Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,16,Mod(47,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.47");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.c (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: | \(68.4928824480\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + 8885809 x^{18} - 79971996 x^{17} + 21106062365235 x^{16} - 168846686224596 x^{15} + \cdots + 85\!\cdots\!61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{194}\cdot 3^{63}\cdot 5^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.15 | ||
Root | \(0.500000 - 124.858i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.47 |
Dual form | 48.16.c.d.47.16 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2222.78 | − | 3067.27i | 0.586795 | − | 0.809735i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 265238.i | 1.51831i | 0.650910 | + | 0.759155i | \(0.274388\pi\) | ||||
−0.650910 | + | 0.759155i | \(0.725612\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85832e6i | 1.31182i | 0.754837 | + | 0.655912i | \(0.227716\pi\) | ||||
−0.754837 | + | 0.655912i | \(0.772284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.46743e6 | − | 1.36357e7i | −0.311343 | − | 0.950298i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.31314e7 | 0.203173 | 0.101587 | − | 0.994827i | \(-0.467608\pi\) | ||||
0.101587 | + | 0.994827i | \(0.467608\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.54218e8 | 1.56565 | 0.782826 | − | 0.622241i | \(-0.213777\pi\) | ||||
0.782826 | + | 0.622241i | \(0.213777\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.13557e8 | + | 5.89565e8i | 1.22943 | + | 0.890937i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.16150e9i | 1.86864i | 0.356434 | + | 0.934321i | \(0.383992\pi\) | ||||
−0.356434 | + | 0.934321i | \(0.616008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.73405e9i | − | 1.72832i | −0.503216 | − | 0.864161i | \(-0.667850\pi\) | ||
0.503216 | − | 0.864161i | \(-0.332150\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.76725e9 | + | 6.35341e9i | 1.06223 | + | 0.769772i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.63863e10 | −1.00351 | −0.501754 | − | 0.865010i | \(-0.667312\pi\) | ||||
−0.501754 | + | 0.865010i | \(0.667312\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.98336e10 | −1.30527 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.17546e10 | − | 1.66064e10i | −0.952184 | − | 0.305525i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.06607e9i | 0.0437713i | 0.999760 | + | 0.0218857i | \(0.00696698\pi\) | ||||
−0.999760 | + | 0.0218857i | \(0.993033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.12231e11i | 0.732657i | 0.930486 | + | 0.366328i | \(0.119385\pi\) | ||||
−0.930486 | + | 0.366328i | \(0.880615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.91882e10 | − | 4.02777e10i | 0.119221 | − | 0.164517i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.58135e11 | −1.99176 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.93505e11 | −0.854632 | −0.427316 | − | 0.904102i | \(-0.640541\pi\) | ||||
−0.427316 | + | 0.904102i | \(0.640541\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.87347e11 | − | 1.08648e12i | 0.918717 | − | 1.26776i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.89518e12i | 1.51975i | 0.650070 | + | 0.759874i | \(0.274739\pi\) | ||||
−0.650070 | + | 0.759874i | \(0.725261\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.30853e11i | 0.410031i | 0.978759 | + | 0.205015i | \(0.0657244\pi\) | ||||
−0.978759 | + | 0.205015i | \(0.934276\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.61671e12 | − | 1.18493e12i | 1.44285 | − | 0.472715i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.27279e12 | 0.654374 | 0.327187 | − | 0.944960i | \(-0.393899\pi\) | ||||
0.327187 | + | 0.944960i | \(0.393899\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.42243e12 | −0.720883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.69718e12 | + | 7.02730e12i | 1.51310 | + | 1.09651i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.07028e12i | − | 0.592874i | −0.955052 | − | 0.296437i | \(-0.904201\pi\) | ||
0.955052 | − | 0.296437i | \(-0.0957985\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.48295e12i | 0.308480i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.06552e13 | − | 1.49683e13i | −1.39948 | − | 1.01417i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.32877e13 | −1.74138 | −0.870690 | − | 0.491833i | \(-0.836327\pi\) | ||||
−0.870690 | + | 0.491833i | \(0.836327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.64456e12 | 0.0670002 | 0.0335001 | − | 0.999439i | \(-0.489335\pi\) | ||||
0.0335001 | + | 0.999439i | \(0.489335\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.89753e13 | − | 1.27693e13i | 1.24662 | − | 0.408427i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.39520e13i | 2.37715i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.08829e13i | 0.219374i | 0.993966 | + | 0.109687i | \(0.0349848\pi\) | ||||
−0.993966 | + | 0.109687i | \(0.965015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.64230e13 | + | 5.02611e13i | −0.588854 | + | 0.812576i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.38204e13 | 0.441308 | 0.220654 | − | 0.975352i | \(-0.429181\pi\) | ||||
0.220654 | + | 0.975352i | \(0.429181\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.67887e13 | −0.389756 | −0.194878 | − | 0.980827i | \(-0.562431\pi\) | ||||
−0.194878 | + | 0.980827i | \(0.562431\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.85411e13 | + | 1.22180e14i | −0.765924 | + | 1.05692i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.75338e13i | 0.266528i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.12245e12i | 0.0241519i | 0.999927 | + | 0.0120760i | \(0.00384399\pi\) | ||||
−0.999927 | + | 0.0120760i | \(0.996156\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.65975e14 | + | 1.21833e14i | −0.806131 | + | 0.591737i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.60341e14 | 0.648571 | 0.324286 | − | 0.945959i | \(-0.394876\pi\) | ||||
0.324286 | + | 0.945959i | \(0.394876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.38549e14 | −2.83718 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.24717e13 | + | 9.03797e12i | 0.0354432 | + | 0.0256848i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.70790e13i | 0.184719i | 0.995726 | + | 0.0923593i | \(0.0294408\pi\) | ||||
−0.995726 | + | 0.0923593i | \(0.970559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.01247e15i | 2.05386i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.44244e14 | + | 2.49465e14i | 0.593258 | + | 0.429920i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.78613e15 | 2.62413 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.27251e14 | −0.662566 | −0.331283 | − | 0.943531i | \(-0.607481\pi\) | ||||
−0.331283 | + | 0.943531i | \(0.607481\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.86637e13 | − | 1.79057e14i | −0.0632566 | − | 0.193075i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.02972e14i | 0.373994i | 0.982360 | + | 0.186997i | \(0.0598755\pi\) | ||||
−0.982360 | + | 0.186997i | \(0.940125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.53605e14i | 0.683877i | 0.939722 | + | 0.341938i | \(0.111083\pi\) | ||||
−0.939722 | + | 0.341938i | \(0.888917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.68516e15 | + | 2.32541e15i | −1.16875 | + | 1.61280i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.52585e14 | 0.272472 | 0.136236 | − | 0.990676i | \(-0.456499\pi\) | ||||
0.136236 | + | 0.990676i | \(0.456499\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.06355e14 | −0.422501 | −0.211250 | − | 0.977432i | \(-0.567754\pi\) | ||||
−0.211250 | + | 0.977432i | \(0.567754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.09695e15 | + | 1.51372e15i | −0.501494 | + | 0.692026i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.53494e15i | 1.41349i | 0.707467 | + | 0.706746i | \(0.249838\pi\) | ||||
−0.707467 | + | 0.706746i | \(0.750162\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.34626e15i | − | 1.52364i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.58244e15 | − | 4.83002e15i | −0.487455 | − | 1.48784i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.03657e15 | −2.45133 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00481e15 | −0.958721 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.81304e15 | + | 4.21256e15i | 1.23059 | + | 0.891781i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.47095e15i | − | 0.463489i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.44998e15i | 1.07407i | 0.843562 | + | 0.537033i | \(0.180455\pi\) | ||||
−0.843562 | + | 0.537033i | \(0.819545\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.24173e15 | + | 1.62452e15i | 0.332016 | + | 0.240604i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.96873e15 | 0.523741 | 0.261871 | − | 0.965103i | \(-0.415661\pi\) | ||||
0.261871 | + | 0.965103i | \(0.415661\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.92481e16 | 2.26725 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.40464e15 | − | 1.37273e16i | 0.463881 | − | 1.44571i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.71165e15i | 0.350076i | 0.984562 | + | 0.175038i | \(0.0560048\pi\) | ||||
−0.984562 | + | 0.175038i | \(0.943995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.48458e16i | − | 1.25601i | −0.778211 | − | 0.628003i | \(-0.783872\pi\) | ||
0.778211 | − | 0.628003i | \(-0.216128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.05191e15 | − | 6.97128e15i | 0.383983 | − | 0.529870i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.65139e15 | 0.318099 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.07848e15 | −0.0664585 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.60731e15 | + | 1.04975e16i | −0.423010 | + | 0.583724i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3.19715e16i | − | 1.60645i | −0.595679 | − | 0.803223i | \(-0.703117\pi\) | ||
0.595679 | − | 0.803223i | \(-0.296883\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.10052e15i | 0.0500346i | 0.999687 | + | 0.0250173i | \(0.00796408\pi\) | ||||
−0.999687 | + | 0.0250173i | \(0.992036\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.31093e16 | − | 1.41238e16i | 1.77577 | − | 0.581788i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.97680e16 | −1.11240 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.72070e16 | −0.584061 | −0.292031 | − | 0.956409i | \(-0.594331\pi\) | ||||
−0.292031 | + | 0.956409i | \(0.594331\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.55519e16 | − | 1.12701e16i | −0.480071 | − | 0.347896i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.68372e16i | − | 1.31643i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.87122e16i | − | 0.735630i | −0.929899 | − | 0.367815i | \(-0.880106\pi\) | ||
0.929899 | − | 0.367815i | \(-0.119894\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.06832e16 | + | 7.74183e15i | 0.249787 | + | 0.181015i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.17903e16 | 0.465469 | 0.232734 | − | 0.972540i | \(-0.425233\pi\) | ||||
0.232734 | + | 0.972540i | \(0.425233\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.42844e16 | 1.45127 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.18237e16 | + | 3.00839e16i | −1.64242 | + | 0.538101i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.08758e16i | 1.32578i | 0.748715 | + | 0.662892i | \(0.230671\pi\) | ||||
−0.748715 | + | 0.662892i | \(0.769329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.13857e17i | − | 1.71228i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.39911e16 | + | 1.02102e17i | −1.02183 | + | 1.41006i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.74113e16 | 0.474904 | 0.237452 | − | 0.971399i | \(-0.423688\pi\) | ||||
0.237452 | + | 0.971399i | \(0.423688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.73789e16 | 0.553345 | 0.276673 | − | 0.960964i | \(-0.410768\pi\) | ||||
0.276673 | + | 0.960964i | \(0.410768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.65549e15 | − | 5.04432e15i | 0.0393154 | − | 0.0542525i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.30896e17i | − | 1.29760i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.15150e16i | 0.379658i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.74663e16 | − | 1.47931e17i | 0.400795 | − | 1.24910i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.91527e15 | 0.0617611 | 0.0308806 | − | 0.999523i | \(-0.490169\pi\) | ||||
0.0308806 | + | 0.999523i | \(0.490169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.44372e17 | −1.04185 | −0.520924 | − | 0.853603i | \(-0.674413\pi\) | ||||
−0.520924 | + | 0.853603i | \(0.674413\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.88176e17 | + | 2.08834e17i | 1.92486 | + | 1.39490i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.11986e17i | 1.31162i | 0.754924 | + | 0.655812i | \(0.227674\pi\) | ||||
−0.754924 | + | 0.655812i | \(0.772326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.69799e17i | 0.973949i | 0.873416 | + | 0.486974i | \(0.161900\pi\) | ||||
−0.873416 | + | 0.486974i | \(0.838100\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.33809e16 | + | 2.41903e16i | 0.177635 | + | 0.128727i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.16221e16 | −0.0574203 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.02674e17 | −2.30745 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.32045e16 | + | 2.23439e17i | 0.312435 | + | 0.953631i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.84277e16i | − | 0.351149i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.06924e17i | − | 1.50451i | −0.658872 | − | 0.752255i | \(-0.728966\pi\) | ||
0.658872 | − | 0.752255i | \(-0.271034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.51753e16 | − | 1.03737e17i | 0.258957 | − | 0.357343i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.93850e17 | −0.622554 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.20793e17 | −0.961117 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.17731e16 | + | 1.12841e17i | −0.228707 | + | 0.315599i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.11986e18i | 2.92564i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.69180e16i | − | 0.114565i | −0.998358 | − | 0.0572827i | \(-0.981756\pi\) | ||
0.998358 | − | 0.0572827i | \(-0.0182436\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.77954e17 | + | 5.43160e17i | 0.406385 | + | 1.24039i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.25067e17 | 0.908372 | 0.454186 | − | 0.890907i | \(-0.349930\pi\) | ||||
0.454186 | + | 0.890907i | \(0.349930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.97232e17 | −0.594744 | −0.297372 | − | 0.954762i | \(-0.596110\pi\) | ||||
−0.297372 | + | 0.954762i | \(0.596110\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.15127e17 | + | 8.34293e16i | 0.215817 | + | 0.156397i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.29822e17i | − | 0.579575i | −0.957091 | − | 0.289788i | \(-0.906415\pi\) | ||
0.957091 | − | 0.289788i | \(-0.0935847\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.02831e17i | 0.993542i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.26447e16 | + | 9.16328e15i | 0.0195567 | + | 0.0141722i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.90050e17 | −1.00207 | −0.501033 | − | 0.865428i | \(-0.667046\pi\) | ||||
−0.501033 | + | 0.865428i | \(0.667046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50839e17 | −0.478608 | −0.239304 | − | 0.970945i | \(-0.576919\pi\) | ||||
−0.239304 | + | 0.970945i | \(0.576919\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.77034e15 | + | 7.79900e17i | 0.00611648 | + | 0.999981i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 9.07759e17i | − | 1.09452i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.38532e18i | − | 2.70595i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.56401e17 | − | 4.91808e17i | 0.380578 | − | 0.525171i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.24796e17 | 0.628327 | 0.314163 | − | 0.949369i | \(-0.398276\pi\) | ||||
0.314163 | + | 0.949369i | \(0.398276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.15175e17 | −0.203886 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.86391e18 | + | 2.57206e18i | −1.66484 | + | 2.29736i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.01441e18i | − | 0.854502i | −0.904133 | − | 0.427251i | \(-0.859482\pi\) | ||
0.904133 | − | 0.427251i | \(-0.140518\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.41060e18i | − | 1.12113i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.54438e16 | − | 1.81649e16i | 0.0415958 | − | 0.0136279i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.59605e18 | 1.83927 | 0.919635 | − | 0.392774i | \(-0.128484\pi\) | ||||
0.919635 | + | 0.392774i | \(0.128484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.34483e18 | 0.900167 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.36422e17 | + | 1.71329e17i | 0.149573 | + | 0.108392i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.31267e18i | − | 0.785257i | −0.919697 | − | 0.392629i | \(-0.871566\pi\) | ||
0.919697 | − | 0.392629i | \(-0.128434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.43658e18i | − | 1.94472i | −0.233485 | − | 0.972360i | \(-0.575013\pi\) | ||
0.233485 | − | 0.972360i | \(-0.424987\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.10552e18 | + | 2.25049e18i | 1.66308 | + | 1.20520i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.23072e17 | −0.265195 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.43682e18 | 1.65028 | 0.825142 | − | 0.564925i | \(-0.191095\pi\) | ||||
0.825142 | + | 0.564925i | \(0.191095\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.53035e18 | − | 5.01385e17i | 0.696242 | − | 0.228108i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.27753e17i | 0.400069i | 0.979789 | + | 0.200034i | \(0.0641054\pi\) | ||||
−0.979789 | + | 0.200034i | \(0.935895\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.14874e18i | 1.28747i | 0.765246 | + | 0.643737i | \(0.222617\pi\) | ||||
−0.765246 | + | 0.643737i | \(0.777383\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.97016e18 | − | 5.47854e18i | 1.53983 | − | 2.12485i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.41703e18 | −1.99364 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.13264e18 | −2.49182 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.17196e18 | + | 1.61722e18i | −0.388791 | + | 0.536503i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.01570e17i | − | 0.0320081i | −0.999872 | − | 0.0160040i | \(-0.994906\pi\) | ||
0.999872 | − | 0.0160040i | \(-0.00509446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8.82915e18i | − | 2.64395i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.79612e17 | − | 2.18065e17i | −0.193458 | − | 0.0620745i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.80430e18 | −1.57114 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.08901e18 | −0.537888 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.23603e18 | + | 8.95717e17i | 0.302836 | + | 0.219458i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.36200e17i | 0.101727i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.48324e18i | − | 0.551418i | −0.961241 | − | 0.275709i | \(-0.911087\pi\) | ||
0.961241 | − | 0.275709i | \(-0.0889126\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.61824e18 | + | 1.89737e18i | 0.553759 | + | 0.401296i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.94556e18 | −0.795070 | −0.397535 | − | 0.917587i | \(-0.630134\pi\) | ||||
−0.397535 | + | 0.917587i | \(0.630134\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.58739e18 | 1.07307 | 0.536533 | − | 0.843879i | \(-0.319734\pi\) | ||||
0.536533 | + | 0.843879i | \(0.319734\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.38692e18 | + | 1.03377e19i | 0.620119 | + | 1.89276i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.66386e17i | − | 0.0814332i | −0.999171 | − | 0.0407166i | \(-0.987036\pi\) | ||
0.999171 | − | 0.0407166i | \(-0.0129641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.33933e16i | 0.00889317i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.00600e18 | − | 1.38820e18i | 0.159885 | − | 0.220630i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.12897e19 | 3.22961 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.41098e19 | −2.04359 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.79235e18 | + | 2.47331e18i | −0.247921 | + | 0.342114i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.49637e18i | 0.858423i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.31036e18i | − | 0.544257i | −0.962261 | − | 0.272128i | \(-0.912272\pi\) | ||
0.962261 | − | 0.272128i | \(-0.0877276\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.20470e18 | + | 6.72931e18i | 0.266084 | + | 0.812154i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.88657e18 | −0.333078 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00174e18 | 0.662298 | 0.331149 | − | 0.943579i | \(-0.392564\pi\) | ||||
0.331149 | + | 0.943579i | \(0.392564\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.08426e19 | + | 7.85738e18i | 1.14455 | + | 0.829430i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.47376e18i | 0.148856i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.78764e18i | 0.366153i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.33312e19 | − | 9.66076e18i | −1.23374 | − | 0.894063i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.71734e18 | 0.418048 | 0.209024 | − | 0.977911i | \(-0.432971\pi\) | ||||
0.209024 | + | 0.977911i | \(0.432971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.92550e18 | −0.418080 | −0.209040 | − | 0.977907i | \(-0.567034\pi\) | ||||
−0.209040 | + | 0.977907i | \(0.567034\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.83324e19 | − | 5.88227e18i | −1.49079 | − | 0.478345i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.72307e18i | 0.212202i | 0.994355 | + | 0.106101i | \(0.0338366\pi\) | ||||
−0.994355 | + | 0.106101i | \(0.966163\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.97046e18i | 0.670042i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.00863e19 | + | 2.77176e19i | −1.43843 | + | 1.98493i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.43785e18 | 0.304764 | 0.152382 | − | 0.988322i | \(-0.451306\pi\) | ||||
0.152382 | + | 0.988322i | \(0.451306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.01663e19 | −1.98709 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.90181e18 | + | 1.22839e19i | −0.562573 | + | 0.776310i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.75776e18i | − | 0.591771i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9.50439e18i | − | 0.553260i | −0.960977 | − | 0.276630i | \(-0.910782\pi\) | ||
0.960977 | − | 0.276630i | \(-0.0892176\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.58422e19 | − | 8.46659e18i | 1.44421 | − | 0.473163i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.44925e19 | 0.777747 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.08165e18 | 0.158843 | 0.0794213 | − | 0.996841i | \(-0.474693\pi\) | ||||
0.0794213 | + | 0.996841i | \(0.474693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.57908e18 | − | 5.49237e18i | −0.375303 | − | 0.271973i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.44027e18i | 0.0685307i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.18315e19i | 1.45567i | 0.685752 | + | 0.727835i | \(0.259473\pi\) | ||||
−0.685752 | + | 0.727835i | \(0.740527\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.97839e19 | + | 1.43369e19i | 0.869709 | + | 0.630256i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.93823e19 | −1.24192 | −0.620962 | − | 0.783841i | \(-0.713258\pi\) | ||||
−0.620962 | + | 0.783841i | \(0.713258\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.95539e18 | −0.404672 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.96571e18 | − | 3.26503e18i | 0.389651 | − | 0.127660i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.46147e19i | 0.925918i | 0.886380 | + | 0.462959i | \(0.153212\pi\) | ||||
−0.886380 | + | 0.462959i | \(0.846788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.18051e19i | − | 1.87520i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.82160e18 | − | 1.21732e19i | 0.307329 | − | 0.424092i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.09343e18 | −0.0366701 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.34981e19 | 0.758758 | 0.379379 | − | 0.925241i | \(-0.376138\pi\) | ||||
0.379379 | + | 0.925241i | \(0.376138\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.27842e19 | − | 5.90391e19i | 1.33041 | − | 1.83588i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.07901e19i | 1.22172i | 0.791738 | + | 0.610860i | \(0.209176\pi\) | ||||
−0.791738 | + | 0.610860i | \(0.790824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.97543e19i | 1.14709i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.23148e19 | − | 4.40229e19i | −0.898440 | − | 1.22396i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.48043e18 | −0.173638 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.87173e19 | 1.77477 | 0.887383 | − | 0.461033i | \(-0.152521\pi\) | ||||
0.887383 | + | 0.461033i | \(0.152521\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.13846e19 | + | 8.25016e18i | 0.283469 | + | 0.205423i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9.51469e19i | − | 2.28438i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.25284e19i | 0.984732i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.55361e19 | − | 3.29988e19i | −1.01703 | − | 0.737018i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.47869e19 | −1.61146 | −0.805732 | − | 0.592281i | \(-0.798228\pi\) | ||||
−0.805732 | + | 0.592281i | \(0.798228\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.28694e19 | 1.72297 | 0.861486 | − | 0.507781i | \(-0.169534\pi\) | ||||
0.861486 | + | 0.507781i | \(0.169534\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.01535e19 | − | 3.09912e19i | −0.203735 | − | 0.621850i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.25934e20i | − | 2.43907i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.70068e18i | 0.0878925i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.03390e19 | − | 1.42671e19i | 0.186659 | − | 0.257576i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.38681e19 | 0.590489 | 0.295245 | − | 0.955422i | \(-0.404599\pi\) | ||||
0.295245 | + | 0.955422i | \(0.404599\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.50108e19 | 0.589580 | 0.294790 | − | 0.955562i | \(-0.404750\pi\) | ||||
0.294790 | + | 0.955562i | \(0.404750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.39721e18 | + | 3.30798e18i | −0.0389975 | + | 0.0538138i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.10346e20i | 1.73438i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.54338e19i | − | 0.690074i | −0.938589 | − | 0.345037i | \(-0.887866\pi\) | ||
0.938589 | − | 0.345037i | \(-0.112134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.52895e19 | + | 4.66674e19i | 0.224442 | + | 0.685053i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.12301e20 | 1.59351 | 0.796754 | − | 0.604304i | \(-0.206549\pi\) | ||||
0.796754 | + | 0.604304i | \(0.206549\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.04443e19 | −0.280460 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.80653e19 | − | 7.10655e19i | −1.30080 | − | 0.942654i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.87480e19i | 1.26672i | 0.773857 | + | 0.633360i | \(0.218325\pi\) | ||||
−0.773857 | + | 0.633360i | \(0.781675\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.48864e19i | 0.308772i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.37559e18 | + | 2.44621e18i | 0.0405148 | + | 0.0293600i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.68545e20 | −3.11840 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.11843e20 | 1.25672 | 0.628361 | − | 0.777922i | \(-0.283726\pi\) | ||||
0.628361 | + | 0.777922i | \(0.283726\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.25010e19 | − | 1.63622e20i | 0.570916 | − | 1.77929i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 9.35080e19i | − | 0.984220i | −0.870533 | − | 0.492110i | \(-0.836226\pi\) | ||
0.870533 | − | 0.492110i | \(-0.163774\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.25066e18i | − | 0.0636896i | −0.999493 | − | 0.0318448i | \(-0.989862\pi\) | ||
0.999493 | − | 0.0318448i | \(-0.0101382\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.61675e19 | + | 9.13065e19i | −0.652751 | + | 0.900750i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.28661e20 | 1.22905 | 0.614524 | − | 0.788898i | \(-0.289348\pi\) | ||||
0.614524 | + | 0.788898i | \(0.289348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.11069e19 | −0.287780 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.82474e19 | + | 5.27787e19i | −0.342724 | + | 0.472935i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.59714e18i | 0.0833073i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.68241e20i | 2.25592i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.91369e19 | + | 2.26511e19i | −0.563407 | + | 0.184587i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.15251e20 | 1.69992 | 0.849962 | − | 0.526843i | \(-0.176625\pi\) | ||||
0.849962 | + | 0.526843i | \(0.176625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.74808e20 | −1.33806 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.43662e20 | − | 1.04109e20i | −1.06596 | − | 0.772473i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.39847e20i | − | 1.00598i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.40847e20i | 1.67986i | 0.542692 | + | 0.839931i | \(0.317405\pi\) | ||||
−0.542692 | + | 0.839931i | \(0.682595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.80681e19 | − | 6.38208e19i | −0.595665 | − | 0.431664i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.64884e19 | 0.239356 | 0.119678 | − | 0.992813i | \(-0.461814\pi\) | ||||
0.119678 | + | 0.992813i | \(0.461814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.28549e19 | −0.0817929 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.74926e19 | − | 1.55598e19i | 0.293148 | − | 0.0960431i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.66697e19i | 0.578918i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.29014e20i | 1.33079i | 0.746493 | + | 0.665393i | \(0.231736\pi\) | ||||
−0.746493 | + | 0.665393i | \(0.768264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.84351e19 | − | 6.68370e19i | 0.273135 | − | 0.376907i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.69943e20 | 1.47745 | 0.738724 | − | 0.674008i | \(-0.235429\pi\) | ||||
0.738724 | + | 0.674008i | \(0.235429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.06883e20 | −0.567839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.65118e20 | − | 2.27850e20i | 0.851596 | − | 1.17514i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.83187e20i | 1.41804i | 0.705187 | + | 0.709022i | \(0.250863\pi\) | ||||
−0.705187 | + | 0.709022i | \(0.749137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.05154e20i | − | 0.511292i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.11828e20 | + | 3.48518e20i | −0.528045 | + | 1.64568i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.26408e20 | −1.03834 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.98450e19 | 0.132951 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.48068e20 | + | 1.79769e20i | 1.07353 | + | 0.777964i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.00854e20i | − | 0.424043i | −0.977265 | − | 0.212022i | \(-0.931995\pi\) | ||
0.977265 | − | 0.212022i | \(-0.0680047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.70261e20i | − | 1.10413i | −0.833800 | − | 0.552067i | \(-0.813839\pi\) | ||
0.833800 | − | 0.552067i | \(-0.186161\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.49231e20 | − | 2.53079e20i | −1.38649 | − | 1.00476i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.54818e20 | −1.36907 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.87407e18 | 0.00702861 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.48710e20 | + | 4.53902e20i | 0.542166 | + | 1.65483i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.71307e20i | 2.37940i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.20043e20i | 0.413697i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.31571e19 | − | 1.14751e20i | 0.278671 | − | 0.384546i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.49415e19 | −0.146464 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.50730e20 | 1.42869 | 0.714343 | − | 0.699796i | \(-0.246726\pi\) | ||||
0.714343 | + | 0.699796i | \(0.246726\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.05313e20 | − | 1.45324e20i | 0.324700 | − | 0.448063i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.13876e20i | − | 0.641487i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.39655e20i | − | 0.407521i | −0.979021 | − | 0.203761i | \(-0.934684\pi\) | ||
0.979021 | − | 0.203761i | \(-0.0653164\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.34697e18 | − | 2.24248e19i | −0.0208601 | − | 0.0636702i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.73811e19 | 0.0756509 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.17833e19 | −0.0316831 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.01495e20 | − | 2.90953e20i | −1.05071 | − | 0.761423i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 2.42202e20i | − | 0.616969i | −0.951229 | − | 0.308484i | \(-0.900178\pi\) | ||
0.951229 | − | 0.308484i | \(-0.0998218\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.58881e20i | 0.641966i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.27338e20 | + | 9.22785e19i | 0.307423 | + | 0.222782i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.76943e20 | −1.59125 | −0.795626 | − | 0.605788i | \(-0.792858\pi\) | ||||
−0.795626 | + | 0.605788i | \(0.792858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.37599e20 | −2.14612 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.48239e20 | − | 4.74410e20i | −0.776255 | − | 1.05750i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 8.30962e20i | − | 1.80401i | −0.431724 | − | 0.902006i | \(-0.642095\pi\) | ||
0.431724 | − | 0.902006i | \(-0.357905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.23859e20i | − | 0.261912i | −0.991388 | − | 0.130956i | \(-0.958195\pi\) | ||
0.991388 | − | 0.130956i | \(-0.0418047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.75939e19 | − | 2.42783e19i | 0.0362411 | − | 0.0500102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.52723e20 | 1.30985 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.61397e20 | 1.09762 | 0.548810 | − | 0.835947i | \(-0.315081\pi\) | ||||
0.548810 | + | 0.835947i | \(0.315081\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.20908e20 | + | 4.42830e20i | −0.611351 | + | 0.843621i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.58305e20i | 0.850811i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.65800e19i | − | 0.120456i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.28110e21 | − | 4.19724e20i | 2.25900 | − | 0.740107i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.26686e19 | −0.0733370 | −0.0366685 | − | 0.999327i | \(-0.511675\pi\) | ||||
−0.0366685 | + | 0.999327i | \(0.511675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.55770e20 | 1.26627 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.50218e20 | + | 4.71197e20i | 1.06207 | + | 0.769655i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.87110e20i | − | 0.775741i | −0.921714 | − | 0.387871i | \(-0.873211\pi\) | ||
0.921714 | − | 0.387871i | \(-0.126789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.39684e21i | − | 3.72188i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.20819e20 | + | 3.77425e20i | 0.788641 | + | 0.571509i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.65145e20 | 1.12991 | 0.564953 | − | 0.825123i | \(-0.308894\pi\) | ||||
0.564953 | + | 0.825123i | \(0.308894\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.29245e20 | −0.474199 | −0.237100 | − | 0.971485i | \(-0.576197\pi\) | ||||
−0.237100 | + | 0.971485i | \(0.576197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.48397e20 | − | 4.86187e19i | 0.208470 | − | 0.0683005i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1.06223e21i | − | 1.45564i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.50006e20i | 1.27002i | 0.772503 | + | 0.635011i | \(0.219004\pi\) | ||||
−0.772503 | + | 0.635011i | \(0.780996\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.58334e19 | + | 3.56483e19i | −0.0336940 | + | 0.0464953i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.05064e20 | 1.02452 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.84462e20 | 0.725776 | 0.362888 | − | 0.931833i | \(-0.381791\pi\) | ||||
0.362888 | + | 0.931833i | \(0.381791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.11733e21 | + | 1.54184e21i | −1.35400 | + | 1.86842i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.05579e21i | 1.24864i | 0.781169 | + | 0.624320i | \(0.214624\pi\) | ||||
−0.781169 | + | 0.624320i | \(0.785376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.18439e20i | − | 0.136714i | −0.997661 | − | 0.0683571i | \(-0.978224\pi\) | ||
0.997661 | − | 0.0683571i | \(-0.0217757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.48064e20 | + | 2.72116e20i | 0.955525 | + | 0.306596i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.20316e20 | −0.242318 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.60234e20 | −0.601546 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.71232e20 | − | 1.96555e20i | −0.284338 | − | 0.206052i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.56022e21i | − | 1.59700i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.07242e21i | − | 1.07188i | −0.844257 | − | 0.535938i | \(-0.819958\pi\) | ||
0.844257 | − | 0.535938i | \(-0.180042\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.24815e21 | − | 9.04502e20i | −1.21826 | − | 0.882839i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.71078e21 | −1.63076 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.21229e21 | −1.12865 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.51090e20 | − | 4.61167e20i | −0.137398 | − | 0.419374i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.09243e20i | 0.541197i | 0.962692 | + | 0.270598i | \(0.0872215\pi\) | ||||
−0.962692 | + | 0.270598i | \(0.912778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.66388e21i | − | 1.44391i | −0.691939 | − | 0.721956i | \(-0.743243\pi\) | ||
0.691939 | − | 0.721956i | \(-0.256757\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.30885e20 | + | 5.94591e20i | −0.365312 | + | 0.504104i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.68486e21 | −1.39566 | −0.697832 | − | 0.716261i | \(-0.745852\pi\) | ||||
−0.697832 | + | 0.716261i | \(0.745852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.37115e20 | −0.353802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.13050e20 | + | 9.83959e20i | −0.563979 | + | 0.778251i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.42205e20i | − | 0.187212i | −0.995609 | − | 0.0936060i | \(-0.970161\pi\) | ||
0.995609 | − | 0.0936060i | \(-0.0298394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.05266e21i | 0.795202i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.64351e20 | + | 5.01641e20i | 0.121348 | + | 0.370384i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.28172e21 | 0.925020 | 0.462510 | − | 0.886614i | \(-0.346949\pi\) | ||||
0.462510 | + | 0.886614i | \(0.346949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.64099e20 | −0.186319 | −0.0931594 | − | 0.995651i | \(-0.529697\pi\) | ||||
−0.0931594 | + | 0.995651i | \(0.529697\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.43491e21 | + | 2.48920e21i | 2.36900 | + | 1.71675i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.10532e21i | 3.44239i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.66276e19i | − | 0.0439249i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.43910e20 | − | 1.04288e20i | −0.0927677 | − | 0.0672264i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.15954e19 | 0.0136127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.59542e20 | 0.159991 | 0.0799953 | − | 0.996795i | \(-0.474509\pi\) | ||||
0.0799953 | + | 0.996795i | \(0.474509\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.06157e21 | + | 6.61490e20i | 1.24285 | + | 0.398791i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.67716e21i | 0.988914i | 0.869202 | + | 0.494457i | \(0.164633\pi\) | ||||
−0.869202 | + | 0.494457i | \(0.835367\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.50705e21i | − | 0.869170i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.44830e20 | − | 1.30380e21i | 0.533029 | − | 0.735541i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.68531e20 | −0.424137 | −0.212068 | − | 0.977255i | \(-0.568020\pi\) | ||||
−0.212068 | + | 0.977255i | \(0.568020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.84469e20 | −0.531524 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.60681e20 | + | 9.11693e20i | −0.348993 | + | 0.481585i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.79598e21i | − | 0.928235i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.04921e20i | − | 0.154206i | −0.997023 | − | 0.0771031i | \(-0.975433\pi\) | ||
0.997023 | − | 0.0771031i | \(-0.0245671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.11801e20 | − | 1.67680e20i | 0.253281 | − | 0.0829815i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.93766e21 | 1.90701 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.99161e21 | −2.83986 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.01165e21 | − | 7.33120e20i | −0.469303 | − | 0.340092i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.41966e21i | − | 0.644612i | −0.946636 | − | 0.322306i | \(-0.895542\pi\) | ||
0.946636 | − | 0.322306i | \(-0.104458\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.32329e21i | 1.47708i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.84905e21 | + | 1.33996e21i | 0.804507 | + | 0.583006i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.15182e21 | −0.490614 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.11904e21 | −0.466659 | −0.233329 | − | 0.972398i | \(-0.574962\pi\) | ||||
−0.233329 | + | 0.972398i | \(0.574962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.62126e19 | − | 1.84167e19i | 0.0229515 | − | 0.00751953i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.83905e21i | − | 0.735227i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.23372e21i | 0.482973i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.53383e21 | + | 2.11657e21i | −0.588007 | + | 0.811408i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.12915e21 | 0.799356 | 0.399678 | − | 0.916656i | \(-0.369122\pi\) | ||||
0.399678 | + | 0.916656i | \(0.369122\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.43988e21 | −0.897126 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.79836e20 | + | 1.07612e21i | −0.280845 | + | 0.387546i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.61966e20i | − | 0.0571332i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.68931e21i | − | 1.27478i | −0.770540 | − | 0.637392i | \(-0.780013\pi\) | ||
0.770540 | − | 0.637392i | \(-0.219987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.40277e21 | + | 1.71891e21i | 0.813309 | + | 0.581831i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.31059e21 | −0.766200 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.40333e21 | 1.10567 | 0.552834 | − | 0.833291i | \(-0.313546\pi\) | ||||
0.552834 | + | 0.833291i | \(0.313546\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.78435e21 | − | 2.01775e21i | −0.886275 | − | 0.642261i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.42908e20i | 0.0445709i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.60817e21i | 1.71391i | 0.515391 | + | 0.856955i | \(0.327647\pi\) | ||||
−0.515391 | + | 0.856955i | \(0.672353\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.31643e21 | − | 5.30204e21i | −2.19110 | − | 1.58784i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.84487e21 | 1.12841 | 0.564203 | − | 0.825636i | \(-0.309183\pi\) | ||||
0.564203 | + | 0.825636i | \(0.309183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.48005e21 | 2.43908 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.16310e20 | − | 2.18636e21i | −0.201928 | − | 0.616336i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.29363e21i | 0.357435i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.67079e21i | − | 0.994168i | −0.867703 | − | 0.497084i | \(-0.834404\pi\) | ||
0.867703 | − | 0.497084i | \(-0.165596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.38878e21 | − | 1.91642e21i | 0.368699 | − | 0.508779i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.91899e20 | −0.0759680 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.72399e21 | 1.46043 | 0.730213 | − | 0.683219i | \(-0.239421\pi\) | ||||
0.730213 | + | 0.683219i | \(0.239421\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.78286e20 | + | 6.60000e20i | −0.119639 | + | 0.165094i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.49082e20i | − | 0.0856135i | −0.999083 | − | 0.0428067i | \(-0.986370\pi\) | ||
0.999083 | − | 0.0428067i | \(-0.0136300\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2.30482e21i | − | 0.554247i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.74616e21 | + | 1.14342e22i | 0.883335 | + | 2.69616i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.17911e22 | −2.72639 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.11183e21 | −0.478863 | −0.239432 | − | 0.970913i | \(-0.576961\pi\) | ||||
−0.239432 | + | 0.970913i | \(0.576961\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.11146e21 | − | 2.25480e21i | −0.691921 | − | 0.501418i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.19464e20i | − | 0.0478648i | −0.999714 | − | 0.0239324i | \(-0.992381\pi\) | ||
0.999714 | − | 0.0239324i | \(-0.00761865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.47057e21i | − | 0.956312i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.32669e21 | − | 3.13544e21i | −0.907816 | − | 0.657872i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.27622e22 | 2.62661 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.44111e20 | 0.0896620 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.75226e19 | − | 2.10438e20i | 0.0133732 | − | 0.0416784i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.56396e21i | − | 0.886786i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.92876e21i | − | 0.558307i | −0.960247 | − | 0.279153i | \(-0.909946\pi\) | ||
0.960247 | − | 0.279153i | \(-0.0900538\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.77045e21 | − | 7.96281e21i | 1.07927 | − | 1.48932i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.01040e22 | −1.85425 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.82533e20 | 0.104899 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.98926e21 | − | 4.12496e21i | 0.528214 | − | 0.728897i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.36696e21i | − | 1.10407i | −0.833822 | − | 0.552033i | \(-0.813852\pi\) | ||
0.833822 | − | 0.552033i | \(-0.186148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.18543e21i | 1.22279i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.05103e21 | − | 3.44345e20i | 0.175538 | − | 0.0575109i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.83088e20 | −0.0791881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.24230e22 | 1.99874 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.02630e21 | − | 2.91776e21i | −0.635851 | − | 0.460785i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.51829e21i | − | 0.700423i | −0.936671 | − | 0.350211i | \(-0.886110\pi\) | ||
0.936671 | − | 0.350211i | \(-0.113890\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.15787e22i | 1.76199i | 0.473129 | + | 0.880993i | \(0.343124\pi\) | ||||
−0.473129 | + | 0.880993i | \(0.656876\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.05409e22 | − | 7.63876e21i | −1.57471 | − | 1.14115i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.61556e21 | 1.11691 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.92160e21 | 0.708665 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.38057e22 | − | 4.52313e21i | 1.95178 | − | 0.639455i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.64272e21i | 1.33852i | 0.743027 | + | 0.669262i | \(0.233389\pi\) | ||||
−0.743027 | + | 0.669262i | \(0.766611\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.10927e22i | 1.51195i | 0.654600 | + | 0.755976i | \(0.272837\pi\) | ||||
−0.654600 | + | 0.755976i | \(0.727163\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.16267e21 | + | 1.60440e21i | −0.155615 | + | 0.214738i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.93415e21 | −1.30569 | −0.652844 | − | 0.757492i | \(-0.726424\pi\) | ||||
−0.652844 | + | 0.757492i | \(0.726424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.15367e22 | −1.48910 | −0.744548 | − | 0.667569i | \(-0.767335\pi\) | ||||
−0.744548 | + | 0.667569i | \(0.767335\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.63929e21 | − | 1.05417e22i | 0.968379 | − | 1.33629i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.08200e22i | − | 1.34707i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.77962e21i | 0.706726i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.86375e21 | − | 5.80848e21i | 0.223845 | − | 0.697624i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.93183e21 | −1.17169 | −0.585847 | − | 0.810421i | \(-0.699238\pi\) | ||||
−0.585847 | + | 0.810421i | \(0.699238\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.61266e21 | 0.998084 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.84567e21 | + | 2.06219e21i | 0.323950 | + | 0.234759i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.97030e22i | 2.20347i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.14470e22i | − | 1.25767i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.65805e21 | + | 6.99895e21i | 1.04251 | + | 0.755484i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.08670e21 | 0.857630 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.94130e20 | −0.0931715 | −0.0465858 | − | 0.998914i | \(-0.514834\pi\) | ||||
−0.0465858 | + | 0.998914i | \(0.514834\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.97939e21 | − | 2.43551e22i | −0.817004 | − | 2.49370i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.82633e22i | 1.83749i | 0.394856 | + | 0.918743i | \(0.370795\pi\) | ||||
−0.394856 | + | 0.918743i | \(0.629205\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.82547e21i | 0.575946i | 0.957639 | + | 0.287973i | \(0.0929814\pi\) | ||||
−0.957639 | + | 0.287973i | \(0.907019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.20409e22 | + | 1.66155e22i | −1.16986 | + | 1.61432i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.79395e21 | 0.553215 | 0.276607 | − | 0.960983i | \(-0.410790\pi\) | ||||
0.276607 | + | 0.960983i | \(0.410790\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.14513e22 | −2.01295 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.58543e22 | + | 2.18778e22i | −1.46219 | + | 2.01771i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.41336e19i | 0.00490703i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.85493e21i | 0.343463i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.35546e21 | + | 7.18945e21i | 0.206285 | + | 0.629635i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.06277e21 | 0.608016 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.91585e21 | 0.754511 | 0.377256 | − | 0.926109i | \(-0.376868\pi\) | ||||
0.377256 | + | 0.926109i | \(0.376868\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.11544e20 | − | 2.25768e20i | −0.0259181 | − | 0.0187822i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.63857e22i | − | 1.34013i | −0.742303 | − | 0.670064i | \(-0.766266\pi\) | ||
0.742303 | − | 0.670064i | \(-0.233734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.37759e22i | 1.10768i | 0.832622 | + | 0.553841i | \(0.186839\pi\) | ||||
−0.832622 | + | 0.553841i | \(0.813161\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.70814e22 | − | 1.96252e22i | −2.14090 | − | 1.55146i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.99476e20 | −0.0232774 | −0.0116387 | − | 0.999932i | \(-0.503705\pi\) | ||||
−0.0116387 | + | 0.999932i | \(0.503705\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.84361e22 | −1.40898 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.17949e21 | + | 1.59985e21i | −0.163784 | + | 0.120225i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.53051e22i | − | 1.13097i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.92291e21i | 0.721051i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.29017e22 | + | 1.78034e22i | −0.921940 | + | 1.27221i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.56340e20 | −0.0320694 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.60297e22 | 1.10787 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.64341e21 | + | 6.40757e21i | −0.315630 | + | 0.435547i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.25667e22i | 0.840149i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 6.76966e21i | − | 0.445156i | −0.974915 | − | 0.222578i | \(-0.928553\pi\) | ||
0.974915 | − | 0.222578i | \(-0.0714471\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.49482e21 | − | 1.80025e21i | 0.355406 | − | 0.116440i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.97929e22 | 1.25928 | 0.629640 | − | 0.776887i | \(-0.283202\pi\) | ||||
0.629640 | + | 0.776887i | \(0.283202\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.10550e21 | 0.131772 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.33795e21 | + | 9.69576e20i | 0.0823721 | + | 0.0596930i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.13439e22i | 0.687056i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.22200e20i | 0.00728123i | 0.999993 | + | 0.00364061i | \(0.00115885\pi\) | ||||
−0.999993 | + | 0.00364061i | \(0.998841\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.61678e21 | − | 5.51969e21i | −0.446503 | − | 0.323570i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.19798e22 | 0.690935 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.96581e22 | 1.11552 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.16395e22 | − | 3.81342e21i | 0.649887 | − | 0.212920i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.55676e21i | 0.140466i | 0.997531 | + | 0.0702331i | \(0.0223743\pi\) | ||||
−0.997531 | + | 0.0702331i | \(0.977626\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.30469e22i | 1.24592i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.77010e21 | + | 1.21021e22i | −0.466543 | + | 0.643797i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.10113e22 | −0.576439 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.63453e22 | −1.35724 | −0.678620 | − | 0.734489i | \(-0.737422\pi\) | ||||
−0.678620 | + | 0.734489i | \(0.737422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.24195e22 | − | 1.71381e22i | 0.629670 | − | 0.868900i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.31671e22i | − | 1.15598i | −0.816044 | − | 0.577989i | \(-0.803837\pi\) | ||
0.816044 | − | 0.577989i | \(-0.196163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.10549e22i | − | 1.52508i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.92370e22 | + | 1.25899e22i | 1.89652 | + | 0.608531i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.82837e22 | 0.869838 | 0.434919 | − | 0.900470i | \(-0.356777\pi\) | ||||
0.434919 | + | 0.900470i | \(0.356777\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.30312e22 | −0.610222 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.43053e21 | − | 1.03667e21i | −0.0659393 | − | 0.0477846i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.69996e22i | 1.67880i | 0.543511 | + | 0.839402i | \(0.317095\pi\) | ||||
−0.543511 | + | 0.839402i | \(0.682905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.09943e21i | 0.0937726i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.63772e20 | + | 1.18681e20i | 0.00720112 | + | 0.00521847i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.06091e22 | −0.459238 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.08694e22 | 0.463214 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.02189e21 | − | 6.17133e21i | −0.0848322 | − | 0.258929i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 3.82930e22i | − | 1.58185i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.31210e21i | − | 0.338074i | −0.985610 | − | 0.169037i | \(-0.945934\pi\) | ||
0.985610 | − | 0.169037i | \(-0.0540658\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.73222e22 | − | 6.53013e22i | 1.89512 | − | 2.61513i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.32751e22 | −0.523472 | −0.261736 | − | 0.965139i | \(-0.584295\pi\) | ||||
−0.261736 | + | 0.965139i | \(0.584295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.24340e22 | 1.64766 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.13628e22 | + | 4.32785e22i | −1.19917 | + | 1.65477i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.04277e21i | − | 0.114567i | −0.998358 | − | 0.0572836i | \(-0.981756\pi\) | ||
0.998358 | − | 0.0572836i | \(-0.0182439\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.01216e21i | 0.0375299i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.60233e21 | + | 1.09952e22i | 0.131543 | + | 0.401501i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.80951e22 | −1.36999 | −0.684996 | − | 0.728547i | \(-0.740196\pi\) | ||||
−0.684996 | + | 0.728547i | \(0.740196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.62266e22 | −1.99145 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.99261e22 | + | 1.44400e22i | 0.695096 | + | 0.503719i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.19759e22i | − | 0.411469i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.06460e22i | − | 0.698689i | −0.936994 | − | 0.349344i | \(-0.886404\pi\) | ||
0.936994 | − | 0.349344i | \(-0.113596\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.32211e22 | − | 9.58098e21i | −0.440704 | − | 0.319367i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.50370e22 | −1.47876 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.02491e22 | −0.331490 | −0.165745 | − | 0.986169i | \(-0.553003\pi\) | ||||
−0.165745 | + | 0.986169i | \(0.553003\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.55412e22 | + | 8.19533e21i | 0.813767 | + | 0.261111i |
(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 | 48.16.c.d.47.15 | yes | 20 | |
3.2 | odd | 2 | inner | 48.16.c.d.47.5 | ✓ | 20 | |
4.3 | odd | 2 | inner | 48.16.c.d.47.6 | yes | 20 | |
12.11 | even | 2 | inner | 48.16.c.d.47.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.16.c.d.47.5 | ✓ | 20 | 3.2 | odd | 2 | inner | |
48.16.c.d.47.6 | yes | 20 | 4.3 | odd | 2 | inner | |
48.16.c.d.47.15 | yes | 20 | 1.1 | even | 1 | trivial | |
48.16.c.d.47.16 | yes | 20 | 12.11 | even | 2 | inner |