Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(1,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("648.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.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: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 72) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.37228 | −1.50813 | −0.754065 | − | 0.656800i | \(-0.771910\pi\) | ||||
−0.754065 | + | 0.656800i | \(0.771910\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.37228 | −0.518674 | −0.259337 | − | 0.965787i | \(-0.583504\pi\) | ||||
−0.259337 | + | 0.965787i | \(0.583504\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.37228 | 1.49000 | 0.745001 | − | 0.667063i | \(-0.232449\pi\) | ||||
0.745001 | + | 0.667063i | \(0.232449\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.372281 | 0.0902915 | 0.0451457 | − | 0.998980i | \(-0.485625\pi\) | ||||
0.0451457 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.37228 | 1.46190 | 0.730951 | − | 0.682430i | \(-0.239077\pi\) | ||||
0.730951 | + | 0.682430i | \(0.239077\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.37228 | 1.12020 | 0.560099 | − | 0.828426i | \(-0.310763\pi\) | ||||
0.560099 | + | 0.828426i | \(0.310763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.37228 | 1.27446 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.37228 | 0.254826 | 0.127413 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127413 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.627719 | 0.112742 | 0.0563708 | − | 0.998410i | \(-0.482047\pi\) | ||||
0.0563708 | + | 0.998410i | \(0.482047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.62772 | 0.782227 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.74456 | −0.451203 | −0.225602 | − | 0.974220i | \(-0.572435\pi\) | ||||
−0.225602 | + | 0.974220i | \(0.572435\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.255437 | −0.0398926 | −0.0199463 | − | 0.999801i | \(-0.506350\pi\) | ||||
−0.0199463 | + | 0.999801i | \(0.506350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.74456 | 1.48603 | 0.743016 | − | 0.669274i | \(-0.233395\pi\) | ||||
0.743016 | + | 0.669274i | \(0.233395\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.37228 | −0.200168 | −0.100084 | − | 0.994979i | \(-0.531911\pi\) | ||||
−0.100084 | + | 0.994979i | \(0.531911\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.11684 | −0.730978 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7446 | −1.47588 | −0.737940 | − | 0.674867i | \(-0.764201\pi\) | ||||
−0.737940 | + | 0.674867i | \(0.764201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.37228 | −0.454718 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.00000 | 0.911322 | 0.455661 | − | 0.890153i | \(-0.349403\pi\) | ||||
0.455661 | + | 0.890153i | \(0.349403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.37228 | −0.431776 | −0.215888 | − | 0.976418i | \(-0.569265\pi\) | ||||
−0.215888 | + | 0.976418i | \(0.569265\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18.1168 | −2.24712 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.74456 | 0.946149 | 0.473074 | − | 0.881022i | \(-0.343144\pi\) | ||||
0.473074 | + | 0.881022i | \(0.343144\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.11684 | 0.598881 | 0.299441 | − | 0.954115i | \(-0.403200\pi\) | ||||
0.299441 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.37228 | −0.156386 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.627719 | −0.0706239 | −0.0353119 | − | 0.999376i | \(-0.511242\pi\) | ||||
−0.0353119 | + | 0.999376i | \(0.511242\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.3723 | 1.68733 | 0.843664 | − | 0.536872i | \(-0.180394\pi\) | ||||
0.843664 | + | 0.536872i | \(0.180394\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.25544 | −0.136171 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.37228 | −0.772825 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.4891 | −2.20474 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.74456 | −0.989410 | −0.494705 | − | 0.869061i | \(-0.664724\pi\) | ||||
−0.494705 | + | 0.869061i | \(0.664724\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1168 | 1.00666 | 0.503332 | − | 0.864093i | \(-0.332107\pi\) | ||||
0.503332 | + | 0.864093i | \(0.332107\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.62772 | −0.653049 | −0.326524 | − | 0.945189i | \(-0.605877\pi\) | ||||
−0.326524 | + | 0.945189i | \(0.605877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.8614 | 1.53338 | 0.766690 | − | 0.642017i | \(-0.221902\pi\) | ||||
0.766690 | + | 0.642017i | \(0.221902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.74456 | 0.646012 | 0.323006 | − | 0.946397i | \(-0.395307\pi\) | ||||
0.323006 | + | 0.946397i | \(0.395307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.37228 | 0.129093 | 0.0645467 | − | 0.997915i | \(-0.479440\pi\) | ||||
0.0645467 | + | 0.997915i | \(0.479440\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.1168 | −1.68940 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.510875 | −0.0468318 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.62772 | −0.413916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.74456 | −0.421012 | −0.210506 | − | 0.977593i | \(-0.567511\pi\) | ||||
−0.210506 | + | 0.977593i | \(0.567511\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.6277 | 1.10329 | 0.551644 | − | 0.834079i | \(-0.314001\pi\) | ||||
0.551644 | + | 0.834079i | \(0.314001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.74456 | −0.758250 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.25544 | 0.534438 | 0.267219 | − | 0.963636i | \(-0.413895\pi\) | ||||
0.267219 | + | 0.963636i | \(0.413895\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.74456 | −0.487247 | −0.243624 | − | 0.969870i | \(-0.578336\pi\) | ||||
−0.243624 | + | 0.969870i | \(0.578336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.37228 | 0.449253 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.62772 | −0.384311 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.62772 | −0.215271 | −0.107636 | − | 0.994190i | \(-0.534328\pi\) | ||||
−0.107636 | + | 0.994190i | \(0.534328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.37228 | −0.437190 | −0.218595 | − | 0.975816i | \(-0.570147\pi\) | ||||
−0.218595 | + | 0.975816i | \(0.570147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.11684 | −0.170029 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1168 | 1.12665 | 0.563323 | − | 0.826236i | \(-0.309523\pi\) | ||||
0.563323 | + | 0.826236i | \(0.309523\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.37228 | −0.581017 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.88316 | −0.145723 | −0.0728615 | − | 0.997342i | \(-0.523213\pi\) | ||||
−0.0728615 | + | 0.997342i | \(0.523213\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.8614 | 1.22011 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.6277 | −0.808010 | −0.404005 | − | 0.914757i | \(-0.632382\pi\) | ||||
−0.404005 | + | 0.914757i | \(0.632382\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.74456 | −0.661027 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.9783 | −1.71748 | −0.858738 | − | 0.512416i | \(-0.828751\pi\) | ||||
−0.858738 | + | 0.512416i | \(0.828751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.4891 | −1.74593 | −0.872966 | − | 0.487780i | \(-0.837807\pi\) | ||||
−0.872966 | + | 0.487780i | \(0.837807\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.25544 | 0.680473 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.372281 | 0.0272239 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8614 | −1.36476 | −0.682382 | − | 0.730996i | \(-0.739056\pi\) | ||||
−0.682382 | + | 0.730996i | \(0.739056\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.74456 | −0.701429 | −0.350714 | − | 0.936482i | \(-0.614061\pi\) | ||||
−0.350714 | + | 0.936482i | \(0.614061\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.7446 | 1.90547 | 0.952736 | − | 0.303801i | \(-0.0982557\pi\) | ||||
0.952736 | + | 0.303801i | \(0.0982557\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.2337 | 1.29255 | 0.646276 | − | 0.763104i | \(-0.276326\pi\) | ||||
0.646276 | + | 0.763104i | \(0.276326\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.88316 | −0.132172 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.861407 | 0.0601632 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.37228 | 0.440780 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.3723 | −1.05827 | −0.529136 | − | 0.848537i | \(-0.677484\pi\) | ||||
−0.529136 | + | 0.848537i | \(0.677484\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −32.8614 | −2.24113 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.861407 | −0.0584761 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.6060 | 1.71470 | 0.857351 | − | 0.514732i | \(-0.172108\pi\) | ||||
0.857351 | + | 0.514732i | \(0.172108\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.0000 | −0.995585 | −0.497792 | − | 0.867296i | \(-0.665856\pi\) | ||||
−0.497792 | + | 0.867296i | \(0.665856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.6060 | −1.16344 | −0.581718 | − | 0.813391i | \(-0.697619\pi\) | ||||
−0.581718 | + | 0.813391i | \(0.697619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.372281 | −0.0243890 | −0.0121945 | − | 0.999926i | \(-0.503882\pi\) | ||||
−0.0121945 | + | 0.999926i | \(0.503882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.62772 | 0.301879 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8614 | 0.961304 | 0.480652 | − | 0.876911i | \(-0.340400\pi\) | ||||
0.480652 | + | 0.876911i | \(0.340400\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.74456 | −0.370040 | −0.185020 | − | 0.982735i | \(-0.559235\pi\) | ||||
−0.185020 | + | 0.982735i | \(0.559235\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.2554 | 1.10241 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.2337 | 2.17824 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.1168 | 1.71160 | 0.855800 | − | 0.517307i | \(-0.173065\pi\) | ||||
0.855800 | + | 0.517307i | \(0.173065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.37228 | 0.337752 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.4891 | −1.15332 | −0.576660 | − | 0.816984i | \(-0.695644\pi\) | ||||
−0.576660 | + | 0.816984i | \(0.695644\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.76631 | 0.234027 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.88316 | −0.239446 | −0.119723 | − | 0.992807i | \(-0.538201\pi\) | ||||
−0.119723 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.2337 | 2.22582 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.25544 | −0.0765454 | −0.0382727 | − | 0.999267i | \(-0.512186\pi\) | ||||
−0.0382727 | + | 0.999267i | \(0.512186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.48913 | 0.0904579 | 0.0452290 | − | 0.998977i | \(-0.485598\pi\) | ||||
0.0452290 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.37228 | 0.384263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.8832 | 0.713990 | 0.356995 | − | 0.934106i | \(-0.383801\pi\) | ||||
0.356995 | + | 0.934106i | \(0.383801\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8614 | 0.886557 | 0.443279 | − | 0.896384i | \(-0.353815\pi\) | ||||
0.443279 | + | 0.896384i | \(0.353815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.86141 | −0.288981 | −0.144490 | − | 0.989506i | \(-0.546154\pi\) | ||||
−0.144490 | + | 0.989506i | \(0.546154\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.350532 | 0.0206912 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8614 | −0.991847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.3723 | 1.48226 | 0.741132 | − | 0.671359i | \(-0.234289\pi\) | ||||
0.741132 | + | 0.671359i | \(0.234289\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.6060 | −1.37439 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.8614 | 1.66910 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.3723 | −0.770765 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.3723 | 0.651175 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6277 | 1.46265 | 0.731326 | − | 0.682029i | \(-0.238902\pi\) | ||||
0.731326 | + | 0.682029i | \(0.238902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.1168 | −1.59436 | −0.797180 | − | 0.603742i | \(-0.793676\pi\) | ||||
−0.797180 | + | 0.603742i | \(0.793676\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.2337 | −1.31325 | −0.656623 | − | 0.754219i | \(-0.728016\pi\) | ||||
−0.656623 | + | 0.754219i | \(0.728016\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.60597 | −0.539525 | −0.269762 | − | 0.962927i | \(-0.586945\pi\) | ||||
−0.269762 | + | 0.962927i | \(0.586945\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.37228 | 0.0768330 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.37228 | 0.131997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.2337 | 1.89894 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.88316 | 0.103822 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.13859 | −0.172513 | −0.0862563 | − | 0.996273i | \(-0.527490\pi\) | ||||
−0.0862563 | + | 0.996273i | \(0.527490\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.1168 | −1.42692 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.9783 | 1.41513 | 0.707563 | − | 0.706651i | \(-0.249795\pi\) | ||||
0.707563 | + | 0.706651i | \(0.249795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.627719 | 0.0339929 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6277 | 0.897812 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.7228 | −1.54192 | −0.770961 | − | 0.636883i | \(-0.780224\pi\) | ||||
−0.770961 | + | 0.636883i | \(0.780224\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.1168 | 1.82623 | 0.913116 | − | 0.407699i | \(-0.133669\pi\) | ||||
0.913116 | + | 0.407699i | \(0.133669\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.9783 | 1.16978 | 0.584892 | − | 0.811111i | \(-0.301137\pi\) | ||||
0.584892 | + | 0.811111i | \(0.301137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.4891 | 0.715928 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2337 | −0.751225 | −0.375613 | − | 0.926777i | \(-0.622568\pi\) | ||||
−0.375613 | + | 0.926777i | \(0.622568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.6060 | 1.13716 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.2554 | −0.903191 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.3723 | 1.22002 | 0.610012 | − | 0.792393i | \(-0.291165\pi\) | ||||
0.610012 | + | 0.792393i | \(0.291165\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.7446 | 0.765500 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.88316 | 0.201062 | 0.100531 | − | 0.994934i | \(-0.467946\pi\) | ||||
0.100531 | + | 0.994934i | \(0.467946\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.37228 | 0.379692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.1168 | −1.18743 | −0.593716 | − | 0.804674i | \(-0.702340\pi\) | ||||
−0.593716 | + | 0.804674i | \(0.702340\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.3505 | −1.55084 | −0.775420 | − | 0.631446i | \(-0.782462\pi\) | ||||
−0.775420 | + | 0.631446i | \(0.782462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.62772 | 0.235850 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.6060 | −1.50108 | −0.750541 | − | 0.660824i | \(-0.770207\pi\) | ||||
−0.750541 | + | 0.660824i | \(0.770207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.11684 | 0.106510 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2337 | 0.814745 | 0.407373 | − | 0.913262i | \(-0.366445\pi\) | ||||
0.407373 | + | 0.913262i | \(0.366445\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.2337 | 0.860609 | 0.430305 | − | 0.902684i | \(-0.358406\pi\) | ||||
0.430305 | + | 0.902684i | \(0.358406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.37228 | 0.167985 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.74456 | −0.136043 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.74456 | −0.284050 | −0.142025 | − | 0.989863i | \(-0.545361\pi\) | ||||
−0.142025 | + | 0.989863i | \(0.545361\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.60597 | −0.472679 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −51.8397 | −2.54471 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.6060 | 1.34864 | 0.674320 | − | 0.738439i | \(-0.264437\pi\) | ||||
0.674320 | + | 0.738439i | \(0.264437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.8832 | −0.871572 | −0.435786 | − | 0.900050i | \(-0.643529\pi\) | ||||
−0.435786 | + | 0.900050i | \(0.643529\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.37228 | 0.115073 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.62772 | 0.223951 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.7446 | −0.613884 | −0.306942 | − | 0.951728i | \(-0.599306\pi\) | ||||
−0.306942 | + | 0.951728i | \(0.599306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8832 | 0.715239 | 0.357619 | − | 0.933867i | \(-0.383589\pi\) | ||||
0.357619 | + | 0.933867i | \(0.383589\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.2337 | 1.63762 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.1168 | −0.482851 | −0.241425 | − | 0.970419i | \(-0.577615\pi\) | ||||
−0.241425 | + | 0.970419i | \(0.577615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.7228 | −1.26964 | −0.634820 | − | 0.772660i | \(-0.718926\pi\) | ||||
−0.634820 | + | 0.772660i | \(0.718926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.2337 | −0.959169 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.1168 | −1.56288 | −0.781440 | − | 0.623980i | \(-0.785515\pi\) | ||||
−0.781440 | + | 0.623980i | \(0.785515\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.255437 | −0.0120281 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.8614 | 1.16552 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.74456 | 0.362275 | 0.181138 | − | 0.983458i | \(-0.442022\pi\) | ||||
0.181138 | + | 0.983458i | \(0.442022\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.1168 | −1.12323 | −0.561617 | − | 0.827398i | \(-0.689820\pi\) | ||||
−0.561617 | + | 0.827398i | \(0.689820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3505 | −0.481030 | −0.240515 | − | 0.970645i | \(-0.577316\pi\) | ||||
−0.240515 | + | 0.970645i | \(0.577316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.62772 | 0.0753218 | 0.0376609 | − | 0.999291i | \(-0.488009\pi\) | ||||
0.0376609 | + | 0.999291i | \(0.488009\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6277 | −0.490742 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.74456 | 0.448055 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.6060 | 1.86313 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.6060 | 1.35273 | 0.676366 | − | 0.736566i | \(-0.263554\pi\) | ||||
0.676366 | + | 0.736566i | \(0.263554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.7446 | −0.672294 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 32.8614 | 1.49216 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.74456 | −0.214997 | −0.107498 | − | 0.994205i | \(-0.534284\pi\) | ||||
−0.107498 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.7446 | 0.530025 | 0.265012 | − | 0.964245i | \(-0.414624\pi\) | ||||
0.265012 | + | 0.964245i | \(0.414624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.510875 | 0.0230086 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.48913 | 0.246221 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.9783 | 1.16295 | 0.581473 | − | 0.813566i | \(-0.302477\pi\) | ||||
0.581473 | + | 0.813566i | \(0.302477\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.4891 | 1.31486 | 0.657428 | − | 0.753518i | \(-0.271645\pi\) | ||||
0.657428 | + | 0.753518i | \(0.271645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.1168 | −1.51818 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.8832 | −0.615360 | −0.307680 | − | 0.951490i | \(-0.599553\pi\) | ||||
−0.307680 | + | 0.951490i | \(0.599553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.02175 | −0.310624 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.3505 | 0.984882 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.37228 | −0.0603529 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.11684 | −0.224173 | −0.112087 | − | 0.993698i | \(-0.535753\pi\) | ||||
−0.112087 | + | 0.993698i | \(0.535753\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.48913 | 0.414930 | 0.207465 | − | 0.978242i | \(-0.433479\pi\) | ||||
0.207465 | + | 0.978242i | \(0.433479\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.233688 | 0.0101796 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.86141 | 0.254844 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.37228 | −0.0594401 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −53.4891 | −2.31254 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.11684 | −0.220398 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.2337 | −1.38583 | −0.692917 | − | 0.721017i | \(-0.743675\pi\) | ||||
−0.692917 | + | 0.721017i | \(0.743675\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.7446 | −0.974270 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.7446 | −1.18627 | −0.593136 | − | 0.805102i | \(-0.702110\pi\) | ||||
−0.593136 | + | 0.805102i | \(0.702110\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.74456 | 0.372531 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.861407 | 0.0366307 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.3505 | 2.21419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.74456 | −0.0735245 | −0.0367623 | − | 0.999324i | \(-0.511704\pi\) | ||||
−0.0367623 | + | 0.999324i | \(0.511704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.62772 | −0.194690 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.23369 | −0.303252 | −0.151626 | − | 0.988438i | \(-0.548451\pi\) | ||||
−0.151626 | + | 0.988438i | \(0.548451\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.51087 | −0.146926 | −0.0734628 | − | 0.997298i | \(-0.523405\pi\) | ||||
−0.0734628 | + | 0.997298i | \(0.523405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.2337 | 1.42764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.8614 | −0.577058 | −0.288529 | − | 0.957471i | \(-0.593166\pi\) | ||||
−0.288529 | + | 0.957471i | \(0.593166\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.0951 | −0.875172 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.7446 | −0.444994 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.2337 | −1.04151 | −0.520753 | − | 0.853707i | \(-0.674349\pi\) | ||||
−0.520753 | + | 0.853707i | \(0.674349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.0000 | −1.06769 | −0.533846 | − | 0.845582i | \(-0.679254\pi\) | ||||
−0.533846 | + | 0.845582i | \(0.679254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.72281 | 0.0706285 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.1386 | 0.455111 | 0.227555 | − | 0.973765i | \(-0.426927\pi\) | ||||
0.227555 | + | 0.973765i | \(0.426927\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.9783 | −1.63075 | −0.815373 | − | 0.578935i | \(-0.803468\pi\) | ||||
−0.815373 | + | 0.578935i | \(0.803468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.7228 | 1.37103 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.11684 | 0.248275 | 0.124138 | − | 0.992265i | \(-0.460384\pi\) | ||||
0.124138 | + | 0.992265i | \(0.460384\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.37228 | −0.298251 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.25544 | −0.0507066 | −0.0253533 | − | 0.999679i | \(-0.508071\pi\) | ||||
−0.0253533 | + | 0.999679i | \(0.508071\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.97825 | −0.321192 | −0.160596 | − | 0.987020i | \(-0.551342\pi\) | ||||
−0.160596 | + | 0.987020i | \(0.551342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.2337 | −0.531907 | −0.265953 | − | 0.963986i | \(-0.585687\pi\) | ||||
−0.265953 | + | 0.963986i | \(0.585687\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.23369 | −0.329876 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.2554 | −0.650217 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.02175 | −0.0407398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0000 | 0.634941 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.4891 | −1.08916 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.2337 | −1.23366 | −0.616828 | − | 0.787098i | \(-0.711583\pi\) | ||||
−0.616828 | + | 0.787098i | \(0.711583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.00000 | 0.118308 | 0.0591542 | − | 0.998249i | \(-0.481160\pi\) | ||||
0.0591542 | + | 0.998249i | \(0.481160\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.7228 | −0.932640 | −0.466320 | − | 0.884616i | \(-0.654420\pi\) | ||||
−0.466320 | + | 0.884616i | \(0.654420\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.00000 | 0.274774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.1168 | −1.56989 | −0.784947 | − | 0.619563i | \(-0.787310\pi\) | ||||
−0.784947 | + | 0.619563i | \(0.787310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −42.5842 | −1.66390 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.88316 | 0.0733573 | 0.0366787 | − | 0.999327i | \(-0.488322\pi\) | ||||
0.0366787 | + | 0.999327i | \(0.488322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0951 | 0.664922 | 0.332461 | − | 0.943117i | \(-0.392121\pi\) | ||||
0.332461 | + | 0.943117i | \(0.392121\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29.4891 | 1.14354 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.37228 | 0.285456 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.37228 | −0.130185 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.37228 | 0.207086 | 0.103543 | − | 0.994625i | \(-0.466982\pi\) | ||||
0.103543 | + | 0.994625i | \(0.466982\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.6060 | 0.753519 | 0.376759 | − | 0.926311i | \(-0.377038\pi\) | ||||
0.376759 | + | 0.926311i | \(0.377038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3723 | 0.513181 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.62772 | −0.368394 | −0.184197 | − | 0.982889i | \(-0.558969\pi\) | ||||
−0.184197 | + | 0.982889i | \(0.558969\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.0951 | −0.806002 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.7228 | −2.19906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.11684 | −0.0805285 | −0.0402643 | − | 0.999189i | \(-0.512820\pi\) | ||||
−0.0402643 | + | 0.999189i | \(0.512820\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.3723 | 0.734833 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0950946 | −0.00360196 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.5109 | −0.472529 | −0.236265 | − | 0.971689i | \(-0.575923\pi\) | ||||
−0.236265 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.4891 | −0.659615 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.8832 | −0.522130 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.6060 | 0.435871 | 0.217936 | − | 0.975963i | \(-0.430068\pi\) | ||||
0.217936 | + | 0.975963i | \(0.430068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.37228 | 0.126293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.1168 | −0.677532 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.5109 | 0.839514 | 0.419757 | − | 0.907637i | \(-0.362115\pi\) | ||||
0.419757 | + | 0.907637i | \(0.362115\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.09509 | 0.338719 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.74456 | 0.324765 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.1168 | 1.04280 | 0.521398 | − | 0.853314i | \(-0.325411\pi\) | ||||
0.521398 | + | 0.853314i | \(0.325411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.62772 | 0.134176 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.13859 | −0.337542 | −0.168771 | − | 0.985655i | \(-0.553980\pi\) | ||||
−0.168771 | + | 0.985655i | \(0.553980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.74456 | 0.285275 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8832 | 0.915342 | 0.457671 | − | 0.889122i | \(-0.348684\pi\) | ||||
0.457671 | + | 0.889122i | \(0.348684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.3723 | 1.51780 | 0.758901 | − | 0.651206i | \(-0.225737\pi\) | ||||
0.758901 | + | 0.651206i | \(0.225737\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.86141 | 0.324657 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.7663 | −0.795324 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.3723 | −1.58268 | −0.791339 | − | 0.611378i | \(-0.790615\pi\) | ||||
−0.791339 | + | 0.611378i | \(0.790615\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.1168 | 0.659339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.4891 | 1.14449 | 0.572246 | − | 0.820082i | \(-0.306072\pi\) | ||||
0.572246 | + | 0.820082i | \(0.306072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.3505 | 1.17271 | 0.586353 | − | 0.810056i | \(-0.300563\pi\) | ||||
0.586353 | + | 0.810056i | \(0.300563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.25544 | −0.335069 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.6060 | 1.35787 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.8832 | 0.572761 | 0.286381 | − | 0.958116i | \(-0.407548\pi\) | ||||
0.286381 | + | 0.958116i | \(0.407548\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.9783 | −0.610665 | −0.305333 | − | 0.952246i | \(-0.598768\pi\) | ||||
−0.305333 | + | 0.952246i | \(0.598768\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.62772 | −0.0583191 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −47.6060 | −1.69913 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.8397 | −1.13496 | −0.567481 | − | 0.823387i | \(-0.692082\pi\) | ||||
−0.567481 | + | 0.823387i | \(0.692082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.88316 | −0.0669573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.1168 | −0.643348 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.6060 | 1.54460 | 0.772301 | − | 0.635256i | \(-0.219106\pi\) | ||||
0.772301 | + | 0.635256i | \(0.219106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.510875 | −0.0180734 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.11684 | 0.180570 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.8614 | 0.876249 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.8614 | 1.47177 | 0.735884 | − | 0.677107i | \(-0.236767\pi\) | ||||
0.735884 | + | 0.677107i | \(0.236767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.3505 | −1.45201 | −0.726007 | − | 0.687688i | \(-0.758626\pi\) | ||||
−0.726007 | + | 0.687688i | \(0.758626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.4674 | 1.41751 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 62.0951 | 2.17243 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.3723 | 0.885499 | 0.442749 | − | 0.896645i | \(-0.354003\pi\) | ||||
0.442749 | + | 0.896645i | \(0.354003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.1168 | 1.46810 | 0.734050 | − | 0.679095i | \(-0.237628\pi\) | ||||
0.734050 | + | 0.679095i | \(0.237628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.9783 | −0.520845 | −0.260422 | − | 0.965495i | \(-0.583862\pi\) | ||||
−0.260422 | + | 0.965495i | \(0.583862\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.48913 | −0.260108 | −0.130054 | − | 0.991507i | \(-0.541515\pi\) | ||||
−0.130054 | + | 0.991507i | \(0.541515\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.90491 | −0.0660011 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.35053 | 0.219769 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.0951 | −1.14257 | −0.571285 | − | 0.820752i | \(-0.693555\pi\) | ||||
−0.571285 | + | 0.820752i | \(0.693555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1168 | −0.935064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −53.4891 | −1.84008 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7228 | 0.471521 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.7446 | −0.505437 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.8832 | 0.543829 | 0.271914 | − | 0.962321i | \(-0.412343\pi\) | ||||
0.271914 | + | 0.962321i | \(0.412343\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.8832 | 0.679196 | 0.339598 | − | 0.940571i | \(-0.389709\pi\) | ||||
0.339598 | + | 0.940571i | \(0.389709\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.4891 | 0.699080 | 0.349540 | − | 0.936921i | \(-0.386338\pi\) | ||||
0.349540 | + | 0.936921i | \(0.386338\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.9783 | 0.918350 | 0.459175 | − | 0.888346i | \(-0.348145\pi\) | ||||
0.459175 | + | 0.888346i | \(0.348145\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.8397 | 1.21858 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.627719 | −0.0212939 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.6060 | 1.40976 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.35053 | 0.214687 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.861407 | −0.0290876 | −0.0145438 | − | 0.999894i | \(-0.504630\pi\) | ||||
−0.0145438 | + | 0.999894i | \(0.504630\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.9783 | −0.706775 | −0.353388 | − | 0.935477i | \(-0.614970\pi\) | ||||
−0.353388 | + | 0.935477i | \(0.614970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.8397 | −1.44167 | −0.720835 | − | 0.693107i | \(-0.756241\pi\) | ||||
−0.720835 | + | 0.693107i | \(0.756241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.8614 | −0.566151 | −0.283075 | − | 0.959098i | \(-0.591355\pi\) | ||||
−0.283075 | + | 0.959098i | \(0.591355\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.51087 | 0.218368 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.74456 | −0.292626 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 77.4891 | 2.59018 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.861407 | 0.0287295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 79.2119 | 2.63309 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0000 | 1.22856 | 0.614282 | − | 0.789086i | \(-0.289446\pi\) | ||||
0.614282 | + | 0.789086i | \(0.289446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.1168 | −0.600238 | −0.300119 | − | 0.953902i | \(-0.597026\pi\) | ||||
−0.300119 | + | 0.953902i | \(0.597026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3723 | 0.508748 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.3288 | −0.572247 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.76631 | 0.0582653 | 0.0291326 | − | 0.999576i | \(-0.490725\pi\) | ||||
0.0291326 | + | 0.999576i | \(0.490725\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.4891 | −0.707323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.4891 | −0.575039 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.5842 | −1.59400 | −0.796998 | − | 0.603982i | \(-0.793580\pi\) | ||||
−0.796998 | + | 0.603982i | \(0.793580\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.6060 | −1.06862 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.25544 | −0.0410572 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.8397 | −1.55953 | −0.779764 | − | 0.626073i | \(-0.784661\pi\) | ||||
−0.779764 | + | 0.626073i | \(0.784661\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.37228 | −0.0446876 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.2554 | −1.37312 | −0.686559 | − | 0.727074i | \(-0.740879\pi\) | ||||
−0.686559 | + | 0.727074i | \(0.740879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.4891 | 0.892335 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.1168 | −0.813614 | −0.406807 | − | 0.913514i | \(-0.633358\pi\) | ||||
−0.406807 | + | 0.913514i | \(0.633358\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.6060 | 2.05824 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.58422 | −0.277199 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6060 | −0.987289 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.8614 | 1.05785 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.62772 | −0.0845017 | −0.0422509 | − | 0.999107i | \(-0.513453\pi\) | ||||
−0.0422509 | + | 0.999107i | \(0.513453\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.4891 | 0.561253 | 0.280626 | − | 0.959817i | \(-0.409458\pi\) | ||||
0.280626 | + | 0.959817i | \(0.409458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.88316 | 0.252722 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.7446 | 0.375742 | 0.187871 | − | 0.982194i | \(-0.439841\pi\) | ||||
0.187871 | + | 0.982194i | \(0.439841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.8832 | 1.20829 | 0.604143 | − | 0.796876i | \(-0.293516\pi\) | ||||
0.604143 | + | 0.796876i | \(0.293516\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −90.1902 | −2.87370 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52.3505 | 1.66465 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.02175 | 0.159521 | 0.0797606 | − | 0.996814i | \(-0.474584\pi\) | ||||
0.0797606 | + | 0.996814i | \(0.474584\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −61.4891 | −1.94934 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.35053 | −0.0744421 | −0.0372210 | − | 0.999307i | \(-0.511851\pi\) | ||||
−0.0372210 | + | 0.999307i | \(0.511851\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 648.2.a.f.1.1 | 2 | ||
3.2 | odd | 2 | 648.2.a.g.1.2 | 2 | |||
4.3 | odd | 2 | 1296.2.a.n.1.1 | 2 | |||
8.3 | odd | 2 | 5184.2.a.bs.1.2 | 2 | |||
8.5 | even | 2 | 5184.2.a.bt.1.2 | 2 | |||
9.2 | odd | 6 | 216.2.i.b.145.1 | 4 | |||
9.4 | even | 3 | 72.2.i.b.25.1 | ✓ | 4 | ||
9.5 | odd | 6 | 216.2.i.b.73.1 | 4 | |||
9.7 | even | 3 | 72.2.i.b.49.1 | yes | 4 | ||
12.11 | even | 2 | 1296.2.a.p.1.2 | 2 | |||
24.5 | odd | 2 | 5184.2.a.bp.1.1 | 2 | |||
24.11 | even | 2 | 5184.2.a.bo.1.1 | 2 | |||
36.7 | odd | 6 | 144.2.i.d.49.2 | 4 | |||
36.11 | even | 6 | 432.2.i.d.145.1 | 4 | |||
36.23 | even | 6 | 432.2.i.d.289.1 | 4 | |||
36.31 | odd | 6 | 144.2.i.d.97.2 | 4 | |||
72.5 | odd | 6 | 1728.2.i.i.1153.2 | 4 | |||
72.11 | even | 6 | 1728.2.i.j.577.2 | 4 | |||
72.13 | even | 6 | 576.2.i.j.385.2 | 4 | |||
72.29 | odd | 6 | 1728.2.i.i.577.2 | 4 | |||
72.43 | odd | 6 | 576.2.i.l.193.1 | 4 | |||
72.59 | even | 6 | 1728.2.i.j.1153.2 | 4 | |||
72.61 | even | 6 | 576.2.i.j.193.2 | 4 | |||
72.67 | odd | 6 | 576.2.i.l.385.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.i.b.25.1 | ✓ | 4 | 9.4 | even | 3 | ||
72.2.i.b.49.1 | yes | 4 | 9.7 | even | 3 | ||
144.2.i.d.49.2 | 4 | 36.7 | odd | 6 | |||
144.2.i.d.97.2 | 4 | 36.31 | odd | 6 | |||
216.2.i.b.73.1 | 4 | 9.5 | odd | 6 | |||
216.2.i.b.145.1 | 4 | 9.2 | odd | 6 | |||
432.2.i.d.145.1 | 4 | 36.11 | even | 6 | |||
432.2.i.d.289.1 | 4 | 36.23 | even | 6 | |||
576.2.i.j.193.2 | 4 | 72.61 | even | 6 | |||
576.2.i.j.385.2 | 4 | 72.13 | even | 6 | |||
576.2.i.l.193.1 | 4 | 72.43 | odd | 6 | |||
576.2.i.l.385.1 | 4 | 72.67 | odd | 6 | |||
648.2.a.f.1.1 | 2 | 1.1 | even | 1 | trivial | ||
648.2.a.g.1.2 | 2 | 3.2 | odd | 2 | |||
1296.2.a.n.1.1 | 2 | 4.3 | odd | 2 | |||
1296.2.a.p.1.2 | 2 | 12.11 | even | 2 | |||
1728.2.i.i.577.2 | 4 | 72.29 | odd | 6 | |||
1728.2.i.i.1153.2 | 4 | 72.5 | odd | 6 | |||
1728.2.i.j.577.2 | 4 | 72.11 | even | 6 | |||
1728.2.i.j.1153.2 | 4 | 72.59 | even | 6 | |||
5184.2.a.bo.1.1 | 2 | 24.11 | even | 2 | |||
5184.2.a.bp.1.1 | 2 | 24.5 | odd | 2 | |||
5184.2.a.bs.1.2 | 2 | 8.3 | odd | 2 | |||
5184.2.a.bt.1.2 | 2 | 8.5 | even | 2 |