Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(609,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.d (of order \(2\), degree \(1\), not 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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.16516096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 13x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.1 | ||
Root | \(0.285442i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.609 |
Dual form | 1520.2.d.h.609.6 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 3.21789i | − | 1.85785i | −0.370268 | − | 0.928925i | \(-0.620734\pi\) | ||
0.370268 | − | 0.928925i | \(-0.379266\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.370556 | − | 2.20515i | −0.165718 | − | 0.986173i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59637i | 0.981334i | 0.871347 | + | 0.490667i | \(0.163247\pi\) | ||||
−0.871347 | + | 0.490667i | \(0.836753\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.35482 | −2.45161 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.741113 | −0.223454 | −0.111727 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111727 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.78878i | − | 1.05082i | −0.850850 | − | 0.525409i | \(-0.823912\pi\) | ||
0.850850 | − | 0.525409i | \(-0.176088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.09593 | + | 1.19241i | −1.83216 | + | 0.307879i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.16725i | 0.768171i | 0.923298 | + | 0.384086i | \(0.125483\pi\) | ||||
−0.923298 | + | 0.384086i | \(0.874517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.35482 | 1.82317 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.570885i | − | 0.119038i | −0.998227 | − | 0.0595189i | \(-0.981043\pi\) | ||
0.998227 | − | 0.0595189i | \(-0.0189566\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.72538 | + | 1.63427i | −0.945075 | + | 0.326853i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.0133i | 2.69687i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.83705 | −1.04836 | −0.524182 | − | 0.851606i | \(-0.675629\pi\) | ||||
−0.524182 | + | 0.851606i | \(0.675629\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.38482i | 0.415144i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.72538 | − | 0.962100i | 0.967765 | − | 0.162625i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.40396i | 0.230809i | 0.993319 | + | 0.115404i | \(0.0368164\pi\) | ||||
−0.993319 | + | 0.115404i | \(0.963184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.1919 | −1.95226 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.83705 | −0.599246 | −0.299623 | − | 0.954058i | \(-0.596861\pi\) | ||||
−0.299623 | + | 0.954058i | \(0.596861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.59637i | 0.395942i | 0.980208 | + | 0.197971i | \(0.0634352\pi\) | ||||
−0.980208 | + | 0.197971i | \(0.936565\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.72538 | + | 16.2185i | 0.406275 | + | 2.41771i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.08247i | 0.741354i | 0.928762 | + | 0.370677i | \(0.120874\pi\) | ||||
−0.928762 | + | 0.370677i | \(0.879126\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.258887 | 0.0369839 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.1919 | 1.42715 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.160905i | − | 0.0221020i | −0.999939 | − | 0.0110510i | \(-0.996482\pi\) | ||
0.999939 | − | 0.0110510i | \(-0.00351771\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.274624 | + | 1.63427i | 0.0370303 | + | 0.220364i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.21789i | 0.426220i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.35482 | 1.08770 | 0.543852 | − | 0.839181i | \(-0.316965\pi\) | ||||
0.543852 | + | 0.839181i | \(0.316965\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.57816 | −1.09832 | −0.549160 | − | 0.835717i | \(-0.685052\pi\) | ||||
−0.549160 | + | 0.835717i | \(0.685052\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 19.0958i | − | 2.40584i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.35482 | + | 1.40396i | −1.03629 | + | 0.174139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.8464i | − | 1.81378i | −0.421371 | − | 0.906888i | \(-0.638451\pi\) | ||
0.421371 | − | 0.906888i | \(-0.361549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.83705 | −0.221154 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.64518 | −0.432603 | −0.216302 | − | 0.976327i | \(-0.569399\pi\) | ||||
−0.216302 | + | 0.976327i | \(0.569399\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.8461i | − | 1.26944i | −0.772743 | − | 0.634719i | \(-0.781116\pi\) | ||
0.772743 | − | 0.634719i | \(-0.218884\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.25889 | + | 15.2057i | 0.607244 | + | 1.75581i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.92420i | − | 0.219283i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.83705 | 0.206684 | 0.103342 | − | 0.994646i | \(-0.467046\pi\) | ||||
0.103342 | + | 0.994646i | \(0.467046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.0289 | 2.55877 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.19876i | 0.460873i | 0.973087 | + | 0.230437i | \(0.0740154\pi\) | ||||
−0.973087 | + | 0.230437i | \(0.925985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.98426 | − | 1.17365i | 0.757550 | − | 0.127300i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.3073i | 2.06996i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.9015 | 1.79156 | 0.895778 | − | 0.444502i | \(-0.146619\pi\) | ||||
0.895778 | + | 0.444502i | \(0.146619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.83705 | 1.03120 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.7830i | 1.94770i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.370556 | + | 2.20515i | 0.0380183 | + | 0.226244i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.78878i | 0.384692i | 0.981327 | + | 0.192346i | \(0.0616096\pi\) | ||||
−0.981327 | + | 0.192346i | \(0.938390\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.45075 | 0.547821 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.35482 | 0.831336 | 0.415668 | − | 0.909517i | \(-0.363548\pi\) | ||||
0.415668 | + | 0.909517i | \(0.363548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.07612i | − | 0.204566i | −0.994755 | − | 0.102283i | \(-0.967385\pi\) | ||
0.994755 | − | 0.102283i | \(-0.0326148\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.09593 | − | 18.4236i | −0.302132 | − | 1.79796i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.70399i | − | 0.551426i | −0.961240 | − | 0.275713i | \(-0.911086\pi\) | ||
0.961240 | − | 0.275713i | \(-0.0889139\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.64518 | −0.157580 | −0.0787899 | − | 0.996891i | \(-0.525106\pi\) | ||||
−0.0787899 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.51777 | 0.428808 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.89006i | − | 0.365946i | −0.983118 | − | 0.182973i | \(-0.941428\pi\) | ||
0.983118 | − | 0.182973i | \(-0.0585720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.25889 | + | 0.211545i | −0.117392 | + | 0.0197267i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 27.8658i | 2.57619i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.22334 | −0.753832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4508 | −0.950068 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.3472i | 1.11331i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.35482 | + | 9.81458i | 0.478950 | + | 0.877842i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.4233i | − | 1.27986i | −0.768432 | − | 0.639931i | \(-0.778963\pi\) | ||
0.768432 | − | 0.639931i | \(-0.221037\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.35482 | 0.735601 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.96853 | −0.870954 | −0.435477 | − | 0.900200i | \(-0.643420\pi\) | ||||
−0.435477 | + | 0.900200i | \(0.643420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.59637i | − | 0.225133i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 30.9015 | − | 5.19273i | 2.65958 | − | 0.446919i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.70431i | 0.829095i | 0.910028 | + | 0.414548i | \(0.136060\pi\) | ||||
−0.910028 | + | 0.414548i | \(0.863940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.4508 | −1.14088 | −0.570439 | − | 0.821340i | \(-0.693227\pi\) | ||||
−0.570439 | + | 0.821340i | \(0.693227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.3548 | 1.37732 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.80791i | 0.234809i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.22334 | + | 13.2309i | 0.184638 | + | 1.09877i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 0.833070i | − | 0.0687105i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0959 | −1.23671 | −0.618353 | − | 0.785900i | \(-0.712200\pi\) | ||||
−0.618353 | + | 0.785900i | \(0.712200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1919 | −1.15492 | −0.577459 | − | 0.816420i | \(-0.695956\pi\) | ||||
−0.577459 | + | 0.816420i | \(0.695956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 23.2946i | − | 1.88325i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.16295 | + | 12.8716i | 0.173733 | + | 1.03387i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.57755i | 0.604754i | 0.953188 | + | 0.302377i | \(0.0977802\pi\) | ||||
−0.953188 | + | 0.302377i | \(0.902220\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.517774 | −0.0410622 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.48223 | 0.116816 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.6757i | − | 1.54112i | −0.637369 | − | 0.770559i | \(-0.719977\pi\) | ||
0.637369 | − | 0.770559i | \(-0.280023\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.25889 | − | 0.883711i | 0.409404 | − | 0.0687968i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.7954i | 0.835376i | 0.908590 | + | 0.417688i | \(0.137160\pi\) | ||||
−0.908590 | + | 0.417688i | \(0.862840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.35482 | −0.104217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.35482 | 0.562437 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 20.3895i | − | 1.55018i | −0.631848 | − | 0.775092i | \(-0.717703\pi\) | ||
0.631848 | − | 0.775092i | \(-0.282297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.24315 | − | 12.2688i | −0.320752 | − | 0.927434i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 26.8849i | − | 2.02079i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.0645 | 1.87341 | 0.936703 | − | 0.350126i | \(-0.113861\pi\) | ||||
0.936703 | + | 0.350126i | \(0.113861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.4193 | −1.44342 | −0.721712 | − | 0.692194i | \(-0.756644\pi\) | ||||
−0.721712 | + | 0.692194i | \(0.756644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.6036i | 2.04051i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.09593 | − | 0.520245i | 0.227617 | − | 0.0382491i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.34729i | − | 0.171651i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −36.3837 | −2.64653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.4508 | −0.828547 | −0.414274 | − | 0.910152i | \(-0.635964\pi\) | ||||
−0.414274 | + | 0.910152i | \(0.635964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.78878i | − | 0.272722i | −0.990659 | − | 0.136361i | \(-0.956459\pi\) | ||
0.990659 | − | 0.136361i | \(-0.0435407\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.51777 | + | 26.8849i | 0.323525 | + | 1.92527i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.28354i | 0.162695i | 0.996686 | + | 0.0813477i | \(0.0259224\pi\) | ||||
−0.996686 | + | 0.0813477i | \(0.974078\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.4508 | −1.37883 | −0.689414 | − | 0.724368i | \(-0.742132\pi\) | ||||
−0.689414 | + | 0.724368i | \(0.742132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −47.7741 | −3.36972 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 15.5782i | − | 1.09337i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.42184 | + | 8.46126i | 0.0993057 | + | 0.590960i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.19876i | 0.291834i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.741113 | 0.0512639 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2274 | −0.772927 | −0.386463 | − | 0.922305i | \(-0.626303\pi\) | ||||
−0.386463 | + | 0.922305i | \(0.626303\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.7298i | 0.803712i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.72538 | − | 0.962100i | 0.390467 | − | 0.0656147i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 15.1551i | − | 1.02880i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −34.9015 | −2.35843 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.03785i | − | 0.270394i | −0.990819 | − | 0.135197i | \(-0.956833\pi\) | ||
0.990819 | − | 0.135197i | \(-0.0431668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 34.7543 | − | 12.0197i | 2.31695 | − | 0.801315i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.2185i | 0.744600i | 0.928112 | + | 0.372300i | \(0.121431\pi\) | ||||
−0.928112 | + | 0.372300i | \(0.878569\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1315 | −1.06600 | −0.532999 | − | 0.846116i | \(-0.678935\pi\) | ||||
−0.532999 | + | 0.846116i | \(0.678935\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.19186 | −0.407395 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.12676i | 0.139329i | 0.997570 | + | 0.0696644i | \(0.0221928\pi\) | ||||
−0.997570 | + | 0.0696644i | \(0.977807\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.2076 | − | 1.88334i | 0.731103 | − | 0.122856i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.91141i | − | 0.383987i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.4152 | −0.932442 | −0.466221 | − | 0.884668i | \(-0.654385\pi\) | ||||
−0.466221 | + | 0.884668i | \(0.654385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.162955 | −0.0104968 | −0.00524842 | − | 0.999986i | \(-0.501671\pi\) | ||||
−0.00524842 | + | 0.999986i | \(0.501671\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 32.0645i | − | 2.05694i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0959323 | − | 0.570885i | −0.00612889 | − | 0.0364725i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.78878i | 0.241074i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5111 | 0.856233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9330 | −0.816322 | −0.408161 | − | 0.912910i | \(-0.633830\pi\) | ||||
−0.408161 | + | 0.912910i | \(0.633830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.423090i | 0.0265995i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.77666 | − | 22.4746i | −0.236504 | − | 1.40741i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.0445i | − | 0.688938i | −0.938798 | − | 0.344469i | \(-0.888059\pi\) | ||
0.938798 | − | 0.344469i | \(-0.111941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.64518 | −0.226501 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 44.1289 | 2.73151 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.8527i | 1.10085i | 0.834885 | + | 0.550424i | \(0.185534\pi\) | ||||
−0.834885 | + | 0.550424i | \(0.814466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.354819 | + | 0.0596243i | −0.0217964 | + | 0.00366269i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 54.3872i | − | 3.32844i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.9934 | −1.52387 | −0.761936 | − | 0.647652i | \(-0.775751\pi\) | ||||
−0.761936 | + | 0.647652i | \(0.775751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8660 | 1.44975 | 0.724877 | − | 0.688879i | \(-0.241897\pi\) | ||||
0.724877 | + | 0.688879i | \(0.241897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 31.6545i | − | 1.91582i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.50204 | − | 1.21118i | 0.211181 | − | 0.0730366i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.2315i | − | 1.27568i | −0.770169 | − | 0.637840i | \(-0.779828\pi\) | ||
0.770169 | − | 0.637840i | \(-0.220172\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 42.9304 | 2.57018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.83705 | 0.228899 | 0.114449 | − | 0.993429i | \(-0.463490\pi\) | ||||
0.114449 | + | 0.993429i | \(0.463490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.211545i | 0.0125751i | 0.999980 | + | 0.00628753i | \(0.00200139\pi\) | ||||
−0.999980 | + | 0.00628753i | \(0.997999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.09593 | − | 1.19241i | 0.420327 | − | 0.0706323i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.96237i | − | 0.588060i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.96853 | 0.409913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.1919 | 0.714700 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9942i | 0.875970i | 0.898982 | + | 0.437985i | \(0.144308\pi\) | ||||
−0.898982 | + | 0.437985i | \(0.855692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.09593 | − | 18.4236i | −0.180252 | − | 1.07267i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 10.3855i | − | 0.602626i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.16295 | −0.125087 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.74111 | −0.388551 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 26.8849i | − | 1.54450i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.17869 | + | 18.9161i | 0.182011 | + | 1.08313i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.65303i | − | 0.0943434i | −0.998887 | − | 0.0471717i | \(-0.984979\pi\) | ||
0.998887 | − | 0.0471717i | \(-0.0150208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.68073 | −0.380053 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.741113 | 0.0420247 | 0.0210123 | − | 0.999779i | \(-0.493311\pi\) | ||||
0.0210123 | + | 0.999779i | \(0.493311\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.8849i | 1.51962i | 0.650143 | + | 0.759812i | \(0.274709\pi\) | ||||
−0.650143 | + | 0.759812i | \(0.725291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −42.1091 | + | 7.07607i | −2.37258 | + | 0.398691i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.16155i | − | 0.458398i | −0.973380 | − | 0.229199i | \(-0.926389\pi\) | ||
0.973380 | − | 0.229199i | \(-0.0736107\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.44668 | 0.248966 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.3548 | −1.02447 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.16725i | − | 0.176231i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.19186 | + | 17.9034i | 0.343463 | + | 0.993101i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.29401i | 0.292759i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.1959 | −0.727516 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 10.3258i | − | 0.565852i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −32.7385 | + | 5.50143i | −1.78870 | + | 0.300575i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.90275i | − | 0.539437i | −0.962939 | − | 0.269718i | \(-0.913069\pi\) | ||
0.962939 | − | 0.269718i | \(-0.0869306\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.5178 | −0.679872 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.32591 | 0.234261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8467i | 1.01763i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.680729 | + | 4.05096i | 0.0366492 | + | 0.218096i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.2781i | 1.14227i | 0.820858 | + | 0.571133i | \(0.193496\pi\) | ||||
−0.820858 | + | 0.571133i | \(0.806504\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.4152 | 0.878686 | 0.439343 | − | 0.898319i | \(-0.355211\pi\) | ||||
0.439343 | + | 0.898319i | \(0.355211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 53.0934 | 2.83391 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 23.8744i | − | 1.27071i | −0.772221 | − | 0.635354i | \(-0.780854\pi\) | ||
0.772221 | − | 0.635354i | \(-0.219146\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.35075 | + | 8.03817i | 0.0716901 | + | 0.426622i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26.4618i | 1.40051i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.22334 | 0.117343 | 0.0586717 | − | 0.998277i | \(-0.481313\pi\) | ||||
0.0586717 | + | 0.998277i | \(0.481313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 33.6294i | 1.76508i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.9172 | + | 4.01909i | −1.25189 | + | 0.210369i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.52057i | 0.235972i | 0.993015 | + | 0.117986i | \(0.0376437\pi\) | ||||
−0.993015 | + | 0.117986i | \(0.962356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.2208 | 1.46911 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.417768 | 0.0216894 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.5186i | − | 0.803521i | −0.915745 | − | 0.401760i | \(-0.868398\pi\) | ||
0.915745 | − | 0.401760i | \(-0.131602\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.5822 | − | 17.2312i | 1.63090 | − | 0.889817i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.7327i | 1.17079i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.9015 | −0.970905 | −0.485453 | − | 0.874263i | \(-0.661345\pi\) | ||||
−0.485453 | + | 0.874263i | \(0.661345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −46.4126 | −2.37779 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 13.7046i | − | 0.700274i | −0.936699 | − | 0.350137i | \(-0.886135\pi\) | ||
0.936699 | − | 0.350137i | \(-0.113865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.24315 | + | 0.713025i | −0.216251 | + | 0.0363391i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 19.0958i | − | 0.970694i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7411 | −0.646000 | −0.323000 | − | 0.946399i | \(-0.604691\pi\) | ||||
−0.323000 | + | 0.946399i | \(0.604691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.80814 | 0.0914413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.0776i | 1.61810i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.680729 | − | 4.05096i | −0.0342512 | − | 0.203826i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 38.6522i | − | 1.93990i | −0.243306 | − | 0.969950i | \(-0.578232\pi\) | ||
0.243306 | − | 0.969950i | \(-0.421768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.35482 | −0.418264 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.8660 | 1.59131 | 0.795655 | − | 0.605750i | \(-0.207127\pi\) | ||||
0.795655 | + | 0.605750i | \(0.207127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.1153i | 1.10164i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.53351 | − | 50.7822i | −0.424034 | − | 2.52339i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.04049i | − | 0.0515751i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0645 | −0.547102 | −0.273551 | − | 0.961857i | \(-0.588198\pi\) | ||||
−0.273551 | + | 0.961857i | \(0.588198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.2274 | 1.54033 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.6922i | 1.06740i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.25889 | − | 1.55588i | 0.454501 | − | 0.0763749i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 43.2830i | 2.11958i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.7452 | −1.25773 | −0.628867 | − | 0.777513i | \(-0.716481\pi\) | ||||
−0.628867 | + | 0.777513i | \(0.716481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4482 | 1.33774 | 0.668871 | − | 0.743378i | \(-0.266778\pi\) | ||||
0.668871 | + | 0.743378i | \(0.266778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 37.3806i | − | 1.81751i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.17613 | − | 14.9664i | −0.251079 | − | 0.725979i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 22.2720i | − | 1.07782i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.03555 | 0.436240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.74519 | −0.0840627 | −0.0420314 | − | 0.999116i | \(-0.513383\pi\) | ||||
−0.0420314 | + | 0.999116i | \(0.513383\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5208i | 0.890052i | 0.895518 | + | 0.445026i | \(0.146806\pi\) | ||||
−0.895518 | + | 0.445026i | \(0.853194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 42.5756 | − | 7.15446i | 2.04134 | − | 0.343030i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.570885i | 0.0273091i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.4482 | 1.40549 | 0.702743 | − | 0.711444i | \(-0.251959\pi\) | ||||
0.702743 | + | 0.711444i | \(0.251959\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.90407 | −0.0906699 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.7388i | 0.557726i | 0.960331 | + | 0.278863i | \(0.0899576\pi\) | ||||
−0.960331 | + | 0.278863i | \(0.910042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.26296 | − | 37.2704i | −0.296893 | − | 1.76678i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 48.5771i | 2.29762i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.06446 | 0.333392 | 0.166696 | − | 0.986008i | \(-0.446690\pi\) | ||||
0.166696 | + | 0.986008i | \(0.446690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.84368 | 0.133904 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 45.6679i | 2.14566i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.64518 | − | 21.6922i | −0.170889 | − | 1.01694i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 34.5000i | − | 1.61384i | −0.590660 | − | 0.806920i | \(-0.701133\pi\) | ||
0.590660 | − | 0.806920i | \(-0.298867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −44.3837 | −2.07166 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.03147 | 0.374063 | 0.187032 | − | 0.982354i | \(-0.440113\pi\) | ||||
0.187032 | + | 0.982354i | \(0.440113\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.3290i | − | 1.17714i | −0.808447 | − | 0.588570i | \(-0.799691\pi\) | ||
0.808447 | − | 0.588570i | \(-0.200309\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 41.4193 | − | 6.96015i | 1.92077 | − | 0.322769i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 26.8759i | − | 1.24367i | −0.783149 | − | 0.621834i | \(-0.786388\pi\) | ||
0.783149 | − | 0.621834i | \(-0.213612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.5467 | 1.77992 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.3837 | 1.12354 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.92420i | − | 0.0884748i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.72538 | − | 1.63427i | 0.216815 | − | 0.0749852i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.18343i | 0.0541854i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.9015 | −1.32054 | −0.660272 | − | 0.751027i | \(-0.729559\pi\) | ||||
−0.660272 | + | 0.751027i | \(0.729559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.31927 | 0.242538 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.76964i | − | 0.217026i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.35482 | − | 1.40396i | 0.379373 | − | 0.0637503i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7294i | 0.803395i | 0.915773 | + | 0.401697i | \(0.131580\pi\) | ||||
−0.915773 | + | 0.401697i | \(0.868420\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −63.3141 | −2.86316 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.1645 | 1.58695 | 0.793475 | − | 0.608603i | \(-0.208270\pi\) | ||||
0.793475 | + | 0.608603i | \(0.208270\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 19.0035i | − | 0.855875i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.01981 | − | 12.0197i | −0.0907838 | − | 0.540247i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 9.46422i | − | 0.424528i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.4508 | 0.960268 | 0.480134 | − | 0.877195i | \(-0.340588\pi\) | ||||
0.480134 | + | 0.877195i | \(0.340588\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.7385 | 1.55200 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.34053i | − | 0.238122i | −0.992887 | − | 0.119061i | \(-0.962012\pi\) | ||
0.992887 | − | 0.119061i | \(-0.0379884\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.09593 | − | 18.4236i | −0.137767 | − | 0.819841i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.35966i | 0.193619i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.1919 | −1.60418 | −0.802088 | − | 0.597206i | \(-0.796278\pi\) | ||||
−0.802088 | + | 0.597206i | \(0.796278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.1604 | 1.24574 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 14.0133i | − | 0.618704i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.57816 | + | 0.769320i | −0.201738 | + | 0.0339003i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.76668i | − | 0.165658i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −65.6111 | −2.88001 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.77259 | −0.121469 | −0.0607346 | − | 0.998154i | \(-0.519344\pi\) | ||||
−0.0607346 | + | 0.998154i | \(0.519344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.5373i | − | 0.898033i | −0.893524 | − | 0.449016i | \(-0.851774\pi\) | ||
0.893524 | − | 0.449016i | \(-0.148226\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −39.4797 | + | 13.6540i | −1.72303 | + | 0.595909i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 18.4874i | − | 0.805323i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.6741 | 0.985830 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −61.4482 | −2.66662 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.5377i | 0.629698i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.5782 | + | 2.11365i | −0.543801 | + | 0.0913811i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 80.6547i | − | 3.48051i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.191865 | −0.00826419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.4797 | 1.52539 | 0.762695 | − | 0.646758i | \(-0.223876\pi\) | ||||
0.762695 | + | 0.646758i | \(0.223876\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 62.4891i | 2.68166i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.609632 | + | 3.62787i | 0.0261138 | + | 0.155401i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 43.0756i | − | 1.84178i | −0.389822 | − | 0.920890i | \(-0.627463\pi\) | ||
0.389822 | − | 0.920890i | \(-0.372537\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 63.0908 | 2.69265 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.76964i | 0.202826i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.67409 | − | 9.96237i | −0.0710612 | − | 0.422879i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.4376i | 1.71340i | 0.515818 | + | 0.856698i | \(0.327488\pi\) | ||||
−0.515818 | + | 0.856698i | \(0.672512\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.83705 | 0.416063 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.55332 | −0.318902 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.7173i | 0.830986i | 0.909596 | + | 0.415493i | \(0.136391\pi\) | ||||
−0.909596 | + | 0.415493i | \(0.863609\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.57816 | + | 1.44149i | −0.360886 | + | 0.0606437i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 59.7915i | 2.51101i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.6807 | −0.783137 | −0.391568 | − | 0.920149i | \(-0.628067\pi\) | ||||
−0.391568 | + | 0.920149i | \(0.628067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.9371 | 1.25283 | 0.626413 | − | 0.779491i | \(-0.284522\pi\) | ||||
0.626413 | + | 0.779491i | \(0.284522\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.8473i | 1.53932i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.932977 | + | 2.69765i | 0.0389079 | + | 0.112500i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.156779i | − | 0.00652679i | −0.999995 | − | 0.00326339i | \(-0.998961\pi\) | ||
0.999995 | − | 0.00326339i | \(-0.00103877\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.1919 | −0.506677 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9015 | −0.452271 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.119249i | 0.00493877i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 61.4482 | − | 10.3258i | 2.54057 | − | 0.426921i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 31.1474i | − | 1.28559i | −0.766038 | − | 0.642795i | \(-0.777775\pi\) | ||
0.766038 | − | 0.642795i | \(-0.222225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.83705 | 0.240511 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.34818 | 0.302264 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.8728i | − | 1.18567i | −0.805326 | − | 0.592833i | \(-0.798009\pi\) | ||
0.805326 | − | 0.592833i | \(-0.201991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.04721 | + | 18.1337i | 0.124923 | + | 0.743409i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 62.5904i | 2.56165i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.3274 | 1.03485 | 0.517425 | − | 0.855728i | \(-0.326891\pi\) | ||||
0.517425 | + | 0.855728i | \(0.326891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8370 | −0.809170 | −0.404585 | − | 0.914500i | \(-0.632584\pi\) | ||||
−0.404585 | + | 0.914500i | \(0.632584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 109.193i | 4.44667i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.87259 | + | 23.0455i | 0.157443 | + | 0.936932i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.49921i | 0.101440i | 0.998713 | + | 0.0507199i | \(0.0161516\pi\) | ||||
−0.998713 | + | 0.0507199i | \(0.983848\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −50.1289 | −2.03133 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.2563 | 0.779027 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.883711i | 0.0356927i | 0.999841 | + | 0.0178464i | \(0.00568098\pi\) | ||||
−0.999841 | + | 0.0178464i | \(0.994319\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.2274 | − | 4.57533i | 1.09792 | − | 0.184495i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 29.4085i | − | 1.18394i | −0.805959 | − | 0.591971i | \(-0.798350\pi\) | ||
0.805959 | − | 0.591971i | \(-0.201650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.3208 | 1.21870 | 0.609348 | − | 0.792903i | \(-0.291431\pi\) | ||||
0.609348 | + | 0.792903i | \(0.291431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 43.8825i | 1.75811i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.6584 | − | 15.4450i | 0.786334 | − | 0.617801i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 2.38482i | − | 0.0952405i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.44668 | −0.177301 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.7767 | −0.707678 | −0.353839 | − | 0.935306i | \(-0.615124\pi\) | ||||
−0.353839 | + | 0.935306i | \(0.615124\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.1286i | 1.43598i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.8056 | + | 5.34465i | −1.26217 | + | 0.212096i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.980865i | − | 0.0388633i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.8096 | 1.06057 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.6675 | −1.29029 | −0.645143 | − | 0.764062i | \(-0.723202\pi\) | ||||
−0.645143 | + | 0.764062i | \(0.723202\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.8661i | 1.25668i | 0.777941 | + | 0.628338i | \(0.216264\pi\) | ||||
−0.777941 | + | 0.628338i | \(0.783736\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.09593 | − | 18.4236i | −0.121902 | − | 0.725430i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 21.2601i | − | 0.835820i | −0.908488 | − | 0.417910i | \(-0.862763\pi\) | ||
0.908488 | − | 0.417910i | \(-0.137237\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.19186 | −0.243052 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −48.7675 | −1.91135 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 12.8340i | − | 0.502234i | −0.967957 | − | 0.251117i | \(-0.919202\pi\) | ||
0.967957 | − | 0.251117i | \(-0.0807980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.69390 | + | 21.9821i | 0.144333 | + | 0.858912i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 79.7710i | 3.11216i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.3548 | 0.792911 | 0.396456 | − | 0.918054i | \(-0.370240\pi\) | ||||
0.396456 | + | 0.918054i | \(0.370240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.7385 | −1.19559 | −0.597795 | − | 0.801649i | \(-0.703957\pi\) | ||||
−0.597795 | + | 0.801649i | \(0.703957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 38.6147i | − | 1.49967i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.72538 | + | 0.962100i | −0.222021 | + | 0.0373086i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.42531i | 0.132629i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9934 | −0.502352 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.35738 | 0.245424 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 21.2094i | − | 0.817564i | −0.912632 | − | 0.408782i | \(-0.865954\pi\) | ||
0.912632 | − | 0.408782i | \(-0.134046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.9015 | − | 66.2183i | −0.881479 | − | 2.54874i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.2650i | 0.432951i | 0.976288 | + | 0.216475i | \(0.0694561\pi\) | ||||
−0.976288 | + | 0.216475i | \(0.930544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.83705 | −0.377511 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.1000 | 1.38336 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 12.3603i | − | 0.472954i | −0.971637 | − | 0.236477i | \(-0.924007\pi\) | ||
0.971637 | − | 0.236477i | \(-0.0759928\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.3995 | − | 3.59600i | 0.817632 | − | 0.137396i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.9093i | 1.98046i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.609632 | −0.0232251 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.7493 | −0.865423 | −0.432711 | − | 0.901533i | \(-0.642443\pi\) | ||||
−0.432711 | + | 0.901533i | \(0.642443\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.1521i | 0.537595i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.98426 | + | 29.6609i | 0.189064 | + | 1.12510i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.1529i | − | 0.460323i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.84368 | 0.258852 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.0289 | −0.605404 | −0.302702 | − | 0.953085i | \(-0.597889\pi\) | ||||
−0.302702 | + | 0.953085i | \(0.597889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.40396i | − | 0.0529512i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.06038 | − | 36.0648i | −0.228247 | − | 1.35828i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.6922i | 0.815818i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.4193 | −1.17998 | −0.589988 | − | 0.807412i | \(-0.700867\pi\) | ||||
−0.589988 | + | 0.807412i | \(0.700867\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.5111 | −0.506707 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.33228i | 0.124795i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.19186 | − | 1.04049i | 0.231563 | − | 0.0389121i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 46.3865i | 1.73234i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2589 | 0.419886 | 0.209943 | − | 0.977714i | \(-0.432672\pi\) | ||||
0.209943 | + | 0.977714i | \(0.432672\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.39037 | 0.200748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.524371i | 0.0195016i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.3523 | − | 9.80559i | 1.05298 | − | 0.364171i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 48.9829i | − | 1.81668i | −0.418237 | − | 0.908338i | \(-0.637352\pi\) | ||
0.418237 | − | 0.908338i | \(-0.362648\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.0934 | −1.26272 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.22334 | −0.304151 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.9260i | 1.32696i | 0.748195 | + | 0.663479i | \(0.230921\pi\) | ||||
−0.748195 | + | 0.663479i | \(0.769079\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.83705 | + | 0.308700i | −0.0677604 | + | 0.0113866i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0029i | 0.405296i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3523 | 0.527956 | 0.263978 | − | 0.964529i | \(-0.414965\pi\) | ||||
0.263978 | + | 0.964529i | \(0.414965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.1919 | 0.447879 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.5629i | 0.460887i | 0.973086 | + | 0.230443i | \(0.0740176\pi\) | ||||
−0.973086 | + | 0.230443i | \(0.925982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.59390 | + | 33.2888i | 0.204944 | + | 1.21961i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 30.8811i | − | 1.12988i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.8096 | 0.541133 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.4548 | −0.965350 | −0.482675 | − | 0.875799i | \(-0.660335\pi\) | ||||
−0.482675 | + | 0.875799i | \(0.660335\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 41.6169i | 1.51660i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.25889 | + | 31.2952i | 0.191390 | + | 1.13895i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 15.7350i | − | 0.571897i | −0.958245 | − | 0.285949i | \(-0.907691\pi\) | ||
0.958245 | − | 0.285949i | \(-0.0923087\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.36146 | 0.0494178 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9619 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.27149i | − | 0.154638i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −51.3680 | + | 8.63195i | −1.85721 | + | 0.312089i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 31.6545i | − | 1.14298i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.9974 | −1.51447 | −0.757233 | − | 0.653145i | \(-0.773449\pi\) | ||||
−0.757233 | + | 0.653145i | \(0.773449\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.5400 | −1.27994 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.9579i | 1.47315i | 0.676355 | + | 0.736576i | \(0.263559\pi\) | ||||
−0.676355 | + | 0.736576i | \(0.736441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.5822 | − | 9.53928i | 0.990783 | − | 0.342661i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.7298i | 0.420804i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.83705 | 0.137476 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.70149 | 0.0966669 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 84.0800i | − | 3.00477i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.7096 | − | 2.80791i | 0.596393 | − | 0.100219i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.5379i | 1.01727i | 0.860983 | + | 0.508634i | \(0.169849\pi\) | ||||
−0.860983 | + | 0.508634i | \(0.830151\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 57.4482 | 2.04521 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.1000 | 0.359115 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.5007i | 1.15413i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.191865 | + | 1.14177i | 0.00680473 | + | 0.0404944i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.2790i | − | 1.17880i | −0.807840 | − | 0.589402i | \(-0.799364\pi\) | ||
0.807840 | − | 0.589402i | \(-0.200636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0974 | −0.569487 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −124.308 | −4.39219 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.03817i | 0.283661i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.549248 | − | 3.26853i | −0.0193585 | − | 0.115201i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 80.4259i | 2.83113i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.4234 | 1.21026 | 0.605130 | − | 0.796126i | \(-0.293121\pi\) | ||||
0.605130 | + | 0.796126i | \(0.293121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2563 | 0.395263 | 0.197631 | − | 0.980276i | \(-0.436675\pi\) | ||||
0.197631 | + | 0.980276i | \(0.436675\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 76.7980i | − | 2.69342i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −43.3878 | + | 7.29095i | −1.51981 | + | 0.255391i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.59637i | − | 0.0908353i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −72.3497 | −2.52810 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.3167 | −1.09296 | −0.546480 | − | 0.837472i | \(-0.684033\pi\) | ||||
−0.546480 | + | 0.837472i | \(0.684033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.4800i | 0.469882i | 0.972010 | + | 0.234941i | \(0.0754898\pi\) | ||||
−0.972010 | + | 0.234941i | \(0.924510\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.89743 | − | 11.2692i | −0.135691 | − | 0.392342i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.9882i | 0.555963i | 0.960586 | + | 0.277982i | \(0.0896654\pi\) | ||||
−0.960586 | + | 0.277982i | \(0.910335\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.4837 | 1.68391 | 0.841955 | − | 0.539548i | \(-0.181405\pi\) | ||||
0.841955 | + | 0.539548i | \(0.181405\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −68.3208 | −2.37002 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.819960i | 0.0284099i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.8056 | − | 4.00032i | 0.823826 | − | 0.138437i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 81.7965i | − | 2.82730i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.9934 | −0.655724 | −0.327862 | − | 0.944726i | \(-0.606328\pi\) | ||||
−0.327862 | + | 0.944726i | \(0.606328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 12.3472i | − | 0.425260i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.502037 | + | 2.98758i | 0.0172706 | + | 0.102776i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 27.1340i | − | 0.932334i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.680729 | 0.0233626 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.801497 | 0.0274750 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44.1210i | − | 1.51067i | −0.655337 | − | 0.755337i | \(-0.727473\pi\) | ||
0.655337 | − | 0.755337i | \(-0.272527\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.72538 | − | 16.2185i | −0.0932059 | − | 0.554660i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.4149i | 1.10727i | 0.832759 | + | 0.553635i | \(0.186760\pi\) | ||||
−0.832759 | + | 0.553635i | \(0.813240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.29444 | 0.214763 | 0.107382 | − | 0.994218i | \(-0.465753\pi\) | ||||
0.107382 | + | 0.994218i | \(0.465753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.0578 | −1.09253 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 17.4338i | − | 0.593453i | −0.954963 | − | 0.296726i | \(-0.904105\pi\) | ||
0.954963 | − | 0.296726i | \(-0.0958950\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.9619 | + | 7.55546i | −1.52875 | + | 0.256893i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 22.4240i | − | 0.761557i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.36146 | −0.0461843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −56.2497 | −1.90595 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 27.8658i | − | 0.943113i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25.4822 | + | 13.9031i | −0.861456 | + | 0.470009i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.2904i | 0.786462i | 0.919440 | + | 0.393231i | \(0.128643\pi\) | ||||
−0.919440 | + | 0.393231i | \(0.871357\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 48.2497 | 1.62742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.9619 | 0.975751 | 0.487875 | − | 0.872913i | \(-0.337772\pi\) | ||||
0.487875 | + | 0.872913i | \(0.337772\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 37.3627i | − | 1.25735i | −0.777667 | − | 0.628677i | \(-0.783597\pi\) | ||
0.777667 | − | 0.628677i | \(-0.216403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −59.2852 | + | 9.96237i | −1.99285 | + | 0.334881i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.0234i | 0.773050i | 0.922279 | + | 0.386525i | \(0.126325\pi\) | ||||
−0.922279 | + | 0.386525i | \(0.873675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.4482 | 1.25597 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.0670 | −0.571767 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.08247i | − | 0.170078i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.28780 | − | 55.2709i | −0.310457 | − | 1.84750i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.96015i | 0.232393i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.0223 | 1.16806 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.509626 | 0.0169781 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.6922i | 0.721870i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.19594 | + | 42.8224i | 0.239201 | + | 1.42347i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.2693i | 1.17110i | 0.810637 | + | 0.585549i | \(0.199121\pi\) | ||||
−0.810637 | + | 0.585549i | \(0.800879\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −61.4482 | −2.03811 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.97260 | 0.164750 | 0.0823748 | − | 0.996601i | \(-0.473750\pi\) | ||||
0.0823748 | + | 0.996601i | \(0.473750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.11175i | − | 0.102984i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 60.8700 | − | 10.2287i | 2.01230 | − | 0.338150i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 25.8819i | − | 0.854697i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.7096 | −1.60678 | −0.803391 | − | 0.595451i | \(-0.796973\pi\) | ||||
−0.803391 | + | 0.595451i | \(0.796973\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.31927 | −0.175276 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.8108i | 0.454587i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.29444 | − | 6.63422i | −0.0754406 | − | 0.218132i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.2695i | 0.501516i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.5126 | −1.06671 | −0.533353 | − | 0.845893i | \(-0.679068\pi\) | ||||
−0.533353 | + | 0.845893i | \(0.679068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.258887 | −0.00848468 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 2.38482i | − | 0.0780755i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.17613 | + | 0.869804i | −0.169277 | + | 0.0284456i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.385560i | − | 0.0125957i | −0.999980 | − | 0.00629785i | \(-0.997995\pi\) | ||
0.999980 | − | 0.00629785i | \(-0.00200468\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 86.5126 | 2.82323 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.3482 | 1.47831 | 0.739154 | − | 0.673536i | \(-0.235225\pi\) | ||||
0.739154 | + | 0.673536i | \(0.235225\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.19051i | 0.0713329i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.4822 | + | 80.2316i | 0.438577 | + | 2.60993i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 9.61202i | − | 0.312349i | −0.987730 | − | 0.156174i | \(-0.950084\pi\) | ||
0.987730 | − | 0.156174i | \(-0.0499161\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.0934 | −1.33395 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.2630 | −0.851635 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 59.8421i | 1.93848i | 0.246126 | + | 0.969238i | \(0.420842\pi\) | ||||
−0.246126 | + | 0.969238i | \(0.579158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.24315 | + | 25.2506i | 0.137305 | + | 0.817091i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 14.3089i | − | 0.462542i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.1959 | −0.813619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.07110 | 0.0990676 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.9518i | 1.35188i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.35482 | + | 1.40396i | −0.268951 | + | 0.0451949i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.368324i | 0.0118445i | 0.999982 | + | 0.00592225i | \(0.00188512\pi\) | ||||
−0.999982 | + | 0.00592225i | \(0.998115\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.1919 | −0.327410 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.8370 | 1.47098 | 0.735490 | − | 0.677535i | \(-0.236952\pi\) | ||||
0.735490 | + | 0.677535i | \(0.236952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 34.9231i | − | 1.11958i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 57.6111 | − | 19.9247i | 1.84503 | − | 0.638102i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.0337i | 0.928872i | 0.885607 | + | 0.464436i | \(0.153743\pi\) | ||||
−0.885607 | + | 0.464436i | \(0.846257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5259 | −0.400330 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.1000 | 0.386323 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 11.0160i | − | 0.351355i | −0.984448 | − | 0.175677i | \(-0.943788\pi\) | ||
0.984448 | − | 0.175677i | \(-0.0562116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.03555 | − | 0.846180i | 0.160446 | − | 0.0269615i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.4631i | 1.35161i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.48223 | 0.0471320 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6822 | 0.815823 | 0.407912 | − | 0.913021i | \(-0.366257\pi\) | ||||
0.407912 | + | 0.913021i | \(0.366257\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.7431i | 0.816933i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.20760 | + | 42.8918i | 0.228496 | + | 1.35976i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.3854i | 0.645611i | 0.946465 | + | 0.322805i | \(0.104626\pi\) | ||||
−0.946465 | + | 0.322805i | \(0.895374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.6741 | −0.622461 |
(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 | 1520.2.d.h.609.1 | 6 | ||
4.3 | odd | 2 | 95.2.b.b.39.4 | yes | 6 | ||
5.2 | odd | 4 | 7600.2.a.ck.1.1 | 6 | |||
5.3 | odd | 4 | 7600.2.a.ck.1.6 | 6 | |||
5.4 | even | 2 | inner | 1520.2.d.h.609.6 | 6 | ||
12.11 | even | 2 | 855.2.c.d.514.3 | 6 | |||
20.3 | even | 4 | 475.2.a.j.1.4 | 6 | |||
20.7 | even | 4 | 475.2.a.j.1.3 | 6 | |||
20.19 | odd | 2 | 95.2.b.b.39.3 | ✓ | 6 | ||
60.23 | odd | 4 | 4275.2.a.br.1.3 | 6 | |||
60.47 | odd | 4 | 4275.2.a.br.1.4 | 6 | |||
60.59 | even | 2 | 855.2.c.d.514.4 | 6 | |||
76.75 | even | 2 | 1805.2.b.e.1084.3 | 6 | |||
380.227 | odd | 4 | 9025.2.a.bx.1.4 | 6 | |||
380.303 | odd | 4 | 9025.2.a.bx.1.3 | 6 | |||
380.379 | even | 2 | 1805.2.b.e.1084.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.b.b.39.3 | ✓ | 6 | 20.19 | odd | 2 | ||
95.2.b.b.39.4 | yes | 6 | 4.3 | odd | 2 | ||
475.2.a.j.1.3 | 6 | 20.7 | even | 4 | |||
475.2.a.j.1.4 | 6 | 20.3 | even | 4 | |||
855.2.c.d.514.3 | 6 | 12.11 | even | 2 | |||
855.2.c.d.514.4 | 6 | 60.59 | even | 2 | |||
1520.2.d.h.609.1 | 6 | 1.1 | even | 1 | trivial | ||
1520.2.d.h.609.6 | 6 | 5.4 | even | 2 | inner | ||
1805.2.b.e.1084.3 | 6 | 76.75 | even | 2 | |||
1805.2.b.e.1084.4 | 6 | 380.379 | even | 2 | |||
4275.2.a.br.1.3 | 6 | 60.23 | odd | 4 | |||
4275.2.a.br.1.4 | 6 | 60.47 | odd | 4 | |||
7600.2.a.ck.1.1 | 6 | 5.2 | odd | 4 | |||
7600.2.a.ck.1.6 | 6 | 5.3 | odd | 4 | |||
9025.2.a.bx.1.3 | 6 | 380.303 | odd | 4 | |||
9025.2.a.bx.1.4 | 6 | 380.227 | odd | 4 |