Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, 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("3072.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.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: | \(24.5300435009\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 48) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.27133\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1 |
$q$-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 | ||||||||
\(5\) | 1.79793 | 0.804060 | 0.402030 | − | 0.915627i | \(-0.368305\pi\) | ||||
0.402030 | + | 0.915627i | \(0.368305\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.158942 | 0.0600743 | 0.0300371 | − | 0.999549i | \(-0.490437\pi\) | ||||
0.0300371 | + | 0.999549i | \(0.490437\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.37109 | −1.61944 | −0.809722 | − | 0.586814i | \(-0.800382\pi\) | ||||
−0.809722 | + | 0.586814i | \(0.800382\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.95687 | −1.65214 | −0.826070 | − | 0.563568i | \(-0.809428\pi\) | ||||
−0.826070 | + | 0.563568i | \(0.809428\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.79793 | 0.464224 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.05320 | −0.740511 | −0.370255 | − | 0.928930i | \(-0.620730\pi\) | ||||
−0.370255 | + | 0.928930i | \(0.620730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.05320 | 0.700453 | 0.350227 | − | 0.936665i | \(-0.386105\pi\) | ||||
0.350227 | + | 0.936665i | \(0.386105\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.158942 | 0.0346839 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.76744 | −0.353488 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.96951 | −0.551423 | −0.275712 | − | 0.961240i | \(-0.588913\pi\) | ||||
−0.275712 | + | 0.961240i | \(0.588913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.15894 | −0.746968 | −0.373484 | − | 0.927637i | \(-0.621837\pi\) | ||||
−0.373484 | + | 0.927637i | \(0.621837\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.37109 | −0.934986 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.285766 | 0.0483033 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.46742 | −1.39203 | −0.696017 | − | 0.718025i | \(-0.745046\pi\) | ||||
−0.696017 | + | 0.718025i | \(0.745046\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.95687 | −0.953863 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.60365 | 0.406622 | 0.203311 | − | 0.979114i | \(-0.434830\pi\) | ||||
0.203311 | + | 0.979114i | \(0.434830\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.13853 | 1.24111 | 0.620557 | − | 0.784162i | \(-0.286907\pi\) | ||||
0.620557 | + | 0.784162i | \(0.286907\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.79793 | 0.268020 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.97474 | −0.996391 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.05320 | −0.427534 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.03049 | −0.690992 | −0.345496 | − | 0.938420i | \(-0.612289\pi\) | ||||
−0.345496 | + | 0.938420i | \(0.612289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.65685 | −1.30213 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.05320 | 0.404407 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.65685 | −0.736460 | −0.368230 | − | 0.929735i | \(-0.620036\pi\) | ||||
−0.368230 | + | 0.929735i | \(0.620036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.18944 | −0.664439 | −0.332220 | − | 0.943202i | \(-0.607798\pi\) | ||||
−0.332220 | + | 0.943202i | \(0.607798\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.158942 | 0.0200248 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.7101 | −1.32842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.08532 | 0.132593 | 0.0662966 | − | 0.997800i | \(-0.478882\pi\) | ||||
0.0662966 | + | 0.997800i | \(0.478882\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843 | 0.340503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.317883 | −0.0377258 | −0.0188629 | − | 0.999822i | \(-0.506005\pi\) | ||||
−0.0188629 | + | 0.999822i | \(0.506005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.33897 | 0.156715 | 0.0783573 | − | 0.996925i | \(-0.475032\pi\) | ||||
0.0783573 | + | 0.996925i | \(0.475032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.76744 | −0.204086 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.853690 | −0.0972870 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.69382 | −1.09064 | −0.545320 | − | 0.838228i | \(-0.683592\pi\) | ||||
−0.545320 | + | 0.838228i | \(0.683592\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.163788 | −0.0179781 | −0.00898906 | − | 0.999960i | \(-0.502861\pi\) | ||||
−0.00898906 | + | 0.999960i | \(0.502861\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.48946 | −0.595415 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.96951 | −0.318364 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.3990 | 1.52629 | 0.763147 | − | 0.646225i | \(-0.223653\pi\) | ||||
0.763147 | + | 0.646225i | \(0.223653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.946795 | −0.0992511 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.15894 | −0.431262 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.48946 | 0.563206 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.571533 | −0.0580304 | −0.0290152 | − | 0.999579i | \(-0.509237\pi\) | ||||
−0.0290152 | + | 0.999579i | \(0.509237\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.37109 | −0.539815 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1158 | −1.00656 | −0.503281 | − | 0.864123i | \(-0.667874\pi\) | ||||
−0.503281 | + | 0.864123i | \(0.667874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3507 | 1.11841 | 0.559207 | − | 0.829028i | \(-0.311106\pi\) | ||||
0.559207 | + | 0.829028i | \(0.311106\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.285766 | 0.0278879 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.02109 | −0.0987123 | −0.0493561 | − | 0.998781i | \(-0.515717\pi\) | ||||
−0.0493561 | + | 0.998781i | \(0.515717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.04313 | −0.195696 | −0.0978480 | − | 0.995201i | \(-0.531196\pi\) | ||||
−0.0978480 | + | 0.995201i | \(0.531196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.46742 | −0.803692 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.53488 | 0.332533 | 0.166267 | − | 0.986081i | \(-0.446829\pi\) | ||||
0.166267 | + | 0.986081i | \(0.446829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.08532 | 0.474209 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.95687 | −0.550713 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.485281 | −0.0444857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.8486 | 1.62260 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.60365 | 0.234763 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1674 | −1.08829 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.49791 | 0.132918 | 0.0664591 | − | 0.997789i | \(-0.478830\pi\) | ||||
0.0664591 | + | 0.997789i | \(0.478830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.13853 | 0.716557 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.7422 | 1.28803 | 0.644015 | − | 0.765013i | \(-0.277267\pi\) | ||||
0.644015 | + | 0.765013i | \(0.277267\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.485281 | 0.0420792 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.79793 | 0.154741 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.7954 | 1.17862 | 0.589309 | − | 0.807907i | \(-0.299400\pi\) | ||||
0.589309 | + | 0.807907i | \(0.299400\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.42847 | −0.290799 | −0.145399 | − | 0.989373i | \(-0.546447\pi\) | ||||
−0.145399 | + | 0.989373i | \(0.546447\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.82843 | −0.238197 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.9949 | 2.67555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.33897 | −0.443377 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.97474 | −0.575267 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.14108 | −0.339250 | −0.169625 | − | 0.985509i | \(-0.554256\pi\) | ||||
−0.169625 | + | 0.985509i | \(0.554256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.6644 | 1.84440 | 0.922201 | − | 0.386712i | \(-0.126389\pi\) | ||||
0.922201 | + | 0.386712i | \(0.126389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.05320 | −0.246837 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.47750 | −0.600607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.93161 | 0.313777 | 0.156888 | − | 0.987616i | \(-0.449854\pi\) | ||||
0.156888 | + | 0.987616i | \(0.449854\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.03049 | −0.398944 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.449555 | 0.0354299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.68897 | −0.602247 | −0.301123 | − | 0.953585i | \(-0.597362\pi\) | ||||
−0.301123 | + | 0.953585i | \(0.597362\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.65685 | −0.751785 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.95458 | 0.306015 | 0.153007 | − | 0.988225i | \(-0.451104\pi\) | ||||
0.153007 | + | 0.988225i | \(0.451104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.4844 | 1.72957 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.05320 | 0.233484 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.6011 | −1.71833 | −0.859165 | − | 0.511699i | \(-0.829016\pi\) | ||||
−0.859165 | + | 0.511699i | \(0.829016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.280920 | −0.0212355 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.65685 | −0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2981 | 1.29292 | 0.646462 | − | 0.762946i | \(-0.276248\pi\) | ||||
0.646462 | + | 0.762946i | \(0.276248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.14953 | −0.605750 | −0.302875 | − | 0.953030i | \(-0.597946\pi\) | ||||
−0.302875 | + | 0.953030i | \(0.597946\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.18944 | −0.383614 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.2238 | −1.11928 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.3990 | 1.19922 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.158942 | 0.0115613 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1674 | 1.16983 | 0.584916 | − | 0.811094i | \(-0.301127\pi\) | ||||
0.584916 | + | 0.811094i | \(0.301127\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.1454 | −1.59406 | −0.797030 | − | 0.603940i | \(-0.793597\pi\) | ||||
−0.797030 | + | 0.603940i | \(0.793597\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.7101 | −0.766963 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.2222 | −1.44077 | −0.720387 | − | 0.693572i | \(-0.756036\pi\) | ||||
−0.720387 | + | 0.693572i | \(0.756036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.0075 | −1.77274 | −0.886368 | − | 0.462981i | \(-0.846780\pi\) | ||||
−0.886368 | + | 0.462981i | \(0.846780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.08532 | 0.0765527 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.471978 | −0.0331264 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.68119 | 0.326948 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.3990 | −1.13434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0559 | −1.79376 | −0.896881 | − | 0.442273i | \(-0.854172\pi\) | ||||
−0.896881 | + | 0.442273i | \(0.854172\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.317883 | −0.0217810 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.6325 | 0.997930 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.661029 | −0.0448736 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.33897 | 0.0904793 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.1876 | 1.22343 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3465 | −1.22857 | −0.614286 | − | 0.789083i | \(-0.710556\pi\) | ||||
−0.614286 | + | 0.789083i | \(0.710556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.76744 | −0.117829 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.163788 | −0.0108710 | −0.00543551 | − | 0.999985i | \(-0.501730\pi\) | ||||
−0.00543551 | + | 0.999985i | \(0.501730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.02756 | 0.266148 | 0.133074 | − | 0.991106i | \(-0.457515\pi\) | ||||
0.133074 | + | 0.991106i | \(0.457515\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.853690 | −0.0561687 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.7211 | −0.767874 | −0.383937 | − | 0.923359i | \(-0.625432\pi\) | ||||
−0.383937 | + | 0.923359i | \(0.625432\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.08532 | −0.331730 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.69382 | −0.629681 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6517 | −0.883058 | −0.441529 | − | 0.897247i | \(-0.645564\pi\) | ||||
−0.441529 | + | 0.897247i | \(0.645564\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.13167 | −0.137313 | −0.0686565 | − | 0.997640i | \(-0.521871\pi\) | ||||
−0.0686565 | + | 0.997640i | \(0.521871\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.5401 | −0.801158 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.1876 | −1.15725 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.163788 | −0.0103797 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.27020 | 0.395771 | 0.197886 | − | 0.980225i | \(-0.436593\pi\) | ||||
0.197886 | + | 0.980225i | \(0.436593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.1917 | −0.955096 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.48946 | −0.343763 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0853 | 0.940997 | 0.470498 | − | 0.882401i | \(-0.344074\pi\) | ||||
0.470498 | + | 0.882401i | \(0.344074\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.34583 | −0.0836255 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.96951 | −0.183808 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.1706 | 1.61375 | 0.806875 | − | 0.590722i | \(-0.201157\pi\) | ||||
0.806875 | + | 0.590722i | \(0.201157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.04449 | −0.555599 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.3990 | 0.881206 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.1580 | 0.741286 | 0.370643 | − | 0.928775i | \(-0.379137\pi\) | ||||
0.370643 | + | 0.928775i | \(0.379137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6644 | 0.647815 | 0.323907 | − | 0.946089i | \(-0.395003\pi\) | ||||
0.323907 | + | 0.946089i | \(0.395003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.946795 | −0.0573027 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.49307 | 0.572453 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.76421 | 0.226170 | 0.113085 | − | 0.993585i | \(-0.463927\pi\) | ||||
0.113085 | + | 0.993585i | \(0.463927\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.15894 | −0.248989 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4496 | 0.623368 | 0.311684 | − | 0.950186i | \(-0.399107\pi\) | ||||
0.311684 | + | 0.950186i | \(0.399107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.6569 | 1.04959 | 0.524796 | − | 0.851228i | \(-0.324142\pi\) | ||||
0.524796 | + | 0.851228i | \(0.324142\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.48946 | 0.325167 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.413828 | 0.0244275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.67794 | −0.451644 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.571533 | −0.0335038 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.7465 | 1.79623 | 0.898114 | − | 0.439762i | \(-0.144937\pi\) | ||||
0.898114 | + | 0.439762i | \(0.144937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1706 | −0.592158 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.37109 | −0.311662 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.8486 | −0.974379 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.29355 | 0.0745590 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1158 | −0.581138 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.33026 | −0.534249 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.2981 | −1.21555 | −0.607775 | − | 0.794110i | \(-0.707938\pi\) | ||||
−0.607775 | + | 0.794110i | \(0.707938\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.3507 | 0.645717 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.77883 | −0.100868 | −0.0504342 | − | 0.998727i | \(-0.516061\pi\) | ||||
−0.0504342 | + | 0.998727i | \(0.516061\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.70320 | −0.152794 | −0.0763971 | − | 0.997077i | \(-0.524342\pi\) | ||||
−0.0763971 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.285766 | 0.0161011 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.0653 | −1.23931 | −0.619655 | − | 0.784874i | \(-0.712728\pi\) | ||||
−0.619655 | + | 0.784874i | \(0.712728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.9495 | 0.892999 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.02109 | −0.0569916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.32206 | −0.518693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.5284 | 0.584011 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.04313 | −0.112985 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.449555 | −0.0247848 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8431 | 1.20060 | 0.600302 | − | 0.799774i | \(-0.295047\pi\) | ||||
0.600302 | + | 0.799774i | \(0.295047\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.46742 | −0.464012 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.95133 | 0.106613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.8738 | 1.02812 | 0.514062 | − | 0.857753i | \(-0.328140\pi\) | ||||
0.514062 | + | 0.857753i | \(0.328140\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.53488 | 0.191988 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.3380 | 1.20967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.22117 | −0.119932 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.08532 | 0.273785 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.0490 | −1.50575 | −0.752875 | − | 0.658163i | \(-0.771334\pi\) | ||||
−0.752875 | + | 0.658163i | \(0.771334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.9307 | −0.906279 | −0.453139 | − | 0.891440i | \(-0.649696\pi\) | ||||
−0.453139 | + | 0.891440i | \(0.649696\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.95687 | −0.317954 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6202 | −0.671705 | −0.335853 | − | 0.941915i | \(-0.609024\pi\) | ||||
−0.335853 | + | 0.941915i | \(0.609024\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.571533 | −0.0303338 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.485281 | −0.0256838 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.0867 | 1.42958 | 0.714790 | − | 0.699339i | \(-0.246522\pi\) | ||||
0.714790 | + | 0.699339i | \(0.246522\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.67794 | −0.509365 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.8486 | 0.936808 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.40738 | 0.126008 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.4937 | −1.06976 | −0.534882 | − | 0.844927i | \(-0.679644\pi\) | ||||
−0.534882 | + | 0.844927i | \(0.679644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.60365 | 0.135541 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.799555 | −0.0415108 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.46190 | −0.0756943 | −0.0378471 | − | 0.999284i | \(-0.512050\pi\) | ||||
−0.0378471 | + | 0.999284i | \(0.512050\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1674 | −0.628322 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.6890 | 0.911028 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.9871 | −1.28350 | −0.641751 | − | 0.766913i | \(-0.721792\pi\) | ||||
−0.641751 | + | 0.766913i | \(0.721792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.49791 | 0.0767404 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.0958 | 1.58892 | 0.794460 | − | 0.607316i | \(-0.207754\pi\) | ||||
0.794460 | + | 0.607316i | \(0.207754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.53488 | −0.0782245 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.13853 | 0.413705 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.62218 | −0.183652 | −0.0918260 | − | 0.995775i | \(-0.529270\pi\) | ||||
−0.0918260 | + | 0.995775i | \(0.529270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.63577 | −0.436729 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.7422 | 0.743644 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.4288 | −0.876940 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.20959 | −0.361839 | −0.180920 | − | 0.983498i | \(-0.557907\pi\) | ||||
−0.180920 | + | 0.983498i | \(0.557907\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.485281 | 0.0242945 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.2660 | 0.762349 | 0.381174 | − | 0.924503i | \(-0.375520\pi\) | ||||
0.381174 | + | 0.924503i | \(0.375520\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.7743 | 1.23410 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.79793 | 0.0893400 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.4792 | 2.25432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.3779 | −0.562603 | −0.281302 | − | 0.959619i | \(-0.590766\pi\) | ||||
−0.281302 | + | 0.959619i | \(0.590766\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.7954 | 0.680476 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.899110 | −0.0442423 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.294481 | −0.0144555 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.42847 | −0.167893 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.9618 | 1.61029 | 0.805146 | − | 0.593077i | \(-0.202087\pi\) | ||||
0.805146 | + | 0.593077i | \(0.202087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.9119 | −1.21413 | −0.607065 | − | 0.794652i | \(-0.707653\pi\) | ||||
−0.607065 | + | 0.794652i | \(0.707653\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82843 | −0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.39635 | 0.261761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.824818 | −0.0399157 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.9949 | 1.54473 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3211 | 0.497151 | 0.248576 | − | 0.968612i | \(-0.420038\pi\) | ||||
0.248576 | + | 0.968612i | \(0.420038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3137 | 0.735930 | 0.367965 | − | 0.929840i | \(-0.380055\pi\) | ||||
0.367965 | + | 0.929840i | \(0.380055\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.33897 | −0.255984 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.63577 | 0.413105 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.5735 | −1.07738 | −0.538688 | − | 0.842505i | \(-0.681080\pi\) | ||||
−0.538688 | + | 0.842505i | \(0.681080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.97474 | −0.332130 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.5334 | −1.59322 | −0.796610 | − | 0.604494i | \(-0.793375\pi\) | ||||
−0.796610 | + | 0.604494i | \(0.793375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.8885 | 1.22723 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.14108 | −0.195866 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.75506 | −0.0828266 | −0.0414133 | − | 0.999142i | \(-0.513186\pi\) | ||||
−0.0414133 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.9844 | −0.658501 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.6644 | 1.06487 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.70227 | −0.0798039 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.7422 | −1.25095 | −0.625473 | − | 0.780246i | \(-0.715094\pi\) | ||||
−0.625473 | + | 0.780246i | \(0.715094\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.05320 | −0.142511 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0662 | 0.608555 | 0.304277 | − | 0.952584i | \(-0.401585\pi\) | ||||
0.304277 | + | 0.952584i | \(0.401585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4474 | 1.36854 | 0.684268 | − | 0.729231i | \(-0.260122\pi\) | ||||
0.684268 | + | 0.729231i | \(0.260122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.47750 | −0.346761 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.7040 | 1.28199 | 0.640995 | − | 0.767545i | \(-0.278522\pi\) | ||||
0.640995 | + | 0.767545i | \(0.278522\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.172503 | 0.00796544 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.93161 | 0.181159 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −43.7127 | −2.00991 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.39635 | −0.247602 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.03049 | −0.230331 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.5499 | −1.62432 | −0.812159 | − | 0.583436i | \(-0.801708\pi\) | ||||
−0.812159 | + | 0.583436i | \(0.801708\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.4393 | 2.29984 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.449555 | 0.0204555 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.02758 | −0.0466599 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.86632 | −0.447086 | −0.223543 | − | 0.974694i | \(-0.571762\pi\) | ||||
−0.223543 | + | 0.974694i | \(0.571762\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.68897 | −0.347707 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.635767 | −0.0286917 | −0.0143459 | − | 0.999897i | \(-0.504567\pi\) | ||||
−0.0143459 | + | 0.999897i | \(0.504567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.06651 | 0.408335 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.65685 | −0.434043 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0505249 | −0.00226635 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.82750 | −0.171342 | −0.0856712 | − | 0.996323i | \(-0.527303\pi\) | ||||
−0.0856712 | + | 0.996323i | \(0.527303\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.95458 | 0.176678 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.6719 | −1.05548 | −0.527739 | − | 0.849407i | \(-0.676960\pi\) | ||||
−0.527739 | + | 0.849407i | \(0.676960\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.1876 | −0.809336 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.4844 | 0.998565 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.7970 | 1.54235 | 0.771175 | − | 0.636623i | \(-0.219669\pi\) | ||||
0.771175 | + | 0.636623i | \(0.219669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.212818 | 0.00941453 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.05320 | 0.134802 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.4077 | 0.899273 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.1917 | 0.668132 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.6011 | −0.992078 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.4889 | −0.634770 | −0.317385 | − | 0.948297i | \(-0.602805\pi\) | ||||
−0.317385 | + | 0.948297i | \(0.602805\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.5742 | −1.20574 | −0.602868 | − | 0.797841i | \(-0.705975\pi\) | ||||
−0.602868 | + | 0.797841i | \(0.705975\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.280920 | −0.0122603 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6981 | 0.553138 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.65685 | −0.245487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.5096 | −0.671796 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.83585 | −0.0793706 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.2981 | 0.746470 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.4619 | 1.61360 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1982 | 0.610428 | 0.305214 | − | 0.952284i | \(-0.401272\pi\) | ||||
0.305214 | + | 0.952284i | \(0.401272\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.14953 | −0.349730 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.67340 | −0.157351 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.1807 | −0.435295 | −0.217648 | − | 0.976027i | \(-0.569838\pi\) | ||||
−0.217648 | + | 0.976027i | \(0.569838\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.18944 | −0.221480 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.06651 | −0.386246 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.54075 | −0.0655194 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.2238 | −0.646216 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.44432 | 0.0611979 | 0.0305990 | − | 0.999532i | \(-0.490259\pi\) | ||||
0.0305990 | + | 0.999532i | \(0.490259\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.4802 | −2.05049 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.3990 | 0.692368 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.48585 | −0.399781 | −0.199890 | − | 0.979818i | \(-0.564059\pi\) | ||||
−0.199890 | + | 0.979818i | \(0.564059\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.35547 | 0.267377 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.158942 | 0.00667492 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.98711 | 0.376759 | 0.188380 | − | 0.982096i | \(-0.439676\pi\) | ||||
0.188380 | + | 0.982096i | \(0.439676\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9706 | 0.542801 | 0.271401 | − | 0.962466i | \(-0.412513\pi\) | ||||
0.271401 | + | 0.962466i | \(0.412513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.1674 | 0.675403 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.99907 | −0.208476 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.5013 | 1.22815 | 0.614077 | − | 0.789246i | \(-0.289528\pi\) | ||||
0.614077 | + | 0.789246i | \(0.289528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.1454 | −0.920331 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0260328 | −0.00108002 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.0192 | 1.11902 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.7101 | −0.442806 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.57988 | 0.106483 | 0.0532416 | − | 0.998582i | \(-0.483045\pi\) | ||||
0.0532416 | + | 0.998582i | \(0.483045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.6981 | −0.523216 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.2222 | −0.831831 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.4338 | 1.45509 | 0.727546 | − | 0.686058i | \(-0.240661\pi\) | ||||
0.727546 | + | 0.686058i | \(0.240661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.872503 | −0.0357691 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.0075 | −1.02349 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.1632 | 1.10986 | 0.554930 | − | 0.831897i | \(-0.312745\pi\) | ||||
0.554930 | + | 0.831897i | \(0.312745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.33897 | −0.217781 | −0.108891 | − | 0.994054i | \(-0.534730\pi\) | ||||
−0.108891 | + | 0.994054i | \(0.534730\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.08532 | 0.0441977 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.0906 | 1.30467 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1084 | −0.653820 | −0.326910 | − | 0.945055i | \(-0.606007\pi\) | ||||
−0.326910 | + | 0.945055i | \(0.606007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.471978 | −0.0191255 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.8486 | 0.681621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.617903 | 0.0249569 | 0.0124784 | − | 0.999922i | \(-0.496028\pi\) | ||||
0.0124784 | + | 0.999922i | \(0.496028\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.68119 | 0.188764 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.80641 | 0.354533 | 0.177266 | − | 0.984163i | \(-0.443275\pi\) | ||||
0.177266 | + | 0.984163i | \(0.443275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.72847 | 0.109666 | 0.0548332 | − | 0.998496i | \(-0.482537\pi\) | ||||
0.0548332 | + | 0.998496i | \(0.482537\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.82843 | 0.113501 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.28861 | 0.0916910 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.0390 | −0.521559 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.3990 | −0.654914 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.8528 | 1.03082 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.7864 | −1.54406 | −0.772030 | − | 0.635586i | \(-0.780759\pi\) | ||||
−0.772030 | + | 0.635586i | \(0.780759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.0559 | −1.03563 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.69315 | 0.106874 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 41.5476 | 1.64618 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.317883 | −0.0125753 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.1091 | 1.30773 | 0.653865 | − | 0.756611i | \(-0.273146\pi\) | ||||
0.653865 | + | 0.756611i | \(0.273146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.2797 | −1.07581 | −0.537904 | − | 0.843006i | \(-0.680784\pi\) | ||||
−0.537904 | + | 0.843006i | \(0.680784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.6325 | 0.576155 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.8477 | −1.64520 | −0.822601 | − | 0.568620i | \(-0.807478\pi\) | ||||
−0.822601 | + | 0.568620i | \(0.807478\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.3835 | 1.19266 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.661029 | −0.0259078 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.8937 | 0.817634 | 0.408817 | − | 0.912616i | \(-0.365941\pi\) | ||||
0.408817 | + | 0.912616i | \(0.365941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.5054 | 1.03565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.33897 | 0.0522382 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.15142 | 0.122762 | 0.0613809 | − | 0.998114i | \(-0.480450\pi\) | ||||
0.0613809 | + | 0.998114i | \(0.480450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5527 | 0.993886 | 0.496943 | − | 0.867783i | \(-0.334456\pi\) | ||||
0.496943 | + | 0.867783i | \(0.334456\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.1876 | 0.706346 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.872503 | 0.0338342 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.39903 | −0.325212 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.3465 | −0.709317 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.8729 | 1.07602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7981 | 0.801706 | 0.400853 | − | 0.916142i | \(-0.368714\pi\) | ||||
0.400853 | + | 0.916142i | \(0.368714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.76744 | −0.0680287 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0423 | 1.57738 | 0.788692 | − | 0.614789i | \(-0.210759\pi\) | ||||
0.788692 | + | 0.614789i | \(0.210759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0908404 | −0.00348613 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.163788 | −0.00627639 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.5784 | −1.01699 | −0.508497 | − | 0.861064i | \(-0.669799\pi\) | ||||
−0.508497 | + | 0.861064i | \(0.669799\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.8032 | 0.947680 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.02756 | 0.153661 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.9660 | 1.14161 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.7899 | −0.562633 | −0.281316 | − | 0.959615i | \(-0.590771\pi\) | ||||
−0.281316 | + | 0.959615i | \(0.590771\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.853690 | −0.0324290 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.16415 | −0.233820 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.94948 | −0.301108 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.7211 | −0.443332 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.9245 | −0.979155 | −0.489577 | − | 0.871960i | \(-0.662849\pi\) | ||||
−0.489577 | + | 0.871960i | \(0.662849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.8528 | −0.975055 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.08532 | −0.191524 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.60782 | −0.0604685 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.6082 | 0.773958 | 0.386979 | − | 0.922089i | \(-0.373519\pi\) | ||||
0.386979 | + | 0.922089i | \(0.373519\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.69382 | −0.363547 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.7633 | −0.440538 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 57.5247 | 2.15130 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.6517 | −0.509834 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.0949 | 1.64446 | 0.822230 | − | 0.569155i | \(-0.192730\pi\) | ||||
0.822230 | + | 0.569155i | \(0.192730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.80409 | 0.0671880 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.13167 | −0.0792777 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.24842 | 0.194921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.23457 | 0.342491 | 0.171246 | − | 0.985228i | \(-0.445221\pi\) | ||||
0.171246 | + | 0.985228i | \(0.445221\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.8486 | −0.919058 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.8467 | −0.954670 | −0.477335 | − | 0.878721i | \(-0.658397\pi\) | ||||
−0.477335 | + | 0.878721i | \(0.658397\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.5401 | −0.462549 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.82936 | −0.214727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0403 | 0.884337 | 0.442169 | − | 0.896932i | \(-0.354209\pi\) | ||||
0.442169 | + | 0.896932i | \(0.354209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.1876 | −0.668137 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.8748 | 0.655762 | 0.327881 | − | 0.944719i | \(-0.393665\pi\) | ||||
0.327881 | + | 0.944719i | \(0.393665\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.44538 | −0.272778 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.163788 | −0.00599271 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.162293 | −0.00593007 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.0731 | −1.27984 | −0.639918 | − | 0.768443i | \(-0.721032\pi\) | ||||
−0.639918 | + | 0.768443i | \(0.721032\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.27020 | 0.228499 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.7490 | 1.48301 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.3962 | 1.68630 | 0.843150 | − | 0.537679i | \(-0.180699\pi\) | ||||
0.843150 | + | 0.537679i | \(0.180699\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.1917 | −0.551425 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.5531 | −0.382550 | −0.191275 | − | 0.981536i | \(-0.561262\pi\) | ||||
−0.191275 | + | 0.981536i | \(0.561262\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.324738 | −0.0117563 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.48946 | −0.198472 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.6972 | 1.21673 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.2068 | −1.26959 | −0.634795 | − | 0.772681i | \(-0.718915\pi\) | ||||
−0.634795 | + | 0.772681i | \(0.718915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0853 | 0.543285 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.4212 | −0.986271 | −0.493136 | − | 0.869952i | \(-0.664149\pi\) | ||||
−0.493136 | + | 0.869952i | \(0.664149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.35067 | 0.264044 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.34583 | −0.0482812 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.94948 | 0.284820 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.70738 | 0.0610948 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.96951 | −0.106121 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.06877 | 0.252295 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.46058 | 0.337233 | 0.168617 | − | 0.985682i | \(-0.446070\pi\) | ||||
0.168617 | + | 0.985682i | \(0.446070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.1706 | 0.931700 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.561839 | 0.0199767 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.9128 | 1.09775 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.04449 | −0.320775 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.1791 | −0.679359 | −0.339680 | − | 0.940541i | \(-0.610319\pi\) | ||||
−0.339680 | + | 0.940541i | \(0.610319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.63577 | 0.305511 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3990 | 0.508765 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.19173 | −0.253791 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.808269 | 0.0284878 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.1580 | 0.427982 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.1578 | −1.51735 | −0.758673 | − | 0.651472i | \(-0.774152\pi\) | ||||
−0.758673 | + | 0.651472i | \(0.774152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.87518 | 0.136076 | 0.0680380 | − | 0.997683i | \(-0.478326\pi\) | ||||
0.0680380 | + | 0.997683i | \(0.478326\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.6644 | 0.374016 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.8243 | −0.484242 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.8486 | 0.869342 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.946795 | −0.0330837 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.62084 | −0.196169 | −0.0980843 | − | 0.995178i | \(-0.531271\pi\) | ||||
−0.0980843 | + | 0.995178i | \(0.531271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.5255 | 1.34291 | 0.671457 | − | 0.741043i | \(-0.265669\pi\) | ||||
0.671457 | + | 0.741043i | \(0.265669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.49307 | 0.330506 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.23674 | −0.147326 | −0.0736629 | − | 0.997283i | \(-0.523469\pi\) | ||||
−0.0736629 | + | 0.997283i | \(0.523469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.3128 | 1.22646 | 0.613231 | − | 0.789903i | \(-0.289869\pi\) | ||||
0.613231 | + | 0.789903i | \(0.289869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.76421 | 0.130579 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.2953 | 0.737838 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.11007 | 0.246054 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.15894 | −0.143754 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.6005 | 1.36716 | 0.683580 | − | 0.729876i | \(-0.260422\pi\) | ||||
0.683580 | + | 0.729876i | \(0.260422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1820 | −0.695932 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.4496 | 0.359902 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.4253 | 1.39067 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.83688 | 0.0974765 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.6569 | 0.605982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.9495 | −0.820977 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.8683 | −0.372124 | −0.186062 | − | 0.982538i | \(-0.559572\pi\) | ||||
−0.186062 | + | 0.982538i | \(0.559572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.48946 | 0.187735 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.0082 | −1.16170 | −0.580849 | − | 0.814011i | \(-0.697279\pi\) | ||||
−0.580849 | + | 0.814011i | \(0.697279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9973 | −0.443463 | −0.221731 | − | 0.975108i | \(-0.571171\pi\) | ||||
−0.221731 | + | 0.975108i | \(0.571171\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.413828 | 0.0141032 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.8307 | 0.879289 | 0.439644 | − | 0.898172i | \(-0.355104\pi\) | ||||
0.439644 | + | 0.898172i | \(0.355104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.6353 | −1.38164 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.67794 | −0.260757 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.0663 | 1.76623 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.46512 | −0.219062 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.571533 | −0.0193435 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.93391 | −0.0653780 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.2150 | 1.52680 | 0.763400 | − | 0.645926i | \(-0.223528\pi\) | ||||
0.763400 | + | 0.645926i | \(0.223528\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.7465 | 1.03705 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.7403 | −1.17043 | −0.585215 | − | 0.810878i | \(-0.698990\pi\) | ||||
−0.585215 | + | 0.810878i | \(0.698990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.9366 | 1.64685 | 0.823424 | − | 0.567427i | \(-0.192061\pi\) | ||||
0.823424 | + | 0.567427i | \(0.192061\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.1706 | −0.341882 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.9284 | −0.769860 | −0.384930 | − | 0.922946i | \(-0.625774\pi\) | ||||
−0.384930 | + | 0.922946i | \(0.625774\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.238081 | 0.00798497 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.37109 | −0.179938 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.63577 | −0.288985 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.1009 | 1.03959 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.8486 | −0.562558 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.3500 | 0.411896 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.3591 | 0.511687 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.29355 | 0.0430467 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.6523 | −0.487059 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.1680 | −0.769280 | −0.384640 | − | 0.923067i | \(-0.625674\pi\) | ||||
−0.384640 | + | 0.923067i | \(0.625674\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.1158 | −0.335520 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.4078 | −0.974324 | −0.487162 | − | 0.873312i | \(-0.661968\pi\) | ||||
−0.487162 | + | 0.873312i | \(0.661968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.879722 | 0.0291146 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.33026 | −0.308449 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.34315 | 0.0773775 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.86029 | 0.226300 | 0.113150 | − | 0.993578i | \(-0.463906\pi\) | ||||
0.113150 | + | 0.993578i | \(0.463906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.2981 | −0.701798 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.89359 | 0.0623283 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.9656 | 0.492067 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3507 | 0.372805 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.1385 | 0.529488 | 0.264744 | − | 0.964319i | \(-0.414713\pi\) | ||||
0.264744 | + | 0.964319i | \(0.414713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.2953 | −0.697925 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.77883 | −0.0582363 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.4844 | 0.964241 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.7669 | −1.13579 | −0.567893 | − | 0.823102i | \(-0.692241\pi\) | ||||
−0.567893 | + | 0.823102i | \(0.692241\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.70320 | −0.0882157 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.7024 | −1.71805 | −0.859025 | − | 0.511934i | \(-0.828929\pi\) | ||||
−0.859025 | + | 0.511934i | \(0.828929\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.36423 | 0.239812 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.285766 | 0.00929598 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.1972 | −0.851296 | −0.425648 | − | 0.904889i | \(-0.639954\pi\) | ||||
−0.425648 | + | 0.904889i | \(0.639954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.97608 | −0.258915 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.0653 | −0.715516 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.1752 | −0.362000 | −0.181000 | − | 0.983483i | \(-0.557933\pi\) | ||||
−0.181000 | + | 0.983483i | \(0.557933\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.0679 | 0.940615 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.9495 | 0.515573 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.19266 | 0.0708047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7032 | −0.442039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.02109 | −0.0329041 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.8159 | −1.28172 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8452 | 0.413075 | 0.206537 | − | 0.978439i | \(-0.433780\pi\) | ||||
0.206537 | + | 0.978439i | \(0.433780\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.32206 | −0.299468 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.40774 | 0.269817 | 0.134909 | − | 0.990858i | \(-0.456926\pi\) | ||||
0.134909 | + | 0.990858i | \(0.456926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.544926 | −0.0174695 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.5284 | 0.337179 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.4156 | −1.29301 | −0.646504 | − | 0.762910i | \(-0.723770\pi\) | ||||
−0.646504 | + | 0.762910i | \(0.723770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −77.3385 | −2.47175 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.04313 | −0.0652320 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.9202 | 0.443985 | 0.221993 | − | 0.975048i | \(-0.428744\pi\) | ||||
0.221993 | + | 0.975048i | \(0.428744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.3582 | −1.15847 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.449555 | −0.0143095 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.0192 | 0.731969 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0309 | −1.30339 | −0.651695 | − | 0.758481i | \(-0.725942\pi\) | ||||
−0.651695 | + | 0.758481i | \(0.725942\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.8431 | 0.693169 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −44.9618 | −1.42539 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.6427 | 1.22383 | 0.611913 | − | 0.790925i | \(-0.290400\pi\) | ||||
0.611913 | + | 0.790925i | \(0.290400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.46742 | −0.267897 |
(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 | 3072.2.a.o.1.4 | 4 | ||
3.2 | odd | 2 | 9216.2.a.bn.1.1 | 4 | |||
4.3 | odd | 2 | 3072.2.a.i.1.4 | 4 | |||
8.3 | odd | 2 | 3072.2.a.t.1.1 | 4 | |||
8.5 | even | 2 | 3072.2.a.n.1.1 | 4 | |||
12.11 | even | 2 | 9216.2.a.bo.1.1 | 4 | |||
16.3 | odd | 4 | 3072.2.d.f.1537.1 | 8 | |||
16.5 | even | 4 | 3072.2.d.i.1537.4 | 8 | |||
16.11 | odd | 4 | 3072.2.d.f.1537.8 | 8 | |||
16.13 | even | 4 | 3072.2.d.i.1537.5 | 8 | |||
24.5 | odd | 2 | 9216.2.a.x.1.4 | 4 | |||
24.11 | even | 2 | 9216.2.a.y.1.4 | 4 | |||
32.3 | odd | 8 | 384.2.j.b.289.1 | 8 | |||
32.5 | even | 8 | 192.2.j.a.49.2 | 8 | |||
32.11 | odd | 8 | 384.2.j.b.97.1 | 8 | |||
32.13 | even | 8 | 192.2.j.a.145.2 | 8 | |||
32.19 | odd | 8 | 48.2.j.a.13.1 | ✓ | 8 | ||
32.21 | even | 8 | 384.2.j.a.97.3 | 8 | |||
32.27 | odd | 8 | 48.2.j.a.37.1 | yes | 8 | ||
32.29 | even | 8 | 384.2.j.a.289.3 | 8 | |||
96.5 | odd | 8 | 576.2.k.b.433.2 | 8 | |||
96.11 | even | 8 | 1152.2.k.c.865.3 | 8 | |||
96.29 | odd | 8 | 1152.2.k.f.289.3 | 8 | |||
96.35 | even | 8 | 1152.2.k.c.289.3 | 8 | |||
96.53 | odd | 8 | 1152.2.k.f.865.3 | 8 | |||
96.59 | even | 8 | 144.2.k.b.37.4 | 8 | |||
96.77 | odd | 8 | 576.2.k.b.145.2 | 8 | |||
96.83 | even | 8 | 144.2.k.b.109.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.1 | ✓ | 8 | 32.19 | odd | 8 | ||
48.2.j.a.37.1 | yes | 8 | 32.27 | odd | 8 | ||
144.2.k.b.37.4 | 8 | 96.59 | even | 8 | |||
144.2.k.b.109.4 | 8 | 96.83 | even | 8 | |||
192.2.j.a.49.2 | 8 | 32.5 | even | 8 | |||
192.2.j.a.145.2 | 8 | 32.13 | even | 8 | |||
384.2.j.a.97.3 | 8 | 32.21 | even | 8 | |||
384.2.j.a.289.3 | 8 | 32.29 | even | 8 | |||
384.2.j.b.97.1 | 8 | 32.11 | odd | 8 | |||
384.2.j.b.289.1 | 8 | 32.3 | odd | 8 | |||
576.2.k.b.145.2 | 8 | 96.77 | odd | 8 | |||
576.2.k.b.433.2 | 8 | 96.5 | odd | 8 | |||
1152.2.k.c.289.3 | 8 | 96.35 | even | 8 | |||
1152.2.k.c.865.3 | 8 | 96.11 | even | 8 | |||
1152.2.k.f.289.3 | 8 | 96.29 | odd | 8 | |||
1152.2.k.f.865.3 | 8 | 96.53 | odd | 8 | |||
3072.2.a.i.1.4 | 4 | 4.3 | odd | 2 | |||
3072.2.a.n.1.1 | 4 | 8.5 | even | 2 | |||
3072.2.a.o.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3072.2.a.t.1.1 | 4 | 8.3 | odd | 2 | |||
3072.2.d.f.1537.1 | 8 | 16.3 | odd | 4 | |||
3072.2.d.f.1537.8 | 8 | 16.11 | odd | 4 | |||
3072.2.d.i.1537.4 | 8 | 16.5 | even | 4 | |||
3072.2.d.i.1537.5 | 8 | 16.13 | even | 4 | |||
9216.2.a.x.1.4 | 4 | 24.5 | odd | 2 | |||
9216.2.a.y.1.4 | 4 | 24.11 | even | 2 | |||
9216.2.a.bn.1.1 | 4 | 3.2 | odd | 2 | |||
9216.2.a.bo.1.1 | 4 | 12.11 | even | 2 |