Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,10,Mod(199,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("225.199");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.b (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: | \(115.883063137\) |
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: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-27.7229i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.199 |
Dual form | 225.10.b.m.199.6 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 31.7828i | − 1.40461i | −0.711875 | − | 0.702306i | \(-0.752154\pi\) | ||||
0.711875 | − | 0.702306i | \(-0.247846\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −498.143 | −0.972936 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 637.237i | − 0.100314i | −0.998741 | − | 0.0501568i | \(-0.984028\pi\) | ||||
0.998741 | − | 0.0501568i | \(-0.0159721\pi\) | |||||||
\(8\) | − 440.406i | − 0.0380144i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(0.885123\pi\) | |||||||
\(14\) | −20253.2 | −0.140902 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −269047. | −1.02633 | ||||||||
\(17\) | 67319.3i | 0.195488i | 0.995212 | + | 0.0977439i | \(0.0311626\pi\) | ||||
−0.995212 | + | 0.0977439i | \(0.968837\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −341136. | −0.600532 | −0.300266 | − | 0.953855i | \(-0.597075\pi\) | ||||
−0.300266 | + | 0.953855i | \(0.597075\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 1.55871e6i | − 1.41861i | ||||||||
\(23\) | 134355.i | 0.100110i | 0.998746 | + | 0.0500550i | \(0.0159397\pi\) | ||||
−0.998746 | + | 0.0500550i | \(0.984060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.31144e6 | 0.991978 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 317435.i | 0.0975988i | ||||||||
\(29\) | 4.45784e6 | 1.17040 | 0.585199 | − | 0.810890i | \(-0.301016\pi\) | ||||
0.585199 | + | 0.810890i | \(0.301016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 456520. | 0.0887834 | 0.0443917 | − | 0.999014i | \(-0.485865\pi\) | ||||
0.0443917 | + | 0.999014i | \(0.485865\pi\) | |||||||
\(32\) | 8.32555e6i | 1.40358i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.13959e6 | 0.274585 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.30516e7i | − 1.14487i | −0.819951 | − | 0.572433i | \(-0.805999\pi\) | ||||
0.819951 | − | 0.572433i | \(-0.194001\pi\) | |||||||
\(38\) | 1.08422e7i | 0.843515i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.56667e7 | 1.41854 | 0.709272 | − | 0.704935i | \(-0.249024\pi\) | ||||
0.709272 | + | 0.704935i | \(0.249024\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.42710e6i | 0.152869i | 0.997075 | + | 0.0764344i | \(0.0243536\pi\) | ||||
−0.997075 | + | 0.0764344i | \(0.975646\pi\) | |||||||
\(44\) | −2.44302e7 | −0.982631 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.27016e6 | 0.140616 | ||||||||
\(47\) | − 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 3.62281e7i | − 0.687116i | ||||||||
\(53\) | 8.42456e7i | 1.46658i | 0.679916 | + | 0.733290i | \(0.262016\pi\) | ||||
−0.679916 | + | 0.733290i | \(0.737984\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −280643. | −0.00381337 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 1.41682e8i | − 1.64396i | ||||||||
\(59\) | −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 | \(0.192249\pi\) | |||||||
\(62\) | − 1.45094e7i | − 0.124706i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.26857e8 | 0.945159 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.94299e7i | − 0.420930i | −0.977601 | − | 0.210465i | \(-0.932502\pi\) | ||||
0.977601 | − | 0.210465i | \(-0.0674978\pi\) | |||||||
\(68\) | − 3.35347e7i | − 0.190197i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.214248\pi\) | |||||||
\(74\) | −4.14815e8 | −1.60809 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.69935e8 | 0.584279 | ||||||||
\(77\) | − 3.12518e7i | − 0.101313i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.72244e8 | −1.07524 | −0.537621 | − | 0.843187i | \(-0.680677\pi\) | ||||
−0.537621 | + | 0.843187i | \(0.680677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 8.15758e8i | − 1.99250i | ||||||||
\(83\) | − 4.50079e8i | − 1.04097i | −0.853872 | − | 0.520484i | \(-0.825752\pi\) | ||||
0.853872 | − | 0.520484i | \(-0.174248\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.08923e8 | 0.214721 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 2.15987e7i | − 0.0383932i | ||||||||
\(89\) | 5.82741e7 | 0.0984511 | 0.0492255 | − | 0.998788i | \(-0.484325\pi\) | ||||
0.0492255 | + | 0.998788i | \(0.484325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.63438e7 | 0.0708444 | ||||||||
\(92\) | − 6.69279e7i | − 0.0974006i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.08002e9 | −1.42678 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 7.85850e8i | − 0.901295i | −0.892702 | − | 0.450647i | \(-0.851193\pi\) | ||||
0.892702 | − | 0.450647i | \(-0.148807\pi\) | |||||||
\(98\) | − 1.26964e9i | − 1.39048i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.60460e8 | 0.153433 | 0.0767167 | − | 0.997053i | \(-0.475556\pi\) | ||||
0.0767167 | + | 0.997053i | \(0.475556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.39454e9i | − 1.22085i | −0.792074 | − | 0.610425i | \(-0.790999\pi\) | ||||
0.792074 | − | 0.610425i | \(-0.209001\pi\) | |||||||
\(104\) | 3.20291e7 | 0.0268469 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.67756e9 | 2.05998 | ||||||||
\(107\) | − 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.71447e8i | 0.102955i | ||||||||
\(113\) | 1.81056e9i | 1.04463i | 0.852754 | + | 0.522313i | \(0.174931\pi\) | ||||
−0.852754 | + | 0.522313i | \(0.825069\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.22064e9 | −1.13872 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.37213e9i | 1.12634i | ||||||||
\(119\) | 4.28984e7 | 0.0196101 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.72275e7 | 0.0200291 | ||||||||
\(122\) | − 5.65786e9i | − 2.31224i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.27412e8 | −0.0863806 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.06491e9i | 1.04545i | 0.852503 | + | 0.522723i | \(0.175084\pi\) | ||||
−0.852503 | + | 0.522723i | \(0.824916\pi\) | |||||||
\(128\) | 2.30815e8i | 0.0760010i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | −2.20667e9 | −0.591243 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.96478e7 | 0.00743136 | ||||||||
\(137\) | − 4.62426e9i | − 1.12150i | −0.827984 | − | 0.560751i | \(-0.810512\pi\) | ||||
0.827984 | − | 0.560751i | \(-0.189488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.57140e8 | −0.0584255 | −0.0292128 | − | 0.999573i | \(-0.509300\pi\) | ||||
−0.0292128 | + | 0.999573i | \(0.509300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 6.60637e9i | − 1.36353i | ||||||||
\(143\) | 3.56668e9i | 0.713267i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.61479e9 | −1.75127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.50155e9i | 1.11388i | ||||||||
\(149\) | 3.14809e9 | 0.523250 | 0.261625 | − | 0.965170i | \(-0.415742\pi\) | ||||
0.261625 | + | 0.965170i | \(0.415742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.02772e10 | −1.60871 | −0.804356 | − | 0.594147i | \(-0.797490\pi\) | ||||
−0.804356 | + | 0.594147i | \(0.797490\pi\) | |||||||
\(152\) | 1.50238e8i | 0.0228289i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.93267e8 | −0.142306 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.25077e9i | − 0.427009i | −0.976942 | − | 0.213505i | \(-0.931512\pi\) | ||||
0.976942 | − | 0.213505i | \(-0.0684878\pi\) | |||||||
\(158\) | 1.18309e10i | 1.51030i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.56158e7 | 0.0100424 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.40049e9i | 0.377309i | 0.982043 | + | 0.188655i | \(0.0604127\pi\) | ||||
−0.982043 | + | 0.188655i | \(0.939587\pi\) | |||||||
\(164\) | −1.27857e10 | −1.38015 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.43047e10 | −1.46216 | ||||||||
\(167\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 1.70719e9i | − 0.148732i | ||||||||
\(173\) | − 6.58861e9i | − 0.559224i | −0.960113 | − | 0.279612i | \(-0.909794\pi\) | ||||
0.960113 | − | 0.279612i | \(-0.0902059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.31947e10 | −1.03656 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 1.85211e9i | − 0.138286i | ||||||||
\(179\) | −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 | \(0.856440\pi\) | |||||||
\(182\) | − 1.47293e9i | − 0.0995090i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.91706e7 | 0.00380562 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.30151e9i | 0.197436i | ||||||||
\(188\) | 1.69276e10i | 0.988292i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(0.881408\pi\) | |||||||
\(194\) | −2.49765e10 | −1.26597 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.98996e10 | −0.963146 | ||||||||
\(197\) | − 2.57285e10i | − 1.21707i | −0.793526 | − | 0.608536i | \(-0.791757\pi\) | ||||
0.793526 | − | 0.608536i | \(-0.208243\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.94367e10 | 1.33061 | 0.665303 | − | 0.746573i | \(-0.268302\pi\) | ||||
0.665303 | + | 0.746573i | \(0.268302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 5.09985e9i | − 0.215515i | ||||||||
\(203\) | − 2.84070e9i | − 0.117407i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.43222e10 | −1.71482 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 1.95667e10i | − 0.724825i | ||||||||
\(209\) | −1.67302e10 | −0.606516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.17275e10 | 0.407319 | 0.203659 | − | 0.979042i | \(-0.434716\pi\) | ||||
0.203659 | + | 0.979042i | \(0.434716\pi\) | |||||||
\(212\) | − 4.19664e10i | − 1.42689i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.97283e10 | −1.62084 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.90911e8i | − 0.00890619i | ||||||||
\(218\) | 3.96341e10i | 1.18854i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.89588e9 | −0.138059 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.58340e10i | 0.699550i | 0.936834 | + | 0.349775i | \(0.113742\pi\) | ||||
−0.936834 | + | 0.349775i | \(0.886258\pi\) | |||||||
\(224\) | 5.30535e9 | 0.140799 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.75447e10 | 1.46729 | ||||||||
\(227\) | − 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 1.96326e9i | − 0.0444920i | ||||||||
\(233\) | − 3.17197e10i | − 0.705062i | −0.935800 | − | 0.352531i | \(-0.885321\pi\) | ||||
0.935800 | − | 0.352531i | \(-0.114679\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.71793e10 | 0.780185 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 1.36343e9i | − 0.0275446i | ||||||||
\(239\) | 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 | \(0.564512\pi\) | |||||||
\(242\) | − 1.50102e9i | − 0.0281331i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.86778e10 | −1.60162 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.48095e10i | − 0.424113i | ||||||||
\(248\) | − 2.01054e8i | − 0.00337505i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(254\) | 9.74114e10 | 1.46845 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.22868e10 | 1.05191 | ||||||||
\(257\) | − 3.30815e10i | − 0.473027i | −0.971628 | − | 0.236514i | \(-0.923995\pi\) | ||||
0.971628 | − | 0.236514i | \(-0.0760048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.31695e9 | −0.114846 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 5.83240e10i | − 0.764701i | ||||||||
\(263\) | − 6.05028e10i | − 0.779784i | −0.920861 | − | 0.389892i | \(-0.872512\pi\) | ||||
0.920861 | − | 0.389892i | \(-0.127488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.90908e9 | 0.0846161 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.45860e10i | 0.409538i | ||||||||
\(269\) | 2.61933e10 | 0.305004 | 0.152502 | − | 0.988303i | \(-0.451267\pi\) | ||||
0.152502 | + | 0.988303i | \(0.451267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.42857e10 | 0.611398 | 0.305699 | − | 0.952128i | \(-0.401110\pi\) | ||||
0.305699 | + | 0.952128i | \(0.401110\pi\) | |||||||
\(272\) | − 1.81120e10i | − 0.200635i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.46972e11 | −1.57528 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.76561e11i | − 1.80192i | −0.433900 | − | 0.900961i | \(-0.642863\pi\) | ||||
0.433900 | − | 0.900961i | \(-0.357137\pi\) | |||||||
\(278\) | 8.17261e9i | 0.0820652i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.91126e9 | 0.0756950 | 0.0378475 | − | 0.999284i | \(-0.487950\pi\) | ||||
0.0378475 | + | 0.999284i | \(0.487950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.34806e11i | − 1.24931i | −0.780899 | − | 0.624657i | \(-0.785239\pi\) | ||||
0.780899 | − | 0.624657i | \(-0.214761\pi\) | |||||||
\(284\) | −1.03544e11 | −0.944480 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.13359e11 | 1.00186 | ||||||||
\(287\) | − 1.63558e10i | − 0.142299i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.14056e11 | 0.961785 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.50696e11i | 1.21305i | ||||||||
\(293\) | − 1.02784e11i | − 0.814741i | −0.913263 | − | 0.407370i | \(-0.866446\pi\) | ||||
0.913263 | − | 0.407370i | \(-0.133554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.74799e9 | −0.0435215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 1.00055e11i | − 0.734964i | ||||||||
\(299\) | −9.77110e9 | −0.0707006 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18388e9 | 0.0153348 | ||||||||
\(302\) | 3.26638e11i | 2.25962i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.17815e10 | 0.616345 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.61472e11i | 1.67998i | 0.542606 | + | 0.839988i | \(0.317438\pi\) | ||||
−0.542606 | + | 0.839988i | \(0.682562\pi\) | |||||||
\(308\) | 1.55679e10i | 0.0985713i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.130910\pi\) | |||||||
\(314\) | −1.03318e11 | −0.599783 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.85431e11 | 1.04614 | ||||||||
\(317\) | − 9.06853e10i | − 0.504394i | −0.967676 | − | 0.252197i | \(-0.918847\pi\) | ||||
0.967676 | − | 0.252197i | \(-0.0811531\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.18624e11 | 1.18206 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 2.72111e9i | − 0.0141057i | ||||||||
\(323\) | − 2.29650e10i | − 0.117397i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.08077e11 | 0.529973 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 1.13038e10i | − 0.0539251i | ||||||||
\(329\) | −2.16542e10 | −0.101897 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.45169e11 | −1.58054 | −0.790271 | − | 0.612758i | \(-0.790060\pi\) | ||||
−0.790271 | + | 0.612758i | \(0.790060\pi\) | |||||||
\(332\) | 2.24204e11i | 1.01279i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.67745e11 | 0.737546 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 8.39418e10i | − 0.354523i | −0.984164 | − | 0.177261i | \(-0.943276\pi\) | ||||
0.984164 | − | 0.177261i | \(-0.0567238\pi\) | |||||||
\(338\) | − 1.68938e11i | − 0.704048i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.23889e10 | 0.0896681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 5.11709e10i | − 0.199618i | ||||||||
\(344\) | 1.50932e9 | 0.00581122 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.09404e11 | −0.785493 | ||||||||
\(347\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.08307e11i | 1.41757i | ||||||||
\(353\) | 2.83875e11i | 0.973064i | 0.873663 | + | 0.486532i | \(0.161738\pi\) | ||||
−0.873663 | + | 0.486532i | \(0.838262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.90288e10 | −0.0957866 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.93034e11i | 1.26461i | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 8.26079e11i | 2.52833i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.30859e10 | −0.0689271 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4.97260e11i | − 1.43082i | −0.698702 | − | 0.715412i | \(-0.746239\pi\) | ||||
0.698702 | − | 0.715412i | \(-0.253761\pi\) | |||||||
\(368\) | − 3.61477e10i | − 0.102746i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | \(0.940398\pi\) | |||||||
\(374\) | 1.04931e11 | 0.277321 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.49656e10 | −0.0386144 | ||||||||
\(377\) | 3.24202e11i | 0.826569i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.65247e11 | 1.40722 | 0.703610 | − | 0.710587i | \(-0.251570\pi\) | ||||
0.703610 | + | 0.710587i | \(0.251570\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.78350e11i | 1.14937i | ||||||||
\(383\) | 5.38864e11i | 1.27963i | 0.768528 | + | 0.639816i | \(0.220989\pi\) | ||||
−0.768528 | + | 0.639816i | \(0.779011\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.46004e11 | 1.02258 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.91466e11i | 0.876902i | ||||||||
\(389\) | 7.67552e11 | 1.69955 | 0.849776 | − | 0.527144i | \(-0.176737\pi\) | ||||
0.849776 | + | 0.527144i | \(0.176737\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.04466e9 | −0.0195703 | ||||||||
\(392\) | − 1.75931e10i | − 0.0376319i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.17722e11 | −1.70951 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.25258e11i | 1.26329i | 0.775259 | + | 0.631643i | \(0.217619\pi\) | ||||
−0.775259 | + | 0.631643i | \(0.782381\pi\) | |||||||
\(398\) | − 9.35578e11i | − 1.86899i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.61329e11 | 0.311574 | 0.155787 | − | 0.987791i | \(-0.450209\pi\) | ||||
0.155787 | + | 0.987791i | \(0.450209\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.32009e10i | 0.0627014i | ||||||||
\(404\) | −7.99320e10 | −0.149281 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.02853e10 | −0.164911 | ||||||||
\(407\) | − 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.94679e11i | 1.18781i | ||||||||
\(413\) | 4.75607e10i | 0.0804403i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.05486e11 | −0.991252 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.31731e11i | 0.851920i | ||||||||
\(419\) | 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 | \(0.516203\pi\) | |||||||
\(422\) | − 3.72732e11i | − 0.572125i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.71023e10 | 0.0557512 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.13439e11i | − 0.165134i | ||||||||
\(428\) | 7.79410e11i | 1.12271i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.183777\pi\) | |||||||
\(434\) | −9.24596e9 | −0.0125097 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.21201e11 | 0.823271 | ||||||||
\(437\) | − 4.58332e10i | − 0.0601193i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.98379e11 | −1.02593 | −0.512966 | − | 0.858409i | \(-0.671453\pi\) | ||||
−0.512966 | + | 0.858409i | \(0.671453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.55604e11i | 0.193920i | ||||||||
\(443\) | − 7.56642e11i | − 0.933413i | −0.884412 | − | 0.466707i | \(-0.845440\pi\) | ||||
0.884412 | − | 0.466707i | \(-0.154560\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.21074e11 | 0.982597 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 8.08381e10i | − 0.0948124i | ||||||||
\(449\) | −6.39419e11 | −0.742467 | −0.371234 | − | 0.928540i | \(-0.621065\pi\) | ||||
−0.371234 | + | 0.928540i | \(0.621065\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.25876e12 | 1.43268 | ||||||||
\(452\) | − 9.01919e11i | − 1.01635i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.97418e11 | −0.880916 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1.34276e12i | − 1.44005i | −0.693949 | − | 0.720024i | \(-0.744131\pi\) | ||||
0.693949 | − | 0.720024i | \(-0.255869\pi\) | |||||||
\(458\) | − 7.32474e11i | − 0.777853i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.47112e11 | −0.357945 | −0.178972 | − | 0.983854i | \(-0.557277\pi\) | ||||
−0.178972 | + | 0.983854i | \(0.557277\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7.20214e11i | − 0.728362i | −0.931328 | − | 0.364181i | \(-0.881349\pi\) | ||||
0.931328 | − | 0.364181i | \(-0.118651\pi\) | |||||||
\(464\) | −1.19937e12 | −1.20122 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.00814e12 | −0.990339 | ||||||||
\(467\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.28701e10i | 0.0304833i | ||||||||
\(473\) | 1.68074e11i | 0.154392i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.13695e10 | −0.0190794 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 7.11279e11i | − 0.623181i | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 6.70052e11i | 0.565454i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.35261e10 | −0.0194870 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.24384e12i | − 1.00204i | −0.865435 | − | 0.501021i | \(-0.832958\pi\) | ||||
0.865435 | − | 0.501021i | \(-0.167042\pi\) | |||||||
\(488\) | − 7.83997e10i | − 0.0625785i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(494\) | −7.88515e11 | −0.595715 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.22825e11 | −0.0911212 | ||||||||
\(497\) | − 1.32456e11i | − 0.0973798i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.75452e10 | −0.0271083 | −0.0135542 | − | 0.999908i | \(-0.504315\pi\) | ||||
−0.0135542 | + | 0.999908i | \(0.504315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 2.53153e12i | − 1.77916i | ||||||||
\(503\) | − 2.86189e11i | − 0.199341i | −0.995020 | − | 0.0996707i | \(-0.968221\pi\) | ||||
0.995020 | − | 0.0996707i | \(-0.0317789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.09420e11 | 0.142017 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 1.52677e12i | − 1.01715i | ||||||||
\(509\) | −1.48505e12 | −0.980646 | −0.490323 | − | 0.871541i | \(-0.663121\pi\) | ||||
−0.490323 | + | 0.871541i | \(0.663121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.92774e11 | −0.125071 | ||||||||
\(512\) | − 2.17930e12i | − 1.40153i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.05142e12 | −0.664420 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.66654e12i | − 1.02590i | ||||||||
\(518\) | 2.64336e11i | 0.161314i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.77521e12 | 1.05556 | 0.527778 | − | 0.849383i | \(-0.323025\pi\) | ||||
0.527778 | + | 0.849383i | \(0.323025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.20614e12i | 0.704922i | 0.935826 | + | 0.352461i | \(0.114655\pi\) | ||||
−0.935826 | + | 0.352461i | \(0.885345\pi\) | |||||||
\(524\) | −9.14135e11 | −0.529687 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.92294e12 | −1.09529 | ||||||||
\(527\) | 3.07326e10i | 0.0173561i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.78310e12 | 0.989978 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 1.08289e11i | − 0.0586112i | ||||||||
\(533\) | 1.86664e12i | 1.00182i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.05773e10 | −0.0160014 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 8.32495e11i | − 0.428412i | ||||||||
\(539\) | 1.95913e12 | 0.999802 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.24195e12 | 1.62711 | 0.813557 | − | 0.581485i | \(-0.197528\pi\) | ||||
0.813557 | + | 0.581485i | \(0.197528\pi\) | |||||||
\(542\) | − 1.72535e12i | − 0.858777i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.60471e11 | −0.274383 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9.33463e11i | − 0.445814i | −0.974840 | − | 0.222907i | \(-0.928445\pi\) | ||||
0.974840 | − | 0.222907i | \(-0.0715547\pi\) | |||||||
\(548\) | 2.30355e12i | 1.09115i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.52073e12 | −0.702861 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.37208e11i | 0.107861i | ||||||||
\(554\) | −5.61160e12 | −2.53100 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.28092e11 | 0.0568443 | ||||||||
\(557\) | − 1.31760e12i | − 0.580012i | −0.957025 | − | 0.290006i | \(-0.906343\pi\) | ||||
0.957025 | − | 0.290006i | \(-0.0936572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.49240e11 | −0.107960 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 2.51442e11i | − 0.106322i | ||||||||
\(563\) | 4.33363e12i | 1.81788i | 0.416931 | + | 0.908938i | \(0.363106\pi\) | ||||
−0.416931 | + | 0.908938i | \(0.636894\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.28452e12 | −1.75480 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 9.15429e10i | − 0.0369026i | ||||||||
\(569\) | 3.08940e12 | 1.23558 | 0.617788 | − | 0.786345i | \(-0.288029\pi\) | ||||
0.617788 | + | 0.786345i | \(0.288029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.43095e11 | −0.292538 | −0.146269 | − | 0.989245i | \(-0.546726\pi\) | ||||
−0.146269 | + | 0.989245i | \(0.546726\pi\) | |||||||
\(572\) | − 1.77672e12i | − 0.693963i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.19832e11 | −0.199875 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.25852e12i | 0.848269i | 0.905599 | + | 0.424134i | \(0.139422\pi\) | ||||
−0.905599 | + | 0.424134i | \(0.860578\pi\) | |||||||
\(578\) | − 3.62501e12i | − 1.35093i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.86807e11 | −0.104423 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.13162e12i | 1.48119i | ||||||||
\(584\) | −1.33230e11 | −0.0473962 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.26674e12 | −1.14440 | ||||||||
\(587\) | − 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.51148e12i | 1.17501i | ||||||||
\(593\) | 2.01077e12i | 0.667755i | 0.942616 | + | 0.333878i | \(0.108357\pi\) | ||||
−0.942616 | + | 0.333878i | \(0.891643\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.56820e12 | −0.509089 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.10552e11i | 0.0993070i | ||||||||
\(599\) | −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 | \(0.600635\pi\) | |||||||
\(602\) | − 6.94096e10i | − 0.0215395i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.11952e12 | 1.56517 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.11631e12i | 1.23072i | 0.788246 | + | 0.615360i | \(0.210989\pi\) | ||||
−0.788246 | + | 0.615360i | \(0.789011\pi\) | |||||||
\(608\) | − 2.84015e12i | − 0.842897i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | \(0.904395\pi\) | |||||||
\(614\) | 8.31031e12 | 2.35971 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.37635e10 | −0.00385137 | ||||||||
\(617\) | 5.42058e12i | 1.50578i | 0.658145 | + | 0.752891i | \(0.271341\pi\) | ||||
−0.658145 | + | 0.752891i | \(0.728659\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.87240e12 | −1.06016 | −0.530081 | − | 0.847947i | \(-0.677838\pi\) | ||||
−0.530081 | + | 0.847947i | \(0.677838\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 2.62153e12i | − 0.702260i | ||||||||
\(623\) | − 3.71344e10i | − 0.00987599i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.31500e12 | −1.12304 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.61935e12i | 0.415453i | ||||||||
\(629\) | 8.78623e11 | 0.223807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.22937e12 | −0.810933 | −0.405467 | − | 0.914110i | \(-0.632891\pi\) | ||||
−0.405467 | + | 0.914110i | \(0.632891\pi\) | |||||||
\(632\) | 1.63939e11i | 0.0408747i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.88223e12 | −0.708478 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.90523e12i | 0.699123i | ||||||||
\(638\) | − 6.94847e12i | − 1.66034i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.10935e12 | −0.259543 | −0.129771 | − | 0.991544i | \(-0.541424\pi\) | ||||
−0.129771 | + | 0.991544i | \(0.541424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.83993e12i | 0.655177i | 0.944821 | + | 0.327588i | \(0.106236\pi\) | ||||
−0.944821 | + | 0.327588i | \(0.893764\pi\) | |||||||
\(644\) | −4.26489e10 | −0.00977061 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.29892e11 | −0.164897 | ||||||||
\(647\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 1.69393e12i | − 0.367098i | ||||||||
\(653\) | 4.72156e12i | 1.01619i | 0.861300 | + | 0.508097i | \(0.169651\pi\) | ||||
−0.861300 | + | 0.508097i | \(0.830349\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.90554e12 | −1.45590 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.88231e11i | 0.143126i | ||||||||
\(659\) | 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 | \(0.804151\pi\) | |||||||
\(662\) | 1.09704e13i | 2.22005i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.98218e11 | −0.0395718 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.98931e11i | 0.117168i | ||||||||
\(668\) | − 2.62912e12i | − 0.510878i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | \(-0.108286\pi\) | |||||||
\(674\) | −2.66790e12 | −0.497967 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.64783e12 | −0.487675 | ||||||||
\(677\) | − 6.06872e12i | − 1.11032i | −0.831744 | − | 0.555160i | \(-0.812657\pi\) | ||||
0.831744 | − | 0.555160i | \(-0.187343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.00773e11 | −0.0904122 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 7.11581e11i | − 0.125949i | ||||||||
\(683\) | − 9.96514e11i | − 0.175223i | −0.996155 | − | 0.0876113i | \(-0.972077\pi\) | ||||
0.996155 | − | 0.0876113i | \(-0.0279233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.62635e12 | −0.280386 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 9.22050e11i | − 0.156894i | ||||||||
\(689\) | −6.12686e12 | −1.03574 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.02702e13 | 1.71367 | 0.856835 | − | 0.515591i | \(-0.172428\pi\) | ||||
0.856835 | + | 0.515591i | \(0.172428\pi\) | |||||||
\(692\) | 3.28207e12i | 0.544090i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.96299e12 | 0.812130 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.72786e12i | 0.277308i | ||||||||
\(698\) | 2.00823e11i | 0.0320232i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.26127e12 | 1.29216 | 0.646079 | − | 0.763270i | \(-0.276408\pi\) | ||||
0.646079 | + | 0.763270i | \(0.276408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.45236e12i | 0.687529i | ||||||||
\(704\) | 6.22140e12 | 0.954578 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.02234e12 | 1.36678 | ||||||||
\(707\) | − 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 2.56643e10i | − 0.00374256i | ||||||||
\(713\) | 6.13355e10i | 0.00888810i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.16017e12 | 0.875960 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 1.90929e13i | − 2.68110i | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 6.55723e12i | 0.898055i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.29475e13 | 1.75130 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.35040e13i | 1.79290i | 0.443145 | + | 0.896450i | \(0.353863\pi\) | ||||
−0.443145 | + | 0.896450i | \(0.646137\pi\) | |||||||
\(728\) | − 2.04101e10i | − 0.00269311i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | \(0.937747\pi\) | |||||||
\(734\) | −1.58043e13 | −2.00975 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.11858e12 | −0.140513 | ||||||||
\(737\) | − 3.40502e12i | − 0.425124i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.29483e12 | −0.899736 | −0.449868 | − | 0.893095i | \(-0.648529\pi\) | ||||
−0.449868 | + | 0.893095i | \(0.648529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 1.70624e12i | − 0.206644i | ||||||||
\(743\) | 1.18034e13i | 1.42088i | 0.703756 | + | 0.710442i | \(0.251505\pi\) | ||||
−0.703756 | + | 0.710442i | \(0.748495\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.42362e12 | 0.522941 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 1.64463e12i | − 0.192092i | ||||||||
\(749\) | −9.97041e11 | −0.115756 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.20855e13 | 1.38639 | 0.693197 | − | 0.720748i | \(-0.256202\pi\) | ||||
0.693197 | + | 0.720748i | \(0.256202\pi\) | |||||||
\(752\) | 9.14258e12i | 1.04253i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.03040e13 | 1.16101 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.48077e13i | − 1.63891i | −0.573144 | − | 0.819455i | \(-0.694276\pi\) | ||||
0.573144 | − | 0.819455i | \(-0.305724\pi\) | |||||||
\(758\) | − 1.79651e13i | − 1.97660i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.75185e13 | 1.89350 | 0.946749 | − | 0.321972i | \(-0.104346\pi\) | ||||
0.946749 | + | 0.321972i | \(0.104346\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.94656e11i | 0.0848826i | ||||||||
\(764\) | 7.49736e12 | 0.796138 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.71266e13 | 1.79739 | ||||||||
\(767\) | − 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 6.99039e12i | − 0.708311i | ||||||||
\(773\) | 1.05896e13i | 1.06677i | 0.845872 | + | 0.533386i | \(0.179081\pi\) | ||||
−0.845872 | + | 0.533386i | \(0.820919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.46093e11 | −0.0342622 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 2.43949e13i | − 2.38721i | ||||||||
\(779\) | −8.75583e12 | −0.851881 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.01940e13 | 0.980426 | ||||||||
\(782\) | 2.87464e11i | 0.0274887i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.07478e13 | −1.01600 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.50861e12i | − 0.233102i | −0.993185 | − | 0.116551i | \(-0.962816\pi\) | ||||
0.993185 | − | 0.116551i | \(-0.0371839\pi\) | |||||||
\(788\) | 1.28165e13i | 1.18413i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.15376e12 | 0.104790 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.29465e13i | 1.16258i | ||||||||
\(794\) | 1.98724e13 | 1.77443 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.46637e13 | −1.29460 | ||||||||
\(797\) | 1.85822e13i | 1.63131i | 0.578541 | + | 0.815653i | \(0.303622\pi\) | ||||
−0.578541 | + | 0.815653i | \(0.696378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.28760e12 | 0.198573 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 5.12746e12i | − 0.437641i | ||||||||
\(803\) | − 1.48362e13i | − 1.25922i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.05522e12 | 0.0880712 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 7.06675e10i | − 0.00583268i | ||||||||
\(809\) | −4.47333e12 | −0.367166 | −0.183583 | − | 0.983004i | \(-0.558770\pi\) | ||||
−0.183583 | + | 0.983004i | \(0.558770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.49582e12 | −0.283763 | −0.141881 | − | 0.989884i | \(-0.545315\pi\) | ||||
−0.141881 | + | 0.989884i | \(0.545315\pi\) | |||||||
\(812\) | 1.41508e12i | 0.114229i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.03436e13 | −1.62412 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.16911e12i | − 0.0918026i | ||||||||
\(818\) | − 2.30108e13i | − 1.79698i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.84197e12 | 0.525578 | 0.262789 | − | 0.964853i | \(-0.415358\pi\) | ||||
0.262789 | + | 0.964853i | \(0.415358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.11058e12i | 0.616244i | 0.951347 | + | 0.308122i | \(0.0997005\pi\) | ||||
−0.951347 | + | 0.308122i | \(0.900300\pi\) | |||||||
\(824\) | −6.14163e11 | −0.0464099 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.51161e12 | 0.112987 | ||||||||
\(827\) | − 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 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.22584e12i | 0.667499i | ||||||||
\(833\) | 2.68924e12i | 0.193521i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.33403e12 | 0.590102 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 8.90044e12i | − 0.623467i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 2.08468e12i | 0.142934i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.84197e12 | −0.396295 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.00951e10i | − 0.00200919i | ||||||||
\(848\) | − 2.26660e13i | − 1.50520i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | \(0.956416\pi\) | |||||||
\(854\) | −3.60540e12 | −0.231949 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.89073e11 | −0.0438665 | ||||||||
\(857\) | − 7.57740e12i | − 0.479851i | −0.970791 | − | 0.239926i | \(-0.922877\pi\) | ||||
0.970791 | − | 0.239926i | \(-0.0771230\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.41463e13 | −0.886486 | −0.443243 | − | 0.896401i | \(-0.646172\pi\) | ||||
−0.443243 | + | 0.896401i | \(0.646172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.18757e13i | 1.96642i | ||||||||
\(863\) | − 1.52498e13i | − 0.935868i | −0.883763 | − | 0.467934i | \(-0.844998\pi\) | ||||
0.883763 | − | 0.467934i | \(-0.155002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.53780e13 | −1.53330 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.44915e11i | 0.00866515i | ||||||||
\(869\) | −1.82558e13 | −1.08596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.04937e12 | 0.297273 | ||||||||
\(872\) | 5.49201e11i | 0.0321668i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.45671e12 | −0.0844443 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.30350e12i | − 0.188572i | −0.995545 | − | 0.0942858i | \(-0.969943\pi\) | ||||
0.995545 | − | 0.0942858i | \(-0.0300568\pi\) | |||||||
\(878\) | 2.53747e13i | 1.44104i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.14728e13 | −1.76013 | −0.880063 | − | 0.474856i | \(-0.842500\pi\) | ||||
−0.880063 | + | 0.474856i | \(0.842500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.10669e13i | 0.612637i | 0.951929 | + | 0.306318i | \(0.0990973\pi\) | ||||
−0.951929 | + | 0.306318i | \(0.900903\pi\) | |||||||
\(884\) | 2.43885e12 | 0.134323 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.40482e13 | −1.31108 | ||||||||
\(887\) | − 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 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 1.28690e13i | − 0.680618i | ||||||||
\(893\) | 1.15923e13i | 0.610010i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.47084e11 | 0.00762394 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.03225e13i | 1.04288i | ||||||||
\(899\) | 2.03509e12 | 0.103912 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.67136e12 | −0.286699 | ||||||||
\(902\) | − 4.00069e13i | − 2.01236i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.97383e11 | 0.0397108 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.00486e13i | 0.983676i | 0.870687 | + | 0.491838i | \(0.163675\pi\) | ||||
−0.870687 | + | 0.491838i | \(0.836325\pi\) | |||||||
\(908\) | 1.24982e13i | 0.610186i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | −4.26768e13 | −2.02271 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.14803e13 | −0.538797 | ||||||||
\(917\) | − 1.16938e12i | − 0.0546129i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.15926e12 | 0.284845 | 0.142423 | − | 0.989806i | \(-0.454511\pi\) | ||||
0.142423 | + | 0.989806i | \(0.454511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.10322e13i | 0.502774i | ||||||||
\(923\) | 1.51169e13i | 0.685574i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.28904e13 | −1.02307 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.71140e13i | 1.64275i | ||||||||
\(929\) | 2.20000e13 | 0.969061 | 0.484531 | − | 0.874774i | \(-0.338990\pi\) | ||||
0.484531 | + | 0.874774i | \(0.338990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.36275e13 | −0.594489 | ||||||||
\(932\) | 1.58010e13i | 0.685980i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.32508e12 | 0.0999715 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.49274e12i | − 0.105645i | −0.998604 | − | 0.0528225i | \(-0.983178\pi\) | ||||
0.998604 | − | 0.0528225i | \(-0.0168217\pi\) | |||||||
\(938\) | 1.40617e12i | 0.0593098i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.26366e13 | 0.525382 | 0.262691 | − | 0.964880i | \(-0.415390\pi\) | ||||
0.262691 | + | 0.964880i | \(0.415390\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.44844e12i | 0.142010i | ||||||||
\(944\) | 2.00805e13 | 0.823002 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.34185e12 | 0.216861 | ||||||||
\(947\) | − 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 1.88927e10i | 0 0.000745466i | ||||||||
\(953\) | 2.97887e13i | 1.16986i | 0.811084 | + | 0.584929i | \(0.198878\pi\) | ||||
−0.811084 | + | 0.584929i | \(0.801122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.11481e13 | −0.431660 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.52655e12i | 0.0585553i | ||||||||
\(959\) | −2.94675e12 | −0.112502 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.62312e13 | −0.992118 | ||||||||
\(962\) | − 3.01679e13i | − 1.13568i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.05020e13 | 0.391674 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.74473e13i | − 0.641664i | −0.947136 | − | 0.320832i | \(-0.896037\pi\) | ||||
0.947136 | − | 0.320832i | \(-0.103963\pi\) | |||||||
\(968\) | − 2.07993e10i | 0 0.000761394i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(974\) | −3.95328e13 | −1.40748 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.78948e13 | −1.68952 | ||||||||
\(977\) | 3.23029e13i | 1.13427i | 0.823625 | + | 0.567135i | \(0.191948\pi\) | ||||
−0.823625 | + | 0.567135i | \(0.808052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.85791e12 | 0.0994321 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 8.36348e12i | − 0.287002i | ||||||||
\(983\) | 1.78014e13i | 0.608083i | 0.952659 | + | 0.304041i | \(0.0983361\pi\) | ||||
−0.952659 | + | 0.304041i | \(0.901664\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.53796e12 | 0.321373 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.23587e13i | 0.412635i | ||||||||
\(989\) | −4.60447e11 | −0.0153037 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.38638e12 | −0.111533 | −0.0557666 | − | 0.998444i | \(-0.517760\pi\) | ||||
−0.0557666 | + | 0.998444i | \(0.517760\pi\) | |||||||
\(992\) | 3.80078e12i | 0.124615i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.20982e12 | −0.136781 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.17766e13i | − 1.33908i | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
0.742778 | − | 0.669538i | \(-0.233508\pi\) | |||||||
\(998\) | 1.19329e12i | 0.0380767i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.10.b.m.199.1 | 6 | ||
3.2 | odd | 2 | 25.10.b.c.24.6 | 6 | |||
5.2 | odd | 4 | 225.10.a.p.1.3 | 3 | |||
5.3 | odd | 4 | 225.10.a.m.1.1 | 3 | |||
5.4 | even | 2 | inner | 225.10.b.m.199.6 | 6 | ||
12.11 | even | 2 | 400.10.c.q.49.6 | 6 | |||
15.2 | even | 4 | 25.10.a.c.1.1 | ✓ | 3 | ||
15.8 | even | 4 | 25.10.a.d.1.3 | yes | 3 | ||
15.14 | odd | 2 | 25.10.b.c.24.1 | 6 | |||
60.23 | odd | 4 | 400.10.a.u.1.1 | 3 | |||
60.47 | odd | 4 | 400.10.a.y.1.3 | 3 | |||
60.59 | even | 2 | 400.10.c.q.49.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.1 | ✓ | 3 | 15.2 | even | 4 | ||
25.10.a.d.1.3 | yes | 3 | 15.8 | even | 4 | ||
25.10.b.c.24.1 | 6 | 15.14 | odd | 2 | |||
25.10.b.c.24.6 | 6 | 3.2 | odd | 2 | |||
225.10.a.m.1.1 | 3 | 5.3 | odd | 4 | |||
225.10.a.p.1.3 | 3 | 5.2 | odd | 4 | |||
225.10.b.m.199.1 | 6 | 1.1 | even | 1 | trivial | ||
225.10.b.m.199.6 | 6 | 5.4 | even | 2 | inner | ||
400.10.a.u.1.1 | 3 | 60.23 | odd | 4 | |||
400.10.a.y.1.3 | 3 | 60.47 | odd | 4 | |||
400.10.c.q.49.1 | 6 | 60.59 | even | 2 | |||
400.10.c.q.49.6 | 6 | 12.11 | even | 2 |