Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,18,Mod(17,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.17");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(58.6310679503\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 83403052 x^{14} - 583821224 x^{13} + \cdots + 21\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{240}\cdot 3^{14}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.14 | ||
Root | \(0.500000 - 3466.80i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 32.17 |
Dual form | 32.18.b.a.17.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 13867.2i | 1.22028i | 0.792295 | + | 0.610138i | \(0.208886\pi\) | ||||
−0.792295 | + | 0.610138i | \(0.791114\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 665059.i | 0.761404i | 0.924698 | + | 0.380702i | \(0.124318\pi\) | ||||
−0.924698 | + | 0.380702i | \(0.875682\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.57536e6 | 0.496672 | 0.248336 | − | 0.968674i | \(-0.420116\pi\) | ||||
0.248336 | + | 0.968674i | \(0.420116\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.31593e7 | −0.489075 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.97863e8i | − 0.278308i | −0.990271 | − | 0.139154i | \(-0.955562\pi\) | ||||
0.990271 | − | 0.139154i | \(-0.0444384\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.74981e9i | 1.61495i | 0.589905 | + | 0.807473i | \(0.299165\pi\) | ||||
−0.589905 | + | 0.807473i | \(0.700835\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.22251e9 | −0.929124 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.37447e10 | 1.17325 | 0.586624 | − | 0.809859i | \(-0.300457\pi\) | ||||
0.586624 | + | 0.809859i | \(0.300457\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00829e11i | 1.36201i | 0.732278 | + | 0.681005i | \(0.238457\pi\) | ||||
−0.732278 | + | 0.681005i | \(0.761543\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.05049e11i | 0.606078i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.16250e11 | −0.842062 | −0.421031 | − | 0.907046i | \(-0.638332\pi\) | ||||
−0.421031 | + | 0.907046i | \(0.638332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.20636e11 | 0.420264 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.14971e11i | 0.623469i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.54291e12i | 1.31516i | 0.753386 | + | 0.657578i | \(0.228419\pi\) | ||||
−0.753386 | + | 0.657578i | \(0.771581\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76965e11 | −0.0583245 | −0.0291623 | − | 0.999575i | \(-0.509284\pi\) | ||||
−0.0291623 | + | 0.999575i | \(0.509284\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.74380e12 | 0.339613 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.03806e12i | 0.378168i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.12889e13i | − 0.996412i | −0.867059 | − | 0.498206i | \(-0.833992\pi\) | ||||
0.867059 | − | 0.498206i | \(-0.166008\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.58666e13 | −1.97068 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.47798e13 | 1.65817 | 0.829086 | − | 0.559121i | \(-0.188861\pi\) | ||||
0.829086 | + | 0.559121i | \(0.188861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.38239e14i | − 1.80363i | −0.432122 | − | 0.901815i | \(-0.642235\pi\) | ||||
0.432122 | − | 0.901815i | \(-0.357765\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4.20047e13i | − 0.372384i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.21469e13 | −0.503221 | −0.251611 | − | 0.967829i | \(-0.580960\pi\) | ||||
−0.251611 | + | 0.967829i | \(0.580960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.75244e14 | −0.753317 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.67945e14i | 1.43169i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.16386e14i | 0.698028i | 0.937118 | + | 0.349014i | \(0.113483\pi\) | ||||
−0.937118 | + | 0.349014i | \(0.886517\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.31590e14 | 0.211905 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.39822e15 | −1.66203 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.29635e14i | 0.292275i | 0.989264 | + | 0.146138i | \(0.0466842\pi\) | ||||
−0.989264 | + | 0.146138i | \(0.953316\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.60732e14i | 0.441288i | 0.975354 | + | 0.220644i | \(0.0708159\pi\) | ||||
−0.975354 | + | 0.220644i | \(0.929184\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.78454e14 | −0.242910 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.15891e15 | −1.22963 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.64311e15i | − 1.09607i | −0.836457 | − | 0.548033i | \(-0.815377\pi\) | ||||
0.836457 | − | 0.548033i | \(-0.184623\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 4.38551e15i | − 1.02755i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.19058e15 | −1.68907 | −0.844534 | − | 0.535502i | \(-0.820122\pi\) | ||||
−0.844534 | + | 0.535502i | \(0.820122\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.44264e15 | −0.789888 | −0.394944 | − | 0.918705i | \(-0.629236\pi\) | ||||
−0.394944 | + | 0.918705i | \(0.629236\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.44633e15i | 0.512838i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.49888e15i | − 0.138228i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.06400e16 | −0.789059 | −0.394529 | − | 0.918883i | \(-0.629092\pi\) | ||||
−0.394529 | + | 0.918883i | \(0.629092\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.08445e16 | −1.24988 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 9.38898e15i | − 0.457567i | −0.973477 | − | 0.228783i | \(-0.926525\pi\) | ||||
0.973477 | − | 0.228783i | \(-0.0734748\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.24422e16i | 0.893316i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.91303e16 | −1.60485 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.24169e16 | 0.603616 | 0.301808 | − | 0.953369i | \(-0.402410\pi\) | ||||
0.301808 | + | 0.953369i | \(0.402410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.59815e16i | 0.802099i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3.84074e15i | − 0.0711721i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.70573e16 | −1.03704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00962e16 | −0.519450 | −0.259725 | − | 0.965683i | \(-0.583632\pi\) | ||||
−0.259725 | + | 0.965683i | \(0.583632\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.24969e16i | 0.136114i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 3.80297e16i | − 0.349455i | −0.984617 | − | 0.174728i | \(-0.944096\pi\) | ||||
0.984617 | − | 0.174728i | \(-0.0559045\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.07629e17 | 1.61500 | 0.807498 | − | 0.589870i | \(-0.200821\pi\) | ||||
0.807498 | + | 0.589870i | \(0.200821\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.98638e16 | −0.461470 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.68191e17i | − 0.946325i | −0.880975 | − | 0.473162i | \(-0.843112\pi\) | ||||
0.880975 | − | 0.473162i | \(-0.156888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.08973e15i | 0.0196593i | 0.999952 | + | 0.00982967i | \(0.00312893\pi\) | ||||
−0.999952 | + | 0.00982967i | \(0.996871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.95218e17 | 1.21590 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.83148e16 | 0.100195 | 0.0500976 | − | 0.998744i | \(-0.484047\pi\) | ||||
0.0500976 | + | 0.998744i | \(0.484047\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.10325e17i | − 0.641149i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.99995e17i | − 0.789830i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.55628e17 | 0.582720 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.66297e17 | 0.922544 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.17566e18i | 2.02343i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.20642e17i | 1.08139i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.04849e17 | 0.137478 | 0.0687388 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687388 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.91698e18 | 2.20093 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.82237e17i | − 0.788011i | −0.919108 | − | 0.394005i | \(-0.871089\pi\) | ||||
0.919108 | − | 0.394005i | \(-0.128911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.63817e17i | 0.676473i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.08509e17 | −0.474712 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.27442e17 | 0.431965 | 0.215983 | − | 0.976397i | \(-0.430705\pi\) | ||||
0.215983 | + | 0.976397i | \(0.430705\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.57262e17i | 0.156585i | 0.996930 | + | 0.0782924i | \(0.0249468\pi\) | ||||
−0.996930 | + | 0.0782924i | \(0.975053\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 1.13915e18i | − 0.614069i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.39811e17 | 0.449453 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.35625e18 | −1.00137 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.43015e18i | − 0.919255i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.12586e18i | − 1.72855i | −0.503016 | − | 0.864277i | \(-0.667776\pi\) | ||||
0.503016 | − | 0.864277i | \(-0.332224\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.51399e18 | 0.455848 | 0.227924 | − | 0.973679i | \(-0.426806\pi\) | ||||
0.227924 | + | 0.973679i | \(0.426806\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.13129e18 | −0.573807 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.84198e17i | − 0.0444085i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.31795e18i | 1.36593i | 0.730450 | + | 0.682966i | \(0.239310\pi\) | ||||
−0.730450 | + | 0.682966i | \(0.760690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.38739e18 | −0.851787 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.39571e18 | −0.418229 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.62696e18i | 1.19883i | 0.800439 | + | 0.599414i | \(0.204600\pi\) | ||||
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.82479e18i | 0.258583i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.60518e18 | −0.972791 | −0.486396 | − | 0.873739i | \(-0.661689\pi\) | ||||
−0.486396 | + | 0.873739i | \(0.661689\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.39103e19 | −1.60805 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 6.36830e18i | − 0.666126i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.85927e18i | 0.934228i | 0.884197 | + | 0.467114i | \(0.154706\pi\) | ||||
−0.884197 | + | 0.467114i | \(0.845294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.42893e18 | 0.208734 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.57112e18 | −0.356657 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.05371e19i | 0.747257i | 0.927578 | + | 0.373628i | \(0.121886\pi\) | ||||
−0.927578 | + | 0.373628i | \(0.878114\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2.64819e19i | − 1.70876i | −0.519649 | − | 0.854380i | \(-0.673937\pi\) | ||||
0.519649 | − | 0.854380i | \(-0.326063\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.16251e18 | −0.538493 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.41584e19 | 0.758672 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.67682e18i | − 0.326525i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.93123e18i | 0.309660i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.32908e19 | −0.951484 | −0.475742 | − | 0.879585i | \(-0.657820\pi\) | ||||
−0.475742 | + | 0.879585i | \(0.657820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.61228e17 | −0.00976748 | −0.00488374 | − | 0.999988i | \(-0.501555\pi\) | ||||
−0.00488374 | + | 0.999988i | \(0.501555\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 4.38052e19i | − 1.50048i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.46253e18i | − 0.202974i | −0.994837 | − | 0.101487i | \(-0.967640\pi\) | ||||
0.994837 | − | 0.101487i | \(-0.0323600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.82250e19 | 0.525311 | 0.262655 | − | 0.964890i | \(-0.415402\pi\) | ||||
0.262655 | + | 0.964890i | \(0.415402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.05198e19 | 1.33750 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.68388e19i | 0.653202i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.63836e19i | 1.26254i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.99741e19 | 0.411832 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.99503e19 | 0.379059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.73859e19i | 1.35600i | 0.735060 | + | 0.678002i | \(0.237154\pi\) | ||||
−0.735060 | + | 0.678002i | \(0.762846\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.27448e20i | − 2.06113i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.19369e19 | 1.37329 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.09811e18 | −0.0289682 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 7.54743e19i | − 0.963882i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.60281e20i | 1.89473i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.34556e20 | 1.47337 | 0.736685 | − | 0.676236i | \(-0.236390\pi\) | ||||
0.736685 | + | 0.676236i | \(0.236390\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.02511e19 | −0.205541 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.95558e19i | 0.748949i | 0.927237 | + | 0.374474i | \(0.122177\pi\) | ||||
−0.927237 | + | 0.374474i | \(0.877823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.46397e19i | 0.302673i | 0.988482 | + | 0.151336i | \(0.0483576\pi\) | ||||
−0.988482 | + | 0.151336i | \(0.951642\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.07853e19 | 0.168676 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.21528e20 | −0.916538 | −0.458269 | − | 0.888814i | \(-0.651530\pi\) | ||||
−0.458269 | + | 0.888814i | \(0.651530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 5.46325e19i | − 0.383155i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.47546e20i | − 0.962870i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.25849e19 | 0.137226 | 0.0686129 | − | 0.997643i | \(-0.478143\pi\) | ||||
0.0686129 | + | 0.997643i | \(0.478143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.85622e20 | 1.61677 | 0.808383 | − | 0.588657i | \(-0.200343\pi\) | ||||
0.808383 | + | 0.588657i | \(0.200343\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.70895e20i | − 0.901731i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.16548e20i | − 0.573578i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.78920e20 | −2.19957 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.30199e20 | 0.558358 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.47186e20i | 0.589713i | 0.955541 | + | 0.294857i | \(0.0952719\pi\) | ||||
−0.955541 | + | 0.294857i | \(0.904728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.25741e19i | 0.234353i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.11211e20 | −1.09009 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.49632e20 | −1.14599 | −0.572993 | − | 0.819560i | \(-0.694218\pi\) | ||||
−0.572993 | + | 0.819560i | \(0.694218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.61271e20i | − 0.494890i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2.23768e20i | − 0.643211i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.56287e20 | 0.690402 | 0.345201 | − | 0.938529i | \(-0.387811\pi\) | ||||
0.345201 | + | 0.938529i | \(0.387811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.10415e20 | −0.531481 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.10860e20i | 0.736579i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.85596e20i | 1.52466i | 0.647187 | + | 0.762331i | \(0.275945\pi\) | ||||
−0.647187 | + | 0.762331i | \(0.724055\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.06814e20 | −1.05830 | −0.529151 | − | 0.848528i | \(-0.677489\pi\) | ||||
−0.529151 | + | 0.848528i | \(0.677489\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.98964e20 | −0.978783 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 6.34419e19i | − 0.116963i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.87639e20i | 1.01867i | 0.860569 | + | 0.509334i | \(0.170108\pi\) | ||||
−0.860569 | + | 0.509334i | \(0.829892\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.74929e19 | 0.0285251 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.24336e20 | −0.804647 | −0.402324 | − | 0.915498i | \(-0.631797\pi\) | ||||
−0.402324 | + | 0.915498i | \(0.631797\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.51546e20i | 1.08585i | 0.839780 | + | 0.542927i | \(0.182684\pi\) | ||||
−0.839780 | + | 0.542927i | \(0.817316\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 9.29898e20i | − 1.26548i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.42237e20 | 0.823568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.11465e20 | 0.376511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 5.56023e20i | − 0.633873i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7.51033e20i | − 0.807764i | −0.914811 | − | 0.403882i | \(-0.867661\pi\) | ||||
0.914811 | − | 0.403882i | \(-0.132339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.19227e20 | −0.222539 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.81039e20 | 0.173517 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.50213e21i | − 1.35988i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.04721e21i | − 0.895813i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.27366e20 | 0.426432 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.39426e20 | −0.335998 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.89249e19i | 0.0426209i | 0.999773 | + | 0.0213105i | \(0.00678384\pi\) | ||||
−0.999773 | + | 0.0213105i | \(0.993216\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.87923e21i | 1.97074i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.05717e20 | 0.586853 | 0.293427 | − | 0.955982i | \(-0.405204\pi\) | ||||
0.293427 | + | 0.955982i | \(0.405204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.51738e21 | 1.54462 | 0.772311 | − | 0.635245i | \(-0.219101\pi\) | ||||
0.772311 | + | 0.635245i | \(0.219101\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 3.18200e20i | − 0.184953i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.88675e21i | − 1.03923i | −0.854401 | − | 0.519614i | \(-0.826076\pi\) | ||||
0.854401 | − | 0.519614i | \(-0.173924\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.01010e20 | 0.366019 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.33234e21 | 1.15478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.40245e21i | 1.59798i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.52296e21i | 0.678704i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.67131e19 | −0.0239898 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.22292e20 | −0.249936 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.03084e21i | 0.393236i | 0.980480 | + | 0.196618i | \(0.0629959\pi\) | ||||
−0.980480 | + | 0.196618i | \(0.937004\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.34459e21i | 0.487321i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.42288e21 | 0.834549 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.14822e21 | 0.703435 | 0.351717 | − | 0.936106i | \(-0.385598\pi\) | ||||
0.351717 | + | 0.936106i | \(0.385598\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.92648e20i | 0.122266i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.48012e19i | 0.0162322i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.08980e21 | −0.870824 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.91662e21 | 0.782380 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.67482e21i | − 1.19389i | −0.802282 | − | 0.596945i | \(-0.796381\pi\) | ||||
0.802282 | − | 0.596945i | \(-0.203619\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 4.72313e21i | − 1.14872i | −0.818603 | − | 0.574360i | \(-0.805251\pi\) | ||||
0.818603 | − | 0.574360i | \(-0.194749\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.34594e21 | −1.00687 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.29922e21 | −0.949084 | −0.474542 | − | 0.880233i | \(-0.657386\pi\) | ||||
−0.474542 | + | 0.880233i | \(0.657386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6.11228e21i | − 1.28606i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.54485e21i | 0.711079i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.26993e21 | 1.00810 | 0.504048 | − | 0.863675i | \(-0.331843\pi\) | ||||
0.504048 | + | 0.863675i | \(0.331843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.68613e21 | −0.855073 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.46624e21i | 1.12576i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 3.61968e21i | − 0.601424i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.39416e21 | 1.17281 | 0.586405 | − | 0.810018i | \(-0.300543\pi\) | ||||
0.586405 | + | 0.810018i | \(0.300543\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.35463e21 | −0.810971 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.39674e21i | 0.346691i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3.45714e21i | − 0.477740i | −0.971052 | − | 0.238870i | \(-0.923223\pi\) | ||||
0.971052 | − | 0.238870i | \(-0.0767769\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.99329e21 | −1.31960 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.68282e22 | −2.12391 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3.17249e21i | − 0.382795i | −0.981513 | − | 0.191398i | \(-0.938698\pi\) | ||||
0.981513 | − | 0.191398i | \(-0.0613020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.45396e21i | 0.167761i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.27971e21 | −0.361947 | −0.180974 | − | 0.983488i | \(-0.557925\pi\) | ||||
−0.180974 | + | 0.983488i | \(0.557925\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.96845e20 | 0.105247 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.73105e21i | 0.882112i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.09936e22i | 1.06308i | 0.847032 | + | 0.531542i | \(0.178387\pi\) | ||||
−0.847032 | + | 0.531542i | \(0.821613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.06718e22 | −0.987947 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.08474e22 | 0.961591 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 7.07620e21i | − 0.600792i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.01100e21i | 0.732915i | 0.930435 | + | 0.366458i | \(0.119430\pi\) | ||||
−0.930435 | + | 0.366458i | \(0.880570\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.05920e22 | −0.825484 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.05004e22 | 0.784296 | 0.392148 | − | 0.919902i | \(-0.371732\pi\) | ||||
0.392148 | + | 0.919902i | \(0.371732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.31553e21i | − 0.0941910i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.38628e22i | − 0.951664i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.21228e21 | −0.277310 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.86541e21 | 0.370382 | 0.185191 | − | 0.982703i | \(-0.440710\pi\) | ||||
0.185191 | + | 0.982703i | \(0.440710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.70087e21i | 0.527117i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.49711e21i | 0.145165i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.24423e21 | 0.348393 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.56750e21 | −0.191077 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 5.02281e21i | − 0.258302i | −0.991625 | − | 0.129151i | \(-0.958775\pi\) | ||||
0.991625 | − | 0.129151i | \(-0.0412252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.55885e22i | − 0.769848i | −0.922948 | − | 0.384924i | \(-0.874228\pi\) | ||||
0.922948 | − | 0.384924i | \(-0.125772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.18834e21 | 0.246113 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.08198e22 | 0.493074 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.00528e21i | 0.219175i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.30326e22i | 0.548457i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.78561e22 | 1.12684 | 0.563421 | − | 0.826170i | \(-0.309485\pi\) | ||||
0.563421 | + | 0.826170i | \(0.309485\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.24470e21 | −0.0484079 | −0.0242040 | − | 0.999707i | \(-0.507705\pi\) | ||||
−0.0242040 | + | 0.999707i | \(0.507705\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 3.26745e22i | − 1.22194i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.18872e22i | − 1.14690i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.09614e22 | 0.725224 | 0.362612 | − | 0.931940i | \(-0.381885\pi\) | ||||
0.362612 | + | 0.931940i | \(0.381885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.10683e22 | 0.368429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.11978e22i | 0.358674i | 0.983788 | + | 0.179337i | \(0.0573952\pi\) | ||||
−0.983788 | + | 0.179337i | \(0.942605\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.49086e22i | 0.459596i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.10813e22 | 2.10931 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.44200e22 | −0.411975 | −0.205987 | − | 0.978555i | \(-0.566041\pi\) | ||||
−0.205987 | + | 0.978555i | \(0.566041\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.67748e22i | − 0.461483i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.09949e22i | 0.556261i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.39298e22 | −0.610721 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.99851e22 | 0.737254 | 0.368627 | − | 0.929577i | \(-0.379828\pi\) | ||||
0.368627 | + | 0.929577i | \(0.379828\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.08754e22i | 0.731484i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.32706e22i | 0.987950i | 0.869476 | + | 0.493975i | \(0.164456\pi\) | ||||
−0.869476 | + | 0.493975i | \(0.835544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.79925e22 | 0.395962 | 0.197981 | − | 0.980206i | \(-0.436562\pi\) | ||||
0.197981 | + | 0.980206i | \(0.436562\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.55432e21 | 0.0541907 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.53566e22i | 1.13234i | 0.824289 | + | 0.566169i | \(0.191575\pi\) | ||||
−0.824289 | + | 0.566169i | \(0.808425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.75979e22i | − 0.544386i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.76123e22 | −1.66682 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.73523e22 | −0.501965 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.23295e22i | 0.572404i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.99827e22i | − 0.341388i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.18108e22 | 0.194727 | 0.0973637 | − | 0.995249i | \(-0.468959\pi\) | ||||
0.0973637 | + | 0.995249i | \(0.468959\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.01118e23 | 1.60915 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3.32218e22i | − 0.510355i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2.66664e22i | − 0.395511i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.16692e22 | −0.310347 | −0.155173 | − | 0.987887i | \(-0.549594\pi\) | ||||
−0.155173 | + | 0.987887i | \(0.549594\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.05765e23 | −1.46290 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.30265e23i | − 1.74034i | −0.492749 | − | 0.870172i | \(-0.664008\pi\) | ||||
0.492749 | − | 0.870172i | \(-0.335992\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.19555e23i | 1.54300i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.31116e21 | −0.103638 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.96220e22 | −0.838913 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.17276e22i | 0.602376i | 0.953565 | + | 0.301188i | \(0.0973832\pi\) | ||||
−0.953565 | + | 0.301188i | \(0.902617\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1.05463e23i | − 1.18707i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.07219e23 | −1.16665 | −0.583327 | − | 0.812237i | \(-0.698249\pi\) | ||||
−0.583327 | + | 0.812237i | \(0.698249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.52920e22 | 0.266076 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.92897e23i | − 1.96227i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.48328e23i | − 1.45922i | −0.683861 | − | 0.729612i | \(-0.739701\pi\) | ||||
0.683861 | − | 0.729612i | \(-0.260299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.12300e22 | −0.392316 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.22557e22 | −0.849172 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.38086e23i | 1.22966i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.62538e22i | 0.140051i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.36721e23 | −1.14002 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.01242e22 | 0.565910 | 0.282955 | − | 0.959133i | \(-0.408685\pi\) | ||||
0.282955 | + | 0.959133i | \(0.408685\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.14598e23i | 1.67634i | 0.545410 | + | 0.838169i | \(0.316374\pi\) | ||||
−0.545410 | + | 0.838169i | \(0.683626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.36825e22i | 0.254713i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.34612e21 | −0.0684291 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.10359e22 | −0.290932 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2.08195e22i | − 0.142945i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.02688e23i | 2.67786i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.11857e23 | 0.720536 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.46120e23 | −0.911860 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.46743e22i | 0.209654i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.34761e23i | − 0.789565i | −0.918775 | − | 0.394783i | \(-0.870820\pi\) | ||||
0.918775 | − | 0.394783i | \(-0.129180\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.67230e23 | 2.08516 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.71991e21 | −0.0149687 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.17960e23i | − 1.16274i | −0.813638 | − | 0.581372i | \(-0.802516\pi\) | ||||
0.813638 | − | 0.581372i | \(-0.197484\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4.17314e22i | − 0.215823i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.57229e23 | −1.79126 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.06015e22 | −0.391904 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.96337e23i | 0.925790i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 7.39588e22i | − 0.338237i | −0.985596 | − | 0.169118i | \(-0.945908\pi\) | ||||
0.985596 | − | 0.169118i | \(-0.0540920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.56608e23 | 2.91277 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.25888e22 | 0.398450 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.46778e21i | 0.0270044i | 0.999909 | + | 0.0135022i | \(0.00429801\pi\) | ||||
−0.999909 | + | 0.0135022i | \(0.995702\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.88310e22i | 0.0762891i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.57904e23 | −0.620781 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.40211e23 | 1.29806 | 0.649029 | − | 0.760764i | \(-0.275176\pi\) | ||||
0.649029 | + | 0.760764i | \(0.275176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 4.01054e23i | − 1.48524i | −0.669715 | − | 0.742619i | \(-0.733584\pi\) | ||||
0.669715 | − | 0.742619i | \(-0.266416\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3.22979e23i | − 1.16107i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.01401e23 | −0.353888 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.92304e23 | 0.651619 | 0.325810 | − | 0.945435i | \(-0.394363\pi\) | ||||
0.325810 | + | 0.945435i | \(0.394363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 3.62250e21i | − 0.0119190i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 7.11249e22i | − 0.227261i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.26010e22 | 0.194267 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.99514e23 | 0.601380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.13316e23i | 0.331793i | 0.986143 | + | 0.165896i | \(0.0530517\pi\) | ||||
−0.986143 | + | 0.165896i | \(0.946948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.79262e22i | − 0.0794386i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.96173e22 | 0.247684 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.06278e23 | 1.09108 | 0.545542 | − | 0.838084i | \(-0.316324\pi\) | ||||
0.545542 | + | 0.838084i | \(0.316324\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.70008e23i | 0.443685i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.52730e23i | 0.641025i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.15444e23 | −1.27073 | −0.635365 | − | 0.772212i | \(-0.719150\pi\) | ||||
−0.635365 | + | 0.772212i | \(0.719150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.97639e23 | 0.952918 | 0.476459 | − | 0.879197i | \(-0.341920\pi\) | ||||
0.476459 | + | 0.879197i | \(0.341920\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.30096e23i | 0.536059i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.10115e23i | 0.702429i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.76629e23 | 1.49021 | 0.745104 | − | 0.666948i | \(-0.232400\pi\) | ||||
0.745104 | + | 0.666948i | \(0.232400\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.72180e23 | −0.797087 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 3.90182e23i | − 0.812675i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.69956e23i | 1.35716i | 0.734525 | + | 0.678582i | \(0.237405\pi\) | ||||
−0.734525 | + | 0.678582i | \(0.762595\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.81882e23 | −1.54065 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.38236e23 | −0.456649 | −0.228325 | − | 0.973585i | \(-0.573325\pi\) | ||||
−0.228325 | + | 0.973585i | \(0.573325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.75944e23i | 0.328099i | 0.986452 | + | 0.164049i | \(0.0524556\pi\) | ||||
−0.986452 | + | 0.164049i | \(0.947544\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.89360e23i | − 0.525000i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.69816e23 | 0.299799 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.34643e23 | −0.403114 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.76655e23i | 0.462557i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 7.18388e23i | − 1.16904i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.34532e23 | 0.846689 | 0.423344 | − | 0.905969i | \(-0.360856\pi\) | ||||
0.423344 | + | 0.905969i | \(0.360856\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.07313e24 | −1.65470 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.97306e22i | 0.104676i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8.32378e23i | − 1.21657i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.80471e23 | 0.826082 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.21663e24 | −1.68603 | −0.843017 | − | 0.537887i | \(-0.819223\pi\) | ||||
−0.843017 | + | 0.537887i | \(0.819223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.18465e23i | 0.294842i | 0.989074 | + | 0.147421i | \(0.0470972\pi\) | ||||
−0.989074 | + | 0.147421i | \(0.952903\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.27491e24i | 1.67580i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.14703e24 | −1.46855 | −0.734275 | − | 0.678852i | \(-0.762478\pi\) | ||||
−0.734275 | + | 0.678852i | \(0.762478\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.52226e22 | 0.0813426 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.90950e22i | − 0.0353492i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.50867e23i | 0.178580i | 0.996006 | + | 0.0892898i | \(0.0284597\pi\) | ||||
−0.996006 | + | 0.0892898i | \(0.971540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.20234e23 | 0.599995 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.43754e23 | 0.386315 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.33218e24i | − 1.45894i | −0.684013 | − | 0.729470i | \(-0.739767\pi\) | ||||
0.684013 | − | 0.729470i | \(-0.260233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.50165e24i | − 1.60272i | −0.598183 | − | 0.801359i | \(-0.704111\pi\) | ||||
0.598183 | − | 0.801359i | \(-0.295889\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.22265e24 | −2.31210 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.07983e23 | −0.515069 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.12045e24i | − 1.10744i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.86592e24i | 1.79792i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.30734e23 | 0.122814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.95354e24 | 1.78935 | 0.894673 | − | 0.446722i | \(-0.147409\pi\) | ||||
0.894673 | + | 0.446722i | \(0.147409\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.93373e23i | 0.262022i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.79219e24i | − 1.56092i | −0.625208 | − | 0.780458i | \(-0.714986\pi\) | ||||
0.625208 | − | 0.780458i | \(-0.285014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.03743e23 | −0.257997 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.10322e24 | −0.913925 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.23745e24i | 1.80791i | 0.427628 | + | 0.903955i | \(0.359349\pi\) | ||||
−0.427628 | + | 0.903955i | \(0.640651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.17286e23i | 0.328900i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.80356e23 | −0.369344 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.50278e24 | −1.12728 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.07548e24i | 0.787114i | 0.919300 | + | 0.393557i | \(0.128756\pi\) | ||||
−0.919300 | + | 0.393557i | \(0.871244\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.46683e22i | 0.0676040i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.71094e23 | −0.119224 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.86087e24 | 1.94545 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.68525e24i | − 1.11843i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.83049e23i | 0.312887i | 0.987687 | + | 0.156444i | \(0.0500030\pi\) | ||||
−0.987687 | + | 0.156444i | \(0.949997\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.14654e24 | 1.35712 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.57600e23 | 0.467555 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.88089e23i | − 0.173565i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.46817e23i | 0.380442i | 0.981741 | + | 0.190221i | \(0.0609204\pi\) | ||||
−0.981741 | + | 0.190221i | \(0.939080\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.72012e23 | 0.385909 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.75904e22 | 0.0491129 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.25030e23i | 0.342215i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.13189e23i | 0.167454i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.08660e24 | 1.08954 | 0.544770 | − | 0.838586i | \(-0.316617\pi\) | ||||
0.544770 | + | 0.838586i | \(0.316617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.57286e24 | 0.802124 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.96078e24i | 1.97290i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.13599e24i | 0.552713i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.50710e24 | −1.19160 | −0.595799 | − | 0.803134i | \(-0.703164\pi\) | ||||
−0.595799 | + | 0.803134i | \(0.703164\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.22019e23 | −0.149519 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 4.66482e24i | − 2.11611i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.50202e24i | 1.10894i | 0.832205 | + | 0.554469i | \(0.187079\pi\) | ||||
−0.832205 | + | 0.554469i | \(0.812921\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.61619e24 | 0.699924 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.20836e23 | −0.305044 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.98150e24i | − 0.819440i | −0.912211 | − | 0.409720i | \(-0.865626\pi\) | ||||
0.912211 | − | 0.409720i | \(-0.134374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 6.64128e24i | − 2.68409i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.48113e24 | 0.585043 | 0.292521 | − | 0.956259i | \(-0.405506\pi\) | ||||
0.292521 | + | 0.956259i | \(0.405506\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.40900e24 | 1.31613 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.93001e23i | 0.223785i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.27411e24i | − 0.470013i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.06055e24 | 1.82498 | 0.912490 | − | 0.409100i | \(-0.134157\pi\) | ||||
0.912490 | + | 0.409100i | \(0.134157\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.04106e24 | −0.719614 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00690e24i | 0.347085i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.15475e23i | − 0.0389200i | −0.999811 | − | 0.0194600i | \(-0.993805\pi\) | ||||
0.999811 | − | 0.0194600i | \(-0.00619470\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.67728e23 | −0.285975 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.07347e24 | −0.990510 | −0.495255 | − | 0.868748i | \(-0.664925\pi\) | ||||
−0.495255 | + | 0.868748i | \(0.664925\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.09811e22i | 0.00976425i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.41743e24i | − 0.436899i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.56571e24 | −0.472008 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.56828e24 | 0.462434 | 0.231217 | − | 0.972902i | \(-0.425729\pi\) | ||||
0.231217 | + | 0.972902i | \(0.425729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 4.84842e24i | − 1.39842i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.06812e24i | 0.865659i | 0.901476 | + | 0.432830i | \(0.142485\pi\) | ||||
−0.901476 | + | 0.432830i | \(0.857515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.88051e22 | −0.0245117 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.23638e24 | 0.603903 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.54827e24i | 2.25845i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.81847e24i | 0.470082i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.24166e24 | −0.819960 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.20181e24 | −1.04003 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 7.03196e23i | − 0.170330i | −0.996367 | − | 0.0851650i | \(-0.972858\pi\) | ||||
0.996367 | − | 0.0851650i | \(-0.0271417\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.55398e24i | 0.842482i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.14495e23 | 0.0497642 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.13835e24 | −0.712656 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 2.91788e24i | − 0.648554i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.69599e24i | 1.02172i | 0.859664 | + | 0.510859i | \(0.170673\pi\) | ||||
−0.859664 | + | 0.510859i | \(0.829327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.77202e24 | −0.590403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.41584e24 | −0.295214 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.07690e24i | 0.219832i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.59329e24i | − 0.318441i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.50730e24 | −1.86051 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.37783e24 | −0.838873 | −0.419436 | − | 0.907785i | \(-0.637772\pi\) | ||||
−0.419436 | + | 0.907785i | \(0.637772\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.61180e24i | 1.61591i | 0.589245 | + | 0.807954i | \(0.299425\pi\) | ||||
−0.589245 | + | 0.807954i | \(0.700575\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.02809e24i | − 1.29142i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.07238e24 | −0.912793 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.39385e25 | 2.45656 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 2.27257e24i | − 0.392287i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.09648e24i | 0.692619i | 0.938120 | + | 0.346309i | \(0.112565\pi\) | ||||
−0.938120 | + | 0.346309i | \(0.887435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.02308e24 | 0.666284 | 0.333142 | − | 0.942877i | \(-0.391891\pi\) | ||||
0.333142 | + | 0.942877i | \(0.391891\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.79762e23 | 0.142727 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6.80277e24i | − 1.08116i | −0.841294 | − | 0.540579i | \(-0.818205\pi\) | ||||
0.841294 | − | 0.540579i | \(-0.181795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 9.06827e24i | − 1.41192i | −0.708251 | − | 0.705961i | \(-0.750515\pi\) | ||||
0.708251 | − | 0.705961i | \(-0.249485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.14891e24 | −1.24306 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.91357e24 | −0.883827 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 5.05790e24i | − 0.740687i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2.53415e23i | − 0.0363636i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.26281e24 | 0.318179 | 0.159090 | − | 0.987264i | \(-0.449144\pi\) | ||||
0.159090 | + | 0.987264i | \(0.449144\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.29508e24 | −0.729637 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 7.27107e24i | − 0.981892i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 9.25117e24i | − 1.22438i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.53237e24 | 0.458202 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.04219e25 | −1.32504 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.73262e24i | 0.839040i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.22743e24i | 1.12723i | 0.826036 | + | 0.563617i | \(0.190591\pi\) | ||||
−0.826036 | + | 0.563617i | \(0.809409\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.23529e24 | 0.507191 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.23968e24 | 0.497733 | 0.248867 | − | 0.968538i | \(-0.419942\pi\) | ||||
0.248867 | + | 0.968538i | \(0.419942\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.28165e24i | − 0.262608i | −0.991342 | − | 0.131304i | \(-0.958084\pi\) | ||||
0.991342 | − | 0.131304i | \(-0.0419164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.90604e24i | 1.00498i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.03258e25 | 1.14244 | 0.571220 | − | 0.820797i | \(-0.306470\pi\) | ||||
0.571220 | + | 0.820797i | \(0.306470\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.55700e24 | −0.711325 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.31915e24i | 0.459447i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.10525e24i | 0.219602i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.73041e25 | 1.77009 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.53245e24 | 0.254050 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.45912e24i | 0.537099i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.49582e24i | 0.144338i | 0.997392 | + | 0.0721692i | \(0.0229921\pi\) | ||||
−0.997392 | + | 0.0721692i | \(0.977008\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.04147e25 | 0.985695 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.02128e24 | 0.837477 | 0.418739 | − | 0.908107i | \(-0.362472\pi\) | ||||
0.418739 | + | 0.908107i | \(0.362472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.61859e24i | 0.511636i | 0.966725 | + | 0.255818i | \(0.0823448\pi\) | ||||
−0.966725 | + | 0.255818i | \(0.917655\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 3.04007e24i | − 0.271560i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.48729e25 | −1.30330 | −0.651649 | − | 0.758521i | \(-0.725922\pi\) | ||||
−0.651649 | + | 0.758521i | \(0.725922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.94267e23 | 0.0682813 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.12435e24i | 0.347852i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.28280e24i | − 0.685393i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.00778e24 | −0.568964 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.08303e25 | 1.65944 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 9.81264e23i | − 0.0767059i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.06764e25i | 0.818959i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.45218e25 | 1.09314 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.76120e25 | 1.30106 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.26650e25i | 0.918215i | 0.888381 | + | 0.459107i | \(0.151831\pi\) | ||||
−0.888381 | + | 0.459107i | \(0.848169\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.40193e24i | 0.170910i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.22052e25 | −1.55077 | −0.775387 | − | 0.631487i | \(-0.782445\pi\) | ||||
−0.775387 | + | 0.631487i | \(0.782445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.85773e24 | −0.127345 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 6.09361e24i | − 0.410011i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 5.92572e24i | − 0.391383i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.34055e25 | 1.51753 | 0.758763 | − | 0.651367i | \(-0.225804\pi\) | ||||
0.758763 | + | 0.651367i | \(0.225804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.17124e23 | −0.0520093 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 4.36536e25i | − 2.72775i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.82599e24i | − 0.418756i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.31137e25 | −0.789855 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.30561e24 | 0.372901 | 0.186450 | − | 0.982464i | \(-0.440302\pi\) | ||||
0.186450 | + | 0.982464i | \(0.440302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.76697e25i | − 1.02603i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.25598e25i | 0.716123i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.44048e24 | 0.248617 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.24230e23 | −0.0453171 | −0.0226586 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226586 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.49090e25i | 1.88487i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 6.73452e24i | − 0.357104i | −0.983930 | − | 0.178552i | \(-0.942859\pi\) | ||||
0.983930 | − | 0.178552i | \(-0.0571413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.68116e25 | −1.39628 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.60968e24 | −0.235776 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.19407e25i | 1.10224i | 0.834426 | + | 0.551119i | \(0.185799\pi\) | ||||
−0.834426 | + | 0.551119i | \(0.814201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.58515e25i | − 1.27563i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.61639e25 | 1.26814 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.04120e25 | 0.495727 | 0.247864 | − | 0.968795i | \(-0.420272\pi\) | ||||
0.247864 | + | 0.968795i | \(0.420272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.54898e25i | − 0.724464i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.72106e24i | 0.446645i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.75310e24 | 0.214545 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.24734e25 | −0.996598 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.06228e25i | 0.462824i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.73732e23i | − 0.00743700i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.11036e25 | −0.887630 | −0.443815 | − | 0.896118i | \(-0.646375\pi\) | ||||
−0.443815 | + | 0.896118i | \(0.646375\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.71825e25 | −1.94997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 6.24704e24i | − 0.253694i | −0.991922 | − | 0.126847i | \(-0.959514\pi\) | ||||
0.991922 | − | 0.126847i | \(-0.0404858\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.94885e24i | 0.0777713i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.11192e25 | −0.828206 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.86564e25 | −0.718992 | −0.359496 | − | 0.933147i | \(-0.617051\pi\) | ||||
−0.359496 | + | 0.933147i | \(0.617051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 4.43547e24i | − 0.167991i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 2.58304e23i | − 0.00961490i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.39881e25 | 0.877589 | 0.438794 | − | 0.898588i | \(-0.355406\pi\) | ||||
0.438794 | + | 0.898588i | \(0.355406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.29797e24 | 0.154545 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 8.62945e24i | − 0.304991i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.37180e25i | 1.51877i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.85777e25 | −0.975889 | −0.487945 | − | 0.872875i | \(-0.662253\pi\) | ||||
−0.487945 | + | 0.872875i | \(0.662253\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.42949e25 | −0.479857 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.21207e25i | 0.399974i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.00050e25i | − 0.324571i | −0.986744 | − | 0.162285i | \(-0.948113\pi\) | ||||
0.986744 | − | 0.162285i | \(-0.0518865\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.94787e25 | 0.621232 |
(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 | 32.18.b.a.17.14 | 16 | ||
4.3 | odd | 2 | 8.18.b.a.5.2 | yes | 16 | ||
8.3 | odd | 2 | 8.18.b.a.5.1 | ✓ | 16 | ||
8.5 | even | 2 | inner | 32.18.b.a.17.3 | 16 | ||
12.11 | even | 2 | 72.18.d.b.37.15 | 16 | |||
24.11 | even | 2 | 72.18.d.b.37.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.b.a.5.1 | ✓ | 16 | 8.3 | odd | 2 | ||
8.18.b.a.5.2 | yes | 16 | 4.3 | odd | 2 | ||
32.18.b.a.17.3 | 16 | 8.5 | even | 2 | inner | ||
32.18.b.a.17.14 | 16 | 1.1 | even | 1 | trivial | ||
72.18.d.b.37.15 | 16 | 12.11 | even | 2 | |||
72.18.d.b.37.16 | 16 | 24.11 | even | 2 |