Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,2,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, 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("1088.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(8.68772373992\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 544) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-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 | ||||||||
\(3\) | 2.90321 | 1.67617 | 0.838085 | − | 0.545540i | \(-0.183675\pi\) | ||||
0.838085 | + | 0.545540i | \(0.183675\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.622216 | 0.278263 | 0.139132 | − | 0.990274i | \(-0.455569\pi\) | ||||
0.139132 | + | 0.990274i | \(0.455569\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.52543 | 0.576557 | 0.288279 | − | 0.957547i | \(-0.406917\pi\) | ||||
0.288279 | + | 0.957547i | \(0.406917\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.42864 | 1.80955 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09679 | 0.330694 | 0.165347 | − | 0.986235i | \(-0.447126\pi\) | ||||
0.165347 | + | 0.986235i | \(0.447126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.42864 | −0.673583 | −0.336792 | − | 0.941579i | \(-0.609342\pi\) | ||||
−0.336792 | + | 0.941579i | \(0.609342\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.80642 | 0.466417 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.80642 | 1.33208 | 0.666042 | − | 0.745914i | \(-0.267987\pi\) | ||||
0.666042 | + | 0.745914i | \(0.267987\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.42864 | 0.966408 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.57628 | −1.78828 | −0.894139 | − | 0.447789i | \(-0.852212\pi\) | ||||
−0.894139 | + | 0.447789i | \(0.852212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61285 | −0.922570 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.05086 | 1.35694 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.37778 | 0.627239 | 0.313619 | − | 0.949549i | \(-0.398458\pi\) | ||||
0.313619 | + | 0.949549i | \(0.398458\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.33185 | 0.598418 | 0.299209 | − | 0.954188i | \(-0.403277\pi\) | ||||
0.299209 | + | 0.954188i | \(0.403277\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.18421 | 0.554300 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.949145 | 0.160435 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.37778 | 0.555304 | 0.277652 | − | 0.960682i | \(-0.410444\pi\) | ||||
0.277652 | + | 0.960682i | \(0.410444\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.05086 | −1.12904 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.85728 | −1.07093 | −0.535464 | − | 0.844558i | \(-0.679863\pi\) | ||||
−0.535464 | + | 0.844558i | \(0.679863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.05086 | −1.07525 | −0.537623 | − | 0.843186i | \(-0.680677\pi\) | ||||
−0.537623 | + | 0.843186i | \(0.680677\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.37778 | 0.503530 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.24443 | 0.181519 | 0.0907595 | − | 0.995873i | \(-0.471071\pi\) | ||||
0.0907595 | + | 0.995873i | \(0.471071\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.67307 | −0.667582 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.90321 | 0.406531 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.8573 | 1.49136 | 0.745681 | − | 0.666303i | \(-0.232124\pi\) | ||||
0.745681 | + | 0.666303i | \(0.232124\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.682439 | 0.0920200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.8573 | 2.23280 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.56199 | −0.593921 | −0.296960 | − | 0.954890i | \(-0.595973\pi\) | ||||
−0.296960 | + | 0.954890i | \(0.595973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.9906 | 1.91935 | 0.959677 | − | 0.281105i | \(-0.0907011\pi\) | ||||
0.959677 | + | 0.281105i | \(0.0907011\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.28100 | 1.04331 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.51114 | −0.187434 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6128 | −1.41874 | −0.709368 | − | 0.704839i | \(-0.751019\pi\) | ||||
−0.709368 | + | 0.704839i | \(0.751019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −24.8988 | −2.99746 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2810 | −1.45749 | −0.728743 | − | 0.684787i | \(-0.759895\pi\) | ||||
−0.728743 | + | 0.684787i | \(0.759895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6128 | 1.59326 | 0.796632 | − | 0.604465i | \(-0.206613\pi\) | ||||
0.796632 | + | 0.604465i | \(0.206613\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.3921 | −1.54638 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.67307 | 0.190664 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1891 | −1.37138 | −0.685692 | − | 0.727892i | \(-0.740500\pi\) | ||||
−0.685692 | + | 0.727892i | \(0.740500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.18421 | 0.464912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.05086 | 0.773932 | 0.386966 | − | 0.922094i | \(-0.373523\pi\) | ||||
0.386966 | + | 0.922094i | \(0.373523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.622216 | 0.0674888 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.80642 | 1.05136 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.67307 | 0.813344 | 0.406672 | − | 0.913574i | \(-0.366689\pi\) | ||||
0.406672 | + | 0.913574i | \(0.366689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.70471 | −0.388360 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.67307 | 1.00305 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.61285 | 0.370670 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.61285 | 0.569898 | 0.284949 | − | 0.958543i | \(-0.408023\pi\) | ||||
0.284949 | + | 0.958543i | \(0.408023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.95407 | 0.598406 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4286 | −1.03769 | −0.518844 | − | 0.854869i | \(-0.673638\pi\) | ||||
−0.518844 | + | 0.854869i | \(0.673638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.75557 | 0.268916 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.46520 | −0.334994 | −0.167497 | − | 0.985873i | \(-0.553568\pi\) | ||||
−0.167497 | + | 0.985873i | \(0.553568\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.47949 | −0.524840 | −0.262420 | − | 0.964954i | \(-0.584521\pi\) | ||||
−0.262420 | + | 0.964954i | \(0.584521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.80642 | 0.930785 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.4701 | −1.73752 | −0.868762 | − | 0.495230i | \(-0.835084\pi\) | ||||
−0.868762 | + | 0.495230i | \(0.835084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.33630 | −0.497612 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.1842 | −1.21888 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.52543 | 0.139836 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.79706 | −0.890641 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.9081 | −1.79506 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.98126 | −0.534981 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.94914 | 0.439166 | 0.219583 | − | 0.975594i | \(-0.429530\pi\) | ||||
0.219583 | + | 0.975594i | \(0.429530\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.4701 | −1.80229 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65878 | 0.494410 | 0.247205 | − | 0.968963i | \(-0.420488\pi\) | ||||
0.247205 | + | 0.968963i | \(0.420488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.85728 | 0.768023 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.38715 | 0.377586 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.7971 | 1.43507 | 0.717535 | − | 0.696523i | \(-0.245270\pi\) | ||||
0.717535 | + | 0.696523i | \(0.245270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8113 | −0.917006 | −0.458503 | − | 0.888693i | \(-0.651614\pi\) | ||||
−0.458503 | + | 0.888693i | \(0.651614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.61285 | 0.304257 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.66370 | −0.222750 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.10171 | 0.174538 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.5669 | −1.11898 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.48886 | −0.695435 | −0.347717 | − | 0.937599i | \(-0.613043\pi\) | ||||
−0.347717 | + | 0.937599i | \(0.613043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.561993 | 0.0457343 | 0.0228672 | − | 0.999739i | \(-0.492721\pi\) | ||||
0.0228672 | + | 0.999739i | \(0.492721\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.42864 | 0.438879 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.07313 | 0.166518 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1017 | 1.28506 | 0.642528 | − | 0.766262i | \(-0.277886\pi\) | ||||
0.642528 | + | 0.766262i | \(0.277886\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 31.5210 | 2.49978 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.0825 | −1.03105 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.95407 | 0.779663 | 0.389831 | − | 0.920886i | \(-0.372533\pi\) | ||||
0.389831 | + | 0.920886i | \(0.372533\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.98126 | 0.154241 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.1383 | −1.63573 | −0.817864 | − | 0.575411i | \(-0.804842\pi\) | ||||
−0.817864 | + | 0.575411i | \(0.804842\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.10171 | −0.546285 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.5210 | 2.41047 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.99063 | 0.531488 | 0.265744 | − | 0.964044i | \(-0.414382\pi\) | ||||
0.265744 | + | 0.964044i | \(0.414382\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.03657 | −0.531914 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.2444 | −0.995512 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.4193 | 1.30198 | 0.650989 | − | 0.759087i | \(-0.274354\pi\) | ||||
0.650989 | + | 0.759087i | \(0.274354\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.99063 | 0.519610 | 0.259805 | − | 0.965661i | \(-0.416342\pi\) | ||||
0.259805 | + | 0.965661i | \(0.416342\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 43.5210 | 3.21716 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.10171 | 0.154521 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.09679 | 0.0802051 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.7556 | 0.782353 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.24443 | −0.668904 | −0.334452 | − | 0.942413i | \(-0.608551\pi\) | ||||
−0.334452 | + | 0.942413i | \(0.608551\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.8573 | 1.35738 | 0.678688 | − | 0.734426i | \(-0.262549\pi\) | ||||
0.678688 | + | 0.734426i | \(0.262549\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.38715 | −0.314171 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.86665 | −0.132993 | −0.0664965 | − | 0.997787i | \(-0.521182\pi\) | ||||
−0.0664965 | + | 0.997787i | \(0.521182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.7003 | 1.25474 | 0.627369 | − | 0.778722i | \(-0.284132\pi\) | ||||
0.627369 | + | 0.778722i | \(0.284132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −33.7146 | −2.37804 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.15257 | 0.361639 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.26671 | −0.298000 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −46.5575 | −3.23597 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.36842 | 0.440513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.65878 | −0.389567 | −0.194783 | − | 0.980846i | \(-0.562400\pi\) | ||||
−0.194783 | + | 0.980846i | \(0.562400\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −35.6543 | −2.44299 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.38715 | −0.299201 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.08250 | 0.345022 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39.5210 | 2.67058 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.42864 | −0.163368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.9304 | 1.80339 | 0.901697 | − | 0.432369i | \(-0.142322\pi\) | ||||
0.901697 | + | 0.432369i | \(0.142322\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.0415 | −1.66943 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.8622 | −1.45105 | −0.725523 | − | 0.688198i | \(-0.758402\pi\) | ||||
−0.725523 | + | 0.688198i | \(0.758402\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.67307 | 0.242723 | 0.121362 | − | 0.992608i | \(-0.461274\pi\) | ||||
0.121362 | + | 0.992608i | \(0.461274\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.85728 | 0.319585 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.3461 | −1.13638 | −0.568192 | − | 0.822896i | \(-0.692357\pi\) | ||||
−0.568192 | + | 0.822896i | \(0.692357\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.774305 | 0.0505101 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −35.3876 | −2.29867 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1427 | −0.720763 | −0.360381 | − | 0.932805i | \(-0.617353\pi\) | ||||
−0.360381 | + | 0.932805i | \(0.617353\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.755569 | −0.0486705 | −0.0243352 | − | 0.999704i | \(-0.507747\pi\) | ||||
−0.0243352 | + | 0.999704i | \(0.507747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.00492 | −0.577666 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.90766 | −0.185763 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.1017 | −0.897270 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.4701 | 1.29724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.40636 | −0.591373 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.80642 | 0.113123 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.4286 | 0.650521 | 0.325260 | − | 0.945625i | \(-0.394548\pi\) | ||||
0.325260 | + | 0.945625i | \(0.394548\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.15257 | 0.320165 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.3368 | 1.13502 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.56199 | −0.527955 | −0.263978 | − | 0.964529i | \(-0.585034\pi\) | ||||
−0.263978 | + | 0.964529i | \(0.585034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.75557 | 0.414991 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.2766 | 1.36330 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.5018 | −1.00613 | −0.503065 | − | 0.864248i | \(-0.667794\pi\) | ||||
−0.503065 | + | 0.864248i | \(0.667794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.3684 | −1.11580 | −0.557901 | − | 0.829908i | \(-0.688393\pi\) | ||||
−0.557901 | + | 0.829908i | \(0.688393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.7556 | −0.650957 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.05932 | −0.305088 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.5625 | −1.77624 | −0.888118 | − | 0.459615i | \(-0.847987\pi\) | ||||
−0.888118 | + | 0.459615i | \(0.847987\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.0874 | 1.08287 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.1017 | −1.19917 | −0.599584 | − | 0.800312i | \(-0.704667\pi\) | ||||
−0.599584 | + | 0.800312i | \(0.704667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.39207 | −0.558301 | −0.279150 | − | 0.960247i | \(-0.590053\pi\) | ||||
−0.279150 | + | 0.960247i | \(0.590053\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.4889 | 0.621307 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4603 | −0.617451 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.2953 | 0.955247 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.7146 | −1.85278 | −0.926392 | − | 0.376560i | \(-0.877107\pi\) | ||||
−0.926392 | + | 0.376560i | \(0.877107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.83854 | −0.165266 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.73329 | 0.448731 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.8287 | 1.20455 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7556 | −0.619941 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −30.2766 | −1.73934 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.32741 | 0.534086 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.1427 | 0.635949 | 0.317974 | − | 0.948099i | \(-0.396997\pi\) | ||||
0.317974 | + | 0.948099i | \(0.396997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.5254 | −0.993776 | −0.496888 | − | 0.867815i | \(-0.665524\pi\) | ||||
−0.496888 | + | 0.867815i | \(0.665524\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4479 | 1.09926 | 0.549629 | − | 0.835409i | \(-0.314769\pi\) | ||||
0.549629 | + | 0.835409i | \(0.314769\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.15257 | 0.290314 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.6222 | 0.933597 | 0.466798 | − | 0.884364i | \(-0.345407\pi\) | ||||
0.466798 | + | 0.884364i | \(0.345407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.70471 | 0.207424 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0602 | −0.561507 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.80642 | 0.323078 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.2029 | 0.621428 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.9081 | −0.879722 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.89829 | 0.104656 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.7654 | −1.80095 | −0.900475 | − | 0.434908i | \(-0.856781\pi\) | ||||
−0.900475 | + | 0.434908i | \(0.856781\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.3368 | 1.00485 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.22570 | −0.394782 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.1017 | 0.877116 | 0.438558 | − | 0.898703i | \(-0.355489\pi\) | ||||
0.438558 | + | 0.898703i | \(0.355489\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −53.6227 | −2.91238 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.65433 | 0.197893 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8064 | −0.961457 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.4924 | −0.834083 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.830082 | 0.0445611 | 0.0222806 | − | 0.999752i | \(-0.492907\pi\) | ||||
0.0222806 | + | 0.999752i | \(0.492907\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.85728 | 0.152947 | 0.0764733 | − | 0.997072i | \(-0.475634\pi\) | ||||
0.0764733 | + | 0.997072i | \(0.475634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.1240 | −0.914011 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.61285 | −0.0858432 | −0.0429216 | − | 0.999078i | \(-0.513667\pi\) | ||||
−0.0429216 | + | 0.999078i | \(0.513667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.64143 | −0.405565 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.42864 | 0.234388 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.6227 | 1.35231 | 0.676157 | − | 0.736758i | \(-0.263644\pi\) | ||||
0.676157 | + | 0.736758i | \(0.263644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.7146 | 0.774450 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28.4429 | −1.49287 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.47013 | 0.443347 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.7190 | −0.611727 | −0.305864 | − | 0.952075i | \(-0.598945\pi\) | ||||
−0.305864 | + | 0.952075i | \(0.598945\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −37.2257 | −1.93789 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.5620 | 0.859856 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.0005 | 1.70870 | 0.854350 | − | 0.519698i | \(-0.173956\pi\) | ||||
0.854350 | + | 0.519698i | \(0.173956\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.3649 | −0.896718 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.20342 | −0.422498 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.90321 | 0.149128 | 0.0745640 | − | 0.997216i | \(-0.476243\pi\) | ||||
0.0745640 | + | 0.997216i | \(0.476243\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.3684 | 0.736116 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.6637 | 1.56684 | 0.783421 | − | 0.621491i | \(-0.213473\pi\) | ||||
0.783421 | + | 0.621491i | \(0.213473\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.04101 | 0.0530548 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −38.2766 | −1.94571 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.16193 | 0.312422 | 0.156211 | − | 0.987724i | \(-0.450072\pi\) | ||||
0.156211 | + | 0.987724i | \(0.450072\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.57628 | −0.433721 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.4286 | 0.828715 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.58427 | −0.381606 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.8889 | 0.847631 | 0.423815 | − | 0.905749i | \(-0.360691\pi\) | ||||
0.423815 | + | 0.905749i | \(0.360691\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.7146 | 1.28734 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.47013 | 0.323103 | 0.161551 | − | 0.986864i | \(-0.448350\pi\) | ||||
0.161551 | + | 0.986864i | \(0.448350\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.09187 | −0.403085 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.60348 | 0.129368 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.70471 | 0.183636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 48.7654 | 2.40542 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.95899 | −0.342429 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.38715 | 0.215357 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.3876 | −1.53706 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.3002 | 0.845170 | 0.422585 | − | 0.906323i | \(-0.361123\pi\) | ||||
0.422585 | + | 0.906323i | \(0.361123\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.5714 | 1.44122 | 0.720610 | − | 0.693341i | \(-0.243862\pi\) | ||||
0.720610 | + | 0.693341i | \(0.243862\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.75557 | 0.328467 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.61285 | −0.223756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.8671 | 1.10662 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.73329 | −0.373367 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.70027 | −0.467245 | −0.233623 | − | 0.972327i | \(-0.575058\pi\) | ||||
−0.233623 | + | 0.972327i | \(0.575058\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.83807 | 0.0883318 | 0.0441659 | − | 0.999024i | \(-0.485937\pi\) | ||||
0.0441659 | + | 0.999024i | \(0.485937\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.10171 | 0.292555 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −49.7975 | −2.38214 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.9224 | 0.759936 | 0.379968 | − | 0.925000i | \(-0.375935\pi\) | ||||
0.379968 | + | 0.925000i | \(0.375935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.3684 | −1.20802 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.10171 | −0.289901 | −0.144951 | − | 0.989439i | \(-0.546302\pi\) | ||||
−0.144951 | + | 0.989439i | \(0.546302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.77430 | 0.226324 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.6450 | −1.16567 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.22570 | 0.435387 | 0.217694 | − | 0.976017i | \(-0.430147\pi\) | ||||
0.217694 | + | 0.976017i | \(0.430147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.52098 | −0.354149 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.63158 | 0.0766585 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.30513 | −0.108066 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0192 | 0.515457 | 0.257729 | − | 0.966217i | \(-0.417026\pi\) | ||||
0.257729 | + | 0.966217i | \(0.417026\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.05086 | 0.329106 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.3461 | −1.18049 | −0.590244 | − | 0.807225i | \(-0.700968\pi\) | ||||
−0.590244 | + | 0.807225i | \(0.700968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.1240 | 1.16761 | 0.583805 | − | 0.811894i | \(-0.301563\pi\) | ||||
0.583805 | + | 0.811894i | \(0.301563\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.01874 | 0.279112 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.1338 | 0.885408 | 0.442704 | − | 0.896668i | \(-0.354019\pi\) | ||||
0.442704 | + | 0.896668i | \(0.354019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.7146 | −0.817982 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.7467 | 2.15397 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.73329 | −0.355577 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.7841 | −1.22894 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 58.9403 | 2.69869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0143 | −1.09724 | −0.548620 | − | 0.836072i | \(-0.684847\pi\) | ||||
−0.548620 | + | 0.836072i | \(0.684847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.20342 | −0.374044 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −37.9813 | −1.72821 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.49240 | 0.158582 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.484417 | 0.0219510 | 0.0109755 | − | 0.999940i | \(-0.496506\pi\) | ||||
0.0109755 | + | 0.999940i | \(0.496506\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.8988 | 1.30685 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.60300 | 0.0723425 | 0.0361713 | − | 0.999346i | \(-0.488484\pi\) | ||||
0.0361713 | + | 0.999346i | \(0.488484\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.37778 | 0.152128 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.70471 | 0.166514 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.7338 | −0.840324 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.1798 | 0.590007 | 0.295004 | − | 0.955496i | \(-0.404679\pi\) | ||||
0.295004 | + | 0.955496i | \(0.404679\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −61.3689 | −2.74176 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.8716 | 1.64402 | 0.822011 | − | 0.569472i | \(-0.192852\pi\) | ||||
0.822011 | + | 0.569472i | \(0.192852\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.48886 | −0.288751 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.6178 | −0.915667 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.2257 | 0.763516 | 0.381758 | − | 0.924262i | \(-0.375319\pi\) | ||||
0.381758 | + | 0.924262i | \(0.375319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.7654 | 0.918608 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 40.9403 | 1.80756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36488 | 0.0600272 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.2953 | 0.890864 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.0607 | 1.71128 | 0.855640 | − | 0.517571i | \(-0.173164\pi\) | ||||
0.855640 | + | 0.517571i | \(0.173164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.71456 | 0.0749724 | 0.0374862 | − | 0.999297i | \(-0.488065\pi\) | ||||
0.0374862 | + | 0.999297i | \(0.488065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −20.4286 | −0.891579 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.33185 | 0.145138 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.5526 | 2.19794 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.7654 | −1.07473 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.6539 | 0.721359 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.15610 | −0.0932165 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 50.5718 | 2.18234 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.12537 | −0.220765 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.9496 | −1.80356 | −0.901778 | − | 0.432200i | \(-0.857737\pi\) | ||||
−0.901778 | + | 0.432200i | \(0.857737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.2953 | 0.870954 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.40943 | −0.146044 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.27163 | 0.0543709 | 0.0271855 | − | 0.999630i | \(-0.491346\pi\) | ||||
0.0271855 | + | 0.999630i | \(0.491346\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 81.3787 | 3.47316 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.6128 | 0.835535 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.5936 | −0.790682 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.10171 | 0.259003 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.0005 | 1.05930 | 0.529652 | − | 0.848215i | \(-0.322322\pi\) | ||||
0.529652 | + | 0.848215i | \(0.322322\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.1240 | 0.724267 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.18421 | 0.134437 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.5022 | 1.24337 | 0.621686 | − | 0.783267i | \(-0.286448\pi\) | ||||
0.621686 | + | 0.783267i | \(0.286448\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.4924 | −0.483489 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.38271 | 0.268048 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.3497 | 1.10464 | 0.552318 | − | 0.833633i | \(-0.313743\pi\) | ||||
0.552318 | + | 0.833633i | \(0.313743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.6079 | 1.11351 | 0.556754 | − | 0.830678i | \(-0.312047\pi\) | ||||
0.556754 | + | 0.830678i | \(0.312047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.8385 | −1.12120 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 39.5611 | 1.64981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.14320 | −0.339006 | −0.169503 | − | 0.985530i | \(-0.554216\pi\) | ||||
−0.169503 | + | 0.985530i | \(0.554216\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 54.7467 | 2.27519 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.7556 | 0.446216 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.9081 | 0.493185 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.20342 | −0.339170 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.8064 | −1.23024 | −0.615121 | − | 0.788432i | \(-0.710893\pi\) | ||||
−0.615121 | + | 0.788432i | \(0.710893\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.3461 | 0.797144 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.41927 | −0.222919 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.8163 | −1.22441 | −0.612204 | − | 0.790700i | \(-0.709717\pi\) | ||||
−0.612204 | + | 0.790700i | \(0.709717\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.949145 | 0.0389111 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 51.3876 | 2.10316 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.8163 | −1.29998 | −0.649989 | − | 0.759944i | \(-0.725226\pi\) | ||||
−0.649989 | + | 0.759944i | \(0.725226\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.20342 | −0.0898794 | −0.0449397 | − | 0.998990i | \(-0.514310\pi\) | ||||
−0.0449397 | + | 0.998990i | \(0.514310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −63.0420 | −2.56727 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.09588 | −0.247833 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.43356 | 0.382896 | 0.191448 | − | 0.981503i | \(-0.438682\pi\) | ||||
0.191448 | + | 0.981503i | \(0.438682\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.9590 | 0.606169 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.02227 | −0.122268 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0223 | 0.525965 | 0.262982 | − | 0.964801i | \(-0.415294\pi\) | ||||
0.262982 | + | 0.964801i | \(0.415294\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.3872 | −0.499498 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.85728 | −0.276064 | −0.138032 | − | 0.990428i | \(-0.544078\pi\) | ||||
−0.138032 | + | 0.990428i | \(0.544078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.56691 | 0.223753 | 0.111877 | − | 0.993722i | \(-0.464314\pi\) | ||||
0.111877 | + | 0.993722i | \(0.464314\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −60.4701 | −2.42658 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.7047 | 0.468939 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.3426 | 0.773704 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.4889 | 0.738374 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.37778 | 0.134681 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.0098 | −1.19467 | −0.597337 | − | 0.801991i | \(-0.703774\pi\) | ||||
−0.597337 | + | 0.801991i | \(0.703774\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.4286 | −0.652980 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.07944 | 0.122204 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.3492 | 0.449672 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −66.6691 | −2.63739 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.07944 | 0.200626 | 0.100313 | − | 0.994956i | \(-0.468016\pi\) | ||||
0.100313 | + | 0.994956i | \(0.468016\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.3546 | 1.63087 | 0.815433 | − | 0.578851i | \(-0.196499\pi\) | ||||
0.815433 | + | 0.578851i | \(0.196499\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.7368 | −0.501512 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.3087 | −1.38813 | −0.694064 | − | 0.719914i | \(-0.744181\pi\) | ||||
−0.694064 | + | 0.719914i | \(0.744181\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.00354 | −0.196406 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.7556 | 0.578316 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.2351 | −0.635327 | −0.317664 | − | 0.948203i | \(-0.602898\pi\) | ||||
−0.317664 | + | 0.948203i | \(0.602898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.52098 | 0.137576 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 73.8992 | 2.88308 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.4479 | −1.14713 | −0.573563 | − | 0.819162i | \(-0.694439\pi\) | ||||
−0.573563 | + | 0.819162i | \(0.694439\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.6735 | 1.34864 | 0.674322 | − | 0.738437i | \(-0.264436\pi\) | ||||
0.674322 | + | 0.738437i | \(0.264436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.05086 | −0.273833 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.51114 | 0.213713 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.9688 | −1.12168 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 78.1847 | 3.02279 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.4415 | 0.634719 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.5111 | 0.906288 | 0.453144 | − | 0.891437i | \(-0.350302\pi\) | ||||
0.453144 | + | 0.891437i | \(0.350302\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −32.5245 | −1.25187 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.25734 | 0.278922 | 0.139461 | − | 0.990228i | \(-0.455463\pi\) | ||||
0.139461 | + | 0.990228i | \(0.455463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.56199 | 0.328579 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −63.4706 | −2.43220 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.0049 | 1.26290 | 0.631449 | − | 0.775417i | \(-0.282460\pi\) | ||||
0.631449 | + | 0.775417i | \(0.282460\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.4514 | 0.399327 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.6637 | 0.406846 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.3684 | −1.00456 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.1985 | 0.882512 | 0.441256 | − | 0.897381i | \(-0.354533\pi\) | ||||
0.441256 | + | 0.897381i | \(0.354533\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.08250 | 0.345016 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.72699 | −0.255169 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.85728 | −0.259738 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −50.3595 | −1.90477 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9175 | −0.487887 | −0.243944 | − | 0.969789i | \(-0.578441\pi\) | ||||
−0.243944 | + | 0.969789i | \(0.578441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.6128 | 0.739713 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.24797 | 0.0846635 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.9081 | −0.598287 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.4197 | 1.29266 | 0.646330 | − | 0.763058i | \(-0.276303\pi\) | ||||
0.646330 | + | 0.763058i | \(0.276303\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −66.1704 | −2.48158 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.5749 | −1.07014 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.65740 | −0.0619832 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.3497 | −1.20812 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.1704 | 0.677641 | 0.338821 | − | 0.940851i | \(-0.389972\pi\) | ||||
0.338821 | + | 0.940851i | \(0.389972\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.19358 | −0.0815800 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.5812 | −0.578671 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.75557 | 0.250550 | 0.125275 | − | 0.992122i | \(-0.460019\pi\) | ||||
0.125275 | + | 0.992122i | \(0.460019\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.6958 | −1.43318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.05086 | −0.260785 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.73329 | 0.0640207 | 0.0320103 | − | 0.999488i | \(-0.489809\pi\) | ||||
0.0320103 | + | 0.999488i | \(0.489809\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.44155 | −0.311371 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.7368 | −0.469167 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.9081 | 1.61519 | 0.807593 | − | 0.589740i | \(-0.200770\pi\) | ||||
0.807593 | + | 0.589740i | \(0.200770\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −40.9403 | −1.50398 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.8207 | 0.507033 | 0.253516 | − | 0.967331i | \(-0.418413\pi\) | ||||
0.253516 | + | 0.967331i | \(0.418413\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.28190 | −0.193514 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 38.2766 | 1.40047 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.28592 | −0.193143 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.69042 | −0.134665 | −0.0673327 | − | 0.997731i | \(-0.521449\pi\) | ||||
−0.0673327 | + | 0.997731i | \(0.521449\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.349681 | 0.0127262 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.4099 | 1.46872 | 0.734361 | − | 0.678759i | \(-0.237482\pi\) | ||||
0.734361 | + | 0.678759i | \(0.237482\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.3087 | −0.991242 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.9175 | −1.19326 | −0.596629 | − | 0.802517i | \(-0.703494\pi\) | ||||
−0.596629 | + | 0.802517i | \(0.703494\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.35857 | −0.302601 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.37778 | 0.122124 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.0794 | 0.400055 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.0005 | 1.33427 | 0.667136 | − | 0.744936i | \(-0.267520\pi\) | ||||
0.667136 | + | 0.744936i | \(0.267520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.2766 | 1.09038 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.67307 | 0.132111 | 0.0660556 | − | 0.997816i | \(-0.478959\pi\) | ||||
0.0660556 | + | 0.997816i | \(0.478959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.3693 | −0.552082 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.9590 | 0.536651 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.8163 | −1.42657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.4697 | −0.481982 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.8163 | 0.851124 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0187 | 0.357584 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.16638 | 0.0772231 | 0.0386115 | − | 0.999254i | \(-0.487707\pi\) | ||||
0.0386115 | + | 0.999254i | \(0.487707\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.8573 | −0.884943 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.1748 | −1.00178 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.4068 | −1.29284 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.6128 | 0.695596 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.1847 | 0.573291 | 0.286645 | − | 0.958037i | \(-0.407460\pi\) | ||||
0.286645 | + | 0.958037i | \(0.407460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.24443 | 0.0440248 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.6543 | 1.47178 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.9304 | 0.526883 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.14013 | −0.286902 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.9081 | −1.68645 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.67259 | 0.164280 | 0.0821398 | − | 0.996621i | \(-0.473825\pi\) | ||||
0.0821398 | + | 0.996621i | \(0.473825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.0879 | 1.30233 | 0.651166 | − | 0.758935i | \(-0.274280\pi\) | ||||
0.651166 | + | 0.758935i | \(0.274280\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −53.3274 | −1.87027 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.19358 | 0.216952 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.9403 | −1.43232 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.1116 | −0.702755 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.7275 | −0.828094 | −0.414047 | − | 0.910255i | \(-0.635885\pi\) | ||||
−0.414047 | + | 0.910255i | \(0.635885\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.7003 | −1.17472 | −0.587359 | − | 0.809327i | \(-0.699832\pi\) | ||||
−0.587359 | + | 0.809327i | \(0.699832\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.6883 | −0.511380 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.86220 | −0.342942 | −0.171471 | − | 0.985189i | \(-0.554852\pi\) | ||||
−0.171471 | + | 0.985189i | \(0.554852\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.1017 | 0.559236 | 0.279618 | − | 0.960111i | \(-0.409792\pi\) | ||||
0.279618 | + | 0.960111i | \(0.409792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −85.8261 | −2.97727 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.67307 | −0.161912 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.1526 | −0.455163 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.4924 | 0.812016 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.6494 | 0.367659 | 0.183829 | − | 0.982958i | \(-0.441151\pi\) | ||||
0.183829 | + | 0.982958i | \(0.441151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5906 | −0.606571 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −58.3595 | −2.01001 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.41880 | −0.152011 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.9447 | −0.513506 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.2672 | −0.935807 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.9688 | −0.993039 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.0513 | 1.23437 | 0.617187 | − | 0.786816i | \(-0.288272\pi\) | ||||
0.617187 | + | 0.786816i | \(0.288272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.6128 | 0.670745 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.24443 | 0.247465 | 0.123733 | − | 0.992316i | \(-0.460514\pi\) | ||||
0.123733 | + | 0.992316i | \(0.460514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.6414 | 1.35255 | 0.676274 | − | 0.736650i | \(-0.263594\pi\) | ||||
0.676274 | + | 0.736650i | \(0.263594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.3684 | −1.03495 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.5906 | 0.564750 | 0.282375 | − | 0.959304i | \(-0.408878\pi\) | ||||
0.282375 | + | 0.959304i | \(0.408878\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.34968 | 0.147894 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.90321 | 0.0985982 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.3689 | −0.453509 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.2034 | 0.955636 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.4701 | 1.03126 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.12399 | −0.308447 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.1941 | −1.32349 | −0.661745 | − | 0.749729i | \(-0.730184\pi\) | ||||
−0.661745 | + | 0.749729i | \(0.730184\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −92.0741 | −3.10558 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.5531 | 1.02936 | 0.514680 | − | 0.857382i | \(-0.327911\pi\) | ||||
0.514680 | + | 0.857382i | \(0.327911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.3274 | 1.52539 | 0.762694 | − | 0.646759i | \(-0.223876\pi\) | ||||
0.762694 | + | 0.646759i | \(0.223876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.24089 | −0.277015 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.8243 | 0.900670 | 0.450335 | − | 0.892860i | \(-0.351305\pi\) | ||||
0.450335 | + | 0.892860i | \(0.351305\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.54956 | 0.253204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.58919 | 0.153744 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.22570 | 0.241799 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.8385 | 0.362293 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 60.4701 | 2.01904 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.2543 | 0.375351 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.8573 | 0.361708 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.2257 | −1.03913 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.34968 | 0.144588 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.5580 | −1.64555 | −0.822774 | − | 0.568369i | \(-0.807575\pi\) | ||||
−0.822774 | + | 0.568369i | \(0.807575\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −56.6133 | −1.87775 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.19802 | 0.139087 | 0.0695433 | − | 0.997579i | \(-0.477846\pi\) | ||||
0.0695433 | + | 0.997579i | \(0.477846\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.73329 | 0.255935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.0794 | 0.895219 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.63206 | 0.285056 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.5941 | −1.63596 | −0.817979 | − | 0.575248i | \(-0.804906\pi\) | ||||
−0.817979 | + | 0.575248i | \(0.804906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.3497 | 1.06596 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.8261 | 0.981738 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.5812 | −0.512307 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.755569 | −0.0247894 | −0.0123947 | − | 0.999923i | \(-0.503945\pi\) | ||||
−0.0123947 | + | 0.999923i | \(0.503945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.1338 | −0.889275 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −50.8800 | −1.66574 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.682439 | 0.0223181 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.28544 | −0.139999 | −0.0699996 | − | 0.997547i | \(-0.522300\pi\) | ||||
−0.0699996 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 56.4612 | 1.84254 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4385 | 0.535879 | 0.267940 | − | 0.963436i | \(-0.413657\pi\) | ||||
0.267940 | + | 0.963436i | \(0.413657\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.8100 | 1.91512 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.69228 | 0.217700 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.0370 | −0.846090 | −0.423045 | − | 0.906109i | \(-0.639039\pi\) | ||||
−0.423045 | + | 0.906109i | \(0.639039\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.0607 | −1.07320 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.2578 | 1.56487 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3876 | 0.563241 | 0.281620 | − | 0.959526i | \(-0.409128\pi\) | ||||
0.281620 | + | 0.959526i | \(0.409128\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.75203 | −0.186131 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.7556 | 0.347678 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.6227 | 0.827400 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.8988 | −0.641896 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.8113 | −0.606187 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.7333 | 0.377708 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.44155 | 0.271462 | 0.135731 | − | 0.990746i | \(-0.456662\pi\) | ||||
0.135731 | + | 0.990746i | \(0.456662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.8573 | 0.541534 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.8671 | −0.990573 | −0.495287 | − | 0.868730i | \(-0.664937\pi\) | ||||
−0.495287 | + | 0.868730i | \(0.664937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.4919 | −0.528707 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.5245 | 1.04162 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58.5531 | −1.87328 | −0.936640 | − | 0.350294i | \(-0.886082\pi\) | ||||
−0.936640 | + | 0.350294i | \(0.886082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.41573 | 0.268968 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.7462 | −0.949723 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.1990 | −0.835618 | −0.417809 | − | 0.908535i | \(-0.637202\pi\) | ||||
−0.417809 | + | 0.908535i | \(0.637202\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.16146 | −0.0370071 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.51114 | 0.175421 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60.4701 | 1.92284 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.4844 | −1.79429 | −0.897143 | − | 0.441740i | \(-0.854362\pi\) | ||||
−0.897143 | + | 0.441740i | \(0.854362\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −95.1249 | −3.01870 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.0134 | 0.349148 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.9077 | 0.725493 | 0.362746 | − | 0.931888i | \(-0.381839\pi\) | ||||
0.362746 | + | 0.931888i | \(0.381839\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.8163 | 0.753513 |
(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 | 1088.2.a.v.1.3 | 3 | ||
3.2 | odd | 2 | 9792.2.a.dc.1.2 | 3 | |||
4.3 | odd | 2 | 1088.2.a.u.1.1 | 3 | |||
8.3 | odd | 2 | 544.2.a.j.1.3 | yes | 3 | ||
8.5 | even | 2 | 544.2.a.i.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 9792.2.a.dd.1.2 | 3 | |||
24.5 | odd | 2 | 4896.2.a.be.1.2 | 3 | |||
24.11 | even | 2 | 4896.2.a.bf.1.2 | 3 | |||
136.67 | odd | 2 | 9248.2.a.t.1.1 | 3 | |||
136.101 | even | 2 | 9248.2.a.u.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
544.2.a.i.1.1 | ✓ | 3 | 8.5 | even | 2 | ||
544.2.a.j.1.3 | yes | 3 | 8.3 | odd | 2 | ||
1088.2.a.u.1.1 | 3 | 4.3 | odd | 2 | |||
1088.2.a.v.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4896.2.a.be.1.2 | 3 | 24.5 | odd | 2 | |||
4896.2.a.bf.1.2 | 3 | 24.11 | even | 2 | |||
9248.2.a.t.1.1 | 3 | 136.67 | odd | 2 | |||
9248.2.a.u.1.3 | 3 | 136.101 | even | 2 | |||
9792.2.a.dc.1.2 | 3 | 3.2 | odd | 2 | |||
9792.2.a.dd.1.2 | 3 | 12.11 | even | 2 |