Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,15,Mod(21,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.21");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.3523729934\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 38299509 x^{12} + 1255603312 x^{11} + 548839279225666 x^{10} + \cdots + 61\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{56}\cdot 3^{6}\cdot 11^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.11 | ||
Root | \(320.191 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.21 |
Dual form | 22.15.b.a.21.4 |
$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 90.5097i | 0.707107i | ||||||||
\(3\) | −6.19137 | −0.00283099 | −0.00141549 | − | 0.999999i | \(-0.500451\pi\) | ||||
−0.00141549 | + | 0.999999i | \(0.500451\pi\) | |||||||
\(4\) | −8192.00 | −0.500000 | ||||||||
\(5\) | −140247. | −1.79516 | −0.897578 | − | 0.440856i | \(-0.854675\pi\) | ||||
−0.897578 | + | 0.440856i | \(0.854675\pi\) | |||||||
\(6\) | − | 560.379i | − | 0.00200181i | ||||||
\(7\) | − | 1.02360e6i | − | 1.24292i | −0.783446 | − | 0.621459i | \(-0.786540\pi\) | ||
0.783446 | − | 0.621459i | \(-0.213460\pi\) | |||||||
\(8\) | − | 741455.i | − | 0.353553i | ||||||
\(9\) | −4.78293e6 | −0.999992 | ||||||||
\(10\) | − | 1.26937e7i | − | 1.26937i | ||||||
\(11\) | 1.50426e7 | + | 1.23882e7i | 0.771926 | + | 0.635713i | ||||
\(12\) | 50719.7 | 0.00141549 | ||||||||
\(13\) | 6.57004e7i | 1.04704i | 0.852012 | + | 0.523522i | \(0.175382\pi\) | ||||
−0.852012 | + | 0.523522i | \(0.824618\pi\) | |||||||
\(14\) | 9.26454e7 | 0.878876 | ||||||||
\(15\) | 868318. | 0.00508206 | ||||||||
\(16\) | 6.71089e7 | 0.250000 | ||||||||
\(17\) | − | 6.20507e8i | − | 1.51218i | −0.654466 | − | 0.756092i | \(-0.727106\pi\) | ||
0.654466 | − | 0.756092i | \(-0.272894\pi\) | |||||||
\(18\) | − | 4.32901e8i | − | 0.707101i | ||||||
\(19\) | 5.75368e8i | 0.643680i | 0.946794 | + | 0.321840i | \(0.104301\pi\) | ||||
−0.946794 | + | 0.321840i | \(0.895699\pi\) | |||||||
\(20\) | 1.14890e9 | 0.897578 | ||||||||
\(21\) | 6.33747e6i | 0.00351869i | ||||||||
\(22\) | −1.12126e9 | + | 1.36150e9i | −0.449517 | + | 0.545834i | ||||
\(23\) | 1.11162e8 | 0.0326485 | 0.0163242 | − | 0.999867i | \(-0.494804\pi\) | ||||
0.0163242 | + | 0.999867i | \(0.494804\pi\) | |||||||
\(24\) | 4.59062e6i | 0.00100090i | ||||||||
\(25\) | 1.35656e10 | 2.22259 | ||||||||
\(26\) | −5.94652e9 | −0.740371 | ||||||||
\(27\) | 5.92260e7 | 0.00566195 | ||||||||
\(28\) | 8.38531e9i | 0.621459i | ||||||||
\(29\) | 1.74829e10i | 1.01351i | 0.862091 | + | 0.506754i | \(0.169155\pi\) | ||||
−0.862091 | + | 0.506754i | \(0.830845\pi\) | |||||||
\(30\) | 7.85912e7i | 0.00359356i | ||||||||
\(31\) | −2.49786e10 | −0.907897 | −0.453949 | − | 0.891028i | \(-0.649985\pi\) | ||||
−0.453949 | + | 0.891028i | \(0.649985\pi\) | |||||||
\(32\) | 6.07400e9i | 0.176777i | ||||||||
\(33\) | −9.31345e7 | − | 7.67002e7i | −0.00218531 | − | 0.00179969i | ||||
\(34\) | 5.61619e10 | 1.06928 | ||||||||
\(35\) | 1.43556e11i | 2.23123i | ||||||||
\(36\) | 3.91818e10 | 0.499996 | ||||||||
\(37\) | 1.40576e11 | 1.48081 | 0.740405 | − | 0.672161i | \(-0.234634\pi\) | ||||
0.740405 | + | 0.672161i | \(0.234634\pi\) | |||||||
\(38\) | −5.20763e10 | −0.455151 | ||||||||
\(39\) | − | 4.06775e8i | − | 0.00296416i | ||||||
\(40\) | 1.03987e11i | 0.634684i | ||||||||
\(41\) | 8.64115e10i | 0.443695i | 0.975081 | + | 0.221847i | \(0.0712087\pi\) | ||||
−0.975081 | + | 0.221847i | \(0.928791\pi\) | |||||||
\(42\) | −5.73602e8 | −0.00248809 | ||||||||
\(43\) | − | 1.26825e11i | − | 0.466578i | −0.972407 | − | 0.233289i | \(-0.925051\pi\) | ||
0.972407 | − | 0.233289i | \(-0.0749488\pi\) | |||||||
\(44\) | −1.23229e11 | − | 1.01485e11i | −0.385963 | − | 0.317856i | ||||
\(45\) | 6.70790e11 | 1.79514 | ||||||||
\(46\) | 1.00613e10i | 0.0230860i | ||||||||
\(47\) | 3.18992e11 | 0.629643 | 0.314821 | − | 0.949151i | \(-0.398055\pi\) | ||||
0.314821 | + | 0.949151i | \(0.398055\pi\) | |||||||
\(48\) | −4.15496e8 | −0.000707747 | ||||||||
\(49\) | −3.69528e11 | −0.544848 | ||||||||
\(50\) | 1.22782e12i | 1.57161i | ||||||||
\(51\) | 3.84179e9i | 0.00428097i | ||||||||
\(52\) | − | 5.38218e11i | − | 0.523522i | ||||||
\(53\) | 1.37130e12 | 1.16735 | 0.583677 | − | 0.811986i | \(-0.301613\pi\) | ||||
0.583677 | + | 0.811986i | \(0.301613\pi\) | |||||||
\(54\) | 5.36053e9i | 0.00400360i | ||||||||
\(55\) | −2.10968e12 | − | 1.73741e12i | −1.38573 | − | 1.14120i | ||||
\(56\) | −7.58951e11 | −0.439438 | ||||||||
\(57\) | − | 3.56231e9i | − | 0.00182225i | ||||||
\(58\) | −1.58237e12 | −0.716658 | ||||||||
\(59\) | −3.22811e12 | −1.29713 | −0.648565 | − | 0.761159i | \(-0.724631\pi\) | ||||
−0.648565 | + | 0.761159i | \(0.724631\pi\) | |||||||
\(60\) | −7.11326e9 | −0.00254103 | ||||||||
\(61\) | − | 1.96411e12i | − | 0.624967i | −0.949923 | − | 0.312484i | \(-0.898839\pi\) | ||
0.949923 | − | 0.312484i | \(-0.101161\pi\) | |||||||
\(62\) | − | 2.26081e12i | − | 0.641980i | ||||||
\(63\) | 4.89579e12i | 1.24291i | ||||||||
\(64\) | −5.49756e11 | −0.125000 | ||||||||
\(65\) | − | 9.21426e12i | − | 1.87961i | ||||||
\(66\) | 6.94211e9 | − | 8.42958e9i | 0.00127258 | − | 0.00154525i | ||||
\(67\) | 6.50801e12 | 1.07380 | 0.536902 | − | 0.843645i | \(-0.319595\pi\) | ||||
0.536902 | + | 0.843645i | \(0.319595\pi\) | |||||||
\(68\) | 5.08320e12i | 0.756092i | ||||||||
\(69\) | −6.88247e8 | −9.24274e−5 | ||||||||
\(70\) | −1.29932e13 | −1.57772 | ||||||||
\(71\) | 2.49479e12 | 0.274300 | 0.137150 | − | 0.990550i | \(-0.456206\pi\) | ||||
0.137150 | + | 0.990550i | \(0.456206\pi\) | |||||||
\(72\) | 3.54633e12i | 0.353551i | ||||||||
\(73\) | − | 1.88866e13i | − | 1.70960i | −0.518957 | − | 0.854800i | \(-0.673680\pi\) | ||
0.518957 | − | 0.854800i | \(-0.326320\pi\) | |||||||
\(74\) | 1.27235e13i | 1.04709i | ||||||||
\(75\) | −8.39895e10 | −0.00629211 | ||||||||
\(76\) | − | 4.71341e12i | − | 0.321840i | ||||||
\(77\) | 1.26806e13 | − | 1.53976e13i | 0.790140 | − | 0.959441i | ||||
\(78\) | 3.68171e10 | 0.00209598 | ||||||||
\(79\) | − | 2.28648e13i | − | 1.19063i | −0.803491 | − | 0.595317i | \(-0.797026\pi\) | ||
0.803491 | − | 0.595317i | \(-0.202974\pi\) | |||||||
\(80\) | −9.41179e12 | −0.448789 | ||||||||
\(81\) | 2.28762e13 | 0.999976 | ||||||||
\(82\) | −7.82107e12 | −0.313740 | ||||||||
\(83\) | 4.23928e13i | 1.56223i | 0.624387 | + | 0.781115i | \(0.285349\pi\) | ||||
−0.624387 | + | 0.781115i | \(0.714651\pi\) | |||||||
\(84\) | − | 5.19165e10i | − | 0.00175934i | ||||||
\(85\) | 8.70240e13i | 2.71461i | ||||||||
\(86\) | 1.14788e13 | 0.329920 | ||||||||
\(87\) | − | 1.08243e11i | − | 0.00286923i | ||||||
\(88\) | 9.18533e12 | − | 1.11534e13i | 0.224758 | − | 0.272917i | ||||
\(89\) | −1.04167e13 | −0.235504 | −0.117752 | − | 0.993043i | \(-0.537569\pi\) | ||||
−0.117752 | + | 0.993043i | \(0.537569\pi\) | |||||||
\(90\) | 6.07129e13i | 1.26936i | ||||||||
\(91\) | 6.72507e13 | 1.30139 | ||||||||
\(92\) | −9.10642e11 | −0.0163242 | ||||||||
\(93\) | 1.54652e11 | 0.00257024 | ||||||||
\(94\) | 2.88718e13i | 0.445225i | ||||||||
\(95\) | − | 8.06933e13i | − | 1.15551i | ||||||
\(96\) | − | 3.76064e10i | − | 0.000500452i | ||||||
\(97\) | −3.99411e13 | −0.494331 | −0.247165 | − | 0.968973i | \(-0.579499\pi\) | ||||
−0.247165 | + | 0.968973i | \(0.579499\pi\) | |||||||
\(98\) | − | 3.34459e13i | − | 0.385265i | ||||||
\(99\) | −7.19479e13 | − | 5.92521e13i | −0.771919 | − | 0.635708i | ||||
\(100\) | −1.11129e14 | −1.11129 | ||||||||
\(101\) | 9.32804e13i | 0.870043i | 0.900420 | + | 0.435021i | \(0.143259\pi\) | ||||
−0.900420 | + | 0.435021i | \(0.856741\pi\) | |||||||
\(102\) | −3.47719e11 | −0.00302710 | ||||||||
\(103\) | 2.19326e14 | 1.78332 | 0.891662 | − | 0.452702i | \(-0.149540\pi\) | ||||
0.891662 | + | 0.452702i | \(0.149540\pi\) | |||||||
\(104\) | 4.87139e13 | 0.370186 | ||||||||
\(105\) | − | 8.88808e11i | − | 0.00631659i | ||||||
\(106\) | 1.24116e14i | 0.825444i | ||||||||
\(107\) | − | 3.33533e13i | − | 0.207708i | −0.994593 | − | 0.103854i | \(-0.966883\pi\) | ||
0.994593 | − | 0.103854i | \(-0.0331174\pi\) | |||||||
\(108\) | −4.85179e11 | −0.00283097 | ||||||||
\(109\) | − | 1.92543e13i | − | 0.105328i | −0.998612 | − | 0.0526639i | \(-0.983229\pi\) | ||
0.998612 | − | 0.0526639i | \(-0.0167712\pi\) | |||||||
\(110\) | 1.57252e14 | − | 1.90946e14i | 0.806953 | − | 0.979857i | ||||
\(111\) | −8.70358e11 | −0.00419215 | ||||||||
\(112\) | − | 6.86924e13i | − | 0.310730i | ||||||
\(113\) | −2.25881e14 | −0.960131 | −0.480065 | − | 0.877233i | \(-0.659387\pi\) | ||||
−0.480065 | + | 0.877233i | \(0.659387\pi\) | |||||||
\(114\) | 3.22424e11 | 0.00128853 | ||||||||
\(115\) | −1.55901e13 | −0.0586091 | ||||||||
\(116\) | − | 1.43220e14i | − | 0.506754i | ||||||
\(117\) | − | 3.14240e14i | − | 1.04703i | ||||||
\(118\) | − | 2.92175e14i | − | 0.917210i | ||||||
\(119\) | −6.35150e14 | −1.87952 | ||||||||
\(120\) | − | 6.43819e11i | − | 0.00179678i | ||||||
\(121\) | 7.28125e13 | + | 3.72704e14i | 0.191738 | + | 0.981446i | ||||
\(122\) | 1.77771e14 | 0.441918 | ||||||||
\(123\) | − | 5.35005e11i | − | 0.00125609i | ||||||
\(124\) | 2.04625e14 | 0.453949 | ||||||||
\(125\) | −1.04653e15 | −2.19473 | ||||||||
\(126\) | −4.43117e14 | −0.878869 | ||||||||
\(127\) | − | 6.96740e14i | − | 1.30751i | −0.756707 | − | 0.653755i | \(-0.773193\pi\) | ||
0.756707 | − | 0.653755i | \(-0.226807\pi\) | |||||||
\(128\) | − | 4.97582e13i | − | 0.0883883i | ||||||
\(129\) | 7.85217e11i | 0.00132088i | ||||||||
\(130\) | 8.33979e14 | 1.32908 | ||||||||
\(131\) | 1.14010e15i | 1.72205i | 0.508566 | + | 0.861023i | \(0.330176\pi\) | ||||
−0.508566 | + | 0.861023i | \(0.669824\pi\) | |||||||
\(132\) | 7.62958e11 | + | 6.28328e11i | 0.00109266 | + | 0.000899847i | ||||
\(133\) | 5.88945e14 | 0.800043 | ||||||||
\(134\) | 5.89038e14i | 0.759294i | ||||||||
\(135\) | −8.30624e12 | −0.0101641 | ||||||||
\(136\) | −4.60078e14 | −0.534638 | ||||||||
\(137\) | 1.39699e15 | 1.54224 | 0.771118 | − | 0.636693i | \(-0.219698\pi\) | ||||
0.771118 | + | 0.636693i | \(0.219698\pi\) | |||||||
\(138\) | − | 6.22930e10i | − | 6.53560e-5i | ||||||
\(139\) | 1.29804e15i | 1.29475i | 0.762173 | + | 0.647374i | \(0.224133\pi\) | ||||
−0.762173 | + | 0.647374i | \(0.775867\pi\) | |||||||
\(140\) | − | 1.17601e15i | − | 1.11562i | ||||||
\(141\) | −1.97499e12 | −0.00178251 | ||||||||
\(142\) | 2.25803e14i | 0.193959i | ||||||||
\(143\) | −8.13913e14 | + | 9.88308e14i | −0.665619 | + | 0.808239i | ||||
\(144\) | −3.20977e14 | −0.249998 | ||||||||
\(145\) | − | 2.45191e15i | − | 1.81940i | ||||||
\(146\) | 1.70942e15 | 1.20887 | ||||||||
\(147\) | 2.28788e12 | 0.00154246 | ||||||||
\(148\) | −1.15160e15 | −0.740405 | ||||||||
\(149\) | 6.79049e14i | 0.416483i | 0.978077 | + | 0.208241i | \(0.0667740\pi\) | ||||
−0.978077 | + | 0.208241i | \(0.933226\pi\) | |||||||
\(150\) | − | 7.60186e12i | − | 0.00444919i | ||||||
\(151\) | − | 1.05477e15i | − | 0.589277i | −0.955609 | − | 0.294639i | \(-0.904801\pi\) | ||
0.955609 | − | 0.294639i | \(-0.0951993\pi\) | |||||||
\(152\) | 4.26609e14 | 0.227575 | ||||||||
\(153\) | 2.96784e15i | 1.51217i | ||||||||
\(154\) | 1.39363e15 | + | 1.14771e15i | 0.678427 | + | 0.558713i | ||||
\(155\) | 3.50317e15 | 1.62982 | ||||||||
\(156\) | 3.33230e12i | 0.00148208i | ||||||||
\(157\) | 9.34964e13 | 0.0397647 | 0.0198823 | − | 0.999802i | \(-0.493671\pi\) | ||||
0.0198823 | + | 0.999802i | \(0.493671\pi\) | |||||||
\(158\) | 2.06949e15 | 0.841906 | ||||||||
\(159\) | −8.49025e12 | −0.00330476 | ||||||||
\(160\) | − | 8.51858e14i | − | 0.317342i | ||||||
\(161\) | − | 1.13785e14i | − | 0.0405794i | ||||||
\(162\) | 2.07052e15i | 0.707090i | ||||||||
\(163\) | −2.94755e15 | −0.964156 | −0.482078 | − | 0.876128i | \(-0.660118\pi\) | ||||
−0.482078 | + | 0.876128i | \(0.660118\pi\) | |||||||
\(164\) | − | 7.07883e14i | − | 0.221847i | ||||||
\(165\) | 1.30618e13 | + | 1.07569e13i | 0.00392297 | + | 0.00323073i | ||||
\(166\) | −3.83695e15 | −1.10466 | ||||||||
\(167\) | 3.56447e15i | 0.983966i | 0.870605 | + | 0.491983i | \(0.163728\pi\) | ||||
−0.870605 | + | 0.491983i | \(0.836272\pi\) | |||||||
\(168\) | 4.69895e12 | 0.00124404 | ||||||||
\(169\) | −3.79166e14 | −0.0962992 | ||||||||
\(170\) | −7.87652e15 | −1.91952 | ||||||||
\(171\) | − | 2.75194e15i | − | 0.643675i | ||||||
\(172\) | 1.03895e15i | 0.233289i | ||||||||
\(173\) | − | 1.29150e15i | − | 0.278466i | −0.990260 | − | 0.139233i | \(-0.955536\pi\) | ||
0.990260 | − | 0.139233i | \(-0.0444637\pi\) | |||||||
\(174\) | 9.79703e12 | 0.00202885 | ||||||||
\(175\) | − | 1.38857e16i | − | 2.76249i | ||||||
\(176\) | 1.00949e15 | + | 8.31361e14i | 0.192981 | + | 0.158928i | ||||
\(177\) | 1.99864e13 | 0.00367216 | ||||||||
\(178\) | − | 9.42809e14i | − | 0.166527i | ||||||
\(179\) | 3.91080e15 | 0.664192 | 0.332096 | − | 0.943246i | \(-0.392244\pi\) | ||||
0.332096 | + | 0.943246i | \(0.392244\pi\) | |||||||
\(180\) | −5.49511e15 | −0.897571 | ||||||||
\(181\) | 8.28150e15 | 1.30125 | 0.650623 | − | 0.759401i | \(-0.274508\pi\) | ||||
0.650623 | + | 0.759401i | \(0.274508\pi\) | |||||||
\(182\) | 6.08684e15i | 0.920221i | ||||||||
\(183\) | 1.21605e13i | 0.00176927i | ||||||||
\(184\) | − | 8.24219e13i | − | 0.0115430i | ||||||
\(185\) | −1.97153e16 | −2.65829 | ||||||||
\(186\) | 1.39975e13i | 0.00181744i | ||||||||
\(187\) | 7.68700e15 | − | 9.33407e15i | 0.961315 | − | 1.16729i | ||||
\(188\) | −2.61318e15 | −0.314821 | ||||||||
\(189\) | − | 6.06236e13i | − | 0.00703735i | ||||||
\(190\) | 7.30353e15 | 0.817067 | ||||||||
\(191\) | −1.89679e15 | −0.204544 | −0.102272 | − | 0.994756i | \(-0.532611\pi\) | ||||
−0.102272 | + | 0.994756i | \(0.532611\pi\) | |||||||
\(192\) | 3.40374e12 | 0.000353873 | ||||||||
\(193\) | 1.43375e16i | 1.43738i | 0.695330 | + | 0.718690i | \(0.255258\pi\) | ||||
−0.695330 | + | 0.718690i | \(0.744742\pi\) | |||||||
\(194\) | − | 3.61505e15i | − | 0.349545i | ||||||
\(195\) | 5.70488e13i | 0.00532114i | ||||||||
\(196\) | 3.02718e15 | 0.272424 | ||||||||
\(197\) | − | 9.49470e15i | − | 0.824551i | −0.911059 | − | 0.412276i | \(-0.864734\pi\) | ||
0.911059 | − | 0.412276i | \(-0.135266\pi\) | |||||||
\(198\) | 5.36289e15 | − | 6.51198e15i | 0.449513 | − | 0.545829i | ||||
\(199\) | 1.18215e15 | 0.0956535 | 0.0478267 | − | 0.998856i | \(-0.484770\pi\) | ||||
0.0478267 | + | 0.998856i | \(0.484770\pi\) | |||||||
\(200\) | − | 1.00583e16i | − | 0.785803i | ||||||
\(201\) | −4.02935e13 | −0.00303992 | ||||||||
\(202\) | −8.44278e15 | −0.615213 | ||||||||
\(203\) | 1.78954e16 | 1.25971 | ||||||||
\(204\) | − | 3.14719e13i | − | 0.00214049i | ||||||
\(205\) | − | 1.21189e16i | − | 0.796501i | ||||||
\(206\) | 1.98512e16i | 1.26100i | ||||||||
\(207\) | −5.31682e14 | −0.0326482 | ||||||||
\(208\) | 4.40908e15i | 0.261761i | ||||||||
\(209\) | −7.12780e15 | + | 8.65505e15i | −0.409196 | + | 0.496873i | ||||
\(210\) | 8.04457e13 | 0.00446650 | ||||||||
\(211\) | 2.01589e16i | 1.08265i | 0.840813 | + | 0.541326i | \(0.182077\pi\) | ||||
−0.840813 | + | 0.541326i | \(0.817923\pi\) | |||||||
\(212\) | −1.12337e16 | −0.583677 | ||||||||
\(213\) | −1.54462e13 | −0.000776539 | ||||||||
\(214\) | 3.01880e15 | 0.146872 | ||||||||
\(215\) | 1.77867e16i | 0.837580i | ||||||||
\(216\) | − | 4.39134e13i | − | 0.00200180i | ||||||
\(217\) | 2.55680e16i | 1.12844i | ||||||||
\(218\) | 1.74270e15 | 0.0744779 | ||||||||
\(219\) | 1.16934e14i | 0.00483986i | ||||||||
\(220\) | 1.72825e16 | + | 1.42329e16i | 0.692863 | + | 0.570602i | ||||
\(221\) | 4.07676e16 | 1.58332 | ||||||||
\(222\) | − | 7.87759e13i | − | 0.00296430i | ||||||
\(223\) | 2.53275e16 | 0.923545 | 0.461772 | − | 0.886999i | \(-0.347214\pi\) | ||||
0.461772 | + | 0.886999i | \(0.347214\pi\) | |||||||
\(224\) | 6.21733e15 | 0.219719 | ||||||||
\(225\) | −6.48832e16 | −2.22257 | ||||||||
\(226\) | − | 2.04444e16i | − | 0.678915i | ||||||
\(227\) | 5.22912e15i | 0.168363i | 0.996450 | + | 0.0841817i | \(0.0268276\pi\) | ||||
−0.996450 | + | 0.0841817i | \(0.973172\pi\) | |||||||
\(228\) | 2.91825e13i | 0.000911125i | ||||||||
\(229\) | −1.59457e16 | −0.482832 | −0.241416 | − | 0.970422i | \(-0.577612\pi\) | ||||
−0.241416 | + | 0.970422i | \(0.577612\pi\) | |||||||
\(230\) | − | 1.41106e15i | − | 0.0414429i | ||||||
\(231\) | −7.85101e13 | + | 9.53323e13i | −0.00223687 | + | 0.00271616i | ||||
\(232\) | 1.29628e16 | 0.358329 | ||||||||
\(233\) | − | 7.51530e15i | − | 0.201583i | −0.994908 | − | 0.100792i | \(-0.967862\pi\) | ||
0.994908 | − | 0.100792i | \(-0.0321376\pi\) | |||||||
\(234\) | 2.84418e16 | 0.740365 | ||||||||
\(235\) | −4.47375e16 | −1.13031 | ||||||||
\(236\) | 2.64447e16 | 0.648565 | ||||||||
\(237\) | 1.41565e14i | 0.00337067i | ||||||||
\(238\) | − | 5.74872e16i | − | 1.32902i | ||||||
\(239\) | − | 5.88675e16i | − | 1.32157i | −0.750575 | − | 0.660786i | \(-0.770223\pi\) | ||
0.750575 | − | 0.660786i | \(-0.229777\pi\) | |||||||
\(240\) | 5.82718e13 | 0.00127052 | ||||||||
\(241\) | 8.01899e16i | 1.69824i | 0.528196 | + | 0.849122i | \(0.322869\pi\) | ||||
−0.528196 | + | 0.849122i | \(0.677131\pi\) | |||||||
\(242\) | −3.37333e16 | + | 6.59024e15i | −0.693987 | + | 0.135579i | ||||
\(243\) | −4.24911e14 | −0.00849287 | ||||||||
\(244\) | 1.60900e16i | 0.312484i | ||||||||
\(245\) | 5.18251e16 | 0.978087 | ||||||||
\(246\) | 4.84231e13 | 0.000888193 | ||||||||
\(247\) | −3.78019e16 | −0.673961 | ||||||||
\(248\) | 1.85205e16i | 0.320990i | ||||||||
\(249\) | − | 2.62469e14i | − | 0.00442265i | ||||||
\(250\) | − | 9.47210e16i | − | 1.55191i | ||||||
\(251\) | −8.72292e15 | −0.138978 | −0.0694889 | − | 0.997583i | \(-0.522137\pi\) | ||||
−0.0694889 | + | 0.997583i | \(0.522137\pi\) | |||||||
\(252\) | − | 4.01063e16i | − | 0.621455i | ||||||
\(253\) | 1.67218e15 | + | 1.37711e15i | 0.0252022 | + | 0.0207551i | ||||
\(254\) | 6.30617e16 | 0.924549 | ||||||||
\(255\) | − | 5.38798e14i | − | 0.00768501i | ||||||
\(256\) | 4.50360e15 | 0.0625000 | ||||||||
\(257\) | −3.93472e16 | −0.531352 | −0.265676 | − | 0.964062i | \(-0.585595\pi\) | ||||
−0.265676 | + | 0.964062i | \(0.585595\pi\) | |||||||
\(258\) | −7.10698e13 | −0.000934000 | ||||||||
\(259\) | − | 1.43893e17i | − | 1.84053i | ||||||
\(260\) | 7.54832e16i | 0.939803i | ||||||||
\(261\) | − | 8.36194e16i | − | 1.01350i | ||||||
\(262\) | −1.03190e17 | −1.21767 | ||||||||
\(263\) | 4.28104e16i | 0.491880i | 0.969285 | + | 0.245940i | \(0.0790966\pi\) | ||||
−0.969285 | + | 0.245940i | \(0.920903\pi\) | |||||||
\(264\) | −5.68697e13 | + | 6.90551e13i | −0.000636288 | + | 0.000772624i | ||||
\(265\) | −1.92321e17 | −2.09558 | ||||||||
\(266\) | 5.33052e16i | 0.565715i | ||||||||
\(267\) | 6.44934e13 | 0.000666709 | ||||||||
\(268\) | −5.33136e16 | −0.536902 | ||||||||
\(269\) | 1.74537e16 | 0.171246 | 0.0856231 | − | 0.996328i | \(-0.472712\pi\) | ||||
0.0856231 | + | 0.996328i | \(0.472712\pi\) | |||||||
\(270\) | − | 7.51795e14i | − | 0.00718709i | ||||||
\(271\) | − | 1.28554e17i | − | 1.19757i | −0.800908 | − | 0.598787i | \(-0.795650\pi\) | ||
0.800908 | − | 0.598787i | \(-0.204350\pi\) | |||||||
\(272\) | − | 4.16415e16i | − | 0.378046i | ||||||
\(273\) | −4.16374e14 | −0.00368422 | ||||||||
\(274\) | 1.26442e17i | 1.09053i | ||||||||
\(275\) | 2.04062e17 | + | 1.68054e17i | 1.71567 | + | 1.41293i | ||||
\(276\) | 5.63812e12 | 4.62137e−5 | ||||||||
\(277\) | 2.19932e16i | 0.175764i | 0.996131 | + | 0.0878821i | \(0.0280099\pi\) | ||||
−0.996131 | + | 0.0878821i | \(0.971990\pi\) | |||||||
\(278\) | −1.17485e17 | −0.915524 | ||||||||
\(279\) | 1.19471e17 | 0.907890 | ||||||||
\(280\) | 1.06440e17 | 0.788860 | ||||||||
\(281\) | 2.42855e17i | 1.75551i | 0.479111 | + | 0.877754i | \(0.340959\pi\) | ||||
−0.479111 | + | 0.877754i | \(0.659041\pi\) | |||||||
\(282\) | − | 1.78756e14i | − | 0.00126043i | ||||||
\(283\) | − | 1.02752e17i | − | 0.706782i | −0.935476 | − | 0.353391i | \(-0.885029\pi\) | ||
0.935476 | − | 0.353391i | \(-0.114971\pi\) | |||||||
\(284\) | −2.04373e16 | −0.137150 | ||||||||
\(285\) | 4.99602e14i | 0.00327122i | ||||||||
\(286\) | −8.94514e16 | − | 7.36670e16i | −0.571512 | − | 0.470664i | ||||
\(287\) | 8.84505e16 | 0.551477 | ||||||||
\(288\) | − | 2.90515e16i | − | 0.176775i | ||||||
\(289\) | −2.16652e17 | −1.28670 | ||||||||
\(290\) | 2.21922e17 | 1.28651 | ||||||||
\(291\) | 2.47290e14 | 0.00139944 | ||||||||
\(292\) | 1.54719e17i | 0.854800i | ||||||||
\(293\) | − | 8.86884e15i | − | 0.0478403i | −0.999714 | − | 0.0239201i | \(-0.992385\pi\) | ||
0.999714 | − | 0.0239201i | \(-0.00761474\pi\) | |||||||
\(294\) | 2.07076e14i | 0.00109068i | ||||||||
\(295\) | 4.52731e17 | 2.32855 | ||||||||
\(296\) | − | 1.04231e17i | − | 0.523546i | ||||||
\(297\) | 8.90916e14 | + | 7.33706e14i | 0.00437060 | + | 0.00359937i | ||||
\(298\) | −6.14605e16 | −0.294498 | ||||||||
\(299\) | 7.30341e15i | 0.0341844i | ||||||||
\(300\) | 6.88042e14 | 0.00314605 | ||||||||
\(301\) | −1.29817e17 | −0.579919 | ||||||||
\(302\) | 9.54670e16 | 0.416682 | ||||||||
\(303\) | − | 5.77533e14i | − | 0.00246308i | ||||||
\(304\) | 3.86123e16i | 0.160920i | ||||||||
\(305\) | 2.75460e17i | 1.12191i | ||||||||
\(306\) | −2.68619e17 | −1.06927 | ||||||||
\(307\) | − | 3.64134e17i | − | 1.41675i | −0.705838 | − | 0.708374i | \(-0.749429\pi\) | ||
0.705838 | − | 0.708374i | \(-0.250571\pi\) | |||||||
\(308\) | −1.03879e17 | + | 1.26137e17i | −0.395070 | + | 0.479720i | ||||
\(309\) | −1.35793e15 | −0.00504857 | ||||||||
\(310\) | 3.17070e17i | 1.15245i | ||||||||
\(311\) | 5.02416e17 | 1.78542 | 0.892710 | − | 0.450631i | \(-0.148801\pi\) | ||||
0.892710 | + | 0.450631i | \(0.148801\pi\) | |||||||
\(312\) | −3.01606e14 | −0.00104799 | ||||||||
\(313\) | 2.26040e17 | 0.768024 | 0.384012 | − | 0.923328i | \(-0.374542\pi\) | ||||
0.384012 | + | 0.923328i | \(0.374542\pi\) | |||||||
\(314\) | 8.46233e15i | 0.0281179i | ||||||||
\(315\) | − | 6.86618e17i | − | 2.23122i | ||||||
\(316\) | 1.87309e17i | 0.595317i | ||||||||
\(317\) | −9.50564e16 | −0.295506 | −0.147753 | − | 0.989024i | \(-0.547204\pi\) | ||||
−0.147753 | + | 0.989024i | \(0.547204\pi\) | |||||||
\(318\) | − | 7.68450e14i | − | 0.00233682i | ||||||
\(319\) | −2.16582e17 | + | 2.62989e17i | −0.644300 | + | 0.782352i | ||||
\(320\) | 7.71014e16 | 0.224395 | ||||||||
\(321\) | 2.06503e14i | 0.000588018i | ||||||||
\(322\) | 1.02987e16 | 0.0286940 | ||||||||
\(323\) | 3.57020e17 | 0.973363 | ||||||||
\(324\) | −1.87402e17 | −0.499988 | ||||||||
\(325\) | 8.91264e17i | 2.32714i | ||||||||
\(326\) | − | 2.66781e17i | − | 0.681761i | ||||||
\(327\) | 1.19211e14i | 0.000298181i | ||||||||
\(328\) | 6.40702e16 | 0.156870 | ||||||||
\(329\) | − | 3.26519e17i | − | 0.782595i | ||||||
\(330\) | −9.73607e14 | + | 1.18222e15i | −0.00228447 | + | 0.00277396i | ||||
\(331\) | −3.76099e17 | −0.863986 | −0.431993 | − | 0.901877i | \(-0.642189\pi\) | ||||
−0.431993 | + | 0.901877i | \(0.642189\pi\) | |||||||
\(332\) | − | 3.47281e17i | − | 0.781115i | ||||||
\(333\) | −6.72366e17 | −1.48080 | ||||||||
\(334\) | −3.22619e17 | −0.695769 | ||||||||
\(335\) | −9.12726e17 | −1.92764 | ||||||||
\(336\) | 4.25300e14i | 0.000879672i | ||||||||
\(337\) | − | 3.82968e17i | − | 0.775806i | −0.921700 | − | 0.387903i | \(-0.873200\pi\) | ||
0.921700 | − | 0.387903i | \(-0.126800\pi\) | |||||||
\(338\) | − | 3.43182e16i | − | 0.0680938i | ||||||
\(339\) | 1.39851e15 | 0.00271812 | ||||||||
\(340\) | − | 7.12901e17i | − | 1.35730i | ||||||
\(341\) | −3.75745e17 | − | 3.09441e17i | −0.700829 | − | 0.577162i | ||||
\(342\) | 2.49078e17 | 0.455147 | ||||||||
\(343\) | − | 3.15979e17i | − | 0.565718i | ||||||
\(344\) | −9.40347e16 | −0.164960 | ||||||||
\(345\) | 9.65242e13 | 0.000165922 | ||||||||
\(346\) | 1.16893e17 | 0.196905 | ||||||||
\(347\) | 9.92625e17i | 1.63862i | 0.573349 | + | 0.819311i | \(0.305644\pi\) | ||||
−0.573349 | + | 0.819311i | \(0.694356\pi\) | |||||||
\(348\) | 8.86726e14i | 0.00143461i | ||||||||
\(349\) | − | 8.70181e17i | − | 1.37985i | −0.723882 | − | 0.689924i | \(-0.757644\pi\) | ||
0.723882 | − | 0.689924i | \(-0.242356\pi\) | |||||||
\(350\) | 1.25679e18 | 1.95338 | ||||||||
\(351\) | 3.89117e15i | 0.00592831i | ||||||||
\(352\) | −7.52462e16 | + | 9.13690e16i | −0.112379 | + | 0.136458i | ||||
\(353\) | 6.19745e17 | 0.907382 | 0.453691 | − | 0.891159i | \(-0.350107\pi\) | ||||
0.453691 | + | 0.891159i | \(0.350107\pi\) | |||||||
\(354\) | 1.80896e15i | 0.00259661i | ||||||||
\(355\) | −3.49886e17 | −0.492411 | ||||||||
\(356\) | 8.53333e16 | 0.117752 | ||||||||
\(357\) | 3.93244e15 | 0.00532090 | ||||||||
\(358\) | 3.53965e17i | 0.469655i | ||||||||
\(359\) | − | 2.11459e14i | − | 0.000275147i | −1.00000 | 0.000137573i | \(-0.999956\pi\) | |||
1.00000 | 0.000137573i | \(-4.37910e-5\pi\) | ||||||||
\(360\) | − | 4.97360e17i | − | 0.634678i | ||||||
\(361\) | 4.67959e17 | 0.585676 | ||||||||
\(362\) | 7.49556e17i | 0.920119i | ||||||||
\(363\) | −4.50809e14 | − | 2.30755e15i | −0.000542808 | − | 0.00277846i | ||||
\(364\) | −5.50918e17 | −0.650695 | ||||||||
\(365\) | 2.64879e18i | 3.06900i | ||||||||
\(366\) | −1.10065e15 | −0.00125107 | ||||||||
\(367\) | −1.15764e17 | −0.129096 | −0.0645478 | − | 0.997915i | \(-0.520561\pi\) | ||||
−0.0645478 | + | 0.997915i | \(0.520561\pi\) | |||||||
\(368\) | 7.45998e15 | 0.00816212 | ||||||||
\(369\) | − | 4.13300e17i | − | 0.443691i | ||||||
\(370\) | − | 1.78443e18i | − | 1.87969i | ||||||
\(371\) | − | 1.40366e18i | − | 1.45093i | ||||||
\(372\) | −1.26691e15 | −0.00128512 | ||||||||
\(373\) | − | 8.28323e17i | − | 0.824590i | −0.911050 | − | 0.412295i | \(-0.864727\pi\) | ||
0.911050 | − | 0.412295i | \(-0.135273\pi\) | |||||||
\(374\) | 8.44824e17 | + | 6.95748e17i | 0.825401 | + | 0.679752i | ||||
\(375\) | 6.47945e15 | 0.00621325 | ||||||||
\(376\) | − | 2.36518e17i | − | 0.222612i | ||||||
\(377\) | −1.14863e18 | −1.06119 | ||||||||
\(378\) | 5.48702e15 | 0.00497615 | ||||||||
\(379\) | 2.14377e18 | 1.90855 | 0.954273 | − | 0.298935i | \(-0.0966314\pi\) | ||||
0.954273 | + | 0.298935i | \(0.0966314\pi\) | |||||||
\(380\) | 6.61040e17i | 0.577753i | ||||||||
\(381\) | 4.31377e15i | 0.00370154i | ||||||||
\(382\) | − | 1.71678e17i | − | 0.144634i | ||||||
\(383\) | 4.77226e17 | 0.394759 | 0.197380 | − | 0.980327i | \(-0.436757\pi\) | ||||
0.197380 | + | 0.980327i | \(0.436757\pi\) | |||||||
\(384\) | 3.08071e14i | 0.000250226i | ||||||||
\(385\) | −1.77841e18 | + | 2.15946e18i | −1.41842 | + | 1.72235i | ||||
\(386\) | −1.29768e18 | −1.01638 | ||||||||
\(387\) | 6.06593e17i | 0.466574i | ||||||||
\(388\) | 3.27197e17 | 0.247165 | ||||||||
\(389\) | 1.36394e18 | 1.01192 | 0.505960 | − | 0.862557i | \(-0.331138\pi\) | ||||
0.505960 | + | 0.862557i | \(0.331138\pi\) | |||||||
\(390\) | −5.16347e15 | −0.00376261 | ||||||||
\(391\) | − | 6.89770e16i | − | 0.0493705i | ||||||
\(392\) | 2.73989e17i | 0.192633i | ||||||||
\(393\) | − | 7.05879e15i | − | 0.00487509i | ||||||
\(394\) | 8.59362e17 | 0.583046 | ||||||||
\(395\) | 3.20672e18i | 2.13738i | ||||||||
\(396\) | 5.89397e17 | + | 4.85393e17i | 0.385960 | + | 0.317854i | ||||
\(397\) | −8.81694e17 | −0.567263 | −0.283632 | − | 0.958933i | \(-0.591539\pi\) | ||||
−0.283632 | + | 0.958933i | \(0.591539\pi\) | |||||||
\(398\) | 1.06996e17i | 0.0676372i | ||||||||
\(399\) | −3.64637e15 | −0.00226491 | ||||||||
\(400\) | 9.10371e17 | 0.555646 | ||||||||
\(401\) | 1.19545e18 | 0.717001 | 0.358501 | − | 0.933529i | \(-0.383288\pi\) | ||||
0.358501 | + | 0.933529i | \(0.383288\pi\) | |||||||
\(402\) | − | 3.64695e15i | − | 0.00214955i | ||||||
\(403\) | − | 1.64111e18i | − | 0.950607i | ||||||
\(404\) | − | 7.64153e17i | − | 0.435021i | ||||||
\(405\) | −3.20831e18 | −1.79511 | ||||||||
\(406\) | 1.61971e18i | 0.890748i | ||||||||
\(407\) | 2.11464e18 | + | 1.74149e18i | 1.14308 | + | 0.941371i | ||||
\(408\) | 2.84851e15 | 0.00151355 | ||||||||
\(409\) | − | 7.10803e17i | − | 0.371267i | −0.982619 | − | 0.185634i | \(-0.940566\pi\) | ||
0.982619 | − | 0.185634i | \(-0.0594337\pi\) | |||||||
\(410\) | 1.09688e18 | 0.563212 | ||||||||
\(411\) | −8.64931e15 | −0.00436605 | ||||||||
\(412\) | −1.79672e18 | −0.891662 | ||||||||
\(413\) | 3.30428e18i | 1.61223i | ||||||||
\(414\) | − | 4.81223e16i | − | 0.0230858i | ||||||
\(415\) | − | 5.94544e18i | − | 2.80445i | ||||||
\(416\) | −3.99064e17 | −0.185093 | ||||||||
\(417\) | − | 8.03665e15i | − | 0.00366541i | ||||||
\(418\) | −7.83366e17 | − | 6.45134e17i | −0.351342 | − | 0.289345i | ||||
\(419\) | 2.10618e18 | 0.928960 | 0.464480 | − | 0.885584i | \(-0.346241\pi\) | ||||
0.464480 | + | 0.885584i | \(0.346241\pi\) | |||||||
\(420\) | 7.28111e15i | 0.00315830i | ||||||||
\(421\) | 3.91041e17 | 0.166820 | 0.0834099 | − | 0.996515i | \(-0.473419\pi\) | ||||
0.0834099 | + | 0.996515i | \(0.473419\pi\) | |||||||
\(422\) | −1.82457e18 | −0.765550 | ||||||||
\(423\) | −1.52572e18 | −0.629638 | ||||||||
\(424\) | − | 1.01676e18i | − | 0.412722i | ||||||
\(425\) | − | 8.41755e18i | − | 3.36096i | ||||||
\(426\) | − | 1.39803e15i | − | 0.000549096i | ||||||
\(427\) | −2.01046e18 | −0.776783 | ||||||||
\(428\) | 2.73231e17i | 0.103854i | ||||||||
\(429\) | 5.03923e15 | − | 6.11898e15i | 0.00188436 | − | 0.00228811i | ||||
\(430\) | −1.60987e18 | −0.592259 | ||||||||
\(431\) | − | 5.26408e17i | − | 0.190538i | −0.995452 | − | 0.0952689i | \(-0.969629\pi\) | ||
0.995452 | − | 0.0952689i | \(-0.0303711\pi\) | |||||||
\(432\) | 3.97459e15 | 0.00141549 | ||||||||
\(433\) | 4.20656e18 | 1.47405 | 0.737024 | − | 0.675866i | \(-0.236230\pi\) | ||||
0.737024 | + | 0.675866i | \(0.236230\pi\) | |||||||
\(434\) | −2.31416e18 | −0.797929 | ||||||||
\(435\) | 1.51807e16i | 0.00515071i | ||||||||
\(436\) | 1.57731e17i | 0.0526639i | ||||||||
\(437\) | 6.39592e16i | 0.0210152i | ||||||||
\(438\) | −1.05837e16 | −0.00342229 | ||||||||
\(439\) | − | 1.00723e18i | − | 0.320535i | −0.987074 | − | 0.160267i | \(-0.948764\pi\) | ||
0.987074 | − | 0.160267i | \(-0.0512357\pi\) | |||||||
\(440\) | −1.28821e18 | + | 1.56423e18i | −0.403477 | + | 0.489928i | ||||
\(441\) | 1.76743e18 | 0.544843 | ||||||||
\(442\) | 3.68986e18i | 1.11958i | ||||||||
\(443\) | −5.95687e17 | −0.177907 | −0.0889533 | − | 0.996036i | \(-0.528352\pi\) | ||||
−0.0889533 | + | 0.996036i | \(0.528352\pi\) | |||||||
\(444\) | 7.12998e15 | 0.00209608 | ||||||||
\(445\) | 1.46090e18 | 0.422767 | ||||||||
\(446\) | 2.29238e18i | 0.653045i | ||||||||
\(447\) | − | 4.20424e15i | − | 0.00117906i | ||||||
\(448\) | 5.62729e17i | 0.155365i | ||||||||
\(449\) | 3.81287e18 | 1.03640 | 0.518200 | − | 0.855259i | \(-0.326602\pi\) | ||||
0.518200 | + | 0.855259i | \(0.326602\pi\) | |||||||
\(450\) | − | 5.87256e18i | − | 1.57159i | ||||||
\(451\) | −1.07049e18 | + | 1.29986e18i | −0.282063 | + | 0.342499i | ||||
\(452\) | 1.85042e18 | 0.480065 | ||||||||
\(453\) | 6.53048e15i | 0.00166824i | ||||||||
\(454\) | −4.73286e17 | −0.119051 | ||||||||
\(455\) | −9.43169e18 | −2.33620 | ||||||||
\(456\) | −2.64129e15 | −0.000644263 | ||||||||
\(457\) | 5.43729e18i | 1.30608i | 0.757324 | + | 0.653039i | \(0.226506\pi\) | ||||
−0.757324 | + | 0.653039i | \(0.773494\pi\) | |||||||
\(458\) | − | 1.44324e18i | − | 0.341414i | ||||||
\(459\) | − | 3.67502e16i | − | 0.00856191i | ||||||
\(460\) | 1.27714e17 | 0.0293045 | ||||||||
\(461\) | − | 5.85799e18i | − | 1.32386i | −0.749566 | − | 0.661930i | \(-0.769738\pi\) | ||
0.749566 | − | 0.661930i | \(-0.230262\pi\) | |||||||
\(462\) | −8.62849e15 | − | 7.10592e15i | −0.00192062 | − | 0.00158171i | ||||
\(463\) | −9.37770e17 | −0.205603 | −0.102801 | − | 0.994702i | \(-0.532781\pi\) | ||||
−0.102801 | + | 0.994702i | \(0.532781\pi\) | |||||||
\(464\) | 1.17326e18i | 0.253377i | ||||||||
\(465\) | −2.16894e16 | −0.00461399 | ||||||||
\(466\) | 6.80207e17 | 0.142541 | ||||||||
\(467\) | −2.51221e18 | −0.518605 | −0.259303 | − | 0.965796i | \(-0.583493\pi\) | ||||
−0.259303 | + | 0.965796i | \(0.583493\pi\) | |||||||
\(468\) | 2.57426e18i | 0.523517i | ||||||||
\(469\) | − | 6.66158e18i | − | 1.33465i | ||||||
\(470\) | − | 4.04918e18i | − | 0.799248i | ||||||
\(471\) | −5.78871e14 | −0.000112573 | ||||||||
\(472\) | 2.39350e18i | 0.458605i | ||||||||
\(473\) | 1.57113e18 | − | 1.90778e18i | 0.296610 | − | 0.360163i | ||||
\(474\) | −1.28130e16 | −0.00238342 | ||||||||
\(475\) | 7.80520e18i | 1.43063i | ||||||||
\(476\) | 5.20315e18 | 0.939761 | ||||||||
\(477\) | −6.55885e18 | −1.16735 | ||||||||
\(478\) | 5.32808e18 | 0.934492 | ||||||||
\(479\) | 1.11409e19i | 1.92563i | 0.270157 | + | 0.962816i | \(0.412924\pi\) | ||||
−0.270157 | + | 0.962816i | \(0.587076\pi\) | |||||||
\(480\) | 5.27416e15i | 0.000898390i | ||||||||
\(481\) | 9.23591e18i | 1.55047i | ||||||||
\(482\) | −7.25796e18 | −1.20084 | ||||||||
\(483\) | 7.04487e14i | 0.000114880i | ||||||||
\(484\) | −5.96480e17 | − | 3.05319e18i | −0.0958691 | − | 0.490723i | ||||
\(485\) | 5.60160e18 | 0.887401 | ||||||||
\(486\) | − | 3.84586e16i | − | 0.00600536i | ||||||
\(487\) | 6.90285e18 | 1.06249 | 0.531246 | − | 0.847218i | \(-0.321724\pi\) | ||||
0.531246 | + | 0.847218i | \(0.321724\pi\) | |||||||
\(488\) | −1.45630e18 | −0.220959 | ||||||||
\(489\) | 1.82493e16 | 0.00272951 | ||||||||
\(490\) | 4.69067e18i | 0.691612i | ||||||||
\(491\) | − | 6.74613e17i | − | 0.0980583i | −0.998797 | − | 0.0490291i | \(-0.984387\pi\) | ||
0.998797 | − | 0.0490291i | \(-0.0156127\pi\) | |||||||
\(492\) | 4.38276e15i | 0.000628047i | ||||||||
\(493\) | 1.08483e19 | 1.53261 | ||||||||
\(494\) | − | 3.42144e18i | − | 0.476562i | ||||||
\(495\) | 1.00905e19 | + | 8.30991e18i | 1.38572 | + | 1.14119i | ||||
\(496\) | −1.67629e18 | −0.226974 | ||||||||
\(497\) | − | 2.55366e18i | − | 0.340933i | ||||||
\(498\) | 2.37560e16 | 0.00312729 | ||||||||
\(499\) | 4.08215e18 | 0.529889 | 0.264944 | − | 0.964264i | \(-0.414646\pi\) | ||||
0.264944 | + | 0.964264i | \(0.414646\pi\) | |||||||
\(500\) | 8.57317e18 | 1.09737 | ||||||||
\(501\) | − | 2.20690e16i | − | 0.00278559i | ||||||
\(502\) | − | 7.89508e17i | − | 0.0982722i | ||||||
\(503\) | − | 4.25871e18i | − | 0.522760i | −0.965236 | − | 0.261380i | \(-0.915822\pi\) | ||
0.965236 | − | 0.261380i | \(-0.0841776\pi\) | |||||||
\(504\) | 3.63001e18 | 0.439435 | ||||||||
\(505\) | − | 1.30823e19i | − | 1.56186i | ||||||
\(506\) | −1.24641e17 | + | 1.51348e17i | −0.0146760 | + | 0.0178206i | ||||
\(507\) | 2.34756e15 | 0.000272622 | ||||||||
\(508\) | 5.70770e18i | 0.653755i | ||||||||
\(509\) | −3.10960e18 | −0.351301 | −0.175651 | − | 0.984453i | \(-0.556203\pi\) | ||||
−0.175651 | + | 0.984453i | \(0.556203\pi\) | |||||||
\(510\) | 4.87664e16 | 0.00543412 | ||||||||
\(511\) | −1.93323e19 | −2.12489 | ||||||||
\(512\) | 4.07619e17i | 0.0441942i | ||||||||
\(513\) | 3.40767e16i | 0.00364449i | ||||||||
\(514\) | − | 3.56130e18i | − | 0.375722i | ||||||
\(515\) | −3.07598e19 | −3.20134 | ||||||||
\(516\) | − | 6.43250e15i | − | 0.000660438i | ||||||
\(517\) | 4.79848e18 | + | 3.95175e18i | 0.486037 | + | 0.400272i | ||||
\(518\) | 1.30237e19 | 1.30145 | ||||||||
\(519\) | 7.99615e15i | 0.000788333i | ||||||||
\(520\) | −6.83196e18 | −0.664541 | ||||||||
\(521\) | 6.47563e18 | 0.621466 | 0.310733 | − | 0.950497i | \(-0.399425\pi\) | ||||
0.310733 | + | 0.950497i | \(0.399425\pi\) | |||||||
\(522\) | 7.56836e18 | 0.716652 | ||||||||
\(523\) | − | 1.65910e18i | − | 0.155010i | −0.996992 | − | 0.0775050i | \(-0.975305\pi\) | ||
0.996992 | − | 0.0775050i | \(-0.0246954\pi\) | |||||||
\(524\) | − | 9.33972e18i | − | 0.861023i | ||||||
\(525\) | 8.59714e16i | 0.00782058i | ||||||||
\(526\) | −3.87476e18 | −0.347812 | ||||||||
\(527\) | 1.54994e19i | 1.37291i | ||||||||
\(528\) | −6.25015e15 | − | 5.14726e15i | −0.000546328 | − | 0.000449924i | ||||
\(529\) | −1.15805e19 | −0.998934 | ||||||||
\(530\) | − | 1.74069e19i | − | 1.48180i | ||||||
\(531\) | 1.54398e19 | 1.29712 | ||||||||
\(532\) | −4.82464e18 | −0.400021 | ||||||||
\(533\) | −5.67727e18 | −0.464568 | ||||||||
\(534\) | 5.83728e15i | 0.000471435i | ||||||||
\(535\) | 4.67769e18i | 0.372868i | ||||||||
\(536\) | − | 4.82540e18i | − | 0.379647i | ||||||
\(537\) | −2.42132e16 | −0.00188032 | ||||||||
\(538\) | 1.57973e18i | 0.121089i | ||||||||
\(539\) | −5.55868e18 | − | 4.57781e18i | −0.420582 | − | 0.346367i | ||||
\(540\) | 6.80447e16 | 0.00508204 | ||||||||
\(541\) | − | 5.01328e18i | − | 0.369608i | −0.982775 | − | 0.184804i | \(-0.940835\pi\) | ||
0.982775 | − | 0.184804i | \(-0.0591650\pi\) | |||||||
\(542\) | 1.16354e19 | 0.846812 | ||||||||
\(543\) | −5.12738e16 | −0.00368381 | ||||||||
\(544\) | 3.76896e18 | 0.267319 | ||||||||
\(545\) | 2.70035e18i | 0.189080i | ||||||||
\(546\) | − | 3.76859e16i | − | 0.00260513i | ||||||
\(547\) | − | 1.70318e19i | − | 1.16238i | −0.813767 | − | 0.581191i | \(-0.802587\pi\) | ||
0.813767 | − | 0.581191i | \(-0.197413\pi\) | |||||||
\(548\) | −1.14442e19 | −0.771118 | ||||||||
\(549\) | 9.39421e18i | 0.624962i | ||||||||
\(550\) | −1.52105e19 | + | 1.84696e19i | −0.999090 | + | 1.21316i | ||||
\(551\) | −1.00591e19 | −0.652375 | ||||||||
\(552\) | 5.10304e14i | 3.26780e-5i | ||||||||
\(553\) | −2.34044e19 | −1.47986 | ||||||||
\(554\) | −1.99060e18 | −0.124284 | ||||||||
\(555\) | 1.22065e17 | 0.00752557 | ||||||||
\(556\) | − | 1.06336e19i | − | 0.647374i | ||||||
\(557\) | − | 4.28571e18i | − | 0.257654i | −0.991667 | − | 0.128827i | \(-0.958879\pi\) | ||
0.991667 | − | 0.128827i | \(-0.0411211\pi\) | |||||||
\(558\) | 1.08133e19i | 0.641975i | ||||||||
\(559\) | 8.33242e18 | 0.488527 | ||||||||
\(560\) | 9.63388e18i | 0.557808i | ||||||||
\(561\) | −4.75930e16 | + | 5.77907e16i | −0.00272147 | + | 0.00330459i | ||||
\(562\) | −2.19807e19 | −1.24133 | ||||||||
\(563\) | − | 9.47779e18i | − | 0.528626i | −0.964437 | − | 0.264313i | \(-0.914855\pi\) | ||
0.964437 | − | 0.264313i | \(-0.0851451\pi\) | |||||||
\(564\) | 1.61792e16 | 0.000891255 | ||||||||
\(565\) | 3.16790e19 | 1.72358 | ||||||||
\(566\) | 9.30005e18 | 0.499770 | ||||||||
\(567\) | − | 2.34161e19i | − | 1.24289i | ||||||
\(568\) | − | 1.84978e18i | − | 0.0969797i | ||||||
\(569\) | − | 3.40436e19i | − | 1.76299i | −0.472192 | − | 0.881496i | \(-0.656537\pi\) | ||
0.472192 | − | 0.881496i | \(-0.343463\pi\) | |||||||
\(570\) | −4.52188e16 | −0.00231310 | ||||||||
\(571\) | 4.30046e18i | 0.217301i | 0.994080 | + | 0.108651i | \(0.0346530\pi\) | ||||
−0.994080 | + | 0.108651i | \(0.965347\pi\) | |||||||
\(572\) | 6.66757e18 | − | 8.09622e18i | 0.332809 | − | 0.404120i | ||||
\(573\) | 1.17437e16 | 0.000579061 | ||||||||
\(574\) | 8.00563e18i | 0.389953i | ||||||||
\(575\) | 1.50798e18 | 0.0725640 | ||||||||
\(576\) | 2.62944e18 | 0.124999 | ||||||||
\(577\) | −1.09117e18 | −0.0512460 | −0.0256230 | − | 0.999672i | \(-0.508157\pi\) | ||||
−0.0256230 | + | 0.999672i | \(0.508157\pi\) | |||||||
\(578\) | − | 1.96091e19i | − | 0.909834i | ||||||
\(579\) | − | 8.87686e16i | − | 0.00406920i | ||||||
\(580\) | 2.00861e19i | 0.909702i | ||||||||
\(581\) | 4.33931e19 | 1.94173 | ||||||||
\(582\) | 2.23821e16i | 0.000989556i | ||||||||
\(583\) | 2.06280e19 | + | 1.69881e19i | 0.901111 | + | 0.742102i | ||||
\(584\) | −1.40036e19 | −0.604435 | ||||||||
\(585\) | 4.40711e19i | 1.87959i | ||||||||
\(586\) | 8.02716e17 | 0.0338282 | ||||||||
\(587\) | −4.48356e19 | −1.86705 | −0.933525 | − | 0.358513i | \(-0.883284\pi\) | ||||
−0.933525 | + | 0.358513i | \(0.883284\pi\) | |||||||
\(588\) | −1.87424e16 | −0.000771228 | ||||||||
\(589\) | − | 1.43719e19i | − | 0.584395i | ||||||
\(590\) | 4.09765e19i | 1.64654i | ||||||||
\(591\) | 5.87852e16i | 0.00233429i | ||||||||
\(592\) | 9.43391e18 | 0.370203 | ||||||||
\(593\) | 9.35070e18i | 0.362628i | 0.983425 | + | 0.181314i | \(0.0580350\pi\) | ||||
−0.983425 | + | 0.181314i | \(0.941965\pi\) | |||||||
\(594\) | −6.64075e16 | + | 8.06365e16i | −0.00254514 | + | 0.00309048i | ||||
\(595\) | 8.90776e19 | 3.37403 | ||||||||
\(596\) | − | 5.56277e18i | − | 0.208241i | ||||||
\(597\) | −7.31912e15 | −0.000270794 | ||||||||
\(598\) | −6.61029e17 | −0.0241720 | ||||||||
\(599\) | 7.44750e18 | 0.269168 | 0.134584 | − | 0.990902i | \(-0.457030\pi\) | ||||
0.134584 | + | 0.990902i | \(0.457030\pi\) | |||||||
\(600\) | 6.22745e16i | 0.00222460i | ||||||||
\(601\) | 3.77235e19i | 1.33196i | 0.745970 | + | 0.665980i | \(0.231986\pi\) | ||||
−0.745970 | + | 0.665980i | \(0.768014\pi\) | |||||||
\(602\) | − | 1.17497e19i | − | 0.410064i | ||||||
\(603\) | −3.11274e19 | −1.07379 | ||||||||
\(604\) | 8.64069e18i | 0.294639i | ||||||||
\(605\) | −1.02117e19 | − | 5.22705e19i | −0.344200 | − | 1.76185i | ||||
\(606\) | 5.22723e16 | 0.00174166 | ||||||||
\(607\) | 1.65517e19i | 0.545157i | 0.962134 | + | 0.272579i | \(0.0878765\pi\) | ||||
−0.962134 | + | 0.272579i | \(0.912124\pi\) | |||||||
\(608\) | −3.49478e18 | −0.113788 | ||||||||
\(609\) | −1.10797e17 | −0.00356622 | ||||||||
\(610\) | −2.49318e19 | −0.793313 | ||||||||
\(611\) | 2.09579e19i | 0.659263i | ||||||||
\(612\) | − | 2.43126e19i | − | 0.756086i | ||||||
\(613\) | 1.82203e19i | 0.560187i | 0.959973 | + | 0.280093i | \(0.0903655\pi\) | ||||
−0.959973 | + | 0.280093i | \(0.909635\pi\) | |||||||
\(614\) | 3.29576e19 | 1.00179 | ||||||||
\(615\) | 7.50326e16i | 0.00225488i | ||||||||
\(616\) | −1.14166e19 | − | 9.40208e18i | −0.339214 | − | 0.279357i | ||||
\(617\) | −1.22988e19 | −0.361298 | −0.180649 | − | 0.983548i | \(-0.557820\pi\) | ||||
−0.180649 | + | 0.983548i | \(0.557820\pi\) | |||||||
\(618\) | − | 1.22906e17i | − | 0.00356988i | ||||||
\(619\) | −5.38341e19 | −1.54605 | −0.773025 | − | 0.634376i | \(-0.781257\pi\) | ||||
−0.773025 | + | 0.634376i | \(0.781257\pi\) | |||||||
\(620\) | −2.86979e19 | −0.814908 | ||||||||
\(621\) | 6.58370e15 | 0.000184854 | ||||||||
\(622\) | 4.54735e19i | 1.26248i | ||||||||
\(623\) | 1.06625e19i | 0.292713i | ||||||||
\(624\) | − | 2.72982e16i | − | 0.000741041i | ||||||
\(625\) | 6.39744e19 | 1.71730 | ||||||||
\(626\) | 2.04588e19i | 0.543075i | ||||||||
\(627\) | 4.41308e16 | − | 5.35866e16i | 0.00115843 | − | 0.00140664i | ||||
\(628\) | −7.65923e17 | −0.0198823 | ||||||||
\(629\) | − | 8.72285e19i | − | 2.23926i | ||||||
\(630\) | 6.21456e19 | 1.57771 | ||||||||
\(631\) | 2.28025e19 | 0.572502 | 0.286251 | − | 0.958155i | \(-0.407591\pi\) | ||||
0.286251 | + | 0.958155i | \(0.407591\pi\) | |||||||
\(632\) | −1.69533e19 | −0.420953 | ||||||||
\(633\) | − | 1.24811e17i | − | 0.00306497i | ||||||
\(634\) | − | 8.60353e18i | − | 0.208954i | ||||||
\(635\) | 9.77154e19i | 2.34718i | ||||||||
\(636\) | 6.95521e16 | 0.00165238 | ||||||||
\(637\) | − | 2.42782e19i | − | 0.570479i | ||||||
\(638\) | −2.38030e19 | − | 1.96028e19i | −0.553207 | − | 0.455589i | ||||
\(639\) | −1.19324e19 | −0.274298 | ||||||||
\(640\) | 6.97842e18i | 0.158671i | ||||||||
\(641\) | −5.76223e19 | −1.29594 | −0.647969 | − | 0.761667i | \(-0.724381\pi\) | ||||
−0.647969 | + | 0.761667i | \(0.724381\pi\) | |||||||
\(642\) | −1.86905e16 | −0.000415792 | ||||||||
\(643\) | 7.35305e19 | 1.61805 | 0.809023 | − | 0.587777i | \(-0.199997\pi\) | ||||
0.809023 | + | 0.587777i | \(0.199997\pi\) | |||||||
\(644\) | 9.32130e17i | 0.0202897i | ||||||||
\(645\) | − | 1.10124e17i | − | 0.00237118i | ||||||
\(646\) | 3.23137e19i | 0.688271i | ||||||||
\(647\) | −8.97802e19 | −1.89169 | −0.945846 | − | 0.324615i | \(-0.894765\pi\) | ||||
−0.945846 | + | 0.324615i | \(0.894765\pi\) | |||||||
\(648\) | − | 1.69617e19i | − | 0.353545i | ||||||
\(649\) | −4.85593e19 | − | 3.99906e19i | −1.00129 | − | 0.824603i | ||||
\(650\) | −8.06680e19 | −1.64554 | ||||||||
\(651\) | − | 1.58301e17i | − | 0.00319461i | ||||||
\(652\) | 2.41463e19 | 0.482078 | ||||||||
\(653\) | 8.44362e19 | 1.66777 | 0.833886 | − | 0.551937i | \(-0.186111\pi\) | ||||
0.833886 | + | 0.551937i | \(0.186111\pi\) | |||||||
\(654\) | −1.07897e16 | −0.000210846 | ||||||||
\(655\) | − | 1.59895e20i | − | 3.09134i | ||||||
\(656\) | 5.79898e18i | 0.110924i | ||||||||
\(657\) | 9.03335e19i | 1.70959i | ||||||||
\(658\) | 2.95531e19 | 0.553378 | ||||||||
\(659\) | − | 6.10282e19i | − | 1.13066i | −0.824864 | − | 0.565331i | \(-0.808748\pi\) | ||
0.824864 | − | 0.565331i | \(-0.191252\pi\) | |||||||
\(660\) | −1.07002e17 | − | 8.81208e16i | −0.00196149 | − | 0.00161537i | ||||
\(661\) | −2.05061e19 | −0.371939 | −0.185970 | − | 0.982555i | \(-0.559543\pi\) | ||||
−0.185970 | + | 0.982555i | \(0.559543\pi\) | |||||||
\(662\) | − | 3.40406e19i | − | 0.610930i | ||||||
\(663\) | −2.52407e17 | −0.00448236 | ||||||||
\(664\) | 3.14323e19 | 0.552332 | ||||||||
\(665\) | −8.25975e19 | −1.43620 | ||||||||
\(666\) | − | 6.08556e19i | − | 1.04708i | ||||||
\(667\) | 1.94344e18i | 0.0330895i | ||||||||
\(668\) | − | 2.92002e19i | − | 0.491983i | ||||||
\(669\) | −1.56812e17 | −0.00261454 | ||||||||
\(670\) | − | 8.26106e19i | − | 1.36305i | ||||||
\(671\) | 2.43319e19 | − | 2.95454e19i | 0.397300 | − | 0.482428i | ||||
\(672\) | −3.84938e16 | −0.000622022 | ||||||||
\(673\) | 2.08739e19i | 0.333810i | 0.985973 | + | 0.166905i | \(0.0533773\pi\) | ||||
−0.985973 | + | 0.166905i | \(0.946623\pi\) | |||||||
\(674\) | 3.46623e19 | 0.548577 | ||||||||
\(675\) | 8.03435e17 | 0.0125842 | ||||||||
\(676\) | 3.10613e18 | 0.0481496 | ||||||||
\(677\) | 1.09156e20i | 1.67467i | 0.546691 | + | 0.837334i | \(0.315887\pi\) | ||||
−0.546691 | + | 0.837334i | \(0.684113\pi\) | |||||||
\(678\) | 1.26579e17i | 0.00192200i | ||||||||
\(679\) | 4.08836e19i | 0.614413i | ||||||||
\(680\) | 6.45244e19 | 0.959758 | ||||||||
\(681\) | − | 3.23754e16i | − | 0.000476635i | ||||||
\(682\) | 2.80074e19 | − | 3.40085e19i | 0.408115 | − | 0.495561i | ||||
\(683\) | 5.50592e19 | 0.794118 | 0.397059 | − | 0.917793i | \(-0.370031\pi\) | ||||
0.397059 | + | 0.917793i | \(0.370031\pi\) | |||||||
\(684\) | 2.25439e19i | 0.321838i | ||||||||
\(685\) | −1.95924e20 | −2.76855 | ||||||||
\(686\) | 2.85992e19 | 0.400023 | ||||||||
\(687\) | 9.87259e16 | 0.00136689 | ||||||||
\(688\) | − | 8.51105e18i | − | 0.116644i | ||||||
\(689\) | 9.00953e19i | 1.22227i | ||||||||
\(690\) | 8.73638e15i | 0.000117324i | ||||||||
\(691\) | −3.15374e19 | −0.419256 | −0.209628 | − | 0.977781i | \(-0.567225\pi\) | ||||
−0.209628 | + | 0.977781i | \(0.567225\pi\) | |||||||
\(692\) | 1.05800e19i | 0.139233i | ||||||||
\(693\) | −6.06503e19 | + | 7.36457e19i | −0.790133 | + | 0.959433i | ||||
\(694\) | −8.98421e19 | −1.15868 | ||||||||
\(695\) | − | 1.82046e20i | − | 2.32427i | ||||||
\(696\) | −8.02573e16 | −0.00101442 | ||||||||
\(697\) | 5.36189e19 | 0.670948 | ||||||||
\(698\) | 7.87598e19 | 0.975700 | ||||||||
\(699\) | 4.65300e16i | 0.000570680i | ||||||||
\(700\) | 1.13752e20i | 1.38125i | ||||||||
\(701\) | 3.24746e19i | 0.390407i | 0.980763 | + | 0.195204i | \(0.0625368\pi\) | ||||
−0.980763 | + | 0.195204i | \(0.937463\pi\) | |||||||
\(702\) | −3.52189e17 | −0.00419194 | ||||||||
\(703\) | 8.08830e19i | 0.953169i | ||||||||
\(704\) | −8.26978e18 | − | 6.81051e18i | −0.0964907 | − | 0.0794641i | ||||
\(705\) | 2.76986e17 | 0.00319988 | ||||||||
\(706\) | 5.60929e19i | 0.641616i | ||||||||
\(707\) | 9.54815e19 | 1.08139 | ||||||||
\(708\) | −1.63729e17 | −0.00183608 | ||||||||
\(709\) | 4.78036e18 | 0.0530808 | 0.0265404 | − | 0.999648i | \(-0.491551\pi\) | ||||
0.0265404 | + | 0.999648i | \(0.491551\pi\) | |||||||
\(710\) | − | 3.16681e19i | − | 0.348187i | ||||||
\(711\) | 1.09361e20i | 1.19063i | ||||||||
\(712\) | 7.72349e18i | 0.0832633i | ||||||||
\(713\) | −2.77668e18 | −0.0296414 | ||||||||
\(714\) | 3.55924e17i | 0.00376244i | ||||||||
\(715\) | 1.14148e20 | − | 1.38607e20i | 1.19489 | − | 1.45092i | ||||
\(716\) | −3.20372e19 | −0.332096 | ||||||||
\(717\) | 3.64471e17i | 0.00374135i | ||||||||
\(718\) | 1.91391e16 | 0.000194558 | ||||||||
\(719\) | −4.85384e18 | −0.0488633 | −0.0244317 | − | 0.999702i | \(-0.507778\pi\) | ||||
−0.0244317 | + | 0.999702i | \(0.507778\pi\) | |||||||
\(720\) | 4.50159e19 | 0.448785 | ||||||||
\(721\) | − | 2.24502e20i | − | 2.21653i | ||||||
\(722\) | 4.23548e19i | 0.414135i | ||||||||
\(723\) | − | 4.96485e17i | − | 0.00480771i | ||||||
\(724\) | −6.78421e19 | −0.650623 | ||||||||
\(725\) | 2.37165e20i | 2.25261i | ||||||||
\(726\) | 2.08855e17 | − | 4.08026e16i | 0.00196467 | − | 0.000383823i | ||||
\(727\) | 1.72840e20 | 1.61029 | 0.805144 | − | 0.593079i | \(-0.202088\pi\) | ||||
0.805144 | + | 0.593079i | \(0.202088\pi\) | |||||||
\(728\) | − | 4.98634e19i | − | 0.460111i | ||||||
\(729\) | −1.09414e20 | −0.999952 | ||||||||
\(730\) | −2.39741e20 | −2.17011 | ||||||||
\(731\) | −7.86956e19 | −0.705551 | ||||||||
\(732\) | − | 9.96191e16i | − | 0.000884637i | ||||||
\(733\) | 1.28441e20i | 1.12973i | 0.825183 | + | 0.564866i | \(0.191072\pi\) | ||||
−0.825183 | + | 0.564866i | \(0.808928\pi\) | |||||||
\(734\) | − | 1.04778e19i | − | 0.0912844i | ||||||
\(735\) | −3.20868e17 | −0.00276895 | ||||||||
\(736\) | 6.75200e17i | 0.00577149i | ||||||||
\(737\) | 9.78977e19 | + | 8.06228e19i | 0.828896 | + | 0.682631i | ||||
\(738\) | 3.74076e19 | 0.313737 | ||||||||
\(739\) | 8.41404e19i | 0.699026i | 0.936931 | + | 0.349513i | \(0.113653\pi\) | ||||
−0.936931 | + | 0.349513i | \(0.886347\pi\) | |||||||
\(740\) | 1.61508e20 | 1.32914 | ||||||||
\(741\) | 2.34045e17 | 0.00190797 | ||||||||
\(742\) | 1.27045e20 | 1.02596 | ||||||||
\(743\) | 1.48627e20i | 1.18899i | 0.804101 | + | 0.594493i | \(0.202647\pi\) | ||||
−0.804101 | + | 0.594493i | \(0.797353\pi\) | |||||||
\(744\) | − | 1.14667e17i | − | 0.000908719i | ||||||
\(745\) | − | 9.52342e19i | − | 0.747652i | ||||||
\(746\) | 7.49713e19 | 0.583073 | ||||||||
\(747\) | − | 2.02762e20i | − | 1.56222i | ||||||
\(748\) | −6.29719e19 | + | 7.64647e19i | −0.480657 | + | 0.583647i | ||||
\(749\) | −3.41404e19 | −0.258164 | ||||||||
\(750\) | 5.86453e17i | 0.00439343i | ||||||||
\(751\) | 2.03222e20 | 1.50831 | 0.754156 | − | 0.656696i | \(-0.228046\pi\) | ||||
0.754156 | + | 0.656696i | \(0.228046\pi\) | |||||||
\(752\) | 2.14072e19 | 0.157411 | ||||||||
\(753\) | 5.40068e16 | 0.000393444 | ||||||||
\(754\) | − | 1.03962e20i | − | 0.750372i | ||||||
\(755\) | 1.47928e20i | 1.05785i | ||||||||
\(756\) | 4.96628e17i | 0.00351867i | ||||||||
\(757\) | 1.55760e20 | 1.09342 | 0.546709 | − | 0.837323i | \(-0.315881\pi\) | ||||
0.546709 | + | 0.837323i | \(0.315881\pi\) | |||||||
\(758\) | 1.94032e20i | 1.34955i | ||||||||
\(759\) | −1.03531e16 | − | 8.52617e15i | −7.13470e−5 | − | 5.87573e-5i | ||||
\(760\) | −5.98305e19 | −0.408533 | ||||||||
\(761\) | − | 5.08678e19i | − | 0.344152i | −0.985084 | − | 0.172076i | \(-0.944952\pi\) | ||
0.985084 | − | 0.172076i | \(-0.0550475\pi\) | |||||||
\(762\) | −3.90438e17 | −0.00261738 | ||||||||
\(763\) | −1.97087e19 | −0.130914 | ||||||||
\(764\) | 1.55385e19 | 0.102272 | ||||||||
\(765\) | − | 4.16230e20i | − | 2.71458i | ||||||
\(766\) | 4.31935e19i | 0.279137i | ||||||||
\(767\) | − | 2.12088e20i | − | 1.35815i | ||||||
\(768\) | −2.78834e16 | −0.000176937 | ||||||||
\(769\) | − | 7.57297e19i | − | 0.476192i | −0.971242 | − | 0.238096i | \(-0.923477\pi\) | ||
0.971242 | − | 0.238096i | \(-0.0765232\pi\) | |||||||
\(770\) | −1.95452e20 | − | 1.60963e20i | −1.21788 | − | 1.00298i | ||||
\(771\) | 2.43613e17 | 0.00150425 | ||||||||
\(772\) | − | 1.17453e20i | − | 0.718690i | ||||||
\(773\) | −1.53500e20 | −0.930793 | −0.465397 | − | 0.885102i | \(-0.654088\pi\) | ||||
−0.465397 | + | 0.885102i | \(0.654088\pi\) | |||||||
\(774\) | −5.49025e19 | −0.329918 | ||||||||
\(775\) | −3.38850e20 | −2.01788 | ||||||||
\(776\) | 2.96145e19i | 0.174772i | ||||||||
\(777\) | 8.90897e17i | 0.00521051i | ||||||||
\(778\) | 1.23449e20i | 0.715536i | ||||||||
\(779\) | −4.97184e19 | −0.285598 | ||||||||
\(780\) | − | 4.67344e17i | − | 0.00266057i | ||||||
\(781\) | 3.75283e19 | + | 3.09061e19i | 0.211739 | + | 0.174376i | ||||
\(782\) | 6.24309e18 | 0.0349102 | ||||||||
\(783\) | 1.03544e18i | 0.00573843i | ||||||||
\(784\) | −2.47986e19 | −0.136212 | ||||||||
\(785\) | −1.31126e19 | −0.0713838 | ||||||||
\(786\) | 6.38889e17 | 0.00344721 | ||||||||
\(787\) | − | 1.04441e20i | − | 0.558531i | −0.960214 | − | 0.279266i | \(-0.909909\pi\) | ||
0.960214 | − | 0.279266i | \(-0.0900910\pi\) | |||||||
\(788\) | 7.77806e19i | 0.412276i | ||||||||
\(789\) | − | 2.65055e17i | − | 0.00139251i | ||||||
\(790\) | −2.90239e20 | −1.51135 | ||||||||
\(791\) | 2.31211e20i | 1.19336i | ||||||||
\(792\) | −4.39328e19 | + | 5.33462e19i | −0.224757 | + | 0.272915i | ||||
\(793\) | 1.29043e20 | 0.654367 | ||||||||
\(794\) | − | 7.98019e19i | − | 0.401116i | ||||||
\(795\) | 1.19073e18 | 0.00593257 | ||||||||
\(796\) | −9.68416e18 | −0.0478267 | ||||||||
\(797\) | −1.12925e20 | −0.552818 | −0.276409 | − | 0.961040i | \(-0.589144\pi\) | ||||
−0.276409 | + | 0.961040i | \(0.589144\pi\) | |||||||
\(798\) | − | 3.30032e17i | − | 0.00160153i | ||||||
\(799\) | − | 1.97937e20i | − | 0.952136i | ||||||
\(800\) | 8.23974e19i | 0.392901i | ||||||||
\(801\) | 4.98222e19 | 0.235502 | ||||||||
\(802\) | 1.08200e20i | 0.506996i | ||||||||
\(803\) | 2.33972e20 | − | 2.84105e20i | 1.08682 | − | 1.31968i | ||||
\(804\) | 3.30084e17 | 0.00151996 | ||||||||
\(805\) | 1.59580e19i | 0.0728464i | ||||||||
\(806\) | 1.48536e20 | 0.672181 | ||||||||
\(807\) | −1.08062e17 | −0.000484796 | ||||||||
\(808\) | 6.91632e19 | 0.307607 | ||||||||
\(809\) | 8.41856e19i | 0.371192i | 0.982626 | + | 0.185596i | \(0.0594215\pi\) | ||||
−0.982626 | + | 0.185596i | \(0.940578\pi\) | |||||||
\(810\) | − | 2.90383e20i | − | 1.26934i | ||||||
\(811\) | 3.43628e20i | 1.48917i | 0.667530 | + | 0.744583i | \(0.267352\pi\) | ||||
−0.667530 | + | 0.744583i | \(0.732648\pi\) | |||||||
\(812\) | −1.46599e20 | −0.629854 | ||||||||
\(813\) | 7.95928e17i | 0.00339031i | ||||||||
\(814\) | −1.57622e20 | + | 1.91395e20i | −0.665649 | + | 0.808277i | ||||
\(815\) | 4.13383e20 | 1.73081 | ||||||||
\(816\) | 2.57818e17i | 0.00107024i | ||||||||
\(817\) | 7.29708e19 | 0.300327 | ||||||||
\(818\) | 6.43346e19 | 0.262525 | ||||||||
\(819\) | −3.21656e20 | −1.30138 | ||||||||
\(820\) | 9.92781e19i | 0.398251i | ||||||||
\(821\) | 5.38083e18i | 0.0214017i | 0.999943 | + | 0.0107008i | \(0.00340624\pi\) | ||||
−0.999943 | + | 0.0107008i | \(0.996594\pi\) | |||||||
\(822\) | − | 7.82846e17i | − | 0.00308726i | ||||||
\(823\) | −3.25916e20 | −1.27440 | −0.637202 | − | 0.770697i | \(-0.719908\pi\) | ||||
−0.637202 | + | 0.770697i | \(0.719908\pi\) | |||||||
\(824\) | − | 1.62621e20i | − | 0.630500i | ||||||
\(825\) | −1.26342e18 | − | 1.04048e18i | −0.00485704 | − | 0.00399997i | ||||
\(826\) | −2.99069e20 | −1.14002 | ||||||||
\(827\) | 2.89840e17i | 0.00109552i | 1.00000 | 0.000547759i | \(0.000174357\pi\) | |||||
−1.00000 | 0.000547759i | \(0.999826\pi\) | ||||||||
\(828\) | 4.35554e18 | 0.0163241 | ||||||||
\(829\) | −8.65860e19 | −0.321785 | −0.160893 | − | 0.986972i | \(-0.551437\pi\) | ||||
−0.160893 | + | 0.986972i | \(0.551437\pi\) | |||||||
\(830\) | 5.38120e20 | 1.98304 | ||||||||
\(831\) | − | 1.36168e17i | − | 0.000497586i | ||||||
\(832\) | − | 3.61192e19i | − | 0.130880i | ||||||
\(833\) | 2.29295e20i | 0.823910i | ||||||||
\(834\) | 7.27395e17 | 0.00259184 | ||||||||
\(835\) | − | 4.99905e20i | − | 1.76637i | ||||||
\(836\) | 5.83909e19 | − | 7.09022e19i | 0.204598 | − | 0.248437i | ||||
\(837\) | −1.47938e18 | −0.00514047 | ||||||||
\(838\) | 1.90629e20i | 0.656874i | ||||||||
\(839\) | −3.29986e20 | −1.12762 | −0.563808 | − | 0.825906i | \(-0.690664\pi\) | ||||
−0.563808 | + | 0.825906i | \(0.690664\pi\) | |||||||
\(840\) | −6.59011e17 | −0.00223325 | ||||||||
\(841\) | −8.09288e18 | −0.0271976 | ||||||||
\(842\) | 3.53930e19i | 0.117959i | ||||||||
\(843\) | − | 1.50361e18i | − | 0.00496982i | ||||||
\(844\) | − | 1.65141e20i | − | 0.541326i | ||||||
\(845\) | 5.31768e19 | 0.172872 | ||||||||
\(846\) | − | 1.38092e20i | − | 0.445221i | ||||||
\(847\) | 3.81499e20 | − | 7.45307e19i | 1.21986 | − | 0.238315i | ||||
\(848\) | 9.20267e19 | 0.291839 | ||||||||
\(849\) | 6.36176e17i | 0.00200089i | ||||||||
\(850\) | 7.61869e20 | 2.37656 | ||||||||
\(851\) | 1.56268e19 | 0.0483462 | ||||||||
\(852\) | 1.26535e17 | 0.000388270 | ||||||||
\(853\) | 3.37389e20i | 1.02681i | 0.858148 | + | 0.513403i | \(0.171615\pi\) | ||||
−0.858148 | + | 0.513403i | \(0.828385\pi\) | |||||||
\(854\) | − | 1.81966e20i | − | 0.549269i | ||||||
\(855\) | 3.85951e20i | 1.15550i | ||||||||
\(856\) | −2.47300e19 | −0.0734358 | ||||||||
\(857\) | 4.79566e20i | 1.41248i | 0.707972 | + | 0.706240i | \(0.249610\pi\) | ||||
−0.707972 | + | 0.706240i | \(0.750390\pi\) | |||||||
\(858\) | 5.53827e17 | + | 4.56099e17i | 0.00161794 | + | 0.00133244i | ||||
\(859\) | −4.35174e20 | −1.26099 | −0.630493 | − | 0.776195i | \(-0.717147\pi\) | ||||
−0.630493 | + | 0.776195i | \(0.717147\pi\) | |||||||
\(860\) | − | 1.45709e20i | − | 0.418790i | ||||||
\(861\) | −5.47630e17 | −0.00156122 | ||||||||
\(862\) | 4.76450e19 | 0.134731 | ||||||||
\(863\) | 6.37261e20 | 1.78748 | 0.893741 | − | 0.448583i | \(-0.148071\pi\) | ||||
0.893741 | + | 0.448583i | \(0.148071\pi\) | |||||||
\(864\) | 3.59739e17i | 0.00100090i | ||||||||
\(865\) | 1.81128e20i | 0.499889i | ||||||||
\(866\) | 3.80734e20i | 1.04231i | ||||||||
\(867\) | 1.34137e18 | 0.00364263 | ||||||||
\(868\) | − | 2.09453e20i | − | 0.564221i | ||||||
\(869\) | 2.83255e20 | − | 3.43948e20i | 0.756902 | − | 0.919082i | ||||
\(870\) | −1.37400e18 | −0.00364210 | ||||||||
\(871\) | 4.27579e20i | 1.12432i | ||||||||
\(872\) | −1.42762e19 | −0.0372390 | ||||||||
\(873\) | 1.91035e20 | 0.494327 | ||||||||
\(874\) | −5.78893e18 | −0.0148600 | ||||||||
\(875\) | 1.07122e21i | 2.72787i | ||||||||
\(876\) | − | 9.57924e17i | − | 0.00241993i | ||||||
\(877\) | − | 5.28557e20i | − | 1.32463i | −0.749225 | − | 0.662315i | \(-0.769574\pi\) | ||
0.749225 | − | 0.662315i | \(-0.230426\pi\) | |||||||
\(878\) | 9.11637e19 | 0.226652 | ||||||||
\(879\) | 5.49103e16i | 0.000135435i | ||||||||
\(880\) | −1.41578e20 | − | 1.16596e20i | −0.346432 | − | 0.285301i | ||||
\(881\) | 6.44389e18 | 0.0156429 | 0.00782144 | − | 0.999969i | \(-0.497510\pi\) | ||||
0.00782144 | + | 0.999969i | \(0.497510\pi\) | |||||||
\(882\) | 1.59969e20i | 0.385262i | ||||||||
\(883\) | 2.19065e20 | 0.523418 | 0.261709 | − | 0.965147i | \(-0.415714\pi\) | ||||
0.261709 | + | 0.965147i | \(0.415714\pi\) | |||||||
\(884\) | −3.33968e20 | −0.791661 | ||||||||
\(885\) | −2.80302e18 | −0.00659210 | ||||||||
\(886\) | − | 5.39154e19i | − | 0.125799i | ||||||
\(887\) | − | 4.53853e20i | − | 1.05063i | −0.850908 | − | 0.525315i | \(-0.823947\pi\) | ||
0.850908 | − | 0.525315i | \(-0.176053\pi\) | |||||||
\(888\) | 6.45332e17i | 0.00148215i | ||||||||
\(889\) | −7.13181e20 | −1.62513 | ||||||||
\(890\) | 1.32226e20i | 0.298941i | ||||||||
\(891\) | 3.44119e20 | + | 2.83397e20i | 0.771907 | + | 0.635698i | ||||
\(892\) | −2.07483e20 | −0.461772 | ||||||||
\(893\) | 1.83537e20i | 0.405289i | ||||||||
\(894\) | 3.80524e17 | 0.000833719 | ||||||||
\(895\) | −5.48476e20 | −1.19233 | ||||||||
\(896\) | −5.09324e19 | −0.109860 | ||||||||
\(897\) | − | 4.52181e16i | − | 9.67754e-5i | ||||||
\(898\) | 3.45102e20i | 0.732846i | ||||||||
\(899\) | − | 4.36698e20i | − | 0.920161i | ||||||
\(900\) | 5.31524e20 | 1.11128 | ||||||||
\(901\) | − | 8.50905e20i | − | 1.76525i | ||||||
\(902\) | −1.17650e20 | − | 9.68894e19i | −0.242184 | − | 0.199448i | ||||
\(903\) | 8.03746e17 | 0.00164174 | ||||||||
\(904\) | 1.67481e20i | 0.339457i | ||||||||
\(905\) | −1.16145e21 | −2.33594 | ||||||||
\(906\) | −5.91071e17 | −0.00117962 | ||||||||
\(907\) | −9.17499e20 | −1.81700 | −0.908499 | − | 0.417886i | \(-0.862771\pi\) | ||||
−0.908499 | + | 0.417886i | \(0.862771\pi\) | |||||||
\(908\) | − | 4.28370e19i | − | 0.0841817i | ||||||
\(909\) | − | 4.46154e20i | − | 0.870036i | ||||||
\(910\) | − | 8.53659e20i | − | 1.65194i | ||||||
\(911\) | 4.23528e20 | 0.813305 | 0.406653 | − | 0.913583i | \(-0.366696\pi\) | ||||
0.406653 | + | 0.913583i | \(0.366696\pi\) | |||||||
\(912\) | − | 2.39063e17i | − | 0.000455563i | ||||||
\(913\) | −5.25172e20 | + | 6.37699e20i | −0.993130 | + | 1.20593i | ||||
\(914\) | −4.92127e20 | −0.923537 | ||||||||
\(915\) | − | 1.70547e18i | − | 0.00317612i | ||||||
\(916\) | 1.30627e20 | 0.241416 | ||||||||
\(917\) | 1.16701e21 | 2.14036 | ||||||||
\(918\) | 3.32625e18 | 0.00605418 | ||||||||
\(919\) | − | 6.33613e20i | − | 1.14450i | −0.820079 | − | 0.572250i | \(-0.806071\pi\) | ||
0.820079 | − | 0.572250i | \(-0.193929\pi\) | |||||||
\(920\) | 1.15594e19i | 0.0207214i | ||||||||
\(921\) | 2.25449e18i | 0.00401079i | ||||||||
\(922\) | 5.30205e20 | 0.936111 | ||||||||
\(923\) | 1.63909e20i | 0.287204i | ||||||||
\(924\) | 6.43155e17 | − | 7.80962e17i | 0.00111844 | − | 0.00135808i | ||||
\(925\) | 1.90700e21 | 3.29123 | ||||||||
\(926\) | − | 8.48773e19i | − | 0.145383i | ||||||
\(927\) | −1.04902e21 | −1.78331 | ||||||||
\(928\) | −1.06191e20 | −0.179165 | ||||||||
\(929\) | −5.34578e20 | −0.895161 | −0.447580 | − | 0.894244i | \(-0.647714\pi\) | ||||
−0.447580 | + | 0.894244i | \(0.647714\pi\) | |||||||
\(930\) | − | 1.96310e18i | − | 0.00326258i | ||||||
\(931\) | − | 2.12615e20i | − | 0.350708i | ||||||
\(932\) | 6.15653e19i | 0.100792i | ||||||||
\(933\) | −3.11064e18 | −0.00505450 | ||||||||
\(934\) | − | 2.27379e20i | − | 0.366709i | ||||||
\(935\) | −1.07808e21 | + | 1.30907e21i | −1.72571 | + | 2.09547i | ||||
\(936\) | −2.32995e20 | −0.370183 | ||||||||
\(937\) | − | 2.21764e20i | − | 0.349715i | −0.984594 | − | 0.174857i | \(-0.944054\pi\) | ||
0.984594 | − | 0.174857i | \(-0.0559465\pi\) | |||||||
\(938\) | 6.02938e20 | 0.943740 | ||||||||
\(939\) | −1.39950e18 | −0.00217427 | ||||||||
\(940\) | 3.66489e20 | 0.565154 | ||||||||
\(941\) | − | 2.53556e20i | − | 0.388102i | −0.980991 | − | 0.194051i | \(-0.937837\pi\) | ||
0.980991 | − | 0.194051i | \(-0.0621628\pi\) | |||||||
\(942\) | − | 5.23934e16i | − | 7.96013e-5i | ||||||
\(943\) | 9.60570e18i | 0.0144860i | ||||||||
\(944\) | −2.16635e20 | −0.324283 | ||||||||
\(945\) | 8.50225e18i | 0.0126331i | ||||||||
\(946\) | 1.72672e20 | + | 1.42203e20i | 0.254674 | + | 0.209735i | ||||
\(947\) | 1.37825e20 | 0.201780 | 0.100890 | − | 0.994898i | \(-0.467831\pi\) | ||||
0.100890 | + | 0.994898i | \(0.467831\pi\) | |||||||
\(948\) | − | 1.15970e18i | − | 0.00168534i | ||||||
\(949\) | 1.24086e21 | 1.79003 | ||||||||
\(950\) | −7.06446e20 | −1.01161 | ||||||||
\(951\) | 5.88529e17 | 0.000836574 | ||||||||
\(952\) | 4.70935e20i | 0.664511i | ||||||||
\(953\) | − | 9.38386e20i | − | 1.31441i | −0.753711 | − | 0.657206i | \(-0.771738\pi\) | ||
0.753711 | − | 0.657206i | \(-0.228262\pi\) | |||||||
\(954\) | − | 5.93640e20i | − | 0.825438i | ||||||
\(955\) | 2.66019e20 | 0.367188 | ||||||||
\(956\) | 4.82243e20i | 0.660786i | ||||||||
\(957\) | 1.34094e18 | − | 1.62826e18i | 0.00182400 | − | 0.00221483i | ||||
\(958\) | −1.00836e21 | −1.36163 | ||||||||
\(959\) | − | 1.42996e21i | − | 1.91687i | ||||||
\(960\) | −4.77363e17 | −0.000635258 | ||||||||
\(961\) | −1.33012e20 | −0.175723 | ||||||||
\(962\) | −8.35939e20 | −1.09635 | ||||||||
\(963\) | 1.59527e20i | 0.207706i | ||||||||
\(964\) | − | 6.56916e20i | − | 0.849122i | ||||||
\(965\) | − | 2.01078e21i | − | 2.58032i | ||||||
\(966\) | −6.37629e16 | −8.12322e−5 | ||||||||
\(967\) | 1.21304e21i | 1.53423i | 0.641511 | + | 0.767114i | \(0.278308\pi\) | ||||
−0.641511 | + | 0.767114i | \(0.721692\pi\) | |||||||
\(968\) | 2.76343e20 | − | 5.39872e19i | 0.346994 | − | 0.0677897i | ||||
\(969\) | −2.21044e18 | −0.00275558 | ||||||||
\(970\) | 5.06999e20i | 0.627487i | ||||||||
\(971\) | −2.90380e20 | −0.356806 | −0.178403 | − | 0.983957i | \(-0.557093\pi\) | ||||
−0.178403 | + | 0.983957i | \(0.557093\pi\) | |||||||
\(972\) | 3.48087e18 | 0.00424643 | ||||||||
\(973\) | 1.32867e21 | 1.60927 | ||||||||
\(974\) | 6.24774e20i | 0.751295i | ||||||||
\(975\) | − | 5.51814e18i | − | 0.00658811i | ||||||
\(976\) | − | 1.31809e20i | − | 0.156242i | ||||||
\(977\) | −2.10367e20 | −0.247580 | −0.123790 | − | 0.992308i | \(-0.539505\pi\) | ||||
−0.123790 | + | 0.992308i | \(0.539505\pi\) | |||||||
\(978\) | 1.65174e18i | 0.00193006i | ||||||||
\(979\) | −1.56694e20 | − | 1.29044e20i | −0.181792 | − | 0.149713i | ||||
\(980\) | −4.24551e20 | −0.489043 | ||||||||
\(981\) | 9.20921e19i | 0.105327i | ||||||||
\(982\) | 6.10590e19 | 0.0693377 | ||||||||
\(983\) | 1.03646e21 | 1.16864 | 0.584318 | − | 0.811525i | \(-0.301362\pi\) | ||||
0.584318 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(984\) | −3.96682e17 | −0.000444096 | ||||||||
\(985\) | 1.33160e21i | 1.48020i | ||||||||
\(986\) | 9.81872e20i | 1.08372i | ||||||||
\(987\) | 2.02160e18i | 0.00221552i | ||||||||
\(988\) | 3.09673e20 | 0.336981 | ||||||||
\(989\) | − | 1.40981e19i | − | 0.0152331i | ||||||
\(990\) | −7.52127e20 | + | 9.13283e20i | −0.806947 | + | 0.979849i | ||||
\(991\) | 3.47514e20 | 0.370217 | 0.185109 | − | 0.982718i | \(-0.440736\pi\) | ||||
0.185109 | + | 0.982718i | \(0.440736\pi\) | |||||||
\(992\) | − | 1.51720e20i | − | 0.160495i | ||||||
\(993\) | 2.32857e18 | 0.00244593 | ||||||||
\(994\) | 2.31131e20 | 0.241076 | ||||||||
\(995\) | −1.65792e20 | −0.171713 | ||||||||
\(996\) | 2.15015e18i | 0.00221133i | ||||||||
\(997\) | − | 2.31343e20i | − | 0.236260i | −0.992998 | − | 0.118130i | \(-0.962310\pi\) | ||
0.992998 | − | 0.118130i | \(-0.0376899\pi\) | |||||||
\(998\) | 3.69474e20i | 0.374688i | ||||||||
\(999\) | 8.32576e18 | 0.00838428 |
(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 | 22.15.b.a.21.11 | yes | 14 | |
4.3 | odd | 2 | 176.15.h.e.65.8 | 14 | |||
11.10 | odd | 2 | inner | 22.15.b.a.21.4 | ✓ | 14 | |
44.43 | even | 2 | 176.15.h.e.65.7 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.15.b.a.21.4 | ✓ | 14 | 11.10 | odd | 2 | inner | |
22.15.b.a.21.11 | yes | 14 | 1.1 | even | 1 | trivial | |
176.15.h.e.65.7 | 14 | 44.43 | even | 2 | |||
176.15.h.e.65.8 | 14 | 4.3 | odd | 2 |