Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(431,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.f (of order \(2\), degree \(1\), not 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.23123460096.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{6} + 6x^{4} + 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 431.8 | ||
Root | \(0.563016 + 1.29731i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.431 |
Dual form | 864.2.f.a.431.7 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.07638 | 1.37580 | 0.687899 | − | 0.725806i | \(-0.258533\pi\) | ||||
0.687899 | + | 0.725806i | \(0.258533\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.99102i | 1.50846i | 0.656609 | + | 0.754231i | \(0.271990\pi\) | ||||
−0.656609 | + | 0.754231i | \(0.728010\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.89939i | 0.572689i | 0.958127 | + | 0.286344i | \(0.0924401\pi\) | ||||
−0.958127 | + | 0.286344i | \(0.907560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.06939i | − 0.296595i | −0.988943 | − | 0.148298i | \(-0.952621\pi\) | ||||
0.988943 | − | 0.148298i | \(-0.0473794\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.08863i | 1.71925i | 0.510929 | + | 0.859623i | \(0.329302\pi\) | ||||
−0.510929 | + | 0.859623i | \(0.670698\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.73205 | −0.856191 | −0.428096 | − | 0.903733i | \(-0.640815\pi\) | ||||
−0.428096 | + | 0.903733i | \(0.640815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.824313 | 0.171881 | 0.0859406 | − | 0.996300i | \(-0.472610\pi\) | ||||
0.0859406 | + | 0.996300i | \(0.472610\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410 | 0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.50413 | −0.836396 | −0.418198 | − | 0.908356i | \(-0.637338\pi\) | ||||
−0.418198 | + | 0.908356i | \(0.637338\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 5.84325i | − 1.04948i | −0.851263 | − | 0.524740i | \(-0.824163\pi\) | ||||
0.851263 | − | 0.524740i | \(-0.175837\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.2779i | 2.07534i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.91264i | − 1.13643i | −0.822880 | − | 0.568216i | \(-0.807634\pi\) | ||||
0.822880 | − | 0.568216i | \(-0.192366\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.79879i | 0.593271i | 0.954991 | + | 0.296635i | \(0.0958646\pi\) | ||||
−0.954991 | + | 0.296635i | \(0.904135\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.97707 | 1.01771 | 0.508855 | − | 0.860852i | \(-0.330069\pi\) | ||||
0.508855 | + | 0.860852i | \(0.330069\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.92820 | −1.27546 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.6569 | 1.46384 | 0.731918 | − | 0.681393i | \(-0.238625\pi\) | ||||
0.731918 | + | 0.681393i | \(0.238625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.84325i | 0.787904i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.89939i | 0.247280i | 0.992327 | + | 0.123640i | \(0.0394568\pi\) | ||||
−0.992327 | + | 0.123640i | \(0.960543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.06939i | 0.136921i | 0.997654 | + | 0.0684606i | \(0.0218088\pi\) | ||||
−0.997654 | + | 0.0684606i | \(0.978191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 3.28985i | − 0.408055i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.19615 | 1.12349 | 0.561744 | − | 0.827311i | \(-0.310130\pi\) | ||||
0.561744 | + | 0.827311i | \(0.310130\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6569 | 1.26474 | 0.632370 | − | 0.774667i | \(-0.282082\pi\) | ||||
0.632370 | + | 0.774667i | \(0.282082\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.92820 | 0.693844 | 0.346922 | − | 0.937894i | \(-0.387227\pi\) | ||||
0.346922 | + | 0.937894i | \(0.387227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.58051 | −0.863879 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6.12979i | − 0.689656i | −0.938666 | − | 0.344828i | \(-0.887937\pi\) | ||||
0.938666 | − | 0.344828i | \(-0.112063\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 10.3785i | − 1.13919i | −0.821927 | − | 0.569593i | \(-0.807101\pi\) | ||||
0.821927 | − | 0.569593i | \(-0.192899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.8073i | 2.36534i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.6683i | 1.44884i | 0.689359 | + | 0.724420i | \(0.257892\pi\) | ||||
−0.689359 | + | 0.724420i | \(0.742108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.26795 | 0.447403 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.4812 | −1.17795 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3923 | −1.15671 | −0.578357 | − | 0.815784i | \(-0.696306\pi\) | ||||
−0.578357 | + | 0.815784i | \(0.696306\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.15276 | 0.612222 | 0.306111 | − | 0.951996i | \(-0.400972\pi\) | ||||
0.306111 | + | 0.951996i | \(0.400972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 3.99102i | − 0.393246i | −0.980479 | − | 0.196623i | \(-0.937002\pi\) | ||||
0.980479 | − | 0.196623i | \(-0.0629976\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.47908i | 0.819704i | 0.912152 | + | 0.409852i | \(0.134420\pi\) | ||||
−0.912152 | + | 0.409852i | \(0.865580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1208i | 0.969398i | 0.874681 | + | 0.484699i | \(0.161071\pi\) | ||||
−0.874681 | + | 0.484699i | \(0.838929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 10.8874i | − 1.02420i | −0.858925 | − | 0.512101i | \(-0.828867\pi\) | ||||
0.858925 | − | 0.512101i | \(-0.171133\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.53590 | 0.236474 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28.2908 | −2.59342 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.39230 | 0.672028 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.64863 | −0.147458 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 10.3785i | − 0.906772i | −0.891314 | − | 0.453386i | \(-0.850216\pi\) | ||||
0.891314 | − | 0.453386i | \(-0.149784\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 14.8947i | − 1.29153i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 17.4671i | − 1.49232i | −0.665769 | − | 0.746158i | \(-0.731896\pi\) | ||||
0.665769 | − | 0.746158i | \(-0.268104\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.19615 | 0.271094 | 0.135547 | − | 0.990771i | \(-0.456721\pi\) | ||||
0.135547 | + | 0.990771i | \(0.456721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.03119 | 0.169857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.8564 | −1.15071 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.15276 | −0.504053 | −0.252027 | − | 0.967720i | \(-0.581097\pi\) | ||||
−0.252027 | + | 0.967720i | \(0.581097\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 9.83427i | − 0.800301i | −0.916449 | − | 0.400151i | \(-0.868958\pi\) | ||||
0.916449 | − | 0.400151i | \(-0.131042\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 17.9761i | − 1.44387i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 21.8073i | − 1.74041i | −0.492687 | − | 0.870207i | \(-0.663985\pi\) | ||||
0.492687 | − | 0.870207i | \(-0.336015\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.28985i | 0.259276i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.80385 | −0.689571 | −0.344785 | − | 0.938682i | \(-0.612048\pi\) | ||||
−0.344785 | + | 0.938682i | \(0.612048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.1381 | 1.71310 | 0.856548 | − | 0.516067i | \(-0.172604\pi\) | ||||
0.856548 | + | 0.516067i | \(0.172604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8564 | 0.912031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.64863 | −0.125343 | −0.0626714 | − | 0.998034i | \(-0.519962\pi\) | ||||
−0.0626714 | + | 0.998034i | \(0.519962\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.8163i | 1.34679i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.79879i | − 0.283935i | −0.989871 | − | 0.141967i | \(-0.954657\pi\) | ||||
0.989871 | − | 0.141967i | \(-0.0453428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3.20817i | − 0.238461i | −0.992867 | − | 0.119231i | \(-0.961957\pi\) | ||||
0.992867 | − | 0.119231i | \(-0.0380428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 21.2659i | − 1.56350i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4641 | −0.984593 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.97707 | 0.504843 | 0.252421 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252421 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.39230 | −0.388147 | −0.194073 | − | 0.980987i | \(-0.562170\pi\) | ||||
−0.194073 | + | 0.980987i | \(0.562170\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.0305 | −1.21337 | −0.606687 | − | 0.794941i | \(-0.707502\pi\) | ||||
−0.606687 | + | 0.794941i | \(0.707502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 15.6775i | − 1.11135i | −0.831400 | − | 0.555675i | \(-0.812460\pi\) | ||||
0.831400 | − | 0.555675i | \(-0.187540\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 17.9761i | − 1.26167i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6865i | 0.816221i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 7.08863i | − 0.490331i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.0526 | −1.44932 | −0.724659 | − | 0.689108i | \(-0.758003\pi\) | ||||
−0.724659 | + | 0.689108i | \(0.758003\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.15276 | −0.419614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.3205 | 1.58310 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.58051 | 0.509920 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.0849i | 1.74677i | 0.487029 | + | 0.873386i | \(0.338081\pi\) | ||||
−0.487029 | + | 0.873386i | \(0.661919\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3.79879i | − 0.252134i | −0.992022 | − | 0.126067i | \(-0.959765\pi\) | ||||
0.992022 | − | 0.126067i | \(-0.0402355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 11.6865i | − 0.772266i | −0.922443 | − | 0.386133i | \(-0.873811\pi\) | ||||
0.922443 | − | 0.386133i | \(-0.126189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.1773i | − 0.928784i | −0.885630 | − | 0.464392i | \(-0.846273\pi\) | ||||
0.885630 | − | 0.464392i | \(-0.153727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.4641 | 1.40016 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.3055 | −0.795977 | −0.397989 | − | 0.917390i | \(-0.630292\pi\) | ||||
−0.397989 | + | 0.917390i | \(0.630292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.39230 | −0.347349 | −0.173674 | − | 0.984803i | \(-0.555564\pi\) | ||||
−0.173674 | + | 0.984803i | \(0.555564\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −27.4665 | −1.75477 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.99102i | 0.253942i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1773i | 0.894861i | 0.894319 | + | 0.447431i | \(0.147661\pi\) | ||||
−0.894319 | + | 0.447431i | \(0.852339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.56569i | 0.0984344i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.79879i | 0.236962i | 0.992956 | + | 0.118481i | \(0.0378024\pi\) | ||||
−0.992956 | + | 0.118481i | \(0.962198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.5885 | 1.71426 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.29725 | −0.203317 | −0.101659 | − | 0.994819i | \(-0.532415\pi\) | ||||
−0.101659 | + | 0.994819i | \(0.532415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.7846 | 2.01394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.8860 | 1.21247 | 0.606236 | − | 0.795285i | \(-0.292679\pi\) | ||||
0.606236 | + | 0.795285i | \(0.292679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.9730i | 0.727311i | 0.931534 | + | 0.363655i | \(0.118471\pi\) | ||||
−0.931534 | + | 0.363655i | \(0.881529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.47908i | 0.511308i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.8073i | 1.31027i | 0.755510 | + | 0.655137i | \(0.227389\pi\) | ||||
−0.755510 | + | 0.655137i | \(0.772611\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3785i | 0.619128i | 0.950879 | + | 0.309564i | \(0.100183\pi\) | ||||
−0.950879 | + | 0.309564i | \(0.899817\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.8564 | −1.65589 | −0.827946 | − | 0.560808i | \(-0.810491\pi\) | ||||
−0.827946 | + | 0.560808i | \(0.810491\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.1610 | −0.894926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.2487 | −1.95581 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.58051 | −0.442858 | −0.221429 | − | 0.975176i | \(-0.571072\pi\) | ||||
−0.221429 | + | 0.975176i | \(0.571072\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.84325i | 0.340207i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 0.881512i | − 0.0509791i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.98203i | − 0.460077i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.28985i | 0.188376i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9282 | −1.19444 | −0.597218 | − | 0.802079i | \(-0.703727\pi\) | ||||
−0.597218 | + | 0.802079i | \(0.703727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.4895 | −1.16185 | −0.580925 | − | 0.813957i | \(-0.697309\pi\) | ||||
−0.580925 | + | 0.813957i | \(0.697309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.39230 | 0.530884 | 0.265442 | − | 0.964127i | \(-0.414482\pi\) | ||||
0.265442 | + | 0.964127i | \(0.414482\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.8096 | 0.944124 | 0.472062 | − | 0.881565i | \(-0.343510\pi\) | ||||
0.472062 | + | 0.881565i | \(0.343510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 8.55511i | − 0.478994i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 26.4551i | − 1.47200i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.77386i | − 0.264806i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.8456i | 1.53518i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.87564 | −0.103095 | −0.0515474 | − | 0.998671i | \(-0.516415\pi\) | ||||
−0.0515474 | + | 0.998671i | \(0.516415\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.2908 | 1.54569 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3923 | −0.620578 | −0.310289 | − | 0.950642i | \(-0.600426\pi\) | ||||
−0.310289 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.0986 | 0.601025 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 7.69549i | − 0.415517i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.59757i | 0.407859i | 0.978986 | + | 0.203930i | \(0.0653714\pi\) | ||||
−0.978986 | + | 0.203930i | \(0.934629\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 2.63508i | − 0.141053i | −0.997510 | − | 0.0705264i | \(-0.977532\pi\) | ||||
0.997510 | − | 0.0705264i | \(-0.0224679\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 7.59757i | − 0.404378i | −0.979347 | − | 0.202189i | \(-0.935194\pi\) | ||||
0.979347 | − | 0.202189i | \(-0.0648055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32.7846 | 1.74003 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.7867 | 1.25541 | 0.627707 | − | 0.778449i | \(-0.283993\pi\) | ||||
0.627707 | + | 0.778449i | \(0.283993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.07180 | −0.266937 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.2374 | 0.954589 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 37.4848i | − 1.95669i | −0.206975 | − | 0.978346i | \(-0.566362\pi\) | ||||
0.206975 | − | 0.978346i | \(-0.433638\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 42.5318i | 2.20814i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 18.5991i | − 0.963027i | −0.876439 | − | 0.481514i | \(-0.840087\pi\) | ||||
0.876439 | − | 0.481514i | \(-0.159913\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.81667i | 0.248071i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.2679 | 1.34929 | 0.674647 | − | 0.738141i | \(-0.264296\pi\) | ||||
0.674647 | + | 0.738141i | \(0.264296\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.64863 | −0.0842409 | −0.0421204 | − | 0.999113i | \(-0.513411\pi\) | ||||
−0.0421204 | + | 0.999113i | \(0.513411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.3205 | −1.18852 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.3819 | 0.779893 | 0.389946 | − | 0.920838i | \(-0.372494\pi\) | ||||
0.389946 | + | 0.920838i | \(0.372494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.84325i | 0.295506i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 18.8576i | − 0.948827i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.1208i | 0.507949i | 0.967211 | + | 0.253974i | \(0.0817379\pi\) | ||||
−0.967211 | + | 0.253974i | \(0.918262\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.1951i | 0.758809i | 0.925231 | + | 0.379405i | \(0.123871\pi\) | ||||
−0.925231 | + | 0.379405i | \(0.876129\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.24871 | −0.311270 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.1298 | 0.650821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.60770 | −0.425623 | −0.212812 | − | 0.977093i | \(-0.568262\pi\) | ||||
−0.212812 | + | 0.977093i | \(0.568262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.58051 | −0.373012 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 31.9281i | − 1.56729i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.4551i | 1.29242i | 0.763160 | + | 0.646209i | \(0.223647\pi\) | ||||
−0.763160 | + | 0.646209i | \(0.776353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.77386i | 0.232664i | 0.993210 | + | 0.116332i | \(0.0371136\pi\) | ||||
−0.993210 | + | 0.116332i | \(0.962886\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.6444i | 1.53498i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.26795 | −0.206541 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.382565 | −0.0184275 | −0.00921375 | − | 0.999958i | \(-0.502933\pi\) | ||||
−0.00921375 | + | 0.999958i | \(0.502933\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.53590 | 0.217981 | 0.108991 | − | 0.994043i | \(-0.465238\pi\) | ||||
0.108991 | + | 0.994043i | \(0.465238\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.07638 | −0.147163 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 14.3984i | − 0.687197i | −0.939117 | − | 0.343598i | \(-0.888354\pi\) | ||||
0.939117 | − | 0.343598i | \(-0.111646\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.3366i | 1.29880i | 0.760446 | + | 0.649402i | \(0.224981\pi\) | ||||
−0.760446 | + | 0.649402i | \(0.775019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 42.0489i | 1.99331i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 24.0468i | − 1.13484i | −0.823429 | − | 0.567419i | \(-0.807942\pi\) | ||||
0.823429 | − | 0.567419i | \(-0.192058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.21539 | −0.339759 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.1298 | 0.615536 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.39230 | 0.299019 | 0.149510 | − | 0.988760i | \(-0.452230\pi\) | ||||
0.149510 | + | 0.988760i | \(0.452230\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.93188 | −0.276275 | −0.138138 | − | 0.990413i | \(-0.544112\pi\) | ||||
−0.138138 | + | 0.990413i | \(0.544112\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.42532i | 0.112714i | 0.998411 | + | 0.0563571i | \(0.0179485\pi\) | ||||
−0.998411 | + | 0.0563571i | \(0.982051\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.8754i | 0.919726i | 0.887990 | + | 0.459863i | \(0.152101\pi\) | ||||
−0.887990 | + | 0.459863i | \(0.847899\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.7020i | 1.69474i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3.79879i | − 0.174668i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.6603 | −0.764425 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.15276 | −0.281127 | −0.140563 | − | 0.990072i | \(-0.544891\pi\) | ||||
−0.140563 | + | 0.990072i | \(0.544891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.39230 | −0.337060 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.0470 | −1.59140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.2073i | 1.50477i | 0.658726 | + | 0.752383i | \(0.271096\pi\) | ||||
−0.658726 | + | 0.752383i | \(0.728904\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0348i | 1.49084i | 0.666595 | + | 0.745420i | \(0.267751\pi\) | ||||
−0.666595 | + | 0.745420i | \(0.732249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 31.9281i | − 1.43797i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.5318i | 1.90781i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.60770 | 0.251035 | 0.125517 | − | 0.992091i | \(-0.459941\pi\) | ||||
0.125517 | + | 0.992091i | \(0.459941\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.4977 | −1.31524 | −0.657619 | − | 0.753351i | \(-0.728436\pi\) | ||||
−0.657619 | + | 0.753351i | \(0.728436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9282 | 0.842294 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.220874 | 0.00979007 | 0.00489503 | − | 0.999988i | \(-0.498442\pi\) | ||||
0.00489503 | + | 0.999988i | \(0.498442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.6595i | 1.04664i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 12.2779i | − 0.541028i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2522i | 0.582831i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.08863i | 0.310559i | 0.987871 | + | 0.155279i | \(0.0496278\pi\) | ||||
−0.987871 | + | 0.155279i | \(0.950372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.5885 | 1.64363 | 0.821814 | − | 0.569756i | \(-0.192962\pi\) | ||||
0.821814 | + | 0.569756i | \(0.192962\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 41.4207 | 1.80431 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3205 | −0.970457 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.06238 | 0.175961 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.0849i | 1.12775i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 16.9582i | − 0.730440i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 34.5632i | − 1.48599i | −0.669298 | − | 0.742994i | \(-0.733405\pi\) | ||||
0.669298 | − | 0.742994i | \(-0.266595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.1354i | 1.33370i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.5885 | 1.35062 | 0.675312 | − | 0.737532i | \(-0.264009\pi\) | ||||
0.675312 | + | 0.737532i | \(0.264009\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.8096 | 0.716115 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.4641 | 1.04032 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.9401 | −0.633034 | −0.316517 | − | 0.948587i | \(-0.602513\pi\) | ||||
−0.316517 | + | 0.948587i | \(0.602513\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.13878i | 0.0904607i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 34.9342i | − 1.47230i | −0.676817 | − | 0.736151i | \(-0.736641\pi\) | ||||
0.676817 | − | 0.736151i | \(-0.263359\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 33.4938i | − 1.40910i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 6.07075i | − 0.254499i | −0.991871 | − | 0.127250i | \(-0.959385\pi\) | ||||
0.991871 | − | 0.127250i | \(-0.0406149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.19615 | 0.133755 | 0.0668774 | − | 0.997761i | \(-0.478696\pi\) | ||||
0.0668774 | + | 0.997761i | \(0.478696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.67982 | 0.153459 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9282 | 0.496578 | 0.248289 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248289 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.4207 | 1.71842 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.2416i | 0.838322i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.0348i | 1.36349i | 0.731588 | + | 0.681747i | \(0.238779\pi\) | ||||
−0.731588 | + | 0.681747i | \(0.761221\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.8073i | 0.898555i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 38.7330i | − 1.59057i | −0.606233 | − | 0.795287i | \(-0.707320\pi\) | ||||
0.606233 | − | 0.795287i | \(-0.292680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −87.0333 | −3.56802 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.5207 | 0.920169 | 0.460084 | − | 0.887875i | \(-0.347819\pi\) | ||||
0.460084 | + | 0.887875i | \(0.347819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.3923 | 1.23973 | 0.619864 | − | 0.784709i | \(-0.287188\pi\) | ||||
0.619864 | + | 0.784709i | \(0.287188\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.7415 | 0.924574 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 35.3461i | − 1.43465i | −0.696738 | − | 0.717326i | \(-0.745366\pi\) | ||||
0.696738 | − | 0.717326i | \(-0.254634\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 7.46120i | − 0.301848i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.91264i | 0.279199i | 0.990208 | + | 0.139599i | \(0.0445815\pi\) | ||||
−0.990208 | + | 0.139599i | \(0.955418\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 28.8635i | − 1.16200i | −0.813904 | − | 0.581000i | \(-0.802662\pi\) | ||||
0.813904 | − | 0.581000i | \(-0.197338\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.1962 | −1.49504 | −0.747520 | − | 0.664240i | \(-0.768755\pi\) | ||||
−0.747520 | + | 0.664240i | \(0.768755\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −54.5505 | −2.18552 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.3923 | −1.09569 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 49.0012 | 1.95380 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0939i | 0.879542i | 0.898110 | + | 0.439771i | \(0.144940\pi\) | ||||
−0.898110 | + | 0.439771i | \(0.855060\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.54773i | 0.378295i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.9342i | 1.37982i | 0.723896 | + | 0.689909i | \(0.242350\pi\) | ||||
−0.723896 | + | 0.689909i | \(0.757650\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.7846 | 0.740793 | 0.370396 | − | 0.928874i | \(-0.379222\pi\) | ||||
0.370396 | + | 0.928874i | \(0.379222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.7720 | −1.56360 | −0.781800 | − | 0.623529i | \(-0.785698\pi\) | ||||
−0.781800 | + | 0.623529i | \(0.785698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.60770 | −0.141614 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.4124 | −1.26840 | −0.634198 | − | 0.773171i | \(-0.718669\pi\) | ||||
−0.634198 | + | 0.773171i | \(0.718669\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 31.9281i | − 1.24753i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 21.7748i | − 0.848227i | −0.905609 | − | 0.424114i | \(-0.860586\pi\) | ||||
0.905609 | − | 0.424114i | \(-0.139414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 45.2571i | − 1.76030i | −0.474698 | − | 0.880149i | \(-0.657443\pi\) | ||||
0.474698 | − | 0.880149i | \(-0.342557\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 45.8216i | − 1.77689i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.71281 | −0.143761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.03119 | −0.0784133 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2487 | 1.35874 | 0.679369 | − | 0.733797i | \(-0.262254\pi\) | ||||
0.679369 | + | 0.733797i | \(0.262254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.4970 | 1.71016 | 0.855080 | − | 0.518496i | \(-0.173508\pi\) | ||||
0.855080 | + | 0.518496i | \(0.173508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 45.4669i | − 1.74486i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 39.7509i | − 1.52103i | −0.649323 | − | 0.760513i | \(-0.724948\pi\) | ||||
0.649323 | − | 0.760513i | \(-0.275052\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 53.7354i | − 2.05313i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 11.3964i | − 0.434167i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.85641 | −0.146705 | −0.0733523 | − | 0.997306i | \(-0.523370\pi\) | ||||
−0.0733523 | + | 0.997306i | \(0.523370\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.83257 | 0.372971 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.9282 | −1.01998 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.8567 | −1.95860 | −0.979300 | − | 0.202415i | \(-0.935121\pi\) | ||||
−0.979300 | + | 0.202415i | \(0.935121\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.7983i | 0.973002i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.5557i | 0.923514i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.1363i | 1.31957i | 0.751454 | + | 0.659786i | \(0.229353\pi\) | ||||
−0.751454 | + | 0.659786i | \(0.770647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.81667i | − 0.180386i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.24871 | 0.233689 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.80138 | 0.290942 | 0.145471 | − | 0.989362i | \(-0.453530\pi\) | ||||
0.145471 | + | 0.989362i | \(0.453530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9282 | 0.593197 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.1069 | −0.746751 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.0849i | 0.967434i | 0.875224 | + | 0.483717i | \(0.160714\pi\) | ||||
−0.875224 | + | 0.483717i | \(0.839286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 14.1773i | − 0.524365i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2522i | 0.489481i | 0.969589 | + | 0.244741i | \(0.0787028\pi\) | ||||
−0.969589 | + | 0.244741i | \(0.921297\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4671i | 0.643409i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.6410 | 0.759292 | 0.379646 | − | 0.925132i | \(-0.376046\pi\) | ||||
0.379646 | + | 0.925132i | \(0.376046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.6950 | −1.89651 | −0.948253 | − | 0.317517i | \(-0.897151\pi\) | ||||
−0.948253 | + | 0.317517i | \(0.897151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.9282 | −0.693476 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.8402 | −1.23649 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.9551i | 0.728171i | 0.931366 | + | 0.364086i | \(0.118618\pi\) | ||||
−0.931366 | + | 0.364086i | \(0.881382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 30.2539i | − 1.10105i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 52.0930i | − 1.89335i | −0.322189 | − | 0.946675i | \(-0.604419\pi\) | ||||
0.322189 | − | 0.946675i | \(-0.395581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.0407i | 1.56023i | 0.625639 | + | 0.780113i | \(0.284838\pi\) | ||||
−0.625639 | + | 0.780113i | \(0.715162\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.3923 | −1.46230 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.03119 | 0.0733421 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.07180 | 0.146833 | 0.0734164 | − | 0.997301i | \(-0.476610\pi\) | ||||
0.0734164 | + | 0.997301i | \(0.476610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.7179 | −1.60839 | −0.804196 | − | 0.594364i | \(-0.797404\pi\) | ||||
−0.804196 | + | 0.594364i | \(0.797404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 26.0849i | − 0.936996i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 14.1773i | − 0.507953i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.2416i | 0.724302i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 67.0875i | − 2.39446i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.44486 | −0.265381 | −0.132690 | − | 0.991158i | \(-0.542362\pi\) | ||||
−0.132690 | + | 0.991158i | \(0.542362\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.4519 | 1.54497 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14359 | 0.0406102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.4665 | −0.972914 | −0.486457 | − | 0.873704i | \(-0.661711\pi\) | ||||
−0.486457 | + | 0.873704i | \(0.661711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.4579i | 1.74969i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.2600i | 0.397356i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1208i | 0.356712i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 14.1773i | − 0.498446i | −0.968446 | − | 0.249223i | \(-0.919825\pi\) | ||||
0.968446 | − | 0.249223i | \(-0.0801752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0718 | 0.950619 | 0.475310 | − | 0.879819i | \(-0.342336\pi\) | ||||
0.475310 | + | 0.879819i | \(0.342336\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.0840 | −0.948710 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.46410 | 0.261136 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.8778 | −0.379636 | −0.189818 | − | 0.981819i | \(-0.560790\pi\) | ||||
−0.189818 | + | 0.981819i | \(0.560790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 24.2326i | − 0.844697i | −0.906434 | − | 0.422348i | \(-0.861206\pi\) | ||||
0.906434 | − | 0.422348i | \(-0.138794\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 40.6324i | − 1.41293i | −0.707749 | − | 0.706464i | \(-0.750289\pi\) | ||||
0.707749 | − | 0.706464i | \(-0.249711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5632i | 1.20043i | 0.799839 | + | 0.600215i | \(0.204918\pi\) | ||||
−0.799839 | + | 0.600215i | \(0.795082\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 63.2888i | − 2.19283i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 68.1051 | 2.35687 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.0528 | 0.864918 | 0.432459 | − | 0.901654i | \(-0.357646\pi\) | ||||
0.432459 | + | 0.901654i | \(0.357646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.71281 | −0.300442 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.4748 | 1.25477 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.5028i | 1.01373i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 5.69818i | − 0.195331i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.8947i | 0.509984i | 0.966943 | + | 0.254992i | \(0.0820728\pi\) | ||||
−0.966943 | + | 0.254992i | \(0.917927\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1.01788i | − 0.0347702i | −0.999849 | − | 0.0173851i | \(-0.994466\pi\) | ||||
0.999849 | − | 0.0173851i | \(-0.00553413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5885 | −0.395393 | −0.197697 | − | 0.980263i | \(-0.563346\pi\) | ||||
−0.197697 | + | 0.980263i | \(0.563346\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.9853 | 0.544147 | 0.272073 | − | 0.962276i | \(-0.412291\pi\) | ||||
0.272073 | + | 0.962276i | \(0.412291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07180 | −0.172446 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.6429 | 0.394958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 9.83427i | − 0.333221i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.57969i | − 0.222434i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.1722i | 0.647400i | 0.946160 | + | 0.323700i | \(0.104927\pi\) | ||||
−0.946160 | + | 0.323700i | \(0.895073\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 6.07075i | − 0.204529i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) | ||||
0.994757 | − | 0.102264i | \(-0.0326088\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.1244 | −1.48490 | −0.742451 | − | 0.669900i | \(-0.766337\pi\) | ||||
−0.742451 | + | 0.669900i | \(0.766337\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.8179 | −0.866880 | −0.433440 | − | 0.901182i | \(-0.642700\pi\) | ||||
−0.433440 | + | 0.901182i | \(0.642700\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.0388 | −0.871354 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 11.6865i | − 0.390637i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.3188i | 0.877780i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 75.5427i | 2.51669i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 9.86954i | − 0.328075i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.3731 | 1.53979 | 0.769896 | − | 0.638169i | \(-0.220308\pi\) | ||||
0.769896 | + | 0.638169i | \(0.220308\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.441748 | −0.0146358 | −0.00731788 | − | 0.999973i | \(-0.502329\pi\) | ||||
−0.00731788 | + | 0.999973i | \(0.502329\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.7128 | 0.652399 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41.4207 | 1.36783 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 58.0130i | − 1.91367i | −0.290628 | − | 0.956836i | \(-0.593864\pi\) | ||||
0.290628 | − | 0.956836i | \(-0.406136\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 11.3964i | − 0.375116i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 30.8587i | − 1.01463i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 20.7570i | − 0.681014i | −0.940242 | − | 0.340507i | \(-0.889401\pi\) | ||||
0.940242 | − | 0.340507i | \(-0.110599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.3205 | 1.09204 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −41.4207 | −1.35460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3923 | −0.764193 | −0.382097 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382097 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.6791 | 0.608923 | 0.304461 | − | 0.952525i | \(-0.401524\pi\) | ||||
0.304461 | + | 0.952525i | \(0.401524\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.13139i | 0.101972i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 29.2360i | − 0.950044i | −0.879974 | − | 0.475022i | \(-0.842440\pi\) | ||||
0.879974 | − | 0.475022i | \(-0.157560\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 6.33956i | − 0.205791i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 15.7041i | − 0.508705i | −0.967112 | − | 0.254353i | \(-0.918138\pi\) | ||||
0.967112 | − | 0.254353i | \(-0.0818624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4641 | 0.694562 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 69.7115 | 2.25110 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.14359 | −0.101406 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.5888 | −0.534011 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.83427i | 0.316249i | 0.987419 | + | 0.158124i | \(0.0505447\pi\) | ||||
−0.987419 | + | 0.158124i | \(0.949455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.8275i | 1.79159i | 0.444466 | + | 0.895796i | \(0.353393\pi\) | ||||
−0.444466 | + | 0.895796i | \(0.646607\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.7559i | 0.408935i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.5379i | 0.753043i | 0.926408 | + | 0.376521i | \(0.122880\pi\) | ||||
−0.926408 | + | 0.376521i | \(0.877120\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.9615 | −0.829734 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55.3156 | 1.76429 | 0.882147 | − | 0.470974i | \(-0.156097\pi\) | ||||
0.882147 | + | 0.470974i | \(0.156097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.3923 | −1.66936 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.64863 | −0.0524233 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 25.7983i | − 0.819511i | −0.912195 | − | 0.409755i | \(-0.865614\pi\) | ||||
0.912195 | − | 0.409755i | \(-0.134386\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 48.2300i | − 1.52899i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.56569i | 0.0495860i | 0.999693 | + | 0.0247930i | \(0.00789267\pi\) | ||||
−0.999693 | + | 0.0247930i | \(0.992107\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 864.2.f.a.431.8 | 8 | ||
3.2 | odd | 2 | inner | 864.2.f.a.431.2 | 8 | ||
4.3 | odd | 2 | 216.2.f.a.107.4 | yes | 8 | ||
8.3 | odd | 2 | inner | 864.2.f.a.431.1 | 8 | ||
8.5 | even | 2 | 216.2.f.a.107.6 | yes | 8 | ||
9.2 | odd | 6 | 2592.2.p.f.2159.8 | 16 | |||
9.4 | even | 3 | 2592.2.p.f.431.1 | 16 | |||
9.5 | odd | 6 | 2592.2.p.f.431.7 | 16 | |||
9.7 | even | 3 | 2592.2.p.f.2159.2 | 16 | |||
12.11 | even | 2 | 216.2.f.a.107.5 | yes | 8 | ||
24.5 | odd | 2 | 216.2.f.a.107.3 | ✓ | 8 | ||
24.11 | even | 2 | inner | 864.2.f.a.431.7 | 8 | ||
36.7 | odd | 6 | 648.2.l.f.539.8 | 16 | |||
36.11 | even | 6 | 648.2.l.f.539.1 | 16 | |||
36.23 | even | 6 | 648.2.l.f.107.6 | 16 | |||
36.31 | odd | 6 | 648.2.l.f.107.3 | 16 | |||
72.5 | odd | 6 | 648.2.l.f.107.8 | 16 | |||
72.11 | even | 6 | 2592.2.p.f.2159.1 | 16 | |||
72.13 | even | 6 | 648.2.l.f.107.1 | 16 | |||
72.29 | odd | 6 | 648.2.l.f.539.3 | 16 | |||
72.43 | odd | 6 | 2592.2.p.f.2159.7 | 16 | |||
72.59 | even | 6 | 2592.2.p.f.431.2 | 16 | |||
72.61 | even | 6 | 648.2.l.f.539.6 | 16 | |||
72.67 | odd | 6 | 2592.2.p.f.431.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.f.a.107.3 | ✓ | 8 | 24.5 | odd | 2 | ||
216.2.f.a.107.4 | yes | 8 | 4.3 | odd | 2 | ||
216.2.f.a.107.5 | yes | 8 | 12.11 | even | 2 | ||
216.2.f.a.107.6 | yes | 8 | 8.5 | even | 2 | ||
648.2.l.f.107.1 | 16 | 72.13 | even | 6 | |||
648.2.l.f.107.3 | 16 | 36.31 | odd | 6 | |||
648.2.l.f.107.6 | 16 | 36.23 | even | 6 | |||
648.2.l.f.107.8 | 16 | 72.5 | odd | 6 | |||
648.2.l.f.539.1 | 16 | 36.11 | even | 6 | |||
648.2.l.f.539.3 | 16 | 72.29 | odd | 6 | |||
648.2.l.f.539.6 | 16 | 72.61 | even | 6 | |||
648.2.l.f.539.8 | 16 | 36.7 | odd | 6 | |||
864.2.f.a.431.1 | 8 | 8.3 | odd | 2 | inner | ||
864.2.f.a.431.2 | 8 | 3.2 | odd | 2 | inner | ||
864.2.f.a.431.7 | 8 | 24.11 | even | 2 | inner | ||
864.2.f.a.431.8 | 8 | 1.1 | even | 1 | trivial | ||
2592.2.p.f.431.1 | 16 | 9.4 | even | 3 | |||
2592.2.p.f.431.2 | 16 | 72.59 | even | 6 | |||
2592.2.p.f.431.7 | 16 | 9.5 | odd | 6 | |||
2592.2.p.f.431.8 | 16 | 72.67 | odd | 6 | |||
2592.2.p.f.2159.1 | 16 | 72.11 | even | 6 | |||
2592.2.p.f.2159.2 | 16 | 9.7 | even | 3 | |||
2592.2.p.f.2159.7 | 16 | 72.43 | odd | 6 | |||
2592.2.p.f.2159.8 | 16 | 9.2 | odd | 6 |