Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7581,2,Mod(1,7581)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7581, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7581.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7581 = 3 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7581.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: | \(60.5345897723\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.8512625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 8x^{4} + 17x^{3} + 11x^{2} - 31x + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.14337\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7581.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.14337 | 0.808485 | 0.404243 | − | 0.914652i | \(-0.367535\pi\) | ||||
0.404243 | + | 0.914652i | \(0.367535\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.692703 | −0.346352 | ||||||||
\(5\) | 2.31074 | 1.03339 | 0.516697 | − | 0.856169i | \(-0.327162\pi\) | ||||
0.516697 | + | 0.856169i | \(0.327162\pi\) | |||||||
\(6\) | 1.14337 | 0.466779 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.07876 | −1.08851 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.64203 | 0.835483 | ||||||||
\(11\) | −3.82746 | −1.15402 | −0.577011 | − | 0.816736i | \(-0.695781\pi\) | ||||
−0.577011 | + | 0.816736i | \(0.695781\pi\) | |||||||
\(12\) | −0.692703 | −0.199966 | ||||||||
\(13\) | 4.12491 | 1.14404 | 0.572022 | − | 0.820239i | \(-0.306159\pi\) | ||||
0.572022 | + | 0.820239i | \(0.306159\pi\) | |||||||
\(14\) | −1.14337 | −0.305579 | ||||||||
\(15\) | 2.31074 | 0.596630 | ||||||||
\(16\) | −2.13476 | −0.533689 | ||||||||
\(17\) | −3.31074 | −0.802972 | −0.401486 | − | 0.915865i | \(-0.631506\pi\) | ||||
−0.401486 | + | 0.915865i | \(0.631506\pi\) | |||||||
\(18\) | 1.14337 | 0.269495 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.60065 | −0.357917 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −4.37621 | −0.933010 | ||||||||
\(23\) | −7.29960 | −1.52207 | −0.761035 | − | 0.648710i | \(-0.775309\pi\) | ||||
−0.761035 | + | 0.648710i | \(0.775309\pi\) | |||||||
\(24\) | −3.07876 | −0.628449 | ||||||||
\(25\) | 0.339506 | 0.0679012 | ||||||||
\(26\) | 4.71630 | 0.924942 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.692703 | 0.130909 | ||||||||
\(29\) | −4.25822 | −0.790732 | −0.395366 | − | 0.918524i | \(-0.629382\pi\) | ||||
−0.395366 | + | 0.918524i | \(0.629382\pi\) | |||||||
\(30\) | 2.64203 | 0.482366 | ||||||||
\(31\) | 8.41762 | 1.51185 | 0.755924 | − | 0.654659i | \(-0.227188\pi\) | ||||
0.755924 | + | 0.654659i | \(0.227188\pi\) | |||||||
\(32\) | 3.71670 | 0.657026 | ||||||||
\(33\) | −3.82746 | −0.666275 | ||||||||
\(34\) | −3.78540 | −0.649191 | ||||||||
\(35\) | −2.31074 | −0.390586 | ||||||||
\(36\) | −0.692703 | −0.115451 | ||||||||
\(37\) | 3.32338 | 0.546361 | 0.273180 | − | 0.961963i | \(-0.411924\pi\) | ||||
0.273180 | + | 0.961963i | \(0.411924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.12491 | 0.660514 | ||||||||
\(40\) | −7.11420 | −1.12485 | ||||||||
\(41\) | 7.10106 | 1.10900 | 0.554500 | − | 0.832184i | \(-0.312910\pi\) | ||||
0.554500 | + | 0.832184i | \(0.312910\pi\) | |||||||
\(42\) | −1.14337 | −0.176426 | ||||||||
\(43\) | −5.75888 | −0.878221 | −0.439110 | − | 0.898433i | \(-0.644706\pi\) | ||||
−0.439110 | + | 0.898433i | \(0.644706\pi\) | |||||||
\(44\) | 2.65129 | 0.399697 | ||||||||
\(45\) | 2.31074 | 0.344464 | ||||||||
\(46\) | −8.34614 | −1.23057 | ||||||||
\(47\) | −0.140137 | −0.0204411 | −0.0102206 | − | 0.999948i | \(-0.503253\pi\) | ||||
−0.0102206 | + | 0.999948i | \(0.503253\pi\) | |||||||
\(48\) | −2.13476 | −0.308126 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.388181 | 0.0548971 | ||||||||
\(51\) | −3.31074 | −0.463596 | ||||||||
\(52\) | −2.85734 | −0.396241 | ||||||||
\(53\) | 13.9466 | 1.91571 | 0.957857 | − | 0.287246i | \(-0.0927398\pi\) | ||||
0.957857 | + | 0.287246i | \(0.0927398\pi\) | |||||||
\(54\) | 1.14337 | 0.155593 | ||||||||
\(55\) | −8.84425 | −1.19256 | ||||||||
\(56\) | 3.07876 | 0.411416 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.86873 | −0.639295 | ||||||||
\(59\) | −13.9651 | −1.81810 | −0.909049 | − | 0.416690i | \(-0.863190\pi\) | ||||
−0.909049 | + | 0.416690i | \(0.863190\pi\) | |||||||
\(60\) | −1.60065 | −0.206644 | ||||||||
\(61\) | −5.75901 | −0.737365 | −0.368683 | − | 0.929555i | \(-0.620191\pi\) | ||||
−0.368683 | + | 0.929555i | \(0.620191\pi\) | |||||||
\(62\) | 9.62446 | 1.22231 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 8.51908 | 1.06488 | ||||||||
\(65\) | 9.53157 | 1.18225 | ||||||||
\(66\) | −4.37621 | −0.538674 | ||||||||
\(67\) | −12.2720 | −1.49926 | −0.749630 | − | 0.661858i | \(-0.769768\pi\) | ||||
−0.749630 | + | 0.661858i | \(0.769768\pi\) | |||||||
\(68\) | 2.29336 | 0.278111 | ||||||||
\(69\) | −7.29960 | −0.878768 | ||||||||
\(70\) | −2.64203 | −0.315783 | ||||||||
\(71\) | −6.29536 | −0.747121 | −0.373561 | − | 0.927606i | \(-0.621863\pi\) | ||||
−0.373561 | + | 0.927606i | \(0.621863\pi\) | |||||||
\(72\) | −3.07876 | −0.362835 | ||||||||
\(73\) | −11.6138 | −1.35929 | −0.679643 | − | 0.733543i | \(-0.737865\pi\) | ||||
−0.679643 | + | 0.733543i | \(0.737865\pi\) | |||||||
\(74\) | 3.79986 | 0.441725 | ||||||||
\(75\) | 0.339506 | 0.0392028 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.82746 | 0.436179 | ||||||||
\(78\) | 4.71630 | 0.534016 | ||||||||
\(79\) | −13.3734 | −1.50463 | −0.752314 | − | 0.658804i | \(-0.771062\pi\) | ||||
−0.752314 | + | 0.658804i | \(0.771062\pi\) | |||||||
\(80\) | −4.93286 | −0.551511 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.11915 | 0.896610 | ||||||||
\(83\) | −13.1411 | −1.44242 | −0.721209 | − | 0.692718i | \(-0.756413\pi\) | ||||
−0.721209 | + | 0.692718i | \(0.756413\pi\) | |||||||
\(84\) | 0.692703 | 0.0755801 | ||||||||
\(85\) | −7.65024 | −0.829785 | ||||||||
\(86\) | −6.58453 | −0.710028 | ||||||||
\(87\) | −4.25822 | −0.456529 | ||||||||
\(88\) | 11.7838 | 1.25616 | ||||||||
\(89\) | −5.44718 | −0.577400 | −0.288700 | − | 0.957420i | \(-0.593223\pi\) | ||||
−0.288700 | + | 0.957420i | \(0.593223\pi\) | |||||||
\(90\) | 2.64203 | 0.278494 | ||||||||
\(91\) | −4.12491 | −0.432408 | ||||||||
\(92\) | 5.05645 | 0.527172 | ||||||||
\(93\) | 8.41762 | 0.872866 | ||||||||
\(94\) | −0.160229 | −0.0165263 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.71670 | 0.379334 | ||||||||
\(97\) | −2.60598 | −0.264597 | −0.132299 | − | 0.991210i | \(-0.542236\pi\) | ||||
−0.132299 | + | 0.991210i | \(0.542236\pi\) | |||||||
\(98\) | 1.14337 | 0.115498 | ||||||||
\(99\) | −3.82746 | −0.384674 | ||||||||
\(100\) | −0.235177 | −0.0235177 | ||||||||
\(101\) | 1.52918 | 0.152159 | 0.0760797 | − | 0.997102i | \(-0.475760\pi\) | ||||
0.0760797 | + | 0.997102i | \(0.475760\pi\) | |||||||
\(102\) | −3.78540 | −0.374810 | ||||||||
\(103\) | −18.1334 | −1.78674 | −0.893368 | − | 0.449326i | \(-0.851664\pi\) | ||||
−0.893368 | + | 0.449326i | \(0.851664\pi\) | |||||||
\(104\) | −12.6996 | −1.24530 | ||||||||
\(105\) | −2.31074 | −0.225505 | ||||||||
\(106\) | 15.9461 | 1.54883 | ||||||||
\(107\) | 1.96763 | 0.190218 | 0.0951091 | − | 0.995467i | \(-0.469680\pi\) | ||||
0.0951091 | + | 0.995467i | \(0.469680\pi\) | |||||||
\(108\) | −0.692703 | −0.0666554 | ||||||||
\(109\) | −16.2152 | −1.55313 | −0.776567 | − | 0.630034i | \(-0.783041\pi\) | ||||
−0.776567 | + | 0.630034i | \(0.783041\pi\) | |||||||
\(110\) | −10.1123 | −0.964166 | ||||||||
\(111\) | 3.32338 | 0.315442 | ||||||||
\(112\) | 2.13476 | 0.201715 | ||||||||
\(113\) | 14.1452 | 1.33067 | 0.665334 | − | 0.746546i | \(-0.268289\pi\) | ||||
0.665334 | + | 0.746546i | \(0.268289\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.8674 | −1.57290 | ||||||||
\(116\) | 2.94968 | 0.273871 | ||||||||
\(117\) | 4.12491 | 0.381348 | ||||||||
\(118\) | −15.9673 | −1.46990 | ||||||||
\(119\) | 3.31074 | 0.303495 | ||||||||
\(120\) | −7.11420 | −0.649435 | ||||||||
\(121\) | 3.64944 | 0.331768 | ||||||||
\(122\) | −6.58468 | −0.596149 | ||||||||
\(123\) | 7.10106 | 0.640281 | ||||||||
\(124\) | −5.83091 | −0.523631 | ||||||||
\(125\) | −10.7692 | −0.963224 | ||||||||
\(126\) | −1.14337 | −0.101860 | ||||||||
\(127\) | −8.64735 | −0.767329 | −0.383664 | − | 0.923473i | \(-0.625338\pi\) | ||||
−0.383664 | + | 0.923473i | \(0.625338\pi\) | |||||||
\(128\) | 2.30707 | 0.203918 | ||||||||
\(129\) | −5.75888 | −0.507041 | ||||||||
\(130\) | 10.8981 | 0.955829 | ||||||||
\(131\) | 13.3604 | 1.16731 | 0.583653 | − | 0.812004i | \(-0.301623\pi\) | ||||
0.583653 | + | 0.812004i | \(0.301623\pi\) | |||||||
\(132\) | 2.65129 | 0.230765 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.0314 | −1.21213 | ||||||||
\(135\) | 2.31074 | 0.198877 | ||||||||
\(136\) | 10.1930 | 0.874039 | ||||||||
\(137\) | 4.20944 | 0.359637 | 0.179819 | − | 0.983700i | \(-0.442449\pi\) | ||||
0.179819 | + | 0.983700i | \(0.442449\pi\) | |||||||
\(138\) | −8.34614 | −0.710471 | ||||||||
\(139\) | −5.35031 | −0.453807 | −0.226904 | − | 0.973917i | \(-0.572860\pi\) | ||||
−0.226904 | + | 0.973917i | \(0.572860\pi\) | |||||||
\(140\) | 1.60065 | 0.135280 | ||||||||
\(141\) | −0.140137 | −0.0118017 | ||||||||
\(142\) | −7.19793 | −0.604037 | ||||||||
\(143\) | −15.7879 | −1.32025 | ||||||||
\(144\) | −2.13476 | −0.177896 | ||||||||
\(145\) | −9.83963 | −0.817137 | ||||||||
\(146\) | −13.2788 | −1.09896 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −2.30212 | −0.189233 | ||||||||
\(149\) | 12.2291 | 1.00185 | 0.500925 | − | 0.865491i | \(-0.332993\pi\) | ||||
0.500925 | + | 0.865491i | \(0.332993\pi\) | |||||||
\(150\) | 0.388181 | 0.0316949 | ||||||||
\(151\) | 0.237459 | 0.0193241 | 0.00966206 | − | 0.999953i | \(-0.496924\pi\) | ||||
0.00966206 | + | 0.999953i | \(0.496924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.31074 | −0.267657 | ||||||||
\(154\) | 4.37621 | 0.352645 | ||||||||
\(155\) | 19.4509 | 1.56233 | ||||||||
\(156\) | −2.85734 | −0.228770 | ||||||||
\(157\) | 14.8067 | 1.18170 | 0.590851 | − | 0.806781i | \(-0.298792\pi\) | ||||
0.590851 | + | 0.806781i | \(0.298792\pi\) | |||||||
\(158\) | −15.2908 | −1.21647 | ||||||||
\(159\) | 13.9466 | 1.10604 | ||||||||
\(160\) | 8.58831 | 0.678966 | ||||||||
\(161\) | 7.29960 | 0.575289 | ||||||||
\(162\) | 1.14337 | 0.0898317 | ||||||||
\(163\) | −6.61997 | −0.518516 | −0.259258 | − | 0.965808i | \(-0.583478\pi\) | ||||
−0.259258 | + | 0.965808i | \(0.583478\pi\) | |||||||
\(164\) | −4.91893 | −0.384104 | ||||||||
\(165\) | −8.84425 | −0.688524 | ||||||||
\(166\) | −15.0251 | −1.16617 | ||||||||
\(167\) | −2.27563 | −0.176094 | −0.0880469 | − | 0.996116i | \(-0.528063\pi\) | ||||
−0.0880469 | + | 0.996116i | \(0.528063\pi\) | |||||||
\(168\) | 3.07876 | 0.237531 | ||||||||
\(169\) | 4.01485 | 0.308835 | ||||||||
\(170\) | −8.74706 | −0.670869 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.98919 | 0.304173 | ||||||||
\(173\) | 1.61272 | 0.122612 | 0.0613062 | − | 0.998119i | \(-0.480473\pi\) | ||||
0.0613062 | + | 0.998119i | \(0.480473\pi\) | |||||||
\(174\) | −4.86873 | −0.369097 | ||||||||
\(175\) | −0.339506 | −0.0256642 | ||||||||
\(176\) | 8.17069 | 0.615889 | ||||||||
\(177\) | −13.9651 | −1.04968 | ||||||||
\(178\) | −6.22815 | −0.466820 | ||||||||
\(179\) | 15.6750 | 1.17160 | 0.585802 | − | 0.810454i | \(-0.300780\pi\) | ||||
0.585802 | + | 0.810454i | \(0.300780\pi\) | |||||||
\(180\) | −1.60065 | −0.119306 | ||||||||
\(181\) | 0.292251 | 0.0217228 | 0.0108614 | − | 0.999941i | \(-0.496543\pi\) | ||||
0.0108614 | + | 0.999941i | \(0.496543\pi\) | |||||||
\(182\) | −4.71630 | −0.349595 | ||||||||
\(183\) | −5.75901 | −0.425718 | ||||||||
\(184\) | 22.4737 | 1.65678 | ||||||||
\(185\) | 7.67947 | 0.564606 | ||||||||
\(186\) | 9.62446 | 0.705699 | ||||||||
\(187\) | 12.6717 | 0.926647 | ||||||||
\(188\) | 0.0970735 | 0.00707982 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.76336 | −0.489380 | −0.244690 | − | 0.969601i | \(-0.578686\pi\) | ||||
−0.244690 | + | 0.969601i | \(0.578686\pi\) | |||||||
\(192\) | 8.51908 | 0.614811 | ||||||||
\(193\) | 10.4078 | 0.749172 | 0.374586 | − | 0.927192i | \(-0.377785\pi\) | ||||
0.374586 | + | 0.927192i | \(0.377785\pi\) | |||||||
\(194\) | −2.97960 | −0.213923 | ||||||||
\(195\) | 9.53157 | 0.682570 | ||||||||
\(196\) | −0.692703 | −0.0494788 | ||||||||
\(197\) | −3.81353 | −0.271702 | −0.135851 | − | 0.990729i | \(-0.543377\pi\) | ||||
−0.135851 | + | 0.990729i | \(0.543377\pi\) | |||||||
\(198\) | −4.37621 | −0.311003 | ||||||||
\(199\) | 3.43449 | 0.243464 | 0.121732 | − | 0.992563i | \(-0.461155\pi\) | ||||
0.121732 | + | 0.992563i | \(0.461155\pi\) | |||||||
\(200\) | −1.04526 | −0.0739108 | ||||||||
\(201\) | −12.2720 | −0.865598 | ||||||||
\(202\) | 1.74842 | 0.123019 | ||||||||
\(203\) | 4.25822 | 0.298868 | ||||||||
\(204\) | 2.29336 | 0.160567 | ||||||||
\(205\) | 16.4087 | 1.14603 | ||||||||
\(206\) | −20.7332 | −1.44455 | ||||||||
\(207\) | −7.29960 | −0.507357 | ||||||||
\(208\) | −8.80567 | −0.610563 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.64203 | −0.182317 | ||||||||
\(211\) | 2.67876 | 0.184413 | 0.0922067 | − | 0.995740i | \(-0.470608\pi\) | ||||
0.0922067 | + | 0.995740i | \(0.470608\pi\) | |||||||
\(212\) | −9.66086 | −0.663510 | ||||||||
\(213\) | −6.29536 | −0.431351 | ||||||||
\(214\) | 2.24973 | 0.153789 | ||||||||
\(215\) | −13.3073 | −0.907547 | ||||||||
\(216\) | −3.07876 | −0.209483 | ||||||||
\(217\) | −8.41762 | −0.571425 | ||||||||
\(218\) | −18.5400 | −1.25569 | ||||||||
\(219\) | −11.6138 | −0.784785 | ||||||||
\(220\) | 6.12644 | 0.413045 | ||||||||
\(221\) | −13.6565 | −0.918634 | ||||||||
\(222\) | 3.79986 | 0.255030 | ||||||||
\(223\) | −17.2704 | −1.15651 | −0.578256 | − | 0.815855i | \(-0.696267\pi\) | ||||
−0.578256 | + | 0.815855i | \(0.696267\pi\) | |||||||
\(224\) | −3.71670 | −0.248332 | ||||||||
\(225\) | 0.339506 | 0.0226337 | ||||||||
\(226\) | 16.1732 | 1.07583 | ||||||||
\(227\) | 7.62974 | 0.506404 | 0.253202 | − | 0.967413i | \(-0.418516\pi\) | ||||
0.253202 | + | 0.967413i | \(0.418516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.31366 | 0.152891 | 0.0764455 | − | 0.997074i | \(-0.475643\pi\) | ||||
0.0764455 | + | 0.997074i | \(0.475643\pi\) | |||||||
\(230\) | −19.2857 | −1.27166 | ||||||||
\(231\) | 3.82746 | 0.251828 | ||||||||
\(232\) | 13.1100 | 0.860716 | ||||||||
\(233\) | −5.70396 | −0.373679 | −0.186839 | − | 0.982390i | \(-0.559824\pi\) | ||||
−0.186839 | + | 0.982390i | \(0.559824\pi\) | |||||||
\(234\) | 4.71630 | 0.308314 | ||||||||
\(235\) | −0.323820 | −0.0211237 | ||||||||
\(236\) | 9.67365 | 0.629701 | ||||||||
\(237\) | −13.3734 | −0.868698 | ||||||||
\(238\) | 3.78540 | 0.245371 | ||||||||
\(239\) | 8.82770 | 0.571017 | 0.285508 | − | 0.958376i | \(-0.407838\pi\) | ||||
0.285508 | + | 0.958376i | \(0.407838\pi\) | |||||||
\(240\) | −4.93286 | −0.318415 | ||||||||
\(241\) | 29.2185 | 1.88213 | 0.941063 | − | 0.338231i | \(-0.109829\pi\) | ||||
0.941063 | + | 0.338231i | \(0.109829\pi\) | |||||||
\(242\) | 4.17267 | 0.268229 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.98928 | 0.255388 | ||||||||
\(245\) | 2.31074 | 0.147628 | ||||||||
\(246\) | 8.11915 | 0.517658 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −25.9158 | −1.64566 | ||||||||
\(249\) | −13.1411 | −0.832780 | ||||||||
\(250\) | −12.3132 | −0.778753 | ||||||||
\(251\) | −6.86118 | −0.433074 | −0.216537 | − | 0.976274i | \(-0.569476\pi\) | ||||
−0.216537 | + | 0.976274i | \(0.569476\pi\) | |||||||
\(252\) | 0.692703 | 0.0436362 | ||||||||
\(253\) | 27.9389 | 1.75650 | ||||||||
\(254\) | −9.88713 | −0.620374 | ||||||||
\(255\) | −7.65024 | −0.479077 | ||||||||
\(256\) | −14.4003 | −0.900020 | ||||||||
\(257\) | −1.60871 | −0.100348 | −0.0501741 | − | 0.998740i | \(-0.515978\pi\) | ||||
−0.0501741 | + | 0.998740i | \(0.515978\pi\) | |||||||
\(258\) | −6.58453 | −0.409935 | ||||||||
\(259\) | −3.32338 | −0.206505 | ||||||||
\(260\) | −6.60255 | −0.409473 | ||||||||
\(261\) | −4.25822 | −0.263577 | ||||||||
\(262\) | 15.2759 | 0.943749 | ||||||||
\(263\) | 18.4455 | 1.13740 | 0.568699 | − | 0.822545i | \(-0.307447\pi\) | ||||
0.568699 | + | 0.822545i | \(0.307447\pi\) | |||||||
\(264\) | 11.7838 | 0.725244 | ||||||||
\(265\) | 32.2269 | 1.97969 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.44718 | −0.333362 | ||||||||
\(268\) | 8.50083 | 0.519271 | ||||||||
\(269\) | 5.16887 | 0.315152 | 0.157576 | − | 0.987507i | \(-0.449632\pi\) | ||||
0.157576 | + | 0.987507i | \(0.449632\pi\) | |||||||
\(270\) | 2.64203 | 0.160789 | ||||||||
\(271\) | −17.5641 | −1.06694 | −0.533472 | − | 0.845818i | \(-0.679113\pi\) | ||||
−0.533472 | + | 0.845818i | \(0.679113\pi\) | |||||||
\(272\) | 7.06762 | 0.428537 | ||||||||
\(273\) | −4.12491 | −0.249651 | ||||||||
\(274\) | 4.81295 | 0.290761 | ||||||||
\(275\) | −1.29945 | −0.0783595 | ||||||||
\(276\) | 5.05645 | 0.304363 | ||||||||
\(277\) | −12.4135 | −0.745852 | −0.372926 | − | 0.927861i | \(-0.621645\pi\) | ||||
−0.372926 | + | 0.927861i | \(0.621645\pi\) | |||||||
\(278\) | −6.11739 | −0.366896 | ||||||||
\(279\) | 8.41762 | 0.503949 | ||||||||
\(280\) | 7.11420 | 0.425155 | ||||||||
\(281\) | −15.9626 | −0.952250 | −0.476125 | − | 0.879378i | \(-0.657959\pi\) | ||||
−0.476125 | + | 0.879378i | \(0.657959\pi\) | |||||||
\(282\) | −0.160229 | −0.00954149 | ||||||||
\(283\) | −19.4069 | −1.15362 | −0.576810 | − | 0.816878i | \(-0.695703\pi\) | ||||
−0.576810 | + | 0.816878i | \(0.695703\pi\) | |||||||
\(284\) | 4.36081 | 0.258767 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.0514 | −1.06740 | ||||||||
\(287\) | −7.10106 | −0.419162 | ||||||||
\(288\) | 3.71670 | 0.219009 | ||||||||
\(289\) | −6.03902 | −0.355236 | ||||||||
\(290\) | −11.2503 | −0.660643 | ||||||||
\(291\) | −2.60598 | −0.152765 | ||||||||
\(292\) | 8.04488 | 0.470791 | ||||||||
\(293\) | 12.3471 | 0.721323 | 0.360661 | − | 0.932697i | \(-0.382551\pi\) | ||||
0.360661 | + | 0.932697i | \(0.382551\pi\) | |||||||
\(294\) | 1.14337 | 0.0666827 | ||||||||
\(295\) | −32.2696 | −1.87881 | ||||||||
\(296\) | −10.2319 | −0.594717 | ||||||||
\(297\) | −3.82746 | −0.222092 | ||||||||
\(298\) | 13.9824 | 0.809981 | ||||||||
\(299\) | −30.1101 | −1.74131 | ||||||||
\(300\) | −0.235177 | −0.0135779 | ||||||||
\(301\) | 5.75888 | 0.331936 | ||||||||
\(302\) | 0.271503 | 0.0156233 | ||||||||
\(303\) | 1.52918 | 0.0878493 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.3075 | −0.761988 | ||||||||
\(306\) | −3.78540 | −0.216397 | ||||||||
\(307\) | −8.92723 | −0.509504 | −0.254752 | − | 0.967006i | \(-0.581994\pi\) | ||||
−0.254752 | + | 0.967006i | \(0.581994\pi\) | |||||||
\(308\) | −2.65129 | −0.151071 | ||||||||
\(309\) | −18.1334 | −1.03157 | ||||||||
\(310\) | 22.2396 | 1.26312 | ||||||||
\(311\) | 25.1416 | 1.42565 | 0.712825 | − | 0.701342i | \(-0.247415\pi\) | ||||
0.712825 | + | 0.701342i | \(0.247415\pi\) | |||||||
\(312\) | −12.6996 | −0.718973 | ||||||||
\(313\) | −13.1928 | −0.745702 | −0.372851 | − | 0.927891i | \(-0.621620\pi\) | ||||
−0.372851 | + | 0.927891i | \(0.621620\pi\) | |||||||
\(314\) | 16.9295 | 0.955388 | ||||||||
\(315\) | −2.31074 | −0.130195 | ||||||||
\(316\) | 9.26382 | 0.521130 | ||||||||
\(317\) | −5.70141 | −0.320223 | −0.160112 | − | 0.987099i | \(-0.551185\pi\) | ||||
−0.160112 | + | 0.987099i | \(0.551185\pi\) | |||||||
\(318\) | 15.9461 | 0.894215 | ||||||||
\(319\) | 16.2982 | 0.912522 | ||||||||
\(320\) | 19.6853 | 1.10044 | ||||||||
\(321\) | 1.96763 | 0.109823 | ||||||||
\(322\) | 8.34614 | 0.465112 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.692703 | −0.0384835 | ||||||||
\(325\) | 1.40043 | 0.0776819 | ||||||||
\(326\) | −7.56908 | −0.419212 | ||||||||
\(327\) | −16.2152 | −0.896703 | ||||||||
\(328\) | −21.8624 | −1.20715 | ||||||||
\(329\) | 0.140137 | 0.00772602 | ||||||||
\(330\) | −10.1123 | −0.556662 | ||||||||
\(331\) | −32.1319 | −1.76613 | −0.883064 | − | 0.469253i | \(-0.844523\pi\) | ||||
−0.883064 | + | 0.469253i | \(0.844523\pi\) | |||||||
\(332\) | 9.10285 | 0.499584 | ||||||||
\(333\) | 3.32338 | 0.182120 | ||||||||
\(334\) | −2.60189 | −0.142369 | ||||||||
\(335\) | −28.3573 | −1.54932 | ||||||||
\(336\) | 2.13476 | 0.116460 | ||||||||
\(337\) | 20.1482 | 1.09754 | 0.548771 | − | 0.835972i | \(-0.315096\pi\) | ||||
0.548771 | + | 0.835972i | \(0.315096\pi\) | |||||||
\(338\) | 4.59046 | 0.249688 | ||||||||
\(339\) | 14.1452 | 0.768262 | ||||||||
\(340\) | 5.29935 | 0.287397 | ||||||||
\(341\) | −32.2181 | −1.74471 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 17.7302 | 0.955948 | ||||||||
\(345\) | −16.8674 | −0.908113 | ||||||||
\(346\) | 1.84393 | 0.0991304 | ||||||||
\(347\) | 30.9762 | 1.66289 | 0.831444 | − | 0.555609i | \(-0.187515\pi\) | ||||
0.831444 | + | 0.555609i | \(0.187515\pi\) | |||||||
\(348\) | 2.94968 | 0.158120 | ||||||||
\(349\) | −13.1310 | −0.702889 | −0.351444 | − | 0.936209i | \(-0.614309\pi\) | ||||
−0.351444 | + | 0.936209i | \(0.614309\pi\) | |||||||
\(350\) | −0.388181 | −0.0207492 | ||||||||
\(351\) | 4.12491 | 0.220171 | ||||||||
\(352\) | −14.2255 | −0.758222 | ||||||||
\(353\) | −2.37288 | −0.126296 | −0.0631479 | − | 0.998004i | \(-0.520114\pi\) | ||||
−0.0631479 | + | 0.998004i | \(0.520114\pi\) | |||||||
\(354\) | −15.9673 | −0.848650 | ||||||||
\(355\) | −14.5469 | −0.772070 | ||||||||
\(356\) | 3.77328 | 0.199983 | ||||||||
\(357\) | 3.31074 | 0.175223 | ||||||||
\(358\) | 17.9223 | 0.947225 | ||||||||
\(359\) | 21.3112 | 1.12476 | 0.562380 | − | 0.826879i | \(-0.309886\pi\) | ||||
0.562380 | + | 0.826879i | \(0.309886\pi\) | |||||||
\(360\) | −7.11420 | −0.374951 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0.334151 | 0.0175626 | ||||||||
\(363\) | 3.64944 | 0.191546 | ||||||||
\(364\) | 2.85734 | 0.149765 | ||||||||
\(365\) | −26.8363 | −1.40468 | ||||||||
\(366\) | −6.58468 | −0.344187 | ||||||||
\(367\) | −0.568943 | −0.0296986 | −0.0148493 | − | 0.999890i | \(-0.504727\pi\) | ||||
−0.0148493 | + | 0.999890i | \(0.504727\pi\) | |||||||
\(368\) | 15.5829 | 0.812312 | ||||||||
\(369\) | 7.10106 | 0.369666 | ||||||||
\(370\) | 8.78048 | 0.456475 | ||||||||
\(371\) | −13.9466 | −0.724072 | ||||||||
\(372\) | −5.83091 | −0.302319 | ||||||||
\(373\) | −7.29725 | −0.377837 | −0.188919 | − | 0.981993i | \(-0.560498\pi\) | ||||
−0.188919 | + | 0.981993i | \(0.560498\pi\) | |||||||
\(374\) | 14.4885 | 0.749181 | ||||||||
\(375\) | −10.7692 | −0.556118 | ||||||||
\(376\) | 0.431449 | 0.0222503 | ||||||||
\(377\) | −17.5648 | −0.904631 | ||||||||
\(378\) | −1.14337 | −0.0588087 | ||||||||
\(379\) | 36.0003 | 1.84921 | 0.924606 | − | 0.380925i | \(-0.124394\pi\) | ||||
0.924606 | + | 0.380925i | \(0.124394\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.64735 | −0.443017 | ||||||||
\(382\) | −7.73303 | −0.395656 | ||||||||
\(383\) | 4.26136 | 0.217745 | 0.108873 | − | 0.994056i | \(-0.465276\pi\) | ||||
0.108873 | + | 0.994056i | \(0.465276\pi\) | |||||||
\(384\) | 2.30707 | 0.117732 | ||||||||
\(385\) | 8.84425 | 0.450745 | ||||||||
\(386\) | 11.9000 | 0.605694 | ||||||||
\(387\) | −5.75888 | −0.292740 | ||||||||
\(388\) | 1.80517 | 0.0916436 | ||||||||
\(389\) | −36.7023 | −1.86088 | −0.930440 | − | 0.366445i | \(-0.880575\pi\) | ||||
−0.930440 | + | 0.366445i | \(0.880575\pi\) | |||||||
\(390\) | 10.8981 | 0.551848 | ||||||||
\(391\) | 24.1670 | 1.22218 | ||||||||
\(392\) | −3.07876 | −0.155501 | ||||||||
\(393\) | 13.3604 | 0.673944 | ||||||||
\(394\) | −4.36027 | −0.219667 | ||||||||
\(395\) | −30.9025 | −1.55487 | ||||||||
\(396\) | 2.65129 | 0.133232 | ||||||||
\(397\) | −34.6530 | −1.73919 | −0.869593 | − | 0.493770i | \(-0.835619\pi\) | ||||
−0.869593 | + | 0.493770i | \(0.835619\pi\) | |||||||
\(398\) | 3.92689 | 0.196837 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.724763 | −0.0362381 | ||||||||
\(401\) | −29.9894 | −1.49760 | −0.748798 | − | 0.662798i | \(-0.769369\pi\) | ||||
−0.748798 | + | 0.662798i | \(0.769369\pi\) | |||||||
\(402\) | −14.0314 | −0.699823 | ||||||||
\(403\) | 34.7219 | 1.72962 | ||||||||
\(404\) | −1.05927 | −0.0527007 | ||||||||
\(405\) | 2.31074 | 0.114821 | ||||||||
\(406\) | 4.86873 | 0.241631 | ||||||||
\(407\) | −12.7201 | −0.630513 | ||||||||
\(408\) | 10.1930 | 0.504627 | ||||||||
\(409\) | 19.0836 | 0.943621 | 0.471811 | − | 0.881700i | \(-0.343601\pi\) | ||||
0.471811 | + | 0.881700i | \(0.343601\pi\) | |||||||
\(410\) | 18.7612 | 0.926550 | ||||||||
\(411\) | 4.20944 | 0.207637 | ||||||||
\(412\) | 12.5611 | 0.618839 | ||||||||
\(413\) | 13.9651 | 0.687176 | ||||||||
\(414\) | −8.34614 | −0.410191 | ||||||||
\(415\) | −30.3655 | −1.49058 | ||||||||
\(416\) | 15.3310 | 0.751666 | ||||||||
\(417\) | −5.35031 | −0.262006 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.57241 | −0.223377 | −0.111688 | − | 0.993743i | \(-0.535626\pi\) | ||||
−0.111688 | + | 0.993743i | \(0.535626\pi\) | |||||||
\(420\) | 1.60065 | 0.0781040 | ||||||||
\(421\) | 2.43380 | 0.118616 | 0.0593082 | − | 0.998240i | \(-0.481111\pi\) | ||||
0.0593082 | + | 0.998240i | \(0.481111\pi\) | |||||||
\(422\) | 3.06282 | 0.149096 | ||||||||
\(423\) | −0.140137 | −0.00681371 | ||||||||
\(424\) | −42.9382 | −2.08526 | ||||||||
\(425\) | −1.12402 | −0.0545227 | ||||||||
\(426\) | −7.19793 | −0.348741 | ||||||||
\(427\) | 5.75901 | 0.278698 | ||||||||
\(428\) | −1.36298 | −0.0658824 | ||||||||
\(429\) | −15.7879 | −0.762248 | ||||||||
\(430\) | −15.2151 | −0.733738 | ||||||||
\(431\) | 31.8687 | 1.53506 | 0.767530 | − | 0.641013i | \(-0.221486\pi\) | ||||
0.767530 | + | 0.641013i | \(0.221486\pi\) | |||||||
\(432\) | −2.13476 | −0.102709 | ||||||||
\(433\) | −38.8760 | −1.86826 | −0.934131 | − | 0.356931i | \(-0.883823\pi\) | ||||
−0.934131 | + | 0.356931i | \(0.883823\pi\) | |||||||
\(434\) | −9.62446 | −0.461989 | ||||||||
\(435\) | −9.83963 | −0.471774 | ||||||||
\(436\) | 11.2323 | 0.537931 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −13.2788 | −0.634487 | ||||||||
\(439\) | −13.6766 | −0.652747 | −0.326374 | − | 0.945241i | \(-0.605827\pi\) | ||||
−0.326374 | + | 0.945241i | \(0.605827\pi\) | |||||||
\(440\) | 27.2293 | 1.29811 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −15.6144 | −0.742702 | ||||||||
\(443\) | 41.2201 | 1.95843 | 0.979214 | − | 0.202831i | \(-0.0650142\pi\) | ||||
0.979214 | + | 0.202831i | \(0.0650142\pi\) | |||||||
\(444\) | −2.30212 | −0.109254 | ||||||||
\(445\) | −12.5870 | −0.596681 | ||||||||
\(446\) | −19.7465 | −0.935024 | ||||||||
\(447\) | 12.2291 | 0.578419 | ||||||||
\(448\) | −8.51908 | −0.402489 | ||||||||
\(449\) | −4.35463 | −0.205508 | −0.102754 | − | 0.994707i | \(-0.532765\pi\) | ||||
−0.102754 | + | 0.994707i | \(0.532765\pi\) | |||||||
\(450\) | 0.388181 | 0.0182990 | ||||||||
\(451\) | −27.1790 | −1.27981 | ||||||||
\(452\) | −9.79842 | −0.460879 | ||||||||
\(453\) | 0.237459 | 0.0111568 | ||||||||
\(454\) | 8.72363 | 0.409420 | ||||||||
\(455\) | −9.53157 | −0.446847 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.12125 | 0.239562 | 0.119781 | − | 0.992800i | \(-0.461781\pi\) | ||||
0.119781 | + | 0.992800i | \(0.461781\pi\) | |||||||
\(458\) | 2.64537 | 0.123610 | ||||||||
\(459\) | −3.31074 | −0.154532 | ||||||||
\(460\) | 11.6841 | 0.544775 | ||||||||
\(461\) | 14.7013 | 0.684708 | 0.342354 | − | 0.939571i | \(-0.388776\pi\) | ||||
0.342354 | + | 0.939571i | \(0.388776\pi\) | |||||||
\(462\) | 4.37621 | 0.203599 | ||||||||
\(463\) | 24.5665 | 1.14170 | 0.570851 | − | 0.821053i | \(-0.306613\pi\) | ||||
0.570851 | + | 0.821053i | \(0.306613\pi\) | |||||||
\(464\) | 9.09026 | 0.422005 | ||||||||
\(465\) | 19.4509 | 0.902014 | ||||||||
\(466\) | −6.52174 | −0.302114 | ||||||||
\(467\) | 30.8040 | 1.42544 | 0.712719 | − | 0.701449i | \(-0.247463\pi\) | ||||
0.712719 | + | 0.701449i | \(0.247463\pi\) | |||||||
\(468\) | −2.85734 | −0.132080 | ||||||||
\(469\) | 12.2720 | 0.566667 | ||||||||
\(470\) | −0.370247 | −0.0170782 | ||||||||
\(471\) | 14.8067 | 0.682256 | ||||||||
\(472\) | 42.9951 | 1.97901 | ||||||||
\(473\) | 22.0419 | 1.01349 | ||||||||
\(474\) | −15.2908 | −0.702329 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.29336 | −0.105116 | ||||||||
\(477\) | 13.9466 | 0.638571 | ||||||||
\(478\) | 10.0933 | 0.461658 | ||||||||
\(479\) | 8.08205 | 0.369279 | 0.184639 | − | 0.982806i | \(-0.440888\pi\) | ||||
0.184639 | + | 0.982806i | \(0.440888\pi\) | |||||||
\(480\) | 8.58831 | 0.392001 | ||||||||
\(481\) | 13.7086 | 0.625061 | ||||||||
\(482\) | 33.4075 | 1.52167 | ||||||||
\(483\) | 7.29960 | 0.332143 | ||||||||
\(484\) | −2.52798 | −0.114908 | ||||||||
\(485\) | −6.02173 | −0.273433 | ||||||||
\(486\) | 1.14337 | 0.0518644 | ||||||||
\(487\) | 33.0673 | 1.49842 | 0.749211 | − | 0.662332i | \(-0.230433\pi\) | ||||
0.749211 | + | 0.662332i | \(0.230433\pi\) | |||||||
\(488\) | 17.7306 | 0.802626 | ||||||||
\(489\) | −6.61997 | −0.299365 | ||||||||
\(490\) | 2.64203 | 0.119355 | ||||||||
\(491\) | −3.82131 | −0.172453 | −0.0862266 | − | 0.996276i | \(-0.527481\pi\) | ||||
−0.0862266 | + | 0.996276i | \(0.527481\pi\) | |||||||
\(492\) | −4.91893 | −0.221762 | ||||||||
\(493\) | 14.0978 | 0.634935 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.84425 | −0.397520 | ||||||||
\(496\) | −17.9696 | −0.806857 | ||||||||
\(497\) | 6.29536 | 0.282385 | ||||||||
\(498\) | −15.0251 | −0.673291 | ||||||||
\(499\) | 32.3677 | 1.44898 | 0.724489 | − | 0.689286i | \(-0.242076\pi\) | ||||
0.724489 | + | 0.689286i | \(0.242076\pi\) | |||||||
\(500\) | 7.45984 | 0.333614 | ||||||||
\(501\) | −2.27563 | −0.101668 | ||||||||
\(502\) | −7.84488 | −0.350134 | ||||||||
\(503\) | −7.13720 | −0.318232 | −0.159116 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159116 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(504\) | 3.07876 | 0.137139 | ||||||||
\(505\) | 3.53354 | 0.157241 | ||||||||
\(506\) | 31.9445 | 1.42011 | ||||||||
\(507\) | 4.01485 | 0.178306 | ||||||||
\(508\) | 5.99005 | 0.265765 | ||||||||
\(509\) | −33.8240 | −1.49922 | −0.749612 | − | 0.661877i | \(-0.769760\pi\) | ||||
−0.749612 | + | 0.661877i | \(0.769760\pi\) | |||||||
\(510\) | −8.74706 | −0.387327 | ||||||||
\(511\) | 11.6138 | 0.513762 | ||||||||
\(512\) | −21.0790 | −0.931571 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.83935 | −0.0811301 | ||||||||
\(515\) | −41.9015 | −1.84640 | ||||||||
\(516\) | 3.98919 | 0.175614 | ||||||||
\(517\) | 0.536370 | 0.0235895 | ||||||||
\(518\) | −3.79986 | −0.166956 | ||||||||
\(519\) | 1.61272 | 0.0707903 | ||||||||
\(520\) | −29.3454 | −1.28688 | ||||||||
\(521\) | −13.3647 | −0.585518 | −0.292759 | − | 0.956186i | \(-0.594573\pi\) | ||||
−0.292759 | + | 0.956186i | \(0.594573\pi\) | |||||||
\(522\) | −4.86873 | −0.213098 | ||||||||
\(523\) | 10.9315 | 0.478002 | 0.239001 | − | 0.971019i | \(-0.423180\pi\) | ||||
0.239001 | + | 0.971019i | \(0.423180\pi\) | |||||||
\(524\) | −9.25480 | −0.404298 | ||||||||
\(525\) | −0.339506 | −0.0148173 | ||||||||
\(526\) | 21.0901 | 0.919570 | ||||||||
\(527\) | −27.8685 | −1.21397 | ||||||||
\(528\) | 8.17069 | 0.355584 | ||||||||
\(529\) | 30.2841 | 1.31670 | ||||||||
\(530\) | 36.8473 | 1.60055 | ||||||||
\(531\) | −13.9651 | −0.606032 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.2912 | 1.26874 | ||||||||
\(534\) | −6.22815 | −0.269518 | ||||||||
\(535\) | 4.54668 | 0.196570 | ||||||||
\(536\) | 37.7824 | 1.63195 | ||||||||
\(537\) | 15.6750 | 0.676426 | ||||||||
\(538\) | 5.90994 | 0.254795 | ||||||||
\(539\) | −3.82746 | −0.164860 | ||||||||
\(540\) | −1.60065 | −0.0688812 | ||||||||
\(541\) | −32.4127 | −1.39353 | −0.696766 | − | 0.717299i | \(-0.745378\pi\) | ||||
−0.696766 | + | 0.717299i | \(0.745378\pi\) | |||||||
\(542\) | −20.0823 | −0.862608 | ||||||||
\(543\) | 0.292251 | 0.0125417 | ||||||||
\(544\) | −12.3050 | −0.527573 | ||||||||
\(545\) | −37.4691 | −1.60500 | ||||||||
\(546\) | −4.71630 | −0.201839 | ||||||||
\(547\) | 35.2365 | 1.50660 | 0.753301 | − | 0.657676i | \(-0.228460\pi\) | ||||
0.753301 | + | 0.657676i | \(0.228460\pi\) | |||||||
\(548\) | −2.91589 | −0.124561 | ||||||||
\(549\) | −5.75901 | −0.245788 | ||||||||
\(550\) | −1.48575 | −0.0633525 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 22.4737 | 0.956544 | ||||||||
\(553\) | 13.3734 | 0.568696 | ||||||||
\(554\) | −14.1932 | −0.603010 | ||||||||
\(555\) | 7.67947 | 0.325975 | ||||||||
\(556\) | 3.70617 | 0.157177 | ||||||||
\(557\) | 0.695473 | 0.0294681 | 0.0147341 | − | 0.999891i | \(-0.495310\pi\) | ||||
0.0147341 | + | 0.999891i | \(0.495310\pi\) | |||||||
\(558\) | 9.62446 | 0.407436 | ||||||||
\(559\) | −23.7548 | −1.00472 | ||||||||
\(560\) | 4.93286 | 0.208451 | ||||||||
\(561\) | 12.6717 | 0.535000 | ||||||||
\(562\) | −18.2512 | −0.769880 | ||||||||
\(563\) | −4.08062 | −0.171977 | −0.0859887 | − | 0.996296i | \(-0.527405\pi\) | ||||
−0.0859887 | + | 0.996296i | \(0.527405\pi\) | |||||||
\(564\) | 0.0970735 | 0.00408753 | ||||||||
\(565\) | 32.6858 | 1.37510 | ||||||||
\(566\) | −22.1893 | −0.932685 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 19.3819 | 0.813246 | ||||||||
\(569\) | 21.4625 | 0.899755 | 0.449878 | − | 0.893090i | \(-0.351468\pi\) | ||||
0.449878 | + | 0.893090i | \(0.351468\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5520 | 0.734530 | 0.367265 | − | 0.930116i | \(-0.380294\pi\) | ||||
0.367265 | + | 0.930116i | \(0.380294\pi\) | |||||||
\(572\) | 10.9363 | 0.457271 | ||||||||
\(573\) | −6.76336 | −0.282544 | ||||||||
\(574\) | −8.11915 | −0.338887 | ||||||||
\(575\) | −2.47826 | −0.103350 | ||||||||
\(576\) | 8.51908 | 0.354962 | ||||||||
\(577\) | 35.3442 | 1.47140 | 0.735699 | − | 0.677308i | \(-0.236854\pi\) | ||||
0.735699 | + | 0.677308i | \(0.236854\pi\) | |||||||
\(578\) | −6.90484 | −0.287203 | ||||||||
\(579\) | 10.4078 | 0.432535 | ||||||||
\(580\) | 6.81594 | 0.283017 | ||||||||
\(581\) | 13.1411 | 0.545183 | ||||||||
\(582\) | −2.97960 | −0.123508 | ||||||||
\(583\) | −53.3801 | −2.21078 | ||||||||
\(584\) | 35.7559 | 1.47959 | ||||||||
\(585\) | 9.53157 | 0.394082 | ||||||||
\(586\) | 14.1173 | 0.583179 | ||||||||
\(587\) | −25.3110 | −1.04470 | −0.522348 | − | 0.852732i | \(-0.674944\pi\) | ||||
−0.522348 | + | 0.852732i | \(0.674944\pi\) | |||||||
\(588\) | −0.692703 | −0.0285666 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −36.8961 | −1.51899 | ||||||||
\(591\) | −3.81353 | −0.156867 | ||||||||
\(592\) | −7.09461 | −0.291587 | ||||||||
\(593\) | 37.7609 | 1.55065 | 0.775327 | − | 0.631559i | \(-0.217585\pi\) | ||||
0.775327 | + | 0.631559i | \(0.217585\pi\) | |||||||
\(594\) | −4.37621 | −0.179558 | ||||||||
\(595\) | 7.65024 | 0.313629 | ||||||||
\(596\) | −8.47117 | −0.346992 | ||||||||
\(597\) | 3.43449 | 0.140564 | ||||||||
\(598\) | −34.4271 | −1.40783 | ||||||||
\(599\) | −8.70691 | −0.355755 | −0.177877 | − | 0.984053i | \(-0.556923\pi\) | ||||
−0.177877 | + | 0.984053i | \(0.556923\pi\) | |||||||
\(600\) | −1.04526 | −0.0426724 | ||||||||
\(601\) | 1.02636 | 0.0418661 | 0.0209330 | − | 0.999781i | \(-0.493336\pi\) | ||||
0.0209330 | + | 0.999781i | \(0.493336\pi\) | |||||||
\(602\) | 6.58453 | 0.268366 | ||||||||
\(603\) | −12.2720 | −0.499753 | ||||||||
\(604\) | −0.164488 | −0.00669294 | ||||||||
\(605\) | 8.43291 | 0.342846 | ||||||||
\(606\) | 1.74842 | 0.0710249 | ||||||||
\(607\) | −7.38240 | −0.299642 | −0.149821 | − | 0.988713i | \(-0.547870\pi\) | ||||
−0.149821 | + | 0.988713i | \(0.547870\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.25822 | 0.172552 | ||||||||
\(610\) | −15.2155 | −0.616056 | ||||||||
\(611\) | −0.578053 | −0.0233855 | ||||||||
\(612\) | 2.29336 | 0.0927035 | ||||||||
\(613\) | 27.8123 | 1.12333 | 0.561663 | − | 0.827366i | \(-0.310162\pi\) | ||||
0.561663 | + | 0.827366i | \(0.310162\pi\) | |||||||
\(614\) | −10.2071 | −0.411926 | ||||||||
\(615\) | 16.4087 | 0.661662 | ||||||||
\(616\) | −11.7838 | −0.474784 | ||||||||
\(617\) | 17.6673 | 0.711260 | 0.355630 | − | 0.934627i | \(-0.384266\pi\) | ||||
0.355630 | + | 0.934627i | \(0.384266\pi\) | |||||||
\(618\) | −20.7332 | −0.834011 | ||||||||
\(619\) | 9.05361 | 0.363895 | 0.181948 | − | 0.983308i | \(-0.441760\pi\) | ||||
0.181948 | + | 0.983308i | \(0.441760\pi\) | |||||||
\(620\) | −13.4737 | −0.541117 | ||||||||
\(621\) | −7.29960 | −0.292923 | ||||||||
\(622\) | 28.7462 | 1.15262 | ||||||||
\(623\) | 5.44718 | 0.218237 | ||||||||
\(624\) | −8.80567 | −0.352509 | ||||||||
\(625\) | −26.5823 | −1.06329 | ||||||||
\(626\) | −15.0843 | −0.602889 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.2566 | −0.409284 | ||||||||
\(629\) | −11.0029 | −0.438712 | ||||||||
\(630\) | −2.64203 | −0.105261 | ||||||||
\(631\) | −1.10545 | −0.0440071 | −0.0220036 | − | 0.999758i | \(-0.507005\pi\) | ||||
−0.0220036 | + | 0.999758i | \(0.507005\pi\) | |||||||
\(632\) | 41.1736 | 1.63780 | ||||||||
\(633\) | 2.67876 | 0.106471 | ||||||||
\(634\) | −6.51883 | −0.258896 | ||||||||
\(635\) | −19.9818 | −0.792952 | ||||||||
\(636\) | −9.66086 | −0.383078 | ||||||||
\(637\) | 4.12491 | 0.163435 | ||||||||
\(638\) | 18.6348 | 0.737761 | ||||||||
\(639\) | −6.29536 | −0.249040 | ||||||||
\(640\) | 5.33103 | 0.210727 | ||||||||
\(641\) | 21.5483 | 0.851106 | 0.425553 | − | 0.904934i | \(-0.360080\pi\) | ||||
0.425553 | + | 0.904934i | \(0.360080\pi\) | |||||||
\(642\) | 2.24973 | 0.0887899 | ||||||||
\(643\) | −41.9439 | −1.65411 | −0.827053 | − | 0.562124i | \(-0.809984\pi\) | ||||
−0.827053 | + | 0.562124i | \(0.809984\pi\) | |||||||
\(644\) | −5.05645 | −0.199252 | ||||||||
\(645\) | −13.3073 | −0.523973 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.78996 | 0.345569 | 0.172784 | − | 0.984960i | \(-0.444724\pi\) | ||||
0.172784 | + | 0.984960i | \(0.444724\pi\) | |||||||
\(648\) | −3.07876 | −0.120945 | ||||||||
\(649\) | 53.4507 | 2.09812 | ||||||||
\(650\) | 1.60121 | 0.0628047 | ||||||||
\(651\) | −8.41762 | −0.329912 | ||||||||
\(652\) | 4.58567 | 0.179589 | ||||||||
\(653\) | −15.4159 | −0.603270 | −0.301635 | − | 0.953424i | \(-0.597532\pi\) | ||||
−0.301635 | + | 0.953424i | \(0.597532\pi\) | |||||||
\(654\) | −18.5400 | −0.724971 | ||||||||
\(655\) | 30.8724 | 1.20628 | ||||||||
\(656\) | −15.1590 | −0.591861 | ||||||||
\(657\) | −11.6138 | −0.453096 | ||||||||
\(658\) | 0.160229 | 0.00624637 | ||||||||
\(659\) | −27.6618 | −1.07755 | −0.538775 | − | 0.842449i | \(-0.681113\pi\) | ||||
−0.538775 | + | 0.842449i | \(0.681113\pi\) | |||||||
\(660\) | 6.12644 | 0.238471 | ||||||||
\(661\) | 14.4566 | 0.562296 | 0.281148 | − | 0.959664i | \(-0.409285\pi\) | ||||
0.281148 | + | 0.959664i | \(0.409285\pi\) | |||||||
\(662\) | −36.7386 | −1.42789 | ||||||||
\(663\) | −13.6565 | −0.530374 | ||||||||
\(664\) | 40.4581 | 1.57008 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.79986 | 0.147242 | ||||||||
\(667\) | 31.0833 | 1.20355 | ||||||||
\(668\) | 1.57634 | 0.0609903 | ||||||||
\(669\) | −17.2704 | −0.667713 | ||||||||
\(670\) | −32.4229 | −1.25261 | ||||||||
\(671\) | 22.0424 | 0.850936 | ||||||||
\(672\) | −3.71670 | −0.143375 | ||||||||
\(673\) | −18.6438 | −0.718664 | −0.359332 | − | 0.933210i | \(-0.616995\pi\) | ||||
−0.359332 | + | 0.933210i | \(0.616995\pi\) | |||||||
\(674\) | 23.0369 | 0.887347 | ||||||||
\(675\) | 0.339506 | 0.0130676 | ||||||||
\(676\) | −2.78110 | −0.106965 | ||||||||
\(677\) | 15.8037 | 0.607386 | 0.303693 | − | 0.952770i | \(-0.401780\pi\) | ||||
0.303693 | + | 0.952770i | \(0.401780\pi\) | |||||||
\(678\) | 16.1732 | 0.621128 | ||||||||
\(679\) | 2.60598 | 0.100008 | ||||||||
\(680\) | 23.5532 | 0.903226 | ||||||||
\(681\) | 7.62974 | 0.292372 | ||||||||
\(682\) | −36.8372 | −1.41057 | ||||||||
\(683\) | −39.7638 | −1.52152 | −0.760760 | − | 0.649033i | \(-0.775174\pi\) | ||||
−0.760760 | + | 0.649033i | \(0.775174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.72692 | 0.371646 | ||||||||
\(686\) | −1.14337 | −0.0436541 | ||||||||
\(687\) | 2.31366 | 0.0882717 | ||||||||
\(688\) | 12.2938 | 0.468697 | ||||||||
\(689\) | 57.5284 | 2.19166 | ||||||||
\(690\) | −19.2857 | −0.734196 | ||||||||
\(691\) | −35.6119 | −1.35474 | −0.677371 | − | 0.735642i | \(-0.736881\pi\) | ||||
−0.677371 | + | 0.735642i | \(0.736881\pi\) | |||||||
\(692\) | −1.11713 | −0.0424670 | ||||||||
\(693\) | 3.82746 | 0.145393 | ||||||||
\(694\) | 35.4173 | 1.34442 | ||||||||
\(695\) | −12.3632 | −0.468961 | ||||||||
\(696\) | 13.1100 | 0.496934 | ||||||||
\(697\) | −23.5097 | −0.890495 | ||||||||
\(698\) | −15.0137 | −0.568275 | ||||||||
\(699\) | −5.70396 | −0.215743 | ||||||||
\(700\) | 0.235177 | 0.00888885 | ||||||||
\(701\) | −19.1094 | −0.721751 | −0.360876 | − | 0.932614i | \(-0.617522\pi\) | ||||
−0.360876 | + | 0.932614i | \(0.617522\pi\) | |||||||
\(702\) | 4.71630 | 0.178005 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −32.6064 | −1.22890 | ||||||||
\(705\) | −0.323820 | −0.0121958 | ||||||||
\(706\) | −2.71309 | −0.102108 | ||||||||
\(707\) | −1.52918 | −0.0575109 | ||||||||
\(708\) | 9.67365 | 0.363558 | ||||||||
\(709\) | −46.0824 | −1.73066 | −0.865330 | − | 0.501202i | \(-0.832891\pi\) | ||||
−0.865330 | + | 0.501202i | \(0.832891\pi\) | |||||||
\(710\) | −16.6325 | −0.624207 | ||||||||
\(711\) | −13.3734 | −0.501543 | ||||||||
\(712\) | 16.7706 | 0.628503 | ||||||||
\(713\) | −61.4452 | −2.30114 | ||||||||
\(714\) | 3.78540 | 0.141665 | ||||||||
\(715\) | −36.4817 | −1.36434 | ||||||||
\(716\) | −10.8581 | −0.405787 | ||||||||
\(717\) | 8.82770 | 0.329677 | ||||||||
\(718\) | 24.3666 | 0.909353 | ||||||||
\(719\) | 30.4417 | 1.13528 | 0.567642 | − | 0.823275i | \(-0.307856\pi\) | ||||
0.567642 | + | 0.823275i | \(0.307856\pi\) | |||||||
\(720\) | −4.93286 | −0.183837 | ||||||||
\(721\) | 18.1334 | 0.675323 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.2185 | 1.08665 | ||||||||
\(724\) | −0.202443 | −0.00752373 | ||||||||
\(725\) | −1.44569 | −0.0536916 | ||||||||
\(726\) | 4.17267 | 0.154862 | ||||||||
\(727\) | −43.2668 | −1.60468 | −0.802339 | − | 0.596869i | \(-0.796411\pi\) | ||||
−0.802339 | + | 0.596869i | \(0.796411\pi\) | |||||||
\(728\) | 12.6996 | 0.470678 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −30.6839 | −1.13566 | ||||||||
\(731\) | 19.0661 | 0.705186 | ||||||||
\(732\) | 3.98928 | 0.147448 | ||||||||
\(733\) | 51.6443 | 1.90753 | 0.953763 | − | 0.300559i | \(-0.0971733\pi\) | ||||
0.953763 | + | 0.300559i | \(0.0971733\pi\) | |||||||
\(734\) | −0.650513 | −0.0240109 | ||||||||
\(735\) | 2.31074 | 0.0852328 | ||||||||
\(736\) | −27.1304 | −1.00004 | ||||||||
\(737\) | 46.9704 | 1.73018 | ||||||||
\(738\) | 8.11915 | 0.298870 | ||||||||
\(739\) | −0.861365 | −0.0316858 | −0.0158429 | − | 0.999874i | \(-0.505043\pi\) | ||||
−0.0158429 | + | 0.999874i | \(0.505043\pi\) | |||||||
\(740\) | −5.31959 | −0.195552 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.9461 | −0.585401 | ||||||||
\(743\) | −21.4297 | −0.786180 | −0.393090 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393090 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(744\) | −25.9158 | −0.950119 | ||||||||
\(745\) | 28.2583 | 1.03531 | ||||||||
\(746\) | −8.34347 | −0.305476 | ||||||||
\(747\) | −13.1411 | −0.480806 | ||||||||
\(748\) | −8.77773 | −0.320946 | ||||||||
\(749\) | −1.96763 | −0.0718957 | ||||||||
\(750\) | −12.3132 | −0.449613 | ||||||||
\(751\) | 1.42871 | 0.0521345 | 0.0260672 | − | 0.999660i | \(-0.491702\pi\) | ||||
0.0260672 | + | 0.999660i | \(0.491702\pi\) | |||||||
\(752\) | 0.299159 | 0.0109092 | ||||||||
\(753\) | −6.86118 | −0.250035 | ||||||||
\(754\) | −20.0830 | −0.731381 | ||||||||
\(755\) | 0.548705 | 0.0199694 | ||||||||
\(756\) | 0.692703 | 0.0251934 | ||||||||
\(757\) | 18.0813 | 0.657176 | 0.328588 | − | 0.944473i | \(-0.393427\pi\) | ||||
0.328588 | + | 0.944473i | \(0.393427\pi\) | |||||||
\(758\) | 41.1617 | 1.49506 | ||||||||
\(759\) | 27.9389 | 1.01412 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0824 | 1.01799 | 0.508993 | − | 0.860771i | \(-0.330018\pi\) | ||||
0.508993 | + | 0.860771i | \(0.330018\pi\) | |||||||
\(762\) | −9.88713 | −0.358173 | ||||||||
\(763\) | 16.2152 | 0.587030 | ||||||||
\(764\) | 4.68500 | 0.169497 | ||||||||
\(765\) | −7.65024 | −0.276595 | ||||||||
\(766\) | 4.87232 | 0.176044 | ||||||||
\(767\) | −57.6046 | −2.07998 | ||||||||
\(768\) | −14.4003 | −0.519627 | ||||||||
\(769\) | −24.9615 | −0.900135 | −0.450068 | − | 0.892994i | \(-0.648600\pi\) | ||||
−0.450068 | + | 0.892994i | \(0.648600\pi\) | |||||||
\(770\) | 10.1123 | 0.364421 | ||||||||
\(771\) | −1.60871 | −0.0579361 | ||||||||
\(772\) | −7.20954 | −0.259477 | ||||||||
\(773\) | 18.6401 | 0.670438 | 0.335219 | − | 0.942140i | \(-0.391190\pi\) | ||||
0.335219 | + | 0.942140i | \(0.391190\pi\) | |||||||
\(774\) | −6.58453 | −0.236676 | ||||||||
\(775\) | 2.85783 | 0.102656 | ||||||||
\(776\) | 8.02318 | 0.288015 | ||||||||
\(777\) | −3.32338 | −0.119226 | ||||||||
\(778\) | −41.9643 | −1.50449 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −6.60255 | −0.236409 | ||||||||
\(781\) | 24.0952 | 0.862195 | ||||||||
\(782\) | 27.6319 | 0.988114 | ||||||||
\(783\) | −4.25822 | −0.152176 | ||||||||
\(784\) | −2.13476 | −0.0762413 | ||||||||
\(785\) | 34.2143 | 1.22116 | ||||||||
\(786\) | 15.2759 | 0.544874 | ||||||||
\(787\) | 13.4619 | 0.479866 | 0.239933 | − | 0.970790i | \(-0.422875\pi\) | ||||
0.239933 | + | 0.970790i | \(0.422875\pi\) | |||||||
\(788\) | 2.64164 | 0.0941046 | ||||||||
\(789\) | 18.4455 | 0.656678 | ||||||||
\(790\) | −35.3330 | −1.25709 | ||||||||
\(791\) | −14.1452 | −0.502945 | ||||||||
\(792\) | 11.7838 | 0.418720 | ||||||||
\(793\) | −23.7554 | −0.843577 | ||||||||
\(794\) | −39.6213 | −1.40611 | ||||||||
\(795\) | 32.2269 | 1.14297 | ||||||||
\(796\) | −2.37908 | −0.0843243 | ||||||||
\(797\) | 13.2754 | 0.470238 | 0.235119 | − | 0.971967i | \(-0.424452\pi\) | ||||
0.235119 | + | 0.971967i | \(0.424452\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.463958 | 0.0164136 | ||||||||
\(800\) | 1.26184 | 0.0446128 | ||||||||
\(801\) | −5.44718 | −0.192467 | ||||||||
\(802\) | −34.2890 | −1.21079 | ||||||||
\(803\) | 44.4512 | 1.56865 | ||||||||
\(804\) | 8.50083 | 0.299801 | ||||||||
\(805\) | 16.8674 | 0.594499 | ||||||||
\(806\) | 39.7000 | 1.39837 | ||||||||
\(807\) | 5.16887 | 0.181953 | ||||||||
\(808\) | −4.70799 | −0.165626 | ||||||||
\(809\) | 11.7919 | 0.414581 | 0.207290 | − | 0.978279i | \(-0.433536\pi\) | ||||
0.207290 | + | 0.978279i | \(0.433536\pi\) | |||||||
\(810\) | 2.64203 | 0.0928315 | ||||||||
\(811\) | −47.0891 | −1.65352 | −0.826761 | − | 0.562553i | \(-0.809819\pi\) | ||||
−0.826761 | + | 0.562553i | \(0.809819\pi\) | |||||||
\(812\) | −2.94968 | −0.103514 | ||||||||
\(813\) | −17.5641 | −0.616000 | ||||||||
\(814\) | −14.5438 | −0.509760 | ||||||||
\(815\) | −15.2970 | −0.535831 | ||||||||
\(816\) | 7.06762 | 0.247416 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 21.8196 | 0.762904 | ||||||||
\(819\) | −4.12491 | −0.144136 | ||||||||
\(820\) | −11.3663 | −0.396930 | ||||||||
\(821\) | −47.1480 | −1.64548 | −0.822739 | − | 0.568419i | \(-0.807555\pi\) | ||||
−0.822739 | + | 0.568419i | \(0.807555\pi\) | |||||||
\(822\) | 4.81295 | 0.167871 | ||||||||
\(823\) | −37.5960 | −1.31052 | −0.655258 | − | 0.755406i | \(-0.727440\pi\) | ||||
−0.655258 | + | 0.755406i | \(0.727440\pi\) | |||||||
\(824\) | 55.8283 | 1.94487 | ||||||||
\(825\) | −1.29945 | −0.0452409 | ||||||||
\(826\) | 15.9673 | 0.555572 | ||||||||
\(827\) | 18.0488 | 0.627620 | 0.313810 | − | 0.949486i | \(-0.398395\pi\) | ||||
0.313810 | + | 0.949486i | \(0.398395\pi\) | |||||||
\(828\) | 5.05645 | 0.175724 | ||||||||
\(829\) | −53.5059 | −1.85834 | −0.929168 | − | 0.369658i | \(-0.879475\pi\) | ||||
−0.929168 | + | 0.369658i | \(0.879475\pi\) | |||||||
\(830\) | −34.7190 | −1.20512 | ||||||||
\(831\) | −12.4135 | −0.430618 | ||||||||
\(832\) | 35.1404 | 1.21827 | ||||||||
\(833\) | −3.31074 | −0.114710 | ||||||||
\(834\) | −6.11739 | −0.211828 | ||||||||
\(835\) | −5.25839 | −0.181974 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.41762 | 0.290955 | ||||||||
\(838\) | −5.22796 | −0.180597 | ||||||||
\(839\) | −37.7365 | −1.30281 | −0.651404 | − | 0.758731i | \(-0.725819\pi\) | ||||
−0.651404 | + | 0.758731i | \(0.725819\pi\) | |||||||
\(840\) | 7.11420 | 0.245463 | ||||||||
\(841\) | −10.8676 | −0.374743 | ||||||||
\(842\) | 2.78274 | 0.0958996 | ||||||||
\(843\) | −15.9626 | −0.549782 | ||||||||
\(844\) | −1.85559 | −0.0638719 | ||||||||
\(845\) | 9.27727 | 0.319148 | ||||||||
\(846\) | −0.160229 | −0.00550878 | ||||||||
\(847\) | −3.64944 | −0.125396 | ||||||||
\(848\) | −29.7726 | −1.02240 | ||||||||
\(849\) | −19.4069 | −0.666043 | ||||||||
\(850\) | −1.28517 | −0.0440808 | ||||||||
\(851\) | −24.2594 | −0.831600 | ||||||||
\(852\) | 4.36081 | 0.149399 | ||||||||
\(853\) | −37.6641 | −1.28959 | −0.644797 | − | 0.764354i | \(-0.723058\pi\) | ||||
−0.644797 | + | 0.764354i | \(0.723058\pi\) | |||||||
\(854\) | 6.58468 | 0.225323 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.05786 | −0.207054 | ||||||||
\(857\) | 16.7648 | 0.572676 | 0.286338 | − | 0.958129i | \(-0.407562\pi\) | ||||
0.286338 | + | 0.958129i | \(0.407562\pi\) | |||||||
\(858\) | −18.0514 | −0.616266 | ||||||||
\(859\) | 37.3684 | 1.27499 | 0.637496 | − | 0.770454i | \(-0.279970\pi\) | ||||
0.637496 | + | 0.770454i | \(0.279970\pi\) | |||||||
\(860\) | 9.21798 | 0.314330 | ||||||||
\(861\) | −7.10106 | −0.242003 | ||||||||
\(862\) | 36.4377 | 1.24107 | ||||||||
\(863\) | 37.6588 | 1.28192 | 0.640960 | − | 0.767574i | \(-0.278536\pi\) | ||||
0.640960 | + | 0.767574i | \(0.278536\pi\) | |||||||
\(864\) | 3.71670 | 0.126445 | ||||||||
\(865\) | 3.72656 | 0.126707 | ||||||||
\(866\) | −44.4497 | −1.51046 | ||||||||
\(867\) | −6.03902 | −0.205096 | ||||||||
\(868\) | 5.83091 | 0.197914 | ||||||||
\(869\) | 51.1863 | 1.73637 | ||||||||
\(870\) | −11.2503 | −0.381422 | ||||||||
\(871\) | −50.6207 | −1.71522 | ||||||||
\(872\) | 49.9227 | 1.69060 | ||||||||
\(873\) | −2.60598 | −0.0881990 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.7692 | 0.364065 | ||||||||
\(876\) | 8.04488 | 0.271811 | ||||||||
\(877\) | −13.3402 | −0.450467 | −0.225234 | − | 0.974305i | \(-0.572315\pi\) | ||||
−0.225234 | + | 0.974305i | \(0.572315\pi\) | |||||||
\(878\) | −15.6374 | −0.527736 | ||||||||
\(879\) | 12.3471 | 0.416456 | ||||||||
\(880\) | 18.8803 | 0.636456 | ||||||||
\(881\) | 38.9372 | 1.31183 | 0.655913 | − | 0.754836i | \(-0.272284\pi\) | ||||
0.655913 | + | 0.754836i | \(0.272284\pi\) | |||||||
\(882\) | 1.14337 | 0.0384993 | ||||||||
\(883\) | −40.1789 | −1.35213 | −0.676064 | − | 0.736843i | \(-0.736316\pi\) | ||||
−0.676064 | + | 0.736843i | \(0.736316\pi\) | |||||||
\(884\) | 9.45989 | 0.318170 | ||||||||
\(885\) | −32.2696 | −1.08473 | ||||||||
\(886\) | 47.1299 | 1.58336 | ||||||||
\(887\) | −31.7850 | −1.06724 | −0.533619 | − | 0.845725i | \(-0.679168\pi\) | ||||
−0.533619 | + | 0.845725i | \(0.679168\pi\) | |||||||
\(888\) | −10.2319 | −0.343360 | ||||||||
\(889\) | 8.64735 | 0.290023 | ||||||||
\(890\) | −14.3916 | −0.482408 | ||||||||
\(891\) | −3.82746 | −0.128225 | ||||||||
\(892\) | 11.9633 | 0.400560 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 13.9824 | 0.467643 | ||||||||
\(895\) | 36.2208 | 1.21073 | ||||||||
\(896\) | −2.30707 | −0.0770737 | ||||||||
\(897\) | −30.1101 | −1.00535 | ||||||||
\(898\) | −4.97895 | −0.166150 | ||||||||
\(899\) | −35.8441 | −1.19547 | ||||||||
\(900\) | −0.235177 | −0.00783923 | ||||||||
\(901\) | −46.1735 | −1.53826 | ||||||||
\(902\) | −31.0757 | −1.03471 | ||||||||
\(903\) | 5.75888 | 0.191643 | ||||||||
\(904\) | −43.5496 | −1.44844 | ||||||||
\(905\) | 0.675314 | 0.0224482 | ||||||||
\(906\) | 0.271503 | 0.00902009 | ||||||||
\(907\) | 44.5936 | 1.48071 | 0.740354 | − | 0.672217i | \(-0.234658\pi\) | ||||
0.740354 | + | 0.672217i | \(0.234658\pi\) | |||||||
\(908\) | −5.28515 | −0.175394 | ||||||||
\(909\) | 1.52918 | 0.0507198 | ||||||||
\(910\) | −10.8981 | −0.361269 | ||||||||
\(911\) | −22.5134 | −0.745903 | −0.372951 | − | 0.927851i | \(-0.621654\pi\) | ||||
−0.372951 | + | 0.927851i | \(0.621654\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.2968 | 1.66458 | ||||||||
\(914\) | 5.85549 | 0.193682 | ||||||||
\(915\) | −13.3075 | −0.439934 | ||||||||
\(916\) | −1.60268 | −0.0529541 | ||||||||
\(917\) | −13.3604 | −0.441200 | ||||||||
\(918\) | −3.78540 | −0.124937 | ||||||||
\(919\) | 21.6807 | 0.715181 | 0.357591 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357591 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(920\) | 51.9308 | 1.71211 | ||||||||
\(921\) | −8.92723 | −0.294162 | ||||||||
\(922\) | 16.8090 | 0.553577 | ||||||||
\(923\) | −25.9678 | −0.854739 | ||||||||
\(924\) | −2.65129 | −0.0872211 | ||||||||
\(925\) | 1.12831 | 0.0370986 | ||||||||
\(926\) | 28.0886 | 0.923050 | ||||||||
\(927\) | −18.1334 | −0.595578 | ||||||||
\(928\) | −15.8265 | −0.519531 | ||||||||
\(929\) | −18.0298 | −0.591537 | −0.295768 | − | 0.955260i | \(-0.595576\pi\) | ||||
−0.295768 | + | 0.955260i | \(0.595576\pi\) | |||||||
\(930\) | 22.2396 | 0.729265 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.95115 | 0.129424 | ||||||||
\(933\) | 25.1416 | 0.823099 | ||||||||
\(934\) | 35.2204 | 1.15245 | ||||||||
\(935\) | 29.2810 | 0.957591 | ||||||||
\(936\) | −12.6996 | −0.415099 | ||||||||
\(937\) | −5.32482 | −0.173954 | −0.0869771 | − | 0.996210i | \(-0.527721\pi\) | ||||
−0.0869771 | + | 0.996210i | \(0.527721\pi\) | |||||||
\(938\) | 14.0314 | 0.458142 | ||||||||
\(939\) | −13.1928 | −0.430531 | ||||||||
\(940\) | 0.224311 | 0.00731623 | ||||||||
\(941\) | −18.8787 | −0.615429 | −0.307715 | − | 0.951479i | \(-0.599564\pi\) | ||||
−0.307715 | + | 0.951479i | \(0.599564\pi\) | |||||||
\(942\) | 16.9295 | 0.551594 | ||||||||
\(943\) | −51.8349 | −1.68798 | ||||||||
\(944\) | 29.8120 | 0.970299 | ||||||||
\(945\) | −2.31074 | −0.0751683 | ||||||||
\(946\) | 25.2020 | 0.819389 | ||||||||
\(947\) | −31.3180 | −1.01770 | −0.508849 | − | 0.860856i | \(-0.669929\pi\) | ||||
−0.508849 | + | 0.860856i | \(0.669929\pi\) | |||||||
\(948\) | 9.26382 | 0.300875 | ||||||||
\(949\) | −47.9056 | −1.55508 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.70141 | −0.184881 | ||||||||
\(952\) | −10.1930 | −0.330356 | ||||||||
\(953\) | 33.2382 | 1.07669 | 0.538346 | − | 0.842724i | \(-0.319050\pi\) | ||||
0.538346 | + | 0.842724i | \(0.319050\pi\) | |||||||
\(954\) | 15.9461 | 0.516275 | ||||||||
\(955\) | −15.6284 | −0.505722 | ||||||||
\(956\) | −6.11498 | −0.197772 | ||||||||
\(957\) | 16.2982 | 0.526845 | ||||||||
\(958\) | 9.24079 | 0.298556 | ||||||||
\(959\) | −4.20944 | −0.135930 | ||||||||
\(960\) | 19.6853 | 0.635342 | ||||||||
\(961\) | 39.8562 | 1.28569 | ||||||||
\(962\) | 15.6741 | 0.505352 | ||||||||
\(963\) | 1.96763 | 0.0634061 | ||||||||
\(964\) | −20.2397 | −0.651877 | ||||||||
\(965\) | 24.0498 | 0.774189 | ||||||||
\(966\) | 8.34614 | 0.268533 | ||||||||
\(967\) | 24.1065 | 0.775211 | 0.387606 | − | 0.921825i | \(-0.373302\pi\) | ||||
0.387606 | + | 0.921825i | \(0.373302\pi\) | |||||||
\(968\) | −11.2358 | −0.361131 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.88507 | −0.221066 | ||||||||
\(971\) | 16.6715 | 0.535012 | 0.267506 | − | 0.963556i | \(-0.413800\pi\) | ||||
0.267506 | + | 0.963556i | \(0.413800\pi\) | |||||||
\(972\) | −0.692703 | −0.0222185 | ||||||||
\(973\) | 5.35031 | 0.171523 | ||||||||
\(974\) | 37.8082 | 1.21145 | ||||||||
\(975\) | 1.40043 | 0.0448497 | ||||||||
\(976\) | 12.2941 | 0.393524 | ||||||||
\(977\) | −48.9492 | −1.56602 | −0.783011 | − | 0.622008i | \(-0.786317\pi\) | ||||
−0.783011 | + | 0.622008i | \(0.786317\pi\) | |||||||
\(978\) | −7.56908 | −0.242032 | ||||||||
\(979\) | 20.8489 | 0.666333 | ||||||||
\(980\) | −1.60065 | −0.0511310 | ||||||||
\(981\) | −16.2152 | −0.517712 | ||||||||
\(982\) | −4.36917 | −0.139426 | ||||||||
\(983\) | 26.3637 | 0.840871 | 0.420436 | − | 0.907322i | \(-0.361877\pi\) | ||||
0.420436 | + | 0.907322i | \(0.361877\pi\) | |||||||
\(984\) | −21.8624 | −0.696949 | ||||||||
\(985\) | −8.81206 | −0.280775 | ||||||||
\(986\) | 16.1191 | 0.513336 | ||||||||
\(987\) | 0.140137 | 0.00446062 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.0375 | 1.33671 | ||||||||
\(990\) | −10.1123 | −0.321389 | ||||||||
\(991\) | 11.6852 | 0.371194 | 0.185597 | − | 0.982626i | \(-0.440578\pi\) | ||||
0.185597 | + | 0.982626i | \(0.440578\pi\) | |||||||
\(992\) | 31.2857 | 0.993323 | ||||||||
\(993\) | −32.1319 | −1.01967 | ||||||||
\(994\) | 7.19793 | 0.228304 | ||||||||
\(995\) | 7.93620 | 0.251594 | ||||||||
\(996\) | 9.10285 | 0.288435 | ||||||||
\(997\) | 50.8039 | 1.60898 | 0.804488 | − | 0.593969i | \(-0.202440\pi\) | ||||
0.804488 | + | 0.593969i | \(0.202440\pi\) | |||||||
\(998\) | 37.0083 | 1.17148 | ||||||||
\(999\) | 3.32338 | 0.105147 |
(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 | 7581.2.a.be.1.4 | yes | 6 | |
19.18 | odd | 2 | 7581.2.a.z.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7581.2.a.z.1.3 | ✓ | 6 | 19.18 | odd | 2 | ||
7581.2.a.be.1.4 | yes | 6 | 1.1 | even | 1 | trivial |