Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(47,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.bh (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{18})\) |
Coefficient field: | 12.0.101559956668416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 8x^{6} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 815.2 | ||
Root | \(-1.39273 + 0.245576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.815 |
Dual form | 864.2.bh.a.335.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{18}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −0.456003 | − | 1.67095i | −0.263274 | − | 0.964721i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.58412 | + | 1.52391i | −0.861374 | + | 0.507971i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.18893 | + | 6.01403i | −0.659987 | + | 1.81330i | −0.0829925 | + | 0.996550i | \(0.526448\pi\) |
−0.576994 | + | 0.816748i | \(0.695774\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.09286 | + | 4.09506i | 1.72027 | + | 0.993199i | 0.918351 | + | 0.395768i | \(0.129521\pi\) |
0.801920 | + | 0.597431i | \(0.203812\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.511376 | + | 0.885729i | 0.117318 | + | 0.203200i | 0.918704 | − | 0.394947i | \(-0.129237\pi\) |
−0.801386 | + | 0.598147i | \(0.795904\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.83022 | + | 3.21394i | −0.766044 | + | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.72474 | + | 3.62302i | 0.716827 | + | 0.697251i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.0473 | + | 0.915165i | 1.92308 | + | 0.159310i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.15282 | − | 9.71615i | 1.27326 | − | 1.51741i | 0.530831 | − | 0.847477i | \(-0.321880\pi\) |
0.742424 | − | 0.669930i | \(-0.233676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.07316 | − | 0.754568i | −0.316154 | − | 0.115071i | 0.179069 | − | 0.983836i | \(-0.442691\pi\) |
−0.495223 | + | 0.868766i | \(0.664914\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.57785 | + | 2.39414i | −0.939693 | + | 0.342020i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.60827 | − | 13.7191i | 0.505258 | − | 1.92106i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.24682 | − | 1.25838i | 0.165145 | − | 0.166676i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.84333 | + | 10.5595i | 0.500359 | + | 1.37472i | 0.890925 | + | 0.454150i | \(0.150057\pi\) |
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.53904 | + | 3.80871i | 0.554532 | + | 0.465308i | 0.876472 | − | 0.481452i | \(-0.159891\pi\) |
−0.321940 | + | 0.946760i | \(0.604335\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.68819 | + | 8.12018i | 0.548711 | + | 0.950395i | 0.998363 | + | 0.0571917i | \(0.0182146\pi\) |
−0.449652 | + | 0.893204i | \(0.648452\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.11691 | + | 4.93453i | 0.821790 | + | 0.569790i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.35538 | − | 7.87596i | 0.483931 | − | 0.875106i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.9291 | + | 13.0248i | 1.19963 | + | 1.42966i | 0.875210 | + | 0.483743i | \(0.160723\pi\) |
0.324415 | + | 0.945915i | \(0.394833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0505 | + | 6.38002i | −1.17135 | + | 0.676280i | −0.953998 | − | 0.299813i | \(-0.903076\pi\) |
−0.217354 | + | 0.976093i | \(0.569742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0731 | − | 5.12218i | −1.42890 | − | 0.520079i | −0.492287 | − | 0.870433i | \(-0.663839\pi\) |
−0.936617 | + | 0.350354i | \(0.886061\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.50840 | − | 18.8767i | −0.352608 | − | 1.89718i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.3102i | − | 1.09340i | −0.837330 | − | 0.546698i | \(-0.815885\pi\) | ||
0.837330 | − | 0.546698i | \(-0.184115\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.26632 | + | 19.9641i | 0.683558 | + | 1.87806i | 0.377048 | + | 0.926194i | \(0.376939\pi\) |
0.306510 | + | 0.951867i | \(0.400839\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −22.9507 | − | 19.2579i | −2.08642 | − | 1.75072i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.9529 | − | 9.19232i | −1.79909 | − | 0.828844i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.315476 | + | 3.80822i | −0.0277761 | + | 0.335295i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.38799 | + | 1.47903i | 0.732862 | + | 0.129223i | 0.527611 | − | 0.849486i | \(-0.323088\pi\) |
0.205251 | + | 0.978709i | \(0.434199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.27249 | + | 1.51649i | 0.108716 | + | 0.129562i | 0.817658 | − | 0.575704i | \(-0.195272\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.11445 | − | 11.9916i | 0.179345 | − | 1.01712i | −0.753663 | − | 0.657262i | \(-0.771715\pi\) |
0.933008 | − | 0.359856i | \(-0.117174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.00000 | + | 9.89949i | 0.577350 | + | 0.816497i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −24.5693 | + | 0.226755i | −1.98631 | + | 0.0183321i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.0454 | −1.64840 | −0.824202 | − | 0.566296i | \(-0.808376\pi\) | ||||
−0.824202 | + | 0.566296i | \(0.808376\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.25743 | + | 12.8025i | 0.173648 | + | 0.984808i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.67123 | − | 1.50954i | −0.204274 | − | 0.115437i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.8917 | − | 11.2371i | 1.19449 | − | 0.844635i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.0732 | − | 12.7440i | −1.64983 | − | 0.952529i | −0.977138 | − | 0.212607i | \(-0.931805\pi\) |
−0.672692 | − | 0.739923i | \(-0.734862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −40.1536 | + | 33.6929i | −2.93632 | + | 2.46387i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.58197 | − | 14.6431i | 0.185854 | − | 1.05403i | −0.738999 | − | 0.673707i | \(-0.764701\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.29433 | − | 9.32127i | 0.302899 | − | 0.657472i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.44617 | + | 1.13663i | −0.445891 | + | 0.0786226i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1381 | − | 5.14583i | 0.973304 | − | 0.354254i | 0.194071 | − | 0.980988i | \(-0.437831\pi\) |
0.779233 | + | 0.626734i | \(0.215609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.4306 | − | 11.5365i | 0.772406 | − | 0.779567i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | − | 14.1421i | 0.333333 | − | 0.942809i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.33644 | + | 20.1567i | −0.486937 | + | 1.33785i | 0.416503 | + | 0.909134i | \(0.363255\pi\) |
−0.903440 | + | 0.428714i | \(0.858967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.4895 | − | 7.78815i | −0.883725 | − | 0.510219i | −0.0118403 | − | 0.999930i | \(-0.503769\pi\) |
−0.871885 | + | 0.489711i | \(0.837102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2613 | − | 13.6448i | 1.04748 | − | 0.878941i | 0.0546547 | − | 0.998505i | \(-0.482594\pi\) |
0.992826 | + | 0.119564i | \(0.0381497\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1464 | − | 3.68614i | −0.971640 | − | 0.236466i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.7800 | − | 24.2013i | 1.06339 | − | 1.53369i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9806 | − | 13.8452i | 1.51364 | − | 0.873902i | 0.513771 | − | 0.857927i | \(-0.328248\pi\) |
0.999872 | − | 0.0159750i | \(-0.00508522\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.7278 | − | 21.1272i | 1.10583 | − | 1.31788i | 0.162247 | − | 0.986750i | \(-0.448126\pi\) |
0.943585 | − | 0.331130i | \(-0.107430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.6997 | + | 15.5555i | 0.960808 | + | 0.951981i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.9446 | − | 30.0702i | −0.659987 | − | 1.81330i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.1685 | + | 27.9376i | −0.606600 | + | 1.66662i | 0.131002 | + | 0.991382i | \(0.458181\pi\) |
−0.737601 | + | 0.675236i | \(0.764042\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.3143 | − | 21.2412i | −1.50478 | − | 1.26266i | −0.873219 | − | 0.487327i | \(-0.837972\pi\) |
−0.631557 | − | 0.775330i | \(-0.717584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.0391 | + | 43.3690i | 1.47289 | + | 2.55112i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.14152 | + | 25.8511i | −0.125538 | + | 1.51542i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −29.9422 | + | 14.4702i | −1.73742 | + | 0.839646i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4258 | − | 30.1824i | 0.994545 | − | 1.72260i | 0.406942 | − | 0.913454i | \(-0.366595\pi\) |
0.587603 | − | 0.809149i | \(-0.300072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.7387 | − | 7.18430i | −1.11570 | − | 0.406080i | −0.282617 | − | 0.959233i | \(-0.591202\pi\) |
−0.833080 | + | 0.553153i | \(0.813425\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.8987 | + | 5.15748i | −1.05482 | + | 0.287862i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.37647i | 0.466079i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.57072 | − | 8.90799i | −0.0863345 | − | 0.489627i | −0.997061 | − | 0.0766165i | \(-0.975588\pi\) |
0.910726 | − | 0.413011i | \(-0.135523\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.9283 | + | 20.9173i | 1.35793 | + | 1.13944i | 0.976616 | + | 0.214993i | \(0.0689729\pi\) |
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 30.0454 | − | 21.2453i | 1.63184 | − | 1.15389i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.0481 | + | 6.35625i | 1.93516 | + | 0.341222i | 0.999918 | − | 0.0127797i | \(-0.00406802\pi\) |
0.935245 | + | 0.354001i | \(0.115179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.25345 | + | 1.49380i | 0.0667144 | + | 0.0795071i | 0.798369 | − | 0.602168i | \(-0.205696\pi\) |
−0.731655 | + | 0.681675i | \(0.761252\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.97699 | − | 15.5486i | 0.472473 | − | 0.818347i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.7133 | + | 47.1310i | −1.13965 | + | 2.47374i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.26131 | + | 37.5319i | −0.325951 | + | 1.95383i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.8062 | 1.68514 | 0.842570 | − | 0.538587i | \(-0.181042\pi\) | ||||
0.842570 | + | 0.538587i | \(0.181042\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.50720 | − | 1.20942i | 0.330779 | − | 0.0614782i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.35357 | − | 14.6903i | −0.0682787 | − | 0.741029i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.6237 | + | 6.10509i | 1.72902 | + | 0.304874i | 0.947679 | − | 0.319225i | \(-0.103423\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.861982 | − | 4.88854i | 0.0426223 | − | 0.241723i | −0.956052 | − | 0.293197i | \(-0.905281\pi\) |
0.998674 | + | 0.0514740i | \(0.0163919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.95372 | − | 2.81778i | 0.0963697 | − | 0.138991i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.0016 | + | 1.93509i | −1.02845 | + | 0.0947619i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.8376 | + | 26.0250i | −1.06684 | + | 1.27140i | −0.105976 | + | 0.994369i | \(0.533797\pi\) |
−0.960860 | + | 0.277036i | \(0.910648\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −40.3285 | + | 7.11100i | −1.95622 | + | 0.344934i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.2012 | 0.874695 | 0.437347 | − | 0.899293i | \(-0.355918\pi\) | ||||
0.437347 | + | 0.899293i | \(0.355918\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.3495 | − | 16.2108i | 0.635691 | − | 0.771944i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.82211 | − | 15.9961i | 0.276617 | − | 0.759998i | −0.721124 | − | 0.692807i | \(-0.756374\pi\) |
0.997740 | − | 0.0671913i | \(-0.0214038\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.9698 | − | 20.1898i | −1.65033 | − | 0.952816i | −0.976937 | − | 0.213528i | \(-0.931505\pi\) |
−0.673389 | − | 0.739288i | \(-0.735162\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.5873 | + | 70.2992i | 1.91118 | + | 3.31026i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.82334 | + | 8.24276i | −0.459516 | + | 0.385580i | −0.842953 | − | 0.537987i | \(-0.819185\pi\) |
0.383437 | + | 0.923567i | \(0.374740\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.5826 | + | 40.9506i | 0.540629 | + | 1.91141i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.2054 | + | 19.7485i | −1.58284 | + | 0.913851i | −0.588393 | + | 0.808575i | \(0.700239\pi\) |
−0.994443 | + | 0.105276i | \(0.966427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.07600 | − | 10.8164i | 0.417315 | − | 0.497336i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.80536 | − | 1.74901i | −0.220485 | − | 0.0802500i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.59677 | + | 35.1657i | 0.433981 | + | 1.59025i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9388 | − | 35.5491i | −0.583921 | − | 1.60431i | −0.781419 | − | 0.624006i | \(-0.785504\pi\) |
0.197499 | − | 0.980303i | \(-0.436718\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.6754 | + | 10.6359i | 0.567428 | + | 0.476129i | 0.880791 | − | 0.473504i | \(-0.157011\pi\) |
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.3629 | − | 9.61002i | 0.904348 | − | 0.426796i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.30427 | + | 5.15184i | −0.0575849 | + | 0.227459i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.6827 | − | 15.4052i | 1.16899 | − | 0.674916i | 0.215547 | − | 0.976493i | \(-0.430847\pi\) |
0.953442 | + | 0.301577i | \(0.0975132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.52270 | − | 2.63740i | 0.0665832 | − | 0.115325i | −0.830812 | − | 0.556553i | \(-0.812124\pi\) |
0.897395 | + | 0.441228i | \(0.145457\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6129 | + | 7.86646i | 0.939693 | + | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.0233 | − | 21.4300i | −1.12932 | − | 0.929984i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.2290 | + | 42.6944i | −0.484569 | + | 1.84240i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 44.8000i | − | 1.92967i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.17190 | + | 29.3313i | 0.221135 | + | 1.25412i | 0.869938 | + | 0.493161i | \(0.164159\pi\) |
−0.648803 | + | 0.760956i | \(0.724730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 74.6091 | + | 51.7304i | 3.15000 | + | 2.18406i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.8074 | + | 4.02156i | 0.961218 | + | 0.169489i | 0.632175 | − | 0.774826i | \(-0.282163\pi\) |
0.329044 | + | 0.944315i | \(0.393274\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.43393 | + | 5.28415i | 0.185880 | + | 0.221523i | 0.850935 | − | 0.525271i | \(-0.176036\pi\) |
−0.665055 | + | 0.746795i | \(0.731592\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.66208 | − | 43.4538i | 0.320648 | − | 1.81848i | −0.217994 | − | 0.975950i | \(-0.569951\pi\) |
0.538642 | − | 0.842535i | \(-0.318938\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.6648 | − | 34.0604i | 0.818655 | − | 1.41795i | −0.0880190 | − | 0.996119i | \(-0.528054\pi\) |
0.906674 | − | 0.421833i | \(-0.138613\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.6452 | + | 2.36296i | −1.06578 | + | 0.0982011i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.40364 | + | 0.423827i | −0.0992090 | + | 0.0174932i | −0.223032 | − | 0.974811i | \(-0.571596\pi\) |
0.123823 | + | 0.992304i | \(0.460484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 38.2159i | − | 1.56934i | −0.619915 | − | 0.784669i | \(-0.712833\pi\) | ||
0.619915 | − | 0.784669i | \(-0.287167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.51507 | + | 8.59237i | 0.0618009 | + | 0.350490i | 0.999990 | + | 0.00436841i | \(0.00139051\pi\) |
−0.938190 | + | 0.346122i | \(0.887498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.5336 | − | 2.92506i | −0.714022 | − | 0.119118i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.8670 | − | 6.32433i | −1.44395 | − | 0.254608i | −0.603877 | − | 0.797077i | \(-0.706378\pi\) |
−0.840076 | + | 0.542469i | \(0.817489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.8318 | − | 25.0319i | 1.19904 | − | 1.00612i | 0.199386 | − | 0.979921i | \(-0.436105\pi\) |
0.999657 | − | 0.0261952i | \(-0.00833914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.34120 | − | 24.6202i | 0.173648 | − | 0.984808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.83873 | + | 10.2529i | 0.193240 | + | 0.409461i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.0454 | − | 21.2774i | −0.598001 | − | 0.845702i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.3213 | − | 7.10974i | 1.59260 | − | 0.280818i | 0.694127 | − | 0.719852i | \(-0.255791\pi\) |
0.898470 | + | 0.439034i | \(0.144679\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.306376 | − | 0.111512i | 0.0120823 | − | 0.00439759i | −0.335972 | − | 0.941872i | \(-0.609065\pi\) |
0.348054 | + | 0.937474i | \(0.386843\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −71.9177 | −2.82302 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.4893 | − | 13.8392i | −0.955419 | − | 0.539917i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.89116 | + | 7.94338i | −0.112623 | + | 0.309430i | −0.983180 | − | 0.182637i | \(-0.941537\pi\) |
0.870557 | + | 0.492068i | \(0.163759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.9453 | + | 25.1271i | −1.15431 | + | 0.968578i | −0.999812 | − | 0.0194154i | \(-0.993820\pi\) |
−0.154495 | + | 0.987994i | \(0.549375\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9108 | − | 1.90587i | −0.997306 | − | 0.0733571i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.0262 | + | 3.06728i | 1.41885 | + | 0.117538i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.1416 | + | 17.9796i | −1.19160 | + | 0.687971i | −0.958670 | − | 0.284522i | \(-0.908165\pi\) |
−0.232932 | + | 0.972493i | \(0.574832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.3288 | + | 15.4064i | 1.61026 | + | 0.586088i | 0.981492 | − | 0.191501i | \(-0.0613355\pi\) |
0.628772 | + | 0.777589i | \(0.283558\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 97.6150 | − | 35.5290i | 3.69743 | − | 1.34576i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.86234 | + | 26.0916i | −0.259558 | + | 0.986876i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.2150 | − | 20.9496i | −1.12371 | − | 0.779125i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.747449 | + | 26.9897i | 0.0276833 | + | 0.999617i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6146 | − | 13.8418i | −0.429582 | − | 0.511956i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.8413 | + | 18.9609i | −1.20973 | + | 0.698435i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.9389 | − | 31.0711i | 0.659893 | − | 1.14297i | −0.320749 | − | 0.947164i | \(-0.603935\pi\) |
0.980643 | − | 0.195805i | \(-0.0627319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −48.0908 | − | 17.0027i | −1.75955 | − | 0.622095i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −34.0699 | − | 33.7569i | −1.24157 | − | 1.23017i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.86952 | − | 10.6314i | −0.140270 | − | 0.385388i | 0.849589 | − | 0.527446i | \(-0.176850\pi\) |
−0.989858 | + | 0.142058i | \(0.954628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.3490 | − | 21.2704i | −0.914110 | − | 0.767029i | 0.0587868 | − | 0.998271i | \(-0.481277\pi\) |
−0.972896 | + | 0.231242i | \(0.925721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.3864 | − | 19.9882i | −1.56252 | − | 0.719857i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.7750 | + | 2.25258i | 0.457713 | + | 0.0807071i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.513060 | − | 2.90971i | 0.0182886 | − | 0.103720i | −0.974297 | − | 0.225267i | \(-0.927675\pi\) |
0.992586 | + | 0.121547i | \(0.0387856\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.8333 | − | 33.3268i | 0.665441 | − | 1.17754i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −59.0971 | + | 10.4204i | −2.08549 | + | 0.367729i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 47.1907i | − | 1.65914i | −0.558404 | − | 0.829569i | \(-0.688586\pi\) | ||
0.558404 | − | 0.829569i | \(-0.311414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.3805 | −1.69887 | −0.849434 | − | 0.527694i | \(-0.823057\pi\) | ||||
−0.849434 | + | 0.527694i | \(0.823057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.391821 | − | 2.22213i | −0.0137081 | − | 0.0777424i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −45.2548 | + | 32.0000i | −1.57557 | + | 1.11410i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.1464 | + | 9.89949i | 0.596240 | + | 0.344239i | 0.767561 | − | 0.640976i | \(-0.221470\pi\) |
−0.171321 | + | 0.985215i | \(0.554804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −56.4599 | − | 9.95540i | −1.95622 | − | 0.344934i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03580 | + | 28.5594i | −0.173648 | + | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 51.3191 | + | 4.25131i | 1.76752 | + | 0.146423i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.9495 | + | 51.9848i | −0.821944 | + | 1.78411i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.2837 | − | 3.92921i | 0.761195 | − | 0.134219i | 0.220441 | − | 0.975400i | \(-0.429250\pi\) |
0.540754 | + | 0.841181i | \(0.318139\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.3166 | + | 6.30274i | −0.590836 | + | 0.215047i | −0.620097 | − | 0.784525i | \(-0.712907\pi\) |
0.0292613 | + | 0.999572i | \(0.490684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 61.0493 | − | 61.6154i | 2.07334 | − | 2.09257i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 44.1723 | − | 8.20981i | 1.49501 | − | 0.277860i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.9949 | − | 6.34791i | −0.370428 | − | 0.213866i | 0.303218 | − | 0.952921i | \(-0.401939\pi\) |
−0.673645 | + | 0.739055i | \(0.735272\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8559 | + | 34.3914i | 0.668203 | + | 1.15736i | 0.978406 | + | 0.206691i | \(0.0662696\pi\) |
−0.310203 | + | 0.950670i | \(0.600397\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.8326 | + | 43.4333i | 1.26744 | + | 1.45507i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −56.5987 | − | 20.6002i | −1.87933 | − | 0.684020i | −0.942311 | − | 0.334738i | \(-0.891352\pi\) |
−0.937018 | − | 0.349281i | \(-0.886426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −102.255 | + | 37.2176i | −3.38413 | + | 1.23172i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −58.3795 | − | 15.3544i | −1.92367 | − | 0.505943i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.67379 | − | 26.5785i | 0.317387 | − | 0.872013i | −0.673725 | − | 0.738982i | \(-0.735307\pi\) |
0.991112 | − | 0.133031i | \(-0.0424710\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.48431 | − | 4.60189i | −0.179741 | − | 0.150821i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5454 | + | 23.4613i | 0.442509 | + | 0.766448i | 0.997875 | − | 0.0651578i | \(-0.0207551\pi\) |
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.00367 | + | 36.2583i | −0.0980210 | + | 1.18325i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.8571 | − | 46.3081i | −1.26269 | − | 1.50481i | −0.775252 | − | 0.631652i | \(-0.782377\pi\) |
−0.487435 | − | 0.873160i | \(-0.662067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.6261 | − | 24.6102i | 1.38079 | − | 0.797202i | 0.388540 | − | 0.921432i | \(-0.372979\pi\) |
0.992253 | + | 0.124230i | \(0.0396461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1305 | − | 10.6026i | −0.939693 | − | 0.342020i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.2357 | + | 29.2269i | 0.555414 | + | 0.941823i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.9966 | − | 3.81970i | 0.449636 | − | 0.122706i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.1127i | 0.998454i | 0.866471 | + | 0.499227i | \(0.166383\pi\) | ||||
−0.866471 | + | 0.499227i | \(0.833617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.7007 | + | 56.8748i | 0.662275 | + | 1.81959i | 0.566296 | + | 0.824202i | \(0.308376\pi\) |
0.0959785 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1808 | − | 80.4235i | −0.453221 | − | 2.57035i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.1685 | + | 6.68666i | −0.449624 | + | 0.212195i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.bh.a.815.2 | 12 | ||
4.3 | odd | 2 | 216.2.v.a.59.2 | yes | 12 | ||
8.3 | odd | 2 | CM | 864.2.bh.a.815.2 | 12 | ||
8.5 | even | 2 | 216.2.v.a.59.2 | yes | 12 | ||
12.11 | even | 2 | 648.2.v.a.611.1 | 12 | |||
24.5 | odd | 2 | 648.2.v.a.611.1 | 12 | |||
27.11 | odd | 18 | inner | 864.2.bh.a.335.2 | 12 | ||
108.11 | even | 18 | 216.2.v.a.11.2 | ✓ | 12 | ||
108.43 | odd | 18 | 648.2.v.a.35.1 | 12 | |||
216.11 | even | 18 | inner | 864.2.bh.a.335.2 | 12 | ||
216.173 | odd | 18 | 216.2.v.a.11.2 | ✓ | 12 | ||
216.205 | even | 18 | 648.2.v.a.35.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.v.a.11.2 | ✓ | 12 | 108.11 | even | 18 | ||
216.2.v.a.11.2 | ✓ | 12 | 216.173 | odd | 18 | ||
216.2.v.a.59.2 | yes | 12 | 4.3 | odd | 2 | ||
216.2.v.a.59.2 | yes | 12 | 8.5 | even | 2 | ||
648.2.v.a.35.1 | 12 | 108.43 | odd | 18 | |||
648.2.v.a.35.1 | 12 | 216.205 | even | 18 | |||
648.2.v.a.611.1 | 12 | 12.11 | even | 2 | |||
648.2.v.a.611.1 | 12 | 24.5 | odd | 2 | |||
864.2.bh.a.335.2 | 12 | 27.11 | odd | 18 | inner | ||
864.2.bh.a.335.2 | 12 | 216.11 | even | 18 | inner | ||
864.2.bh.a.815.2 | 12 | 1.1 | even | 1 | trivial | ||
864.2.bh.a.815.2 | 12 | 8.3 | odd | 2 | CM |