Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 12x^{4} + 28x^{3} + 16x^{2} - 60x + 27 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 836) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.64714\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | −1.64714 | −0.950978 | −0.475489 | − | 0.879722i | \(-0.657729\pi\) | ||||
−0.475489 | + | 0.879722i | \(0.657729\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.84900 | 0.826897 | 0.413449 | − | 0.910527i | \(-0.364324\pi\) | ||||
0.413449 | + | 0.910527i | \(0.364324\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.60453 | −1.36238 | −0.681192 | − | 0.732105i | \(-0.738538\pi\) | ||||
−0.681192 | + | 0.732105i | \(0.738538\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.286920 | −0.0956400 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.60764 | −1.27793 | −0.638965 | − | 0.769236i | \(-0.720637\pi\) | ||||
−0.638965 | + | 0.769236i | \(0.720637\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.04556 | −0.786361 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.53875 | 1.10081 | 0.550405 | − | 0.834898i | \(-0.314473\pi\) | ||||
0.550405 | + | 0.834898i | \(0.314473\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.93718 | 1.29560 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.43020 | −1.54930 | −0.774652 | − | 0.632387i | \(-0.782075\pi\) | ||||
−0.774652 | + | 0.632387i | \(0.782075\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.58121 | −0.316241 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.41403 | 1.04193 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.20922 | −0.224547 | −0.112273 | − | 0.993677i | \(-0.535813\pi\) | ||||
−0.112273 | + | 0.993677i | \(0.535813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.16972 | 1.46733 | 0.733663 | − | 0.679514i | \(-0.237809\pi\) | ||||
0.733663 | + | 0.679514i | \(0.237809\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.64714 | 0.286731 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.66477 | −1.12655 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.67467 | −0.439713 | −0.219857 | − | 0.975532i | \(-0.570559\pi\) | ||||
−0.219857 | + | 0.975532i | \(0.570559\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.58945 | 1.21528 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.6575 | −1.66442 | −0.832208 | − | 0.554464i | \(-0.812923\pi\) | ||||
−0.832208 | + | 0.554464i | \(0.812923\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.58121 | −1.15612 | −0.578062 | − | 0.815993i | \(-0.696191\pi\) | ||||
−0.578062 | + | 0.815993i | \(0.696191\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.530515 | −0.0790844 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.21528 | 1.05246 | 0.526229 | − | 0.850343i | \(-0.323606\pi\) | ||||
0.526229 | + | 0.850343i | \(0.323606\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.99263 | 0.856091 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.47598 | −1.04685 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.86813 | 1.35549 | 0.677746 | − | 0.735296i | \(-0.262957\pi\) | ||||
0.677746 | + | 0.735296i | \(0.262957\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.84900 | −0.249319 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.64714 | 0.218169 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.61190 | 0.990984 | 0.495492 | − | 0.868612i | \(-0.334988\pi\) | ||||
0.495492 | + | 0.868612i | \(0.334988\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0950 | 1.67664 | 0.838320 | − | 0.545179i | \(-0.183538\pi\) | ||||
0.838320 | + | 0.545179i | \(0.183538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.03421 | 0.130298 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.51952 | −1.05672 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.37878 | −1.14580 | −0.572900 | − | 0.819625i | \(-0.694182\pi\) | ||||
−0.572900 | + | 0.819625i | \(0.694182\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.2386 | 1.47336 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9414 | 1.29851 | 0.649254 | − | 0.760571i | \(-0.275081\pi\) | ||||
0.649254 | + | 0.760571i | \(0.275081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.17013 | 0.956241 | 0.478121 | − | 0.878294i | \(-0.341318\pi\) | ||||
0.478121 | + | 0.878294i | \(0.341318\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.60447 | 0.300739 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.60453 | 0.410774 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.1049 | −1.58692 | −0.793461 | − | 0.608621i | \(-0.791723\pi\) | ||||
−0.793461 | + | 0.608621i | \(0.791723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.05692 | −0.895213 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.3819 | 1.68838 | 0.844191 | − | 0.536042i | \(-0.180081\pi\) | ||||
0.844191 | + | 0.536042i | \(0.180081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.39215 | 0.910256 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.99176 | 0.213539 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.58945 | 0.698480 | 0.349240 | − | 0.937033i | \(-0.386440\pi\) | ||||
0.349240 | + | 0.937033i | \(0.386440\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.6084 | 1.74103 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.4567 | −1.39539 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.84900 | −0.189703 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8914 | −1.30893 | −0.654464 | − | 0.756093i | \(-0.727106\pi\) | ||||
−0.654464 | + | 0.756093i | \(0.727106\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.286920 | 0.0288365 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.942465 | 0.0937787 | 0.0468894 | − | 0.998900i | \(-0.485069\pi\) | ||||
0.0468894 | + | 0.998900i | \(0.485069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5386 | 1.03840 | 0.519199 | − | 0.854653i | \(-0.326230\pi\) | ||||
0.519199 | + | 0.854653i | \(0.326230\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.9778 | 1.07133 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.04516 | −0.681081 | −0.340540 | − | 0.940230i | \(-0.610610\pi\) | ||||
−0.340540 | + | 0.940230i | \(0.610610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.2076 | −0.977708 | −0.488854 | − | 0.872366i | \(-0.662585\pi\) | ||||
−0.488854 | + | 0.872366i | \(0.662585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.40557 | 0.418158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.83490 | 0.360757 | 0.180378 | − | 0.983597i | \(-0.442268\pi\) | ||||
0.180378 | + | 0.983597i | \(0.442268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.7384 | −1.28112 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.32202 | 0.122221 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.3601 | −1.49973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.5544 | 1.58282 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1686 | −1.08840 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6913 | −0.948696 | −0.474348 | − | 0.880337i | \(-0.657316\pi\) | ||||
−0.474348 | + | 0.880337i | \(0.657316\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4873 | 1.09945 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2811 | 0.898260 | 0.449130 | − | 0.893466i | \(-0.351734\pi\) | ||||
0.449130 | + | 0.893466i | \(0.351734\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.60453 | 0.312552 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.0105 | 0.861569 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.15505 | 0.440425 | 0.220213 | − | 0.975452i | \(-0.429325\pi\) | ||||
0.220213 | + | 0.975452i | \(0.429325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.23710 | −0.189749 | −0.0948743 | − | 0.995489i | \(-0.530245\pi\) | ||||
−0.0948743 | + | 0.995489i | \(0.530245\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8846 | −1.00086 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.60764 | 0.385310 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.23585 | −0.185677 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.87073 | −0.814124 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.7042 | −1.12269 | −0.561347 | − | 0.827581i | \(-0.689717\pi\) | ||||
−0.561347 | + | 0.827581i | \(0.689717\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4420 | 1.33803 | 0.669014 | − | 0.743250i | \(-0.266717\pi\) | ||||
0.669014 | + | 0.743250i | \(0.266717\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.30226 | −0.105281 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.1058 | 1.21333 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.4827 | −1.71451 | −0.857254 | − | 0.514894i | \(-0.827831\pi\) | ||||
−0.857254 | + | 0.514894i | \(0.827831\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.2542 | −1.28904 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.7824 | 2.11075 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.1301 | −1.34173 | −0.670865 | − | 0.741580i | \(-0.734077\pi\) | ||||
−0.670865 | + | 0.741580i | \(0.734077\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.04556 | 0.237097 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.8782 | 1.46084 | 0.730419 | − | 0.682999i | \(-0.239325\pi\) | ||||
0.730419 | + | 0.682999i | \(0.239325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.23037 | 0.633105 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.286920 | 0.0219413 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.79779 | 0.744912 | 0.372456 | − | 0.928050i | \(-0.378516\pi\) | ||||
0.372456 | + | 0.928050i | \(0.378516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.69950 | 0.430842 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.5379 | −0.942405 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.54923 | 0.713743 | 0.356872 | − | 0.934153i | \(-0.383843\pi\) | ||||
0.356872 | + | 0.934153i | \(0.383843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.9124 | 1.55441 | 0.777203 | − | 0.629249i | \(-0.216638\pi\) | ||||
0.777203 | + | 0.629249i | \(0.216638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.5693 | −1.59445 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.94546 | −0.363598 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.53875 | −0.331907 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.5150 | −1.41951 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.5827 | 1.70639 | 0.853193 | − | 0.521596i | \(-0.174663\pi\) | ||||
0.853193 | + | 0.521596i | \(0.174663\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.8780 | 1.21491 | 0.607454 | − | 0.794355i | \(-0.292191\pi\) | ||||
0.607454 | + | 0.794355i | \(0.292191\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.0329 | 1.00491 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2427 | 1.15724 | 0.578621 | − | 0.815597i | \(-0.303591\pi\) | ||||
0.578621 | + | 0.815597i | \(0.303591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.0695 | 1.56446 | 0.782232 | − | 0.622988i | \(-0.214081\pi\) | ||||
0.782232 | + | 0.622988i | \(0.214081\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.4482 | 1.08963 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.35867 | 0.305919 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.7056 | −1.37630 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.13187 | 0.148175 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.06376 | 0.0732323 | 0.0366162 | − | 0.999329i | \(-0.488342\pi\) | ||||
0.0366162 | + | 0.999329i | \(0.488342\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.0221 | −1.23485 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0176 | −0.955995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.4480 | −1.99906 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.4574 | −0.909365 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.9130 | −1.40676 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.85252 | 0.257984 | 0.128992 | − | 0.991646i | \(-0.458826\pi\) | ||||
0.128992 | + | 0.991646i | \(0.458826\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.453680 | 0.0302453 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.38224 | 0.0917428 | 0.0458714 | − | 0.998947i | \(-0.485394\pi\) | ||||
0.0458714 | + | 0.998947i | \(0.485394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.79798 | −0.317060 | −0.158530 | − | 0.987354i | \(-0.550675\pi\) | ||||
−0.158530 | + | 0.987354i | \(0.550675\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.93718 | −0.390637 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.77649 | 0.443943 | 0.221971 | − | 0.975053i | \(-0.428751\pi\) | ||||
0.221971 | + | 0.975053i | \(0.428751\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.3410 | 0.870274 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.2327 | 1.50913 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.8035 | 1.15161 | 0.575807 | − | 0.817586i | \(-0.304688\pi\) | ||||
0.575807 | + | 0.817586i | \(0.304688\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.9019 | 1.08875 | 0.544373 | − | 0.838843i | \(-0.316768\pi\) | ||||
0.544373 | + | 0.838843i | \(0.316768\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.97119 | −0.190602 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.0804 | 0.707899 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.60764 | 0.293177 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.3362 | −1.60561 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.7083 | 1.49645 | 0.748226 | − | 0.663444i | \(-0.230906\pi\) | ||||
0.748226 | + | 0.663444i | \(0.230906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.43020 | 0.467133 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.8231 | −0.865634 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.23002 | 0.0767263 | 0.0383632 | − | 0.999264i | \(-0.487786\pi\) | ||||
0.0383632 | + | 0.999264i | \(0.487786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.64094 | 0.599059 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.346950 | 0.0214756 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.29315 | −0.511377 | −0.255689 | − | 0.966759i | \(-0.582302\pi\) | ||||
−0.255689 | + | 0.966759i | \(0.582302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.2461 | 1.12085 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.8538 | −0.664239 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.8457 | 1.27098 | 0.635492 | − | 0.772108i | \(-0.280797\pi\) | ||||
0.635492 | + | 0.772108i | \(0.280797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.06428 | −0.489870 | −0.244935 | − | 0.969539i | \(-0.578767\pi\) | ||||
−0.244935 | + | 0.969539i | \(0.578767\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.3564 | −1.65568 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.58121 | 0.0953503 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.94531 | −0.537472 | −0.268736 | − | 0.963214i | \(-0.586606\pi\) | ||||
−0.268736 | + | 0.963214i | \(0.586606\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.34406 | −0.140335 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.65424 | −0.337304 | −0.168652 | − | 0.985676i | \(-0.553941\pi\) | ||||
−0.168652 | + | 0.985676i | \(0.553941\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.2519 | −1.67940 | −0.839700 | − | 0.543051i | \(-0.817269\pi\) | ||||
−0.839700 | + | 0.543051i | \(0.817269\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.04556 | 0.180404 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 38.4151 | 2.26757 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.60029 | 0.211782 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.2341 | 1.24476 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.67042 | 0.214428 | 0.107214 | − | 0.994236i | \(-0.465807\pi\) | ||||
0.107214 | + | 0.994236i | \(0.465807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.0744 | 0.819442 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.41403 | −0.314154 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 34.2357 | 1.97990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.3267 | 1.57508 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.55237 | −0.0891816 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.2126 | 1.38641 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.06344 | −0.517278 | −0.258639 | − | 0.965974i | \(-0.583274\pi\) | ||||
−0.258639 | + | 0.965974i | \(0.583274\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.3586 | −0.987494 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7300 | 0.891968 | 0.445984 | − | 0.895041i | \(-0.352854\pi\) | ||||
0.445984 | + | 0.895041i | \(0.352854\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.58157 | −0.258966 | −0.129483 | − | 0.991582i | \(-0.541332\pi\) | ||||
−0.129483 | + | 0.991582i | \(0.541332\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.91226 | 0.107743 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.37416 | −0.301843 | −0.150921 | − | 0.988546i | \(-0.548224\pi\) | ||||
−0.150921 | + | 0.988546i | \(0.548224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.20922 | 0.0677034 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6044 | 0.647693 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.53875 | −0.252543 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.28563 | 0.404134 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.8133 | 0.929779 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.0077 | −1.43385 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.7794 | −0.812349 | −0.406174 | − | 0.913796i | \(-0.633137\pi\) | ||||
−0.406174 | + | 0.913796i | \(0.633137\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.767417 | 0.0420542 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.3413 | −0.947459 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3056 | 0.670331 | 0.335165 | − | 0.942159i | \(-0.391208\pi\) | ||||
0.335165 | + | 0.942159i | \(0.391208\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.31663 | −0.343072 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.16972 | −0.442415 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.63108 | 0.196060 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.6292 | 1.21831 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.6446 | −0.893530 | −0.446765 | − | 0.894651i | \(-0.647424\pi\) | ||||
−0.446765 | + | 0.894651i | \(0.647424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.8958 | −0.690297 | −0.345149 | − | 0.938548i | \(-0.612171\pi\) | ||||
−0.345149 | + | 0.938548i | \(0.612171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.9459 | −1.33151 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.50692 | 0.506003 | 0.253001 | − | 0.967466i | \(-0.418582\pi\) | ||||
0.253001 | + | 0.967466i | \(0.418582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.2307 | 1.07373 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26.9474 | 1.42621 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.5140 | −1.02991 | −0.514954 | − | 0.857218i | \(-0.672191\pi\) | ||||
−0.514954 | + | 0.857218i | \(0.672191\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.64714 | −0.0864526 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.1066 | 0.790713 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.2094 | 1.36812 | 0.684060 | − | 0.729425i | \(-0.260212\pi\) | ||||
0.684060 | + | 0.729425i | \(0.260212\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.05784 | 0.159185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.5700 | −1.84670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.3119 | 0.792821 | 0.396410 | − | 0.918073i | \(-0.370256\pi\) | ||||
0.396410 | + | 0.918073i | \(0.370256\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.0435 | 1.03504 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.57166 | 0.286955 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.9993 | 0.616361 | 0.308180 | − | 0.951328i | \(-0.400280\pi\) | ||||
0.308180 | + | 0.951328i | \(0.400280\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.6100 | 0.902190 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.5695 | −1.40874 | −0.704369 | − | 0.709834i | \(-0.748770\pi\) | ||||
−0.704369 | + | 0.709834i | \(0.748770\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.66477 | 0.339668 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.17520 | 0.110572 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.3579 | −1.33640 | −0.668198 | − | 0.743983i | \(-0.732934\pi\) | ||||
−0.668198 | + | 0.743983i | \(0.732934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.7239 | −1.70549 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.9344 | −0.854226 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.0799 | −1.31222 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6384 | −0.734683 | −0.367341 | − | 0.930086i | \(-0.619732\pi\) | ||||
−0.367341 | + | 0.930086i | \(0.619732\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.93718 | −0.297231 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.884350 | 0.0441623 | 0.0220812 | − | 0.999756i | \(-0.492971\pi\) | ||||
0.0220812 | + | 0.999756i | \(0.492971\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.6432 | −1.87514 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.8972 | −0.740249 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.67467 | 0.132579 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6864 | 1.07233 | 0.536163 | − | 0.844115i | \(-0.319873\pi\) | ||||
0.536163 | + | 0.844115i | \(0.319873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.49110 | −0.418835 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.4373 | −1.35010 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.4411 | 1.39612 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.68483 | 0.180447 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.6191 | −1.44699 | −0.723494 | − | 0.690331i | \(-0.757465\pi\) | ||||
−0.723494 | + | 0.690331i | \(0.757465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.1830 | 1.61724 | 0.808621 | − | 0.588329i | \(-0.200214\pi\) | ||||
0.808621 | + | 0.588329i | \(0.200214\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.07021 | −0.100657 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.17671 | −0.348121 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −47.2012 | −2.28423 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.58945 | −0.366422 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.37951 | 0.259122 | 0.129561 | − | 0.991571i | \(-0.458643\pi\) | ||||
0.129561 | + | 0.991571i | \(0.458643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.5638 | 1.56491 | 0.782457 | − | 0.622704i | \(-0.213966\pi\) | ||||
0.782457 | + | 0.622704i | \(0.213966\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.68276 | 0.176575 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.43020 | 0.355435 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.6281 | −1.22316 | −0.611580 | − | 0.791182i | \(-0.709466\pi\) | ||||
−0.611580 | + | 0.791182i | \(0.709466\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.71941 | −0.0818765 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.87249 | −0.469056 | −0.234528 | − | 0.972109i | \(-0.575355\pi\) | ||||
−0.234528 | + | 0.972109i | \(0.575355\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.1839 | 0.577571 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.5728 | 1.06766 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.43358 | −0.0676550 | −0.0338275 | − | 0.999428i | \(-0.510770\pi\) | ||||
−0.0338275 | + | 0.999428i | \(0.510770\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.6575 | 0.501840 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.0823 | −1.27244 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30.7089 | 1.43965 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.81542 | −0.0849217 | −0.0424609 | − | 0.999098i | \(-0.513520\pi\) | ||||
−0.0424609 | + | 0.999098i | \(0.513520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.5729 | 1.14697 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.3391 | −1.41303 | −0.706517 | − | 0.707696i | \(-0.749735\pi\) | ||||
−0.706517 | + | 0.707696i | \(0.749735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.1414 | 1.12195 | 0.560974 | − | 0.827833i | \(-0.310427\pi\) | ||||
0.560974 | + | 0.827833i | \(0.310427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.8814 | −1.15385 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.7532 | −0.636421 | −0.318210 | − | 0.948020i | \(-0.603082\pi\) | ||||
−0.318210 | + | 0.948020i | \(0.603082\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.8061 | 1.56102 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.3851 | 1.63046 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.58121 | 0.348584 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.58121 | 0.0725507 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.83136 | −0.129639 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.1851 | 0.876588 | 0.438294 | − | 0.898832i | \(-0.355583\pi\) | ||||
0.438294 | + | 0.898832i | \(0.355583\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.3239 | 0.561923 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −44.1144 | −2.00728 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.8363 | −1.08235 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.3820 | −0.651711 | −0.325855 | − | 0.945420i | \(-0.605652\pi\) | ||||
−0.325855 | + | 0.945420i | \(0.605652\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.2157 | 1.27596 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.7834 | −1.47950 | −0.739748 | − | 0.672885i | \(-0.765055\pi\) | ||||
−0.739748 | + | 0.672885i | \(0.765055\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.48836 | −0.247183 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.530515 | 0.0238449 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −39.4387 | −1.76907 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.89797 | 0.353562 | 0.176781 | − | 0.984250i | \(-0.443432\pi\) | ||||
0.176781 | + | 0.984250i | \(0.443432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.0951 | −1.38923 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.50370 | 0.111634 | 0.0558172 | − | 0.998441i | \(-0.482224\pi\) | ||||
0.0558172 | + | 0.998441i | \(0.482224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.74262 | 0.0775454 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.5566 | −0.602069 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.5076 | 1.26358 | 0.631788 | − | 0.775142i | \(-0.282321\pi\) | ||||
0.631788 | + | 0.775142i | \(0.282321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.4495 | −1.30277 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.41403 | −0.239035 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.4858 | 0.858649 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.21528 | −0.317328 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.1384 | −0.708396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.6574 | 1.47456 | 0.737279 | − | 0.675588i | \(-0.236110\pi\) | ||||
0.737279 | + | 0.675588i | \(0.236110\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.2318 | −0.753492 | −0.376746 | − | 0.926317i | \(-0.622957\pi\) | ||||
−0.376746 | + | 0.926317i | \(0.622957\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.38790 | −0.409721 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.0804 | 1.61525 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.2079 | 1.40034 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.18400 | −0.0947777 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.1058 | 2.12701 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.0265 | −0.563184 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.7290 | −0.678754 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.99263 | −0.258121 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.6025 | 1.78863 | 0.894315 | − | 0.447438i | \(-0.147663\pi\) | ||||
0.894315 | + | 0.447438i | \(0.147663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.4457 | −1.47821 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.8738 | −0.808464 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.872294 | −0.0372966 | −0.0186483 | − | 0.999826i | \(-0.505936\pi\) | ||||
−0.0186483 | + | 0.999826i | \(0.505936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.75721 | −0.160354 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.20922 | 0.0515146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.8414 | 2.16200 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.14589 | 0.345774 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.76642 | −0.413816 | −0.206908 | − | 0.978360i | \(-0.566340\pi\) | ||||
−0.206908 | + | 0.978360i | \(0.566340\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.9315 | 1.47744 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.47598 | 0.315636 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.0277 | −0.464762 | −0.232381 | − | 0.972625i | \(-0.574652\pi\) | ||||
−0.232381 | + | 0.972625i | \(0.574652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.09072 | 0.298309 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.0414 | 1.21962 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.57307 | 0.233635 | 0.116818 | − | 0.993153i | \(-0.462731\pi\) | ||||
0.116818 | + | 0.993153i | \(0.462731\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.86690 | 0.371068 | 0.185534 | − | 0.982638i | \(-0.440598\pi\) | ||||
0.185534 | + | 0.982638i | \(0.440598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −38.8441 | −1.62274 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.7487 | 0.489954 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.3329 | −1.30440 | −0.652202 | − | 0.758045i | \(-0.726155\pi\) | ||||
−0.652202 | + | 0.758045i | \(0.726155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.8005 | −1.15535 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −55.4445 | −2.30022 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.86813 | −0.408696 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.44442 | 0.101064 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.2704 | 0.795376 | 0.397688 | − | 0.917521i | \(-0.369813\pi\) | ||||
0.397688 | + | 0.917521i | \(0.369813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.16972 | −0.336627 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.7540 | −1.10051 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.5232 | −1.21237 | −0.606186 | − | 0.795323i | \(-0.707301\pi\) | ||||
−0.606186 | + | 0.795323i | \(0.707301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.2497 | −1.24012 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.3516 | −1.48777 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.5386 | −0.512313 | −0.256157 | − | 0.966635i | \(-0.582456\pi\) | ||||
−0.256157 | + | 0.966635i | \(0.582456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.36819 | 0.218973 | 0.109486 | − | 0.993988i | \(-0.465079\pi\) | ||||
0.109486 | + | 0.993988i | \(0.465079\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.69096 | 0.109584 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.84900 | 0.0751725 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.5693 | 1.93078 | 0.965389 | − | 0.260814i | \(-0.0839910\pi\) | ||||
0.965389 | + | 0.260814i | \(0.0839910\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.17936 | −0.290922 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.2455 | −1.34497 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0498 | 0.486688 | 0.243344 | − | 0.969940i | \(-0.421756\pi\) | ||||
0.243344 | + | 0.969940i | \(0.421756\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.4580 | 1.30883 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.65285 | −0.106800 | −0.0534000 | − | 0.998573i | \(-0.517006\pi\) | ||||
−0.0534000 | + | 0.998573i | \(0.517006\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.1495 | −0.930458 | −0.465229 | − | 0.885190i | \(-0.654028\pi\) | ||||
−0.465229 | + | 0.885190i | \(0.654028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.2273 | −1.61427 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.7519 | −0.951598 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.5938 | −0.583750 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.64714 | −0.0657806 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.1397 | −0.484041 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.9858 | −0.835433 | −0.417717 | − | 0.908577i | \(-0.637170\pi\) | ||||
−0.417717 | + | 0.908577i | \(0.637170\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.75217 | −0.0696424 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.7681 | −0.784474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.6119 | −1.09402 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.13931 | −0.124189 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7666 | 0.938724 | 0.469362 | − | 0.883006i | \(-0.344484\pi\) | ||||
0.469362 | + | 0.883006i | \(0.344484\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.8230 | −0.939486 | −0.469743 | − | 0.882803i | \(-0.655653\pi\) | ||||
−0.469743 | + | 0.882803i | \(0.655653\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.0891 | 0.909130 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.4698 | −1.00132 | −0.500661 | − | 0.865643i | \(-0.666910\pi\) | ||||
−0.500661 | + | 0.865643i | \(0.666910\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.61190 | −0.298793 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 48.5051 | 1.90106 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.5654 | −1.58745 | −0.793724 | − | 0.608278i | \(-0.791861\pi\) | ||||
−0.793724 | + | 0.608278i | \(0.791861\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.0097 | 0.742769 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.34417 | −0.0914549 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.3240 | −1.18126 | −0.590628 | − | 0.806944i | \(-0.701120\pi\) | ||||
−0.590628 | + | 0.806944i | \(0.701120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.02555 | −0.0787847 | −0.0393923 | − | 0.999224i | \(-0.512542\pi\) | ||||
−0.0393923 | + | 0.999224i | \(0.512542\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.4466 | 1.33780 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.66477 | 0.258449 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.98476 | 0.347891 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.34565 | −0.245337 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0950 | −0.505526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.5899 | −1.87300 | −0.936501 | − | 0.350664i | \(-0.885956\pi\) | ||||
−0.936501 | + | 0.350664i | \(0.885956\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.56069 | −0.329501 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.4471 | −0.632115 | −0.316057 | − | 0.948740i | \(-0.602359\pi\) | ||||
−0.316057 | + | 0.948740i | \(0.602359\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 46.4676 | 1.78326 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.27675 | −0.0872454 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.22449 | 0.199910 | 0.0999549 | − | 0.994992i | \(-0.468130\pi\) | ||||
0.0999549 | + | 0.994992i | \(0.468130\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.53167 | 0.364186 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.90296 | 0.301517 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45.4688 | −1.73222 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.93791 | −0.0737217 | −0.0368608 | − | 0.999320i | \(-0.511736\pi\) | ||||
−0.0368608 | + | 0.999320i | \(0.511736\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.03421 | −0.0392865 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.13640 | −0.156903 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −48.3716 | −1.83220 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.1618 | −0.422180 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0143 | −0.680391 | −0.340196 | − | 0.940355i | \(-0.610493\pi\) | ||||
−0.340196 | + | 0.940355i | \(0.610493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.67467 | 0.100877 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.9746 | −0.827612 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.39714 | −0.127763 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.68923 | 0.251219 | 0.125610 | − | 0.992080i | \(-0.459911\pi\) | ||||
0.125610 | + | 0.992080i | \(0.459911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.04697 | 0.151773 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −60.7027 | −2.27333 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.51952 | 0.318612 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.3249 | −1.09516 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.4030 | −1.32031 | −0.660155 | − | 0.751129i | \(-0.729510\pi\) | ||||
−0.660155 | + | 0.751129i | \(0.729510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.9867 | −1.41470 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.8398 | −1.03537 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.91203 | 0.0710109 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.7973 | −1.14221 | −0.571104 | − | 0.820878i | \(-0.693485\pi\) | ||||
−0.571104 | + | 0.820878i | \(0.693485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0647 | 1.07647 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.4092 | −1.27267 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.1274 | 1.85150 | 0.925748 | − | 0.378140i | \(-0.123436\pi\) | ||||
0.925748 | + | 0.378140i | \(0.123436\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.2510 | −0.673197 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.37878 | 0.345472 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.52288 | −0.276734 | −0.138367 | − | 0.990381i | \(-0.544185\pi\) | ||||
−0.138367 | + | 0.990381i | \(0.544185\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.58945 | −0.278805 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.3485 | 1.59030 | 0.795151 | − | 0.606412i | \(-0.207392\pi\) | ||||
0.795151 | + | 0.606412i | \(0.207392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.3391 | −0.928352 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.41337 | −0.161477 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.3945 | 0.927894 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.77361 | 0.283663 | 0.141832 | − | 0.989891i | \(-0.454701\pi\) | ||||
0.141832 | + | 0.989891i | \(0.454701\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −39.0509 | −1.42309 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.4012 | 1.10641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8968 | 0.577779 | 0.288890 | − | 0.957362i | \(-0.406714\pi\) | ||||
0.288890 | + | 0.957362i | \(0.406714\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.2386 | −0.444233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.6717 | 1.07560 | 0.537798 | − | 0.843073i | \(-0.319256\pi\) | ||||
0.537798 | + | 0.843073i | \(0.319256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.7935 | 1.33201 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.40788 | −0.0870569 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.0729 | −1.26641 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.8509 | −0.896145 | −0.448073 | − | 0.893997i | \(-0.647889\pi\) | ||||
−0.448073 | + | 0.893997i | \(0.647889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.02601 | −0.0729651 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5033 | 0.377779 | 0.188890 | − | 0.981998i | \(-0.439511\pi\) | ||||
0.188890 | + | 0.981998i | \(0.439511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.9180 | −0.464029 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.8800 | −0.569692 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.6575 | 0.381843 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.9414 | −0.391515 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.54676 | −0.233962 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.7215 | −1.41772 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.5264 | −0.517809 | −0.258905 | − | 0.965903i | \(-0.583362\pi\) | ||||
−0.258905 | + | 0.965903i | \(0.583362\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.6600 | 0.486309 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.8230 | −0.491489 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −60.3370 | −2.14263 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.0540 | −1.06591 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.5101 | 1.08072 | 0.540361 | − | 0.841433i | \(-0.318288\pi\) | ||||
0.540361 | + | 0.841433i | \(0.318288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.7484 | 1.15856 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.89064 | −0.0668026 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.17013 | −0.288318 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 49.5206 | 1.74537 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.3358 | −1.20868 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.17703 | −0.111698 | −0.0558492 | − | 0.998439i | \(-0.517787\pi\) | ||||
−0.0558492 | + | 0.998439i | \(0.517787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.0867 | −0.599994 | −0.299997 | − | 0.953940i | \(-0.596986\pi\) | ||||
−0.299997 | + | 0.953940i | \(0.596986\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.2830 | 0.465856 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.6734 | −1.10947 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.58121 | 0.265233 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.76528 | −0.166512 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5078 | −0.471425 | −0.235713 | − | 0.971823i | \(-0.575742\pi\) | ||||
−0.235713 | + | 0.971823i | \(0.575742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.83242 | −0.307879 | −0.153939 | − | 0.988080i | \(-0.549196\pi\) | ||||
−0.153939 | + | 0.988080i | \(0.549196\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.60447 | −0.0906761 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.46414 | −0.120460 | −0.0602299 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602299 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.5694 | 1.47850 | 0.739249 | − | 0.673433i | \(-0.235181\pi\) | ||||
0.739249 | + | 0.673433i | \(0.235181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.7342 | 0.511124 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.1991 | 0.942393 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.9057 | 1.20796 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 44.2311 | 1.52885 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.5545 | 0.640573 | 0.320287 | − | 0.947321i | \(-0.396221\pi\) | ||||
0.320287 | + | 0.947321i | \(0.396221\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5378 | −0.949579 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.31335 | 0.320769 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.2179 | 0.523513 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.60453 | −0.123853 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 46.5349 | 1.59707 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.8734 | 0.681250 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.0092 | 0.650863 | 0.325431 | − | 0.945566i | \(-0.394491\pi\) | ||||
0.325431 | + | 0.945566i | \(0.394491\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.530515 | 0.0181432 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.84122 | −0.302010 | −0.151005 | − | 0.988533i | \(-0.548251\pi\) | ||||
−0.151005 | + | 0.988533i | \(0.548251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.6032 | 0.532375 | 0.266188 | − | 0.963921i | \(-0.414236\pi\) | ||||
0.266188 | + | 0.963921i | \(0.414236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −63.2752 | −2.15641 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.2438 | 0.927388 | 0.463694 | − | 0.885995i | \(-0.346524\pi\) | ||||
0.463694 | + | 0.885995i | \(0.346524\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.1161 | 0.615966 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.93020 | −0.201400 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.1049 | 0.478475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.2141 | 1.46425 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.69881 | 0.125186 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 43.8622 | 1.48281 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.09546 | 0.0369910 | 0.0184955 | − | 0.999829i | \(-0.494112\pi\) | ||||
0.0184955 | + | 0.999829i | \(0.494112\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.04571 | −0.203917 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.6772 | 1.06723 | 0.533615 | − | 0.845727i | \(-0.320833\pi\) | ||||
0.533615 | + | 0.845727i | \(0.320833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.3127 | −0.414355 | −0.207178 | − | 0.978303i | \(-0.566428\pi\) | ||||
−0.207178 | + | 0.978303i | \(0.566428\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.1825 | −0.779272 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.3490 | 1.25406 | 0.627029 | − | 0.778996i | \(-0.284271\pi\) | ||||
0.627029 | + | 0.778996i | \(0.284271\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.5370 | 1.29249 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.05692 | 0.269917 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.21528 | −0.241450 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.6565 | 0.590192 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −56.3911 | −1.88285 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.87900 | −0.329483 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7890 | 1.49214 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −45.0110 | −1.49787 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38.6670 | 1.28533 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.3443 | −0.509498 | −0.254749 | − | 0.967007i | \(-0.581993\pi\) | ||||
−0.254749 | + | 0.967007i | \(0.581993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.270412 | −0.00896900 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.4470 | −1.14128 | −0.570641 | − | 0.821200i | \(-0.693305\pi\) | ||||
−0.570641 | + | 0.821200i | \(0.693305\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.3819 | −0.509066 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.8816 | −1.31844 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.0584 | −1.22378 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.1740 | 0.335608 | 0.167804 | − | 0.985820i | \(-0.446332\pi\) | ||||
0.167804 | + | 0.985820i | \(0.446332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.9288 | 0.491920 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −50.4142 | −1.65940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.22921 | 0.139056 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.02373 | −0.0993124 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.8942 | 0.390235 | 0.195117 | − | 0.980780i | \(-0.437491\pi\) | ||||
0.195117 | + | 0.980780i | \(0.437491\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.99263 | −0.196401 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.9096 | −0.848242 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.39215 | −0.274453 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.9975 | −0.816634 | −0.408317 | − | 0.912840i | \(-0.633884\pi\) | ||||
−0.408317 | + | 0.912840i | \(0.633884\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.54650 | 0.246271 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.255522 | 0.00832978 | 0.00416489 | − | 0.999991i | \(-0.498674\pi\) | ||||
0.00416489 | + | 0.999991i | \(0.498674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 79.1871 | 2.57869 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −36.0832 | −1.17379 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.7242 | 1.77830 | 0.889149 | − | 0.457618i | \(-0.151297\pi\) | ||||
0.889149 | + | 0.457618i | \(0.151297\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.6450 | −1.22201 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.85201 | 0.287046 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.40355 | 0.0778587 | 0.0389293 | − | 0.999242i | \(-0.487605\pi\) | ||||
0.0389293 | + | 0.999242i | \(0.487605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.6044 | 1.41100 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.99176 | −0.0643845 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.5815 | −0.600028 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.7443 | 1.15304 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.02140 | 0.0651386 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.2075 | 1.00460 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.0910 | −1.22492 | −0.612462 | − | 0.790500i | \(-0.709821\pi\) | ||||
−0.612462 | + | 0.790500i | \(0.709821\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.47598 | 0.240163 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.2442 | 1.51614 | 0.758069 | − | 0.652175i | \(-0.226143\pi\) | ||||
0.758069 | + | 0.652175i | \(0.226143\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.06370 | 0.258510 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0005 | −0.384323 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.37638 | 0.140013 | 0.0700065 | − | 0.997547i | \(-0.477698\pi\) | ||||
0.0700065 | + | 0.997547i | \(0.477698\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.58945 | −0.210600 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.92875 | 0.0935080 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.8315 | −1.23853 | −0.619266 | − | 0.785181i | \(-0.712570\pi\) | ||||
−0.619266 | + | 0.785181i | \(0.712570\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.0326 | 0.956919 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.8384 | 1.36356 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.3299 | 1.79119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.7975 | 0.533591 | 0.266795 | − | 0.963753i | \(-0.414035\pi\) | ||||
0.266795 | + | 0.963753i | \(0.414035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.3438 | 0.772526 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.8064 | 1.29365 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.1556 | −1.30341 | −0.651706 | − | 0.758471i | \(-0.725946\pi\) | ||||
−0.651706 | + | 0.758471i | \(0.725946\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.4807 | −0.458151 |
(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 | 3344.2.a.x.1.2 | 6 | ||
4.3 | odd | 2 | 836.2.a.d.1.5 | ✓ | 6 | ||
12.11 | even | 2 | 7524.2.a.r.1.3 | 6 | |||
44.43 | even | 2 | 9196.2.a.k.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
836.2.a.d.1.5 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.x.1.2 | 6 | 1.1 | even | 1 | trivial | ||
7524.2.a.r.1.3 | 6 | 12.11 | even | 2 | |||
9196.2.a.k.1.5 | 6 | 44.43 | even | 2 |