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: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 13x^{7} + 32x^{6} + 40x^{5} - 79x^{4} - 39x^{3} + 58x^{2} + 9x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.39711\) 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 | ||||||||
\(5\) | 1.20115 | 0.537171 | 0.268585 | − | 0.963256i | \(-0.413444\pi\) | ||||
0.268585 | + | 0.963256i | \(0.413444\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.61263 | −0.609517 | −0.304759 | − | 0.952430i | \(-0.598576\pi\) | ||||
−0.304759 | + | 0.952430i | \(0.598576\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.338239 | 0.101983 | 0.0509915 | − | 0.998699i | \(-0.483762\pi\) | ||||
0.0509915 | + | 0.998699i | \(0.483762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.11150 | 0.862976 | 0.431488 | − | 0.902119i | \(-0.357989\pi\) | ||||
0.431488 | + | 0.902119i | \(0.357989\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.20115 | −0.310136 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.639136 | −0.155013 | −0.0775066 | − | 0.996992i | \(-0.524696\pi\) | ||||
−0.0775066 | + | 0.996992i | \(0.524696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.596248 | 0.136789 | 0.0683944 | − | 0.997658i | \(-0.478212\pi\) | ||||
0.0683944 | + | 0.997658i | \(0.478212\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.61263 | 0.351905 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.55724 | −0.711447 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.81971 | 1.22486 | 0.612428 | − | 0.790527i | \(-0.290193\pi\) | ||||
0.612428 | + | 0.790527i | \(0.290193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.338239 | −0.0588799 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.93701 | −0.327415 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.39475 | −1.54449 | −0.772243 | − | 0.635327i | \(-0.780865\pi\) | ||||
−0.772243 | + | 0.635327i | \(0.780865\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.11150 | −0.498239 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.25774 | −1.13347 | −0.566734 | − | 0.823901i | \(-0.691793\pi\) | ||||
−0.566734 | + | 0.823901i | \(0.691793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1340 | −1.54543 | −0.772713 | − | 0.634756i | \(-0.781101\pi\) | ||||
−0.772713 | + | 0.634756i | \(0.781101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.20115 | 0.179057 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.35438 | 1.21861 | 0.609306 | − | 0.792935i | \(-0.291448\pi\) | ||||
0.609306 | + | 0.792935i | \(0.291448\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.39942 | −0.628489 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.639136 | 0.0894969 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.58270 | −0.492122 | −0.246061 | − | 0.969254i | \(-0.579136\pi\) | ||||
−0.246061 | + | 0.969254i | \(0.579136\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.406277 | 0.0547823 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.596248 | −0.0789750 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.07731 | −0.921388 | −0.460694 | − | 0.887559i | \(-0.652399\pi\) | ||||
−0.460694 | + | 0.887559i | \(0.652399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.15381 | 0.275767 | 0.137883 | − | 0.990448i | \(-0.455970\pi\) | ||||
0.137883 | + | 0.990448i | \(0.455970\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.61263 | −0.203172 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.73739 | 0.463566 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.3862 | 1.75756 | 0.878780 | − | 0.477227i | \(-0.158358\pi\) | ||||
0.878780 | + | 0.477227i | \(0.158358\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.94972 | 0.350067 | 0.175034 | − | 0.984562i | \(-0.443997\pi\) | ||||
0.175034 | + | 0.984562i | \(0.443997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.80159 | −0.327901 | −0.163951 | − | 0.986469i | \(-0.552424\pi\) | ||||
−0.163951 | + | 0.986469i | \(0.552424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.55724 | 0.410754 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.545455 | −0.0621604 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0498286 | −0.00560616 | −0.00280308 | − | 0.999996i | \(-0.500892\pi\) | ||||
−0.00280308 | + | 0.999996i | \(0.500892\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.56713 | −0.172015 | −0.0860074 | − | 0.996294i | \(-0.527411\pi\) | ||||
−0.0860074 | + | 0.996294i | \(0.527411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.767698 | −0.0832685 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00920 | 0.106975 | 0.0534876 | − | 0.998569i | \(-0.482966\pi\) | ||||
0.0534876 | + | 0.998569i | \(0.482966\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.01771 | −0.525999 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.81971 | −0.707171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.716184 | 0.0734789 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.80229 | 0.690667 | 0.345334 | − | 0.938480i | \(-0.387766\pi\) | ||||
0.345334 | + | 0.938480i | \(0.387766\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.338239 | 0.0339943 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.8893 | −1.78005 | −0.890024 | − | 0.455913i | \(-0.849313\pi\) | ||||
−0.890024 | + | 0.455913i | \(0.849313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.803404 | 0.0791618 | 0.0395809 | − | 0.999216i | \(-0.487398\pi\) | ||||
0.0395809 | + | 0.999216i | \(0.487398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.93701 | 0.189033 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.26733 | 0.605886 | 0.302943 | − | 0.953009i | \(-0.402031\pi\) | ||||
0.302943 | + | 0.953009i | \(0.402031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.86541 | 0.561804 | 0.280902 | − | 0.959736i | \(-0.409366\pi\) | ||||
0.280902 | + | 0.959736i | \(0.409366\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.39475 | 0.891710 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.1926 | 1.71141 | 0.855707 | − | 0.517461i | \(-0.173123\pi\) | ||||
0.855707 | + | 0.517461i | \(0.173123\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.20115 | −0.112008 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.11150 | 0.287659 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.03069 | 0.0944832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8856 | −0.989599 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.25774 | 0.654408 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.2785 | −0.919340 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.35561 | 0.386498 | 0.193249 | − | 0.981150i | \(-0.438097\pi\) | ||||
0.193249 | + | 0.981150i | \(0.438097\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.1340 | 0.892252 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.07738 | 0.705724 | 0.352862 | − | 0.935675i | \(-0.385209\pi\) | ||||
0.352862 | + | 0.935675i | \(0.385209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.961528 | −0.0833751 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.20115 | −0.103379 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.7999 | −1.86249 | −0.931245 | − | 0.364392i | \(-0.881277\pi\) | ||||
−0.931245 | + | 0.364392i | \(0.881277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.45828 | 0.717422 | 0.358711 | − | 0.933449i | \(-0.383216\pi\) | ||||
0.358711 | + | 0.933449i | \(0.383216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.35438 | −0.703566 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.05243 | 0.0880089 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.20115 | 0.0997501 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.39942 | 0.362858 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.71469 | −0.222396 | −0.111198 | − | 0.993798i | \(-0.535469\pi\) | ||||
−0.111198 | + | 0.993798i | \(0.535469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.0192 | −1.22225 | −0.611123 | − | 0.791536i | \(-0.709282\pi\) | ||||
−0.611123 | + | 0.791536i | \(0.709282\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.639136 | −0.0516710 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.19150 | 0.657957 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.5542 | −1.16155 | −0.580775 | − | 0.814064i | \(-0.697251\pi\) | ||||
−0.580775 | + | 0.814064i | \(0.697251\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.58270 | 0.284127 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.61263 | 0.127093 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.681185 | 0.0533545 | 0.0266773 | − | 0.999644i | \(-0.491507\pi\) | ||||
0.0266773 | + | 0.999644i | \(0.491507\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.406277 | −0.0316286 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.6805 | −0.903863 | −0.451931 | − | 0.892053i | \(-0.649265\pi\) | ||||
−0.451931 | + | 0.892053i | \(0.649265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.31854 | −0.255272 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.596248 | 0.0455962 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.91936 | −0.754155 | −0.377077 | − | 0.926182i | \(-0.623071\pi\) | ||||
−0.377077 | + | 0.926182i | \(0.623071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.73651 | 0.433639 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.07731 | 0.531963 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.993143 | 0.0742310 | 0.0371155 | − | 0.999311i | \(-0.488183\pi\) | ||||
0.0371155 | + | 0.999311i | \(0.488183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.2303 | −0.834738 | −0.417369 | − | 0.908737i | \(-0.637048\pi\) | ||||
−0.417369 | + | 0.908737i | \(0.637048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.15381 | −0.159214 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.2845 | −0.829653 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.216181 | −0.0158087 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.61263 | 0.117302 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.98963 | −0.505752 | −0.252876 | − | 0.967499i | \(-0.581376\pi\) | ||||
−0.252876 | + | 0.967499i | \(0.581376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.6537 | 1.70263 | 0.851316 | − | 0.524653i | \(-0.175805\pi\) | ||||
0.851316 | + | 0.524653i | \(0.175805\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.73739 | −0.267640 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.5658 | −0.895279 | −0.447640 | − | 0.894214i | \(-0.647735\pi\) | ||||
−0.447640 | + | 0.894214i | \(0.647735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2327 | −0.938043 | −0.469022 | − | 0.883187i | \(-0.655393\pi\) | ||||
−0.469022 | + | 0.883187i | \(0.655393\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.3862 | −1.01473 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.61263 | −0.113184 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.71764 | −0.608866 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.201675 | 0.0139501 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0732 | 1.17537 | 0.587684 | − | 0.809091i | \(-0.300040\pi\) | ||||
0.587684 | + | 0.809091i | \(0.300040\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.94972 | −0.202111 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.1725 | −0.830158 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.9977 | −0.746570 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.80159 | 0.189314 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.98867 | −0.133773 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.73917 | −0.183428 | −0.0917141 | − | 0.995785i | \(-0.529235\pi\) | ||||
−0.0917141 | + | 0.995785i | \(0.529235\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.55724 | −0.237149 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.3610 | 1.01954 | 0.509772 | − | 0.860309i | \(-0.329730\pi\) | ||||
0.509772 | + | 0.860309i | \(0.329730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.5282 | −0.893966 | −0.446983 | − | 0.894543i | \(-0.647502\pi\) | ||||
−0.446983 | + | 0.894543i | \(0.647502\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.545455 | 0.0358883 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.16344 | 0.141732 | 0.0708660 | − | 0.997486i | \(-0.477424\pi\) | ||||
0.0708660 | + | 0.997486i | \(0.477424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0349 | 0.654603 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.0498286 | 0.00323672 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.642665 | −0.0415705 | −0.0207853 | − | 0.999784i | \(-0.506617\pi\) | ||||
−0.0207853 | + | 0.999784i | \(0.506617\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7133 | −1.26985 | −0.634924 | − | 0.772575i | \(-0.718969\pi\) | ||||
−0.634924 | + | 0.772575i | \(0.718969\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.28437 | −0.337606 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.85523 | 0.118045 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.56713 | 0.0993128 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.4803 | 1.41895 | 0.709473 | − | 0.704732i | \(-0.248933\pi\) | ||||
0.709473 | + | 0.704732i | \(0.248933\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.338239 | −0.0212649 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.767698 | 0.0480751 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.21026 | 0.200250 | 0.100125 | − | 0.994975i | \(-0.468076\pi\) | ||||
0.100125 | + | 0.994975i | \(0.468076\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.1503 | 0.941391 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0263 | 0.679911 | 0.339955 | − | 0.940442i | \(-0.389588\pi\) | ||||
0.339955 | + | 0.940442i | \(0.389588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.30337 | −0.264354 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.00920 | −0.0617621 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.7003 | 1.81086 | 0.905429 | − | 0.424498i | \(-0.139549\pi\) | ||||
0.905429 | + | 0.424498i | \(0.139549\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.89141 | −0.357877 | −0.178939 | − | 0.983860i | \(-0.557266\pi\) | ||||
−0.178939 | + | 0.983860i | \(0.557266\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.01771 | 0.303685 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.20320 | −0.0725556 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.94396 | 0.176886 | 0.0884428 | − | 0.996081i | \(-0.471811\pi\) | ||||
0.0884428 | + | 0.996081i | \(0.471811\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.81971 | 0.408285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.01684 | −0.239625 | −0.119812 | − | 0.992797i | \(-0.538229\pi\) | ||||
−0.119812 | + | 0.992797i | \(0.538229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.45516 | −0.264831 | −0.132416 | − | 0.991194i | \(-0.542273\pi\) | ||||
−0.132416 | + | 0.991194i | \(0.542273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.716184 | −0.0424231 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.7041 | 0.690868 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5915 | −0.975971 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.80229 | −0.398757 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.7830 | −1.27258 | −0.636288 | − | 0.771452i | \(-0.719531\pi\) | ||||
−0.636288 | + | 0.771452i | \(0.719531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.50092 | −0.494943 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.338239 | −0.0196266 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.11150 | −0.179943 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.3425 | 0.941963 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.8893 | 1.02771 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.58705 | 0.148134 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.41091 | −0.537109 | −0.268554 | − | 0.963265i | \(-0.586546\pi\) | ||||
−0.268554 | + | 0.963265i | \(0.586546\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.803404 | −0.0457041 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.3265 | −1.54954 | −0.774770 | − | 0.632243i | \(-0.782135\pi\) | ||||
−0.774770 | + | 0.632243i | \(0.782135\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.68271 | −0.264682 | −0.132341 | − | 0.991204i | \(-0.542249\pi\) | ||||
−0.132341 | + | 0.991204i | \(0.542249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.93701 | −0.109138 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0704 | 0.565608 | 0.282804 | − | 0.959178i | \(-0.408735\pi\) | ||||
0.282804 | + | 0.959178i | \(0.408735\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.338239 | 0.0189378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.26733 | −0.349808 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.381083 | −0.0212041 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.0684 | −0.613962 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.86541 | −0.324358 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.4725 | −0.742765 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1249 | −0.611481 | −0.305741 | − | 0.952115i | \(-0.598904\pi\) | ||||
−0.305741 | + | 0.952115i | \(0.598904\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.39475 | −0.514829 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.2800 | 0.944110 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.15480 | −0.335273 | −0.167637 | − | 0.985849i | \(-0.553614\pi\) | ||||
−0.167637 | + | 0.985849i | \(0.553614\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.1926 | −0.988085 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.30669 | 0.124914 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3831 | 0.992592 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.20115 | 0.0646678 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.9824 | −1.18008 | −0.590039 | − | 0.807375i | \(-0.700888\pi\) | ||||
−0.590039 | + | 0.807375i | \(0.700888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.02475 | −0.161911 | −0.0809557 | − | 0.996718i | \(-0.525797\pi\) | ||||
−0.0809557 | + | 0.996718i | \(0.525797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.11150 | −0.166080 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.90540 | −0.420762 | −0.210381 | − | 0.977619i | \(-0.567470\pi\) | ||||
−0.210381 | + | 0.977619i | \(0.567470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.54306 | 0.188046 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.03069 | −0.0545499 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.1058 | −1.64170 | −0.820850 | − | 0.571143i | \(-0.806500\pi\) | ||||
−0.820850 | + | 0.571143i | \(0.806500\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6445 | −0.981289 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8856 | 0.571346 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.36513 | −0.176139 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.8879 | −1.45574 | −0.727868 | − | 0.685717i | \(-0.759489\pi\) | ||||
−0.727868 | + | 0.685717i | \(0.759489\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.25774 | −0.377823 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.77758 | 0.299957 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.19547 | 0.424345 | 0.212173 | − | 0.977232i | \(-0.431946\pi\) | ||||
0.212173 | + | 0.977232i | \(0.431946\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2785 | 0.530781 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.11150 | 0.160251 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.785868 | −0.0403673 | −0.0201837 | − | 0.999796i | \(-0.506425\pi\) | ||||
−0.0201837 | + | 0.999796i | \(0.506425\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.35561 | −0.223145 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.00046 | 0.0511212 | 0.0255606 | − | 0.999673i | \(-0.491863\pi\) | ||||
0.0255606 | + | 0.999673i | \(0.491863\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.655174 | −0.0333908 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.1340 | −0.515142 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.73378 | 0.0879061 | 0.0439531 | − | 0.999034i | \(-0.486005\pi\) | ||||
0.0439531 | + | 0.999034i | \(0.486005\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.639136 | 0.0323225 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.07738 | −0.407450 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.0598517 | −0.00301147 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.10969 | 0.206259 | 0.103130 | − | 0.994668i | \(-0.467114\pi\) | ||||
0.103130 | + | 0.994668i | \(0.467114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.961528 | 0.0481366 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.7878 | −1.28778 | −0.643890 | − | 0.765118i | \(-0.722680\pi\) | ||||
−0.643890 | + | 0.765118i | \(0.722680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2195 | 1.05702 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.20115 | 0.0596857 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.17767 | −0.157511 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9038 | 0.835837 | 0.417919 | − | 0.908484i | \(-0.362760\pi\) | ||||
0.417919 | + | 0.908484i | \(0.362760\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.7999 | 1.07531 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4131 | 0.561602 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.88236 | −0.0924013 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.45828 | −0.414204 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.4626 | −1.14622 | −0.573111 | − | 0.819478i | \(-0.694264\pi\) | ||||
−0.573111 | + | 0.819478i | \(0.694264\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.82889 | −0.381557 | −0.190778 | − | 0.981633i | \(-0.561101\pi\) | ||||
−0.190778 | + | 0.981633i | \(0.561101\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.35438 | 0.406204 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.27356 | 0.110284 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.47329 | −0.168085 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.05243 | −0.0508120 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.45370 | −0.166359 | −0.0831795 | − | 0.996535i | \(-0.526507\pi\) | ||||
−0.0831795 | + | 0.996535i | \(0.526507\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.84877 | −0.377188 | −0.188594 | − | 0.982055i | \(-0.560393\pi\) | ||||
−0.188594 | + | 0.982055i | \(0.560393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.20115 | −0.0575908 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.596248 | −0.0285224 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.5186 | −1.93385 | −0.966925 | − | 0.255062i | \(-0.917904\pi\) | ||||
−0.966925 | + | 0.255062i | \(0.917904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.39942 | −0.209496 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.7763 | −1.41472 | −0.707358 | − | 0.706856i | \(-0.750113\pi\) | ||||
−0.707358 | + | 0.706856i | \(0.750113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.21220 | 0.0574639 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.71469 | 0.128401 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.0566 | 1.56004 | 0.780018 | − | 0.625757i | \(-0.215210\pi\) | ||||
0.780018 | + | 0.625757i | \(0.215210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.45485 | −0.115595 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.0192 | 0.705664 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.02702 | −0.282551 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.8554 | 0.741682 | 0.370841 | − | 0.928696i | \(-0.379069\pi\) | ||||
0.370841 | + | 0.928696i | \(0.379069\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.639136 | 0.0298323 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.78319 | −0.0830516 | −0.0415258 | − | 0.999137i | \(-0.513222\pi\) | ||||
−0.0415258 | + | 0.999137i | \(0.513222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.3951 | 1.59848 | 0.799238 | − | 0.601015i | \(-0.205237\pi\) | ||||
0.799238 | + | 0.601015i | \(0.205237\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.19150 | −0.379872 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.8508 | −0.826038 | −0.413019 | − | 0.910722i | \(-0.635526\pi\) | ||||
−0.413019 | + | 0.910722i | \(0.635526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.1997 | −1.07126 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.5542 | 0.670622 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.42773 | −0.157607 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.12100 | −0.0973180 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.58270 | −0.164041 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.8933 | −0.680492 | −0.340246 | − | 0.940337i | \(-0.610510\pi\) | ||||
−0.340246 | + | 0.940337i | \(0.610510\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.2318 | −1.33285 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.61263 | −0.0733772 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.17057 | 0.371006 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.3135 | 1.41895 | 0.709476 | − | 0.704730i | \(-0.248932\pi\) | ||||
0.709476 | + | 0.704730i | \(0.248932\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.681185 | −0.0308042 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.662539 | 0.0299000 | 0.0149500 | − | 0.999888i | \(-0.495241\pi\) | ||||
0.0149500 | + | 0.999888i | \(0.495241\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.639136 | −0.0287852 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.406277 | 0.0182608 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.75681 | −0.213372 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.89940 | 0.264093 | 0.132047 | − | 0.991244i | \(-0.457845\pi\) | ||||
0.132047 | + | 0.991244i | \(0.457845\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.6805 | 0.521845 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.24014 | −0.233646 | −0.116823 | − | 0.993153i | \(-0.537271\pi\) | ||||
−0.116823 | + | 0.993153i | \(0.537271\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.4877 | −0.956190 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.31854 | 0.147382 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.61806 | 0.204692 | 0.102346 | − | 0.994749i | \(-0.467365\pi\) | ||||
0.102346 | + | 0.994749i | \(0.467365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.51793 | 0.199862 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.596248 | −0.0263250 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.965010 | 0.0425234 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.82578 | 0.124278 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.91936 | 0.435412 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.4262 | −1.85873 | −0.929363 | − | 0.369168i | \(-0.879643\pi\) | ||||
−0.929363 | + | 0.369168i | \(0.879643\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.74382 | 0.382341 | 0.191170 | − | 0.981557i | \(-0.438772\pi\) | ||||
0.191170 | + | 0.981557i | \(0.438772\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.73651 | −0.250362 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.35872 | −0.189869 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.07731 | −0.307129 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.5825 | −0.978156 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.52801 | 0.325464 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.993143 | −0.0428573 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.48806 | −0.0640952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6159 | −1.01533 | −0.507663 | − | 0.861556i | \(-0.669490\pi\) | ||||
−0.507663 | + | 0.861556i | \(0.669490\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.2303 | 0.481936 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.04524 | 0.301785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.05500 | 0.258893 | 0.129447 | − | 0.991586i | \(-0.458680\pi\) | ||||
0.129447 | + | 0.991586i | \(0.458680\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.15381 | 0.0919222 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.596248 | 0.0254010 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0803552 | 0.00341705 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.2845 | 0.479001 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.7879 | −1.68587 | −0.842935 | − | 0.538016i | \(-0.819174\pi\) | ||||
−0.842935 | + | 0.538016i | \(0.819174\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.5321 | −1.33366 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.216181 | 0.00912716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.8818 | 0.711483 | 0.355741 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355741 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.8520 | 0.919321 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.61263 | −0.0677241 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00577 | −0.209853 | −0.104926 | − | 0.994480i | \(-0.533461\pi\) | ||||
−0.104926 | + | 0.994480i | \(0.533461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.7880 | 1.79062 | 0.895310 | − | 0.445444i | \(-0.146954\pi\) | ||||
0.895310 | + | 0.445444i | \(0.146954\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.98963 | 0.291996 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.55724 | 0.148347 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.5686 | 0.731391 | 0.365696 | − | 0.930734i | \(-0.380831\pi\) | ||||
0.365696 | + | 0.930734i | \(0.380831\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.6537 | −0.983015 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.52720 | 0.104846 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.21181 | −0.0501881 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.73739 | 0.154522 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.9948 | −0.907821 | −0.453910 | − | 0.891047i | \(-0.649971\pi\) | ||||
−0.453910 | + | 0.891047i | \(0.649971\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.06624 | 0.167546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.5658 | 0.516890 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.4911 | −0.841468 | −0.420734 | − | 0.907184i | \(-0.638227\pi\) | ||||
−0.420734 | + | 0.907184i | \(0.638227\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.23801 | 0.0507536 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.2327 | 0.541580 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.4985 | −1.24613 | −0.623067 | − | 0.782169i | \(-0.714113\pi\) | ||||
−0.623067 | + | 0.782169i | \(0.714113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.9470 | 1.34394 | 0.671969 | − | 0.740580i | \(-0.265449\pi\) | ||||
0.671969 | + | 0.740580i | \(0.265449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3862 | 0.585853 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.0752 | −0.531584 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.9288 | 0.646531 | 0.323266 | − | 0.946308i | \(-0.395219\pi\) | ||||
0.323266 | + | 0.946308i | \(0.395219\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.61263 | 0.0653471 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.9947 | 1.05163 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.2801 | 1.66729 | 0.833643 | − | 0.552303i | \(-0.186251\pi\) | ||||
0.833643 | + | 0.552303i | \(0.186251\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.71764 | 0.351529 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0064 | 0.966460 | 0.483230 | − | 0.875493i | \(-0.339464\pi\) | ||||
0.483230 | + | 0.875493i | \(0.339464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.4600 | −1.06352 | −0.531759 | − | 0.846896i | \(-0.678469\pi\) | ||||
−0.531759 | + | 0.846896i | \(0.678469\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.62747 | −0.0652032 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.44012 | 0.217605 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.201675 | −0.00805411 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00452 | 0.239416 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.25857 | −0.129722 | −0.0648609 | − | 0.997894i | \(-0.520660\pi\) | ||||
−0.0648609 | + | 0.997894i | \(0.520660\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.0732 | −0.678599 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.23175 | 0.207615 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.6888 | −0.542371 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.94972 | 0.116689 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.165723 | 0.00654567 | 0.00327283 | − | 0.999995i | \(-0.498958\pi\) | ||||
0.00327283 | + | 0.999995i | \(0.498958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.6352 | −1.20813 | −0.604067 | − | 0.796934i | \(-0.706454\pi\) | ||||
−0.604067 | + | 0.796934i | \(0.706454\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.1725 | 0.479292 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.14154 | −0.202135 | −0.101067 | − | 0.994880i | \(-0.532226\pi\) | ||||
−0.101067 | + | 0.994880i | \(0.532226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.39383 | −0.0939659 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.9977 | 0.431033 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.3580 | 0.718402 | 0.359201 | − | 0.933260i | \(-0.383049\pi\) | ||||
0.359201 | + | 0.933260i | \(0.383049\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.70215 | 0.379094 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.80159 | −0.109300 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.1689 | −1.60371 | −0.801857 | − | 0.597516i | \(-0.796154\pi\) | ||||
−0.801857 | + | 0.597516i | \(0.796154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.4208 | 1.29992 | 0.649958 | − | 0.759970i | \(-0.274786\pi\) | ||||
0.649958 | + | 0.759970i | \(0.274786\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.98867 | 0.0772337 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.15494 | −0.0447867 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.73917 | 0.105902 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.728502 | 0.0281235 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2889 | 1.36029 | 0.680143 | − | 0.733080i | \(-0.261918\pi\) | ||||
0.680143 | + | 0.733080i | \(0.261918\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.55724 | 0.136918 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2575 | −0.624827 | −0.312414 | − | 0.949946i | \(-0.601137\pi\) | ||||
−0.312414 | + | 0.949946i | \(0.601137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9696 | −0.420974 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.3610 | −0.588634 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.3035 | −1.46564 | −0.732821 | − | 0.680421i | \(-0.761797\pi\) | ||||
−0.732821 | + | 0.680421i | \(0.761797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.1850 | −1.00048 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.5282 | 0.516131 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1476 | −0.424690 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.64282 | 0.214663 | 0.107331 | − | 0.994223i | \(-0.465769\pi\) | ||||
0.107331 | + | 0.994223i | \(0.465769\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.545455 | −0.0207201 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.1597 | 0.385378 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.63868 | 0.175702 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.16344 | −0.0818290 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.2253 | 0.537283 | 0.268641 | − | 0.963240i | \(-0.413425\pi\) | ||||
0.268641 | + | 0.963240i | \(0.413425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.60160 | −0.211268 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.0349 | −0.377935 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.8488 | 1.08497 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.2154 | −0.721650 | −0.360825 | − | 0.932633i | \(-0.617505\pi\) | ||||
−0.360825 | + | 0.932633i | \(0.617505\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0498286 | −0.00186872 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.81971 | −0.255400 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.26413 | 0.0472758 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.642665 | 0.0240008 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.53093 | −0.131682 | −0.0658408 | − | 0.997830i | \(-0.520973\pi\) | ||||
−0.0658408 | + | 0.997830i | \(0.520973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.29559 | −0.0482505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.7133 | 0.733147 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.55724 | −0.132112 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.63590 | 0.171936 | 0.0859679 | − | 0.996298i | \(-0.472602\pi\) | ||||
0.0859679 | + | 0.996298i | \(0.472602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.47702 | 0.239561 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.6038 | −1.68442 | −0.842208 | − | 0.539153i | \(-0.818745\pi\) | ||||
−0.842208 | + | 0.539153i | \(0.818745\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.28437 | 0.194917 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.86600 | 0.179241 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.44161 | 0.163387 | 0.0816936 | − | 0.996657i | \(-0.473967\pi\) | ||||
0.0816936 | + | 0.996657i | \(0.473967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.85523 | −0.0681535 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.66431 | −0.0610578 | −0.0305289 | − | 0.999534i | \(-0.509719\pi\) | ||||
−0.0305289 | + | 0.999534i | \(0.509719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.26076 | −0.119465 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.56713 | −0.0573383 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1069 | −0.369298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.9356 | 1.05588 | 0.527938 | − | 0.849283i | \(-0.322965\pi\) | ||||
0.527938 | + | 0.849283i | \(0.322965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.4803 | −0.819229 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.0403 | −0.656555 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0491 | −0.365240 | −0.182620 | − | 0.983184i | \(-0.558458\pi\) | ||||
−0.182620 | + | 0.983184i | \(0.558458\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.338239 | 0.0122773 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.78753 | −0.173548 | −0.0867740 | − | 0.996228i | \(-0.527656\pi\) | ||||
−0.0867740 | + | 0.996228i | \(0.527656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.45873 | −0.342429 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.767698 | −0.0277562 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.0211 | −0.795135 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.8260 | −1.00343 | −0.501715 | − | 0.865033i | \(-0.667297\pi\) | ||||
−0.501715 | + | 0.865033i | \(0.667297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.21026 | −0.115615 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.4542 | 1.41907 | 0.709534 | − | 0.704672i | \(-0.248906\pi\) | ||||
0.709534 | + | 0.704672i | \(0.248906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.2593 | −0.871420 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.1503 | −0.543512 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.32741 | −0.155046 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.997711 | 0.0357009 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.4818 | −0.623951 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.7369 | 1.13130 | 0.565649 | − | 0.824646i | \(-0.308626\pi\) | ||||
0.565649 | + | 0.824646i | \(0.308626\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0263 | −0.392547 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.3379 | −1.04314 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.70158 | 0.237980 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.30337 | 0.152625 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.81985 | 0.0998843 | 0.0499422 | − | 0.998752i | \(-0.484096\pi\) | ||||
0.0499422 | + | 0.998752i | \(0.484096\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.33958 | −0.188901 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00920 | 0.0356584 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.947609 | −0.0334404 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.93701 | 0.0682707 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.7003 | −1.04550 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.1839 | −0.744788 | −0.372394 | − | 0.928075i | \(-0.621463\pi\) | ||||
−0.372394 | + | 0.928075i | \(0.621463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9950 | 0.491432 | 0.245716 | − | 0.969342i | \(-0.420977\pi\) | ||||
0.245716 | + | 0.969342i | \(0.420977\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.89141 | 0.206621 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.818206 | 0.0286605 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.04240 | −0.211397 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.01771 | −0.175333 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.808941 | 0.0282322 | 0.0141161 | − | 0.999900i | \(-0.495507\pi\) | ||||
0.0141161 | + | 0.999900i | \(0.495507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.6231 | 0.579444 | 0.289722 | − | 0.957111i | \(-0.406437\pi\) | ||||
0.289722 | + | 0.957111i | \(0.406437\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.20320 | 0.0418900 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.0968 | −1.60294 | −0.801472 | − | 0.598033i | \(-0.795949\pi\) | ||||
−0.801472 | + | 0.598033i | \(0.795949\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.7905 | −1.17359 | −0.586796 | − | 0.809735i | \(-0.699611\pi\) | ||||
−0.586796 | + | 0.809735i | \(0.699611\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.94396 | −0.102125 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.81183 | 0.0974240 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0300 | −0.485529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.81971 | −0.235724 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.78694 | 0.0616919 | 0.0308460 | − | 0.999524i | \(-0.490180\pi\) | ||||
0.0308460 | + | 0.999524i | \(0.490180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.01684 | 0.138347 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.98607 | −0.137125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.5544 | 0.603178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.45516 | 0.152901 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.39475 | 0.322048 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.6350 | 1.93915 | 0.969573 | − | 0.244802i | \(-0.0787231\pi\) | ||||
0.969573 | + | 0.244802i | \(0.0787231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.716184 | 0.0244930 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.1805 | −0.791830 | −0.395915 | − | 0.918287i | \(-0.629573\pi\) | ||||
−0.395915 | + | 0.918287i | \(0.629573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.7068 | −0.365312 | −0.182656 | − | 0.983177i | \(-0.558469\pi\) | ||||
−0.182656 | + | 0.983177i | \(0.558469\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.7041 | −0.398873 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.3716 | −0.421133 | −0.210567 | − | 0.977580i | \(-0.567531\pi\) | ||||
−0.210567 | + | 0.977580i | \(0.567531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.9146 | −0.405110 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.5915 | 0.563477 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.0168540 | −0.000571733 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.7629 | 1.51673 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.80229 | 0.230222 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.5755 | 0.560353 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.1193 | −1.38850 | −0.694250 | − | 0.719734i | \(-0.744264\pi\) | ||||
−0.694250 | + | 0.719734i | \(0.744264\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.7830 | 0.734722 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.6496 | −1.13368 | −0.566842 | − | 0.823826i | \(-0.691835\pi\) | ||||
−0.566842 | + | 0.823826i | \(0.691835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.7557 | −1.23693 | −0.618463 | − | 0.785814i | \(-0.712244\pi\) | ||||
−0.618463 | + | 0.785814i | \(0.712244\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.50092 | 0.285755 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.9939 | 1.34287 | 0.671433 | − | 0.741066i | \(-0.265679\pi\) | ||||
0.671433 | + | 0.741066i | \(0.265679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.02399 | −0.235577 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.338239 | 0.0113314 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.98129 | 0.166692 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.19291 | 0.0398747 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.11150 | 0.103890 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.81971 | 0.227450 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.28983 | 0.0762854 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.3425 | −0.543843 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.4892 | −0.448397 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.5832 | 0.982294 | 0.491147 | − | 0.871077i | \(-0.336578\pi\) | ||||
0.491147 | + | 0.871077i | \(0.336578\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.8893 | −0.593350 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.07788 | −0.201369 | −0.100685 | − | 0.994918i | \(-0.532103\pi\) | ||||
−0.100685 | + | 0.994918i | \(0.532103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.530065 | −0.0175426 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.58705 | −0.0855251 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.0258 | −0.430151 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.9627 | 0.955392 | 0.477696 | − | 0.878525i | \(-0.341472\pi\) | ||||
0.477696 | + | 0.878525i | \(0.341472\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.41091 | 0.310100 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.17806 | 0.302100 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.4193 | 1.09882 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.803404 | 0.0263873 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.76667 | −0.287625 | −0.143813 | − | 0.989605i | \(-0.545936\pi\) | ||||
−0.143813 | + | 0.989605i | \(0.545936\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.62315 | −0.0859702 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.3265 | 0.894628 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.259666 | −0.00849198 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.90935 | −0.0950442 | −0.0475221 | − | 0.998870i | \(-0.515132\pi\) | ||||
−0.0475221 | + | 0.998870i | \(0.515132\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.68271 | 0.152814 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.4834 | 0.341748 | 0.170874 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170874 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.25774 | 0.236344 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.93701 | 0.0630110 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.4324 | −1.02142 | −0.510708 | − | 0.859754i | \(-0.670617\pi\) | ||||
−0.510708 | + | 0.859754i | \(0.670617\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.71716 | −0.282971 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.0704 | −0.326554 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.1720 | −0.944973 | −0.472487 | − | 0.881338i | \(-0.656643\pi\) | ||||
−0.472487 | + | 0.881338i | \(0.656643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.39560 | −0.271675 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.338239 | −0.0109337 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.1552 | 1.13522 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5084 | 0.500271 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.26733 | 0.201962 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.4117 | 0.914605 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.4493 | 1.46155 | 0.730775 | − | 0.682618i | \(-0.239159\pi\) | ||||
0.730775 | + | 0.682618i | \(0.239159\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.381083 | 0.0122422 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.45579 | −0.110902 | −0.0554508 | − | 0.998461i | \(-0.517660\pi\) | ||||
−0.0554508 | + | 0.998461i | \(0.517660\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.6401 | −0.437281 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.0684 | 0.354471 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.5352 | −0.976907 | −0.488453 | − | 0.872590i | \(-0.662439\pi\) | ||||
−0.488453 | + | 0.872590i | \(0.662439\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.341352 | 0.0109097 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.86541 | 0.187268 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.9381 | −1.36951 | −0.684756 | − | 0.728773i | \(-0.740091\pi\) | ||||
−0.684756 | + | 0.728773i | \(0.740091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.0935 | −0.480918 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.4725 | 0.428836 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.1340 | 0.322243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.0808830 | −0.00256933 | −0.00128467 | − | 0.999999i | \(-0.500409\pi\) | ||||
−0.00128467 | + | 0.999999i | \(0.500409\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.1249 | 0.353039 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.8945 | −0.503890 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0203 | 1.29912 | 0.649562 | − | 0.760308i | \(-0.274952\pi\) | ||||
0.649562 | + | 0.760308i | \(0.274952\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.39475 | 0.297237 |
(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.e.1.7 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.e.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial |