Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6020,2,Mod(1,6020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6020 = 2^{2} \cdot 5 \cdot 7 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6020.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: | \(48.0699420168\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 27 x^{11} - 2 x^{10} + 268 x^{9} + 37 x^{8} - 1201 x^{7} - 189 x^{6} + 2384 x^{5} + 231 x^{4} - 1729 x^{3} + 20 x^{2} + 105 x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.54322\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.54322 | −1.46833 | −0.734164 | − | 0.678972i | \(-0.762426\pi\) | ||||
−0.734164 | + | 0.678972i | \(0.762426\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.46796 | 1.15599 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.23106 | −0.974202 | −0.487101 | − | 0.873346i | \(-0.661946\pi\) | ||||
−0.487101 | + | 0.873346i | \(0.661946\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.70161 | −1.30399 | −0.651996 | − | 0.758222i | \(-0.726068\pi\) | ||||
−0.651996 | + | 0.758222i | \(0.726068\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.54322 | −0.656656 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.826062 | −0.200349 | −0.100175 | − | 0.994970i | \(-0.531940\pi\) | ||||
−0.100175 | + | 0.994970i | \(0.531940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65222 | −1.29671 | −0.648354 | − | 0.761339i | \(-0.724542\pi\) | ||||
−0.648354 | + | 0.761339i | \(0.724542\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.54322 | 0.554976 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.98232 | −1.66443 | −0.832215 | − | 0.554453i | \(-0.812927\pi\) | ||||
−0.832215 | + | 0.554453i | \(0.812927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.19012 | −0.229038 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.88745 | −0.536187 | −0.268093 | − | 0.963393i | \(-0.586394\pi\) | ||||
−0.268093 | + | 0.963393i | \(0.586394\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.99139 | −1.61490 | −0.807451 | − | 0.589935i | \(-0.799153\pi\) | ||||
−0.807451 | + | 0.589935i | \(0.799153\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.21730 | 1.43045 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.79116 | 0.787662 | 0.393831 | − | 0.919183i | \(-0.371149\pi\) | ||||
0.393831 | + | 0.919183i | \(0.371149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.9572 | 1.91469 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.32201 | −0.362637 | −0.181319 | − | 0.983424i | \(-0.558037\pi\) | ||||
−0.181319 | + | 0.983424i | \(0.558037\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.46796 | 0.516973 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.524113 | 0.0764497 | 0.0382248 | − | 0.999269i | \(-0.487830\pi\) | ||||
0.0382248 | + | 0.999269i | \(0.487830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.10085 | 0.294179 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.07174 | −0.834018 | −0.417009 | − | 0.908902i | \(-0.636922\pi\) | ||||
−0.417009 | + | 0.908902i | \(0.636922\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.23106 | −0.435676 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.3748 | 1.90399 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.71720 | −0.614127 | −0.307063 | − | 0.951689i | \(-0.599346\pi\) | ||||
−0.307063 | + | 0.951689i | \(0.599346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.31640 | −0.552658 | −0.276329 | − | 0.961063i | \(-0.589118\pi\) | ||||
−0.276329 | + | 0.961063i | \(0.589118\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.46796 | −0.436922 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.70161 | −0.583163 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6915 | 1.42835 | 0.714173 | − | 0.699969i | \(-0.246803\pi\) | ||||
0.714173 | + | 0.699969i | \(0.246803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.3008 | 2.44393 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.06811 | 0.245440 | 0.122720 | − | 0.992441i | \(-0.460838\pi\) | ||||
0.122720 | + | 0.992441i | \(0.460838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.28496 | 0.735598 | 0.367799 | − | 0.929905i | \(-0.380111\pi\) | ||||
0.367799 | + | 0.929905i | \(0.380111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.54322 | −0.293666 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23106 | 0.368214 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6842 | −1.53959 | −0.769796 | − | 0.638290i | \(-0.779642\pi\) | ||||
−0.769796 | + | 0.638290i | \(0.779642\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.37714 | −0.819682 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.4005 | 1.25137 | 0.625683 | − | 0.780078i | \(-0.284820\pi\) | ||||
0.625683 | + | 0.780078i | \(0.284820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.826062 | −0.0895990 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.34343 | 0.787298 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7618 | −1.24675 | −0.623376 | − | 0.781922i | \(-0.714239\pi\) | ||||
−0.623376 | + | 0.781922i | \(0.714239\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.70161 | 0.492863 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.8671 | 2.37120 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.65222 | −0.579905 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9020 | 1.31000 | 0.654998 | − | 0.755631i | \(-0.272670\pi\) | ||||
0.654998 | + | 0.755631i | \(0.272670\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.2052 | −1.12616 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.64856 | 0.263542 | 0.131771 | − | 0.991280i | \(-0.457934\pi\) | ||||
0.131771 | + | 0.991280i | \(0.457934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2293 | −1.30353 | −0.651763 | − | 0.758423i | \(-0.725970\pi\) | ||||
−0.651763 | + | 0.758423i | \(0.725970\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.54322 | 0.248193 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.56234 | −0.344384 | −0.172192 | − | 0.985063i | \(-0.555085\pi\) | ||||
−0.172192 | + | 0.985063i | \(0.555085\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8358 | 1.70836 | 0.854179 | − | 0.519979i | \(-0.174060\pi\) | ||||
0.854179 | + | 0.519979i | \(0.174060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.1850 | −1.15655 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.17570 | 0.110600 | 0.0553001 | − | 0.998470i | \(-0.482388\pi\) | ||||
0.0553001 | + | 0.998470i | \(0.482388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.98232 | −0.744356 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.3050 | −1.50740 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.826062 | 0.0757250 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.560233 | −0.0509303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.90538 | 0.532470 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.59158 | 0.229966 | 0.114983 | − | 0.993367i | \(-0.463319\pi\) | ||||
0.114983 | + | 0.993367i | \(0.463319\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.54322 | −0.223918 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.53621 | 0.221589 | 0.110795 | − | 0.993843i | \(-0.464660\pi\) | ||||
0.110795 | + | 0.993843i | \(0.464660\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.65222 | 0.490110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.19012 | −0.102429 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.6291 | 1.59160 | 0.795798 | − | 0.605563i | \(-0.207052\pi\) | ||||
0.795798 | + | 0.605563i | \(0.207052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.7700 | −1.59205 | −0.796027 | − | 0.605261i | \(-0.793069\pi\) | ||||
−0.796027 | + | 0.605261i | \(0.793069\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.33293 | −0.112253 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.1912 | 1.27035 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.88745 | −0.239790 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.54322 | −0.209761 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.2059 | −1.57341 | −0.786704 | − | 0.617330i | \(-0.788214\pi\) | ||||
−0.786704 | + | 0.617330i | \(0.788214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1547 | −1.15190 | −0.575948 | − | 0.817486i | \(-0.695367\pi\) | ||||
−0.575948 | + | 0.817486i | \(0.695367\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.86475 | −0.231601 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.99139 | −0.722206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8703 | −1.26659 | −0.633293 | − | 0.773912i | \(-0.718297\pi\) | ||||
−0.633293 | + | 0.773912i | \(0.718297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.4418 | 1.22461 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.98232 | 0.629095 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0290 | −0.785536 | −0.392768 | − | 0.919638i | \(-0.628482\pi\) | ||||
−0.392768 | + | 0.919638i | \(0.628482\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.21730 | 0.639716 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.6275 | −1.59621 | −0.798103 | − | 0.602521i | \(-0.794163\pi\) | ||||
−0.798103 | + | 0.602521i | \(0.794163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.10515 | 0.700396 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.6017 | −1.49898 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.1560 | −0.924202 | −0.462101 | − | 0.886827i | \(-0.652904\pi\) | ||||
−0.462101 | + | 0.886827i | \(0.652904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.9969 | 0.901739 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.4334 | 1.90098 | 0.950492 | − | 0.310749i | \(-0.100580\pi\) | ||||
0.950492 | + | 0.310749i | \(0.100580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.06167 | −0.450560 | −0.225280 | − | 0.974294i | \(-0.572330\pi\) | ||||
−0.225280 | + | 0.974294i | \(0.572330\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.9775 | 0.811483 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.79116 | 0.352253 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.66906 | 0.195181 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.19012 | 0.0865684 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.94351 | 0.502415 | 0.251207 | − | 0.967933i | \(-0.419172\pi\) | ||||
0.251207 | + | 0.967933i | \(0.419172\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7134 | −0.771171 | −0.385585 | − | 0.922672i | \(-0.626000\pi\) | ||||
−0.385585 | + | 0.922672i | \(0.626000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.9572 | 0.856274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.86251 | 0.346440 | 0.173220 | − | 0.984883i | \(-0.444583\pi\) | ||||
0.173220 | + | 0.984883i | \(0.444583\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.92150 | 0.703316 | 0.351658 | − | 0.936128i | \(-0.385618\pi\) | ||||
0.351658 | + | 0.936128i | \(0.385618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.7341 | −2.09728 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.88745 | 0.202660 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.32201 | −0.162176 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −27.6824 | −1.92406 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.2627 | 1.26326 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5109 | 0.723601 | 0.361800 | − | 0.932256i | \(-0.382162\pi\) | ||||
0.361800 | + | 0.932256i | \(0.382162\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.25966 | −0.360386 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.99139 | 0.610375 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.9840 | −1.08010 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.88382 | 0.261254 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.08545 | −0.608407 | −0.304203 | − | 0.952607i | \(-0.598390\pi\) | ||||
−0.304203 | + | 0.952607i | \(0.598390\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.46796 | 0.231197 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.8035 | 1.51352 | 0.756760 | − | 0.653693i | \(-0.226781\pi\) | ||||
0.756760 | + | 0.653693i | \(0.226781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.21632 | 0.146458 | 0.0732291 | − | 0.997315i | \(-0.476670\pi\) | ||||
0.0732291 | + | 0.997315i | \(0.476670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.21730 | −0.540658 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1345 | 0.794957 | 0.397478 | − | 0.917612i | \(-0.369885\pi\) | ||||
0.397478 | + | 0.917612i | \(0.369885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.524113 | 0.0341893 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34.8019 | 2.26062 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.846447 | 0.0547521 | 0.0273760 | − | 0.999625i | \(-0.491285\pi\) | ||||
0.0273760 | + | 0.999625i | \(0.491285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.8902 | 0.765917 | 0.382958 | − | 0.923766i | \(-0.374905\pi\) | ||||
0.382958 | + | 0.923766i | \(0.374905\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3320 | 1.43260 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.5745 | 1.69090 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.9939 | −1.83741 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.32084 | −0.0833709 | −0.0416855 | − | 0.999131i | \(-0.513273\pi\) | ||||
−0.0416855 | + | 0.999131i | \(0.513273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.7914 | 1.62149 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.10085 | 0.131561 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.58738 | 0.0990178 | 0.0495089 | − | 0.998774i | \(-0.484234\pi\) | ||||
0.0495089 | + | 0.998774i | \(0.484234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.79116 | −0.297708 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.0136 | −0.619824 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.3740 | −1.25632 | −0.628158 | − | 0.778086i | \(-0.716191\pi\) | ||||
−0.628158 | + | 0.778086i | \(0.716191\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.07174 | −0.372984 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.9129 | 1.83064 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.01643 | −0.122944 | −0.0614718 | − | 0.998109i | \(-0.519579\pi\) | ||||
−0.0614718 | + | 0.998109i | \(0.519579\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.44996 | 0.331062 | 0.165531 | − | 0.986205i | \(-0.447066\pi\) | ||||
0.165531 | + | 0.986205i | \(0.447066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.9572 | −0.723684 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.23106 | −0.194840 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.91936 | 0.595997 | 0.297998 | − | 0.954566i | \(-0.403681\pi\) | ||||
0.297998 | + | 0.954566i | \(0.403681\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −31.1818 | −1.86680 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.29128 | −0.375306 | −0.187653 | − | 0.982235i | \(-0.560088\pi\) | ||||
−0.187653 | + | 0.982235i | \(0.560088\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3795 | 1.21144 | 0.605719 | − | 0.795679i | \(-0.292886\pi\) | ||||
0.605719 | + | 0.795679i | \(0.292886\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.3748 | 0.851491 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.32201 | 0.137064 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3176 | −0.959860 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.8125 | −1.92350 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.3636 | 1.18966 | 0.594828 | − | 0.803853i | \(-0.297220\pi\) | ||||
0.594828 | + | 0.803853i | \(0.297220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.71720 | −0.274646 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.84535 | 0.223130 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37.5298 | 2.17040 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | −0.0576390 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.73588 | −0.386966 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.31640 | −0.247156 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.9777 | 1.02604 | 0.513021 | − | 0.858376i | \(-0.328526\pi\) | ||||
0.513021 | + | 0.858376i | \(0.328526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 33.6451 | 1.91400 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.8813 | −1.29748 | −0.648740 | − | 0.761010i | \(-0.724704\pi\) | ||||
−0.648740 | + | 0.761010i | \(0.724704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.2726 | −1.88068 | −0.940339 | − | 0.340238i | \(-0.889492\pi\) | ||||
−0.940339 | + | 0.340238i | \(0.889492\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.46796 | −0.195397 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.06981 | 0.284749 | 0.142374 | − | 0.989813i | \(-0.454526\pi\) | ||||
0.142374 | + | 0.989813i | \(0.454526\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.32955 | 0.522354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.05980 | 0.505669 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.66908 | 0.259795 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.70161 | −0.260798 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −45.3603 | −2.50843 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.524113 | −0.0288953 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1196 | 0.721116 | 0.360558 | − | 0.932737i | \(-0.382586\pi\) | ||||
0.360558 | + | 0.932737i | \(0.382586\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.6155 | 0.910526 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.6915 | 0.638776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7963 | 1.18732 | 0.593661 | − | 0.804715i | \(-0.297682\pi\) | ||||
0.593661 | + | 0.804715i | \(0.297682\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.99005 | −0.162397 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.0517 | 1.57324 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.3008 | 1.09296 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.70002 | −0.198628 | −0.0993138 | − | 0.995056i | \(-0.531665\pi\) | ||||
−0.0993138 | + | 0.995056i | \(0.531665\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.3883 | 0.984301 | 0.492151 | − | 0.870510i | \(-0.336211\pi\) | ||||
0.492151 | + | 0.870510i | \(0.336211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.59548 | 0.298664 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.2852 | −1.02645 | −0.513225 | − | 0.858254i | \(-0.671549\pi\) | ||||
−0.513225 | + | 0.858254i | \(0.671549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.06811 | 0.109764 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.10085 | −0.111189 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.86451 | 0.151183 | 0.0755915 | − | 0.997139i | \(-0.475916\pi\) | ||||
0.0755915 | + | 0.997139i | \(0.475916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.9476 | 0.681452 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.42480 | 0.0747824 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.28496 | 0.328970 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.9686 | −1.40775 | −0.703873 | − | 0.710325i | \(-0.748548\pi\) | ||||
−0.703873 | + | 0.710325i | \(0.748548\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.05263 | −0.419203 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.07174 | 0.315229 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.0224 | 1.45095 | 0.725473 | − | 0.688251i | \(-0.241621\pi\) | ||||
0.725473 | + | 0.688251i | \(0.241621\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.54322 | −0.131331 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.5757 | 0.699184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1535 | 0.572915 | 0.286458 | − | 0.958093i | \(-0.407522\pi\) | ||||
0.286458 | + | 0.958093i | \(0.407522\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.59096 | −0.337665 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.99036 | −0.203898 | −0.101949 | − | 0.994790i | \(-0.532508\pi\) | ||||
−0.101949 | + | 0.994790i | \(0.532508\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.23106 | 0.164670 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.46796 | 0.176286 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.89279 | 0.298776 | 0.149388 | − | 0.988779i | \(-0.452270\pi\) | ||||
0.149388 | + | 0.988779i | \(0.452270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.59389 | 0.333467 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.45012 | −0.325366 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.6842 | −0.688526 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.3012 | −0.868320 | −0.434160 | − | 0.900836i | \(-0.642955\pi\) | ||||
−0.434160 | + | 0.900836i | \(0.642955\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.3748 | −0.719641 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.48895 | −0.124292 | −0.0621462 | − | 0.998067i | \(-0.519795\pi\) | ||||
−0.0621462 | + | 0.998067i | \(0.519795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.2740 | 2.10582 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.37714 | −0.366573 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.4805 | −0.767342 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.50827 | −0.272367 | −0.136183 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136183 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −47.3780 | −2.33698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.71720 | 0.232118 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.4005 | 0.559628 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47.7363 | 2.33766 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.2976 | 0.698485 | 0.349242 | − | 0.937032i | \(-0.386439\pi\) | ||||
0.349242 | + | 0.937032i | \(0.386439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.46188 | −0.217459 | −0.108729 | − | 0.994071i | \(-0.534678\pi\) | ||||
−0.108729 | + | 0.994071i | \(0.534678\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.81760 | 0.0883748 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.826062 | −0.0400699 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.31640 | 0.208885 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −38.6345 | −1.86529 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.3253 | 1.46072 | 0.730359 | − | 0.683063i | \(-0.239353\pi\) | ||||
0.730359 | + | 0.683063i | \(0.239353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.7065 | 1.86011 | 0.930057 | − | 0.367414i | \(-0.119757\pi\) | ||||
0.930057 | + | 0.367414i | \(0.119757\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.34343 | 0.352090 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 45.1178 | 2.15828 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.29330 | 0.395818 | 0.197909 | − | 0.980220i | \(-0.436585\pi\) | ||||
0.197909 | + | 0.980220i | \(0.436585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.46796 | 0.165141 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.64506 | 0.363228 | 0.181614 | − | 0.983370i | \(-0.441868\pi\) | ||||
0.181614 | + | 0.983370i | \(0.441868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7618 | −0.557565 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 48.8448 | 2.31028 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.5289 | 0.685659 | 0.342829 | − | 0.939398i | \(-0.388615\pi\) | ||||
0.342829 | + | 0.939398i | \(0.388615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.50256 | 0.353282 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.9986 | 1.69136 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.70161 | 0.220415 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.8478 | 1.34945 | 0.674723 | − | 0.738071i | \(-0.264263\pi\) | ||||
0.674723 | + | 0.738071i | \(0.264263\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.983112 | 0.0458877 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.7276 | 1.01196 | 0.505978 | − | 0.862546i | \(-0.331132\pi\) | ||||
0.505978 | + | 0.862546i | \(0.331132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.1384 | 1.26123 | 0.630615 | − | 0.776096i | \(-0.282803\pi\) | ||||
0.630615 | + | 0.776096i | \(0.282803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.8671 | 1.06043 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.07991 | 0.235070 | 0.117535 | − | 0.993069i | \(-0.462501\pi\) | ||||
0.117535 | + | 0.993069i | \(0.462501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.6915 | −0.539864 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.3616 | 1.85976 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.23106 | −0.148564 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.65222 | −0.259342 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.0565 | −0.964113 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.4541 | −0.660423 | −0.330211 | − | 0.943907i | \(-0.607120\pi\) | ||||
−0.330211 | + | 0.943907i | \(0.607120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.5262 | −1.02711 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.3008 | −0.923718 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.9020 | 0.585848 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.1656 | −0.777848 | −0.388924 | − | 0.921270i | \(-0.627153\pi\) | ||||
−0.388924 | + | 0.921270i | \(0.627153\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.5061 | 1.15342 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4552 | −0.742613 | −0.371307 | − | 0.928510i | \(-0.621090\pi\) | ||||
−0.371307 | + | 0.928510i | \(0.621090\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.38522 | 0.107425 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.2052 | −0.503636 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.06811 | −0.0927674 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.1019 | −0.855120 | −0.427560 | − | 0.903987i | \(-0.640627\pi\) | ||||
−0.427560 | + | 0.903987i | \(0.640627\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 52.4603 | 2.34375 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.3764 | −0.863952 | −0.431976 | − | 0.901885i | \(-0.642183\pi\) | ||||
−0.431976 | + | 0.901885i | \(0.642183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.64856 | 0.117860 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.1564 | −1.02841 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.30352 | 0.279399 | 0.139699 | − | 0.990194i | \(-0.455386\pi\) | ||||
0.139699 | + | 0.990194i | \(0.455386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.28496 | −0.278030 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.72681 | 0.296996 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.2293 | −0.582954 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.69344 | −0.0744775 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.9153 | 1.35703 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.52354 | −0.285801 | −0.142901 | − | 0.989737i | \(-0.545643\pi\) | ||||
−0.142901 | + | 0.989737i | \(0.545643\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.4101 | −0.979925 | −0.489963 | − | 0.871743i | \(-0.662990\pi\) | ||||
−0.489963 | + | 0.871743i | \(0.662990\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.54322 | 0.110995 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.42744 | 0.323544 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.7175 | 1.77033 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.3590 | −0.709922 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.9172 | 0.472876 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.56234 | −0.154013 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −64.6828 | −2.79127 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.23106 | −0.139172 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.1446 | −1.46799 | −0.733996 | − | 0.679154i | \(-0.762347\pi\) | ||||
−0.733996 | + | 0.679154i | \(0.762347\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.4161 | 0.661570 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.8358 | 0.764001 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1558 | −1.03283 | −0.516413 | − | 0.856339i | \(-0.672733\pi\) | ||||
−0.516413 | + | 0.856339i | \(0.672733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.9691 | −0.638865 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.3205 | 0.695278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.6842 | 0.581911 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.1850 | −0.517223 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.1381 | 0.471938 | 0.235969 | − | 0.971761i | \(-0.424174\pi\) | ||||
0.235969 | + | 0.971761i | \(0.424174\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.70161 | −0.198857 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.78799 | −0.286589 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.4073 | −1.78726 | −0.893628 | − | 0.448808i | \(-0.851849\pi\) | ||||
−0.893628 | + | 0.448808i | \(0.851849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.17570 | 0.0494619 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.37714 | 0.309811 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.5083 | −1.19513 | −0.597566 | − | 0.801820i | \(-0.703865\pi\) | ||||
−0.597566 | + | 0.801820i | \(0.703865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.3986 | 1.14659 | 0.573297 | − | 0.819347i | \(-0.305664\pi\) | ||||
0.573297 | + | 0.819347i | \(0.305664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.6589 | −0.737709 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.98232 | −0.332886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.16264 | −0.214924 | −0.107462 | − | 0.994209i | \(-0.534272\pi\) | ||||
−0.107462 | + | 0.994209i | \(0.534272\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.2466 | 1.13233 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.4005 | −0.472972 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.6182 | 0.812502 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.3050 | −0.674128 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.4702 | −1.21637 | −0.608183 | − | 0.793796i | \(-0.708102\pi\) | ||||
−0.608183 | + | 0.793796i | \(0.708102\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 50.8213 | 2.09406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.3664 | −0.508687 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.8935 | 1.67930 | 0.839648 | − | 0.543131i | \(-0.182761\pi\) | ||||
0.839648 | + | 0.543131i | \(0.182761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.826062 | 0.0338652 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.2325 | −1.03270 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.90595 | −0.0778751 | −0.0389376 | − | 0.999242i | \(-0.512397\pi\) | ||||
−0.0389376 | + | 0.999242i | \(0.512397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.6359 | −1.08650 | −0.543251 | − | 0.839570i | \(-0.682807\pi\) | ||||
−0.543251 | + | 0.839570i | \(0.682807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.5457 | 1.65115 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.560233 | −0.0227767 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.6611 | −1.52862 | −0.764309 | − | 0.644850i | \(-0.776920\pi\) | ||||
−0.764309 | + | 0.644850i | \(0.776920\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.34343 | −0.297571 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.46417 | −0.0996898 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.5251 | 0.990558 | 0.495279 | − | 0.868734i | \(-0.335066\pi\) | ||||
0.495279 | + | 0.868734i | \(0.335066\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.90538 | 0.238128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.5372 | 1.06835 | 0.534174 | − | 0.845374i | \(-0.320623\pi\) | ||||
0.534174 | + | 0.845374i | \(0.320623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.4489 | 0.500363 | 0.250181 | − | 0.968199i | \(-0.419510\pi\) | ||||
0.250181 | + | 0.968199i | \(0.419510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.49991 | 0.381218 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.7618 | 0.471228 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −46.4460 | −1.85487 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.95780 | −0.157808 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0114 | −0.398546 | −0.199273 | − | 0.979944i | \(-0.563858\pi\) | ||||
−0.199273 | + | 0.979944i | \(0.563858\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.7315 | −1.06248 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.59158 | 0.102844 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.70161 | −0.186285 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.17212 | 0.283725 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.0043 | −1.38259 | −0.691294 | − | 0.722574i | \(-0.742959\pi\) | ||||
−0.691294 | + | 0.722574i | \(0.742959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.41630 | 0.371342 | 0.185671 | − | 0.982612i | \(-0.440554\pi\) | ||||
0.185671 | + | 0.982612i | \(0.440554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.54322 | −0.100139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.2706 | −1.50457 | −0.752286 | − | 0.658836i | \(-0.771049\pi\) | ||||
−0.752286 | + | 0.658836i | \(0.771049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2416 | 0.598283 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.8671 | −0.896231 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.55237 | 0.0607489 | 0.0303745 | − | 0.999539i | \(-0.490330\pi\) | ||||
0.0303745 | + | 0.999539i | \(0.490330\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.53621 | 0.0990978 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.7960 | 0.850341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3540 | 0.598107 | 0.299054 | − | 0.954236i | \(-0.403329\pi\) | ||||
0.299054 | + | 0.954236i | \(0.403329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.7984 | −0.770069 | −0.385035 | − | 0.922902i | \(-0.625810\pi\) | ||||
−0.385035 | + | 0.922902i | \(0.625810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.87740 | −0.383607 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.65222 | 0.219184 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.0486 | 0.892445 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.1063 | 0.893340 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.9466 | 0.538401 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.5922 | 1.06360 | 0.531801 | − | 0.846869i | \(-0.321515\pi\) | ||||
0.531801 | + | 0.846869i | \(0.321515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.19012 | −0.0458077 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.31356 | −0.0504841 | −0.0252421 | − | 0.999681i | \(-0.508036\pi\) | ||||
−0.0252421 | + | 0.999681i | \(0.508036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.9020 | −0.495132 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −57.9942 | −2.22234 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.0362 | 1.22583 | 0.612916 | − | 0.790148i | \(-0.289996\pi\) | ||||
0.612916 | + | 0.790148i | \(0.289996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.6291 | 0.711783 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.63657 | −0.215049 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.5470 | 1.08755 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0286 | 0.609755 | 0.304878 | − | 0.952392i | \(-0.401384\pi\) | ||||
0.304878 | + | 0.952392i | \(0.401384\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.2052 | 0.425650 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.7700 | −0.711988 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.91812 | 0.0726541 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.8606 | −1.16726 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.8591 | −1.58100 | −0.790498 | − | 0.612464i | \(-0.790178\pi\) | ||||
−0.790498 | + | 0.612464i | \(0.790178\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.0807 | −1.02137 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.33293 | −0.0502012 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.64856 | −0.0996095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.1658 | 0.870010 | 0.435005 | − | 0.900428i | \(-0.356747\pi\) | ||||
0.435005 | + | 0.900428i | \(0.356747\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −47.4562 | −1.77975 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 71.7722 | 2.68789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.1912 | 0.568119 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.15270 | −0.0803940 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.82345 | −0.254472 | −0.127236 | − | 0.991872i | \(-0.540611\pi\) | ||||
−0.127236 | + | 0.991872i | \(0.540611\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.2293 | 0.492686 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.2394 | −1.12462 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.88745 | −0.107237 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.5855 | 1.35688 | 0.678440 | − | 0.734656i | \(-0.262656\pi\) | ||||
0.678440 | + | 0.734656i | \(0.262656\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.6638 | −1.28384 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.826062 | −0.0305530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.20968 | −0.229360 | −0.114680 | − | 0.993402i | \(-0.536584\pi\) | ||||
−0.114680 | + | 0.993402i | \(0.536584\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.54322 | −0.0938080 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.7760 | −1.39150 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.70123 | 0.136152 | 0.0680760 | − | 0.997680i | \(-0.478314\pi\) | ||||
0.0680760 | + | 0.997680i | \(0.478314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −67.5848 | −2.48279 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.9570 | −1.31913 | −0.659566 | − | 0.751646i | \(-0.729260\pi\) | ||||
−0.659566 | + | 0.751646i | \(0.729260\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.2059 | −0.703649 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.5364 | 1.44656 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.56234 | 0.130165 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.3333 | 1.28933 | 0.644666 | − | 0.764464i | \(-0.276996\pi\) | ||||
0.644666 | + | 0.764464i | \(0.276996\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.35919 | 0.122416 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.1547 | −0.515143 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.5795 | −1.11143 | −0.555716 | − | 0.831373i | \(-0.687556\pi\) | ||||
−0.555716 | + | 0.831373i | \(0.687556\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −65.5931 | −2.38088 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.7467 | −0.897067 | −0.448533 | − | 0.893766i | \(-0.648054\pi\) | ||||
−0.448533 | + | 0.893766i | \(0.648054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.8358 | −0.645699 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.86475 | −0.103575 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.1784 | 0.800816 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.6176 | 1.42865 | 0.714324 | − | 0.699815i | \(-0.246734\pi\) | ||||
0.714324 | + | 0.699815i | \(0.246734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.03704 | −0.145391 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.70111 | −0.169087 | −0.0845435 | − | 0.996420i | \(-0.526943\pi\) | ||||
−0.0845435 | + | 0.996420i | \(0.526943\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.99139 | −0.322980 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.1850 | 0.437133 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.1245 | 0.470235 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.68219 | −0.239108 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.43641 | 0.122807 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.8703 | −0.566434 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.24502 | −0.151319 | −0.0756594 | − | 0.997134i | \(-0.524106\pi\) | ||||
−0.0756594 | + | 0.997134i | \(0.524106\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51.8156 | 1.84468 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.17570 | −0.0418029 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.2940 | 0.720662 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.4418 | 0.547663 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.3478 | 0.579069 | 0.289535 | − | 0.957168i | \(-0.406500\pi\) | ||||
0.289535 | + | 0.957168i | \(0.406500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.432949 | −0.0153166 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −40.7896 | −1.44123 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.3071 | −0.716621 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.98232 | 0.281340 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.12821 | 0.180522 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.6565 | −0.831719 | −0.415860 | − | 0.909429i | \(-0.636519\pi\) | ||||
−0.415860 | + | 0.909429i | \(0.636519\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.78363 | −0.308435 | −0.154217 | − | 0.988037i | \(-0.549286\pi\) | ||||
−0.154217 | + | 0.988037i | \(0.549286\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.8604 | −0.486107 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0290 | −0.351302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.65222 | −0.197746 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.3050 | 0.569742 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.55306 | −0.0542023 | −0.0271011 | − | 0.999633i | \(-0.508628\pi\) | ||||
−0.0271011 | + | 0.999633i | \(0.508628\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.7299 | 1.76833 | 0.884166 | − | 0.467173i | \(-0.154727\pi\) | ||||
0.884166 | + | 0.467173i | \(0.154727\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.21730 | 0.286090 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.92543 | 0.310368 | 0.155184 | − | 0.987886i | \(-0.450403\pi\) | ||||
0.155184 | + | 0.987886i | \(0.450403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.0578 | −1.04395 | −0.521975 | − | 0.852961i | \(-0.674805\pi\) | ||||
−0.521975 | + | 0.852961i | \(0.674805\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.2271 | −0.875118 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.826062 | −0.0286213 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.6275 | −0.713845 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.7008 | 0.369875 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.6236 | 1.16082 | 0.580408 | − | 0.814326i | \(-0.302893\pi\) | ||||
0.580408 | + | 0.814326i | \(0.302893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.6626 | −0.712504 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.0001 | 0.551072 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.10515 | 0.313227 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.560233 | 0.0192498 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −51.8296 | −1.77879 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.2446 | −1.31101 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.3386 | 0.799098 | 0.399549 | − | 0.916712i | \(-0.369167\pi\) | ||||
0.399549 | + | 0.916712i | \(0.369167\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.6017 | −0.670363 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.38382 | 0.0814298 | 0.0407149 | − | 0.999171i | \(-0.487036\pi\) | ||||
0.0407149 | + | 0.999171i | \(0.487036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.69240 | −0.296581 | −0.148290 | − | 0.988944i | \(-0.547377\pi\) | ||||
−0.148290 | + | 0.988944i | \(0.547377\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.90538 | −0.201255 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.6653 | 1.82679 | 0.913393 | − | 0.407078i | \(-0.133452\pi\) | ||||
0.913393 | + | 0.407078i | \(0.133452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.1560 | −0.413316 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.4993 | 1.40939 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.2145 | 1.49987 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.9690 | −1.86255 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 44.7435 | 1.51434 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.1380 | −1.55797 | −0.778985 | − | 0.627043i | \(-0.784265\pi\) | ||||
−0.778985 | + | 0.627043i | \(0.784265\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −51.7892 | −1.74681 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.1977 | −0.747858 | −0.373929 | − | 0.927457i | \(-0.621990\pi\) | ||||
−0.373929 | + | 0.927457i | \(0.621990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.6248 | 0.963301 | 0.481650 | − | 0.876363i | \(-0.340038\pi\) | ||||
0.481650 | + | 0.876363i | \(0.340038\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.9969 | 0.403270 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.9140 | 1.34018 | 0.670091 | − | 0.742279i | \(-0.266255\pi\) | ||||
0.670091 | + | 0.742279i | \(0.266255\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.59158 | −0.0869189 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.8360 | 0.798536 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.96240 | −0.0991329 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.4334 | 0.850146 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −95.4464 | −3.18686 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.9622 | 0.865889 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.01563 | 0.167095 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.54322 | 0.0846330 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.06167 | −0.201497 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.8337 | 0.924203 | 0.462101 | − | 0.886827i | \(-0.347096\pi\) | ||||
0.462101 | + | 0.886827i | \(0.347096\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.18511 | 0.304651 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.81976 | −0.0934228 | −0.0467114 | − | 0.998908i | \(-0.514874\pi\) | ||||
−0.0467114 | + | 0.998908i | \(0.514874\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.8357 | −1.21908 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.9775 | 0.362906 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.53621 | −0.0837529 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.3219 | 1.46204 | 0.731022 | − | 0.682354i | \(-0.239044\pi\) | ||||
0.731022 | + | 0.682354i | \(0.239044\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.7212 | −1.50656 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.72345 | −0.320051 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.79116 | 0.157532 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.8788 | −1.50686 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.54170 | 0.280244 | 0.140122 | − | 0.990134i | \(-0.455251\pi\) | ||||
0.140122 | + | 0.990134i | \(0.455251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.65222 | −0.185244 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 58.1922 | 1.90513 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.66906 | 0.0872875 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.35442 | −0.0442469 | −0.0221234 | − | 0.999755i | \(-0.507043\pi\) | ||||
−0.0221234 | + | 0.999755i | \(0.507043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 84.6195 | 2.76145 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.3210 | −1.18403 | −0.592016 | − | 0.805926i | \(-0.701668\pi\) | ||||
−0.592016 | + | 0.805926i | \(0.701668\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.5350 | 0.603584 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.19012 | 0.0387146 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.4358 | −1.86641 | −0.933207 | − | 0.359339i | \(-0.883002\pi\) | ||||
−0.933207 | + | 0.359339i | \(0.883002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.5494 | −0.959215 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.8936 | −0.418105 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.6811 | −1.28540 | −0.642698 | − | 0.766120i | \(-0.722185\pi\) | ||||
−0.642698 | + | 0.766120i | \(0.722185\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.94351 | 0.224687 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.7271 | −0.766987 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.6291 | −0.601567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.8451 | 1.60791 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.3540 | −0.398103 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.7134 | −0.344878 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.4196 | −1.36412 | −0.682061 | − | 0.731295i | \(-0.738916\pi\) | ||||
−0.682061 | + | 0.731295i | \(0.738916\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.8745 | −0.381464 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.5379 | −1.20465 | −0.602324 | − | 0.798252i | \(-0.705758\pi\) | ||||
−0.602324 | + | 0.798252i | \(0.705758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.7700 | 0.601740 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.9572 | 0.382938 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.3123 | −1.19373 | −0.596864 | − | 0.802343i | \(-0.703587\pi\) | ||||
−0.596864 | + | 0.802343i | \(0.703587\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.0032 | 1.21459 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 61.8537 | 1.97484 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.6499 | −0.371574 | −0.185787 | − | 0.982590i | \(-0.559484\pi\) | ||||
−0.185787 | + | 0.982590i | \(0.559484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.86251 | 0.154933 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.33293 | 0.0424277 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.98232 | −0.253823 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.3456 | −0.646298 | −0.323149 | − | 0.946348i | \(-0.604742\pi\) | ||||
−0.323149 | + | 0.946348i | \(0.604742\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.3659 | −1.05883 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.92150 | 0.314533 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.2181 | −1.33706 | −0.668530 | − | 0.743685i | \(-0.733076\pi\) | ||||
−0.668530 | + | 0.743685i | \(0.733076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.70205 | −0.180405 |
(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 | 6020.2.a.k.1.2 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6020.2.a.k.1.2 | ✓ | 13 | 1.1 | even | 1 | trivial |