Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.41421 | 0.577350 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.41421 | 1.02942 | 0.514712 | − | 0.857363i | \(-0.327899\pi\) | ||||
0.514712 | + | 0.857363i | \(0.327899\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58579 | −0.439818 | −0.219909 | − | 0.975520i | \(-0.570576\pi\) | ||||
−0.219909 | + | 0.975520i | \(0.570576\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −6.24264 | −1.51406 | −0.757031 | − | 0.653379i | \(-0.773351\pi\) | ||||
−0.757031 | + | 0.653379i | \(0.773351\pi\) | |||||||
\(18\) | −1.41421 | −0.333333 | ||||||||
\(19\) | 6.65685 | 1.52719 | 0.763594 | − | 0.645697i | \(-0.223433\pi\) | ||||
0.763594 | + | 0.645697i | \(0.223433\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.82843 | −1.02942 | ||||||||
\(23\) | 6.24264 | 1.30168 | 0.650840 | − | 0.759215i | \(-0.274417\pi\) | ||||
0.650840 | + | 0.759215i | \(0.274417\pi\) | |||||||
\(24\) | −2.82843 | −0.577350 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.24264 | 0.439818 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.242641 | −0.0450572 | −0.0225286 | − | 0.999746i | \(-0.507172\pi\) | ||||
−0.0225286 | + | 0.999746i | \(0.507172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.171573 | 0.0308154 | 0.0154077 | − | 0.999881i | \(-0.495095\pi\) | ||||
0.0154077 | + | 0.999881i | \(0.495095\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.41421 | −0.594338 | ||||||||
\(34\) | 8.82843 | 1.51406 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.58579 | 0.918298 | 0.459149 | − | 0.888359i | \(-0.348154\pi\) | ||||
0.459149 | + | 0.888359i | \(0.348154\pi\) | |||||||
\(38\) | −9.41421 | −1.52719 | ||||||||
\(39\) | 1.58579 | 0.253929 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.24264 | −0.350242 | −0.175121 | − | 0.984547i | \(-0.556032\pi\) | ||||
−0.175121 | + | 0.984547i | \(0.556032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4142 | 1.58815 | 0.794076 | − | 0.607818i | \(-0.207955\pi\) | ||||
0.794076 | + | 0.607818i | \(0.207955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.82843 | −1.30168 | ||||||||
\(47\) | 9.31371 | 1.35854 | 0.679272 | − | 0.733887i | \(-0.262296\pi\) | ||||
0.679272 | + | 0.733887i | \(0.262296\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.24264 | 0.874145 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.17157 | −0.160928 | −0.0804640 | − | 0.996758i | \(-0.525640\pi\) | ||||
−0.0804640 | + | 0.996758i | \(0.525640\pi\) | |||||||
\(54\) | 1.41421 | 0.192450 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.65685 | −0.881722 | ||||||||
\(58\) | 0.343146 | 0.0450572 | ||||||||
\(59\) | −1.41421 | −0.184115 | −0.0920575 | − | 0.995754i | \(-0.529344\pi\) | ||||
−0.0920575 | + | 0.995754i | \(0.529344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4853 | −1.59858 | −0.799288 | − | 0.600948i | \(-0.794790\pi\) | ||||
−0.799288 | + | 0.600948i | \(0.794790\pi\) | |||||||
\(62\) | −0.242641 | −0.0308154 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.82843 | 0.594338 | ||||||||
\(67\) | −11.7279 | −1.43279 | −0.716397 | − | 0.697693i | \(-0.754210\pi\) | ||||
−0.716397 | + | 0.697693i | \(0.754210\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.24264 | −0.751526 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.41421 | −0.405193 | −0.202596 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202596 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(72\) | 2.82843 | 0.333333 | ||||||||
\(73\) | 2.07107 | 0.242400 | 0.121200 | − | 0.992628i | \(-0.461326\pi\) | ||||
0.121200 | + | 0.992628i | \(0.461326\pi\) | |||||||
\(74\) | −7.89949 | −0.918298 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.24264 | −0.253929 | ||||||||
\(79\) | −4.65685 | −0.523937 | −0.261969 | − | 0.965076i | \(-0.584372\pi\) | ||||
−0.261969 | + | 0.965076i | \(0.584372\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.17157 | 0.350242 | ||||||||
\(83\) | 5.41421 | 0.594287 | 0.297144 | − | 0.954833i | \(-0.403966\pi\) | ||||
0.297144 | + | 0.954833i | \(0.403966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.7279 | −1.58815 | ||||||||
\(87\) | 0.242641 | 0.0260138 | ||||||||
\(88\) | 9.65685 | 1.02942 | ||||||||
\(89\) | 3.75736 | 0.398279 | 0.199140 | − | 0.979971i | \(-0.436185\pi\) | ||||
0.199140 | + | 0.979971i | \(0.436185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.171573 | −0.0177913 | ||||||||
\(94\) | −13.1716 | −1.35854 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8284 | −1.09946 | −0.549730 | − | 0.835342i | \(-0.685269\pi\) | ||||
−0.549730 | + | 0.835342i | \(0.685269\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.41421 | 0.343141 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.24264 | 0.621166 | 0.310583 | − | 0.950546i | \(-0.399476\pi\) | ||||
0.310583 | + | 0.950546i | \(0.399476\pi\) | |||||||
\(102\) | −8.82843 | −0.874145 | ||||||||
\(103\) | −1.24264 | −0.122441 | −0.0612205 | − | 0.998124i | \(-0.519499\pi\) | ||||
−0.0612205 | + | 0.998124i | \(0.519499\pi\) | |||||||
\(104\) | −4.48528 | −0.439818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.65685 | 0.160928 | ||||||||
\(107\) | −15.4142 | −1.49015 | −0.745074 | − | 0.666982i | \(-0.767586\pi\) | ||||
−0.745074 | + | 0.666982i | \(0.767586\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4853 | −1.29166 | −0.645828 | − | 0.763483i | \(-0.723488\pi\) | ||||
−0.645828 | + | 0.763483i | \(0.723488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.58579 | −0.530179 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.34315 | 0.408569 | 0.204284 | − | 0.978912i | \(-0.434513\pi\) | ||||
0.204284 | + | 0.978912i | \(0.434513\pi\) | |||||||
\(114\) | 9.41421 | 0.881722 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.58579 | −0.146606 | ||||||||
\(118\) | 2.00000 | 0.184115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.656854 | 0.0597140 | ||||||||
\(122\) | 17.6569 | 1.59858 | ||||||||
\(123\) | 2.24264 | 0.202212 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0711 | 1.60355 | 0.801774 | − | 0.597627i | \(-0.203890\pi\) | ||||
0.801774 | + | 0.597627i | \(0.203890\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | −10.4142 | −0.916920 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4853 | 0.916103 | 0.458052 | − | 0.888926i | \(-0.348547\pi\) | ||||
0.458052 | + | 0.888926i | \(0.348547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.5858 | 1.43279 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.6569 | −1.51406 | ||||||||
\(137\) | 2.92893 | 0.250236 | 0.125118 | − | 0.992142i | \(-0.460069\pi\) | ||||
0.125118 | + | 0.992142i | \(0.460069\pi\) | |||||||
\(138\) | 8.82843 | 0.751526 | ||||||||
\(139\) | −11.4853 | −0.974169 | −0.487084 | − | 0.873355i | \(-0.661940\pi\) | ||||
−0.487084 | + | 0.873355i | \(0.661940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.31371 | −0.784356 | ||||||||
\(142\) | 4.82843 | 0.405193 | ||||||||
\(143\) | −5.41421 | −0.452759 | ||||||||
\(144\) | −4.00000 | −0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.92893 | −0.242400 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6569 | 1.44651 | 0.723253 | − | 0.690583i | \(-0.242646\pi\) | ||||
0.723253 | + | 0.690583i | \(0.242646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.48528 | −0.527765 | −0.263882 | − | 0.964555i | \(-0.585003\pi\) | ||||
−0.263882 | + | 0.964555i | \(0.585003\pi\) | |||||||
\(152\) | 18.8284 | 1.52719 | ||||||||
\(153\) | −6.24264 | −0.504688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.1421 | −1.28828 | −0.644141 | − | 0.764906i | \(-0.722785\pi\) | ||||
−0.644141 | + | 0.764906i | \(0.722785\pi\) | |||||||
\(158\) | 6.58579 | 0.523937 | ||||||||
\(159\) | 1.17157 | 0.0929118 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.41421 | −0.111111 | ||||||||
\(163\) | 19.3137 | 1.51277 | 0.756383 | − | 0.654129i | \(-0.226965\pi\) | ||||
0.756383 | + | 0.654129i | \(0.226965\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.65685 | −0.594287 | ||||||||
\(167\) | 11.7574 | 0.909812 | 0.454906 | − | 0.890540i | \(-0.349673\pi\) | ||||
0.454906 | + | 0.890540i | \(0.349673\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4853 | −0.806560 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.65685 | 0.509062 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.82843 | −0.215041 | −0.107521 | − | 0.994203i | \(-0.534291\pi\) | ||||
−0.107521 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(174\) | −0.343146 | −0.0260138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.6569 | −1.02942 | ||||||||
\(177\) | 1.41421 | 0.106299 | ||||||||
\(178\) | −5.31371 | −0.398279 | ||||||||
\(179\) | 19.6569 | 1.46922 | 0.734611 | − | 0.678488i | \(-0.237365\pi\) | ||||
0.734611 | + | 0.678488i | \(0.237365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.656854 | −0.0488236 | −0.0244118 | − | 0.999702i | \(-0.507771\pi\) | ||||
−0.0244118 | + | 0.999702i | \(0.507771\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4853 | 0.922939 | ||||||||
\(184\) | 17.6569 | 1.30168 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.242641 | 0.0177913 | ||||||||
\(187\) | −21.3137 | −1.55861 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9706 | 1.37266 | 0.686331 | − | 0.727289i | \(-0.259220\pi\) | ||||
0.686331 | + | 0.727289i | \(0.259220\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | 6.75736 | 0.486405 | 0.243203 | − | 0.969975i | \(-0.421802\pi\) | ||||
0.243203 | + | 0.969975i | \(0.421802\pi\) | |||||||
\(194\) | 15.3137 | 1.09946 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.55635 | −0.395873 | −0.197937 | − | 0.980215i | \(-0.563424\pi\) | ||||
−0.197937 | + | 0.980215i | \(0.563424\pi\) | |||||||
\(198\) | −4.82843 | −0.343141 | ||||||||
\(199\) | −5.51472 | −0.390928 | −0.195464 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195464 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.7279 | 0.827224 | ||||||||
\(202\) | −8.82843 | −0.621166 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.75736 | 0.122441 | ||||||||
\(207\) | 6.24264 | 0.433894 | ||||||||
\(208\) | 6.34315 | 0.439818 | ||||||||
\(209\) | 22.7279 | 1.57212 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.142136 | 0.00978502 | 0.00489251 | − | 0.999988i | \(-0.498443\pi\) | ||||
0.00489251 | + | 0.999988i | \(0.498443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.41421 | 0.233938 | ||||||||
\(214\) | 21.7990 | 1.49015 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.82843 | −0.192450 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 19.0711 | 1.29166 | ||||||||
\(219\) | −2.07107 | −0.139950 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.89949 | 0.665912 | ||||||||
\(222\) | 7.89949 | 0.530179 | ||||||||
\(223\) | 17.1716 | 1.14989 | 0.574947 | − | 0.818191i | \(-0.305023\pi\) | ||||
0.574947 | + | 0.818191i | \(0.305023\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.14214 | −0.408569 | ||||||||
\(227\) | 23.0711 | 1.53128 | 0.765640 | − | 0.643269i | \(-0.222422\pi\) | ||||
0.765640 | + | 0.643269i | \(0.222422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.3137 | 0.945876 | 0.472938 | − | 0.881096i | \(-0.343193\pi\) | ||||
0.472938 | + | 0.881096i | \(0.343193\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.686292 | −0.0450572 | ||||||||
\(233\) | 22.4853 | 1.47306 | 0.736530 | − | 0.676405i | \(-0.236463\pi\) | ||||
0.736530 | + | 0.676405i | \(0.236463\pi\) | |||||||
\(234\) | 2.24264 | 0.146606 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.65685 | 0.302495 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.3137 | 1.11993 | 0.559965 | − | 0.828516i | \(-0.310814\pi\) | ||||
0.559965 | + | 0.828516i | \(0.310814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3431 | 0.666261 | 0.333130 | − | 0.942881i | \(-0.391895\pi\) | ||||
0.333130 | + | 0.942881i | \(0.391895\pi\) | |||||||
\(242\) | −0.928932 | −0.0597140 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.17157 | −0.202212 | ||||||||
\(247\) | −10.5563 | −0.671684 | ||||||||
\(248\) | 0.485281 | 0.0308154 | ||||||||
\(249\) | −5.41421 | −0.343112 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.41421 | 0.341742 | 0.170871 | − | 0.985293i | \(-0.445342\pi\) | ||||
0.170871 | + | 0.985293i | \(0.445342\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.3137 | 1.33998 | ||||||||
\(254\) | −25.5563 | −1.60355 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.8995 | −1.86508 | −0.932540 | − | 0.361068i | \(-0.882412\pi\) | ||||
−0.932540 | + | 0.361068i | \(0.882412\pi\) | |||||||
\(258\) | 14.7279 | 0.916920 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.242641 | −0.0150191 | ||||||||
\(262\) | −14.8284 | −0.916103 | ||||||||
\(263\) | −1.17157 | −0.0722423 | −0.0361211 | − | 0.999347i | \(-0.511500\pi\) | ||||
−0.0361211 | + | 0.999347i | \(0.511500\pi\) | |||||||
\(264\) | −9.65685 | −0.594338 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.75736 | −0.229947 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.14214 | −0.496435 | −0.248217 | − | 0.968704i | \(-0.579845\pi\) | ||||
−0.248217 | + | 0.968704i | \(0.579845\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.1421 | −1.22355 | −0.611774 | − | 0.791033i | \(-0.709544\pi\) | ||||
−0.611774 | + | 0.791033i | \(0.709544\pi\) | |||||||
\(272\) | 24.9706 | 1.51406 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.14214 | −0.250236 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3848 | 1.40506 | 0.702528 | − | 0.711657i | \(-0.252055\pi\) | ||||
0.702528 | + | 0.711657i | \(0.252055\pi\) | |||||||
\(278\) | 16.2426 | 0.974169 | ||||||||
\(279\) | 0.171573 | 0.0102718 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.65685 | 0.576080 | 0.288040 | − | 0.957618i | \(-0.406996\pi\) | ||||
0.288040 | + | 0.957618i | \(0.406996\pi\) | |||||||
\(282\) | 13.1716 | 0.784356 | ||||||||
\(283\) | −13.2426 | −0.787193 | −0.393597 | − | 0.919283i | \(-0.628769\pi\) | ||||
−0.393597 | + | 0.919283i | \(0.628769\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.65685 | 0.452759 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.9706 | 1.29239 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8284 | 0.634774 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3137 | −0.894636 | −0.447318 | − | 0.894375i | \(-0.647621\pi\) | ||||
−0.447318 | + | 0.894375i | \(0.647621\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.7990 | 0.918298 | ||||||||
\(297\) | −3.41421 | −0.198113 | ||||||||
\(298\) | −24.9706 | −1.44651 | ||||||||
\(299\) | −9.89949 | −0.572503 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.17157 | 0.527765 | ||||||||
\(303\) | −6.24264 | −0.358630 | ||||||||
\(304\) | −26.6274 | −1.52719 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.82843 | 0.504688 | ||||||||
\(307\) | 1.58579 | 0.0905056 | 0.0452528 | − | 0.998976i | \(-0.485591\pi\) | ||||
0.0452528 | + | 0.998976i | \(0.485591\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.24264 | 0.0706914 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.0711 | 0.968011 | 0.484006 | − | 0.875065i | \(-0.339181\pi\) | ||||
0.484006 | + | 0.875065i | \(0.339181\pi\) | |||||||
\(312\) | 4.48528 | 0.253929 | ||||||||
\(313\) | 26.2132 | 1.48166 | 0.740829 | − | 0.671694i | \(-0.234433\pi\) | ||||
0.740829 | + | 0.671694i | \(0.234433\pi\) | |||||||
\(314\) | 22.8284 | 1.28828 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.100505 | −0.00564493 | −0.00282246 | − | 0.999996i | \(-0.500898\pi\) | ||||
−0.00282246 | + | 0.999996i | \(0.500898\pi\) | |||||||
\(318\) | −1.65685 | −0.0929118 | ||||||||
\(319\) | −0.828427 | −0.0463830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.4142 | 0.860338 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −41.5563 | −2.31226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.3137 | −1.51277 | ||||||||
\(327\) | 13.4853 | 0.745738 | ||||||||
\(328\) | −6.34315 | −0.350242 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.6274 | −1.51854 | −0.759270 | − | 0.650776i | \(-0.774444\pi\) | ||||
−0.759270 | + | 0.650776i | \(0.774444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.58579 | 0.306099 | ||||||||
\(334\) | −16.6274 | −0.909812 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.899495 | 0.0489986 | 0.0244993 | − | 0.999700i | \(-0.492201\pi\) | ||||
0.0244993 | + | 0.999700i | \(0.492201\pi\) | |||||||
\(338\) | 14.8284 | 0.806560 | ||||||||
\(339\) | −4.34315 | −0.235887 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.585786 | 0.0317221 | ||||||||
\(342\) | −9.41421 | −0.509062 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 29.4558 | 1.58815 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.00000 | 0.215041 | ||||||||
\(347\) | 24.9706 | 1.34049 | 0.670245 | − | 0.742140i | \(-0.266189\pi\) | ||||
0.670245 | + | 0.742140i | \(0.266189\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.6274 | 0.890045 | 0.445023 | − | 0.895519i | \(-0.353196\pi\) | ||||
0.445023 | + | 0.895519i | \(0.353196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.58579 | 0.0846430 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.89949 | 0.313998 | 0.156999 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.156999 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(354\) | −2.00000 | −0.106299 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −27.7990 | −1.46922 | ||||||||
\(359\) | −26.5858 | −1.40314 | −0.701572 | − | 0.712599i | \(-0.747518\pi\) | ||||
−0.701572 | + | 0.712599i | \(0.747518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.3137 | 1.33230 | ||||||||
\(362\) | 0.928932 | 0.0488236 | ||||||||
\(363\) | −0.656854 | −0.0344759 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −17.6569 | −0.922939 | ||||||||
\(367\) | −19.5858 | −1.02237 | −0.511185 | − | 0.859471i | \(-0.670793\pi\) | ||||
−0.511185 | + | 0.859471i | \(0.670793\pi\) | |||||||
\(368\) | −24.9706 | −1.30168 | ||||||||
\(369\) | −2.24264 | −0.116747 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.2426 | −0.996346 | −0.498173 | − | 0.867078i | \(-0.665996\pi\) | ||||
−0.498173 | + | 0.867078i | \(0.665996\pi\) | |||||||
\(374\) | 30.1421 | 1.55861 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26.3431 | 1.35854 | ||||||||
\(377\) | 0.384776 | 0.0198170 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7990 | 0.760173 | 0.380087 | − | 0.924951i | \(-0.375894\pi\) | ||||
0.380087 | + | 0.924951i | \(0.375894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0711 | −0.925809 | ||||||||
\(382\) | −26.8284 | −1.37266 | ||||||||
\(383\) | 12.4853 | 0.637968 | 0.318984 | − | 0.947760i | \(-0.396658\pi\) | ||||
0.318984 | + | 0.947760i | \(0.396658\pi\) | |||||||
\(384\) | 11.3137 | 0.577350 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.55635 | −0.486405 | ||||||||
\(387\) | 10.4142 | 0.529384 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.8701 | 0.855346 | 0.427673 | − | 0.903934i | \(-0.359334\pi\) | ||||
0.427673 | + | 0.903934i | \(0.359334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38.9706 | −1.97083 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.4853 | −0.528912 | ||||||||
\(394\) | 7.85786 | 0.395873 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.2132 | −1.21523 | −0.607613 | − | 0.794233i | \(-0.707873\pi\) | ||||
−0.607613 | + | 0.794233i | \(0.707873\pi\) | |||||||
\(398\) | 7.79899 | 0.390928 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.485281 | 0.0242338 | 0.0121169 | − | 0.999927i | \(-0.496143\pi\) | ||||
0.0121169 | + | 0.999927i | \(0.496143\pi\) | |||||||
\(402\) | −16.5858 | −0.827224 | ||||||||
\(403\) | −0.272078 | −0.0135532 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.0711 | 0.945318 | ||||||||
\(408\) | 17.6569 | 0.874145 | ||||||||
\(409\) | 26.3137 | 1.30113 | 0.650565 | − | 0.759451i | \(-0.274532\pi\) | ||||
0.650565 | + | 0.759451i | \(0.274532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.92893 | −0.144474 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.82843 | −0.433894 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.4853 | 0.562437 | ||||||||
\(418\) | −32.1421 | −1.57212 | ||||||||
\(419\) | 3.17157 | 0.154941 | 0.0774707 | − | 0.996995i | \(-0.475316\pi\) | ||||
0.0774707 | + | 0.996995i | \(0.475316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4853 | 1.33955 | 0.669775 | − | 0.742564i | \(-0.266390\pi\) | ||||
0.669775 | + | 0.742564i | \(0.266390\pi\) | |||||||
\(422\) | −0.201010 | −0.00978502 | ||||||||
\(423\) | 9.31371 | 0.452848 | ||||||||
\(424\) | −3.31371 | −0.160928 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.82843 | −0.233938 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.41421 | 0.261401 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.8284 | 1.77396 | 0.886981 | − | 0.461805i | \(-0.152798\pi\) | ||||
0.886981 | + | 0.461805i | \(0.152798\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | −24.5563 | −1.18010 | −0.590051 | − | 0.807366i | \(-0.700893\pi\) | ||||
−0.590051 | + | 0.807366i | \(0.700893\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.5563 | 1.98791 | ||||||||
\(438\) | 2.92893 | 0.139950 | ||||||||
\(439\) | −0.343146 | −0.0163775 | −0.00818873 | − | 0.999966i | \(-0.502607\pi\) | ||||
−0.00818873 | + | 0.999966i | \(0.502607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | −0.485281 | −0.0230564 | −0.0115282 | − | 0.999934i | \(-0.503670\pi\) | ||||
−0.0115282 | + | 0.999934i | \(0.503670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.2843 | −1.14989 | ||||||||
\(447\) | −17.6569 | −0.835141 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.97056 | −0.328961 | −0.164481 | − | 0.986380i | \(-0.552595\pi\) | ||||
−0.164481 | + | 0.986380i | \(0.552595\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.65685 | −0.360547 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.48528 | 0.304705 | ||||||||
\(454\) | −32.6274 | −1.53128 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.8284 | −0.881722 | ||||||||
\(457\) | 20.8995 | 0.977637 | 0.488819 | − | 0.872385i | \(-0.337428\pi\) | ||||
0.488819 | + | 0.872385i | \(0.337428\pi\) | |||||||
\(458\) | −20.2426 | −0.945876 | ||||||||
\(459\) | 6.24264 | 0.291382 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.0711 | 1.26083 | 0.630413 | − | 0.776260i | \(-0.282886\pi\) | ||||
0.630413 | + | 0.776260i | \(0.282886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.4142 | 0.483990 | 0.241995 | − | 0.970278i | \(-0.422198\pi\) | ||||
0.241995 | + | 0.970278i | \(0.422198\pi\) | |||||||
\(464\) | 0.970563 | 0.0450572 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −31.7990 | −1.47306 | ||||||||
\(467\) | 6.68629 | 0.309405 | 0.154702 | − | 0.987961i | \(-0.450558\pi\) | ||||
0.154702 | + | 0.987961i | \(0.450558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.1421 | 0.743790 | ||||||||
\(472\) | −4.00000 | −0.184115 | ||||||||
\(473\) | 35.5563 | 1.63488 | ||||||||
\(474\) | −6.58579 | −0.302495 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.17157 | −0.0536426 | ||||||||
\(478\) | −24.4853 | −1.11993 | ||||||||
\(479\) | 34.6274 | 1.58217 | 0.791084 | − | 0.611708i | \(-0.209517\pi\) | ||||
0.791084 | + | 0.611708i | \(0.209517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.85786 | −0.403884 | ||||||||
\(482\) | −14.6274 | −0.666261 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.41421 | 0.0641500 | ||||||||
\(487\) | −0.899495 | −0.0407600 | −0.0203800 | − | 0.999792i | \(-0.506488\pi\) | ||||
−0.0203800 | + | 0.999792i | \(0.506488\pi\) | |||||||
\(488\) | −35.3137 | −1.59858 | ||||||||
\(489\) | −19.3137 | −0.873396 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1421 | −0.457708 | −0.228854 | − | 0.973461i | \(-0.573498\pi\) | ||||
−0.228854 | + | 0.973461i | \(0.573498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.51472 | 0.0682195 | ||||||||
\(494\) | 14.9289 | 0.671684 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.686292 | −0.0308154 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.65685 | 0.343112 | ||||||||
\(499\) | 8.79899 | 0.393897 | 0.196948 | − | 0.980414i | \(-0.436897\pi\) | ||||
0.196948 | + | 0.980414i | \(0.436897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.7574 | −0.525280 | ||||||||
\(502\) | −7.65685 | −0.341742 | ||||||||
\(503\) | −18.4853 | −0.824218 | −0.412109 | − | 0.911135i | \(-0.635208\pi\) | ||||
−0.412109 | + | 0.911135i | \(0.635208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −30.1421 | −1.33998 | ||||||||
\(507\) | 10.4853 | 0.465668 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.7990 | −0.611629 | −0.305815 | − | 0.952091i | \(-0.598929\pi\) | ||||
−0.305815 | + | 0.952091i | \(0.598929\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −6.65685 | −0.293907 | ||||||||
\(514\) | 42.2843 | 1.86508 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.7990 | 1.39852 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.82843 | 0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.1127 | 1.71356 | 0.856779 | − | 0.515683i | \(-0.172462\pi\) | ||||
0.856779 | + | 0.515683i | \(0.172462\pi\) | |||||||
\(522\) | 0.343146 | 0.0150191 | ||||||||
\(523\) | −7.58579 | −0.331703 | −0.165852 | − | 0.986151i | \(-0.553037\pi\) | ||||
−0.165852 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.65685 | 0.0722423 | ||||||||
\(527\) | −1.07107 | −0.0466564 | ||||||||
\(528\) | 13.6569 | 0.594338 | ||||||||
\(529\) | 15.9706 | 0.694372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.41421 | −0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.55635 | 0.154043 | ||||||||
\(534\) | 5.31371 | 0.229947 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −33.1716 | −1.43279 | ||||||||
\(537\) | −19.6569 | −0.848256 | ||||||||
\(538\) | 11.5147 | 0.496435 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.3137 | 1.38927 | 0.694637 | − | 0.719360i | \(-0.255565\pi\) | ||||
0.694637 | + | 0.719360i | \(0.255565\pi\) | |||||||
\(542\) | 28.4853 | 1.22355 | ||||||||
\(543\) | 0.656854 | 0.0281883 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.7990 | 1.35963 | 0.679813 | − | 0.733385i | \(-0.262061\pi\) | ||||
0.679813 | + | 0.733385i | \(0.262061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.4853 | −0.532859 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.61522 | −0.0688108 | ||||||||
\(552\) | −17.6569 | −0.751526 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −33.0711 | −1.40506 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.34315 | 0.353510 | 0.176755 | − | 0.984255i | \(-0.443440\pi\) | ||||
0.176755 | + | 0.984255i | \(0.443440\pi\) | |||||||
\(558\) | −0.242641 | −0.0102718 | ||||||||
\(559\) | −16.5147 | −0.698498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.3137 | 0.899865 | ||||||||
\(562\) | −13.6569 | −0.576080 | ||||||||
\(563\) | −14.2843 | −0.602010 | −0.301005 | − | 0.953623i | \(-0.597322\pi\) | ||||
−0.301005 | + | 0.953623i | \(0.597322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.7279 | 0.787193 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.65685 | −0.405193 | ||||||||
\(569\) | −36.8701 | −1.54567 | −0.772837 | − | 0.634605i | \(-0.781163\pi\) | ||||
−0.772837 | + | 0.634605i | \(0.781163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.9706 | 1.17053 | 0.585266 | − | 0.810841i | \(-0.300990\pi\) | ||||
0.585266 | + | 0.810841i | \(0.300990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.9706 | −0.792507 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.00000 | 0.333333 | ||||||||
\(577\) | 6.55635 | 0.272944 | 0.136472 | − | 0.990644i | \(-0.456424\pi\) | ||||
0.136472 | + | 0.990644i | \(0.456424\pi\) | |||||||
\(578\) | −31.0711 | −1.29239 | ||||||||
\(579\) | −6.75736 | −0.280826 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −15.3137 | −0.634774 | ||||||||
\(583\) | −4.00000 | −0.165663 | ||||||||
\(584\) | 5.85786 | 0.242400 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.6569 | 0.894636 | ||||||||
\(587\) | 30.2426 | 1.24825 | 0.624124 | − | 0.781326i | \(-0.285456\pi\) | ||||
0.624124 | + | 0.781326i | \(0.285456\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.14214 | 0.0470609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.55635 | 0.228558 | ||||||||
\(592\) | −22.3431 | −0.918298 | ||||||||
\(593\) | 13.4142 | 0.550856 | 0.275428 | − | 0.961322i | \(-0.411180\pi\) | ||||
0.275428 | + | 0.961322i | \(0.411180\pi\) | |||||||
\(594\) | 4.82843 | 0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.51472 | 0.225702 | ||||||||
\(598\) | 14.0000 | 0.572503 | ||||||||
\(599\) | −42.1421 | −1.72188 | −0.860940 | − | 0.508706i | \(-0.830124\pi\) | ||||
−0.860940 | + | 0.508706i | \(0.830124\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.1716 | 0.985979 | 0.492990 | − | 0.870035i | \(-0.335904\pi\) | ||||
0.492990 | + | 0.870035i | \(0.335904\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.7279 | −0.477598 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.82843 | 0.358630 | ||||||||
\(607\) | −1.24264 | −0.0504372 | −0.0252186 | − | 0.999682i | \(-0.508028\pi\) | ||||
−0.0252186 | + | 0.999682i | \(0.508028\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.7696 | −0.597512 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.1421 | −0.409637 | −0.204818 | − | 0.978800i | \(-0.565660\pi\) | ||||
−0.204818 | + | 0.978800i | \(0.565660\pi\) | |||||||
\(614\) | −2.24264 | −0.0905056 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.82843 | 0.355419 | 0.177710 | − | 0.984083i | \(-0.443131\pi\) | ||||
0.177710 | + | 0.984083i | \(0.443131\pi\) | |||||||
\(618\) | −1.75736 | −0.0706914 | ||||||||
\(619\) | −39.9706 | −1.60655 | −0.803276 | − | 0.595607i | \(-0.796912\pi\) | ||||
−0.803276 | + | 0.595607i | \(0.796912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.24264 | −0.250509 | ||||||||
\(622\) | −24.1421 | −0.968011 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.34315 | −0.253929 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −37.0711 | −1.48166 | ||||||||
\(627\) | −22.7279 | −0.907666 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.8701 | −1.39036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | −13.1716 | −0.523937 | ||||||||
\(633\) | −0.142136 | −0.00564938 | ||||||||
\(634\) | 0.142136 | 0.00564493 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.17157 | 0.0463830 | ||||||||
\(639\) | −3.41421 | −0.135064 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2132 | −0.521890 | −0.260945 | − | 0.965354i | \(-0.584034\pi\) | ||||
−0.260945 | + | 0.965354i | \(0.584034\pi\) | |||||||
\(642\) | −21.7990 | −0.860338 | ||||||||
\(643\) | 24.5563 | 0.968408 | 0.484204 | − | 0.874955i | \(-0.339109\pi\) | ||||
0.484204 | + | 0.874955i | \(0.339109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 58.7696 | 2.31226 | ||||||||
\(647\) | 9.61522 | 0.378013 | 0.189007 | − | 0.981976i | \(-0.439473\pi\) | ||||
0.189007 | + | 0.981976i | \(0.439473\pi\) | |||||||
\(648\) | 2.82843 | 0.111111 | ||||||||
\(649\) | −4.82843 | −0.189532 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.75736 | −0.303569 | −0.151784 | − | 0.988414i | \(-0.548502\pi\) | ||||
−0.151784 | + | 0.988414i | \(0.548502\pi\) | |||||||
\(654\) | −19.0711 | −0.745738 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.97056 | 0.350242 | ||||||||
\(657\) | 2.07107 | 0.0808001 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.3137 | −1.06399 | −0.531996 | − | 0.846747i | \(-0.678558\pi\) | ||||
−0.531996 | + | 0.846747i | \(0.678558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.3137 | −1.25686 | −0.628429 | − | 0.777867i | \(-0.716302\pi\) | ||||
−0.628429 | + | 0.777867i | \(0.716302\pi\) | |||||||
\(662\) | 39.0711 | 1.51854 | ||||||||
\(663\) | −9.89949 | −0.384465 | ||||||||
\(664\) | 15.3137 | 0.594287 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.89949 | −0.306099 | ||||||||
\(667\) | −1.51472 | −0.0586501 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.1716 | −0.663891 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.6274 | −1.64561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.27208 | −0.0875822 | −0.0437911 | − | 0.999041i | \(-0.513944\pi\) | ||||
−0.0437911 | + | 0.999041i | \(0.513944\pi\) | |||||||
\(674\) | −1.27208 | −0.0489986 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.89949 | 0.149870 | 0.0749349 | − | 0.997188i | \(-0.476125\pi\) | ||||
0.0749349 | + | 0.997188i | \(0.476125\pi\) | |||||||
\(678\) | 6.14214 | 0.235887 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.0711 | −0.884085 | ||||||||
\(682\) | −0.828427 | −0.0317221 | ||||||||
\(683\) | −20.5858 | −0.787693 | −0.393847 | − | 0.919176i | \(-0.628856\pi\) | ||||
−0.393847 | + | 0.919176i | \(0.628856\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.3137 | −0.546102 | ||||||||
\(688\) | −41.6569 | −1.58815 | ||||||||
\(689\) | 1.85786 | 0.0707790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.3137 | −1.15319 | −0.576594 | − | 0.817031i | \(-0.695619\pi\) | ||||
−0.576594 | + | 0.817031i | \(0.695619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.3137 | −1.34049 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.686292 | 0.0260138 | ||||||||
\(697\) | 14.0000 | 0.530288 | ||||||||
\(698\) | −23.5147 | −0.890045 | ||||||||
\(699\) | −22.4853 | −0.850471 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.2132 | 1.55660 | 0.778301 | − | 0.627892i | \(-0.216082\pi\) | ||||
0.778301 | + | 0.627892i | \(0.216082\pi\) | |||||||
\(702\) | −2.24264 | −0.0846430 | ||||||||
\(703\) | 37.1838 | 1.40241 | ||||||||
\(704\) | 27.3137 | 1.02942 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.34315 | −0.313998 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.1127 | −0.417346 | −0.208673 | − | 0.977985i | \(-0.566914\pi\) | ||||
−0.208673 | + | 0.977985i | \(0.566914\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.65685 | −0.174646 | ||||||||
\(712\) | 10.6274 | 0.398279 | ||||||||
\(713\) | 1.07107 | 0.0401118 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.3137 | −0.646592 | ||||||||
\(718\) | 37.5980 | 1.40314 | ||||||||
\(719\) | −17.5147 | −0.653189 | −0.326594 | − | 0.945165i | \(-0.605901\pi\) | ||||
−0.326594 | + | 0.945165i | \(0.605901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −35.7990 | −1.33230 | ||||||||
\(723\) | −10.3431 | −0.384666 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.928932 | 0.0344759 | ||||||||
\(727\) | 4.75736 | 0.176441 | 0.0882203 | − | 0.996101i | \(-0.471882\pi\) | ||||
0.0882203 | + | 0.996101i | \(0.471882\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −65.0122 | −2.40456 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.7574 | −0.397332 | −0.198666 | − | 0.980067i | \(-0.563661\pi\) | ||||
−0.198666 | + | 0.980067i | \(0.563661\pi\) | |||||||
\(734\) | 27.6985 | 1.02237 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.0416 | −1.47495 | ||||||||
\(738\) | 3.17157 | 0.116747 | ||||||||
\(739\) | −35.1421 | −1.29272 | −0.646362 | − | 0.763031i | \(-0.723710\pi\) | ||||
−0.646362 | + | 0.763031i | \(0.723710\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.5563 | 0.387797 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.72792 | 0.173451 | 0.0867253 | − | 0.996232i | \(-0.472360\pi\) | ||||
0.0867253 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(744\) | −0.485281 | −0.0177913 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 27.2132 | 0.996346 | ||||||||
\(747\) | 5.41421 | 0.198096 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.6274 | 0.716215 | 0.358107 | − | 0.933680i | \(-0.383422\pi\) | ||||
0.358107 | + | 0.933680i | \(0.383422\pi\) | |||||||
\(752\) | −37.2548 | −1.35854 | ||||||||
\(753\) | −5.41421 | −0.197305 | ||||||||
\(754\) | −0.544156 | −0.0198170 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.5980 | −1.51190 | −0.755952 | − | 0.654627i | \(-0.772826\pi\) | ||||
−0.755952 | + | 0.654627i | \(0.772826\pi\) | |||||||
\(758\) | −20.9289 | −0.760173 | ||||||||
\(759\) | −21.3137 | −0.773639 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.9289 | 0.758673 | 0.379337 | − | 0.925259i | \(-0.376152\pi\) | ||||
0.379337 | + | 0.925259i | \(0.376152\pi\) | |||||||
\(762\) | 25.5563 | 0.925809 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.6569 | −0.637968 | ||||||||
\(767\) | 2.24264 | 0.0809771 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9706 | 0.575913 | 0.287957 | − | 0.957643i | \(-0.407024\pi\) | ||||
0.287957 | + | 0.957643i | \(0.407024\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.8995 | 1.07680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.9289 | 0.896631 | 0.448316 | − | 0.893875i | \(-0.352024\pi\) | ||||
0.448316 | + | 0.893875i | \(0.352024\pi\) | |||||||
\(774\) | −14.7279 | −0.529384 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −30.6274 | −1.09946 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.8579 | −0.855346 | ||||||||
\(779\) | −14.9289 | −0.534885 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6569 | −0.417115 | ||||||||
\(782\) | 55.1127 | 1.97083 | ||||||||
\(783\) | 0.242641 | 0.00867127 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.8284 | 0.528912 | ||||||||
\(787\) | 13.1716 | 0.469516 | 0.234758 | − | 0.972054i | \(-0.424570\pi\) | ||||
0.234758 | + | 0.972054i | \(0.424570\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.17157 | 0.0417091 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.65685 | 0.343141 | ||||||||
\(793\) | 19.7990 | 0.703083 | ||||||||
\(794\) | 34.2426 | 1.21523 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.4437 | 0.369933 | 0.184967 | − | 0.982745i | \(-0.440782\pi\) | ||||
0.184967 | + | 0.982745i | \(0.440782\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58.1421 | −2.05692 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.75736 | 0.132760 | ||||||||
\(802\) | −0.686292 | −0.0242338 | ||||||||
\(803\) | 7.07107 | 0.249533 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.384776 | 0.0135532 | ||||||||
\(807\) | 8.14214 | 0.286617 | ||||||||
\(808\) | 17.6569 | 0.621166 | ||||||||
\(809\) | −4.62742 | −0.162691 | −0.0813457 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813457 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.9706 | 0.806606 | 0.403303 | − | 0.915067i | \(-0.367862\pi\) | ||||
0.403303 | + | 0.915067i | \(0.367862\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.1421 | 0.706416 | ||||||||
\(814\) | −26.9706 | −0.945318 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −24.9706 | −0.874145 | ||||||||
\(817\) | 69.3259 | 2.42541 | ||||||||
\(818\) | −37.2132 | −1.30113 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.5563 | 0.473120 | 0.236560 | − | 0.971617i | \(-0.423980\pi\) | ||||
0.236560 | + | 0.971617i | \(0.423980\pi\) | |||||||
\(822\) | 4.14214 | 0.144474 | ||||||||
\(823\) | −22.2843 | −0.776781 | −0.388390 | − | 0.921495i | \(-0.626969\pi\) | ||||
−0.388390 | + | 0.921495i | \(0.626969\pi\) | |||||||
\(824\) | −3.51472 | −0.122441 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.8284 | −0.446088 | −0.223044 | − | 0.974808i | \(-0.571599\pi\) | ||||
−0.223044 | + | 0.974808i | \(0.571599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.6569 | 0.647979 | 0.323990 | − | 0.946061i | \(-0.394976\pi\) | ||||
0.323990 | + | 0.946061i | \(0.394976\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.3848 | −0.811209 | ||||||||
\(832\) | −12.6863 | −0.439818 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.2426 | −0.562437 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.171573 | −0.00593043 | ||||||||
\(838\) | −4.48528 | −0.154941 | ||||||||
\(839\) | 7.27208 | 0.251060 | 0.125530 | − | 0.992090i | \(-0.459937\pi\) | ||||
0.125530 | + | 0.992090i | \(0.459937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9411 | −0.997970 | ||||||||
\(842\) | −38.8701 | −1.33955 | ||||||||
\(843\) | −9.65685 | −0.332600 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.1716 | −0.452848 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.68629 | 0.160928 | ||||||||
\(849\) | 13.2426 | 0.454486 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.8701 | 1.19533 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0122 | 1.30151 | 0.650756 | − | 0.759287i | \(-0.274452\pi\) | ||||
0.650756 | + | 0.759287i | \(0.274452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −43.5980 | −1.49015 | ||||||||
\(857\) | −6.24264 | −0.213245 | −0.106622 | − | 0.994300i | \(-0.534004\pi\) | ||||
−0.106622 | + | 0.994300i | \(0.534004\pi\) | |||||||
\(858\) | −7.65685 | −0.261401 | ||||||||
\(859\) | −15.6569 | −0.534205 | −0.267102 | − | 0.963668i | \(-0.586066\pi\) | ||||
−0.267102 | + | 0.963668i | \(0.586066\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −52.0833 | −1.77396 | ||||||||
\(863\) | 9.79899 | 0.333561 | 0.166781 | − | 0.985994i | \(-0.446663\pi\) | ||||
0.166781 | + | 0.985994i | \(0.446663\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.7279 | 1.18010 | ||||||||
\(867\) | −21.9706 | −0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.8995 | −0.539353 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.5980 | 0.630169 | ||||||||
\(872\) | −38.1421 | −1.29166 | ||||||||
\(873\) | −10.8284 | −0.366487 | ||||||||
\(874\) | −58.7696 | −1.98791 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.0000 | 0.607817 | 0.303908 | − | 0.952701i | \(-0.401708\pi\) | ||||
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(878\) | 0.485281 | 0.0163775 | ||||||||
\(879\) | 15.3137 | 0.516519 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.6569 | 0.729638 | 0.364819 | − | 0.931078i | \(-0.381131\pi\) | ||||
0.364819 | + | 0.931078i | \(0.381131\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.07107 | −0.271613 | −0.135807 | − | 0.990735i | \(-0.543363\pi\) | ||||
−0.135807 | + | 0.990735i | \(0.543363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.686292 | 0.0230564 | ||||||||
\(887\) | 5.21320 | 0.175042 | 0.0875211 | − | 0.996163i | \(-0.472105\pi\) | ||||
0.0875211 | + | 0.996163i | \(0.472105\pi\) | |||||||
\(888\) | −15.7990 | −0.530179 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.41421 | 0.114380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 62.0000 | 2.07475 | ||||||||
\(894\) | 24.9706 | 0.835141 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.89949 | 0.330535 | ||||||||
\(898\) | 9.85786 | 0.328961 | ||||||||
\(899\) | −0.0416306 | −0.00138846 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.31371 | 0.243655 | ||||||||
\(902\) | 10.8284 | 0.360547 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.2843 | 0.408569 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.17157 | −0.304705 | ||||||||
\(907\) | 8.61522 | 0.286064 | 0.143032 | − | 0.989718i | \(-0.454315\pi\) | ||||
0.143032 | + | 0.989718i | \(0.454315\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.24264 | 0.207055 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24264 | 0.140565 | 0.0702825 | − | 0.997527i | \(-0.477610\pi\) | ||||
0.0702825 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(912\) | 26.6274 | 0.881722 | ||||||||
\(913\) | 18.4853 | 0.611774 | ||||||||
\(914\) | −29.5563 | −0.977637 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.82843 | −0.291382 | ||||||||
\(919\) | −46.6569 | −1.53907 | −0.769534 | − | 0.638606i | \(-0.779511\pi\) | ||||
−0.769534 | + | 0.638606i | \(0.779511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.58579 | −0.0522534 | ||||||||
\(922\) | −38.2843 | −1.26083 | ||||||||
\(923\) | 5.41421 | 0.178211 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.7279 | −0.483990 | ||||||||
\(927\) | −1.24264 | −0.0408137 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.0122 | 1.67366 | 0.836828 | − | 0.547466i | \(-0.184407\pi\) | ||||
0.836828 | + | 0.547466i | \(0.184407\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.0711 | −0.558882 | ||||||||
\(934\) | −9.45584 | −0.309405 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.48528 | −0.146606 | ||||||||
\(937\) | −7.92893 | −0.259027 | −0.129513 | − | 0.991578i | \(-0.541342\pi\) | ||||
−0.129513 | + | 0.991578i | \(0.541342\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.2132 | −0.855436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.2721 | 0.367459 | 0.183730 | − | 0.982977i | \(-0.441183\pi\) | ||||
0.183730 | + | 0.982977i | \(0.441183\pi\) | |||||||
\(942\) | −22.8284 | −0.743790 | ||||||||
\(943\) | −14.0000 | −0.455903 | ||||||||
\(944\) | 5.65685 | 0.184115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −50.2843 | −1.63488 | ||||||||
\(947\) | 4.92893 | 0.160169 | 0.0800844 | − | 0.996788i | \(-0.474481\pi\) | ||||
0.0800844 | + | 0.996788i | \(0.474481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.28427 | −0.106612 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.100505 | 0.00325910 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.4853 | −1.57059 | −0.785296 | − | 0.619120i | \(-0.787489\pi\) | ||||
−0.785296 | + | 0.619120i | \(0.787489\pi\) | |||||||
\(954\) | 1.65685 | 0.0536426 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.828427 | 0.0267792 | ||||||||
\(958\) | −48.9706 | −1.58217 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9706 | −0.999050 | ||||||||
\(962\) | 12.5269 | 0.403884 | ||||||||
\(963\) | −15.4142 | −0.496716 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.3848 | −0.752004 | −0.376002 | − | 0.926619i | \(-0.622701\pi\) | ||||
−0.376002 | + | 0.926619i | \(0.622701\pi\) | |||||||
\(968\) | 1.85786 | 0.0597140 | ||||||||
\(969\) | 41.5563 | 1.33498 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.3431 | −0.460293 | −0.230147 | − | 0.973156i | \(-0.573921\pi\) | ||||
−0.230147 | + | 0.973156i | \(0.573921\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.27208 | 0.0407600 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 49.9411 | 1.59858 | ||||||||
\(977\) | −13.6985 | −0.438253 | −0.219127 | − | 0.975696i | \(-0.570321\pi\) | ||||
−0.219127 | + | 0.975696i | \(0.570321\pi\) | |||||||
\(978\) | 27.3137 | 0.873396 | ||||||||
\(979\) | 12.8284 | 0.409998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.4853 | −0.430552 | ||||||||
\(982\) | 14.3431 | 0.457708 | ||||||||
\(983\) | 53.1543 | 1.69536 | 0.847680 | − | 0.530508i | \(-0.177999\pi\) | ||||
0.847680 | + | 0.530508i | \(0.177999\pi\) | |||||||
\(984\) | 6.34315 | 0.202212 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.14214 | −0.0682195 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 65.0122 | 2.06727 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.6569 | −0.973847 | −0.486924 | − | 0.873445i | \(-0.661881\pi\) | ||||
−0.486924 | + | 0.873445i | \(0.661881\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.6274 | 0.876730 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.757359 | 0.0239858 | 0.0119929 | − | 0.999928i | \(-0.496182\pi\) | ||||
0.0119929 | + | 0.999928i | \(0.496182\pi\) | |||||||
\(998\) | −12.4437 | −0.393897 | ||||||||
\(999\) | −5.58579 | −0.176726 |
(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 | 3675.2.a.x.1.1 | 2 | ||
5.4 | even | 2 | 735.2.a.j.1.2 | 2 | |||
7.3 | odd | 6 | 525.2.i.g.226.2 | 4 | |||
7.5 | odd | 6 | 525.2.i.g.151.2 | 4 | |||
7.6 | odd | 2 | 3675.2.a.z.1.1 | 2 | |||
15.14 | odd | 2 | 2205.2.a.s.1.1 | 2 | |||
35.3 | even | 12 | 525.2.r.g.499.2 | 8 | |||
35.4 | even | 6 | 735.2.i.j.226.1 | 4 | |||
35.9 | even | 6 | 735.2.i.j.361.1 | 4 | |||
35.12 | even | 12 | 525.2.r.g.424.2 | 8 | |||
35.17 | even | 12 | 525.2.r.g.499.3 | 8 | |||
35.19 | odd | 6 | 105.2.i.c.46.1 | yes | 4 | ||
35.24 | odd | 6 | 105.2.i.c.16.1 | ✓ | 4 | ||
35.33 | even | 12 | 525.2.r.g.424.3 | 8 | |||
35.34 | odd | 2 | 735.2.a.i.1.2 | 2 | |||
105.59 | even | 6 | 315.2.j.d.226.2 | 4 | |||
105.89 | even | 6 | 315.2.j.d.46.2 | 4 | |||
105.104 | even | 2 | 2205.2.a.u.1.1 | 2 | |||
140.19 | even | 6 | 1680.2.bg.p.1201.1 | 4 | |||
140.59 | even | 6 | 1680.2.bg.p.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.c.16.1 | ✓ | 4 | 35.24 | odd | 6 | ||
105.2.i.c.46.1 | yes | 4 | 35.19 | odd | 6 | ||
315.2.j.d.46.2 | 4 | 105.89 | even | 6 | |||
315.2.j.d.226.2 | 4 | 105.59 | even | 6 | |||
525.2.i.g.151.2 | 4 | 7.5 | odd | 6 | |||
525.2.i.g.226.2 | 4 | 7.3 | odd | 6 | |||
525.2.r.g.424.2 | 8 | 35.12 | even | 12 | |||
525.2.r.g.424.3 | 8 | 35.33 | even | 12 | |||
525.2.r.g.499.2 | 8 | 35.3 | even | 12 | |||
525.2.r.g.499.3 | 8 | 35.17 | even | 12 | |||
735.2.a.i.1.2 | 2 | 35.34 | odd | 2 | |||
735.2.a.j.1.2 | 2 | 5.4 | even | 2 | |||
735.2.i.j.226.1 | 4 | 35.4 | even | 6 | |||
735.2.i.j.361.1 | 4 | 35.9 | even | 6 | |||
1680.2.bg.p.961.1 | 4 | 140.59 | even | 6 | |||
1680.2.bg.p.1201.1 | 4 | 140.19 | even | 6 | |||
2205.2.a.s.1.1 | 2 | 15.14 | odd | 2 | |||
2205.2.a.u.1.1 | 2 | 105.104 | even | 2 | |||
3675.2.a.x.1.1 | 2 | 1.1 | even | 1 | trivial | ||
3675.2.a.z.1.1 | 2 | 7.6 | odd | 2 |