Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(961,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.g (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.4 | ||
Root | \(3.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.961 |
Dual form | 1560.2.g.f.961.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.70156i | 1.77702i | 0.458854 | + | 0.888512i | \(0.348260\pi\) | ||||
−0.458854 | + | 0.888512i | \(0.651740\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.70156i | − | 0.814552i | −0.913305 | − | 0.407276i | \(-0.866479\pi\) | ||
0.913305 | − | 0.407276i | \(-0.133521\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.00000i | 0.554700 | − | 0.832050i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.00000i | − | 0.258199i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.70156 | 1.62537 | 0.812684 | − | 0.582705i | \(-0.198006\pi\) | ||||
0.812684 | + | 0.582705i | \(0.198006\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.40312i | − | 1.69839i | −0.528077 | − | 0.849197i | \(-0.677087\pi\) | ||
0.528077 | − | 0.849197i | \(-0.322913\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.70156i | − | 1.02596i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.70156 | 0.563315 | 0.281657 | − | 0.959515i | \(-0.409116\pi\) | ||||
0.281657 | + | 0.959515i | \(0.409116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.40312i | 1.68885i | 0.535673 | + | 0.844425i | \(0.320058\pi\) | ||||
−0.535673 | + | 0.844425i | \(0.679942\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.70156i | 0.470282i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.70156 | −0.794709 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.70156i | 0.444134i | 0.975031 | + | 0.222067i | \(0.0712804\pi\) | ||||
−0.975031 | + | 0.222067i | \(0.928720\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | + | 3.00000i | −0.320256 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.70156i | 1.35896i | 0.733696 | + | 0.679478i | \(0.237794\pi\) | ||||
−0.733696 | + | 0.679478i | \(0.762206\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.40312 | −0.213974 | −0.106987 | − | 0.994260i | \(-0.534120\pi\) | ||||
−0.106987 | + | 0.994260i | \(0.534120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.1047 | −2.15781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.70156 | −0.938406 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.70156 | 1.19525 | 0.597626 | − | 0.801775i | \(-0.296111\pi\) | ||||
0.597626 | + | 0.801775i | \(0.296111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.70156 | 0.364279 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.40312i | 0.980568i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.596876i | 0.0777066i | 0.999245 | + | 0.0388533i | \(0.0123705\pi\) | ||||
−0.999245 | + | 0.0388533i | \(0.987629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.70156 | 0.858047 | 0.429024 | − | 0.903293i | \(-0.358858\pi\) | ||||
0.429024 | + | 0.903293i | \(0.358858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.70156i | 0.592341i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | + | 2.00000i | 0.372104 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.70156 | −0.325230 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.701562i | − | 0.0832601i | −0.999133 | − | 0.0416301i | \(-0.986745\pi\) | ||
0.999133 | − | 0.0416301i | \(-0.0132551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.8062i | − | 1.49886i | −0.662085 | − | 0.749429i | \(-0.730328\pi\) | ||
0.662085 | − | 0.749429i | \(-0.269672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.7016 | 1.44748 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.29844 | −0.371103 | −0.185552 | − | 0.982635i | \(-0.559407\pi\) | ||||
−0.185552 | + | 0.982635i | \(0.559407\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.40312i | 1.03213i | 0.856550 | + | 0.516063i | \(0.172603\pi\) | ||||
−0.856550 | + | 0.516063i | \(0.827397\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.70156i | 0.726886i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.70156i | 0.498365i | 0.968457 | + | 0.249182i | \(0.0801618\pi\) | ||||
−0.968457 | + | 0.249182i | \(0.919838\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.1047 | + | 9.40312i | 1.47857 | + | 0.985715i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 9.40312i | − | 0.975059i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.40312 | 0.759545 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 16.1047i | − | 1.63518i | −0.575799 | − | 0.817592i | \(-0.695309\pi\) | ||
0.575799 | − | 0.817592i | \(-0.304691\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.70156i | − | 0.271517i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.80625 | −0.876254 | −0.438127 | − | 0.898913i | \(-0.644358\pi\) | ||||
−0.438127 | + | 0.898913i | \(0.644358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.40312 | −0.335320 | −0.167660 | − | 0.985845i | \(-0.553621\pi\) | ||||
−0.167660 | + | 0.985845i | \(0.553621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.70156 | 0.458825 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.10469 | −0.590162 | −0.295081 | − | 0.955472i | \(-0.595347\pi\) | ||||
−0.295081 | + | 0.955472i | \(0.595347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000i | 0.574696i | 0.957826 | + | 0.287348i | \(0.0927736\pi\) | ||||
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.70156i | − | 0.256421i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.70156i | 0.251922i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | − | 3.00000i | 0.184900 | − | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 31.5078i | 2.88832i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.70156 | 0.336506 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.70156i | − | 0.784593i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.80625 | 0.781428 | 0.390714 | − | 0.920512i | \(-0.372228\pi\) | ||||
0.390714 | + | 0.920512i | \(0.372228\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.40312 | 0.123538 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34.8062 | 3.01808 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.80625i | − | 0.752369i | −0.926545 | − | 0.376184i | \(-0.877236\pi\) | ||
0.926545 | − | 0.376184i | \(-0.122764\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1047 | 0.857068 | 0.428534 | − | 0.903526i | \(-0.359030\pi\) | ||||
0.428534 | + | 0.903526i | \(0.359030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 8.00000i | − | 0.673722i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.10469 | − | 5.40312i | −0.677748 | − | 0.451832i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000i | 0.166091i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.1047 | 1.24581 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.7016i | 1.20440i | 0.798346 | + | 0.602199i | \(0.205709\pi\) | ||||
−0.798346 | + | 0.602199i | \(0.794291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.40312i | − | 0.439700i | −0.975534 | − | 0.219850i | \(-0.929443\pi\) | ||
0.975534 | − | 0.219850i | \(-0.0705568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.70156 | 0.541789 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.40312 | −0.755277 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.8062 | −1.82014 | −0.910068 | − | 0.414458i | \(-0.863971\pi\) | ||||
−0.910068 | + | 0.414458i | \(0.863971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.70156 | −0.690079 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.7016i | 1.00102i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.29844i | − | 0.571658i | −0.958281 | − | 0.285829i | \(-0.907731\pi\) | ||
0.958281 | − | 0.285829i | \(-0.0922689\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.70156 | −0.210316 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | − | 12.0000i | −0.384615 | − | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 7.40312i | − | 0.566131i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5969 | 0.805666 | 0.402833 | − | 0.915274i | \(-0.368026\pi\) | ||||
0.402833 | + | 0.915274i | \(0.368026\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.70156i | − | 0.355405i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.596876i | − | 0.0448639i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.80625 | 0.508723 | 0.254361 | − | 0.967109i | \(-0.418135\pi\) | ||||
0.254361 | + | 0.967109i | \(0.418135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.10469 | 0.602417 | 0.301208 | − | 0.953558i | \(-0.402610\pi\) | ||||
0.301208 | + | 0.953558i | \(0.402610\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.70156 | −0.495394 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.70156 | −0.198623 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 18.1047i | − | 1.32395i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 4.70156i | − | 0.341988i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.5078i | 1.83609i | 0.396473 | + | 0.918046i | \(0.370234\pi\) | ||||
−0.396473 | + | 0.918046i | \(0.629766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.00000 | − | 2.00000i | −0.214834 | − | 0.143223i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.8062i | 0.912407i | 0.889875 | + | 0.456204i | \(0.150791\pi\) | ||||
−0.889875 | + | 0.456204i | \(0.849209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8062 | −1.04959 | −0.524794 | − | 0.851230i | \(-0.675857\pi\) | ||||
−0.524794 | + | 0.851230i | \(0.675857\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.00000i | − | 0.564276i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.40312i | 0.659970i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.70156 | −0.607743 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.70156 | 0.187772 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.0000 | −1.38343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.6125 | −1.76324 | −0.881619 | − | 0.471963i | \(-0.843546\pi\) | ||||
−0.881619 | + | 0.471963i | \(0.843546\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.701562i | 0.0480702i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.40312i | − | 0.0956923i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44.2094 | −3.00113 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.8062i | 0.865366i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.4031 | − | 20.1047i | 0.901592 | − | 1.35239i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.0000i | − | 1.60716i | −0.595198 | − | 0.803579i | \(-0.702926\pi\) | ||
0.595198 | − | 0.803579i | \(-0.297074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8062i | 0.717236i | 0.933484 | + | 0.358618i | \(0.116752\pi\) | ||||
−0.933484 | + | 0.358618i | \(0.883248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8062i | 1.11059i | 0.831654 | + | 0.555294i | \(0.187394\pi\) | ||||
−0.831654 | + | 0.555294i | \(0.812606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.7016 | −0.835701 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.70156 | −0.176985 | −0.0884926 | − | 0.996077i | \(-0.528205\pi\) | ||||
−0.0884926 | + | 0.996077i | \(0.528205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.29844 | 0.214257 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.29844i | 0.213358i | 0.994294 | + | 0.106679i | \(0.0340218\pi\) | ||||
−0.994294 | + | 0.106679i | \(0.965978\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.40312i | 0.0903832i | 0.998978 | + | 0.0451916i | \(0.0143898\pi\) | ||||
−0.998978 | + | 0.0451916i | \(0.985610\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 15.1047i | − | 0.965003i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.2094 | − | 14.8062i | −1.41315 | − | 0.942099i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 9.40312i | − | 0.595899i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.4031 | 1.85591 | 0.927954 | − | 0.372694i | \(-0.121566\pi\) | ||||
0.927954 | + | 0.372694i | \(0.121566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.29844i | − | 0.458849i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 6.70156i | − | 0.419668i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.8062 | 1.29786 | 0.648929 | − | 0.760849i | \(-0.275217\pi\) | ||||
0.648929 | + | 0.760849i | \(0.275217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.7016 | −0.789237 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.2094 | 1.12284 | 0.561419 | − | 0.827532i | \(-0.310256\pi\) | ||||
0.561419 | + | 0.827532i | \(0.310256\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.70156i | 0.534533i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.70156i | − | 0.287731i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.596876 | −0.0363922 | −0.0181961 | − | 0.999834i | \(-0.505792\pi\) | ||||
−0.0181961 | + | 0.999834i | \(0.505792\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.59688i | − | 0.157749i | −0.996885 | − | 0.0788745i | \(-0.974867\pi\) | ||
0.996885 | − | 0.0788745i | \(-0.0251326\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.1047 | − | 9.40312i | −0.853654 | − | 0.569103i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.70156i | 0.162910i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.8062 | 0.649285 | 0.324642 | − | 0.945837i | \(-0.394756\pi\) | ||||
0.324642 | + | 0.945837i | \(0.394756\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.40312i | 0.562950i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.4031i | − | 1.03818i | −0.854719 | − | 0.519092i | \(-0.826270\pi\) | ||
0.854719 | − | 0.519092i | \(-0.173730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4031 | 0.796733 | 0.398367 | − | 0.917226i | \(-0.369577\pi\) | ||||
0.398367 | + | 0.917226i | \(0.369577\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.40312 | −0.438523 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.9109 | −2.41490 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.9109 | 1.64182 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.1047i | 0.944073i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.596876 | −0.0347515 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.70156i | 0.156761i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.40312 | − | 8.10469i | 0.312471 | − | 0.468706i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.59688i | − | 0.380238i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.80625 | 0.505906 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.70156i | 0.383730i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.1047i | − | 0.576705i | −0.957524 | − | 0.288352i | \(-0.906893\pi\) | ||
0.957524 | − | 0.288352i | \(-0.0931075\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.40312 | 0.193597 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.40312 | 0.306383 | 0.153192 | − | 0.988197i | \(-0.451045\pi\) | ||||
0.153192 | + | 0.988197i | \(0.451045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.20937 | 0.350974 | 0.175487 | − | 0.984482i | \(-0.443850\pi\) | ||||
0.175487 | + | 0.984482i | \(0.443850\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.70156 | −0.264903 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 28.8062i | − | 1.61792i | −0.587864 | − | 0.808960i | \(-0.700031\pi\) | ||
0.587864 | − | 0.808960i | \(-0.299969\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.40312i | − | 0.302517i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.10469 | 0.340730 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 49.6125i | − | 2.76051i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | + | 3.00000i | −0.110940 | + | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 6.00000i | − | 0.331801i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.6125 | −2.07364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 15.4031i | − | 0.846632i | −0.905982 | − | 0.423316i | \(-0.860866\pi\) | ||
0.905982 | − | 0.423316i | \(-0.139134\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.70156i | 0.148045i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.19375 | −0.391869 | −0.195934 | − | 0.980617i | \(-0.562774\pi\) | ||||
−0.195934 | + | 0.980617i | \(0.562774\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.0000 | −0.760376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.4031 | 1.37566 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 38.1047i | − | 2.05746i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2.70156i | − | 0.145447i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.5078 | 1.69143 | 0.845714 | − | 0.533637i | \(-0.179175\pi\) | ||||
0.845714 | + | 0.533637i | \(0.179175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.80625i | − | 0.471388i | −0.971827 | − | 0.235694i | \(-0.924264\pi\) | ||
0.971827 | − | 0.235694i | \(-0.0757363\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | + | 3.00000i | −0.106752 | + | 0.160128i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.2094i | 1.60788i | 0.594709 | + | 0.803941i | \(0.297267\pi\) | ||||
−0.594709 | + | 0.803941i | \(0.702733\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.701562 | 0.0372351 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 31.5078i | − | 1.66757i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0000i | 0.844448i | 0.906492 | + | 0.422224i | \(0.138750\pi\) | ||||
−0.906492 | + | 0.422224i | \(0.861250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.8062 | −1.88454 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.70156 | −0.194282 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.8062 | 0.670310 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.70156i | 0.452985i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.9109i | 2.12399i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.6125 | −1.74039 | −0.870195 | − | 0.492708i | \(-0.836007\pi\) | ||||
−0.870195 | + | 0.492708i | \(0.836007\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | − | 6.00000i | 0.206010 | − | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.80625i | 0.246880i | 0.992352 | + | 0.123440i | \(0.0393927\pi\) | ||||
−0.992352 | + | 0.123440i | \(0.960607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.80625 | −0.451158 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 6.59688i | − | 0.337085i | −0.985694 | − | 0.168542i | \(-0.946094\pi\) | ||
0.985694 | − | 0.168542i | \(-0.0539060\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.7016i | 0.647332i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.40312 | −0.0713248 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.1047 | 0.915593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.29844i | − | 0.165962i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 17.2984i | − | 0.868184i | −0.900869 | − | 0.434092i | \(-0.857069\pi\) | ||
0.900869 | − | 0.434092i | \(-0.142931\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.8062 | −1.74249 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 28.2094i | − | 1.40871i | −0.709848 | − | 0.704354i | \(-0.751237\pi\) | ||
0.709848 | − | 0.704354i | \(-0.248763\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.2094 | + | 18.8062i | 1.40521 | + | 0.936806i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.29844 | 0.361770 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.80625i | − | 0.336547i | −0.985740 | − | 0.168274i | \(-0.946181\pi\) | ||
0.985740 | − | 0.168274i | \(-0.0538192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.80625i | 0.434380i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.80625 | −0.138086 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.40312 | −0.461581 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.1047 | −0.494829 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.4031 | −1.04561 | −0.522806 | − | 0.852452i | \(-0.675115\pi\) | ||||
−0.522806 | + | 0.852452i | \(0.675115\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.8062i | − | 0.624138i | −0.950059 | − | 0.312069i | \(-0.898978\pi\) | ||
0.950059 | − | 0.312069i | \(-0.101022\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.70156 | −0.325074 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.5078i | 1.52477i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.10469 | + | 5.40312i | 0.391298 | + | 0.260865i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 30.8062i | − | 1.48388i | −0.670464 | − | 0.741942i | \(-0.733905\pi\) | ||
0.670464 | − | 0.741942i | \(-0.266095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6125 | −1.13474 | −0.567372 | − | 0.823462i | \(-0.692040\pi\) | ||||
−0.567372 | + | 0.823462i | \(0.692040\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 2.00000i | − | 0.0958927i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 20.0000i | − | 0.956730i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.89531 | 0.472278 | 0.236139 | − | 0.971719i | \(-0.424118\pi\) | ||||
0.236139 | + | 0.971719i | \(0.424118\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.1047 | −0.719271 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.2984 | −0.536805 | −0.268402 | − | 0.963307i | \(-0.586496\pi\) | ||||
−0.268402 | + | 0.963307i | \(0.586496\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.70156 | −0.222875 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.7016i | − | 0.695360i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9109i | 0.798076i | 0.916934 | + | 0.399038i | \(0.130656\pi\) | ||||
−0.916934 | + | 0.399038i | \(0.869344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.5078 | 1.10694 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.40312i | 0.253861i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.40312 | + | 14.1047i | −0.440825 | + | 0.661238i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.8953i | 0.743551i | 0.928323 | + | 0.371776i | \(0.121251\pi\) | ||||
−0.928323 | + | 0.371776i | \(0.878749\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.70156 | −0.312802 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.7172i | 1.57037i | 0.619264 | + | 0.785183i | \(0.287431\pi\) | ||||
−0.619264 | + | 0.785183i | \(0.712569\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.50781i | 0.348918i | 0.984664 | + | 0.174459i | \(0.0558176\pi\) | ||||
−0.984664 | + | 0.174459i | \(0.944182\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.40312 | 0.436059 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.1047 | 1.39308 | 0.696539 | − | 0.717519i | \(-0.254722\pi\) | ||||
0.696539 | + | 0.717519i | \(0.254722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.6125 | −1.73678 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.8062 | 1.05086 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.79063i | 0.174293i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.40312i | 0.339679i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.70156 | 0.398417 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 26.3141i | − | 1.20232i | −0.799129 | − | 0.601160i | \(-0.794705\pi\) | ||
0.799129 | − | 0.601160i | \(-0.205295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.10469 | + | 5.40312i | 0.369542 | + | 0.246361i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 12.7016i | − | 0.577941i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.1047 | 0.731276 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5078i | 0.702726i | 0.936239 | + | 0.351363i | \(0.114282\pi\) | ||||
−0.936239 | + | 0.351363i | \(0.885718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.29844i | 0.330047i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.6125 | −1.51691 | −0.758455 | − | 0.651725i | \(-0.774046\pi\) | ||||
−0.758455 | + | 0.651725i | \(0.774046\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4031 | 0.603646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.70156 | 0.121426 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.29844 | 0.147955 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 27.4031i | − | 1.22673i | −0.789799 | − | 0.613366i | \(-0.789815\pi\) | ||
0.789799 | − | 0.613366i | \(-0.210185\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 8.00000i | − | 0.357414i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.4031 | −1.04349 | −0.521747 | − | 0.853100i | \(-0.674719\pi\) | ||||
−0.521747 | + | 0.853100i | \(0.674719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.80625i | − | 0.391873i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | + | 12.0000i | 0.222058 | + | 0.532939i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 33.7172i | − | 1.49449i | −0.664550 | − | 0.747244i | \(-0.731377\pi\) | ||
0.664550 | − | 0.747244i | \(-0.268623\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 60.2094 | 2.66351 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.40312i | 0.326856i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.40312i | − | 0.149960i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.6125 | 0.950517 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.5969 | −0.465151 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.20937 | 0.272038 | 0.136019 | − | 0.990706i | \(-0.456569\pi\) | ||||
0.136019 | + | 0.990706i | \(0.456569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.59688 | 0.288461 | 0.144231 | − | 0.989544i | \(-0.453929\pi\) | ||||
0.144231 | + | 0.989544i | \(0.453929\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.70156i | 0.205193i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 63.0156i | 2.74500i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7016 | −0.682677 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.596876i | 0.0259022i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.1047 | + | 17.4031i | 1.13072 | + | 0.753813i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.10469i | − | 0.263929i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.80625 | −0.293711 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 40.8062i | 1.75765i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 27.4031i | − | 1.17815i | −0.808078 | − | 0.589076i | \(-0.799492\pi\) | ||
0.808078 | − | 0.589076i | \(-0.200508\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.10469 | −0.347805 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.5969 | −0.795145 | −0.397572 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397572 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.70156 | 0.286016 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 14.8062i | − | 0.630767i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.5078i | − | 0.659459i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.70156 | 0.114675 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14.0000i | − | 0.593199i | −0.955002 | − | 0.296600i | \(-0.904147\pi\) | ||
0.955002 | − | 0.296600i | \(-0.0958526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.80625 | + | 4.20937i | −0.118692 | + | 0.178037i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.1047i | 0.764380i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.1047 | 1.60592 | 0.802961 | − | 0.596032i | \(-0.203257\pi\) | ||||
0.802961 | + | 0.596032i | \(0.203257\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000i | 0.588984i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.70156i | 0.197447i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.0000 | −1.08998 | −0.544988 | − | 0.838444i | \(-0.683466\pi\) | ||||
−0.544988 | + | 0.838444i | \(0.683466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3141 | −1.60339 | −0.801697 | − | 0.597731i | \(-0.796069\pi\) | ||||
−0.801697 | + | 0.597731i | \(0.796069\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.70156 | −0.112663 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.5078i | 1.39495i | 0.716610 | + | 0.697474i | \(0.245693\pi\) | ||||
−0.716610 | + | 0.697474i | \(0.754307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 25.5078i | − | 1.06007i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −44.2094 | −1.83411 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 23.5078i | − | 0.973594i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | + | 2.00000i | 0.124035 | + | 0.0826898i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 32.2094i | − | 1.32942i | −0.747100 | − | 0.664712i | \(-0.768554\pi\) | ||
0.747100 | − | 0.664712i | \(-0.231446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 69.6125 | 2.86833 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 12.8062i | − | 0.526779i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.0000i | 0.903432i | 0.892162 | + | 0.451716i | \(0.149188\pi\) | ||||
−0.892162 | + | 0.451716i | \(0.850812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −31.5078 | −1.29169 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.8062 | 0.605979 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.8062 | −1.74902 | −0.874508 | − | 0.485011i | \(-0.838816\pi\) | ||||
−0.874508 | + | 0.485011i | \(0.838816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.1203 | −1.92208 | −0.961039 | − | 0.276414i | \(-0.910854\pi\) | ||||
−0.961039 | + | 0.276414i | \(0.910854\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.70156i | 0.150490i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.2094 | 1.38852 | 0.694258 | − | 0.719726i | \(-0.255733\pi\) | ||||
0.694258 | + | 0.719726i | \(0.255733\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 9.40312i | − | 0.381034i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | + | 16.0000i | 0.970936 | + | 0.647291i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16.1047i | − | 0.650462i | −0.945635 | − | 0.325231i | \(-0.894558\pi\) | ||
0.945635 | − | 0.325231i | \(-0.105442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.70156 | 0.350881 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6125i | 0.950603i | 0.879823 | + | 0.475302i | \(0.157661\pi\) | ||||
−0.879823 | + | 0.475302i | \(0.842339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000i | 0.884255i | 0.896952 | + | 0.442127i | \(0.145776\pi\) | ||||
−0.896952 | + | 0.442127i | \(0.854224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.70156 | −0.108410 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.1047 | −0.885606 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0000 | 0.798723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.1047i | 0.721881i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 32.2094i | − | 1.28223i | −0.767443 | − | 0.641117i | \(-0.778471\pi\) | ||
0.767443 | − | 0.641117i | \(-0.221529\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.6125 | 1.01801 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.80625i | 0.349465i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.2094 | + | 45.3141i | −1.19694 | + | 1.79541i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 0.701562i | − | 0.0277534i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.0156 | 1.77801 | 0.889005 | − | 0.457897i | \(-0.151397\pi\) | ||||
0.889005 | + | 0.457897i | \(0.151397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.50781i | − | 0.296079i | −0.988981 | − | 0.148040i | \(-0.952704\pi\) | ||
0.988981 | − | 0.148040i | \(-0.0472963\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.40312i | 0.0552480i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.9109 | 0.586209 | 0.293105 | − | 0.956080i | \(-0.405312\pi\) | ||||
0.293105 | + | 0.956080i | \(0.405312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.61250 | 0.0632960 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 44.2094 | 1.73270 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.40312 | −0.0549085 | −0.0274542 | − | 0.999623i | \(-0.508740\pi\) | ||||
−0.0274542 | + | 0.999623i | \(0.508740\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.0000i | − | 0.468879i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.8062i | − | 0.499619i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.0156 | −1.67565 | −0.837825 | − | 0.545938i | \(-0.816173\pi\) | ||||
−0.837825 | + | 0.545938i | \(0.816173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5969i | 0.489962i | 0.969528 | + | 0.244981i | \(0.0787817\pi\) | ||||
−0.969528 | + | 0.244981i | \(0.921218\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.4031 | + | 20.1047i | −0.520534 | + | 0.780801i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 34.8062i | 1.34973i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.40312 | 0.209210 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000i | 0.927894i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18.1047i | − | 0.698924i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.4031 | 1.05631 | 0.528156 | − | 0.849147i | \(-0.322883\pi\) | ||||
0.528156 | + | 0.849147i | \(0.322883\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.29844 | −0.126769 | −0.0633846 | − | 0.997989i | \(-0.520189\pi\) | ||||
−0.0633846 | + | 0.997989i | \(0.520189\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 75.7172 | 2.90576 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 10.8062i | − | 0.414096i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 49.4031i | − | 1.89036i | −0.326553 | − | 0.945179i | \(-0.605887\pi\) | ||
0.326553 | − | 0.945179i | \(-0.394113\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.80625 | 0.336469 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 16.8062i | − | 0.641198i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.4031 | − | 26.1047i | 0.663006 | − | 0.994509i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 19.6125i | − | 0.746095i | −0.927812 | − | 0.373047i | \(-0.878313\pi\) | ||
0.927812 | − | 0.373047i | \(-0.121687\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.7016 | 0.482492 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.1047i | 0.383293i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 58.3141i | 2.20880i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.70156 | 0.102182 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.0156 | −1.09590 | −0.547952 | − | 0.836509i | \(-0.684593\pi\) | ||||
−0.547952 | + | 0.836509i | \(0.684593\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 41.4031i | − | 1.55712i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.2094i | 0.383421i | 0.981452 | + | 0.191711i | \(0.0614035\pi\) | ||||
−0.981452 | + | 0.191711i | \(0.938597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.29844 | −0.123701 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.4031i | 0.951354i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.40312 | − | 8.10469i | 0.202065 | − | 0.303098i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 3.29844i | − | 0.123182i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.59688 | 0.0968471 | 0.0484236 | − | 0.998827i | \(-0.484580\pi\) | ||||
0.0484236 | + | 0.998827i | \(0.484580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 16.0000i | − | 0.595871i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.40312i | − | 0.0521828i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.8062 | −1.36507 | −0.682534 | − | 0.730854i | \(-0.739122\pi\) | ||||
−0.682534 | + | 0.730854i | \(0.739122\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.40312 | −0.347787 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.2984i | 1.37765i | 0.724928 | + | 0.688825i | \(0.241873\pi\) | ||||
−0.724928 | + | 0.688825i | \(0.758127\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.1047i | 0.557145i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.6125 | 0.796107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 11.1938i | − | 0.411769i | −0.978576 | − | 0.205884i | \(-0.933993\pi\) | ||
0.978576 | − | 0.205884i | \(-0.0660071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.2094 | + | 14.8062i | 0.815882 | + | 0.543921i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40.0000i | − | 1.46746i | −0.679442 | − | 0.733729i | \(-0.737778\pi\) | ||
0.679442 | − | 0.733729i | \(-0.262222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.7016 | −0.538624 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.40312i | 0.344042i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 28.7016i | − | 1.04873i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.7016 | 1.77715 | 0.888573 | − | 0.458736i | \(-0.151698\pi\) | ||||
0.888573 | + | 0.458736i | \(0.151698\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.4031 | −1.07151 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.40312 | 0.196640 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.8062 | −0.683525 | −0.341762 | − | 0.939786i | \(-0.611024\pi\) | ||||
−0.341762 | + | 0.939786i | \(0.611024\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.29844i | 0.264917i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.40312i | 0.0508632i | 0.999677 | + | 0.0254316i | \(0.00809600\pi\) | ||||
−0.999677 | + | 0.0254316i | \(0.991904\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.2094 | −1.02125 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.70156i | 0.242295i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.79063 | + | 1.19375i | 0.0646558 | + | 0.0431039i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.19375i | 0.187291i | 0.995606 | + | 0.0936457i | \(0.0298521\pi\) | ||||
−0.995606 | + | 0.0936457i | \(0.970148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.8062 | −0.749319 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.1938i | 0.690351i | 0.938538 | + | 0.345176i | \(0.112181\pi\) | ||||
−0.938538 | + | 0.345176i | \(0.887819\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 9.40312i | − | 0.337770i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.7016 | 0.455666 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 64.4187 | 2.30804 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.89531 | −0.0678197 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 22.8062i | − | 0.813990i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.0000i | 1.85360i | 0.375555 | + | 0.926800i | \(0.377452\pi\) | ||||
−0.375555 | + | 0.926800i | \(0.622548\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.2094 | −0.648271 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 65.8219i | 2.34036i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.4031 | − | 20.1047i | 0.475959 | − | 0.713938i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 8.70156i | − | 0.308613i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.5234 | −1.50626 | −0.753129 | − | 0.657873i | \(-0.771456\pi\) | ||||
−0.753129 | + | 0.657873i | \(0.771456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.6125i | 1.89667i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.70156i | 0.166122i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.5969 | −1.22090 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.7016 | −0.447671 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.596876 | 0.0210110 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.5969 | −0.583515 | −0.291758 | − | 0.956492i | \(-0.594240\pi\) | ||||
−0.291758 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.19375i | − | 0.252607i | −0.991992 | − | 0.126303i | \(-0.959689\pi\) | ||
0.991992 | − | 0.126303i | \(-0.0403113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.59688i | 0.0910764i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.29844 | 0.255653 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3875i | 0.363413i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.1047 | + | 9.40312i | 0.492858 | + | 0.328572i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 25.5078i | − | 0.890229i | −0.895474 | − | 0.445114i | \(-0.853163\pi\) | ||
0.895474 | − | 0.445114i | \(-0.146837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.61250 | −0.125924 | −0.0629619 | − | 0.998016i | \(-0.520055\pi\) | ||||
−0.0629619 | + | 0.998016i | \(0.520055\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.70156i | − | 0.0940563i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 30.8062i | − | 1.07124i | −0.844460 | − | 0.535619i | \(-0.820078\pi\) | ||
0.844460 | − | 0.535619i | \(-0.179922\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.8062 | −0.374865 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −101.225 | −3.50724 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.40312i | − | 0.325020i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.70156i | 0.300411i | 0.988655 | + | 0.150206i | \(0.0479936\pi\) | ||||
−0.988655 | + | 0.150206i | \(0.952006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.4031i | 0.599395i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0000 | − | 5.00000i | 0.412813 | − | 0.172005i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.4031i | 0.597978i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.4031 | −0.459994 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.29844i | 0.250187i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.1047i | 0.414457i | 0.978293 | + | 0.207228i | \(0.0664443\pi\) | ||||
−0.978293 | + | 0.207228i | \(0.933556\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.40312 | 0.253182 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.3141 | −0.420640 | −0.210320 | − | 0.977633i | \(-0.567451\pi\) | ||||
−0.210320 | + | 0.977633i | \(0.567451\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.5078 | −0.665598 | −0.332799 | − | 0.942998i | \(-0.607993\pi\) | ||||
−0.332799 | + | 0.942998i | \(0.607993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.9109 | 1.39424 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 30.5969i | − | 1.04153i | −0.853700 | − | 0.520765i | \(-0.825647\pi\) | ||
0.853700 | − | 0.520765i | \(-0.174353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5969i | 0.360305i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.9109 | −0.947905 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.91093i | 0.302283i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | + | 16.0000i | 0.813209 | + | 0.542139i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 16.1047i | − | 0.545061i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.70156 | 0.158942 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 51.6125i | − | 1.74283i | −0.490546 | − | 0.871415i | \(-0.663203\pi\) | ||
0.490546 | − | 0.871415i | \(-0.336797\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.00000i | 0.202375i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.2094 | −1.28731 | −0.643653 | − | 0.765317i | \(-0.722582\pi\) | ||||
−0.643653 | + | 0.765317i | \(0.722582\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.4187 | 1.09098 | 0.545489 | − | 0.838118i | \(-0.316344\pi\) | ||||
0.545489 | + | 0.838118i | \(0.316344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.596876 | 0.0200638 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.3141 | 1.75653 | 0.878267 | − | 0.478170i | \(-0.158700\pi\) | ||||
0.878267 | + | 0.478170i | \(0.158700\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.4031i | 1.38862i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.70156i | − | 0.0905057i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 59.2250 | 1.98189 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.80625i | 0.227508i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.40312 | + | 8.10469i | −0.180405 | + | 0.270608i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.8062i | 0.627224i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.3141 | 1.94272 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.59688i | 0.219530i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.10469i | 0.269409i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0000 | 0.796907 | 0.398453 | − | 0.917189i | \(-0.369547\pi\) | ||||
0.398453 | + | 0.917189i | \(0.369547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.80625 | −0.292085 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.8219 | 1.25309 | 0.626547 | − | 0.779383i | \(-0.284468\pi\) | ||||
0.626547 | + | 0.779383i | \(0.284468\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.4031 | 0.840721 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 6.70156i | − | 0.221547i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 56.4187i | − | 1.86311i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.29844 | −0.240753 | −0.120377 | − | 0.992728i | \(-0.538410\pi\) | ||||
−0.120377 | + | 0.992728i | \(0.538410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.1047i | 0.332961i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.10469 | − | 1.40312i | −0.0692766 | − | 0.0461844i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.70156i | − | 0.0888268i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.40312 | −0.111773 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 7.50781i | − | 0.246323i | −0.992387 | − | 0.123162i | \(-0.960697\pi\) | ||
0.992387 | − | 0.123162i | \(-0.0393034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 111.822i | 3.66481i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.40312 | −0.176890 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.1047 | 0.592087 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.38750 | −0.274008 | −0.137004 | − | 0.990571i | \(-0.543747\pi\) | ||||
−0.137004 | + | 0.990571i | \(0.543747\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.20937 | −0.202635 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.5078i | 1.09232i | 0.837680 | + | 0.546162i | \(0.183912\pi\) | ||||
−0.837680 | + | 0.546162i | \(0.816088\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.5078i | 0.765520i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.70156 | 0.152942 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 20.0000i | − | 0.649913i | −0.945729 | − | 0.324956i | \(-0.894650\pi\) | ||
0.945729 | − | 0.324956i | \(-0.105350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.4187 | − | 25.6125i | −1.24713 | − | 0.831417i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.8062i | 0.934107i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.1203 | 0.878513 | 0.439256 | − | 0.898362i | \(-0.355242\pi\) | ||||
0.439256 | + | 0.898362i | \(0.355242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.00000i | 0.129437i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.40312i | 0.174658i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 41.4031 | 1.33698 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −57.4187 | −1.85222 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.10469 | −0.196721 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.5078 | −0.821125 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.6125i | 1.59378i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.209373 | −0.00671909 | −0.00335955 | − | 0.999994i | \(-0.501069\pi\) | ||||
−0.00335955 | + | 0.999994i | \(0.501069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.5078i | 1.52303i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00000 | − | 3.00000i | 0.0640513 | − | 0.0960769i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.5969i | 0.403010i | 0.979488 | + | 0.201505i | \(0.0645832\pi\) | ||||
−0.979488 | + | 0.201505i | \(0.935417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7016 | 0.405944 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000i | 0.191565i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.4187i | 1.54432i | 0.635429 | + | 0.772159i | \(0.280823\pi\) | ||||
−0.635429 | + | 0.772159i | \(0.719177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.8062 | −0.408041 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 37.6125 | 1.19722 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.79063 | −0.120535 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.1047 | 1.08337 | 0.541686 | − | 0.840581i | \(-0.317786\pi\) | ||||
0.541686 | + | 0.840581i | \(0.317786\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.4031i | 0.488803i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 14.8062i | − | 0.469390i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.0000 | −1.39349 | −0.696747 | − | 0.717317i | \(-0.745370\pi\) | ||||
−0.696747 | + | 0.717317i | \(0.745370\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 2.70156i | − | 0.0854736i |
(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 | 1560.2.g.f.961.4 | yes | 4 | |
3.2 | odd | 2 | 4680.2.g.h.2521.2 | 4 | |||
4.3 | odd | 2 | 3120.2.g.r.961.3 | 4 | |||
13.12 | even | 2 | inner | 1560.2.g.f.961.1 | ✓ | 4 | |
39.38 | odd | 2 | 4680.2.g.h.2521.3 | 4 | |||
52.51 | odd | 2 | 3120.2.g.r.961.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.g.f.961.1 | ✓ | 4 | 13.12 | even | 2 | inner | |
1560.2.g.f.961.4 | yes | 4 | 1.1 | even | 1 | trivial | |
3120.2.g.r.961.2 | 4 | 52.51 | odd | 2 | |||
3120.2.g.r.961.3 | 4 | 4.3 | odd | 2 | |||
4680.2.g.h.2521.2 | 4 | 3.2 | odd | 2 | |||
4680.2.g.h.2521.3 | 4 | 39.38 | odd | 2 |