Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3720,2,Mod(1,3720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3720, 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("3720.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3720 = 2^{3} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3720.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: | \(29.7043495519\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.78292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 10x^{2} + 8x + 18 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.09502\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3720.1 |
$q$-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 | ||||||||
\(7\) | −1.09502 | −0.413877 | −0.206939 | − | 0.978354i | \(-0.566350\pi\) | ||||
−0.206939 | + | 0.978354i | \(0.566350\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.25711 | 1.58508 | 0.792539 | − | 0.609822i | \(-0.208759\pi\) | ||||
0.792539 | + | 0.609822i | \(0.208759\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.24976 | 0.346620 | 0.173310 | − | 0.984867i | \(-0.444554\pi\) | ||||
0.173310 | + | 0.984867i | \(0.444554\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.64620 | −0.641798 | −0.320899 | − | 0.947113i | \(-0.603985\pi\) | ||||
−0.320899 | + | 0.947113i | \(0.603985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.25711 | 0.747232 | 0.373616 | − | 0.927584i | \(-0.378118\pi\) | ||||
0.373616 | + | 0.927584i | \(0.378118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.09502 | 0.238952 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.99097 | −1.45772 | −0.728859 | − | 0.684664i | \(-0.759949\pi\) | ||||
−0.728859 | + | 0.684664i | \(0.759949\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.89596 | 1.09485 | 0.547426 | − | 0.836854i | \(-0.315608\pi\) | ||||
0.547426 | + | 0.836854i | \(0.315608\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.25711 | −0.915145 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.09502 | 0.185092 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.24976 | −0.534257 | −0.267128 | − | 0.963661i | \(-0.586075\pi\) | ||||
−0.267128 | + | 0.963661i | \(0.586075\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.24976 | −0.200121 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.34477 | −0.662571 | −0.331286 | − | 0.943530i | \(-0.607482\pi\) | ||||
−0.331286 | + | 0.943530i | \(0.607482\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.14571 | 1.04231 | 0.521155 | − | 0.853462i | \(-0.325502\pi\) | ||||
0.521155 | + | 0.853462i | \(0.325502\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.80094 | −0.828706 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.64620 | 0.370542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.80094 | 0.934181 | 0.467090 | − | 0.884210i | \(-0.345302\pi\) | ||||
0.467090 | + | 0.884210i | \(0.345302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.25711 | −0.708868 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.25711 | −0.431414 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.80829 | −1.14674 | −0.573371 | − | 0.819296i | \(-0.694365\pi\) | ||||
−0.573371 | + | 0.819296i | \(0.694365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.91234 | 0.372886 | 0.186443 | − | 0.982466i | \(-0.440304\pi\) | ||||
0.186443 | + | 0.982466i | \(0.440304\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.09502 | −0.137959 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.24976 | −0.155013 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.43979 | 0.175898 | 0.0879491 | − | 0.996125i | \(-0.471969\pi\) | ||||
0.0879491 | + | 0.996125i | \(0.471969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.99097 | 0.841614 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.24073 | −0.503282 | −0.251641 | − | 0.967821i | \(-0.580970\pi\) | ||||
−0.251641 | + | 0.967821i | \(0.580970\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.69689 | −1.01789 | −0.508947 | − | 0.860798i | \(-0.669965\pi\) | ||||
−0.508947 | + | 0.860798i | \(0.669965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.75662 | −0.656027 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0933 | 1.36061 | 0.680304 | − | 0.732931i | \(-0.261848\pi\) | ||||
0.680304 | + | 0.732931i | \(0.261848\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0433434 | 0.00475755 | 0.00237878 | − | 0.999997i | \(-0.499243\pi\) | ||||
0.00237878 | + | 0.999997i | \(0.499243\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.64620 | 0.287021 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.89596 | −0.632113 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.63885 | 0.491717 | 0.245858 | − | 0.969306i | \(-0.420930\pi\) | ||||
0.245858 | + | 0.969306i | \(0.420930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.36850 | −0.143458 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.25711 | −0.334172 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.309478 | 0.0314228 | 0.0157114 | − | 0.999877i | \(-0.494999\pi\) | ||||
0.0157114 | + | 0.999877i | \(0.494999\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.25711 | 0.528359 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.4789 | 1.63971 | 0.819857 | − | 0.572568i | \(-0.194053\pi\) | ||||
0.819857 | + | 0.572568i | \(0.194053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0417 | −1.48210 | −0.741050 | − | 0.671450i | \(-0.765672\pi\) | ||||
−0.741050 | + | 0.671450i | \(0.765672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.09502 | −0.106863 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0786 | −0.974339 | −0.487169 | − | 0.873308i | \(-0.661971\pi\) | ||||
−0.487169 | + | 0.873308i | \(0.661971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2481 | 0.981588 | 0.490794 | − | 0.871276i | \(-0.336707\pi\) | ||||
0.490794 | + | 0.871276i | \(0.336707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.24976 | 0.308453 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1547 | 0.955278 | 0.477639 | − | 0.878556i | \(-0.341493\pi\) | ||||
0.477639 | + | 0.878556i | \(0.341493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.99097 | 0.651911 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.24976 | 0.115540 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.89763 | 0.265626 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.6372 | 1.51247 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.00000 | −0.360668 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.7033 | 1.92585 | 0.962927 | − | 0.269763i | \(-0.0869453\pi\) | ||||
0.962927 | + | 0.269763i | \(0.0869453\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.34477 | 0.382536 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.0997 | −1.66875 | −0.834375 | − | 0.551197i | \(-0.814171\pi\) | ||||
−0.834375 | + | 0.551197i | \(0.814171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.56659 | −0.309262 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3367 | 0.883126 | 0.441563 | − | 0.897230i | \(-0.354424\pi\) | ||||
0.441563 | + | 0.897230i | \(0.354424\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.80997 | −0.153519 | −0.0767597 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767597 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.14571 | −0.601777 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.57010 | 0.549419 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.89596 | −0.489632 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.80094 | 0.478453 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.2571 | 1.24991 | 0.624955 | − | 0.780660i | \(-0.285117\pi\) | ||||
0.624955 | + | 0.780660i | \(0.285117\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.26613 | 0.509931 | 0.254965 | − | 0.966950i | \(-0.417936\pi\) | ||||
0.254965 | + | 0.966950i | \(0.417936\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.64620 | −0.213933 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.2391 | 1.69506 | 0.847530 | − | 0.530747i | \(-0.178089\pi\) | ||||
0.847530 | + | 0.530747i | \(0.178089\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.80094 | −0.539350 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.65523 | 0.603317 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.3511 | 1.20239 | 0.601197 | − | 0.799101i | \(-0.294691\pi\) | ||||
0.601197 | + | 0.799101i | \(0.294691\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.25711 | 0.409265 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6690 | 1.44465 | 0.722323 | − | 0.691555i | \(-0.243074\pi\) | ||||
0.722323 | + | 0.691555i | \(0.243074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4381 | −0.879855 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.25711 | 0.249077 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.4118 | 1.01968 | 0.509842 | − | 0.860268i | \(-0.329704\pi\) | ||||
0.509842 | + | 0.860268i | \(0.329704\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.09502 | −0.0827755 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.80829 | 0.662072 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.4962 | −1.83093 | −0.915464 | − | 0.402399i | \(-0.868176\pi\) | ||||
−0.915464 | + | 0.402399i | \(0.868176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0343 | 1.26615 | 0.633075 | − | 0.774090i | \(-0.281792\pi\) | ||||
0.633075 | + | 0.774090i | \(0.281792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.91234 | −0.215286 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.24976 | 0.238927 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.9114 | −1.01730 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.09502 | 0.0796507 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4988 | 0.904382 | 0.452191 | − | 0.891921i | \(-0.350642\pi\) | ||||
0.452191 | + | 0.891921i | \(0.350642\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.60188 | −0.403232 | −0.201616 | − | 0.979465i | \(-0.564619\pi\) | ||||
−0.201616 | + | 0.979465i | \(0.564619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.24976 | 0.0894968 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.2481 | 1.72760 | 0.863802 | − | 0.503831i | \(-0.168077\pi\) | ||||
0.863802 | + | 0.503831i | \(0.168077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.61091 | −0.326859 | −0.163429 | − | 0.986555i | \(-0.552256\pi\) | ||||
−0.163429 | + | 0.986555i | \(0.552256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.43979 | −0.101555 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.45617 | −0.453134 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | −0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.99097 | −0.485906 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.1230 | 1.18442 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.35947 | −0.162433 | −0.0812165 | − | 0.996696i | \(-0.525881\pi\) | ||||
−0.0812165 | + | 0.996696i | \(0.525881\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.24073 | 0.290570 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.34477 | 0.296311 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.09502 | −0.0743346 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.69689 | 0.587682 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.30710 | −0.222460 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.792889 | 0.0530958 | 0.0265479 | − | 0.999648i | \(-0.491549\pi\) | ||||
0.0265479 | + | 0.999648i | \(0.491549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.7976 | 1.51313 | 0.756564 | − | 0.653919i | \(-0.226876\pi\) | ||||
0.756564 | + | 0.653919i | \(0.226876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.60539 | −0.436497 | −0.218248 | − | 0.975893i | \(-0.570034\pi\) | ||||
−0.218248 | + | 0.975893i | \(0.570034\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.75662 | 0.378758 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.7417 | 1.88293 | 0.941466 | − | 0.337109i | \(-0.109449\pi\) | ||||
0.941466 | + | 0.337109i | \(0.109449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.14571 | −0.466135 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0933 | −0.785547 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.10139 | −0.135928 | −0.0679638 | − | 0.997688i | \(-0.521650\pi\) | ||||
−0.0679638 | + | 0.997688i | \(0.521650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.11945 | 0.265357 | 0.132678 | − | 0.991159i | \(-0.457642\pi\) | ||||
0.132678 | + | 0.991159i | \(0.457642\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.80094 | 0.370608 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.07059 | 0.259005 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0433434 | −0.00274677 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.1161 | 1.52219 | 0.761097 | − | 0.648638i | \(-0.224661\pi\) | ||||
0.761097 | + | 0.648638i | \(0.224661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.7523 | −2.31060 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.64620 | −0.165711 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.09334 | −0.255336 | −0.127668 | − | 0.991817i | \(-0.540749\pi\) | ||||
−0.127668 | + | 0.991817i | \(0.540749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.55854 | 0.221117 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.89596 | 0.364950 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5289 | 0.649241 | 0.324620 | − | 0.945844i | \(-0.394763\pi\) | ||||
0.324620 | + | 0.945844i | \(0.394763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.80094 | −0.417778 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.63885 | −0.283893 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.61728 | −0.342492 | −0.171246 | − | 0.985228i | \(-0.554779\pi\) | ||||
−0.171246 | + | 0.985228i | \(0.554779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.8556 | −1.63136 | −0.815682 | − | 0.578501i | \(-0.803638\pi\) | ||||
−0.815682 | + | 0.578501i | \(0.803638\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.36850 | 0.0828255 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.25711 | 0.317015 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.1578 | −1.87209 | −0.936044 | − | 0.351883i | \(-0.885542\pi\) | ||||
−0.936044 | + | 0.351883i | \(0.885542\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.3948 | 1.33596 | 0.667980 | − | 0.744179i | \(-0.267159\pi\) | ||||
0.667980 | + | 0.744179i | \(0.267159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.616096 | −0.0366231 | −0.0183116 | − | 0.999832i | \(-0.505829\pi\) | ||||
−0.0183116 | + | 0.999832i | \(0.505829\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.25711 | 0.192934 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.38007 | −0.258547 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.99762 | −0.588096 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.309478 | −0.0181419 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.0400 | −1.63811 | −0.819057 | − | 0.573712i | \(-0.805503\pi\) | ||||
−0.819057 | + | 0.573712i | \(0.805503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.80829 | 0.512839 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.25711 | −0.305048 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.73701 | −0.505274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.75760 | 0.274223 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.4789 | −0.946689 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.91234 | −0.166760 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6118 | −1.11930 | −0.559651 | − | 0.828728i | \(-0.689065\pi\) | ||||
−0.559651 | + | 0.828728i | \(0.689065\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0417 | 0.855691 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.2750 | 1.77344 | 0.886722 | − | 0.462302i | \(-0.152976\pi\) | ||||
0.886722 | + | 0.462302i | \(0.152976\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.630799 | −0.0356549 | −0.0178274 | − | 0.999841i | \(-0.505675\pi\) | ||||
−0.0178274 | + | 0.999841i | \(0.505675\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.09502 | 0.0616972 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.88272 | −0.218075 | −0.109038 | − | 0.994038i | \(-0.534777\pi\) | ||||
−0.109038 | + | 0.994038i | \(0.534777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.9957 | 1.73542 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0786 | 0.562535 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.61896 | −0.479572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.24976 | 0.0693240 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.2481 | −0.566720 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.82467 | −0.431388 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3504 | −0.623877 | −0.311938 | − | 0.950102i | \(-0.600978\pi\) | ||||
−0.311938 | + | 0.950102i | \(0.600978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.24976 | −0.178086 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.43979 | −0.0786640 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6435 | 1.12453 | 0.562263 | − | 0.826959i | \(-0.309931\pi\) | ||||
0.562263 | + | 0.826959i | \(0.309931\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.1547 | −0.551530 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.25711 | 0.284688 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.0172 | 0.756860 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.99097 | −0.376381 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.6166 | −1.16044 | −0.580219 | − | 0.814460i | \(-0.697033\pi\) | ||||
−0.580219 | + | 0.814460i | \(0.697033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.42341 | −0.236780 | −0.118390 | − | 0.992967i | \(-0.537773\pi\) | ||||
−0.118390 | + | 0.992967i | \(0.537773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.24976 | −0.0667070 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8680 | 0.844569 | 0.422285 | − | 0.906463i | \(-0.361228\pi\) | ||||
0.422285 | + | 0.906463i | \(0.361228\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.24073 | 0.225074 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.89763 | −0.153359 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.59767 | 0.453768 | 0.226884 | − | 0.973922i | \(-0.427146\pi\) | ||||
0.226884 | + | 0.973922i | \(0.427146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.39126 | −0.441645 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.6372 | −0.873225 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.69689 | 0.455216 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.3389 | −0.644084 | −0.322042 | − | 0.946725i | \(-0.604369\pi\) | ||||
−0.322042 | + | 0.946725i | \(0.604369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.44714 | −0.386636 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2528 | 1.46287 | 0.731437 | − | 0.681909i | \(-0.238850\pi\) | ||||
0.731437 | + | 0.681909i | \(0.238850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.36850 | 0.379497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.0172 | −1.64462 | −0.822308 | − | 0.569043i | \(-0.807314\pi\) | ||||
−0.822308 | + | 0.569043i | \(0.807314\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.7033 | −1.11189 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.0082 | 0.562493 | 0.281247 | − | 0.959636i | \(-0.409252\pi\) | ||||
0.281247 | + | 0.959636i | \(0.409252\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.75662 | 0.293384 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.34477 | −0.220857 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.60020 | −0.233239 | −0.116620 | − | 0.993177i | \(-0.537206\pi\) | ||||
−0.116620 | + | 0.993177i | \(0.537206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.4995 | 0.935560 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.0997 | 0.963453 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0933 | −0.608482 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.47892 | −0.325168 | −0.162584 | − | 0.986695i | \(-0.551983\pi\) | ||||
−0.162584 | + | 0.986695i | \(0.551983\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.56659 | 0.178553 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.0506947 | 0.00253157 | 0.00126579 | − | 0.999999i | \(-0.499597\pi\) | ||||
0.00126579 | + | 0.999999i | \(0.499597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.24976 | 0.0622548 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.0843 | −0.846838 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1867 | 0.899273 | 0.449637 | − | 0.893212i | \(-0.351553\pi\) | ||||
0.449637 | + | 0.893212i | \(0.351553\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.3367 | −0.509873 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.64522 | 0.474610 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0433434 | −0.00212764 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.80997 | 0.0886345 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.4798 | 0.658530 | 0.329265 | − | 0.944238i | \(-0.393199\pi\) | ||||
0.329265 | + | 0.944238i | \(0.393199\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.14571 | 0.348261 | 0.174130 | − | 0.984723i | \(-0.444289\pi\) | ||||
0.174130 | + | 0.984723i | \(0.444289\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.14571 | 0.347436 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.64620 | −0.128360 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.18905 | −0.154329 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.57010 | −0.317207 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.6551 | 1.91012 | 0.955060 | − | 0.296414i | \(-0.0957907\pi\) | ||||
0.955060 | + | 0.296414i | \(0.0957907\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4011 | 0.644018 | 0.322009 | − | 0.946737i | \(-0.395642\pi\) | ||||
0.322009 | + | 0.946737i | \(0.395642\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.89596 | 0.282689 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.7703 | −1.08925 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.8943 | −1.28359 | −0.641797 | − | 0.766875i | \(-0.721811\pi\) | ||||
−0.641797 | + | 0.766875i | \(0.721811\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.80094 | −0.276235 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7692 | −0.844238 | −0.422119 | − | 0.906540i | \(-0.638714\pi\) | ||||
−0.422119 | + | 0.906540i | \(0.638714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.63885 | −0.219903 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.2571 | −0.721636 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.8642 | 0.795870 | 0.397935 | − | 0.917414i | \(-0.369727\pi\) | ||||
0.397935 | + | 0.917414i | \(0.369727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0284 | 0.990190 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.26613 | −0.294409 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.36850 | 0.0641564 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.67728 | 0.452684 | 0.226342 | − | 0.974048i | \(-0.427323\pi\) | ||||
0.226342 | + | 0.974048i | \(0.427323\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.64620 | 0.123514 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2442 | 0.709995 | 0.354998 | − | 0.934867i | \(-0.384482\pi\) | ||||
0.354998 | + | 0.934867i | \(0.384482\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.3028 | −1.96598 | −0.982988 | − | 0.183668i | \(-0.941203\pi\) | ||||
−0.982988 | + | 0.183668i | \(0.941203\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1277 | 0.607475 | 0.303738 | − | 0.952756i | \(-0.401765\pi\) | ||||
0.303738 | + | 0.952756i | \(0.401765\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.57659 | −0.0728002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.2391 | −0.978644 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.8409 | −1.05023 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.25711 | 0.149446 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.80094 | 0.311394 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.0791 | 0.871747 | 0.435874 | − | 0.900008i | \(-0.356439\pi\) | ||||
0.435874 | + | 0.900008i | \(0.356439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.06140 | −0.185184 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.65523 | −0.348325 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.309478 | −0.0140527 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.2365 | 0.962318 | 0.481159 | − | 0.876633i | \(-0.340216\pi\) | ||||
0.481159 | + | 0.876633i | \(0.340216\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.3511 | −0.694203 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.66797 | −0.346051 | −0.173025 | − | 0.984917i | \(-0.555354\pi\) | ||||
−0.173025 | + | 0.984917i | \(0.555354\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.6019 | −0.702673 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.25711 | −0.236289 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.64367 | 0.208297 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.7582 | −1.73505 | −0.867527 | − | 0.497390i | \(-0.834292\pi\) | ||||
−0.867527 | + | 0.497390i | \(0.834292\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.6690 | −0.834067 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.9249 | −0.576292 | −0.288146 | − | 0.957587i | \(-0.593039\pi\) | ||||
−0.288146 | + | 0.957587i | \(0.593039\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.4789 | −0.733302 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4381 | 0.507984 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.05421 | −0.135375 | −0.0676877 | − | 0.997707i | \(-0.521562\pi\) | ||||
−0.0676877 | + | 0.997707i | \(0.521562\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.52324 | 0.421283 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.25711 | −0.143805 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.0417 | 0.662815 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.5658 | 1.65214 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.4118 | −0.588715 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.13415 | −0.268742 | −0.134371 | − | 0.990931i | \(-0.542901\pi\) | ||||
−0.134371 | + | 0.990931i | \(0.542901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.6984 | 0.642714 | 0.321357 | − | 0.946958i | \(-0.395861\pi\) | ||||
0.321357 | + | 0.946958i | \(0.395861\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.09502 | 0.0477904 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.64620 | −0.115270 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.8737 | 1.12494 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.80829 | −0.382247 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.99902 | 0.216532 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0786 | 0.435737 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.4962 | 1.05709 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.4962 | −1.31356 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5542 | 0.883694 | 0.441847 | − | 0.897090i | \(-0.354323\pi\) | ||||
0.441847 | + | 0.897090i | \(0.354323\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.0343 | −0.731012 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.2481 | −0.438979 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.08285 | 0.302841 | 0.151420 | − | 0.988469i | \(-0.451615\pi\) | ||||
0.151420 | + | 0.988469i | \(0.451615\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.91234 | 0.124295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.2038 | 0.818108 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.2424 | −0.563124 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.24976 | −0.137944 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.18338 | 0.0925128 | 0.0462564 | − | 0.998930i | \(-0.485271\pi\) | ||||
0.0462564 | + | 0.998930i | \(0.485271\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.42990 | −0.229660 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.9114 | 0.587338 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.5164 | −1.45469 | −0.727346 | − | 0.686271i | \(-0.759246\pi\) | ||||
−0.727346 | + | 0.686271i | \(0.759246\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1547 | −0.427213 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.09502 | −0.0459864 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.65453 | 0.237050 | 0.118525 | − | 0.992951i | \(-0.462183\pi\) | ||||
0.118525 | + | 0.992951i | \(0.462183\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.1900 | 0.426440 | 0.213220 | − | 0.977004i | \(-0.431605\pi\) | ||||
0.213220 | + | 0.977004i | \(0.431605\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.4988 | −0.522145 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.99097 | −0.291544 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.70327 | 0.0709080 | 0.0354540 | − | 0.999371i | \(-0.488712\pi\) | ||||
0.0354540 | + | 0.999371i | \(0.488712\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.60188 | 0.232806 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0474617 | −0.00196904 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.7533 | 1.48075 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.24976 | −0.0516710 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.7042 | 0.524360 | 0.262180 | − | 0.965019i | \(-0.415559\pi\) | ||||
0.262180 | + | 0.965019i | \(0.415559\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.25711 | 0.134207 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.2481 | −0.997433 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.7023 | −1.17866 | −0.589331 | − | 0.807892i | \(-0.700609\pi\) | ||||
−0.589331 | + | 0.807892i | \(0.700609\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.89763 | −0.118791 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.61091 | 0.188712 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.8597 | 0.525432 | 0.262716 | − | 0.964873i | \(-0.415382\pi\) | ||||
0.262716 | + | 0.964873i | \(0.415382\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5289 | 0.511065 | 0.255533 | − | 0.966800i | \(-0.417749\pi\) | ||||
0.255533 | + | 0.966800i | \(0.417749\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.43979 | 0.0586327 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.6372 | −0.676397 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.22916 | −0.212245 | −0.106123 | − | 0.994353i | \(-0.533844\pi\) | ||||
−0.106123 | + | 0.994353i | \(0.533844\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.45617 | 0.261617 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.93039 | 0.361285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.8697 | −0.681360 | −0.340680 | − | 0.940179i | \(-0.610657\pi\) | ||||
−0.340680 | + | 0.940179i | \(0.610657\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.00000 | 0.161296 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.3551 | 1.74541 | 0.872706 | − | 0.488246i | \(-0.162363\pi\) | ||||
0.872706 | + | 0.488246i | \(0.162363\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.5448 | −0.584605 | −0.292303 | − | 0.956326i | \(-0.594421\pi\) | ||||
−0.292303 | + | 0.956326i | \(0.594421\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.99097 | 0.280538 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.07962 | −0.203510 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.1230 | −0.683825 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.59950 | 0.342885 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.4970 | 0.417878 | 0.208939 | − | 0.977929i | \(-0.432999\pi\) | ||||
0.208939 | + | 0.977929i | \(0.432999\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.35947 | 0.0937807 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.7033 | −0.861268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.24976 | −0.287246 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.24073 | −0.167761 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.2864 | −1.31473 | −0.657367 | − | 0.753571i | \(-0.728330\pi\) | ||||
−0.657367 | + | 0.753571i | \(0.728330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.3585 | 0.763425 | 0.381712 | − | 0.924281i | \(-0.375335\pi\) | ||||
0.381712 | + | 0.924281i | \(0.375335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.34477 | −0.171075 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.3732 | −0.761639 | −0.380820 | − | 0.924649i | \(-0.624358\pi\) | ||||
−0.380820 | + | 0.924649i | \(0.624358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.3061 | −1.81767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.09502 | 0.0429171 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.456168 | 0.0178512 | 0.00892561 | − | 0.999960i | \(-0.497159\pi\) | ||||
0.00892561 | + | 0.999960i | \(0.497159\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.0997 | 0.746288 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.69689 | −0.339298 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.2158 | 1.91718 | 0.958588 | − | 0.284797i | \(-0.0919263\pi\) | ||||
0.958588 | + | 0.284797i | \(0.0919263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.1984 | −1.75802 | −0.879008 | − | 0.476807i | \(-0.841794\pi\) | ||||
−0.879008 | + | 0.476807i | \(0.841794\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.30710 | 0.128437 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.56659 | 0.138306 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.2185 | −1.59599 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.792889 | −0.0306549 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3105 | 0.591054 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.1611 | 0.584418 | 0.292209 | − | 0.956354i | \(-0.405610\pi\) | ||||
0.292209 | + | 0.956354i | \(0.405610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.78386 | −0.145426 | −0.0727128 | − | 0.997353i | \(-0.523166\pi\) | ||||
−0.0727128 | + | 0.997353i | \(0.523166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.338884 | −0.0130052 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.7976 | −0.873605 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.3479 | −0.969911 | −0.484955 | − | 0.874539i | \(-0.661164\pi\) | ||||
−0.484955 | + | 0.874539i | \(0.661164\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.3367 | −0.394946 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.60539 | 0.252011 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.49951 | 0.323806 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0500 | 0.838821 | 0.419411 | − | 0.907797i | \(-0.362237\pi\) | ||||
0.419411 | + | 0.907797i | \(0.362237\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.75662 | −0.218676 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.80997 | 0.0686560 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.5848 | −0.400928 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.7417 | −1.08711 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.72819 | −0.178581 | −0.0892906 | − | 0.996006i | \(-0.528460\pi\) | ||||
−0.0892906 | + | 0.996006i | \(0.528460\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5848 | −0.399213 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.14571 | 0.269123 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.0447 | −0.678640 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.5305 | −1.55971 | −0.779855 | − | 0.625960i | \(-0.784707\pi\) | ||||
−0.779855 | + | 0.625960i | \(0.784707\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0933 | 0.453536 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.99097 | −0.261814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.57010 | −0.245708 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.10139 | 0.0784778 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2028 | −0.678849 | −0.339425 | − | 0.940633i | \(-0.610232\pi\) | ||||
−0.339425 | + | 0.940633i | \(0.610232\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.4709 | 0.613407 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.11945 | −0.153204 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.89596 | 0.218970 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.21209 | 0.0820418 | 0.0410209 | − | 0.999158i | \(-0.486939\pi\) | ||||
0.0410209 | + | 0.999158i | \(0.486939\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.4971 | 0.425237 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.0578 | −1.44263 | −0.721317 | − | 0.692605i | \(-0.756463\pi\) | ||||
−0.721317 | + | 0.692605i | \(0.756463\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.80094 | −0.213971 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.56912 | 0.278812 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.11491 | −0.0410126 | −0.0205063 | − | 0.999790i | \(-0.506528\pi\) | ||||
−0.0205063 | + | 0.999790i | \(0.506528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.07059 | −0.149537 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.7556 | −0.981569 | −0.490785 | − | 0.871281i | \(-0.663290\pi\) | ||||
−0.490785 | + | 0.871281i | \(0.663290\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.2571 | −0.558977 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0433434 | 0.00158585 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.0363 | 0.403257 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0783 | −0.513723 | −0.256862 | − | 0.966448i | \(-0.582688\pi\) | ||||
−0.256862 | + | 0.966448i | \(0.582688\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.1161 | −0.878839 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.26613 | −0.228048 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.16209 | 0.0785825 | 0.0392913 | − | 0.999228i | \(-0.487490\pi\) | ||||
0.0392913 | + | 0.999228i | \(0.487490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.7523 | 1.33402 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.46450 | −0.125588 | −0.0627940 | − | 0.998027i | \(-0.520001\pi\) | ||||
−0.0627940 | + | 0.998027i | \(0.520001\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2218 | −0.406257 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.64620 | 0.0956736 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.0082 | −0.397483 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0786 | −0.507689 | −0.253844 | − | 0.967245i | \(-0.581695\pi\) | ||||
−0.253844 | + | 0.967245i | \(0.581695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.09334 | 0.147418 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.8327 | −1.64849 | −0.824244 | − | 0.566235i | \(-0.808400\pi\) | ||||
−0.824244 | + | 0.566235i | \(0.808400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.55854 | −0.127662 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.0284 | 0.466792 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.2940 | −0.797740 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.89596 | −0.210704 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.2391 | −0.758054 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6234 | 0.449977 | 0.224989 | − | 0.974361i | \(-0.427765\pi\) | ||||
0.224989 | + | 0.974361i | \(0.427765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5289 | −0.374839 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.1196 | −0.395368 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.63971 | 0.129250 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.80094 | 0.241204 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.9841 | 0.424499 | 0.212249 | − | 0.977216i | \(-0.431921\pi\) | ||||
0.212249 | + | 0.977216i | \(0.431921\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.9090 | −0.668952 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.63885 | 0.163906 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −45.7205 | −1.61344 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.65523 | −0.269811 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.61728 | 0.197738 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.9611 | 0.526003 | 0.263002 | − | 0.964795i | \(-0.415288\pi\) | ||||
0.263002 | + | 0.964795i | \(0.415288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.9604 | 0.595559 | 0.297780 | − | 0.954635i | \(-0.403754\pi\) | ||||
0.297780 | + | 0.954635i | \(0.403754\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.8556 | 0.941868 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.3511 | −0.537727 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1514 | −0.495094 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.36850 | −0.0478194 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.8167 | −0.377506 | −0.188753 | − | 0.982025i | \(-0.560445\pi\) | ||||
−0.188753 | + | 0.982025i | \(0.560445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4085 | −0.397675 | −0.198838 | − | 0.980032i | \(-0.563717\pi\) | ||||
−0.198838 | + | 0.980032i | \(0.563717\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.25711 | −0.183029 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.6556 | 1.41373 | 0.706867 | − | 0.707347i | \(-0.250108\pi\) | ||||
0.706867 | + | 0.707347i | \(0.250108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0078 | 0.451781 | 0.225890 | − | 0.974153i | \(-0.427471\pi\) | ||||
0.225890 | + | 0.974153i | \(0.427471\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.1578 | 1.08085 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.3504 | 0.531861 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.6690 | −0.646066 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.8677 | −1.89424 | −0.947121 | − | 0.320876i | \(-0.896023\pi\) | ||||
−0.947121 | + | 0.320876i | \(0.896023\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.76229 | 0.198700 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.3948 | −0.771317 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.4381 | 0.393483 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.2180 | −0.625977 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.616096 | 0.0211444 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.7189 | 0.778796 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −57.6338 | −1.97334 | −0.986672 | − | 0.162721i | \(-0.947973\pi\) | ||||
−0.986672 | + | 0.162721i | \(0.947973\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.25711 | −0.111391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.34731 | −0.285139 | −0.142569 | − | 0.989785i | \(-0.545536\pi\) | ||||
−0.142569 | + | 0.989785i | \(0.545536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.7886 | −0.879894 | −0.439947 | − | 0.898024i | \(-0.645003\pi\) | ||||
−0.439947 | + | 0.898024i | \(0.645003\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.38007 | 0.149272 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.32672 | 0.283445 | 0.141722 | − | 0.989906i | \(-0.454736\pi\) | ||||
0.141722 | + | 0.989906i | \(0.454736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.4118 | −0.456016 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.99762 | 0.339537 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 63.5760 | 2.15667 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.79938 | 0.0609698 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.309478 | 0.0104743 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.09502 | 0.0370183 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.7377 | 1.94967 | 0.974833 | − | 0.222938i | \(-0.0715649\pi\) | ||||
0.974833 | + | 0.222938i | \(0.0715649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.0400 | 0.945765 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.6002 | −1.09833 | −0.549164 | − | 0.835714i | \(-0.685054\pi\) | ||||
−0.549164 | + | 0.835714i | \(0.685054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0955 | −0.945489 | −0.472744 | − | 0.881200i | \(-0.656737\pi\) | ||||
−0.472744 | + | 0.881200i | \(0.656737\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.80829 | −0.296087 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.1741 | −1.21461 | −0.607304 | − | 0.794469i | \(-0.707749\pi\) | ||||
−0.607304 | + | 0.794469i | \(0.707749\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.7654 | −0.797067 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.25711 | 0.176120 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.2743 | 0.778846 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.4962 | 0.818816 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.73701 | 0.291720 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.89596 | 0.196641 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.9966 | −0.599555 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.75760 | −0.158323 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.0343 | −0.566240 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.3488 | −0.476443 | −0.238222 | − | 0.971211i | \(-0.576564\pi\) | ||||
−0.238222 | + | 0.971211i | \(0.576564\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.4789 | 0.546571 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.48579 | 0.248015 | 0.124008 | − | 0.992281i | \(-0.460425\pi\) | ||||
0.124008 | + | 0.992281i | \(0.460425\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.227861 | 0.00754109 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.91234 | 0.0962788 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.9145 | 0.690658 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.84077 | −0.324617 | −0.162309 | − | 0.986740i | \(-0.551894\pi\) | ||||
−0.162309 | + | 0.986740i | \(0.551894\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.6118 | 0.646230 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.29987 | −0.174447 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.24976 | −0.106851 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.0417 | −0.494033 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.2227 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.8943 | −0.619235 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.2750 | −1.02390 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.9114 | 0.454950 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.5838 | −1.68517 | −0.842585 | − | 0.538563i | \(-0.818967\pi\) | ||||
−0.842585 | + | 0.538563i | \(0.818967\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.630799 | 0.0205853 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.44628 | 0.210143 | 0.105071 | − | 0.994465i | \(-0.466493\pi\) | ||||
0.105071 | + | 0.994465i | \(0.466493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.9639 | −0.910629 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.09502 | −0.0356209 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.2584 | 0.950772 | 0.475386 | − | 0.879777i | \(-0.342308\pi\) | ||||
0.475386 | + | 0.879777i | \(0.342308\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.8690 | −0.352822 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.88272 | 0.125906 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.3471 | 1.59851 | 0.799255 | − | 0.600993i | \(-0.205228\pi\) | ||||
0.799255 | + | 0.600993i | \(0.205228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.4988 | −0.404452 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.9957 | −1.00195 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.3189 | −0.365506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.0786 | −0.324780 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.60188 | 0.180331 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.6842 | 1.62990 | 0.814948 | − | 0.579535i | \(-0.196766\pi\) | ||||
0.814948 | + | 0.579535i | \(0.196766\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.61896 | 0.276881 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.76711 | 0.217167 | 0.108583 | − | 0.994087i | \(-0.465369\pi\) | ||||
0.108583 | + | 0.994087i | \(0.465369\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.98194 | 0.0635382 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.24976 | −0.0400242 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.5848 | 0.530595 | 0.265297 | − | 0.964167i | \(-0.414530\pi\) | ||||
0.265297 | + | 0.964167i | \(0.414530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.3869 | 0.779409 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.2481 | 0.327196 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.1171 | 0.482160 | 0.241080 | − | 0.970505i | \(-0.422498\pi\) | ||||
0.241080 | + | 0.970505i | \(0.422498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.2481 | −0.772608 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.82467 | 0.249062 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.3742 | 0.965843 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.9948 | 1.93757 | 0.968783 | − | 0.247912i | \(-0.0797443\pi\) | ||||
0.968783 | + | 0.247912i | \(0.0797443\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.3504 | 0.360196 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.61091 | 0.146176 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.2355 | 1.27427 | 0.637136 | − | 0.770751i | \(-0.280119\pi\) | ||||
0.637136 | + | 0.770751i | \(0.280119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.24976 | 0.102818 |
(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 | 3720.2.a.r.1.2 | ✓ | 4 | |
4.3 | odd | 2 | 7440.2.a.bx.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3720.2.a.r.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7440.2.a.bx.1.3 | 4 | 4.3 | odd | 2 |