Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3120,2,Mod(1,3120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3120.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3120.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: | \(24.9133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1849.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 14x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1560) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.50331\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3120.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50331 | 0.946161 | 0.473081 | − | 0.881019i | \(-0.343142\pi\) | ||||
0.473081 | + | 0.881019i | \(0.343142\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.27316 | −0.986896 | −0.493448 | − | 0.869775i | \(-0.664264\pi\) | ||||
−0.493448 | + | 0.869775i | \(0.664264\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.50331 | 1.09221 | 0.546106 | − | 0.837716i | \(-0.316109\pi\) | ||||
0.546106 | + | 0.837716i | \(0.316109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.23014 | −0.741046 | −0.370523 | − | 0.928823i | \(-0.620821\pi\) | ||||
−0.370523 | + | 0.928823i | \(0.620821\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50331 | −0.546267 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.50331 | 0.521976 | 0.260988 | − | 0.965342i | \(-0.415952\pi\) | ||||
0.260988 | + | 0.965342i | \(0.415952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.77647 | −1.44405 | −0.722027 | − | 0.691865i | \(-0.756790\pi\) | ||||
−0.722027 | + | 0.691865i | \(0.756790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00662 | 0.899215 | 0.449607 | − | 0.893226i | \(-0.351564\pi\) | ||||
0.449607 | + | 0.893226i | \(0.351564\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.27316 | 0.569785 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.50331 | −0.423136 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.73345 | 1.27137 | 0.635686 | − | 0.771948i | \(-0.280717\pi\) | ||||
0.635686 | + | 0.771948i | \(0.280717\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.73345 | 1.20776 | 0.603881 | − | 0.797074i | \(-0.293620\pi\) | ||||
0.603881 | + | 0.797074i | \(0.293620\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00662 | −1.31375 | −0.656875 | − | 0.754000i | \(-0.728122\pi\) | ||||
−0.656875 | + | 0.754000i | \(0.728122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.733451 | −0.104779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50331 | −0.630589 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.27978 | 0.862594 | 0.431297 | − | 0.902210i | \(-0.358056\pi\) | ||||
0.431297 | + | 0.902210i | \(0.358056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.27316 | 0.441353 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.23014 | 0.427843 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.27316 | 1.18731 | 0.593654 | − | 0.804721i | \(-0.297685\pi\) | ||||
0.593654 | + | 0.804721i | \(0.297685\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.50331 | 0.315387 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5529 | −1.90009 | −0.950047 | − | 0.312106i | \(-0.898966\pi\) | ||||
−0.950047 | + | 0.312106i | \(0.898966\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.50331 | −0.301363 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.73345 | −0.680435 | −0.340218 | − | 0.940347i | \(-0.610501\pi\) | ||||
−0.340218 | + | 0.940347i | \(0.610501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.7765 | 1.84650 | 0.923248 | − | 0.384204i | \(-0.125524\pi\) | ||||
0.923248 | + | 0.384204i | \(0.125524\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.19374 | −0.933763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.72684 | 0.531811 | 0.265905 | − | 0.963999i | \(-0.414329\pi\) | ||||
0.265905 | + | 0.963999i | \(0.414329\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.5529 | 1.26810 | 0.634050 | − | 0.773292i | \(-0.281391\pi\) | ||||
0.634050 | + | 0.773292i | \(0.281391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50331 | −0.488452 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.77647 | 0.833725 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.2864 | −1.62035 | −0.810177 | − | 0.586185i | \(-0.800629\pi\) | ||||
−0.810177 | + | 0.586185i | \(0.800629\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50331 | 0.262418 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.00662 | −0.519162 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.23014 | 0.331406 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.5033 | 1.26952 | 0.634759 | − | 0.772710i | \(-0.281099\pi\) | ||||
0.634759 | + | 0.772710i | \(0.281099\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.27316 | −0.328965 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.23014 | 0.520419 | 0.260209 | − | 0.965552i | \(-0.416208\pi\) | ||||
0.260209 | + | 0.965552i | \(0.416208\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.50331 | 0.244298 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.726836 | 0.0702659 | 0.0351329 | − | 0.999383i | \(-0.488815\pi\) | ||||
0.0351329 | + | 0.999383i | \(0.488815\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.7831 | 1.60753 | 0.803764 | − | 0.594948i | \(-0.202827\pi\) | ||||
0.803764 | + | 0.594948i | \(0.202827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.73345 | −0.734027 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.77647 | −0.355261 | −0.177630 | − | 0.984097i | \(-0.556843\pi\) | ||||
−0.177630 | + | 0.984097i | \(0.556843\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.50331 | −0.233435 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.2732 | 1.03341 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.286395 | −0.0260359 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.73345 | −0.697302 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.54633 | 0.580893 | 0.290446 | − | 0.956891i | \(-0.406196\pi\) | ||||
0.290446 | + | 0.956891i | \(0.406196\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2301 | 0.981182 | 0.490591 | − | 0.871390i | \(-0.336781\pi\) | ||||
0.490591 | + | 0.871390i | \(0.336781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.08604 | −0.701149 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.5529 | −1.15791 | −0.578953 | − | 0.815361i | \(-0.696539\pi\) | ||||
−0.578953 | + | 0.815361i | \(0.696539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.7335 | 1.84341 | 0.921704 | − | 0.387895i | \(-0.126798\pi\) | ||||
0.921704 | + | 0.387895i | \(0.126798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.00662 | 0.758494 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.27316 | −0.273716 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.77647 | 0.645801 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.733451 | 0.0604940 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.27978 | 0.186767 | 0.0933834 | − | 0.995630i | \(-0.470232\pi\) | ||||
0.0933834 | + | 0.995630i | \(0.470232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.46029 | 0.525731 | 0.262865 | − | 0.964833i | \(-0.415333\pi\) | ||||
0.262865 | + | 0.964833i | \(0.415333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50331 | 0.364071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.00662 | −0.402141 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.53971 | −0.282500 | −0.141250 | − | 0.989974i | \(-0.545112\pi\) | ||||
−0.141250 | + | 0.989974i | \(0.545112\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.27978 | −0.498019 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.26655 | 0.493873 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7401 | 1.46784 | 0.733918 | − | 0.679238i | \(-0.237690\pi\) | ||||
0.733918 | + | 0.679238i | \(0.237690\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.27316 | −0.254816 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.00000 | 0.309529 | 0.154765 | − | 0.987951i | \(-0.450538\pi\) | ||||
0.154765 | + | 0.987951i | \(0.450538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.23014 | −0.247015 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.46029 | −0.643224 | −0.321612 | − | 0.946872i | \(-0.604225\pi\) | ||||
−0.321612 | + | 0.946872i | \(0.604225\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50331 | 0.189232 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.76986 | 0.356516 | 0.178258 | − | 0.983984i | \(-0.442954\pi\) | ||||
0.178258 | + | 0.983984i | \(0.442954\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7335 | 1.16946 | 0.584729 | − | 0.811229i | \(-0.301201\pi\) | ||||
0.584729 | + | 0.811229i | \(0.301201\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.27316 | −0.685492 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.73345 | −0.568575 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.7401 | −1.07790 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50331 | −0.182089 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.0132 | 1.88225 | 0.941126 | − | 0.338057i | \(-0.109770\pi\) | ||||
0.941126 | + | 0.338057i | \(0.109770\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.503308 | −0.0362289 | −0.0181144 | − | 0.999836i | \(-0.505766\pi\) | ||||
−0.0181144 | + | 0.999836i | \(0.505766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0066 | −0.784189 | −0.392094 | − | 0.919925i | \(-0.628249\pi\) | ||||
−0.392094 | + | 0.919925i | \(0.628249\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.01323 | −0.142714 | −0.0713571 | − | 0.997451i | \(-0.522733\pi\) | ||||
−0.0713571 | + | 0.997451i | \(0.522733\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.5529 | 1.09702 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.4669 | −1.36631 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.73345 | −0.540128 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.50331 | 0.173992 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5728 | 0.731335 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.73345 | 0.392850 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.5331 | 0.850802 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.7765 | −1.06608 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.50331 | 0.302925 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.7897 | −1.59308 | −0.796538 | − | 0.604588i | \(-0.793338\pi\) | ||||
−0.796538 | + | 0.604588i | \(0.793338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.0198 | 1.52788 | 0.763940 | − | 0.645287i | \(-0.223262\pi\) | ||||
0.763940 | + | 0.645287i | \(0.223262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.77647 | −0.513884 | −0.256942 | − | 0.966427i | \(-0.582715\pi\) | ||||
−0.256942 | + | 0.966427i | \(0.582715\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.19374 | 0.539108 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.9702 | 1.57034 | 0.785170 | − | 0.619280i | \(-0.212575\pi\) | ||||
0.785170 | + | 0.619280i | \(0.212575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00662 | 0.587527 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.72684 | −0.307041 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.812878 | −0.0525807 | −0.0262903 | − | 0.999654i | \(-0.508369\pi\) | ||||
−0.0262903 | + | 0.999654i | \(0.508369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0132 | 1.28917 | 0.644583 | − | 0.764535i | \(-0.277031\pi\) | ||||
0.644583 | + | 0.764535i | \(0.277031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.733451 | 0.0468585 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.23014 | −0.205529 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.5529 | −0.732138 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.3162 | 0.714271 | 0.357136 | − | 0.934053i | \(-0.383753\pi\) | ||||
0.357136 | + | 0.934053i | \(0.383753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.19374 | −0.515136 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.50331 | 0.282008 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3294 | 1.20574 | 0.602868 | − | 0.797841i | \(-0.294025\pi\) | ||||
0.602868 | + | 0.797841i | \(0.294025\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.3592 | 1.20292 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.77647 | −0.481352 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.2368 | 0.754551 | 0.377275 | − | 0.926101i | \(-0.376861\pi\) | ||||
0.377275 | + | 0.926101i | \(0.376861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.27978 | −0.385764 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.2864 | 0.935512 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.76986 | −0.168881 | −0.0844406 | − | 0.996429i | \(-0.526910\pi\) | ||||
−0.0844406 | + | 0.996429i | \(0.526910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0860423 | 0.00522670 | 0.00261335 | − | 0.999997i | \(-0.499168\pi\) | ||||
0.00261335 | + | 0.999997i | \(0.499168\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.50331 | −0.151507 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.27316 | −0.197379 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.5529 | 1.05465 | 0.527327 | − | 0.849662i | \(-0.323194\pi\) | ||||
0.527327 | + | 0.849662i | \(0.323194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00662 | 0.299738 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.0132 | 1.43251 | 0.716255 | − | 0.697839i | \(-0.245855\pi\) | ||||
0.716255 | + | 0.697839i | \(0.245855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.0132 | −1.30855 | −0.654275 | − | 0.756256i | \(-0.727026\pi\) | ||||
−0.654275 | + | 0.756256i | \(0.727026\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.23014 | −0.191337 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.3592 | 1.14274 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.27978 | 0.192928 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.5033 | −0.732957 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.99338 | −0.525399 | −0.262700 | − | 0.964878i | \(-0.584613\pi\) | ||||
−0.262700 | + | 0.964878i | \(0.584613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.27316 | 0.189928 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.50331 | 0.144770 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0132 | −0.577153 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.23014 | −0.300464 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.27316 | −0.530980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.2930 | 1.27233 | 0.636165 | − | 0.771553i | \(-0.280520\pi\) | ||||
0.636165 | + | 0.771553i | \(0.280520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5529 | −0.992151 | −0.496076 | − | 0.868279i | \(-0.665226\pi\) | ||||
−0.496076 | + | 0.868279i | \(0.665226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.50331 | −0.141045 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.54633 | −0.255347 | −0.127674 | − | 0.991816i | \(-0.540751\pi\) | ||||
−0.127674 | + | 0.991816i | \(0.540751\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.4537 | 1.42513 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.726836 | −0.0405680 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.5463 | −0.809379 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.7831 | −0.928107 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.5463 | −1.24302 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.7897 | −1.08774 | −0.543870 | − | 0.839169i | \(-0.683042\pi\) | ||||
−0.543870 | + | 0.839169i | \(0.683042\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.73345 | 0.423790 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.5529 | 0.849748 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.0198 | −0.709236 | −0.354618 | − | 0.935011i | \(-0.615389\pi\) | ||||
−0.354618 | + | 0.935011i | \(0.615389\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.77647 | 0.205110 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.3875 | −0.887432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.3592 | −1.04530 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.50331 | 0.134774 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.18712 | 0.385825 | 0.192912 | − | 0.981216i | \(-0.438207\pi\) | ||||
0.192912 | + | 0.981216i | \(0.438207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2301 | −0.922308 | −0.461154 | − | 0.887320i | \(-0.652565\pi\) | ||||
−0.461154 | + | 0.887320i | \(0.652565\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.5662 | −1.68010 | −0.840049 | − | 0.542511i | \(-0.817474\pi\) | ||||
−0.840049 | + | 0.542511i | \(0.817474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.73345 | 0.304300 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.2732 | −0.596639 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.46029 | 0.129849 | 0.0649245 | − | 0.997890i | \(-0.479319\pi\) | ||||
0.0649245 | + | 0.997890i | \(0.479319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.56617 | −0.450851 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.286395 | 0.0150318 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.7765 | −0.825778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.09266 | −0.265835 | −0.132917 | − | 0.991127i | \(-0.542434\pi\) | ||||
−0.132917 | + | 0.991127i | \(0.542434\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.73345 | 0.402587 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.7202 | 0.816153 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0066 | 0.569901 | 0.284950 | − | 0.958542i | \(-0.408023\pi\) | ||||
0.284950 | + | 0.958542i | \(0.408023\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.77647 | −0.400509 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3360 | 1.35279 | 0.676396 | − | 0.736539i | \(-0.263541\pi\) | ||||
0.676396 | + | 0.736539i | \(0.263541\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.54633 | −0.335379 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.5463 | −0.947673 | −0.473837 | − | 0.880613i | \(-0.657131\pi\) | ||||
−0.473837 | + | 0.880613i | \(0.657131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.19374 | 0.417592 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.7699 | −0.951670 | −0.475835 | − | 0.879535i | \(-0.657854\pi\) | ||||
−0.475835 | + | 0.879535i | \(0.657854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.2732 | 0.570108 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.2301 | −0.566486 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.72684 | −0.237833 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.266549 | −0.0133777 | −0.00668886 | − | 0.999978i | \(-0.502129\pi\) | ||||
−0.00668886 | + | 0.999978i | \(0.502129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.08604 | 0.404808 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.5662 | 1.77609 | 0.888045 | − | 0.459757i | \(-0.152063\pi\) | ||||
0.888045 | + | 0.459757i | \(0.152063\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.00662 | 0.249397 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.3129 | −1.25471 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.460287 | 0.0227597 | 0.0113799 | − | 0.999935i | \(-0.496378\pi\) | ||||
0.0113799 | + | 0.999935i | \(0.496378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5529 | 0.668517 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.5529 | −0.567112 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.7335 | −1.06429 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.32280 | 0.406595 | 0.203298 | − | 0.979117i | \(-0.434834\pi\) | ||||
0.203298 | + | 0.979117i | \(0.434834\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.3228 | 0.503103 | 0.251551 | − | 0.967844i | \(-0.419059\pi\) | ||||
0.251551 | + | 0.967844i | \(0.419059\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.00662 | −0.437917 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.50331 | 0.218443 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.2136 | 1.12338 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.27316 | 0.158030 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5662 | −0.846133 | −0.423066 | − | 0.906099i | \(-0.639046\pi\) | ||||
−0.423066 | + | 0.906099i | \(0.639046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00662 | 0.336716 | 0.168358 | − | 0.985726i | \(-0.446153\pi\) | ||||
0.168358 | + | 0.985726i | \(0.446153\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.77647 | −0.372853 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.08604 | −0.386808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.25993 | 0.0601334 | 0.0300667 | − | 0.999548i | \(-0.490428\pi\) | ||||
0.0300667 | + | 0.999548i | \(0.490428\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.733451 | −0.0349262 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.8261 | −1.27455 | −0.637273 | − | 0.770638i | \(-0.719938\pi\) | ||||
−0.637273 | + | 0.770638i | \(0.719938\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.2864 | 0.724645 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.27978 | −0.107830 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.7401 | −1.54510 | −0.772550 | − | 0.634954i | \(-0.781019\pi\) | ||||
−0.772550 | + | 0.634954i | \(0.781019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.3129 | −1.19194 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.46029 | −0.303531 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.50331 | −0.117357 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.5960 | 1.57155 | 0.785776 | − | 0.618511i | \(-0.212264\pi\) | ||||
0.785776 | + | 0.618511i | \(0.212264\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.50331 | −0.210196 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.8327 | −1.94834 | −0.974172 | − | 0.225807i | \(-0.927498\pi\) | ||||
−0.974172 | + | 0.225807i | \(0.927498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.05625 | 0.281458 | 0.140729 | − | 0.990048i | \(-0.455055\pi\) | ||||
0.140729 | + | 0.990048i | \(0.455055\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.00662 | 0.232176 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.2996 | −1.26328 | −0.631638 | − | 0.775263i | \(-0.717617\pi\) | ||||
−0.631638 | + | 0.775263i | \(0.717617\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.9338 | −1.79780 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.53971 | 0.163101 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.0927 | 0.602001 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.23014 | −0.148209 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.27978 | 0.287531 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.2798 | −1.29214 | −0.646068 | − | 0.763280i | \(-0.723588\pi\) | ||||
−0.646068 | + | 0.763280i | \(0.723588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.73345 | 0.352615 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.26655 | −0.285138 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.5033 | −0.567746 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.9636 | −1.13121 | −0.565604 | − | 0.824677i | \(-0.691357\pi\) | ||||
−0.565604 | + | 0.824677i | \(0.691357\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.7401 | −0.847455 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.22353 | −0.280864 | −0.140432 | − | 0.990090i | \(-0.544849\pi\) | ||||
−0.140432 | + | 0.990090i | \(0.544849\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.0198 | −1.57721 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.27316 | 0.147118 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.3526 | −0.643802 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.2301 | 0.860859 | 0.430430 | − | 0.902624i | \(-0.358362\pi\) | ||||
0.430430 | + | 0.902624i | \(0.358362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.00000 | −0.178707 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.6970 | −0.476958 | −0.238479 | − | 0.971148i | \(-0.576649\pi\) | ||||
−0.238479 | + | 0.971148i | \(0.576649\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.23014 | −0.232738 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.740066 | 0.0328029 | 0.0164014 | − | 0.999865i | \(-0.494779\pi\) | ||||
0.0164014 | + | 0.999865i | \(0.494779\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.4934 | 1.74708 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.23014 | 0.142614 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.4801 | 1.29653 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.46029 | 0.371365 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.5662 | −1.55818 | −0.779091 | − | 0.626911i | \(-0.784319\pi\) | ||||
−0.779091 | + | 0.626911i | \(0.784319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0132 | −0.612756 | −0.306378 | − | 0.951910i | \(-0.599117\pi\) | ||||
−0.306378 | + | 0.951910i | \(0.599117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.50331 | −0.109253 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.5463 | 0.982134 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7335 | −0.727541 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.73345 | 0.334973 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.726836 | −0.0314238 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.76986 | −0.205835 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.40071 | 0.103406 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7765 | 0.506310 | 0.253155 | − | 0.967426i | \(-0.418532\pi\) | ||||
0.253155 | + | 0.967426i | \(0.418532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.7335 | −0.675187 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.7831 | −0.718908 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | 0.171028 | 0.0855138 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855138 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.27316 | 0.395769 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.1191 | 1.07011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8327 | 0.503179 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.73345 | 0.328267 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.0265 | −1.78072 | −0.890359 | − | 0.455259i | \(-0.849547\pi\) | ||||
−0.890359 | + | 0.455259i | \(0.849547\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.7401 | 0.622326 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.3724 | 1.06932 | 0.534660 | − | 0.845067i | \(-0.320440\pi\) | ||||
0.534660 | + | 0.845067i | \(0.320440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.77647 | 0.158877 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.50331 | 0.105129 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.0993 | 1.51336 | 0.756680 | − | 0.653785i | \(-0.226820\pi\) | ||||
0.756680 | + | 0.653785i | \(0.226820\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1871 | 0.970351 | 0.485175 | − | 0.874417i | \(-0.338756\pi\) | ||||
0.485175 | + | 0.874417i | \(0.338756\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.0132 | −1.08672 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.50331 | 0.104395 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.9636 | 1.45555 | 0.727777 | − | 0.685814i | \(-0.240554\pi\) | ||||
0.727777 | + | 0.685814i | \(0.240554\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.503308 | 0.0209168 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.9206 | 1.19983 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.5548 | −0.851291 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.9934 | −0.783941 | −0.391970 | − | 0.919978i | \(-0.628206\pi\) | ||||
−0.391970 | + | 0.919978i | \(0.628206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.1721 | −0.666359 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0066 | 0.452752 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5331 | 0.432543 | 0.216271 | − | 0.976333i | \(-0.430610\pi\) | ||||
0.216271 | + | 0.976333i | \(0.430610\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2732 | −0.462155 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.01323 | 0.0823960 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.1059 | 0.944081 | 0.472040 | − | 0.881577i | \(-0.343518\pi\) | ||||
0.472040 | + | 0.881577i | \(0.343518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.8129 | −0.767393 | −0.383697 | − | 0.923459i | \(-0.625349\pi\) | ||||
−0.383697 | + | 0.923459i | \(0.625349\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.5529 | −0.633365 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.286395 | 0.0116436 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.09266 | 0.206705 | 0.103352 | − | 0.994645i | \(-0.467043\pi\) | ||||
0.103352 | + | 0.994645i | \(0.467043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.4669 | 0.788839 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.00662 | −0.364369 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.2004 | 1.09861 | 0.549306 | − | 0.835621i | \(-0.314892\pi\) | ||||
0.549306 | + | 0.835621i | \(0.314892\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.73345 | 0.311843 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.460287 | −0.0185304 | −0.00926522 | − | 0.999957i | \(-0.502949\pi\) | ||||
−0.00926522 | + | 0.999957i | \(0.502949\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.21691 | 0.0489119 | 0.0244559 | − | 0.999701i | \(-0.492215\pi\) | ||||
0.0244559 | + | 0.999701i | \(0.492215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.50331 | −0.100454 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.2665 | −1.53312 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.5728 | −0.422237 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.8261 | 1.38861 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.01323 | −0.0801454 | −0.0400727 | − | 0.999197i | \(-0.512759\pi\) | ||||
−0.0400727 | + | 0.999197i | \(0.512759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.54633 | −0.259783 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.733451 | −0.0290604 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.73345 | −0.226812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.37424 | −0.172772 | −0.0863861 | − | 0.996262i | \(-0.527532\pi\) | ||||
−0.0863861 | + | 0.996262i | \(0.527532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.72022 | −0.146711 | −0.0733556 | − | 0.997306i | \(-0.523371\pi\) | ||||
−0.0733556 | + | 0.997306i | \(0.523371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.00000 | −0.157500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.4305 | 0.488693 | 0.244347 | − | 0.969688i | \(-0.421427\pi\) | ||||
0.244347 | + | 0.969688i | \(0.421427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.5331 | −0.491211 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.0000 | 0.860927 | 0.430463 | − | 0.902608i | \(-0.358350\pi\) | ||||
0.430463 | + | 0.902608i | \(0.358350\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.2301 | −0.438798 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.7765 | 0.615499 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.3294 | −1.14251 | −0.571256 | − | 0.820772i | \(-0.693544\pi\) | ||||
−0.571256 | + | 0.820772i | \(0.693544\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.32280 | 0.0903465 | 0.0451732 | − | 0.998979i | \(-0.485616\pi\) | ||||
0.0451732 | + | 0.998979i | \(0.485616\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.50331 | −0.174894 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.08604 | 0.313563 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.4669 | −0.753761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.7897 | 0.919763 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.3526 | −1.17175 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.1059 | −0.813572 | −0.406786 | − | 0.913523i | \(-0.633351\pi\) | ||||
−0.406786 | + | 0.913523i | \(0.633351\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.1937 | −1.31417 | −0.657086 | − | 0.753816i | \(-0.728211\pi\) | ||||
−0.657086 | + | 0.753816i | \(0.728211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.2996 | 1.20117 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.0198 | −0.882122 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.4735 | 1.24256 | 0.621282 | − | 0.783587i | \(-0.286612\pi\) | ||||
0.621282 | + | 0.783587i | \(0.286612\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.5529 | 0.517831 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.77647 | 0.296691 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.27978 | 0.239241 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.8095 | 1.32422 | 0.662109 | − | 0.749408i | \(-0.269662\pi\) | ||||
0.662109 | + | 0.749408i | \(0.269662\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.19374 | −0.311254 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.7335 | −0.824397 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.8261 | 1.31913 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.9702 | −0.906637 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1507 | 0.685543 | 0.342772 | − | 0.939419i | \(-0.388634\pi\) | ||||
0.342772 | + | 0.939419i | \(0.388634\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.9802 | −0.942144 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.00662 | −0.339209 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.0927 | 0.492400 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.2434 | −0.422254 | −0.211127 | − | 0.977459i | \(-0.567713\pi\) | ||||
−0.211127 | + | 0.977459i | \(0.567713\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.72684 | 0.177270 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.5331 | 0.469368 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.27316 | 0.122409 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.812878 | 0.0303575 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.53971 | 0.355771 | 0.177886 | − | 0.984051i | \(-0.443074\pi\) | ||||
0.177886 | + | 0.984051i | \(0.443074\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.0132 | −0.744300 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.77647 | −0.288811 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.1125 | −1.33934 | −0.669669 | − | 0.742659i | \(-0.733564\pi\) | ||||
−0.669669 | + | 0.742659i | \(0.733564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0132 | −0.666243 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.2798 | −1.26615 | −0.633076 | − | 0.774089i | \(-0.718208\pi\) | ||||
−0.633076 | + | 0.774089i | \(0.718208\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.733451 | −0.0270537 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 50.9073 | 1.87520 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.8625 | −0.951368 | −0.475684 | − | 0.879616i | \(-0.657799\pi\) | ||||
−0.475684 | + | 0.879616i | \(0.657799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.23014 | 0.118662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.55956 | 0.167274 | 0.0836370 | − | 0.996496i | \(-0.473346\pi\) | ||||
0.0836370 | + | 0.996496i | \(0.473346\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.27978 | −0.0835247 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.5529 | 0.422700 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.81949 | 0.0664828 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.8327 | −1.30755 | −0.653777 | − | 0.756687i | \(-0.726817\pi\) | ||||
−0.653777 | + | 0.756687i | \(0.726817\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.3162 | −0.412385 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.46029 | −0.235114 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.4669 | −1.07099 | −0.535496 | − | 0.844538i | \(-0.679875\pi\) | ||||
−0.535496 | + | 0.844538i | \(0.679875\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.19374 | 0.297414 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.4735 | 0.814664 | 0.407332 | − | 0.913280i | \(-0.366459\pi\) | ||||
0.407332 | + | 0.913280i | \(0.366459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.0132 | 1.52098 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.50331 | −0.162817 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.4669 | −1.20685 | −0.603424 | − | 0.797421i | \(-0.706197\pi\) | ||||
−0.603424 | + | 0.797421i | \(0.706197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.3294 | −0.696132 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.0860 | −0.794380 | −0.397190 | − | 0.917736i | \(-0.630015\pi\) | ||||
−0.397190 | + | 0.917736i | \(0.630015\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00662 | 0.179843 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.3592 | −0.694508 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.9802 | −0.895007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.7665 | 0.671519 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.77647 | 0.277908 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.53971 | 0.126338 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0000 | 0.998092 | 0.499046 | − | 0.866575i | \(-0.333684\pi\) | ||||
0.499046 | + | 0.866575i | \(0.333684\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.2368 | −0.435640 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.45367 | −0.336134 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.27316 | 0.329300 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.27978 | 0.222721 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.1739 | −0.395800 | −0.197900 | − | 0.980222i | \(-0.563412\pi\) | ||||
−0.197900 | + | 0.980222i | \(0.563412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.5596 | −1.43489 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.2864 | −0.540118 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −51.6390 | −1.82230 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.26655 | −0.220867 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.76986 | 0.0975036 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.68381 | −0.164471 | −0.0822355 | − | 0.996613i | \(-0.526206\pi\) | ||||
−0.0822355 | + | 0.996613i | \(0.526206\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.0860423 | −0.00301763 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7401 | −0.656436 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9206 | 0.452034 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.50331 | 0.0874726 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.8129 | 0.516973 | 0.258487 | − | 0.966015i | \(-0.416776\pi\) | ||||
0.258487 | + | 0.966015i | \(0.416776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0265 | −0.698079 | −0.349039 | − | 0.937108i | \(-0.613492\pi\) | ||||
−0.349039 | + | 0.937108i | \(0.613492\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.27316 | 0.113957 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.9272 | −1.45795 | −0.728976 | − | 0.684540i | \(-0.760003\pi\) | ||||
−0.728976 | + | 0.684540i | \(0.760003\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5529 | −0.608905 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.30295 | −0.114441 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | −0.138426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.00662 | −0.173054 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.83934 | −0.167073 | −0.0835363 | − | 0.996505i | \(-0.526621\pi\) | ||||
−0.0835363 | + | 0.996505i | \(0.526621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.4735 | 1.08529 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.0132 | −0.827060 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.716935 | −0.0246342 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.0132 | 0.755492 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.3592 | 0.663625 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.6673 | −1.18698 | −0.593492 | − | 0.804840i | \(-0.702251\pi\) | ||||
−0.593492 | + | 0.804840i | \(0.702251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.23014 | 0.110469 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.6026 | 0.772089 | 0.386045 | − | 0.922480i | \(-0.373841\pi\) | ||||
0.386045 | + | 0.922480i | \(0.373841\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.16728 | 0.278664 | 0.139332 | − | 0.990246i | \(-0.455504\pi\) | ||||
0.139332 | + | 0.990246i | \(0.455504\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.3592 | −0.659760 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.4934 | −1.75285 | −0.876427 | − | 0.481534i | \(-0.840080\pi\) | ||||
−0.876427 | + | 0.481534i | \(0.840080\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.46029 | 0.287658 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.27978 | −0.111387 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.4717 | −0.524842 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.5529 | −0.526991 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.5033 | 0.423173 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.50331 | −0.0846272 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.1323 | −1.79415 | −0.897076 | − | 0.441876i | \(-0.854313\pi\) | ||||
−0.897076 | + | 0.441876i | \(0.854313\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.99338 | 0.303339 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.4471 | 0.486734 | 0.243367 | − | 0.969934i | \(-0.421748\pi\) | ||||
0.243367 | + | 0.969934i | \(0.421748\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.98677 | 0.0668601 | 0.0334301 | − | 0.999441i | \(-0.489357\pi\) | ||||
0.0334301 | + | 0.999441i | \(0.489357\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.0761 | 1.78212 | 0.891060 | − | 0.453885i | \(-0.149962\pi\) | ||||
0.891060 | + | 0.453885i | \(0.149962\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.3875 | 0.549618 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.27316 | −0.109655 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.0927 | 0.973549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.76986 | −0.159439 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.50331 | −0.0835830 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.9338 | −1.29852 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.2798 | 0.942136 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.0132 | 0.333219 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.7335 | −0.522998 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.46690 | 0.247934 | 0.123967 | − | 0.992286i | \(-0.460438\pi\) | ||||
0.123967 | + | 0.992286i | \(0.460438\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.23014 | 0.173473 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.6456 | −1.87675 | −0.938376 | − | 0.345615i | \(-0.887670\pi\) | ||||
−0.938376 | + | 0.345615i | \(0.887670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.8147 | −1.25148 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.27316 | 0.306561 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.1125 | 0.928357 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.7533 | 1.60822 | 0.804111 | − | 0.594479i | \(-0.202642\pi\) | ||||
0.804111 | + | 0.594479i | \(0.202642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.2930 | −0.734580 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.73345 | −0.188719 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.73345 | 0.254274 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.3923 | −1.78455 | −0.892276 | − | 0.451489i | \(-0.850893\pi\) | ||||
−0.892276 | + | 0.451489i | \(0.850893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.36915 | 0.0776458 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.7401 | 0.482052 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.5529 | 0.572819 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.8526 | −1.07096 | −0.535482 | − | 0.844547i | \(-0.679870\pi\) | ||||
−0.535482 | + | 0.844547i | \(0.679870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.3592 | 0.630423 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.50331 | 0.0814326 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.63237 | 0.215523 | 0.107762 | − | 0.994177i | \(-0.465632\pi\) | ||||
0.107762 | + | 0.994177i | \(0.465632\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.7765 | 0.512126 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.54633 | 0.147425 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.5298 | 1.31289 | 0.656444 | − | 0.754375i | \(-0.272060\pi\) | ||||
0.656444 | + | 0.754375i | \(0.272060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.0132 | −0.841768 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.4537 | −0.822800 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.9272 | −1.09557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.93380 | −0.191413 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.726836 | 0.0234220 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.503308 | 0.0162020 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.3426 | −1.39381 | −0.696903 | − | 0.717166i | \(-0.745439\pi\) | ||||
−0.696903 | + | 0.717166i | \(0.745439\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.5463 | 0.467295 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.78970 | −0.121617 | −0.0608087 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608087 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54.4055 | 1.74416 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.4669 | 0.558816 | 0.279408 | − | 0.960173i | \(-0.409862\pi\) | ||||
0.279408 | + | 0.960173i | \(0.409862\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.0349 | 1.59912 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.7831 | 0.535843 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0265 | 0.511165 | 0.255582 | − | 0.966787i | \(-0.417733\pi\) | ||||
0.255582 | + | 0.966787i | \(0.417733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.0066 | 0.350700 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.5463 | 0.717658 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.0132 | −0.318402 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.3923 | 1.15604 | 0.578019 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578019 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.7897 | 0.628007 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.01323 | 0.0638237 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.0331 | −0.602784 | −0.301392 | − | 0.953500i | \(-0.597451\pi\) | ||||
−0.301392 | + | 0.953500i | \(0.597451\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.73345 | −0.244676 |
(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 | 3120.2.a.bh.1.3 | 3 | ||
3.2 | odd | 2 | 9360.2.a.db.1.3 | 3 | |||
4.3 | odd | 2 | 1560.2.a.p.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 4680.2.a.bl.1.1 | 3 | |||
20.19 | odd | 2 | 7800.2.a.bf.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.a.p.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
3120.2.a.bh.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4680.2.a.bl.1.1 | 3 | 12.11 | even | 2 | |||
7800.2.a.bf.1.3 | 3 | 20.19 | odd | 2 | |||
9360.2.a.db.1.3 | 3 | 3.2 | odd | 2 |