Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, 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("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.284630\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.51334 | −0.676785 | −0.338392 | − | 0.941005i | \(-0.609883\pi\) | ||||
−0.338392 | + | 0.941005i | \(0.609883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59435 | −0.980573 | −0.490286 | − | 0.871561i | \(-0.663108\pi\) | ||||
−0.490286 | + | 0.871561i | \(0.663108\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.51334 | 0.478559 | ||||||||
\(11\) | 5.00714 | 1.50971 | 0.754855 | − | 0.655892i | \(-0.227707\pi\) | ||||
0.754855 | + | 0.655892i | \(0.227707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.82306 | −1.33768 | −0.668838 | − | 0.743408i | \(-0.733208\pi\) | ||||
−0.668838 | + | 0.743408i | \(0.733208\pi\) | |||||||
\(14\) | 2.59435 | 0.693370 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.863693 | 0.209476 | 0.104738 | − | 0.994500i | \(-0.466600\pi\) | ||||
0.104738 | + | 0.994500i | \(0.466600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00158 | −1.60627 | −0.803137 | − | 0.595795i | \(-0.796837\pi\) | ||||
−0.803137 | + | 0.595795i | \(0.796837\pi\) | |||||||
\(20\) | −1.51334 | −0.338392 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.00714 | −1.06753 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.70981 | −0.541962 | ||||||||
\(26\) | 4.82306 | 0.945880 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.59435 | −0.490286 | ||||||||
\(29\) | −3.11362 | −0.578185 | −0.289093 | − | 0.957301i | \(-0.593354\pi\) | ||||
−0.289093 | + | 0.957301i | \(0.593354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.17428 | −0.210907 | −0.105453 | − | 0.994424i | \(-0.533629\pi\) | ||||
−0.105453 | + | 0.994424i | \(0.533629\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.863693 | −0.148122 | ||||||||
\(35\) | 3.92613 | 0.663637 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.602123 | −0.0989883 | −0.0494942 | − | 0.998774i | \(-0.515761\pi\) | ||||
−0.0494942 | + | 0.998774i | \(0.515761\pi\) | |||||||
\(38\) | 7.00158 | 1.13581 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.51334 | 0.239280 | ||||||||
\(41\) | −5.29335 | −0.826683 | −0.413341 | − | 0.910576i | \(-0.635638\pi\) | ||||
−0.413341 | + | 0.910576i | \(0.635638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.45925 | 0.222534 | 0.111267 | − | 0.993791i | \(-0.464509\pi\) | ||||
0.111267 | + | 0.993791i | \(0.464509\pi\) | |||||||
\(44\) | 5.00714 | 0.754855 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.6797 | 1.84952 | 0.924760 | − | 0.380552i | \(-0.124266\pi\) | ||||
0.924760 | + | 0.380552i | \(0.124266\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.269342 | −0.0384774 | ||||||||
\(50\) | 2.70981 | 0.383225 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.82306 | −0.668838 | ||||||||
\(53\) | −4.23281 | −0.581422 | −0.290711 | − | 0.956811i | \(-0.593892\pi\) | ||||
−0.290711 | + | 0.956811i | \(0.593892\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.57749 | −1.02175 | ||||||||
\(56\) | 2.59435 | 0.346685 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.11362 | 0.408839 | ||||||||
\(59\) | −3.98142 | −0.518337 | −0.259168 | − | 0.965832i | \(-0.583448\pi\) | ||||
−0.259168 | + | 0.965832i | \(0.583448\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.26229 | −0.929841 | −0.464920 | − | 0.885352i | \(-0.653917\pi\) | ||||
−0.464920 | + | 0.885352i | \(0.653917\pi\) | |||||||
\(62\) | 1.17428 | 0.149134 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.29891 | 0.905319 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.1371 | −1.97146 | −0.985729 | − | 0.168340i | \(-0.946159\pi\) | ||||
−0.985729 | + | 0.168340i | \(0.946159\pi\) | |||||||
\(68\) | 0.863693 | 0.104738 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.92613 | −0.469262 | ||||||||
\(71\) | −5.88463 | −0.698377 | −0.349188 | − | 0.937053i | \(-0.613543\pi\) | ||||
−0.349188 | + | 0.937053i | \(0.613543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.3814 | 1.68322 | 0.841608 | − | 0.540089i | \(-0.181609\pi\) | ||||
0.841608 | + | 0.540089i | \(0.181609\pi\) | |||||||
\(74\) | 0.602123 | 0.0699953 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.00158 | −0.803137 | ||||||||
\(77\) | −12.9903 | −1.48038 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3402 | 1.16336 | 0.581681 | − | 0.813417i | \(-0.302395\pi\) | ||||
0.581681 | + | 0.813417i | \(0.302395\pi\) | |||||||
\(80\) | −1.51334 | −0.169196 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.29335 | 0.584553 | ||||||||
\(83\) | −2.64101 | −0.289888 | −0.144944 | − | 0.989440i | \(-0.546300\pi\) | ||||
−0.144944 | + | 0.989440i | \(0.546300\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.30706 | −0.141770 | ||||||||
\(86\) | −1.45925 | −0.157355 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.00714 | −0.533763 | ||||||||
\(89\) | 5.23754 | 0.555178 | 0.277589 | − | 0.960700i | \(-0.410465\pi\) | ||||
0.277589 | + | 0.960700i | \(0.410465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.5127 | 1.31169 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.6797 | −1.30781 | ||||||||
\(95\) | 10.5958 | 1.08710 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9518 | 1.51812 | 0.759062 | − | 0.651018i | \(-0.225658\pi\) | ||||
0.759062 | + | 0.651018i | \(0.225658\pi\) | |||||||
\(98\) | 0.269342 | 0.0272077 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.70981 | −0.270981 | ||||||||
\(101\) | 0.530283 | 0.0527652 | 0.0263826 | − | 0.999652i | \(-0.491601\pi\) | ||||
0.0263826 | + | 0.999652i | \(0.491601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.919917 | 0.0906421 | 0.0453211 | − | 0.998972i | \(-0.485569\pi\) | ||||
0.0453211 | + | 0.998972i | \(0.485569\pi\) | |||||||
\(104\) | 4.82306 | 0.472940 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.23281 | 0.411127 | ||||||||
\(107\) | −13.4562 | −1.30086 | −0.650428 | − | 0.759568i | \(-0.725410\pi\) | ||||
−0.650428 | + | 0.759568i | \(0.725410\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.97597 | −0.476611 | −0.238306 | − | 0.971190i | \(-0.576592\pi\) | ||||
−0.238306 | + | 0.971190i | \(0.576592\pi\) | |||||||
\(110\) | 7.57749 | 0.722486 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.59435 | −0.245143 | ||||||||
\(113\) | 13.6038 | 1.27974 | 0.639869 | − | 0.768484i | \(-0.278989\pi\) | ||||
0.639869 | + | 0.768484i | \(0.278989\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.11362 | −0.289093 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.98142 | 0.366519 | ||||||||
\(119\) | −2.24072 | −0.205407 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.0715 | 1.27922 | ||||||||
\(122\) | 7.26229 | 0.657497 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.17428 | −0.105453 | ||||||||
\(125\) | 11.6675 | 1.04358 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.73013 | 0.597203 | 0.298601 | − | 0.954378i | \(-0.403480\pi\) | ||||
0.298601 | + | 0.954378i | \(0.403480\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.29891 | −0.640157 | ||||||||
\(131\) | −18.9969 | −1.65976 | −0.829882 | − | 0.557939i | \(-0.811592\pi\) | ||||
−0.829882 | + | 0.557939i | \(0.811592\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.1646 | 1.57507 | ||||||||
\(134\) | 16.1371 | 1.39403 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.863693 | −0.0740611 | ||||||||
\(137\) | 2.62684 | 0.224426 | 0.112213 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112213 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.4268 | −1.56294 | −0.781471 | − | 0.623941i | \(-0.785530\pi\) | ||||
−0.781471 | + | 0.623941i | \(0.785530\pi\) | |||||||
\(140\) | 3.92613 | 0.331818 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.88463 | 0.493827 | ||||||||
\(143\) | −24.1497 | −2.01950 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.71196 | 0.391307 | ||||||||
\(146\) | −14.3814 | −1.19021 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.602123 | −0.0494942 | ||||||||
\(149\) | 3.95602 | 0.324090 | 0.162045 | − | 0.986783i | \(-0.448191\pi\) | ||||
0.162045 | + | 0.986783i | \(0.448191\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.2471 | −1.32217 | −0.661085 | − | 0.750311i | \(-0.729904\pi\) | ||||
−0.661085 | + | 0.750311i | \(0.729904\pi\) | |||||||
\(152\) | 7.00158 | 0.567903 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.9903 | 1.04679 | ||||||||
\(155\) | 1.77708 | 0.142739 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3422 | 1.62349 | 0.811743 | − | 0.584015i | \(-0.198519\pi\) | ||||
0.811743 | + | 0.584015i | \(0.198519\pi\) | |||||||
\(158\) | −10.3402 | −0.822621 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.51334 | 0.119640 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.9527 | −1.17119 | −0.585593 | − | 0.810605i | \(-0.699138\pi\) | ||||
−0.585593 | + | 0.810605i | \(0.699138\pi\) | |||||||
\(164\) | −5.29335 | −0.413341 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.64101 | 0.204982 | ||||||||
\(167\) | 12.0503 | 0.932477 | 0.466238 | − | 0.884659i | \(-0.345609\pi\) | ||||
0.466238 | + | 0.884659i | \(0.345609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2619 | 0.789376 | ||||||||
\(170\) | 1.30706 | 0.100247 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.45925 | 0.111267 | ||||||||
\(173\) | −15.5014 | −1.17855 | −0.589273 | − | 0.807934i | \(-0.700586\pi\) | ||||
−0.589273 | + | 0.807934i | \(0.700586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.03020 | 0.531433 | ||||||||
\(176\) | 5.00714 | 0.377428 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.23754 | −0.392570 | ||||||||
\(179\) | −7.21524 | −0.539292 | −0.269646 | − | 0.962960i | \(-0.586907\pi\) | ||||
−0.269646 | + | 0.962960i | \(0.586907\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.34058 | 0.248304 | 0.124152 | − | 0.992263i | \(-0.460379\pi\) | ||||
0.124152 | + | 0.992263i | \(0.460379\pi\) | |||||||
\(182\) | −12.5127 | −0.927504 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.911214 | 0.0669938 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.32463 | 0.316249 | ||||||||
\(188\) | 12.6797 | 0.924760 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.5958 | −0.768697 | ||||||||
\(191\) | 17.0123 | 1.23097 | 0.615485 | − | 0.788149i | \(-0.288960\pi\) | ||||
0.615485 | + | 0.788149i | \(0.288960\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.7417 | −1.63698 | −0.818491 | − | 0.574519i | \(-0.805189\pi\) | ||||
−0.818491 | + | 0.574519i | \(0.805189\pi\) | |||||||
\(194\) | −14.9518 | −1.07348 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.269342 | −0.0192387 | ||||||||
\(197\) | −10.0792 | −0.718116 | −0.359058 | − | 0.933315i | \(-0.616902\pi\) | ||||
−0.359058 | + | 0.933315i | \(0.616902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.43241 | −0.668646 | −0.334323 | − | 0.942459i | \(-0.608508\pi\) | ||||
−0.334323 | + | 0.942459i | \(0.608508\pi\) | |||||||
\(200\) | 2.70981 | 0.191613 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.530283 | −0.0373106 | ||||||||
\(203\) | 8.07783 | 0.566952 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.01063 | 0.559487 | ||||||||
\(206\) | −0.919917 | −0.0640937 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.82306 | −0.334419 | ||||||||
\(209\) | −35.0579 | −2.42501 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.37926 | −0.232638 | −0.116319 | − | 0.993212i | \(-0.537109\pi\) | ||||
−0.116319 | + | 0.993212i | \(0.537109\pi\) | |||||||
\(212\) | −4.23281 | −0.290711 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.4562 | 0.919844 | ||||||||
\(215\) | −2.20834 | −0.150608 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.04649 | 0.206809 | ||||||||
\(218\) | 4.97597 | 0.337015 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.57749 | −0.510875 | ||||||||
\(221\) | −4.16564 | −0.280211 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3295 | −1.16047 | −0.580236 | − | 0.814448i | \(-0.697040\pi\) | ||||
−0.580236 | + | 0.814448i | \(0.697040\pi\) | |||||||
\(224\) | 2.59435 | 0.173342 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.6038 | −0.904911 | ||||||||
\(227\) | −11.9206 | −0.791197 | −0.395598 | − | 0.918424i | \(-0.629463\pi\) | ||||
−0.395598 | + | 0.918424i | \(0.629463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9000 | 1.11678 | 0.558390 | − | 0.829578i | \(-0.311419\pi\) | ||||
0.558390 | + | 0.829578i | \(0.311419\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.11362 | 0.204419 | ||||||||
\(233\) | −28.4924 | −1.86660 | −0.933299 | − | 0.359099i | \(-0.883084\pi\) | ||||
−0.933299 | + | 0.359099i | \(0.883084\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.1886 | −1.25173 | ||||||||
\(236\) | −3.98142 | −0.259168 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.24072 | 0.145245 | ||||||||
\(239\) | 22.0994 | 1.42949 | 0.714745 | − | 0.699385i | \(-0.246543\pi\) | ||||
0.714745 | + | 0.699385i | \(0.246543\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.59815 | −0.102946 | −0.0514728 | − | 0.998674i | \(-0.516392\pi\) | ||||
−0.0514728 | + | 0.998674i | \(0.516392\pi\) | |||||||
\(242\) | −14.0715 | −0.904548 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.26229 | −0.464920 | ||||||||
\(245\) | 0.407605 | 0.0260410 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.7690 | 2.14867 | ||||||||
\(248\) | 1.17428 | 0.0745668 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.6675 | −0.737920 | ||||||||
\(251\) | 17.5887 | 1.11019 | 0.555094 | − | 0.831787i | \(-0.312682\pi\) | ||||
0.555094 | + | 0.831787i | \(0.312682\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.73013 | −0.422286 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.6964 | 1.29101 | 0.645504 | − | 0.763757i | \(-0.276648\pi\) | ||||
0.645504 | + | 0.763757i | \(0.276648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.56212 | 0.0970653 | ||||||||
\(260\) | 7.29891 | 0.452659 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.9969 | 1.17363 | ||||||||
\(263\) | 27.5247 | 1.69724 | 0.848622 | − | 0.529000i | \(-0.177433\pi\) | ||||
0.848622 | + | 0.529000i | \(0.177433\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.40567 | 0.393497 | ||||||||
\(266\) | −18.1646 | −1.11374 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.1371 | −0.985729 | ||||||||
\(269\) | 13.2757 | 0.809434 | 0.404717 | − | 0.914442i | \(-0.367370\pi\) | ||||
0.404717 | + | 0.914442i | \(0.367370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0786 | 1.46267 | 0.731335 | − | 0.682019i | \(-0.238898\pi\) | ||||
0.731335 | + | 0.682019i | \(0.238898\pi\) | |||||||
\(272\) | 0.863693 | 0.0523691 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.62684 | −0.158693 | ||||||||
\(275\) | −13.5684 | −0.818206 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.3404 | −1.10197 | −0.550983 | − | 0.834516i | \(-0.685747\pi\) | ||||
−0.550983 | + | 0.834516i | \(0.685747\pi\) | |||||||
\(278\) | 18.4268 | 1.10517 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.92613 | −0.234631 | ||||||||
\(281\) | 0.0199733 | 0.00119151 | 0.000595754 | − | 1.00000i | \(-0.499810\pi\) | ||||
0.000595754 | 1.00000i | \(0.499810\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.5537 | 1.04346 | 0.521729 | − | 0.853111i | \(-0.325287\pi\) | ||||
0.521729 | + | 0.853111i | \(0.325287\pi\) | |||||||
\(284\) | −5.88463 | −0.349188 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.1497 | 1.42800 | ||||||||
\(287\) | 13.7328 | 0.810623 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2540 | −0.956120 | ||||||||
\(290\) | −4.71196 | −0.276696 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.3814 | 0.841608 | ||||||||
\(293\) | 2.90645 | 0.169797 | 0.0848983 | − | 0.996390i | \(-0.472943\pi\) | ||||
0.0848983 | + | 0.996390i | \(0.472943\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.02523 | 0.350803 | ||||||||
\(296\) | 0.602123 | 0.0349977 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.95602 | −0.229166 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.78581 | −0.218211 | ||||||||
\(302\) | 16.2471 | 0.934915 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.00158 | −0.401568 | ||||||||
\(305\) | 10.9903 | 0.629302 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.7120 | −0.725511 | −0.362755 | − | 0.931884i | \(-0.618164\pi\) | ||||
−0.362755 | + | 0.931884i | \(0.618164\pi\) | |||||||
\(308\) | −12.9903 | −0.740190 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.77708 | −0.100931 | ||||||||
\(311\) | 21.3006 | 1.20785 | 0.603924 | − | 0.797042i | \(-0.293603\pi\) | ||||
0.603924 | + | 0.797042i | \(0.293603\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.89134 | 0.106905 | 0.0534524 | − | 0.998570i | \(-0.482977\pi\) | ||||
0.0534524 | + | 0.998570i | \(0.482977\pi\) | |||||||
\(314\) | −20.3422 | −1.14798 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.3402 | 0.581681 | ||||||||
\(317\) | 21.8115 | 1.22505 | 0.612527 | − | 0.790450i | \(-0.290153\pi\) | ||||
0.612527 | + | 0.790450i | \(0.290153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5903 | −0.872892 | ||||||||
\(320\) | −1.51334 | −0.0845981 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.04722 | −0.336476 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0696 | 0.724970 | ||||||||
\(326\) | 14.9527 | 0.828153 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.29335 | 0.292277 | ||||||||
\(329\) | −32.8955 | −1.81359 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.4183 | 0.957396 | 0.478698 | − | 0.877980i | \(-0.341109\pi\) | ||||
0.478698 | + | 0.877980i | \(0.341109\pi\) | |||||||
\(332\) | −2.64101 | −0.144944 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.0503 | −0.659361 | ||||||||
\(335\) | 24.4208 | 1.33425 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.9480 | −0.977689 | −0.488844 | − | 0.872371i | \(-0.662581\pi\) | ||||
−0.488844 | + | 0.872371i | \(0.662581\pi\) | |||||||
\(338\) | −10.2619 | −0.558173 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.30706 | −0.0708852 | ||||||||
\(341\) | −5.87978 | −0.318408 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8592 | 1.01830 | ||||||||
\(344\) | −1.45925 | −0.0786776 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.5014 | 0.833358 | ||||||||
\(347\) | 4.82518 | 0.259029 | 0.129515 | − | 0.991578i | \(-0.458658\pi\) | ||||
0.129515 | + | 0.991578i | \(0.458658\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3559 | 0.554337 | 0.277169 | − | 0.960821i | \(-0.410604\pi\) | ||||
0.277169 | + | 0.960821i | \(0.410604\pi\) | |||||||
\(350\) | −7.03020 | −0.375780 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.00714 | −0.266882 | ||||||||
\(353\) | 29.3716 | 1.56329 | 0.781646 | − | 0.623723i | \(-0.214381\pi\) | ||||
0.781646 | + | 0.623723i | \(0.214381\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.90543 | 0.472651 | ||||||||
\(356\) | 5.23754 | 0.277589 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.21524 | 0.381337 | ||||||||
\(359\) | 9.99774 | 0.527660 | 0.263830 | − | 0.964569i | \(-0.415014\pi\) | ||||
0.263830 | + | 0.964569i | \(0.415014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0222 | 1.58011 | ||||||||
\(362\) | −3.34058 | −0.175577 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.5127 | 0.655844 | ||||||||
\(365\) | −21.7639 | −1.13918 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.7049 | 0.871991 | 0.435995 | − | 0.899949i | \(-0.356396\pi\) | ||||
0.435995 | + | 0.899949i | \(0.356396\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.911214 | −0.0473718 | ||||||||
\(371\) | 10.9814 | 0.570126 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.2235 | 1.72025 | 0.860125 | − | 0.510084i | \(-0.170386\pi\) | ||||
0.860125 | + | 0.510084i | \(0.170386\pi\) | |||||||
\(374\) | −4.32463 | −0.223622 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.6797 | −0.653904 | ||||||||
\(377\) | 15.0172 | 0.773424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.45299 | 0.434201 | 0.217100 | − | 0.976149i | \(-0.430340\pi\) | ||||
0.217100 | + | 0.976149i | \(0.430340\pi\) | |||||||
\(380\) | 10.5958 | 0.543551 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.0123 | −0.870427 | ||||||||
\(383\) | 4.40327 | 0.224997 | 0.112498 | − | 0.993652i | \(-0.464115\pi\) | ||||
0.112498 | + | 0.993652i | \(0.464115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.6587 | 1.00190 | ||||||||
\(386\) | 22.7417 | 1.15752 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.9518 | 0.759062 | ||||||||
\(389\) | −20.2882 | −1.02865 | −0.514325 | − | 0.857595i | \(-0.671958\pi\) | ||||
−0.514325 | + | 0.857595i | \(0.671958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.269342 | 0.0136038 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.0792 | 0.507784 | ||||||||
\(395\) | −15.6482 | −0.787346 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.3569 | −0.720555 | −0.360277 | − | 0.932845i | \(-0.617318\pi\) | ||||
−0.360277 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(398\) | 9.43241 | 0.472804 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.70981 | −0.135491 | ||||||||
\(401\) | 11.5320 | 0.575879 | 0.287940 | − | 0.957649i | \(-0.407030\pi\) | ||||
0.287940 | + | 0.957649i | \(0.407030\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.66362 | 0.282125 | ||||||||
\(404\) | 0.530283 | 0.0263826 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.07783 | −0.400896 | ||||||||
\(407\) | −3.01491 | −0.149444 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.6704 | −1.17042 | −0.585212 | − | 0.810880i | \(-0.698989\pi\) | ||||
−0.585212 | + | 0.810880i | \(0.698989\pi\) | |||||||
\(410\) | −8.01063 | −0.395617 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.919917 | 0.0453211 | ||||||||
\(413\) | 10.3292 | 0.508267 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.99674 | 0.196192 | ||||||||
\(416\) | 4.82306 | 0.236470 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 35.0579 | 1.71474 | ||||||||
\(419\) | 2.23033 | 0.108959 | 0.0544794 | − | 0.998515i | \(-0.482650\pi\) | ||||
0.0544794 | + | 0.998515i | \(0.482650\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0322 | −0.878834 | −0.439417 | − | 0.898283i | \(-0.644815\pi\) | ||||
−0.439417 | + | 0.898283i | \(0.644815\pi\) | |||||||
\(422\) | 3.37926 | 0.164500 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.23281 | 0.205564 | ||||||||
\(425\) | −2.34045 | −0.113528 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.8409 | 0.911776 | ||||||||
\(428\) | −13.4562 | −0.650428 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.20834 | 0.106496 | ||||||||
\(431\) | −22.3676 | −1.07741 | −0.538705 | − | 0.842495i | \(-0.681086\pi\) | ||||
−0.538705 | + | 0.842495i | \(0.681086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.5048 | 0.841227 | 0.420614 | − | 0.907240i | \(-0.361815\pi\) | ||||
0.420614 | + | 0.907240i | \(0.361815\pi\) | |||||||
\(434\) | −3.04649 | −0.146236 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.97597 | −0.238306 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.1141 | −0.721357 | −0.360678 | − | 0.932690i | \(-0.617455\pi\) | ||||
−0.360678 | + | 0.932690i | \(0.617455\pi\) | |||||||
\(440\) | 7.57749 | 0.361243 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.16564 | 0.198139 | ||||||||
\(443\) | 11.8244 | 0.561794 | 0.280897 | − | 0.959738i | \(-0.409368\pi\) | ||||
0.280897 | + | 0.959738i | \(0.409368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.92616 | −0.375736 | ||||||||
\(446\) | 17.3295 | 0.820578 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.59435 | −0.122572 | ||||||||
\(449\) | 4.68716 | 0.221201 | 0.110600 | − | 0.993865i | \(-0.464723\pi\) | ||||
0.110600 | + | 0.993865i | \(0.464723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.5046 | −1.24805 | ||||||||
\(452\) | 13.6038 | 0.639869 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.9206 | 0.559461 | ||||||||
\(455\) | −18.9359 | −0.887731 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.8624 | −1.35013 | −0.675064 | − | 0.737759i | \(-0.735884\pi\) | ||||
−0.675064 | + | 0.737759i | \(0.735884\pi\) | |||||||
\(458\) | −16.9000 | −0.789683 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.23414 | 0.0574794 | 0.0287397 | − | 0.999587i | \(-0.490851\pi\) | ||||
0.0287397 | + | 0.999587i | \(0.490851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.545786 | 0.0253648 | 0.0126824 | − | 0.999920i | \(-0.495963\pi\) | ||||
0.0126824 | + | 0.999920i | \(0.495963\pi\) | |||||||
\(464\) | −3.11362 | −0.144546 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.4924 | 1.31988 | ||||||||
\(467\) | −15.9286 | −0.737089 | −0.368544 | − | 0.929610i | \(-0.620144\pi\) | ||||
−0.368544 | + | 0.929610i | \(0.620144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.8653 | 1.93316 | ||||||||
\(470\) | 19.1886 | 0.885104 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.98142 | 0.183260 | ||||||||
\(473\) | 7.30668 | 0.335962 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.9730 | 0.870539 | ||||||||
\(476\) | −2.24072 | −0.102703 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.0994 | −1.01080 | ||||||||
\(479\) | 0.255466 | 0.0116725 | 0.00583626 | − | 0.999983i | \(-0.498142\pi\) | ||||
0.00583626 | + | 0.999983i | \(0.498142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.90407 | 0.132414 | ||||||||
\(482\) | 1.59815 | 0.0727935 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.0715 | 0.639612 | ||||||||
\(485\) | −22.6271 | −1.02744 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.5758 | 1.15895 | 0.579476 | − | 0.814989i | \(-0.303257\pi\) | ||||
0.579476 | + | 0.814989i | \(0.303257\pi\) | |||||||
\(488\) | 7.26229 | 0.328748 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.407605 | −0.0184137 | ||||||||
\(491\) | 7.52661 | 0.339671 | 0.169836 | − | 0.985472i | \(-0.445676\pi\) | ||||
0.169836 | + | 0.985472i | \(0.445676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.68921 | −0.121116 | ||||||||
\(494\) | −33.7690 | −1.51934 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.17428 | −0.0527267 | ||||||||
\(497\) | 15.2668 | 0.684809 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.1412 | −1.79697 | −0.898483 | − | 0.439007i | \(-0.855330\pi\) | ||||
−0.898483 | + | 0.439007i | \(0.855330\pi\) | |||||||
\(500\) | 11.6675 | 0.521788 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.5887 | −0.785022 | ||||||||
\(503\) | 24.1482 | 1.07671 | 0.538357 | − | 0.842717i | \(-0.319045\pi\) | ||||
0.538357 | + | 0.842717i | \(0.319045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.802497 | −0.0357107 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.73013 | 0.298601 | ||||||||
\(509\) | −0.639983 | −0.0283667 | −0.0141834 | − | 0.999899i | \(-0.504515\pi\) | ||||
−0.0141834 | + | 0.999899i | \(0.504515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.3104 | −1.65052 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.6964 | −0.912880 | ||||||||
\(515\) | −1.39214 | −0.0613452 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 63.4889 | 2.79224 | ||||||||
\(518\) | −1.56212 | −0.0686355 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.29891 | −0.320079 | ||||||||
\(521\) | −22.7385 | −0.996191 | −0.498095 | − | 0.867122i | \(-0.665967\pi\) | ||||
−0.498095 | + | 0.867122i | \(0.665967\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.840829 | 0.0367669 | 0.0183834 | − | 0.999831i | \(-0.494148\pi\) | ||||
0.0183834 | + | 0.999831i | \(0.494148\pi\) | |||||||
\(524\) | −18.9969 | −0.829882 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.5247 | −1.20013 | ||||||||
\(527\) | −1.01422 | −0.0441800 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −6.40567 | −0.278245 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.1646 | 0.787534 | ||||||||
\(533\) | 25.5302 | 1.10583 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.3637 | 0.880399 | ||||||||
\(536\) | 16.1371 | 0.697016 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.2757 | −0.572356 | ||||||||
\(539\) | −1.34863 | −0.0580898 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8587 | 0.982773 | 0.491386 | − | 0.870942i | \(-0.336490\pi\) | ||||
0.491386 | + | 0.870942i | \(0.336490\pi\) | |||||||
\(542\) | −24.0786 | −1.03426 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.863693 | −0.0370305 | ||||||||
\(545\) | 7.53032 | 0.322563 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4614 | 0.447296 | 0.223648 | − | 0.974670i | \(-0.428203\pi\) | ||||
0.223648 | + | 0.974670i | \(0.428203\pi\) | |||||||
\(548\) | 2.62684 | 0.112213 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.5684 | 0.578559 | ||||||||
\(551\) | 21.8003 | 0.928723 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.8261 | −1.14076 | ||||||||
\(554\) | 18.3404 | 0.779208 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.4268 | −0.781471 | ||||||||
\(557\) | 26.2874 | 1.11383 | 0.556916 | − | 0.830569i | \(-0.311984\pi\) | ||||
0.556916 | + | 0.830569i | \(0.311984\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.03806 | −0.297678 | ||||||||
\(560\) | 3.92613 | 0.165909 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.0199733 | −0.000842524 0 | ||||||||
\(563\) | 27.8694 | 1.17456 | 0.587278 | − | 0.809386i | \(-0.300200\pi\) | ||||
0.587278 | + | 0.809386i | \(0.300200\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.5871 | −0.866107 | ||||||||
\(566\) | −17.5537 | −0.737836 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.88463 | 0.246914 | ||||||||
\(569\) | 32.2063 | 1.35016 | 0.675080 | − | 0.737745i | \(-0.264109\pi\) | ||||
0.675080 | + | 0.737745i | \(0.264109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4966 | 0.690361 | 0.345181 | − | 0.938536i | \(-0.387818\pi\) | ||||
0.345181 | + | 0.938536i | \(0.387818\pi\) | |||||||
\(572\) | −24.1497 | −1.00975 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.7328 | −0.573197 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.57419 | −0.273687 | −0.136844 | − | 0.990593i | \(-0.543696\pi\) | ||||
−0.136844 | + | 0.990593i | \(0.543696\pi\) | |||||||
\(578\) | 16.2540 | 0.676079 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.71196 | 0.195653 | ||||||||
\(581\) | 6.85170 | 0.284257 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.1943 | −0.877778 | ||||||||
\(584\) | −14.3814 | −0.595107 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.90645 | −0.120064 | ||||||||
\(587\) | 15.4230 | 0.636574 | 0.318287 | − | 0.947994i | \(-0.396892\pi\) | ||||
0.318287 | + | 0.947994i | \(0.396892\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.22181 | 0.338774 | ||||||||
\(590\) | −6.02523 | −0.248055 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.602123 | −0.0247471 | ||||||||
\(593\) | 14.3695 | 0.590086 | 0.295043 | − | 0.955484i | \(-0.404666\pi\) | ||||
0.295043 | + | 0.955484i | \(0.404666\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.39097 | 0.139016 | ||||||||
\(596\) | 3.95602 | 0.162045 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.73316 | −0.315968 | −0.157984 | − | 0.987442i | \(-0.550500\pi\) | ||||
−0.157984 | + | 0.987442i | \(0.550500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.0245 | 1.30631 | 0.653153 | − | 0.757226i | \(-0.273446\pi\) | ||||
0.653153 | + | 0.757226i | \(0.273446\pi\) | |||||||
\(602\) | 3.78581 | 0.154298 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.2471 | −0.661085 | ||||||||
\(605\) | −21.2949 | −0.865760 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.918396 | −0.0372765 | −0.0186383 | − | 0.999826i | \(-0.505933\pi\) | ||||
−0.0186383 | + | 0.999826i | \(0.505933\pi\) | |||||||
\(608\) | 7.00158 | 0.283952 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.9903 | −0.444984 | ||||||||
\(611\) | −61.1548 | −2.47406 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.7621 | 0.798182 | 0.399091 | − | 0.916911i | \(-0.369326\pi\) | ||||
0.399091 | + | 0.916911i | \(0.369326\pi\) | |||||||
\(614\) | 12.7120 | 0.513013 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.9903 | 0.523393 | ||||||||
\(617\) | −6.90005 | −0.277786 | −0.138893 | − | 0.990307i | \(-0.544354\pi\) | ||||
−0.138893 | + | 0.990307i | \(0.544354\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.7324 | 0.913691 | 0.456846 | − | 0.889546i | \(-0.348979\pi\) | ||||
0.456846 | + | 0.889546i | \(0.348979\pi\) | |||||||
\(620\) | 1.77708 | 0.0713693 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.3006 | −0.854077 | ||||||||
\(623\) | −13.5880 | −0.544392 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.10787 | −0.164315 | ||||||||
\(626\) | −1.89134 | −0.0755931 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.3422 | 0.811743 | ||||||||
\(629\) | −0.520049 | −0.0207357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.6909 | 1.34121 | 0.670607 | − | 0.741813i | \(-0.266034\pi\) | ||||
0.670607 | + | 0.741813i | \(0.266034\pi\) | |||||||
\(632\) | −10.3402 | −0.411311 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.8115 | −0.866244 | ||||||||
\(635\) | −10.1850 | −0.404178 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.29905 | 0.0514704 | ||||||||
\(638\) | 15.5903 | 0.617228 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.51334 | 0.0598199 | ||||||||
\(641\) | 4.23932 | 0.167443 | 0.0837216 | − | 0.996489i | \(-0.473319\pi\) | ||||
0.0837216 | + | 0.996489i | \(0.473319\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.0914 | 1.58105 | 0.790525 | − | 0.612430i | \(-0.209808\pi\) | ||||
0.790525 | + | 0.612430i | \(0.209808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.04722 | 0.237925 | ||||||||
\(647\) | 5.69698 | 0.223971 | 0.111986 | − | 0.993710i | \(-0.464279\pi\) | ||||
0.111986 | + | 0.993710i | \(0.464279\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.9355 | −0.782538 | ||||||||
\(650\) | −13.0696 | −0.512631 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.9527 | −0.585593 | ||||||||
\(653\) | −32.2988 | −1.26395 | −0.631975 | − | 0.774989i | \(-0.717755\pi\) | ||||
−0.631975 | + | 0.774989i | \(0.717755\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.7487 | 1.12330 | ||||||||
\(656\) | −5.29335 | −0.206671 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32.8955 | 1.28240 | ||||||||
\(659\) | −9.24211 | −0.360021 | −0.180011 | − | 0.983665i | \(-0.557613\pi\) | ||||
−0.180011 | + | 0.983665i | \(0.557613\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.3877 | −1.25974 | −0.629868 | − | 0.776702i | \(-0.716891\pi\) | ||||
−0.629868 | + | 0.776702i | \(0.716891\pi\) | |||||||
\(662\) | −17.4183 | −0.676981 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.64101 | 0.102491 | ||||||||
\(665\) | −27.4891 | −1.06598 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 12.0503 | 0.466238 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.4208 | −0.943459 | ||||||||
\(671\) | −36.3633 | −1.40379 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.7223 | 1.49264 | 0.746318 | − | 0.665590i | \(-0.231820\pi\) | ||||
0.746318 | + | 0.665590i | \(0.231820\pi\) | |||||||
\(674\) | 17.9480 | 0.691330 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.2619 | 0.394688 | ||||||||
\(677\) | −29.2630 | −1.12467 | −0.562334 | − | 0.826910i | \(-0.690097\pi\) | ||||
−0.562334 | + | 0.826910i | \(0.690097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.7902 | −1.48863 | ||||||||
\(680\) | 1.30706 | 0.0501234 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.87978 | 0.225148 | ||||||||
\(683\) | 32.8985 | 1.25883 | 0.629413 | − | 0.777071i | \(-0.283295\pi\) | ||||
0.629413 | + | 0.777071i | \(0.283295\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.97529 | −0.151888 | ||||||||
\(686\) | −18.8592 | −0.720049 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.45925 | 0.0556335 | ||||||||
\(689\) | 20.4151 | 0.777754 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.3215 | −0.468730 | −0.234365 | − | 0.972149i | \(-0.575301\pi\) | ||||
−0.234365 | + | 0.972149i | \(0.575301\pi\) | |||||||
\(692\) | −15.5014 | −0.589273 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.82518 | −0.183161 | ||||||||
\(695\) | 27.8860 | 1.05778 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.57183 | −0.173171 | ||||||||
\(698\) | −10.3559 | −0.391976 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.03020 | 0.265717 | ||||||||
\(701\) | 27.3050 | 1.03129 | 0.515647 | − | 0.856801i | \(-0.327552\pi\) | ||||
0.515647 | + | 0.856801i | \(0.327552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.21581 | 0.159002 | ||||||||
\(704\) | 5.00714 | 0.188714 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.3716 | −1.10541 | ||||||||
\(707\) | −1.37574 | −0.0517401 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1293 | 0.417969 | 0.208985 | − | 0.977919i | \(-0.432984\pi\) | ||||
0.208985 | + | 0.977919i | \(0.432984\pi\) | |||||||
\(710\) | −8.90543 | −0.334215 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.23754 | −0.196285 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.5467 | 1.36677 | ||||||||
\(716\) | −7.21524 | −0.269646 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.99774 | −0.373112 | ||||||||
\(719\) | −25.7081 | −0.958750 | −0.479375 | − | 0.877610i | \(-0.659137\pi\) | ||||
−0.479375 | + | 0.877610i | \(0.659137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.38659 | −0.0888812 | ||||||||
\(722\) | −30.0222 | −1.11731 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.34058 | 0.124152 | ||||||||
\(725\) | 8.43733 | 0.313354 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.0480451 | 0.00178189 | 0.000890947 | − | 1.00000i | \(-0.499716\pi\) | ||||
0.000890947 | 1.00000i | \(0.499716\pi\) | ||||||||
\(728\) | −12.5127 | −0.463752 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.7639 | 0.805518 | ||||||||
\(731\) | 1.26035 | 0.0466156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.6005 | 1.13026 | 0.565128 | − | 0.825003i | \(-0.308827\pi\) | ||||
0.565128 | + | 0.825003i | \(0.308827\pi\) | |||||||
\(734\) | −16.7049 | −0.616591 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −80.8007 | −2.97633 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.0286 | −0.442481 | −0.221240 | − | 0.975219i | \(-0.571011\pi\) | ||||
−0.221240 | + | 0.975219i | \(0.571011\pi\) | |||||||
\(740\) | 0.911214 | 0.0334969 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.9814 | −0.403140 | ||||||||
\(743\) | 10.1814 | 0.373521 | 0.186760 | − | 0.982405i | \(-0.440201\pi\) | ||||
0.186760 | + | 0.982405i | \(0.440201\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.98679 | −0.219339 | ||||||||
\(746\) | −33.2235 | −1.21640 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.32463 | 0.158124 | ||||||||
\(749\) | 34.9100 | 1.27558 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.06980 | −0.330962 | −0.165481 | − | 0.986213i | \(-0.552918\pi\) | ||||
−0.165481 | + | 0.986213i | \(0.552918\pi\) | |||||||
\(752\) | 12.6797 | 0.462380 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.0172 | −0.546893 | ||||||||
\(755\) | 24.5873 | 0.894824 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.5078 | 0.636333 | 0.318166 | − | 0.948035i | \(-0.396933\pi\) | ||||
0.318166 | + | 0.948035i | \(0.396933\pi\) | |||||||
\(758\) | −8.45299 | −0.307026 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.5958 | −0.384348 | ||||||||
\(761\) | 24.9741 | 0.905310 | 0.452655 | − | 0.891686i | \(-0.350477\pi\) | ||||
0.452655 | + | 0.891686i | \(0.350477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.9094 | 0.467352 | ||||||||
\(764\) | 17.0123 | 0.615485 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.40327 | −0.159097 | ||||||||
\(767\) | 19.2026 | 0.693367 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.51279 | −0.306979 | −0.153490 | − | 0.988150i | \(-0.549051\pi\) | ||||
−0.153490 | + | 0.988150i | \(0.549051\pi\) | |||||||
\(770\) | −19.6587 | −0.708450 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.7417 | −0.818491 | ||||||||
\(773\) | −49.0834 | −1.76541 | −0.882703 | − | 0.469931i | \(-0.844279\pi\) | ||||
−0.882703 | + | 0.469931i | \(0.844279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.18207 | 0.114303 | ||||||||
\(776\) | −14.9518 | −0.536738 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.2882 | 0.727366 | ||||||||
\(779\) | 37.0619 | 1.32788 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.4652 | −1.05435 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.269342 | −0.00961936 | ||||||||
\(785\) | −30.7846 | −1.09875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.33510 | 0.154530 | 0.0772649 | − | 0.997011i | \(-0.475381\pi\) | ||||
0.0772649 | + | 0.997011i | \(0.475381\pi\) | |||||||
\(788\) | −10.0792 | −0.359058 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.6482 | 0.556738 | ||||||||
\(791\) | −35.2930 | −1.25488 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.0264 | 1.24383 | ||||||||
\(794\) | 14.3569 | 0.509509 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.43241 | −0.334323 | ||||||||
\(797\) | 4.48314 | 0.158801 | 0.0794005 | − | 0.996843i | \(-0.474699\pi\) | ||||
0.0794005 | + | 0.996843i | \(0.474699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.9513 | 0.387431 | ||||||||
\(800\) | 2.70981 | 0.0958063 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.5320 | −0.407208 | ||||||||
\(803\) | 72.0097 | 2.54117 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.66362 | −0.199492 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.530283 | −0.0186553 | ||||||||
\(809\) | −28.1045 | −0.988100 | −0.494050 | − | 0.869433i | \(-0.664484\pi\) | ||||
−0.494050 | + | 0.869433i | \(0.664484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.7318 | 1.53563 | 0.767815 | − | 0.640672i | \(-0.221344\pi\) | ||||
0.767815 | + | 0.640672i | \(0.221344\pi\) | |||||||
\(812\) | 8.07783 | 0.283476 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.01491 | 0.105673 | ||||||||
\(815\) | 22.6285 | 0.792641 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.2171 | −0.357450 | ||||||||
\(818\) | 23.6704 | 0.827615 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.01063 | 0.279743 | ||||||||
\(821\) | 6.53023 | 0.227907 | 0.113953 | − | 0.993486i | \(-0.463649\pi\) | ||||
0.113953 | + | 0.993486i | \(0.463649\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.913788 | −0.0318527 | −0.0159263 | − | 0.999873i | \(-0.505070\pi\) | ||||
−0.0159263 | + | 0.999873i | \(0.505070\pi\) | |||||||
\(824\) | −0.919917 | −0.0320468 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.3292 | −0.359399 | ||||||||
\(827\) | 19.0247 | 0.661554 | 0.330777 | − | 0.943709i | \(-0.392689\pi\) | ||||
0.330777 | + | 0.943709i | \(0.392689\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.2601 | 0.495272 | 0.247636 | − | 0.968853i | \(-0.420346\pi\) | ||||
0.247636 | + | 0.968853i | \(0.420346\pi\) | |||||||
\(830\) | −3.99674 | −0.138729 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.82306 | −0.167209 | ||||||||
\(833\) | −0.232629 | −0.00806012 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.2361 | −0.631086 | ||||||||
\(836\) | −35.0579 | −1.21250 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.23033 | −0.0770456 | ||||||||
\(839\) | −55.4731 | −1.91514 | −0.957571 | − | 0.288196i | \(-0.906944\pi\) | ||||
−0.957571 | + | 0.288196i | \(0.906944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.3054 | −0.665702 | ||||||||
\(842\) | 18.0322 | 0.621430 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.37926 | −0.116319 | ||||||||
\(845\) | −15.5297 | −0.534238 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.5063 | −1.25437 | ||||||||
\(848\) | −4.23281 | −0.145355 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.34045 | 0.0802766 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.42049 | −0.254073 | −0.127036 | − | 0.991898i | \(-0.540547\pi\) | ||||
−0.127036 | + | 0.991898i | \(0.540547\pi\) | |||||||
\(854\) | −18.8409 | −0.644723 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.4562 | 0.459922 | ||||||||
\(857\) | 25.9013 | 0.884772 | 0.442386 | − | 0.896825i | \(-0.354132\pi\) | ||||
0.442386 | + | 0.896825i | \(0.354132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.1780 | −1.40498 | −0.702488 | − | 0.711695i | \(-0.747928\pi\) | ||||
−0.702488 | + | 0.711695i | \(0.747928\pi\) | |||||||
\(860\) | −2.20834 | −0.0753038 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.3676 | 0.761843 | ||||||||
\(863\) | −50.2342 | −1.70999 | −0.854995 | − | 0.518636i | \(-0.826440\pi\) | ||||
−0.854995 | + | 0.518636i | \(0.826440\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.4588 | 0.797622 | ||||||||
\(866\) | −17.5048 | −0.594837 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.04649 | 0.103405 | ||||||||
\(869\) | 51.7748 | 1.75634 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 77.8301 | 2.63717 | ||||||||
\(872\) | 4.97597 | 0.168508 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.2697 | −1.02330 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.5028 | 0.624794 | 0.312397 | − | 0.949952i | \(-0.398868\pi\) | ||||
0.312397 | + | 0.949952i | \(0.398868\pi\) | |||||||
\(878\) | 15.1141 | 0.510076 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.57749 | −0.255437 | ||||||||
\(881\) | −13.6757 | −0.460746 | −0.230373 | − | 0.973102i | \(-0.573995\pi\) | ||||
−0.230373 | + | 0.973102i | \(0.573995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.23466 | −0.0415497 | −0.0207749 | − | 0.999784i | \(-0.506613\pi\) | ||||
−0.0207749 | + | 0.999784i | \(0.506613\pi\) | |||||||
\(884\) | −4.16564 | −0.140106 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.8244 | −0.397248 | ||||||||
\(887\) | 13.0032 | 0.436606 | 0.218303 | − | 0.975881i | \(-0.429948\pi\) | ||||
0.218303 | + | 0.975881i | \(0.429948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.4603 | −0.585601 | ||||||||
\(890\) | 7.92616 | 0.265686 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.3295 | −0.580236 | ||||||||
\(893\) | −88.7777 | −2.97083 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.9191 | 0.364985 | ||||||||
\(896\) | 2.59435 | 0.0866712 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.68716 | −0.156412 | ||||||||
\(899\) | 3.65626 | 0.121943 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.65585 | −0.121794 | ||||||||
\(902\) | 26.5046 | 0.882506 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.6038 | −0.452455 | ||||||||
\(905\) | −5.05543 | −0.168048 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.84547 | −0.260505 | −0.130252 | − | 0.991481i | \(-0.541579\pi\) | ||||
−0.130252 | + | 0.991481i | \(0.541579\pi\) | |||||||
\(908\) | −11.9206 | −0.395598 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.9359 | 0.627720 | ||||||||
\(911\) | 43.3450 | 1.43608 | 0.718042 | − | 0.696000i | \(-0.245039\pi\) | ||||
0.718042 | + | 0.696000i | \(0.245039\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.2239 | −0.437647 | ||||||||
\(914\) | 28.8624 | 0.954685 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.9000 | 0.558390 | ||||||||
\(917\) | 49.2846 | 1.62752 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.3327 | −1.29747 | −0.648733 | − | 0.761016i | \(-0.724701\pi\) | ||||
−0.648733 | + | 0.761016i | \(0.724701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.23414 | −0.0406441 | ||||||||
\(923\) | 28.3819 | 0.934202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.63164 | 0.0536479 | ||||||||
\(926\) | −0.545786 | −0.0179357 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.11362 | 0.102210 | ||||||||
\(929\) | −29.5966 | −0.971033 | −0.485516 | − | 0.874228i | \(-0.661368\pi\) | ||||
−0.485516 | + | 0.874228i | \(0.661368\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.88582 | 0.0618053 | ||||||||
\(932\) | −28.4924 | −0.933299 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.9286 | 0.521200 | ||||||||
\(935\) | −6.54463 | −0.214032 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.1762 | −0.822470 | −0.411235 | − | 0.911529i | \(-0.634902\pi\) | ||||
−0.411235 | + | 0.911529i | \(0.634902\pi\) | |||||||
\(938\) | −41.8653 | −1.36695 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.1886 | −0.625863 | ||||||||
\(941\) | −16.8886 | −0.550552 | −0.275276 | − | 0.961365i | \(-0.588769\pi\) | ||||
−0.275276 | + | 0.961365i | \(0.588769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −3.98142 | −0.129584 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.30668 | −0.237561 | ||||||||
\(947\) | 15.4544 | 0.502200 | 0.251100 | − | 0.967961i | \(-0.419208\pi\) | ||||
0.251100 | + | 0.967961i | \(0.419208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −69.3624 | −2.25160 | ||||||||
\(950\) | −18.9730 | −0.615564 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.24072 | 0.0726223 | ||||||||
\(953\) | −1.03906 | −0.0336585 | −0.0168292 | − | 0.999858i | \(-0.505357\pi\) | ||||
−0.0168292 | + | 0.999858i | \(0.505357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.7454 | −0.833102 | ||||||||
\(956\) | 22.0994 | 0.714745 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.255466 | −0.00825372 | ||||||||
\(959\) | −6.81495 | −0.220066 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6211 | −0.955518 | ||||||||
\(962\) | −2.90407 | −0.0936311 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.59815 | −0.0514728 | ||||||||
\(965\) | 34.4158 | 1.10789 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.1795 | 0.745404 | 0.372702 | − | 0.927951i | \(-0.378431\pi\) | ||||
0.372702 | + | 0.927951i | \(0.378431\pi\) | |||||||
\(968\) | −14.0715 | −0.452274 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.6271 | 0.726512 | ||||||||
\(971\) | −6.18163 | −0.198378 | −0.0991890 | − | 0.995069i | \(-0.531625\pi\) | ||||
−0.0991890 | + | 0.995069i | \(0.531625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.8056 | 1.53258 | ||||||||
\(974\) | −25.5758 | −0.819502 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.26229 | −0.232460 | ||||||||
\(977\) | 30.4534 | 0.974292 | 0.487146 | − | 0.873321i | \(-0.338038\pi\) | ||||
0.487146 | + | 0.873321i | \(0.338038\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.2251 | 0.838158 | ||||||||
\(980\) | 0.407605 | 0.0130205 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.52661 | −0.240184 | ||||||||
\(983\) | −1.47151 | −0.0469338 | −0.0234669 | − | 0.999725i | \(-0.507470\pi\) | ||||
−0.0234669 | + | 0.999725i | \(0.507470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.2533 | 0.486010 | ||||||||
\(986\) | 2.68921 | 0.0856420 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.7690 | 1.07434 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.5601 | −1.00254 | −0.501269 | − | 0.865291i | \(-0.667133\pi\) | ||||
−0.501269 | + | 0.865291i | \(0.667133\pi\) | |||||||
\(992\) | 1.17428 | 0.0372834 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.2668 | −0.484233 | ||||||||
\(995\) | 14.2744 | 0.452529 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.3785 | 0.487042 | 0.243521 | − | 0.969896i | \(-0.421698\pi\) | ||||
0.243521 | + | 0.969896i | \(0.421698\pi\) | |||||||
\(998\) | 40.1412 | 1.27065 | ||||||||
\(999\) | 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 | 9522.2.a.bt.1.1 | 5 | ||
3.2 | odd | 2 | 3174.2.a.bc.1.5 | 5 | |||
23.2 | even | 11 | 414.2.i.d.73.1 | 10 | |||
23.12 | even | 11 | 414.2.i.d.397.1 | 10 | |||
23.22 | odd | 2 | 9522.2.a.bq.1.5 | 5 | |||
69.2 | odd | 22 | 138.2.e.a.73.1 | ✓ | 10 | ||
69.35 | odd | 22 | 138.2.e.a.121.1 | yes | 10 | ||
69.68 | even | 2 | 3174.2.a.bd.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.a.73.1 | ✓ | 10 | 69.2 | odd | 22 | ||
138.2.e.a.121.1 | yes | 10 | 69.35 | odd | 22 | ||
414.2.i.d.73.1 | 10 | 23.2 | even | 11 | |||
414.2.i.d.397.1 | 10 | 23.12 | even | 11 | |||
3174.2.a.bc.1.5 | 5 | 3.2 | odd | 2 | |||
3174.2.a.bd.1.1 | 5 | 69.68 | even | 2 | |||
9522.2.a.bq.1.5 | 5 | 23.22 | odd | 2 | |||
9522.2.a.bt.1.1 | 5 | 1.1 | even | 1 | trivial |