Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,22,Mod(33,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.33");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(178.865500344\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 33.24 | ||
Character | \(\chi\) | \(=\) | 64.33 |
Dual form | 64.22.b.c.33.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 114658.i | 1.12107i | 0.828131 | + | 0.560534i | \(0.189404\pi\) | ||||
−0.828131 | + | 0.560534i | \(0.810596\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.31189e7i | 0.600775i | 0.953817 | + | 0.300387i | \(0.0971159\pi\) | ||||
−0.953817 | + | 0.300387i | \(0.902884\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.14201e8 | 1.08944 | 0.544719 | − | 0.838619i | \(-0.316636\pi\) | ||||
0.544719 | + | 0.838619i | \(0.316636\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.68616e9 | −0.256795 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.24608e11i | − 1.44852i | −0.689527 | − | 0.724260i | \(-0.742182\pi\) | ||||
0.689527 | − | 0.724260i | \(-0.257818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.76398e11i | 0.354886i | 0.984131 | + | 0.177443i | \(0.0567825\pi\) | ||||
−0.984131 | + | 0.177443i | \(0.943217\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.50419e12 | −0.673509 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.32868e12 | −0.400459 | −0.200229 | − | 0.979749i | \(-0.564169\pi\) | ||||
−0.200229 | + | 0.979749i | \(0.564169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.75236e13i | − 0.655708i | −0.944728 | − | 0.327854i | \(-0.893675\pi\) | ||||
0.944728 | − | 0.327854i | \(-0.106325\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.33549e13i | 1.22133i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.65572e14 | −1.33672 | −0.668360 | − | 0.743838i | \(-0.733003\pi\) | ||||
−0.668360 | + | 0.743838i | \(0.733003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.04732e14 | 0.639070 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.91375e14i | 0.833184i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.38411e14i | − 0.325926i | −0.986632 | − | 0.162963i | \(-0.947895\pi\) | ||||
0.986632 | − | 0.162963i | \(-0.0521051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.12499e15 | 0.465650 | 0.232825 | − | 0.972519i | \(-0.425203\pi\) | ||||
0.232825 | + | 0.972519i | \(0.425203\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.42874e16 | 1.62389 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.06814e16i | 0.654506i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.13429e16i | 1.07157i | 0.844354 | + | 0.535785i | \(0.179984\pi\) | ||||
−0.844354 | + | 0.535785i | \(0.820016\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.02255e16 | −0.397852 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.67346e15 | 0.0427411 | 0.0213705 | − | 0.999772i | \(-0.493197\pi\) | ||||
0.0213705 | + | 0.999772i | \(0.493197\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.60426e17i | − 1.13202i | −0.824397 | − | 0.566012i | \(-0.808485\pi\) | ||||
0.824397 | − | 0.566012i | \(-0.191515\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 3.52394e16i | − 0.154276i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.23709e17 | 1.17501 | 0.587504 | − | 0.809222i | \(-0.300111\pi\) | ||||
0.587504 | + | 0.809222i | \(0.300111\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.04377e17 | 0.186874 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.81660e17i | − 0.448942i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.51790e18i | − 1.19219i | −0.802912 | − | 0.596097i | \(-0.796717\pi\) | ||||
0.802912 | − | 0.596097i | \(-0.203283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.63472e18 | 0.870234 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00923e18 | 0.735094 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.75219e18i | 0.701022i | 0.936559 | + | 0.350511i | \(0.113992\pi\) | ||||
−0.936559 | + | 0.350511i | \(0.886008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.67390e18i | 0.300446i | 0.988652 | + | 0.150223i | \(0.0479991\pi\) | ||||
−0.988652 | + | 0.150223i | \(0.952001\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.18708e18 | −0.279762 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.31415e18 | −0.213207 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.15114e19i | 1.44173i | 0.693075 | + | 0.720865i | \(0.256255\pi\) | ||||
−0.693075 | + | 0.720865i | \(0.743745\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 3.04501e19i | − 1.49855i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.67913e19 | 1.34132 | 0.670660 | − | 0.741765i | \(-0.266011\pi\) | ||||
0.670660 | + | 0.741765i | \(0.266011\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.73277e19 | 1.56126 | 0.780629 | − | 0.624994i | \(-0.214899\pi\) | ||||
0.780629 | + | 0.624994i | \(0.214899\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.49401e19i | 0.716441i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.01456e20i | − 1.57807i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.95602e19 | 1.18304 | 0.591522 | − | 0.806289i | \(-0.298527\pi\) | ||||
0.591522 | + | 0.806289i | \(0.298527\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.30302e20 | −1.19085 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.00024e20i | − 0.707596i | −0.935322 | − | 0.353798i | \(-0.884890\pi\) | ||||
0.935322 | − | 0.353798i | \(-0.115110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 4.36685e19i | − 0.240585i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.46649e19 | 0.365385 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.88634e20 | 1.32113 | 0.660566 | − | 0.750768i | \(-0.270317\pi\) | ||||
0.660566 | + | 0.750768i | \(0.270317\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.43624e20i | 0.386626i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.43648e20i | 0.522025i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.29890e20 | 0.393933 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.38790e20 | 0.604162 | 0.302081 | − | 0.953282i | \(-0.402319\pi\) | ||||
0.302081 | + | 0.953282i | \(0.402319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.34719e20i | 0.371972i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 3.97827e20i | − 0.358360i | −0.983816 | − | 0.179180i | \(-0.942656\pi\) | ||||
0.983816 | − | 0.179180i | \(-0.0573445\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.02232e20 | −0.661496 | −0.330748 | − | 0.943719i | \(-0.607301\pi\) | ||||
−0.330748 | + | 0.943719i | \(0.607301\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.22471e21 | −0.733746 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.14459e20i | − 0.400258i | −0.979770 | − | 0.200129i | \(-0.935864\pi\) | ||||
0.979770 | − | 0.200129i | \(-0.0641361\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.54780e21i | 1.43542i | 0.696340 | + | 0.717712i | \(0.254811\pi\) | ||||
−0.696340 | + | 0.717712i | \(0.745189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.59372e21 | −1.20130 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.17475e21 | −1.15693 | −0.578464 | − | 0.815708i | \(-0.696348\pi\) | ||||
−0.578464 | + | 0.815708i | \(0.696348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.48401e21i | − 0.803068i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.73834e20i | − 0.0911328i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.71021e21 | −0.436275 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.12702e21 | −1.09821 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.21193e20i | 0.0479156i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.02533e22i | 0.984712i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00609e22 | 0.817896 | 0.408948 | − | 0.912558i | \(-0.365896\pi\) | ||||
0.408948 | + | 0.912558i | \(0.365896\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.83942e22 | 1.26908 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.16162e21i | 0.302996i | 0.988458 | + | 0.151498i | \(0.0484098\pi\) | ||||
−0.988458 | + | 0.151498i | \(0.951590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.42677e22i | − 0.714353i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.16938e22 | −0.500556 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.18447e21 | 0.153488 | 0.0767441 | − | 0.997051i | \(-0.475548\pi\) | ||||
0.0767441 | + | 0.997051i | \(0.475548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.91283e21i | 0.217771i | 0.994054 | + | 0.108886i | \(0.0347282\pi\) | ||||
−0.994054 | + | 0.108886i | \(0.965272\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.85818e22i | 1.31726i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.19807e22 | 0.514059 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.68712e21 | 0.195808 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.19677e22i | 0.209498i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 6.29440e22i | − 0.956090i | −0.878335 | − | 0.478045i | \(-0.841346\pi\) | ||||
0.878335 | − | 0.478045i | \(-0.158654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.40998e23 | 1.86189 | 0.930947 | − | 0.365155i | \(-0.118984\pi\) | ||||
0.930947 | + | 0.365155i | \(0.118984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.94136e21 | 0.102836 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.78775e22i | 0.279751i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.68616e23i | − 1.47894i | −0.673187 | − | 0.739472i | \(-0.735075\pi\) | ||||
0.673187 | − | 0.739472i | \(-0.264925\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.74040e23 | 1.33653 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.16229e23 | −1.45627 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.06801e23i | 1.22344i | 0.791074 | + | 0.611720i | \(0.209522\pi\) | ||||
−0.791074 | + | 0.611720i | \(0.790478\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.87435e23i | 0.975592i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.28331e23 | −1.04723 | −0.523615 | − | 0.851955i | \(-0.675417\pi\) | ||||
−0.523615 | + | 0.851955i | \(0.675417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.15948e23 | 0.874056 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.70712e22i | 0.168382i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.81019e23i | 1.52292i | 0.648210 | + | 0.761462i | \(0.275518\pi\) | ||||
−0.648210 | + | 0.761462i | \(0.724482\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.48113e23 | 0.696227 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.15561e23 | −0.785894 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.75630e23i | − 0.388724i | −0.980930 | − | 0.194362i | \(-0.937736\pi\) | ||||
0.980930 | − | 0.194362i | \(-0.0622636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.48571e23i | 1.08046i | 0.841518 | + | 0.540229i | \(0.181662\pi\) | ||||
−0.841518 | + | 0.540229i | \(0.818338\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.91926e23 | −0.336820 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.11183e23 | −0.643773 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.14781e23i | 0.580072i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.25759e23i | 0.907702i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.02164e24 | 1.14405 | 0.572027 | − | 0.820235i | \(-0.306157\pi\) | ||||
0.572027 | + | 0.820235i | \(0.306157\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.01129e22 | 0.0101514 | 0.00507569 | − | 0.999987i | \(-0.498384\pi\) | ||||
0.00507569 | + | 0.999987i | \(0.498384\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 2.65336e23i | − 0.239019i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.16736e24i | 1.75402i | 0.480468 | + | 0.877012i | \(0.340467\pi\) | ||||
−0.480468 | + | 0.877012i | \(0.659533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.20832e24 | 0.879477 | 0.439738 | − | 0.898126i | \(-0.355071\pi\) | ||||
0.439738 | + | 0.898126i | \(0.355071\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.46646e24 | −1.61628 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 6.01215e23i | − 0.355076i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.81917e22i | 0.0256777i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.13370e23 | 0.343262 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.18359e24 | −0.949806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.51453e24i | 0.989672i | 0.868987 | + | 0.494836i | \(0.164772\pi\) | ||||
−0.868987 | + | 0.494836i | \(0.835228\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.21843e24i | 1.50371i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.10461e24 | 0.680092 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.73017e24 | 0.507296 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.57310e24i | 1.75028i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 5.87172e23i | − 0.142117i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.94567e24 | 1.74956 | 0.874781 | − | 0.484519i | \(-0.161005\pi\) | ||||
0.874781 | + | 0.484519i | \(0.161005\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.18560e23 | −0.164110 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.16629e24i | 1.30925i | 0.755954 | + | 0.654625i | \(0.227174\pi\) | ||||
−0.755954 | + | 0.654625i | \(0.772826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4.42950e23i | − 0.0738044i | −0.999319 | − | 0.0369022i | \(-0.988251\pi\) | ||||
0.999319 | − | 0.0369022i | \(-0.0117490\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.16328e25 | 1.76913 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.26907e24 | 0.315218 | 0.157609 | − | 0.987502i | \(-0.449621\pi\) | ||||
0.157609 | + | 0.987502i | \(0.449621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.55859e24i | 0.705914i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.14154e25i | 1.32627i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.22558e25 | 1.30366 | 0.651828 | − | 0.758367i | \(-0.274002\pi\) | ||||
0.651828 | + | 0.758367i | \(0.274002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.81847e25 | −1.77226 | −0.886128 | − | 0.463440i | \(-0.846615\pi\) | ||||
−0.886128 | + | 0.463440i | \(0.846615\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 5.61607e24i | − 0.501841i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.36932e24i | 0.112269i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.09113e24 | 0.232702 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.14686e25 | 0.793263 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.93006e25i | − 1.22743i | −0.789527 | − | 0.613716i | \(-0.789674\pi\) | ||||
0.789527 | − | 0.613716i | \(-0.210326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.30926e25i | 1.93627i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.00695e24 | 0.269713 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.60236e25 | −1.78768 | −0.893839 | − | 0.448387i | \(-0.851999\pi\) | ||||
−0.893839 | + | 0.448387i | \(0.851999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.55194e25i | 1.16741i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.98349e24i | 0.0836960i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.63224e25 | 1.02516 | 0.512578 | − | 0.858641i | \(-0.328691\pi\) | ||||
0.512578 | + | 0.858641i | \(0.328691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.99132e25 | 0.716240 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.45601e25i | 1.48108i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.54840e25i | 0.475865i | 0.971282 | + | 0.237933i | \(0.0764698\pi\) | ||||
−0.971282 | + | 0.237933i | \(0.923530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.42811e25 | −1.54337 | −0.771687 | − | 0.636002i | \(-0.780587\pi\) | ||||
−0.771687 | + | 0.636002i | \(0.780587\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.64676e25 | −0.433434 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 3.79722e25i | − 0.925705i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.04508e25i | 1.36573i | 0.730545 | + | 0.682864i | \(0.239266\pi\) | ||||
−0.730545 | + | 0.682864i | \(0.760734\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.70807e24 | −0.119576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.29873e25 | −0.641106 | −0.320553 | − | 0.947231i | \(-0.603869\pi\) | ||||
−0.320553 | + | 0.947231i | \(0.603869\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.20492e25i | − 0.397773i | −0.980022 | − | 0.198887i | \(-0.936267\pi\) | ||||
0.980022 | − | 0.198887i | \(-0.0637326\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.63588e25i | 0.441626i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.99094e24 | 0.0465637 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.80119e25 | −0.839633 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.03109e25i | 0.677307i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6.77166e25i | − 0.848369i | −0.905576 | − | 0.424185i | \(-0.860561\pi\) | ||||
0.905576 | − | 0.424185i | \(-0.139439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.61056e25 | −0.421156 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.11073e26 | 1.20688 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.68465e25i | − 0.474383i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.30619e26i | − 1.23327i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.56141e25 | 0.401746 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.19597e25 | −0.180500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.44941e25i | − 0.725190i | −0.931947 | − | 0.362595i | \(-0.881891\pi\) | ||||
0.931947 | − | 0.362595i | \(-0.118109\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.03448e26i | − 0.741582i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.92541e26 | 1.28985 | 0.644925 | − | 0.764246i | \(-0.276889\pi\) | ||||
0.644925 | + | 0.764246i | \(0.276889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.47024e26 | 1.54712 | 0.773558 | − | 0.633726i | \(-0.218475\pi\) | ||||
0.773558 | + | 0.633726i | \(0.218475\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.86920e25i | − 0.168074i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.73540e26i | − 1.49933i | −0.661816 | − | 0.749667i | \(-0.730214\pi\) | ||||
0.661816 | − | 0.749667i | \(-0.269786\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.20123e25 | −0.472110 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.33845e25 | 0.448716 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.83304e25i | 0.262584i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.37542e25i | 0.226797i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.06784e26 | −1.60921 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.44985e26 | 1.28010 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.81293e26i | 0.979410i | 0.871888 | + | 0.489705i | \(0.162896\pi\) | ||||
−0.871888 | + | 0.489705i | \(0.837104\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 8.41921e25i | − 0.275174i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.82206e26 | −0.866155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.38854e26 | −0.977010 | −0.488505 | − | 0.872561i | \(-0.662458\pi\) | ||||
−0.488505 | + | 0.872561i | \(0.662458\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 4.78669e26i | − 1.29700i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2.64792e26i | − 0.674503i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.69784e26 | −0.885850 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.99470e26 | 0.900294 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6.52881e26i | − 1.38476i | −0.721533 | − | 0.692380i | \(-0.756562\pi\) | ||||
0.721533 | − | 0.692380i | \(-0.243438\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8.30091e26i | − 1.65752i | −0.559605 | − | 0.828759i | \(-0.689047\pi\) | ||||
0.559605 | − | 0.828759i | \(-0.310953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.57237e26 | −0.295685 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.48358e26 | −1.14863 | −0.574315 | − | 0.818634i | \(-0.694732\pi\) | ||||
−0.574315 | + | 0.818634i | \(0.694732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.82660e26i | 0.805831i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.10748e26i | − 0.489094i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.89871e26 | −1.32079 | −0.660397 | − | 0.750917i | \(-0.729612\pi\) | ||||
−0.660397 | + | 0.750917i | \(0.729612\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.07133e26 | 0.570047 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 9.31830e26i | − 1.23117i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.52075e26i | 0.937964i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.55739e26 | −0.301164 | −0.150582 | − | 0.988598i | \(-0.548115\pi\) | ||||
−0.150582 | + | 0.988598i | \(0.548115\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.86752e24 | −0.0109757 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.23588e27i | − 1.29882i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.08913e26i | − 0.108178i | −0.998536 | − | 0.0540888i | \(-0.982775\pi\) | ||||
0.998536 | − | 0.0540888i | \(-0.0172254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.17563e27 | −1.10393 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.30254e26 | 0.115667 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.03293e26i | 0.254771i | 0.991853 | + | 0.127386i | \(0.0406585\pi\) | ||||
−0.991853 | + | 0.127386i | \(0.959341\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.15357e27i | 0.916917i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.88044e26 | −0.592875 | −0.296438 | − | 0.955052i | \(-0.595799\pi\) | ||||
−0.296438 | + | 0.955052i | \(0.595799\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.33099e27 | 0.948065 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.30930e26i | 0.290698i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 5.00122e26i | − 0.319599i | −0.987150 | − | 0.159799i | \(-0.948915\pi\) | ||||
0.987150 | − | 0.159799i | \(-0.0510847\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.84004e26 | 0.535301 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.91822e26 | −0.339680 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.30612e27i | 0.710743i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.48390e27i | − 1.28184i | −0.767607 | − | 0.640920i | \(-0.778553\pi\) | ||||
0.767607 | − | 0.640920i | \(-0.221447\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.63591e27 | 0.800839 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.69255e27 | 1.71518 | 0.857590 | − | 0.514333i | \(-0.171961\pi\) | ||||
0.857590 | + | 0.514333i | \(0.171961\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.74845e26i | 0.165253i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.70941e27i | − 0.715433i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.90559e27 | 1.55219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.04322e27 | −1.52627 | −0.763137 | − | 0.646236i | \(-0.776342\pi\) | ||||
−0.763137 | + | 0.646236i | \(0.776342\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.79784e26i | 0.172071i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.24083e27i | 0.763720i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.31221e27 | 0.425106 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.92613e26 | −0.244136 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.53519e27i | 0.449693i | 0.974394 | + | 0.224846i | \(0.0721880\pi\) | ||||
−0.974394 | + | 0.224846i | \(0.927812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.47068e27i | − 0.409786i | −0.978784 | − | 0.204893i | \(-0.934315\pi\) | ||||
0.978784 | − | 0.204893i | \(-0.0656846\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.13815e27 | −0.301735 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.01435e27 | −0.255921 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.36289e27i | 0.327317i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.52027e27i | 0.576296i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.28715e27 | 0.498063 | 0.249031 | − | 0.968495i | \(-0.419888\pi\) | ||||
0.249031 | + | 0.968495i | \(0.419888\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.26337e27 | −1.50666 | −0.753330 | − | 0.657643i | \(-0.771554\pi\) | ||||
−0.753330 | + | 0.657643i | \(0.771554\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.11071e27i | 0.219514i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.65378e27i | 0.876498i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.82811e27 | 1.04629 | 0.523143 | − | 0.852245i | \(-0.324759\pi\) | ||||
0.523143 | + | 0.852245i | \(0.324759\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.80375e26 | −0.0479881 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.06036e27i | 0.825928i | 0.910747 | + | 0.412964i | \(0.135506\pi\) | ||||
−0.910747 | + | 0.412964i | \(0.864494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.09844e27i | 0.793702i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.21705e27 | 1.07184 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.03689e28 | 1.46943 | 0.734713 | − | 0.678378i | \(-0.237317\pi\) | ||||
0.734713 | + | 0.678378i | \(0.237317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 4.57745e26i | − 0.0619113i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.61666e28i | 2.08731i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.88418e27 | −0.232275 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.56627e27 | −0.537578 | −0.268789 | − | 0.963199i | \(-0.586623\pi\) | ||||
−0.268789 | + | 0.963199i | \(0.586623\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.96710e27i | − 0.333656i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.22037e27i | − 0.238542i | −0.992862 | − | 0.119271i | \(-0.961944\pi\) | ||||
0.992862 | − | 0.119271i | \(-0.0380558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.54922e28 | −1.59043 | −0.795213 | − | 0.606330i | \(-0.792641\pi\) | ||||
−0.795213 | + | 0.606330i | \(0.792641\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.19639e27 | −0.313620 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.66026e27i | 0.906069i | 0.891493 | + | 0.453035i | \(0.149659\pi\) | ||||
−0.891493 | + | 0.453035i | \(0.850341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.75146e28i | 1.57067i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.93332e28 | 1.65800 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.99904e28 | −1.63976 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.34001e27i | − 0.419043i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.07733e27i | 0.306149i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.55119e27 | 0.470758 | 0.235379 | − | 0.971904i | \(-0.424367\pi\) | ||||
0.235379 | + | 0.971904i | \(0.424367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.52883e27 | −0.380286 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.47925e28i | − 1.63258i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.75643e27i | 0.362965i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.88451e27 | −0.234575 | −0.117288 | − | 0.993098i | \(-0.537420\pi\) | ||||
−0.117288 | + | 0.993098i | \(0.537420\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.37114e28 | −1.37156 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.06166e28i | 0.588342i | 0.955753 | + | 0.294171i | \(0.0950436\pi\) | ||||
−0.955753 | + | 0.294171i | \(0.904956\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.45793e27i | 0.130520i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.39113e27 | −0.223471 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.99555e28 | 1.46128 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.58203e28i | 1.67522i | 0.546265 | + | 0.837612i | \(0.316049\pi\) | ||||
−0.546265 | + | 0.837612i | \(0.683951\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 2.61801e28i | − 1.17402i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.68066e28 | 0.722798 | 0.361399 | − | 0.932411i | \(-0.382299\pi\) | ||||
0.361399 | + | 0.932411i | \(0.382299\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.21904e27 | 0.215294 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.47602e28i | 0.979877i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.08041e28i | − 0.410255i | −0.978735 | − | 0.205127i | \(-0.934239\pi\) | ||||
0.978735 | − | 0.205127i | \(-0.0657608\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.66763e28 | 1.70089 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.56201e28 | 0.546326 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.18363e28i | − 0.397410i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5.27978e28i | − 1.70202i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.51528e28 | −1.70730 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.39234e28 | 0.413951 | 0.206976 | − | 0.978346i | \(-0.433638\pi\) | ||||
0.206976 | + | 0.978346i | \(0.433638\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.30668e28i | − 0.373166i | −0.982439 | − | 0.186583i | \(-0.940259\pi\) | ||||
0.982439 | − | 0.186583i | \(-0.0597413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.84482e28i | 0.780518i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.07341e27 | −0.186474 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.10571e28 | 0.786821 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 7.39282e27i | − 0.180019i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.47992e26i | 0.0151682i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.06848e28 | 0.240465 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.01374e28 | 0.435786 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.30063e28i | − 0.270690i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.99689e28i | − 0.800111i | −0.916491 | − | 0.400056i | \(-0.868991\pi\) | ||||
0.916491 | − | 0.400056i | \(-0.131009\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.28982e28 | −1.21127 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.65431e28 | −0.862367 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4.09401e28i | − 0.729930i | −0.931021 | − | 0.364965i | \(-0.881081\pi\) | ||||
0.931021 | − | 0.364965i | \(-0.118919\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4.49636e27i | − 0.0771528i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.29396e28 | −0.213712 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.10620e28 | 1.28885 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 4.71456e28i | − 0.721713i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9.63372e28i | − 1.42009i | −0.704158 | − | 0.710043i | \(-0.748675\pi\) | ||||
0.704158 | − | 0.710043i | \(-0.251325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.82989e28 | 0.401740 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.75581e28 | −0.650301 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.10402e29i | − 1.45425i | −0.686503 | − | 0.727127i | \(-0.740855\pi\) | ||||
0.686503 | − | 0.727127i | \(-0.259145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.47680e28i | − 0.695053i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.06092e29 | −1.29736 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.27031e28 | 0.503247 | 0.251623 | − | 0.967825i | \(-0.419036\pi\) | ||||
0.251623 | + | 0.967825i | \(0.419036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.84895e28i | 0.550767i | 0.961334 | + | 0.275384i | \(0.0888049\pi\) | ||||
−0.961334 | + | 0.275384i | \(0.911195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.17139e29i | 1.28256i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.09284e28 | −0.854258 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.65903e28 | −0.372409 | −0.186205 | − | 0.982511i | \(-0.559619\pi\) | ||||
−0.186205 | + | 0.982511i | \(0.559619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.15953e27i | 0.0113804i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 8.14398e28i | − 0.770881i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.89144e29 | −1.72692 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.21617e27 | 0.0547503 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 8.80312e27i | − 0.0748060i | −0.999300 | − | 0.0374030i | \(-0.988091\pi\) | ||||
0.999300 | − | 0.0374030i | \(-0.0119085\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.72375e28i | − 0.305330i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.48506e29 | −1.96638 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.35815e29 | −1.03723 | −0.518613 | − | 0.855009i | \(-0.673551\pi\) | ||||
−0.518613 | + | 0.855009i | \(0.673551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.55549e28i | − 0.262103i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.38544e29i | 0.985954i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.49105e28 | 0.514708 | 0.257354 | − | 0.966317i | \(-0.417149\pi\) | ||||
0.257354 | + | 0.966317i | \(0.417149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.82014e29 | 1.87106 | 0.935531 | − | 0.353244i | \(-0.114922\pi\) | ||||
0.935531 | + | 0.353244i | \(0.114922\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5.77832e28i | − 0.370229i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1.06617e29i | − 0.659776i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.17396e29 | 0.701736 | 0.350868 | − | 0.936425i | \(-0.385887\pi\) | ||||
0.350868 | + | 0.936425i | \(0.385887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.89342e28 | 0.398065 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.47416e28i | 0.416994i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3.83941e28i | − 0.206980i | −0.994630 | − | 0.103490i | \(-0.966999\pi\) | ||||
0.994630 | − | 0.103490i | \(-0.0330011\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.52558e27 | −0.0287865 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.53635e27 | −0.0329110 | −0.0164555 | − | 0.999865i | \(-0.505238\pi\) | ||||
−0.0164555 | + | 0.999865i | \(0.505238\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.35329e29i | 0.658625i | 0.944221 | + | 0.329312i | \(0.106817\pi\) | ||||
−0.944221 | + | 0.329312i | \(0.893183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.36725e29i | − 1.11373i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.16426e29 | 1.43929 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.07957e28 | 0.0474801 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.50367e29i | − 1.06480i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.04330e29i | − 0.429120i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.42416e29 | 1.76004 | 0.880019 | − | 0.474938i | \(-0.157530\pi\) | ||||
0.880019 | + | 0.474938i | \(0.157530\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.88312e29 | −1.10949 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.31988e29i | 0.491371i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.84120e28i | 0.0663188i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.88274e28 | −0.344444 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.08677e28 | 0.171566 | 0.0857832 | − | 0.996314i | \(-0.472661\pi\) | ||||
0.0857832 | + | 0.996314i | \(0.472661\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.61728e28i | − 0.183363i | −0.995788 | − | 0.0916813i | \(-0.970776\pi\) | ||||
0.995788 | − | 0.0916813i | \(-0.0292241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.41311e29i | 0.762429i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.68341e29 | 0.514868 | 0.257434 | − | 0.966296i | \(-0.417123\pi\) | ||||
0.257434 | + | 0.966296i | \(0.417123\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.42946e29 | 1.01544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.98378e29i | 0.568714i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.42886e29i | − 0.396645i | −0.980137 | − | 0.198322i | \(-0.936451\pi\) | ||||
0.980137 | − | 0.198322i | \(-0.0635493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.77146e28 | −0.182033 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.53992e29 | −0.400923 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.69706e29i | 0.680133i | 0.940401 | + | 0.340066i | \(0.110450\pi\) | ||||
−0.940401 | + | 0.340066i | \(0.889550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.69427e29i | 1.14671i | 0.819307 | + | 0.573354i | \(0.194358\pi\) | ||||
−0.819307 | + | 0.573354i | \(0.805642\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.73242e28 | 0.159323 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.87177e29 | 0.429165 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.96101e29i | 0.435672i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.11036e29i | 1.96138i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.08582e29 | 0.435202 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.03975e29 | −1.42364 | −0.711818 | − | 0.702364i | \(-0.752128\pi\) | ||||
−0.711818 | + | 0.702364i | \(0.752128\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.71631e29i | 0.532463i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.19335e29i | − 0.416798i | −0.978044 | − | 0.208399i | \(-0.933175\pi\) | ||||
0.978044 | − | 0.208399i | \(-0.0668253\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.57263e29 | 0.658197 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.21674e29 | −1.46776 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.89835e29i | 1.54132i | 0.637248 | + | 0.770659i | \(0.280073\pi\) | ||||
−0.637248 | + | 0.770659i | \(0.719927\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.48956e28i | 0.0922118i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.07879e28 | 0.0827398 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.67755e29 | 0.423093 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 9.42228e29i | − 1.44423i | −0.691773 | − | 0.722115i | \(-0.743170\pi\) | ||||
0.691773 | − | 0.722115i | \(-0.256830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.72528e29i | 0.405240i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.06886e28 | −0.130831 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.22278e28 | −0.0171160 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.60168e29i | 0.353381i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.18589e30i | 1.56316i | 0.623804 | + | 0.781581i | \(0.285586\pi\) | ||||
−0.623804 | + | 0.781581i | \(0.714414\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.49240e29 | 0.702638 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.37338e29 | −0.791378 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 3.23911e29i | − 0.390411i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.56974e29i | 0.534695i | 0.963600 | + | 0.267348i | \(0.0861472\pi\) | ||||
−0.963600 | + | 0.267348i | \(0.913853\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.67435e29 | −0.303799 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.64339e29 | −0.622443 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.88362e29i | 0.308834i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.40523e30i | 1.46149i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.01293e28 | −0.0910359 | −0.0455179 | − | 0.998964i | \(-0.514494\pi\) | ||||
−0.0455179 | + | 0.998964i | \(0.514494\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.34598e29 | −0.720658 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.08502e30i | − 1.98682i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.25018e29i | − 0.208290i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.62357e28 | −0.0325856 | −0.0162928 | − | 0.999867i | \(-0.505186\pi\) | ||||
−0.0162928 | + | 0.999867i | \(0.505186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.19073e29 | −0.628253 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.34006e29i | 0.453329i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.40449e30i | − 1.15858i | −0.815120 | − | 0.579292i | \(-0.803329\pi\) | ||||
0.815120 | − | 0.579292i | \(-0.196671\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.57003e29 | −0.125861 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.68051e30 | 2.08838 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.28167e30i | 0.970528i | 0.874368 | + | 0.485264i | \(0.161277\pi\) | ||||
−0.874368 | + | 0.485264i | \(0.838723\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.54424e29i | 0.260875i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.67917e30 | 1.91698 | 0.958490 | − | 0.285128i | \(-0.0920360\pi\) | ||||
0.958490 | + | 0.285128i | \(0.0920360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.25755e29 | 0.574395 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.68681e29i | 0.181707i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 6.63133e29i | − 0.436056i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.59720e30 | 1.02127 | 0.510635 | − | 0.859798i | \(-0.329410\pi\) | ||||
0.510635 | + | 0.859798i | \(0.329410\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.21298e30 | 1.37603 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.84973e30i | 1.11858i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.95679e30i | − 1.15090i | −0.817836 | − | 0.575451i | \(-0.804826\pi\) | ||||
0.817836 | − | 0.575451i | \(-0.195174\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.79434e30 | −2.17069 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.12382e30 | −1.18189 | −0.590947 | − | 0.806710i | \(-0.701246\pi\) | ||||
−0.590947 | + | 0.806710i | \(0.701246\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.88862e30i | 1.56381i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.17301e29i | 0.0617810i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.85481e29 | −0.248783 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.94984e30 | 0.972236 | 0.486118 | − | 0.873893i | \(-0.338413\pi\) | ||||
0.486118 | + | 0.873893i | \(0.338413\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 4.13040e30i | − 2.00411i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.54317e30i | − 0.728667i | −0.931268 | − | 0.364334i | \(-0.881297\pi\) | ||||
0.931268 | − | 0.364334i | \(-0.118703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.47553e29 | 0.297583 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.92601e30 | −1.30875 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.43723e28i | − 0.0280257i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 4.58451e30i | − 1.94293i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.58201e29 | 0.271556 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.21205e30 | 0.888512 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.29401e30i | − 0.897140i | −0.893748 | − | 0.448570i | \(-0.851933\pi\) | ||||
0.893748 | − | 0.448570i | \(-0.148067\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.01808e30i | 1.14927i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.39908e30 | −1.26040 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.95273e29 | −0.106624 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.28321e30i | 0.802954i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.11630e30i | − 0.382356i | −0.981555 | − | 0.191178i | \(-0.938769\pi\) | ||||
0.981555 | − | 0.191178i | \(-0.0612308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.41039e30 | −0.470542 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.04393e30 | −0.339259 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.14352e30i | − 2.26151i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.83668e30i | − 0.874892i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.77537e30 | −0.533478 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.22000e30 | 1.23553 | 0.617764 | − | 0.786363i | \(-0.288039\pi\) | ||||
0.617764 | + | 0.786363i | \(0.288039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.17983e29i | − 0.0621877i | −0.999516 | − | 0.0310938i | \(-0.990101\pi\) | ||||
0.999516 | − | 0.0310938i | \(-0.00989907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.22378e30i | − 1.73023i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.71300e30 | −0.735012 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.81124e30 | −0.742278 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 3.85796e29i | − 0.0992835i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.48715e30i | 0.373037i | 0.982451 | + | 0.186518i | \(0.0597204\pi\) | ||||
−0.982451 | + | 0.186518i | \(0.940280\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.35473e29 | 0.0331248 | 0.0165624 | − | 0.999863i | \(-0.494728\pi\) | ||||
0.0165624 | + | 0.999863i | \(0.494728\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.35383e30 | 1.03778 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.26860e30i | 0.759546i | 0.925080 | + | 0.379773i | \(0.123998\pi\) | ||||
−0.925080 | + | 0.379773i | \(0.876002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.32938e30i | 1.43396i | 0.697092 | + | 0.716982i | \(0.254477\pi\) | ||||
−0.697092 | + | 0.716982i | \(0.745523\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.93118e30 | −1.53107 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.47439e29 | −0.0748352 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.99545e30i | − 0.629149i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.89416e30i | 0.387972i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.73795e29 | −0.0746677 | −0.0373338 | − | 0.999303i | \(-0.511886\pi\) | ||||
−0.0373338 | + | 0.999303i | \(0.511886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.58759e30 | 0.893772 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 3.78226e30i | − 0.718724i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.83300e30i | 0.525111i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.61703e30 | −1.19643 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.52813e30 | 0.445931 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8.32380e30i | − 1.43239i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.46122e30i | − 0.245329i | −0.992448 | − | 0.122665i | \(-0.960856\pi\) | ||||
0.992448 | − | 0.122665i | \(-0.0391440\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.17522e29 | −0.101160 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.94598e30 | −0.790595 | −0.395297 | − | 0.918553i | \(-0.629358\pi\) | ||||
−0.395297 | + | 0.918553i | \(0.629358\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.79146e30i | 1.52728i | 0.645641 | + | 0.763641i | \(0.276590\pi\) | ||||
−0.645641 | + | 0.763641i | \(0.723410\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.42936e29i | 0.0522011i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.46950e30 | 0.218301 | 0.109151 | − | 0.994025i | \(-0.465187\pi\) | ||||
0.109151 | + | 0.994025i | \(0.465187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.31043e30 | −0.914934 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 6.65154e30i | − 0.941286i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.24060e31i | − 1.71366i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.79458e30 | −0.511650 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.17866e30 | −0.155146 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.34826e30i | 1.07278i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.85727e30i | 0.358472i | 0.983806 | + | 0.179236i | \(0.0573625\pi\) | ||||
−0.983806 | + | 0.179236i | \(0.942637\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.76427e30 | 0.951080 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.34495e30 | −0.400076 | −0.200038 | − | 0.979788i | \(-0.564107\pi\) | ||||
−0.200038 | + | 0.979788i | \(0.564107\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.96693e30i | − 0.463305i | −0.972799 | − | 0.231652i | \(-0.925587\pi\) | ||||
0.972799 | − | 0.231652i | \(-0.0744132\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 4.13981e30i | − 0.472145i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.17546e31 | 1.30921 | 0.654607 | − | 0.755969i | \(-0.272834\pi\) | ||||
0.654607 | + | 0.755969i | \(0.272834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.19160e30 | 0.891046 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.62367e31i | 1.72497i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7.42491e30i | − 0.770462i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.30406e30 | 0.233535 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.37133e30 | 0.531816 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.56912e30i | − 0.151767i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.05260e30i | 0.477425i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.49765e31 | 1.38258 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.19664e30 | −0.649112 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.54097e30i | 0.400195i | 0.979776 | + | 0.200098i | \(0.0641259\pi\) | ||||
−0.979776 | + | 0.200098i | \(0.935874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.06863e30i | 0.0920249i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.58505e31 | 1.33383 | 0.666916 | − | 0.745133i | \(-0.267614\pi\) | ||||
0.666916 | + | 0.745133i | \(0.267614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.24639e31 | −1.02497 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.51786e30i | − 0.202353i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.20260e30i | 0.330096i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.50687e30 | −0.576297 | −0.288148 | − | 0.957586i | \(-0.593040\pi\) | ||||
−0.288148 | + | 0.957586i | \(0.593040\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.08345e31 | 0.812988 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.48992e30i | 0.476016i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.55119e30i | 0.684809i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.42354e30 | 0.169869 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.48338e30 | −0.101645 | −0.0508225 | − | 0.998708i | \(-0.516184\pi\) | ||||
−0.0508225 | + | 0.998708i | \(0.516184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.82907e30i | − 0.122535i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.20764e31i | 1.44601i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.44146e30 | −0.348493 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.05541e30 | 0.504455 | 0.252227 | − | 0.967668i | \(-0.418837\pi\) | ||||
0.252227 | + | 0.967668i | \(0.418837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.83233e31i | 1.73442i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.58565e31i | 1.54839i | 0.632949 | + | 0.774193i | \(0.281844\pi\) | ||||
−0.632949 | + | 0.774193i | \(0.718156\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.75570e29 | −0.0571328 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.52114e30 | −0.545324 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.22907e31i | − 1.24868i | −0.781154 | − | 0.624338i | \(-0.785369\pi\) | ||||
0.781154 | − | 0.624338i | \(-0.214631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.01125e31i | 0.554069i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.13636e31 | 1.68086 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.08594e29 | 0.0476315 | 0.0238157 | − | 0.999716i | \(-0.492418\pi\) | ||||
0.0238157 | + | 0.999716i | \(0.492418\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.34027e31i | 0.687318i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.05500e31i | − 0.529268i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.40700e30 | 0.167216 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.63099e31 | −0.783170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.18777e30i | 0.102784i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.32670e29i | 0.00609870i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.53441e31 | 0.690183 | 0.345091 | − | 0.938569i | \(-0.387848\pi\) | ||||
0.345091 | + | 0.938569i | \(0.387848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.68806e30 | −0.294375 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 8.48542e30i | − 0.365486i | −0.983161 | − | 0.182743i | \(-0.941502\pi\) | ||||
0.983161 | − | 0.182743i | \(-0.0584977\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.62843e30i | 0.237248i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.16336e30 | −0.254255 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.57089e31 | −1.03798 | −0.518992 | − | 0.854779i | \(-0.673692\pi\) | ||||
−0.518992 | + | 0.854779i | \(0.673692\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 4.84271e31i | − 1.91368i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 9.52995e30i | − 0.368609i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.49539e31 | −1.70199 | −0.850993 | − | 0.525178i | \(-0.823999\pi\) | ||||
−0.850993 | + | 0.525178i | \(0.823999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.84333e31 | −1.05377 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.95553e31i | 1.43508i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.26047e31i | 1.51320i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.88864e31 | 1.35215 | 0.676075 | − | 0.736833i | \(-0.263680\pi\) | ||||
0.676075 | + | 0.736833i | \(0.263680\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.22525e31 | −1.09799 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.58518e31i | 0.528367i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.29787e31i | 1.72903i | 0.502608 | + | 0.864514i | \(0.332374\pi\) | ||||
−0.502608 | + | 0.864514i | \(0.667626\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.79383e31 | −0.892816 |
(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 | 64.22.b.c.33.24 | yes | 28 | |
4.3 | odd | 2 | inner | 64.22.b.c.33.6 | yes | 28 | |
8.3 | odd | 2 | inner | 64.22.b.c.33.23 | yes | 28 | |
8.5 | even | 2 | inner | 64.22.b.c.33.5 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.22.b.c.33.5 | ✓ | 28 | 8.5 | even | 2 | inner | |
64.22.b.c.33.6 | yes | 28 | 4.3 | odd | 2 | inner | |
64.22.b.c.33.23 | yes | 28 | 8.3 | odd | 2 | inner | |
64.22.b.c.33.24 | yes | 28 | 1.1 | even | 1 | trivial |