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: | \(0\) |
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 | 1.19 | ||
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 | \(-0.148633\pi\) | ||||
0.892948 | + | 0.450159i | \(0.148633\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.53432 | 1.13338 | 0.566691 | − | 0.823930i | \(-0.308223\pi\) | ||||
0.566691 | + | 0.823930i | \(0.308223\pi\) | |||||||
\(6\) | 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 | \(-0.460528\pi\) | ||||
0.123686 | + | 0.992321i | \(0.460528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.83932 | 2.02410 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.35119 | −0.327712 | −0.163856 | − | 0.986484i | \(-0.552393\pi\) | ||||
−0.163856 | + | 0.986484i | \(0.552393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.44412 | 1.70780 | 0.853899 | − | 0.520439i | \(-0.174232\pi\) | ||||
0.853899 | + | 0.520439i | \(0.174232\pi\) | |||||||
\(20\) | 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 | \(-0.754157\pi\) | ||||
−0.716280 | + | 0.697813i | \(0.754157\pi\) | |||||||
\(32\) | 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 | \(-0.191215\pi\) | ||||
0.824929 | + | 0.565237i | \(0.191215\pi\) | |||||||
\(48\) | 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 | \(-0.390987\pi\) | ||||
0.335818 | + | 0.941927i | \(0.390987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0219 | −1.53925 | −0.769626 | − | 0.638495i | \(-0.779557\pi\) | ||||
−0.769626 | + | 0.638495i | \(0.779557\pi\) | |||||||
\(62\) | 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 | \(-0.779398\pi\) | ||||
−0.769307 | + | 0.638879i | \(0.779398\pi\) | |||||||
\(74\) | 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 | \(-0.405682\pi\) | ||||
0.291993 | + | 0.956420i | \(0.405682\pi\) | |||||||
\(84\) | 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 | \(-0.528701\pi\) | ||||
−0.0900437 | + | 0.995938i | \(0.528701\pi\) | |||||||
\(90\) | 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 | \(-0.382811\pi\) | ||||
0.359899 | + | 0.932991i | \(0.382811\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.8591 | 1.59390 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7826 | −1.07291 | −0.536453 | − | 0.843930i | \(-0.680236\pi\) | ||||
−0.536453 | + | 0.843930i | \(0.680236\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5587 | −1.43451 | −0.717253 | − | 0.696813i | \(-0.754601\pi\) | ||||
−0.717253 | + | 0.696813i | \(0.754601\pi\) | |||||||
\(104\) | 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 | \(-0.666237\pi\) | ||||
−0.498830 | + | 0.866700i | \(0.666237\pi\) | |||||||
\(132\) | 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 | \(-0.572306\pi\) | ||||
−0.225209 | + | 0.974311i | \(0.572306\pi\) | |||||||
\(140\) | 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 | \(-0.377764\pi\) | ||||
0.374646 | + | 0.927168i | \(0.377764\pi\) | |||||||
\(158\) | 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 | \(-0.529615\pi\) | ||||
−0.0929054 | + | 0.995675i | \(0.529615\pi\) | |||||||
\(168\) | 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 | \(-0.438451\pi\) | ||||
0.192158 | + | 0.981364i | \(0.438451\pi\) | |||||||
\(174\) | 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 | \(-0.448849\pi\) | ||||
0.160005 | + | 0.987116i | \(0.448849\pi\) | |||||||
\(182\) | 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 | \(-0.589689\pi\) | ||||
−0.278052 | + | 0.960566i | \(0.589689\pi\) | |||||||
\(200\) | 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 | \(-0.544864\pi\) | ||||
−0.140478 | + | 0.990084i | \(0.544864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.34521 | 0.623014 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.1726 | −0.675179 | −0.337590 | − | 0.941293i | \(-0.609612\pi\) | ||||
−0.337590 | + | 0.941293i | \(0.609612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.6246 | 1.23075 | 0.615373 | − | 0.788236i | \(-0.289005\pi\) | ||||
0.615373 | + | 0.788236i | \(0.289005\pi\) | |||||||
\(230\) | 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 | \(-0.378659\pi\) | ||||
0.372039 | + | 0.928217i | \(0.378659\pi\) | |||||||
\(242\) | 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 | \(-0.566180\pi\) | ||||
−0.206415 | + | 0.978465i | \(0.566180\pi\) | |||||||
\(252\) | 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 | \(-0.495523\pi\) | ||||
0.0140633 | + | 0.999901i | \(0.495523\pi\) | |||||||
\(258\) | 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 | \(-0.406312\pi\) | ||||
0.290099 | + | 0.956997i | \(0.406312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.2628 | −1.53460 | −0.767302 | − | 0.641286i | \(-0.778401\pi\) | ||||
−0.767302 | + | 0.641286i | \(0.778401\pi\) | |||||||
\(272\) | 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 | \(-0.637415\pi\) | ||||
−0.418417 | + | 0.908255i | \(0.637415\pi\) | |||||||
\(284\) | 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 | \(-0.364352\pi\) | ||||
0.413370 | + | 0.910563i | \(0.364352\pi\) | |||||||
\(294\) | 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 | \(-0.823161\pi\) | ||||
−0.849608 | + | 0.527415i | \(0.823161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −45.0337 | −2.56188 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4152 | 1.27105 | 0.635524 | − | 0.772081i | \(-0.280784\pi\) | ||||
0.635524 | + | 0.772081i | \(0.280784\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8733 | 1.46244 | 0.731222 | − | 0.682139i | \(-0.238950\pi\) | ||||
0.731222 | + | 0.682139i | \(0.238950\pi\) | |||||||
\(314\) | 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 | \(-0.475796\pi\) | ||||
0.0759650 | + | 0.997110i | \(0.475796\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.84462 | 0.525467 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.5144 | −1.09187 | −0.545935 | − | 0.837828i | \(-0.683825\pi\) | ||||
−0.545935 | + | 0.837828i | \(0.683825\pi\) | |||||||
\(354\) | 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 | \(-0.209076\pi\) | ||||
0.791931 | + | 0.610610i | \(0.209076\pi\) | |||||||
\(368\) | 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 | \(-0.275096\pi\) | ||||
0.649219 | + | 0.760602i | \(0.275096\pi\) | |||||||
\(384\) | 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 | \(-0.435711\pi\) | ||||
0.200600 | + | 0.979673i | \(0.435711\pi\) | |||||||
\(398\) | 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 | \(-0.330075\pi\) | ||||
0.508840 | + | 0.860861i | \(0.330075\pi\) | |||||||
\(410\) | 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 | \(-0.687477\pi\) | ||||
−0.555509 | + | 0.831511i | \(0.687477\pi\) | |||||||
\(420\) | 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 | \(-0.353758\pi\) | ||||
0.443439 | + | 0.896305i | \(0.353758\pi\) | |||||||
\(434\) | 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 | \(-0.282733\pi\) | ||||
0.630784 | + | 0.775958i | \(0.282733\pi\) | |||||||
\(440\) | 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 | \(-0.356430\pi\) | ||||
0.435900 | + | 0.899995i | \(0.356430\pi\) | |||||||
\(462\) | 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 | \(-0.258638\pi\) | ||||
0.687659 | + | 0.726034i | \(0.258638\pi\) | |||||||
\(468\) | 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 | \(-0.583557\pi\) | ||||
−0.259498 | + | 0.965744i | \(0.583557\pi\) | |||||||
\(480\) | 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 | \(-0.446024\pi\) | ||||
0.168760 | + | 0.985657i | \(0.446024\pi\) | |||||||
\(504\) | 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 | \(-0.796093\pi\) | ||||
−0.801741 | + | 0.597672i | \(0.796093\pi\) | |||||||
\(510\) | 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 | \(-0.509410\pi\) | ||||
−0.0295594 | + | 0.999563i | \(0.509410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.5118 | 1.11555 | 0.557776 | − | 0.829991i | \(-0.311655\pi\) | ||||
0.557776 | + | 0.829991i | \(0.311655\pi\) | |||||||
\(524\) | 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 | \(-0.205788\pi\) | ||||
0.798197 | + | 0.602397i | \(0.205788\pi\) | |||||||
\(564\) | 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 | \(-0.494745\pi\) | ||||
0.0165085 | + | 0.999864i | \(0.494745\pi\) | |||||||
\(578\) | 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 | \(-0.457555\pi\) | ||||
0.132949 | + | 0.991123i | \(0.457555\pi\) | |||||||
\(588\) | 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 | \(-0.524417\pi\) | ||||
−0.0766338 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(594\) | 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 | \(-0.182757\pi\) | ||||
0.839655 | + | 0.543121i | \(0.182757\pi\) | |||||||
\(602\) | 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 | \(-0.734564\pi\) | ||||
−0.671998 | + | 0.740553i | \(0.734564\pi\) | |||||||
\(608\) | 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 | \(-0.799220\pi\) | ||||
−0.807574 | + | 0.589766i | \(0.799220\pi\) | |||||||
\(620\) | 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 | \(-0.678264\pi\) | ||||
−0.531215 | + | 0.847237i | \(0.678264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −79.5575 | −3.13257 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6010 | 0.652654 | 0.326327 | − | 0.945257i | \(-0.394189\pi\) | ||||
0.326327 | + | 0.945257i | \(0.394189\pi\) | |||||||
\(648\) | 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 | \(-0.505777\pi\) | ||||
−0.0181484 | + | 0.999835i | \(0.505777\pi\) | |||||||
\(662\) | 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 | \(-0.584239\pi\) | ||||
−0.261567 | + | 0.965185i | \(0.584239\pi\) | |||||||
\(678\) | 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 | \(-0.144157\pi\) | ||||
0.899190 | + | 0.437558i | \(0.144157\pi\) | |||||||
\(692\) | 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 | \(-0.742062\pi\) | ||||
−0.689254 | + | 0.724520i | \(0.742062\pi\) | |||||||
\(720\) | 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 | \(-0.719459\pi\) | ||||
−0.636114 | + | 0.771595i | \(0.719459\pi\) | |||||||
\(728\) | 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 | \(-0.500930\pi\) | ||||
−0.00292034 | + | 0.999996i | \(0.500930\pi\) | |||||||
\(734\) | 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 | \(-0.281707\pi\) | ||||
0.633282 | + | 0.773921i | \(0.281707\pi\) | |||||||
\(762\) | 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 | \(-0.342566\pi\) | ||||
0.474673 | + | 0.880162i | \(0.342566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.39476 | 0.0502312 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.96790 | 0.106748 | 0.0533740 | − | 0.998575i | \(-0.483002\pi\) | ||||
0.0533740 | + | 0.998575i | \(0.483002\pi\) | |||||||
\(774\) | 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 | \(-0.229043\pi\) | ||||
0.752095 | + | 0.659054i | \(0.229043\pi\) | |||||||
\(788\) | 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 | \(-0.740629\pi\) | ||||
−0.685986 | + | 0.727615i | \(0.740629\pi\) | |||||||
\(798\) | 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 | \(-0.494443\pi\) | ||||
0.0174569 | + | 0.999848i | \(0.494443\pi\) | |||||||
\(812\) | 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 | \(-0.722787\pi\) | ||||
−0.644146 | + | 0.764902i | \(0.722787\pi\) | |||||||
\(830\) | 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 | \(-0.200261\pi\) | ||||
0.808535 | + | 0.588448i | \(0.200261\pi\) | |||||||
\(840\) | 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 | \(-0.417137\pi\) | ||||
0.257392 | + | 0.966307i | \(0.417137\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 123.916 | 4.23783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.1946 | 1.09975 | 0.549873 | − | 0.835248i | \(-0.314676\pi\) | ||||
0.549873 | + | 0.835248i | \(0.314676\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.1032 | 1.02711 | 0.513554 | − | 0.858057i | \(-0.328329\pi\) | ||||
0.513554 | + | 0.858057i | \(0.328329\pi\) | |||||||
\(860\) | 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 | \(-0.769060\pi\) | ||||
−0.748154 | + | 0.663525i | \(0.769060\pi\) | |||||||
\(882\) | 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 | \(-0.626790\pi\) | ||||
−0.387872 | + | 0.921713i | \(0.626790\pi\) | |||||||
\(888\) | 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 | \(-0.461044\pi\) | ||||
0.122079 | + | 0.992520i | \(0.461044\pi\) | |||||||
\(930\) | 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 | \(-0.427245\pi\) | ||||
0.226582 | + | 0.973992i | \(0.427245\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 80.0329 | 2.61177 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.3238 | −1.15152 | −0.575761 | − | 0.817618i | \(-0.695294\pi\) | ||||
−0.575761 | + | 0.817618i | \(0.695294\pi\) | |||||||
\(942\) | 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 | \(-0.743960\pi\) | ||||
−0.693564 | + | 0.720395i | \(0.743960\pi\) | |||||||
\(972\) | 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 | \(-0.641560\pi\) | ||||
−0.430209 | + | 0.902729i | \(0.641560\pi\) | |||||||
\(984\) | 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 | \(-0.232073\pi\) | ||||
0.745789 | + | 0.666183i | \(0.232073\pi\) | |||||||
\(998\) | 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.t.1.19 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.2 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.19 | yes | 20 | 1.1 | even | 1 | trivial |