Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, 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("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 19x^{7} + 16x^{6} + 106x^{5} - 87x^{4} - 153x^{3} + 149x^{2} - 26x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-2.81781\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | 2.81781 | 1.62686 | 0.813431 | − | 0.581661i | \(-0.197597\pi\) | ||||
0.813431 | + | 0.581661i | \(0.197597\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.974186 | −0.368208 | −0.184104 | − | 0.982907i | \(-0.558938\pi\) | ||||
−0.184104 | + | 0.982907i | \(0.558938\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.94004 | 1.64668 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.42555 | −1.03284 | −0.516421 | − | 0.856335i | \(-0.672736\pi\) | ||||
−0.516421 | + | 0.856335i | \(0.672736\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.81781 | 0.727555 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.283829 | 0.0688387 | 0.0344193 | − | 0.999407i | \(-0.489042\pi\) | ||||
0.0344193 | + | 0.999407i | \(0.489042\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.03105 | 1.38362 | 0.691809 | − | 0.722081i | \(-0.256814\pi\) | ||||
0.691809 | + | 0.722081i | \(0.256814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.74507 | −0.599023 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.91511 | 1.85893 | 0.929465 | − | 0.368911i | \(-0.120269\pi\) | ||||
0.929465 | + | 0.368911i | \(0.120269\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.46666 | 1.05206 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.461096 | 0.0856233 | 0.0428117 | − | 0.999083i | \(-0.486368\pi\) | ||||
0.0428117 | + | 0.999083i | \(0.486368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.96959 | 1.43138 | 0.715690 | − | 0.698418i | \(-0.246112\pi\) | ||||
0.715690 | + | 0.698418i | \(0.246112\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.65254 | −1.68029 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.974186 | −0.164668 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.95339 | −0.485535 | −0.242767 | − | 0.970085i | \(-0.578055\pi\) | ||||
−0.242767 | + | 0.970085i | \(0.578055\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.76466 | −1.36881 | −0.684405 | − | 0.729102i | \(-0.739938\pi\) | ||||
−0.684405 | + | 0.729102i | \(0.739938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.81154 | 1.34375 | 0.671873 | − | 0.740666i | \(-0.265490\pi\) | ||||
0.671873 | + | 0.740666i | \(0.265490\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.94004 | 0.736418 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.3775 | −1.51372 | −0.756859 | − | 0.653578i | \(-0.773267\pi\) | ||||
−0.756859 | + | 0.653578i | \(0.773267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.05096 | −0.864423 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.799776 | 0.111991 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.96945 | 0.682606 | 0.341303 | − | 0.939953i | \(-0.389132\pi\) | ||||
0.341303 | + | 0.939953i | \(0.389132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.42555 | −0.461901 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.9943 | 2.25096 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.88601 | 1.02667 | 0.513336 | − | 0.858188i | \(-0.328410\pi\) | ||||
0.513336 | + | 0.858188i | \(0.328410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4869 | 1.47075 | 0.735375 | − | 0.677661i | \(-0.237006\pi\) | ||||
0.735375 | + | 0.677661i | \(0.237006\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.81252 | −0.606320 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.96340 | −0.484206 | −0.242103 | − | 0.970251i | \(-0.577837\pi\) | ||||
−0.242103 | + | 0.970251i | \(0.577837\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 25.1211 | 3.02422 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.22524 | −0.738801 | −0.369400 | − | 0.929270i | \(-0.620437\pi\) | ||||
−0.369400 | + | 0.929270i | \(0.620437\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.94784 | 1.16431 | 0.582153 | − | 0.813079i | \(-0.302210\pi\) | ||||
0.582153 | + | 0.813079i | \(0.302210\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.81781 | 0.325372 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.33712 | 0.380301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.63735 | 0.746760 | 0.373380 | − | 0.927679i | \(-0.378199\pi\) | ||||
0.373380 | + | 0.927679i | \(0.378199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.583871 | 0.0648745 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.05049 | 0.773891 | 0.386946 | − | 0.922103i | \(-0.373530\pi\) | ||||
0.386946 | + | 0.922103i | \(0.373530\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.283829 | 0.0307856 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.29928 | 0.139297 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.66990 | 0.919007 | 0.459504 | − | 0.888176i | \(-0.348027\pi\) | ||||
0.459504 | + | 0.888176i | \(0.348027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.4568 | 2.32866 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.03105 | 0.618773 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.332881 | −0.0337990 | −0.0168995 | − | 0.999857i | \(-0.505380\pi\) | ||||
−0.0168995 | + | 0.999857i | \(0.505380\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.9224 | −1.70076 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.0197 | −1.39501 | −0.697506 | − | 0.716579i | \(-0.745707\pi\) | ||||
−0.697506 | + | 0.716579i | \(0.745707\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.6039 | −1.83310 | −0.916549 | − | 0.399923i | \(-0.869037\pi\) | ||||
−0.916549 | + | 0.399923i | \(0.869037\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.74507 | −0.267891 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8007 | −1.04414 | −0.522071 | − | 0.852902i | \(-0.674840\pi\) | ||||
−0.522071 | + | 0.852902i | \(0.674840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.87817 | 0.275679 | 0.137839 | − | 0.990455i | \(-0.455984\pi\) | ||||
0.137839 | + | 0.990455i | \(0.455984\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.32209 | −0.789898 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.77628 | 0.919675 | 0.459838 | − | 0.888003i | \(-0.347908\pi\) | ||||
0.459838 | + | 0.888003i | \(0.347908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.91511 | 0.831338 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.276502 | −0.0253469 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.734394 | 0.0667631 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.6971 | −2.22686 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3824 | 1.27623 | 0.638114 | − | 0.769942i | \(-0.279715\pi\) | ||||
0.638114 | + | 0.769942i | \(0.279715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.8292 | 2.18609 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9106 | 1.47749 | 0.738745 | − | 0.673985i | \(-0.235419\pi\) | ||||
0.738745 | + | 0.673985i | \(0.235419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.87537 | −0.509459 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.46666 | 0.470495 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.71889 | 0.659469 | 0.329735 | − | 0.944074i | \(-0.393041\pi\) | ||||
0.329735 | + | 0.944074i | \(0.393041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.7958 | −1.59424 | −0.797120 | − | 0.603821i | \(-0.793644\pi\) | ||||
−0.797120 | + | 0.603821i | \(0.793644\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.2419 | −2.46261 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.461096 | 0.0382919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.0504 | −1.40630 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.52113 | 0.288462 | 0.144231 | − | 0.989544i | \(-0.453929\pi\) | ||||
0.144231 | + | 0.989544i | \(0.453929\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0498 | −0.899217 | −0.449608 | − | 0.893226i | \(-0.648436\pi\) | ||||
−0.449608 | + | 0.893226i | \(0.648436\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.40213 | 0.113355 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.96959 | 0.640133 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.47826 | 0.357404 | 0.178702 | − | 0.983903i | \(-0.442810\pi\) | ||||
0.178702 | + | 0.983903i | \(0.442810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.0029 | 1.11051 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.68498 | −0.684472 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3490 | −0.888923 | −0.444462 | − | 0.895798i | \(-0.646605\pi\) | ||||
−0.444462 | + | 0.895798i | \(0.646605\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.65254 | −0.751449 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.82022 | −0.682529 | −0.341265 | − | 0.939967i | \(-0.610855\pi\) | ||||
−0.341265 | + | 0.939967i | \(0.610855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 29.7936 | 2.27838 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.64718 | −0.353319 | −0.176659 | − | 0.984272i | \(-0.556529\pi\) | ||||
−0.176659 | + | 0.984272i | \(0.556529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.974186 | −0.0736416 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.2213 | 1.67025 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.3186 | −1.89240 | −0.946200 | − | 0.323581i | \(-0.895113\pi\) | ||||
−0.946200 | + | 0.323581i | \(0.895113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.32715 | 0.321635 | 0.160817 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160817 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.3679 | 2.39271 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.95339 | −0.217138 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.972271 | −0.0710995 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.32554 | −0.387376 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.62340 | −0.189823 | −0.0949114 | − | 0.995486i | \(-0.530257\pi\) | ||||
−0.0949114 | + | 0.995486i | \(0.530257\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.6639 | −1.55940 | −0.779700 | − | 0.626153i | \(-0.784629\pi\) | ||||
−0.779700 | + | 0.626153i | \(0.784629\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.8601 | 1.48622 | 0.743110 | − | 0.669169i | \(-0.233350\pi\) | ||||
0.743110 | + | 0.669169i | \(0.233350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7819 | 1.61497 | 0.807485 | − | 0.589888i | \(-0.200828\pi\) | ||||
0.807485 | + | 0.589888i | \(0.200828\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.1681 | −0.787736 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.449193 | −0.0315272 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.76466 | −0.612150 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 44.0410 | 3.06106 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.6597 | −1.42906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9891 | 1.10073 | 0.550366 | − | 0.834923i | \(-0.314488\pi\) | ||||
0.550366 | + | 0.834923i | \(0.314488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.5415 | −1.20193 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.81154 | 0.600942 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.76387 | −0.527046 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28.0311 | 1.89417 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.54613 | −0.505326 | −0.252663 | − | 0.967554i | \(-0.581306\pi\) | ||||
−0.252663 | + | 0.967554i | \(0.581306\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.94004 | 0.329336 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.4988 | −1.89153 | −0.945765 | − | 0.324853i | \(-0.894685\pi\) | ||||
−0.945765 | + | 0.324853i | \(0.894685\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.3902 | −1.28134 | −0.640671 | − | 0.767815i | \(-0.721344\pi\) | ||||
−0.640671 | + | 0.767815i | \(0.721344\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.40337 | 0.618696 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7622 | −0.836080 | −0.418040 | − | 0.908429i | \(-0.637283\pi\) | ||||
−0.418040 | + | 0.908429i | \(0.637283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.3775 | −0.676955 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.7028 | 1.21488 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1424 | −0.720741 | −0.360371 | − | 0.932809i | \(-0.617350\pi\) | ||||
−0.360371 | + | 0.932809i | \(0.617350\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.48277 | −0.353176 | −0.176588 | − | 0.984285i | \(-0.556506\pi\) | ||||
−0.176588 | + | 0.984285i | \(0.556506\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7547 | −0.946517 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.05096 | −0.386582 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.8669 | 1.25901 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.4904 | −1.54582 | −0.772910 | − | 0.634516i | \(-0.781199\pi\) | ||||
−0.772910 | + | 0.634516i | \(0.781199\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.5392 | −1.91998 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.799776 | 0.0500839 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.7828 | −0.922128 | −0.461064 | − | 0.887367i | \(-0.652532\pi\) | ||||
−0.461064 | + | 0.887367i | \(0.652532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.87715 | 0.178778 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.27783 | 0.140994 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.01732 | 0.186056 | 0.0930279 | − | 0.995664i | \(-0.470345\pi\) | ||||
0.0930279 | + | 0.995664i | \(0.470345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.96945 | 0.305271 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.4301 | 1.49510 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.46709 | −0.516248 | −0.258124 | − | 0.966112i | \(-0.583104\pi\) | ||||
−0.258124 | + | 0.966112i | \(0.583104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7542 | 1.56445 | 0.782227 | − | 0.622994i | \(-0.214084\pi\) | ||||
0.782227 | + | 0.622994i | \(0.214084\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.42555 | −0.206568 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.6848 | 0.882322 | 0.441161 | − | 0.897428i | \(-0.354567\pi\) | ||||
0.441161 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 39.3701 | 2.35703 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.1933 | 1.50290 | 0.751452 | − | 0.659788i | \(-0.229354\pi\) | ||||
0.751452 | + | 0.659788i | \(0.229354\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.3058 | −1.14761 | −0.573807 | − | 0.818991i | \(-0.694534\pi\) | ||||
−0.573807 | + | 0.818991i | \(0.694534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.9943 | 1.00666 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.53841 | 0.504006 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9194 | −0.995261 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.937995 | −0.0549862 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.23340 | 0.0720561 | 0.0360281 | − | 0.999351i | \(-0.488529\pi\) | ||||
0.0360281 | + | 0.999351i | \(0.488529\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.88601 | 0.459141 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.7263 | −1.08661 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.58408 | −0.494778 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −39.5048 | −2.26949 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.4869 | 0.657739 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.36503 | 0.420344 | 0.210172 | − | 0.977664i | \(-0.432598\pi\) | ||||
0.210172 | + | 0.977664i | \(0.432598\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −52.4222 | −2.98220 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.77672 | −0.440977 | −0.220489 | − | 0.975390i | \(-0.570765\pi\) | ||||
−0.220489 | + | 0.975390i | \(0.570765\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.104459 | 0.00590438 | 0.00295219 | − | 0.999996i | \(-0.499060\pi\) | ||||
0.00295219 | + | 0.999996i | \(0.499060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.81252 | −0.271155 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.3972 | 1.81961 | 0.909803 | − | 0.415040i | \(-0.136232\pi\) | ||||
0.909803 | + | 0.415040i | \(0.136232\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.57951 | −0.0884354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.4342 | −1.69867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.71179 | 0.0952464 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.11013 | 0.448491 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.1096 | 0.557363 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1973 | −1.05518 | −0.527589 | − | 0.849500i | \(-0.676904\pi\) | ||||
−0.527589 | + | 0.849500i | \(0.676904\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.5899 | −0.799520 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.96340 | −0.216543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.6042 | −1.17686 | −0.588429 | − | 0.808549i | \(-0.700253\pi\) | ||||
−0.588429 | + | 0.808549i | \(0.700253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.5477 | 1.49618 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.3002 | −1.47839 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.7141 | 0.686495 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.1211 | 1.35247 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.4830 | −0.670120 | −0.335060 | − | 0.942197i | \(-0.608757\pi\) | ||||
−0.335060 | + | 0.942197i | \(0.608757\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1232 | 1.39834 | 0.699171 | − | 0.714954i | \(-0.253552\pi\) | ||||
0.699171 | + | 0.714954i | \(0.253552\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.7057 | −1.04883 | −0.524413 | − | 0.851464i | \(-0.675715\pi\) | ||||
−0.524413 | + | 0.851464i | \(0.675715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.22524 | −0.330402 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.779130 | −0.0412360 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.56325 | −0.346395 | −0.173198 | − | 0.984887i | \(-0.555410\pi\) | ||||
−0.173198 | + | 0.984887i | \(0.555410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3736 | 0.914399 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.06938 | 0.108614 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.94784 | 0.520694 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.1532 | −1.73058 | −0.865291 | − | 0.501270i | \(-0.832866\pi\) | ||||
−0.865291 | + | 0.501270i | \(0.832866\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −43.2978 | −2.25399 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.84117 | −0.251341 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.0243 | 1.55460 | 0.777300 | − | 0.629130i | \(-0.216589\pi\) | ||||
0.777300 | + | 0.629130i | \(0.216589\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.81781 | 0.145511 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1570 | −0.573097 | −0.286549 | − | 0.958066i | \(-0.592508\pi\) | ||||
−0.286549 | + | 0.958066i | \(0.592508\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 40.5267 | 2.07625 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.5707 | −0.591233 | −0.295616 | − | 0.955307i | \(-0.595525\pi\) | ||||
−0.295616 | + | 0.955307i | \(0.595525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.33712 | 0.170076 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 43.5293 | 2.21272 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6724 | −0.946727 | −0.473363 | − | 0.880867i | \(-0.656960\pi\) | ||||
−0.473363 | + | 0.880867i | \(0.656960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.53037 | 0.127966 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 47.6509 | 2.40367 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.63735 | 0.333961 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7838 | 0.741977 | 0.370988 | − | 0.928638i | \(-0.379019\pi\) | ||||
0.370988 | + | 0.928638i | \(0.379019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.5557 | −0.828819 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5374 | −0.676025 | −0.338012 | − | 0.941142i | \(-0.609755\pi\) | ||||
−0.338012 | + | 0.941142i | \(0.609755\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.583871 | 0.0290128 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.1170 | 0.501481 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.79211 | 0.484189 | 0.242094 | − | 0.970253i | \(-0.422166\pi\) | ||||
0.242094 | + | 0.970253i | \(0.422166\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.7504 | 1.07287 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.68244 | −0.378028 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.05049 | 0.346095 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −52.9630 | −2.59361 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.3450 | −0.945065 | −0.472533 | − | 0.881313i | \(-0.656660\pi\) | ||||
−0.472533 | + | 0.881313i | \(0.656660\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.8582 | 0.529199 | 0.264599 | − | 0.964358i | \(-0.414760\pi\) | ||||
0.264599 | + | 0.964358i | \(0.414760\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −51.2654 | −2.49261 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.283829 | 0.0137677 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.1904 | −0.541541 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.47538 | 0.408245 | 0.204122 | − | 0.978945i | \(-0.434566\pi\) | ||||
0.204122 | + | 0.978945i | \(0.434566\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6325 | −0.703193 | −0.351596 | − | 0.936152i | \(-0.614361\pi\) | ||||
−0.351596 | + | 0.936152i | \(0.614361\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.29928 | 0.0622957 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 53.7675 | 2.57205 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2299 | 0.488245 | 0.244123 | − | 0.969744i | \(-0.421500\pi\) | ||||
0.244123 | + | 0.969744i | \(0.421500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.8920 | −1.42343 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.89017 | 0.0898045 | 0.0449023 | − | 0.998991i | \(-0.485702\pi\) | ||||
0.0449023 | + | 0.998991i | \(0.485702\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.66990 | 0.410993 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.92185 | 0.469288 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6031 | 0.500393 | 0.250196 | − | 0.968195i | \(-0.419505\pi\) | ||||
0.250196 | + | 0.968195i | \(0.419505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.0238 | 1.41376 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.1361 | −1.46290 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.2158 | −1.31988 | −0.659939 | − | 0.751319i | \(-0.729418\pi\) | ||||
−0.659939 | + | 0.751319i | \(0.729418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.55160 | 0.0724223 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1918 | −0.660976 | −0.330488 | − | 0.943810i | \(-0.607213\pi\) | ||||
−0.330488 | + | 0.943810i | \(0.607213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.9826 | −0.882195 | −0.441098 | − | 0.897459i | \(-0.645411\pi\) | ||||
−0.441098 | + | 0.897459i | \(0.645411\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.4568 | 1.04141 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.88823 | −0.457573 | −0.228786 | − | 0.973477i | \(-0.573476\pi\) | ||||
−0.228786 | + | 0.973477i | \(0.573476\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.86109 | 0.178288 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6189 | 0.581447 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.1844 | −1.38788 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.03105 | 0.276724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.5493 | 1.12403 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.4914 | 1.21042 | 0.605211 | − | 0.796065i | \(-0.293089\pi\) | ||||
0.605211 | + | 0.796065i | \(0.293089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.4726 | −1.11354 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.332881 | −0.0151154 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.8349 | 1.57852 | 0.789261 | − | 0.614058i | \(-0.210464\pi\) | ||||
0.789261 | + | 0.614058i | \(0.210464\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.9793 | −1.44616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.113245 | −0.00511068 | −0.00255534 | − | 0.999997i | \(-0.500813\pi\) | ||||
−0.00255534 | + | 0.999997i | \(0.500813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.130872 | 0.00589420 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.9224 | −0.760603 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.06455 | 0.272032 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.69924 | 0.344665 | 0.172333 | − | 0.985039i | \(-0.444870\pi\) | ||||
0.172333 | + | 0.985039i | \(0.444870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.8537 | −1.11038 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.09165 | −0.0486742 | −0.0243371 | − | 0.999704i | \(-0.507748\pi\) | ||||
−0.0243371 | + | 0.999704i | \(0.507748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0197 | −0.623869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.78054 | 0.167569 | 0.0837847 | − | 0.996484i | \(-0.473299\pi\) | ||||
0.0837847 | + | 0.996484i | \(0.473299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.69105 | −0.428707 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.9697 | 1.45565 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.6039 | −0.819786 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.5487 | 1.56343 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.0949 | −0.574800 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.70631 | −0.381430 | −0.190715 | − | 0.981645i | \(-0.561081\pi\) | ||||
−0.190715 | + | 0.981645i | \(0.561081\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.8023 | −0.516077 | −0.258038 | − | 0.966135i | \(-0.583076\pi\) | ||||
−0.258038 | + | 0.966135i | \(0.583076\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.74507 | −0.119805 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.26200 | 0.0985343 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.4792 | 2.45562 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 38.9572 | 1.69060 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.8007 | −0.466954 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −71.3429 | −3.07867 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.7279 | 0.892813 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0010 | −0.902902 | −0.451451 | − | 0.892296i | \(-0.649093\pi\) | ||||
−0.451451 | + | 0.892296i | \(0.649093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.1931 | 0.523255 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.87817 | 0.123287 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6759 | −0.841282 | −0.420641 | − | 0.907227i | \(-0.638195\pi\) | ||||
−0.420641 | + | 0.907227i | \(0.638195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 56.7458 | 2.42185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.78089 | 0.118470 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.46601 | −0.274963 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.32209 | −0.353253 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.5516 | 0.913172 | 0.456586 | − | 0.889679i | \(-0.349072\pi\) | ||||
0.456586 | + | 0.889679i | \(0.349072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.73967 | −0.115669 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6586 | 0.449205 | 0.224602 | − | 0.974450i | \(-0.427892\pi\) | ||||
0.224602 | + | 0.974450i | \(0.427892\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.77628 | 0.411291 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.568799 | −0.0238873 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.5445 | 1.15473 | 0.577363 | − | 0.816488i | \(-0.304082\pi\) | ||||
0.577363 | + | 0.816488i | \(0.304082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.1038 | −1.76199 | −0.880994 | − | 0.473127i | \(-0.843125\pi\) | ||||
−0.880994 | + | 0.473127i | \(0.843125\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.39224 | −0.308815 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.91511 | 0.371786 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.7205 | 1.40380 | 0.701901 | − | 0.712274i | \(-0.252335\pi\) | ||||
0.701901 | + | 0.712274i | \(0.252335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −61.0447 | −2.53693 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.86849 | −0.284953 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.0231 | −0.705024 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3282 | 0.550114 | 0.275057 | − | 0.961428i | \(-0.411303\pi\) | ||||
0.275057 | + | 0.961428i | \(0.411303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.0650 | 1.98048 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 58.7797 | 2.41788 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.07378 | −0.0440949 | −0.0220474 | − | 0.999757i | \(-0.507018\pi\) | ||||
−0.0220474 | + | 0.999757i | \(0.507018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.276502 | −0.0113355 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 64.1951 | 2.62733 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3111 | −0.748169 | −0.374085 | − | 0.927395i | \(-0.622043\pi\) | ||||
−0.374085 | + | 0.927395i | \(0.622043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.14497 | −0.0467043 | −0.0233521 | − | 0.999727i | \(-0.507434\pi\) | ||||
−0.0233521 | + | 0.999727i | \(0.507434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.5793 | −0.797332 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.734394 | 0.0298573 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.3920 | −0.462385 | −0.231193 | − | 0.972908i | \(-0.574263\pi\) | ||||
−0.231193 | + | 0.972908i | \(0.574263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.26574 | −0.0512904 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.51518 | 0.263146 | 0.131573 | − | 0.991306i | \(-0.457997\pi\) | ||||
0.131573 | + | 0.991306i | \(0.457997\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.6971 | −0.995884 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.43338 | −0.178481 | −0.0892405 | − | 0.996010i | \(-0.528444\pi\) | ||||
−0.0892405 | + | 0.996010i | \(0.528444\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.32341 | 0.0933857 | 0.0466929 | − | 0.998909i | \(-0.485132\pi\) | ||||
0.0466929 | + | 0.998909i | \(0.485132\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 48.7359 | 1.95570 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.44610 | −0.338386 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −58.2150 | −2.32488 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.838259 | −0.0334236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4463 | 1.01300 | 0.506501 | − | 0.862239i | \(-0.330939\pi\) | ||||
0.506501 | + | 0.862239i | \(0.330939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.0541 | 1.79074 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.3824 | 0.570746 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −30.7530 | −1.21657 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.30285 | 0.367440 | 0.183720 | − | 0.982979i | \(-0.441186\pi\) | ||||
0.183720 | + | 0.982979i | \(0.441186\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.3771 | 1.94724 | 0.973621 | − | 0.228172i | \(-0.0732747\pi\) | ||||
0.973621 | + | 0.228172i | \(0.0732747\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.8292 | 0.977649 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.1654 | 1.02867 | 0.514334 | − | 0.857590i | \(-0.328039\pi\) | ||||
0.514334 | + | 0.857590i | \(0.328039\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.0139 | −1.06039 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.8771 | −0.857430 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.5177 | −0.489857 | −0.244929 | − | 0.969541i | \(-0.578765\pi\) | ||||
−0.244929 | + | 0.969541i | \(0.578765\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.9106 | 0.660753 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 49.1427 | 1.91724 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.30544 | −0.362488 | −0.181244 | − | 0.983438i | \(-0.558012\pi\) | ||||
−0.181244 | + | 0.983438i | \(0.558012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.778487 | −0.0302796 | −0.0151398 | − | 0.999885i | \(-0.504819\pi\) | ||||
−0.0151398 | + | 0.999885i | \(0.504819\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.87537 | −0.227837 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.11072 | 0.159168 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.2635 | −0.822096 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39.3490 | −1.51905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6069 | 0.717243 | 0.358621 | − | 0.933483i | \(-0.383247\pi\) | ||||
0.358621 | + | 0.933483i | \(0.383247\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.46666 | 0.210412 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.451238 | 0.0173425 | 0.00867125 | − | 0.999962i | \(-0.497240\pi\) | ||||
0.00867125 | + | 0.999962i | \(0.497240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.324288 | 0.0124450 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −80.3040 | −3.07726 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3929 | 1.35427 | 0.677136 | − | 0.735858i | \(-0.263221\pi\) | ||||
0.677136 | + | 0.735858i | \(0.263221\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.71889 | 0.294924 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −54.6379 | −2.08457 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.0369 | −1.48503 | −0.742516 | − | 0.669828i | \(-0.766368\pi\) | ||||
−0.742516 | + | 0.669828i | \(0.766368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.4855 | 0.626233 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.7958 | −0.712966 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.48767 | −0.0942270 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35.9614 | −1.36019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0395 | 0.681344 | 0.340672 | − | 0.940182i | \(-0.389345\pi\) | ||||
0.340672 | + | 0.940182i | \(0.389345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.8121 | −0.671795 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.2419 | −1.10131 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.6578 | 0.513654 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.7805 | −0.742871 | −0.371436 | − | 0.928459i | \(-0.621134\pi\) | ||||
−0.371436 | + | 0.928459i | \(0.621134\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.7888 | 1.22967 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 71.0498 | 2.66084 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.3971 | −1.17255 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.2849 | −0.383562 | −0.191781 | − | 0.981438i | \(-0.561426\pi\) | ||||
−0.191781 | + | 0.981438i | \(0.561426\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.1237 | 0.674961 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.4494 | −0.574569 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.461096 | 0.0171247 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.08016 | −0.262589 | −0.131294 | − | 0.991343i | \(-0.541913\pi\) | ||||
−0.131294 | + | 0.991343i | \(0.541913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.3276 | −1.60473 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50097 | 0.0925017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.29532 | 0.232523 | 0.116261 | − | 0.993219i | \(-0.462909\pi\) | ||||
0.116261 | + | 0.993219i | \(0.462909\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.0504 | −0.628915 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.5768 | 0.500108 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.4301 | −1.22975 | −0.614873 | − | 0.788626i | \(-0.710793\pi\) | ||||
−0.614873 | + | 0.788626i | \(0.710793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.84274 | −0.140976 | −0.0704882 | − | 0.997513i | \(-0.522456\pi\) | ||||
−0.0704882 | + | 0.997513i | \(0.522456\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.52113 | 0.129004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.8297 | 1.27435 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5219 | 0.384461 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.7285 | −1.26726 | −0.633630 | − | 0.773636i | \(-0.718436\pi\) | ||||
−0.633630 | + | 0.773636i | \(0.718436\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −69.0092 | −2.51483 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.0498 | −0.402142 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.10935 | 0.294739 | 0.147370 | − | 0.989081i | \(-0.452919\pi\) | ||||
0.147370 | + | 0.989081i | \(0.452919\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −86.0535 | −3.12354 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.4717 | 0.379598 | 0.189799 | − | 0.981823i | \(-0.439216\pi\) | ||||
0.189799 | + | 0.981823i | \(0.439216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.80388 | −0.101507 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.40213 | 0.0506940 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.2939 | −1.59728 | −0.798639 | − | 0.601810i | \(-0.794446\pi\) | ||||
−0.798639 | + | 0.601810i | \(0.794446\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.6552 | −1.50017 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2760 | −0.441537 | −0.220769 | − | 0.975326i | \(-0.570857\pi\) | ||||
−0.220769 | + | 0.975326i | \(0.570857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.96959 | 0.286276 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.10727 | 0.290847 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52.8601 | −1.89391 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.3249 | 0.763064 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.52065 | 0.0900808 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.47826 | 0.159836 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.08241 | −0.252461 | −0.126230 | − | 0.992001i | \(-0.540288\pi\) | ||||
−0.126230 | + | 0.992001i | \(0.540288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.50222 | 0.302687 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.52392 | −0.338632 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.0029 | 0.496633 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.6799 | −0.697099 | −0.348550 | − | 0.937290i | \(-0.613326\pi\) | ||||
−0.348550 | + | 0.937290i | \(0.613326\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.94544 | −0.104202 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42.8296 | 1.51331 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.0768 | −1.20254 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.68498 | −0.306105 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.8586 | −0.839864 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.3066 | 0.924890 | 0.462445 | − | 0.886648i | \(-0.346972\pi\) | ||||
0.462445 | + | 0.886648i | \(0.346972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.2096 | 1.83333 | 0.916663 | − | 0.399662i | \(-0.130872\pi\) | ||||
0.916663 | + | 0.399662i | \(0.130872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 72.5702 | 2.54515 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.3490 | −0.397539 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.1428 | 1.85923 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.9551 | −1.70855 | −0.854273 | − | 0.519825i | \(-0.825997\pi\) | ||||
−0.854273 | + | 0.519825i | \(0.825997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.3073 | 0.986731 | 0.493366 | − | 0.869822i | \(-0.335767\pi\) | ||||
0.493366 | + | 0.869822i | \(0.335767\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.65254 | −0.336058 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.1223 | 0.386759 | 0.193380 | − | 0.981124i | \(-0.438055\pi\) | ||||
0.193380 | + | 0.981124i | \(0.438055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.14566 | −0.0397905 | −0.0198952 | − | 0.999802i | \(-0.506333\pi\) | ||||
−0.0198952 | + | 0.999802i | \(0.506333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.3788 | 1.43542 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.71744 | −0.0595057 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.82022 | −0.305236 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 43.5670 | 1.50590 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.3167 | −0.977602 | −0.488801 | − | 0.872395i | \(-0.662566\pi\) | ||||
−0.488801 | + | 0.872395i | \(0.662566\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7874 | −0.992669 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 70.9898 | 2.44502 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.715436 | −0.0245827 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.4002 | −1.86701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.3298 | −0.902574 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6180 | 1.01410 | 0.507051 | − | 0.861916i | \(-0.330736\pi\) | ||||
0.507051 | + | 0.861916i | \(0.330736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.7936 | 1.01892 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.3690 | 0.490835 | 0.245417 | − | 0.969418i | \(-0.421075\pi\) | ||||
0.245417 | + | 0.969418i | \(0.421075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.17850 | −0.313166 | −0.156583 | − | 0.987665i | \(-0.550048\pi\) | ||||
−0.156583 | + | 0.987665i | \(0.550048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.0596 | 0.819949 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.1458 | −1.09426 | −0.547128 | − | 0.837049i | \(-0.684279\pi\) | ||||
−0.547128 | + | 0.837049i | \(0.684279\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.64718 | −0.158009 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −47.6757 | −1.61915 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.7366 | −0.771285 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.64445 | −0.0556561 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.974186 | −0.0329335 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.9633 | −0.876720 | −0.438360 | − | 0.898800i | \(-0.644440\pi\) | ||||
−0.438360 | + | 0.898800i | \(0.644440\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.47549 | 0.117225 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.1165 | −0.576671 | −0.288335 | − | 0.957529i | \(-0.593102\pi\) | ||||
−0.288335 | + | 0.957529i | \(0.593102\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.3273 | −0.616762 | −0.308381 | − | 0.951263i | \(-0.599787\pi\) | ||||
−0.308381 | + | 0.951263i | \(0.599787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.2213 | 0.746960 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.2866 | −1.21838 | −0.609192 | − | 0.793023i | \(-0.708506\pi\) | ||||
−0.609192 | + | 0.793023i | \(0.708506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.0111 | −0.469917 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00008 | −0.0670051 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −62.5874 | −2.09441 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.3186 | −0.846307 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.67475 | 0.122560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.41047 | 0.0469897 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.1883 | −0.804935 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.32715 | 0.143839 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.7409 | 0.356645 | 0.178323 | − | 0.983972i | \(-0.442933\pi\) | ||||
0.178323 | + | 0.983972i | \(0.442933\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −69.2579 | −2.29714 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.8649 | −1.05573 | −0.527866 | − | 0.849327i | \(-0.677008\pi\) | ||||
−0.527866 | + | 0.849327i | \(0.677008\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.1518 | −0.799308 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.3679 | 1.07005 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.4741 | −0.544023 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.6467 | 0.483149 | 0.241574 | − | 0.970382i | \(-0.422336\pi\) | ||||
0.241574 | + | 0.970382i | \(0.422336\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.7532 | 0.683842 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.95339 | −0.0971069 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −91.9040 | −3.01852 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.9334 | −1.86792 | −0.933962 | − | 0.357373i | \(-0.883672\pi\) | ||||
−0.933962 | + | 0.357373i | \(0.883672\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.4937 | −1.19603 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.9133 | −0.717409 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.972271 | −0.0317967 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.76516 | 0.123002 | 0.0615012 | − | 0.998107i | \(-0.480411\pi\) | ||||
0.0615012 | + | 0.998107i | \(0.480411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.294346 | 0.00960562 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.9802 | −0.944728 | −0.472364 | − | 0.881404i | \(-0.656599\pi\) | ||||
−0.472364 | + | 0.881404i | \(0.656599\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −78.1379 | −2.54452 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.32554 | −0.173240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.77047 | −0.317498 | −0.158749 | − | 0.987319i | \(-0.550746\pi\) | ||||
−0.158749 | + | 0.987319i | \(0.550746\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 91.2890 | 2.96025 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.3749 | 1.37266 | 0.686330 | − | 0.727291i | \(-0.259221\pi\) | ||||
0.686330 | + | 0.727291i | \(0.259221\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.62340 | −0.0848913 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.45075 | −0.143872 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.51964 | −0.242822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.5144 | 1.04885 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −53.3558 | −1.71937 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.6639 | −0.697385 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.65301 | −0.181788 | −0.0908942 | − | 0.995861i | \(-0.528973\pi\) | ||||
−0.0908942 | + | 0.995861i | \(0.528973\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.82349 | 0.154953 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0547 | 1.28542 | 0.642709 | − | 0.766111i | \(-0.277811\pi\) | ||||
0.642709 | + | 0.766111i | \(0.277811\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.3106 | 0.587012 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.7119 | 0.502668 | 0.251334 | − | 0.967900i | \(-0.419131\pi\) | ||||
0.251334 | + | 0.967900i | \(0.419131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.6992 | −0.949190 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.2183 | 0.453955 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.6671 | 1.48845 | 0.744225 | − | 0.667929i | \(-0.232819\pi\) | ||||
0.744225 | + | 0.667929i | \(0.232819\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.8601 | 0.664658 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.4870 | 0.906752 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 78.5558 | 2.49793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.23358 | 0.0391859 | 0.0195930 | − | 0.999808i | \(-0.493763\pi\) | ||||
0.0195930 | + | 0.999808i | \(0.493763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −54.0942 | −1.71663 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.7819 | 0.722236 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9285 | 1.04286 | 0.521428 | − | 0.853295i | \(-0.325400\pi\) | ||||
0.521428 | + | 0.853295i | \(0.325400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.1452 | −0.510811 |
(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 | 3380.2.a.s.1.9 | yes | 9 | |
13.5 | odd | 4 | 3380.2.f.j.3041.17 | 18 | |||
13.8 | odd | 4 | 3380.2.f.j.3041.18 | 18 | |||
13.12 | even | 2 | 3380.2.a.r.1.9 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.r.1.9 | ✓ | 9 | 13.12 | even | 2 | ||
3380.2.a.s.1.9 | yes | 9 | 1.1 | even | 1 | trivial | |
3380.2.f.j.3041.17 | 18 | 13.5 | odd | 4 | |||
3380.2.f.j.3041.18 | 18 | 13.8 | odd | 4 |