Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, 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("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + 6652 x^{11} - 67665 x^{10} - 17345 x^{9} + 174105 x^{8} + 41499 x^{7} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-1.76710\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 | ||||||||
\(3\) | 1.76710 | 1.02024 | 0.510119 | − | 0.860104i | \(-0.329601\pi\) | ||||
0.510119 | + | 0.860104i | \(0.329601\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0387940 | 0.0146628 | 0.00733138 | − | 0.999973i | \(-0.497666\pi\) | ||||
0.00733138 | + | 0.999973i | \(0.497666\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.122653 | 0.0408842 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.56985 | −1.37786 | −0.688931 | − | 0.724827i | \(-0.741920\pi\) | ||||
−0.688931 | + | 0.724827i | \(0.741920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.95916 | 0.820724 | 0.410362 | − | 0.911923i | \(-0.365402\pi\) | ||||
0.410362 | + | 0.911923i | \(0.365402\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.76710 | 0.456264 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.20092 | −0.776338 | −0.388169 | − | 0.921588i | \(-0.626892\pi\) | ||||
−0.388169 | + | 0.921588i | \(0.626892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.27921 | 0.522886 | 0.261443 | − | 0.965219i | \(-0.415802\pi\) | ||||
0.261443 | + | 0.965219i | \(0.415802\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0685530 | 0.0149595 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.32494 | 1.11033 | 0.555163 | − | 0.831741i | \(-0.312656\pi\) | ||||
0.555163 | + | 0.831741i | \(0.312656\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.08457 | −0.978526 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.46209 | −1.75707 | −0.878533 | − | 0.477682i | \(-0.841477\pi\) | ||||
−0.878533 | + | 0.477682i | \(0.841477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.25733 | −1.48306 | −0.741530 | − | 0.670920i | \(-0.765899\pi\) | ||||
−0.741530 | + | 0.670920i | \(0.765899\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.07539 | −1.40575 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0387940 | 0.00655738 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.02356 | −1.31906 | −0.659532 | − | 0.751676i | \(-0.729246\pi\) | ||||
−0.659532 | + | 0.751676i | \(0.729246\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.22914 | 0.837333 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.45591 | −0.227375 | −0.113688 | − | 0.993517i | \(-0.536266\pi\) | ||||
−0.113688 | + | 0.993517i | \(0.536266\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.90058 | −0.747332 | −0.373666 | − | 0.927563i | \(-0.621899\pi\) | ||||
−0.373666 | + | 0.927563i | \(0.621899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.122653 | 0.0182840 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.28585 | −0.916885 | −0.458442 | − | 0.888724i | \(-0.651592\pi\) | ||||
−0.458442 | + | 0.888724i | \(0.651592\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99850 | −0.999785 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.65636 | −0.792049 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.800929 | −0.110016 | −0.0550080 | − | 0.998486i | \(-0.517518\pi\) | ||||
−0.0550080 | + | 0.998486i | \(0.517518\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.56985 | −0.616198 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.02760 | 0.533468 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.10666 | −0.925208 | −0.462604 | − | 0.886565i | \(-0.653085\pi\) | ||||
−0.462604 | + | 0.886565i | \(0.653085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2872 | 1.57322 | 0.786608 | − | 0.617453i | \(-0.211835\pi\) | ||||
0.786608 | + | 0.617453i | \(0.211835\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.00475819 | 0.000599475 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.95916 | 0.367039 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.7703 | −1.43797 | −0.718986 | − | 0.695024i | \(-0.755394\pi\) | ||||
−0.718986 | + | 0.695024i | \(0.755394\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.40972 | 1.13280 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.1978 | 1.56629 | 0.783147 | − | 0.621837i | \(-0.213613\pi\) | ||||
0.783147 | + | 0.621837i | \(0.213613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9471 | 1.39830 | 0.699150 | − | 0.714975i | \(-0.253562\pi\) | ||||
0.699150 | + | 0.714975i | \(0.253562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.76710 | 0.204047 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.177283 | −0.0202032 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5301 | 1.18473 | 0.592366 | − | 0.805669i | \(-0.298194\pi\) | ||||
0.592366 | + | 0.805669i | \(0.298194\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.35291 | −1.03921 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.60891 | 0.286365 | 0.143182 | − | 0.989696i | \(-0.454266\pi\) | ||||
0.143182 | + | 0.989696i | \(0.454266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20092 | −0.347189 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.7205 | −1.79262 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.97946 | −0.209822 | −0.104911 | − | 0.994482i | \(-0.533456\pi\) | ||||
−0.104911 | + | 0.994482i | \(0.533456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.114798 | 0.0120341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.5915 | −1.51307 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.27921 | 0.233842 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.49362 | 0.659327 | 0.329664 | − | 0.944098i | \(-0.393065\pi\) | ||||
0.329664 | + | 0.944098i | \(0.393065\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.560504 | −0.0563328 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.67550 | 0.564733 | 0.282367 | − | 0.959307i | \(-0.408881\pi\) | ||||
0.282367 | + | 0.959307i | \(0.408881\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.74080 | 0.270059 | 0.135030 | − | 0.990842i | \(-0.456887\pi\) | ||||
0.135030 | + | 0.990842i | \(0.456887\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0685530 | 0.00669009 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.83326 | −0.950617 | −0.475309 | − | 0.879819i | \(-0.657664\pi\) | ||||
−0.475309 | + | 0.879819i | \(0.657664\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.08385 | 0.582728 | 0.291364 | − | 0.956612i | \(-0.405891\pi\) | ||||
0.291364 | + | 0.956612i | \(0.405891\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.1785 | −1.34576 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.26544 | −0.495331 | −0.247666 | − | 0.968846i | \(-0.579663\pi\) | ||||
−0.247666 | + | 0.968846i | \(0.579663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.32494 | 0.496553 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.362949 | 0.0335547 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.124177 | −0.0113833 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.88353 | 0.898502 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.57275 | −0.231977 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8506 | −1.58398 | −0.791992 | − | 0.610531i | \(-0.790956\pi\) | ||||
−0.791992 | + | 0.610531i | \(0.790956\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.65983 | −0.762456 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.79650 | −0.156961 | −0.0784804 | − | 0.996916i | \(-0.525007\pi\) | ||||
−0.0784804 | + | 0.996916i | \(0.525007\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0884197 | 0.00766696 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.08457 | −0.437610 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.61311 | −0.223253 | −0.111626 | − | 0.993750i | \(-0.535606\pi\) | ||||
−0.111626 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3106 | −1.29863 | −0.649313 | − | 0.760521i | \(-0.724944\pi\) | ||||
−0.649313 | + | 0.760521i | \(0.724944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.1077 | −0.935440 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.5229 | −1.13084 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.46209 | −0.785784 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.3671 | −1.02002 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.28565 | −0.514941 | −0.257470 | − | 0.966286i | \(-0.582889\pi\) | ||||
−0.257470 | + | 0.966286i | \(0.582889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.392602 | −0.0317400 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.25733 | −0.663244 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.1820 | 1.37127 | 0.685635 | − | 0.727946i | \(-0.259525\pi\) | ||||
0.685635 | + | 0.727946i | \(0.259525\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.41532 | −0.112242 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.206576 | 0.0162805 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.15053 | 0.560073 | 0.280036 | − | 0.959989i | \(-0.409653\pi\) | ||||
0.280036 | + | 0.959989i | \(0.409653\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.07539 | −0.628669 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.33831 | −0.180944 | −0.0904720 | − | 0.995899i | \(-0.528838\pi\) | ||||
−0.0904720 | + | 0.995899i | \(0.528838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.24336 | −0.326412 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.279551 | 0.0213778 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.3007 | −0.859179 | −0.429589 | − | 0.903024i | \(-0.641342\pi\) | ||||
−0.429589 | + | 0.903024i | \(0.641342\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0387940 | 0.00293255 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.5582 | −0.943932 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.0976 | 0.978964 | 0.489482 | − | 0.872013i | \(-0.337186\pi\) | ||||
0.489482 | + | 0.872013i | \(0.337186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.3326 | −1.06533 | −0.532667 | − | 0.846325i | \(-0.678810\pi\) | ||||
−0.532667 | + | 0.846325i | \(0.678810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.7128 | 1.60505 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.02356 | −0.589904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.6277 | 1.06969 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.197251 | −0.0143479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.61903 | 0.478936 | 0.239468 | − | 0.970904i | \(-0.423027\pi\) | ||||
0.239468 | + | 0.970904i | \(0.423027\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.71813 | −0.627545 | −0.313772 | − | 0.949498i | \(-0.601593\pi\) | ||||
−0.313772 | + | 0.949498i | \(0.601593\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.22914 | 0.374467 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.0485 | −1.42840 | −0.714198 | − | 0.699944i | \(-0.753208\pi\) | ||||
−0.714198 | + | 0.699944i | \(0.753208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.44127 | −0.102169 | −0.0510846 | − | 0.998694i | \(-0.516268\pi\) | ||||
−0.0510846 | + | 0.998694i | \(0.516268\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.7993 | −1.46707 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.367072 | −0.0257634 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.45591 | −0.101685 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.653118 | 0.0453949 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.4156 | −0.720465 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9084 | 1.30171 | 0.650855 | − | 0.759202i | \(-0.274411\pi\) | ||||
0.650855 | + | 0.759202i | \(0.274411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.3219 | 1.59799 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.90058 | −0.334217 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.320335 | −0.0217457 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.1117 | 1.42660 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.47205 | −0.637159 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.41547 | −0.362647 | −0.181323 | − | 0.983424i | \(-0.558038\pi\) | ||||
−0.181323 | + | 0.983424i | \(0.558038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.122653 | 0.00817685 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.2785 | −1.21319 | −0.606594 | − | 0.795012i | \(-0.707465\pi\) | ||||
−0.606594 | + | 0.795012i | \(0.707465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.23060 | −0.0813205 | −0.0406602 | − | 0.999173i | \(-0.512946\pi\) | ||||
−0.0406602 | + | 0.999173i | \(0.512946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.313277 | −0.0206121 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.6000 | 1.67711 | 0.838555 | − | 0.544817i | \(-0.183401\pi\) | ||||
0.838555 | + | 0.544817i | \(0.183401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.28585 | −0.410043 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.6078 | 1.20871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.4541 | 0.805590 | 0.402795 | − | 0.915290i | \(-0.368039\pi\) | ||||
0.402795 | + | 0.915290i | \(0.368039\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3219 | 1.18022 | 0.590108 | − | 0.807324i | \(-0.299085\pi\) | ||||
0.590108 | + | 0.807324i | \(0.299085\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.27386 | −0.0817179 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.99850 | −0.447117 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.74455 | 0.429145 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.61021 | 0.292160 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.6627 | −1.43046 | −0.715230 | − | 0.698889i | \(-0.753678\pi\) | ||||
−0.715230 | + | 0.698889i | \(0.753678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.3342 | −1.52988 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.65636 | −0.354215 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.7215 | −1.23019 | −0.615096 | − | 0.788452i | \(-0.710883\pi\) | ||||
−0.615096 | + | 0.788452i | \(0.710883\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.311266 | −0.0193411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.16055 | −0.0718363 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.0741 | −1.29948 | −0.649741 | − | 0.760155i | \(-0.725123\pi\) | ||||
−0.649741 | + | 0.760155i | \(0.725123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.800929 | −0.0492007 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.49791 | −0.214068 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.51179 | 0.0921756 | 0.0460878 | − | 0.998937i | \(-0.485325\pi\) | ||||
0.0460878 | + | 0.998937i | \(0.485325\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5008 | −0.941607 | −0.470803 | − | 0.882238i | \(-0.656036\pi\) | ||||
−0.470803 | + | 0.882238i | \(0.656036\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.202859 | 0.0122776 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.56985 | −0.275572 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.5766 | 1.41658 | 0.708292 | − | 0.705920i | \(-0.249466\pi\) | ||||
0.708292 | + | 0.705920i | \(0.249466\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.01278 | −0.0606337 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.81071 | 0.465948 | 0.232974 | − | 0.972483i | \(-0.425154\pi\) | ||||
0.232974 | + | 0.972483i | \(0.425154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.56257 | −0.211773 | −0.105886 | − | 0.994378i | \(-0.533768\pi\) | ||||
−0.105886 | + | 0.994378i | \(0.533768\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.02760 | 0.238574 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0564807 | −0.00333395 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.75409 | −0.397299 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4749 | 0.672670 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.02125 | −0.351765 | −0.175882 | − | 0.984411i | \(-0.556278\pi\) | ||||
−0.175882 | + | 0.984411i | \(0.556278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.10666 | −0.413766 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.2357 | 1.34827 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.7574 | 0.911272 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.190113 | −0.0109579 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.0292 | 0.576162 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.2872 | 0.703564 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0560 | 1.31587 | 0.657936 | − | 0.753074i | \(-0.271430\pi\) | ||||
0.657936 | + | 0.753074i | \(0.271430\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.84328 | 0.275524 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.3684 | 1.15498 | 0.577492 | − | 0.816396i | \(-0.304032\pi\) | ||||
0.577492 | + | 0.816396i | \(0.304032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2529 | 0.862143 | 0.431072 | − | 0.902318i | \(-0.358136\pi\) | ||||
0.431072 | + | 0.902318i | \(0.358136\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.00475819 | 0.000268094 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.23641 | 0.181775 | 0.0908874 | − | 0.995861i | \(-0.471030\pi\) | ||||
0.0908874 | + | 0.995861i | \(0.471030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.2403 | 2.42099 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.3764 | −0.969855 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.29557 | −0.405937 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.95916 | 0.164145 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.7508 | 0.594520 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.243853 | −0.0134441 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.7991 | −0.648537 | −0.324268 | − | 0.945965i | \(-0.605118\pi\) | ||||
−0.324268 | + | 0.945965i | \(0.605118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.984111 | −0.0539289 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.7703 | −0.643081 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3246 | 1.10715 | 0.553575 | − | 0.832799i | \(-0.313263\pi\) | ||||
0.553575 | + | 0.832799i | \(0.313263\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.30458 | −0.505355 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.7347 | 2.04345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.543058 | −0.0293224 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.40972 | 0.506602 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.62496 | −0.301963 | −0.150982 | − | 0.988537i | \(-0.548243\pi\) | ||||
−0.150982 | + | 0.988537i | \(0.548243\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0986 | 1.07585 | 0.537927 | − | 0.842991i | \(-0.319207\pi\) | ||||
0.537927 | + | 0.842991i | \(0.319207\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.0461 | −0.803100 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6630 | −0.673984 | −0.336992 | − | 0.941508i | \(-0.609410\pi\) | ||||
−0.336992 | + | 0.941508i | \(0.609410\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.1978 | 0.700468 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.219433 | −0.0116136 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.1956 | −1.01311 | −0.506553 | − | 0.862209i | \(-0.669081\pi\) | ||||
−0.506553 | + | 0.862209i | \(0.669081\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.8052 | −0.726590 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.4652 | 0.916686 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.9471 | 0.625338 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.36036 | −0.279809 | −0.139904 | − | 0.990165i | \(-0.544679\pi\) | ||||
−0.139904 | + | 0.990165i | \(0.544679\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.178572 | −0.00929606 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0310712 | −0.00161314 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.61435 | 0.135366 | 0.0676831 | − | 0.997707i | \(-0.478439\pi\) | ||||
0.0676831 | + | 0.997707i | \(0.478439\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.76710 | 0.0912528 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.9999 | −1.44207 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.5377 | −1.00359 | −0.501793 | − | 0.864988i | \(-0.667326\pi\) | ||||
−0.501793 | + | 0.864988i | \(0.667326\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.5438 | −1.61604 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.6004 | −1.10373 | −0.551865 | − | 0.833933i | \(-0.686084\pi\) | ||||
−0.551865 | + | 0.833933i | \(0.686084\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.177283 | −0.00903517 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.601070 | −0.0305541 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.8691 | −0.551083 | −0.275542 | − | 0.961289i | \(-0.588857\pi\) | ||||
−0.275542 | + | 0.961289i | \(0.588857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.0447 | −0.861989 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.17460 | −0.160137 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.5301 | 0.529828 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.11621 | 0.256775 | 0.128388 | − | 0.991724i | \(-0.459020\pi\) | ||||
0.128388 | + | 0.991724i | \(0.459020\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.156247 | 0.00782212 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6595 | 0.532308 | 0.266154 | − | 0.963930i | \(-0.414247\pi\) | ||||
0.266154 | + | 0.963930i | \(0.414247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.4348 | −1.21718 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.35291 | −0.464750 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.6665 | 1.81749 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.4102 | 1.20700 | 0.603502 | − | 0.797361i | \(-0.293771\pi\) | ||||
0.603502 | + | 0.797361i | \(0.293771\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.61763 | −0.227771 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.275696 | −0.0135661 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.60891 | 0.128066 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.0554 | −1.32491 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.51427 | −0.464802 | −0.232401 | − | 0.972620i | \(-0.574658\pi\) | ||||
−0.232401 | + | 0.972620i | \(0.574658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.28534 | −0.452540 | −0.226270 | − | 0.974065i | \(-0.572653\pi\) | ||||
−0.226270 | + | 0.974065i | \(0.572653\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.770976 | −0.0374861 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.20092 | −0.155268 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.476670 | 0.0230677 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.8964 | −1.15373 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.19193 | 0.0574132 | 0.0287066 | − | 0.999588i | \(-0.490861\pi\) | ||||
0.0287066 | + | 0.999588i | \(0.490861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.166866 | −0.00801906 | −0.00400953 | − | 0.999992i | \(-0.501276\pi\) | ||||
−0.00400953 | + | 0.999992i | \(0.501276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.7205 | −0.801686 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.1367 | 0.580575 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2855 | −0.777263 | −0.388632 | − | 0.921393i | \(-0.627052\pi\) | ||||
−0.388632 | + | 0.921393i | \(0.627052\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.858384 | −0.0408754 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.9686 | −0.663666 | −0.331833 | − | 0.943338i | \(-0.607667\pi\) | ||||
−0.331833 | + | 0.943338i | \(0.607667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.97946 | −0.0938353 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.1074 | −0.525362 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.7196 | −0.647470 | −0.323735 | − | 0.946148i | \(-0.604939\pi\) | ||||
−0.323735 | + | 0.946148i | \(0.604939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.65330 | 0.313292 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.76710 | 0.0830257 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.114798 | 0.00538180 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9449 | −0.839427 | −0.419714 | − | 0.907657i | \(-0.637869\pi\) | ||||
−0.419714 | + | 0.907657i | \(0.637869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.2753 | 0.759667 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.8821 | −1.43832 | −0.719160 | − | 0.694844i | \(-0.755473\pi\) | ||||
−0.719160 | + | 0.694844i | \(0.755473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.9285 | 0.740262 | 0.370131 | − | 0.928979i | \(-0.379313\pi\) | ||||
0.370131 | + | 0.928979i | \(0.379313\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.5915 | −0.676667 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.60709 | 0.0743673 | 0.0371836 | − | 0.999308i | \(-0.488161\pi\) | ||||
0.0371836 | + | 0.999308i | \(0.488161\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.456617 | −0.0210846 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.3623 | 1.39902 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.3949 | 1.02972 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.27921 | 0.104577 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0982360 | −0.00449792 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.1231 | −1.28498 | −0.642489 | − | 0.766295i | \(-0.722098\pi\) | ||||
−0.642489 | + | 0.766295i | \(0.722098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.7430 | −1.08259 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.365041 | 0.0166099 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.49362 | 0.294860 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.4637 | −1.78827 | −0.894135 | − | 0.447797i | \(-0.852209\pi\) | ||||
−0.894135 | + | 0.447797i | \(0.852209\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.6357 | 0.571407 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.1021 | −0.681549 | −0.340775 | − | 0.940145i | \(-0.610689\pi\) | ||||
−0.340775 | + | 0.940145i | \(0.610689\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.2874 | 1.36408 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.560504 | −0.0251928 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.511996 | 0.0229662 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.1026 | 1.07898 | 0.539489 | − | 0.841993i | \(-0.318617\pi\) | ||||
0.539489 | + | 0.841993i | \(0.318617\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.13204 | −0.184606 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.77947 | −0.302282 | −0.151141 | − | 0.988512i | \(-0.548295\pi\) | ||||
−0.151141 | + | 0.988512i | \(0.548295\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.67550 | 0.252556 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.49845 | −0.333018 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.1741 | 1.07150 | 0.535748 | − | 0.844378i | \(-0.320030\pi\) | ||||
0.535748 | + | 0.844378i | \(0.320030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.463475 | 0.0205029 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.5888 | −0.511658 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.74080 | 0.120774 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.7254 | 1.26334 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.9696 | −0.876566 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.1397 | 1.36426 | 0.682129 | − | 0.731232i | \(-0.261054\pi\) | ||||
0.682129 | + | 0.731232i | \(0.261054\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.7975 | 0.996867 | 0.498433 | − | 0.866928i | \(-0.333909\pi\) | ||||
0.498433 | + | 0.866928i | \(0.333909\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0685530 | 0.00299190 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.4311 | 1.15136 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.35499 | 0.232826 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.871651 | −0.0378264 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.30828 | −0.186612 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.83326 | −0.425129 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.1449 | 0.998776 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.9821 | 1.37757 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.3365 | −0.616374 | −0.308187 | − | 0.951326i | \(-0.599722\pi\) | ||||
−0.308187 | + | 0.951326i | \(0.599722\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.3272 | −1.08689 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.08385 | 0.260604 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.02146 | 0.129188 | 0.0645941 | − | 0.997912i | \(-0.479425\pi\) | ||||
0.0645941 | + | 0.997912i | \(0.479425\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.50706 | 0.0643197 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.5661 | −0.918746 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.408506 | 0.0173714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.1785 | −0.601842 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.3291 | 0.903744 | 0.451872 | − | 0.892083i | \(-0.350756\pi\) | ||||
0.451872 | + | 0.892083i | \(0.350756\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.5016 | −0.613353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.8487 | 1.09133 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.3960 | −1.70249 | −0.851245 | − | 0.524769i | \(-0.824152\pi\) | ||||
−0.851245 | + | 0.524769i | \(0.824152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.26544 | −0.221519 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.362837 | −0.0152377 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.3561 | 1.35644 | 0.678219 | − | 0.734860i | \(-0.262752\pi\) | ||||
0.678219 | + | 0.734860i | \(0.262752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.79143 | −0.200515 | −0.100258 | − | 0.994962i | \(-0.531967\pi\) | ||||
−0.100258 | + | 0.994962i | \(0.531967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.6965 | 0.488629 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.32494 | 0.222065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9158 | 0.787473 | 0.393737 | − | 0.919223i | \(-0.371182\pi\) | ||||
0.393737 | + | 0.919223i | \(0.371182\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.4058 | −0.640245 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.101210 | 0.00419890 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.66012 | 0.151587 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.362949 | 0.0150061 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.6739 | 0.770753 | 0.385376 | − | 0.922759i | \(-0.374072\pi\) | ||||
0.385376 | + | 0.922759i | \(0.374072\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.8202 | −0.775472 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.4277 | −1.45730 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.9862 | 1.06712 | 0.533562 | − | 0.845761i | \(-0.320853\pi\) | ||||
0.533562 | + | 0.845761i | \(0.320853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.124177 | −0.00509075 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.54688 | −0.104237 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.3171 | 0.830134 | 0.415067 | − | 0.909791i | \(-0.363758\pi\) | ||||
0.415067 | + | 0.909791i | \(0.363758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.9972 | 1.67231 | 0.836155 | − | 0.548493i | \(-0.184798\pi\) | ||||
0.836155 | + | 0.548493i | \(0.184798\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.44366 | −0.0587904 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.88353 | 0.401823 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.75068 | −0.395768 | −0.197884 | − | 0.980225i | \(-0.563407\pi\) | ||||
−0.197884 | + | 0.980225i | \(0.563407\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.648655 | −0.0262848 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.6008 | −0.752509 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.6381 | 1.03551 | 0.517756 | − | 0.855528i | \(-0.326767\pi\) | ||||
0.517756 | + | 0.855528i | \(0.326767\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.57275 | −0.103743 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.53450 | −0.142294 | −0.0711468 | − | 0.997466i | \(-0.522666\pi\) | ||||
−0.0711468 | + | 0.997466i | \(0.522666\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.1241 | 0.648081 | 0.324041 | − | 0.946043i | \(-0.394959\pi\) | ||||
0.324041 | + | 0.946043i | \(0.394959\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.0750 | −1.08648 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0767911 | −0.00307657 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.4055 | −0.735045 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.6828 | 1.02404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.0961 | −0.999060 | −0.499530 | − | 0.866297i | \(-0.666494\pi\) | ||||
−0.499530 | + | 0.866297i | \(0.666494\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.4131 | 1.32805 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.8506 | −0.708379 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.7097 | −0.820548 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.61875 | 0.0640367 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.65432 | 0.223332 | 0.111666 | − | 0.993746i | \(-0.464381\pi\) | ||||
0.111666 | + | 0.993746i | \(0.464381\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.4400 | 1.20044 | 0.600218 | − | 0.799836i | \(-0.295080\pi\) | ||||
0.600218 | + | 0.799836i | \(0.295080\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.65983 | −0.340981 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.26228 | 0.0496254 | 0.0248127 | − | 0.999692i | \(-0.492101\pi\) | ||||
0.0248127 | + | 0.999692i | \(0.492101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.4764 | 1.27481 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.566065 | −0.0221858 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.4840 | 0.840733 | 0.420366 | − | 0.907354i | \(-0.361902\pi\) | ||||
0.420366 | + | 0.907354i | \(0.361902\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.79650 | −0.0701950 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.46534 | 0.0571684 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.9084 | 1.20402 | 0.602010 | − | 0.798489i | \(-0.294367\pi\) | ||||
0.602010 | + | 0.798489i | \(0.294367\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.2710 | −0.944033 | −0.472016 | − | 0.881590i | \(-0.656474\pi\) | ||||
−0.472016 | + | 0.881590i | \(0.656474\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.7381 | −0.650054 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0884197 | 0.00342877 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.3851 | −1.95092 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.56969 | −0.369986 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −56.1507 | −2.16767 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0862 | −1.08264 | −0.541322 | − | 0.840815i | \(-0.682076\pi\) | ||||
−0.541322 | + | 0.840815i | \(0.682076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.08457 | −0.195705 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.41113 | 0.323266 | 0.161633 | − | 0.986851i | \(-0.448324\pi\) | ||||
0.161633 | + | 0.986851i | \(0.448324\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.251914 | 0.00966755 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.3000 | −1.23774 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.8456 | 1.79250 | 0.896249 | − | 0.443551i | \(-0.146282\pi\) | ||||
0.896249 | + | 0.443551i | \(0.146282\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.61311 | −0.0998416 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.17460 | −0.0829662 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.37008 | −0.0902928 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.6065 | 0.441531 | 0.220766 | − | 0.975327i | \(-0.429144\pi\) | ||||
0.220766 | + | 0.975327i | \(0.429144\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0217442 | −0.000825994 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.3106 | −0.580764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.66026 | 0.176520 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 45.2378 | 1.71105 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.3597 | −0.920055 | −0.460027 | − | 0.887905i | \(-0.652160\pi\) | ||||
−0.460027 | + | 0.887905i | \(0.652160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.2874 | −0.689721 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.1077 | −0.418342 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.220175 | 0.00828055 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.2668 | −0.385579 | −0.192789 | − | 0.981240i | \(-0.561753\pi\) | ||||
−0.192789 | + | 0.981240i | \(0.561753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.29155 | 0.0484368 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.9698 | −1.64668 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.5229 | −0.505729 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.0077 | 0.821893 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.1952 | 0.454806 | 0.227403 | − | 0.973801i | \(-0.426977\pi\) | ||||
0.227403 | + | 0.973801i | \(0.426977\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.106327 | 0.00395981 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.3766 | 1.20410 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.46209 | −0.351413 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.2674 | −0.974203 | −0.487102 | − | 0.873345i | \(-0.661946\pi\) | ||||
−0.487102 | + | 0.873345i | \(0.661946\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.8077 | 0.955841 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.6864 | 0.580182 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.6577 | 0.726073 | 0.363036 | − | 0.931775i | \(-0.381740\pi\) | ||||
0.363036 | + | 0.931775i | \(0.381740\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.3671 | −0.456166 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.7885 | 1.98133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.5196 | 1.08590 | 0.542948 | − | 0.839766i | \(-0.317308\pi\) | ||||
0.542948 | + | 0.839766i | \(0.317308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.9183 | 0.437830 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.9633 | −1.86966 | −0.934832 | − | 0.355091i | \(-0.884450\pi\) | ||||
−0.934832 | + | 0.355091i | \(0.884450\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.28565 | −0.230288 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.319990 | 0.0117078 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.381472 | −0.0139387 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0252 | −0.657748 | −0.328874 | − | 0.944374i | \(-0.606669\pi\) | ||||
−0.328874 | + | 0.944374i | \(0.606669\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −40.0474 | −1.45941 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.5850 | 1.43874 | 0.719370 | − | 0.694627i | \(-0.244431\pi\) | ||||
0.719370 | + | 0.694627i | \(0.244431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −43.0010 | −1.56084 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.4089 | 1.06607 | 0.533036 | − | 0.846093i | \(-0.321051\pi\) | ||||
0.533036 | + | 0.846093i | \(0.321051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.236017 | 0.00854439 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.392602 | −0.0141946 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.0298 | −0.759340 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.506255 | 0.0182560 | 0.00912802 | − | 0.999958i | \(-0.497094\pi\) | ||||
0.00912802 | + | 0.999958i | \(0.497094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34.8499 | −1.25509 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.48236 | 0.233154 | 0.116577 | − | 0.993182i | \(-0.462808\pi\) | ||||
0.116577 | + | 0.993182i | \(0.462808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.25733 | −0.296612 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.550039 | −0.0197325 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.31833 | −0.118891 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.3121 | −2.15814 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 48.1106 | 1.71933 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.1820 | 0.613251 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6830 | 0.380806 | 0.190403 | − | 0.981706i | \(-0.439021\pi\) | ||||
0.190403 | + | 0.981706i | \(0.439021\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.2400 | −1.32578 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.204268 | −0.00726292 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.3599 | 1.29118 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.41532 | −0.0501963 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.48024 | −0.194120 | −0.0970601 | − | 0.995279i | \(-0.530944\pi\) | ||||
−0.0970601 | + | 0.995279i | \(0.530944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.1205 | 0.711812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.242786 | −0.00857842 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −54.5963 | −1.92666 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.206576 | 0.00728084 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.67149 | 0.0940410 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.0241 | 1.75876 | 0.879378 | − | 0.476125i | \(-0.157959\pi\) | ||||
0.879378 | + | 0.476125i | \(0.157959\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0612 | −0.458641 | −0.229320 | − | 0.973351i | \(-0.573650\pi\) | ||||
−0.229320 | + | 0.973351i | \(0.573650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.3915 | −0.960662 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.15053 | 0.250472 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.1695 | −0.390770 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0140803 | 0.000492004 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.4173 | −1.34077 | −0.670386 | − | 0.742012i | \(-0.733872\pi\) | ||||
−0.670386 | + | 0.742012i | \(0.733872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.1835 | −0.773269 | −0.386635 | − | 0.922233i | \(-0.626363\pi\) | ||||
−0.386635 | + | 0.922233i | \(0.626363\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.07539 | −0.281149 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.7872 | −1.41831 | −0.709155 | − | 0.705053i | \(-0.750923\pi\) | ||||
−0.709155 | + | 0.705053i | \(0.750923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.8876 | −1.59374 | −0.796872 | − | 0.604149i | \(-0.793513\pi\) | ||||
−0.796872 | + | 0.604149i | \(0.793513\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.6624 | 1.44525 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.4016 | 0.776171 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.33831 | −0.0809206 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.9849 | 1.45121 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.4757 | 1.70809 | 0.854045 | − | 0.520199i | \(-0.174142\pi\) | ||||
0.854045 | + | 0.520199i | \(0.174142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.5311 | 2.08728 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.8023 | 0.475378 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.24336 | −0.145976 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.383422 | 0.0131745 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.29543 | −0.216059 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −42.7250 | −1.46459 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0309 | 0.822801 | 0.411401 | − | 0.911455i | \(-0.365040\pi\) | ||||
0.411401 | + | 0.911455i | \(0.365040\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.279551 | 0.00956045 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.8225 | −1.08704 | −0.543518 | − | 0.839397i | \(-0.682908\pi\) | ||||
−0.543518 | + | 0.839397i | \(0.682908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6715 | −0.432346 | −0.216173 | − | 0.976355i | \(-0.569358\pi\) | ||||
−0.216173 | + | 0.976355i | \(0.569358\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0998071 | −0.00340142 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.669733 | 0.0227980 | 0.0113990 | − | 0.999935i | \(-0.496372\pi\) | ||||
0.0113990 | + | 0.999935i | \(0.496372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3007 | −0.384236 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.9352 | −0.405340 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.1211 | −1.63240 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.8303 | −1.18018 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.796460 | 0.0269561 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.0387940 | 0.00131148 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.1381 | −1.72681 | −0.863406 | − | 0.504509i | \(-0.831673\pi\) | ||||
−0.863406 | + | 0.504509i | \(0.831673\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.6402 | −0.358884 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.38097 | −0.214980 | −0.107490 | − | 0.994206i | \(-0.534281\pi\) | ||||
−0.107490 | + | 0.994206i | \(0.534281\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.6058 | −0.390566 | −0.195283 | − | 0.980747i | \(-0.562563\pi\) | ||||
−0.195283 | + | 0.980747i | \(0.562563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.5582 | −0.422139 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.1963 | 1.21535 | 0.607677 | − | 0.794184i | \(-0.292102\pi\) | ||||
0.607677 | + | 0.794184i | \(0.292102\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.692496 | −0.0232256 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 42.7414 | 1.43189 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.3268 | −0.479427 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.0976 | 0.437806 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.8449 | 0.929714 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 78.1316 | 2.60583 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.56371 | 0.0854096 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.335950 | −0.0111797 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.3326 | −0.476431 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.1081 | 1.33177 | 0.665884 | − | 0.746055i | \(-0.268055\pi\) | ||||
0.665884 | + | 0.746055i | \(0.268055\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.696115 | 0.0230887 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.6097 | −1.24607 | −0.623033 | − | 0.782196i | \(-0.714100\pi\) | ||||
−0.623033 | + | 0.782196i | \(0.714100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.9223 | −0.394571 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.7128 | 0.717802 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.0696934 | −0.00230148 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.3608 | −0.671642 | −0.335821 | − | 0.941926i | \(-0.609014\pi\) | ||||
−0.335821 | + | 0.941926i | \(0.609014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.7422 | 1.34250 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.0545 | 1.28549 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.02356 | −0.263813 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.336167 | 0.0110412 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.2860 | 0.501518 | 0.250759 | − | 0.968050i | \(-0.419320\pi\) | ||||
0.250759 | + | 0.968050i | \(0.419320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.9510 | −0.522774 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.9930 | 1.17836 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.6277 | 0.478378 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6942 | 1.10074 | 0.550371 | − | 0.834920i | \(-0.314486\pi\) | ||||
0.550371 | + | 0.834920i | \(0.314486\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.9534 | 0.879591 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.5975 | 1.68203 | 0.841014 | − | 0.541013i | \(-0.181959\pi\) | ||||
0.841014 | + | 0.541013i | \(0.181959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.75264 | −0.252461 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.197251 | −0.00641657 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.7964 | 1.35820 | 0.679100 | − | 0.734046i | \(-0.262370\pi\) | ||||
0.679100 | + | 0.734046i | \(0.262370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.3533 | 1.14762 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.71907 | 0.185453 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.4569 | 1.47249 | 0.736246 | − | 0.676714i | \(-0.236596\pi\) | ||||
0.736246 | + | 0.676714i | \(0.236596\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.61903 | 0.214187 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 76.4101 | 2.46999 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.101373 | −0.00327350 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.1834 | 1.19947 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.20608 | −0.0388653 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.71813 | −0.280647 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.7130 | −0.826876 | −0.413438 | − | 0.910532i | \(-0.635672\pi\) | ||||
−0.413438 | + | 0.910532i | \(0.635672\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.8920 | −0.414152 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.9973 | −1.57240 | −0.786199 | − | 0.617973i | \(-0.787954\pi\) | ||||
−0.786199 | + | 0.617973i | \(0.787954\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.593959 | −0.0190415 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.22914 | 0.167467 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.1109 | 1.02732 | 0.513659 | − | 0.857995i | \(-0.328290\pi\) | ||||
0.513659 | + | 0.857995i | \(0.328290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.04583 | 0.289106 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.746201 | 0.0238244 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.0689 | −1.18232 | −0.591158 | − | 0.806556i | \(-0.701329\pi\) | ||||
−0.591158 | + | 0.806556i | \(0.701329\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.0485 | −0.638798 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.430914 | −0.0137161 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.0953 | −0.829783 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.2142 | 1.53158 | 0.765788 | − | 0.643093i | \(-0.222349\pi\) | ||||
0.765788 | + | 0.643093i | \(0.222349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.8502 | −0.661662 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.44127 | −0.0456915 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.74238 | −0.213533 | −0.106767 | − | 0.994284i | \(-0.534050\pi\) | ||||
−0.106767 | + | 0.994284i | \(0.534050\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.7963 | 1.29074 |
(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 | 6040.2.a.p.1.15 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.15 | ✓ | 19 | 1.1 | even | 1 | trivial |