Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(2177,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.2177");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.h (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: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.959512576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2177.4 | ||
Root | \(0.819051 - 1.52616i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.2177 |
Dual form | 2304.3.h.l.2177.3 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −5.21904 | −1.04381 | −0.521904 | − | 0.853004i | \(-0.674778\pi\) | ||||
−0.521904 | + | 0.853004i | \(0.674778\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.285714 | 0.142857 | − | 0.989743i | \(-0.454371\pi\) | ||||
0.142857 | + | 0.989743i | \(0.454371\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.78122 | −0.434656 | −0.217328 | − | 0.976099i | \(-0.569734\pi\) | ||||
−0.217328 | + | 0.976099i | \(0.569734\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.38083i | 0.106218i | 0.998589 | + | 0.0531089i | \(0.0169130\pi\) | ||||
−0.998589 | + | 0.0531089i | \(0.983087\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 14.6807i | − 0.863571i | −0.901976 | − | 0.431786i | \(-0.857884\pi\) | ||||
0.901976 | − | 0.431786i | \(-0.142116\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.7617i | 1.40851i | 0.709948 | + | 0.704254i | \(0.248719\pi\) | ||||
−0.709948 | + | 0.704254i | \(0.751281\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 18.0477i | − 0.784683i | −0.919820 | − | 0.392342i | \(-0.871665\pi\) | ||||
0.919820 | − | 0.392342i | \(-0.128335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.23834 | 0.0895335 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 25.0180 | 0.862691 | 0.431345 | − | 0.902187i | \(-0.358039\pi\) | ||||
0.431345 | + | 0.902187i | \(0.358039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −39.5233 | −1.27495 | −0.637473 | − | 0.770473i | \(-0.720020\pi\) | ||||
−0.637473 | + | 0.770473i | \(0.720020\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.4381 | −0.298231 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.0000i | 0.702703i | 0.936244 | + | 0.351351i | \(0.114278\pi\) | ||||
−0.936244 | + | 0.351351i | \(0.885722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 28.8228i | 0.702996i | 0.936189 | + | 0.351498i | \(0.114328\pi\) | ||||
−0.936189 | + | 0.351498i | \(0.885672\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.52333i | 0.221473i | 0.993850 | + | 0.110736i | \(0.0353209\pi\) | ||||
−0.993850 | + | 0.110736i | \(0.964679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 80.2731i | − 1.70794i | −0.520323 | − | 0.853969i | \(-0.674189\pi\) | ||||
0.520323 | − | 0.853969i | \(-0.325811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45.0000 | −0.918367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.79874 | −0.184882 | −0.0924409 | − | 0.995718i | \(-0.529467\pi\) | ||||
−0.0924409 | + | 0.995718i | \(0.529467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24.9533 | 0.453697 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 73.5391 | 1.24643 | 0.623213 | − | 0.782052i | \(-0.285827\pi\) | ||||
0.623213 | + | 0.782052i | \(0.285827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 67.5233i | − 1.10694i | −0.832869 | − | 0.553470i | \(-0.813303\pi\) | ||||
0.832869 | − | 0.553470i | \(-0.186697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 7.20661i | − 0.110871i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 102.762i | 1.53376i | 0.641793 | + | 0.766878i | \(0.278191\pi\) | ||||
−0.641793 | + | 0.766878i | \(0.721809\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 21.9533i | 0.309201i | 0.987977 | + | 0.154601i | \(0.0494091\pi\) | ||||
−0.987977 | + | 0.154601i | \(0.950591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 140.570 | 1.92562 | 0.962808 | − | 0.270186i | \(-0.0870853\pi\) | ||||
0.962808 | + | 0.270186i | \(0.0870853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.56244 | −0.124187 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.476674 | −0.00603385 | −0.00301692 | − | 0.999995i | \(-0.500960\pi\) | ||||
−0.00301692 | + | 0.999995i | \(0.500960\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −31.3142 | −0.377280 | −0.188640 | − | 0.982046i | \(-0.560408\pi\) | ||||
−0.188640 | + | 0.982046i | \(0.560408\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 76.6192i | 0.901402i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 13.1310i | − 0.147539i | −0.997275 | − | 0.0737694i | \(-0.976497\pi\) | ||||
0.997275 | − | 0.0737694i | \(-0.0235029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.76166i | 0.0303479i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 139.670i | − 1.47021i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −69.2383 | −0.713797 | −0.356899 | − | 0.934143i | \(-0.616166\pi\) | ||||
−0.356899 | + | 0.934143i | \(0.616166\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −78.5566 | −0.777788 | −0.388894 | − | 0.921282i | \(-0.627143\pi\) | ||||
−0.388894 | + | 0.921282i | \(0.627143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 198.570 | 1.92786 | 0.963932 | − | 0.266149i | \(-0.0857513\pi\) | ||||
0.963932 | + | 0.266149i | \(0.0857513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 177.517 | 1.65904 | 0.829518 | − | 0.558480i | \(-0.188615\pi\) | ||||
0.829518 | + | 0.558480i | \(0.188615\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 137.381i | − 1.26037i | −0.776443 | − | 0.630187i | \(-0.782978\pi\) | ||||
0.776443 | − | 0.630187i | \(-0.217022\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 72.5279i | − 0.641840i | −0.947106 | − | 0.320920i | \(-0.896008\pi\) | ||||
0.947106 | − | 0.320920i | \(-0.103992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 94.1917i | 0.819058i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 29.3614i | − 0.246735i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −98.1400 | −0.811074 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 118.794 | 0.950352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 81.0467 | 0.638163 | 0.319081 | − | 0.947727i | \(-0.396626\pi\) | ||||
0.319081 | + | 0.947727i | \(0.396626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 164.452 | 1.25536 | 0.627679 | − | 0.778473i | \(-0.284005\pi\) | ||||
0.627679 | + | 0.778473i | \(0.284005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 53.5233i | 0.402431i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 224.790i | 1.64081i | 0.571786 | + | 0.820403i | \(0.306251\pi\) | ||||
−0.571786 | + | 0.820403i | \(0.693749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 170.378i | − 1.22574i | −0.790183 | − | 0.612872i | \(-0.790014\pi\) | ||||
0.790183 | − | 0.612872i | \(-0.209986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 6.60206i | − 0.0461682i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −130.570 | −0.900483 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −59.5637 | −0.399756 | −0.199878 | − | 0.979821i | \(-0.564055\pi\) | ||||
−0.199878 | + | 0.979821i | \(0.564055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 242.570 | 1.60642 | 0.803212 | − | 0.595693i | \(-0.203123\pi\) | ||||
0.803212 | + | 0.595693i | \(0.203123\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 206.274 | 1.33080 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 161.617i | 1.02941i | 0.857369 | + | 0.514703i | \(0.172098\pi\) | ||||
−0.857369 | + | 0.514703i | \(0.827902\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 36.0954i | − 0.224195i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 80.9533i | 0.496646i | 0.968677 | + | 0.248323i | \(0.0798795\pi\) | ||||
−0.968677 | + | 0.248323i | \(0.920121\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 179.268i | − 1.07346i | −0.843754 | − | 0.536731i | \(-0.819659\pi\) | ||||
0.843754 | − | 0.536731i | \(-0.180341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 167.093 | 0.988718 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 26.4982 | 0.153169 | 0.0765844 | − | 0.997063i | \(-0.475599\pi\) | ||||
0.0765844 | + | 0.997063i | \(0.475599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.47667 | 0.0255810 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 306.679 | 1.71329 | 0.856646 | − | 0.515905i | \(-0.172544\pi\) | ||||
0.856646 | + | 0.515905i | \(0.172544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 57.3808i | 0.317021i | 0.987357 | + | 0.158511i | \(0.0506692\pi\) | ||||
−0.987357 | + | 0.158511i | \(0.949331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 135.695i | − 0.733486i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 70.1917i | 0.375357i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 216.712i | − 1.13462i | −0.823506 | − | 0.567308i | \(-0.807985\pi\) | ||||
0.823506 | − | 0.567308i | \(-0.192015\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 187.140 | 0.969637 | 0.484819 | − | 0.874615i | \(-0.338886\pi\) | ||||
0.484819 | + | 0.874615i | \(0.338886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −65.8947 | −0.334491 | −0.167245 | − | 0.985915i | \(-0.553487\pi\) | ||||
−0.167245 | + | 0.985915i | \(0.553487\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 114.953 | 0.577655 | 0.288828 | − | 0.957381i | \(-0.406735\pi\) | ||||
0.288828 | + | 0.957381i | \(0.406735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 50.0361 | 0.246483 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 150.427i | − 0.733793i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 127.953i | − 0.612217i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 103.332i | 0.489723i | 0.969558 | + | 0.244862i | \(0.0787426\pi\) | ||||
−0.969558 | + | 0.244862i | \(0.921257\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 49.7026i | − 0.231175i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −79.0467 | −0.364270 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.2716 | 0.0917267 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 241.047 | 1.08093 | 0.540463 | − | 0.841368i | \(-0.318249\pi\) | ||||
0.540463 | + | 0.841368i | \(0.318249\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.5579 | −0.0993738 | −0.0496869 | − | 0.998765i | \(-0.515822\pi\) | ||||
−0.0496869 | + | 0.998765i | \(0.515822\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 212.997i | − 0.930120i | −0.885279 | − | 0.465060i | \(-0.846033\pi\) | ||||
0.885279 | − | 0.465060i | \(-0.153967\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 63.9107i | − 0.274295i | −0.990551 | − | 0.137147i | \(-0.956207\pi\) | ||||
0.990551 | − | 0.137147i | \(-0.0437934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 418.948i | 1.78276i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 174.417i | − 0.729779i | −0.931051 | − | 0.364890i | \(-0.881107\pi\) | ||||
0.931051 | − | 0.364890i | \(-0.118893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −47.3316 | −0.196397 | −0.0981984 | − | 0.995167i | \(-0.531308\pi\) | ||||
−0.0981984 | + | 0.995167i | \(0.531308\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 234.857 | 0.958598 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.9533 | −0.149609 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 205.731 | 0.819647 | 0.409824 | − | 0.912165i | \(-0.365590\pi\) | ||||
0.409824 | + | 0.912165i | \(0.365590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 86.2901i | 0.341067i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 251.796i | 0.979751i | 0.871792 | + | 0.489875i | \(0.162958\pi\) | ||||
−0.871792 | + | 0.489875i | \(0.837042\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 52.0000i | 0.200772i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 206.607i | − 0.785578i | −0.919629 | − | 0.392789i | \(-0.871510\pi\) | ||||
0.919629 | − | 0.392789i | \(-0.128490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 51.1400 | 0.192981 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −430.963 | −1.60209 | −0.801047 | − | 0.598601i | \(-0.795723\pi\) | ||||
−0.801047 | + | 0.598601i | \(0.795723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 290.953 | 1.07363 | 0.536814 | − | 0.843700i | \(-0.319628\pi\) | ||||
0.536814 | + | 0.843700i | \(0.319628\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.7020 | −0.0389163 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 57.9508i | 0.209209i | 0.994514 | + | 0.104604i | \(0.0333576\pi\) | ||||
−0.994514 | + | 0.104604i | \(0.966642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 124.517i | − 0.443120i | −0.975147 | − | 0.221560i | \(-0.928885\pi\) | ||||
0.975147 | − | 0.221560i | \(-0.0711149\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 254.093i | 0.897856i | 0.893568 | + | 0.448928i | \(0.148194\pi\) | ||||
−0.893568 | + | 0.448928i | \(0.851806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 57.6457i | 0.200856i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 73.4767 | 0.254245 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 239.909 | 0.818802 | 0.409401 | − | 0.912355i | \(-0.365738\pi\) | ||||
0.409401 | + | 0.912355i | \(0.365738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −383.803 | −1.30103 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.9209 | 0.0833473 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.0467i | 0.0632779i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 352.407i | 1.15543i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.71501i | 0.0121010i | 0.999982 | + | 0.00605051i | \(0.00192595\pi\) | ||||
−0.999982 | + | 0.00605051i | \(0.998074\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 473.828i | − 1.52356i | −0.647835 | − | 0.761781i | \(-0.724325\pi\) | ||||
0.647835 | − | 0.761781i | \(-0.275675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −310.000 | −0.990415 | −0.495208 | − | 0.868775i | \(-0.664908\pi\) | ||||
−0.495208 | + | 0.868775i | \(0.664908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 475.342 | 1.49950 | 0.749752 | − | 0.661719i | \(-0.230173\pi\) | ||||
0.749752 | + | 0.661719i | \(0.230173\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −119.617 | −0.374974 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 392.880 | 1.21635 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.09077i | 0.00951005i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 160.546i | − 0.487982i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 390.762i | 1.18055i | 0.807203 | + | 0.590274i | \(0.200980\pi\) | ||||
−0.807203 | + | 0.590274i | \(0.799020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 536.317i | − 1.60095i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 316.000 | 0.937685 | 0.468843 | − | 0.883282i | \(-0.344671\pi\) | ||||
0.468843 | + | 0.883282i | \(0.344671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 188.970 | 0.554163 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −188.000 | −0.548105 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −485.475 | −1.39906 | −0.699531 | − | 0.714602i | \(-0.746608\pi\) | ||||
−0.699531 | + | 0.714602i | \(0.746608\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 561.233i | 1.60812i | 0.594549 | + | 0.804059i | \(0.297330\pi\) | ||||
−0.594549 | + | 0.804059i | \(0.702670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 114.280i | − 0.323740i | −0.986812 | − | 0.161870i | \(-0.948247\pi\) | ||||
0.986812 | − | 0.161870i | \(-0.0517525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 114.575i | − 0.322747i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 217.789i | − 0.606654i | −0.952886 | − | 0.303327i | \(-0.901903\pi\) | ||||
0.952886 | − | 0.303327i | \(-0.0980975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −355.187 | −0.983896 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −733.640 | −2.00997 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 143.907 | 0.392116 | 0.196058 | − | 0.980592i | \(-0.437186\pi\) | ||||
0.196058 | + | 0.980592i | \(0.437186\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.5975 | −0.0528234 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 400.663i | − 1.07416i | −0.843530 | − | 0.537082i | \(-0.819527\pi\) | ||||
0.843530 | − | 0.537082i | \(-0.180473\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.5457i | 0.0916331i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 156.668i | 0.413373i | 0.978407 | + | 0.206686i | \(0.0662680\pi\) | ||||
−0.978407 | + | 0.206686i | \(0.933732\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 483.390i | 1.26211i | 0.775736 | + | 0.631057i | \(0.217379\pi\) | ||||
−0.775736 | + | 0.631057i | \(0.782621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 49.9067 | 0.129628 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −726.933 | −1.86872 | −0.934362 | − | 0.356326i | \(-0.884029\pi\) | ||||
−0.934362 | + | 0.356326i | \(0.884029\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −264.953 | −0.677630 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.48778 | 0.00629817 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 94.1866i | 0.237246i | 0.992939 | + | 0.118623i | \(0.0378480\pi\) | ||||
−0.992939 | + | 0.118623i | \(0.962152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.42898i | 0.00605731i | 0.999995 | + | 0.00302865i | \(0.000964052\pi\) | ||||
−0.999995 | + | 0.00302865i | \(0.999036\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 54.5751i | − 0.135422i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 124.312i | − 0.305434i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 66.7617 | 0.163231 | 0.0816157 | − | 0.996664i | \(-0.473992\pi\) | ||||
0.0816157 | + | 0.996664i | \(0.473992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 147.078 | 0.356122 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 163.430 | 0.393807 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 241.021 | 0.575229 | 0.287614 | − | 0.957746i | \(-0.407138\pi\) | ||||
0.287614 | + | 0.957746i | \(0.407138\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 698.806i | − 1.65987i | −0.557859 | − | 0.829936i | \(-0.688377\pi\) | ||||
0.557859 | − | 0.829936i | \(-0.311623\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 32.8604i | − 0.0773185i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 135.047i | − 0.316269i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 783.599i | 1.81810i | 0.416692 | + | 0.909048i | \(0.363189\pi\) | ||||
−0.416692 | + | 0.909048i | \(0.636811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 317.233 | 0.732640 | 0.366320 | − | 0.930489i | \(-0.380617\pi\) | ||||
0.366320 | + | 0.930489i | \(0.380617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 482.987 | 1.10523 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 219.140 | 0.499180 | 0.249590 | − | 0.968352i | \(-0.419704\pi\) | ||||
0.249590 | + | 0.968352i | \(0.419704\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −229.707 | −0.518526 | −0.259263 | − | 0.965807i | \(-0.583480\pi\) | ||||
−0.259263 | + | 0.965807i | \(0.583480\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 68.5309i | 0.154002i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 107.074i | − 0.238471i | −0.992866 | − | 0.119236i | \(-0.961956\pi\) | ||||
0.992866 | − | 0.119236i | \(-0.0380444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 137.808i | − 0.305562i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 14.4132i | − 0.0316774i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −605.042 | −1.32394 | −0.661971 | − | 0.749529i | \(-0.730280\pi\) | ||||
−0.661971 | + | 0.749529i | \(0.730280\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −305.435 | −0.662550 | −0.331275 | − | 0.943534i | \(-0.607479\pi\) | ||||
−0.331275 | + | 0.943534i | \(0.607479\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 59.1400 | 0.127732 | 0.0638660 | − | 0.997958i | \(-0.479657\pi\) | ||||
0.0638660 | + | 0.997958i | \(0.479657\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 565.477 | 1.21087 | 0.605435 | − | 0.795894i | \(-0.292999\pi\) | ||||
0.605435 | + | 0.795894i | \(0.292999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 205.523i | 0.438216i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 45.5331i | − 0.0962645i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 59.9016i | 0.126109i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 249.576i | − 0.521035i | −0.965469 | − | 0.260517i | \(-0.916107\pi\) | ||||
0.965469 | − | 0.260517i | \(-0.0838932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.9016 | −0.0746395 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 361.357 | 0.745067 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 435.897 | 0.895065 | 0.447532 | − | 0.894268i | \(-0.352303\pi\) | ||||
0.447532 | + | 0.894268i | \(0.352303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −335.506 | −0.683311 | −0.341655 | − | 0.939825i | \(-0.610988\pi\) | ||||
−0.341655 | + | 0.939825i | \(0.610988\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 367.282i | − 0.744995i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 43.9066i | 0.0883433i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 712.373i | − 1.42760i | −0.700349 | − | 0.713801i | \(-0.746972\pi\) | ||||
0.700349 | − | 0.713801i | \(-0.253028\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 527.832i | 1.04937i | 0.851297 | + | 0.524683i | \(0.175816\pi\) | ||||
−0.851297 | + | 0.524683i | \(0.824184\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 409.990 | 0.811861 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 736.294 | 1.44655 | 0.723275 | − | 0.690560i | \(-0.242636\pi\) | ||||
0.723275 | + | 0.690560i | \(0.242636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 281.140 | 0.550176 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1036.34 | −2.01232 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 383.803i | 0.742366i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 372.001i | − 0.714013i | −0.934102 | − | 0.357006i | \(-0.883797\pi\) | ||||
0.934102 | − | 0.357006i | \(-0.116203\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 251.135i | − 0.480181i | −0.970750 | − | 0.240091i | \(-0.922823\pi\) | ||||
0.970750 | − | 0.240091i | \(-0.0771772\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 580.231i | 1.10101i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 203.280 | 0.384272 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −39.7995 | −0.0746707 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −926.467 | −1.73171 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 215.155 | 0.399174 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 966.992i | 1.78742i | 0.448648 | + | 0.893708i | \(0.351906\pi\) | ||||
−0.448648 | + | 0.893708i | \(0.648094\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 716.996i | 1.31559i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 293.710i | − 0.536947i | −0.963287 | − | 0.268473i | \(-0.913481\pi\) | ||||
0.963287 | − | 0.268473i | \(-0.0865192\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 669.524i | 1.21511i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.953348 | −0.00172396 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −566.193 | −1.01650 | −0.508252 | − | 0.861208i | \(-0.669708\pi\) | ||||
−0.508252 | + | 0.861208i | \(0.669708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.1501 | −0.0235243 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −150.108 | −0.266622 | −0.133311 | − | 0.991074i | \(-0.542561\pi\) | ||||
−0.133311 | + | 0.991074i | \(0.542561\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 378.526i | 0.669957i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 899.707i | 1.58121i | 0.612328 | + | 0.790604i | \(0.290233\pi\) | ||||
−0.612328 | + | 0.790604i | \(0.709767\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 680.570i | − 1.19189i | −0.803025 | − | 0.595946i | \(-0.796777\pi\) | ||||
0.803025 | − | 0.595946i | \(-0.203223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 40.3969i | − 0.0702554i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −249.233 | −0.431947 | −0.215973 | − | 0.976399i | \(-0.569292\pi\) | ||||
−0.215973 | + | 0.976399i | \(0.569292\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −62.6284 | −0.107794 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.8499 | 0.0803600 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 602.587 | 1.02655 | 0.513277 | − | 0.858223i | \(-0.328431\pi\) | ||||
0.513277 | + | 0.858223i | \(0.328431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1057.71i | − 1.79577i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 154.142i | 0.259936i | 0.991518 | + | 0.129968i | \(0.0414875\pi\) | ||||
−0.991518 | + | 0.129968i | \(0.958513\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 153.238i | 0.257543i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 309.244i | 0.516267i | 0.966109 | + | 0.258133i | \(0.0831074\pi\) | ||||
−0.966109 | + | 0.258133i | \(0.916893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 811.327 | 1.34996 | 0.674981 | − | 0.737836i | \(-0.264152\pi\) | ||||
0.674981 | + | 0.737836i | \(0.264152\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 512.196 | 0.846605 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −202.197 | −0.333108 | −0.166554 | − | 0.986032i | \(-0.553264\pi\) | ||||
−0.166554 | + | 0.986032i | \(0.553264\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 110.844 | 0.181413 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 694.560i | − 1.13305i | −0.824044 | − | 0.566525i | \(-0.808287\pi\) | ||||
0.824044 | − | 0.566525i | \(-0.191713\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 896.267i | − 1.45262i | −0.687367 | − | 0.726311i | \(-0.741233\pi\) | ||||
0.687367 | − | 0.726311i | \(-0.258767\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 672.570i | − 1.08654i | −0.839557 | − | 0.543271i | \(-0.817185\pi\) | ||||
0.839557 | − | 0.543271i | \(-0.182815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 26.2619i | − 0.0421540i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −675.948 | −1.08152 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 381.699 | 0.606834 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 218.953 | 0.346994 | 0.173497 | − | 0.984834i | \(-0.444493\pi\) | ||||
0.173497 | + | 0.984834i | \(0.444493\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −422.985 | −0.666119 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 62.1374i | − 0.0975470i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1193.18i | − 1.86144i | −0.365734 | − | 0.930720i | \(-0.619182\pi\) | ||||
0.365734 | − | 0.930720i | \(-0.380818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1009.33i | − 1.56971i | −0.619676 | − | 0.784857i | \(-0.712736\pi\) | ||||
0.619676 | − | 0.784857i | \(-0.287264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 637.605i | 0.985479i | 0.870177 | + | 0.492740i | \(0.164005\pi\) | ||||
−0.870177 | + | 0.492740i | \(0.835995\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −351.606 | −0.541767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −939.073 | −1.43809 | −0.719045 | − | 0.694964i | \(-0.755420\pi\) | ||||
−0.719045 | + | 0.694964i | \(0.755420\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −858.280 | −1.31035 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1224.84 | −1.85864 | −0.929318 | − | 0.369281i | \(-0.879604\pi\) | ||||
−0.929318 | + | 0.369281i | \(0.879604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1034.18i | 1.56456i | 0.622925 | + | 0.782282i | \(0.285944\pi\) | ||||
−0.622925 | + | 0.782282i | \(0.714056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 279.340i | − 0.420060i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 451.518i | − 0.676939i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 322.844i | 0.481138i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.9533 | −0.0281625 | −0.0140812 | − | 0.999901i | \(-0.504482\pi\) | ||||
−0.0140812 | + | 0.999901i | \(0.504482\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1024.66 | −1.51353 | −0.756767 | − | 0.653685i | \(-0.773222\pi\) | ||||
−0.756767 | + | 0.653685i | \(0.773222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −138.477 | −0.203942 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −965.904 | −1.41421 | −0.707104 | − | 0.707109i | \(-0.749999\pi\) | ||||
−0.707104 | + | 0.707109i | \(0.749999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1173.19i | − 1.71268i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 13.5304i | − 0.0196377i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 419.233i | 0.606705i | 0.952878 | + | 0.303353i | \(0.0981060\pi\) | ||||
−0.952878 | + | 0.303353i | \(0.901894\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 889.210i | 1.27944i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 423.140 | 0.607087 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1085.27 | 1.54817 | 0.774086 | − | 0.633081i | \(-0.218210\pi\) | ||||
0.774086 | + | 0.633081i | \(0.218210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −695.803 | −0.989763 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −157.113 | −0.222225 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 369.469i | 0.521113i | 0.965459 | + | 0.260556i | \(0.0839060\pi\) | ||||
−0.965459 | + | 0.260556i | \(0.916094\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 713.306i | 1.00043i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.4564i | 0.0481907i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 468.567i | 0.651692i | 0.945423 | + | 0.325846i | \(0.105649\pi\) | ||||
−0.945423 | + | 0.325846i | \(0.894351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 397.140 | 0.550818 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 55.9988 | 0.0772397 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 502.570 | 0.691293 | 0.345646 | − | 0.938365i | \(-0.387660\pi\) | ||||
0.345646 | + | 0.938365i | \(0.387660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 139.809 | 0.191257 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1189.37i | 1.62261i | 0.584625 | + | 0.811303i | \(0.301241\pi\) | ||||
−0.584625 | + | 0.811303i | \(0.698759\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 491.326i | − 0.666657i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1431.04i | 1.93645i | 0.250081 | + | 0.968225i | \(0.419543\pi\) | ||||
−0.250081 | + | 0.968225i | \(0.580457\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 203.508i | − 0.273900i | −0.990578 | − | 0.136950i | \(-0.956270\pi\) | ||||
0.990578 | − | 0.136950i | \(-0.0437300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 310.865 | 0.417269 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 355.034 | 0.474010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −930.570 | −1.23911 | −0.619554 | − | 0.784954i | \(-0.712686\pi\) | ||||
−0.619554 | + | 0.784954i | \(0.712686\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1265.98 | −1.67680 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 306.894i | − 0.405408i | −0.979240 | − | 0.202704i | \(-0.935027\pi\) | ||||
0.979240 | − | 0.202704i | \(-0.0649730\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 939.701i | 1.23482i | 0.786640 | + | 0.617412i | \(0.211819\pi\) | ||||
−0.786640 | + | 0.617412i | \(0.788181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 274.762i | − 0.360107i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 101.545i | 0.132393i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1238.19 | −1.61013 | −0.805063 | − | 0.593190i | \(-0.797868\pi\) | ||||
−0.805063 | + | 0.593190i | \(0.797868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −697.502 | −0.902332 | −0.451166 | − | 0.892440i | \(-0.648992\pi\) | ||||
−0.451166 | + | 0.892440i | \(0.648992\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −88.4665 | −0.114150 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −771.347 | −0.990176 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 104.964i | − 0.134396i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 843.483i | − 1.07450i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 206.575i | − 0.262484i | −0.991350 | − | 0.131242i | \(-0.958103\pi\) | ||||
0.991350 | − | 0.131242i | \(-0.0418965\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 145.056i | − 0.183383i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 93.2383 | 0.117577 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 566.596 | 0.710911 | 0.355455 | − | 0.934693i | \(-0.384326\pi\) | ||||
0.355455 | + | 0.934693i | \(0.384326\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1178.47 | −1.47493 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −672.096 | −0.836981 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 188.383i | 0.234017i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 806.091i | 0.996404i | 0.867061 | + | 0.498202i | \(0.166006\pi\) | ||||
−0.867061 | + | 0.498202i | \(0.833994\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 420.472i | − 0.518461i | −0.965816 | − | 0.259230i | \(-0.916531\pi\) | ||||
0.965816 | − | 0.259230i | \(-0.0834689\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 422.498i | − 0.518403i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −254.860 | −0.311946 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −386.042 | −0.470209 | −0.235105 | − | 0.971970i | \(-0.575543\pi\) | ||||
−0.235105 | + | 0.971970i | \(0.575543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −998.570 | −1.21333 | −0.606665 | − | 0.794958i | \(-0.707493\pi\) | ||||
−0.606665 | + | 0.794958i | \(0.707493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −684.604 | −0.827816 | −0.413908 | − | 0.910319i | \(-0.635837\pi\) | ||||
−0.413908 | + | 0.910319i | \(0.635837\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 533.567i | − 0.643628i | −0.946803 | − | 0.321814i | \(-0.895707\pi\) | ||||
0.946803 | − | 0.321814i | \(-0.104293\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 660.632i | 0.793076i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 935.606i | 1.12049i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1441.02i | 1.71754i | 0.512360 | + | 0.858771i | \(0.328771\pi\) | ||||
−0.512360 | + | 0.858771i | \(0.671229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −215.098 | −0.255765 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −872.066 | −1.03203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −196.280 | −0.231735 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 469.241 | 0.551399 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 670.383i | 0.785913i | 0.919557 | + | 0.392956i | \(0.128548\pi\) | ||||
−0.919557 | + | 0.392956i | \(0.871452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 223.046i | 0.260264i | 0.991497 | + | 0.130132i | \(0.0415401\pi\) | ||||
−0.991497 | + | 0.130132i | \(0.958460\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1174.48i | − 1.36726i | −0.729829 | − | 0.683630i | \(-0.760400\pi\) | ||||
0.729829 | − | 0.683630i | \(-0.239600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 780.785i | 0.904734i | 0.891832 | + | 0.452367i | \(0.149420\pi\) | ||||
−0.891832 | + | 0.452367i | \(0.850580\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −138.295 | −0.159879 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.27908 | 0.00262265 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −141.897 | −0.162912 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 237.588 | 0.271529 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1096.28i | − 1.25003i | −0.780611 | − | 0.625017i | \(-0.785092\pi\) | ||||
0.780611 | − | 0.625017i | \(-0.214908\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1164.43i | 1.32171i | 0.750514 | + | 0.660854i | \(0.229806\pi\) | ||||
−0.750514 | + | 0.660854i | \(0.770194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8032i | 0.0133672i | 0.999978 | + | 0.00668360i | \(0.00212747\pi\) | ||||
−0.999978 | + | 0.00668360i | \(0.997873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 295.505i | − 0.333151i | −0.986029 | − | 0.166575i | \(-0.946729\pi\) | ||||
0.986029 | − | 0.166575i | \(-0.0532709\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 162.093 | 0.182332 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2148.24 | 2.40565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1600.57 | −1.78835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −988.796 | −1.09988 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 143.852i | 0.159659i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 299.473i | − 0.330909i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 423.617i | − 0.467053i | −0.972350 | − | 0.233526i | \(-0.924974\pi\) | ||||
0.972350 | − | 0.233526i | \(-0.0750265\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1008.39i | − 1.10691i | −0.832880 | − | 0.553454i | \(-0.813309\pi\) | ||||
0.832880 | − | 0.553454i | \(-0.186691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 149.720 | 0.163987 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 328.904 | 0.358674 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1067.51 | 1.16160 | 0.580802 | − | 0.814045i | \(-0.302739\pi\) | ||||
0.580802 | + | 0.814045i | \(0.302739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.3138 | −0.0328427 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 58.1968i | 0.0629154i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 720.842i | − 0.775934i | −0.921673 | − | 0.387967i | \(-0.873178\pi\) | ||||
0.921673 | − | 0.387967i | \(-0.126822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1204.27i | − 1.29353i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 366.333i | − 0.391800i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1032.47 | 1.10189 | 0.550943 | − | 0.834543i | \(-0.314268\pi\) | ||||
0.550943 | + | 0.834543i | \(0.314268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1597.62 | −1.69779 | −0.848893 | − | 0.528565i | \(-0.822730\pi\) | ||||
−0.848893 | + | 0.528565i | \(0.822730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 520.187 | 0.551629 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −625.214 | −0.660205 | −0.330103 | − | 0.943945i | \(-0.607083\pi\) | ||||
−0.330103 | + | 0.943945i | \(0.607083\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 194.103i | 0.204535i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 807.036i | − 0.846838i | −0.905934 | − | 0.423419i | \(-0.860830\pi\) | ||||
0.905934 | − | 0.423419i | \(-0.139170\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1131.03i | 1.18432i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 449.581i | 0.468802i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 601.093 | 0.625487 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −976.690 | −1.01211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1296.47 | −1.34071 | −0.670355 | − | 0.742041i | \(-0.733858\pi\) | ||||
−0.670355 | + | 0.742041i | \(0.733858\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −200.075 | −0.206050 | −0.103025 | − | 0.994679i | \(-0.532852\pi\) | ||||
−0.103025 | + | 0.994679i | \(0.532852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 340.757i | − 0.350212i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1309.95i | − 1.34079i | −0.742003 | − | 0.670396i | \(-0.766124\pi\) | ||||
0.742003 | − | 0.670396i | \(-0.233876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 62.7820i | 0.0641287i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1553.47i | 1.58033i | 0.612893 | + | 0.790166i | \(0.290006\pi\) | ||||
−0.612893 | + | 0.790166i | \(0.709994\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 343.907 | 0.349144 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 171.874 | 0.173786 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 922.757 | 0.931137 | 0.465568 | − | 0.885012i | \(-0.345850\pi\) | ||||
0.465568 | + | 0.885012i | \(0.345850\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −599.946 | −0.602960 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 787.710i | − 0.790080i | −0.918664 | − | 0.395040i | \(-0.870731\pi\) | ||||
0.918664 | − | 0.395040i | \(-0.129269\pi\) | |||||||
\(998\) | 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 | 2304.3.h.l.2177.4 | 8 | ||
3.2 | odd | 2 | inner | 2304.3.h.l.2177.6 | 8 | ||
4.3 | odd | 2 | 2304.3.h.j.2177.4 | 8 | |||
8.3 | odd | 2 | 2304.3.h.j.2177.5 | 8 | |||
8.5 | even | 2 | inner | 2304.3.h.l.2177.5 | 8 | ||
12.11 | even | 2 | 2304.3.h.j.2177.6 | 8 | |||
16.3 | odd | 4 | 1152.3.e.g.1025.3 | yes | 4 | ||
16.5 | even | 4 | 1152.3.e.a.1025.2 | ✓ | 4 | ||
16.11 | odd | 4 | 1152.3.e.e.1025.2 | yes | 4 | ||
16.13 | even | 4 | 1152.3.e.c.1025.3 | yes | 4 | ||
24.5 | odd | 2 | inner | 2304.3.h.l.2177.3 | 8 | ||
24.11 | even | 2 | 2304.3.h.j.2177.3 | 8 | |||
48.5 | odd | 4 | 1152.3.e.a.1025.3 | yes | 4 | ||
48.11 | even | 4 | 1152.3.e.e.1025.3 | yes | 4 | ||
48.29 | odd | 4 | 1152.3.e.c.1025.2 | yes | 4 | ||
48.35 | even | 4 | 1152.3.e.g.1025.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.e.a.1025.2 | ✓ | 4 | 16.5 | even | 4 | ||
1152.3.e.a.1025.3 | yes | 4 | 48.5 | odd | 4 | ||
1152.3.e.c.1025.2 | yes | 4 | 48.29 | odd | 4 | ||
1152.3.e.c.1025.3 | yes | 4 | 16.13 | even | 4 | ||
1152.3.e.e.1025.2 | yes | 4 | 16.11 | odd | 4 | ||
1152.3.e.e.1025.3 | yes | 4 | 48.11 | even | 4 | ||
1152.3.e.g.1025.2 | yes | 4 | 48.35 | even | 4 | ||
1152.3.e.g.1025.3 | yes | 4 | 16.3 | odd | 4 | ||
2304.3.h.j.2177.3 | 8 | 24.11 | even | 2 | |||
2304.3.h.j.2177.4 | 8 | 4.3 | odd | 2 | |||
2304.3.h.j.2177.5 | 8 | 8.3 | odd | 2 | |||
2304.3.h.j.2177.6 | 8 | 12.11 | even | 2 | |||
2304.3.h.l.2177.3 | 8 | 24.5 | odd | 2 | inner | ||
2304.3.h.l.2177.4 | 8 | 1.1 | even | 1 | trivial | ||
2304.3.h.l.2177.5 | 8 | 8.5 | even | 2 | inner | ||
2304.3.h.l.2177.6 | 8 | 3.2 | odd | 2 | inner |