.900359i | \(-0.356696\pi\) | ||||
0.435149 | + | 0.900359i | \(0.356696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.9049 | 1.09017 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −88.6694 | −3.33948 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.2860 | −1.25008 | −0.625041 | − | 0.780592i | \(-0.714918\pi\) | ||||
−0.625041 | + | 0.780592i | \(0.714918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 66.6626 | 2.50004 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 60.2452 | 2.25620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.45773 | 0.204107 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 61.1489 | 2.28365 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.9635 | 1.37851 | 0.689254 | − | 0.724520i | \(-0.257938\pi\) | ||||
0.689254 | + | 0.724520i | \(0.257938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 35.7309 | 1.32885 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.1130 | −0.487005 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.3030 | 1.27223 | 0.636114 | − | 0.771595i | \(-0.280541\pi\) | ||||
0.636114 | + | 0.771595i | \(0.280541\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.59756 | −0.281391 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.7126 | −0.507179 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.158131 | 0.00584069 | 0.00292034 | − | 0.999996i | \(-0.499070\pi\) | ||||
0.00292034 | + | 0.999996i | \(0.499070\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.8725 | 0.916191 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.1280 | −0.556494 | −0.278247 | − | 0.960510i | \(-0.589753\pi\) | ||||
−0.278247 | + | 0.960510i | \(0.589753\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.5378 | −0.754474 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.9477 | −0.768497 | −0.384249 | − | 0.923230i | \(-0.625539\pi\) | ||||
−0.384249 | + | 0.923230i | \(0.625539\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.2668 | 1.47526 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −34.9456 | −1.27859 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3640 | −0.414678 | −0.207339 | − | 0.978269i | \(-0.566480\pi\) | ||||
−0.207339 | + | 0.978269i | \(0.566480\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.2313 | −0.737270 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.4774 | 0.781643 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.23584 | 0.226645 | 0.113323 | − | 0.993558i | \(-0.463851\pi\) | ||||
0.113323 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −56.4122 | −2.04763 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.9397 | −1.26656 | −0.633282 | − | 0.773921i | \(-0.718293\pi\) | ||||
−0.633282 | + | 0.773921i | \(0.718293\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.4921 | −0.813204 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.60133 | 0.166144 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.3262 | −0.949347 | −0.474673 | − | 0.880162i | \(-0.657434\pi\) | ||||
−0.474673 | + | 0.880162i | \(0.657434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.39476 | 0.0502312 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.96790 | −0.106748 | −0.0533740 | − | 0.998575i | \(-0.516998\pi\) | ||||
−0.0533740 | + | 0.998575i | \(0.516998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.3483 | 0.407643 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.44412 | −0.266713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.60247 | −0.200472 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 101.728 | 3.63547 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.7937 | 0.849235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.1978 | −1.50419 | −0.752095 | − | 0.659054i | \(-0.770957\pi\) | ||||
−0.752095 | + | 0.659054i | \(0.770957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −56.7309 | −2.01967 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7225 | −0.380768 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 53.0566 | 1.88173 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.7324 | 1.37197 | 0.685986 | − | 0.727615i | \(-0.259371\pi\) | ||||
0.685986 | + | 0.727615i | \(0.259371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.2831 | −0.540679 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.1591 | 0.394288 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.7408 | 1.12011 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.4353 | 1.03617 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.5673 | 1.74269 | 0.871347 | − | 0.490667i | \(-0.163247\pi\) | ||||
0.871347 | + | 0.490667i | \(0.163247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.994275 | −0.0349137 | −0.0174569 | − | 0.999848i | \(-0.505557\pi\) | ||||
−0.0174569 | + | 0.999848i | \(0.505557\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −78.1444 | −2.74064 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.83562 | −0.239441 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 75.5467 | 2.64305 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.8508 | 1.73980 | 0.869902 | − | 0.493224i | \(-0.164182\pi\) | ||||
0.869902 | + | 0.493224i | \(0.164182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6941 | 0.825924 | 0.412962 | − | 0.910748i | \(-0.364494\pi\) | ||||
0.412962 | + | 0.910748i | \(0.364494\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.6263 | −0.369960 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.2592 | −0.843574 | −0.421787 | − | 0.906695i | \(-0.638597\pi\) | ||||
−0.421787 | + | 0.906695i | \(0.638597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.0930 | 1.28829 | 0.644146 | − | 0.764902i | \(-0.277213\pi\) | ||||
0.644146 | + | 0.764902i | \(0.277213\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56.8470 | 1.97200 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.08542 | −0.210595 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −88.0379 | −3.04304 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.8392 | −1.61707 | −0.808535 | − | 0.588448i | \(-0.799739\pi\) | ||||
−0.808535 | + | 0.588448i | \(0.799739\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.9435 | 1.92909 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.4730 | 0.567359 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.9301 | 1.06403 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.5461 | −1.49450 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.3283 | −1.00536 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0349 | −0.514784 | −0.257392 | − | 0.966307i | \(-0.582863\pi\) | ||||
−0.257392 | + | 0.966307i | \(0.582863\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 123.916 | 4.23783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.1946 | −1.09975 | −0.549873 | − | 0.835248i | \(-0.685324\pi\) | ||||
−0.549873 | + | 0.835248i | \(0.685324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.1032 | −1.02711 | −0.513554 | − | 0.858057i | \(-0.671671\pi\) | ||||
−0.513554 | + | 0.858057i | \(0.671671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.6664 | 0.805615 | 0.402807 | − | 0.915285i | \(-0.368034\pi\) | ||||
0.402807 | + | 0.915285i | \(0.368034\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.8107 | 0.435577 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 46.9381 | 1.59410 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.5052 | 0.831281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.18788 | −0.311320 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −46.5638 | −1.57595 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.8653 | −1.00848 | −0.504239 | − | 0.863564i | \(-0.668227\pi\) | ||||
−0.504239 | + | 0.863564i | \(0.668227\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 43.7744 | 1.47647 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.4129 | 1.49631 | 0.748154 | − | 0.663525i | \(-0.230940\pi\) | ||||
0.748154 | + | 0.663525i | \(0.230940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.0274 | 0.741281 | 0.370640 | − | 0.928776i | \(-0.379138\pi\) | ||||
0.370640 | + | 0.928776i | \(0.379138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −40.4426 | −1.35946 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.1036 | 0.775743 | 0.387872 | − | 0.921713i | \(-0.373210\pi\) | ||||
0.387872 | + | 0.921713i | \(0.373210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34.8593 | 1.16783 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 84.1993 | 2.81762 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.8399 | −1.06429 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.8386 | 0.695782 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −73.5121 | −2.45177 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.14489 | 0.304660 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.9110 | 0.362693 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1097 | −0.568117 | −0.284058 | − | 0.958807i | \(-0.591681\pi\) | ||||
−0.284058 | + | 0.958807i | \(0.591681\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 70.8230 | 2.34905 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8392 | −0.392249 | −0.196124 | − | 0.980579i | \(-0.562836\pi\) | ||||
−0.196124 | + | 0.980579i | \(0.562836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.8460 | −0.425141 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 94.2438 | 3.11560 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.3855 | −1.10129 | −0.550644 | − | 0.834740i | \(-0.685618\pi\) | ||||
−0.550644 | + | 0.834740i | \(0.685618\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −92.0947 | −3.03462 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.06955 | 0.0681200 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.52454 | −0.181646 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 95.6253 | 3.14075 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.44181 | −0.244158 | −0.122079 | − | 0.992520i | \(-0.538956\pi\) | ||||
−0.122079 | + | 0.992520i | \(0.538956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 69.3361 | 2.26996 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.26810 | −0.270396 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.8715 | −0.453163 | −0.226582 | − | 0.973992i | \(-0.572755\pi\) | ||||
−0.226582 | + | 0.973992i | \(0.572755\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 80.0329 | 2.61177 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.3238 | 1.15152 | 0.575761 | − | 0.817618i | \(-0.304706\pi\) | ||||
0.575761 | + | 0.817618i | \(0.304706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.55317 | 0.245965 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.9480 | −1.88306 | −0.941529 | − | 0.336933i | \(-0.890611\pi\) | ||||
−0.941529 | + | 0.336933i | \(0.890611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.7250 | −0.380611 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −70.6662 | −2.29151 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.9224 | −1.42279 | −0.711394 | − | 0.702794i | \(-0.751936\pi\) | ||||
−0.711394 | + | 0.702794i | \(0.751936\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.6188 | 1.44383 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 68.8350 | 2.22512 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.6191 | 1.05223 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 62.0052 | 1.99809 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −51.6660 | −1.66319 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.9160 | 1.50872 | 0.754358 | − | 0.656463i | \(-0.227948\pi\) | ||||
0.754358 | + | 0.656463i | \(0.227948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.1134 | 0.999506 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.2241 | 1.38713 | 0.693564 | − | 0.720395i | \(-0.256040\pi\) | ||||
0.693564 | + | 0.720395i | \(0.256040\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.92534 | 0.125712 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.7307 | −1.20711 | −0.603556 | − | 0.797321i | \(-0.706250\pi\) | ||||
−0.603556 | + | 0.797321i | \(0.706250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.10209 | 0.131104 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −76.4652 | −2.44134 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.9765 | 0.860418 | 0.430209 | − | 0.902729i | \(-0.358440\pi\) | ||||
0.430209 | + | 0.902729i | \(0.358440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.5191 | −0.940557 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −76.6534 | −2.43744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.4937 | 1.22279 | 0.611396 | − | 0.791325i | \(-0.290608\pi\) | ||||
0.611396 | + | 0.791325i | \(0.290608\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.5613 | 0.938098 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.8812 | −0.630278 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.0970 | −1.49158 | −0.745789 | − | 0.666183i | \(-0.767927\pi\) | ||||
−0.745789 | + | 0.666183i | \(0.767927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.8582 | 1.35597 |
(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 | 8036.2.a.s.1.2 | ✓ | 20 | |
7.6 | odd | 2 | 8036.2.a.t.1.19 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
8036.2.a.t.1.19 | yes | 20 | 7.6 | odd | 2 |