Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.321637\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.21819 | 1.59432 | 0.797162 | − | 0.603765i | \(-0.206333\pi\) | ||||
0.797162 | + | 0.603765i | \(0.206333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.57491 | −1.68090 | −0.840450 | − | 0.541890i | \(-0.817709\pi\) | ||||
−0.840450 | + | 0.541890i | \(0.817709\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.21819 | −0.615214 | −0.307607 | − | 0.951513i | \(-0.599528\pi\) | ||||
−0.307607 | + | 0.951513i | \(0.599528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.643274 | 0.156017 | 0.0780085 | − | 0.996953i | \(-0.475144\pi\) | ||||
0.0780085 | + | 0.996953i | \(0.475144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.21819 | −0.920484 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.35673 | −0.282897 | −0.141448 | − | 0.989946i | \(-0.545176\pi\) | ||||
−0.141448 | + | 0.989946i | \(0.545176\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.86146 | 0.902751 | 0.451375 | − | 0.892334i | \(-0.350934\pi\) | ||||
0.451375 | + | 0.892334i | \(0.350934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.64327 | −0.474746 | −0.237373 | − | 0.971419i | \(-0.576286\pi\) | ||||
−0.237373 | + | 0.971419i | \(0.576286\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.57491 | 0.970468 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.21819 | −0.713004 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.21819 | −0.364668 | −0.182334 | − | 0.983237i | \(-0.558365\pi\) | ||||
−0.182334 | + | 0.983237i | \(0.558365\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.21819 | 0.355194 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.57491 | 0.558308 | 0.279154 | − | 0.960246i | \(-0.409946\pi\) | ||||
0.279154 | + | 0.960246i | \(0.409946\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.218187 | 0.0332732 | 0.0166366 | − | 0.999862i | \(-0.494704\pi\) | ||||
0.0166366 | + | 0.999862i | \(0.494704\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.35673 | 0.197899 | 0.0989494 | − | 0.995092i | \(-0.468452\pi\) | ||||
0.0989494 | + | 0.995092i | \(0.468452\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.7931 | 1.54187 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.643274 | −0.0900764 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.643274 | 0.0883605 | 0.0441803 | − | 0.999024i | \(-0.485932\pi\) | ||||
0.0441803 | + | 0.999024i | \(0.485932\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.57491 | 0.751721 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.43637 | 0.577567 | 0.288783 | − | 0.957394i | \(-0.406749\pi\) | ||||
0.288783 | + | 0.957394i | \(0.406749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0796 | 1.67468 | 0.837339 | − | 0.546685i | \(-0.184110\pi\) | ||||
0.837339 | + | 0.546685i | \(0.184110\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.21819 | 0.531442 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.21819 | 0.275132 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.28655 | −0.157177 | −0.0785885 | − | 0.996907i | \(-0.525041\pi\) | ||||
−0.0785885 | + | 0.996907i | \(0.525041\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.35673 | 0.163331 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.1498 | −1.32324 | −0.661620 | − | 0.749839i | \(-0.730131\pi\) | ||||
−0.661620 | + | 0.749839i | \(0.730131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −23.5160 | −2.67990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.28655 | 0.144748 | 0.0723740 | − | 0.997378i | \(-0.476942\pi\) | ||||
0.0723740 | + | 0.997378i | \(0.476942\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3662 | −1.35737 | −0.678683 | − | 0.734431i | \(-0.737449\pi\) | ||||
−0.678683 | + | 0.734431i | \(0.737449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.643274 | −0.0697729 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.86146 | −0.521203 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0113 | 1.27319 | 0.636597 | − | 0.771197i | \(-0.280342\pi\) | ||||
0.636597 | + | 0.771197i | \(0.280342\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.35673 | −0.980851 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.64327 | 0.274095 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.78181 | 0.587054 | 0.293527 | − | 0.955951i | \(-0.405171\pi\) | ||||
0.293527 | + | 0.955951i | \(0.405171\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.57491 | −0.560300 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.43637 | −0.640443 | −0.320222 | − | 0.947343i | \(-0.603757\pi\) | ||||
−0.320222 | + | 0.947343i | \(0.603757\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.28655 | 0.126767 | 0.0633837 | − | 0.997989i | \(-0.479811\pi\) | ||||
0.0633837 | + | 0.997989i | \(0.479811\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.21819 | 0.411653 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.28655 | 0.124375 | 0.0621877 | − | 0.998064i | \(-0.480192\pi\) | ||||
0.0621877 | + | 0.998064i | \(0.480192\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.4364 | 1.76588 | 0.882942 | − | 0.469482i | \(-0.155559\pi\) | ||||
0.882942 | + | 0.469482i | \(0.155559\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.21819 | 0.210541 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0796 | 1.23043 | 0.615215 | − | 0.788359i | \(-0.289069\pi\) | ||||
0.615215 | + | 0.788359i | \(0.289069\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.35673 | 0.126515 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.21819 | −0.205071 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.71345 | 0.248742 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.0796 | 1.82542 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.57491 | −0.322339 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.28655 | 0.824048 | 0.412024 | − | 0.911173i | \(-0.364822\pi\) | ||||
0.412024 | + | 0.911173i | \(0.364822\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.218187 | −0.0192103 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.86146 | −0.250007 | −0.125004 | − | 0.992156i | \(-0.539894\pi\) | ||||
−0.125004 | + | 0.992156i | \(0.539894\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.21819 | 0.365763 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.8727 | −1.27066 | −0.635332 | − | 0.772239i | \(-0.719137\pi\) | ||||
−0.635332 | + | 0.772239i | \(0.719137\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.850175 | −0.0721109 | −0.0360555 | − | 0.999350i | \(-0.511479\pi\) | ||||
−0.0360555 | + | 0.999350i | \(0.511479\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.35673 | −0.114257 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.3662 | 1.03411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.86146 | −0.403722 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.7931 | −0.890200 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.1593 | −1.65151 | −0.825757 | − | 0.564026i | \(-0.809252\pi\) | ||||
−0.825757 | + | 0.564026i | \(0.809252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5160 | −0.937161 | −0.468580 | − | 0.883421i | \(-0.655234\pi\) | ||||
−0.468580 | + | 0.883421i | \(0.655234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.643274 | 0.0520056 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.64327 | 0.212313 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.14982 | 0.730236 | 0.365118 | − | 0.930961i | \(-0.381029\pi\) | ||||
0.365118 | + | 0.930961i | \(0.381029\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.643274 | −0.0510150 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.72292 | −0.451029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.50474 | 0.431164 | 0.215582 | − | 0.976486i | \(-0.430835\pi\) | ||||
0.215582 | + | 0.976486i | \(0.430835\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.57491 | −0.434006 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.920352 | 0.0712190 | 0.0356095 | − | 0.999366i | \(-0.488663\pi\) | ||||
0.0356095 | + | 0.999366i | \(0.488663\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.07965 | −0.621511 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.6658 | −1.26708 | −0.633540 | − | 0.773710i | \(-0.718399\pi\) | ||||
−0.633540 | + | 0.773710i | \(0.718399\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.21819 | 0.318865 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.43637 | −0.333458 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.0226 | 1.79553 | 0.897766 | − | 0.440473i | \(-0.145189\pi\) | ||||
0.897766 | + | 0.440473i | \(0.145189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.14982 | −0.680101 | −0.340051 | − | 0.940407i | \(-0.610444\pi\) | ||||
−0.340051 | + | 0.940407i | \(0.610444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.0796 | −0.966875 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.21819 | 0.163084 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.58620 | −0.262249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.21819 | −0.306828 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.2884 | 1.17858 | 0.589292 | − | 0.807920i | \(-0.299407\pi\) | ||||
0.589292 | + | 0.807920i | \(0.299407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5047 | 1.40398 | 0.701991 | − | 0.712186i | \(-0.252295\pi\) | ||||
0.701991 | + | 0.712186i | \(0.252295\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.21819 | −0.158848 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.51602 | 0.677988 | 0.338994 | − | 0.940788i | \(-0.389913\pi\) | ||||
0.338994 | + | 0.940788i | \(0.389913\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.27708 | 0.161418 | 0.0807089 | − | 0.996738i | \(-0.474282\pi\) | ||||
0.0807089 | + | 0.996738i | \(0.474282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.28655 | 0.0907461 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.5066 | 1.43928 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.57491 | −0.249683 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.35673 | −0.0942990 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.57491 | −0.385625 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.42690 | −0.0982320 | −0.0491160 | − | 0.998793i | \(-0.515640\pi\) | ||||
−0.0491160 | + | 0.998793i | \(0.515640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.1498 | 0.763973 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.218187 | −0.0148802 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.1498 | −0.756899 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.0000 | −0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.42690 | −0.0959839 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.71345 | 0.449566 | 0.224783 | − | 0.974409i | \(-0.427833\pi\) | ||||
0.224783 | + | 0.974409i | \(0.427833\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7931 | 0.915480 | 0.457740 | − | 0.889086i | \(-0.348659\pi\) | ||||
0.457740 | + | 0.889086i | \(0.348659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5066 | −0.958620 | −0.479310 | − | 0.877646i | \(-0.659113\pi\) | ||||
−0.479310 | + | 0.877646i | \(0.659113\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.5160 | 1.54724 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.2996 | 1.59192 | 0.795961 | − | 0.605347i | \(-0.206966\pi\) | ||||
0.795961 | + | 0.605347i | \(0.206966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.35673 | −0.0885030 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.28655 | −0.0835703 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.57491 | 0.360611 | 0.180306 | − | 0.983611i | \(-0.442291\pi\) | ||||
0.180306 | + | 0.983611i | \(0.442291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.2996 | 1.56528 | 0.782639 | − | 0.622476i | \(-0.213873\pi\) | ||||
0.782639 | + | 0.622476i | \(0.213873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.7931 | −0.689546 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.21819 | −0.141140 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.3662 | 0.783676 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.0113 | −0.884385 | −0.442192 | − | 0.896920i | \(-0.645799\pi\) | ||||
−0.442192 | + | 0.896920i | \(0.645799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.56363 | 0.475521 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.643274 | 0.0402834 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.9204 | −0.681193 | −0.340596 | − | 0.940210i | \(-0.610629\pi\) | ||||
−0.340596 | + | 0.940210i | \(0.610629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.35673 | −0.581399 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.86146 | 0.300917 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.6658 | −0.657684 | −0.328842 | − | 0.944385i | \(-0.606658\pi\) | ||||
−0.328842 | + | 0.944385i | \(0.606658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.643274 | −0.0395160 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0113 | −0.735079 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.0113 | 0.976225 | 0.488113 | − | 0.872781i | \(-0.337686\pi\) | ||||
0.488113 | + | 0.872781i | \(0.337686\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.7360 | 1.86708 | 0.933540 | − | 0.358473i | \(-0.116702\pi\) | ||||
0.933540 | + | 0.358473i | \(0.116702\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.35673 | 0.566295 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.57491 | −0.336180 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.2996 | 1.21969 | 0.609844 | − | 0.792522i | \(-0.291232\pi\) | ||||
0.609844 | + | 0.792522i | \(0.291232\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.64327 | −0.158249 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.5844 | −1.10865 | −0.554326 | − | 0.832300i | \(-0.687024\pi\) | ||||
−0.554326 | + | 0.832300i | \(0.687024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.0909 | 1.49150 | 0.745751 | − | 0.666225i | \(-0.232091\pi\) | ||||
0.745751 | + | 0.666225i | \(0.232091\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.0796 | 0.890123 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5862 | −0.975659 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.78181 | −0.338936 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.7931 | 0.688960 | 0.344480 | − | 0.938794i | \(-0.388055\pi\) | ||||
0.344480 | + | 0.938794i | \(0.388055\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.43637 | −0.258296 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.57491 | 0.323489 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00947 | 0.174042 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.920352 | 0.0530482 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.43637 | 0.369760 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.0796 | −0.748938 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.85018 | 0.505106 | 0.252553 | − | 0.967583i | \(-0.418730\pi\) | ||||
0.252553 | + | 0.967583i | \(0.418730\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.28655 | −0.0731892 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.8709 | 1.24019 | 0.620093 | − | 0.784528i | \(-0.287095\pi\) | ||||
0.620093 | + | 0.784528i | \(0.287095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.14982 | −0.0649919 | −0.0324960 | − | 0.999472i | \(-0.510346\pi\) | ||||
−0.0324960 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.21819 | −0.237668 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.1022 | 1.63454 | 0.817272 | − | 0.576252i | \(-0.195486\pi\) | ||||
0.817272 | + | 0.576252i | \(0.195486\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.1022 | −1.51743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.28655 | −0.0718081 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.643274 | 0.0357927 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.21819 | −0.123043 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.4364 | −1.01953 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.72292 | 0.315515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.94292 | 0.491548 | 0.245774 | − | 0.969327i | \(-0.420958\pi\) | ||||
0.245774 | + | 0.969327i | \(0.420958\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.21819 | −0.121556 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.28655 | 0.0702917 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3775 | 1.11003 | 0.555016 | − | 0.831840i | \(-0.312712\pi\) | ||||
0.555016 | + | 0.831840i | \(0.312712\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.0796 | −0.710389 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7360 | 0.798000 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0000 | 0.863919 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.35673 | −0.0730437 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.07965 | −0.380055 | −0.190028 | − | 0.981779i | \(-0.560858\pi\) | ||||
−0.190028 | + | 0.981779i | \(0.560858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.1593 | 1.93556 | 0.967781 | − | 0.251792i | \(-0.0810199\pi\) | ||||
0.967781 | + | 0.251792i | \(0.0810199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.21819 | 0.118398 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.1593 | 1.71167 | 0.855833 | − | 0.517252i | \(-0.173045\pi\) | ||||
0.855833 | + | 0.517252i | \(0.173045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.1498 | 0.591771 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.71345 | −0.143611 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.86146 | 0.151022 | 0.0755111 | − | 0.997145i | \(-0.475941\pi\) | ||||
0.0755111 | + | 0.997145i | \(0.475941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.0796 | −1.05391 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0000 | −0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3585 | 0.645111 | 0.322555 | − | 0.946551i | \(-0.395458\pi\) | ||||
0.322555 | + | 0.946551i | \(0.395458\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.57491 | 0.186103 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.71345 | 0.140875 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.495265 | 0.0256438 | 0.0128219 | − | 0.999918i | \(-0.495919\pi\) | ||||
0.0128219 | + | 0.999918i | \(0.495919\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.7836 | −0.555385 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.78363 | −0.142985 | −0.0714927 | − | 0.997441i | \(-0.522776\pi\) | ||||
−0.0714927 | + | 0.997441i | \(0.522776\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.28655 | −0.475764 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.0131 | 1.68689 | 0.843445 | − | 0.537215i | \(-0.180524\pi\) | ||||
0.843445 | + | 0.537215i | \(0.180524\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.5160 | 1.19849 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.218187 | 0.0110911 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.4589 | 1.54433 | 0.772165 | − | 0.635422i | \(-0.219174\pi\) | ||||
0.772165 | + | 0.635422i | \(0.219174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.872747 | −0.0441367 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.86146 | 0.144342 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.28655 | −0.0647333 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.2865 | −0.767210 | −0.383605 | − | 0.923497i | \(-0.625318\pi\) | ||||
−0.383605 | + | 0.923497i | \(0.625318\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.21819 | −0.211173 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.0339 | −1.79944 | −0.899722 | − | 0.436462i | \(-0.856231\pi\) | ||||
−0.899722 | + | 0.436462i | \(0.856231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.86328 | 0.292071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.3662 | 0.612970 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.0226 | −1.68231 | −0.841154 | − | 0.540796i | \(-0.818123\pi\) | ||||
−0.841154 | + | 0.540796i | \(0.818123\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.8727 | 0.733618 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.7135 | 0.920829 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.3662 | 0.607033 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.850175 | 0.0416333 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.72474 | 0.426231 | 0.213116 | − | 0.977027i | \(-0.431639\pi\) | ||||
0.213116 | + | 0.977027i | \(0.431639\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0131 | 1.70643 | 0.853217 | − | 0.521556i | \(-0.174648\pi\) | ||||
0.853217 | + | 0.521556i | \(0.174648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.35673 | 0.0659663 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.643274 | 0.0312034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 55.1724 | 2.66998 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.3662 | −0.597046 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8633 | 0.667771 | 0.333885 | − | 0.942614i | \(-0.391640\pi\) | ||||
0.333885 | + | 0.942614i | \(0.391640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.2408 | −1.45328 | −0.726639 | − | 0.687019i | \(-0.758919\pi\) | ||||
−0.726639 | + | 0.687019i | \(0.758919\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.86146 | 0.233089 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.35673 | −0.0649010 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.5862 | −1.50753 | −0.753763 | − | 0.657146i | \(-0.771764\pi\) | ||||
−0.753763 | + | 0.657146i | \(0.771764\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.7931 | 0.513957 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.2295 | −0.866108 | −0.433054 | − | 0.901368i | \(-0.642564\pi\) | ||||
−0.433054 | + | 0.901368i | \(0.642564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0113 | −0.569390 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.1593 | 0.953502 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.71164 | −0.458320 | −0.229160 | − | 0.973389i | \(-0.573598\pi\) | ||||
−0.229160 | + | 0.973389i | \(0.573598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.9298 | −0.938459 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5160 | 0.541070 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.35673 | 0.438650 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.8633 | −0.929165 | −0.464582 | − | 0.885530i | \(-0.653796\pi\) | ||||
−0.464582 | + | 0.885530i | \(0.653796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.643274 | −0.0300255 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.2996 | −0.945449 | −0.472724 | − | 0.881210i | \(-0.656729\pi\) | ||||
−0.472724 | + | 0.881210i | \(0.656729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.2408 | −1.49836 | −0.749178 | − | 0.662369i | \(-0.769551\pi\) | ||||
−0.749178 | + | 0.662369i | \(0.769551\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.64327 | −0.122579 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.2295 | 1.21376 | 0.606878 | − | 0.794795i | \(-0.292422\pi\) | ||||
0.606878 | + | 0.794795i | \(0.292422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.42690 | −0.250591 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.14982 | −0.421602 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.21637 | −0.0559288 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.643274 | 0.0294535 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.1611 | −1.51517 | −0.757585 | − | 0.652737i | \(-0.773621\pi\) | ||||
−0.757585 | + | 0.652737i | \(0.773621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.92035 | 0.224349 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.72292 | 0.260402 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.78181 | −0.262539 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.5636 | 0.886513 | 0.443256 | − | 0.896395i | \(-0.353823\pi\) | ||||
0.443256 | + | 0.896395i | \(0.353823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.50474 | −0.248933 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8615 | 1.21224 | 0.606120 | − | 0.795373i | \(-0.292725\pi\) | ||||
0.606120 | + | 0.795373i | \(0.292725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.12725 | 0.140844 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.57491 | 0.250574 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −47.0320 | −2.10968 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.0226 | −1.79166 | −0.895828 | − | 0.444401i | \(-0.853417\pi\) | ||||
−0.895828 | + | 0.444401i | \(0.853417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.920352 | −0.0411183 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.6527 | 0.787097 | 0.393549 | − | 0.919304i | \(-0.371247\pi\) | ||||
0.393549 | + | 0.919304i | \(0.371247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.43637 | 0.286415 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.07965 | 0.358830 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.8615 | −0.747371 | −0.373686 | − | 0.927555i | \(-0.621906\pi\) | ||||
−0.373686 | + | 0.927555i | \(0.621906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.1819 | 1.86602 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.28655 | −0.0566921 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.56363 | −0.332648 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.6658 | 0.731549 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.57491 | 0.156620 | 0.0783099 | − | 0.996929i | \(-0.475048\pi\) | ||||
0.0783099 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.4364 | 1.24344 | 0.621718 | − | 0.783241i | \(-0.286435\pi\) | ||||
0.621718 | + | 0.783241i | \(0.286435\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.21819 | −0.184097 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.70035 | −0.0740684 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1593 | −0.919969 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.43637 | 0.192522 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.92982 | −0.343479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.28655 | −0.0556224 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.0226 | −1.03665 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −60.1706 | −2.59173 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.573097 | 0.0246394 | 0.0123197 | − | 0.999924i | \(-0.496078\pi\) | ||||
0.0123197 | + | 0.999924i | \(0.496078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.14982 | 0.392657 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4364 | −0.789727 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.85018 | 0.378406 | 0.189203 | − | 0.981938i | \(-0.439410\pi\) | ||||
0.189203 | + | 0.981938i | \(0.439410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.0796 | 0.558226 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.86146 | 0.207105 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.42690 | 0.230775 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.21819 | −0.0941568 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.29965 | 0.351667 | 0.175834 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175834 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.483979 | −0.0204701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.58620 | 0.151409 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.3793 | −0.732450 | −0.366225 | − | 0.930526i | \(-0.619350\pi\) | ||||
−0.366225 | + | 0.930526i | \(0.619350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.0796 | −0.550265 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.21819 | 0.177147 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.4346 | 0.814739 | 0.407370 | − | 0.913263i | \(-0.366446\pi\) | ||||
0.407370 | + | 0.913263i | \(0.366446\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.1629 | −1.34598 | −0.672988 | − | 0.739653i | \(-0.734990\pi\) | ||||
−0.672988 | + | 0.739653i | \(0.734990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.2884 | −0.680456 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.35673 | −0.0565794 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.1688 | −1.29757 | −0.648786 | − | 0.760971i | \(-0.724723\pi\) | ||||
−0.648786 | + | 0.760971i | \(0.724723\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.5047 | −0.810589 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −52.1629 | −2.16408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.58620 | −0.148525 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.21819 | 0.0917107 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.5160 | −0.970610 | −0.485305 | − | 0.874345i | \(-0.661291\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.64327 | −0.108914 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.51602 | −0.391437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.0131 | −1.27356 | −0.636778 | − | 0.771047i | \(-0.719733\pi\) | ||||
−0.636778 | + | 0.771047i | \(0.719733\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.71345 | −0.111241 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.27708 | −0.0931946 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.1724 | −1.60054 | −0.800270 | − | 0.599639i | \(-0.795311\pi\) | ||||
−0.800270 | + | 0.599639i | \(0.795311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.86328 | −0.157586 | −0.0787932 | − | 0.996891i | \(-0.525107\pi\) | ||||
−0.0787932 | + | 0.996891i | \(0.525107\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.28655 | −0.0523923 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.0796 | −0.816354 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.02257 | −0.325626 | −0.162813 | − | 0.986657i | \(-0.552057\pi\) | ||||
−0.162813 | + | 0.986657i | \(0.552057\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.5066 | −0.830967 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00947 | −0.121750 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.8633 | 0.802270 | 0.401135 | − | 0.916019i | \(-0.368616\pi\) | ||||
0.401135 | + | 0.916019i | \(0.368616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.57491 | 0.144154 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.3888 | 0.740304 | 0.370152 | − | 0.928971i | \(-0.379306\pi\) | ||||
0.370152 | + | 0.928971i | \(0.379306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.4364 | −0.499860 | −0.249930 | − | 0.968264i | \(-0.580408\pi\) | ||||
−0.249930 | + | 0.968264i | \(0.580408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.35673 | 0.0544435 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 50.6658 | 2.02988 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.57491 | 0.222641 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.42690 | −0.0568943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6182 | −1.69661 | −0.848303 | − | 0.529512i | \(-0.822375\pi\) | ||||
−0.848303 | + | 0.529512i | \(0.822375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.42690 | 0.0567143 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.28655 | −0.368525 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.9411 | −0.948581 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.1498 | −0.441080 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.16111 | −0.124856 | −0.0624282 | − | 0.998049i | \(-0.519884\pi\) | ||||
−0.0624282 | + | 0.998049i | \(0.519884\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.5368 | −1.44087 | −0.720435 | − | 0.693523i | \(-0.756058\pi\) | ||||
−0.720435 | + | 0.693523i | \(0.756058\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.218187 | 0.00859109 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.6527 | 0.694001 | 0.347001 | − | 0.937865i | \(-0.387200\pi\) | ||||
0.347001 | + | 0.937865i | \(0.387200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.7324 | −0.970831 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1498 | 0.436996 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.51602 | −0.215859 | −0.107929 | − | 0.994159i | \(-0.534422\pi\) | ||||
−0.107929 | + | 0.994159i | \(0.534422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.86146 | 0.111807 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.0000 | 0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2996 | −0.712853 | −0.356427 | − | 0.934323i | \(-0.616005\pi\) | ||||
−0.356427 | + | 0.934323i | \(0.616005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.72292 | 0.300387 | 0.150193 | − | 0.988657i | \(-0.452010\pi\) | ||||
0.150193 | + | 0.988657i | \(0.452010\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.42690 | 0.0554163 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.21819 | −0.163574 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.59567 | −0.255385 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.71345 | −0.259557 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −72.9179 | −2.81496 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9637 | 1.54049 | 0.770243 | − | 0.637750i | \(-0.220135\pi\) | ||||
0.770243 | + | 0.637750i | \(0.220135\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.2295 | −1.85361 | −0.926805 | − | 0.375544i | \(-0.877456\pi\) | ||||
−0.926805 | + | 0.375544i | \(0.877456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.3888 | 0.935955 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.7931 | −0.528553 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5862 | 0.596389 | 0.298195 | − | 0.954505i | \(-0.403616\pi\) | ||||
0.298195 | + | 0.954505i | \(0.403616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.8727 | 0.568258 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.5066 | 0.553459 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.42690 | −0.0543607 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.8633 | −1.28822 | −0.644110 | − | 0.764933i | \(-0.722772\pi\) | ||||
−0.644110 | + | 0.764933i | \(0.722772\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23.5160 | −0.893300 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.850175 | 0.0322490 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.29965 | 0.0871054 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.2996 | −0.919097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.3317 | 1.18338 | 0.591691 | − | 0.806165i | \(-0.298461\pi\) | ||||
0.591691 | + | 0.806165i | \(0.298461\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.21819 | −0.0836605 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.35673 | 0.0510972 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.1498 | −1.02107 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.939294 | −0.0352759 | −0.0176380 | − | 0.999844i | \(-0.505615\pi\) | ||||
−0.0176380 | + | 0.999844i | \(0.505615\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.28655 | 0.0482493 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.58620 | 0.134304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.3662 | −0.462470 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.57491 | −0.208199 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.1611 | 1.23670 | 0.618350 | − | 0.785903i | \(-0.287801\pi\) | ||||
0.618350 | + | 0.785903i | \(0.287801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.42690 | 0.202108 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.2996 | −0.903714 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.86146 | 0.180550 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.2408 | 1.19574 | 0.597872 | − | 0.801592i | \(-0.296013\pi\) | ||||
0.597872 | + | 0.801592i | \(0.296013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.140354 | 0.00519118 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.5862 | 0.649561 | 0.324781 | − | 0.945789i | \(-0.394710\pi\) | ||||
0.324781 | + | 0.945789i | \(0.394710\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.7931 | 0.398109 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.17240 | 0.264199 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.5731 | −0.536080 | −0.268040 | − | 0.963408i | \(-0.586376\pi\) | ||||
−0.268040 | + | 0.963408i | \(0.586376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.21819 | 0.0814871 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.5862 | 1.01204 | 0.506020 | − | 0.862522i | \(-0.331116\pi\) | ||||
0.506020 | + | 0.862522i | \(0.331116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.1593 | 0.738579 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.3662 | −0.452455 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.42690 | 0.198295 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.5160 | 0.420226 | 0.210113 | − | 0.977677i | \(-0.432617\pi\) | ||||
0.210113 | + | 0.977677i | \(0.432617\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.0113 | 0.510600 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.5160 | 0.419111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.2902 | −0.483040 | −0.241520 | − | 0.970396i | \(-0.577646\pi\) | ||||
−0.241520 | + | 0.970396i | \(0.577646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.56363 | −0.274542 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.84070 | −0.284225 | −0.142113 | − | 0.989850i | \(-0.545390\pi\) | ||||
−0.142113 | + | 0.989850i | \(0.545390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 77.7681 | 2.81539 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.643274 | −0.0232576 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.84070 | −0.355327 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.2996 | −1.88597 | −0.942987 | − | 0.332830i | \(-0.891996\pi\) | ||||
−0.942987 | + | 0.332830i | \(0.891996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9204 | 0.393287 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.2426 | −0.907912 | −0.453956 | − | 0.891024i | \(-0.649988\pi\) | ||||
−0.453956 | + | 0.891024i | \(0.649988\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.64327 | −0.0949492 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.35673 | 0.335671 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.57491 | 0.128085 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.1593 | 2.22423 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.86146 | −0.173734 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.14982 | −0.326571 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.8633 | 0.636757 | 0.318379 | − | 0.947964i | \(-0.396862\pi\) | ||||
0.318379 | + | 0.947964i | \(0.396862\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.6658 | 0.379714 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 55.1724 | 1.96170 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.0131 | −1.03029 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.643274 | 0.0228146 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.50655 | 0.230474 | 0.115237 | − | 0.993338i | \(-0.463237\pi\) | ||||
0.115237 | + | 0.993338i | \(0.463237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.872747 | 0.0308756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0113 | 0.424398 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −55.7491 | −1.96734 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.72292 | 0.201707 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.0113 | −0.563624 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.84070 | 0.135032 | 0.0675160 | − | 0.997718i | \(-0.478493\pi\) | ||||
0.0675160 | + | 0.997718i | \(0.478493\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.44584 | 0.261459 | 0.130729 | − | 0.991418i | \(-0.458268\pi\) | ||||
0.130729 | + | 0.991418i | \(0.458268\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.7360 | −1.07796 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.50474 | −0.192822 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.218187 | 0.00763339 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.35673 | −0.326950 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.2960 | −1.05734 | −0.528669 | − | 0.848828i | \(-0.677309\pi\) | ||||
−0.528669 | + | 0.848828i | \(0.677309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.3811 | −1.12873 | −0.564367 | − | 0.825524i | \(-0.690880\pi\) | ||||
−0.564367 | + | 0.825524i | \(0.690880\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.57491 | 0.194094 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.9524 | 0.415625 | 0.207813 | − | 0.978169i | \(-0.433366\pi\) | ||||
0.207813 | + | 0.978169i | \(0.433366\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.5767 | −0.784122 | −0.392061 | − | 0.919939i | \(-0.628238\pi\) | ||||
−0.392061 | + | 0.919939i | \(0.628238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.2996 | −0.704187 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.94292 | 0.240558 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.920352 | −0.0318501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.64327 | 0.0913649 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.14982 | 0.108744 | 0.0543720 | − | 0.998521i | \(-0.482684\pi\) | ||||
0.0543720 | + | 0.998521i | \(0.482684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.36620 | −0.185041 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.5844 | 0.640080 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.07965 | 0.277948 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 84.6997 | 2.91032 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.0909 | −0.861119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.00947 | 0.103163 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.5826 | 0.396580 | 0.198290 | − | 0.980143i | \(-0.436461\pi\) | ||||
0.198290 | + | 0.980143i | \(0.436461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.91088 | 0.133593 | 0.0667966 | − | 0.997767i | \(-0.478722\pi\) | ||||
0.0667966 | + | 0.997767i | \(0.478722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.01310 | 0.171045 | 0.0855224 | − | 0.996336i | \(-0.472744\pi\) | ||||
0.0855224 | + | 0.996336i | \(0.472744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0796 | −0.513913 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.7324 | −1.38655 | −0.693273 | − | 0.720675i | \(-0.743832\pi\) | ||||
−0.693273 | + | 0.720675i | \(0.743832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6658 | 0.566656 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.5862 | 0.563297 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.17240 | −0.243307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.85381 | 0.0966975 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.78181 | 0.195685 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.21819 | −0.142601 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.2371 | 1.22364 | 0.611820 | − | 0.790997i | \(-0.290438\pi\) | ||||
0.611820 | + | 0.790997i | \(0.290438\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.7931 | −0.397771 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0226 | −0.607196 | −0.303598 | − | 0.952800i | \(-0.598188\pi\) | ||||
−0.303598 | + | 0.952800i | \(0.598188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.6771 | 1.77273 | 0.886363 | − | 0.462990i | \(-0.153224\pi\) | ||||
0.886363 | + | 0.462990i | \(0.153224\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.43637 | 0.149127 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.8727 | −1.10376 | −0.551879 | − | 0.833924i | \(-0.686089\pi\) | ||||
−0.551879 | + | 0.833924i | \(0.686089\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.1724 | 1.31380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.57491 | −0.186767 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.35673 | 0.0454011 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0226 | −0.802986 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.00947 | −0.100483 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.8502 | −0.428577 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.413802 | 0.0137857 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.920352 | −0.0306274 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.14982 | 0.304150 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.5957 | 0.883095 | 0.441547 | − | 0.897238i | \(-0.354430\pi\) | ||||
0.441547 | + | 0.897238i | \(0.354430\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.43637 | −0.213481 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.15930 | −0.204067 | −0.102033 | − | 0.994781i | \(-0.532535\pi\) | ||||
−0.102033 | + | 0.994781i | \(0.532535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68.9405 | 2.28160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.0796 | 0.432400 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.0702 | −0.398592 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.8858 | 1.11779 | 0.558895 | − | 0.829238i | \(-0.311225\pi\) | ||||
0.558895 | + | 0.829238i | \(0.311225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.85018 | −0.291623 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.7324 | 0.814077 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.21819 | −0.0729335 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.28655 | 0.0422558 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.8953 | −1.14488 | −0.572439 | − | 0.819947i | \(-0.694003\pi\) | ||||
−0.572439 | + | 0.819947i | \(0.694003\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.7931 | 0.353730 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.8709 | −0.716022 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.58620 | 0.117281 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.29602 | −0.205682 | −0.102841 | − | 0.994698i | \(-0.532793\pi\) | ||||
−0.102841 | + | 0.994698i | \(0.532793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.14982 | 0.0375231 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.8651 | 0.354192 | 0.177096 | − | 0.984194i | \(-0.443330\pi\) | ||||
0.177096 | + | 0.984194i | \(0.443330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.85018 | −0.157943 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.21819 | 0.137218 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.79310 | 0.318233 | 0.159116 | − | 0.987260i | \(-0.449135\pi\) | ||||
0.159116 | + | 0.987260i | \(0.449135\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.1819 | −0.720054 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.1022 | −0.943704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.35310 | 0.0438311 | 0.0219155 | − | 0.999760i | \(-0.493024\pi\) | ||||
0.0219155 | + | 0.999760i | \(0.493024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.2884 | −0.527079 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.1022 | 0.876090 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −62.7360 | −2.02585 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0131 | −0.774616 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.28655 | 0.0414585 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5047 | −0.627880 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.9637 | −0.706304 | −0.353152 | − | 0.935566i | \(-0.614890\pi\) | ||||
−0.353152 | + | 0.935566i | \(0.614890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.643274 | −0.0206649 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.7455 | 0.441114 | 0.220557 | − | 0.975374i | \(-0.429213\pi\) | ||||
0.220557 | + | 0.975374i | \(0.429213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.58620 | −0.114968 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.21819 | 0.0710388 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.3698 | 1.54749 | 0.773744 | − | 0.633498i | \(-0.218382\pi\) | ||||
0.773744 | + | 0.633498i | \(0.218382\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −66.9619 | −2.14011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.4364 | 0.588628 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.0665 | −0.448653 | −0.224327 | − | 0.974514i | \(-0.572018\pi\) | ||||
−0.224327 | + | 0.974514i | \(0.572018\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.51602 | −0.303206 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.72292 | −0.182163 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.296019 | −0.00941287 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.2865 | 1.05738 | 0.528691 | − | 0.848814i | \(-0.322683\pi\) | ||||
0.528691 | + | 0.848814i | \(0.322683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.94292 | −0.283795 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.27708 | −0.0721882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.5957 | −1.53904 | −0.769520 | − | 0.638623i | \(-0.779505\pi\) | ||||
−0.769520 | + | 0.638623i | \(0.779505\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.21819 | 0.0701803 |
(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 | 4560.2.a.bq.1.3 | 3 | ||
4.3 | odd | 2 | 2280.2.a.t.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 6840.2.a.bn.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.t.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
4560.2.a.bq.1.3 | 3 | 1.1 | even | 1 | trivial | ||
6840.2.a.bn.1.1 | 3 | 12.11 | even | 2 |