Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.39605.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 8x^{2} + 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.318315\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.681685 | −0.304859 | −0.152429 | − | 0.988314i | \(-0.548710\pi\) | ||||
−0.152429 | + | 0.988314i | \(0.548710\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.71255 | 1.11938 | 0.559688 | − | 0.828704i | \(-0.310921\pi\) | ||||
0.559688 | + | 0.828704i | \(0.310921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.66749 | 1.01718 | 0.508590 | − | 0.861009i | \(-0.330167\pi\) | ||||
0.508590 | + | 0.861009i | \(0.330167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.681685 | 0.176010 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.21699 | 0.537699 | 0.268850 | − | 0.963182i | \(-0.413357\pi\) | ||||
0.268850 | + | 0.963182i | \(0.413357\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34918 | −0.997770 | −0.498885 | − | 0.866668i | \(-0.666257\pi\) | ||||
−0.498885 | + | 0.866668i | \(0.666257\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.53531 | −0.907061 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.63226 | −0.860189 | −0.430095 | − | 0.902784i | \(-0.641520\pi\) | ||||
−0.430095 | + | 0.902784i | \(0.641520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.21699 | −1.47582 | −0.737908 | − | 0.674902i | \(-0.764186\pi\) | ||||
−0.737908 | + | 0.674902i | \(0.764186\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.71255 | −0.646272 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.681685 | −0.115226 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.93391 | 0.646730 | 0.323365 | − | 0.946274i | \(-0.395186\pi\) | ||||
0.323365 | + | 0.946274i | \(0.395186\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.66749 | −0.587269 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.99563 | −0.936360 | −0.468180 | − | 0.883633i | \(-0.655090\pi\) | ||||
−0.468180 | + | 0.883633i | \(0.655090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.16305 | −0.787358 | −0.393679 | − | 0.919248i | \(-0.628798\pi\) | ||||
−0.393679 | + | 0.919248i | \(0.628798\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.681685 | −0.101620 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.41527 | −0.935763 | −0.467882 | − | 0.883791i | \(-0.654983\pi\) | ||||
−0.467882 | + | 0.883791i | \(0.654983\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.21699 | −0.310441 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.60140 | −0.494690 | −0.247345 | − | 0.968927i | \(-0.579558\pi\) | ||||
−0.247345 | + | 0.968927i | \(0.579558\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.53079 | −0.341251 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.34918 | 0.576063 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.83258 | −0.889526 | −0.444763 | − | 0.895648i | \(-0.646712\pi\) | ||||
−0.444763 | + | 0.895648i | \(0.646712\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.71939 | −0.604256 | −0.302128 | − | 0.953267i | \(-0.597697\pi\) | ||||
−0.302128 | + | 0.953267i | \(0.597697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.50007 | −0.310096 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.96477 | 0.362204 | 0.181102 | − | 0.983464i | \(-0.442034\pi\) | ||||
0.181102 | + | 0.983464i | \(0.442034\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.12003 | −0.370280 | −0.185140 | − | 0.982712i | \(-0.559274\pi\) | ||||
−0.185140 | + | 0.982712i | \(0.559274\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2787 | 1.20303 | 0.601516 | − | 0.798860i | \(-0.294563\pi\) | ||||
0.601516 | + | 0.798860i | \(0.294563\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.53531 | 0.523692 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.71255 | 0.423084 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6137 | 1.30664 | 0.653322 | − | 0.757080i | \(-0.273375\pi\) | ||||
0.653322 | + | 0.757080i | \(0.273375\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.5520 | −1.26799 | −0.633997 | − | 0.773335i | \(-0.718587\pi\) | ||||
−0.633997 | + | 0.773335i | \(0.718587\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.51129 | −0.163922 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.63226 | 0.496631 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.88885 | 0.200218 | 0.100109 | − | 0.994976i | \(-0.468081\pi\) | ||||
0.100109 | + | 0.994976i | \(0.468081\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.66749 | 0.384458 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.21699 | 0.852062 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.96477 | 0.304179 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.33062 | 0.744311 | 0.372156 | − | 0.928170i | \(-0.378619\pi\) | ||||
0.372156 | + | 0.928170i | \(0.378619\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.71255 | 0.373125 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.59251 | 0.456972 | 0.228486 | − | 0.973547i | \(-0.426622\pi\) | ||||
0.228486 | + | 0.973547i | \(0.426622\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3448 | −1.41344 | −0.706718 | − | 0.707495i | \(-0.749825\pi\) | ||||
−0.706718 | + | 0.707495i | \(0.749825\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.681685 | 0.0665256 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.44613 | −0.139803 | −0.0699015 | − | 0.997554i | \(-0.522269\pi\) | ||||
−0.0699015 | + | 0.997554i | \(0.522269\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.11567 | 0.873122 | 0.436561 | − | 0.899675i | \(-0.356196\pi\) | ||||
0.436561 | + | 0.899675i | \(0.356196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.93391 | −0.373390 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.8051 | 1.20461 | 0.602303 | − | 0.798268i | \(-0.294250\pi\) | ||||
0.602303 | + | 0.798268i | \(0.294250\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.681685 | −0.0635675 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.66749 | 0.339060 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.21699 | 0.203231 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.78301 | 0.253001 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.99563 | 0.540608 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.50007 | 0.581384 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.5069 | −1.55349 | −0.776744 | − | 0.629816i | \(-0.783130\pi\) | ||||
−0.776744 | + | 0.629816i | \(0.783130\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.16305 | 0.454581 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.08480 | −0.182150 | −0.0910751 | − | 0.995844i | \(-0.529030\pi\) | ||||
−0.0910751 | + | 0.995844i | \(0.529030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.34918 | −0.377122 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.681685 | 0.0586701 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.9163 | −1.27438 | −0.637192 | − | 0.770705i | \(-0.719904\pi\) | ||||
−0.637192 | + | 0.770705i | \(0.719904\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.45050 | −0.462306 | −0.231153 | − | 0.972917i | \(-0.574250\pi\) | ||||
−0.231153 | + | 0.972917i | \(0.574250\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.41527 | 0.540263 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.6157 | 1.13861 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.15774 | 0.262236 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.09900 | 0.581572 | 0.290786 | − | 0.956788i | \(-0.406083\pi\) | ||||
0.290786 | + | 0.956788i | \(0.406083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.29197 | −0.756170 | −0.378085 | − | 0.925771i | \(-0.623417\pi\) | ||||
−0.378085 | + | 0.925771i | \(0.623417\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.21699 | 0.179233 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.60140 | 0.449915 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.33499 | −0.106543 | −0.0532717 | − | 0.998580i | \(-0.516965\pi\) | ||||
−0.0532717 | + | 0.998580i | \(0.516965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.60140 | 0.285610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.49760 | −0.587257 | −0.293629 | − | 0.955920i | \(-0.594863\pi\) | ||||
−0.293629 | + | 0.955920i | \(0.594863\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.53079 | 0.197022 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.34918 | −0.336549 | −0.168275 | − | 0.985740i | \(-0.553820\pi\) | ||||
−0.168275 | + | 0.985740i | \(0.553820\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.450502 | 0.0346540 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.34918 | −0.332590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.7459 | 1.80537 | 0.902683 | − | 0.430306i | \(-0.141594\pi\) | ||||
0.902683 | + | 0.430306i | \(0.141594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.53531 | −0.342837 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.83258 | 0.513568 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.28512 | 0.469772 | 0.234886 | − | 0.972023i | \(-0.424528\pi\) | ||||
0.234886 | + | 0.972023i | \(0.424528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.97692 | −0.146943 | −0.0734717 | − | 0.997297i | \(-0.523408\pi\) | ||||
−0.0734717 | + | 0.997297i | \(0.523408\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.71939 | 0.348868 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.68168 | −0.197161 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.23068 | 0.601887 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6279 | 0.769007 | 0.384504 | − | 0.923123i | \(-0.374373\pi\) | ||||
0.384504 | + | 0.923123i | \(0.374373\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.9531 | −1.22031 | −0.610154 | − | 0.792283i | \(-0.708892\pi\) | ||||
−0.610154 | + | 0.792283i | \(0.708892\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.50007 | 0.179034 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.45596 | −0.459968 | −0.229984 | − | 0.973194i | \(-0.573867\pi\) | ||||
−0.229984 | + | 0.973194i | \(0.573867\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.0256 | −1.06513 | −0.532567 | − | 0.846388i | \(-0.678772\pi\) | ||||
−0.532567 | + | 0.846388i | \(0.678772\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.96477 | −0.209119 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.63226 | −0.325121 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.08713 | 0.285458 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.1465 | −1.11688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.68416 | 0.115943 | 0.0579713 | − | 0.998318i | \(-0.481537\pi\) | ||||
0.0579713 | + | 0.998318i | \(0.481537\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.12003 | 0.213781 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.51957 | 0.240033 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.21699 | −0.557806 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.2787 | −0.694571 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.13080 | 0.546937 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.742472 | 0.0497196 | 0.0248598 | − | 0.999691i | \(-0.492086\pi\) | ||||
0.0248598 | + | 0.999691i | \(0.492086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.53531 | −0.302354 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.0500 | 1.33077 | 0.665383 | − | 0.746502i | \(-0.268268\pi\) | ||||
0.665383 | + | 0.746502i | \(0.268268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.7710 | −0.777850 | −0.388925 | − | 0.921269i | \(-0.627153\pi\) | ||||
−0.388925 | + | 0.921269i | \(0.627153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.71255 | −0.244268 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.0882 | 1.11949 | 0.559743 | − | 0.828666i | \(-0.310900\pi\) | ||||
0.559743 | + | 0.828666i | \(0.310900\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.37319 | 0.285276 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.6137 | −0.754391 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.5838 | −1.59019 | −0.795096 | − | 0.606483i | \(-0.792580\pi\) | ||||
−0.795096 | + | 0.606483i | \(0.792580\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3963 | −0.798514 | −0.399257 | − | 0.916839i | \(-0.630732\pi\) | ||||
−0.399257 | + | 0.916839i | \(0.630732\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.681685 | −0.0435513 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.9506 | −1.01491 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.5520 | 0.732077 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.40653 | −0.404377 | −0.202188 | − | 0.979347i | \(-0.564805\pi\) | ||||
−0.202188 | + | 0.979347i | \(0.564805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.71255 | 0.233406 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.51129 | 0.0946406 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.3262 | −1.82932 | −0.914661 | − | 0.404223i | \(-0.867542\pi\) | ||||
−0.914661 | + | 0.404223i | \(0.867542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.93391 | 0.244441 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.63226 | −0.286730 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.0905 | 1.30050 | 0.650249 | − | 0.759721i | \(-0.274664\pi\) | ||||
0.650249 | + | 0.759721i | \(0.274664\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.45502 | 0.150811 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.88885 | −0.115596 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.7302 | 0.959085 | 0.479542 | − | 0.877519i | \(-0.340803\pi\) | ||||
0.479542 | + | 0.877519i | \(0.340803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.0055 | −1.27599 | −0.637995 | − | 0.770040i | \(-0.720236\pi\) | ||||
−0.637995 | + | 0.770040i | \(0.720236\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.66749 | −0.221967 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.8375 | −1.01534 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.643976 | −0.0386928 | −0.0193464 | − | 0.999813i | \(-0.506159\pi\) | ||||
−0.0193464 | + | 0.999813i | \(0.506159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.21699 | −0.491938 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.8404 | −1.30289 | −0.651444 | − | 0.758697i | \(-0.725836\pi\) | ||||
−0.651444 | + | 0.758697i | \(0.725836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.89431 | 0.409824 | 0.204912 | − | 0.978780i | \(-0.434309\pi\) | ||||
0.204912 | + | 0.978780i | \(0.434309\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.96477 | −0.175618 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.99563 | −0.353911 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0850 | −0.710880 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.33062 | −0.429728 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.30164 | −0.309725 | −0.154863 | − | 0.987936i | \(-0.549494\pi\) | ||||
−0.154863 | + | 0.987936i | \(0.549494\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.65767 | 0.271180 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.71255 | −0.215424 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.66749 | 0.212097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.16305 | −0.297593 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.59251 | −0.263833 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.21714 | 0.184213 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.87218 | −0.449289 | −0.224645 | − | 0.974441i | \(-0.572122\pi\) | ||||
−0.224645 | + | 0.974441i | \(0.572122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.3448 | 0.816048 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.7390 | 0.608955 | 0.304478 | − | 0.952519i | \(-0.401518\pi\) | ||||
0.304478 | + | 0.952519i | \(0.401518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.1038 | −0.797194 | −0.398597 | − | 0.917126i | \(-0.630503\pi\) | ||||
−0.398597 | + | 0.917126i | \(0.630503\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.681685 | −0.0384086 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3800 | 0.976160 | 0.488080 | − | 0.872799i | \(-0.337697\pi\) | ||||
0.488080 | + | 0.872799i | \(0.337697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.1975 | −0.962875 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.44613 | 0.0807153 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.64209 | −0.536500 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.6332 | −0.922644 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.11567 | −0.504097 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.41527 | −0.353685 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.4251 | −1.50742 | −0.753710 | − | 0.657207i | \(-0.771738\pi\) | ||||
−0.753710 | + | 0.657207i | \(0.771738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.93391 | 0.215577 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.02104 | −0.110421 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.8803 | 1.35531 | 0.677657 | − | 0.735378i | \(-0.262995\pi\) | ||||
0.677657 | + | 0.735378i | \(0.262995\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.8051 | −0.695479 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.5060 | −1.65199 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.681685 | 0.0367007 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.84380 | 0.313711 | 0.156856 | − | 0.987622i | \(-0.449864\pi\) | ||||
0.156856 | + | 0.987622i | \(0.449864\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.5750 | −1.52959 | −0.764793 | − | 0.644276i | \(-0.777159\pi\) | ||||
−0.764793 | + | 0.644276i | \(0.777159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.66749 | −0.195756 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.57039 | −0.0835833 | −0.0417916 | − | 0.999126i | \(-0.513307\pi\) | ||||
−0.0417916 | + | 0.999126i | \(0.513307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.12688 | 0.112883 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.21699 | −0.117336 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.1441 | −0.904828 | −0.452414 | − | 0.891808i | \(-0.649437\pi\) | ||||
−0.452414 | + | 0.891808i | \(0.649437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0846542 | −0.00445549 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.78301 | −0.146070 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.00685 | −0.366755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.56850 | −0.342873 | −0.171436 | − | 0.985195i | \(-0.554841\pi\) | ||||
−0.171436 | + | 0.985195i | \(0.554841\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.99563 | −0.312120 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.60140 | −0.186975 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.8449 | 0.768639 | 0.384319 | − | 0.923200i | \(-0.374436\pi\) | ||||
0.384319 | + | 0.923200i | \(0.374436\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.50007 | −0.335662 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.9888 | −0.874967 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.81606 | 0.504217 | 0.252109 | − | 0.967699i | \(-0.418876\pi\) | ||||
0.252109 | + | 0.967699i | \(0.418876\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.5069 | 0.896907 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.4198 | 1.09450 | 0.547250 | − | 0.836969i | \(-0.315675\pi\) | ||||
0.547250 | + | 0.836969i | \(0.315675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.53079 | −0.128981 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.16305 | −0.262453 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.34044 | 0.220069 | 0.110035 | − | 0.993928i | \(-0.464904\pi\) | ||||
0.110035 | + | 0.993928i | \(0.464904\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.21699 | 0.112118 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.08480 | 0.105164 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.91689 | −0.398342 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.8551 | 1.64895 | 0.824476 | − | 0.565897i | \(-0.191470\pi\) | ||||
0.824476 | + | 0.565897i | \(0.191470\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.34918 | 0.217731 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.9153 | 0.644962 | 0.322481 | − | 0.946576i | \(-0.395483\pi\) | ||||
0.322481 | + | 0.946576i | \(0.395483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.1358 | −1.50117 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.681685 | −0.0338732 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.6048 | 0.723934 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.0301 | −1.63323 | −0.816616 | − | 0.577182i | \(-0.804152\pi\) | ||||
−0.816616 | + | 0.577182i | \(0.804152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.9163 | 0.735766 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.83258 | −0.336209 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.87481 | 0.386559 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.45050 | 0.266912 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.522051 | 0.0255039 | 0.0127519 | − | 0.999919i | \(-0.495941\pi\) | ||||
0.0127519 | + | 0.999919i | \(0.495941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9888 | −0.925457 | −0.462728 | − | 0.886500i | \(-0.653129\pi\) | ||||
−0.462728 | + | 0.886500i | \(0.653129\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.41527 | −0.311921 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.0547 | −0.487726 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.71939 | −0.228387 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.6157 | −0.657374 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.9978 | 1.68579 | 0.842893 | − | 0.538081i | \(-0.180851\pi\) | ||||
0.842893 | + | 0.538081i | \(0.180851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.71707 | 0.418915 | 0.209458 | − | 0.977818i | \(-0.432830\pi\) | ||||
0.209458 | + | 0.977818i | \(0.432830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.15774 | −0.151402 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.34918 | −0.208049 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.3316 | −0.922645 | −0.461322 | − | 0.887233i | \(-0.652625\pi\) | ||||
−0.461322 | + | 0.887233i | \(0.652625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.7504 | 0.605790 | 0.302895 | − | 0.953024i | \(-0.402047\pi\) | ||||
0.302895 | + | 0.953024i | \(0.402047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.28760 | −0.0610382 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.09900 | −0.335771 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.9080 | −0.609166 | −0.304583 | − | 0.952486i | \(-0.598517\pi\) | ||||
−0.304583 | + | 0.952486i | \(0.598517\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.2591 | −1.04814 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.29197 | 0.436575 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.50007 | −0.117205 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.4516 | −0.676017 | −0.338008 | − | 0.941143i | \(-0.609753\pi\) | ||||
−0.338008 | + | 0.941143i | \(0.609753\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.21699 | −0.103480 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.5309 | −1.46854 | −0.734271 | − | 0.678856i | \(-0.762476\pi\) | ||||
−0.734271 | + | 0.678856i | \(0.762476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9672 | 0.649113 | 0.324557 | − | 0.945866i | \(-0.394785\pi\) | ||||
0.324557 | + | 0.945866i | \(0.394785\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.60140 | −0.259759 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.37662 | 0.387624 | 0.193812 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193812 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.96477 | 0.136900 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.33499 | 0.0615129 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.1681 | −0.881349 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.7248 | 0.905038 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.60140 | −0.164897 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.17957 | −0.282352 | −0.141176 | − | 0.989985i | \(-0.545088\pi\) | ||||
−0.141176 | + | 0.989985i | \(0.545088\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.4276 | 0.657841 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.99717 | −0.226910 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.84567 | −0.264893 | −0.132446 | − | 0.991190i | \(-0.542283\pi\) | ||||
−0.132446 | + | 0.991190i | \(0.542283\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.49760 | 0.339053 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0877 | 1.35784 | 0.678920 | − | 0.734212i | \(-0.262448\pi\) | ||||
0.678920 | + | 0.734212i | \(0.262448\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2697 | −0.462523 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.53079 | −0.113750 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.12003 | −0.139953 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.3086 | −0.685309 | −0.342654 | − | 0.939462i | \(-0.611326\pi\) | ||||
−0.342654 | + | 0.939462i | \(0.611326\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.34918 | 0.194307 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.0402 | −0.670609 | −0.335304 | − | 0.942110i | \(-0.608839\pi\) | ||||
−0.335304 | + | 0.942110i | \(0.608839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.13065 | −0.139312 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.450502 | −0.0200075 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.4870 | 1.35131 | 0.675656 | − | 0.737217i | \(-0.263861\pi\) | ||||
0.675656 | + | 0.737217i | \(0.263861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2787 | 0.454704 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.34918 | 0.192021 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.77864 | 0.430898 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.8170 | −1.04747 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.7459 | −1.04233 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.1500 | −0.444678 | −0.222339 | − | 0.974969i | \(-0.571369\pi\) | ||||
−0.222339 | + | 0.974969i | \(0.571369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.26437 | 0.0990142 | 0.0495071 | − | 0.998774i | \(-0.484235\pi\) | ||||
0.0495071 | + | 0.998774i | \(0.484235\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.53531 | 0.197937 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.2170 | −0.793545 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.83258 | −0.296509 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.9889 | −0.952446 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.985808 | 0.0426202 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.28512 | −0.271223 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.71255 | 0.159911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7512 | 1.36509 | 0.682545 | − | 0.730843i | \(-0.260873\pi\) | ||||
0.682545 | + | 0.730843i | \(0.260873\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.97692 | 0.0848378 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.21401 | −0.266179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.7710 | −1.10189 | −0.550944 | − | 0.834542i | \(-0.685732\pi\) | ||||
−0.550944 | + | 0.834542i | \(0.685732\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.71939 | −0.201419 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.1465 | 0.858271 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6137 | 0.493865 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.68168 | 0.113831 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.65613 | −0.0701724 | −0.0350862 | − | 0.999384i | \(-0.511171\pi\) | ||||
−0.0350862 | + | 0.999384i | \(0.511171\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.9354 | −0.800884 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.23068 | −0.347500 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.00233 | 0.337258 | 0.168629 | − | 0.985680i | \(-0.446066\pi\) | ||||
0.168629 | + | 0.985680i | \(0.446066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.72907 | −0.367235 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.58080 | −0.275881 | −0.137941 | − | 0.990440i | \(-0.544048\pi\) | ||||
−0.137941 | + | 0.990440i | \(0.544048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.9820 | 1.46395 | 0.731976 | − | 0.681330i | \(-0.238598\pi\) | ||||
0.731976 | + | 0.681330i | \(0.238598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.6279 | −0.443987 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.53531 | −0.189135 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.2558 | 0.468585 | 0.234292 | − | 0.972166i | \(-0.424723\pi\) | ||||
0.234292 | + | 0.972166i | \(0.424723\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.9531 | 0.704545 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.5520 | −0.479257 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3704 | −0.553744 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.50007 | −0.103365 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.3805 | 0.676095 | 0.338047 | − | 0.941129i | \(-0.390234\pi\) | ||||
0.338047 | + | 0.941129i | \(0.390234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.7372 | 1.47252 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.45596 | 0.265563 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.2920 | −0.463706 | −0.231853 | − | 0.972751i | \(-0.574479\pi\) | ||||
−0.231853 | + | 0.972751i | \(0.574479\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.51129 | −0.0619568 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.0256 | 0.614955 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.0456 | −0.573889 | −0.286945 | − | 0.957947i | \(-0.592640\pi\) | ||||
−0.286945 | + | 0.957947i | \(0.592640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.71596 | 0.273950 | 0.136975 | − | 0.990575i | \(-0.456262\pi\) | ||||
0.136975 | + | 0.990575i | \(0.456262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.96477 | 0.120735 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.89714 | −0.0771295 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.5453 | −1.68627 | −0.843135 | − | 0.537701i | \(-0.819293\pi\) | ||||
−0.843135 | + | 0.537701i | \(0.819293\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.63226 | 0.187709 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.5280 | −0.951839 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.99376 | −0.403644 | −0.201822 | − | 0.979422i | \(-0.564686\pi\) | ||||
−0.201822 | + | 0.979422i | \(0.564686\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.08713 | −0.164809 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.6157 | −0.628666 | −0.314333 | − | 0.949313i | \(-0.601781\pi\) | ||||
−0.314333 | + | 0.949313i | \(0.601781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.23272 | −0.170127 | −0.0850637 | − | 0.996376i | \(-0.527109\pi\) | ||||
−0.0850637 | + | 0.996376i | \(0.527109\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.88885 | 0.0756752 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.2455 | 0.729821 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.1465 | 0.644830 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.72143 | 0.347746 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.1468 | 1.67784 | 0.838919 | − | 0.544256i | \(-0.183188\pi\) | ||||
0.838919 | + | 0.544256i | \(0.183188\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.68416 | −0.0669395 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.9342 | 0.473594 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.66749 | 0.145311 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.12003 | −0.123427 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.66749 | −0.381843 | −0.190922 | − | 0.981605i | \(-0.561148\pi\) | ||||
−0.190922 | + | 0.981605i | \(0.561148\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.8753 | −1.21760 | −0.608802 | − | 0.793322i | \(-0.708349\pi\) | ||||
−0.608802 | + | 0.793322i | \(0.708349\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.51957 | −0.138583 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.1106 | 0.436805 | 0.218402 | − | 0.975859i | \(-0.429915\pi\) | ||||
0.218402 | + | 0.975859i | \(0.429915\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.3663 | −0.995714 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.21699 | 0.322049 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.6203 | 1.58959 | 0.794797 | − | 0.606876i | \(-0.207577\pi\) | ||||
0.794797 | + | 0.606876i | \(0.207577\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.42118 | 0.0555301 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.2787 | 0.401011 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.13764 | −0.278043 | −0.139022 | − | 0.990289i | \(-0.544396\pi\) | ||||
−0.139022 | + | 0.990289i | \(0.544396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5980 | −0.412214 | −0.206107 | − | 0.978529i | \(-0.566079\pi\) | ||||
−0.206107 | + | 0.978529i | \(0.566079\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.13080 | −0.315774 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.96477 | 0.114969 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.63226 | −0.179362 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.742472 | −0.0287056 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.5210 | −0.676390 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.8352 | −1.26570 | −0.632852 | − | 0.774273i | \(-0.718116\pi\) | ||||
−0.632852 | + | 0.774273i | \(0.718116\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.53531 | 0.174564 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.2542 | 1.00903 | 0.504516 | − | 0.863402i | \(-0.331671\pi\) | ||||
0.504516 | + | 0.863402i | \(0.331671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.33062 | 0.281323 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0500 | −0.768318 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.8203 | 0.490554 | 0.245277 | − | 0.969453i | \(-0.421121\pi\) | ||||
0.245277 | + | 0.969453i | \(0.421121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1682 | 0.388507 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.7710 | 0.449092 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.2081 | −0.503189 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.2581 | 1.79778 | 0.898892 | − | 0.438171i | \(-0.144374\pi\) | ||||
0.898892 | + | 0.438171i | \(0.144374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.71255 | 0.141028 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.71553 | 0.140938 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.2923 | −0.503480 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.0882 | −0.646336 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.3948 | 0.543685 | 0.271842 | − | 0.962342i | \(-0.412367\pi\) | ||||
0.271842 | + | 0.962342i | \(0.412367\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.1093 | −0.645288 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.37319 | −0.164704 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.59251 | 0.172719 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.40406 | −0.127842 | −0.0639210 | − | 0.997955i | \(-0.520361\pi\) | ||||
−0.0639210 | + | 0.997955i | \(0.520361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.6137 | 0.435548 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.21699 | −0.307729 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.28165 | −0.347114 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.5838 | 0.918098 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.6326 | −1.44075 | −0.720376 | − | 0.693584i | \(-0.756031\pi\) | ||||
−0.720376 | + | 0.693584i | \(0.756031\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.3448 | −0.534229 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.3963 | 0.461022 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.0087 | 0.780244 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.7830 | −0.659535 | −0.329768 | − | 0.944062i | \(-0.606970\pi\) | ||||
−0.329768 | + | 0.944062i | \(0.606970\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.4464 | −0.423362 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.92050 | 0.0709354 | 0.0354677 | − | 0.999371i | \(-0.488708\pi\) | ||||
0.0354677 | + | 0.999371i | \(0.488708\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.681685 | 0.0251443 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0068 | 0.405442 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.58925 | 0.315961 | 0.157980 | − | 0.987442i | \(-0.449502\pi\) | ||||
0.157980 | + | 0.987442i | \(0.449502\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.9506 | 0.585959 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5308 | 0.386337 | 0.193169 | − | 0.981166i | \(-0.438124\pi\) | ||||
0.193169 | + | 0.981166i | \(0.438124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.83928 | −0.177297 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.5520 | −0.422665 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.44613 | −0.0528406 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.8659 | 1.12631 | 0.563157 | − | 0.826350i | \(-0.309587\pi\) | ||||
0.563157 | + | 0.826350i | \(0.309587\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.40653 | 0.233467 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.33420 | 0.230525 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.50567 | −0.236453 | −0.118226 | − | 0.992987i | \(-0.537721\pi\) | ||||
−0.118226 | + | 0.992987i | \(0.537721\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.71255 | −0.134757 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.7554 | −1.18738 | −0.593692 | − | 0.804693i | \(-0.702330\pi\) | ||||
−0.593692 | + | 0.804693i | \(0.702330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.11567 | 0.330009 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.51129 | −0.0546408 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.0584 | −0.904808 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.5298 | 0.704264 | 0.352132 | − | 0.935950i | \(-0.385457\pi\) | ||||
0.352132 | + | 0.935950i | \(0.385457\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.3262 | 1.05616 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.4062 | −1.66911 | −0.834557 | − | 0.550921i | \(-0.814276\pi\) | ||||
−0.834557 | + | 0.550921i | \(0.814276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.2666 | 1.33865 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.93391 | −0.141128 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.0761 | 0.934272 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.5833 | −0.414482 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.63226 | 0.165544 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.910039 | 0.0324807 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.4937 | −1.08698 | −0.543491 | − | 0.839415i | \(-0.682898\pi\) | ||||
−0.543491 | + | 0.839415i | \(0.682898\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.0905 | −0.750843 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.8051 | 0.455298 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.3083 | −0.614637 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.45502 | −0.0870706 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.9621 | −1.38011 | −0.690054 | − | 0.723758i | \(-0.742413\pi\) | ||||
−0.690054 | + | 0.723758i | \(0.742413\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.2226 | −0.503159 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.88885 | 0.0667393 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.1602 | 1.34664 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.681685 | −0.0240262 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.7302 | −0.553728 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.82728 | 0.240034 | 0.120017 | − | 0.992772i | \(-0.461705\pi\) | ||||
0.120017 | + | 0.992772i | \(0.461705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.1986 | −1.69248 | −0.846241 | − | 0.532801i | \(-0.821139\pi\) | ||||
−0.846241 | + | 0.532801i | \(0.821139\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.0055 | 0.736693 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.11100 | 0.179030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.4550 | 0.785602 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.66749 | 0.128153 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 56.3174 | 1.96549 | 0.982745 | − | 0.184967i | \(-0.0592178\pi\) | ||||
0.982745 | + | 0.184967i | \(0.0592178\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.86484 | −0.274151 | −0.137075 | − | 0.990561i | \(-0.543770\pi\) | ||||
−0.137075 | + | 0.990561i | \(0.543770\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.8375 | 0.586208 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.8131 | 0.619422 | 0.309711 | − | 0.950831i | \(-0.399768\pi\) | ||||
0.309711 | + | 0.950831i | \(0.399768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.7175 | −1.86569 | −0.932843 | − | 0.360283i | \(-0.882680\pi\) | ||||
−0.932843 | + | 0.360283i | \(0.882680\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.643976 | 0.0223393 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.21699 | 0.0768142 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.96477 | 0.102600 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.21699 | 0.284021 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.38033 | −0.116702 | −0.0583510 | − | 0.998296i | \(-0.518584\pi\) | ||||
−0.0583510 | + | 0.998296i | \(0.518584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.54215 | −0.260074 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.8404 | 0.752222 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.307100 | −0.0105646 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.78301 | 0.0956253 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.89431 | −0.236612 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.93391 | 0.134853 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9072 | 0.989764 | 0.494882 | − | 0.868960i | \(-0.335211\pi\) | ||||
0.494882 | + | 0.868960i | \(0.335211\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.96477 | 0.101393 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.4329 | −0.663815 | −0.331908 | − | 0.943312i | \(-0.607692\pi\) | ||||
−0.331908 | + | 0.943312i | \(0.607692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.8159 | 0.437273 | 0.218637 | − | 0.975806i | \(-0.429839\pi\) | ||||
0.218637 | + | 0.975806i | \(0.429839\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.99563 | 0.204331 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.25957 | 0.110957 | 0.0554785 | − | 0.998460i | \(-0.482332\pi\) | ||||
0.0554785 | + | 0.998460i | \(0.482332\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.1872 | −0.550382 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.0850 | 0.410427 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.1164 | 1.46262 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.8733 | 0.368427 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.33062 | 0.248104 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.50007 | 0.219743 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9913 | −0.472451 | −0.236226 | − | 0.971698i | \(-0.575910\pi\) | ||||
−0.236226 | + | 0.971698i | \(0.575910\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.30164 | 0.178820 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.174264 | −0.00587111 | −0.00293555 | − | 0.999996i | \(-0.500934\pi\) | ||||
−0.00293555 | + | 0.999996i | \(0.500934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.5852 | −1.73598 | −0.867989 | − | 0.496583i | \(-0.834588\pi\) | ||||
−0.867989 | + | 0.496583i | \(0.834588\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.65767 | −0.156566 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.4004 | 1.42367 | 0.711833 | − | 0.702348i | \(-0.247865\pi\) | ||||
0.711833 | + | 0.702348i | \(0.247865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.5069 | −0.587163 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.71255 | 0.124375 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.9012 | 0.933676 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.28447 | −0.143214 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.66749 | −0.122454 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.0633 | 1.26948 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.98427 | −0.265995 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.16305 | 0.171816 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.34764 | 0.0447970 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.1863 | −0.338230 | −0.169115 | − | 0.985596i | \(-0.554091\pi\) | ||||
−0.169115 | + | 0.985596i | \(0.554091\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.59251 | 0.152324 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.4173 | −0.974639 | −0.487319 | − | 0.873224i | \(-0.662025\pi\) | ||||
−0.487319 | + | 0.873224i | \(0.662025\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.8873 | −1.41936 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.21714 | −0.106355 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.08480 | −0.0688463 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.7597 | 1.41051 | 0.705257 | − | 0.708952i | \(-0.250832\pi\) | ||||
0.705257 | + | 0.708952i | \(0.250832\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.87218 | 0.259397 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.4427 | −0.376641 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.8415 | −0.586624 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.3448 | −0.471145 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.12936 | 0.233907 | 0.116953 | − | 0.993137i | \(-0.462687\pi\) | ||||
0.116953 | + | 0.993137i | \(0.462687\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.34918 | −0.142539 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.7390 | −0.351580 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.61073 | −0.183491 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.4494 | −1.68078 | −0.840389 | − | 0.541983i | \(-0.817674\pi\) | ||||
−0.840389 | + | 0.541983i | \(0.817674\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.1038 | 0.460260 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0999 | −0.687838 | −0.343919 | − | 0.938999i | \(-0.611755\pi\) | ||||
−0.343919 | + | 0.938999i | \(0.611755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.99563 | −0.195245 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.681685 | 0.0221752 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.17333 | −0.200606 | −0.100303 | − | 0.994957i | \(-0.531981\pi\) | ||||
−0.100303 | + | 0.994957i | \(0.531981\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.6971 | 1.22370 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.3800 | −0.563586 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.1838 | −1.04254 | −0.521268 | − | 0.853393i | \(-0.674541\pi\) | ||||
−0.521268 | + | 0.853393i | \(0.674541\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.24488 | −0.234439 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.1975 | 0.555916 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.9163 | −0.481672 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.5189 | 1.17803 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.44613 | −0.0466010 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.5566 | 0.372021 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.21822 | 0.264280 | 0.132140 | − | 0.991231i | \(-0.457815\pi\) | ||||
0.132140 | + | 0.991231i | \(0.457815\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.64209 | 0.309748 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.611810 | −0.0196339 | −0.00981697 | − | 0.999952i | \(-0.503125\pi\) | ||||
−0.00981697 | + | 0.999952i | \(0.503125\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.45050 | −0.174735 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.6332 | 0.532689 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.8950 | −1.72426 | −0.862128 | − | 0.506691i | \(-0.830868\pi\) | ||||
−0.862128 | + | 0.506691i | \(0.830868\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.01245 | 0.224119 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.11567 | 0.291041 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.9487 | −0.349209 | −0.174604 | − | 0.984639i | \(-0.555865\pi\) | ||||
−0.174604 | + | 0.984639i | \(0.555865\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.40093 | 0.140225 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.41527 | 0.204200 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.16305 | −0.164175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.22384 | −0.293005 | −0.146502 | − | 0.989210i | \(-0.546802\pi\) | ||||
−0.146502 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.4251 | 0.870309 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.2427 | 0.324715 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.8410 | −1.07175 | −0.535877 | − | 0.844296i | \(-0.680019\pi\) | ||||
−0.535877 | + | 0.844296i | \(0.680019\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.93391 | −0.124463 |
(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 | 7728.2.a.bz.1.2 | 4 | ||
4.3 | odd | 2 | 3864.2.a.t.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.t.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
7728.2.a.bz.1.2 | 4 | 1.1 | even | 1 | trivial |