Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,22,Mod(1,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.a (trivial) |
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: | yes |
Analytic conductor: | \(33.5372813144\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 12.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.12681e7 | −0.516018 | −0.258009 | − | 0.966142i | \(-0.583067\pi\) | ||||
−0.258009 | + | 0.966142i | \(0.583067\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.81914e8 | 0.377214 | 0.188607 | − | 0.982053i | \(-0.439603\pi\) | ||||
0.188607 | + | 0.982053i | \(0.439603\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.61721e10 | −0.420485 | −0.210242 | − | 0.977649i | \(-0.567425\pi\) | ||||
−0.210242 | + | 0.977649i | \(0.567425\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.49099e11 | −0.903517 | −0.451759 | − | 0.892140i | \(-0.649203\pi\) | ||||
−0.451759 | + | 0.892140i | \(0.649203\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.65369e11 | −0.297923 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.12186e12 | 0.255272 | 0.127636 | − | 0.991821i | \(-0.459261\pi\) | ||||
0.127636 | + | 0.991821i | \(0.459261\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.60941e12 | −0.172477 | −0.0862387 | − | 0.996275i | \(-0.527485\pi\) | ||||
−0.0862387 | + | 0.996275i | \(0.527485\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.66467e13 | 0.217784 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.50953e13 | 0.478648 | 0.239324 | − | 0.970940i | \(-0.423074\pi\) | ||||
0.239324 | + | 0.970940i | \(0.423074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.49867e14 | −0.733725 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.24574e15 | −0.991245 | −0.495622 | − | 0.868538i | \(-0.665060\pi\) | ||||
−0.495622 | + | 0.868538i | \(0.665060\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.15569e15 | −0.691508 | −0.345754 | − | 0.938325i | \(-0.612377\pi\) | ||||
−0.345754 | + | 0.938325i | \(0.612377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.13593e15 | −0.242767 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.17663e15 | −0.194649 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.81785e16 | −0.621498 | −0.310749 | − | 0.950492i | \(-0.600580\pi\) | ||||
−0.310749 | + | 0.950492i | \(0.600580\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.65188e16 | −0.521646 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.69650e17 | −1.97389 | −0.986944 | − | 0.161061i | \(-0.948508\pi\) | ||||
−0.986944 | + | 0.161061i | \(0.948508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.58969e17 | −1.12174 | −0.560870 | − | 0.827904i | \(-0.689533\pi\) | ||||
−0.560870 | + | 0.827904i | \(0.689533\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.92894e16 | −0.172006 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.34697e17 | −0.373536 | −0.186768 | − | 0.982404i | \(-0.559801\pi\) | ||||
−0.186768 | + | 0.982404i | \(0.559801\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.79070e17 | −0.857710 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.25294e17 | 0.147381 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.56374e16 | −0.0122819 | −0.00614097 | − | 0.999981i | \(-0.501955\pi\) | ||||
−0.00614097 | + | 0.999981i | \(0.501955\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.07590e17 | 0.216978 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.72181e17 | −0.0995799 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.97724e18 | 0.758347 | 0.379173 | − | 0.925326i | \(-0.376208\pi\) | ||||
0.379173 | + | 0.925326i | \(0.376208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.60386e18 | 0.646851 | 0.323425 | − | 0.946254i | \(-0.395166\pi\) | ||||
0.323425 | + | 0.946254i | \(0.395166\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.82974e17 | 0.125738 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.06048e18 | 0.466232 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.10662e19 | 1.41189 | 0.705945 | − | 0.708267i | \(-0.250523\pi\) | ||||
0.705945 | + | 0.708267i | \(0.250523\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.61528e18 | 0.276348 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.19801e19 | 0.801340 | 0.400670 | − | 0.916222i | \(-0.368777\pi\) | ||||
0.400670 | + | 0.916222i | \(0.368777\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.70544e19 | −0.464458 | −0.232229 | − | 0.972661i | \(-0.574602\pi\) | ||||
−0.232229 | + | 0.972661i | \(0.574602\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.06593e19 | −0.423616 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.01974e19 | −0.158613 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.15020e20 | −1.36675 | −0.683375 | − | 0.730067i | \(-0.739489\pi\) | ||||
−0.683375 | + | 0.730067i | \(0.739489\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.66285e19 | −0.683574 | −0.341787 | − | 0.939777i | \(-0.611032\pi\) | ||||
−0.341787 | + | 0.939777i | \(0.611032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.39093e19 | −0.131725 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.32609e20 | −0.572295 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.04276e19 | 0.205419 | 0.102709 | − | 0.994711i | \(-0.467249\pi\) | ||||
0.102709 | + | 0.994711i | \(0.467249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.26607e20 | −0.340819 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.86341e20 | −0.399242 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.19392e19 | 0.0890015 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.07820e20 | −0.561520 | −0.280760 | − | 0.959778i | \(-0.590587\pi\) | ||||
−0.280760 | + | 0.959778i | \(0.590587\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.26124e20 | −0.140162 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.95076e21 | 1.75724 | 0.878618 | − | 0.477525i | \(-0.158466\pi\) | ||||
0.878618 | + | 0.477525i | \(0.158466\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.98058e20 | 0.658436 | 0.329218 | − | 0.944254i | \(-0.393215\pi\) | ||||
0.329218 | + | 0.944254i | \(0.393215\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.87577e20 | −0.112381 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.22013e21 | 1.58250 | 0.791250 | − | 0.611493i | \(-0.209431\pi\) | ||||
0.791250 | + | 0.611493i | \(0.209431\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.55319e20 | −0.224680 | −0.112340 | − | 0.993670i | \(-0.535835\pi\) | ||||
−0.112340 | + | 0.993670i | \(0.535835\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.07342e21 | −0.358822 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00790e21 | 1.11069 | 0.555346 | − | 0.831620i | \(-0.312586\pi\) | ||||
0.555346 | + | 0.831620i | \(0.312586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.07154e21 | −0.246991 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.56591e21 | −0.301172 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.98182e20 | 0.0962920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.09183e21 | −0.823193 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00176e22 | −1.13963 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.31538e21 | 0.894634 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.78249e22 | −1.44906 | −0.724532 | − | 0.689241i | \(-0.757944\pi\) | ||||
−0.724532 | + | 0.689241i | \(0.757944\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.38693e21 | −0.647637 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.43009e21 | 0.318756 | 0.159378 | − | 0.987218i | \(-0.449051\pi\) | ||||
0.159378 | + | 0.987218i | \(0.449051\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.29946e21 | −0.0650608 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.32000e21 | −0.0993078 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.64038e22 | 0.968502 | 0.484251 | − | 0.874929i | \(-0.339092\pi\) | ||||
0.484251 | + | 0.874929i | \(0.339092\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.41795e22 | −1.39176 | −0.695882 | − | 0.718156i | \(-0.744986\pi\) | ||||
−0.695882 | + | 0.718156i | \(0.744986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.95375e21 | −0.215661 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.62448e22 | 0.379915 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.53052e22 | 0.511501 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.82886e22 | −0.495199 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.19466e23 | 1.81464 | 0.907319 | − | 0.420444i | \(-0.138126\pi\) | ||||
0.907319 | + | 0.420444i | \(0.138126\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.87257e21 | 0.0775479 | 0.0387739 | − | 0.999248i | \(-0.487655\pi\) | ||||
0.0387739 | + | 0.999248i | \(0.487655\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.39846e21 | 0.0850906 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.55586e22 | 0.356831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.96848e23 | 1.72657 | 0.863286 | − | 0.504716i | \(-0.168403\pi\) | ||||
0.863286 | + | 0.504716i | \(0.168403\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.23371e20 | −0.00709099 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.68087e22 | 0.180553 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.93738e23 | −1.14616 | −0.573079 | − | 0.819500i | \(-0.694251\pi\) | ||||
−0.573079 | + | 0.819500i | \(0.694251\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.40678e22 | 0.125272 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.08785e23 | −0.957585 | −0.478792 | − | 0.877928i | \(-0.658925\pi\) | ||||
−0.478792 | + | 0.877928i | \(0.658925\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.53750e22 | −0.183656 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.60720e22 | −0.0574925 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.48568e23 | −0.786975 | −0.393488 | − | 0.919330i | \(-0.628732\pi\) | ||||
−0.393488 | + | 0.919330i | \(0.628732\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.86325e22 | −0.276771 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.75803e23 | 0.437832 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.15674e23 | −1.58401 | −0.792006 | − | 0.610513i | \(-0.790963\pi\) | ||||
−0.792006 | + | 0.610513i | \(0.790963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.74196e22 | 0.0540052 | 0.0270026 | − | 0.999635i | \(-0.491404\pi\) | ||||
0.0270026 | + | 0.999635i | \(0.491404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.12804e23 | 0.373459 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.04837e23 | 0.320705 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.67521e22 | −0.107338 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.80436e22 | 0.0725948 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.35303e24 | −1.51516 | −0.757580 | − | 0.652742i | \(-0.773618\pi\) | ||||
−0.757580 | + | 0.652742i | \(0.773618\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.27470e24 | 1.27955 | 0.639774 | − | 0.768563i | \(-0.279028\pi\) | ||||
0.639774 | + | 0.768563i | \(0.279028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.98816e23 | 0.269179 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.36579e23 | −0.110532 | −0.0552659 | − | 0.998472i | \(-0.517601\pi\) | ||||
−0.0552659 | + | 0.998472i | \(0.517601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.10960e24 | 0.807625 | 0.403813 | − | 0.914842i | \(-0.367685\pi\) | ||||
0.403813 | + | 0.914842i | \(0.367685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.24394e24 | 0.815155 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.33107e23 | −0.373911 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.91163e24 | 1.01856 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.31577e23 | 0.159549 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.66732e23 | 0.0725241 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.25779e23 | −0.167579 | −0.0837893 | − | 0.996483i | \(-0.526702\pi\) | ||||
−0.0837893 | + | 0.996483i | \(0.526702\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.29790e24 | 0.462654 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.79127e24 | 0.578839 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.89635e23 | −0.260846 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00705e24 | −0.268155 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.52924e23 | −0.230642 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.06482e23 | −0.0234463 | −0.0117231 | − | 0.999931i | \(-0.503732\pi\) | ||||
−0.0117231 | + | 0.999931i | \(0.503732\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.21991e24 | −0.244575 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.78572e24 | −1.05703 | −0.528513 | − | 0.848925i | \(-0.677250\pi\) | ||||
−0.528513 | + | 0.848925i | \(0.677250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.95470e24 | −1.32541 | −0.662707 | − | 0.748879i | \(-0.730592\pi\) | ||||
−0.662707 | + | 0.748879i | \(0.730592\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.02148e23 | −0.0915750 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.84067e24 | −0.950302 | −0.475151 | − | 0.879904i | \(-0.657607\pi\) | ||||
−0.475151 | + | 0.879904i | \(0.657607\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.51778e24 | 0.192751 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.79182e24 | −0.789094 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.71539e25 | 1.82467 | 0.912335 | − | 0.409445i | \(-0.134278\pi\) | ||||
0.912335 | + | 0.409445i | \(0.134278\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00591e24 | −0.585329 | −0.292664 | − | 0.956215i | \(-0.594542\pi\) | ||||
−0.292664 | + | 0.956215i | \(0.594542\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.39821e24 | 0.442594 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.07008e24 | 0.155836 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.70582e24 | −0.394661 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.48883e25 | 0.946829 | 0.473415 | − | 0.880840i | \(-0.343021\pi\) | ||||
0.473415 | + | 0.880840i | \(0.343021\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.43979e24 | −0.201264 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.41182e24 | −0.0760514 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.76815e25 | 0.877445 | 0.438723 | − | 0.898622i | \(-0.355431\pi\) | ||||
0.438723 | + | 0.898622i | \(0.355431\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.12478e24 | −0.234438 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.83042e24 | −0.330415 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.25801e25 | 1.26887 | 0.634434 | − | 0.772977i | \(-0.281233\pi\) | ||||
0.634434 | + | 0.772977i | \(0.281233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.76203e23 | 0.00633771 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.56819e24 | 0.118599 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.09117e25 | 0.642674 | 0.321337 | − | 0.946965i | \(-0.395868\pi\) | ||||
0.321337 | + | 0.946965i | \(0.395868\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.57378e25 | 0.447474 | 0.223737 | − | 0.974650i | \(-0.428174\pi\) | ||||
0.223737 | + | 0.974650i | \(0.428174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.47603e24 | −0.196772 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.26554e25 | 0.308520 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.23463e25 | −0.278934 | −0.139467 | − | 0.990227i | \(-0.544539\pi\) | ||||
−0.139467 | + | 0.990227i | \(0.544539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.10032e25 | −0.230503 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.51786e25 | −1.07239 | −0.536197 | − | 0.844093i | \(-0.680140\pi\) | ||||
−0.536197 | + | 0.844093i | \(0.680140\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.45585e25 | 0.262639 | 0.131320 | − | 0.991340i | \(-0.458079\pi\) | ||||
0.131320 | + | 0.991340i | \(0.458079\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.06696e24 | 0.0513851 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.78267e25 | −0.744578 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.45896e25 | −0.934836 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.40814e25 | −0.324194 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.86675e25 | −0.359153 | −0.179576 | − | 0.983744i | \(-0.557473\pi\) | ||||
−0.179576 | + | 0.983744i | \(0.557473\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.35478e25 | −0.391321 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.44751e24 | −0.0809223 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.27072e25 | −0.432467 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.48155e25 | −0.423136 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.15191e26 | 1.01454 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.06086e25 | −0.333787 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.31398e25 | 0.638052 | 0.319026 | − | 0.947746i | \(-0.396644\pi\) | ||||
0.319026 | + | 0.947746i | \(0.396644\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.30294e25 | 0.380148 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.80388e26 | −1.20843 | −0.604217 | − | 0.796820i | \(-0.706514\pi\) | ||||
−0.604217 | + | 0.796820i | \(0.706514\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.33157e26 | 1.46027 | 0.730133 | − | 0.683305i | \(-0.239458\pi\) | ||||
0.730133 | + | 0.683305i | \(0.239458\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.10762e25 | −0.0648831 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.51585e25 | 0.466773 | 0.233387 | − | 0.972384i | \(-0.425019\pi\) | ||||
0.233387 | + | 0.972384i | \(0.425019\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.12332e25 | 0.416803 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.90145e26 | 0.913657 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.78051e24 | −0.0440286 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.57125e26 | 0.662933 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.27910e25 | −0.129719 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.79731e25 | −0.140903 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.68513e25 | 0.197946 | 0.0989730 | − | 0.995090i | \(-0.468444\pi\) | ||||
0.0989730 | + | 0.995090i | \(0.468444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.33845e25 | −0.207166 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.37376e26 | −0.728561 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.08109e26 | 0.600034 | 0.300017 | − | 0.953934i | \(-0.403008\pi\) | ||||
0.300017 | + | 0.953934i | \(0.403008\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.36663e26 | 0.641258 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.14148e26 | 0.290768 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.92519e26 | −0.700754 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.32735e25 | −0.142601 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.50754e26 | −1.16815 | −0.584075 | − | 0.811700i | \(-0.698543\pi\) | ||||
−0.584075 | + | 0.811700i | \(0.698543\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.04674e25 | −0.0408692 | −0.0204346 | − | 0.999791i | \(-0.506505\pi\) | ||||
−0.0204346 | + | 0.999791i | \(0.506505\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.24654e25 | −0.173882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.92034e26 | 1.04885 | 0.524424 | − | 0.851458i | \(-0.324281\pi\) | ||||
0.524424 | + | 0.851458i | \(0.324281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.47674e26 | −0.413506 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.53220e25 | 0.0555942 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.22516e26 | −0.775547 | −0.387773 | − | 0.921755i | \(-0.626756\pi\) | ||||
−0.387773 | + | 0.921755i | \(0.626756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.92963e26 | −0.970252 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.59716e26 | −0.475270 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.92171e26 | 0.239669 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.15652e27 | −1.36195 | −0.680974 | − | 0.732308i | \(-0.738443\pi\) | ||||
−0.680974 | + | 0.732308i | \(0.738443\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.91532e26 | −0.657963 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.40840e24 | −0.00463292 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.94328e26 | 0.292340 | 0.146170 | − | 0.989259i | \(-0.453305\pi\) | ||||
0.146170 | + | 0.989259i | \(0.453305\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.50064e26 | 0.516517 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00856e27 | 0.895607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.24279e27 | 1.04397 | 0.521984 | − | 0.852955i | \(-0.325192\pi\) | ||||
0.521984 | + | 0.852955i | \(0.325192\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.05254e27 | −0.836618 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.18301e27 | 1.64236 | 0.821181 | − | 0.570668i | \(-0.193316\pi\) | ||||
0.821181 | + | 0.570668i | \(0.193316\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.14905e26 | 0.0818470 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.54289e26 | −0.373914 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.52211e27 | 0.972690 | 0.486345 | − | 0.873767i | \(-0.338330\pi\) | ||||
0.486345 | + | 0.873767i | \(0.338330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.01779e26 | 0.122185 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.20642e26 | 0.184034 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.29606e27 | 0.705269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.32566e26 | −0.326441 | −0.163221 | − | 0.986590i | \(-0.552188\pi\) | ||||
−0.163221 | + | 0.986590i | \(0.552188\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.67316e25 | −0.0375629 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.76087e26 | −0.174692 | −0.0873459 | − | 0.996178i | \(-0.527839\pi\) | ||||
−0.0873459 | + | 0.996178i | \(0.527839\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.41722e27 | 0.624789 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.36994e26 | −0.0573354 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.57554e26 | 0.261331 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.84109e27 | −1.44997 | −0.724986 | − | 0.688764i | \(-0.758154\pi\) | ||||
−0.724986 | + | 0.688764i | \(0.758154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.55912e27 | 0.559165 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.39326e26 | 0.286059 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.08882e27 | 0.352737 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.60876e27 | −0.803535 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.15090e27 | −0.630048 | −0.315024 | − | 0.949084i | \(-0.602013\pi\) | ||||
−0.315024 | + | 0.949084i | \(0.602013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.87739e27 | −0.523109 | −0.261554 | − | 0.965189i | \(-0.584235\pi\) | ||||
−0.261554 | + | 0.965189i | \(0.584235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.69661e26 | −0.124512 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.42369e26 | −0.187299 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.01598e27 | 0.244001 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.59241e26 | 0.219344 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.68016e27 | −1.23694 | −0.618471 | − | 0.785807i | \(-0.712248\pi\) | ||||
−0.618471 | + | 0.785807i | \(0.712248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.55781e27 | −0.530574 | −0.265287 | − | 0.964170i | \(-0.585467\pi\) | ||||
−0.265287 | + | 0.964170i | \(0.585467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.49425e27 | 0.295315 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.38333e26 | −0.0825560 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.04971e27 | 0.727020 | 0.363510 | − | 0.931590i | \(-0.381578\pi\) | ||||
0.363510 | + | 0.931590i | \(0.381578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.67041e27 | −0.285903 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.15784e28 | −1.88978 | −0.944890 | − | 0.327388i | \(-0.893831\pi\) | ||||
−0.944890 | + | 0.327388i | \(0.893831\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.80903e26 | −0.106000 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.05437e27 | 1.04768 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.09657e27 | −0.155399 | −0.0776997 | − | 0.996977i | \(-0.524758\pi\) | ||||
−0.0776997 | + | 0.996977i | \(0.524758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.13658e27 | 0.829990 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.46769e26 | 0.0447723 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.42662e27 | 0.175869 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.08169e27 | −0.127345 | −0.0636725 | − | 0.997971i | \(-0.520281\pi\) | ||||
−0.0636725 | + | 0.997971i | \(0.520281\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.36872e26 | 0.0491271 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.20305e27 | 0.129248 | 0.0646238 | − | 0.997910i | \(-0.479415\pi\) | ||||
0.0646238 | + | 0.997910i | \(0.479415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.71985e27 | 0.997836 | 0.498918 | − | 0.866649i | \(-0.333731\pi\) | ||||
0.498918 | + | 0.866649i | \(0.333731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.09970e27 | 0.206016 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.01684e27 | 0.0953729 | 0.0476865 | − | 0.998862i | \(-0.484815\pi\) | ||||
0.0476865 | + | 0.998862i | \(0.484815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.93886e27 | 0.532584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.16237e28 | 0.996836 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.75022e27 | 0.471675 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.61268e27 | 0.126551 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.45242e25 | −0.00409398 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.80013e27 | −0.416788 | −0.208394 | − | 0.978045i | \(-0.566824\pi\) | ||||
−0.208394 | + | 0.978045i | \(0.566824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.16394e27 | 0.561535 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.58303e27 | 0.104242 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.59535e27 | 0.289755 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.92907e27 | −0.478815 | −0.239408 | − | 0.970919i | \(-0.576953\pi\) | ||||
−0.239408 | + | 0.970919i | \(0.576953\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.14400e28 | −0.661735 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.94270e28 | −1.07659 | −0.538294 | − | 0.842757i | \(-0.680931\pi\) | ||||
−0.538294 | + | 0.842757i | \(0.680931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.76515e27 | −0.253037 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.42118e27 | 0.0723260 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.19650e27 | 0.302276 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.12364e27 | −0.333155 | −0.166578 | − | 0.986028i | \(-0.553272\pi\) | ||||
−0.166578 | + | 0.986028i | \(0.553272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.23286e28 | −0.552862 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.58499e28 | −1.54179 | −0.770893 | − | 0.636964i | \(-0.780190\pi\) | ||||
−0.770893 | + | 0.636964i | \(0.780190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.19814e28 | −0.906766 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.67935e27 | −0.106034 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.53859e28 | 1.72339 | 0.861696 | − | 0.507425i | \(-0.169402\pi\) | ||||
0.861696 | + | 0.507425i | \(0.169402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.80788e27 | −0.175200 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.49036e26 | −0.0331933 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.01194e28 | −0.339765 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.87229e27 | 0.157066 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.46777e28 | −0.454360 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.13279e28 | 1.22870 | 0.614352 | − | 0.789032i | \(-0.289417\pi\) | ||||
0.614352 | + | 0.789032i | \(0.289417\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.57605e28 | −0.735675 | −0.367837 | − | 0.929890i | \(-0.619902\pi\) | ||||
−0.367837 | + | 0.929890i | \(0.619902\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.82415e27 | −0.159794 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.69594e27 | −0.176522 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.04285e28 | −0.770896 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.03810e28 | 0.252782 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.61895e28 | 1.78344 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.62847e28 | −0.816599 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.22598e28 | −0.914530 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.73290e28 | 0.360654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00618e28 | 1.00216 | 0.501078 | − | 0.865402i | \(-0.332937\pi\) | ||||
0.501078 | + | 0.865402i | \(0.332937\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.61910e27 | 0.0311799 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.25739e27 | 0.115939 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.69499e28 | 1.37196 | 0.685979 | − | 0.727621i | \(-0.259374\pi\) | ||||
0.685979 | + | 0.727621i | \(0.259374\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.25659e28 | 0.215617 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.03515e28 | 0.170967 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.24258e28 | −0.515557 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.20954e28 | 0.185159 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.27070e28 | 1.36657 | 0.683287 | − | 0.730150i | \(-0.260550\pi\) | ||||
0.683287 | + | 0.730150i | \(0.260550\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.13926e28 | 1.01351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.53213e27 | −0.0619716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.62203e28 | −0.477104 | −0.238552 | − | 0.971130i | \(-0.576673\pi\) | ||||
−0.238552 | + | 0.971130i | \(0.576673\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.51614e28 | −0.573137 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.42742e27 | 0.0419126 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.10807e28 | −0.130583 | −0.0652917 | − | 0.997866i | \(-0.520798\pi\) | ||||
−0.0652917 | + | 0.997866i | \(0.520798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.89713e28 | 0.215485 | 0.107743 | − | 0.994179i | \(-0.465638\pi\) | ||||
0.107743 | + | 0.994179i | \(0.465638\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.98953e28 | −0.874778 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.32707e28 | −0.351196 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.05096e29 | −1.06965 | −0.534825 | − | 0.844963i | \(-0.679623\pi\) | ||||
−0.534825 | + | 0.844963i | \(0.679623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.52698e28 | 0.738748 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.72409e28 | −0.257853 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.65636e26 | 0.00516437 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.76448e28 | 0.155411 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.07068e29 | −0.909825 | −0.454912 | − | 0.890536i | \(-0.650329\pi\) | ||||
−0.454912 | + | 0.890536i | \(0.650329\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.45459e28 | 0.119269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.06483e27 | −0.0638155 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.26566e29 | −1.73029 | −0.865147 | − | 0.501519i | \(-0.832775\pi\) | ||||
−0.865147 | + | 0.501519i | \(0.832775\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.74037e27 | −0.0496885 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.55209e28 | 0.466283 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.58466e29 | −1.08882 | −0.544408 | − | 0.838821i | \(-0.683245\pi\) | ||||
−0.544408 | + | 0.838821i | \(0.683245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.75299e29 | −1.16304 | −0.581522 | − | 0.813530i | \(-0.697543\pi\) | ||||
−0.581522 | + | 0.813530i | \(0.697543\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.34533e28 | 0.470630 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.86433e28 | 0.424783 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.39496e29 | 0.833834 | 0.416917 | − | 0.908945i | \(-0.363111\pi\) | ||||
0.416917 | + | 0.908945i | \(0.363111\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.73843e28 | −0.215878 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.04924e28 | 0.337496 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.79163e29 | 0.965858 | 0.482929 | − | 0.875660i | \(-0.339573\pi\) | ||||
0.482929 | + | 0.875660i | \(0.339573\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.12880e29 | 0.588068 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.93960e29 | −0.976604 | −0.488302 | − | 0.872675i | \(-0.662384\pi\) | ||||
−0.488302 | + | 0.872675i | \(0.662384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.29272e29 | 0.629150 | 0.314575 | − | 0.949233i | \(-0.398138\pi\) | ||||
0.314575 | + | 0.949233i | \(0.398138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.95793e28 | 0.0921159 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.70354e28 | 0.0774868 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.18632e28 | 0.272077 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.84535e27 | 0.0418718 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.85722e28 | −0.158651 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.99938e29 | 0.795401 | 0.397701 | − | 0.917515i | \(-0.369808\pi\) | ||||
0.397701 | + | 0.917515i | \(0.369808\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.51418e28 | −0.0967516 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.00852e29 | 0.747744 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.15150e29 | 0.774956 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.66398e28 | 0.267113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.98808e29 | −0.670539 | −0.335269 | − | 0.942122i | \(-0.608827\pi\) | ||||
−0.335269 | + | 0.942122i | \(0.608827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.68097e29 | −0.548712 | −0.274356 | − | 0.961628i | \(-0.588465\pi\) | ||||
−0.274356 | + | 0.961628i | \(0.588465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.05773e29 | 0.334193 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.67978e27 | 0.0265469 | 0.0132735 | − | 0.999912i | \(-0.495775\pi\) | ||||
0.0132735 | + | 0.999912i | \(0.495775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07693e29 | −0.318873 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.25320e28 | −0.150600 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.07947e29 | 1.41003 | 0.705017 | − | 0.709190i | \(-0.250939\pi\) | ||||
0.705017 | + | 0.709190i | \(0.250939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.11868e28 | −0.164484 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.94651e28 | −0.154819 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.42808e28 | 0.0864477 | 0.0432239 | − | 0.999065i | \(-0.486237\pi\) | ||||
0.0432239 | + | 0.999065i | \(0.486237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.03536e28 | 0.123003 | 0.0615015 | − | 0.998107i | \(-0.480411\pi\) | ||||
0.0615015 | + | 0.998107i | \(0.480411\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.62692e28 | −0.133161 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.46424e28 | 0.0335726 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.13559e29 | −0.474458 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.28764e27 | −0.0135367 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.30359e29 | −0.271991 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.22880e29 | −0.855182 | −0.427591 | − | 0.903972i | \(-0.640638\pi\) | ||||
−0.427591 | + | 0.903972i | \(0.640638\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.20346e28 | −0.141205 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.94132e27 | −0.00558936 | −0.00279468 | − | 0.999996i | \(-0.500890\pi\) | ||||
−0.00279468 | + | 0.999996i | \(0.500890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.14970e29 | −0.211813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.41641e29 | −0.610274 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.09159e29 | −0.362293 | −0.181147 | − | 0.983456i | \(-0.557981\pi\) | ||||
−0.181147 | + | 0.983456i | \(0.557981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.97520e29 | −0.499765 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.69717e29 | −0.765228 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.02272e27 | 0.0110970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.10396e29 | −1.08888 | −0.544442 | − | 0.838799i | \(-0.683258\pi\) | ||||
−0.544442 | + | 0.838799i | \(0.683258\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.55562e28 | −0.0528709 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.97819e29 | 0.718176 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.59973e29 | −0.503878 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.03935e29 | −0.548657 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.10616e29 | 1.06850 | 0.534252 | − | 0.845325i | \(-0.320593\pi\) | ||||
0.534252 | + | 0.845325i | \(0.320593\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.37921e28 | 0.107194 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.96236e28 | 0.111285 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.49948e29 | 0.662854 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.31827e30 | 1.54248 | 0.771241 | − | 0.636544i | \(-0.219637\pi\) | ||||
0.771241 | + | 0.636544i | \(0.219637\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.01050e29 | −0.455584 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.00092e29 | −0.330989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.83048e29 | −0.196043 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.01292e30 | 1.05347 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.04204e30 | 1.05252 | 0.526262 | − | 0.850323i | \(-0.323593\pi\) | ||||
0.526262 | + | 0.850323i | \(0.323593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.53175e29 | 0.248371 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.54643e29 | −0.337940 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.85712e29 | 0.727301 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.06635e30 | −0.958933 | −0.479467 | − | 0.877560i | \(-0.659170\pi\) | ||||
−0.479467 | + | 0.877560i | \(0.659170\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.37309e29 | −0.286349 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.08122e30 | 1.71682 | 0.858412 | − | 0.512961i | \(-0.171451\pi\) | ||||
0.858412 | + | 0.512961i | \(0.171451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.18759e29 | 0.255532 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.62008e29 | −0.593678 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.80814e29 | 0.136920 | 0.0684598 | − | 0.997654i | \(-0.478192\pi\) | ||||
0.0684598 | + | 0.997654i | \(0.478192\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.22236e29 | 0.0899721 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.87745e29 | 0.348988 | 0.174494 | − | 0.984658i | \(-0.444171\pi\) | ||||
0.174494 | + | 0.984658i | \(0.444171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.34616e30 | −0.936386 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.36923e29 | −0.227858 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.07800e29 | 0.596941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.22610e29 | −0.589928 | −0.294964 | − | 0.955508i | \(-0.595308\pi\) | ||||
−0.294964 | + | 0.955508i | \(0.595308\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.79141e29 | 0.546652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.61726e28 | −0.0400161 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.92184e30 | 1.13035 | 0.565173 | − | 0.824972i | \(-0.308809\pi\) | ||||
0.565173 | + | 0.824972i | \(0.308809\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.03116e29 | −0.116200 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.51722e30 | −1.95732 | −0.978658 | − | 0.205496i | \(-0.934119\pi\) | ||||
−0.978658 | + | 0.205496i | \(0.934119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.56552e29 | −0.0847524 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.33666e28 | −0.0439083 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.33707e30 | −0.685180 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.78079e29 | 0.0887946 | 0.0443973 | − | 0.999014i | \(-0.485863\pi\) | ||||
0.0443973 | + | 0.999014i | \(0.485863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.04407e30 | 0.506593 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.21079e30 | −1.98829 | −0.994143 | − | 0.108071i | \(-0.965533\pi\) | ||||
−0.994143 | + | 0.108071i | \(0.965533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.10407e30 | 0.507376 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.02613e29 | −0.135353 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.81985e29 | 0.340451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.95066e29 | −0.336951 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.62378e29 | −0.190765 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.21810e30 | −0.890943 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.65263e29 | 0.142847 | 0.0714235 | − | 0.997446i | \(-0.477246\pi\) | ||||
0.0714235 | + | 0.997446i | \(0.477246\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.92382e30 | 0.732581 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.12988e30 | 0.418968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.61849e30 | −0.584441 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.04046e28 | 0.00365908 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.15540e30 | −1.08079 | −0.540396 | − | 0.841411i | \(-0.681726\pi\) | ||||
−0.540396 | + | 0.841411i | \(0.681726\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.85809e29 | −0.0953531 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.10698e29 | 0.0684729 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.16894e29 | 0.195298 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.02083e29 | −0.0931686 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.23482e30 | 0.371048 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.77681e30 | −0.520214 | −0.260107 | − | 0.965580i | \(-0.583758\pi\) | ||||
−0.260107 | + | 0.965580i | \(0.583758\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.55440e30 | 1.01402 | 0.507010 | − | 0.861940i | \(-0.330751\pi\) | ||||
0.507010 | + | 0.861940i | \(0.330751\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.29304e29 | 0.258349 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.18305e30 | 0.591439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.32751e29 | 0.193475 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.41452e29 | −0.113606 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.53502e30 | 0.635884 | 0.317942 | − | 0.948110i | \(-0.397008\pi\) | ||||
0.317942 | + | 0.948110i | \(0.397008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.71174e30 | −0.418543 | −0.209272 | − | 0.977858i | \(-0.567109\pi\) | ||||
−0.209272 | + | 0.977858i | \(0.567109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.47290e29 | 0.178124 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.61940e30 | 1.53819 | 0.769097 | − | 0.639132i | \(-0.220706\pi\) | ||||
0.769097 | + | 0.639132i | \(0.220706\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.52629e30 | 1.47858 | 0.739288 | − | 0.673389i | \(-0.235162\pi\) | ||||
0.739288 | + | 0.673389i | \(0.235162\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.29039e29 | −0.161042 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.01652e30 | −0.218949 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.35261e30 | 0.494131 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.49729e29 | −0.133081 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.94428e30 | 0.787894 | 0.393947 | − | 0.919133i | \(-0.371109\pi\) | ||||
0.393947 | + | 0.919133i | \(0.371109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.94839e28 | −0.0174336 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.25824e30 | −0.619147 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.11290e29 | 0.0947701 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.71737e30 | −0.310519 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.59666e29 | 0.151635 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.72869e30 | −0.297479 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.15149e31 | −1.93329 | −0.966644 | − | 0.256124i | \(-0.917554\pi\) | ||||
−0.966644 | + | 0.256124i | \(0.917554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.81101e29 | 0.0296672 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.63232e29 | 0.0420766 | 0.0210383 | − | 0.999779i | \(-0.493303\pi\) | ||||
0.0210383 | + | 0.999779i | \(0.493303\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.57894e30 | 0.402266 | 0.201133 | − | 0.979564i | \(-0.435538\pi\) | ||||
0.201133 | + | 0.979564i | \(0.435538\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.82412e30 | −0.429882 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.33890e30 | −0.496009 | −0.248005 | − | 0.968759i | \(-0.579775\pi\) | ||||
−0.248005 | + | 0.968759i | \(0.579775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.80089e30 | 0.406094 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.81395e30 | −0.539728 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.16052e30 | 0.574698 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.46080e30 | −1.27567 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.42198e30 | −0.187173 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.62614e30 | 0.337468 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.94355e30 | −0.243838 | −0.121919 | − | 0.992540i | \(-0.538905\pi\) | ||||
−0.121919 | + | 0.992540i | \(0.538905\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.69278e30 | −0.207357 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.05871e30 | 0.365840 | 0.182920 | − | 0.983128i | \(-0.441445\pi\) | ||||
0.182920 | + | 0.983128i | \(0.441445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.12080e31 | −1.30901 | −0.654503 | − | 0.756060i | \(-0.727122\pi\) | ||||
−0.654503 | + | 0.756060i | \(0.727122\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.98097e30 | −0.225929 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.65586e30 | 0.629942 | 0.314971 | − | 0.949101i | \(-0.398005\pi\) | ||||
0.314971 | + | 0.949101i | \(0.398005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.02509e30 | −0.546607 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.39768e29 | −0.0467205 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.20875e29 | 0.0644264 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.06428e30 | 0.817380 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.52181e30 | −0.249685 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.08687e30 | 0.685453 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.31803e28 | −0.00313523 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.64631e30 | −0.244298 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.08966e29 | −0.0278677 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.28972e31 | −1.13663 | −0.568314 | − | 0.822812i | \(-0.692404\pi\) | ||||
−0.568314 | + | 0.822812i | \(0.692404\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.80189e30 | 0.585745 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.11830e31 | −0.941058 | −0.470529 | − | 0.882384i | \(-0.655937\pi\) | ||||
−0.470529 | + | 0.882384i | \(0.655937\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.49525e30 | 0.287432 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.39790e30 | −0.192712 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.53082e30 | 0.120239 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.99044e31 | 1.52804 | 0.764022 | − | 0.645190i | \(-0.223222\pi\) | ||||
0.764022 | + | 0.645190i | \(0.223222\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.90932e30 | 0.368379 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.87123e30 | −0.724025 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.36006e30 | 0.456009 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.13134e30 | 0.219479 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.46924e31 | 1.69199 | 0.845995 | − | 0.533190i | \(-0.179007\pi\) | ||||
0.845995 | + | 0.533190i | \(0.179007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.20823e30 | 0.147936 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.06517e31 | −0.697690 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.64849e29 | 0.0553883 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.80473e31 | 1.75641 | 0.878204 | − | 0.478286i | \(-0.158742\pi\) | ||||
0.878204 | + | 0.478286i | \(0.158742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.37677e31 | 0.843086 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.99005e30 | 0.538358 | 0.269179 | − | 0.963090i | \(-0.413248\pi\) | ||||
0.269179 | + | 0.963090i | \(0.413248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.61329e31 | −0.944799 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.54041e29 | −0.0374603 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.54170e31 | −1.42380 | −0.711901 | − | 0.702280i | \(-0.752166\pi\) | ||||
−0.711901 | + | 0.702280i | \(0.752166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.65911e30 | 0.419646 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.02852e30 | 0.269492 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.08338e30 | −0.476181 | −0.238090 | − | 0.971243i | \(-0.576521\pi\) | ||||
−0.238090 | + | 0.971243i | \(0.576521\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.52461e31 | 0.781851 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.79674e30 | 0.240642 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.44360e30 | 0.365332 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.08671e31 | −0.521817 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.12279e31 | 0.527500 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.43635e31 | −0.660271 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.32705e31 | −0.596909 | −0.298455 | − | 0.954424i | \(-0.596471\pi\) | ||||
−0.298455 | + | 0.954424i | \(0.596471\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.77529e29 | −0.0254199 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.95025e31 | −1.70146 | −0.850732 | − | 0.525600i | \(-0.823841\pi\) | ||||
−0.850732 | + | 0.525600i | \(0.823841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.24548e31 | −0.524992 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.27807e30 | 0.382745 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.04812e31 | 0.423172 | 0.211586 | − | 0.977359i | \(-0.432137\pi\) | ||||
0.211586 | + | 0.977359i | \(0.432137\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.18579e30 | −0.0863755 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.93628e30 | −0.0748933 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.33201e31 | −1.64013 | −0.820063 | − | 0.572273i | \(-0.806062\pi\) | ||||
−0.820063 | + | 0.572273i | \(0.806062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.53898e30 | 0.0570364 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.24227e30 | −0.0813502 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.51172e31 | −0.536919 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.71476e31 | 0.943968 | 0.471984 | − | 0.881607i | \(-0.343538\pi\) | ||||
0.471984 | + | 0.881607i | \(0.343538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.35701e30 | 0.114284 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.25031e31 | −0.416750 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.18699e31 | −1.69284 | −0.846421 | − | 0.532515i | \(-0.821247\pi\) | ||||
−0.846421 | + | 0.532515i | \(0.821247\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.74279e30 | −0.119607 |
(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 | 12.22.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 36.22.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.22.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.22.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
36.22.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
48.22.a.b.1.1 | 1 | 4.3 | odd | 2 |