Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,10,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(206.014334466\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 1305x^{4} + 433104x^{2} + 16000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.6 | ||
Root | \(-27.7229i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.10.c.q.49.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 268.664i | 1.91498i | 0.288470 | + | 0.957489i | \(0.406854\pi\) | ||||
−0.288470 | + | 0.957489i | \(0.593146\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 637.237i | 0.100314i | 0.998741 | + | 0.0501568i | \(0.0159721\pi\) | ||||
−0.998741 | + | 0.0501568i | \(0.984028\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −52497.3 | −2.66714 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 49042.6 | 1.00996 | 0.504982 | − | 0.863130i | \(-0.331499\pi\) | ||||
0.504982 | + | 0.863130i | \(0.331499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72726.2i | 0.706229i | 0.935580 | + | 0.353115i | \(0.114877\pi\) | ||||
−0.935580 | + | 0.353115i | \(0.885123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 67319.3i | − 0.195488i | −0.995212 | − | 0.0977439i | \(-0.968837\pi\) | ||||
0.995212 | − | 0.0977439i | \(-0.0311626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 341136. | 0.600532 | 0.300266 | − | 0.953855i | \(-0.402925\pi\) | ||||
0.300266 | + | 0.953855i | \(0.402925\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −171203. | −0.192098 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 134355.i | 0.100110i | 0.998746 | + | 0.0500550i | \(0.0159397\pi\) | ||||
−0.998746 | + | 0.0500550i | \(0.984060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 8.81603e6i | − 3.19254i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.45784e6 | −1.17040 | −0.585199 | − | 0.810890i | \(-0.698984\pi\) | ||||
−0.585199 | + | 0.810890i | \(0.698984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −456520. | −0.0887834 | −0.0443917 | − | 0.999014i | \(-0.514135\pi\) | ||||
−0.0443917 | + | 0.999014i | \(0.514135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.31760e7i | 1.93406i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.30516e7i | − 1.14487i | −0.819951 | − | 0.572433i | \(-0.805999\pi\) | ||||
0.819951 | − | 0.572433i | \(-0.194001\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.95389e7 | −1.35241 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.56667e7 | −1.41854 | −0.709272 | − | 0.704935i | \(-0.750976\pi\) | ||||
−0.709272 | + | 0.704935i | \(0.750976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.42710e6i | − 0.152869i | −0.997075 | − | 0.0764344i | \(-0.975646\pi\) | ||||
0.997075 | − | 0.0764344i | \(-0.0243536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 3.39814e7i | − 1.01578i | −0.861421 | − | 0.507891i | \(-0.830425\pi\) | ||||
0.861421 | − | 0.507891i | \(-0.169575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.99475e7 | 0.989937 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.80863e7 | 0.374355 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.42456e7i | − 1.46658i | −0.679916 | − | 0.733290i | \(-0.737984\pi\) | ||||
0.679916 | − | 0.733290i | \(-0.262016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.16509e7i | 1.15001i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.46358e7 | −0.801887 | −0.400944 | − | 0.916103i | \(-0.631318\pi\) | ||||
−0.400944 | + | 0.916103i | \(0.631318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.78017e8 | 1.64618 | 0.823088 | − | 0.567913i | \(-0.192249\pi\) | ||||
0.823088 | + | 0.567913i | \(0.192249\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3.34533e7i | − 0.267551i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.94299e7i | 0.420930i | 0.977601 | + | 0.210465i | \(0.0674978\pi\) | ||||
−0.977601 | + | 0.210465i | \(0.932502\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.60963e7 | −0.191708 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.07860e8 | 0.970753 | 0.485376 | − | 0.874305i | \(-0.338683\pi\) | ||||
0.485376 | + | 0.874305i | \(0.338683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 3.02516e8i | − 1.24680i | −0.781905 | − | 0.623398i | \(-0.785752\pi\) | ||||
0.781905 | − | 0.623398i | \(-0.214248\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.12518e7i | 0.101313i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.72244e8 | 1.07524 | 0.537621 | − | 0.843187i | \(-0.319323\pi\) | ||||
0.537621 | + | 0.843187i | \(0.319323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.33524e9 | 3.44650 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.50079e8i | − 1.04097i | −0.853872 | − | 0.520484i | \(-0.825752\pi\) | ||||
0.853872 | − | 0.520484i | \(-0.174248\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.19766e9i | − 2.24129i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.82741e7 | −0.0984511 | −0.0492255 | − | 0.998788i | \(-0.515675\pi\) | ||||
−0.0492255 | + | 0.998788i | \(0.515675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.63438e7 | −0.0708444 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1.22650e8i | − 0.170018i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 7.85850e8i | − 0.901295i | −0.892702 | − | 0.450647i | \(-0.851193\pi\) | ||||
0.892702 | − | 0.450647i | \(-0.148807\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.57461e9 | −2.69372 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.60460e8 | −0.153433 | −0.0767167 | − | 0.997053i | \(-0.524444\pi\) | ||||
−0.0767167 | + | 0.997053i | \(0.524444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.39454e9i | 1.22085i | 0.792074 | + | 0.610425i | \(0.209001\pi\) | ||||
−0.792074 | + | 0.610425i | \(0.790999\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.56463e9i | − 1.15394i | −0.816764 | − | 0.576972i | \(-0.804234\pi\) | ||||
0.816764 | − | 0.576972i | \(-0.195766\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.24703e9 | −0.846172 | −0.423086 | − | 0.906089i | \(-0.639053\pi\) | ||||
−0.423086 | + | 0.906089i | \(0.639053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50649e9 | 2.19240 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1.81056e9i | − 1.04463i | −0.852754 | − | 0.522313i | \(-0.825069\pi\) | ||||
0.852754 | − | 0.522313i | \(-0.174931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 3.81793e9i | − 1.88361i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.28984e7 | 0.0196101 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.72275e7 | 0.0200291 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 6.89572e9i | − 2.71648i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.06491e9i | − 1.04545i | −0.852503 | − | 0.522723i | \(-0.824916\pi\) | ||||
0.852503 | − | 0.522723i | \(-0.175084\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.20739e8 | 0.292740 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.83508e9 | 0.544421 | 0.272211 | − | 0.962238i | \(-0.412245\pi\) | ||||
0.272211 | + | 0.962238i | \(0.412245\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.17385e8i | 0.0602416i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.62426e9i | 1.12150i | 0.827984 | + | 0.560751i | \(0.189488\pi\) | ||||
−0.827984 | + | 0.560751i | \(0.810512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.57140e8 | 0.0584255 | 0.0292128 | − | 0.999573i | \(-0.490700\pi\) | ||||
0.0292128 | + | 0.999573i | \(0.490700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.12958e9 | 1.94520 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.56668e9i | 0.713267i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.07325e10i | 1.89571i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.14809e9 | −0.523250 | −0.261625 | − | 0.965170i | \(-0.584258\pi\) | ||||
−0.261625 | + | 0.965170i | \(0.584258\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.02772e10 | 1.60871 | 0.804356 | − | 0.594147i | \(-0.202510\pi\) | ||||
0.804356 | + | 0.594147i | \(0.202510\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.53408e9i | 0.521393i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.25077e9i | − 0.427009i | −0.976942 | − | 0.213505i | \(-0.931512\pi\) | ||||
0.976942 | − | 0.213505i | \(-0.0684878\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.26338e10 | 2.80847 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.56158e7 | −0.0100424 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3.40049e9i | − 0.377309i | −0.982043 | − | 0.188655i | \(-0.939587\pi\) | ||||
0.982043 | − | 0.188655i | \(-0.0604127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.27785e9i | 0.525089i | 0.964920 | + | 0.262544i | \(0.0845616\pi\) | ||||
−0.964920 | + | 0.262544i | \(0.915438\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.31540e9 | 0.501240 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.79087e10 | −1.60170 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.58861e9i | 0.559224i | 0.960113 | + | 0.279612i | \(0.0902059\pi\) | ||||
−0.960113 | + | 0.279612i | \(0.909794\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 2.00520e10i | − 1.53560i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.23663e10 | −0.900326 | −0.450163 | − | 0.892946i | \(-0.648634\pi\) | ||||
−0.450163 | + | 0.892946i | \(0.648634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.59914e10 | −1.80002 | −0.900009 | − | 0.435872i | \(-0.856440\pi\) | ||||
−0.900009 | + | 0.435872i | \(0.856440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.78267e10i | 3.15239i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.30151e9i | − 0.197436i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.61790e9 | 0.320255 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.50506e10 | −0.818284 | −0.409142 | − | 0.912471i | \(-0.634172\pi\) | ||||
−0.409142 | + | 0.912471i | \(0.634172\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.40329e10i | 0.728014i | 0.931396 | + | 0.364007i | \(0.118592\pi\) | ||||
−0.931396 | + | 0.364007i | \(0.881408\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.57285e10i | 1.21707i | 0.793526 | + | 0.608536i | \(0.208243\pi\) | ||||
−0.793526 | + | 0.608536i | \(0.791757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.94367e10 | −1.33061 | −0.665303 | − | 0.746573i | \(-0.731698\pi\) | ||||
−0.665303 | + | 0.746573i | \(0.731698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.86533e10 | −0.806072 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.84070e9i | − 0.117407i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 7.05326e9i | − 0.267007i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.67302e10 | 0.606516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.17275e10 | −0.407319 | −0.203659 | − | 0.979042i | \(-0.565284\pi\) | ||||
−0.203659 | + | 0.979042i | \(0.565284\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.58445e10i | 1.85897i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.90911e8i | − 0.00890619i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.12751e10 | 2.38759 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.89588e9 | 0.138059 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.58340e10i | − 0.699550i | −0.936834 | − | 0.349775i | \(-0.886258\pi\) | ||||
0.936834 | − | 0.349775i | \(-0.113742\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.50896e10i | − 0.627159i | −0.949562 | − | 0.313580i | \(-0.898472\pi\) | ||||
0.949562 | − | 0.313580i | \(-0.101528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.30463e10 | 0.553785 | 0.276892 | − | 0.960901i | \(-0.410695\pi\) | ||||
0.276892 | + | 0.960901i | \(0.410695\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.39622e9 | −0.194013 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.17197e10i | 0.705062i | 0.935800 | + | 0.352531i | \(0.114679\pi\) | ||||
−0.935800 | + | 0.352531i | \(0.885321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.00009e11i | 2.05906i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.23794e10 | 0.443668 | 0.221834 | − | 0.975084i | \(-0.428796\pi\) | ||||
0.221834 | + | 0.975084i | \(0.428796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.10823e10 | −0.402569 | −0.201285 | − | 0.979533i | \(-0.564512\pi\) | ||||
−0.201285 | + | 0.979533i | \(0.564512\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.85206e11i | 3.40743i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.48095e10i | 0.424113i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.20920e11 | 1.99343 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.96509e10 | 1.26666 | 0.633329 | − | 0.773883i | \(-0.281688\pi\) | ||||
0.633329 | + | 0.773883i | \(0.281688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.58910e9i | 0.101108i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.30815e10i | 0.473027i | 0.971628 | + | 0.236514i | \(0.0760048\pi\) | ||||
−0.971628 | + | 0.236514i | \(0.923995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.31695e9 | 0.114846 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.34025e11 | 3.12162 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 6.05028e10i | − 0.779784i | −0.920861 | − | 0.389892i | \(-0.872512\pi\) | ||||
0.920861 | − | 0.389892i | \(-0.127488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.56562e10i | − 0.188532i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.61933e10 | −0.305004 | −0.152502 | − | 0.988303i | \(-0.548733\pi\) | ||||
−0.152502 | + | 0.988303i | \(0.548733\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.42857e10 | −0.611398 | −0.305699 | − | 0.952128i | \(-0.598890\pi\) | ||||
−0.305699 | + | 0.952128i | \(0.598890\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 1.24509e10i | − 0.135666i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.76561e11i | − 1.80192i | −0.433900 | − | 0.900961i | \(-0.642863\pi\) | ||||
0.433900 | − | 0.900961i | \(-0.357137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.39661e10 | 0.236798 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.91126e9 | −0.0756950 | −0.0378475 | − | 0.999284i | \(-0.512050\pi\) | ||||
−0.0378475 | + | 0.999284i | \(0.512050\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.34806e11i | 1.24931i | 0.780899 | + | 0.624657i | \(0.214761\pi\) | ||||
−0.780899 | + | 0.624657i | \(0.785239\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.63558e10i | − 0.142299i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.14056e11 | 0.961785 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.11130e11 | 1.72596 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.02784e11i | 0.814741i | 0.913263 | + | 0.407370i | \(0.133554\pi\) | ||||
−0.913263 | + | 0.407370i | \(0.866446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 4.32361e11i | − 3.22435i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.77110e9 | −0.0707006 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18388e9 | 0.0153348 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4.31098e10i | − 0.293822i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.61472e11i | − 1.67998i | −0.542606 | − | 0.839988i | \(-0.682562\pi\) | ||||
0.542606 | − | 0.839988i | \(-0.317438\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.74662e11 | −2.33790 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.24828e10 | 0.499967 | 0.249984 | − | 0.968250i | \(-0.419575\pi\) | ||||
0.249984 | + | 0.968250i | \(0.419575\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.35766e11i | − 0.799540i | −0.916615 | − | 0.399770i | \(-0.869090\pi\) | ||||
0.916615 | − | 0.399770i | \(-0.130910\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.06853e10i | 0.504394i | 0.967676 | + | 0.252197i | \(0.0811531\pi\) | ||||
−0.967676 | + | 0.252197i | \(0.918847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.18624e11 | −1.18206 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.20360e11 | 2.20978 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.29650e10i | − 0.117397i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 3.35033e11i | − 1.62040i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.16542e10 | 0.101897 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.45169e11 | 1.58054 | 0.790271 | − | 0.612758i | \(-0.209940\pi\) | ||||
0.790271 | + | 0.612758i | \(0.209940\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.85173e11i | 3.05352i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 8.39418e10i | − 0.354523i | −0.984164 | − | 0.177261i | \(-0.943276\pi\) | ||||
0.984164 | − | 0.177261i | \(-0.0567238\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.86433e11 | 2.00043 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.23889e10 | −0.0896681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.11709e10i | 0.199618i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.56153e11i | 0.578188i | 0.957301 | + | 0.289094i | \(0.0933540\pi\) | ||||
−0.957301 | + | 0.289094i | \(0.906646\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.31862e9 | −0.0227986 | −0.0113993 | − | 0.999935i | \(-0.503629\pi\) | ||||
−0.0113993 | + | 0.999935i | \(0.503629\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.41156e11 | 2.25466 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2.83875e11i | − 0.973064i | −0.873663 | − | 0.486532i | \(-0.838262\pi\) | ||||
0.873663 | − | 0.486532i | \(-0.161738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.15253e10i | 0.0375529i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00733e11 | 1.90878 | 0.954391 | − | 0.298558i | \(-0.0965058\pi\) | ||||
0.954391 | + | 0.298558i | \(0.0965058\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.06314e11 | −0.639361 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.26883e10i | 0.0383552i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.97260e11i | 1.43082i | 0.698702 | + | 0.715412i | \(0.253761\pi\) | ||||
−0.698702 | + | 0.715412i | \(0.746239\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.34743e12 | 3.78346 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.36845e10 | 0.147118 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.39183e11i | 0.372303i | 0.982521 | + | 0.186151i | \(0.0596015\pi\) | ||||
−0.982521 | + | 0.186151i | \(0.940398\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.24202e11i | − 0.826569i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.65247e11 | −1.40722 | −0.703610 | − | 0.710587i | \(-0.748430\pi\) | ||||
−0.703610 | + | 0.710587i | \(0.748430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.23432e11 | 2.00201 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.38864e11i | 1.27963i | 0.768528 | + | 0.639816i | \(0.220989\pi\) | ||||
−0.768528 | + | 0.639816i | \(0.779011\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.79914e11i | 0.407723i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.67552e11 | −1.69955 | −0.849776 | − | 0.527144i | \(-0.823263\pi\) | ||||
−0.849776 | + | 0.527144i | \(0.823263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.04466e9 | 0.0195703 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.93021e11i | 1.04255i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.25258e11i | 1.26329i | 0.775259 | + | 0.631643i | \(0.217619\pi\) | ||||
−0.775259 | + | 0.631643i | \(0.782381\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.84034e10 | −0.115361 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.61329e11 | −0.311574 | −0.155787 | − | 0.987791i | \(-0.549791\pi\) | ||||
−0.155787 | + | 0.987791i | \(0.549791\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3.32009e10i | − 0.0627014i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6.40083e11i | − 1.15628i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.24004e11 | 1.27934 | 0.639670 | − | 0.768649i | \(-0.279071\pi\) | ||||
0.639670 | + | 0.768649i | \(0.279071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.24237e12 | −2.14765 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.75607e10i | − 0.0804403i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.90842e10i | 0.111884i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.80040e11 | 0.443871 | 0.221936 | − | 0.975061i | \(-0.428763\pi\) | ||||
0.221936 | + | 0.975061i | \(0.428763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.55915e10 | −0.101760 | −0.0508801 | − | 0.998705i | \(-0.516203\pi\) | ||||
−0.0508801 | + | 0.998705i | \(0.516203\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.78393e12i | 2.70924i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.13439e11i | 0.165134i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.58239e11 | −1.36589 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.00292e12 | −1.39997 | −0.699987 | − | 0.714156i | \(-0.746811\pi\) | ||||
−0.699987 | + | 0.714156i | \(0.746811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 7.98482e11i | − 1.09162i | −0.837910 | − | 0.545808i | \(-0.816223\pi\) | ||||
0.837910 | − | 0.545808i | \(-0.183777\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.58332e10i | 0.0601193i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.98379e11 | 1.02593 | 0.512966 | − | 0.858409i | \(-0.328547\pi\) | ||||
0.512966 | + | 0.858409i | \(0.328547\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.09714e12 | −2.64030 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 7.56642e11i | − 0.933413i | −0.884412 | − | 0.466707i | \(-0.845440\pi\) | ||||
0.884412 | − | 0.466707i | \(-0.154560\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 8.45779e11i | − 1.00201i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.39419e11 | 0.742467 | 0.371234 | − | 0.928540i | \(-0.378935\pi\) | ||||
0.371234 | + | 0.928540i | \(0.378935\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.25876e12 | −1.43268 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.76111e12i | 3.08065i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1.34276e12i | − 1.44005i | −0.693949 | − | 0.720024i | \(-0.744131\pi\) | ||||
0.693949 | − | 0.720024i | \(-0.255869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.93489e11 | −0.624102 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.47112e11 | 0.357945 | 0.178972 | − | 0.983854i | \(-0.442723\pi\) | ||||
0.178972 | + | 0.983854i | \(0.442723\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.20214e11i | 0.728362i | 0.931328 | + | 0.364181i | \(0.118651\pi\) | ||||
−0.931328 | + | 0.364181i | \(0.881349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.31553e10i | 0.0711737i | 0.999367 | + | 0.0355869i | \(0.0113300\pi\) | ||||
−0.999367 | + | 0.0355869i | \(0.988670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.42433e10 | −0.0422250 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.73364e11 | 0.817713 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1.68074e11i | − 0.154392i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.42267e12i | 3.91158i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.80307e10 | −0.0416878 | −0.0208439 | − | 0.999783i | \(-0.506635\pi\) | ||||
−0.0208439 | + | 0.999783i | \(0.506635\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.49191e11 | 0.808539 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.30019e10i | − 0.0192310i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.24384e12i | 1.00204i | 0.865435 | + | 0.501021i | \(0.167042\pi\) | ||||
−0.865435 | + | 0.501021i | \(0.832958\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.13590e11 | 0.722539 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.63145e11 | 0.204328 | 0.102164 | − | 0.994768i | \(-0.467423\pi\) | ||||
0.102164 | + | 0.994768i | \(0.467423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00099e11i | 0.228798i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.32456e11i | 0.0973798i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.75452e10 | 0.0271083 | 0.0135542 | − | 0.999908i | \(-0.495685\pi\) | ||||
0.0135542 | + | 0.999908i | \(0.495685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.41797e12 | −1.00553 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.86189e11i | − 0.199341i | −0.995020 | − | 0.0996707i | \(-0.968221\pi\) | ||||
0.995020 | − | 0.0996707i | \(-0.0317789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.42806e12i | 0.959864i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.48505e12 | 0.980646 | 0.490323 | − | 0.871541i | \(-0.336879\pi\) | ||||
0.490323 | + | 0.871541i | \(0.336879\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.92774e11 | 0.125071 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 3.00746e12i | − 1.91722i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.66654e12i | − 1.02590i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.77012e12 | −1.07090 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.77521e12 | −1.05556 | −0.527778 | − | 0.849383i | \(-0.676975\pi\) | ||||
−0.527778 | + | 0.849383i | \(0.676975\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.20614e12i | − 0.704922i | −0.935826 | − | 0.352461i | \(-0.885345\pi\) | ||||
0.935826 | − | 0.352461i | \(-0.114655\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.07326e10i | 0.0173561i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.78310e12 | 0.989978 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.91818e12 | 2.13875 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.86664e12i | − 1.00182i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 3.32237e12i | − 1.72410i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.95913e12 | 0.999802 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.24195e12 | 1.62711 | 0.813557 | − | 0.581485i | \(-0.197528\pi\) | ||||
0.813557 | + | 0.581485i | \(0.197528\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 6.98296e12i | − 3.44699i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.33463e11i | 0.445814i | 0.974840 | + | 0.222907i | \(0.0715547\pi\) | ||||
−0.974840 | + | 0.222907i | \(0.928445\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.34540e12 | −4.39059 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.52073e12 | −0.702861 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.37208e11i | 0.107861i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.31760e12i | 0.580012i | 0.957025 | + | 0.290006i | \(0.0936572\pi\) | ||||
−0.957025 | + | 0.290006i | \(0.906343\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.49240e11 | 0.107960 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.86998e11 | 0.378085 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.33363e12i | 1.81788i | 0.416931 | + | 0.908938i | \(0.363106\pi\) | ||||
−0.416931 | + | 0.908938i | \(0.636894\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.50868e11i | 0.345731i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.08940e12 | −1.23558 | −0.617788 | − | 0.786345i | \(-0.711971\pi\) | ||||
−0.617788 | + | 0.786345i | \(0.711971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.43095e11 | 0.292538 | 0.146269 | − | 0.989245i | \(-0.453274\pi\) | ||||
0.146269 | + | 0.989245i | \(0.453274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4.04356e12i | − 1.56700i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.25852e12i | 0.848269i | 0.905599 | + | 0.424134i | \(0.139422\pi\) | ||||
−0.905599 | + | 0.424134i | \(0.860578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.77013e12 | −1.39413 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.86807e11 | 0.104423 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4.13162e12i | − 1.48119i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4.75794e12i | − 1.65405i | −0.562169 | − | 0.827023i | \(-0.690033\pi\) | ||||
0.562169 | − | 0.827023i | \(-0.309967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.55735e11 | −0.0533173 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.91232e12 | −2.33067 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 2.01077e12i | − 0.667755i | −0.942616 | − | 0.333878i | \(-0.891643\pi\) | ||||
0.942616 | − | 0.333878i | \(-0.108357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 7.90857e12i | − 2.54808i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.29427e12 | −1.04554 | −0.522768 | − | 0.852475i | \(-0.675101\pi\) | ||||
−0.522768 | + | 0.852475i | \(0.675101\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.98887e12 | −0.621830 | −0.310915 | − | 0.950438i | \(-0.600635\pi\) | ||||
−0.310915 | + | 0.950438i | \(0.600635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3.64488e12i | − 1.12268i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4.11631e12i | − 1.23072i | −0.788246 | − | 0.615360i | \(-0.789011\pi\) | ||||
0.788246 | − | 0.615360i | \(-0.210989\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.63194e11 | 0.224832 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.47134e12 | 0.717376 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.06864e12i | 0.591715i | 0.955232 | + | 0.295858i | \(0.0956054\pi\) | ||||
−0.955232 | + | 0.295858i | \(0.904395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 5.42058e12i | − 1.50578i | −0.658145 | − | 0.752891i | \(-0.728659\pi\) | ||||
0.658145 | − | 0.752891i | \(-0.271341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.87240e12 | 1.06016 | 0.530081 | − | 0.847947i | \(-0.322162\pi\) | ||||
0.530081 | + | 0.847947i | \(0.322162\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.18447e12 | 0.319605 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 3.71344e10i | − 0.00987599i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.49480e12i | 1.16147i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.78623e11 | −0.223807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.22937e12 | 0.810933 | 0.405467 | − | 0.914110i | \(-0.367109\pi\) | ||||
0.405467 | + | 0.914110i | \(0.367109\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 3.15076e12i | − 0.780006i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.90523e12i | 0.699123i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.09121e13 | −2.58913 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.10935e12 | 0.259543 | 0.129771 | − | 0.991544i | \(-0.458576\pi\) | ||||
0.129771 | + | 0.991544i | \(0.458576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.83993e12i | − 0.655177i | −0.944821 | − | 0.327588i | \(-0.893764\pi\) | ||||
0.944821 | − | 0.327588i | \(-0.106236\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.66962e12i | 0.598935i | 0.954107 | + | 0.299467i | \(0.0968090\pi\) | ||||
−0.954107 | + | 0.299467i | \(0.903191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.66033e12 | −0.809878 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.81574e10 | 0.0170552 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 4.72156e12i | − 1.01619i | −0.861300 | − | 0.508097i | \(-0.830349\pi\) | ||||
0.861300 | − | 0.508097i | \(-0.169651\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.58813e13i | 3.32538i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.01448e12 | 0.829173 | 0.414586 | − | 0.910010i | \(-0.363926\pi\) | ||||
0.414586 | + | 0.910010i | \(0.363926\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.01591e12 | −1.63323 | −0.816613 | − | 0.577186i | \(-0.804151\pi\) | ||||
−0.816613 | + | 0.577186i | \(0.804151\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.31535e12i | 0.264380i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 5.98931e11i | − 0.117168i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.94065e12 | 1.33962 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.73040e12 | 1.66258 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 3.55147e12i | − 0.667330i | −0.942692 | − | 0.333665i | \(-0.891714\pi\) | ||||
0.942692 | − | 0.333665i | \(-0.108286\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.06872e12i | 1.11032i | 0.831744 | + | 0.555160i | \(0.187343\pi\) | ||||
−0.831744 | + | 0.555160i | \(0.812657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00773e11 | 0.0904122 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.74068e12 | 1.20100 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 9.96514e11i | − 0.175223i | −0.996155 | − | 0.0876113i | \(-0.972077\pi\) | ||||
0.996155 | − | 0.0876113i | \(-0.0279233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.19170e12i | 1.06049i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.12686e12 | 1.03574 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.02702e13 | −1.71367 | −0.856835 | − | 0.515591i | \(-0.827572\pi\) | ||||
−0.856835 | + | 0.515591i | \(0.827572\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.64063e12i | − 0.270217i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.72786e12i | 0.277308i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.52194e12 | −1.35018 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.26127e12 | −1.29216 | −0.646079 | − | 0.763270i | \(-0.723592\pi\) | ||||
−0.646079 | + | 0.763270i | \(0.723592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 4.45236e12i | − 0.687529i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.02251e11i | − 0.0153915i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.11428e12 | 1.20598 | 0.602992 | − | 0.797747i | \(-0.293975\pi\) | ||||
0.602992 | + | 0.797747i | \(0.293975\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.95418e13 | −2.86782 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 6.13355e10i | − 0.00888810i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.01254e12i | 0.849614i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.06399e13 | 1.48476 | 0.742380 | − | 0.669979i | \(-0.233697\pi\) | ||||
0.742380 | + | 0.669979i | \(0.233697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.88651e11 | −0.122468 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 5.66405e12i | − 0.770911i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.35040e13i | − 1.79290i | −0.443145 | − | 0.896450i | \(-0.646137\pi\) | ||||
0.443145 | − | 0.896450i | \(-0.353863\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.34766e13 | −3.07866 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.30710e11 | −0.0298840 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.03764e12i | 0.388659i | 0.980936 | + | 0.194329i | \(0.0622530\pi\) | ||||
−0.980936 | + | 0.194329i | \(0.937747\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.40502e12i | 0.425124i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.29483e12 | 0.899736 | 0.449868 | − | 0.893095i | \(-0.351471\pi\) | ||||
0.449868 | + | 0.893095i | \(0.351471\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.66542e12 | −0.812168 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.18034e13i | 1.42088i | 0.703756 | + | 0.710442i | \(0.251505\pi\) | ||||
−0.703756 | + | 0.710442i | \(0.748495\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.36279e13i | 2.77641i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.97041e11 | 0.115756 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.20855e13 | −1.38639 | −0.693197 | − | 0.720748i | \(-0.743798\pi\) | ||||
−0.693197 | + | 0.720748i | \(0.743798\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.13993e13i | 2.42562i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.48077e13i | − 1.63891i | −0.573144 | − | 0.819455i | \(-0.694276\pi\) | ||||
0.573144 | − | 0.819455i | \(-0.305724\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.77025e12 | −0.193619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.75185e13 | −1.89350 | −0.946749 | − | 0.321972i | \(-0.895654\pi\) | ||||
−0.946749 | + | 0.321972i | \(0.895654\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.94656e11i | − 0.0848826i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 5.42798e12i | − 0.566316i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.16729e12 | −0.429720 | −0.214860 | − | 0.976645i | \(-0.568930\pi\) | ||||
−0.214860 | + | 0.976645i | \(0.568930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.88781e12 | −0.905837 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.05896e13i | − 1.06677i | −0.845872 | − | 0.533386i | \(-0.820919\pi\) | ||||
0.845872 | − | 0.533386i | \(-0.179081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.23446e12i | 0.219927i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.75583e12 | −0.851881 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.01940e13 | 0.980426 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.93004e13i | 3.73654i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.50861e12i | 0.233102i | 0.993185 | + | 0.116551i | \(0.0371839\pi\) | ||||
−0.993185 | + | 0.116551i | \(0.962816\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.62549e13 | 1.49327 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.15376e12 | 0.104790 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.29465e13i | 1.16258i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.85822e13i | − 1.63131i | −0.578541 | − | 0.815653i | \(-0.696378\pi\) | ||||
0.578541 | − | 0.815653i | \(-0.303622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.28760e12 | −0.198573 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.05923e12 | 0.262583 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.48362e13i | − 1.25922i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 7.03720e12i | − 0.584075i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.47333e12 | 0.367166 | 0.183583 | − | 0.983004i | \(-0.441230\pi\) | ||||
0.183583 | + | 0.983004i | \(0.441230\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.49582e12 | 0.283763 | 0.141881 | − | 0.989884i | \(-0.454685\pi\) | ||||
0.141881 | + | 0.989884i | \(0.454685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.45846e13i | − 1.17081i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.16911e12i | − 0.0918026i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.43293e12 | 0.188952 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.84197e12 | −0.525578 | −0.262789 | − | 0.964853i | \(-0.584642\pi\) | ||||
−0.262789 | + | 0.964853i | \(0.584642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 8.11058e12i | − 0.616244i | −0.951347 | − | 0.308122i | \(-0.900300\pi\) | ||||
0.951347 | − | 0.308122i | \(-0.0997005\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 5.06349e10i | − 0.00376422i | −0.999998 | − | 0.00188211i | \(-0.999401\pi\) | ||||
0.999998 | − | 0.00188211i | \(-0.000599095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50474e13 | 1.10654 | 0.553269 | − | 0.833002i | \(-0.313380\pi\) | ||||
0.553269 | + | 0.833002i | \(0.313380\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.74356e13 | 3.45064 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2.68924e12i | − 0.193521i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.02469e12i | 0.283444i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.68352e13 | 1.86972 | 0.934859 | − | 0.355020i | \(-0.115526\pi\) | ||||
0.934859 | + | 0.355020i | \(0.115526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.36519e12 | 0.369831 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.12547e12i | − 0.144954i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00951e10i | 0.00200919i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.62176e13 | −2.39241 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.75354e12 | 0.114613 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.22107e12i | 0.272993i | 0.990641 | + | 0.136497i | \(0.0435843\pi\) | ||||
−0.990641 | + | 0.136497i | \(0.956416\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.57740e12i | 0.479851i | 0.970791 | + | 0.239926i | \(0.0771230\pi\) | ||||
−0.970791 | + | 0.239926i | \(0.922877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.41463e13 | 0.886486 | 0.443243 | − | 0.896401i | \(-0.353828\pi\) | ||||
0.443243 | + | 0.896401i | \(0.353828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.39421e12 | 0.272500 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1.52498e13i | − 0.935868i | −0.883763 | − | 0.467934i | \(-0.844998\pi\) | ||||
0.883763 | − | 0.467934i | \(-0.155002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.06427e13i | 1.84180i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.82558e13 | 1.08596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.04937e12 | −0.297273 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.12550e13i | 2.40388i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.30350e12i | − 0.188572i | −0.995545 | − | 0.0942858i | \(-0.969943\pi\) | ||||
0.995545 | − | 0.0942858i | \(-0.0300568\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.76142e13 | −1.56021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.14728e13 | 1.76013 | 0.880063 | − | 0.474856i | \(-0.157500\pi\) | ||||
0.880063 | + | 0.474856i | \(0.157500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.10669e13i | − 0.612637i | −0.951929 | − | 0.306318i | \(-0.900903\pi\) | ||||
0.951929 | − | 0.306318i | \(-0.0990973\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 6.92035e12i | − 0.375381i | −0.982228 | − | 0.187690i | \(-0.939900\pi\) | ||||
0.982228 | − | 0.187690i | \(-0.0601001\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.95308e12 | 0.104872 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.54838e13 | 3.48084 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.15923e13i | − 0.610010i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 2.62514e12i | − 0.135390i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.03509e12 | 0.103912 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.67136e12 | −0.286699 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.86729e11i | 0.0293659i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.00486e13i | − 0.983676i | −0.870687 | − | 0.491838i | \(-0.836325\pi\) | ||||
0.870687 | − | 0.491838i | \(-0.163675\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.42371e12 | 0.409229 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.53798e13 | −1.22083 | −0.610416 | − | 0.792081i | \(-0.708998\pi\) | ||||
−0.610416 | + | 0.792081i | \(0.708998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 2.20730e13i | − 1.05134i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.16938e12i | 0.0546129i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.15926e12 | −0.284845 | −0.142423 | − | 0.989806i | \(-0.545489\pi\) | ||||
−0.142423 | + | 0.989806i | \(0.545489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.02482e13 | 3.21712 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.51169e13i | 0.685574i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 7.32095e13i | − 3.25618i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.20000e13 | −0.969061 | −0.484531 | − | 0.874774i | \(-0.661010\pi\) | ||||
−0.484531 | + | 0.874774i | \(0.661010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.36275e13 | 0.594489 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.21601e13i | 0.957426i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.49274e12i | − 0.105645i | −0.998604 | − | 0.0528225i | \(-0.983178\pi\) | ||||
0.998604 | − | 0.0528225i | \(-0.0168217\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.64753e13 | 1.53110 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.26366e13 | −0.525382 | −0.262691 | − | 0.964880i | \(-0.584610\pi\) | ||||
−0.262691 | + | 0.964880i | \(0.584610\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 3.44844e12i | − 0.142010i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.05809e13i | − 0.831551i | −0.909467 | − | 0.415775i | \(-0.863510\pi\) | ||||
0.909467 | − | 0.415775i | \(-0.136490\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.20008e13 | 0.880524 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.43639e13 | −0.965904 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 2.97887e13i | − 1.16986i | −0.811084 | − | 0.584929i | \(-0.801122\pi\) | ||||
0.811084 | − | 0.584929i | \(-0.198878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5.87364e13i | − 2.26362i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.94675e12 | −0.112502 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.62312e13 | −0.992118 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.21389e13i | 3.07773i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.74473e13i | 0.641664i | 0.947136 | + | 0.320832i | \(0.103963\pi\) | ||||
−0.947136 | + | 0.320832i | \(0.896037\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.16988e12 | 0.224812 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.53844e13 | 0.916390 | 0.458195 | − | 0.888852i | \(-0.348496\pi\) | ||||
0.458195 | + | 0.888852i | \(0.348496\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.63859e11i | 0.00586088i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 3.23029e13i | − 1.13427i | −0.823625 | − | 0.567135i | \(-0.808052\pi\) | ||||
0.823625 | − | 0.567135i | \(-0.191948\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.85791e12 | −0.0994321 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.54659e13 | 2.25686 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.78014e13i | 0.608083i | 0.952659 | + | 0.304041i | \(0.0983361\pi\) | ||||
−0.952659 | + | 0.304041i | \(0.901664\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.81771e12i | 0.195130i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.60447e11 | 0.0153037 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.38638e12 | 0.111533 | 0.0557666 | − | 0.998444i | \(-0.482240\pi\) | ||||
0.0557666 | + | 0.998444i | \(0.482240\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.27345e13i | 3.02670i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.17766e13i | − 1.33908i | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
0.742778 | − | 0.669538i | \(-0.233508\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.15063e14 | −3.65503 |
(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 | 400.10.c.q.49.6 | 6 | ||
4.3 | odd | 2 | 25.10.b.c.24.6 | 6 | |||
5.2 | odd | 4 | 400.10.a.y.1.3 | 3 | |||
5.3 | odd | 4 | 400.10.a.u.1.1 | 3 | |||
5.4 | even | 2 | inner | 400.10.c.q.49.1 | 6 | ||
12.11 | even | 2 | 225.10.b.m.199.1 | 6 | |||
20.3 | even | 4 | 25.10.a.d.1.3 | yes | 3 | ||
20.7 | even | 4 | 25.10.a.c.1.1 | ✓ | 3 | ||
20.19 | odd | 2 | 25.10.b.c.24.1 | 6 | |||
60.23 | odd | 4 | 225.10.a.m.1.1 | 3 | |||
60.47 | odd | 4 | 225.10.a.p.1.3 | 3 | |||
60.59 | even | 2 | 225.10.b.m.199.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.1 | ✓ | 3 | 20.7 | even | 4 | ||
25.10.a.d.1.3 | yes | 3 | 20.3 | even | 4 | ||
25.10.b.c.24.1 | 6 | 20.19 | odd | 2 | |||
25.10.b.c.24.6 | 6 | 4.3 | odd | 2 | |||
225.10.a.m.1.1 | 3 | 60.23 | odd | 4 | |||
225.10.a.p.1.3 | 3 | 60.47 | odd | 4 | |||
225.10.b.m.199.1 | 6 | 12.11 | even | 2 | |||
225.10.b.m.199.6 | 6 | 60.59 | even | 2 | |||
400.10.a.u.1.1 | 3 | 5.3 | odd | 4 | |||
400.10.a.y.1.3 | 3 | 5.2 | odd | 4 | |||
400.10.c.q.49.1 | 6 | 5.4 | even | 2 | inner | ||
400.10.c.q.49.6 | 6 | 1.1 | even | 1 | trivial |