Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,22,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(201.223687887\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.63 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.22.f.a.35.64 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1049.06 | − | 998.310i | 0.724412 | − | 0.689367i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 103905. | − | 2.09458e6i | 0.0495460 | − | 0.998772i | ||||
\(5\) | −2.17906e7 | −0.997895 | −0.498948 | − | 0.866632i | \(-0.666280\pi\) | ||||
−0.498948 | + | 0.866632i | \(0.666280\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.90529e8i | 1.19157i | 0.803145 | + | 0.595784i | \(0.203158\pi\) | ||||
−0.803145 | + | 0.595784i | \(0.796842\pi\) | |||||||
\(8\) | −1.98203e9 | − | 2.30107e9i | −0.652629 | − | 0.757678i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.28597e10 | + | 2.17538e10i | −0.722888 | + | 0.687916i | ||||
\(11\) | − | 3.82633e10i | − | 0.444794i | −0.974956 | − | 0.222397i | \(-0.928612\pi\) | ||
0.974956 | − | 0.222397i | \(-0.0713882\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.83887e11i | − | 0.973506i | −0.873540 | − | 0.486753i | \(-0.838181\pi\) | ||
0.873540 | − | 0.486753i | \(-0.161819\pi\) | |||||||
\(14\) | 8.89024e11 | + | 9.34219e11i | 0.821427 | + | 0.863186i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.37645e12 | − | 4.35276e11i | −0.995090 | − | 0.0989703i | ||||
\(17\) | − | 2.21884e12i | − | 0.266939i | −0.991053 | − | 0.133470i | \(-0.957388\pi\) | ||
0.991053 | − | 0.133470i | \(-0.0426119\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.16847e13 | 0.437223 | 0.218612 | − | 0.975812i | \(-0.429847\pi\) | ||||
0.218612 | + | 0.975812i | \(0.429847\pi\) | |||||||
\(20\) | −2.26417e12 | + | 4.56422e13i | −0.0494417 | + | 0.996670i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.81986e13 | − | 4.01405e13i | −0.306627 | − | 0.322214i | ||||
\(23\) | −8.76881e13 | −0.441366 | −0.220683 | − | 0.975346i | \(-0.570829\pi\) | ||||
−0.220683 | + | 0.975346i | \(0.570829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00507e12 | −0.00420493 | ||||||||
\(26\) | −4.83069e14 | − | 5.07627e14i | −0.671103 | − | 0.705220i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.86528e15 | + | 9.25308e13i | 1.19010 | + | 0.0590374i | ||||
\(29\) | −4.27624e15 | −1.88748 | −0.943742 | − | 0.330683i | \(-0.892721\pi\) | ||||
−0.943742 | + | 0.330683i | \(0.892721\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.49379e15i | − | 0.546465i | −0.961948 | − | 0.273233i | \(-0.911907\pi\) | ||
0.961948 | − | 0.273233i | \(-0.0880929\pi\) | |||||||
\(32\) | −5.02571e15 | + | 3.91243e15i | −0.789082 | + | 0.614287i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.21509e15 | − | 2.32770e15i | −0.184019 | − | 0.193374i | ||||
\(35\) | − | 1.94052e16i | − | 1.18906i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.91817e15i | 0.202334i | 0.994869 | + | 0.101167i | \(0.0322577\pi\) | ||||
−0.994869 | + | 0.101167i | \(0.967742\pi\) | |||||||
\(38\) | 1.22579e16 | − | 1.16649e16i | 0.316730 | − | 0.301407i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.31898e16 | + | 5.01418e16i | 0.651255 | + | 0.756083i | ||||
\(41\) | − | 2.79351e16i | − | 0.325028i | −0.986706 | − | 0.162514i | \(-0.948040\pi\) | ||
0.986706 | − | 0.162514i | \(-0.0519602\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.17433e16 | −0.365120 | −0.182560 | − | 0.983195i | \(-0.558438\pi\) | ||||
−0.182560 | + | 0.983195i | \(0.558438\pi\) | |||||||
\(44\) | −8.01454e16 | − | 3.97577e15i | −0.444248 | − | 0.0220378i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.19902e16 | + | 8.75400e16i | −0.319731 | + | 0.304263i | ||||
\(47\) | −2.93354e17 | −0.813513 | −0.406756 | − | 0.913537i | \(-0.633340\pi\) | ||||
−0.406756 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.34495e17 | −0.419832 | ||||||||
\(50\) | −2.10344e15 | + | 2.00168e15i | −0.00304610 | + | 0.00289874i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.01354e18 | − | 5.02785e16i | −0.972310 | − | 0.0482333i | ||||
\(53\) | 7.56626e17 | 0.594271 | 0.297136 | − | 0.954835i | \(-0.403969\pi\) | ||||
0.297136 | + | 0.954835i | \(0.403969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.33782e17i | 0.443858i | ||||||||
\(56\) | 2.04917e18 | − | 1.76506e18i | 0.902824 | − | 0.777651i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.48604e18 | + | 4.26901e18i | −1.36732 | + | 1.30117i | ||||
\(59\) | 4.55809e18i | 1.16101i | 0.814256 | + | 0.580506i | \(0.197145\pi\) | ||||
−0.814256 | + | 0.580506i | \(0.802855\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.83311e18i | 1.22646i | 0.789903 | + | 0.613232i | \(0.210131\pi\) | ||||
−0.789903 | + | 0.613232i | \(0.789869\pi\) | |||||||
\(62\) | −2.48958e18 | − | 2.61614e18i | −0.376715 | − | 0.395866i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.36646e18 | + | 9.12159e18i | −0.148151 | + | 0.988965i | ||||
\(65\) | 1.05442e19i | 0.971457i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.07614e18 | 0.139146 | 0.0695731 | − | 0.997577i | \(-0.477836\pi\) | ||||
0.0695731 | + | 0.997577i | \(0.477836\pi\) | |||||||
\(68\) | −4.64753e18 | − | 2.30550e17i | −0.266612 | − | 0.0132258i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.93724e19 | − | 2.03572e19i | −0.819698 | − | 0.861369i | ||||
\(71\) | 1.22268e19 | 0.445758 | 0.222879 | − | 0.974846i | \(-0.428454\pi\) | ||||
0.222879 | + | 0.974846i | \(0.428454\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.26851e19 | 1.70716 | 0.853580 | − | 0.520961i | \(-0.174426\pi\) | ||||
0.853580 | + | 0.520961i | \(0.174426\pi\) | |||||||
\(74\) | 5.90817e18 | + | 6.20852e18i | 0.139483 | + | 0.146573i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.21410e18 | − | 2.44744e19i | 0.0216626 | − | 0.436686i | ||||
\(77\) | 3.40746e19 | 0.530002 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.16868e19i | − | 0.851833i | −0.904762 | − | 0.425917i | \(-0.859952\pi\) | ||
0.904762 | − | 0.425917i | \(-0.140048\pi\) | |||||||
\(80\) | 9.53657e19 | + | 9.48494e18i | 0.992996 | + | 0.0987620i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.78879e19 | − | 2.93057e19i | −0.224063 | − | 0.235454i | ||||
\(83\) | 1.85258e20i | 1.31056i | 0.755385 | + | 0.655282i | \(0.227450\pi\) | ||||
−0.755385 | + | 0.655282i | \(0.772550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.83500e19i | 0.266378i | ||||||||
\(86\) | −5.42819e19 | + | 5.16559e19i | −0.264497 | + | 0.251701i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.80465e19 | + | 7.58392e19i | −0.337011 | + | 0.290286i | ||||
\(89\) | − | 2.85566e20i | − | 0.970758i | −0.874304 | − | 0.485379i | \(-0.838682\pi\) | ||
0.874304 | − | 0.485379i | \(-0.161318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.30915e20 | 1.16000 | ||||||||
\(92\) | −9.11128e18 | + | 1.83670e20i | −0.0218679 | + | 0.440824i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.07746e20 | + | 2.92858e20i | −0.589319 | + | 0.560809i | ||||
\(95\) | −2.54616e20 | −0.436303 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.52477e20 | 1.31145 | 0.655724 | − | 0.755001i | \(-0.272363\pi\) | ||||
0.655724 | + | 0.755001i | \(0.272363\pi\) | |||||||
\(98\) | −2.46000e20 | + | 2.34099e20i | −0.304131 | + | 0.289418i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.08337e17 | + | 4.19976e18i | −0.000208337 | + | 0.00419976i | ||||
\(101\) | −7.40415e20 | −0.666962 | −0.333481 | − | 0.942757i | \(-0.608223\pi\) | ||||
−0.333481 | + | 0.942757i | \(0.608223\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.01409e21i | − | 0.743508i | −0.928331 | − | 0.371754i | \(-0.878756\pi\) | ||
0.928331 | − | 0.371754i | \(-0.121244\pi\) | |||||||
\(104\) | −1.11346e21 | + | 9.59080e20i | −0.737604 | + | 0.635338i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.93747e20 | − | 7.55348e20i | 0.430497 | − | 0.409671i | ||||
\(107\) | − | 1.84528e21i | − | 0.906846i | −0.891295 | − | 0.453423i | \(-0.850203\pi\) | ||
0.891295 | − | 0.453423i | \(-0.149797\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.08113e20i | 0.326960i | 0.986547 | + | 0.163480i | \(0.0522718\pi\) | ||||
−0.986547 | + | 0.163480i | \(0.947728\pi\) | |||||||
\(110\) | 8.32373e20 | + | 8.74688e20i | 0.305981 | + | 0.321536i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.87626e20 | − | 3.89736e21i | 0.117930 | − | 1.18572i | ||||
\(113\) | − | 1.03198e21i | − | 0.285988i | −0.989724 | − | 0.142994i | \(-0.954327\pi\) | ||
0.989724 | − | 0.142994i | \(-0.0456730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.91078e21 | 0.440437 | ||||||||
\(116\) | −4.44325e20 | + | 8.95691e21i | −0.0935172 | + | 1.88517i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.55038e21 | + | 4.78171e21i | 0.800363 | + | 0.841051i | ||||
\(119\) | 1.97594e21 | 0.318076 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.93617e21 | 0.802158 | ||||||||
\(122\) | 6.82156e21 | + | 7.16834e21i | 0.845484 | + | 0.888466i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.22344e21 | − | 2.59119e20i | −0.545794 | − | 0.0270752i | ||||
\(125\) | 1.04343e22 | 1.00209 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.05105e21i | 0.166739i | 0.996519 | + | 0.0833693i | \(0.0265681\pi\) | ||||
−0.996519 | + | 0.0833693i | \(0.973432\pi\) | |||||||
\(128\) | 7.67268e21 | + | 1.09332e22i | 0.574437 | + | 0.818549i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.05264e22 | + | 1.10615e22i | 0.669690 | + | 0.703735i | ||||
\(131\) | 3.08968e22i | 1.81370i | 0.421457 | + | 0.906848i | \(0.361519\pi\) | ||||
−0.421457 | + | 0.906848i | \(0.638481\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.04055e22i | 0.520981i | ||||||||
\(134\) | 2.17800e21 | − | 2.07263e21i | 0.100799 | − | 0.0959227i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.10571e21 | + | 4.39782e21i | −0.202254 | + | 0.174212i | ||||
\(137\) | 4.38025e22i | 1.60669i | 0.595511 | + | 0.803347i | \(0.296949\pi\) | ||||
−0.595511 | + | 0.803347i | \(0.703051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.08156e22 | −0.655744 | −0.327872 | − | 0.944722i | \(-0.606331\pi\) | ||||
−0.327872 | + | 0.944722i | \(0.606331\pi\) | |||||||
\(140\) | −4.06457e22 | − | 2.01631e21i | −1.18760 | − | 0.0589131i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.28266e22 | − | 1.22061e22i | 0.322913 | − | 0.307291i | ||||
\(143\) | −1.85151e22 | −0.433010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.31820e22 | 1.88351 | ||||||||
\(146\) | 6.57605e22 | − | 6.25792e22i | 1.23669 | − | 1.17686i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.23961e22 | + | 6.14931e20i | 0.202086 | + | 0.0100249i | ||||
\(149\) | 2.02470e21 | 0.0307543 | 0.0153772 | − | 0.999882i | \(-0.495105\pi\) | ||||
0.0153772 | + | 0.999882i | \(0.495105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.22747e23i | − | 1.62089i | −0.585817 | − | 0.810443i | \(-0.699226\pi\) | ||
0.585817 | − | 0.810443i | \(-0.300774\pi\) | |||||||
\(152\) | −2.31594e22 | − | 2.68872e22i | −0.285344 | − | 0.331274i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.57463e22 | − | 3.40170e22i | 0.383940 | − | 0.365366i | ||||
\(155\) | 5.43414e22i | 0.545315i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.53066e23i | 1.34256i | 0.741206 | + | 0.671278i | \(0.234254\pi\) | ||||
−0.741206 | + | 0.671278i | \(0.765746\pi\) | |||||||
\(158\) | −7.15656e22 | − | 7.52038e22i | −0.587226 | − | 0.617078i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.09513e23 | − | 8.52543e22i | 0.787422 | − | 0.612994i | ||||
\(161\) | − | 7.80888e22i | − | 0.525917i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.27169e23 | −1.34394 | −0.671968 | − | 0.740580i | \(-0.734551\pi\) | ||||
−0.671968 | + | 0.740580i | \(0.734551\pi\) | |||||||
\(164\) | −5.85123e22 | − | 2.90261e21i | −0.324629 | − | 0.0161038i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.84945e23 | + | 1.94347e23i | 0.903459 | + | 0.949388i | ||||
\(167\) | −3.10645e22 | −0.142476 | −0.0712379 | − | 0.997459i | \(-0.522695\pi\) | ||||
−0.0712379 | + | 0.997459i | \(0.522695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.29181e22 | 0.0522863 | ||||||||
\(170\) | 4.82683e22 | + | 5.07221e22i | 0.183632 | + | 0.192967i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.37641e21 | + | 1.08380e23i | −0.0180902 | + | 0.364671i | ||||
\(173\) | 3.90989e22 | 0.123788 | 0.0618942 | − | 0.998083i | \(-0.480286\pi\) | ||||
0.0618942 | + | 0.998083i | \(0.480286\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.78557e21i | − | 0.00501045i | ||||||
\(176\) | −1.66551e22 | + | 1.67458e23i | −0.0440214 | + | 0.442611i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.85083e23 | − | 2.99576e23i | −0.669208 | − | 0.703229i | ||||
\(179\) | − | 6.34529e23i | − | 1.40441i | −0.711974 | − | 0.702206i | \(-0.752199\pi\) | ||
0.711974 | − | 0.702206i | \(-0.247801\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.93863e23i | 0.578789i | 0.957210 | + | 0.289395i | \(0.0934540\pi\) | ||||
−0.957210 | + | 0.289395i | \(0.906546\pi\) | |||||||
\(182\) | 4.52056e23 | − | 4.30187e23i | 0.840316 | − | 0.799664i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.73801e23 | + | 2.01776e23i | 0.288048 | + | 0.334413i | ||||
\(185\) | − | 1.28961e23i | − | 0.201908i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.49002e22 | −0.118733 | ||||||||
\(188\) | −3.04811e22 | + | 6.14452e23i | −0.0403063 | + | 0.812514i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.67108e23 | + | 2.54186e23i | −0.316063 | + | 0.300773i | ||||
\(191\) | 1.68725e24 | 1.88942 | 0.944712 | − | 0.327902i | \(-0.106342\pi\) | ||||
0.944712 | + | 0.327902i | \(0.106342\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.63739e23 | 0.264742 | 0.132371 | − | 0.991200i | \(-0.457741\pi\) | ||||
0.132371 | + | 0.991200i | \(0.457741\pi\) | |||||||
\(194\) | 9.99206e23 | − | 9.50867e23i | 0.950029 | − | 0.904069i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.43654e22 | + | 4.91169e23i | −0.0208010 | + | 0.419316i | ||||
\(197\) | −1.46868e24 | −1.18859 | −0.594293 | − | 0.804249i | \(-0.702568\pi\) | ||||
−0.594293 | + | 0.804249i | \(0.702568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.49124e23i | 0.399681i | 0.979828 | + | 0.199840i | \(0.0640424\pi\) | ||||
−0.979828 | + | 0.199840i | \(0.935958\pi\) | |||||||
\(200\) | 3.97411e21 | + | 4.61379e21i | 0.00274426 | + | 0.00318598i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.76741e23 | + | 7.39164e23i | −0.483155 | + | 0.459781i | ||||
\(203\) | − | 3.80811e24i | − | 2.24906i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.08725e23i | 0.324344i | ||||||||
\(206\) | −1.01238e24 | − | 1.06384e24i | −0.512550 | − | 0.538606i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.10624e23 | + | 2.11771e24i | −0.0963481 | + | 0.968726i | ||||
\(209\) | − | 4.47093e23i | − | 0.194474i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.90217e24 | 1.14224 | 0.571120 | − | 0.820867i | \(-0.306509\pi\) | ||||
0.571120 | + | 0.820867i | \(0.306509\pi\) | |||||||
\(212\) | 7.86176e22 | − | 1.58481e24i | 0.0294438 | − | 0.593541i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.84217e24 | − | 1.93582e24i | −0.625150 | − | 0.656931i | ||||
\(215\) | 1.12752e24 | 0.364351 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.22079e24 | 0.651150 | ||||||||
\(218\) | 8.06748e23 | + | 8.47760e23i | 0.225395 | + | 0.236853i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.74642e24 | + | 8.66345e22i | 0.443313 | + | 0.0219914i | ||||
\(221\) | −1.07367e24 | −0.259867 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.06044e24i | 0.894072i | 0.894516 | + | 0.447036i | \(0.147520\pi\) | ||||
−0.894516 | + | 0.447036i | \(0.852480\pi\) | |||||||
\(224\) | −3.48413e24 | − | 4.47554e24i | −0.731964 | − | 0.940245i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.03024e24 | − | 1.08261e24i | −0.197151 | − | 0.207173i | ||||
\(227\) | − | 3.65333e24i | − | 0.667448i | −0.942671 | − | 0.333724i | \(-0.891695\pi\) | ||
0.942671 | − | 0.333724i | \(-0.108305\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.39657e24i | 0.565936i | 0.959129 | + | 0.282968i | \(0.0913190\pi\) | ||||
−0.959129 | + | 0.282968i | \(0.908681\pi\) | |||||||
\(230\) | 2.00453e24 | − | 1.90755e24i | 0.319058 | − | 0.303623i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.47565e24 | + | 9.83992e24i | 1.23183 | + | 1.43010i | ||||
\(233\) | 9.47332e24i | 1.31603i | 0.753006 | + | 0.658014i | \(0.228603\pi\) | ||||
−0.753006 | + | 0.658014i | \(0.771397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.39237e24 | 0.811801 | ||||||||
\(236\) | 9.54726e24 | + | 4.73610e23i | 1.15959 | + | 0.0575235i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.07288e24 | − | 1.97260e24i | 0.230418 | − | 0.219271i | ||||
\(239\) | 1.09757e25 | 1.16749 | 0.583745 | − | 0.811937i | \(-0.301587\pi\) | ||||
0.583745 | + | 0.811937i | \(0.301587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.58378e25 | 1.54353 | 0.771767 | − | 0.635905i | \(-0.219373\pi\) | ||||
0.771767 | + | 0.635905i | \(0.219373\pi\) | |||||||
\(242\) | 6.22740e24 | − | 5.92614e24i | 0.581093 | − | 0.552981i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.43125e25 | + | 7.09997e23i | 1.22496 | + | 0.0607664i | ||||
\(245\) | 5.10981e24 | 0.418948 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.65405e24i | − | 0.425639i | ||||||
\(248\) | −5.73839e24 | + | 4.94278e24i | −0.414045 | + | 0.356639i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.09462e25 | − | 1.04166e25i | 0.725927 | − | 0.690809i | ||||
\(251\) | 3.73948e24i | 0.237814i | 0.992905 | + | 0.118907i | \(0.0379390\pi\) | ||||
−0.992905 | + | 0.118907i | \(0.962061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.35524e24i | 0.196317i | ||||||||
\(254\) | 2.04758e24 | + | 2.15167e24i | 0.114944 | + | 0.120788i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.89639e25 | + | 3.80993e24i | 0.980410 | + | 0.196969i | ||||
\(257\) | − | 9.76300e24i | − | 0.484491i | −0.970215 | − | 0.242245i | \(-0.922116\pi\) | ||
0.970215 | − | 0.242245i | \(-0.0778839\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.27030e24 | −0.241095 | ||||||||
\(260\) | 2.20856e25 | + | 1.09560e24i | 0.970264 | + | 0.0481318i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.08446e25 | + | 3.24126e25i | 1.25030 | + | 1.31386i | ||||
\(263\) | −6.53732e24 | −0.254603 | −0.127302 | − | 0.991864i | \(-0.540632\pi\) | ||||
−0.127302 | + | 0.991864i | \(0.540632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.64874e25 | −0.593021 | ||||||||
\(266\) | 1.03879e25 | + | 1.09160e25i | 0.359147 | + | 0.377405i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.15722e23 | − | 4.34863e24i | 0.00689413 | − | 0.138975i | ||||
\(269\) | 1.70394e25 | 0.523666 | 0.261833 | − | 0.965113i | \(-0.415673\pi\) | ||||
0.261833 | + | 0.965113i | \(0.415673\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.01430e25i | 1.99437i | 0.0749517 | + | 0.997187i | \(0.476120\pi\) | ||||
−0.0749517 | + | 0.997187i | \(0.523880\pi\) | |||||||
\(272\) | −9.65809e23 | + | 9.71066e24i | −0.0264191 | + | 0.265629i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.37285e25 | + | 4.59515e25i | 1.10760 | + | 1.16391i | ||||
\(275\) | 7.67204e22i | 0.00187033i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.79027e25i | 1.53409i | 0.641596 | + | 0.767043i | \(0.278273\pi\) | ||||
−0.641596 | + | 0.767043i | \(0.721727\pi\) | |||||||
\(278\) | −2.18369e25 | + | 2.07805e25i | −0.475029 | + | 0.452048i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.46527e25 | + | 3.84617e25i | −0.900924 | + | 0.776014i | ||||
\(281\) | − | 4.29933e25i | − | 0.835573i | −0.908545 | − | 0.417787i | \(-0.862806\pi\) | ||
0.908545 | − | 0.417787i | \(-0.137194\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.56696e25 | 0.823890 | 0.411945 | − | 0.911209i | \(-0.364850\pi\) | ||||
0.411945 | + | 0.911209i | \(0.364850\pi\) | |||||||
\(284\) | 1.27043e24 | − | 2.56099e25i | 0.0220855 | − | 0.445211i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.94235e25 | + | 1.84838e25i | −0.313678 | + | 0.298503i | ||||
\(287\) | 2.48770e25 | 0.387292 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.41687e25 | 0.928743 | ||||||||
\(290\) | 9.77536e25 | − | 9.30246e25i | 1.36444 | − | 1.29843i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.51333e24 | − | 1.31299e26i | 0.0845830 | − | 1.70506i | ||||
\(293\) | 3.33271e25 | 0.417530 | 0.208765 | − | 0.977966i | \(-0.433056\pi\) | ||||
0.208765 | + | 0.977966i | \(0.433056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.93236e25i | − | 1.15857i | ||||||
\(296\) | 1.36181e25 | − | 1.17300e25i | 0.153304 | − | 0.132049i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.12404e24 | − | 2.02128e24i | 0.0222788 | − | 0.0212010i | ||||
\(299\) | 4.24311e25i | 0.429672i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 4.60789e25i | − | 0.435065i | ||||||
\(302\) | −1.22539e26 | − | 1.28769e26i | −1.11739 | − | 1.17419i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.11373e25 | − | 5.08605e24i | −0.435076 | − | 0.0432721i | ||||
\(305\) | − | 1.48898e26i | − | 1.22388i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.51387e26 | 1.16181 | 0.580904 | − | 0.813972i | \(-0.302699\pi\) | ||||
0.580904 | + | 0.813972i | \(0.302699\pi\) | |||||||
\(308\) | 3.54053e24 | − | 7.13718e25i | 0.0262595 | − | 0.529351i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.42495e25 | + | 5.70074e25i | 0.375922 | + | 0.395033i | ||||
\(311\) | −2.67148e26 | −1.78965 | −0.894826 | − | 0.446415i | \(-0.852700\pi\) | ||||
−0.894826 | + | 0.446415i | \(0.852700\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.80737e26 | 1.13196 | 0.565980 | − | 0.824419i | \(-0.308498\pi\) | ||||
0.565980 | + | 0.824419i | \(0.308498\pi\) | |||||||
\(314\) | 1.52807e26 | + | 1.60576e26i | 0.925514 | + | 0.972564i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.50153e26 | − | 7.44865e24i | −0.850787 | − | 0.0422049i | ||||
\(317\) | 1.21047e26 | 0.663486 | 0.331743 | − | 0.943370i | \(-0.392363\pi\) | ||||
0.331743 | + | 0.943370i | \(0.392363\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.63623e26i | 0.839542i | ||||||||
\(320\) | 2.97760e25 | − | 1.98765e26i | 0.147840 | − | 0.986883i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.79568e25 | − | 8.19199e25i | −0.362550 | − | 0.380981i | ||||
\(323\) | − | 2.59264e25i | − | 0.116712i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.70225e23i | 0.00409352i | ||||||||
\(326\) | −2.38314e26 | + | 2.26785e26i | −0.973564 | + | 0.926466i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.42807e25 | + | 5.53684e25i | −0.246266 | + | 0.212122i | ||||
\(329\) | − | 2.61240e26i | − | 0.969355i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.46911e26 | −1.20788 | −0.603941 | − | 0.797029i | \(-0.706404\pi\) | ||||
−0.603941 | + | 0.797029i | \(0.706404\pi\) | |||||||
\(332\) | 3.88038e26 | + | 1.92494e25i | 1.30895 | + | 0.0649331i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.25885e25 | + | 3.10120e25i | −0.103211 | + | 0.0982182i | ||||
\(335\) | −4.52404e25 | −0.138853 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.49146e26 | −1.87167 | −0.935834 | − | 0.352442i | \(-0.885351\pi\) | ||||
−0.935834 | + | 0.352442i | \(0.885351\pi\) | |||||||
\(338\) | 1.35519e25 | − | 1.28963e25i | 0.0378768 | − | 0.0360445i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.01273e26 | + | 5.02383e24i | 0.266050 | + | 0.0131979i | ||||
\(341\) | −9.54208e25 | −0.243065 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.88576e26i | 0.691309i | ||||||||
\(344\) | 1.02557e26 | + | 1.19065e26i | 0.238288 | + | 0.276643i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.10171e25 | − | 3.90328e25i | 0.0896739 | − | 0.0853357i | ||||
\(347\) | − | 1.79370e26i | − | 0.380443i | −0.981741 | − | 0.190221i | \(-0.939079\pi\) | ||
0.981741 | − | 0.190221i | \(-0.0609206\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.75439e25i | 0.134871i | 0.997724 | + | 0.0674356i | \(0.0214817\pi\) | ||||
−0.997724 | + | 0.0674356i | \(0.978518\pi\) | |||||||
\(350\) | −1.78255e24 | − | 1.87317e24i | −0.00345404 | − | 0.00362963i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.49702e26 | + | 1.92300e26i | 0.273232 | + | 0.350979i | ||||
\(353\) | 5.51274e26i | 0.976637i | 0.872666 | + | 0.488318i | \(0.162389\pi\) | ||||
−0.872666 | + | 0.488318i | \(0.837611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.66429e26 | −0.444820 | ||||||||
\(356\) | −5.98139e26 | − | 2.96718e25i | −0.969566 | − | 0.0480972i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.33457e26 | − | 6.65659e26i | −0.968155 | − | 1.01737i | ||||
\(359\) | −2.43646e25 | −0.0361633 | −0.0180817 | − | 0.999837i | \(-0.505756\pi\) | ||||
−0.0180817 | + | 0.999837i | \(0.505756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.77678e26 | −0.808836 | ||||||||
\(362\) | 2.93367e26 | + | 3.08281e26i | 0.398998 | + | 0.419282i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.47744e25 | − | 9.02585e26i | 0.0574732 | − | 1.15857i | ||||
\(365\) | −1.36595e27 | −1.70357 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.16093e26i | − | 0.136714i | −0.997661 | − | 0.0683570i | \(-0.978224\pi\) | ||
0.997661 | − | 0.0683570i | \(-0.0217757\pi\) | |||||||
\(368\) | 3.83763e26 | + | 3.81685e25i | 0.439199 | + | 0.0436821i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.28743e26 | − | 1.35288e26i | −0.139189 | − | 0.146265i | ||||
\(371\) | 6.73797e26i | 0.708114i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.30996e26i | − | 0.825384i | −0.910871 | − | 0.412692i | \(-0.864589\pi\) | ||
0.910871 | − | 0.412692i | \(-0.135411\pi\) | |||||||
\(374\) | −8.90655e25 | + | 8.47568e25i | −0.0860117 | + | 0.0818507i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.81437e26 | + | 6.75027e26i | 0.530922 | + | 0.616381i | ||||
\(377\) | 2.06922e27i | 1.83748i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.09303e27 | 0.918162 | 0.459081 | − | 0.888394i | \(-0.348179\pi\) | ||||
0.459081 | + | 0.888394i | \(0.348179\pi\) | |||||||
\(380\) | −2.64560e25 | + | 5.33313e26i | −0.0216171 | + | 0.435767i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.77003e27 | − | 1.68440e27i | 1.36872 | − | 1.30251i | ||||
\(383\) | −7.09173e26 | −0.533537 | −0.266769 | − | 0.963761i | \(-0.585956\pi\) | ||||
−0.266769 | + | 0.963761i | \(0.585956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.42507e26 | −0.528887 | ||||||||
\(386\) | 2.76678e26 | − | 2.63293e26i | 0.191782 | − | 0.182504i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.89676e25 | − | 1.99504e27i | 0.0649770 | − | 1.30984i | ||||
\(389\) | −1.42899e27 | −0.913187 | −0.456593 | − | 0.889675i | \(-0.650931\pi\) | ||||
−0.456593 | + | 0.889675i | \(0.650931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.94566e26i | 0.117818i | ||||||||
\(392\) | 4.64778e26 | + | 5.39590e26i | 0.273994 | + | 0.318097i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.54073e27 | + | 1.46619e27i | −0.861026 | + | 0.819372i | ||||
\(395\) | 1.56210e27i | 0.850040i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.26565e26i | − | 0.220133i | −0.993924 | − | 0.110066i | \(-0.964894\pi\) | ||
0.993924 | − | 0.110066i | \(-0.0351063\pi\) | |||||||
\(398\) | 5.48196e26 | + | 5.76065e26i | 0.275527 | + | 0.289534i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.77508e24 | + | 8.72757e23i | 0.00418428 | + | 0.000416163i | ||||
\(401\) | 1.44569e27i | 0.671520i | 0.941947 | + | 0.335760i | \(0.108993\pi\) | ||||
−0.941947 | + | 0.335760i | \(0.891007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.20671e27 | −0.531987 | ||||||||
\(404\) | −7.69332e25 | + | 1.55086e27i | −0.0330453 | + | 0.666143i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.80168e27 | − | 3.99494e27i | −1.55043 | − | 1.62925i | ||||
\(407\) | 2.26449e26 | 0.0899972 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.52483e27 | 1.33059 | 0.665294 | − | 0.746581i | \(-0.268306\pi\) | ||||
0.665294 | + | 0.746581i | \(0.268306\pi\) | |||||||
\(410\) | 6.07696e26 | + | 6.38589e26i | 0.223592 | + | 0.234958i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.12409e27 | − | 1.05369e26i | −0.742595 | − | 0.0368378i | ||||
\(413\) | −4.05911e27 | −1.38342 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.03690e27i | − | 1.30780i | ||||||
\(416\) | 1.89317e27 | + | 2.43187e27i | 0.598012 | + | 0.768176i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.46338e26 | − | 4.69028e26i | −0.134064 | − | 0.140880i | ||||
\(419\) | − | 2.28742e27i | − | 0.670037i | −0.942212 | − | 0.335018i | \(-0.891257\pi\) | ||
0.942212 | − | 0.335018i | \(-0.108743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.39946e27i | 1.78312i | 0.452899 | + | 0.891562i | \(0.350390\pi\) | ||||
−0.452899 | + | 0.891562i | \(0.649610\pi\) | |||||||
\(422\) | 3.04455e27 | − | 2.89727e27i | 0.827452 | − | 0.787422i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.49966e27 | − | 1.74105e27i | −0.387839 | − | 0.450266i | ||||
\(425\) | 4.44892e24i | 0.00112246i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.08508e27 | −1.46141 | ||||||||
\(428\) | −3.86509e27 | − | 1.91735e26i | −0.905733 | − | 0.0449306i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.18284e27 | − | 1.12561e27i | 0.263940 | − | 0.251172i | ||||
\(431\) | −7.58568e27 | −1.65190 | −0.825949 | − | 0.563745i | \(-0.809360\pi\) | ||||
−0.825949 | + | 0.563745i | \(0.809360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.38867e27 | 0.702921 | 0.351460 | − | 0.936203i | \(-0.385685\pi\) | ||||
0.351460 | + | 0.936203i | \(0.385685\pi\) | |||||||
\(434\) | 2.32975e27 | − | 2.21704e27i | 0.471701 | − | 0.448881i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.69265e27 | + | 8.39674e25i | 0.326558 | + | 0.0161995i | ||||
\(437\) | −1.02461e27 | −0.192975 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.72632e27i | 1.38706i | 0.720428 | + | 0.693530i | \(0.243945\pi\) | ||||
−0.720428 | + | 0.693530i | \(0.756055\pi\) | |||||||
\(440\) | 1.91859e27 | − | 1.65258e27i | 0.336302 | − | 0.289675i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.12634e27 | + | 1.07185e27i | −0.188251 | + | 0.179144i | ||||
\(443\) | − | 2.46574e27i | − | 0.402447i | −0.979545 | − | 0.201223i | \(-0.935508\pi\) | ||
0.979545 | − | 0.201223i | \(-0.0644917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.22266e27i | 0.968715i | ||||||||
\(446\) | 4.05358e27 | + | 4.25965e27i | 0.616344 | + | 0.647676i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.12304e27 | − | 1.21687e27i | −1.17842 | − | 0.176532i | ||||
\(449\) | − | 1.18937e28i | − | 1.68551i | −0.538295 | − | 0.842756i | \(-0.680931\pi\) | ||
0.538295 | − | 0.842756i | \(-0.319069\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.06889e27 | −0.144570 | ||||||||
\(452\) | −2.16156e27 | − | 1.07228e26i | −0.285637 | − | 0.0141696i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.64716e27 | − | 3.83256e27i | −0.460117 | − | 0.483507i | ||||
\(455\) | −9.38992e27 | −1.15756 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.14169e27 | −1.07623 | −0.538117 | − | 0.842870i | \(-0.680864\pi\) | ||||
−0.538117 | + | 0.842870i | \(0.680864\pi\) | |||||||
\(458\) | 3.39083e27 | + | 3.56320e27i | 0.390138 | + | 0.409971i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.98541e26 | − | 4.00228e27i | 0.0218219 | − | 0.439896i | ||||
\(461\) | −2.04911e27 | −0.220143 | −0.110072 | − | 0.993924i | \(-0.535108\pi\) | ||||
−0.110072 | + | 0.993924i | \(0.535108\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.88888e26i | − | 0.0399231i | −0.999801 | − | 0.0199616i | \(-0.993646\pi\) | ||
0.999801 | − | 0.0199616i | \(-0.00635438\pi\) | |||||||
\(464\) | 1.87148e28 | + | 1.86134e27i | 1.87822 | + | 0.186805i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.45731e27 | + | 9.93809e27i | 0.907226 | + | 0.953346i | ||||
\(467\) | − | 1.67480e27i | − | 0.157086i | −0.996911 | − | 0.0785428i | \(-0.974973\pi\) | ||
0.996911 | − | 0.0785428i | \(-0.0250267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.84886e27i | 0.165802i | ||||||||
\(470\) | 6.70599e27 | − | 6.38157e27i | 0.588078 | − | 0.559629i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.04885e28 | − | 9.03428e27i | 0.879673 | − | 0.757709i | ||||
\(473\) | 1.97987e27i | 0.162403i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.34285e25 | −0.00183849 | ||||||||
\(476\) | 2.05311e26 | − | 4.13876e27i | 0.0157594 | − | 0.317686i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.15141e28 | − | 1.09571e28i | 0.845744 | − | 0.804829i | ||||
\(479\) | 4.04070e27 | 0.290358 | 0.145179 | − | 0.989405i | \(-0.453624\pi\) | ||||
0.145179 | + | 0.989405i | \(0.453624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.86373e27 | 0.196974 | ||||||||
\(482\) | 1.66148e28 | − | 1.58111e28i | 1.11816 | − | 1.06406i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.16801e26 | − | 1.24338e28i | 0.0397437 | − | 0.801173i | ||||
\(485\) | −2.07551e28 | −1.30869 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.41848e28i | 1.46046i | 0.683202 | + | 0.730229i | \(0.260587\pi\) | ||||
−0.683202 | + | 0.730229i | \(0.739413\pi\) | |||||||
\(488\) | 1.57234e28 | − | 1.35434e28i | 0.929265 | − | 0.800426i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.36050e27 | − | 5.10117e27i | 0.303491 | − | 0.288809i | ||||
\(491\) | 5.39692e27i | 0.299082i | 0.988756 | + | 0.149541i | \(0.0477796\pi\) | ||||
−0.988756 | + | 0.149541i | \(0.952220\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.48830e27i | 0.503844i | ||||||||
\(494\) | −5.64450e27 | − | 5.93144e27i | −0.293422 | − | 0.308338i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.08549e27 | + | 1.09140e28i | −0.0540838 | + | 0.543782i | ||||
\(497\) | 1.08883e28i | 0.531151i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.31297e28 | 1.54939 | 0.774696 | − | 0.632333i | \(-0.217903\pi\) | ||||
0.774696 | + | 0.632333i | \(0.217903\pi\) | |||||||
\(500\) | 1.08418e27 | − | 2.18554e28i | 0.0496496 | − | 1.00086i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.73316e27 | + | 3.92294e27i | 0.163941 | + | 0.172275i | ||||
\(503\) | −3.77927e28 | −1.62534 | −0.812670 | − | 0.582724i | \(-0.801987\pi\) | ||||
−0.812670 | + | 0.582724i | \(0.801987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.61341e28 | 0.665558 | ||||||||
\(506\) | 3.34957e27 | + | 3.51985e27i | 0.135334 | + | 0.142214i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.29607e27 | + | 2.13115e26i | 0.166534 | + | 0.00826123i | ||||
\(509\) | −8.98207e27 | −0.341067 | −0.170533 | − | 0.985352i | \(-0.554549\pi\) | ||||
−0.170533 | + | 0.985352i | \(0.554549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.58229e28i | 2.03420i | ||||||||
\(512\) | 2.36978e28 | − | 1.49350e28i | 0.846005 | − | 0.533176i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.74651e27 | − | 1.02420e28i | −0.333992 | − | 0.350971i | ||||
\(515\) | 2.20977e28i | 0.741943i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.12247e28i | 0.361846i | ||||||||
\(518\) | −5.52887e27 | + | 5.26140e27i | −0.174652 | + | 0.166203i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.42629e28 | − | 2.08990e28i | 0.736051 | − | 0.634001i | ||||
\(521\) | − | 2.09029e28i | − | 0.621456i | −0.950499 | − | 0.310728i | \(-0.899427\pi\) | ||
0.950499 | − | 0.310728i | \(-0.100573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.50442e28 | 1.28639 | 0.643193 | − | 0.765704i | \(-0.277609\pi\) | ||||
0.643193 | + | 0.765704i | \(0.277609\pi\) | |||||||
\(524\) | 6.47157e28 | + | 3.21034e27i | 1.81147 | + | 0.0898614i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.85804e27 | + | 6.52627e27i | −0.184438 | + | 0.175515i | ||||
\(527\) | −5.53333e27 | −0.145873 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.17824e28 | −0.805196 | ||||||||
\(530\) | −1.72963e28 | + | 1.64595e28i | −0.429591 | + | 0.408809i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.17952e28 | + | 1.08119e27i | 0.520341 | + | 0.0258125i | ||||
\(533\) | −1.35174e28 | −0.316416 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.02099e28i | 0.904938i | ||||||||
\(536\) | −4.11498e27 | − | 4.77734e27i | −0.0908107 | − | 0.105428i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.78753e28 | − | 1.70106e28i | 0.379350 | − | 0.360998i | ||||
\(539\) | 8.97257e27i | 0.186739i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.97434e28i | 0.995783i | 0.867239 | + | 0.497891i | \(0.165892\pi\) | ||||
−0.867239 | + | 0.497891i | \(0.834108\pi\) | |||||||
\(542\) | 7.00245e28 | + | 7.35843e28i | 1.37486 | + | 1.44475i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.68106e27 | + | 1.11513e28i | 0.163978 | + | 0.210637i | ||||
\(545\) | − | 1.76093e28i | − | 0.326271i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.86434e27 | −0.0688983 | −0.0344491 | − | 0.999406i | \(-0.510968\pi\) | ||||
−0.0344491 | + | 0.999406i | \(0.510968\pi\) | |||||||
\(548\) | 9.17477e28 | + | 4.55132e27i | 1.60472 | + | 0.0796052i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.65908e25 | + | 8.04844e25i | 0.00128934 | + | 0.00135489i | ||||
\(551\) | −4.99664e28 | −0.825251 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.38391e28 | 1.01502 | ||||||||
\(554\) | 6.77880e28 | + | 7.12341e28i | 1.05755 | + | 1.11131i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.16286e27 | + | 4.36000e28i | −0.0324895 | + | 0.654939i | ||||
\(557\) | −1.38397e28 | −0.204008 | −0.102004 | − | 0.994784i | \(-0.532525\pi\) | ||||
−0.102004 | + | 0.994784i | \(0.532525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.50379e28i | 0.355446i | ||||||||
\(560\) | −8.44661e27 | + | 8.49259e28i | −0.117682 | + | 1.18322i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.29207e28 | − | 4.51026e28i | −0.576017 | − | 0.605299i | ||||
\(563\) | − | 8.76099e28i | − | 1.15402i | −0.816736 | − | 0.577012i | \(-0.804219\pi\) | ||
0.816736 | − | 0.577012i | \(-0.195781\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.24875e28i | 0.285386i | ||||||||
\(566\) | 4.79102e28 | − | 4.55924e28i | 0.596836 | − | 0.567963i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.42339e28 | − | 2.81346e28i | −0.290915 | − | 0.337741i | ||||
\(569\) | 5.46180e27i | 0.0643661i | 0.999482 | + | 0.0321830i | \(0.0102459\pi\) | ||||
−0.999482 | + | 0.0321830i | \(0.989754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.60392e28 | −0.295766 | −0.147883 | − | 0.989005i | \(-0.547246\pi\) | ||||
−0.147883 | + | 0.989005i | \(0.547246\pi\) | |||||||
\(572\) | −1.92382e27 | + | 3.87813e28i | −0.0214539 | + | 0.432478i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.60975e28 | − | 2.48350e28i | 0.280559 | − | 0.266987i | ||||
\(575\) | 1.75820e26 | 0.00185591 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.12378e28 | 0.826822 | 0.413411 | − | 0.910544i | \(-0.364337\pi\) | ||||
0.413411 | + | 0.910544i | \(0.364337\pi\) | |||||||
\(578\) | 6.73168e28 | − | 6.40602e28i | 0.672793 | − | 0.640245i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.68212e27 | − | 1.95177e29i | 0.0933204 | − | 1.88120i | ||||
\(581\) | −1.64978e29 | −1.56162 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.89510e28i | − | 0.264328i | ||||||
\(584\) | −1.24244e29 | − | 1.44243e29i | −1.11414 | − | 1.29348i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.49622e28 | − | 3.32708e28i | 0.302464 | − | 0.287831i | ||||
\(587\) | 7.63529e27i | 0.0648822i | 0.999474 | + | 0.0324411i | \(0.0103281\pi\) | ||||
−0.999474 | + | 0.0324411i | \(0.989672\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.91391e28i | − | 0.238927i | ||||||
\(590\) | −9.91558e28 | − | 1.04197e29i | −0.798679 | − | 0.839281i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.57604e27 | − | 2.59006e28i | 0.0200251 | − | 0.201341i | ||||
\(593\) | 3.47952e28i | 0.265733i | 0.991134 | + | 0.132866i | \(0.0424181\pi\) | ||||
−0.991134 | + | 0.132866i | \(0.957582\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.30571e28 | −0.317407 | ||||||||
\(596\) | 2.10378e26 | − | 4.24090e27i | 0.00152375 | − | 0.0307165i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.23594e28 | + | 4.45128e28i | 0.296202 | + | 0.311260i | ||||
\(599\) | −2.41191e29 | −1.65722 | −0.828610 | − | 0.559826i | \(-0.810868\pi\) | ||||
−0.828610 | + | 0.559826i | \(0.810868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.20539e28 | −0.345360 | −0.172680 | − | 0.984978i | \(-0.555243\pi\) | ||||
−0.172680 | + | 0.984978i | \(0.555243\pi\) | |||||||
\(602\) | −4.60010e28 | − | 4.83395e28i | −0.299919 | − | 0.315166i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.57103e29 | − | 1.27541e28i | −1.61890 | − | 0.0803084i | ||||
\(605\) | −1.29353e29 | −0.800470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.89256e27i | 0.0113128i | 0.999984 | + | 0.00565638i | \(0.00180049\pi\) | ||||
−0.999984 | + | 0.00565638i | \(0.998200\pi\) | |||||||
\(608\) | −5.87236e28 | + | 4.57154e28i | −0.345005 | + | 0.268581i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.48646e29 | − | 1.56203e29i | −0.843705 | − | 0.886596i | ||||
\(611\) | 1.41950e29i | 0.791960i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.05961e29i | 0.571230i | 0.958344 | + | 0.285615i | \(0.0921978\pi\) | ||||
−0.958344 | + | 0.285615i | \(0.907802\pi\) | |||||||
\(614\) | 1.58814e29 | − | 1.51131e29i | 0.841628 | − | 0.800912i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.75369e28 | − | 7.84079e28i | −0.345895 | − | 0.401571i | ||||
\(617\) | − | 6.70216e28i | − | 0.337459i | −0.985662 | − | 0.168729i | \(-0.946034\pi\) | ||
0.985662 | − | 0.168729i | \(-0.0539664\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.87251e29 | −1.88469 | −0.942346 | − | 0.334639i | \(-0.891386\pi\) | ||||
−0.942346 | + | 0.334639i | \(0.891386\pi\) | |||||||
\(620\) | 1.13822e29 | + | 5.64636e27i | 0.544646 | + | 0.0270182i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.80255e29 | + | 2.66697e29i | −1.29645 | + | 1.23373i | ||||
\(623\) | 2.54304e29 | 1.15672 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.26414e29 | −0.995777 | ||||||||
\(626\) | 1.89604e29 | − | 1.80431e29i | 0.820006 | − | 0.780336i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.20609e29 | + | 1.59044e28i | 1.34091 | + | 0.0665183i | ||||
\(629\) | 1.31315e28 | 0.0540110 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.06072e28i | − | 0.0819804i | −0.999160 | − | 0.0409902i | \(-0.986949\pi\) | ||
0.999160 | − | 0.0409902i | \(-0.0130512\pi\) | |||||||
\(632\) | −1.64956e29 | + | 1.42086e29i | −0.645415 | + | 0.555931i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.26986e29 | − | 1.20842e29i | 0.480637 | − | 0.457385i | ||||
\(635\) | − | 4.46936e28i | − | 0.166388i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.13469e29i | 0.408709i | ||||||||
\(638\) | 1.63347e29 | + | 1.71651e29i | 0.578753 | + | 0.608174i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.67193e29 | − | 2.38243e29i | −0.573228 | − | 0.816826i | ||||
\(641\) | 4.33253e29i | 1.46128i | 0.682765 | + | 0.730638i | \(0.260777\pi\) | ||||
−0.682765 | + | 0.730638i | \(0.739223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.99623e29 | −1.63090 | −0.815450 | − | 0.578827i | \(-0.803511\pi\) | ||||
−0.815450 | + | 0.578827i | \(0.803511\pi\) | |||||||
\(644\) | −1.63563e29 | − | 8.11385e27i | −0.525271 | − | 0.0260571i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.58826e28 | − | 2.71984e28i | −0.0804575 | − | 0.0845477i | ||||
\(647\) | −1.37434e29 | −0.420338 | −0.210169 | − | 0.977665i | \(-0.567401\pi\) | ||||
−0.210169 | + | 0.977665i | \(0.567401\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.74407e29 | 0.516411 | ||||||||
\(650\) | 9.68585e26 | + | 1.01782e27i | 0.00282194 | + | 0.00296540i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.36041e28 | + | 4.75822e29i | −0.0665867 | + | 1.34229i | ||||
\(653\) | −3.21253e29 | −0.891782 | −0.445891 | − | 0.895087i | \(-0.647113\pi\) | ||||
−0.445891 | + | 0.895087i | \(0.647113\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 6.73261e29i | − | 1.80988i | ||||||
\(656\) | −1.21595e28 | + | 1.22257e29i | −0.0321681 | + | 0.323432i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.60799e29 | − | 2.74057e29i | −0.668241 | − | 0.702213i | ||||
\(659\) | 2.28016e29i | 0.575001i | 0.957781 | + | 0.287500i | \(0.0928242\pi\) | ||||
−0.957781 | + | 0.287500i | \(0.907176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.40304e29i | − | 0.587010i | −0.955958 | − | 0.293505i | \(-0.905178\pi\) | ||
0.955958 | − | 0.293505i | \(-0.0948217\pi\) | |||||||
\(662\) | −3.63931e29 | + | 3.46325e29i | −0.875004 | + | 0.832674i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.26292e29 | − | 3.67188e29i | 0.992985 | − | 0.855311i | ||||
\(665\) | − | 2.26743e29i | − | 0.519884i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.74976e29 | 0.833070 | ||||||||
\(668\) | −3.22777e27 | + | 6.50670e28i | −0.00705911 | + | 0.142301i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.74599e28 | + | 4.51640e28i | −0.100587 | + | 0.0957209i | ||||
\(671\) | 2.61457e29 | 0.545524 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.70562e27 | −0.00344925 | −0.00172462 | − | 0.999999i | \(-0.500549\pi\) | ||||
−0.00172462 | + | 0.999999i | \(0.500549\pi\) | |||||||
\(674\) | −6.80994e29 | + | 6.48049e29i | −1.35586 | + | 1.29027i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.34226e27 | − | 2.70579e28i | 0.00259058 | − | 0.0522221i | ||||
\(677\) | 1.25887e29 | 0.239221 | 0.119610 | − | 0.992821i | \(-0.461835\pi\) | ||||
0.119610 | + | 0.992821i | \(0.461835\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.48208e29i | 1.56268i | ||||||||
\(680\) | 1.11257e29 | − | 9.58313e28i | 0.201828 | − | 0.173846i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.00102e29 | + | 9.52595e28i | −0.176079 | + | 0.167561i | ||||
\(683\) | 3.09146e29i | 0.535483i | 0.963491 | + | 0.267741i | \(0.0862773\pi\) | ||||
−0.963491 | + | 0.267741i | \(0.913723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.54485e29i | − | 1.60331i | ||||||
\(686\) | 2.88089e29 | + | 3.02734e29i | 0.476566 | + | 0.500793i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.26452e29 | + | 2.25226e28i | 0.363327 | + | 0.0361360i | ||||
\(689\) | − | 3.66121e29i | − | 0.578527i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.68187e29 | 0.717629 | 0.358815 | − | 0.933409i | \(-0.383181\pi\) | ||||
0.358815 | + | 0.933409i | \(0.383181\pi\) | |||||||
\(692\) | 4.06259e27 | − | 8.18956e28i | 0.00613322 | − | 0.123636i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.79066e29 | − | 1.88170e29i | −0.262265 | − | 0.275597i | ||||
\(695\) | 4.53586e29 | 0.654364 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.19837e28 | −0.0867627 | ||||||||
\(698\) | 6.74298e28 | + | 7.08577e28i | 0.0929757 | + | 0.0977023i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.74001e27 | − | 1.85530e26i | −0.00500430 | − | 0.000248248i | ||||
\(701\) | 6.27256e29 | 0.826810 | 0.413405 | − | 0.910547i | \(-0.364339\pi\) | ||||
0.413405 | + | 0.910547i | \(0.364339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.91518e28i | 0.0884652i | ||||||||
\(704\) | 3.49022e29 | + | 5.22851e28i | 0.439886 | + | 0.0658969i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.50342e29 | + | 5.78320e29i | 0.673261 | + | 0.707487i | ||||
\(707\) | − | 6.59361e29i | − | 0.794730i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 9.31186e29i | − | 1.08956i | −0.838579 | − | 0.544780i | \(-0.816613\pi\) | ||
0.838579 | − | 0.544780i | \(-0.183387\pi\) | |||||||
\(710\) | −2.79501e29 | + | 2.65979e29i | −0.322233 | + | 0.306644i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.57106e29 | + | 5.66001e29i | −0.735522 | + | 0.633544i | ||||
\(713\) | 2.18676e29i | 0.241191i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.03456e29 | 0.432099 | ||||||||
\(716\) | −1.32907e30 | − | 6.59310e28i | −1.40269 | − | 0.0695830i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.55600e28 | + | 2.43235e28i | −0.0261971 | + | 0.0249298i | ||||
\(719\) | 3.28458e28 | 0.0331762 | 0.0165881 | − | 0.999862i | \(-0.494720\pi\) | ||||
0.0165881 | + | 0.999862i | \(0.494720\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.03076e29 | 0.885940 | ||||||||
\(722\) | −6.06020e29 | + | 5.76702e29i | −0.585931 | + | 0.557585i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.15519e29 | + | 3.05340e28i | 0.578078 | + | 0.0286767i | ||||
\(725\) | 8.57414e27 | 0.00793673 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.05506e30i | 0.948781i | 0.880314 | + | 0.474391i | \(0.157332\pi\) | ||||
−0.880314 | + | 0.474391i | \(0.842668\pi\) | |||||||
\(728\) | −8.54088e29 | − | 9.91565e29i | −0.757048 | − | 0.878904i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.43296e30 | + | 1.36364e30i | −1.23408 | + | 1.17438i | ||||
\(731\) | 1.14810e29i | 0.0974648i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 9.48676e29i | − | 0.782576i | −0.920268 | − | 0.391288i | \(-0.872030\pi\) | ||
0.920268 | − | 0.391288i | \(-0.127970\pi\) | |||||||
\(734\) | −1.15897e29 | − | 1.21789e29i | −0.0942461 | − | 0.0990372i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.40695e29 | − | 3.43074e29i | 0.348274 | − | 0.271125i | ||||
\(737\) | − | 7.94399e28i | − | 0.0618914i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.58334e29 | 0.649965 | 0.324982 | − | 0.945720i | \(-0.394642\pi\) | ||||
0.324982 | + | 0.945720i | \(0.394642\pi\) | |||||||
\(740\) | −2.70118e29 | − | 1.33997e28i | −0.201661 | − | 0.0100038i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.72659e29 | + | 7.06854e29i | 0.488151 | + | 0.512966i | ||||
\(743\) | 2.01870e30 | 1.44441 | 0.722204 | − | 0.691680i | \(-0.243129\pi\) | ||||
0.722204 | + | 0.691680i | \(0.243129\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.41196e28 | −0.0306896 | ||||||||
\(746\) | −8.29592e29 | − | 8.71765e29i | −0.568993 | − | 0.597918i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.82160e27 | + | 1.77830e29i | −0.00588275 | + | 0.118587i | ||||
\(749\) | 1.64328e30 | 1.08057 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5.78878e29i | − | 0.370141i | −0.982725 | − | 0.185071i | \(-0.940749\pi\) | ||
0.982725 | − | 0.185071i | \(-0.0592514\pi\) | |||||||
\(752\) | 1.28385e30 | + | 1.27690e29i | 0.809519 | + | 0.0805136i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.06572e30 | + | 2.17073e30i | 1.26670 | + | 1.33109i | ||||
\(755\) | 2.67473e30i | 1.61747i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.07003e29i | − | 0.121750i | −0.998145 | − | 0.0608752i | \(-0.980611\pi\) | ||
0.998145 | − | 0.0608752i | \(-0.0193892\pi\) | |||||||
\(758\) | 1.14665e30 | − | 1.09118e30i | 0.665128 | − | 0.632951i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.04658e29 | + | 5.85889e29i | 0.284744 | + | 0.330577i | ||||
\(761\) | − | 2.06637e30i | − | 1.14992i | −0.818181 | − | 0.574961i | \(-0.805017\pi\) | ||
0.818181 | − | 0.574961i | \(-0.194983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.19648e29 | −0.389594 | ||||||||
\(764\) | 1.75315e29 | − | 3.53408e30i | 0.0936134 | − | 1.88710i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.43965e29 | + | 7.07974e29i | −0.386501 | + | 0.367803i | ||||
\(767\) | 2.20560e30 | 1.13025 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.98274e28 | 0.0298314 | 0.0149157 | − | 0.999889i | \(-0.495252\pi\) | ||||
0.0149157 | + | 0.999889i | \(0.495252\pi\) | |||||||
\(770\) | −7.78935e29 | + | 7.41252e29i | −0.383132 | + | 0.364597i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.74039e28 | − | 5.52421e29i | 0.0131169 | − | 0.264416i | ||||
\(773\) | 2.71660e30 | 1.28275 | 0.641373 | − | 0.767229i | \(-0.278365\pi\) | ||||
0.641373 | + | 0.767229i | \(0.278365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00022e27i | 0.00229785i | ||||||||
\(776\) | −1.88784e30 | − | 2.19171e30i | −0.855889 | − | 0.993655i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.49910e30 | + | 1.42658e30i | −0.661524 | + | 0.629521i | ||||
\(779\) | − | 3.26412e29i | − | 0.142110i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 4.67837e29i | − | 0.198271i | ||||||
\(782\) | 1.94237e29 | + | 2.04112e29i | 0.0812198 | + | 0.0853487i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.02626e30 | + | 1.02070e29i | 0.417771 | + | 0.0415509i | ||||
\(785\) | − | 3.33541e30i | − | 1.33973i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.56931e30 | −1.78696 | −0.893482 | − | 0.449098i | \(-0.851745\pi\) | ||||
−0.893482 | + | 0.449098i | \(0.851745\pi\) | |||||||
\(788\) | −1.52603e29 | + | 3.07625e30i | −0.0588896 | + | 1.18713i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.55946e30 | + | 1.63874e30i | 0.585990 | + | 0.615780i | ||||
\(791\) | 9.19008e29 | 0.340774 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.30645e30 | 1.19397 | ||||||||
\(794\) | −4.25844e29 | − | 4.47492e29i | −0.151752 | − | 0.159467i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.15018e30 | + | 5.70570e28i | 0.399190 | + | 0.0198026i | ||||
\(797\) | 2.55125e30 | 0.873858 | 0.436929 | − | 0.899496i | \(-0.356066\pi\) | ||||
0.436929 | + | 0.899496i | \(0.356066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.50906e29i | 0.217159i | ||||||||
\(800\) | 1.00769e28 | − | 7.84467e27i | 0.00331803 | − | 0.00258303i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.44325e30 | + | 1.51662e30i | 0.462924 | + | 0.486458i | ||||
\(803\) | − | 2.39854e30i | − | 0.759335i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.70161e30i | 0.524810i | ||||||||
\(806\) | −1.26592e30 | + | 1.20467e30i | −0.385378 | + | 0.366735i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.46753e30 | + | 1.70375e30i | 0.435278 | + | 0.505342i | ||||
\(809\) | − | 4.19734e30i | − | 1.22889i | −0.788958 | − | 0.614447i | \(-0.789379\pi\) | ||
0.788958 | − | 0.614447i | \(-0.210621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.24263e30 | −1.49565 | −0.747826 | − | 0.663895i | \(-0.768902\pi\) | ||||
−0.747826 | + | 0.663895i | \(0.768902\pi\) | |||||||
\(812\) | −7.97639e30 | − | 3.95684e29i | −2.24630 | − | 0.111432i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.37559e29 | − | 2.26066e29i | 0.0651950 | − | 0.0620411i | ||||
\(815\) | 4.95015e30 | 1.34111 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.04602e29 | −0.159639 | ||||||||
\(818\) | 3.69777e30 | − | 3.51888e30i | 0.963895 | − | 0.917264i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.27502e30 | + | 6.32498e28i | 0.323945 | + | 0.0160699i | ||||
\(821\) | −5.54721e30 | −1.39146 | −0.695731 | − | 0.718302i | \(-0.744920\pi\) | ||||
−0.695731 | + | 0.718302i | \(0.744920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4.17017e30i | − | 1.01966i | −0.860275 | − | 0.509830i | \(-0.829708\pi\) | ||
0.860275 | − | 0.509830i | \(-0.170292\pi\) | |||||||
\(824\) | −2.33349e30 | + | 2.00996e30i | −0.563340 | + | 0.485235i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.25825e30 | + | 4.05225e30i | −1.00217 | + | 0.953686i | ||||
\(827\) | − | 3.48635e29i | − | 0.0810145i | −0.999179 | − | 0.0405072i | \(-0.987103\pi\) | ||
0.999179 | − | 0.0405072i | \(-0.0128974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.23470e30i | − | 1.18596i | −0.805218 | − | 0.592979i | \(-0.797952\pi\) | ||
0.805218 | − | 0.592979i | \(-0.202048\pi\) | |||||||
\(830\) | −4.03008e30 | − | 4.23495e30i | −0.901558 | − | 0.947390i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.41382e30 | + | 6.61210e29i | 0.962763 | + | 0.144226i | ||||
\(833\) | 5.20308e29i | 0.112070i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.76915e29 | 0.142176 | ||||||||
\(836\) | −9.36471e29 | − | 4.64555e28i | −0.194235 | − | 0.00963542i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.28356e30 | − | 2.39964e30i | −0.461901 | − | 0.485383i | ||||
\(839\) | 5.25097e29 | 0.104891 | 0.0524456 | − | 0.998624i | \(-0.483298\pi\) | ||||
0.0524456 | + | 0.998624i | \(0.483298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.31534e31 | 2.56259 | ||||||||
\(842\) | 6.38865e30 | + | 6.71342e30i | 1.22923 | + | 1.29172i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.01551e29 | − | 6.07882e30i | 0.0565934 | − | 1.14084i | ||||
\(845\) | −2.81493e29 | −0.0521763 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.28633e30i | 0.955825i | ||||||||
\(848\) | −3.31134e30 | − | 3.29341e29i | −0.591354 | − | 0.0588152i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.44141e27 | + | 4.66719e27i | 0.000773788 | + | 0.000813124i | ||||
\(851\) | − | 5.18954e29i | − | 0.0893034i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.95090e30i | − | 1.16701i | −0.812108 | − | 0.583507i | \(-0.801680\pi\) | ||
0.812108 | − | 0.583507i | \(-0.198320\pi\) | |||||||
\(854\) | −6.38362e30 | + | 6.07479e30i | −1.05867 | + | 1.00745i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.24613e30 | + | 3.65742e30i | −0.687097 | + | 0.591834i | ||||
\(857\) | 6.73384e30i | 1.07638i | 0.842825 | + | 0.538188i | \(0.180891\pi\) | ||||
−0.842825 | + | 0.538188i | \(0.819109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.35510e30 | 1.45922 | 0.729609 | − | 0.683865i | \(-0.239702\pi\) | ||||
0.729609 | + | 0.683865i | \(0.239702\pi\) | |||||||
\(860\) | 1.17155e29 | − | 2.36168e30i | 0.0180521 | − | 0.363904i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.95784e30 | + | 7.57286e30i | −1.19665 | + | 1.13876i | ||||
\(863\) | 7.54466e30 | 1.12080 | 0.560398 | − | 0.828224i | \(-0.310648\pi\) | ||||
0.560398 | + | 0.828224i | \(0.310648\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.51990e29 | −0.123528 | ||||||||
\(866\) | 3.55492e30 | − | 3.38294e30i | 0.509204 | − | 0.484570i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.30753e29 | − | 4.65162e30i | 0.0322619 | − | 0.650350i | ||||
\(869\) | −2.74297e30 | −0.378891 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.00462e30i | − | 0.135460i | ||||||
\(872\) | 1.85952e30 | − | 1.60171e30i | 0.247730 | − | 0.213383i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.07487e30 | + | 1.02287e30i | −0.139794 | + | 0.133031i | ||||
\(875\) | 9.29202e30i | 1.19406i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.20577e31i | − | 1.51276i | −0.654133 | − | 0.756379i | \(-0.726967\pi\) | ||
0.654133 | − | 0.756379i | \(-0.273033\pi\) | |||||||
\(878\) | 7.71326e30 | + | 8.10538e30i | 0.956193 | + | 1.00480i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.62925e29 | − | 3.64901e30i | 0.0439288 | − | 0.441679i | ||||
\(881\) | 1.45171e31i | 1.73634i | 0.496270 | + | 0.868168i | \(0.334703\pi\) | ||||
−0.496270 | + | 0.868168i | \(0.665297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.69439e30 | −1.01543 | −0.507717 | − | 0.861524i | \(-0.669510\pi\) | ||||
−0.507717 | + | 0.861524i | \(0.669510\pi\) | |||||||
\(884\) | −1.11560e29 | + | 2.24888e30i | −0.0128754 | + | 0.259548i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.46157e30 | − | 2.58671e30i | −0.277434 | − | 0.291537i | ||||
\(887\) | 1.42864e31 | 1.59120 | 0.795600 | − | 0.605822i | \(-0.207156\pi\) | ||||
0.795600 | + | 0.605822i | \(0.207156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.82652e30 | −0.198680 | ||||||||
\(890\) | 6.21214e30 | + | 6.52795e30i | 0.667800 | + | 0.701749i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.50491e30 | + | 4.21902e29i | 0.892974 | + | 0.0442977i | ||||
\(893\) | −3.42774e30 | −0.355687 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.38268e31i | 1.40146i | ||||||||
\(896\) | −9.73637e30 | + | 6.83274e30i | −0.975356 | + | 0.684480i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.18736e31 | − | 1.24773e31i | −1.16194 | − | 1.22101i | ||||
\(899\) | 1.06641e31i | 1.03144i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.67883e30i | − | 0.158634i | ||||||
\(902\) | −1.12133e30 | + | 1.06708e30i | −0.104729 | + | 0.0996621i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.37466e30 | + | 2.04542e30i | −0.216687 | + | 0.186644i | ||||
\(905\) | − | 6.40347e30i | − | 0.577571i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.08707e31 | −1.83934 | −0.919668 | − | 0.392698i | \(-0.871542\pi\) | ||||
−0.919668 | + | 0.392698i | \(0.871542\pi\) | |||||||
\(908\) | −7.65218e30 | − | 3.79601e29i | −0.666628 | − | 0.0330694i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.85059e30 | + | 9.37405e30i | −0.838548 | + | 0.797981i | ||||
\(911\) | −9.37384e30 | −0.788814 | −0.394407 | − | 0.918936i | \(-0.629050\pi\) | ||||
−0.394407 | + | 0.918936i | \(0.629050\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.08860e30 | 0.582931 | ||||||||
\(914\) | −9.59019e30 | + | 9.12625e30i | −0.779637 | + | 0.741920i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.11437e30 | + | 3.52922e29i | 0.565241 | + | 0.0280399i | ||||
\(917\) | −2.75145e31 | −2.16114 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.69026e30i | 0.513606i | 0.966464 | + | 0.256803i | \(0.0826692\pi\) | ||||
−0.966464 | + | 0.256803i | \(0.917331\pi\) | |||||||
\(920\) | −3.78723e30 | − | 4.39684e30i | −0.287442 | − | 0.333709i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.14964e30 | + | 2.04565e30i | −0.159474 | + | 0.151760i | ||||
\(923\) | − | 5.91638e30i | − | 0.433948i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.18663e28i | − | 0.000850801i | ||||||
\(926\) | −3.88231e29 | − | 4.07967e29i | −0.0275217 | − | 0.0289208i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.14911e31 | − | 1.67305e31i | 1.48938 | − | 1.15946i | ||||
\(929\) | − | 2.81215e31i | − | 1.92696i | −0.267772 | − | 0.963482i | \(-0.586287\pi\) | ||
0.267772 | − | 0.963482i | \(-0.413713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.74000e30 | −0.183560 | ||||||||
\(932\) | 1.98426e31 | + | 9.84330e29i | 1.31441 | + | 0.0652039i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.67197e30 | − | 1.75697e30i | −0.108290 | − | 0.113795i | ||||
\(935\) | 1.85003e30 | 0.118483 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.22088e31 | −1.39078 | −0.695390 | − | 0.718632i | \(-0.744769\pi\) | ||||
−0.695390 | + | 0.718632i | \(0.744769\pi\) | |||||||
\(938\) | 1.84574e30 | + | 1.93957e30i | 0.114298 | + | 0.120109i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.64202e29 | − | 1.33893e31i | 0.0402215 | − | 0.810804i | ||||
\(941\) | −9.54987e30 | −0.571882 | −0.285941 | − | 0.958247i | \(-0.592306\pi\) | ||||
−0.285941 | + | 0.958247i | \(0.592306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.44958e30i | 0.143456i | ||||||||
\(944\) | 1.98403e30 | − | 1.99483e31i | 0.114906 | − | 1.15531i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.97652e30 | + | 2.07700e30i | 0.111955 | + | 0.117647i | ||||
\(947\) | 1.93975e31i | 1.08660i | 0.839538 | + | 0.543300i | \(0.182825\pi\) | ||||
−0.839538 | + | 0.543300i | \(0.817175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.03325e31i | − | 1.66193i | ||||||
\(950\) | −2.45779e28 | + | 2.33889e28i | −0.00133183 | + | 0.00126740i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.91639e30 | − | 4.54678e30i | −0.207586 | − | 0.240999i | ||||
\(953\) | − | 4.38799e30i | − | 0.230033i | −0.993364 | − | 0.115017i | \(-0.963308\pi\) | ||
0.993364 | − | 0.115017i | \(-0.0366921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.67663e31 | −1.88545 | ||||||||
\(956\) | 1.14043e30 | − | 2.29894e31i | 0.0578445 | − | 1.16606i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.23894e30 | − | 4.03387e30i | 0.210339 | − | 0.200163i | ||||
\(959\) | −3.90074e31 | −1.91448 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.46065e31 | 0.701376 | ||||||||
\(962\) | 3.00422e30 | − | 2.85889e30i | 0.142690 | − | 0.135787i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.64564e30 | − | 3.31735e31i | 0.0764760 | − | 1.54164i | ||||
\(965\) | −5.74704e30 | −0.264184 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.39748e31i | 1.07839i | 0.842180 | + | 0.539197i | \(0.181272\pi\) | ||||
−0.842180 | + | 0.539197i | \(0.818728\pi\) | |||||||
\(968\) | −1.17657e31 | − | 1.36595e31i | −0.523511 | − | 0.607777i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.17733e31 | + | 2.07200e31i | −0.948030 | + | 0.902167i | ||||
\(971\) | 2.98705e31i | 1.28659i | 0.765617 | + | 0.643296i | \(0.222434\pi\) | ||||
−0.765617 | + | 0.643296i | \(0.777566\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.85369e31i | − | 0.781363i | ||||||
\(974\) | 2.41440e31 | + | 2.53714e31i | 1.00679 | + | 1.05797i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.97429e30 | − | 2.99048e31i | 0.121383 | − | 1.22044i | ||||
\(977\) | − | 3.07943e31i | − | 1.24330i | −0.783294 | − | 0.621652i | \(-0.786462\pi\) | ||
0.783294 | − | 0.621652i | \(-0.213538\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.09267e31 | −0.431788 | ||||||||
\(980\) | 5.30937e29 | − | 1.07029e31i | 0.0207572 | − | 0.418434i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.38780e30 | + | 5.66170e30i | 0.206177 | + | 0.216659i | ||||
\(983\) | 7.30276e30 | 0.276487 | 0.138244 | − | 0.990398i | \(-0.455854\pi\) | ||||
0.138244 | + | 0.990398i | \(0.455854\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.20034e31 | 1.18608 | ||||||||
\(986\) | 9.47227e30 | + | 9.95381e30i | 0.347333 | + | 0.364991i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.18428e31 | − | 5.87487e29i | −0.425116 | − | 0.0210887i | ||||
\(989\) | 4.53727e30 | 0.161151 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.01010e31i | 0.698948i | 0.936946 | + | 0.349474i | \(0.113640\pi\) | ||||
−0.936946 | + | 0.349474i | \(0.886360\pi\) | |||||||
\(992\) | 9.75679e30 | + | 1.25331e31i | 0.335687 | + | 0.431206i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.08699e31 | + | 1.14225e31i | 0.366158 | + | 0.384772i | ||||
\(995\) | − | 1.19658e31i | − | 0.398840i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00709e31i | 1.63413i | 0.576546 | + | 0.817065i | \(0.304400\pi\) | ||||
−0.576546 | + | 0.817065i | \(0.695600\pi\) | |||||||
\(998\) | 3.47550e31 | − | 3.30737e31i | 1.12240 | − | 1.06810i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 72.22.f.a.35.63 | yes | 84 | |
3.2 | odd | 2 | inner | 72.22.f.a.35.22 | yes | 84 | |
8.3 | odd | 2 | inner | 72.22.f.a.35.21 | ✓ | 84 | |
24.11 | even | 2 | inner | 72.22.f.a.35.64 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.22.f.a.35.21 | ✓ | 84 | 8.3 | odd | 2 | inner | |
72.22.f.a.35.22 | yes | 84 | 3.2 | odd | 2 | inner | |
72.22.f.a.35.63 | yes | 84 | 1.1 | even | 1 | trivial | |
72.22.f.a.35.64 | yes | 84 | 24.11 | even | 2 | inner |