Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 449x^{6} + 50632x^{4} + 69129x^{2} + 18225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(1.01122i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.d.193.7 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 27.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 69.8856i | − 0.250030i | −0.992155 | − | 0.125015i | \(-0.960102\pi\) | ||||
0.992155 | − | 0.125015i | \(-0.0398980\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −860.192 | −0.947877 | −0.473939 | − | 0.880558i | \(-0.657168\pi\) | ||||
−0.473939 | + | 0.880558i | \(0.657168\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 6106.68i | − 1.38335i | −0.722211 | − | 0.691673i | \(-0.756874\pi\) | ||||
0.722211 | − | 0.691673i | \(-0.243126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5338.61i | − 0.673949i | −0.941514 | − | 0.336974i | \(-0.890596\pi\) | ||||
0.941514 | − | 0.336974i | \(-0.109404\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1886.91 | −0.144355 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 38616.6 | 1.90635 | 0.953175 | − | 0.302419i | \(-0.0977941\pi\) | ||||
0.953175 | + | 0.302419i | \(0.0977941\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13583.6i | 0.454335i | 0.973856 | + | 0.227167i | \(0.0729465\pi\) | ||||
−0.973856 | + | 0.227167i | \(0.927054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 23225.2i | 0.547257i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 99683.6 | 1.70835 | 0.854173 | − | 0.519988i | \(-0.174064\pi\) | ||||
0.854173 | + | 0.519988i | \(0.174064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 73241.0 | 0.937485 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 81173.3i | − 0.618045i | −0.951055 | − | 0.309023i | \(-0.899998\pi\) | ||||
0.951055 | − | 0.309023i | \(-0.100002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −153071. | −0.922839 | −0.461419 | − | 0.887182i | \(-0.652660\pi\) | ||||
−0.461419 | + | 0.887182i | \(0.652660\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −164880. | −0.798675 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 60115.1i | 0.236998i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 467160.i | 1.51621i | 0.652131 | + | 0.758106i | \(0.273875\pi\) | ||||
−0.652131 | + | 0.758106i | \(0.726125\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −144143. | −0.389104 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 384378. | 0.870994 | 0.435497 | − | 0.900190i | \(-0.356573\pi\) | ||||
0.435497 | + | 0.900190i | \(0.356573\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 450696.i | − 0.864458i | −0.901764 | − | 0.432229i | \(-0.857727\pi\) | ||||
0.901764 | − | 0.432229i | \(-0.142273\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 50946.6i | 0.0833435i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 503097. | 0.706821 | 0.353410 | − | 0.935468i | \(-0.385022\pi\) | ||||
0.353410 | + | 0.935468i | \(0.385022\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −83612.9 | −0.101528 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1.04265e6i | − 1.10063i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.61153e6i | − 1.48687i | −0.668810 | − | 0.743434i | \(-0.733196\pi\) | ||||
0.668810 | − | 0.743434i | \(-0.266804\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −426769. | −0.345879 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 366756. | 0.262310 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.58458e6i | 1.00446i | 0.864735 | + | 0.502228i | \(0.167486\pi\) | ||||
−0.864735 | + | 0.502228i | \(0.832514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2.61079e6i | − 1.47271i | −0.676596 | − | 0.736355i | \(-0.736545\pi\) | ||||
0.676596 | − | 0.736355i | \(-0.263455\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 627080. | 0.315959 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −373092. | −0.168508 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52096e6i | 0.617810i | 0.951093 | + | 0.308905i | \(0.0999625\pi\) | ||||
−0.951093 | + | 0.308905i | \(0.900038\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.69146e6i | − 0.986315i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.15058e6 | 0.381515 | 0.190758 | − | 0.981637i | \(-0.438906\pi\) | ||||
0.190758 | + | 0.981637i | \(0.438906\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.52252e6 | 1.05980 | 0.529899 | − | 0.848061i | \(-0.322230\pi\) | ||||
0.529899 | + | 0.848061i | \(0.322230\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.97751e6i | − 0.541257i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.25292e6i | 1.31124i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.64873e6 | −1.74540 | −0.872699 | − | 0.488259i | \(-0.837632\pi\) | ||||
−0.872699 | + | 0.488259i | \(0.837632\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6.34999e6i | − 1.21899i | −0.792790 | − | 0.609495i | \(-0.791372\pi\) | ||||
0.792790 | − | 0.609495i | \(-0.208628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.69875e6i | − 0.476646i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.19168e6 | −0.356829 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.70342e6 | −0.256128 | −0.128064 | − | 0.991766i | \(-0.540876\pi\) | ||||
−0.128064 | + | 0.991766i | \(0.540876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.59223e6i | 0.638821i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.13291e6i | 0.532801i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 949296. | 0.113598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.70830e6 | −0.301297 | −0.150649 | − | 0.988587i | \(-0.548136\pi\) | ||||
−0.150649 | + | 0.988587i | \(0.548136\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.45177e6i | 0.461115i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 621207.i | 0.0599945i | 0.999550 | + | 0.0299973i | \(0.00954986\pi\) | ||||
−0.999550 | + | 0.0299973i | \(0.990450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 772068. | 0.0696186 | 0.0348093 | − | 0.999394i | \(-0.488918\pi\) | ||||
0.0348093 | + | 0.999394i | \(0.488918\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.62311e6 | 0.136831 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.30766e7i | − 1.03193i | −0.856609 | − | 0.515967i | \(-0.827433\pi\) | ||||
0.856609 | − | 0.515967i | \(-0.172567\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.05610e6i | 0.595843i | 0.954590 | + | 0.297922i | \(0.0962934\pi\) | ||||
−0.954590 | + | 0.297922i | \(0.903707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.26133e7 | 0.875386 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.54504e7 | 1.65928 | 0.829642 | − | 0.558296i | \(-0.188545\pi\) | ||||
0.829642 | + | 0.558296i | \(0.188545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 6.96645e6i | − 0.427139i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.89185e6i | 0.224650i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.32177e7 | −1.80699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.78044e7 | −0.913646 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.03782e7i | − 0.502869i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.05783e7i | − 0.484430i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.00240e7 | −1.30063 | −0.650317 | − | 0.759663i | \(-0.725364\pi\) | ||||
−0.650317 | + | 0.759663i | \(0.725364\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.21688e7 | −0.499095 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2.90785e7i | − 1.13012i | −0.825051 | − | 0.565058i | \(-0.808854\pi\) | ||||
0.825051 | − | 0.565058i | \(-0.191146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.16845e7i | − 0.430654i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.37556e6 | 0.0481184 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.43011e7 | −0.475169 | −0.237584 | − | 0.971367i | \(-0.576356\pi\) | ||||
−0.237584 | + | 0.971367i | \(0.576356\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.91992e7i | − 0.922188i | −0.887351 | − | 0.461094i | \(-0.847457\pi\) | ||||
0.887351 | − | 0.461094i | \(-0.152543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 1.35836e7i | − 0.408083i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.26012e7 | −0.932304 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.67285e6 | −0.154530 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.25755e6i | 0.0586174i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.91575e6i | 0.146507i | 0.997313 | + | 0.0732534i | \(0.0233382\pi\) | ||||
−0.997313 | + | 0.0732534i | \(0.976662\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.16205e7 | 0.747394 | 0.373697 | − | 0.927551i | \(-0.378090\pi\) | ||||
0.373697 | + | 0.927551i | \(0.378090\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.81515e7 | −0.635450 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.06974e7i | 0.230738i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.33595e7i | 1.10043i | 0.835023 | + | 0.550216i | \(0.185454\pi\) | ||||
−0.835023 | + | 0.550216i | \(0.814546\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.35113e7 | −0.858443 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.57470e7 | −1.61930 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3.05332e7i | − 0.552225i | −0.961125 | − | 0.276112i | \(-0.910954\pi\) | ||||
0.961125 | − | 0.276112i | \(-0.0890462\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.15228e7i | 0.199693i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.15038e7 | 0.191133 | 0.0955664 | − | 0.995423i | \(-0.469534\pi\) | ||||
0.0955664 | + | 0.995423i | \(0.469534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.42477e7 | 0.545793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 9.90242e6i | − 0.151445i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.06369e8i | 1.56191i | 0.624590 | + | 0.780953i | \(0.285266\pi\) | ||||
−0.624590 | + | 0.780953i | \(0.714734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.30013e7 | −0.888621 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.27836e7 | 0.579923 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.03733e8i | − 1.35186i | −0.736966 | − | 0.675930i | \(-0.763742\pi\) | ||||
0.736966 | − | 0.675930i | \(-0.236258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 9.35733e7i | − 1.17294i | −0.809970 | − | 0.586472i | \(-0.800517\pi\) | ||||
0.809970 | − | 0.586472i | \(-0.199483\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.04913e7 | −0.850269 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.26478e7 | 0.379099 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.35819e8i | − 2.63714i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.69312e7i | − 0.182419i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.06409e8 | −1.10500 | −0.552498 | − | 0.833514i | \(-0.686325\pi\) | ||||
−0.552498 | + | 0.833514i | \(0.686325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.87045e7 | 0.487661 | 0.243831 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243831 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00735e7i | 0.0972880i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2.38283e7i | − 0.222056i | −0.993817 | − | 0.111028i | \(-0.964586\pi\) | ||||
0.993817 | − | 0.111028i | \(-0.0354143\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.99543e8 | −1.79494 | −0.897472 | − | 0.441072i | \(-0.854598\pi\) | ||||
−0.897472 | + | 0.441072i | \(0.854598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.10658e7 | 0.356693 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.98246e7i | 0.585831i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.68625e7i | − 0.217775i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.26693e7 | −0.569449 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.29505e7 | 0.628503 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.62815e7i | − 0.265886i | −0.991124 | − | 0.132943i | \(-0.957557\pi\) | ||||
0.991124 | − | 0.132943i | \(-0.0424428\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3.10656e7i | − 0.220268i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.14972e7 | −0.216141 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.31670e8 | 0.874738 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 9.51079e7i | − 0.611874i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.06159e8i | − 1.28478i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00575e7 | 0.0607328 | 0.0303664 | − | 0.999539i | \(-0.490333\pi\) | ||||
0.0303664 | + | 0.999539i | \(0.490333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.33927e7 | −0.312495 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3.54925e7i | − 0.201394i | −0.994917 | − | 0.100697i | \(-0.967893\pi\) | ||||
0.994917 | − | 0.100697i | \(-0.0321072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.92621e8i | 1.05994i | 0.848017 | + | 0.529969i | \(0.177796\pi\) | ||||
−0.848017 | + | 0.529969i | \(0.822204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.41829e8 | 0.757046 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.85858e7 | 0.407004 | 0.203502 | − | 0.979075i | \(-0.434768\pi\) | ||||
0.203502 | + | 0.979075i | \(0.434768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 3.51593e7i | − 0.176727i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.06516e8i | 1.00771i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.94334e8 | −1.86841 | −0.934205 | − | 0.356737i | \(-0.883889\pi\) | ||||
−0.934205 | + | 0.356737i | \(0.883889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.64677e8 | −1.21802 | −0.609012 | − | 0.793161i | \(-0.708434\pi\) | ||||
−0.609012 | + | 0.793161i | \(0.708434\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.43489e7i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.84334e6i | 0.0253852i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.25174e7 | 0.306198 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.71450e8 | −0.703784 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 3.14631e8i | − 1.25586i | −0.778268 | − | 0.627932i | \(-0.783901\pi\) | ||||
0.778268 | − | 0.627932i | \(-0.216099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6.08736e8i | − 2.36324i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.28661e7 | −0.275192 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.74334e6 | −0.0321301 | −0.0160650 | − | 0.999871i | \(-0.505114\pi\) | ||||
−0.0160650 | + | 0.999871i | \(0.505114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.01848e8i | − 1.43718i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.91754e7i | 0.206015i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.27808e8 | 0.433224 | 0.216612 | − | 0.976258i | \(-0.430499\pi\) | ||||
0.216612 | + | 0.976258i | \(0.430499\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.12623e8 | −0.371762 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.59923e7i | 0.147875i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 7.00994e7i | − 0.219574i | −0.993955 | − | 0.109787i | \(-0.964983\pi\) | ||||
0.993955 | − | 0.109787i | \(-0.0350169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.25699e8 | −1.29930 | −0.649651 | − | 0.760232i | \(-0.725085\pi\) | ||||
−0.649651 | + | 0.760232i | \(0.725085\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.23990e8 | 0.368823 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.47259e8i | − 1.29687i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.13084e7i | 0.0602382i | 0.999546 | + | 0.0301191i | \(0.00958866\pi\) | ||||
−0.999546 | + | 0.0301191i | \(0.990411\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.11588e8 | 0.307613 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.21595e8 | −1.13350 | −0.566752 | − | 0.823889i | \(-0.691800\pi\) | ||||
−0.566752 | + | 0.823889i | \(0.691800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.62621e8i | 1.73785i | 0.494944 | + | 0.868925i | \(0.335189\pi\) | ||||
−0.494944 | + | 0.868925i | \(0.664811\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2.56310e7i | − 0.0655856i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.30639e8 | −0.825596 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.08090e9 | 2.63417 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.31240e7i | 0.173954i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.55155e8i | 0.360354i | 0.983634 | + | 0.180177i | \(0.0576670\pi\) | ||||
−0.983634 | + | 0.180177i | \(0.942333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.10739e8 | 0.251145 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.20198e8 | 0.266225 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5.32172e8i | − 1.15134i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.87685e8i | 0.819400i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.67726e7 | 0.0346379 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.82457e8 | −0.368222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.43544e8i | 1.26939i | 0.772764 | + | 0.634693i | \(0.218873\pi\) | ||||
−0.772764 | + | 0.634693i | \(0.781127\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 2.08458e7i | − 0.0401943i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.58443e8 | 1.05273 | 0.526366 | − | 0.850258i | \(-0.323554\pi\) | ||||
0.526366 | + | 0.850258i | \(0.323554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.78709e8 | 0.882403 | 0.441201 | − | 0.897408i | \(-0.354552\pi\) | ||||
0.441201 | + | 0.897408i | \(0.354552\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 4.38239e7i | − 0.0789994i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.26905e8i | 0.929020i | 0.885568 | + | 0.464510i | \(0.153770\pi\) | ||||
−0.885568 | + | 0.464510i | \(0.846230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.95700e8 | −0.854971 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.53068e8 | −0.595787 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.24551e8i | 0.866122i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3.91005e8i | − 0.631817i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.17515e8 | 0.344010 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.32760e8 | −0.669979 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 5.87362e8i | − 0.890241i | −0.895471 | − | 0.445121i | \(-0.853161\pi\) | ||||
0.895471 | − | 0.445121i | \(-0.146839\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3.40560e8i | − 0.505404i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.06293e8 | 0.154471 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.12323e9 | −1.59869 | −0.799344 | − | 0.600874i | \(-0.794820\pi\) | ||||
−0.799344 | + | 0.600874i | \(0.794820\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 6.87161e8i | − 0.957988i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.34753e8i | 1.27661i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.80328e8 | 1.04411 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.88094e8 | −0.246609 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.10945e9i | 1.42546i | 0.701440 | + | 0.712728i | \(0.252541\pi\) | ||||
−0.701440 | + | 0.712728i | \(0.747459\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.43892e8i | 0.558970i | 0.960150 | + | 0.279485i | \(0.0901637\pi\) | ||||
−0.960150 | + | 0.279485i | \(0.909836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.05080e8 | 0.129701 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.12493e8 | 0.136118 | 0.0680589 | − | 0.997681i | \(-0.478319\pi\) | ||||
0.0680589 | + | 0.997681i | \(0.478319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 8.04089e7i | − 0.0953905i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.96877e8i | 1.04326i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.86420e8 | 0.554856 | 0.277428 | − | 0.960746i | \(-0.410518\pi\) | ||||
0.277428 | + | 0.960746i | \(0.410518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.09358e8 | 0.793580 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.80718e8i | 0.527494i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.46173e8i | − 0.264982i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.24608e9 | −1.31587 | −0.657935 | − | 0.753075i | \(-0.728570\pi\) | ||||
−0.657935 | + | 0.753075i | \(0.728570\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.80212e8 | −0.290331 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.38622e9i | 1.40937i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.04875e9i | − 1.04638i | −0.852215 | − | 0.523192i | \(-0.824741\pi\) | ||||
0.852215 | − | 0.523192i | \(-0.175259\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.85614e8 | −0.279686 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.33353e8 | −0.416531 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.55519e8i | 0.146739i | 0.997305 | + | 0.0733697i | \(0.0233753\pi\) | ||||
−0.997305 | + | 0.0733697i | \(0.976625\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.10647e8i | 0.750922i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.81354e8 | 0.164942 | 0.0824711 | − | 0.996593i | \(-0.473719\pi\) | ||||
0.0824711 | + | 0.996593i | \(0.473719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.67104e8 | 0.327851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.28557e8i | 0.288153i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.90627e8i | − 0.250330i | −0.992136 | − | 0.125165i | \(-0.960054\pi\) | ||||
0.992136 | − | 0.125165i | \(-0.0399460\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.84944e9 | 3.25671 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.85120e8 | −0.652472 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.34536e8i | 0.436403i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.05323e9i | − 1.64691i | −0.567381 | − | 0.823455i | \(-0.692043\pi\) | ||||
0.567381 | − | 0.823455i | \(-0.307957\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.15481e8 | −0.248638 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.73752e8 | −0.366898 | −0.183449 | − | 0.983029i | \(-0.558726\pi\) | ||||
−0.183449 | + | 0.983029i | \(0.558726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.17185e8i | 0.621946i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.71401e7i | − 0.0277812i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.85280e9 | 2.09745 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.63944e7 | 0.0118485 | 0.00592424 | − | 0.999982i | \(-0.498114\pi\) | ||||
0.00592424 | + | 0.999982i | \(0.498114\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.86130e8i | 0.274339i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.36304e9i | − 0.952102i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.43773e8 | −0.304784 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.88379e8 | −0.532425 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.55726e9i | 1.03422i | 0.855920 | + | 0.517109i | \(0.172992\pi\) | ||||
−0.855920 | + | 0.517109i | \(0.827008\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.48339e9i | − 0.968877i | −0.874825 | − | 0.484439i | \(-0.839024\pi\) | ||||
0.874825 | − | 0.484439i | \(-0.160976\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.66758e8 | −0.235607 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.82832e9 | 1.78717 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.24578e9i | 1.39595i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.80233e8i | 0.538266i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.81971e8 | −0.530620 | −0.265310 | − | 0.964163i | \(-0.585474\pi\) | ||||
−0.265310 | + | 0.964163i | \(0.585474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.54428e9 | 1.50611 | 0.753057 | − | 0.657955i | \(-0.228578\pi\) | ||||
0.753057 | + | 0.657955i | \(0.228578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.53167e8i | 0.0892180i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.35406e9i | 0.776162i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.23338e7 | −0.0351640 | −0.0175820 | − | 0.999845i | \(-0.505597\pi\) | ||||
−0.0175820 | + | 0.999845i | \(0.505597\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.09538e7 | 0.0338428 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.60350e9i | − 1.42280i | −0.702786 | − | 0.711401i | \(-0.748061\pi\) | ||||
0.702786 | − | 0.711401i | \(-0.251939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.19045e8i | 0.0640397i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.59725e8 | 0.0845857 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.34950e9 | −0.703577 | −0.351789 | − | 0.936079i | \(-0.614426\pi\) | ||||
−0.351789 | + | 0.936079i | \(0.614426\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.34728e9i | − 1.20489i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 8.53753e8i | − 0.431508i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.20931e8 | 0.159725 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.69773e9 | 0.832072 | 0.416036 | − | 0.909348i | \(-0.363419\pi\) | ||||
0.416036 | + | 0.909348i | \(0.363419\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.60090e8i | 0.366877i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.08982e9i | 1.94425i | 0.234473 | + | 0.972123i | \(0.424663\pi\) | ||||
−0.234473 | + | 0.972123i | \(0.575337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.44026e9 | 1.61086 | 0.805430 | − | 0.592691i | \(-0.201935\pi\) | ||||
0.805430 | + | 0.592691i | \(0.201935\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.88831e8 | 0.133217 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.41766e8i | 0.109847i | 0.998491 | + | 0.0549233i | \(0.0174914\pi\) | ||||
−0.998491 | + | 0.0549233i | \(0.982509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.30831e9i | − 0.585608i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.44071e9 | 0.635334 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.75226e9 | −1.19584 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.94874e8i | 0.425932i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.17480e9i | 0.495622i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.03213e9 | −0.429103 | −0.214551 | − | 0.976713i | \(-0.568829\pi\) | ||||
−0.214551 | + | 0.976713i | \(0.568829\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.49399e9 | 1.02185 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.31517e9i | 0.934905i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.89271e8i | 0.0753335i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.67124e9 | 1.83265 | 0.916327 | − | 0.400431i | \(-0.131139\pi\) | ||||
0.916327 | + | 0.400431i | \(0.131139\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.24397e8 | −0.318827 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.59929e9i | 1.75350i | 0.480947 | + | 0.876750i | \(0.340293\pi\) | ||||
−0.480947 | + | 0.876750i | \(0.659707\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 3.13464e9i | − 1.17821i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.11115e8 | 0.115293 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.89718e8 | −0.361630 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.60308e9i | 1.65843i | 0.558932 | + | 0.829213i | \(0.311211\pi\) | ||||
−0.558932 | + | 0.829213i | \(0.688789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 3.10604e8i | − 0.110351i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.74041e9 | 0.960125 | 0.480063 | − | 0.877234i | \(-0.340614\pi\) | ||||
0.480063 | + | 0.877234i | \(0.340614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.34135e7 | 0.0150005 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9.24688e8i | − 0.315114i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.06630e9i | 1.03063i | 0.857001 | + | 0.515315i | \(0.172325\pi\) | ||||
−0.857001 | + | 0.515315i | \(0.827675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.03004e9 | −1.00456 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.67365e8 | −0.0874368 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 5.39564e7i | − 0.0174068i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3.07225e9i | − 0.977777i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.87197e9 | 0.901767 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.75950e9 | −0.854865 | −0.427433 | − | 0.904047i | \(-0.640582\pi\) | ||||
−0.427433 | + | 0.904047i | \(0.640582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.03158e9i | − 0.620979i | −0.950577 | − | 0.310490i | \(-0.899507\pi\) | ||||
0.950577 | − | 0.310490i | \(-0.100493\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.70104e9i | 0.513045i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.91107e9 | −1.75925 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.53198e9 | 1.91845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.15516e9i | − 0.334819i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2.05205e9i | − 0.587005i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.13867e8 | −0.258015 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.80079e9 | −0.780497 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.10597e8i | 0.140449i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 8.68196e8i | − 0.235737i | −0.993029 | − | 0.117868i | \(-0.962394\pi\) | ||||
0.993029 | − | 0.117868i | \(-0.0376061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.52648e9 | −0.677199 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.63005e8 | 0.148979 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.66370e8i | − 0.0695873i | −0.999395 | − | 0.0347937i | \(-0.988923\pi\) | ||||
0.999395 | − | 0.0347937i | \(-0.0110774\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.90326e9i | 0.490903i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10262e9 | 0.280800 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.57937e9 | 1.65442 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 8.81491e8i | − 0.218873i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 6.92953e9i | − 1.69907i | −0.527535 | − | 0.849533i | \(-0.676884\pi\) | ||||
0.527535 | − | 0.849533i | \(-0.323116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.40609e9 | −0.582600 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.36712e9 | −1.52255 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 6.05174e9i | − 1.42923i | −0.699520 | − | 0.714613i | \(-0.746603\pi\) | ||||
0.699520 | − | 0.714613i | \(-0.253397\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.77862e9i | − 0.414871i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.57141e8 | −0.105320 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.35823e9 | −0.536654 | −0.268327 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268327 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.32039e9i | 0.296808i | 0.988927 | + | 0.148404i | \(0.0474136\pi\) | ||||
−0.988927 | + | 0.148404i | \(0.952586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.87304e9i | 0.637970i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.30092e9 | 1.60155 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.48171e9 | −1.40467 | −0.702334 | − | 0.711847i | \(-0.747859\pi\) | ||||
−0.702334 | + | 0.711847i | \(0.747859\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.31502e9i | − 0.281551i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.46221e9i | 1.15545i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.84109e9 | −2.05685 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.71984e8 | 0.0561692 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.51129e8i | 0.0308399i | 0.999881 | + | 0.0154200i | \(0.00490852\pi\) | ||||
−0.999881 | + | 0.0154200i | \(0.995091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.07924e9i | − 0.419278i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.43365e8 | −0.128204 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.81216e9 | −0.947652 | −0.473826 | − | 0.880619i | \(-0.657127\pi\) | ||||
−0.473826 | + | 0.880619i | \(0.657127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.32144e9i | 0.451802i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.38766e9i | 1.03631i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.95101e9 | 0.751129 | 0.375565 | − | 0.926796i | \(-0.377449\pi\) | ||||
0.375565 | + | 0.926796i | \(0.377449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.30889e9 | −0.809664 | −0.404832 | − | 0.914391i | \(-0.632670\pi\) | ||||
−0.404832 | + | 0.914391i | \(0.632670\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.10878e9i | − 0.205937i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.24427e9i | 0.228439i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.02322e9 | 0.185698 | 0.0928489 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928489 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.88527e9 | 0.338230 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.68584e9i | − 0.476361i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.24790e9i | − 0.394153i | −0.980388 | − | 0.197076i | \(-0.936855\pi\) | ||||
0.980388 | − | 0.197076i | \(-0.0631447\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.25288e8 | −0.125733 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.76194e9 | 0.301990 | 0.150995 | − | 0.988535i | \(-0.451752\pi\) | ||||
0.150995 | + | 0.988535i | \(0.451752\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4.40993e9i | − 0.747333i | −0.927563 | − | 0.373667i | \(-0.878100\pi\) | ||||
0.927563 | − | 0.373667i | \(-0.121900\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.96207e9i | 0.328772i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.46527e9 | 0.242778 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.98268e9 | 0.816362 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.23966e9i | − 0.362866i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.80401e10i | 2.89043i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.94248e9 | −0.466241 | −0.233120 | − | 0.972448i | \(-0.574894\pi\) | ||||
−0.233120 | + | 0.972448i | \(0.574894\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.79600e8 | −0.153510 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.09825e9i | 0.325198i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.46377e8i | 0.0684248i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.38772e8 | −0.127172 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.15137e9 | −0.172669 | −0.0863343 | − | 0.996266i | \(-0.527515\pi\) | ||||
−0.0863343 | + | 0.996266i | \(0.527515\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.10275e9i | − 0.311924i | −0.987763 | − | 0.155962i | \(-0.950152\pi\) | ||||
0.987763 | − | 0.155962i | \(-0.0498478\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.50424e8i | 0.124789i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.11353e10 | −1.61636 | −0.808181 | − | 0.588934i | \(-0.799548\pi\) | ||||
−0.808181 | + | 0.588934i | \(0.799548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.67651e9 | 1.38951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 3.55509e9i | − 0.505030i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 4.60816e9i | − 0.647636i | −0.946119 | − | 0.323818i | \(-0.895033\pi\) | ||||
0.946119 | − | 0.323818i | \(-0.104967\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.03217e9 | −0.282563 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.56791e9 | −0.353266 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.25838e9i | − 0.171282i | −0.996326 | − | 0.0856411i | \(-0.972706\pi\) | ||||
0.996326 | − | 0.0856411i | \(-0.0272938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.45629e10i | − 1.96129i | −0.195791 | − | 0.980646i | \(-0.562727\pi\) | ||||
0.195791 | − | 0.980646i | \(-0.437273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.56629e9 | −0.741769 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.16577e8 | −0.107677 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 8.09164e9i | − 1.05584i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 2.71553e8i | − 0.0350641i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.59432e10 | −2.03727 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.22925e10 | 1.55449 | 0.777243 | − | 0.629200i | \(-0.216617\pi\) | ||||
0.777243 | + | 0.629200i | \(0.216617\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.44160e9i | 0.180419i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.50903e9i | 0.434636i | 0.976101 | + | 0.217318i | \(0.0697309\pi\) | ||||
−0.976101 | + | 0.217318i | \(0.930269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.32965e9 | 0.285593 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.58296e8 | −0.116275 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 6.38859e9i | − 0.767243i | −0.923490 | − | 0.383621i | \(-0.874677\pi\) | ||||
0.923490 | − | 0.383621i | \(-0.125323\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.99442e8i | 0.118807i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.20078e9 | 0.611955 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.60332e9 | −1.00207 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.38774e10i | − 1.60005i | −0.599966 | − | 0.800026i | \(-0.704819\pi\) | ||||
0.599966 | − | 0.800026i | \(-0.295181\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3.82938e9i | − 0.437081i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.04061e9 | −0.230575 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.48434e10 | 1.66042 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 2.12182e9i | − 0.234984i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 5.25165e9i | − 0.575815i | −0.957658 | − | 0.287907i | \(-0.907040\pi\) | ||||
0.957658 | − | 0.287907i | \(-0.0929595\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.34570e9 | −0.688868 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.49300e8 | −0.102033 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5.34358e8i | − 0.0568675i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.13161e10i | − 1.19243i | −0.802824 | − | 0.596215i | \(-0.796670\pi\) | ||||
0.802824 | − | 0.596215i | \(-0.203330\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.57592e9 | 0.581799 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.52586e10 | −1.57653 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.27836e9i | 0.233104i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.06470e10i | 1.07873i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.00326e9 | 0.702666 | 0.351333 | − | 0.936251i | \(-0.385729\pi\) | ||||
0.351333 | + | 0.936251i | \(0.385729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.64126e8 | −0.0659899 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.14627e9i | 0.703227i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 5.94522e9i | − 0.579408i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.14254e9 | 0.206804 | 0.103402 | − | 0.994640i | \(-0.467027\pi\) | ||||
0.103402 | + | 0.994640i | \(0.467027\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.74043e10i | − 1.64796i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.00725e10i | − 1.88251i | −0.337691 | − | 0.941257i | \(-0.609646\pi\) | ||||
0.337691 | − | 0.941257i | \(-0.390354\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.57770e8 | 0.0146561 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.28799e9 | 0.854645 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.84304e8i | 0.0714873i | 0.999361 | + | 0.0357436i | \(0.0113800\pi\) | ||||
−0.999361 | + | 0.0357436i | \(0.988620\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.95797e9i | − 0.176784i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.16696e10 | −1.93816 | −0.969079 | − | 0.246749i | \(-0.920638\pi\) | ||||
−0.969079 | + | 0.246749i | \(0.920638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.13426e8 | 0.0366312 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.62914e9i | 0.406330i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12484e10i | 0.978146i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.78319e9 | −0.153623 | −0.0768117 | − | 0.997046i | \(-0.524474\pi\) | ||||
−0.0768117 | + | 0.997046i | \(0.524474\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.49502e9 | −0.725074 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2.20982e9i | − 0.186871i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.55236e9i | 0.800341i | 0.916441 | + | 0.400171i | \(0.131049\pi\) | ||||
−0.916441 | + | 0.400171i | \(0.868951\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.64359e10 | −1.36441 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.69468e9 | 0.221647 | 0.110823 | − | 0.993840i | \(-0.464651\pi\) | ||||
0.110823 | + | 0.993840i | \(0.464651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 6.92979e9i | − 0.564786i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.96739e9i | 0.158882i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.45944e9 | 0.676952 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.87358e9 | 0.545056 | 0.272528 | − | 0.962148i | \(-0.412140\pi\) | ||||
0.272528 | + | 0.962148i | \(0.412140\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.36070e8i | 0.0185503i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.50956e10i | 1.17550i | 0.809043 | + | 0.587749i | \(0.199986\pi\) | ||||
−0.809043 | + | 0.587749i | \(0.800014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.12110e10 | −0.865147 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.08499e10 | −0.829758 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.22123e9i | 0.395723i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 7.02622e9i | − 0.527768i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.59773e9 | 0.118943 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.72906e9 | 0.275141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 6.42984e9i | − 0.470207i | −0.971970 | − | 0.235103i | \(-0.924457\pi\) | ||||
0.971970 | − | 0.235103i | \(-0.0755429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 3.45081e9i | − 0.250122i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.18922e10 | −1.57280 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.39380e10 | −0.992531 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.04081e9i | 0.214637i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.25537e10i | − 1.57803i | −0.614377 | − | 0.789013i | \(-0.710593\pi\) | ||||
0.614377 | − | 0.789013i | \(-0.289407\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.94279e10 | 1.34745 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.24179e9 | 0.0853759 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.15109e10i | − 1.46607i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.99248e9i | 0.404875i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.89268e9 | −0.126771 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.28393e10 | 0.852556 | 0.426278 | − | 0.904592i | \(-0.359824\pi\) | ||||
0.426278 | + | 0.904592i | \(0.359824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.20292e10i | 0.791891i | 0.918274 | + | 0.395946i | \(0.129583\pi\) | ||||
−0.918274 | + | 0.395946i | \(0.870417\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.14939e10i | 0.750153i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.13383e9 | −0.138073 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.12206e9 | 0.392754 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 3.34774e9i | − 0.212940i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.28268e10i | − 0.808944i | −0.914550 | − | 0.404472i | \(-0.867455\pi\) | ||||
0.914550 | − | 0.404472i | \(-0.132545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.15343e10 | −0.721257 | −0.360628 | − | 0.932710i | \(-0.617438\pi\) | ||||
−0.360628 | + | 0.932710i | \(0.617438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.20760e10 | −0.748746 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.84870e8i | 0.0113657i | 0.999984 | + | 0.00568287i | \(0.00180892\pi\) | ||||
−0.999984 | + | 0.00568287i | \(0.998191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.96965e9i | 0.485845i | 0.970046 | + | 0.242923i | \(0.0781062\pi\) | ||||
−0.970046 | + | 0.242923i | \(0.921894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.75328e8 | 0.0347786 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.22884e9 | −0.193548 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 8.03953e8i | − 0.0477890i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.01289e9i | − 0.177600i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.77023e9 | 0.278851 | 0.139426 | − | 0.990233i | \(-0.455474\pi\) | ||||
0.139426 | + | 0.990233i | \(0.455474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.06608e10 | 0.618020 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.13831e10i | 0.654429i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.39342e9i | − 0.136465i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.53152e10 | 0.866025 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.78908e10 | 1.00335 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.65682e10i | 2.59022i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 5.90759e9i | − 0.325904i | −0.986634 | − | 0.162952i | \(-0.947899\pi\) | ||||
0.986634 | − | 0.162952i | \(-0.0521015\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.92037e8 | −0.0378659 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.61048e9 | 0.141673 | 0.0708367 | − | 0.997488i | \(-0.477433\pi\) | ||||
0.0708367 | + | 0.997488i | \(0.477433\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.45743e10i | − 1.32283i | −0.750019 | − | 0.661416i | \(-0.769956\pi\) | ||||
0.750019 | − | 0.661416i | \(-0.230044\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.92725e9i | 0.476658i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.17420e10 | 1.68111 | 0.840556 | − | 0.541725i | \(-0.182229\pi\) | ||||
0.840556 | + | 0.541725i | \(0.182229\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.43368e9 | 0.390524 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.91844e10i | − 1.52084i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.67083e10i | 2.41449i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.11980e9 | 0.416372 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.97435e9 | 0.100432 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.09938e9i | 0.459181i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.25309e10i | 0.627313i | 0.949537 | + | 0.313657i | \(0.101554\pi\) | ||||
−0.949537 | + | 0.313657i | \(0.898446\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.18918e9 | 0.208050 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.40090e9 | −0.167563 | −0.0837815 | − | 0.996484i | \(-0.526700\pi\) | ||||
−0.0837815 | + | 0.996484i | \(0.526700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.37453e10i | 0.671881i | 0.941883 | + | 0.335941i | \(0.109054\pi\) | ||||
−0.941883 | + | 0.335941i | \(0.890946\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.98996e9i | − 0.144999i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.68738e10 | 0.811858 | 0.405929 | − | 0.913905i | \(-0.366948\pi\) | ||||
0.405929 | + | 0.913905i | \(0.366948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.58264e10 | 1.23284 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 3.24534e9i | − 0.153705i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.83385e9i | 0.321133i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.24945e9 | −0.338006 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.43686e10 | −0.664725 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.24253e10i | 0.570356i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 6.22317e10i | − 2.83449i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.04675e10 | 0.473081 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.53943e9 | −0.293271 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.30493e10i | 1.47074i | 0.677664 | + | 0.735372i | \(0.262992\pi\) | ||||
−0.677664 | + | 0.735372i | \(0.737008\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 4.52860e8i | − 0.0199982i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.26308e10 | 0.991712 | 0.495856 | − | 0.868405i | \(-0.334854\pi\) | ||||
0.495856 | + | 0.868405i | \(0.334854\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.87774e10 | −1.68628 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.92633e9i | 0.212593i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.50131e10i | 1.07121i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.68178e10 | −1.56478 | −0.782391 | − | 0.622788i | \(-0.786000\pi\) | ||||
−0.782391 | + | 0.622788i | \(0.786000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.73757e10 | 0.732880 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 6.14250e9i | − 0.257122i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.42153e10i | 1.42143i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.62837e8 | −0.0232062 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.59562e10 | −1.88057 | −0.940285 | − | 0.340389i | \(-0.889441\pi\) | ||||
−0.940285 | + | 0.340389i | \(0.889441\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.13576e9i | − 0.0461278i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.50780e10i | − 0.607795i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.64804e10 | −0.659366 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.13165e10 | −1.24361 | −0.621806 | − | 0.783171i | \(-0.713601\pi\) | ||||
−0.621806 | + | 0.783171i | \(0.713601\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.29252e10i | − 0.509455i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.02564e9i | − 0.0401264i | −0.999799 | − | 0.0200632i | \(-0.993613\pi\) | ||||
0.999799 | − | 0.0200632i | \(-0.00638674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.83162e10 | 1.48796 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.18324e9 | −0.0456103 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 8.12232e9i | − 0.310781i | −0.987853 | − | 0.155391i | \(-0.950336\pi\) | ||||
0.987853 | − | 0.155391i | \(-0.0496637\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.88054e10i | − 0.714249i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.42264e10 | 0.536370 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.41119e10 | −1.27668 | −0.638338 | − | 0.769757i | \(-0.720378\pi\) | ||||
−0.638338 | + | 0.769757i | \(0.720378\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.43645e9i | 0.276283i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.33839e10i | 0.493617i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.23017e10 | 0.450402 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.08200e9 | −0.148368 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.53284e9i | 0.343978i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3.40374e9i | − 0.121930i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.99763e10 | −1.06607 | −0.533035 | − | 0.846093i | \(-0.678949\pi\) | ||||
−0.533035 | + | 0.846093i | \(0.678949\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.41629e10 | 0.500056 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.45450e9i | 0.121093i | 0.998165 | + | 0.0605463i | \(0.0192843\pi\) | ||||
−0.998165 | + | 0.0605463i | \(0.980716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.51169e10i | 0.874121i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.05571e10 | −0.364779 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.88403e10 | 1.33245 | 0.666226 | − | 0.745750i | \(-0.267909\pi\) | ||||
0.666226 | + | 0.745750i | \(0.267909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.04022e10i | 0.354313i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 5.87289e9i | − 0.198614i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.64409e10 | 1.22363 | 0.611817 | − | 0.790999i | \(-0.290439\pi\) | ||||
0.611817 | + | 0.790999i | \(0.290439\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.66526e9 | −0.0555207 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.16845e10i | 0.386813i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 4.49270e10i | − 1.47679i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.07339e10 | 1.32953 | 0.664764 | − | 0.747053i | \(-0.268532\pi\) | ||||
0.664764 | + | 0.747053i | \(0.268532\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.58588e10 | −0.513981 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.39452e10i | 0.448790i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.26657e10i | 0.724330i | 0.932114 | + | 0.362165i | \(0.117962\pi\) | ||||
−0.932114 | + | 0.362165i | \(0.882038\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.19512e9 | −0.291795 |
(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 | 384.8.d.d.193.2 | yes | 8 | |
4.3 | odd | 2 | 384.8.d.c.193.6 | yes | 8 | ||
8.3 | odd | 2 | 384.8.d.c.193.3 | ✓ | 8 | ||
8.5 | even | 2 | inner | 384.8.d.d.193.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.c.193.3 | ✓ | 8 | 8.3 | odd | 2 | ||
384.8.d.c.193.6 | yes | 8 | 4.3 | odd | 2 | ||
384.8.d.d.193.2 | yes | 8 | 1.1 | even | 1 | trivial | |
384.8.d.d.193.7 | yes | 8 | 8.5 | even | 2 | inner |