Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9450,2,Mod(1,9450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.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: | \(75.4586299101\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1890) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | 0.738549 | 0.369274 | − | 0.929320i | \(-0.379606\pi\) | ||||
0.369274 | + | 0.929320i | \(0.379606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.44949 | 0.402016 | 0.201008 | − | 0.979590i | \(-0.435578\pi\) | ||||
0.201008 | + | 0.979590i | \(0.435578\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.44949 | −1.02078 | −0.510391 | − | 0.859942i | \(-0.670499\pi\) | ||||
−0.510391 | + | 0.859942i | \(0.670499\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.44949 | −0.522233 | ||||||||
\(23\) | −1.44949 | −0.302240 | −0.151120 | − | 0.988515i | \(-0.548288\pi\) | ||||
−0.151120 | + | 0.988515i | \(0.548288\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.44949 | −0.284268 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 2.55051 | 0.473618 | 0.236809 | − | 0.971556i | \(-0.423898\pi\) | ||||
0.236809 | + | 0.971556i | \(0.423898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.44949 | −0.260336 | −0.130168 | − | 0.991492i | \(-0.541552\pi\) | ||||
−0.130168 | + | 0.991492i | \(0.541552\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.34847 | 0.550485 | 0.275242 | − | 0.961375i | \(-0.411242\pi\) | ||||
0.275242 | + | 0.961375i | \(0.411242\pi\) | |||||||
\(38\) | 4.44949 | 0.721803 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.89898 | 0.765092 | 0.382546 | − | 0.923936i | \(-0.375047\pi\) | ||||
0.382546 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.89898 | −0.594589 | −0.297294 | − | 0.954786i | \(-0.596084\pi\) | ||||
−0.297294 | + | 0.954786i | \(0.596084\pi\) | |||||||
\(44\) | 2.44949 | 0.369274 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.44949 | 0.213716 | ||||||||
\(47\) | −11.7980 | −1.72091 | −0.860455 | − | 0.509527i | \(-0.829820\pi\) | ||||
−0.860455 | + | 0.509527i | \(0.829820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.44949 | 0.201008 | ||||||||
\(53\) | 5.44949 | 0.748545 | 0.374272 | − | 0.927319i | \(-0.377892\pi\) | ||||
0.374272 | + | 0.927319i | \(0.377892\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.55051 | −0.334898 | ||||||||
\(59\) | 0.101021 | 0.0131518 | 0.00657588 | − | 0.999978i | \(-0.497907\pi\) | ||||
0.00657588 | + | 0.999978i | \(0.497907\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8990 | 1.39547 | 0.697736 | − | 0.716355i | \(-0.254191\pi\) | ||||
0.697736 | + | 0.716355i | \(0.254191\pi\) | |||||||
\(62\) | 1.44949 | 0.184085 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | −0.610847 | −0.305424 | − | 0.952217i | \(-0.598798\pi\) | ||||
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.44949 | −0.646735 | −0.323368 | − | 0.946273i | \(-0.604815\pi\) | ||||
−0.323368 | + | 0.946273i | \(0.604815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.7980 | −1.38085 | −0.690423 | − | 0.723406i | \(-0.742576\pi\) | ||||
−0.690423 | + | 0.723406i | \(0.742576\pi\) | |||||||
\(74\) | −3.34847 | −0.389252 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.44949 | −0.510391 | ||||||||
\(77\) | −2.44949 | −0.279145 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.44949 | −0.725624 | −0.362812 | − | 0.931862i | \(-0.618183\pi\) | ||||
−0.362812 | + | 0.931862i | \(0.618183\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.89898 | −0.541002 | ||||||||
\(83\) | 10.8990 | 1.19632 | 0.598159 | − | 0.801377i | \(-0.295899\pi\) | ||||
0.598159 | + | 0.801377i | \(0.295899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.89898 | 0.420438 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.44949 | −0.261116 | ||||||||
\(89\) | 11.0000 | 1.16600 | 0.582999 | − | 0.812473i | \(-0.301879\pi\) | ||||
0.582999 | + | 0.812473i | \(0.301879\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.44949 | −0.151948 | ||||||||
\(92\) | −1.44949 | −0.151120 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.7980 | 1.21687 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.55051 | −0.969707 | −0.484854 | − | 0.874595i | \(-0.661127\pi\) | ||||
−0.484854 | + | 0.874595i | \(0.661127\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.2474 | 1.21867 | 0.609333 | − | 0.792914i | \(-0.291437\pi\) | ||||
0.609333 | + | 0.792914i | \(0.291437\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.4495 | −1.52228 | −0.761142 | − | 0.648586i | \(-0.775361\pi\) | ||||
−0.761142 | + | 0.648586i | \(0.775361\pi\) | |||||||
\(104\) | −1.44949 | −0.142134 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.44949 | −0.529301 | ||||||||
\(107\) | −3.34847 | −0.323709 | −0.161854 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161854 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1464 | −1.45076 | −0.725382 | − | 0.688346i | \(-0.758337\pi\) | ||||
−0.725382 | + | 0.688346i | \(0.758337\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 6.44949 | 0.606717 | 0.303358 | − | 0.952877i | \(-0.401892\pi\) | ||||
0.303358 | + | 0.952877i | \(0.401892\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.55051 | 0.236809 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.101021 | −0.00929969 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | −10.8990 | −0.986747 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.44949 | −0.130168 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.89898 | −0.789657 | −0.394828 | − | 0.918755i | \(-0.629196\pi\) | ||||
−0.394828 | + | 0.918755i | \(0.629196\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.7980 | −1.46764 | −0.733822 | − | 0.679342i | \(-0.762266\pi\) | ||||
−0.733822 | + | 0.679342i | \(0.762266\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.44949 | 0.385820 | ||||||||
\(134\) | 5.00000 | 0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −5.10102 | −0.435810 | −0.217905 | − | 0.975970i | \(-0.569922\pi\) | ||||
−0.217905 | + | 0.975970i | \(0.569922\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.2474 | 1.88700 | 0.943502 | − | 0.331367i | \(-0.107510\pi\) | ||||
0.943502 | + | 0.331367i | \(0.107510\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.44949 | 0.457311 | ||||||||
\(143\) | 3.55051 | 0.296909 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.7980 | 0.976406 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.34847 | 0.275242 | ||||||||
\(149\) | 0.550510 | 0.0450996 | 0.0225498 | − | 0.999746i | \(-0.492822\pi\) | ||||
0.0225498 | + | 0.999746i | \(0.492822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2474 | 0.996683 | 0.498342 | − | 0.866981i | \(-0.333943\pi\) | ||||
0.498342 | + | 0.866981i | \(0.333943\pi\) | |||||||
\(152\) | 4.44949 | 0.360901 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.44949 | 0.197386 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.44949 | −0.434917 | −0.217458 | − | 0.976070i | \(-0.569777\pi\) | ||||
−0.217458 | + | 0.976070i | \(0.569777\pi\) | |||||||
\(158\) | 6.44949 | 0.513094 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.44949 | 0.114236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.10102 | −0.321217 | −0.160608 | − | 0.987018i | \(-0.551346\pi\) | ||||
−0.160608 | + | 0.987018i | \(0.551346\pi\) | |||||||
\(164\) | 4.89898 | 0.382546 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.8990 | −0.845925 | ||||||||
\(167\) | −3.55051 | −0.274747 | −0.137373 | − | 0.990519i | \(-0.543866\pi\) | ||||
−0.137373 | + | 0.990519i | \(0.543866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8990 | −0.838383 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.89898 | −0.297294 | ||||||||
\(173\) | 11.1464 | 0.847447 | 0.423724 | − | 0.905792i | \(-0.360723\pi\) | ||||
0.423724 | + | 0.905792i | \(0.360723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.44949 | 0.184637 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.0000 | −0.824485 | ||||||||
\(179\) | −0.898979 | −0.0671929 | −0.0335964 | − | 0.999435i | \(-0.510696\pi\) | ||||
−0.0335964 | + | 0.999435i | \(0.510696\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.44949 | 0.553716 | 0.276858 | − | 0.960911i | \(-0.410707\pi\) | ||||
0.276858 | + | 0.960911i | \(0.410707\pi\) | |||||||
\(182\) | 1.44949 | 0.107443 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.44949 | 0.106858 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.44949 | −0.179124 | ||||||||
\(188\) | −11.7980 | −0.860455 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.6969 | −1.64229 | −0.821146 | − | 0.570718i | \(-0.806665\pi\) | ||||
−0.821146 | + | 0.570718i | \(0.806665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.20204 | −0.518414 | −0.259207 | − | 0.965822i | \(-0.583461\pi\) | ||||
−0.259207 | + | 0.965822i | \(0.583461\pi\) | |||||||
\(194\) | 9.55051 | 0.685687 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 12.8990 | 0.919014 | 0.459507 | − | 0.888174i | \(-0.348026\pi\) | ||||
0.459507 | + | 0.888174i | \(0.348026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.24745 | 0.655534 | 0.327767 | − | 0.944759i | \(-0.393704\pi\) | ||||
0.327767 | + | 0.944759i | \(0.393704\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.2474 | −0.861727 | ||||||||
\(203\) | −2.55051 | −0.179011 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.4495 | 1.07642 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.44949 | 0.100504 | ||||||||
\(209\) | −10.8990 | −0.753898 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0000 | −1.03264 | −0.516321 | − | 0.856395i | \(-0.672699\pi\) | ||||
−0.516321 | + | 0.856395i | \(0.672699\pi\) | |||||||
\(212\) | 5.44949 | 0.374272 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.34847 | 0.228897 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.44949 | 0.0983978 | ||||||||
\(218\) | 15.1464 | 1.02585 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.44949 | −0.0975032 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.44949 | −0.429014 | ||||||||
\(227\) | 11.6969 | 0.776353 | 0.388177 | − | 0.921585i | \(-0.373105\pi\) | ||||
0.388177 | + | 0.921585i | \(0.373105\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.10102 | −0.204921 | −0.102461 | − | 0.994737i | \(-0.532672\pi\) | ||||
−0.102461 | + | 0.994737i | \(0.532672\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.55051 | −0.167449 | ||||||||
\(233\) | 13.1464 | 0.861251 | 0.430626 | − | 0.902531i | \(-0.358293\pi\) | ||||
0.430626 | + | 0.902531i | \(0.358293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.101021 | 0.00657588 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.00000 | −0.0648204 | ||||||||
\(239\) | 20.4949 | 1.32570 | 0.662852 | − | 0.748750i | \(-0.269346\pi\) | ||||
0.662852 | + | 0.748750i | \(0.269346\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6515 | 0.686125 | 0.343063 | − | 0.939313i | \(-0.388536\pi\) | ||||
0.343063 | + | 0.939313i | \(0.388536\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.8990 | 0.697736 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.44949 | −0.410371 | ||||||||
\(248\) | 1.44949 | 0.0920427 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.5959 | 1.74184 | 0.870919 | − | 0.491426i | \(-0.163524\pi\) | ||||
0.870919 | + | 0.491426i | \(0.163524\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.55051 | −0.223219 | ||||||||
\(254\) | 8.89898 | 0.558372 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.0000 | 0.748539 | 0.374270 | − | 0.927320i | \(-0.377893\pi\) | ||||
0.374270 | + | 0.927320i | \(0.377893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.34847 | −0.208064 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.7980 | 1.03778 | ||||||||
\(263\) | −23.9444 | −1.47647 | −0.738237 | − | 0.674541i | \(-0.764341\pi\) | ||||
−0.738237 | + | 0.674541i | \(0.764341\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.44949 | −0.272816 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.00000 | −0.305424 | ||||||||
\(269\) | 3.10102 | 0.189073 | 0.0945363 | − | 0.995521i | \(-0.469863\pi\) | ||||
0.0945363 | + | 0.995521i | \(0.469863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.34847 | −0.264151 | −0.132075 | − | 0.991240i | \(-0.542164\pi\) | ||||
−0.132075 | + | 0.991240i | \(0.542164\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.10102 | 0.308164 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.20204 | −0.372645 | −0.186322 | − | 0.982489i | \(-0.559657\pi\) | ||||
−0.186322 | + | 0.982489i | \(0.559657\pi\) | |||||||
\(278\) | −22.2474 | −1.33431 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.3485 | −0.796303 | −0.398151 | − | 0.917320i | \(-0.630348\pi\) | ||||
−0.398151 | + | 0.917320i | \(0.630348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.5505 | −1.04327 | −0.521635 | − | 0.853169i | \(-0.674678\pi\) | ||||
−0.521635 | + | 0.853169i | \(0.674678\pi\) | |||||||
\(284\) | −5.44949 | −0.323368 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.55051 | −0.209946 | ||||||||
\(287\) | −4.89898 | −0.289178 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.7980 | −0.690423 | ||||||||
\(293\) | −30.4949 | −1.78153 | −0.890765 | − | 0.454463i | \(-0.849831\pi\) | ||||
−0.890765 | + | 0.454463i | \(0.849831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.34847 | −0.194626 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.550510 | −0.0318902 | ||||||||
\(299\) | −2.10102 | −0.121505 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.89898 | 0.224733 | ||||||||
\(302\) | −12.2474 | −0.704761 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.44949 | −0.255196 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.4495 | 1.39541 | 0.697703 | − | 0.716387i | \(-0.254206\pi\) | ||||
0.697703 | + | 0.716387i | \(0.254206\pi\) | |||||||
\(308\) | −2.44949 | −0.139573 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.3485 | −0.756922 | −0.378461 | − | 0.925617i | \(-0.623547\pi\) | ||||
−0.378461 | + | 0.925617i | \(0.623547\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.9444 | −1.63603 | −0.818017 | − | 0.575194i | \(-0.804926\pi\) | ||||
−0.818017 | + | 0.575194i | \(0.804926\pi\) | |||||||
\(314\) | 5.44949 | 0.307532 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.44949 | −0.362812 | ||||||||
\(317\) | 4.20204 | 0.236010 | 0.118005 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118005 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.24745 | 0.349790 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.44949 | −0.0807769 | ||||||||
\(323\) | 4.44949 | 0.247576 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.10102 | 0.227135 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.89898 | −0.270501 | ||||||||
\(329\) | 11.7980 | 0.650443 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | −0.714545 | −0.357272 | − | 0.934000i | \(-0.616293\pi\) | ||||
−0.357272 | + | 0.934000i | \(0.616293\pi\) | |||||||
\(332\) | 10.8990 | 0.598159 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.55051 | 0.194275 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.7980 | −1.24188 | −0.620942 | − | 0.783857i | \(-0.713250\pi\) | ||||
−0.620942 | + | 0.783857i | \(0.713250\pi\) | |||||||
\(338\) | 10.8990 | 0.592826 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.55051 | −0.192271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.89898 | 0.210219 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.1464 | −0.599236 | ||||||||
\(347\) | 13.5959 | 0.729867 | 0.364934 | − | 0.931034i | \(-0.381092\pi\) | ||||
0.364934 | + | 0.931034i | \(0.381092\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.1464 | −1.07841 | −0.539207 | − | 0.842173i | \(-0.681276\pi\) | ||||
−0.539207 | + | 0.842173i | \(0.681276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.44949 | −0.130558 | ||||||||
\(353\) | −15.4949 | −0.824710 | −0.412355 | − | 0.911023i | \(-0.635294\pi\) | ||||
−0.412355 | + | 0.911023i | \(0.635294\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.0000 | 0.582999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.898979 | 0.0475125 | ||||||||
\(359\) | 21.4495 | 1.13206 | 0.566030 | − | 0.824384i | \(-0.308478\pi\) | ||||
0.566030 | + | 0.824384i | \(0.308478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.797959 | 0.0419978 | ||||||||
\(362\) | −7.44949 | −0.391536 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.44949 | −0.0759739 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0454 | 0.785364 | 0.392682 | − | 0.919674i | \(-0.371547\pi\) | ||||
0.392682 | + | 0.919674i | \(0.371547\pi\) | |||||||
\(368\) | −1.44949 | −0.0755599 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.44949 | −0.282923 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.3485 | −1.41605 | −0.708025 | − | 0.706187i | \(-0.750414\pi\) | ||||
−0.708025 | + | 0.706187i | \(0.750414\pi\) | |||||||
\(374\) | 2.44949 | 0.126660 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.7980 | 0.608433 | ||||||||
\(377\) | 3.69694 | 0.190402 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.6969 | 1.16128 | ||||||||
\(383\) | −7.10102 | −0.362845 | −0.181423 | − | 0.983405i | \(-0.558070\pi\) | ||||
−0.181423 | + | 0.983405i | \(0.558070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.20204 | 0.366574 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.55051 | −0.484854 | ||||||||
\(389\) | −28.8990 | −1.46524 | −0.732618 | − | 0.680640i | \(-0.761702\pi\) | ||||
−0.732618 | + | 0.680640i | \(0.761702\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.44949 | 0.0733038 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.8990 | −0.649841 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.6969 | 1.13913 | 0.569563 | − | 0.821947i | \(-0.307112\pi\) | ||||
0.569563 | + | 0.821947i | \(0.307112\pi\) | |||||||
\(398\) | −9.24745 | −0.463533 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.69694 | −0.434304 | −0.217152 | − | 0.976138i | \(-0.569677\pi\) | ||||
−0.217152 | + | 0.976138i | \(0.569677\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.10102 | −0.104659 | ||||||||
\(404\) | 12.2474 | 0.609333 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.55051 | 0.126580 | ||||||||
\(407\) | 8.20204 | 0.406560 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.59592 | −0.474488 | −0.237244 | − | 0.971450i | \(-0.576244\pi\) | ||||
−0.237244 | + | 0.971450i | \(0.576244\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.4495 | −0.761142 | ||||||||
\(413\) | −0.101021 | −0.00497089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.44949 | −0.0710671 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.8990 | 0.533087 | ||||||||
\(419\) | −38.5959 | −1.88553 | −0.942767 | − | 0.333452i | \(-0.891786\pi\) | ||||
−0.942767 | + | 0.333452i | \(0.891786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.7980 | 0.964893 | 0.482447 | − | 0.875925i | \(-0.339748\pi\) | ||||
0.482447 | + | 0.875925i | \(0.339748\pi\) | |||||||
\(422\) | 15.0000 | 0.730189 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.44949 | −0.264651 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8990 | −0.527439 | ||||||||
\(428\) | −3.34847 | −0.161854 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.79796 | −0.375614 | −0.187807 | − | 0.982206i | \(-0.560138\pi\) | ||||
−0.187807 | + | 0.982206i | \(0.560138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.5959 | −1.13395 | −0.566974 | − | 0.823736i | \(-0.691886\pi\) | ||||
−0.566974 | + | 0.823736i | \(0.691886\pi\) | |||||||
\(434\) | −1.44949 | −0.0695777 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.1464 | −0.725382 | ||||||||
\(437\) | 6.44949 | 0.308521 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.34847 | 0.302996 | 0.151498 | − | 0.988458i | \(-0.451590\pi\) | ||||
0.151498 | + | 0.988458i | \(0.451590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.44949 | 0.0689452 | ||||||||
\(443\) | −27.5505 | −1.30896 | −0.654482 | − | 0.756077i | \(-0.727113\pi\) | ||||
−0.654482 | + | 0.756077i | \(0.727113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 32.0000 | 1.51017 | 0.755087 | − | 0.655625i | \(-0.227595\pi\) | ||||
0.755087 | + | 0.655625i | \(0.227595\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 6.44949 | 0.303358 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.6969 | −0.548965 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.101021 | −0.00472554 | −0.00236277 | − | 0.999997i | \(-0.500752\pi\) | ||||
−0.00236277 | + | 0.999997i | \(0.500752\pi\) | |||||||
\(458\) | 3.10102 | 0.144901 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0000 | 0.465746 | 0.232873 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232873 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.75255 | −0.174396 | −0.0871979 | − | 0.996191i | \(-0.527791\pi\) | ||||
−0.0871979 | + | 0.996191i | \(0.527791\pi\) | |||||||
\(464\) | 2.55051 | 0.118404 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.1464 | −0.608997 | ||||||||
\(467\) | −12.2020 | −0.564643 | −0.282322 | − | 0.959320i | \(-0.591105\pi\) | ||||
−0.282322 | + | 0.959320i | \(0.591105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00000 | 0.230879 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.101021 | −0.00464985 | ||||||||
\(473\) | −9.55051 | −0.439133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.00000 | 0.0458349 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.4949 | −0.937415 | ||||||||
\(479\) | −36.0000 | −1.64488 | −0.822441 | − | 0.568850i | \(-0.807388\pi\) | ||||
−0.822441 | + | 0.568850i | \(0.807388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.85357 | 0.221304 | ||||||||
\(482\) | −10.6515 | −0.485164 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | −0.227273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.3939 | −1.78511 | −0.892553 | − | 0.450942i | \(-0.851088\pi\) | ||||
−0.892553 | + | 0.450942i | \(0.851088\pi\) | |||||||
\(488\) | −10.8990 | −0.493374 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.40408 | −0.198753 | −0.0993767 | − | 0.995050i | \(-0.531685\pi\) | ||||
−0.0993767 | + | 0.995050i | \(0.531685\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.55051 | −0.114869 | ||||||||
\(494\) | 6.44949 | 0.290176 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.44949 | −0.0650840 | ||||||||
\(497\) | 5.44949 | 0.244443 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.89898 | 0.129776 | 0.0648881 | − | 0.997893i | \(-0.479331\pi\) | ||||
0.0648881 | + | 0.997893i | \(0.479331\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.5959 | −1.23167 | ||||||||
\(503\) | 6.65153 | 0.296577 | 0.148289 | − | 0.988944i | \(-0.452624\pi\) | ||||
0.148289 | + | 0.988944i | \(0.452624\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.55051 | 0.157839 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.89898 | −0.394828 | ||||||||
\(509\) | 13.1464 | 0.582705 | 0.291353 | − | 0.956616i | \(-0.405895\pi\) | ||||
0.291353 | + | 0.956616i | \(0.405895\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.7980 | 0.521911 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.0000 | −0.529297 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.8990 | −1.27098 | ||||||||
\(518\) | 3.34847 | 0.147123 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.59592 | 0.157239 | 0.0786193 | − | 0.996905i | \(-0.474949\pi\) | ||||
0.0786193 | + | 0.996905i | \(0.474949\pi\) | |||||||
\(524\) | −16.7980 | −0.733822 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.9444 | 1.04402 | ||||||||
\(527\) | 1.44949 | 0.0631408 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8990 | −0.908651 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.44949 | 0.192910 | ||||||||
\(533\) | 7.10102 | 0.307579 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.00000 | 0.215967 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.10102 | −0.133694 | ||||||||
\(539\) | 2.44949 | 0.105507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.75255 | −0.419295 | −0.209647 | − | 0.977777i | \(-0.567232\pi\) | ||||
−0.209647 | + | 0.977777i | \(0.567232\pi\) | |||||||
\(542\) | 4.34847 | 0.186783 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.696938 | −0.0297989 | −0.0148995 | − | 0.999889i | \(-0.504743\pi\) | ||||
−0.0148995 | + | 0.999889i | \(0.504743\pi\) | |||||||
\(548\) | −5.10102 | −0.217905 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3485 | −0.483461 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.44949 | 0.274260 | ||||||||
\(554\) | 6.20204 | 0.263499 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.2474 | 0.943502 | ||||||||
\(557\) | −33.0454 | −1.40018 | −0.700089 | − | 0.714055i | \(-0.746857\pi\) | ||||
−0.700089 | + | 0.714055i | \(0.746857\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65153 | −0.239034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.3485 | 0.563071 | ||||||||
\(563\) | 9.69694 | 0.408677 | 0.204339 | − | 0.978900i | \(-0.434496\pi\) | ||||
0.204339 | + | 0.978900i | \(0.434496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.5505 | 0.737703 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.44949 | 0.228656 | ||||||||
\(569\) | 31.8434 | 1.33494 | 0.667472 | − | 0.744635i | \(-0.267377\pi\) | ||||
0.667472 | + | 0.744635i | \(0.267377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4949 | −0.815836 | −0.407918 | − | 0.913019i | \(-0.633745\pi\) | ||||
−0.407918 | + | 0.913019i | \(0.633745\pi\) | |||||||
\(572\) | 3.55051 | 0.148454 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.89898 | 0.204479 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5505 | 0.813898 | 0.406949 | − | 0.913451i | \(-0.366593\pi\) | ||||
0.406949 | + | 0.913451i | \(0.366593\pi\) | |||||||
\(578\) | 16.0000 | 0.665512 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.8990 | −0.452166 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.3485 | 0.552837 | ||||||||
\(584\) | 11.7980 | 0.488203 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.4949 | 1.25973 | ||||||||
\(587\) | 35.4949 | 1.46503 | 0.732516 | − | 0.680750i | \(-0.238346\pi\) | ||||
0.732516 | + | 0.680750i | \(0.238346\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.44949 | 0.265747 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.34847 | 0.137621 | ||||||||
\(593\) | −16.8990 | −0.693958 | −0.346979 | − | 0.937873i | \(-0.612792\pi\) | ||||
−0.346979 | + | 0.937873i | \(0.612792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.550510 | 0.0225498 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.10102 | 0.0859171 | ||||||||
\(599\) | −5.44949 | −0.222660 | −0.111330 | − | 0.993783i | \(-0.535511\pi\) | ||||
−0.111330 | + | 0.993783i | \(0.535511\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.3031 | −0.542643 | −0.271322 | − | 0.962489i | \(-0.587461\pi\) | ||||
−0.271322 | + | 0.962489i | \(0.587461\pi\) | |||||||
\(602\) | −3.89898 | −0.158911 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.2474 | 0.498342 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.0454 | 0.935384 | 0.467692 | − | 0.883891i | \(-0.345086\pi\) | ||||
0.467692 | + | 0.883891i | \(0.345086\pi\) | |||||||
\(608\) | 4.44949 | 0.180451 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.1010 | −0.691833 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.2474 | 1.94870 | 0.974348 | − | 0.225046i | \(-0.0722534\pi\) | ||||
0.974348 | + | 0.225046i | \(0.0722534\pi\) | |||||||
\(614\) | −24.4495 | −0.986701 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.44949 | 0.0986928 | ||||||||
\(617\) | 38.8990 | 1.56601 | 0.783007 | − | 0.622013i | \(-0.213685\pi\) | ||||
0.783007 | + | 0.622013i | \(0.213685\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.7980 | 1.76039 | 0.880194 | − | 0.474614i | \(-0.157412\pi\) | ||||
0.880194 | + | 0.474614i | \(0.157412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.3485 | 0.535225 | ||||||||
\(623\) | −11.0000 | −0.440706 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.9444 | 1.15685 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.44949 | −0.217458 | ||||||||
\(629\) | −3.34847 | −0.133512 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.89898 | 0.195025 | 0.0975126 | − | 0.995234i | \(-0.468911\pi\) | ||||
0.0975126 | + | 0.995234i | \(0.468911\pi\) | |||||||
\(632\) | 6.44949 | 0.256547 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.20204 | −0.166884 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.44949 | 0.0574309 | ||||||||
\(638\) | −6.24745 | −0.247339 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.55051 | −0.219232 | −0.109616 | − | 0.993974i | \(-0.534962\pi\) | ||||
−0.109616 | + | 0.993974i | \(0.534962\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.8536 | −0.428023 | −0.214012 | − | 0.976831i | \(-0.568653\pi\) | ||||
−0.214012 | + | 0.976831i | \(0.568653\pi\) | |||||||
\(644\) | 1.44949 | 0.0571179 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.44949 | −0.175063 | ||||||||
\(647\) | −13.5959 | −0.534511 | −0.267255 | − | 0.963626i | \(-0.586117\pi\) | ||||
−0.267255 | + | 0.963626i | \(0.586117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.247449 | 0.00971321 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.10102 | −0.160608 | ||||||||
\(653\) | −15.2474 | −0.596679 | −0.298339 | − | 0.954460i | \(-0.596433\pi\) | ||||
−0.298339 | + | 0.954460i | \(0.596433\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.89898 | 0.191273 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.7980 | −0.459932 | ||||||||
\(659\) | −23.7526 | −0.925268 | −0.462634 | − | 0.886549i | \(-0.653096\pi\) | ||||
−0.462634 | + | 0.886549i | \(0.653096\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.4949 | 1.34170 | 0.670848 | − | 0.741595i | \(-0.265930\pi\) | ||||
0.670848 | + | 0.741595i | \(0.265930\pi\) | |||||||
\(662\) | 13.0000 | 0.505259 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.8990 | −0.422962 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.69694 | −0.143146 | ||||||||
\(668\) | −3.55051 | −0.137373 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.6969 | 1.03062 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.4949 | −1.83079 | −0.915397 | − | 0.402553i | \(-0.868123\pi\) | ||||
−0.915397 | + | 0.402553i | \(0.868123\pi\) | |||||||
\(674\) | 22.7980 | 0.878145 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8990 | −0.419192 | ||||||||
\(677\) | −13.7980 | −0.530299 | −0.265149 | − | 0.964207i | \(-0.585421\pi\) | ||||
−0.265149 | + | 0.964207i | \(0.585421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.55051 | 0.366515 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.55051 | 0.135956 | ||||||||
\(683\) | 5.55051 | 0.212384 | 0.106192 | − | 0.994346i | \(-0.466134\pi\) | ||||
0.106192 | + | 0.994346i | \(0.466134\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.89898 | −0.148647 | ||||||||
\(689\) | 7.89898 | 0.300927 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2929 | −0.695893 | −0.347947 | − | 0.937514i | \(-0.613121\pi\) | ||||
−0.347947 | + | 0.937514i | \(0.613121\pi\) | |||||||
\(692\) | 11.1464 | 0.423724 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.5959 | −0.516094 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.89898 | −0.185562 | ||||||||
\(698\) | 20.1464 | 0.762554 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.3939 | −1.48789 | −0.743943 | − | 0.668243i | \(-0.767047\pi\) | ||||
−0.743943 | + | 0.668243i | \(0.767047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.8990 | −0.561926 | ||||||||
\(704\) | 2.44949 | 0.0923186 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.4949 | 0.583158 | ||||||||
\(707\) | −12.2474 | −0.460613 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.1464 | 0.869282 | 0.434641 | − | 0.900604i | \(-0.356875\pi\) | ||||
0.434641 | + | 0.900604i | \(0.356875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.0000 | −0.412242 | ||||||||
\(713\) | 2.10102 | 0.0786838 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.898979 | −0.0335964 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.4495 | −0.800488 | ||||||||
\(719\) | −15.1464 | −0.564866 | −0.282433 | − | 0.959287i | \(-0.591142\pi\) | ||||
−0.282433 | + | 0.959287i | \(0.591142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4495 | 0.575369 | ||||||||
\(722\) | −0.797959 | −0.0296970 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.44949 | 0.276858 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.65153 | 0.135428 | 0.0677139 | − | 0.997705i | \(-0.478429\pi\) | ||||
0.0677139 | + | 0.997705i | \(0.478429\pi\) | |||||||
\(728\) | 1.44949 | 0.0537217 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.89898 | 0.144209 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.4495 | −1.38323 | −0.691614 | − | 0.722267i | \(-0.743100\pi\) | ||||
−0.691614 | + | 0.722267i | \(0.743100\pi\) | |||||||
\(734\) | −15.0454 | −0.555336 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.44949 | 0.0534289 | ||||||||
\(737\) | −12.2474 | −0.451141 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.7980 | 1.61113 | 0.805567 | − | 0.592505i | \(-0.201861\pi\) | ||||
0.805567 | + | 0.592505i | \(0.201861\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.44949 | 0.200057 | ||||||||
\(743\) | 40.3485 | 1.48024 | 0.740121 | − | 0.672474i | \(-0.234768\pi\) | ||||
0.740121 | + | 0.672474i | \(0.234768\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 27.3485 | 1.00130 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.44949 | −0.0895622 | ||||||||
\(749\) | 3.34847 | 0.122350 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.4495 | −1.69497 | −0.847483 | − | 0.530823i | \(-0.821883\pi\) | ||||
−0.847483 | + | 0.530823i | \(0.821883\pi\) | |||||||
\(752\) | −11.7980 | −0.430227 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.69694 | −0.134635 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.5959 | 1.58452 | 0.792260 | − | 0.610183i | \(-0.208904\pi\) | ||||
0.792260 | + | 0.610183i | \(0.208904\pi\) | |||||||
\(758\) | −10.0000 | −0.363216 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.4949 | −1.06919 | −0.534595 | − | 0.845109i | \(-0.679536\pi\) | ||||
−0.534595 | + | 0.845109i | \(0.679536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.1464 | 0.548338 | ||||||||
\(764\) | −22.6969 | −0.821146 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.10102 | 0.256570 | ||||||||
\(767\) | 0.146428 | 0.00528722 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.7423 | −0.747988 | −0.373994 | − | 0.927431i | \(-0.622012\pi\) | ||||
−0.373994 | + | 0.927431i | \(0.622012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.20204 | −0.259207 | ||||||||
\(773\) | 38.6969 | 1.39183 | 0.695916 | − | 0.718123i | \(-0.254999\pi\) | ||||
0.695916 | + | 0.718123i | \(0.254999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.55051 | 0.342843 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.8990 | 1.03608 | ||||||||
\(779\) | −21.7980 | −0.780993 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.3485 | −0.477646 | ||||||||
\(782\) | −1.44949 | −0.0518336 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.2929 | −1.86404 | −0.932020 | − | 0.362408i | \(-0.881955\pi\) | ||||
−0.932020 | + | 0.362408i | \(0.881955\pi\) | |||||||
\(788\) | 12.8990 | 0.459507 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.44949 | −0.229317 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7980 | 0.561002 | ||||||||
\(794\) | −22.6969 | −0.805484 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.24745 | 0.327767 | ||||||||
\(797\) | 2.49490 | 0.0883738 | 0.0441869 | − | 0.999023i | \(-0.485930\pi\) | ||||
0.0441869 | + | 0.999023i | \(0.485930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.7980 | 0.417382 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.69694 | 0.307100 | ||||||||
\(803\) | −28.8990 | −1.01982 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.10102 | 0.0740053 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.2474 | −0.430864 | ||||||||
\(809\) | 6.20204 | 0.218052 | 0.109026 | − | 0.994039i | \(-0.465227\pi\) | ||||
0.109026 | + | 0.994039i | \(0.465227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.1918 | −1.58690 | −0.793450 | − | 0.608635i | \(-0.791717\pi\) | ||||
−0.793450 | + | 0.608635i | \(0.791717\pi\) | |||||||
\(812\) | −2.55051 | −0.0895054 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.20204 | −0.287481 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.3485 | 0.606946 | ||||||||
\(818\) | 9.59592 | 0.335513 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.4495 | −1.86540 | −0.932700 | − | 0.360653i | \(-0.882554\pi\) | ||||
−0.932700 | + | 0.360653i | \(0.882554\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.8434 | −1.94658 | −0.973289 | − | 0.229585i | \(-0.926263\pi\) | ||||
−0.973289 | + | 0.229585i | \(0.926263\pi\) | |||||||
\(824\) | 15.4495 | 0.538208 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.101021 | 0.00351495 | ||||||||
\(827\) | −36.2929 | −1.26203 | −0.631013 | − | 0.775772i | \(-0.717361\pi\) | ||||
−0.631013 | + | 0.775772i | \(0.717361\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.89898 | −0.239611 | −0.119806 | − | 0.992797i | \(-0.538227\pi\) | ||||
−0.119806 | + | 0.992797i | \(0.538227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.44949 | 0.0502520 | ||||||||
\(833\) | −1.00000 | −0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.8990 | −0.376949 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 38.5959 | 1.33327 | ||||||||
\(839\) | −42.4495 | −1.46552 | −0.732760 | − | 0.680488i | \(-0.761768\pi\) | ||||
−0.732760 | + | 0.680488i | \(0.761768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4949 | −0.775686 | ||||||||
\(842\) | −19.7980 | −0.682283 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.0000 | −0.516321 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.00000 | 0.171802 | ||||||||
\(848\) | 5.44949 | 0.187136 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.85357 | −0.166378 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.2474 | 0.453584 | 0.226792 | − | 0.973943i | \(-0.427176\pi\) | ||||
0.226792 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(854\) | 10.8990 | 0.372955 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.34847 | 0.114448 | ||||||||
\(857\) | −0.101021 | −0.00345080 | −0.00172540 | − | 0.999999i | \(-0.500549\pi\) | ||||
−0.00172540 | + | 0.999999i | \(0.500549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.9444 | 0.714613 | 0.357307 | − | 0.933987i | \(-0.383695\pi\) | ||||
0.357307 | + | 0.933987i | \(0.383695\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.79796 | 0.265600 | ||||||||
\(863\) | 0.348469 | 0.0118620 | 0.00593102 | − | 0.999982i | \(-0.498112\pi\) | ||||
0.00593102 | + | 0.999982i | \(0.498112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.5959 | 0.801822 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.44949 | 0.0491989 | ||||||||
\(869\) | −15.7980 | −0.535909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.24745 | −0.245570 | ||||||||
\(872\) | 15.1464 | 0.512923 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.44949 | −0.218157 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3031 | −0.449212 | −0.224606 | − | 0.974450i | \(-0.572110\pi\) | ||||
−0.224606 | + | 0.974450i | \(0.572110\pi\) | |||||||
\(878\) | −6.34847 | −0.214250 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.2929 | 0.447848 | 0.223924 | − | 0.974607i | \(-0.428113\pi\) | ||||
0.223924 | + | 0.974607i | \(0.428113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.10102 | −0.0707050 | −0.0353525 | − | 0.999375i | \(-0.511255\pi\) | ||||
−0.0353525 | + | 0.999375i | \(0.511255\pi\) | |||||||
\(884\) | −1.44949 | −0.0487516 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.5505 | 0.925577 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.89898 | 0.298462 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | 52.4949 | 1.75667 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32.0000 | −1.06785 | ||||||||
\(899\) | −3.69694 | −0.123300 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.44949 | −0.181549 | ||||||||
\(902\) | −12.0000 | −0.399556 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.44949 | −0.214507 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.2020 | 0.604389 | 0.302194 | − | 0.953246i | \(-0.402281\pi\) | ||||
0.302194 | + | 0.953246i | \(0.402281\pi\) | |||||||
\(908\) | 11.6969 | 0.388177 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.20204 | −0.205483 | −0.102741 | − | 0.994708i | \(-0.532761\pi\) | ||||
−0.102741 | + | 0.994708i | \(0.532761\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.6969 | 0.883540 | ||||||||
\(914\) | 0.101021 | 0.00334146 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.10102 | −0.102461 | ||||||||
\(917\) | 16.7980 | 0.554717 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.5959 | −0.580436 | −0.290218 | − | 0.956961i | \(-0.593728\pi\) | ||||
−0.290218 | + | 0.956961i | \(0.593728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.0000 | −0.329332 | ||||||||
\(923\) | −7.89898 | −0.259998 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.75255 | 0.123316 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.55051 | −0.0837246 | ||||||||
\(929\) | −31.5959 | −1.03663 | −0.518314 | − | 0.855190i | \(-0.673440\pi\) | ||||
−0.518314 | + | 0.855190i | \(0.673440\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.44949 | −0.145826 | ||||||||
\(932\) | 13.1464 | 0.430626 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.2020 | 0.399263 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9444 | 1.14158 | 0.570792 | − | 0.821095i | \(-0.306636\pi\) | ||||
0.570792 | + | 0.821095i | \(0.306636\pi\) | |||||||
\(938\) | −5.00000 | −0.163256 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.5959 | −0.964799 | −0.482400 | − | 0.875951i | \(-0.660235\pi\) | ||||
−0.482400 | + | 0.875951i | \(0.660235\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.10102 | −0.231241 | ||||||||
\(944\) | 0.101021 | 0.00328794 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.55051 | 0.310514 | ||||||||
\(947\) | −28.0454 | −0.911353 | −0.455677 | − | 0.890145i | \(-0.650603\pi\) | ||||
−0.455677 | + | 0.890145i | \(0.650603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.1010 | −0.555123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.00000 | −0.0324102 | ||||||||
\(953\) | 46.2929 | 1.49957 | 0.749786 | − | 0.661680i | \(-0.230156\pi\) | ||||
0.749786 | + | 0.661680i | \(0.230156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.4949 | 0.662852 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.0000 | 1.16311 | ||||||||
\(959\) | 5.10102 | 0.164721 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8990 | −0.932225 | ||||||||
\(962\) | −4.85357 | −0.156485 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.6515 | 0.343063 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.8990 | −0.800697 | −0.400349 | − | 0.916363i | \(-0.631111\pi\) | ||||
−0.400349 | + | 0.916363i | \(0.631111\pi\) | |||||||
\(968\) | 5.00000 | 0.160706 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.49490 | 0.304706 | 0.152353 | − | 0.988326i | \(-0.451315\pi\) | ||||
0.152353 | + | 0.988326i | \(0.451315\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.2474 | −0.713220 | ||||||||
\(974\) | 39.3939 | 1.26226 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.8990 | 0.348868 | ||||||||
\(977\) | −35.3939 | −1.13235 | −0.566175 | − | 0.824285i | \(-0.691577\pi\) | ||||
−0.566175 | + | 0.824285i | \(0.691577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.9444 | 0.861146 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.40408 | 0.140540 | ||||||||
\(983\) | 34.6969 | 1.10666 | 0.553330 | − | 0.832962i | \(-0.313357\pi\) | ||||
0.553330 | + | 0.832962i | \(0.313357\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.55051 | 0.0812248 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.44949 | −0.205186 | ||||||||
\(989\) | 5.65153 | 0.179708 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.3939 | 0.870195 | 0.435098 | − | 0.900383i | \(-0.356714\pi\) | ||||
0.435098 | + | 0.900383i | \(0.356714\pi\) | |||||||
\(992\) | 1.44949 | 0.0460213 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.44949 | −0.172847 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.7423 | −1.57536 | −0.787678 | − | 0.616087i | \(-0.788717\pi\) | ||||
−0.787678 | + | 0.616087i | \(0.788717\pi\) | |||||||
\(998\) | −2.89898 | −0.0917656 | ||||||||
\(999\) | 0 | 0 |
(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 | 9450.2.a.ea.1.2 | 2 | ||
3.2 | odd | 2 | 9450.2.a.ep.1.1 | 2 | |||
5.2 | odd | 4 | 1890.2.g.r.379.2 | yes | 4 | ||
5.3 | odd | 4 | 1890.2.g.r.379.4 | yes | 4 | ||
5.4 | even | 2 | 9450.2.a.ev.1.2 | 2 | |||
15.2 | even | 4 | 1890.2.g.m.379.3 | yes | 4 | ||
15.8 | even | 4 | 1890.2.g.m.379.1 | ✓ | 4 | ||
15.14 | odd | 2 | 9450.2.a.ek.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.g.m.379.1 | ✓ | 4 | 15.8 | even | 4 | ||
1890.2.g.m.379.3 | yes | 4 | 15.2 | even | 4 | ||
1890.2.g.r.379.2 | yes | 4 | 5.2 | odd | 4 | ||
1890.2.g.r.379.4 | yes | 4 | 5.3 | odd | 4 | ||
9450.2.a.ea.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9450.2.a.ek.1.1 | 2 | 15.14 | odd | 2 | |||
9450.2.a.ep.1.1 | 2 | 3.2 | odd | 2 | |||
9450.2.a.ev.1.2 | 2 | 5.4 | even | 2 |