Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.11 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.08723 | −0.627715 | −0.313857 | − | 0.949470i | \(-0.601621\pi\) | ||||
−0.313857 | + | 0.949470i | \(0.601621\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.34996i | 1.49815i | 0.662487 | + | 0.749073i | \(0.269501\pi\) | ||||
−0.662487 | + | 0.749073i | \(0.730499\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.81792 | −0.605974 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.52800 | + | 0.743786i | −0.978491 | + | 0.206289i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.64219i | − | 0.940409i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.31834 | 1.04735 | 0.523676 | − | 0.851918i | \(-0.324560\pi\) | ||||
0.523676 | + | 0.851918i | \(0.324560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.13566i | − | 1.63703i | −0.574484 | − | 0.818516i | \(-0.694797\pi\) | ||
0.574484 | − | 0.818516i | \(-0.305203\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.08723i | − | 0.237254i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.49079 | 0.310851 | 0.155426 | − | 0.987848i | \(-0.450325\pi\) | ||||
0.155426 | + | 0.987848i | \(0.450325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.22222 | −1.24444 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.23821 | 1.00809 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.80792 | 0.521417 | 0.260708 | − | 0.965418i | \(-0.416044\pi\) | ||||
0.260708 | + | 0.965418i | \(0.416044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.91308i | − | 1.24163i | −0.783959 | − | 0.620813i | \(-0.786803\pi\) | ||
0.783959 | − | 0.620813i | \(-0.213197\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.08723i | 0.189263i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.34996 | −0.566246 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.56372i | 0.585873i | 0.956132 | + | 0.292936i | \(0.0946324\pi\) | ||||
−0.956132 | + | 0.292936i | \(0.905368\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.83576 | − | 0.808669i | 0.614213 | − | 0.129491i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.88418i | − | 1.38748i | −0.720227 | − | 0.693738i | \(-0.755963\pi\) | ||
0.720227 | − | 0.693738i | \(-0.244037\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.06590 | −0.925040 | −0.462520 | − | 0.886609i | \(-0.653055\pi\) | ||||
−0.462520 | + | 0.886609i | \(0.653055\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 6.08996i | − | 0.907838i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.61283i | − | 0.672850i | −0.941710 | − | 0.336425i | \(-0.890782\pi\) | ||
0.941710 | − | 0.336425i | \(-0.109218\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.69505 | −0.657438 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.9549 | 1.77950 | 0.889749 | − | 0.456451i | \(-0.150879\pi\) | ||||
0.889749 | + | 0.456451i | \(0.150879\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.34996 | 0.451708 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.75813i | 1.02759i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.89042i | 1.28762i | 0.765184 | + | 0.643811i | \(0.222648\pi\) | ||||
−0.765184 | + | 0.643811i | \(0.777352\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.97309 | 0.508701 | 0.254351 | − | 0.967112i | \(-0.418138\pi\) | ||||
0.254351 | + | 0.967112i | \(0.418138\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.81792i | − | 0.229037i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.49165 | − | 11.8187i | −0.309051 | − | 1.46592i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.7654i | − | 1.55954i | −0.626065 | − | 0.779771i | \(-0.715336\pi\) | ||
0.626065 | − | 0.779771i | \(-0.284664\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.62084 | −0.195126 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.59867i | − | 0.783118i | −0.920153 | − | 0.391559i | \(-0.871936\pi\) | ||
0.920153 | − | 0.391559i | \(-0.128064\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0334i | 1.40841i | 0.709998 | + | 0.704204i | \(0.248696\pi\) | ||||
−0.709998 | + | 0.704204i | \(0.751304\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.76501 | 0.781156 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.43515 | 1.06154 | 0.530769 | − | 0.847517i | \(-0.321903\pi\) | ||||
0.530769 | + | 0.847517i | \(0.321903\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.241394 | −0.0268215 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.795337i | 0.0872995i | 0.999047 | + | 0.0436498i | \(0.0138986\pi\) | ||||
−0.999047 | + | 0.0436498i | \(0.986101\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4663i | 1.56909i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.05286 | −0.327301 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.02531i | − | 0.108683i | −0.998522 | − | 0.0543415i | \(-0.982694\pi\) | ||
0.998522 | − | 0.0543415i | \(-0.0173060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.743786 | − | 3.52800i | −0.0779700 | − | 0.369835i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.51614i | 0.779387i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.9041 | 2.45251 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9734i | 1.31725i | 0.752472 | + | 0.658625i | \(0.228861\pi\) | ||||
−0.752472 | + | 0.658625i | \(0.771139\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.81792i | 0.182708i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.21979 | 0.220877 | 0.110439 | − | 0.993883i | \(-0.464774\pi\) | ||||
0.110439 | + | 0.993883i | \(0.464774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.76051 | −0.863199 | −0.431600 | − | 0.902065i | \(-0.642051\pi\) | ||||
−0.431600 | + | 0.902065i | \(0.642051\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.64219 | 0.355441 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.48980 | 0.530719 | 0.265360 | − | 0.964150i | \(-0.414509\pi\) | ||||
0.265360 | + | 0.964150i | \(0.414509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.16288i | 0.398731i | 0.979925 | + | 0.199366i | \(0.0638882\pi\) | ||||
−0.979925 | + | 0.199366i | \(0.936112\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.87460i | − | 0.367761i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.4716 | −1.07916 | −0.539578 | − | 0.841936i | \(-0.681416\pi\) | ||||
−0.539578 | + | 0.841936i | \(0.681416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.99408i | 0.465701i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.41363 | − | 1.35214i | 0.592940 | − | 0.125006i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.31834i | 0.395862i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.65918i | 0.870939i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.09438i | − | 0.366212i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.72215 | −0.419023 | −0.209511 | − | 0.977806i | \(-0.567187\pi\) | ||||
−0.209511 | + | 0.977806i | \(0.567187\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.59505 | 0.580662 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.01648 | 0.0888100 | 0.0444050 | − | 0.999014i | \(-0.485861\pi\) | ||||
0.0444050 | + | 0.999014i | \(0.485861\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.13566 | 0.618740 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.5478i | 1.51027i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.51956i | 0.215261i | 0.994191 | + | 0.107630i | \(0.0343263\pi\) | ||||
−0.994191 | + | 0.107630i | \(0.965674\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.39901 | 0.797213 | 0.398607 | − | 0.917122i | \(-0.369494\pi\) | ||||
0.398607 | + | 0.917122i | \(0.369494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.01523i | 0.422358i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.743786 | + | 3.52800i | 0.0621985 | + | 0.295026i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.40640i | 0.781159i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.08723 | 0.0896736 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 8.40917i | − | 0.688906i | −0.938804 | − | 0.344453i | \(-0.888064\pi\) | ||
0.938804 | − | 0.344453i | \(-0.111936\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.61043i | − | 0.375192i | −0.982246 | − | 0.187596i | \(-0.939930\pi\) | ||
0.982246 | − | 0.187596i | \(-0.0600695\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.85041 | −0.634668 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.1585 | 1.86014 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.0879 | −1.36376 | −0.681880 | − | 0.731464i | \(-0.738838\pi\) | ||||
−0.681880 | + | 0.731464i | \(0.738838\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.0850 | −1.11702 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.49079i | 0.117491i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.8787i | 1.79200i | 0.444057 | + | 0.895999i | \(0.353539\pi\) | ||||
−0.444057 | + | 0.895999i | \(0.646461\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.64219 | −0.283544 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.2131i | 1.33199i | 0.745957 | + | 0.665994i | \(0.231992\pi\) | ||||
−0.745957 | + | 0.665994i | \(0.768008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8936 | − | 5.24815i | 0.914890 | − | 0.403704i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9721i | 0.991999i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.9899 | −0.911575 | −0.455788 | − | 0.890089i | \(-0.650642\pi\) | ||||
−0.455788 | + | 0.890089i | \(0.650642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.22222i | − | 0.470355i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 10.7532i | − | 0.808260i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.8321 | 1.48232 | 0.741162 | − | 0.671327i | \(-0.234275\pi\) | ||||
0.741162 | + | 0.671327i | \(0.234275\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6548 | −1.46093 | −0.730464 | − | 0.682951i | \(-0.760696\pi\) | ||||
−0.730464 | + | 0.682951i | \(0.760696\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.31967 | −0.319319 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.9383 | −0.877723 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.31834i | − | 0.315788i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.23821i | 0.381024i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7595 | 0.995601 | 0.497800 | − | 0.867292i | \(-0.334141\pi\) | ||||
0.497800 | + | 0.867292i | \(0.334141\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.3099i | − | 1.17401i | −0.809582 | − | 0.587007i | \(-0.800306\pi\) | ||
0.809582 | − | 0.587007i | \(-0.199694\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.70901 | + | 12.8496i | 0.193996 | + | 0.920182i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.3513i | − | 1.30748i | −0.756719 | − | 0.653740i | \(-0.773199\pi\) | ||
0.756719 | − | 0.653740i | \(-0.226801\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.4478 | 1.44950 | 0.724752 | − | 0.689010i | \(-0.241954\pi\) | ||||
0.724752 | + | 0.689010i | \(0.241954\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.8790i | 0.978948i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.80792i | 0.197077i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.7616 | 2.07864 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.71014 | −0.188368 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.13566 | −0.493584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8352 | 0.952454 | 0.476227 | − | 0.879322i | \(-0.342004\pi\) | ||||
0.476227 | + | 0.879322i | \(0.342004\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.17430i | 0.491575i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 20.3205i | − | 1.38585i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.91308 | 0.469291 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 13.0832i | − | 0.884079i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.2351 | + | 3.21192i | −1.02482 | + | 0.216057i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.0590i | − | 0.740568i | −0.928919 | − | 0.370284i | \(-0.879260\pi\) | ||
0.928919 | − | 0.370284i | \(-0.120740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.3115 | 0.754100 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.2606i | 1.07925i | 0.841904 | + | 0.539627i | \(0.181435\pi\) | ||||
−0.841904 | + | 0.539627i | \(0.818565\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.6808i | − | 1.16838i | −0.811617 | − | 0.584189i | \(-0.801413\pi\) | ||
0.811617 | − | 0.584189i | \(-0.198587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.08723 | −0.0715348 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8756 | 1.17107 | 0.585535 | − | 0.810647i | \(-0.300885\pi\) | ||||
0.585535 | + | 0.810647i | \(0.300885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.4528 | 1.00803 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.2582 | −0.666343 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3242i | − | 0.667819i | −0.942605 | − | 0.333909i | \(-0.891632\pi\) | ||
0.942605 | − | 0.333909i | \(-0.108368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.774848i | − | 0.0499124i | −0.999689 | − | 0.0249562i | \(-0.992055\pi\) | ||
0.999689 | − | 0.0249562i | \(-0.00794462\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4522 | −0.991258 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3.34996i | − | 0.214021i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.30740 | + | 25.1746i | 0.337702 | + | 1.60182i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 0.864717i | − | 0.0547992i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.64264 | −0.356161 | −0.178080 | − | 0.984016i | \(-0.556989\pi\) | ||||
−0.178080 | + | 0.984016i | \(0.556989\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.49079i | − | 0.0937251i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 15.7282i | − | 0.984939i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.7966 | −0.735853 | −0.367926 | − | 0.929855i | \(-0.619932\pi\) | ||||
−0.367926 | + | 0.929855i | \(0.619932\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.56372 | −0.221439 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.10457 | −0.315965 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.17206 | 0.195598 | 0.0977988 | − | 0.995206i | \(-0.468820\pi\) | ||||
0.0977988 | + | 0.995206i | \(0.468820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 43.3985i | 2.66595i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.11476i | 0.0682220i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9042 | 0.664839 | 0.332420 | − | 0.943132i | \(-0.392135\pi\) | ||||
0.332420 | + | 0.943132i | \(0.392135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.9374i | − | 0.725147i | −0.931955 | − | 0.362574i | \(-0.881898\pi\) | ||
0.931955 | − | 0.362574i | \(-0.118102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.808669 | + | 3.83576i | 0.0489429 | + | 0.232151i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.22222i | 0.375214i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.8415 | 1.55267 | 0.776334 | − | 0.630322i | \(-0.217077\pi\) | ||||
0.776334 | + | 0.630322i | \(0.217077\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.5674i | 0.752393i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.45300i | 0.504264i | 0.967693 | + | 0.252132i | \(0.0811317\pi\) | ||||
−0.967693 | + | 0.252132i | \(0.918868\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.9613 | 1.78102 | 0.890508 | − | 0.454968i | \(-0.150349\pi\) | ||||
0.890508 | + | 0.454968i | \(0.150349\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25.9894 | −1.53948 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.88418 | 0.524417 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.64806 | 0.0969449 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 14.1051i | − | 0.826857i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.86174i | − | 0.284026i | −0.989865 | − | 0.142013i | \(-0.954643\pi\) | ||
0.989865 | − | 0.142013i | \(-0.0453574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.1325 | −1.92905 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.23821i | − | 0.303952i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.25950 | + | 1.10883i | −0.304165 | + | 0.0641252i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.06590i | − | 0.349632i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.41343 | −0.138648 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.3097i | 0.762109i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.5920i | 1.91719i | 0.284765 | + | 0.958597i | \(0.408084\pi\) | ||||
−0.284765 | + | 0.958597i | \(0.591916\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.52473 | 0.541843 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.887922 | −0.0503494 | −0.0251747 | − | 0.999683i | \(-0.508014\pi\) | ||||
−0.0251747 | + | 0.999683i | \(0.508014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.4993 | 1.44131 | 0.720654 | − | 0.693295i | \(-0.243842\pi\) | ||||
0.720654 | + | 0.693295i | \(0.243842\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.08996 | 0.343130 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.0285i | 0.900252i | 0.892965 | + | 0.450126i | \(0.148621\pi\) | ||||
−0.892965 | + | 0.450126i | \(0.851379\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.80792i | − | 0.157213i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.96870 | −0.333140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 30.8142i | − | 1.71455i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.9520 | − | 4.62800i | 1.21768 | − | 0.256715i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.52602i | − | 0.250290i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.61283 | 0.254314 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.4189i | − | 1.45211i | −0.687634 | − | 0.726057i | \(-0.741351\pi\) | ||
0.687634 | − | 0.726057i | \(-0.258649\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.47857i | − | 0.355024i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 42.7635 | 2.33642 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.97919 | 0.325707 | 0.162854 | − | 0.986650i | \(-0.447930\pi\) | ||||
0.162854 | + | 0.986650i | \(0.447930\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.4723 | 0.677402 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.91308 | −0.374364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 5.42974i | − | 0.292327i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.6757 | 0.841517 | 0.420758 | − | 0.907173i | \(-0.361764\pi\) | ||||
0.420758 | + | 0.907173i | \(0.361764\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.5860i | − | 0.673711i | −0.941556 | − | 0.336855i | \(-0.890637\pi\) | ||
0.941556 | − | 0.336855i | \(-0.109363\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.4804 | + | 3.89611i | −0.986411 | + | 0.207959i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.0812i | − | 1.01559i | −0.861478 | − | 0.507794i | \(-0.830461\pi\) | ||
0.861478 | − | 0.507794i | \(-0.169539\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.1053 | 1.17323 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 4.69505i | − | 0.248488i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.2818i | − | 0.964879i | −0.875929 | − | 0.482439i | \(-0.839751\pi\) | ||
0.875929 | − | 0.482439i | \(-0.160249\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.9176 | −1.67987 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.08723 | 0.0570650 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.3115 | −2.11000 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.7377 | 1.76109 | 0.880547 | − | 0.473959i | \(-0.157175\pi\) | ||||
0.880547 | + | 0.473959i | \(0.157175\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.1507i | 0.840774i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.9549i | 0.672587i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.7608 | 1.64451 | 0.822256 | − | 0.569118i | \(-0.192715\pi\) | ||||
0.822256 | + | 0.569118i | \(0.192715\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.45155i | 0.229877i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.90633 | + | 2.08849i | −0.510202 | + | 0.107563i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.77706i | − | 0.399481i | −0.979849 | − | 0.199740i | \(-0.935990\pi\) | ||
0.979849 | − | 0.199740i | \(-0.0640099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.13408 | 0.263027 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 20.9064i | − | 1.06827i | −0.845400 | − | 0.534134i | \(-0.820638\pi\) | ||
0.845400 | − | 0.534134i | \(-0.179362\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.34996i | 0.170730i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.0273 | 0.560550 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.0133 | 1.42033 | 0.710166 | − | 0.704034i | \(-0.248620\pi\) | ||||
0.710166 | + | 0.704034i | \(0.248620\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.43774 | 0.325570 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.10515 | −0.0557474 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 31.6074i | 1.59034i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.5116i | − | 0.828694i | −0.910119 | − | 0.414347i | \(-0.864010\pi\) | ||
0.910119 | − | 0.414347i | \(-0.135990\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.75813 | −0.388392 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.1648i | − | 1.10686i | −0.832896 | − | 0.553430i | \(-0.813319\pi\) | ||
0.832896 | − | 0.553430i | \(-0.186681\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.14185 | + | 24.3894i | 0.256134 | + | 1.21492i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.808658i | − | 0.0401826i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.56372 | 0.176647 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.356646i | 0.0176350i | 0.999961 | + | 0.00881751i | \(0.00280674\pi\) | ||||
−0.999961 | + | 0.00881751i | \(0.997193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.73935i | − | 0.135122i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.89042 | −0.486676 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.66434 | −0.130788 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.2189 | −0.500423 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.5854 | 1.64076 | 0.820378 | − | 0.571821i | \(-0.193763\pi\) | ||||
0.820378 | + | 0.571821i | \(0.193763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.02335i | − | 0.0498752i | −0.999689 | − | 0.0249376i | \(-0.992061\pi\) | ||
0.999689 | − | 0.0249376i | \(-0.00793870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.38576i | 0.407730i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.8697 | −1.30337 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.97309i | 0.192271i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.808669 | − | 3.83576i | −0.0390429 | − | 0.185192i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.8561i | − | 0.860100i | −0.902805 | − | 0.430050i | \(-0.858496\pi\) | ||
0.902805 | − | 0.430050i | \(-0.141504\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.2041 | −0.826775 | −0.413388 | − | 0.910555i | \(-0.635655\pi\) | ||||
−0.413388 | + | 0.910555i | \(0.635655\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 10.2270i | − | 0.490345i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 10.6378i | − | 0.508873i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3419 | −0.732229 | −0.366114 | − | 0.930570i | \(-0.619312\pi\) | ||||
−0.366114 | + | 0.930570i | \(0.619312\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.81792 | 0.0865677 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.0634 | −1.66591 | −0.832955 | − | 0.553340i | \(-0.813353\pi\) | ||||
−0.832955 | + | 0.553340i | \(0.813353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.43476 | 0.162823 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.14273i | 0.432436i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.70661i | 0.316504i | 0.987399 | + | 0.158252i | \(0.0505859\pi\) | ||||
−0.987399 | + | 0.158252i | \(0.949414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.88418 | −0.418340 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.01262i | 0.235513i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.8187 | − | 2.49165i | 0.554067 | − | 0.116810i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 37.6775i | − | 1.76248i | −0.472668 | − | 0.881240i | \(-0.656709\pi\) | ||
0.472668 | − | 0.881240i | \(-0.343291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.6204 | 1.05583 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.6991i | 1.89555i | 0.318947 | + | 0.947773i | \(0.396671\pi\) | ||||
−0.318947 | + | 0.947773i | \(0.603329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.98402i | 0.138679i | 0.997593 | + | 0.0693396i | \(0.0220892\pi\) | ||||
−0.997593 | + | 0.0693396i | \(0.977911\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −25.1787 | −1.16764 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.4650 | −1.22465 | −0.612327 | − | 0.790605i | \(-0.709766\pi\) | ||||
−0.612327 | + | 0.790605i | \(0.709766\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.7654 | 0.589451 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.5785 | 0.856053 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.06590i | 0.278910i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 44.3996i | 2.03719i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.5511 | −1.07833 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 11.4762i | − | 0.524361i | −0.965019 | − | 0.262180i | \(-0.915558\pi\) | ||
0.965019 | − | 0.262180i | \(-0.0844416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.65065 | − | 12.5728i | −0.120859 | − | 0.573271i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.62084i | − | 0.0737506i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −43.4603 | −1.97343 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18.7141i | − | 0.848018i | −0.905658 | − | 0.424009i | \(-0.860622\pi\) | ||
0.905658 | − | 0.424009i | \(-0.139378\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 24.8745i | − | 1.12486i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.55959 | −0.431418 | −0.215709 | − | 0.976458i | \(-0.569206\pi\) | ||||
−0.215709 | + | 0.976458i | \(0.569206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.1255 | 0.546107 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.08996 | −0.273723 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.59867 | 0.295991 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.2878i | − | 0.818672i | −0.912384 | − | 0.409336i | \(-0.865760\pi\) | ||
0.912384 | − | 0.409336i | \(-0.134240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 18.7147i | − | 0.836109i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.0398 | −0.982705 | −0.491352 | − | 0.870961i | \(-0.663497\pi\) | ||||
−0.491352 | + | 0.870961i | \(0.663497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.43620i | 0.330907i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9311 | + | 5.70597i | −0.574290 | + | 0.253411i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 23.5200i | − | 1.04250i | −0.853403 | − | 0.521252i | \(-0.825465\pi\) | ||
0.853403 | − | 0.521252i | \(-0.174535\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0334 | −0.532328 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 37.3781i | − | 1.65028i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 29.3474i | − | 1.29320i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.61283 | −0.202872 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.0358 | 0.572209 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.16958 | −0.314105 | −0.157052 | − | 0.987590i | \(-0.550199\pi\) | ||||
−0.157052 | + | 0.987590i | \(0.550199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.9276 | 1.92082 | 0.960410 | − | 0.278590i | \(-0.0898670\pi\) | ||||
0.960410 | + | 0.278590i | \(0.0898670\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.76501i | 0.295249i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 29.8530i | − | 1.30042i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.7775 | −0.903372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 17.9800i | − | 0.780266i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.60793 | + | 31.3434i | 0.286221 | + | 1.35763i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.3906i | 0.795095i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.5622 | −0.930476 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 5.02702i | − | 0.216129i | −0.994144 | − | 0.108064i | \(-0.965535\pi\) | ||
0.994144 | − | 0.108064i | \(-0.0344652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.3694 | 0.917047 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.9455 | −0.597358 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.2289 | 1.24974 | 0.624868 | − | 0.780730i | \(-0.285153\pi\) | ||||
0.624868 | + | 0.780730i | \(0.285153\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.22276 | −0.308260 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 20.0363i | − | 0.853576i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.43515i | 0.401223i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.9798 | 0.550960 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17.8653i | − | 0.756979i | −0.925606 | − | 0.378489i | \(-0.876444\pi\) | ||
0.925606 | − | 0.378489i | \(-0.123556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.4005 | − | 4.51173i | 0.905144 | − | 0.190826i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.69505i | 0.198225i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.379493 | −0.0159937 | −0.00799685 | − | 0.999968i | \(-0.502546\pi\) | ||||
−0.00799685 | + | 0.999968i | \(0.502546\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 38.4293i | − | 1.61673i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.241394i | − | 0.0101376i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.5588 | 1.49070 | 0.745352 | − | 0.666672i | \(-0.232282\pi\) | ||||
0.745352 | + | 0.666672i | \(0.232282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.3720 | −1.73136 | −0.865682 | − | 0.500595i | \(-0.833115\pi\) | ||||
−0.865682 | + | 0.500595i | \(0.833115\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.9598 | −0.624954 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.27602 | −0.386837 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.7093i | 1.56986i | 0.619585 | + | 0.784929i | \(0.287301\pi\) | ||||
−0.619585 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.7327i | 0.736946i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.795337 | −0.0329961 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 12.9549i | − | 0.536539i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.52963 | + | 21.4854i | 0.187277 | + | 0.888311i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.3211i | 1.33404i | 0.745042 | + | 0.667018i | \(0.232429\pi\) | ||||
−0.745042 | + | 0.667018i | \(0.767571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.3294 | −2.03258 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.9522i | 0.820724i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 31.2125i | − | 1.28174i | −0.767647 | − | 0.640872i | \(-0.778573\pi\) | ||
0.767647 | − | 0.640872i | \(-0.221427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.4663 | −0.593059 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.2315 | −0.909875 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.7899 | −1.17633 | −0.588163 | − | 0.808743i | \(-0.700149\pi\) | ||||
−0.588163 | + | 0.808743i | \(0.700149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.90195 | −0.118373 | −0.0591866 | − | 0.998247i | \(-0.518851\pi\) | ||||
−0.0591866 | + | 0.998247i | \(0.518851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.2065i | 0.945042i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3.34996i | − | 0.136195i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.59972 | −0.267875 | −0.133937 | − | 0.990990i | \(-0.542762\pi\) | ||||
−0.133937 | + | 0.990990i | \(0.542762\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 3.05286i | − | 0.123708i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.43096 | + | 16.2741i | 0.138802 | + | 0.658378i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.0862i | 1.29595i | 0.761662 | + | 0.647975i | \(0.224384\pi\) | ||||
−0.761662 | + | 0.647975i | \(0.775616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −32.3579 | −1.30479 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.3420i | 1.70462i | 0.523034 | + | 0.852312i | \(0.324800\pi\) | ||||
−0.523034 | + | 0.852312i | \(0.675200\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0020i | 0.723562i | 0.932263 | + | 0.361781i | \(0.117831\pi\) | ||||
−0.932263 | + | 0.361781i | \(0.882169\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.80907 | 0.313367 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.02531 | 0.0410783 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.3951 | −0.695804 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.75813 | 0.309830 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.3894i | 0.613614i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0601i | 1.07725i | 0.842547 | + | 0.538623i | \(0.181055\pi\) | ||||
−0.842547 | + | 0.538623i | \(0.818945\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.0421 | −0.597870 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 15.8190i | − | 0.627758i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.52800 | − | 0.743786i | 0.139784 | − | 0.0294699i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.9959i | 0.474549i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.9694 | −1.10472 | −0.552362 | − | 0.833604i | \(-0.686273\pi\) | ||||
−0.552362 | + | 0.833604i | \(0.686273\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.99767i | − | 0.354834i | −0.984136 | − | 0.177417i | \(-0.943226\pi\) | ||
0.984136 | − | 0.177417i | \(-0.0567741\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.0931i | 0.869916i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.2166 | −1.50245 | −0.751225 | − | 0.660046i | \(-0.770537\pi\) | ||||
−0.751225 | + | 0.660046i | \(0.770537\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.89042 | 0.388233 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.51614 | −0.294581 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.7247 | 1.43715 | 0.718574 | − | 0.695451i | \(-0.244795\pi\) | ||||
0.718574 | + | 0.695451i | \(0.244795\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.40516i | 0.133050i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 21.8759i | − | 0.853459i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.5319 | 0.643992 | 0.321996 | − | 0.946741i | \(-0.395646\pi\) | ||||
0.321996 | + | 0.946741i | \(0.395646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 14.2119i | − | 0.552778i | −0.961046 | − | 0.276389i | \(-0.910862\pi\) | ||
0.961046 | − | 0.276389i | \(-0.0891378\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.5641 | − | 3.49211i | 0.643297 | − | 0.135622i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.9041i | 0.926963i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.18601 | 0.162083 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0238i | 0.464866i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.97309i | − | 0.153379i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9327 | 0.459973 | 0.229987 | − | 0.973194i | \(-0.426132\pi\) | ||||
0.229987 | + | 0.973194i | \(0.426132\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −32.5933 | −1.25452 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.7278 | 0.642902 | 0.321451 | − | 0.946926i | \(-0.395830\pi\) | ||||
0.321451 | + | 0.946926i | \(0.395830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.9734 | −0.497873 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 17.6791i | − | 0.677464i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 5.48026i | − | 0.209696i | −0.994488 | − | 0.104848i | \(-0.966564\pi\) | ||
0.994488 | − | 0.104848i | \(-0.0334356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.44043 | −0.322492 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.2231i | 0.733409i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45.7050 | + | 9.63570i | −1.74122 | + | 0.367091i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.8095i | 1.59051i | 0.606275 | + | 0.795255i | \(0.292663\pi\) | ||||
−0.606275 | + | 0.795255i | \(0.707337\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.81792 | −0.0690571 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 31.4863i | 1.19434i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 38.3649i | − | 1.45317i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.4350 | −0.735098 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.566554 | −0.0213984 | −0.0106992 | − | 0.999943i | \(-0.503406\pi\) | ||||
−0.0106992 | + | 0.999943i | \(0.503406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4295 | 0.959092 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.8008 | −0.632754 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.21979i | 0.0834838i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.88377i | 0.333637i | 0.985988 | + | 0.166819i | \(0.0533494\pi\) | ||||
−0.985988 | + | 0.166819i | \(0.946651\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.1524 | −0.643264 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 10.3059i | − | 0.385961i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.8187 | + | 2.49165i | −0.441992 | + | 0.0931825i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.2249i | 0.419200i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.4041 | 1.61870 | 0.809350 | − | 0.587326i | \(-0.199819\pi\) | ||||
0.809350 | + | 0.587326i | \(0.199819\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 8.76051i | − | 0.326259i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.842442i | 0.0313307i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.4715 | −0.648874 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0438 | 0.557943 | 0.278972 | − | 0.960299i | \(-0.410006\pi\) | ||||
0.278972 | + | 0.960299i | \(0.410006\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5243 | 0.649049 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.1946 | −0.968842 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.47061i | 0.202062i | 0.994883 | + | 0.101031i | \(0.0322141\pi\) | ||||
−0.994883 | + | 0.101031i | \(0.967786\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.64219i | 0.134344i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.7654 | −0.470220 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.8229i | 0.545268i | 0.962118 | + | 0.272634i | \(0.0878947\pi\) | ||||
−0.962118 | + | 0.272634i | \(0.912105\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.77039 | − | 27.3707i | −0.211980 | − | 1.00549i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34.1196i | − | 1.25173i | −0.779933 | − | 0.625863i | \(-0.784747\pi\) | ||
0.779933 | − | 0.625863i | \(-0.215253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.1704 | 1.03208 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.44586i | − | 0.0529013i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.48980i | 0.200593i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.1659 | 1.24673 | 0.623366 | − | 0.781930i | \(-0.285765\pi\) | ||||
0.623366 | + | 0.781930i | \(0.285765\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.13487 | 0.223567 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4448 | 0.562092 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0261 | 1.23670 | 0.618350 | − | 0.785903i | \(-0.287801\pi\) | ||||
0.618350 | + | 0.785903i | \(0.287801\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.62084i | 0.0588327i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.9598i | − | 0.723544i | −0.932267 | − | 0.361772i | \(-0.882172\pi\) | ||
0.932267 | − | 0.361772i | \(-0.117828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.16288 | −0.150706 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 26.2985i | − | 0.950825i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.35635 | − | 34.8934i | −0.265623 | − | 1.25993i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.3918i | 1.92536i | 0.270649 | + | 0.962678i | \(0.412762\pi\) | ||||
−0.270649 | + | 0.962678i | \(0.587238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.8257 | 0.461906 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.47357i | − | 0.340741i | −0.985380 | − | 0.170370i | \(-0.945504\pi\) | ||
0.985380 | − | 0.170370i | \(-0.0544964\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.0147i | 1.54513i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.87460 | 0.139001 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −63.3945 | −2.27134 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.59867 | −0.236119 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.7085 | 0.525637 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 57.2437i | − | 2.04311i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 43.0640i | − | 1.53507i | −0.641009 | − | 0.767533i | \(-0.721484\pi\) | ||
0.641009 | − | 0.767533i | \(-0.278516\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.44877 | −0.122779 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.4716i | − | 0.407882i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0170 | + | 2.95513i | −0.497760 | + | 0.104940i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 47.1843i | − | 1.67346i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3563 | −0.402260 | −0.201130 | − | 0.979565i | \(-0.564461\pi\) | ||||
−0.201130 | + | 0.979565i | \(0.564461\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 19.9198i | − | 0.704711i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.86394i | 0.0658591i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.0334 | 0.424651 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.99408 | −0.176018 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.8554 | −0.417330 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.27264 | 0.290850 | 0.145425 | − | 0.989369i | \(-0.453545\pi\) | ||||
0.145425 | + | 0.989369i | \(0.453545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.0311i | 0.843845i | 0.906632 | + | 0.421922i | \(0.138644\pi\) | ||||
−0.906632 | + | 0.421922i | \(0.861356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9788i | 0.455186i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −76.6427 | −2.68468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.2841i | 1.51432i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.35214 | + | 6.41363i | 0.0472478 | + | 0.224110i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.6505i | 1.73281i | 0.499339 | + | 0.866407i | \(0.333576\pi\) | ||||
−0.499339 | + | 0.866407i | \(0.666424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3234 | −0.359850 | −0.179925 | − | 0.983680i | \(-0.557586\pi\) | ||||
−0.179925 | + | 0.983680i | \(0.557586\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.76501i | − | 0.235527i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.7564i | 0.930413i | 0.885202 | + | 0.465206i | \(0.154020\pi\) | ||||
−0.885202 | + | 0.465206i | \(0.845980\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.2214 | −1.08436 | −0.542182 | − | 0.840261i | \(-0.682402\pi\) | ||||
−0.542182 | + | 0.840261i | \(0.682402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.0958 | −0.974633 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.31834 | −0.149622 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −57.6631 | −1.99551 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 36.2122i | − | 1.25168i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 21.8707i | − | 0.755061i | −0.925997 | − | 0.377531i | \(-0.876773\pi\) | ||
0.925997 | − | 0.377531i | \(-0.123227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1156 | −0.728124 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 9.19039i | − | 0.316534i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.5811 | + | 39.8429i | 0.604808 | + | 1.37064i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −32.5750 | −1.11797 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.31276i | 0.182119i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.0838i | 0.721895i | 0.932586 | + | 0.360948i | \(0.117547\pi\) | ||||
−0.932586 | + | 0.360948i | \(0.882453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −43.4559 | −1.48616 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.7184 | −1.18596 | −0.592979 | − | 0.805218i | \(-0.702048\pi\) | ||||
−0.592979 | + | 0.805218i | \(0.702048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4087 | 0.457500 | 0.228750 | − | 0.973485i | \(-0.426536\pi\) | ||||
0.228750 | + | 0.973485i | \(0.426536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.65918 | −0.329184 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 26.7141i | − | 0.909359i | −0.890655 | − | 0.454680i | \(-0.849754\pi\) | ||
0.890655 | − | 0.454680i | \(-0.150246\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 40.1657i | − | 1.36567i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.79183 | −0.0608538 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.43515i | − | 0.320066i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.49473 | + | 45.0363i | 0.321716 | + | 1.52600i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 23.5846i | − | 0.798219i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.09438 | 0.138415 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.42868i | 0.217081i | 0.994092 | + | 0.108541i | \(0.0346177\pi\) | ||||
−0.994092 | + | 0.108541i | \(0.965382\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.28585i | 0.178287i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.8595 | −1.07337 | −0.536687 | − | 0.843782i | \(-0.680324\pi\) | ||||
−0.536687 | + | 0.843782i | \(0.680324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.88272 | 0.0633586 | 0.0316793 | − | 0.999498i | \(-0.489914\pi\) | ||||
0.0316793 | + | 0.999498i | \(0.489914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.0228 | 1.21089 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.605266 | 0.0203228 | 0.0101614 | − | 0.999948i | \(-0.496765\pi\) | ||||
0.0101614 | + | 0.999948i | \(0.496765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.72215i | − | 0.158376i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.241394i | 0.00808699i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.9156 | −1.10148 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 66.4368i | 2.22074i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.71831 | − | 1.20556i | 0.190929 | − | 0.0402523i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 19.4114i | − | 0.647405i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.9438 | 1.86376 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.59505i | 0.219469i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 65.8427i | − | 2.18869i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.4191 | −0.644801 | −0.322400 | − | 0.946603i | \(-0.604490\pi\) | ||||
−0.322400 | + | 0.946603i | \(0.604490\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.03540 | −0.133846 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.5051 | 0.348050 | 0.174025 | − | 0.984741i | \(-0.444323\pi\) | ||||
0.174025 | + | 0.984741i | \(0.444323\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.795337 | 0.0263218 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 14.4707i | − | 0.478387i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.01648i | 0.0335670i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.23099 | −0.172555 | −0.0862773 | − | 0.996271i | \(-0.527497\pi\) | ||||
−0.0862773 | + | 0.996271i | \(0.527497\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 36.5223i | − | 1.20345i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.90800 | + | 23.2801i | 0.161549 | + | 0.766274i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 22.1743i | − | 0.729085i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.9259 | 0.523076 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 0.236803i | − | 0.00776924i | −0.999992 | − | 0.00388462i | \(-0.998763\pi\) | ||
0.999992 | − | 0.00388462i | \(-0.00123652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.13566i | 0.233862i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.965379 | 0.0316051 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.4663 | 0.473097 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −60.0746 | −1.96255 | −0.981276 | − | 0.192607i | \(-0.938306\pi\) | ||||
−0.981276 | + | 0.192607i | \(0.938306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.7237 | −0.904730 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.6019i | 0.410811i | 0.978677 | + | 0.205406i | \(0.0658513\pi\) | ||||
−0.978677 | + | 0.205406i | \(0.934149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 13.2444i | − | 0.431298i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.5478 | −0.570829 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.8695i | 0.613176i | 0.951842 | + | 0.306588i | \(0.0991874\pi\) | ||||
−0.951842 | + | 0.306588i | \(0.900813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.95031 | − | 42.4540i | −0.290539 | − | 1.37811i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 17.4268i | − | 0.565102i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.2874 | 0.398027 | 0.199014 | − | 0.979997i | \(-0.436226\pi\) | ||||
0.199014 | + | 0.979997i | \(0.436226\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.0937i | 1.49156i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.05286i | 0.0986850i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.51956 | −0.0813609 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.7907 | −0.541636 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.98003 | −0.321602 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.6375 | 1.75884 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 54.8891i | − | 1.76511i | −0.470205 | − | 0.882557i | \(-0.655820\pi\) | ||
0.470205 | − | 0.882557i | \(-0.344180\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.5022i | 1.07625i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.77490 | −0.0569591 | −0.0284796 | − | 0.999594i | \(-0.509067\pi\) | ||||
−0.0284796 | + | 0.999594i | \(0.509067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.39901i | 0.301318i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23.8669 | + | 5.03172i | −0.764354 | + | 0.161144i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 52.7699i | − | 1.68826i | −0.536139 | − | 0.844130i | \(-0.680118\pi\) | ||
0.536139 | − | 0.844130i | \(-0.319882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.02531 | −0.0327692 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 7.56779i | − | 0.241621i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 38.3002i | − | 1.22159i | −0.791790 | − | 0.610794i | \(-0.790850\pi\) | ||
0.791790 | − | 0.610794i | \(-0.209150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 61.4762 | 1.95880 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.01523 | −0.159636 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.04297 | −0.287550 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.7153 | 1.42043 | 0.710214 | − | 0.703986i | \(-0.248598\pi\) | ||||
0.710214 | + | 0.703986i | \(0.248598\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.7235i | 0.911514i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 68.4991i | 2.17157i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.1786 | 0.417372 | 0.208686 | − | 0.977983i | \(-0.433081\pi\) | ||||
0.208686 | + | 0.977983i | \(0.433081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.6675i | 0.590615i |
(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 | 4004.2.m.c.2157.11 | ✓ | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.12 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.11 | ✓ | 36 | 1.1 | even | 1 | trivial | |
4004.2.m.c.2157.12 | yes | 36 | 13.12 | even | 2 | inner |