Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(35,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.v (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: | \(5.17430605098\) |
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 | 35.1 | ||
Root | \(0.483690 - 1.32893i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.35 |
Dual form | 648.2.v.a.611.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.909039 | + | 1.08335i | −0.642788 | + | 0.766044i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.347296 | − | 1.96962i | −0.173648 | − | 0.984808i | ||||
\(5\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(8\) | 2.44949 | + | 1.41421i | 0.866025 | + | 0.500000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.18893 | − | 6.01403i | −0.659987 | − | 1.81330i | −0.576994 | − | 0.816748i | \(-0.695774\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.75877 | + | 1.36808i | −0.939693 | + | 0.342020i | ||||
\(17\) | −7.09286 | + | 4.09506i | −1.72027 | + | 0.993199i | −0.801920 | + | 0.597431i | \(0.796188\pi\) |
−0.918351 | + | 0.395768i | \(0.870479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.511376 | + | 0.885729i | −0.117318 | + | 0.203200i | −0.918704 | − | 0.394947i | \(-0.870763\pi\) |
0.801386 | + | 0.598147i | \(0.204096\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.50512 | + | 3.09561i | 1.81330 | + | 0.659987i | ||||
\(23\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.83022 | − | 3.21394i | −0.766044 | − | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(32\) | 1.93476 | − | 5.31570i | 0.342020 | − | 0.939693i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.01130 | − | 11.4066i | 0.344934 | − | 1.95622i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | −0.494694 | − | 1.35916i | −0.0802500 | − | 0.220485i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.15282 | − | 9.71615i | −1.27326 | − | 1.51741i | −0.742424 | − | 0.669930i | \(-0.766324\pi\) |
−0.530831 | − | 0.847477i | \(-0.678120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.07316 | − | 0.754568i | 0.316154 | − | 0.115071i | −0.179069 | − | 0.983836i | \(-0.557309\pi\) |
0.495223 | + | 0.868766i | \(0.335086\pi\) | |||||||
\(44\) | −11.0851 | + | 6.40000i | −1.67114 | + | 0.964836i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.57785 | − | 2.39414i | −0.939693 | − | 0.342020i | ||||
\(50\) | 6.96364 | − | 1.22788i | 0.984808 | − | 0.173648i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.84333 | − | 10.5595i | 0.500359 | − | 1.37472i | −0.390567 | − | 0.920575i | \(-0.627721\pi\) |
0.890925 | − | 0.454150i | \(-0.150057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.00000 | + | 6.92820i | 0.500000 | + | 0.866025i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.53904 | + | 3.80871i | −0.554532 | + | 0.465308i | −0.876472 | − | 0.481452i | \(-0.840109\pi\) |
0.321940 | + | 0.946760i | \(0.395665\pi\) | |||||||
\(68\) | 10.5290 | + | 12.5480i | 1.27683 | + | 1.52167i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.68819 | − | 8.12018i | 0.548711 | − | 0.950395i | −0.449652 | − | 0.893204i | \(-0.648452\pi\) |
0.998363 | − | 0.0571917i | \(-0.0182146\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.92214 | + | 0.699604i | 0.220485 | + | 0.0802500i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 17.9372 | 1.98083 | ||||||||
\(83\) | 10.9291 | − | 13.0248i | 1.19963 | − | 1.42966i | 0.324415 | − | 0.945915i | \(-0.394833\pi\) |
0.875210 | − | 0.483743i | \(-0.160723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.06712 | + | 2.93189i | −0.115071 | + | 0.316154i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.14337 | − | 17.8269i | 0.335084 | − | 1.90036i | ||||
\(89\) | 11.0505 | + | 6.38002i | 1.17135 | + | 0.676280i | 0.953998 | − | 0.299813i | \(-0.0969242\pi\) |
0.217354 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(90\) | 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 | −0.936617 | − | 0.350354i | \(-0.886061\pi\) |
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(98\) | 8.57321 | − | 4.94975i | 0.866025 | − | 0.500000i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | + | 8.66025i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3102i | 1.09340i | 0.837330 | + | 0.546698i | \(0.184115\pi\) | ||||
−0.837330 | + | 0.546698i | \(0.815885\pi\) | |||||||
\(108\) | 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 | −0.306510 | + | 0.951867i | \(0.599161\pi\) |
−0.377048 | + | 0.926194i | \(0.623061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.94586 | + | 13.7626i | 0.731475 | + | 1.26695i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −22.9507 | + | 19.2579i | −2.08642 | + | 1.75072i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | −11.1418 | − | 1.96460i | −0.984808 | − | 0.173648i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.38799 | − | 1.47903i | 0.732862 | − | 0.129223i | 0.205251 | − | 0.978709i | \(-0.434199\pi\) |
0.527611 | + | 0.849486i | \(0.323088\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 8.37963i | − | 0.723890i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −23.1652 | −1.98640 | ||||||||
\(137\) | −1.27249 | + | 1.51649i | −0.108716 | + | 0.129562i | −0.817658 | − | 0.575704i | \(-0.804728\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.11445 | − | 11.9916i | −0.179345 | − | 1.01712i | −0.933008 | − | 0.359856i | \(-0.882826\pi\) |
0.753663 | − | 0.657262i | \(-0.228285\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.53526 | + | 12.4605i | 0.375340 | + | 1.03124i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(152\) | −2.50522 | + | 1.44639i | −0.203200 | + | 0.117318i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0454 | 1.64840 | 0.824202 | − | 0.566296i | \(-0.191624\pi\) | ||||
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(164\) | −16.3056 | + | 19.4323i | −1.27326 | + | 1.51741i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.17544 | + | 23.6801i | 0.324077 | + | 1.83793i | ||||
\(167\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.25743 | − | 12.8025i | 0.173648 | − | 0.984808i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.20621 | − | 3.82127i | −0.168222 | − | 0.291369i | ||||
\(173\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.4554 | + | 19.6107i | 1.24037 | + | 1.47821i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.9571 | + | 6.17189i | −1.27099 | + | 0.462603i | ||||
\(179\) | −22.0732 | + | 12.7440i | −1.64983 | + | 0.952529i | −0.672692 | + | 0.739923i | \(0.734862\pi\) |
−0.977138 | + | 0.212607i | \(0.931805\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(182\) | 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 | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.58197 | + | 14.6431i | 0.185854 | + | 1.05403i | 0.924853 | + | 0.380325i | \(0.124188\pi\) |
−0.738999 | + | 0.673707i | \(0.764701\pi\) | |||||||
\(194\) | 7.24386 | − | 19.9023i | 0.520079 | − | 1.42890i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.43107 | + | 13.7873i | −0.173648 | + | 0.984808i | ||||
\(197\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | −4.83690 | − | 13.2893i | −0.342020 | − | 0.939693i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | \(-0.562169\pi\) |
−0.779233 | + | 0.626734i | \(0.784391\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.2529 | − | 10.2814i | −0.837590 | − | 0.702822i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.0227 | − | 26.0201i | −0.999295 | − | 1.73083i | ||||
\(227\) | −7.33644 | − | 20.1567i | −0.486937 | − | 1.33785i | −0.903440 | − | 0.428714i | \(-0.858967\pi\) |
0.416503 | − | 0.909134i | \(-0.363255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.4895 | − | 7.78815i | 0.883725 | − | 0.510219i | 0.0118403 | − | 0.999930i | \(-0.496231\pi\) |
0.871885 | + | 0.489711i | \(0.162898\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −22.1328 | − | 3.90262i | −1.44073 | − | 0.254039i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2613 | + | 13.6448i | 1.04748 | + | 0.878941i | 0.992826 | − | 0.119564i | \(-0.0381497\pi\) |
0.0546547 | + | 0.998505i | \(0.482594\pi\) | |||||||
\(242\) | − | 42.3698i | − | 2.72363i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9806 | + | 13.8452i | 1.51364 | + | 0.873902i | 0.999872 | + | 0.0159750i | \(0.00508522\pi\) |
0.513771 | + | 0.857927i | \(0.328248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.2567 | − | 10.2846i | 0.766044 | − | 0.642788i | ||||
\(257\) | −17.7278 | − | 21.1272i | −1.10583 | − | 1.31788i | −0.943585 | − | 0.331130i | \(-0.892570\pi\) |
−0.162247 | − | 0.986750i | \(-0.551874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.02270 | + | 10.4316i | −0.372084 | + | 0.644468i | ||||
\(263\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.07808 | + | 7.61741i | 0.554532 | + | 0.465308i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 21.0580 | − | 25.0960i | 1.27683 | − | 1.52167i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.486151 | − | 2.75710i | −0.0293694 | − | 0.166562i | ||||
\(275\) | −10.9446 | + | 30.0702i | −0.659987 | + | 1.81330i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(278\) | 14.9133 | + | 8.61018i | 0.894438 | + | 0.516404i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1685 | + | 27.9376i | 0.606600 | + | 1.66662i | 0.737601 | + | 0.675236i | \(0.235958\pi\) |
−0.131002 | + | 0.991382i | \(0.541819\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.3143 | − | 21.2412i | 1.50478 | − | 1.26266i | 0.631557 | − | 0.775330i | \(-0.282416\pi\) |
0.873219 | − | 0.487327i | \(-0.162028\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17.6218 | − | 6.41382i | −1.03124 | − | 0.375340i | ||||
\(293\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.710396 | − | 4.02886i | 0.0407440 | − | 0.231071i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.4258 | − | 30.1824i | −0.994545 | − | 1.72260i | −0.587603 | − | 0.809149i | \(-0.699928\pi\) |
−0.406942 | − | 0.913454i | \(-0.633405\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.7387 | + | 7.18430i | −1.11570 | + | 0.406080i | −0.833080 | − | 0.553153i | \(-0.813425\pi\) |
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.37647i | − | 0.466079i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.1311 | + | 22.7996i | −1.05957 | + | 1.26275i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.22953 | − | 35.3294i | −0.343968 | − | 1.95074i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.57072 | − | 8.90799i | 0.0863345 | − | 0.489627i | −0.910726 | − | 0.413011i | \(-0.864477\pi\) |
0.997061 | − | 0.0766165i | \(-0.0244117\pi\) | |||||||
\(332\) | −29.4495 | − | 17.0027i | −1.61625 | − | 0.933143i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.9283 | − | 20.9173i | 1.35793 | − | 1.13944i | 0.381314 | − | 0.924445i | \(-0.375472\pi\) |
0.976616 | − | 0.214993i | \(-0.0689729\pi\) | |||||||
\(338\) | 11.8175 | + | 14.0836i | 0.642788 | + | 0.766044i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.14530 | + | 1.08358i | 0.331333 | + | 0.0584229i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.0481 | − | 6.35625i | 1.93516 | − | 0.341222i | 0.935245 | − | 0.354001i | \(-0.115179\pi\) |
0.999918 | + | 0.0127797i | \(0.00406802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −36.2039 | −1.92967 | ||||||||
\(353\) | −1.25345 | + | 1.49380i | −0.0667144 | + | 0.0795071i | −0.798369 | − | 0.602168i | \(-0.794304\pi\) |
0.731655 | + | 0.681675i | \(0.238748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.72837 | − | 23.9810i | 0.462603 | − | 1.27099i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.25922 | − | 35.4978i | 0.330810 | − | 1.87612i | ||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.97699 | + | 15.5486i | 0.472473 | + | 0.818347i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(374\) | −73.0024 | + | 12.8723i | −3.77486 | + | 0.665610i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.8062 | −1.68514 | −0.842570 | − | 0.538587i | \(-0.818958\pi\) | ||||
−0.842570 | + | 0.538587i | \(0.818958\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.2107 | − | 10.5139i | −0.926900 | − | 0.535146i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.9763 | + | 25.9396i | 0.760304 | + | 1.31689i | ||||
\(389\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −12.7265 | − | 15.1669i | −0.642788 | − | 0.766044i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.7939 | + | 6.84040i | 0.939693 | + | 0.342020i | ||||
\(401\) | −34.6237 | + | 6.10509i | −1.72902 | + | 0.304874i | −0.947679 | − | 0.319225i | \(-0.896577\pi\) |
−0.781345 | + | 0.624099i | \(0.785466\pi\) | |||||||
\(402\) | 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 | 0.998674 | − | 0.0514740i | \(-0.0163919\pi\) |
−0.956052 | + | 0.293197i | \(0.905281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.09119 | + | 5.95021i | −0.346841 | + | 0.291034i | ||||
\(419\) | −21.8376 | − | 26.0250i | −1.06684 | − | 1.27140i | −0.960860 | − | 0.277036i | \(-0.910648\pi\) |
−0.105976 | − | 0.994369i | \(-0.533797\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(422\) | 18.4268 | − | 10.6387i | 0.897002 | − | 0.517884i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 40.3285 | + | 7.11100i | 1.95622 | + | 0.344934i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 22.2767 | − | 3.92798i | 1.07679 | − | 0.189866i | ||||
\(429\) | 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 | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.82211 | + | 15.9961i | 0.276617 | + | 0.759998i | 0.997740 | + | 0.0671913i | \(0.0214038\pi\) |
−0.721124 | + | 0.692807i | \(0.756374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.9698 | − | 20.1898i | 1.65033 | − | 0.952816i | 0.673389 | − | 0.739288i | \(-0.264838\pi\) |
0.976937 | − | 0.213528i | \(-0.0684954\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.5873 | + | 70.2992i | −1.91118 | + | 3.31026i | ||||
\(452\) | 41.8451 | + | 7.37842i | 1.96823 | + | 0.347052i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 28.5059 | + | 10.3753i | 1.33785 | + | 0.486937i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.82334 | − | 8.24276i | −0.459516 | − | 0.385580i | 0.383437 | − | 0.923567i | \(-0.374740\pi\) |
−0.842953 | + | 0.537987i | \(0.819185\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.82516 | + | 21.6936i | −0.177197 | + | 1.00494i | ||||
\(467\) | −34.2054 | − | 19.7485i | −1.58284 | − | 0.913851i | −0.994443 | − | 0.105276i | \(-0.966427\pi\) |
−0.588393 | − | 0.808575i | \(-0.700239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 24.3475 | − | 20.4300i | 1.12069 | − | 0.940367i | ||||
\(473\) | −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 | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −29.5643 | + | 5.21298i | −1.34662 | + | 0.237445i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 45.9013 | + | 38.5158i | 2.08642 | + | 1.75072i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9388 | + | 35.5491i | −0.583921 | + | 1.60431i | 0.197499 | + | 0.980303i | \(0.436718\pi\) |
−0.781419 | + | 0.624006i | \(0.785504\pi\) | |||||||
\(492\) | 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 | \(-0.842989\pi\) |
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −36.7985 | + | 13.3936i | −1.64240 | + | 0.597784i | ||||
\(503\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 39.0035 | 1.72037 | ||||||||
\(515\) | 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 | \(-0.569153\pi\) |
−0.953442 | + | 0.301577i | \(0.902487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.52270 | − | 2.63740i | −0.0665832 | − | 0.115325i | 0.830812 | − | 0.556553i | \(-0.187876\pi\) |
−0.897395 | + | 0.441228i | \(0.854543\pi\) | |||||||
\(524\) | −5.82624 | − | 16.0075i | −0.254520 | − | 0.699289i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6129 | − | 7.86646i | 0.939693 | − | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −16.5047 | + | 2.91022i | −0.712893 | + | 0.125702i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(544\) | 8.04518 | + | 45.6265i | 0.344934 | + | 1.95622i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.17190 | + | 29.3313i | −0.221135 | + | 1.25412i | 0.648803 | + | 0.760956i | \(0.275270\pi\) |
−0.869938 | + | 0.493161i | \(0.835841\pi\) | |||||||
\(548\) | 3.42883 | + | 1.97964i | 0.146472 | + | 0.0845659i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.6274 | − | 39.1918i | −0.964836 | − | 1.67114i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.8846 | + | 8.32931i | −0.970522 | + | 0.353241i | ||||
\(557\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −39.5098 | − | 14.3804i | −1.66662 | − | 0.606600i | ||||
\(563\) | 22.8074 | − | 4.02156i | 0.961218 | − | 0.169489i | 0.329044 | − | 0.944315i | \(-0.393274\pi\) |
0.632175 | + | 0.774826i | \(0.282163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 46.7333i | 1.96435i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.43393 | + | 5.28415i | −0.185880 | + | 0.221523i | −0.850935 | − | 0.525271i | \(-0.823964\pi\) |
0.665055 | + | 0.746795i | \(0.268408\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.66208 | − | 43.4538i | −0.320648 | − | 1.81848i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
0.217994 | − | 0.975950i | \(-0.430049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.6648 | + | 34.0604i | 0.818655 | + | 1.41795i | 0.906674 | + | 0.421833i | \(0.138613\pi\) |
−0.0880190 | + | 0.996119i | \(0.528054\pi\) | |||||||
\(578\) | 24.2223 | + | 66.5502i | 1.00751 | + | 2.76812i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 22.9673 | − | 13.2602i | 0.950395 | − | 0.548711i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.40364 | − | 0.423827i | −0.0992090 | − | 0.0174932i | 0.123823 | − | 0.992304i | \(-0.460484\pi\) |
−0.223032 | + | 0.974811i | \(0.571596\pi\) | |||||||
\(588\) | 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 | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.51507 | − | 8.59237i | 0.0618009 | − | 0.350490i | −0.938190 | − | 0.346122i | \(-0.887498\pi\) |
0.999990 | − | 0.00436841i | \(-0.00139051\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(608\) | 3.71889 | + | 4.43199i | 0.150821 | + | 0.179741i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 48.5389 | + | 8.55872i | 1.95887 | + | 0.345402i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.8670 | − | 6.32433i | 1.44395 | − | 0.254608i | 0.603877 | − | 0.797077i | \(-0.293622\pi\) |
0.840076 | + | 0.542469i | \(0.182511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.8318 | − | 25.0319i | −1.19904 | − | 1.00612i | −0.999657 | − | 0.0261952i | \(-0.991661\pi\) |
−0.199386 | − | 0.979921i | \(-0.563895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.34120 | + | 24.6202i | 0.173648 | + | 0.984808i | ||||
\(626\) | 10.1601 | − | 27.9147i | 0.406080 | − | 1.11570i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | \(-0.744209\pi\) |
−0.898470 | + | 0.439034i | \(0.855321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.306376 | − | 0.111512i | −0.0120823 | − | 0.00439759i | 0.335972 | − | 0.941872i | \(-0.390935\pi\) |
−0.348054 | + | 0.937474i | \(0.613157\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.07465 | + | 7.61454i | 0.357037 | + | 0.299590i | ||||
\(647\) | 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 | ||||||||
\(652\) | −7.30899 | − | 41.4514i | −0.286242 | − | 1.62336i | ||||
\(653\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 43.9370 | + | 25.3671i | 1.71545 | + | 0.990417i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.89116 | − | 7.94338i | −0.112623 | − | 0.309430i | 0.870557 | − | 0.492068i | \(-0.163759\pi\) |
−0.983180 | + | 0.182637i | \(0.941537\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(662\) | 8.22263 | + | 9.79935i | 0.319582 | + | 0.380862i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45.1906 | − | 16.4480i | 1.75373 | − | 0.638307i | ||||
\(665\) | 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 | −0.154495 | − | 0.987994i | \(-0.549375\pi\) |
−0.999812 | + | 0.0194154i | \(0.993820\pi\) | |||||||
\(674\) | 46.0207i | 1.77265i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.0000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.1416 | − | 17.9796i | −1.19160 | − | 0.687971i | −0.232932 | − | 0.972493i | \(-0.574832\pi\) |
−0.958670 | + | 0.284522i | \(0.908165\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.76022 | + | 5.67250i | −0.257731 | + | 0.216262i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.3288 | + | 15.4064i | −1.61026 | + | 0.586088i | −0.981492 | − | 0.191501i | \(-0.938665\pi\) |
−0.628772 | + | 0.777589i | \(0.716442\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.8831 | + | 44.8308i | −0.982508 | + | 1.70175i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 97.6150 | + | 35.5290i | 3.69743 | + | 1.34576i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 32.9107 | − | 39.2215i | 1.24037 | − | 1.47821i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.478878 | − | 2.71585i | −0.0180228 | − | 0.102212i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.0454 | + | 31.2556i | 0.676280 | + | 1.17135i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.7667 | + | 39.0498i | 1.22455 | + | 1.45936i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.0050 | − | 4.40906i | −0.930590 | − | 0.164088i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6146 | + | 13.8418i | −0.429582 | + | 0.511956i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(734\) | 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 | −0.980643 | − | 0.195805i | \(-0.937268\pi\) |
0.320749 | − | 0.947164i | \(-0.396065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 52.4168 | − | 90.7886i | 1.91655 | − | 3.31956i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 29.8221 | − | 35.5406i | 1.08319 | − | 1.29089i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.86952 | − | 10.6314i | 0.140270 | − | 0.385388i | −0.849589 | − | 0.527446i | \(-0.823150\pi\) |
0.989858 | + | 0.142058i | \(0.0453719\pi\) | |||||||
\(762\) | 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 | −0.972896 | − | 0.231242i | \(-0.925721\pi\) |
0.0587868 | + | 0.998271i | \(0.481277\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27.9445 | − | 10.1710i | 1.00574 | − | 0.366061i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −41.7157 | − | 7.35561i | −1.49751 | − | 0.264051i | ||||
\(777\) | 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 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.513060 | − | 2.90971i | −0.0182886 | − | 0.103720i | 0.974297 | − | 0.225267i | \(-0.0723255\pi\) |
−0.992586 | + | 0.121547i | \(0.961214\pi\) | |||||||
\(788\) | 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 | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −24.4949 | + | 14.1421i | −0.866025 | + | 0.500000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.8603 | − | 43.0593i | 0.877849 | − | 1.52048i | ||||
\(803\) | −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 | \(-0.176943\pi\) | ||||
0.849434 | + | 0.527694i | \(0.176943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.391821 | + | 2.22213i | −0.0137081 | + | 0.0777424i | ||||
\(818\) | −6.07958 | − | 3.51005i | −0.212568 | − | 0.122726i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.1464 | − | 9.89949i | 0.596240 | − | 0.344239i | −0.171321 | − | 0.985215i | \(-0.554804\pi\) |
0.767561 | + | 0.640976i | \(0.221470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 56.4599 | − | 9.95540i | 1.95622 | − | 0.344934i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 13.0912i | − | 0.452769i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 48.0454 | 1.65970 | ||||||||
\(839\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03580 | − | 28.5594i | −0.173648 | − | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.22522 | + | 29.6337i | −0.179859 | + | 1.02003i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −44.3639 | + | 37.2257i | −1.52167 | + | 1.27683i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.9950 | + | 27.7042i | −0.546698 | + | 0.946909i | ||||
\(857\) | −22.2837 | − | 3.92921i | −0.761195 | − | 0.134219i | −0.220441 | − | 0.975400i | \(-0.570750\pi\) |
−0.540754 | + | 0.841181i | \(0.681861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3166 | + | 6.30274i | 0.590836 | + | 0.215047i | 0.620097 | − | 0.784525i | \(-0.287093\pi\) |
−0.0292613 | + | 0.999572i | \(0.509316\pi\) | |||||||
\(860\) | 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 | ||||||||
\(866\) | −16.5456 | + | 19.7183i | −0.562243 | + | 0.670055i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.9949 | − | 6.34791i | 0.370428 | − | 0.213866i | −0.303218 | − | 0.952921i | \(-0.598061\pi\) |
0.673645 | + | 0.739055i | \(0.264728\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.8559 | + | 34.3914i | −0.668203 | + | 1.15736i | 0.310203 | + | 0.950670i | \(0.399603\pi\) |
−0.978406 | + | 0.206691i | \(0.933730\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.6219 | − | 8.23370i | −0.759998 | − | 0.276617i | ||||
\(887\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.91625 | + | 56.2379i | −0.330910 | + | 1.87668i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −39.2633 | − | 107.875i | −1.30732 | − | 3.59184i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −46.0322 | + | 38.6256i | −1.53101 | + | 1.28467i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.5987 | − | 20.6002i | 1.87933 | − | 0.684020i | 0.937018 | − | 0.349281i | \(-0.113574\pi\) |
0.942311 | − | 0.334738i | \(-0.108648\pi\) | |||||||
\(908\) | −37.1531 | + | 21.4503i | −1.23297 | + | 0.711854i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −102.255 | − | 37.2176i | −3.38413 | − | 1.23172i | ||||
\(914\) | 17.8596 | − | 3.14913i | 0.590743 | − | 0.104164i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | −0.991112 | − | 0.133031i | \(-0.957529\pi\) |
0.673725 | − | 0.738982i | \(-0.264693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.48431 | − | 4.60189i | 0.179741 | − | 0.150821i | ||||
\(932\) | −20.0245 | − | 23.8643i | −0.655925 | − | 0.781701i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 52.4886 | − | 19.1043i | 1.71748 | − | 0.625111i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5454 | − | 23.4613i | 0.442509 | − | 0.766448i | −0.555366 | − | 0.831606i | \(-0.687422\pi\) |
0.997875 | + | 0.0651578i | \(0.0207551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 44.9486i | 1.46295i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.9683 | 0.649226 | ||||||||
\(947\) | −38.8571 | + | 46.3081i | −1.26269 | + | 1.50481i | −0.487435 | + | 0.873160i | \(0.662067\pi\) |
−0.775252 | + | 0.631652i | \(0.782377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.47347 | + | 6.79581i | −0.0802500 | + | 0.220485i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.6261 | − | 24.6102i | −1.38079 | − | 0.797202i | −0.388540 | − | 0.921432i | \(-0.627021\pi\) |
−0.992253 | + | 0.124230i | \(0.960354\pi\) | |||||||
\(954\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.2276 | − | 36.7673i | 0.683695 | − | 1.18419i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(968\) | −83.4522 | + | 14.7149i | −2.68226 | + | 0.472954i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 31.1127i | − | 0.998454i | −0.866471 | − | 0.499227i | \(-0.833617\pi\) | ||
0.866471 | − | 0.499227i | \(-0.166383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.7007 | + | 56.8748i | −0.662275 | + | 1.81959i | −0.0959785 | + | 0.995383i | \(0.530598\pi\) |
−0.566296 | + | 0.824202i | \(0.691624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1808 | − | 80.4235i | 0.453221 | − | 2.57035i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.7503 | − | 46.3328i | −0.853635 | − | 1.47854i | ||||
\(983\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(984\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(998\) | − | 23.4004i | − | 0.740725i | ||||||
\(999\) | 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 | 648.2.v.a.35.1 | 12 | ||
3.2 | odd | 2 | 216.2.v.a.11.2 | ✓ | 12 | ||
8.3 | odd | 2 | CM | 648.2.v.a.35.1 | 12 | ||
12.11 | even | 2 | 864.2.bh.a.335.2 | 12 | |||
24.5 | odd | 2 | 864.2.bh.a.335.2 | 12 | |||
24.11 | even | 2 | 216.2.v.a.11.2 | ✓ | 12 | ||
27.5 | odd | 18 | inner | 648.2.v.a.611.1 | 12 | ||
27.22 | even | 9 | 216.2.v.a.59.2 | yes | 12 | ||
108.103 | odd | 18 | 864.2.bh.a.815.2 | 12 | |||
216.59 | even | 18 | inner | 648.2.v.a.611.1 | 12 | ||
216.157 | even | 18 | 864.2.bh.a.815.2 | 12 | |||
216.211 | odd | 18 | 216.2.v.a.59.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.v.a.11.2 | ✓ | 12 | 3.2 | odd | 2 | ||
216.2.v.a.11.2 | ✓ | 12 | 24.11 | even | 2 | ||
216.2.v.a.59.2 | yes | 12 | 27.22 | even | 9 | ||
216.2.v.a.59.2 | yes | 12 | 216.211 | odd | 18 | ||
648.2.v.a.35.1 | 12 | 1.1 | even | 1 | trivial | ||
648.2.v.a.35.1 | 12 | 8.3 | odd | 2 | CM | ||
648.2.v.a.611.1 | 12 | 27.5 | odd | 18 | inner | ||
648.2.v.a.611.1 | 12 | 216.59 | even | 18 | inner | ||
864.2.bh.a.335.2 | 12 | 12.11 | even | 2 | |||
864.2.bh.a.335.2 | 12 | 24.5 | odd | 2 | |||
864.2.bh.a.815.2 | 12 | 108.103 | odd | 18 | |||
864.2.bh.a.815.2 | 12 | 216.157 | even | 18 |