Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} - 137 x^{8} - 121665 x^{7} + 60168 x^{6} + 172218 x^{5} - 138024 x^{4} + \cdots - 208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(2.30095\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.30095 | 1.02902 | 0.514509 | − | 0.857485i | \(-0.327974\pi\) | ||||
0.514509 | + | 0.857485i | \(0.327974\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.14667 | −1.56729 | −0.783646 | − | 0.621208i | \(-0.786642\pi\) | ||||
−0.783646 | + | 0.621208i | \(0.786642\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.07535 | 0.324229 | 0.162115 | − | 0.986772i | \(-0.448169\pi\) | ||||
0.162115 | + | 0.986772i | \(0.448169\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.08498 | 1.96502 | 0.982510 | − | 0.186208i | \(-0.0596200\pi\) | ||||
0.982510 | + | 0.186208i | \(0.0596200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.30095 | −0.594104 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.59628 | 1.59983 | 0.799916 | − | 0.600112i | \(-0.204877\pi\) | ||||
0.799916 | + | 0.600112i | \(0.204877\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.26448 | −1.43717 | −0.718585 | − | 0.695439i | \(-0.755210\pi\) | ||||
−0.718585 | + | 0.695439i | \(0.755210\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.14667 | 0.904877 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.294386 | 0.0588772 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.73160 | −1.02943 | −0.514713 | − | 0.857363i | \(-0.672102\pi\) | ||||
−0.514713 | + | 0.857363i | \(0.672102\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.07535 | −0.187194 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.54128 | −1.61277 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.95867 | 1.63719 | 0.818597 | − | 0.574368i | \(-0.194752\pi\) | ||||
0.818597 | + | 0.574368i | \(0.194752\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.08498 | −1.13451 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.49984 | −1.48363 | −0.741813 | − | 0.670607i | \(-0.766034\pi\) | ||||
−0.741813 | + | 0.670607i | \(0.766034\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2369 | 1.56111 | 0.780556 | − | 0.625086i | \(-0.214936\pi\) | ||||
0.780556 | + | 0.625086i | \(0.214936\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.30095 | 0.343006 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.32540 | 0.922654 | 0.461327 | − | 0.887230i | \(-0.347373\pi\) | ||||
0.461327 | + | 0.887230i | \(0.347373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.1948 | 1.45640 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.59628 | −0.923663 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.2635 | −1.54716 | −0.773582 | − | 0.633696i | \(-0.781537\pi\) | ||||
−0.773582 | + | 0.633696i | \(0.781537\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.47432 | 0.333638 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.26448 | 0.829751 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.4884 | 1.62585 | 0.812924 | − | 0.582369i | \(-0.197874\pi\) | ||||
0.812924 | + | 0.582369i | \(0.197874\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.914556 | 0.117097 | 0.0585484 | − | 0.998285i | \(-0.481353\pi\) | ||||
0.0585484 | + | 0.998285i | \(0.481353\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.14667 | −0.522431 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.3022 | 2.02204 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.117437 | 0.0143472 | 0.00717360 | − | 0.999974i | \(-0.497717\pi\) | ||||
0.00717360 | + | 0.999974i | \(0.497717\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.86395 | 0.695923 | 0.347961 | − | 0.937509i | \(-0.386874\pi\) | ||||
0.347961 | + | 0.937509i | \(0.386874\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6237 | 1.36045 | 0.680224 | − | 0.733004i | \(-0.261883\pi\) | ||||
0.680224 | + | 0.733004i | \(0.261883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.294386 | −0.0339928 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.45910 | −0.508162 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.13043 | −1.02725 | −0.513627 | − | 0.858014i | \(-0.671698\pi\) | ||||
−0.513627 | + | 0.858014i | \(0.671698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.02819 | −0.222622 | −0.111311 | − | 0.993786i | \(-0.535505\pi\) | ||||
−0.111311 | + | 0.993786i | \(0.535505\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.1777 | 1.64626 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.19189 | −0.550340 | −0.275170 | − | 0.961396i | \(-0.588734\pi\) | ||||
−0.275170 | + | 0.961396i | \(0.588734\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29.3791 | −3.07976 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.73160 | 0.594339 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.4143 | −1.47887 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.6087 | 1.17869 | 0.589344 | − | 0.807882i | \(-0.299386\pi\) | ||||
0.589344 | + | 0.807882i | \(0.299386\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.07535 | 0.108076 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5553 | −1.05029 | −0.525146 | − | 0.851012i | \(-0.675989\pi\) | ||||
−0.525146 | + | 0.851012i | \(0.675989\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.940511 | 0.0926713 | 0.0463356 | − | 0.998926i | \(-0.485246\pi\) | ||||
0.0463356 | + | 0.998926i | \(0.485246\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.54128 | 0.931134 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.02555 | −0.195817 | −0.0979087 | − | 0.995195i | \(-0.531215\pi\) | ||||
−0.0979087 | + | 0.995195i | \(0.531215\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5747 | −1.01287 | −0.506437 | − | 0.862277i | \(-0.669038\pi\) | ||||
−0.506437 | + | 0.862277i | \(0.669038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.95867 | −0.945235 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.23699 | 0.210438 | 0.105219 | − | 0.994449i | \(-0.466446\pi\) | ||||
0.105219 | + | 0.994449i | \(0.466446\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.30095 | 0.214565 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.08498 | 0.655007 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.3525 | −2.50740 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.84363 | −0.894875 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.49984 | 0.856572 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8274 | −0.968432 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.23810 | −0.287334 | −0.143667 | − | 0.989626i | \(-0.545890\pi\) | ||||
−0.143667 | + | 0.989626i | \(0.545890\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.2369 | −0.901308 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.86048 | −0.424662 | −0.212331 | − | 0.977198i | \(-0.568106\pi\) | ||||
−0.212331 | + | 0.977198i | \(0.568106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.9767 | 2.25247 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.30095 | −0.198035 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.469986 | −0.0401536 | −0.0200768 | − | 0.999798i | \(-0.506391\pi\) | ||||
−0.0200768 | + | 0.999798i | \(0.506391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.81811 | −0.408667 | −0.204333 | − | 0.978901i | \(-0.565503\pi\) | ||||
−0.204333 | + | 0.978901i | \(0.565503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.32540 | −0.532695 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.61882 | 0.637117 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.30095 | 0.191084 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.1948 | −0.840856 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6908 | 0.875825 | 0.437912 | − | 0.899018i | \(-0.355718\pi\) | ||||
0.437912 | + | 0.899018i | \(0.355718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.84163 | 0.800901 | 0.400450 | − | 0.916319i | \(-0.368854\pi\) | ||||
0.400450 | + | 0.916319i | \(0.368854\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.59628 | 0.533277 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.1881 | −1.05930 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.109545 | 0.00874268 | 0.00437134 | − | 0.999990i | \(-0.498609\pi\) | ||||
0.00437134 | + | 0.999990i | \(0.498609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.2635 | 0.893255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.14667 | −0.326803 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.53117 | −0.198256 | −0.0991282 | − | 0.995075i | \(-0.531605\pi\) | ||||
−0.0991282 | + | 0.995075i | \(0.531605\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.47432 | −0.192626 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.1472 | −1.63642 | −0.818209 | − | 0.574921i | \(-0.805033\pi\) | ||||
−0.818209 | + | 0.574921i | \(0.805033\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.1970 | 2.86131 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.26448 | −0.479057 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.94554 | 0.299974 | 0.149987 | − | 0.988688i | \(-0.452077\pi\) | ||||
0.149987 | + | 0.988688i | \(0.452077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.22072 | −0.0922778 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.4884 | −0.938684 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.7894 | 0.806440 | 0.403220 | − | 0.915103i | \(-0.367891\pi\) | ||||
0.403220 | + | 0.915103i | \(0.367891\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.6702 | 1.09042 | 0.545212 | − | 0.838298i | \(-0.316449\pi\) | ||||
0.545212 | + | 0.838298i | \(0.316449\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.914556 | −0.0676059 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.9144 | 1.68470 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.09329 | 0.518712 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.14667 | 0.301626 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8055 | 0.854217 | 0.427108 | − | 0.904200i | \(-0.359532\pi\) | ||||
0.427108 | + | 0.904200i | \(0.359532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0127 | 0.720729 | 0.360365 | − | 0.932812i | \(-0.382652\pi\) | ||||
0.360365 | + | 0.932812i | \(0.382652\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.3022 | −1.16743 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.11966 | 0.151019 | 0.0755096 | − | 0.997145i | \(-0.475942\pi\) | ||||
0.0755096 | + | 0.997145i | \(0.475942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.88360 | −0.204413 | −0.102206 | − | 0.994763i | \(-0.532590\pi\) | ||||
−0.102206 | + | 0.994763i | \(0.532590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.117437 | −0.00828335 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.14667 | −0.291039 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.8587 | −1.52668 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.73649 | −0.465973 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.61196 | 0.455186 | 0.227593 | − | 0.973756i | \(-0.426914\pi\) | ||||
0.227593 | + | 0.973756i | \(0.426914\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.86395 | −0.401791 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.5546 | 1.60641 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.7670 | 1.61341 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.6237 | −0.785455 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 46.7345 | 3.14370 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5569 | 1.51052 | 0.755262 | − | 0.655423i | \(-0.227509\pi\) | ||||
0.755262 | + | 0.655423i | \(0.227509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.294386 | 0.0196257 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7717 | 0.914062 | 0.457031 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457031 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.5754 | −1.02925 | −0.514624 | − | 0.857416i | \(-0.672069\pi\) | ||||
−0.514624 | + | 0.857416i | \(0.672069\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.45910 | 0.293388 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.8619 | −1.36671 | −0.683356 | − | 0.730086i | \(-0.739480\pi\) | ||||
−0.683356 | + | 0.730086i | \(0.739480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.5544 | 0.949428 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.13043 | 0.593085 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3213 | 0.667630 | 0.333815 | − | 0.942639i | \(-0.391664\pi\) | ||||
0.333815 | + | 0.942639i | \(0.391664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.34079 | 0.344031 | 0.172015 | − | 0.985094i | \(-0.444972\pi\) | ||||
0.172015 | + | 0.985094i | \(0.444972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.4578 | 1.49867 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −44.3837 | −2.82407 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.02819 | 0.128531 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.13104 | −0.386988 | −0.193494 | − | 0.981101i | \(-0.561982\pi\) | ||||
−0.193494 | + | 0.981101i | \(0.561982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.07535 | 0.0676065 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.1777 | −0.950466 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.88476 | −0.616594 | −0.308297 | − | 0.951290i | \(-0.599759\pi\) | ||||
−0.308297 | + | 0.951290i | \(0.599759\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −41.2953 | −2.56596 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5660 | 1.26815 | 0.634077 | − | 0.773270i | \(-0.281380\pi\) | ||||
0.634077 | + | 0.773270i | \(0.281380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.9168 | −1.59206 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.19189 | 0.317739 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.11530 | −0.433827 | −0.216914 | − | 0.976191i | \(-0.569599\pi\) | ||||
−0.216914 | + | 0.976191i | \(0.569599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.8149 | 1.75038 | 0.875189 | − | 0.483781i | \(-0.160737\pi\) | ||||
0.875189 | + | 0.483781i | \(0.160737\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.3791 | 1.77810 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.316567 | 0.0190897 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.38971 | 0.444005 | 0.222002 | − | 0.975046i | \(-0.428741\pi\) | ||||
0.222002 | + | 0.975046i | \(0.428741\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.73160 | −0.343142 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.755545 | −0.0450720 | −0.0225360 | − | 0.999746i | \(-0.507174\pi\) | ||||
−0.0225360 | + | 0.999746i | \(0.507174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.5928 | 1.69967 | 0.849833 | − | 0.527053i | \(-0.176703\pi\) | ||||
0.849833 | + | 0.527053i | \(0.176703\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.4143 | 0.853828 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.3927 | 2.32528 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.5109 | 1.55946 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.6087 | −0.680516 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.4820 | 0.670787 | 0.335393 | − | 0.942078i | \(-0.391131\pi\) | ||||
0.335393 | + | 0.942078i | \(0.391131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.7352 | 1.67303 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.07535 | −0.0623980 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.08498 | 0.409735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.4490 | −2.44672 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.5553 | 0.606386 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.10435 | 0.120495 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.8578 | −0.676762 | −0.338381 | − | 0.941009i | \(-0.609879\pi\) | ||||
−0.338381 | + | 0.941009i | \(0.609879\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.940511 | −0.0535038 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.6246 | 0.999397 | 0.499699 | − | 0.866199i | \(-0.333444\pi\) | ||||
0.499699 | + | 0.866199i | \(0.333444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7639 | −1.06060 | −0.530300 | − | 0.847810i | \(-0.677921\pi\) | ||||
−0.530300 | + | 0.847810i | \(0.677921\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.54128 | −0.537590 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.2215 | 0.854922 | 0.427461 | − | 0.904034i | \(-0.359408\pi\) | ||||
0.427461 | + | 0.904034i | \(0.359408\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.07535 | 0.0602079 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.02555 | 0.113055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −41.3223 | −2.29923 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.08572 | 0.115695 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.5747 | 0.584783 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.2293 | −1.44607 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.49941 | −0.247310 | −0.123655 | − | 0.992325i | \(-0.539462\pi\) | ||||
−0.123655 | + | 0.992325i | \(0.539462\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.95867 | 0.545732 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.270217 | 0.0147635 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.2540 | −1.26672 | −0.633362 | − | 0.773855i | \(-0.718326\pi\) | ||||
−0.633362 | + | 0.773855i | \(0.718326\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.23699 | −0.121496 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.16346 | −0.333770 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2479 | −0.715319 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.30095 | −0.123879 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.7632 | 1.49040 | 0.745202 | − | 0.666839i | \(-0.232353\pi\) | ||||
0.745202 | + | 0.666839i | \(0.232353\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.4824 | −1.20346 | −0.601728 | − | 0.798701i | \(-0.705521\pi\) | ||||
−0.601728 | + | 0.798701i | \(0.705521\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.08498 | −0.378168 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.35029 | 0.337992 | 0.168996 | − | 0.985617i | \(-0.445948\pi\) | ||||
0.168996 | + | 0.985617i | \(0.445948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.4927 | 0.716117 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.3525 | 1.44765 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.3409 | −1.39022 | −0.695110 | − | 0.718903i | \(-0.744644\pi\) | ||||
−0.695110 | + | 0.718903i | \(0.744644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.2437 | 1.06546 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.84363 | 0.516657 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.7455 | 1.39992 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.66726 | 0.504627 | 0.252314 | − | 0.967646i | \(-0.418809\pi\) | ||||
0.252314 | + | 0.967646i | \(0.418809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.49984 | −0.494542 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.7061 | 2.42486 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.3987 | −0.745535 | −0.372768 | − | 0.927925i | \(-0.621591\pi\) | ||||
−0.372768 | + | 0.927925i | \(0.621591\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.8274 | 0.559124 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.08498 | 0.364895 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8818 | 1.48356 | 0.741780 | − | 0.670644i | \(-0.233982\pi\) | ||||
0.741780 | + | 0.670644i | \(0.233982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.23810 | 0.165893 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.2556 | 0.626230 | 0.313115 | − | 0.949715i | \(-0.398627\pi\) | ||||
0.313115 | + | 0.949715i | \(0.398627\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2602 | −0.522908 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.2369 | 0.520371 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.5051 | 1.54667 | 0.773335 | − | 0.633997i | \(-0.218587\pi\) | ||||
0.773335 | + | 0.633997i | \(0.218587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.59628 | 0.333588 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.86048 | 0.245179 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.0087 | −1.05706 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.6015 | 0.983770 | 0.491885 | − | 0.870660i | \(-0.336308\pi\) | ||||
0.491885 | + | 0.870660i | \(0.336308\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.9767 | −1.30046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.8523 | −0.591876 | −0.295938 | − | 0.955207i | \(-0.595632\pi\) | ||||
−0.295938 | + | 0.955207i | \(0.595632\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.6083 | −2.02284 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.30095 | 0.114335 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.7090 | 0.530827 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5742 | 0.522862 | 0.261431 | − | 0.965222i | \(-0.415806\pi\) | ||||
0.261431 | + | 0.965222i | \(0.415806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.469986 | 0.0231827 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −51.7851 | −2.54818 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.66676 | −0.229082 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.81811 | 0.235944 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.5181 | 1.34435 | 0.672174 | − | 0.740394i | \(-0.265361\pi\) | ||||
0.672174 | + | 0.740394i | \(0.265361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.8114 | −1.45292 | −0.726460 | − | 0.687208i | \(-0.758836\pi\) | ||||
−0.726460 | + | 0.687208i | \(0.758836\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.32540 | 0.307551 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.94185 | 0.0941936 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.79236 | −0.183525 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.61882 | −0.367840 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.5427 | 1.42302 | 0.711511 | − | 0.702675i | \(-0.248011\pi\) | ||||
0.711511 | + | 0.702675i | \(0.248011\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.5886 | −0.797198 | −0.398599 | − | 0.917125i | \(-0.630504\pi\) | ||||
−0.398599 | + | 0.917125i | \(0.630504\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.30095 | −0.110322 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.26448 | −0.299671 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.326091 | 0.0155635 | 0.00778174 | − | 0.999970i | \(-0.497523\pi\) | ||||
0.00778174 | + | 0.999970i | \(0.497523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.1948 | 0.485468 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.6424 | −1.55089 | −0.775444 | − | 0.631417i | \(-0.782474\pi\) | ||||
−0.775444 | + | 0.631417i | \(0.782474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.9463 | −0.566309 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.6908 | −0.505658 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.219120 | 0.0103409 | 0.00517045 | − | 0.999987i | \(-0.498354\pi\) | ||||
0.00517045 | + | 0.999987i | \(0.498354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2156 | −0.481035 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.84163 | −0.462400 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −67.5998 | −3.16913 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.6459 | 1.34000 | 0.669999 | − | 0.742362i | \(-0.266295\pi\) | ||||
0.669999 | + | 0.742362i | \(0.266295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.59628 | −0.307888 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.9950 | −1.25728 | −0.628641 | − | 0.777696i | \(-0.716388\pi\) | ||||
−0.628641 | + | 0.777696i | \(0.716388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8655 | 1.66681 | 0.833405 | − | 0.552663i | \(-0.186388\pi\) | ||||
0.833405 | + | 0.552663i | \(0.186388\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.1881 | 0.611586 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.9580 | 0.553350 | 0.276675 | − | 0.960964i | \(-0.410767\pi\) | ||||
0.276675 | + | 0.960964i | \(0.410767\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.486971 | −0.0224862 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.109545 | −0.00504759 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0082 | 0.506158 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.84418 | −0.0846166 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.2635 | −0.515721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.6505 | 1.49184 | 0.745919 | − | 0.666037i | \(-0.232011\pi\) | ||||
0.745919 | + | 0.666037i | \(0.232011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 70.5570 | 3.21712 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.14667 | 0.188680 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.7111 | 1.21289 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.9040 | 1.49102 | 0.745510 | − | 0.666494i | \(-0.232206\pi\) | ||||
0.745510 | + | 0.666494i | \(0.232206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.53117 | 0.114463 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.13387 | −0.141429 | −0.0707147 | − | 0.997497i | \(-0.522528\pi\) | ||||
−0.0707147 | + | 0.997497i | \(0.522528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.59628 | 0.297081 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.47432 | 0.111213 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.3158 | −1.09071 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.37944 | −0.151285 | −0.0756423 | − | 0.997135i | \(-0.524101\pi\) | ||||
−0.0756423 | + | 0.997135i | \(0.524101\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.1472 | 0.944786 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.30322 | 0.236459 | 0.118229 | − | 0.992986i | \(-0.462278\pi\) | ||||
0.118229 | + | 0.992986i | \(0.462278\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.2872 | −1.08077 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.1970 | −1.65198 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.1426 | 1.51334 | 0.756672 | − | 0.653794i | \(-0.226824\pi\) | ||||
0.756672 | + | 0.653794i | \(0.226824\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.1995 | −2.13222 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.26448 | 0.276584 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.16407 | 0.0953604 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.80200 | 0.299152 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.94554 | −0.173190 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.1152 | 1.45080 | 0.725402 | − | 0.688325i | \(-0.241654\pi\) | ||||
0.725402 | + | 0.688325i | \(0.241654\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.226623 | 0.00990954 | 0.00495477 | − | 0.999988i | \(-0.498423\pi\) | ||||
0.00495477 | + | 0.999988i | \(0.498423\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.22072 | 0.0532766 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37.8072 | −1.64691 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.4884 | 0.541950 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −67.3062 | −2.91536 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.66070 | −0.201500 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.7894 | −0.465598 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.9630 | 0.472209 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.87188 | 0.381432 | 0.190716 | − | 0.981645i | \(-0.438919\pi\) | ||||
0.190716 | + | 0.981645i | \(0.438919\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.6702 | −0.629557 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.3319 | −1.04227 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.1436 | 1.11782 | 0.558909 | − | 0.829229i | \(-0.311220\pi\) | ||||
0.558909 | + | 0.829229i | \(0.311220\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.914556 | 0.0390323 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.26448 | −0.266876 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.8608 | 1.61001 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.9144 | −0.972663 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.38317 | −0.312835 | −0.156418 | − | 0.987691i | \(-0.549995\pi\) | ||||
−0.156418 | + | 0.987691i | \(0.549995\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 72.5282 | 3.06762 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.09329 | −0.299479 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.98968 | 0.126000 | 0.0629999 | − | 0.998014i | \(-0.479933\pi\) | ||||
0.0629999 | + | 0.998014i | \(0.479933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.14720 | 0.216545 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.14667 | −0.174144 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.9097 | 1.17004 | 0.585018 | − | 0.811021i | \(-0.301088\pi\) | ||||
0.585018 | + | 0.811021i | \(0.301088\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.5825 | −1.90757 | −0.953783 | − | 0.300495i | \(-0.902848\pi\) | ||||
−0.953783 | + | 0.300495i | \(0.902848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.8055 | −0.493182 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.294386 | 0.0122767 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.987488 | 0.0411097 | 0.0205548 | − | 0.999789i | \(-0.493457\pi\) | ||||
0.0205548 | + | 0.999789i | \(0.493457\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.0127 | −0.416113 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.41021 | 0.348914 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.1122 | −0.501636 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.3022 | 0.674014 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.1055 | −1.77915 | −0.889577 | − | 0.456785i | \(-0.849001\pi\) | ||||
−0.889577 | + | 0.456785i | \(0.849001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.9055 | 1.47946 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.11966 | −0.0871910 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.0276 | 0.658174 | 0.329087 | − | 0.944300i | \(-0.393259\pi\) | ||||
0.329087 | + | 0.944300i | \(0.393259\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −62.9369 | −2.58016 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.88360 | 0.118018 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.8181 | 1.01404 | 0.507021 | − | 0.861934i | \(-0.330747\pi\) | ||||
0.507021 | + | 0.861934i | \(0.330747\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.1161 | −0.535018 | −0.267509 | − | 0.963555i | \(-0.586200\pi\) | ||||
−0.267509 | + | 0.963555i | \(0.586200\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.117437 | 0.00478240 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.6497 | −0.920842 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5553 | 0.550194 | 0.275097 | − | 0.961416i | \(-0.411290\pi\) | ||||
0.275097 | + | 0.961416i | \(0.411290\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.14667 | 0.168031 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44.8153 | 1.81303 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.84990 | 0.195886 | 0.0979428 | − | 0.995192i | \(-0.468774\pi\) | ||||
0.0979428 | + | 0.995192i | \(0.468774\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.8587 | 0.881428 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.4968 | 0.825170 | 0.412585 | − | 0.910919i | \(-0.364626\pi\) | ||||
0.412585 | + | 0.910919i | \(0.364626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0019 | 0.683364 | 0.341682 | − | 0.939816i | \(-0.389003\pi\) | ||||
0.341682 | + | 0.939816i | \(0.389003\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.5290 | 0.862543 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.3853 | −1.05541 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.73649 | 0.269030 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 65.6901 | 2.61924 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4415 | 1.33129 | 0.665643 | − | 0.746270i | \(-0.268157\pi\) | ||||
0.665643 | + | 0.746270i | \(0.268157\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.61196 | −0.262802 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.45071 | −0.295672 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 72.2302 | 2.86187 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.86395 | 0.231974 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.8861 | −1.73339 | −0.866697 | − | 0.498834i | \(-0.833762\pi\) | ||||
−0.866697 | + | 0.498834i | \(0.833762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.4699 | −1.16218 | −0.581090 | − | 0.813839i | \(-0.697374\pi\) | ||||
−0.581090 | + | 0.813839i | \(0.697374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.5546 | −0.927462 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5982 | −0.652544 | −0.326272 | − | 0.945276i | \(-0.605793\pi\) | ||||
−0.326272 | + | 0.945276i | \(0.605793\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.4293 | 0.527148 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.7670 | −0.931504 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −46.7391 | −1.82904 | −0.914520 | − | 0.404540i | \(-0.867432\pi\) | ||||
−0.914520 | + | 0.404540i | \(0.867432\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.1837 | −0.436985 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.6237 | 0.453483 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.2475 | −0.983505 | −0.491752 | − | 0.870735i | \(-0.663643\pi\) | ||||
−0.491752 | + | 0.870735i | \(0.663643\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.9629 | −1.67106 | −0.835531 | − | 0.549444i | \(-0.814840\pi\) | ||||
−0.835531 | + | 0.549444i | \(0.814840\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −46.7345 | −1.81502 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 59.7712 | 2.31783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.5569 | −0.872102 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.983465 | 0.0379662 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.3303 | 1.36188 | 0.680942 | − | 0.732338i | \(-0.261571\pi\) | ||||
0.680942 | + | 0.732338i | \(0.261571\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.294386 | −0.0113309 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.8478 | 1.30088 | 0.650439 | − | 0.759559i | \(-0.274585\pi\) | ||||
0.650439 | + | 0.759559i | \(0.274585\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48.1375 | −1.84735 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.7717 | −0.527734 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.3826 | 0.397278 | 0.198639 | − | 0.980073i | \(-0.436348\pi\) | ||||
0.198639 | + | 0.980073i | \(0.436348\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.08142 | −0.0413188 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.5754 | 0.594237 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −79.8019 | −3.04021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.9223 | −1.21438 | −0.607190 | − | 0.794557i | \(-0.707703\pi\) | ||||
−0.607190 | + | 0.794557i | \(0.707703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.45910 | −0.169387 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.0862 | −0.420525 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −62.6636 | −2.37355 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.8619 | 0.789071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.8227 | −0.786462 | −0.393231 | − | 0.919440i | \(-0.628643\pi\) | ||||
−0.393231 | + | 0.919440i | \(0.628643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −62.3859 | −2.35293 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.5544 | −0.548152 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43.7693 | 1.64611 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.8372 | 1.30834 | 0.654168 | − | 0.756349i | \(-0.273019\pi\) | ||||
0.654168 | + | 0.756349i | \(0.273019\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.13043 | −0.342418 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.73160 | −0.214650 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.5305 | 0.655605 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.3213 | −0.385456 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.81381 | −0.216819 | −0.108409 | − | 0.994106i | \(-0.534576\pi\) | ||||
−0.108409 | + | 0.994106i | \(0.534576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.89998 | −0.145243 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.34079 | −0.198626 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.294386 | 0.0109332 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4648 | −0.388117 | −0.194059 | − | 0.980990i | \(-0.562165\pi\) | ||||
−0.194059 | + | 0.980990i | \(0.562165\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 67.5254 | 2.49752 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.7216 | −1.87345 | −0.936723 | − | 0.350071i | \(-0.886157\pi\) | ||||
−0.936723 | + | 0.350071i | \(0.886157\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −23.4578 | −0.865255 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.126285 | 0.00465178 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.0674 | −1.25319 | −0.626594 | − | 0.779346i | \(-0.715552\pi\) | ||||
−0.626594 | + | 0.779346i | \(0.715552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 44.3837 | 1.63048 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.4315 | −0.456067 | −0.228034 | − | 0.973653i | \(-0.573230\pi\) | ||||
−0.228034 | + | 0.973653i | \(0.573230\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.5990 | 0.901239 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.02819 | −0.0742075 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.39928 | 0.306903 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.2789 | 0.521045 | 0.260522 | − | 0.965468i | \(-0.416105\pi\) | ||||
0.260522 | + | 0.965468i | \(0.416105\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.13104 | 0.223428 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.6451 | 0.824141 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.57983 | −0.166457 | −0.0832284 | − | 0.996531i | \(-0.526523\pi\) | ||||
−0.0832284 | + | 0.996531i | \(0.526523\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.07535 | −0.0390326 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.9792 | −0.434246 | −0.217123 | − | 0.976144i | \(-0.569667\pi\) | ||||
−0.217123 | + | 0.976144i | \(0.569667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.8498 | 1.58747 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.1777 | 0.548752 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 88.4800 | 3.19483 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.1733 | −1.26838 | −0.634191 | − | 0.773177i | \(-0.718667\pi\) | ||||
−0.634191 | + | 0.773177i | \(0.718667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.88476 | 0.355991 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.45121 | 0.232034 | 0.116017 | − | 0.993247i | \(-0.462987\pi\) | ||||
0.116017 | + | 0.993247i | \(0.462987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.68730 | −0.0606097 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 41.2953 | 1.48146 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59.5116 | 2.13222 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.30578 | 0.225639 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.252059 | 0.00899637 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.6976 | −0.773436 | −0.386718 | − | 0.922198i | \(-0.626391\pi\) | ||||
−0.386718 | + | 0.922198i | \(0.626391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.5660 | −0.732169 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.27604 | −0.329818 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.47961 | 0.230098 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.9168 | 0.919175 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.2348 | −0.964708 | −0.482354 | − | 0.875976i | \(-0.660218\pi\) | ||||
−0.482354 | + | 0.875976i | \(0.660218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.7241 | 1.47609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.19189 | −0.183447 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.4995 | 0.441097 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.54128 | −0.336286 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.11530 | 0.250470 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.7793 | 1.85562 | 0.927811 | − | 0.373049i | \(-0.121688\pi\) | ||||
0.927811 | + | 0.373049i | \(0.121688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.3021 | 1.02893 | 0.514467 | − | 0.857510i | \(-0.327990\pi\) | ||||
0.514467 | + | 0.857510i | \(0.327990\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.8149 | −1.01058 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.82410 | −0.204009 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −64.1288 | −2.24358 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.3791 | −1.02659 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7232 | 0.932645 | 0.466323 | − | 0.884615i | \(-0.345579\pi\) | ||||
0.466323 | + | 0.884615i | \(0.345579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5153 | −0.436257 | −0.218129 | − | 0.975920i | \(-0.569995\pi\) | ||||
−0.218129 | + | 0.975920i | \(0.569995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.316567 | −0.0110215 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.8437 | 0.481394 | 0.240697 | − | 0.970600i | \(-0.422624\pi\) | ||||
0.240697 | + | 0.970600i | \(0.422624\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.9325 | −1.38691 | −0.693456 | − | 0.720499i | \(-0.743913\pi\) | ||||
−0.693456 | + | 0.720499i | \(0.743913\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.38971 | −0.256346 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 67.2479 | 2.33000 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.6587 | −1.68390 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.73160 | 0.198113 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.1482 | −1.48964 | −0.744821 | − | 0.667264i | \(-0.767465\pi\) | ||||
−0.744821 | + | 0.667264i | \(0.767465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.755545 | 0.0260224 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 85.5885 | 2.94433 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.8182 | 1.40253 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.5928 | −0.981302 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.95867 | 0.341379 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.5150 | 1.38721 | 0.693604 | − | 0.720357i | \(-0.256022\pi\) | ||||
0.693604 | + | 0.720357i | \(0.256022\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.4143 | −0.492958 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.5208 | 1.82823 | 0.914117 | − | 0.405450i | \(-0.132885\pi\) | ||||
0.914117 | + | 0.405450i | \(0.132885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.4144 | 1.31068 | 0.655341 | − | 0.755334i | \(-0.272525\pi\) | ||||
0.655341 | + | 0.755334i | \(0.272525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.3927 | −1.34250 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.9820 | −1.32696 | −0.663481 | − | 0.748193i | \(-0.730922\pi\) | ||||
−0.663481 | + | 0.748193i | \(0.730922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.07850 | 0.308678 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.5109 | −0.900356 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.81838 | −0.333066 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.832038 | 0.0281925 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.6087 | 0.392896 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 44.8976 | 1.51782 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.2074 | 1.02003 | 0.510015 | − | 0.860166i | \(-0.329640\pi\) | ||||
0.510015 | + | 0.860166i | \(0.329640\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.4820 | −0.387279 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.5901 | 0.525245 | 0.262622 | − | 0.964899i | \(-0.415413\pi\) | ||||
0.262622 | + | 0.964899i | \(0.415413\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.09079 | −0.137666 | −0.0688330 | − | 0.997628i | \(-0.521928\pi\) | ||||
−0.0688330 | + | 0.997628i | \(0.521928\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.7352 | −0.965923 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.8859 | 0.667702 | 0.333851 | − | 0.942626i | \(-0.391652\pi\) | ||||
0.333851 | + | 0.942626i | \(0.391652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.4273 | 0.450337 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.07535 | 0.0360255 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.6254 | −1.32601 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.8260 | 0.829841 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.08498 | −0.236561 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.73160 | −0.191160 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74.2973 | −2.47520 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42.4490 | 1.41261 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.7553 | 1.12207 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.6632 | −1.15097 | −0.575486 | − | 0.817811i | \(-0.695187\pi\) | ||||
−0.575486 | + | 0.817811i | \(0.695187\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.5553 | −0.350097 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.37318 | −0.310547 | −0.155274 | − | 0.987871i | \(-0.549626\pi\) | ||||
−0.155274 | + | 0.987871i | \(0.549626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.18100 | −0.0721807 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.10435 | −0.0695677 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.1548 | 0.665570 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.8751 | −1.87614 | −0.938068 | − | 0.346450i | \(-0.887387\pi\) | ||||
−0.938068 | + | 0.346450i | \(0.887387\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.8578 | 0.390729 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.5460 | 1.36750 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.93169 | 0.0963934 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.940511 | 0.0308904 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.2034 | −0.367571 | −0.183785 | − | 0.982966i | \(-0.558835\pi\) | ||||
−0.183785 | + | 0.982966i | \(0.558835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −63.8654 | −2.09310 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.6246 | −0.577002 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.3213 | 0.533764 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.59354 | 0.182733 | 0.0913665 | − | 0.995817i | \(-0.470877\pi\) | ||||
0.0913665 | + | 0.995817i | \(0.470877\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.7639 | 0.612337 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.5483 | 1.74562 | 0.872812 | − | 0.488056i | \(-0.162294\pi\) | ||||
0.872812 | + | 0.488056i | \(0.162294\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.49984 | −0.309357 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.54128 | 0.310378 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.5448 | 1.44751 | 0.723756 | − | 0.690056i | \(-0.242414\pi\) | ||||
0.723756 | + | 0.690056i | \(0.242414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 82.3535 | 2.67331 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.2215 | −0.493589 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.7799 | 0.770307 | 0.385154 | − | 0.922852i | \(-0.374148\pi\) | ||||
0.385154 | + | 0.922852i | \(0.374148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.1639 | 0.879004 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.07535 | −0.0347610 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.94888 | 0.0629325 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.85126 | 0.0597181 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.02555 | −0.0652725 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.0387 | 0.741643 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.5573 | −1.69013 | −0.845064 | − | 0.534665i | \(-0.820438\pi\) | ||||
−0.845064 | + | 0.534665i | \(0.820438\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.3223 | 1.32746 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.1202 | 1.41588 | 0.707942 | − | 0.706270i | \(-0.249624\pi\) | ||||
0.707942 | + | 0.706270i | \(0.249624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.9791 | 0.640500 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.08572 | −0.0667965 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 58.0608 | 1.85753 | 0.928765 | − | 0.370670i | \(-0.120872\pi\) | ||||
0.928765 | + | 0.370670i | \(0.120872\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.58309 | −0.178436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.5747 | −0.337625 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.12163 | −0.0995645 | −0.0497823 | − | 0.998760i | \(-0.515853\pi\) | ||||
−0.0497823 | + | 0.998760i | \(0.515853\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.87723 | 0.155401 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.2293 | 0.834888 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.2369 | 0.325514 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.6463 | −0.624085 | −0.312043 | − | 0.950068i | \(-0.601013\pi\) | ||||
−0.312043 | + | 0.950068i | \(0.601013\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.49941 | 0.142785 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.63503 | −0.210344 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.23323 | 0.102397 | 0.0511987 | − | 0.998688i | \(-0.483696\pi\) | ||||
0.0511987 | + | 0.998688i | \(0.483696\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.95867 | −0.315078 |
(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 | 8004.2.a.i.1.12 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.i.1.12 | ✓ | 16 | 1.1 | even | 1 | trivial |