Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,4,Mod(97,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.97");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.3283667211\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.97 |
Dual form | 192.4.d.a.97.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.3923i | 0.929516i | 0.885438 | + | 0.464758i | \(0.153859\pi\) | ||||
−0.885438 | + | 0.464758i | \(0.846141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | −0.187044 | −0.0935220 | − | 0.995617i | \(-0.529813\pi\) | ||||
−0.0935220 | + | 0.995617i | \(0.529813\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 55.4256i | 1.18248i | 0.806494 | + | 0.591242i | \(0.201362\pi\) | ||||
−0.806494 | + | 0.591242i | \(0.798638\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.1769 | −0.536656 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −90.0000 | −1.28401 | −0.642006 | − | 0.766700i | \(-0.721898\pi\) | ||||
−0.642006 | + | 0.766700i | \(0.721898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 116.000i | − 1.40064i | −0.713827 | − | 0.700322i | \(-0.753040\pi\) | ||||
0.713827 | − | 0.700322i | \(-0.246960\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 10.3923i | − 0.107990i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −103.923 | −0.942150 | −0.471075 | − | 0.882093i | \(-0.656134\pi\) | ||||
−0.471075 | + | 0.882093i | \(0.656134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.0000 | 0.136000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 259.808i | 1.66362i | 0.555058 | + | 0.831811i | \(0.312696\pi\) | ||||
−0.555058 | + | 0.831811i | \(0.687304\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −301.377 | −1.74609 | −0.873046 | − | 0.487637i | \(-0.837859\pi\) | ||||
−0.873046 | + | 0.487637i | \(0.837859\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 36.0000i | − 0.173860i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.6410i | 0.153918i | 0.997034 | + | 0.0769588i | \(0.0245210\pi\) | ||||
−0.997034 | + | 0.0769588i | \(0.975479\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −166.277 | −0.682708 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −54.0000 | −0.205692 | −0.102846 | − | 0.994697i | \(-0.532795\pi\) | ||||
−0.102846 | + | 0.994697i | \(0.532795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.0000i | 0.0709296i | 0.999371 | + | 0.0354648i | \(0.0112912\pi\) | ||||
−0.999371 | + | 0.0354648i | \(0.988709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 93.5307i | − 0.309839i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 394.908 | 1.22560 | 0.612800 | − | 0.790238i | \(-0.290043\pi\) | ||||
0.612800 | + | 0.790238i | \(0.290043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −331.000 | −0.965015 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 270.000i | − 0.741325i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 488.438i | 1.26589i | 0.774197 | + | 0.632945i | \(0.218154\pi\) | ||||
−0.774197 | + | 0.632945i | \(0.781846\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 348.000 | 0.808662 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 324.000i | 0.714936i | 0.933925 | + | 0.357468i | \(0.116360\pi\) | ||||
−0.933925 | + | 0.357468i | \(0.883640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 575.041i | − 1.20699i | −0.797366 | − | 0.603495i | \(-0.793774\pi\) | ||||
0.797366 | − | 0.603495i | \(-0.206226\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 31.1769 | 0.0623480 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −576.000 | −1.09914 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 116.000i | 0.211517i | 0.994392 | + | 0.105759i | \(0.0337271\pi\) | ||||
−0.994392 | + | 0.105759i | \(0.966273\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 311.769i | − 0.543951i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1101.58 | 1.84132 | 0.920662 | − | 0.390361i | \(-0.127650\pi\) | ||||
0.920662 | + | 0.390361i | \(0.127650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1106.00 | 1.77325 | 0.886627 | − | 0.462486i | \(-0.153042\pi\) | ||||
0.886627 | + | 0.462486i | \(0.153042\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 51.0000i | 0.0785196i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −148.956 | −0.212138 | −0.106069 | − | 0.994359i | \(-0.533826\pi\) | ||||
−0.106069 | + | 0.994359i | \(0.533826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1152.00i | 1.52348i | 0.647886 | + | 0.761738i | \(0.275653\pi\) | ||||
−0.647886 | + | 0.761738i | \(0.724347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 935.307i | − 1.19351i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −779.423 | −0.960493 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 918.000 | 1.09335 | 0.546673 | − | 0.837346i | \(-0.315894\pi\) | ||||
0.546673 | + | 0.837346i | \(0.315894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 192.000i | − 0.221177i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 904.131i | − 1.00811i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1205.51 | 1.30192 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 190.000 | 0.198882 | 0.0994411 | − | 0.995043i | \(-0.468295\pi\) | ||||
0.0994411 | + | 0.995043i | \(0.468295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.3923i | − 0.0102383i | −0.999987 | − | 0.00511917i | \(-0.998371\pi\) | ||||
0.999987 | − | 0.00511917i | \(-0.00162949\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 793.279 | 0.758875 | 0.379438 | − | 0.925217i | \(-0.376118\pi\) | ||||
0.379438 | + | 0.925217i | \(0.376118\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 108.000 | 0.100378 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 252.000i | − 0.227680i | −0.993499 | − | 0.113840i | \(-0.963685\pi\) | ||||
0.993499 | − | 0.113840i | \(-0.0363151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 457.261i | − 0.401814i | −0.979610 | − | 0.200907i | \(-0.935611\pi\) | ||||
0.979610 | − | 0.200907i | \(-0.0643889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −103.923 | −0.0888643 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2214.00 | −1.84315 | −0.921573 | − | 0.388204i | \(-0.873096\pi\) | ||||
−0.921573 | + | 0.388204i | \(0.873096\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1080.00i | − 0.875744i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 498.831i | − 0.394162i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 311.769 | 0.240167 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1331.00 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 162.000i | − 0.118756i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1475.71i | 1.05593i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −696.284 | −0.486498 | −0.243249 | − | 0.969964i | \(-0.578213\pi\) | ||||
−0.243249 | + | 0.969964i | \(0.578213\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −60.0000 | −0.0409512 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2268.00i | 1.51264i | 0.654201 | + | 0.756321i | \(0.273005\pi\) | ||||
−0.654201 | + | 0.756321i | \(0.726995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 401.836i | 0.261982i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 280.592 | 0.178885 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 522.000 | 0.325529 | 0.162764 | − | 0.986665i | \(-0.447959\pi\) | ||||
0.162764 | + | 0.986665i | \(0.447959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 676.000i | 0.412501i | 0.978499 | + | 0.206250i | \(0.0661261\pi\) | ||||
−0.978499 | + | 0.206250i | \(0.933874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1184.72i | 0.707600i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2700.00 | −1.54636 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 993.000i | − 0.557151i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1465.31i | 0.805660i | 0.915275 | + | 0.402830i | \(0.131973\pi\) | ||||
−0.915275 | + | 0.402830i | \(0.868027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2386.77 | −1.28631 | −0.643153 | − | 0.765738i | \(-0.722374\pi\) | ||||
−0.643153 | + | 0.765738i | \(0.722374\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 810.000 | 0.428004 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3132.00i | − 1.62302i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2016.11i | 1.02486i | 0.858729 | + | 0.512430i | \(0.171254\pi\) | ||||
−0.858729 | + | 0.512430i | \(0.828746\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1465.31 | −0.730862 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 360.000 | 0.176223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 388.000i | 0.186445i | 0.995645 | + | 0.0932224i | \(0.0297168\pi\) | ||||
−0.995645 | + | 0.0932224i | \(0.970283\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2203.17 | −1.02088 | −0.510438 | − | 0.859915i | \(-0.670517\pi\) | ||||
−0.510438 | + | 0.859915i | \(0.670517\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −875.000 | −0.398270 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1044.00i | 0.466881i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 197.454i | 0.0867753i | 0.999058 | + | 0.0433877i | \(0.0138151\pi\) | ||||
−0.999058 | + | 0.0433877i | \(0.986185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −58.8897 | −0.0254380 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −972.000 | −0.412768 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2844.00i | − 1.18754i | −0.804633 | − | 0.593772i | \(-0.797638\pi\) | ||||
0.804633 | − | 0.593772i | \(-0.202362\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 96.9948i | − 0.0398319i | −0.999802 | − | 0.0199159i | \(-0.993660\pi\) | ||||
0.999802 | − | 0.0199159i | \(-0.00633986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1725.12 | 0.696856 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −360.000 | −0.143069 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 93.5307i | 0.0359966i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3200.83 | −1.21259 | −0.606293 | − | 0.795241i | \(-0.707344\pi\) | ||||
−0.606293 | + | 0.795241i | \(0.707344\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1342.00 | −0.500514 | −0.250257 | − | 0.968179i | \(-0.580515\pi\) | ||||
−0.250257 | + | 0.968179i | \(0.580515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1728.00i | − 0.634588i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 966.484i | − 0.349539i | −0.984609 | − | 0.174769i | \(-0.944082\pi\) | ||||
0.984609 | − | 0.174769i | \(-0.0559180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1784.01 | −0.635504 | −0.317752 | − | 0.948174i | \(-0.602928\pi\) | ||||
−0.317752 | + | 0.948174i | \(0.602928\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −348.000 | −0.122120 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 900.000i | − 0.311171i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 561.184i | − 0.191194i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 935.307 | 0.314050 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2764.00i | − 0.901809i | −0.892572 | − | 0.450904i | \(-0.851102\pi\) | ||||
0.892572 | − | 0.450904i | \(-0.148898\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3304.75i | 1.06309i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −207.846 | −0.0659302 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1044.00 | 0.326596 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3318.00i | 1.02379i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 4988.31i | − 1.51832i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4292.02 | 1.28886 | 0.644428 | − | 0.764665i | \(-0.277095\pi\) | ||||
0.644428 | + | 0.764665i | \(0.277095\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −153.000 | −0.0453333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5688.00i | 1.66311i | 0.555443 | + | 0.831555i | \(0.312549\pi\) | ||||
−0.555443 | + | 0.831555i | \(0.687451\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5570.28i | 1.60740i | 0.595036 | + | 0.803699i | \(0.297138\pi\) | ||||
−0.595036 | + | 0.803699i | \(0.702862\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2718.00 | 0.764215 | 0.382108 | − | 0.924118i | \(-0.375198\pi\) | ||||
0.382108 | + | 0.924118i | \(0.375198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4104.00i | 1.13921i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 446.869i | − 0.122478i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3574.95 | −0.967550 | −0.483775 | − | 0.875192i | \(-0.660735\pi\) | ||||
−0.483775 | + | 0.875192i | \(0.660735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4490.00 | 1.20011 | 0.600055 | − | 0.799959i | \(-0.295146\pi\) | ||||
0.600055 | + | 0.799959i | \(0.295146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3439.85i | − 0.896996i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6429.37 | 1.65624 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3456.00 | −0.879579 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4608.00i | − 1.15878i | −0.815050 | − | 0.579391i | \(-0.803290\pi\) | ||||
0.815050 | − | 0.579391i | \(-0.196710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2805.92 | 0.689073 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4626.00 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 120.000i | − 0.0287893i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2338.27i | − 0.554541i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1995.32 | 0.467821 | 0.233910 | − | 0.972258i | \(-0.424848\pi\) | ||||
0.233910 | + | 0.972258i | \(0.424848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5076.00 | −1.17666 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2754.00i | 0.631244i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3148.87i | − 0.713717i | −0.934158 | − | 0.356859i | \(-0.883848\pi\) | ||||
0.934158 | − | 0.356859i | \(-0.116152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5345.11 | 1.19813 | 0.599063 | − | 0.800702i | \(-0.295540\pi\) | ||||
0.599063 | + | 0.800702i | \(0.295540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 576.000 | 0.127696 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 6526.37i | − 1.41564i | −0.706394 | − | 0.707818i | \(-0.749679\pi\) | ||||
0.706394 | − | 0.707818i | \(-0.250321\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2712.39 | 0.582031 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1170.00 | −0.248386 | −0.124193 | − | 0.992258i | \(-0.539634\pi\) | ||||
−0.124193 | + | 0.992258i | \(0.539634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5740.00i | 1.20568i | 0.797862 | + | 0.602840i | \(0.205964\pi\) | ||||
−0.797862 | + | 0.602840i | \(0.794036\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3616.52i | 0.751664i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 187.061 | 0.0384735 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3187.00 | 0.648687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 570.000i | 0.114825i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7991.68i | − 1.59344i | −0.604346 | − | 0.796722i | \(-0.706566\pi\) | ||||
0.604346 | − | 0.796722i | \(-0.293434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3367.11 | −0.664544 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5760.00i | − 1.11408i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 69.2820i | − 0.0132669i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.1769 | 0.00591111 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5976.00 | 1.12192 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5452.00i | − 1.01356i | −0.862076 | − | 0.506779i | \(-0.830836\pi\) | ||||
0.862076 | − | 0.506779i | \(-0.169164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2379.84i | 0.438137i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2203.17 | −0.401705 | −0.200852 | − | 0.979622i | \(-0.564371\pi\) | ||||
−0.200852 | + | 0.979622i | \(0.564371\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1034.00 | −0.186726 | −0.0933628 | − | 0.995632i | \(-0.529762\pi\) | ||||
−0.0933628 | + | 0.995632i | \(0.529762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 324.000i | 0.0579534i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2650.04i | − 0.469530i | −0.972052 | − | 0.234765i | \(-0.924568\pi\) | ||||
0.972052 | − | 0.234765i | \(-0.0754320\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 756.000 | 0.131451 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10440.0i | 1.79844i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 942.236i | 0.160818i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1371.78 | 0.231987 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1368.00 | −0.229241 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4132.00i | 0.686149i | 0.939308 | + | 0.343074i | \(0.111468\pi\) | ||||
−0.939308 | + | 0.343074i | \(0.888532\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 311.769i | − 0.0513058i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1205.51 | −0.196609 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −458.000 | −0.0740322 | −0.0370161 | − | 0.999315i | \(-0.511785\pi\) | ||||
−0.0370161 | + | 0.999315i | \(0.511785\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 6642.00i | − 1.06414i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2334.80 | 0.367544 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3240.00 | 0.505611 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 11016.0i | − 1.70424i | −0.523350 | − | 0.852118i | \(-0.675318\pi\) | ||||
0.523350 | − | 0.852118i | \(-0.324682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2528.79i | 0.387860i | 0.981015 | + | 0.193930i | \(0.0621235\pi\) | ||||
−0.981015 | + | 0.193930i | \(0.937876\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1496.49 | 0.227569 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5562.00 | 0.838627 | 0.419314 | − | 0.907841i | \(-0.362271\pi\) | ||||
0.419314 | + | 0.907841i | \(0.362271\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11448.0i | 1.71154i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 935.307i | 0.138660i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8875.03 | −1.30475 | −0.652376 | − | 0.757895i | \(-0.726228\pi\) | ||||
−0.652376 | + | 0.757895i | \(0.726228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6597.00 | −0.961802 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3993.00i | 0.577350i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11493.9i | 1.64827i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12799.9 | −1.82056 | −0.910282 | − | 0.413989i | \(-0.864135\pi\) | ||||
−0.910282 | + | 0.413989i | \(0.864135\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 486.000 | 0.0685641 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1692.00i | − 0.236777i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4981.38i | 0.691491i | 0.938328 | + | 0.345745i | \(0.112374\pi\) | ||||
−0.938328 | + | 0.345745i | \(0.887626\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4427.12 | −0.609642 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14400.0 | −1.96721 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 9892.00i | − 1.34068i | −0.742054 | − | 0.670340i | \(-0.766148\pi\) | ||||
0.742054 | − | 0.670340i | \(-0.233852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2088.85i | − 0.280880i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8771.11 | 1.17019 | 0.585095 | − | 0.810965i | \(-0.301057\pi\) | ||||
0.585095 | + | 0.810965i | \(0.301057\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 180.000i | − 0.0236432i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9903.87i | 1.29086i | 0.763818 | + | 0.645432i | \(0.223323\pi\) | ||||
−0.763818 | + | 0.645432i | \(0.776677\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9353.07 | 1.20973 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6804.00 | −0.873324 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1548.00i | − 0.197186i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 103.923i | − 0.0131379i | −0.999978 | − | 0.00656895i | \(-0.997909\pi\) | ||||
0.999978 | − | 0.00656895i | \(-0.00209098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1205.51 | −0.151255 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1062.00 | 0.132254 | 0.0661269 | − | 0.997811i | \(-0.478936\pi\) | ||||
0.0661269 | + | 0.997811i | \(0.478936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 16704.0i | − 2.06473i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 841.777i | 0.103280i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8614.00 | −1.04141 | −0.520703 | − | 0.853738i | \(-0.674330\pi\) | ||||
−0.520703 | + | 0.853738i | \(0.674330\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1566.00i | 0.187944i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1122.37i | − 0.133724i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11971.9 | −1.41609 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2028.00 | −0.238157 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10440.0i | 1.21725i | 0.793458 | + | 0.608625i | \(0.208278\pi\) | ||||
−0.793458 | + | 0.608625i | \(0.791722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 900.666i | − 0.104266i | −0.998640 | − | 0.0521328i | \(-0.983398\pi\) | ||||
0.998640 | − | 0.0521328i | \(-0.0166019\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3554.17 | −0.408533 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1530.00 | −0.174626 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1992.00i | 0.225760i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −394.908 | −0.0441346 | −0.0220673 | − | 0.999756i | \(-0.507025\pi\) | ||||
−0.0220673 | + | 0.999756i | \(0.507025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12958.0 | 1.43816 | 0.719078 | − | 0.694929i | \(-0.244564\pi\) | ||||
0.719078 | + | 0.694929i | \(0.244564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 8100.00i | − 0.892794i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12055.1i | 1.31962i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11441.9 | −1.24395 | −0.621974 | − | 0.783038i | \(-0.713669\pi\) | ||||
−0.621974 | + | 0.783038i | \(0.713669\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2979.00 | 0.321672 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1800.00i | − 0.193049i | −0.995331 | − | 0.0965244i | \(-0.969227\pi\) | ||||
0.995331 | − | 0.0965244i | \(-0.0307726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9540.14i | 1.01628i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4395.94 | −0.465148 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13626.0 | −1.43218 | −0.716092 | − | 0.698006i | \(-0.754071\pi\) | ||||
−0.716092 | + | 0.698006i | \(0.754071\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 7160.30i | − 0.742649i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1995.32 | 0.205587 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12602.0 | 1.28993 | 0.644964 | − | 0.764213i | \(-0.276873\pi\) | ||||
0.644964 | + | 0.764213i | \(0.276873\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2430.00i | 0.247108i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1839.44i | − 0.185838i | −0.995674 | − | 0.0929188i | \(-0.970380\pi\) | ||||
0.995674 | − | 0.0929188i | \(-0.0296197\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11012.4 | 1.10538 | 0.552688 | − | 0.833389i | \(-0.313602\pi\) | ||||
0.552688 | + | 0.833389i | \(0.313602\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9396.00 | 0.937052 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9144.00i | 0.906068i | 0.891493 | + | 0.453034i | \(0.149658\pi\) | ||||
−0.891493 | + | 0.453034i | \(0.850342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 401.836i | − 0.0395630i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6048.32 | −0.591703 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1972.00i | − 0.190488i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4395.94i | − 0.421963i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6173.03 | −0.588837 | −0.294418 | − | 0.955677i | \(-0.595126\pi\) | ||||
−0.294418 | + | 0.955677i | \(0.595126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1920.00 | −0.182005 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1080.00i | 0.101743i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1974.54i | 0.184864i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3204.29 | −0.298153 | −0.149076 | − | 0.988826i | \(-0.547630\pi\) | ||||
−0.149076 | + | 0.988826i | \(0.547630\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1164.00 | −0.107644 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 396.000i | 0.0363976i | 0.999834 | + | 0.0181988i | \(0.00579318\pi\) | ||||
−0.999834 | + | 0.0181988i | \(0.994207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 23382.7i | − 2.13611i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3816.00 | −0.344408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 12436.0i | − 1.11565i | −0.829957 | − | 0.557827i | \(-0.811635\pi\) | ||||
0.829957 | − | 0.557827i | \(-0.188365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 6609.51i | − 0.589403i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16482.2 | 1.46104 | 0.730522 | − | 0.682890i | \(-0.239277\pi\) | ||||
0.730522 | + | 0.682890i | \(0.239277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 108.000 | 0.00951671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2625.00i | − 0.229942i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9155.62i | 0.797280i | 0.917107 | + | 0.398640i | \(0.130518\pi\) | ||||
−0.917107 | + | 0.398640i | \(0.869482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3831.30 | −0.331676 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3132.00 | −0.269554 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8244.00i | 0.705386i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −592.361 | −0.0500998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7650.00 | 0.643287 | 0.321644 | − | 0.946861i | \(-0.395765\pi\) | ||||
0.321644 | + | 0.946861i | \(0.395765\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18332.0i | 1.53270i | 0.642423 | + | 0.766350i | \(0.277929\pi\) | ||||
−0.642423 | + | 0.766350i | \(0.722071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 176.669i | − 0.0146866i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27123.9 | 2.24200 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1367.00 | −0.112353 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2916.00i | − 0.238312i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2992.98i | − 0.243228i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2618.86 | 0.211632 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8532.00 | 0.685629 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 16863.2i | − 1.34012i | −0.742305 | − | 0.670062i | \(-0.766267\pi\) | ||||
0.742305 | − | 0.670062i | \(-0.233733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 290.985 | 0.0229969 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4752.00 | 0.373492 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1684.00i | 0.131632i | 0.997832 | + | 0.0658159i | \(0.0209650\pi\) | ||||
−0.997832 | + | 0.0658159i | \(0.979035\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5175.37i | 0.402330i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30137.7 | 2.33014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 516.000 | 0.0396791 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1080.00i | − 0.0826008i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2275.91i | 0.173130i | 0.996246 | + | 0.0865652i | \(0.0275891\pi\) | ||||
−0.996246 | + | 0.0865652i | \(0.972411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1108.51 | −0.0838731 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7992.00i | − 0.598264i | −0.954212 | − | 0.299132i | \(-0.903303\pi\) | ||||
0.954212 | − | 0.299132i | \(-0.0966971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 23008.6i | − 1.71323i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −280.592 | −0.0207827 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5526.00 | −0.407139 | −0.203569 | − | 0.979061i | \(-0.565254\pi\) | ||||
−0.203569 | + | 0.979061i | \(0.565254\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13420.0i | 0.983554i | 0.870721 | + | 0.491777i | \(0.163653\pi\) | ||||
−0.870721 | + | 0.491777i | \(0.836347\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9602.49i | − 0.700087i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1766.69 | −0.128132 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10178.0 | −0.734343 | −0.367171 | − | 0.930153i | \(-0.619674\pi\) | ||||
−0.367171 | + | 0.930153i | \(0.619674\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4026.00i | − 0.288972i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 3990.65i | − 0.284957i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5184.00 | 0.366380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18684.0i | 1.31375i | 0.754000 | + | 0.656875i | \(0.228122\pi\) | ||||
−0.754000 | + | 0.656875i | \(0.771878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34959.7i | 2.44565i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2899.45 | 0.201806 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5094.00 | −0.352758 | −0.176379 | − | 0.984322i | \(-0.556438\pi\) | ||||
−0.176379 | + | 0.984322i | \(0.556438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3240.00i | 0.223239i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5352.04i | − 0.366908i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19433.6 | −1.32560 | −0.662801 | − | 0.748795i | \(-0.730633\pi\) | ||||
−0.662801 | + | 0.748795i | \(0.730633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27722.0 | 1.88154 | 0.940769 | − | 0.339049i | \(-0.110105\pi\) | ||||
0.940769 | + | 0.339049i | \(0.110105\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1044.00i | − 0.0705057i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13832.2i | 0.929516i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26684.0 | 1.78430 | 0.892149 | − | 0.451741i | \(-0.149197\pi\) | ||||
0.892149 | + | 0.451741i | \(0.149197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2700.00 | 0.179654 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21888.0i | 1.44925i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 16911.7i | − 1.11429i | −0.830416 | − | 0.557144i | \(-0.811897\pi\) | ||||
0.830416 | − | 0.557144i | \(-0.188103\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1683.55 | 0.110386 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17694.0 | 1.15451 | 0.577256 | − | 0.816563i | \(-0.304124\pi\) | ||||
0.577256 | + | 0.816563i | \(0.304124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 13652.0i | − 0.886462i | −0.896407 | − | 0.443231i | \(-0.853832\pi\) | ||||
0.896407 | − | 0.443231i | \(-0.146168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2805.92i | 0.181317i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3180.05 | −0.204504 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13211.0 | −0.845504 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 3117.69i | − 0.197632i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9162.55 | −0.578059 | −0.289030 | − | 0.957320i | \(-0.593333\pi\) | ||||
−0.289030 | + | 0.957320i | \(0.593333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8292.00 | 0.520659 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 7236.00i | − 0.452208i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 18345.9i | − 1.14112i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9914.26 | −0.613775 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5202.00 | −0.320541 | −0.160270 | − | 0.987073i | \(-0.551237\pi\) | ||||
−0.160270 | + | 0.987073i | \(0.551237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15892.0i | 0.974680i | 0.873212 | + | 0.487340i | \(0.162033\pi\) | ||||
−0.873212 | + | 0.487340i | \(0.837967\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 623.538i | − 0.0380648i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 478.046 | 0.0290478 | 0.0145239 | − | 0.999895i | \(-0.495377\pi\) | ||||
0.0145239 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3132.00i | 0.188560i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 24660.9i | − 1.47788i | −0.673770 | − | 0.738941i | \(-0.735326\pi\) | ||||
0.673770 | − | 0.738941i | \(-0.264674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23569.7 | −1.40602 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9954.00 | −0.591085 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 28260.0i | − 1.67049i | −0.549878 | − | 0.835245i | \(-0.685326\pi\) | ||||
0.549878 | − | 0.835245i | \(-0.314674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25863.0i | 1.52187i | 0.648830 | + | 0.760933i | \(0.275258\pi\) | ||||
−0.648830 | + | 0.760933i | \(0.724742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14964.9 | 0.876605 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4176.00 | −0.243516 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 27000.0i | − 1.56738i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12876.1i | 0.744122i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 190.000 | 0.0108826 | 0.00544128 | − | 0.999985i | \(-0.498268\pi\) | ||||
0.00544128 | + | 0.999985i | \(0.498268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 459.000i | − 0.0261732i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4998.70i | 0.283775i | 0.989883 | + | 0.141887i | \(0.0453171\pi\) | ||||
−0.989883 | + | 0.141887i | \(0.954683\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −658.179 | −0.0371997 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17064.0 | −0.960197 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 8064.00i | − 0.451772i | −0.974154 | − | 0.225886i | \(-0.927472\pi\) | ||||
0.974154 | − | 0.225886i | \(-0.0725277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5424.78i | 0.302584i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16710.8 | −0.928032 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27072.0 | −1.49690 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 19244.0i | − 1.05944i | −0.848171 | − | 0.529722i | \(-0.822296\pi\) | ||||
0.848171 | − | 0.529722i | \(-0.177704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7025.20 | −0.383426 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4860.00 | 0.264111 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8154.00i | 0.441220i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6204.21i | 0.334279i | 0.985933 | + | 0.167140i | \(0.0534530\pi\) | ||||
−0.985933 | + | 0.167140i | \(0.946547\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4018.36 | 0.215584 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12312.0 | −0.657726 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.0000i | 0.00191502i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15020.3i | 0.795629i | 0.917466 | + | 0.397814i | \(0.130231\pi\) | ||||
−0.917466 | + | 0.397814i | \(0.869769\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1340.61 | 0.0707127 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31320.0 | 1.64508 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 10724.9i | − 0.558615i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30740.4 | −1.59447 | −0.797236 | − | 0.603668i | \(-0.793705\pi\) | ||||
−0.797236 | + | 0.603668i | \(0.793705\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2748.00 | −0.141943 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13470.0i | 0.692883i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4416.73i | 0.226253i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12127.8 | −0.618701 | −0.309351 | − | 0.950948i | \(-0.600112\pi\) | ||||
−0.309351 | + | 0.950948i | \(0.600112\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1800.00i | − 0.0910744i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12387.6i | 0.624212i | 0.950047 | + | 0.312106i | \(0.101034\pi\) | ||||
−0.950047 | + | 0.312106i | \(0.898966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10319.6 | 0.517881 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11180.0i | 0.556513i | 0.960507 | + | 0.278256i | \(0.0897565\pi\) | ||||
−0.960507 | + | 0.278256i | \(0.910244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19288.1i | 0.956230i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35500.1 | −1.75286 | −0.876429 | − | 0.481532i | \(-0.840081\pi\) | ||||
−0.876429 | + | 0.481532i | \(0.840081\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15228.0 | −0.748873 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 10368.0i | − 0.507825i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 872.954i | 0.0425862i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37970.0 | 1.84493 | 0.922467 | − | 0.386076i | \(-0.126170\pi\) | ||||
0.922467 | + | 0.386076i | \(0.126170\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13824.0 | 0.669023 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 24804.0i | − 1.19564i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39047.4i | 1.87477i | 0.348296 | + | 0.937385i | \(0.386760\pi\) | ||||
−0.348296 | + | 0.937385i | \(0.613240\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12222.0 | −0.582191 | −0.291095 | − | 0.956694i | \(-0.594020\pi\) | ||||
−0.291095 | + | 0.956694i | \(0.594020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1584.00i | 0.0751568i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8417.77i | 0.397837i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17957.9 | −0.845401 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34030.0 | −1.59578 | −0.797889 | − | 0.602804i | \(-0.794050\pi\) | ||||
−0.797889 | + | 0.602804i | \(0.794050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13878.0i | 0.648254i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 4873.99i | − 0.226786i | −0.993550 | − | 0.113393i | \(-0.963828\pi\) | ||||
0.993550 | − | 0.113393i | \(-0.0361718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5123.41 | −0.237469 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 360.000 | 0.0166215 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6264.00i | 0.288102i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7014.81 | 0.320164 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20952.0 | −0.952623 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30988.0i | 1.40356i | 0.712393 | + | 0.701781i | \(0.247611\pi\) | ||||
−0.712393 | + | 0.701781i | \(0.752389\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5985.97i | 0.270096i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7669.52 | 0.344749 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31872.0 | 1.42725 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 15228.0i | − 0.679348i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 7160.30i | − 0.318232i | −0.987260 | − | 0.159116i | \(-0.949136\pi\) | ||||
0.987260 | − | 0.159116i | \(-0.0508644\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35541.7 | −1.57369 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8262.00 | −0.364449 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3741.23i | 0.163803i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9446.61 | 0.412065 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37530.0 | 1.63101 | 0.815503 | − | 0.578752i | \(-0.196460\pi\) | ||||
0.815503 | + | 0.578752i | \(0.196460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 10852.0i | − 0.469871i | −0.972011 | − | 0.234935i | \(-0.924512\pi\) | ||||
0.972011 | − | 0.234935i | \(-0.0754879\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16035.3i | 0.691739i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4032.21 | −0.173303 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2320.00 | 0.0993470 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1728.00i | 0.0737255i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 31353.6i | − 1.33282i | −0.745584 | − | 0.666411i | \(-0.767829\pi\) | ||||
0.745584 | − | 0.666411i | \(-0.232171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32947.1 | 1.39546 | 0.697729 | − | 0.716361i | \(-0.254194\pi\) | ||||
0.697729 | + | 0.716361i | \(0.254194\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 10044.0i | − 0.422327i | −0.977451 | − | 0.211163i | \(-0.932275\pi\) | ||||
0.977451 | − | 0.211163i | \(-0.0677252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9796.48i | 0.410429i | 0.978717 | + | 0.205215i | \(0.0657892\pi\) | ||||
−0.978717 | + | 0.205215i | \(0.934211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19579.1 | 0.817318 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29790.0 | 1.23909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 22896.0i | − 0.948921i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8137.17i | 0.336036i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21054.8 | −0.866380 | −0.433190 | − | 0.901303i | \(-0.642612\pi\) | ||||
−0.433190 | + | 0.901303i | \(0.642612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43111.0 | −1.76764 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 3510.00i | − 0.143405i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 9093.27i | − 0.370199i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4610.72 | −0.187044 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17220.0 | −0.696100 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3600.00i | − 0.145013i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 40703.2i | − 1.63382i | −0.576763 | − | 0.816911i | \(-0.695684\pi\) | ||||
0.576763 | − | 0.816911i | \(-0.304316\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10849.6 | −0.433973 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18342.0 | −0.731098 | −0.365549 | − | 0.930792i | \(-0.619119\pi\) | ||||
−0.365549 | + | 0.930792i | \(0.619119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26324.0i | 1.04559i | 0.852458 | + | 0.522796i | \(0.175111\pi\) | ||||
−0.852458 | + | 0.522796i | \(0.824889\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 561.184i | 0.0222127i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12761.8 | 0.503378 | 0.251689 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251689 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2052.00 | −0.0806591 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9561.00i | 0.374520i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6429.37 | −0.250116 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1710.00 | −0.0662941 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5112.00i | − 0.197505i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2459.51i | − 0.0946999i | −0.998878 | − | 0.0473500i | \(-0.984922\pi\) | ||||
0.998878 | − | 0.0473500i | \(-0.0150776\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23975.0 | 0.919975 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37314.0 | 1.42695 | 0.713474 | − | 0.700682i | \(-0.247121\pi\) | ||||
0.713474 | + | 0.700682i | \(0.247121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18244.0i | 0.695311i | 0.937622 | + | 0.347655i | \(0.113022\pi\) | ||||
−0.937622 | + | 0.347655i | \(0.886978\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 10101.3i | − 0.383675i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17957.9 | 0.679783 | 0.339891 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339891 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2412.00 | 0.0909965 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 45809.3i | − 1.71663i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29555.7 | 1.10384 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17280.0 | 0.643213 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 78300.0i | − 2.90484i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 43959.4i | − 1.62542i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 207.846 | 0.00765967 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1008.00 | 0.0370244 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16388.0i | 0.599950i | 0.953947 | + | 0.299975i | \(0.0969783\pi\) | ||||
−0.953947 | + | 0.299975i | \(0.903022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 93.5307i | 0.00341278i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25107.8 | −0.913127 | −0.456564 | − | 0.889691i | \(-0.650920\pi\) | ||||
−0.456564 | + | 0.889691i | \(0.650920\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17928.0i | 0.647739i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 7856.58i | − 0.282930i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27155.1 | 0.974716 | 0.487358 | − | 0.873202i | \(-0.337961\pi\) | ||||
0.487358 | + | 0.873202i | \(0.337961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16356.0 | 0.585178 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61056.0i | 2.17734i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 588.897i | 0.0209328i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7139.51 | −0.252958 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48006.0 | 1.69540 | 0.847700 | − | 0.530477i | \(-0.177987\pi\) | ||||
0.847700 | + | 0.530477i | \(0.177987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38396.0i | 1.35164i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 6609.51i | − 0.231924i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7894.00 | 0.275225 | 0.137612 | − | 0.990486i | \(-0.456057\pi\) | ||||
0.137612 | + | 0.990486i | \(0.456057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 3102.00i | − 0.107806i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2670.82i | − 0.0925253i | −0.998929 | − | 0.0462627i | \(-0.985269\pi\) | ||||
0.998929 | − | 0.0462627i | \(-0.0147311\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5611.84 | 0.193793 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −972.000 | −0.0334594 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22356.0i | 0.767130i | 0.923514 | + | 0.383565i | \(0.125304\pi\) | ||||
−0.923514 | + | 0.383565i | \(0.874696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61300.7i | 2.09685i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7950.11 | 0.271083 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14958.0 | −0.508434 | −0.254217 | − | 0.967147i | \(-0.581818\pi\) | ||||
−0.254217 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 33264.0i | − 1.12712i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1808.26 | −0.0608882 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61037.0 | 2.04884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2268.00i | 0.0758933i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 13946.5i | − 0.465236i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17476.4 | 0.581182 | 0.290591 | − | 0.956847i | \(-0.406148\pi\) | ||||
0.290591 | + | 0.956847i | \(0.406148\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31320.0 | −1.03833 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48528.0i | 1.60385i | 0.597425 | + | 0.801925i | \(0.296190\pi\) | ||||
−0.597425 | + | 0.801925i | \(0.703810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2341.73i | − 0.0771557i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2826.71 | −0.0928483 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39978.0 | −1.30912 | −0.654560 | − | 0.756010i | \(-0.727146\pi\) | ||||
−0.654560 | + | 0.756010i | \(0.727146\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4115.35i | 0.133938i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17957.9 | 0.582674 | 0.291337 | − | 0.956621i | \(-0.405900\pi\) | ||||
0.291337 | + | 0.956621i | \(0.405900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10044.0 | 0.324902 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 4104.00i | − 0.132352i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2078.46i | − 0.0668263i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1666.23 | 0.0534103 | 0.0267052 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267052 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12396.0 | −0.396148 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 18540.0i | − 0.590711i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 41465.3i | − 1.31717i | −0.752506 | − | 0.658585i | \(-0.771155\pi\) | ||||
0.752506 | − | 0.658585i | \(-0.228845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 935.307 | 0.0296214 |
(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 | 192.4.d.a.97.4 | yes | 4 | |
3.2 | odd | 2 | 576.4.d.g.289.1 | 4 | |||
4.3 | odd | 2 | inner | 192.4.d.a.97.2 | yes | 4 | |
8.3 | odd | 2 | inner | 192.4.d.a.97.3 | yes | 4 | |
8.5 | even | 2 | inner | 192.4.d.a.97.1 | ✓ | 4 | |
12.11 | even | 2 | 576.4.d.g.289.2 | 4 | |||
16.3 | odd | 4 | 768.4.a.n.1.2 | 2 | |||
16.5 | even | 4 | 768.4.a.n.1.1 | 2 | |||
16.11 | odd | 4 | 768.4.a.g.1.1 | 2 | |||
16.13 | even | 4 | 768.4.a.g.1.2 | 2 | |||
24.5 | odd | 2 | 576.4.d.g.289.3 | 4 | |||
24.11 | even | 2 | 576.4.d.g.289.4 | 4 | |||
48.5 | odd | 4 | 2304.4.a.be.1.2 | 2 | |||
48.11 | even | 4 | 2304.4.a.bg.1.2 | 2 | |||
48.29 | odd | 4 | 2304.4.a.bg.1.1 | 2 | |||
48.35 | even | 4 | 2304.4.a.be.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
192.4.d.a.97.1 | ✓ | 4 | 8.5 | even | 2 | inner | |
192.4.d.a.97.2 | yes | 4 | 4.3 | odd | 2 | inner | |
192.4.d.a.97.3 | yes | 4 | 8.3 | odd | 2 | inner | |
192.4.d.a.97.4 | yes | 4 | 1.1 | even | 1 | trivial | |
576.4.d.g.289.1 | 4 | 3.2 | odd | 2 | |||
576.4.d.g.289.2 | 4 | 12.11 | even | 2 | |||
576.4.d.g.289.3 | 4 | 24.5 | odd | 2 | |||
576.4.d.g.289.4 | 4 | 24.11 | even | 2 | |||
768.4.a.g.1.1 | 2 | 16.11 | odd | 4 | |||
768.4.a.g.1.2 | 2 | 16.13 | even | 4 | |||
768.4.a.n.1.1 | 2 | 16.5 | even | 4 | |||
768.4.a.n.1.2 | 2 | 16.3 | odd | 4 | |||
2304.4.a.be.1.1 | 2 | 48.35 | even | 4 | |||
2304.4.a.be.1.2 | 2 | 48.5 | odd | 4 | |||
2304.4.a.bg.1.1 | 2 | 48.29 | odd | 4 | |||
2304.4.a.bg.1.2 | 2 | 48.11 | even | 4 |