Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9801,2,Mod(1,9801)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9801, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9801.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9801 = 3^{4} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9801.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: | \(78.2613790211\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 15x^{8} - x^{7} + 75x^{6} + 15x^{5} - 148x^{4} - 54x^{3} + 96x^{2} + 55x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 1089) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.71687\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9801.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71687 | −1.92112 | −0.960559 | − | 0.278078i | \(-0.910303\pi\) | ||||
−0.960559 | + | 0.278078i | \(0.910303\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.38138 | 2.69069 | ||||||||
\(5\) | 1.67141 | 0.747476 | 0.373738 | − | 0.927534i | \(-0.378076\pi\) | ||||
0.373738 | + | 0.927534i | \(0.378076\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59211 | −0.979724 | −0.489862 | − | 0.871800i | \(-0.662953\pi\) | ||||
−0.489862 | + | 0.871800i | \(0.662953\pi\) | |||||||
\(8\) | −9.18678 | −3.24802 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.54100 | −1.43599 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.199351 | −0.0552902 | −0.0276451 | − | 0.999618i | \(-0.508801\pi\) | ||||
−0.0276451 | + | 0.999618i | \(0.508801\pi\) | |||||||
\(14\) | 7.04241 | 1.88216 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.1965 | 3.54913 | ||||||||
\(17\) | 7.79195 | 1.88983 | 0.944913 | − | 0.327321i | \(-0.106146\pi\) | ||||
0.944913 | + | 0.327321i | \(0.106146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.13361 | −0.260067 | −0.130034 | − | 0.991510i | \(-0.541509\pi\) | ||||
−0.130034 | + | 0.991510i | \(0.541509\pi\) | |||||||
\(20\) | 8.99449 | 2.01123 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.79747 | 0.374798 | 0.187399 | − | 0.982284i | \(-0.439994\pi\) | ||||
0.187399 | + | 0.982284i | \(0.439994\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.20639 | −0.441279 | ||||||||
\(26\) | 0.541612 | 0.106219 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −13.9491 | −2.63613 | ||||||||
\(29\) | −4.02665 | −0.747730 | −0.373865 | − | 0.927483i | \(-0.621968\pi\) | ||||
−0.373865 | + | 0.927483i | \(0.621968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.43134 | 0.795892 | 0.397946 | − | 0.917409i | \(-0.369723\pi\) | ||||
0.397946 | + | 0.917409i | \(0.369723\pi\) | |||||||
\(32\) | −20.1965 | −3.57028 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −21.1697 | −3.63058 | ||||||||
\(35\) | −4.33247 | −0.732320 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.55523 | 0.748876 | 0.374438 | − | 0.927252i | \(-0.377836\pi\) | ||||
0.374438 | + | 0.927252i | \(0.377836\pi\) | |||||||
\(38\) | 3.07987 | 0.499620 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −15.3549 | −2.42782 | ||||||||
\(41\) | 4.49550 | 0.702080 | 0.351040 | − | 0.936360i | \(-0.385828\pi\) | ||||
0.351040 | + | 0.936360i | \(0.385828\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.36629 | 0.513354 | 0.256677 | − | 0.966497i | \(-0.417372\pi\) | ||||
0.256677 | + | 0.966497i | \(0.417372\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.88349 | −0.720031 | ||||||||
\(47\) | 8.35219 | 1.21829 | 0.609146 | − | 0.793058i | \(-0.291512\pi\) | ||||
0.609146 | + | 0.793058i | \(0.291512\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.280991 | −0.0401416 | ||||||||
\(50\) | 5.99449 | 0.847749 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.07279 | −0.148769 | ||||||||
\(53\) | 0.660920 | 0.0907844 | 0.0453922 | − | 0.998969i | \(-0.485546\pi\) | ||||
0.0453922 | + | 0.998969i | \(0.485546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 23.8131 | 3.18216 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.9399 | 1.43648 | ||||||||
\(59\) | 4.53865 | 0.590882 | 0.295441 | − | 0.955361i | \(-0.404533\pi\) | ||||
0.295441 | + | 0.955361i | \(0.404533\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.455719 | 0.0583489 | 0.0291745 | − | 0.999574i | \(-0.490712\pi\) | ||||
0.0291745 | + | 0.999574i | \(0.490712\pi\) | |||||||
\(62\) | −12.0394 | −1.52900 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.4783 | 3.30979 | ||||||||
\(65\) | −0.333198 | −0.0413281 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.5434 | −1.41025 | −0.705123 | − | 0.709085i | \(-0.749108\pi\) | ||||
−0.705123 | + | 0.709085i | \(0.749108\pi\) | |||||||
\(68\) | 41.9315 | 5.08494 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.7707 | 1.40687 | ||||||||
\(71\) | 13.4057 | 1.59096 | 0.795481 | − | 0.605979i | \(-0.207218\pi\) | ||||
0.795481 | + | 0.605979i | \(0.207218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7548 | −1.25875 | −0.629375 | − | 0.777101i | \(-0.716689\pi\) | ||||
−0.629375 | + | 0.777101i | \(0.716689\pi\) | |||||||
\(74\) | −12.3760 | −1.43868 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.10038 | −0.699761 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9014 | 1.33901 | 0.669505 | − | 0.742808i | \(-0.266506\pi\) | ||||
0.669505 | + | 0.742808i | \(0.266506\pi\) | |||||||
\(80\) | 23.7282 | 2.65289 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.2137 | −1.34878 | ||||||||
\(83\) | −2.89275 | −0.317521 | −0.158760 | − | 0.987317i | \(-0.550750\pi\) | ||||
−0.158760 | + | 0.987317i | \(0.550750\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.0235 | 1.41260 | ||||||||
\(86\) | −9.14576 | −0.986213 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.6422 | 1.23408 | 0.617038 | − | 0.786933i | \(-0.288333\pi\) | ||||
0.617038 | + | 0.786933i | \(0.288333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.516740 | 0.0541691 | ||||||||
\(92\) | 9.67286 | 1.00847 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −22.6918 | −2.34048 | ||||||||
\(95\) | −1.89472 | −0.194394 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.72812 | −0.480068 | −0.240034 | − | 0.970764i | \(-0.577159\pi\) | ||||
−0.240034 | + | 0.970764i | \(0.577159\pi\) | |||||||
\(98\) | 0.763417 | 0.0771168 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.8735 | −1.18735 | ||||||||
\(101\) | −0.620511 | −0.0617432 | −0.0308716 | − | 0.999523i | \(-0.509828\pi\) | ||||
−0.0308716 | + | 0.999523i | \(0.509828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.1420 | −1.29492 | −0.647461 | − | 0.762099i | \(-0.724169\pi\) | ||||
−0.647461 | + | 0.762099i | \(0.724169\pi\) | |||||||
\(104\) | 1.83140 | 0.179583 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.79563 | −0.174407 | ||||||||
\(107\) | 0.141493 | 0.0136787 | 0.00683933 | − | 0.999977i | \(-0.497823\pi\) | ||||
0.00683933 | + | 0.999977i | \(0.497823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.0135 | −1.53381 | −0.766906 | − | 0.641759i | \(-0.778205\pi\) | ||||
−0.766906 | + | 0.641759i | \(0.778205\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −36.7989 | −3.47717 | ||||||||
\(113\) | 6.23635 | 0.586666 | 0.293333 | − | 0.956010i | \(-0.405236\pi\) | ||||
0.293333 | + | 0.956010i | \(0.405236\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00430 | 0.280153 | ||||||||
\(116\) | −21.6690 | −2.01191 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.3309 | −1.13515 | ||||||||
\(119\) | −20.1976 | −1.85151 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.23813 | −0.112095 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 23.8467 | 2.14150 | ||||||||
\(125\) | −12.0448 | −1.07732 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.73490 | 0.331419 | 0.165709 | − | 0.986175i | \(-0.447009\pi\) | ||||
0.165709 | + | 0.986175i | \(0.447009\pi\) | |||||||
\(128\) | −31.5451 | −2.78822 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.905255 | 0.0793961 | ||||||||
\(131\) | 13.0364 | 1.13900 | 0.569498 | − | 0.821992i | \(-0.307137\pi\) | ||||
0.569498 | + | 0.821992i | \(0.307137\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.93843 | 0.254794 | ||||||||
\(134\) | 31.3618 | 2.70925 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −71.5830 | −6.13819 | ||||||||
\(137\) | −10.9025 | −0.931464 | −0.465732 | − | 0.884926i | \(-0.654209\pi\) | ||||
−0.465732 | + | 0.884926i | \(0.654209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7372 | −1.16517 | −0.582585 | − | 0.812770i | \(-0.697959\pi\) | ||||
−0.582585 | + | 0.812770i | \(0.697959\pi\) | |||||||
\(140\) | −23.3147 | −1.97045 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −36.4215 | −3.05642 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.73018 | −0.558911 | ||||||||
\(146\) | 29.2193 | 2.41821 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 24.5135 | 2.01499 | ||||||||
\(149\) | 5.00287 | 0.409851 | 0.204926 | − | 0.978778i | \(-0.434305\pi\) | ||||
0.204926 | + | 0.978778i | \(0.434305\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.2484 | 1.48503 | 0.742516 | − | 0.669828i | \(-0.233632\pi\) | ||||
0.742516 | + | 0.669828i | \(0.233632\pi\) | |||||||
\(152\) | 10.4142 | 0.844703 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.40658 | 0.594911 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.17899 | −0.253711 | −0.126856 | − | 0.991921i | \(-0.540488\pi\) | ||||
−0.126856 | + | 0.991921i | \(0.540488\pi\) | |||||||
\(158\) | −32.3345 | −2.57239 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −33.7567 | −2.66870 | ||||||||
\(161\) | −4.65922 | −0.367198 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.0397 | −1.17800 | −0.588999 | − | 0.808134i | \(-0.700478\pi\) | ||||
−0.588999 | + | 0.808134i | \(0.700478\pi\) | |||||||
\(164\) | 24.1920 | 1.88908 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.85923 | 0.609995 | ||||||||
\(167\) | −2.30344 | −0.178246 | −0.0891229 | − | 0.996021i | \(-0.528406\pi\) | ||||
−0.0891229 | + | 0.996021i | \(0.528406\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9603 | −0.996943 | ||||||||
\(170\) | −35.3833 | −2.71377 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.1153 | 1.38128 | ||||||||
\(173\) | −19.6981 | −1.49762 | −0.748808 | − | 0.662787i | \(-0.769373\pi\) | ||||
−0.748808 | + | 0.662787i | \(0.769373\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.71921 | 0.432331 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −31.6305 | −2.37080 | ||||||||
\(179\) | −14.2894 | −1.06804 | −0.534022 | − | 0.845471i | \(-0.679320\pi\) | ||||
−0.534022 | + | 0.845471i | \(0.679320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.3355 | 1.06555 | 0.532776 | − | 0.846256i | \(-0.321149\pi\) | ||||
0.532776 | + | 0.846256i | \(0.321149\pi\) | |||||||
\(182\) | −1.40392 | −0.104065 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.5129 | −1.21735 | ||||||||
\(185\) | 7.61366 | 0.559767 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 44.9464 | 3.27805 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.14771 | 0.373454 | ||||||||
\(191\) | −6.70138 | −0.484895 | −0.242448 | − | 0.970165i | \(-0.577950\pi\) | ||||
−0.242448 | + | 0.970165i | \(0.577950\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.7162 | 1.77911 | 0.889555 | − | 0.456828i | \(-0.151015\pi\) | ||||
0.889555 | + | 0.456828i | \(0.151015\pi\) | |||||||
\(194\) | 12.8457 | 0.922267 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.51212 | −0.108009 | ||||||||
\(197\) | 3.16677 | 0.225623 | 0.112811 | − | 0.993616i | \(-0.464014\pi\) | ||||
0.112811 | + | 0.993616i | \(0.464014\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.30214 | −0.588523 | −0.294261 | − | 0.955725i | \(-0.595074\pi\) | ||||
−0.294261 | + | 0.955725i | \(0.595074\pi\) | |||||||
\(200\) | 20.2697 | 1.43328 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.68585 | 0.118616 | ||||||||
\(203\) | 10.4375 | 0.732569 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.51382 | 0.524788 | ||||||||
\(206\) | 35.7052 | 2.48770 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.83010 | −0.196232 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.4934 | 1.54851 | 0.774254 | − | 0.632875i | \(-0.218125\pi\) | ||||
0.774254 | + | 0.632875i | \(0.218125\pi\) | |||||||
\(212\) | 3.55667 | 0.244273 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.384419 | −0.0262783 | ||||||||
\(215\) | 5.62644 | 0.383720 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4865 | −0.779755 | ||||||||
\(218\) | 43.5065 | 2.94663 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.55334 | −0.104489 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6694 | 0.848405 | 0.424203 | − | 0.905567i | \(-0.360554\pi\) | ||||
0.424203 | + | 0.905567i | \(0.360554\pi\) | |||||||
\(224\) | 52.3515 | 3.49788 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.9433 | −1.12705 | ||||||||
\(227\) | 5.69621 | 0.378071 | 0.189035 | − | 0.981970i | \(-0.439464\pi\) | ||||
0.189035 | + | 0.981970i | \(0.439464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.72848 | −0.444630 | −0.222315 | − | 0.974975i | \(-0.571361\pi\) | ||||
−0.222315 | + | 0.974975i | \(0.571361\pi\) | |||||||
\(230\) | −8.16230 | −0.538206 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 36.9920 | 2.42864 | ||||||||
\(233\) | 6.62352 | 0.433921 | 0.216961 | − | 0.976180i | \(-0.430386\pi\) | ||||
0.216961 | + | 0.976180i | \(0.430386\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9599 | 0.910645 | ||||||||
\(236\) | 24.4242 | 1.58988 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 54.8742 | 3.55696 | ||||||||
\(239\) | −4.68001 | −0.302725 | −0.151362 | − | 0.988478i | \(-0.548366\pi\) | ||||
−0.151362 | + | 0.988478i | \(0.548366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.79666 | 0.244564 | 0.122282 | − | 0.992495i | \(-0.460979\pi\) | ||||
0.122282 | + | 0.992495i | \(0.460979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.45240 | 0.156999 | ||||||||
\(245\) | −0.469651 | −0.0300049 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.225986 | 0.0143792 | ||||||||
\(248\) | −40.7097 | −2.58507 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 32.7242 | 2.06966 | ||||||||
\(251\) | 11.5694 | 0.730253 | 0.365126 | − | 0.930958i | \(-0.381026\pi\) | ||||
0.365126 | + | 0.930958i | \(0.381026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.1472 | −0.636694 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 32.7473 | 2.04671 | ||||||||
\(257\) | −13.2795 | −0.828350 | −0.414175 | − | 0.910197i | \(-0.635930\pi\) | ||||
−0.414175 | + | 0.910197i | \(0.635930\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.8076 | −0.733691 | ||||||||
\(260\) | −1.79306 | −0.111201 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −35.4182 | −2.18815 | ||||||||
\(263\) | −16.4771 | −1.01602 | −0.508011 | − | 0.861351i | \(-0.669619\pi\) | ||||
−0.508011 | + | 0.861351i | \(0.669619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.10467 | 0.0678592 | ||||||||
\(266\) | −7.98333 | −0.489490 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −62.1193 | −3.79454 | ||||||||
\(269\) | 16.8816 | 1.02929 | 0.514643 | − | 0.857404i | \(-0.327924\pi\) | ||||
0.514643 | + | 0.857404i | \(0.327924\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.0885 | 1.70625 | 0.853126 | − | 0.521704i | \(-0.174704\pi\) | ||||
0.853126 | + | 0.521704i | \(0.174704\pi\) | |||||||
\(272\) | 110.619 | 6.70724 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 29.6207 | 1.78945 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.4650 | 0.688867 | 0.344433 | − | 0.938811i | \(-0.388071\pi\) | ||||
0.344433 | + | 0.938811i | \(0.388071\pi\) | |||||||
\(278\) | 37.3221 | 2.23843 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 39.8014 | 2.37859 | ||||||||
\(281\) | 12.9124 | 0.770290 | 0.385145 | − | 0.922856i | \(-0.374151\pi\) | ||||
0.385145 | + | 0.922856i | \(0.374151\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.2669 | 1.50196 | 0.750981 | − | 0.660324i | \(-0.229581\pi\) | ||||
0.750981 | + | 0.660324i | \(0.229581\pi\) | |||||||
\(284\) | 72.1411 | 4.28079 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.6528 | −0.687844 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.7146 | 2.57144 | ||||||||
\(290\) | 18.2850 | 1.07373 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −57.8755 | −3.38691 | ||||||||
\(293\) | 2.28505 | 0.133494 | 0.0667471 | − | 0.997770i | \(-0.478738\pi\) | ||||
0.0667471 | + | 0.997770i | \(0.478738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.58594 | 0.441670 | ||||||||
\(296\) | −41.8479 | −2.43236 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.5922 | −0.787372 | ||||||||
\(299\) | −0.358328 | −0.0207226 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.72577 | −0.502945 | ||||||||
\(302\) | −49.5785 | −2.85292 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.0933 | −0.923013 | ||||||||
\(305\) | 0.761693 | 0.0436144 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.56109 | 0.146169 | 0.0730847 | − | 0.997326i | \(-0.476716\pi\) | ||||
0.0730847 | + | 0.997326i | \(0.476716\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.1227 | −1.14289 | ||||||||
\(311\) | −3.41091 | −0.193415 | −0.0967075 | − | 0.995313i | \(-0.530831\pi\) | ||||
−0.0967075 | + | 0.995313i | \(0.530831\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.9763 | 1.58131 | 0.790657 | − | 0.612259i | \(-0.209739\pi\) | ||||
0.790657 | + | 0.612259i | \(0.209739\pi\) | |||||||
\(314\) | 8.63690 | 0.487409 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 64.0458 | 3.60286 | ||||||||
\(317\) | −30.7328 | −1.72613 | −0.863064 | − | 0.505095i | \(-0.831457\pi\) | ||||
−0.863064 | + | 0.505095i | \(0.831457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 44.2561 | 2.47399 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.6585 | 0.705431 | ||||||||
\(323\) | −8.83302 | −0.491482 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.439848 | 0.0243984 | ||||||||
\(326\) | 40.8608 | 2.26307 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −41.2992 | −2.28037 | ||||||||
\(329\) | −21.6498 | −1.19359 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.97755 | −0.328556 | −0.164278 | − | 0.986414i | \(-0.552529\pi\) | ||||
−0.164278 | + | 0.986414i | \(0.552529\pi\) | |||||||
\(332\) | −15.5670 | −0.854350 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.25816 | 0.342431 | ||||||||
\(335\) | −19.2937 | −1.05413 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.31492 | 0.0716280 | 0.0358140 | − | 0.999358i | \(-0.488598\pi\) | ||||
0.0358140 | + | 0.999358i | \(0.488598\pi\) | |||||||
\(338\) | 35.2113 | 1.91524 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 70.0846 | 3.80087 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8731 | 1.01905 | ||||||||
\(344\) | −30.9253 | −1.66738 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 53.5171 | 2.87709 | ||||||||
\(347\) | 17.9358 | 0.962842 | 0.481421 | − | 0.876489i | \(-0.340121\pi\) | ||||
0.481421 | + | 0.876489i | \(0.340121\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.7232 | −1.37693 | −0.688466 | − | 0.725269i | \(-0.741715\pi\) | ||||
−0.688466 | + | 0.725269i | \(0.741715\pi\) | |||||||
\(350\) | −15.5383 | −0.830559 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.9067 | −1.05953 | −0.529763 | − | 0.848145i | \(-0.677719\pi\) | ||||
−0.529763 | + | 0.848145i | \(0.677719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.4064 | 1.18921 | ||||||||
\(356\) | 62.6514 | 3.32052 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 38.8226 | 2.05184 | ||||||||
\(359\) | 29.2180 | 1.54207 | 0.771033 | − | 0.636796i | \(-0.219740\pi\) | ||||
0.771033 | + | 0.636796i | \(0.219740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7149 | −0.932365 | ||||||||
\(362\) | −38.9478 | −2.04705 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.78078 | 0.145752 | ||||||||
\(365\) | −17.9756 | −0.940887 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.1477 | 0.895101 | 0.447550 | − | 0.894259i | \(-0.352297\pi\) | ||||
0.447550 | + | 0.894259i | \(0.352297\pi\) | |||||||
\(368\) | 25.5178 | 1.33021 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.6853 | −1.07538 | ||||||||
\(371\) | −1.71318 | −0.0889436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.2416 | −1.04807 | −0.524034 | − | 0.851697i | \(-0.675574\pi\) | ||||
−0.524034 | + | 0.851697i | \(0.675574\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −76.7297 | −3.95703 | ||||||||
\(377\) | 0.802719 | 0.0413421 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.1090 | −1.03293 | −0.516465 | − | 0.856308i | \(-0.672752\pi\) | ||||
−0.516465 | + | 0.856308i | \(0.672752\pi\) | |||||||
\(380\) | −10.1962 | −0.523055 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.2068 | 0.931540 | ||||||||
\(383\) | −21.3083 | −1.08880 | −0.544402 | − | 0.838824i | \(-0.683243\pi\) | ||||
−0.544402 | + | 0.838824i | \(0.683243\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −67.1507 | −3.41788 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.4438 | −1.29171 | ||||||||
\(389\) | 34.5424 | 1.75137 | 0.875685 | − | 0.482883i | \(-0.160410\pi\) | ||||
0.875685 | + | 0.482883i | \(0.160410\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0058 | 0.708303 | ||||||||
\(392\) | 2.58141 | 0.130381 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.60369 | −0.433448 | ||||||||
\(395\) | 19.8921 | 1.00088 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.61262 | −0.131124 | −0.0655619 | − | 0.997849i | \(-0.520884\pi\) | ||||
−0.0655619 | + | 0.997849i | \(0.520884\pi\) | |||||||
\(398\) | 22.5558 | 1.13062 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −31.3231 | −1.56616 | ||||||||
\(401\) | 10.2520 | 0.511962 | 0.255981 | − | 0.966682i | \(-0.417602\pi\) | ||||
0.255981 | + | 0.966682i | \(0.417602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.883395 | −0.0440050 | ||||||||
\(404\) | −3.33921 | −0.166132 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −28.3573 | −1.40735 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.96459 | 0.196036 | 0.0980181 | − | 0.995185i | \(-0.468750\pi\) | ||||
0.0980181 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(410\) | −20.4141 | −1.00818 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −70.7222 | −3.48423 | ||||||||
\(413\) | −11.7647 | −0.578901 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.83497 | −0.237339 | ||||||||
\(416\) | 4.02621 | 0.197401 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.7769 | 1.60126 | 0.800628 | − | 0.599162i | \(-0.204499\pi\) | ||||
0.800628 | + | 0.599162i | \(0.204499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.5922 | −1.83213 | −0.916066 | − | 0.401029i | \(-0.868653\pi\) | ||||
−0.916066 | + | 0.401029i | \(0.868653\pi\) | |||||||
\(422\) | −61.1116 | −2.97487 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.07173 | −0.294869 | ||||||||
\(425\) | −17.1921 | −0.833941 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.18127 | −0.0571658 | ||||||||
\(428\) | 0.761429 | 0.0368051 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.2863 | −0.737171 | ||||||||
\(431\) | −30.0260 | −1.44630 | −0.723152 | − | 0.690689i | \(-0.757307\pi\) | ||||
−0.723152 | + | 0.690689i | \(0.757307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.8078 | 0.855788 | 0.427894 | − | 0.903829i | \(-0.359256\pi\) | ||||
0.427894 | + | 0.903829i | \(0.359256\pi\) | |||||||
\(434\) | 31.2073 | 1.49800 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −86.1746 | −4.12702 | ||||||||
\(437\) | −2.03762 | −0.0974727 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.34051 | −0.111707 | −0.0558533 | − | 0.998439i | \(-0.517788\pi\) | ||||
−0.0558533 | + | 0.998439i | \(0.517788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.22022 | 0.200735 | ||||||||
\(443\) | 6.40676 | 0.304394 | 0.152197 | − | 0.988350i | \(-0.451365\pi\) | ||||
0.152197 | + | 0.988350i | \(0.451365\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.4589 | 0.922443 | ||||||||
\(446\) | −34.4211 | −1.62989 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −68.6346 | −3.24268 | ||||||||
\(449\) | 21.7677 | 1.02728 | 0.513640 | − | 0.858006i | \(-0.328297\pi\) | ||||
0.513640 | + | 0.858006i | \(0.328297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 33.5602 | 1.57854 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.4759 | −0.726318 | ||||||||
\(455\) | 0.863684 | 0.0404901 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.14228 | −0.334102 | −0.167051 | − | 0.985948i | \(-0.553424\pi\) | ||||
−0.167051 | + | 0.985948i | \(0.553424\pi\) | |||||||
\(458\) | 18.2804 | 0.854187 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.1673 | 0.753804 | ||||||||
\(461\) | 2.88780 | 0.134498 | 0.0672491 | − | 0.997736i | \(-0.478578\pi\) | ||||
0.0672491 | + | 0.997736i | \(0.478578\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.45208 | 0.0674838 | 0.0337419 | − | 0.999431i | \(-0.489258\pi\) | ||||
0.0337419 | + | 0.999431i | \(0.489258\pi\) | |||||||
\(464\) | −57.1644 | −2.65379 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.9953 | −0.833614 | ||||||||
\(467\) | 5.50281 | 0.254640 | 0.127320 | − | 0.991862i | \(-0.459363\pi\) | ||||
0.127320 | + | 0.991862i | \(0.459363\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.9216 | 1.38165 | ||||||||
\(470\) | −37.9273 | −1.74946 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −41.6956 | −1.91919 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50119 | 0.114762 | ||||||||
\(476\) | −108.691 | −4.98184 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.7150 | 0.581570 | ||||||||
\(479\) | −10.4549 | −0.477695 | −0.238848 | − | 0.971057i | \(-0.576770\pi\) | ||||
−0.238848 | + | 0.971057i | \(0.576770\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.908093 | −0.0414055 | ||||||||
\(482\) | −10.3150 | −0.469837 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.90262 | −0.358840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.69868 | 0.258232 | 0.129116 | − | 0.991630i | \(-0.458786\pi\) | ||||
0.129116 | + | 0.991630i | \(0.458786\pi\) | |||||||
\(488\) | −4.18659 | −0.189518 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.27598 | 0.0576430 | ||||||||
\(491\) | −8.30036 | −0.374590 | −0.187295 | − | 0.982304i | \(-0.559972\pi\) | ||||
−0.187295 | + | 0.982304i | \(0.559972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.3755 | −1.41308 | ||||||||
\(494\) | −0.613976 | −0.0276241 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 62.9096 | 2.82472 | ||||||||
\(497\) | −34.7489 | −1.55870 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.9052 | 0.622484 | 0.311242 | − | 0.950331i | \(-0.399255\pi\) | ||||
0.311242 | + | 0.950331i | \(0.399255\pi\) | |||||||
\(500\) | −64.8178 | −2.89874 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −31.4325 | −1.40290 | ||||||||
\(503\) | 29.2592 | 1.30460 | 0.652302 | − | 0.757959i | \(-0.273803\pi\) | ||||
0.652302 | + | 0.757959i | \(0.273803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.03713 | −0.0461516 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.0989 | 0.891746 | ||||||||
\(509\) | −36.6693 | −1.62534 | −0.812669 | − | 0.582726i | \(-0.801986\pi\) | ||||
−0.812669 | + | 0.582726i | \(0.801986\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.8775 | 1.23323 | ||||||||
\(512\) | −25.8799 | −1.14374 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 36.0785 | 1.59136 | ||||||||
\(515\) | −21.9657 | −0.967923 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 32.0798 | 1.40951 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.06101 | 0.134234 | ||||||||
\(521\) | 42.0462 | 1.84208 | 0.921039 | − | 0.389469i | \(-0.127342\pi\) | ||||
0.921039 | + | 0.389469i | \(0.127342\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.3284 | −1.58853 | −0.794264 | − | 0.607573i | \(-0.792143\pi\) | ||||
−0.794264 | + | 0.607573i | \(0.792143\pi\) | |||||||
\(524\) | 70.1539 | 3.06469 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44.7661 | 1.95190 | ||||||||
\(527\) | 34.5288 | 1.50410 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7691 | −0.859527 | ||||||||
\(530\) | −3.00124 | −0.130365 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.8128 | 0.685573 | ||||||||
\(533\) | −0.896186 | −0.0388181 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.236493 | 0.0102245 | ||||||||
\(536\) | 106.046 | 4.58050 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −45.8650 | −1.97738 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.4772 | 0.708409 | 0.354205 | − | 0.935168i | \(-0.384752\pi\) | ||||
0.354205 | + | 0.935168i | \(0.384752\pi\) | |||||||
\(542\) | −76.3127 | −3.27791 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −157.370 | −6.74720 | ||||||||
\(545\) | −26.7650 | −1.14649 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4828 | −0.576484 | −0.288242 | − | 0.957558i | \(-0.593071\pi\) | ||||
−0.288242 | + | 0.957558i | \(0.593071\pi\) | |||||||
\(548\) | −58.6706 | −2.50628 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.56464 | 0.194460 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.8496 | −1.31186 | ||||||||
\(554\) | −31.1490 | −1.32339 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −73.9249 | −3.13511 | ||||||||
\(557\) | −41.2760 | −1.74892 | −0.874460 | − | 0.485098i | \(-0.838784\pi\) | ||||
−0.874460 | + | 0.485098i | \(0.838784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.671074 | −0.0283834 | ||||||||
\(560\) | −61.5059 | −2.59910 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.0814 | −1.47982 | ||||||||
\(563\) | 1.43165 | 0.0603369 | 0.0301685 | − | 0.999545i | \(-0.490396\pi\) | ||||
0.0301685 | + | 0.999545i | \(0.490396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.4235 | 0.438519 | ||||||||
\(566\) | −68.6469 | −2.88545 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −123.155 | −5.16747 | ||||||||
\(569\) | 29.3751 | 1.23147 | 0.615734 | − | 0.787954i | \(-0.288859\pi\) | ||||
0.615734 | + | 0.787954i | \(0.288859\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9706 | −1.00314 | −0.501569 | − | 0.865118i | \(-0.667244\pi\) | ||||
−0.501569 | + | 0.865118i | \(0.667244\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 31.6592 | 1.32143 | ||||||||
\(575\) | −3.96592 | −0.165390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.8351 | 1.74162 | 0.870810 | − | 0.491620i | \(-0.163595\pi\) | ||||
0.870810 | + | 0.491620i | \(0.163595\pi\) | |||||||
\(578\) | −118.767 | −4.94005 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −36.2177 | −1.50386 | ||||||||
\(581\) | 7.49832 | 0.311083 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 98.8017 | 4.08844 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.20819 | −0.256458 | ||||||||
\(587\) | 3.15857 | 0.130368 | 0.0651841 | − | 0.997873i | \(-0.479237\pi\) | ||||
0.0651841 | + | 0.997873i | \(0.479237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.02340 | −0.206986 | ||||||||
\(590\) | −20.6100 | −0.848500 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 64.6685 | 2.65786 | ||||||||
\(593\) | 42.1283 | 1.73000 | 0.865001 | − | 0.501770i | \(-0.167318\pi\) | ||||
0.865001 | + | 0.501770i | \(0.167318\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −33.7584 | −1.38396 | ||||||||
\(596\) | 26.9224 | 1.10278 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.973530 | 0.0398106 | ||||||||
\(599\) | 22.9023 | 0.935762 | 0.467881 | − | 0.883792i | \(-0.345018\pi\) | ||||
0.467881 | + | 0.883792i | \(0.345018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.95721 | 0.120627 | 0.0603136 | − | 0.998179i | \(-0.480790\pi\) | ||||
0.0603136 | + | 0.998179i | \(0.480790\pi\) | |||||||
\(602\) | 23.7068 | 0.966216 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 98.2015 | 3.99576 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.7620 | 0.680348 | 0.340174 | − | 0.940362i | \(-0.389514\pi\) | ||||
0.340174 | + | 0.940362i | \(0.389514\pi\) | |||||||
\(608\) | 22.8949 | 0.928513 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.06942 | −0.0837884 | ||||||||
\(611\) | −1.66502 | −0.0673596 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.4806 | −1.10993 | −0.554965 | − | 0.831874i | \(-0.687268\pi\) | ||||
−0.554965 | + | 0.831874i | \(0.687268\pi\) | |||||||
\(614\) | −6.95816 | −0.280808 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.9473 | −1.44718 | −0.723592 | − | 0.690228i | \(-0.757510\pi\) | ||||
−0.723592 | + | 0.690228i | \(0.757510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.9891 | 1.24556 | 0.622778 | − | 0.782398i | \(-0.286004\pi\) | ||||
0.622778 | + | 0.782398i | \(0.286004\pi\) | |||||||
\(620\) | 39.8576 | 1.60072 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.26700 | 0.371573 | ||||||||
\(623\) | −30.1779 | −1.20905 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.09985 | −0.363994 | ||||||||
\(626\) | −76.0080 | −3.03789 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.1074 | −0.682658 | ||||||||
\(629\) | 35.4942 | 1.41525 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8066 | 0.708868 | 0.354434 | − | 0.935081i | \(-0.384674\pi\) | ||||
0.354434 | + | 0.935081i | \(0.384674\pi\) | |||||||
\(632\) | −109.335 | −4.34912 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 83.4971 | 3.31609 | ||||||||
\(635\) | 6.24254 | 0.247728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0560160 | 0.00221944 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −52.7247 | −2.08413 | ||||||||
\(641\) | 12.8415 | 0.507208 | 0.253604 | − | 0.967308i | \(-0.418384\pi\) | ||||
0.253604 | + | 0.967308i | \(0.418384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.1684 | 0.637620 | 0.318810 | − | 0.947819i | \(-0.396717\pi\) | ||||
0.318810 | + | 0.947819i | \(0.396717\pi\) | |||||||
\(644\) | −25.0731 | −0.988017 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.9982 | 0.944195 | ||||||||
\(647\) | 0.875926 | 0.0344362 | 0.0172181 | − | 0.999852i | \(-0.494519\pi\) | ||||
0.0172181 | + | 0.999852i | \(0.494519\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.19501 | −0.0468722 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −80.9343 | −3.16963 | ||||||||
\(653\) | 31.7262 | 1.24154 | 0.620771 | − | 0.783992i | \(-0.286820\pi\) | ||||
0.620771 | + | 0.783992i | \(0.286820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.7892 | 0.851373 | ||||||||
\(656\) | 63.8205 | 2.49177 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 58.8196 | 2.29303 | ||||||||
\(659\) | 11.9937 | 0.467209 | 0.233605 | − | 0.972332i | \(-0.424948\pi\) | ||||
0.233605 | + | 0.972332i | \(0.424948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.8469 | −0.927536 | −0.463768 | − | 0.885957i | \(-0.653503\pi\) | ||||
−0.463768 | + | 0.885957i | \(0.653503\pi\) | |||||||
\(662\) | 16.2402 | 0.631194 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.5751 | 1.03131 | ||||||||
\(665\) | 4.91132 | 0.190453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.23777 | −0.280248 | ||||||||
\(668\) | −12.3957 | −0.479605 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 52.4184 | 2.02510 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.9721 | 1.27098 | 0.635491 | − | 0.772108i | \(-0.280798\pi\) | ||||
0.635491 | + | 0.772108i | \(0.280798\pi\) | |||||||
\(674\) | −3.57245 | −0.137606 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −69.7441 | −2.68247 | ||||||||
\(677\) | 26.5286 | 1.01958 | 0.509789 | − | 0.860299i | \(-0.329723\pi\) | ||||
0.509789 | + | 0.860299i | \(0.329723\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2558 | 0.470334 | ||||||||
\(680\) | −119.644 | −4.58815 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4229 | 0.666669 | 0.333334 | − | 0.942809i | \(-0.391826\pi\) | ||||
0.333334 | + | 0.942809i | \(0.391826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.2225 | −0.696247 | ||||||||
\(686\) | −51.2757 | −1.95772 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 47.7895 | 1.82196 | ||||||||
\(689\) | −0.131755 | −0.00501948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.4638 | 1.65344 | 0.826721 | − | 0.562613i | \(-0.190204\pi\) | ||||
0.826721 | + | 0.562613i | \(0.190204\pi\) | |||||||
\(692\) | −106.003 | −4.02962 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −48.7292 | −1.84973 | ||||||||
\(695\) | −22.9604 | −0.870938 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.0288 | 1.32681 | ||||||||
\(698\) | 69.8866 | 2.64525 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 30.7772 | 1.16327 | ||||||||
\(701\) | −16.2104 | −0.612258 | −0.306129 | − | 0.951990i | \(-0.599034\pi\) | ||||
−0.306129 | + | 0.951990i | \(0.599034\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.16385 | −0.194758 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54.0839 | 2.03548 | ||||||||
\(707\) | 1.60843 | 0.0604912 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.12098 | 0.342546 | 0.171273 | − | 0.985224i | \(-0.445212\pi\) | ||||
0.171273 | + | 0.985224i | \(0.445212\pi\) | |||||||
\(710\) | −60.8752 | −2.28460 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −106.955 | −4.00830 | ||||||||
\(713\) | 7.96519 | 0.298299 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −76.8970 | −2.87378 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −79.3814 | −2.96249 | ||||||||
\(719\) | 30.5511 | 1.13936 | 0.569682 | − | 0.821865i | \(-0.307066\pi\) | ||||
0.569682 | + | 0.821865i | \(0.307066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.0655 | 1.26867 | ||||||||
\(722\) | 48.1292 | 1.79118 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 77.1451 | 2.86707 | ||||||||
\(725\) | 8.88438 | 0.329958 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.6974 | 0.619271 | 0.309635 | − | 0.950855i | \(-0.399793\pi\) | ||||
0.309635 | + | 0.950855i | \(0.399793\pi\) | |||||||
\(728\) | −4.74718 | −0.175942 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 48.8374 | 1.80755 | ||||||||
\(731\) | 26.2299 | 0.970150 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.3643 | −1.19540 | −0.597702 | − | 0.801718i | \(-0.703919\pi\) | ||||
−0.597702 | + | 0.801718i | \(0.703919\pi\) | |||||||
\(734\) | −46.5880 | −1.71959 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36.3026 | −1.33813 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.6489 | 1.01708 | 0.508541 | − | 0.861038i | \(-0.330185\pi\) | ||||
0.508541 | + | 0.861038i | \(0.330185\pi\) | |||||||
\(740\) | 40.9720 | 1.50616 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.65447 | 0.170871 | ||||||||
\(743\) | 6.85387 | 0.251444 | 0.125722 | − | 0.992066i | \(-0.459875\pi\) | ||||
0.125722 | + | 0.992066i | \(0.459875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.36184 | 0.306354 | ||||||||
\(746\) | 54.9937 | 2.01346 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.366765 | −0.0134013 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.8183 | 0.832653 | 0.416327 | − | 0.909215i | \(-0.363317\pi\) | ||||
0.416327 | + | 0.909215i | \(0.363317\pi\) | |||||||
\(752\) | 118.572 | 4.32388 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.18088 | −0.0794231 | ||||||||
\(755\) | 30.5005 | 1.11003 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.07971 | −0.0755884 | −0.0377942 | − | 0.999286i | \(-0.512033\pi\) | ||||
−0.0377942 | + | 0.999286i | \(0.512033\pi\) | |||||||
\(758\) | 54.6335 | 1.98438 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.4064 | 0.631396 | ||||||||
\(761\) | −21.8445 | −0.791863 | −0.395931 | − | 0.918280i | \(-0.629578\pi\) | ||||
−0.395931 | + | 0.918280i | \(0.629578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.5086 | 1.50271 | ||||||||
\(764\) | −36.0627 | −1.30470 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 57.8920 | 2.09172 | ||||||||
\(767\) | −0.904787 | −0.0326699 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.56817 | 0.128671 | 0.0643357 | − | 0.997928i | \(-0.479507\pi\) | ||||
0.0643357 | + | 0.997928i | \(0.479507\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 133.007 | 4.78704 | ||||||||
\(773\) | −9.24340 | −0.332462 | −0.166231 | − | 0.986087i | \(-0.553160\pi\) | ||||
−0.166231 | + | 0.986087i | \(0.553160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.77729 | −0.351211 | ||||||||
\(776\) | 43.4362 | 1.55927 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −93.8472 | −3.36459 | ||||||||
\(779\) | −5.09614 | −0.182588 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −38.0519 | −1.36073 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.98910 | −0.142468 | ||||||||
\(785\) | −5.31339 | −0.189643 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.7058 | −0.524204 | −0.262102 | − | 0.965040i | \(-0.584416\pi\) | ||||
−0.262102 | + | 0.965040i | \(0.584416\pi\) | |||||||
\(788\) | 17.0416 | 0.607081 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −54.0441 | −1.92280 | ||||||||
\(791\) | −16.1653 | −0.574771 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0908484 | −0.00322612 | ||||||||
\(794\) | 7.09815 | 0.251904 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.6770 | −1.58353 | ||||||||
\(797\) | −21.1269 | −0.748352 | −0.374176 | − | 0.927358i | \(-0.622074\pi\) | ||||
−0.374176 | + | 0.927358i | \(0.622074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 65.0799 | 2.30236 | ||||||||
\(800\) | 44.5615 | 1.57549 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.8534 | −0.983539 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.78747 | −0.274472 | ||||||||
\(806\) | 2.40007 | 0.0845388 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.70050 | 0.200543 | ||||||||
\(809\) | −29.6574 | −1.04270 | −0.521349 | − | 0.853344i | \(-0.674571\pi\) | ||||
−0.521349 | + | 0.853344i | \(0.674571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.19031 | 0.217371 | 0.108686 | − | 0.994076i | \(-0.465336\pi\) | ||||
0.108686 | + | 0.994076i | \(0.465336\pi\) | |||||||
\(812\) | 56.1682 | 1.97112 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.1374 | −0.880526 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.81605 | −0.133507 | ||||||||
\(818\) | −10.7713 | −0.376608 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.4348 | 1.41204 | ||||||||
\(821\) | −21.2591 | −0.741948 | −0.370974 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370974 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.0182 | −1.39495 | −0.697474 | − | 0.716611i | \(-0.745693\pi\) | ||||
−0.697474 | + | 0.716611i | \(0.745693\pi\) | |||||||
\(824\) | 120.733 | 4.20593 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.9630 | 1.11214 | ||||||||
\(827\) | −22.0260 | −0.765919 | −0.382960 | − | 0.923765i | \(-0.625095\pi\) | ||||
−0.382960 | + | 0.923765i | \(0.625095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6206 | −1.06350 | −0.531749 | − | 0.846902i | \(-0.678465\pi\) | ||||
−0.531749 | + | 0.846902i | \(0.678465\pi\) | |||||||
\(830\) | 13.1360 | 0.455957 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.27849 | −0.182999 | ||||||||
\(833\) | −2.18947 | −0.0758607 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.85000 | −0.133235 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −89.0506 | −3.07620 | ||||||||
\(839\) | 8.64337 | 0.298402 | 0.149201 | − | 0.988807i | \(-0.452330\pi\) | ||||
0.149201 | + | 0.988807i | \(0.452330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.7861 | −0.440899 | ||||||||
\(842\) | 102.133 | 3.51974 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 121.045 | 4.16656 | ||||||||
\(845\) | −21.6619 | −0.745191 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.38277 | 0.322206 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 46.7088 | 1.60210 | ||||||||
\(851\) | 8.18789 | 0.280677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.24417 | 0.179557 | 0.0897784 | − | 0.995962i | \(-0.471384\pi\) | ||||
0.0897784 | + | 0.995962i | \(0.471384\pi\) | |||||||
\(854\) | 3.20936 | 0.109822 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.29987 | −0.0444285 | ||||||||
\(857\) | −22.4040 | −0.765306 | −0.382653 | − | 0.923892i | \(-0.624989\pi\) | ||||
−0.382653 | + | 0.923892i | \(0.624989\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.380602 | 0.0129860 | 0.00649299 | − | 0.999979i | \(-0.497933\pi\) | ||||
0.00649299 | + | 0.999979i | \(0.497933\pi\) | |||||||
\(860\) | 30.2780 | 1.03247 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 81.5769 | 2.77852 | ||||||||
\(863\) | 14.6703 | 0.499382 | 0.249691 | − | 0.968326i | \(-0.419671\pi\) | ||||
0.249691 | + | 0.968326i | \(0.419671\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.9235 | −1.11943 | ||||||||
\(866\) | −48.3814 | −1.64407 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −61.8133 | −2.09808 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.30119 | 0.0779727 | ||||||||
\(872\) | 147.112 | 4.98185 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.53596 | 0.187257 | ||||||||
\(875\) | 31.2215 | 1.05548 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.7817 | 0.938123 | 0.469061 | − | 0.883166i | \(-0.344592\pi\) | ||||
0.469061 | + | 0.883166i | \(0.344592\pi\) | |||||||
\(878\) | 6.35887 | 0.214601 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.5329 | 0.422243 | 0.211122 | − | 0.977460i | \(-0.432288\pi\) | ||||
0.211122 | + | 0.977460i | \(0.432288\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.2943 | −1.72619 | −0.863095 | − | 0.505042i | \(-0.831477\pi\) | ||||
−0.863095 | + | 0.505042i | \(0.831477\pi\) | |||||||
\(884\) | −8.35911 | −0.281147 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.4063 | −0.584777 | ||||||||
\(887\) | −2.56217 | −0.0860291 | −0.0430146 | − | 0.999074i | \(-0.513696\pi\) | ||||
−0.0430146 | + | 0.999074i | \(0.513696\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.68126 | −0.324699 | ||||||||
\(890\) | −52.8674 | −1.77212 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 68.1789 | 2.28280 | ||||||||
\(893\) | −9.46811 | −0.316838 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.8835 | −0.798337 | ||||||||
\(896\) | 81.7682 | 2.73168 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −59.1400 | −1.97353 | ||||||||
\(899\) | −17.8435 | −0.595113 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.14986 | 0.171567 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −57.2919 | −1.90550 | ||||||||
\(905\) | 23.9606 | 0.796476 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.9430 | 1.59192 | 0.795960 | − | 0.605349i | \(-0.206966\pi\) | ||||
0.795960 | + | 0.605349i | \(0.206966\pi\) | |||||||
\(908\) | 30.6535 | 1.01727 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.34652 | −0.0777862 | ||||||||
\(911\) | 54.4206 | 1.80303 | 0.901517 | − | 0.432743i | \(-0.142454\pi\) | ||||
0.901517 | + | 0.432743i | \(0.142454\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.4046 | 0.641848 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.2085 | −1.19636 | ||||||||
\(917\) | −33.7918 | −1.11590 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.69832 | −0.121996 | −0.0609982 | − | 0.998138i | \(-0.519428\pi\) | ||||
−0.0609982 | + | 0.998138i | \(0.519428\pi\) | |||||||
\(920\) | −27.5999 | −0.909940 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.84577 | −0.258387 | ||||||||
\(923\) | −2.67244 | −0.0879645 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0506 | −0.330463 | ||||||||
\(926\) | −3.94511 | −0.129644 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 81.3244 | 2.66960 | ||||||||
\(929\) | −25.8407 | −0.847807 | −0.423903 | − | 0.905707i | \(-0.639340\pi\) | ||||
−0.423903 | + | 0.905707i | \(0.639340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.318534 | 0.0104395 | ||||||||
\(932\) | 35.6437 | 1.16755 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.9504 | −0.489192 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.1689 | 0.920239 | 0.460120 | − | 0.887857i | \(-0.347806\pi\) | ||||
0.460120 | + | 0.887857i | \(0.347806\pi\) | |||||||
\(938\) | −81.2931 | −2.65431 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 75.1237 | 2.45026 | ||||||||
\(941\) | 30.4871 | 0.993851 | 0.496925 | − | 0.867793i | \(-0.334462\pi\) | ||||
0.496925 | + | 0.867793i | \(0.334462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.08052 | 0.263138 | ||||||||
\(944\) | 64.4330 | 2.09712 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.8142 | −1.78122 | −0.890611 | − | 0.454766i | \(-0.849723\pi\) | ||||
−0.890611 | + | 0.454766i | \(0.849723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.14398 | 0.0695965 | ||||||||
\(950\) | −6.79540 | −0.220472 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 185.551 | 6.01373 | ||||||||
\(953\) | −38.8502 | −1.25848 | −0.629240 | − | 0.777211i | \(-0.716634\pi\) | ||||
−0.629240 | + | 0.777211i | \(0.716634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.2007 | −0.362448 | ||||||||
\(956\) | −25.1849 | −0.814539 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.4045 | 0.917709 | ||||||||
\(959\) | 28.2604 | 0.912577 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3632 | −0.366555 | ||||||||
\(962\) | 2.46717 | 0.0795448 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.4313 | 0.658047 | ||||||||
\(965\) | 41.3108 | 1.32984 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.8498 | 0.831272 | 0.415636 | − | 0.909531i | \(-0.363559\pi\) | ||||
0.415636 | + | 0.909531i | \(0.363559\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21.4704 | 0.689373 | ||||||||
\(971\) | 14.7459 | 0.473219 | 0.236609 | − | 0.971605i | \(-0.423964\pi\) | ||||
0.236609 | + | 0.971605i | \(0.423964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.6082 | 1.14155 | ||||||||
\(974\) | −15.4826 | −0.496094 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.46963 | 0.207088 | ||||||||
\(977\) | 37.6396 | 1.20420 | 0.602099 | − | 0.798422i | \(-0.294331\pi\) | ||||
0.602099 | + | 0.798422i | \(0.294331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.52737 | −0.0807340 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.5510 | 0.719631 | ||||||||
\(983\) | 6.42972 | 0.205076 | 0.102538 | − | 0.994729i | \(-0.467304\pi\) | ||||
0.102538 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.29296 | 0.168648 | ||||||||
\(986\) | 85.2431 | 2.71469 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.21612 | 0.0386899 | ||||||||
\(989\) | 6.05079 | 0.192404 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.1704 | 1.11722 | 0.558612 | − | 0.829429i | \(-0.311334\pi\) | ||||
0.558612 | + | 0.829429i | \(0.311334\pi\) | |||||||
\(992\) | −89.4977 | −2.84156 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 94.4083 | 2.99445 | ||||||||
\(995\) | −13.8763 | −0.439907 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.128713 | −0.00407637 | −0.00203818 | − | 0.999998i | \(-0.500649\pi\) | ||||
−0.00203818 | + | 0.999998i | \(0.500649\pi\) | |||||||
\(998\) | −37.7787 | −1.19587 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9801.2.a.cd.1.1 | 10 | ||
3.2 | odd | 2 | 9801.2.a.cb.1.10 | 10 | |||
9.4 | even | 3 | 1089.2.e.l.727.10 | yes | 20 | ||
9.7 | even | 3 | 1089.2.e.l.364.10 | ✓ | 20 | ||
11.10 | odd | 2 | 9801.2.a.ce.1.10 | 10 | |||
33.32 | even | 2 | 9801.2.a.cc.1.1 | 10 | |||
99.43 | odd | 6 | 1089.2.e.m.364.1 | yes | 20 | ||
99.76 | odd | 6 | 1089.2.e.m.727.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1089.2.e.l.364.10 | ✓ | 20 | 9.7 | even | 3 | ||
1089.2.e.l.727.10 | yes | 20 | 9.4 | even | 3 | ||
1089.2.e.m.364.1 | yes | 20 | 99.43 | odd | 6 | ||
1089.2.e.m.727.1 | yes | 20 | 99.76 | odd | 6 | ||
9801.2.a.cb.1.10 | 10 | 3.2 | odd | 2 | |||
9801.2.a.cc.1.1 | 10 | 33.32 | even | 2 | |||
9801.2.a.cd.1.1 | 10 | 1.1 | even | 1 | trivial | ||
9801.2.a.ce.1.10 | 10 | 11.10 | odd | 2 |