Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(863,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.863");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.f (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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.58594980096.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 21x^{6} + 341x^{4} - 2100x^{2} + 10000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 863.6 | ||
Root | \(-3.20565 + 1.85078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.863 |
Dual form | 1728.4.f.g.863.5 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 9.35849 | 0.837048 | 0.418524 | − | 0.908206i | \(-0.362548\pi\) | ||||
0.418524 | + | 0.908206i | \(0.362548\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 21.2094i | 1.14520i | 0.819835 | + | 0.572599i | \(0.194065\pi\) | ||||
−0.819835 | + | 0.572599i | \(0.805935\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 50.9277i | − 1.39593i | −0.716130 | − | 0.697967i | \(-0.754088\pi\) | ||||
0.716130 | − | 0.697967i | \(-0.245912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 33.2716i | 0.709837i | 0.934897 | + | 0.354919i | \(0.115491\pi\) | ||||
−0.934897 | + | 0.354919i | \(0.884509\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 120.628i | − 1.72098i | −0.509470 | − | 0.860489i | \(-0.670158\pi\) | ||||
0.509470 | − | 0.860489i | \(-0.329842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −82.1317 | −0.991700 | −0.495850 | − | 0.868408i | \(-0.665143\pi\) | ||||
−0.495850 | + | 0.868408i | \(0.665143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 95.3719 | 0.864627 | 0.432313 | − | 0.901723i | \(-0.357697\pi\) | ||||
0.432313 | + | 0.901723i | \(0.357697\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −37.4187 | −0.299350 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 83.1384 | 0.532359 | 0.266180 | − | 0.963923i | \(-0.414239\pi\) | ||||
0.266180 | + | 0.963923i | \(0.414239\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.4187i | 0.211000i | 0.994419 | + | 0.105500i | \(0.0336443\pi\) | ||||
−0.994419 | + | 0.105500i | \(0.966356\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 198.488i | 0.958587i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 201.724i | 0.896305i | 0.893957 | + | 0.448152i | \(0.147918\pi\) | ||||
−0.893957 | + | 0.448152i | \(0.852082\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 291.769i | − 1.11138i | −0.831389 | − | 0.555690i | \(-0.812454\pi\) | ||||
0.831389 | − | 0.555690i | \(-0.187546\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −457.424 | −1.62224 | −0.811122 | − | 0.584877i | \(-0.801143\pi\) | ||||
−0.811122 | + | 0.584877i | \(0.801143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −628.397 | −1.95024 | −0.975118 | − | 0.221686i | \(-0.928844\pi\) | ||||
−0.975118 | + | 0.221686i | \(0.928844\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −106.837 | −0.311480 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −659.013 | −1.70797 | −0.853985 | − | 0.520298i | \(-0.825821\pi\) | ||||
−0.853985 | + | 0.520298i | \(0.825821\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 476.606i | − 1.16846i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 44.8330i | 0.0989282i | 0.998776 | + | 0.0494641i | \(0.0157513\pi\) | ||||
−0.998776 | + | 0.0494641i | \(0.984249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 149.600i | − 0.314006i | −0.987598 | − | 0.157003i | \(-0.949817\pi\) | ||||
0.987598 | − | 0.157003i | \(-0.0501833\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 311.372i | 0.594168i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 134.256 | 0.244805 | 0.122402 | − | 0.992481i | \(-0.460940\pi\) | ||||
0.122402 | + | 0.992481i | \(0.460940\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −291.769 | −0.487698 | −0.243849 | − | 0.969813i | \(-0.578410\pi\) | ||||
−0.243849 | + | 0.969813i | \(0.578410\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 888.212 | 1.42407 | 0.712037 | − | 0.702142i | \(-0.247773\pi\) | ||||
0.712037 | + | 0.702142i | \(0.247773\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1080.14 | 1.59862 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 714.653i | 1.01778i | 0.860831 | + | 0.508891i | \(0.169944\pi\) | ||||
−0.860831 | + | 0.508891i | \(0.830056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 827.466i | − 1.09429i | −0.837038 | − | 0.547145i | \(-0.815714\pi\) | ||||
0.837038 | − | 0.547145i | \(-0.184286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1128.90i | − 1.44054i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 19.6032i | 0.0233476i | 0.999932 | + | 0.0116738i | \(0.00371596\pi\) | ||||
−0.999932 | + | 0.0116738i | \(0.996284\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −705.670 | −0.812905 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −768.628 | −0.830101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −805.469 | −0.843123 | −0.421562 | − | 0.906800i | \(-0.638518\pi\) | ||||
−0.421562 | + | 0.906800i | \(0.638518\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 421.787 | 0.415538 | 0.207769 | − | 0.978178i | \(-0.433380\pi\) | ||||
0.207769 | + | 0.978178i | \(0.433380\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 372.653i | 0.356491i | 0.983986 | + | 0.178246i | \(0.0570422\pi\) | ||||
−0.983986 | + | 0.178246i | \(0.942958\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 40.9142i | − 0.0369656i | −0.999829 | − | 0.0184828i | \(-0.994116\pi\) | ||||
0.999829 | − | 0.0184828i | \(-0.00588360\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2080.96i | − 1.82862i | −0.405011 | − | 0.914312i | \(-0.632732\pi\) | ||||
0.405011 | − | 0.914312i | \(-0.367268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 614.447i | 0.511525i | 0.966740 | + | 0.255762i | \(0.0823265\pi\) | ||||
−0.966740 | + | 0.255762i | \(0.917674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 892.536 | 0.723734 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2558.45 | 1.97086 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1262.63 | −0.948633 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1519.99 | −1.08762 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1682.24i | − 1.17539i | −0.809083 | − | 0.587695i | \(-0.800036\pi\) | ||||
0.809083 | − | 0.587695i | \(-0.199964\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2008.81i | 1.33978i | 0.742462 | + | 0.669888i | \(0.233658\pi\) | ||||
−0.742462 | + | 0.669888i | \(0.766342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1741.96i | − 1.13569i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2140.40i | − 1.33479i | −0.744703 | − | 0.667396i | \(-0.767409\pi\) | ||||
0.744703 | − | 0.667396i | \(-0.232591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2626.56 | −1.60275 | −0.801373 | − | 0.598165i | \(-0.795897\pi\) | ||||
−0.801373 | + | 0.598165i | \(0.795897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1694.45 | 0.990886 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 778.050 | 0.445611 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 260.728 | 0.143353 | 0.0716766 | − | 0.997428i | \(-0.477165\pi\) | ||||
0.0716766 | + | 0.997428i | \(0.477165\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1825.26i | 0.983692i | 0.870682 | + | 0.491846i | \(0.163678\pi\) | ||||
−0.870682 | + | 0.491846i | \(0.836322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 340.824i | 0.176617i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1731.00i | − 0.879929i | −0.898015 | − | 0.439965i | \(-0.854991\pi\) | ||||
0.898015 | − | 0.439965i | \(-0.145009\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2022.78i | 0.990169i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1066.74 | −0.512597 | −0.256299 | − | 0.966598i | \(-0.582503\pi\) | ||||
−0.256299 | + | 0.966598i | \(0.582503\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1643.93 | 0.761745 | 0.380873 | − | 0.924628i | \(-0.375624\pi\) | ||||
0.380873 | + | 0.924628i | \(0.375624\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1090.00 | 0.496131 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3182.76 | −1.39873 | −0.699367 | − | 0.714763i | \(-0.746535\pi\) | ||||
−0.699367 | + | 0.714763i | \(0.746535\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 793.628i | − 0.342815i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3669.40i | − 1.53220i | −0.642720 | − | 0.766101i | \(-0.722194\pi\) | ||||
0.642720 | − | 0.766101i | \(-0.277806\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1363.16i | − 0.559796i | −0.960030 | − | 0.279898i | \(-0.909699\pi\) | ||||
0.960030 | − | 0.279898i | \(-0.0903006\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1887.83i | 0.750251i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6143.31 | −2.40237 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −807.834 | −0.306036 | −0.153018 | − | 0.988223i | \(-0.548899\pi\) | ||||
−0.153018 | + | 0.988223i | \(0.548899\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 898.681 | 0.335173 | 0.167587 | − | 0.985857i | \(-0.446403\pi\) | ||||
0.167587 | + | 0.985857i | \(0.446403\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4394.80 | 1.58943 | 0.794713 | − | 0.606986i | \(-0.207622\pi\) | ||||
0.794713 | + | 0.606986i | \(0.207622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 878.234i | − 0.312846i | −0.987690 | − | 0.156423i | \(-0.950004\pi\) | ||||
0.987690 | − | 0.156423i | \(-0.0499963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1763.31i | 0.609657i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2730.51i | − 0.930280i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4182.78i | 1.38435i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5015.10 | −1.63627 | −0.818137 | − | 0.575024i | \(-0.804993\pi\) | ||||
−0.818137 | + | 0.575024i | \(0.804993\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4280.79 | −1.35790 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −772.419 | −0.241637 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4013.49 | 1.22161 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1304.69i | 0.391788i | 0.980625 | + | 0.195894i | \(0.0627609\pi\) | ||||
−0.980625 | + | 0.195894i | \(0.937239\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1393.77i | 0.407523i | 0.979021 | + | 0.203762i | \(0.0653168\pi\) | ||||
−0.979021 | + | 0.203762i | \(0.934683\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1153.16i | 0.332763i | 0.986061 | + | 0.166381i | \(0.0532083\pi\) | ||||
−0.986061 | + | 0.166381i | \(0.946792\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3540.43i | − 0.995456i | −0.867333 | − | 0.497728i | \(-0.834168\pi\) | ||||
0.867333 | − | 0.497728i | \(-0.165832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5880.84 | −1.63244 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 78.4127 | 0.0212222 | 0.0106111 | − | 0.999944i | \(-0.496622\pi\) | ||||
0.0106111 | + | 0.999944i | \(0.496622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3906.31 | 1.04410 | 0.522048 | − | 0.852916i | \(-0.325168\pi\) | ||||
0.522048 | + | 0.852916i | \(0.325168\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −999.837 | −0.260723 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2732.65i | − 0.703946i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 5007.89i | − 1.25934i | −0.776861 | − | 0.629672i | \(-0.783189\pi\) | ||||
0.776861 | − | 0.629672i | \(-0.216811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4857.07i | − 1.20696i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2019.77i | − 0.490232i | −0.969494 | − | 0.245116i | \(-0.921174\pi\) | ||||
0.969494 | − | 0.245116i | \(-0.0788261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4278.45 | −1.02645 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6575.74 | −1.54174 | −0.770869 | − | 0.636993i | \(-0.780178\pi\) | ||||
−0.770869 | + | 0.636993i | \(0.780178\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6167.36 | −1.42965 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3661.36 | −0.829876 | −0.414938 | − | 0.909850i | \(-0.636197\pi\) | ||||
−0.414938 | + | 0.909850i | \(0.636197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3645.23i | 0.817092i | 0.912738 | + | 0.408546i | \(0.133964\pi\) | ||||
−0.912738 | + | 0.408546i | \(0.866036\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1905.65i | 0.417873i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5103.76i | − 1.10706i | −0.832830 | − | 0.553529i | \(-0.813281\pi\) | ||||
0.832830 | − | 0.553529i | \(-0.186719\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 487.800i | 0.103558i | 0.998659 | + | 0.0517789i | \(0.0164891\pi\) | ||||
−0.998659 | + | 0.0517789i | \(0.983511\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −339.147 | −0.0712374 | −0.0356187 | − | 0.999365i | \(-0.511340\pi\) | ||||
−0.0356187 | + | 0.999365i | \(0.511340\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6188.23 | 1.27275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9638.14 | −1.96176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9014.85 | −1.79745 | −0.898726 | − | 0.438511i | \(-0.855506\pi\) | ||||
−0.898726 | + | 0.438511i | \(0.855506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 419.569i | 0.0828077i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3173.18i | 0.613744i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 9701.67i | − 1.85779i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 1400.03i | − 0.262838i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4127.92 | −0.767404 | −0.383702 | − | 0.923457i | \(-0.625351\pi\) | ||||
−0.383702 | + | 0.923457i | \(0.625351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2597.65 | −0.473631 | −0.236816 | − | 0.971555i | \(-0.576104\pi\) | ||||
−0.236816 | + | 0.971555i | \(0.576104\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8571.57 | 1.54790 | 0.773952 | − | 0.633245i | \(-0.218277\pi\) | ||||
0.773952 | + | 0.633245i | \(0.218277\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3321.62 | 0.588520 | 0.294260 | − | 0.955725i | \(-0.404927\pi\) | ||||
0.294260 | + | 0.955725i | \(0.404927\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 4234.05i | − 0.743139i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9907.39i | 1.70669i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1244.98i | − 0.212490i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 13327.9i | − 2.23341i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −184.431 | −0.0306262 | −0.0153131 | − | 0.999883i | \(-0.504874\pi\) | ||||
−0.0153131 | + | 0.999883i | \(0.504874\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1256.43 | 0.204914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6322.76 | 1.02202 | 0.511012 | − | 0.859573i | \(-0.329271\pi\) | ||||
0.511012 | + | 0.859573i | \(0.329271\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1854.72 | 0.294542 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5008.86i | 0.788493i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6318.50i | − 0.977507i | −0.872422 | − | 0.488753i | \(-0.837452\pi\) | ||||
0.872422 | − | 0.488753i | \(-0.162548\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8503.65i | − 1.30427i | −0.758103 | − | 0.652135i | \(-0.773874\pi\) | ||||
0.758103 | − | 0.652135i | \(-0.226126\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 7697.59i | − 1.16063i | −0.814393 | − | 0.580313i | \(-0.802930\pi\) | ||||
0.814393 | − | 0.580313i | \(-0.197070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2730.51 | −0.408227 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −903.571 | −0.132838 | −0.0664188 | − | 0.997792i | \(-0.521157\pi\) | ||||
−0.0664188 | + | 0.997792i | \(0.521157\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −113.388 | −0.0165312 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8312.32 | 1.19202 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6619.95i | 0.941576i | 0.882246 | + | 0.470788i | \(0.156030\pi\) | ||||
−0.882246 | + | 0.470788i | \(0.843970\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 13977.2i | − 1.95596i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 11830.0i | − 1.64219i | −0.570794 | − | 0.821093i | \(-0.693364\pi\) | ||||
0.570794 | − | 0.821093i | \(-0.306636\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2766.15i | 0.377888i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3711.81 | 0.503068 | 0.251534 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251534 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1761.92 | 0.235065 | 0.117532 | − | 0.993069i | \(-0.462502\pi\) | ||||
0.117532 | + | 0.993069i | \(0.462502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10108.5 | 1.33812 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4849.66 | 0.632102 | 0.316051 | − | 0.948742i | \(-0.397643\pi\) | ||||
0.316051 | + | 0.948742i | \(0.397643\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 11504.5i | − 1.48800i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6688.07i | 0.851933i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8066.93i | − 1.01982i | −0.860228 | − | 0.509909i | \(-0.829679\pi\) | ||||
0.860228 | − | 0.509909i | \(-0.170321\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14632.2i | 1.82219i | 0.412199 | + | 0.911094i | \(0.364761\pi\) | ||||
−0.412199 | + | 0.911094i | \(0.635239\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1211.71 | −0.149776 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10273.4 | 1.25118 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12812.9 | −1.54904 | −0.774519 | − | 0.632551i | \(-0.782008\pi\) | ||||
−0.774519 | + | 0.632551i | \(0.782008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −950.880 | −0.113292 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 7743.82i | − 0.915974i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 9701.95i | − 1.13120i | −0.824681 | − | 0.565598i | \(-0.808645\pi\) | ||||
0.824681 | − | 0.565598i | \(-0.191355\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16265.0i | 1.88292i | 0.337123 | + | 0.941460i | \(0.390546\pi\) | ||||
−0.337123 | + | 0.941460i | \(0.609454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4513.75i | 0.515175i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3172.93 | 0.359599 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16472.2 | −1.84092 | −0.920460 | − | 0.390837i | \(-0.872185\pi\) | ||||
−0.920460 | + | 0.390837i | \(0.872185\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14696.1 | −1.63106 | −0.815532 | − | 0.578712i | \(-0.803556\pi\) | ||||
−0.815532 | + | 0.578712i | \(0.803556\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7833.05 | −0.857450 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7192.32i | 0.781938i | 0.920404 | + | 0.390969i | \(0.127860\pi\) | ||||
−0.920404 | + | 0.390969i | \(0.872140\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12096.0i | 1.29728i | 0.761094 | + | 0.648642i | \(0.224663\pi\) | ||||
−0.761094 | + | 0.648642i | \(0.775337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 183.456i | 0.0195430i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2061.98i | 0.216728i | 0.994111 | + | 0.108364i | \(0.0345613\pi\) | ||||
−0.994111 | + | 0.108364i | \(0.965439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14859.1 | −1.55142 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6604.00 | −0.680440 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18568.8 | 1.90068 | 0.950340 | − | 0.311215i | \(-0.100736\pi\) | ||||
0.950340 | + | 0.311215i | \(0.100736\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2231.88 | 0.225486 | 0.112743 | − | 0.993624i | \(-0.464036\pi\) | ||||
0.112743 | + | 0.993624i | \(0.464036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3414.82i | − 0.342765i | −0.985205 | − | 0.171383i | \(-0.945177\pi\) | ||||
0.985205 | − | 0.171383i | \(-0.0548234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8313.82i | 0.823806i | 0.911228 | + | 0.411903i | \(0.135136\pi\) | ||||
−0.911228 | + | 0.411903i | \(0.864864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2847.48i | 0.280350i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23295.5i | 2.26455i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3073.26 | 0.296865 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3888.73 | 0.370941 | 0.185470 | − | 0.982650i | \(-0.440619\pi\) | ||||
0.185470 | + | 0.982650i | \(0.440619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6711.69 | −0.636231 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7537.97 | −0.705735 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1477.35i | − 0.137464i | −0.997635 | − | 0.0687320i | \(-0.978105\pi\) | ||||
0.997635 | − | 0.0687320i | \(-0.0218953\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 11772.5i | − 1.08205i | −0.841006 | − | 0.541026i | \(-0.818036\pi\) | ||||
0.841006 | − | 0.541026i | \(-0.181964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 10028.8i | − 0.916178i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6188.23i | − 0.558511i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9378.01 | −0.841318 | −0.420659 | − | 0.907219i | \(-0.638201\pi\) | ||||
−0.420659 | + | 0.907219i | \(0.638201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22078.3 | 1.95710 | 0.978552 | − | 0.205998i | \(-0.0660442\pi\) | ||||
0.978552 | + | 0.205998i | \(0.0660442\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3947.29 | 0.347826 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18081.3 | −1.57453 | −0.787267 | − | 0.616612i | \(-0.788505\pi\) | ||||
−0.787267 | + | 0.616612i | \(0.788505\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18838.4i | 1.63085i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3487.47i | 0.298400i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32002.8i | 2.72240i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8655.05i | 0.727801i | 0.931438 | + | 0.363901i | \(0.118555\pi\) | ||||
−0.931438 | + | 0.363901i | \(0.881445\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9920.20 | 0.829407 | 0.414704 | − | 0.909956i | \(-0.363885\pi\) | ||||
0.414704 | + | 0.909956i | \(0.363885\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4393.12 | 0.363126 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3071.20 | −0.252421 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9707.61 | 0.788900 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 382.895i | − 0.0309420i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5440.99i | 0.434805i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12337.7i | 0.980481i | 0.871587 | + | 0.490241i | \(0.163091\pi\) | ||||
−0.871587 | + | 0.490241i | \(0.836909\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 19474.6i | − 1.53065i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7446.60 | −0.582073 | −0.291036 | − | 0.956712i | \(-0.594000\pi\) | ||||
−0.291036 | + | 0.956712i | \(0.594000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6828.30 | −0.527941 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15157.3 | −1.16556 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10322.9 | 0.785268 | 0.392634 | − | 0.919695i | \(-0.371564\pi\) | ||||
0.392634 | + | 0.919695i | \(0.371564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 15219.2i | − 1.15153i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18218.6i | 1.36381i | 0.731442 | + | 0.681904i | \(0.238848\pi\) | ||||
−0.731442 | + | 0.681904i | \(0.761152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5750.29i | 0.428171i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6399.31i | 0.471481i | 0.971816 | + | 0.235741i | \(0.0757516\pi\) | ||||
−0.971816 | + | 0.235741i | \(0.924248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1999.51 | −0.146545 | −0.0732723 | − | 0.997312i | \(-0.523344\pi\) | ||||
−0.0732723 | + | 0.997312i | \(0.523344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3568.70 | −0.258826 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10659.3 | 0.769067 | 0.384534 | − | 0.923111i | \(-0.374362\pi\) | ||||
0.384534 | + | 0.923111i | \(0.374362\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17550.0 | 1.25318 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33562.0i | 2.38421i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 8379.15i | − 0.589173i | −0.955625 | − | 0.294586i | \(-0.904818\pi\) | ||||
0.955625 | − | 0.294586i | \(-0.0951819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2991.13i | − 0.209249i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 7052.96i | − 0.488416i | −0.969723 | − | 0.244208i | \(-0.921472\pi\) | ||||
0.969723 | − | 0.244208i | \(-0.0785279\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23943.2 | 1.64971 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21730.4 | 1.48227 | 0.741135 | − | 0.671356i | \(-0.234288\pi\) | ||||
0.741135 | + | 0.671356i | \(0.234288\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18068.1 | 1.22631 | 0.613156 | − | 0.789962i | \(-0.289900\pi\) | ||||
0.613156 | + | 0.789962i | \(0.289900\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11816.3 | −0.794052 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 21545.7i | − 1.44071i | −0.693603 | − | 0.720357i | \(-0.743978\pi\) | ||||
0.693603 | − | 0.720357i | \(-0.256022\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 20907.8i | − 1.38435i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19035.8i | 1.25424i | 0.778923 | + | 0.627120i | \(0.215766\pi\) | ||||
−0.778923 | + | 0.627120i | \(0.784234\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 17984.2i | − 1.17344i | −0.809788 | − | 0.586722i | \(-0.800418\pi\) | ||||
0.809788 | − | 0.586722i | \(-0.199582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10517.1 | 0.682907 | 0.341454 | − | 0.939899i | \(-0.389081\pi\) | ||||
0.341454 | + | 0.939899i | \(0.389081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −415.771 | −0.0267376 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9547.49 | −0.611040 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24333.6 | 1.54252 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 23831.9i | − 1.50354i | −0.659425 | − | 0.751771i | \(-0.729200\pi\) | ||||
0.659425 | − | 0.751771i | \(-0.270800\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 15743.2i | − 0.983858i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3554.66i | − 0.221100i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15647.0i | 0.964149i | 0.876130 | + | 0.482075i | \(0.160117\pi\) | ||||
−0.876130 | + | 0.482075i | \(0.839883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29777.2 | 1.82628 | 0.913139 | − | 0.407648i | \(-0.133651\pi\) | ||||
0.913139 | + | 0.407648i | \(0.133651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9149.68 | 0.555968 | 0.277984 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277984 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2283.24 | 0.138097 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19011.7 | −1.13933 | −0.569667 | − | 0.821875i | \(-0.692928\pi\) | ||||
−0.569667 | + | 0.821875i | \(0.692928\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18799.4i | 1.12146i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 299.938i | 0.0177298i | 0.999961 | + | 0.00886490i | \(0.00282182\pi\) | ||||
−0.999961 | + | 0.00886490i | \(0.997178\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23512.2i | 1.38354i | 0.722118 | + | 0.691769i | \(0.243169\pi\) | ||||
−0.722118 | + | 0.691769i | \(0.756831\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 16302.1i | − 0.950630i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7929.07 | 0.460292 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7618.81 | −0.438332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22913.5 | 1.31241 | 0.656204 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656204 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16220.1 | −0.920809 | −0.460405 | − | 0.887709i | \(-0.652296\pi\) | ||||
−0.460405 | + | 0.887709i | \(0.652296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 17083.5i | − 0.965543i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 18445.4i | − 1.03337i | −0.856175 | − | 0.516686i | \(-0.827165\pi\) | ||||
0.856175 | − | 0.516686i | \(-0.172835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 20030.9i | − 1.11729i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 21926.4i | − 1.21238i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18971.8 | 1.04446 | 0.522231 | − | 0.852804i | \(-0.325100\pi\) | ||||
0.522231 | + | 0.852804i | \(0.325100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24580.6 | −1.34158 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35195.5 | −1.91266 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9303.46 | 0.501265 | 0.250632 | − | 0.968082i | \(-0.419361\pi\) | ||||
0.250632 | + | 0.968082i | \(0.419361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 16568.0i | − 0.888865i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8945.84i | 0.475874i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33456.9i | 1.77221i | 0.463481 | + | 0.886107i | \(0.346600\pi\) | ||||
−0.463481 | + | 0.886107i | \(0.653400\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3473.32i | 0.182436i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15857.5 | 0.829420 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19474.6 | −1.01013 | −0.505064 | − | 0.863082i | \(-0.668531\pi\) | ||||
−0.505064 | + | 0.863082i | \(0.668531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7903.74 | −0.408253 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3110.94 | −0.159362 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7641.59i | 0.389836i | 0.980820 | + | 0.194918i | \(0.0624441\pi\) | ||||
−0.980820 | + | 0.194918i | \(0.937556\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 55178.2i | 2.79184i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 23153.2i | − 1.16669i | −0.812224 | − | 0.583345i | \(-0.801743\pi\) | ||||
0.812224 | − | 0.583345i | \(-0.198257\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 6837.33i | − 0.341732i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20627.7 | 1.02680 | 0.513398 | − | 0.858150i | \(-0.328386\pi\) | ||||
0.513398 | + | 0.858150i | \(0.328386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30112.9 | −1.48686 | −0.743429 | − | 0.668815i | \(-0.766802\pi\) | ||||
−0.743429 | + | 0.668815i | \(0.766802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2440.02 | 0.119994 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 867.764 | 0.0423330 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13806.8i | 0.670861i | 0.942065 | + | 0.335431i | \(0.108882\pi\) | ||||
−0.942065 | + | 0.335431i | \(0.891118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17081.7i | 0.823398i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16505.6i | 0.792478i | 0.918147 | + | 0.396239i | \(0.129685\pi\) | ||||
−0.918147 | + | 0.396239i | \(0.870315\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35472.2i | 1.68971i | 0.534997 | + | 0.844854i | \(0.320313\pi\) | ||||
−0.534997 | + | 0.844854i | \(0.679687\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44135.9 | 2.09414 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1491.67 | −0.0702229 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2816.64 | 0.132081 | 0.0660406 | − | 0.997817i | \(-0.478963\pi\) | ||||
0.0660406 | + | 0.997817i | \(0.478963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30378.5 | −1.41351 | −0.706753 | − | 0.707461i | \(-0.749841\pi\) | ||||
−0.706753 | + | 0.707461i | \(0.749841\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1362.74i | − 0.0631628i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23963.5i | 1.10216i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14859.1i | 0.680795i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 16199.5i | − 0.736543i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26302.1 | 1.19132 | 0.595660 | − | 0.803237i | \(-0.296891\pi\) | ||||
0.595660 | + | 0.803237i | \(0.296891\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13032.0 | −0.585797 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4977.45 | 0.222893 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27016.4 | 1.20072 | 0.600358 | − | 0.799731i | \(-0.295025\pi\) | ||||
0.600358 | + | 0.799731i | \(0.295025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 75802.3i | 3.35631i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 45234.6i | − 1.98791i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18930.1i | 0.828819i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33893.5i | 1.47297i | 0.676455 | + | 0.736484i | \(0.263516\pi\) | ||||
−0.676455 | + | 0.736484i | \(0.736484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16820.8 | −0.728309 | −0.364155 | − | 0.931338i | \(-0.618642\pi\) | ||||
−0.364155 | + | 0.931338i | \(0.618642\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9983.05 | −0.429069 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37569.0 | 1.60878 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27615.2 | −1.17391 | −0.586953 | − | 0.809621i | \(-0.699673\pi\) | ||||
−0.586953 | + | 0.809621i | \(0.699673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 27645.0i | − 1.17089i | −0.810712 | − | 0.585445i | \(-0.800920\pi\) | ||||
0.810712 | − | 0.585445i | \(-0.199080\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 33748.9i | − 1.41906i | −0.704674 | − | 0.709531i | \(-0.748907\pi\) | ||||
0.704674 | − | 0.709531i | \(-0.251093\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19289.5i | 0.808145i | 0.914727 | + | 0.404072i | \(0.132406\pi\) | ||||
−0.914727 | + | 0.404072i | \(0.867594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12887.6i | 0.536049i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15384.7 | 0.637618 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8017.26 | 0.329900 | 0.164950 | − | 0.986302i | \(-0.447254\pi\) | ||||
0.164950 | + | 0.986302i | \(0.447254\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17477.0 | −0.716594 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10200.7 | 0.415286 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 26779.6i | − 1.08637i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19238.8i | 0.774969i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23777.8i | 0.954439i | 0.878784 | + | 0.477220i | \(0.158355\pi\) | ||||
−0.878784 | + | 0.477220i | \(0.841645\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 40669.8i | − 1.62107i | −0.585692 | − | 0.810534i | \(-0.699177\pi\) | ||||
0.585692 | − | 0.810534i | \(-0.300823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7166.21 | −0.284642 | −0.142321 | − | 0.989821i | \(-0.545457\pi\) | ||||
−0.142321 | + | 0.989821i | \(0.545457\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30914.4 | 1.21939 | 0.609697 | − | 0.792635i | \(-0.291291\pi\) | ||||
0.609697 | + | 0.792635i | \(0.291291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29785.8 | −1.17081 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36395.6 | 1.42076 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4466.90i | 0.173772i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 32238.1i | − 1.24554i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5414.60i | 0.208481i | 0.994552 | + | 0.104241i | \(0.0332412\pi\) | ||||
−0.994552 | + | 0.104241i | \(0.966759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 6604.46i | − 0.252565i | −0.991994 | − | 0.126283i | \(-0.959695\pi\) | ||||
0.991994 | − | 0.126283i | \(-0.0403046\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35256.0 | 1.34367 | 0.671834 | − | 0.740701i | \(-0.265507\pi\) | ||||
0.671834 | + | 0.740701i | \(0.265507\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17276.2 | 0.653976 | 0.326988 | − | 0.945028i | \(-0.393966\pi\) | ||||
0.326988 | + | 0.945028i | \(0.393966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35679.2 | 1.34605 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51611.3 | 1.93405 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 34340.1i | − 1.28253i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3027.80i | 0.112328i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 79495.5i | 2.93938i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 12757.1i | − 0.468576i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34491.5 | −1.26270 | −0.631351 | − | 0.775497i | \(-0.717499\pi\) | ||||
−0.631351 | + | 0.775497i | \(0.717499\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38213.5 | 1.38976 | 0.694879 | − | 0.719127i | \(-0.255458\pi\) | ||||
0.694879 | + | 0.719127i | \(0.255458\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42140.9 | −1.52756 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42605.6 | −1.53431 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36899.1i | 1.32447i | 0.749295 | + | 0.662236i | \(0.230392\pi\) | ||||
−0.749295 | + | 0.662236i | \(0.769608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 9707.61i | − 0.346186i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 7548.27i | − 0.268309i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 279.002i | − 0.00985335i | −0.999988 | − | 0.00492668i | \(-0.998432\pi\) | ||||
0.999988 | − | 0.00492668i | \(-0.00156822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8774.74 | 0.308894 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −57492.1 | −2.01090 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41546.4 | −1.44852 | −0.724259 | − | 0.689528i | \(-0.757818\pi\) | ||||
−0.724259 | + | 0.689528i | \(0.757818\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18490.9 | −0.640580 | −0.320290 | − | 0.947320i | \(-0.603780\pi\) | ||||
−0.320290 | + | 0.947320i | \(0.603780\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 27826.5i | − 0.960930i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 7862.91i | − 0.269810i | −0.990859 | − | 0.134905i | \(-0.956927\pi\) | ||||
0.990859 | − | 0.134905i | \(-0.0430730\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29552.3i | 1.01086i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 23650.7i | − 0.803904i | −0.915661 | − | 0.401952i | \(-0.868332\pi\) | ||||
0.915661 | − | 0.401952i | \(-0.131668\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7560.11 | −0.256167 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45396.5 | 1.52860 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28464.7 | 0.955479 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8410.29 | 0.280556 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 13515.5i | − 0.449460i | −0.974421 | − | 0.224730i | \(-0.927850\pi\) | ||||
0.974421 | − | 0.224730i | \(-0.0721501\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39505.1i | 1.30564i | 0.757512 | + | 0.652821i | \(0.226415\pi\) | ||||
−0.757512 | + | 0.652821i | \(0.773585\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 55707.6i | − 1.83546i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42131.6i | 1.37964i | 0.723981 | + | 0.689820i | \(0.242310\pi\) | ||||
−0.723981 | + | 0.689820i | \(0.757690\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 998.345 | 0.0325917 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48982.9 | 1.58933 | 0.794665 | − | 0.607049i | \(-0.207647\pi\) | ||||
0.794665 | + | 0.607049i | \(0.207647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41128.7 | 1.33043 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43625.4 | −1.40263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 3555.12i | − 0.113958i | −0.998375 | − | 0.0569788i | \(-0.981853\pi\) | ||||
0.998375 | − | 0.0569788i | \(-0.0181468\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 8218.94i | − 0.261867i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43140.0i | 1.37037i | 0.728370 | + | 0.685184i | \(0.240278\pi\) | ||||
−0.728370 | + | 0.685184i | \(0.759722\pi\) | |||||||
\(998\) | 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 | 1728.4.f.g.863.6 | yes | 8 | |
3.2 | odd | 2 | 1728.4.f.c.863.4 | yes | 8 | ||
4.3 | odd | 2 | 1728.4.f.c.863.5 | yes | 8 | ||
8.3 | odd | 2 | 1728.4.f.c.863.3 | ✓ | 8 | ||
8.5 | even | 2 | inner | 1728.4.f.g.863.4 | yes | 8 | |
12.11 | even | 2 | inner | 1728.4.f.g.863.3 | yes | 8 | |
24.5 | odd | 2 | 1728.4.f.c.863.6 | yes | 8 | ||
24.11 | even | 2 | inner | 1728.4.f.g.863.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.f.c.863.3 | ✓ | 8 | 8.3 | odd | 2 | ||
1728.4.f.c.863.4 | yes | 8 | 3.2 | odd | 2 | ||
1728.4.f.c.863.5 | yes | 8 | 4.3 | odd | 2 | ||
1728.4.f.c.863.6 | yes | 8 | 24.5 | odd | 2 | ||
1728.4.f.g.863.3 | yes | 8 | 12.11 | even | 2 | inner | |
1728.4.f.g.863.4 | yes | 8 | 8.5 | even | 2 | inner | |
1728.4.f.g.863.5 | yes | 8 | 24.11 | even | 2 | inner | |
1728.4.f.g.863.6 | yes | 8 | 1.1 | even | 1 | trivial |