Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,10,Mod(1,225)]
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, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(115.883063137\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 652x + 4000 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-27.7229\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −31.7828 | −1.40461 | −0.702306 | − | 0.711875i | \(-0.747846\pi\) | ||||
−0.702306 | + | 0.711875i | \(0.747846\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 498.143 | 0.972936 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −637.237 | −0.100314 | −0.0501568 | − | 0.998741i | \(-0.515972\pi\) | ||||
−0.0501568 | + | 0.998741i | \(0.515972\pi\) | |||||||
\(8\) | 440.406 | 0.0380144 | ||||||||
\(9\) | 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 | ||||||||
\(13\) | −72726.2 | −0.706229 | −0.353115 | − | 0.935580i | \(-0.614877\pi\) | ||||
−0.353115 | + | 0.935580i | \(0.614877\pi\) | |||||||
\(14\) | 20253.2 | 0.140902 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −269047. | −1.02633 | ||||||||
\(17\) | 67319.3 | 0.195488 | 0.0977439 | − | 0.995212i | \(-0.468837\pi\) | ||||
0.0977439 | + | 0.995212i | \(0.468837\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 341136. | 0.600532 | 0.300266 | − | 0.953855i | \(-0.402925\pi\) | ||||
0.300266 | + | 0.953855i | \(0.402925\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.55871e6 | −1.41861 | ||||||||
\(23\) | −134355. | −0.100110 | −0.0500550 | − | 0.998746i | \(-0.515940\pi\) | ||||
−0.0500550 | + | 0.998746i | \(0.515940\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.31144e6 | 0.991978 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −317435. | −0.0975988 | ||||||||
\(29\) | −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 | \(-0.485865\pi\) | ||||
0.0443917 | + | 0.999014i | \(0.485865\pi\) | |||||||
\(32\) | 8.32555e6 | 1.40358 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.13959e6 | −0.274585 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.30516e7 | −1.14487 | −0.572433 | − | 0.819951i | \(-0.694001\pi\) | ||||
−0.572433 | + | 0.819951i | \(0.694001\pi\) | |||||||
\(38\) | −1.08422e7 | −0.843515 | ||||||||
\(39\) | 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 | ||||||||
\(43\) | −3.42710e6 | −0.152869 | −0.0764344 | − | 0.997075i | \(-0.524354\pi\) | ||||
−0.0764344 | + | 0.997075i | \(0.524354\pi\) | |||||||
\(44\) | 2.44302e7 | 0.982631 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.27016e6 | 0.140616 | ||||||||
\(47\) | −3.39814e7 | −1.01578 | −0.507891 | − | 0.861421i | \(-0.669575\pi\) | ||||
−0.507891 | + | 0.861421i | \(0.669575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.99475e7 | −0.989937 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.62281e7 | −0.687116 | ||||||||
\(53\) | −8.42456e7 | −1.46658 | −0.733290 | − | 0.679916i | \(-0.762016\pi\) | ||||
−0.733290 | + | 0.679916i | \(0.762016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −280643. | −0.00381337 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.41682e8 | 1.64396 | ||||||||
\(59\) | 7.46358e7 | 0.801887 | 0.400944 | − | 0.916103i | \(-0.368682\pi\) | ||||
0.400944 | + | 0.916103i | \(0.368682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.78017e8 | 1.64618 | 0.823088 | − | 0.567913i | \(-0.192249\pi\) | ||||
0.823088 | + | 0.567913i | \(0.192249\pi\) | |||||||
\(62\) | −1.45094e7 | −0.124706 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.26857e8 | −0.945159 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.94299e7 | −0.420930 | −0.210465 | − | 0.977601i | \(-0.567498\pi\) | ||||
−0.210465 | + | 0.977601i | \(0.567498\pi\) | |||||||
\(68\) | 3.35347e7 | 0.190197 | ||||||||
\(69\) | 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 | ||||||||
\(73\) | 3.02516e8 | 1.24680 | 0.623398 | − | 0.781905i | \(-0.285752\pi\) | ||||
0.623398 | + | 0.781905i | \(0.285752\pi\) | |||||||
\(74\) | 4.14815e8 | 1.60809 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.69935e8 | 0.584279 | ||||||||
\(77\) | −3.12518e7 | −0.101313 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.72244e8 | 1.07524 | 0.537621 | − | 0.843187i | \(-0.319323\pi\) | ||||
0.537621 | + | 0.843187i | \(0.319323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.15758e8 | −1.99250 | ||||||||
\(83\) | 4.50079e8 | 1.04097 | 0.520484 | − | 0.853872i | \(-0.325752\pi\) | ||||
0.520484 | + | 0.853872i | \(0.325752\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.08923e8 | 0.214721 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.15987e7 | 0.0383932 | ||||||||
\(89\) | −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 | ||||||||
\(92\) | −6.69279e7 | −0.0974006 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.08002e9 | 1.42678 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.85850e8 | −0.901295 | −0.450647 | − | 0.892702i | \(-0.648807\pi\) | ||||
−0.450647 | + | 0.892702i | \(0.648807\pi\) | |||||||
\(98\) | 1.26964e9 | 1.39048 | ||||||||
\(99\) | 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 | ||||||||
\(103\) | 1.39454e9 | 1.22085 | 0.610425 | − | 0.792074i | \(-0.290999\pi\) | ||||
0.610425 | + | 0.792074i | \(0.290999\pi\) | |||||||
\(104\) | −3.20291e7 | −0.0268469 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.67756e9 | 2.05998 | ||||||||
\(107\) | −1.56463e9 | −1.15394 | −0.576972 | − | 0.816764i | \(-0.695766\pi\) | ||||
−0.576972 | + | 0.816764i | \(0.695766\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.24703e9 | 0.846172 | 0.423086 | − | 0.906089i | \(-0.360947\pi\) | ||||
0.423086 | + | 0.906089i | \(0.360947\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.71447e8 | 0.102955 | ||||||||
\(113\) | −1.81056e9 | −1.04463 | −0.522313 | − | 0.852754i | \(-0.674931\pi\) | ||||
−0.522313 | + | 0.852754i | \(0.674931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.22064e9 | −1.13872 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.37213e9 | −1.12634 | ||||||||
\(119\) | −4.28984e7 | −0.0196101 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.72275e7 | 0.0200291 | ||||||||
\(122\) | −5.65786e9 | −2.31224 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.27412e8 | 0.0863806 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.06491e9 | 1.04545 | 0.522723 | − | 0.852503i | \(-0.324916\pi\) | ||||
0.522723 | + | 0.852503i | \(0.324916\pi\) | |||||||
\(128\) | −2.30815e8 | −0.0760010 | ||||||||
\(129\) | 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 | ||||||||
\(133\) | −2.17385e8 | −0.0602416 | ||||||||
\(134\) | 2.20667e9 | 0.591243 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.96478e7 | 0.00743136 | ||||||||
\(137\) | −4.62426e9 | −1.12150 | −0.560751 | − | 0.827984i | \(-0.689488\pi\) | ||||
−0.560751 | + | 0.827984i | \(0.689488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.57140e8 | 0.0584255 | 0.0292128 | − | 0.999573i | \(-0.490700\pi\) | ||||
0.0292128 | + | 0.999573i | \(0.490700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.60637e9 | −1.36353 | ||||||||
\(143\) | −3.56668e9 | −0.713267 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.61479e9 | −1.75127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.50155e9 | −1.11388 | ||||||||
\(149\) | −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 | \(-0.797490\pi\) | ||||
−0.804356 | + | 0.594147i | \(0.797490\pi\) | |||||||
\(152\) | 1.50238e8 | 0.0228289 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.93267e8 | 0.142306 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.25077e9 | −0.427009 | −0.213505 | − | 0.976942i | \(-0.568488\pi\) | ||||
−0.213505 | + | 0.976942i | \(0.568488\pi\) | |||||||
\(158\) | −1.18309e10 | −1.51030 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.56158e7 | 0.0100424 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.40049e9 | −0.377309 | −0.188655 | − | 0.982043i | \(-0.560413\pi\) | ||||
−0.188655 | + | 0.982043i | \(0.560413\pi\) | |||||||
\(164\) | 1.27857e10 | 1.38015 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.43047e10 | −1.46216 | ||||||||
\(167\) | 5.27785e9 | 0.525089 | 0.262544 | − | 0.964920i | \(-0.415438\pi\) | ||||
0.262544 | + | 0.964920i | \(0.415438\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.31540e9 | −0.501240 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.70719e9 | −0.148732 | ||||||||
\(173\) | 6.58861e9 | 0.559224 | 0.279612 | − | 0.960113i | \(-0.409794\pi\) | ||||
0.279612 | + | 0.960113i | \(0.409794\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.31947e10 | −1.03656 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.85211e9 | 0.138286 | ||||||||
\(179\) | 1.23663e10 | 0.900326 | 0.450163 | − | 0.892946i | \(-0.351366\pi\) | ||||
0.450163 | + | 0.892946i | \(0.351366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.59914e10 | −1.80002 | −0.900009 | − | 0.435872i | \(-0.856440\pi\) | ||||
−0.900009 | + | 0.435872i | \(0.856440\pi\) | |||||||
\(182\) | −1.47293e9 | −0.0995090 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.91706e7 | −0.00380562 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.30151e9 | 0.197436 | ||||||||
\(188\) | −1.69276e10 | −0.988292 | ||||||||
\(189\) | 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 | ||||||||
\(193\) | −1.40329e10 | −0.728014 | −0.364007 | − | 0.931396i | \(-0.618592\pi\) | ||||
−0.364007 | + | 0.931396i | \(0.618592\pi\) | |||||||
\(194\) | 2.49765e10 | 1.26597 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.98996e10 | −0.963146 | ||||||||
\(197\) | −2.57285e10 | −1.21707 | −0.608536 | − | 0.793526i | \(-0.708243\pi\) | ||||
−0.608536 | + | 0.793526i | \(0.708243\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.94367e10 | −1.33061 | −0.665303 | − | 0.746573i | \(-0.731698\pi\) | ||||
−0.665303 | + | 0.746573i | \(0.731698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.09985e9 | −0.215515 | ||||||||
\(203\) | 2.84070e9 | 0.117407 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.43222e10 | −1.71482 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.95667e10 | 0.724825 | ||||||||
\(209\) | 1.67302e10 | 0.606516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.17275e10 | 0.407319 | 0.203659 | − | 0.979042i | \(-0.434716\pi\) | ||||
0.203659 | + | 0.979042i | \(0.434716\pi\) | |||||||
\(212\) | −4.19664e10 | −1.42689 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.97283e10 | 1.62084 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.90911e8 | −0.00890619 | ||||||||
\(218\) | −3.96341e10 | −1.18854 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.89588e9 | −0.138059 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.58340e10 | −0.699550 | −0.349775 | − | 0.936834i | \(-0.613742\pi\) | ||||
−0.349775 | + | 0.936834i | \(0.613742\pi\) | |||||||
\(224\) | −5.30535e9 | −0.140799 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.75447e10 | 1.46729 | ||||||||
\(227\) | −2.50896e10 | −0.627159 | −0.313580 | − | 0.949562i | \(-0.601528\pi\) | ||||
−0.313580 | + | 0.949562i | \(0.601528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.30463e10 | −0.553785 | −0.276892 | − | 0.960901i | \(-0.589305\pi\) | ||||
−0.276892 | + | 0.960901i | \(0.589305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.96326e9 | −0.0444920 | ||||||||
\(233\) | 3.17197e10 | 0.705062 | 0.352531 | − | 0.935800i | \(-0.385321\pi\) | ||||
0.352531 | + | 0.935800i | \(0.385321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.71793e10 | 0.780185 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.36343e9 | 0.0275446 | ||||||||
\(239\) | −2.23794e10 | −0.443668 | −0.221834 | − | 0.975084i | \(-0.571204\pi\) | ||||
−0.221834 | + | 0.975084i | \(0.571204\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.10823e10 | −0.402569 | −0.201285 | − | 0.979533i | \(-0.564512\pi\) | ||||
−0.201285 | + | 0.979533i | \(0.564512\pi\) | |||||||
\(242\) | −1.50102e9 | −0.0281331 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.86778e10 | 1.60162 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.48095e10 | −0.424113 | ||||||||
\(248\) | 2.01054e8 | 0.00337505 | ||||||||
\(249\) | 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 | ||||||||
\(253\) | −6.58910e9 | −0.101108 | ||||||||
\(254\) | −9.74114e10 | −1.46845 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.22868e10 | 1.05191 | ||||||||
\(257\) | −3.30815e10 | −0.473027 | −0.236514 | − | 0.971628i | \(-0.576005\pi\) | ||||
−0.236514 | + | 0.971628i | \(0.576005\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.31695e9 | 0.114846 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.83240e10 | −0.764701 | ||||||||
\(263\) | 6.05028e10 | 0.779784 | 0.389892 | − | 0.920861i | \(-0.372512\pi\) | ||||
0.389892 | + | 0.920861i | \(0.372512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.90908e9 | 0.0846161 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.45860e10 | −0.409538 | ||||||||
\(269\) | −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 | \(-0.401110\pi\) | ||||
0.305699 | + | 0.952128i | \(0.401110\pi\) | |||||||
\(272\) | −1.81120e10 | −0.200635 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.46972e11 | 1.57528 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.76561e11 | −1.80192 | −0.900961 | − | 0.433900i | \(-0.857137\pi\) | ||||
−0.900961 | + | 0.433900i | \(0.857137\pi\) | |||||||
\(278\) | −8.17261e9 | −0.0820652 | ||||||||
\(279\) | 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 | ||||||||
\(283\) | 1.34806e11 | 1.24931 | 0.624657 | − | 0.780899i | \(-0.285239\pi\) | ||||
0.624657 | + | 0.780899i | \(0.285239\pi\) | |||||||
\(284\) | 1.03544e11 | 0.944480 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.13359e11 | 1.00186 | ||||||||
\(287\) | −1.63558e10 | −0.142299 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.14056e11 | −0.961785 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.50696e11 | 1.21305 | ||||||||
\(293\) | 1.02784e11 | 0.814741 | 0.407370 | − | 0.913263i | \(-0.366446\pi\) | ||||
0.407370 | + | 0.913263i | \(0.366446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.74799e9 | −0.0435215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00055e11 | 0.734964 | ||||||||
\(299\) | 9.77110e9 | 0.0707006 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18388e9 | 0.0153348 | ||||||||
\(302\) | 3.26638e11 | 2.25962 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.17815e10 | −0.616345 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.61472e11 | 1.67998 | 0.839988 | − | 0.542606i | \(-0.182562\pi\) | ||||
0.839988 | + | 0.542606i | \(0.182562\pi\) | |||||||
\(308\) | −1.55679e10 | −0.0985713 | ||||||||
\(309\) | 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 | ||||||||
\(313\) | 1.35766e11 | 0.799540 | 0.399770 | − | 0.916615i | \(-0.369090\pi\) | ||||
0.399770 | + | 0.916615i | \(0.369090\pi\) | |||||||
\(314\) | 1.03318e11 | 0.599783 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.85431e11 | 1.04614 | ||||||||
\(317\) | −9.06853e10 | −0.504394 | −0.252197 | − | 0.967676i | \(-0.581153\pi\) | ||||
−0.252197 | + | 0.967676i | \(0.581153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.18624e11 | −1.18206 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.72111e9 | −0.0141057 | ||||||||
\(323\) | 2.29650e10 | 0.117397 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.08077e11 | 0.529973 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.13038e10 | 0.0539251 | ||||||||
\(329\) | 2.16542e10 | 0.101897 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.45169e11 | −1.58054 | −0.790271 | − | 0.612758i | \(-0.790060\pi\) | ||||
−0.790271 | + | 0.612758i | \(0.790060\pi\) | |||||||
\(332\) | 2.24204e11 | 1.01279 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.67745e11 | −0.737546 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.39418e10 | −0.354523 | −0.177261 | − | 0.984164i | \(-0.556724\pi\) | ||||
−0.177261 | + | 0.984164i | \(0.556724\pi\) | |||||||
\(338\) | 1.68938e11 | 0.704048 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.23889e10 | 0.0896681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.11709e10 | 0.199618 | ||||||||
\(344\) | −1.50932e9 | −0.00581122 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.09404e11 | −0.785493 | ||||||||
\(347\) | 1.56153e11 | 0.578188 | 0.289094 | − | 0.957301i | \(-0.406646\pi\) | ||||
0.289094 | + | 0.957301i | \(0.406646\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.31862e9 | 0.0227986 | 0.0113993 | − | 0.999935i | \(-0.496371\pi\) | ||||
0.0113993 | + | 0.999935i | \(0.496371\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.08307e11 | 1.41757 | ||||||||
\(353\) | −2.83875e11 | −0.973064 | −0.486532 | − | 0.873663i | \(-0.661738\pi\) | ||||
−0.486532 | + | 0.873663i | \(0.661738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.90288e10 | −0.0957866 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.93034e11 | −1.26461 | ||||||||
\(359\) | −6.00733e11 | −1.90878 | −0.954391 | − | 0.298558i | \(-0.903494\pi\) | ||||
−0.954391 | + | 0.298558i | \(0.903494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.06314e11 | −0.639361 | ||||||||
\(362\) | 8.26079e11 | 2.52833 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.30859e10 | 0.0689271 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.97260e11 | −1.43082 | −0.715412 | − | 0.698702i | \(-0.753761\pi\) | ||||
−0.715412 | + | 0.698702i | \(0.753761\pi\) | |||||||
\(368\) | 3.61477e10 | 0.102746 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.36845e10 | 0.147118 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.39183e11 | −0.372303 | −0.186151 | − | 0.982521i | \(-0.559602\pi\) | ||||
−0.186151 | + | 0.982521i | \(0.559602\pi\) | |||||||
\(374\) | −1.04931e11 | −0.277321 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.49656e10 | −0.0386144 | ||||||||
\(377\) | 3.24202e11 | 0.826569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.65247e11 | −1.40722 | −0.703610 | − | 0.710587i | \(-0.748430\pi\) | ||||
−0.703610 | + | 0.710587i | \(0.748430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.78350e11 | 1.14937 | ||||||||
\(383\) | −5.38864e11 | −1.27963 | −0.639816 | − | 0.768528i | \(-0.720989\pi\) | ||||
−0.639816 | + | 0.768528i | \(0.720989\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.46004e11 | 1.02258 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.91466e11 | −0.876902 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | −1.75931e10 | −0.0376319 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.17722e11 | 1.70951 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.25258e11 | 1.26329 | 0.631643 | − | 0.775259i | \(-0.282381\pi\) | ||||
0.631643 | + | 0.775259i | \(0.282381\pi\) | |||||||
\(398\) | 9.35578e11 | 1.86899 | ||||||||
\(399\) | 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 | ||||||||
\(403\) | −3.32009e10 | −0.0627014 | ||||||||
\(404\) | 7.99320e10 | 0.149281 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.02853e10 | −0.164911 | ||||||||
\(407\) | −6.40083e11 | −1.15628 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.24004e11 | −1.27934 | −0.639670 | − | 0.768649i | \(-0.720929\pi\) | ||||
−0.639670 | + | 0.768649i | \(0.720929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.94679e11 | 1.18781 | ||||||||
\(413\) | −4.75607e10 | −0.0804403 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.05486e11 | −0.991252 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.31731e11 | −0.851920 | ||||||||
\(419\) | −2.80040e11 | −0.443871 | −0.221936 | − | 0.975061i | \(-0.571237\pi\) | ||||
−0.221936 | + | 0.975061i | \(0.571237\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.55915e10 | −0.101760 | −0.0508801 | − | 0.998705i | \(-0.516203\pi\) | ||||
−0.0508801 | + | 0.998705i | \(0.516203\pi\) | |||||||
\(422\) | −3.72732e11 | −0.572125 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.71023e10 | −0.0557512 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.13439e11 | −0.165134 | ||||||||
\(428\) | −7.79410e11 | −1.12271 | ||||||||
\(429\) | 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 | ||||||||
\(433\) | 7.98482e11 | 1.09162 | 0.545808 | − | 0.837910i | \(-0.316223\pi\) | ||||
0.545808 | + | 0.837910i | \(0.316223\pi\) | |||||||
\(434\) | 9.24596e9 | 0.0125097 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.21201e11 | 0.823271 | ||||||||
\(437\) | −4.58332e10 | −0.0601193 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.98379e11 | 1.02593 | 0.512966 | − | 0.858409i | \(-0.328547\pi\) | ||||
0.512966 | + | 0.858409i | \(0.328547\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.55604e11 | 0.193920 | ||||||||
\(443\) | 7.56642e11 | 0.933413 | 0.466707 | − | 0.884412i | \(-0.345440\pi\) | ||||
0.466707 | + | 0.884412i | \(0.345440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.21074e11 | 0.982597 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.08381e10 | 0.0948124 | ||||||||
\(449\) | 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 | ||||||||
\(452\) | −9.01919e11 | −1.01635 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.97418e11 | 0.880916 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.34276e12 | −1.44005 | −0.720024 | − | 0.693949i | \(-0.755869\pi\) | ||||
−0.720024 | + | 0.693949i | \(0.755869\pi\) | |||||||
\(458\) | 7.32474e11 | 0.777853 | ||||||||
\(459\) | 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 | ||||||||
\(463\) | 7.20214e11 | 0.728362 | 0.364181 | − | 0.931328i | \(-0.381349\pi\) | ||||
0.364181 | + | 0.931328i | \(0.381349\pi\) | |||||||
\(464\) | 1.19937e12 | 1.20122 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.00814e12 | −0.990339 | ||||||||
\(467\) | 7.31553e10 | 0.0711737 | 0.0355869 | − | 0.999367i | \(-0.488670\pi\) | ||||
0.0355869 | + | 0.999367i | \(0.488670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.42433e10 | 0.0422250 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.28701e10 | 0.0304833 | ||||||||
\(473\) | −1.68074e11 | −0.154392 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.13695e10 | −0.0190794 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.11279e11 | 0.623181 | ||||||||
\(479\) | 4.80307e10 | 0.0416878 | 0.0208439 | − | 0.999783i | \(-0.493365\pi\) | ||||
0.0208439 | + | 0.999783i | \(0.493365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.49191e11 | 0.808539 | ||||||||
\(482\) | 6.70052e11 | 0.565454 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.35261e10 | 0.0194870 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.24384e12 | −1.00204 | −0.501021 | − | 0.865435i | \(-0.667042\pi\) | ||||
−0.501021 | + | 0.865435i | \(0.667042\pi\) | |||||||
\(488\) | 7.83997e10 | 0.0625785 | ||||||||
\(489\) | 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 | ||||||||
\(493\) | −3.00099e11 | −0.228798 | ||||||||
\(494\) | 7.88515e11 | 0.595715 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.22825e11 | −0.0911212 | ||||||||
\(497\) | −1.32456e11 | −0.0973798 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.75452e10 | 0.0271083 | 0.0135542 | − | 0.999908i | \(-0.495685\pi\) | ||||
0.0135542 | + | 0.999908i | \(0.495685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.53153e12 | −1.77916 | ||||||||
\(503\) | 2.86189e11 | 0.199341 | 0.0996707 | − | 0.995020i | \(-0.468221\pi\) | ||||
0.0996707 | + | 0.995020i | \(0.468221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.09420e11 | 0.142017 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.52677e12 | 1.01715 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | −2.17930e12 | −1.40153 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.05142e12 | 0.664420 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.66654e12 | −1.02590 | ||||||||
\(518\) | −2.64336e11 | −0.161314 | ||||||||
\(519\) | 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 | ||||||||
\(523\) | −1.20614e12 | −0.704922 | −0.352461 | − | 0.935826i | \(-0.614655\pi\) | ||||
−0.352461 | + | 0.935826i | \(0.614655\pi\) | |||||||
\(524\) | 9.14135e11 | 0.529687 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.92294e12 | −1.09529 | ||||||||
\(527\) | 3.07326e10 | 0.0173561 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.78310e12 | −0.989978 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.08289e11 | −0.0586112 | ||||||||
\(533\) | −1.86664e12 | −1.00182 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.05773e10 | −0.0160014 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.32495e11 | 0.428412 | ||||||||
\(539\) | −1.95913e12 | −0.999802 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.24195e12 | 1.62711 | 0.813557 | − | 0.581485i | \(-0.197528\pi\) | ||||
0.813557 | + | 0.581485i | \(0.197528\pi\) | |||||||
\(542\) | −1.72535e12 | −0.858777 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.60471e11 | 0.274383 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.33463e11 | −0.445814 | −0.222907 | − | 0.974840i | \(-0.571555\pi\) | ||||
−0.222907 | + | 0.974840i | \(0.571555\pi\) | |||||||
\(548\) | −2.30355e12 | −1.09115 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.52073e12 | −0.702861 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.37208e11 | −0.107861 | ||||||||
\(554\) | 5.61160e12 | 2.53100 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.28092e11 | 0.0568443 | ||||||||
\(557\) | −1.31760e12 | −0.580012 | −0.290006 | − | 0.957025i | \(-0.593657\pi\) | ||||
−0.290006 | + | 0.957025i | \(0.593657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.49240e11 | 0.107960 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.51442e11 | −0.106322 | ||||||||
\(563\) | −4.33363e12 | −1.81788 | −0.908938 | − | 0.416931i | \(-0.863106\pi\) | ||||
−0.908938 | + | 0.416931i | \(0.863106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.28452e12 | −1.75480 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.15429e10 | 0.0369026 | ||||||||
\(569\) | −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 | \(-0.546726\pi\) | ||||
−0.146269 | + | 0.989245i | \(0.546726\pi\) | |||||||
\(572\) | −1.77672e12 | −0.693963 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.19832e11 | 0.199875 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.25852e12 | 0.848269 | 0.424134 | − | 0.905599i | \(-0.360578\pi\) | ||||
0.424134 | + | 0.905599i | \(0.360578\pi\) | |||||||
\(578\) | 3.62501e12 | 1.35093 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.86807e11 | −0.104423 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.13162e12 | −1.48119 | ||||||||
\(584\) | 1.33230e11 | 0.0473962 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.26674e12 | −1.14440 | ||||||||
\(587\) | −4.75794e12 | −1.65405 | −0.827023 | − | 0.562169i | \(-0.809967\pi\) | ||||
−0.827023 | + | 0.562169i | \(0.809967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.55735e11 | 0.0533173 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.51148e12 | 1.17501 | ||||||||
\(593\) | −2.01077e12 | −0.667755 | −0.333878 | − | 0.942616i | \(-0.608357\pi\) | ||||
−0.333878 | + | 0.942616i | \(0.608357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.56820e12 | −0.509089 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.10552e11 | −0.0993070 | ||||||||
\(599\) | 3.29427e12 | 1.04554 | 0.522768 | − | 0.852475i | \(-0.324899\pi\) | ||||
0.522768 | + | 0.852475i | \(0.324899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.98887e12 | −0.621830 | −0.310915 | − | 0.950438i | \(-0.600635\pi\) | ||||
−0.310915 | + | 0.950438i | \(0.600635\pi\) | |||||||
\(602\) | −6.94096e10 | −0.0215395 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.11952e12 | −1.56517 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.11631e12 | 1.23072 | 0.615360 | − | 0.788246i | \(-0.289011\pi\) | ||||
0.615360 | + | 0.788246i | \(0.289011\pi\) | |||||||
\(608\) | 2.84015e12 | 0.842897 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.47134e12 | 0.717376 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.06864e12 | −0.591715 | −0.295858 | − | 0.955232i | \(-0.595605\pi\) | ||||
−0.295858 | + | 0.955232i | \(0.595605\pi\) | |||||||
\(614\) | −8.31031e12 | −2.35971 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.37635e10 | −0.00385137 | ||||||||
\(617\) | 5.42058e12 | 1.50578 | 0.752891 | − | 0.658145i | \(-0.228659\pi\) | ||||
0.752891 | + | 0.658145i | \(0.228659\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.87240e12 | 1.06016 | 0.530081 | − | 0.847947i | \(-0.322162\pi\) | ||||
0.530081 | + | 0.847947i | \(0.322162\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.62153e12 | −0.702260 | ||||||||
\(623\) | 3.71344e10 | 0.00987599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.31500e12 | −1.12304 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.61935e12 | −0.415453 | ||||||||
\(629\) | −8.78623e11 | −0.223807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.22937e12 | −0.810933 | −0.405467 | − | 0.914110i | \(-0.632891\pi\) | ||||
−0.405467 | + | 0.914110i | \(0.632891\pi\) | |||||||
\(632\) | 1.63939e11 | 0.0408747 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.88223e12 | 0.708478 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.90523e12 | 0.699123 | ||||||||
\(638\) | 6.94847e12 | 1.66034 | ||||||||
\(639\) | 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 | ||||||||
\(643\) | −2.83993e12 | −0.655177 | −0.327588 | − | 0.944821i | \(-0.606236\pi\) | ||||
−0.327588 | + | 0.944821i | \(0.606236\pi\) | |||||||
\(644\) | 4.26489e10 | 0.00977061 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.29892e11 | −0.164897 | ||||||||
\(647\) | 2.66962e12 | 0.598935 | 0.299467 | − | 0.954107i | \(-0.403191\pi\) | ||||
0.299467 | + | 0.954107i | \(0.403191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.66033e12 | 0.809878 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.69393e12 | −0.367098 | ||||||||
\(653\) | −4.72156e12 | −1.01619 | −0.508097 | − | 0.861300i | \(-0.669651\pi\) | ||||
−0.508097 | + | 0.861300i | \(0.669651\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.90554e12 | −1.45590 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.88231e11 | −0.143126 | ||||||||
\(659\) | −4.01448e12 | −0.829173 | −0.414586 | − | 0.910010i | \(-0.636074\pi\) | ||||
−0.414586 | + | 0.910010i | \(0.636074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.01591e12 | −1.63323 | −0.816613 | − | 0.577186i | \(-0.804151\pi\) | ||||
−0.816613 | + | 0.577186i | \(0.804151\pi\) | |||||||
\(662\) | 1.09704e13 | 2.22005 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.98218e11 | 0.0395718 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.98931e11 | 0.117168 | ||||||||
\(668\) | 2.62912e12 | 0.510878 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.73040e12 | 1.66258 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.55147e12 | 0.667330 | 0.333665 | − | 0.942692i | \(-0.391714\pi\) | ||||
0.333665 | + | 0.942692i | \(0.391714\pi\) | |||||||
\(674\) | 2.66790e12 | 0.497967 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.64783e12 | −0.487675 | ||||||||
\(677\) | −6.06872e12 | −1.11032 | −0.555160 | − | 0.831744i | \(-0.687343\pi\) | ||||
−0.555160 | + | 0.831744i | \(0.687343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00773e11 | 0.0904122 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.11581e11 | −0.125949 | ||||||||
\(683\) | 9.96514e11 | 0.175223 | 0.0876113 | − | 0.996155i | \(-0.472077\pi\) | ||||
0.0876113 | + | 0.996155i | \(0.472077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.62635e12 | −0.280386 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.22050e11 | 0.156894 | ||||||||
\(689\) | 6.12686e12 | 1.03574 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.02702e13 | 1.71367 | 0.856835 | − | 0.515591i | \(-0.172428\pi\) | ||||
0.856835 | + | 0.515591i | \(0.172428\pi\) | |||||||
\(692\) | 3.28207e12 | 0.544090 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.96299e12 | −0.812130 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.72786e12 | 0.277308 | ||||||||
\(698\) | −2.00823e11 | −0.0320232 | ||||||||
\(699\) | 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 | ||||||||
\(703\) | −4.45236e12 | −0.687529 | ||||||||
\(704\) | −6.22140e12 | −0.954578 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.02234e12 | 1.36678 | ||||||||
\(707\) | −1.02251e11 | −0.0153915 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.11428e12 | −1.20598 | −0.602992 | − | 0.797747i | \(-0.706025\pi\) | ||||
−0.602992 | + | 0.797747i | \(0.706025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.56643e10 | −0.00374256 | ||||||||
\(713\) | −6.13355e10 | −0.00888810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.16017e12 | 0.875960 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.90929e13 | 2.68110 | ||||||||
\(719\) | −1.06399e13 | −1.48476 | −0.742380 | − | 0.669979i | \(-0.766303\pi\) | ||||
−0.742380 | + | 0.669979i | \(0.766303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.88651e11 | −0.122468 | ||||||||
\(722\) | 6.55723e12 | 0.898055 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.29475e13 | −1.75130 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.35040e13 | 1.79290 | 0.896450 | − | 0.443145i | \(-0.146137\pi\) | ||||
0.896450 | + | 0.443145i | \(0.146137\pi\) | |||||||
\(728\) | 2.04101e10 | 0.00269311 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.30710e11 | −0.0298840 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.03764e12 | −0.388659 | −0.194329 | − | 0.980936i | \(-0.562253\pi\) | ||||
−0.194329 | + | 0.980936i | \(0.562253\pi\) | |||||||
\(734\) | 1.58043e13 | 2.00975 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.11858e12 | −0.140513 | ||||||||
\(737\) | −3.40502e12 | −0.425124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.29483e12 | 0.899736 | 0.449868 | − | 0.893095i | \(-0.351471\pi\) | ||||
0.449868 | + | 0.893095i | \(0.351471\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.70624e12 | −0.206644 | ||||||||
\(743\) | −1.18034e13 | −1.42088 | −0.710442 | − | 0.703756i | \(-0.751505\pi\) | ||||
−0.710442 | + | 0.703756i | \(0.751505\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.42362e12 | 0.522941 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.64463e12 | 0.192092 | ||||||||
\(749\) | 9.97041e11 | 0.115756 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.20855e13 | 1.38639 | 0.693197 | − | 0.720748i | \(-0.256202\pi\) | ||||
0.693197 | + | 0.720748i | \(0.256202\pi\) | |||||||
\(752\) | 9.14258e12 | 1.04253 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.03040e13 | −1.16101 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.48077e13 | −1.63891 | −0.819455 | − | 0.573144i | \(-0.805724\pi\) | ||||
−0.819455 | + | 0.573144i | \(0.805724\pi\) | |||||||
\(758\) | 1.79651e13 | 1.97660 | ||||||||
\(759\) | 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 | ||||||||
\(763\) | −7.94656e11 | −0.0848826 | ||||||||
\(764\) | −7.49736e12 | −0.796138 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.71266e13 | 1.79739 | ||||||||
\(767\) | −5.42798e12 | −0.566316 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.16729e12 | 0.429720 | 0.214860 | − | 0.976645i | \(-0.431070\pi\) | ||||
0.214860 | + | 0.976645i | \(0.431070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.99039e12 | −0.708311 | ||||||||
\(773\) | −1.05896e13 | −1.06677 | −0.533386 | − | 0.845872i | \(-0.679081\pi\) | ||||
−0.533386 | + | 0.845872i | \(0.679081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.46093e11 | −0.0342622 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.43949e13 | 2.38721 | ||||||||
\(779\) | 8.75583e12 | 0.851881 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.01940e13 | 0.980426 | ||||||||
\(782\) | 2.87464e11 | 0.0274887 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.07478e13 | 1.01600 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.50861e12 | −0.233102 | −0.116551 | − | 0.993185i | \(-0.537184\pi\) | ||||
−0.116551 | + | 0.993185i | \(0.537184\pi\) | |||||||
\(788\) | −1.28165e13 | −1.18413 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.15376e12 | 0.104790 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.29465e13 | −1.16258 | ||||||||
\(794\) | −1.98724e13 | −1.77443 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.46637e13 | −1.29460 | ||||||||
\(797\) | 1.85822e13 | 1.63131 | 0.815653 | − | 0.578541i | \(-0.196378\pi\) | ||||
0.815653 | + | 0.578541i | \(0.196378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.28760e12 | −0.198573 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.12746e12 | −0.437641 | ||||||||
\(803\) | 1.48362e13 | 1.25922 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.05522e12 | 0.0880712 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.06675e10 | 0.00583268 | ||||||||
\(809\) | 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 | \(-0.545315\pi\) | ||||
−0.141881 | + | 0.989884i | \(0.545315\pi\) | |||||||
\(812\) | 1.41508e12 | 0.114229 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.03436e13 | 1.62412 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.16911e12 | −0.0918026 | ||||||||
\(818\) | 2.30108e13 | 1.79698 | ||||||||
\(819\) | 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 | ||||||||
\(823\) | −8.11058e12 | −0.616244 | −0.308122 | − | 0.951347i | \(-0.599700\pi\) | ||||
−0.308122 | + | 0.951347i | \(0.599700\pi\) | |||||||
\(824\) | 6.14163e11 | 0.0464099 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.51161e12 | 0.112987 | ||||||||
\(827\) | −5.06349e10 | −0.00376422 | −0.00188211 | − | 0.999998i | \(-0.500599\pi\) | ||||
−0.00188211 | + | 0.999998i | \(0.500599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.50474e13 | −1.10654 | −0.553269 | − | 0.833002i | \(-0.686620\pi\) | ||||
−0.553269 | + | 0.833002i | \(0.686620\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.22584e12 | 0.667499 | ||||||||
\(833\) | −2.68924e12 | −0.193521 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.33403e12 | 0.590102 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.90044e12 | 0.623467 | ||||||||
\(839\) | −2.68352e13 | −1.86972 | −0.934859 | − | 0.355020i | \(-0.884474\pi\) | ||||
−0.934859 | + | 0.355020i | \(0.884474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.36519e12 | 0.369831 | ||||||||
\(842\) | 2.08468e12 | 0.142934 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.84197e12 | 0.396295 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.00951e10 | −0.00200919 | ||||||||
\(848\) | 2.26660e13 | 1.50520 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.75354e12 | 0.114613 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.22107e12 | −0.272993 | −0.136497 | − | 0.990641i | \(-0.543584\pi\) | ||||
−0.136497 | + | 0.990641i | \(0.543584\pi\) | |||||||
\(854\) | 3.60540e12 | 0.231949 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.89073e11 | −0.0438665 | ||||||||
\(857\) | −7.57740e12 | −0.479851 | −0.239926 | − | 0.970791i | \(-0.577123\pi\) | ||||
−0.239926 | + | 0.970791i | \(0.577123\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.41463e13 | 0.886486 | 0.443243 | − | 0.896401i | \(-0.353828\pi\) | ||||
0.443243 | + | 0.896401i | \(0.353828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.18757e13 | 1.96642 | ||||||||
\(863\) | 1.52498e13 | 0.935868 | 0.467934 | − | 0.883763i | \(-0.344998\pi\) | ||||
0.467934 | + | 0.883763i | \(0.344998\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.53780e13 | −1.53330 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.44915e11 | −0.00866515 | ||||||||
\(869\) | 1.82558e13 | 1.08596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.04937e12 | 0.297273 | ||||||||
\(872\) | 5.49201e11 | 0.0321668 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.45671e12 | 0.0844443 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.30350e12 | −0.188572 | −0.0942858 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942858 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(878\) | −2.53747e13 | −1.44104 | ||||||||
\(879\) | 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 | ||||||||
\(883\) | −1.10669e13 | −0.612637 | −0.306318 | − | 0.951929i | \(-0.599097\pi\) | ||||
−0.306318 | + | 0.951929i | \(0.599097\pi\) | |||||||
\(884\) | −2.43885e12 | −0.134323 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.40482e13 | −1.31108 | ||||||||
\(887\) | −6.92035e12 | −0.375381 | −0.187690 | − | 0.982228i | \(-0.560100\pi\) | ||||
−0.187690 | + | 0.982228i | \(0.560100\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.95308e12 | −0.104872 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.28690e13 | −0.680618 | ||||||||
\(893\) | −1.15923e13 | −0.610010 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.47084e11 | 0.00762394 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.03225e13 | −1.04288 | ||||||||
\(899\) | −2.03509e12 | −0.103912 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.67136e12 | −0.286699 | ||||||||
\(902\) | −4.00069e13 | −2.01236 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.97383e11 | −0.0397108 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.00486e13 | 0.983676 | 0.491838 | − | 0.870687i | \(-0.336325\pi\) | ||||
0.491838 | + | 0.870687i | \(0.336325\pi\) | |||||||
\(908\) | −1.24982e13 | −0.610186 | ||||||||
\(909\) | 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 | ||||||||
\(913\) | 2.20730e13 | 1.05134 | ||||||||
\(914\) | 4.26768e13 | 2.02271 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.14803e13 | −0.538797 | ||||||||
\(917\) | −1.16938e12 | −0.0546129 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.15926e12 | −0.284845 | −0.142423 | − | 0.989806i | \(-0.545489\pi\) | ||||
−0.142423 | + | 0.989806i | \(0.545489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.10322e13 | 0.502774 | ||||||||
\(923\) | −1.51169e13 | −0.685574 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.28904e13 | −1.02307 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.71140e13 | −1.64275 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | 1.58010e13 | 0.685980 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.32508e12 | −0.0999715 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.49274e12 | −0.105645 | −0.0528225 | − | 0.998604i | \(-0.516822\pi\) | ||||
−0.0528225 | + | 0.998604i | \(0.516822\pi\) | |||||||
\(938\) | −1.40617e12 | −0.0593098 | ||||||||
\(939\) | 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 | ||||||||
\(943\) | −3.44844e12 | −0.142010 | ||||||||
\(944\) | −2.00805e13 | −0.823002 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.34185e12 | 0.216861 | ||||||||
\(947\) | −2.05809e13 | −0.831551 | −0.415775 | − | 0.909467i | \(-0.636490\pi\) | ||||
−0.415775 | + | 0.909467i | \(0.636490\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.20008e13 | −0.880524 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.88927e10 | −0.000745466 0 | ||||||||
\(953\) | −2.97887e13 | −1.16986 | −0.584929 | − | 0.811084i | \(-0.698878\pi\) | ||||
−0.584929 | + | 0.811084i | \(0.698878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.11481e13 | −0.431660 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.52655e12 | −0.0585553 | ||||||||
\(959\) | 2.94675e12 | 0.112502 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.62312e13 | −0.992118 | ||||||||
\(962\) | −3.01679e13 | −1.13568 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.05020e13 | −0.391674 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.74473e13 | −0.641664 | −0.320832 | − | 0.947136i | \(-0.603963\pi\) | ||||
−0.320832 | + | 0.947136i | \(0.603963\pi\) | |||||||
\(968\) | 2.07993e10 | 0.000761394 0 | ||||||||
\(969\) | 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 | ||||||||
\(973\) | −1.63859e11 | −0.00586088 | ||||||||
\(974\) | 3.95328e13 | 1.40748 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.78948e13 | −1.68952 | ||||||||
\(977\) | 3.23029e13 | 1.13427 | 0.567135 | − | 0.823625i | \(-0.308052\pi\) | ||||
0.567135 | + | 0.823625i | \(0.308052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.85791e12 | −0.0994321 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.36348e12 | −0.287002 | ||||||||
\(983\) | −1.78014e13 | −0.608083 | −0.304041 | − | 0.952659i | \(-0.598336\pi\) | ||||
−0.304041 | + | 0.952659i | \(0.598336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.53796e12 | 0.321373 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.23587e13 | −0.412635 | ||||||||
\(989\) | 4.60447e11 | 0.0153037 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.38638e12 | −0.111533 | −0.0557666 | − | 0.998444i | \(-0.517760\pi\) | ||||
−0.0557666 | + | 0.998444i | \(0.517760\pi\) | |||||||
\(992\) | 3.80078e12 | 0.124615 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.20982e12 | 0.136781 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.17766e13 | −1.33908 | −0.669538 | − | 0.742778i | \(-0.733508\pi\) | ||||
−0.669538 | + | 0.742778i | \(0.733508\pi\) | |||||||
\(998\) | −1.19329e12 | −0.0380767 | ||||||||
\(999\) | 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.a.m.1.1 | 3 | ||
3.2 | odd | 2 | 25.10.a.d.1.3 | yes | 3 | ||
5.2 | odd | 4 | 225.10.b.m.199.1 | 6 | |||
5.3 | odd | 4 | 225.10.b.m.199.6 | 6 | |||
5.4 | even | 2 | 225.10.a.p.1.3 | 3 | |||
12.11 | even | 2 | 400.10.a.u.1.1 | 3 | |||
15.2 | even | 4 | 25.10.b.c.24.6 | 6 | |||
15.8 | even | 4 | 25.10.b.c.24.1 | 6 | |||
15.14 | odd | 2 | 25.10.a.c.1.1 | ✓ | 3 | ||
60.23 | odd | 4 | 400.10.c.q.49.1 | 6 | |||
60.47 | odd | 4 | 400.10.c.q.49.6 | 6 | |||
60.59 | even | 2 | 400.10.a.y.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.1 | ✓ | 3 | 15.14 | odd | 2 | ||
25.10.a.d.1.3 | yes | 3 | 3.2 | odd | 2 | ||
25.10.b.c.24.1 | 6 | 15.8 | even | 4 | |||
25.10.b.c.24.6 | 6 | 15.2 | even | 4 | |||
225.10.a.m.1.1 | 3 | 1.1 | even | 1 | trivial | ||
225.10.a.p.1.3 | 3 | 5.4 | even | 2 | |||
225.10.b.m.199.1 | 6 | 5.2 | odd | 4 | |||
225.10.b.m.199.6 | 6 | 5.3 | odd | 4 | |||
400.10.a.u.1.1 | 3 | 12.11 | even | 2 | |||
400.10.a.y.1.3 | 3 | 60.59 | even | 2 | |||
400.10.c.q.49.1 | 6 | 60.23 | odd | 4 | |||
400.10.c.q.49.6 | 6 | 60.47 | odd | 4 |