Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,9,Mod(101,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.101");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.g (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: | \(122.213583018\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7378 x^{14} + 23156928 x^{12} - 101588726286 x^{10} + \cdots + 34\!\cdots\!81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{38}\cdot 3^{20}\cdot 5^{18} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.3 | ||
Root | \(74.2942 + 32.2702i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.101 |
Dual form | 300.9.g.h.101.4 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −74.2942 | − | 32.2702i | −0.917213 | − | 0.398398i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4017.33 | 1.67319 | 0.836594 | − | 0.547823i | \(-0.184543\pi\) | ||||
0.836594 | + | 0.547823i | \(0.184543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4478.26 | + | 4794.99i | 0.682558 | + | 0.730831i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11332.6i | 0.774033i | 0.922073 | + | 0.387016i | \(0.126494\pi\) | ||||
−0.922073 | + | 0.387016i | \(0.873506\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14669.4 | −0.513618 | −0.256809 | − | 0.966462i | \(-0.582671\pi\) | ||||
−0.256809 | + | 0.966462i | \(0.582671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 121646.i | 1.45648i | 0.685324 | + | 0.728238i | \(0.259661\pi\) | ||||
−0.685324 | + | 0.728238i | \(0.740339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22809.0 | −0.175022 | −0.0875109 | − | 0.996164i | \(-0.527891\pi\) | ||||
−0.0875109 | + | 0.996164i | \(0.527891\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −298464. | − | 129640.i | −1.53467 | − | 0.666595i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 452115.i | 1.61561i | 0.589448 | + | 0.807806i | \(0.299345\pi\) | ||||
−0.589448 | + | 0.807806i | \(0.700655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −177974. | − | 500754.i | −0.334889 | − | 0.942258i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 925775.i | 1.30892i | 0.756096 | + | 0.654460i | \(0.227104\pi\) | ||||
−0.756096 | + | 0.654460i | \(0.772896\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.24456e6 | −1.34763 | −0.673814 | − | 0.738901i | \(-0.735345\pi\) | ||||
−0.673814 | + | 0.738901i | \(0.735345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 365706. | − | 841948.i | 0.308373 | − | 0.709953i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9962.64 | −0.00531579 | −0.00265789 | − | 0.999996i | \(-0.500846\pi\) | ||||
−0.00265789 | + | 0.999996i | \(0.500846\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.08985e6 | + | 473386.i | 0.471097 | + | 0.204624i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.24930e6i | − | 1.14988i | −0.818194 | − | 0.574942i | \(-0.805024\pi\) | ||
0.818194 | − | 0.574942i | \(-0.194976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −986757. | −0.288627 | −0.144313 | − | 0.989532i | \(-0.546097\pi\) | ||||
−0.144313 | + | 0.989532i | \(0.546097\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 749904.i | − | 0.153679i | −0.997043 | − | 0.0768395i | \(-0.975517\pi\) | ||
0.997043 | − | 0.0768395i | \(-0.0244829\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.03741e7 | 1.79956 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.92556e6 | − | 9.03762e6i | 0.580257 | − | 1.33590i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.98864e6i | − | 0.505500i | −0.967532 | − | 0.252750i | \(-0.918665\pi\) | ||
0.967532 | − | 0.252750i | \(-0.0813350\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.69458e6 | + | 736052.i | 0.160532 | + | 0.0697283i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.17788e7i | − | 0.972061i | −0.873942 | − | 0.486030i | \(-0.838444\pi\) | ||
0.873942 | − | 0.486030i | \(-0.161556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.04000e7 | 1.47337 | 0.736684 | − | 0.676238i | \(-0.236391\pi\) | ||||
0.736684 | + | 0.676238i | \(0.236391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.79906e7 | + | 1.92630e7i | 1.14205 | + | 1.22282i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.35287e7 | −0.671363 | −0.335682 | − | 0.941976i | \(-0.608967\pi\) | ||||
−0.335682 | + | 0.941976i | \(0.608967\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.45898e7 | − | 3.35895e7i | 0.643657 | − | 1.48186i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.35989e7i | 0.535145i | 0.963538 | + | 0.267573i | \(0.0862215\pi\) | ||||
−0.963538 | + | 0.267573i | \(0.913778\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.39793e7 | −1.90080 | −0.950399 | − | 0.311035i | \(-0.899324\pi\) | ||||
−0.950399 | + | 0.311035i | \(0.899324\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.55268e7i | 1.29510i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.08987e7 | −0.279811 | −0.139906 | − | 0.990165i | \(-0.544680\pi\) | ||||
−0.139906 | + | 0.990165i | \(0.544680\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.93705e6 | + | 4.29464e7i | −0.0682292 | + | 0.997670i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.54029e7i | − | 1.16740i | −0.811969 | − | 0.583701i | \(-0.801604\pi\) | ||
0.811969 | − | 0.583701i | \(-0.198396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.98750e7 | − | 6.87797e7i | 0.521471 | − | 1.20056i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.17147e7i | − | 1.30239i | −0.758912 | − | 0.651194i | \(-0.774269\pi\) | ||
0.758912 | − | 0.651194i | \(-0.225731\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.89319e7 | −0.859380 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.24638e7 | + | 4.01623e7i | 1.23606 | + | 0.536892i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.22851e8 | −1.38768 | −0.693841 | − | 0.720128i | \(-0.744083\pi\) | ||||
−0.693841 | + | 0.720128i | \(0.744083\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.43397e7 | + | 5.07504e7i | −0.565687 | + | 0.528322i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.32849e6i | − | 0.0704254i | −0.999380 | − | 0.0352127i | \(-0.988789\pi\) | ||
0.999380 | − | 0.0352127i | \(-0.0112109\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.35738e7 | −0.831391 | −0.415696 | − | 0.909504i | \(-0.636462\pi\) | ||||
−0.415696 | + | 0.909504i | \(0.636462\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.65967e8i | 1.26615i | 0.774090 | + | 0.633076i | \(0.218208\pi\) | ||||
−0.774090 | + | 0.633076i | \(0.781792\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.76976e7 | 0.196217 | 0.0981085 | − | 0.995176i | \(-0.468721\pi\) | ||||
0.0981085 | + | 0.995176i | \(0.468721\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 740167. | + | 321497.i | 0.00487571 | + | 0.00211780i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.57224e7i | − | 0.280424i | −0.990122 | − | 0.140212i | \(-0.955222\pi\) | ||
0.990122 | − | 0.140212i | \(-0.0447784\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.56936e7 | − | 7.03397e7i | −0.350574 | − | 0.375368i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.88693e8i | 2.43696i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.59308e7 | 0.400873 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.04856e8 | + | 2.41404e8i | −0.458112 | + | 1.05469i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.26014e8 | −0.868802 | −0.434401 | − | 0.900720i | \(-0.643040\pi\) | ||||
−0.434401 | + | 0.900720i | \(0.643040\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.33104e7 | + | 3.18429e7i | 0.264732 | + | 0.114988i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.76919e8i | − | 1.95898i | −0.201494 | − | 0.979490i | \(-0.564580\pi\) | ||
0.201494 | − | 0.979490i | \(-0.435420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.16313e7 | −0.292844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.85337e8i | 1.09385i | 0.837181 | + | 0.546926i | \(0.184202\pi\) | ||||
−0.837181 | + | 0.546926i | \(0.815798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.39587e8 | −0.641807 | −0.320903 | − | 0.947112i | \(-0.603987\pi\) | ||||
−0.320903 | + | 0.947112i | \(0.603987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.41996e7 | + | 5.57135e7i | −0.0612254 | + | 0.140956i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.66243e8i | − | 0.397557i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.70736e8 | − | 3.34775e8i | −1.65058 | − | 0.716941i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.07729e6i | − | 0.00827230i | −0.999991 | − | 0.00413615i | \(-0.998683\pi\) | ||
0.999991 | − | 0.00413615i | \(-0.00131658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.75381e8 | −0.529696 | −0.264848 | − | 0.964290i | \(-0.585322\pi\) | ||||
−0.264848 | + | 0.964290i | \(0.585322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.83292e8 | + | 5.44764e8i | −1.06444 | + | 0.994130i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.32870e8 | −1.04164 | −0.520818 | − | 0.853668i | \(-0.674373\pi\) | ||||
−0.520818 | + | 0.853668i | \(0.674373\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.28714e8 | + | 2.96333e8i | −0.201390 | + | 0.463651i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.81629e9i | 2.70322i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.06865e8 | 0.859690 | 0.429845 | − | 0.902903i | \(-0.358568\pi\) | ||||
0.429845 | + | 0.902903i | \(0.358568\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.43132e8i | 1.21257i | 0.795248 | + | 0.606285i | \(0.207341\pi\) | ||||
−0.795248 | + | 0.606285i | \(0.792659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00538e8 | −0.736197 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.02145e8 | − | 1.09369e8i | −0.119463 | − | 0.127911i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.01076e8i | − | 0.782673i | −0.920248 | − | 0.391337i | \(-0.872013\pi\) | ||
0.920248 | − | 0.391337i | \(-0.127987\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.80105e8 | + | 8.75098e8i | −0.387267 | + | 0.891586i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.09833e9i | − | 1.06984i | −0.844901 | − | 0.534922i | \(-0.820341\pi\) | ||
0.844901 | − | 0.534922i | \(-0.179659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.20407e8 | −0.484874 | −0.242437 | − | 0.970167i | \(-0.577947\pi\) | ||||
−0.242437 | + | 0.970167i | \(0.577947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.51560e9 | − | 6.58313e8i | −1.35139 | − | 0.586987i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.37857e9 | −1.12736 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.14978e8 | − | 2.01169e9i | −0.560332 | − | 1.57657i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 9.77875e8i | − | 0.734767i | −0.930069 | − | 0.367384i | \(-0.880254\pi\) | ||
0.930069 | − | 0.367384i | \(-0.119746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.30466e8 | −0.526467 | −0.263233 | − | 0.964732i | \(-0.584789\pi\) | ||||
−0.263233 | + | 0.964732i | \(0.584789\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.83486e8i | − | 0.321010i | −0.987035 | − | 0.160505i | \(-0.948688\pi\) | ||
0.987035 | − | 0.160505i | \(-0.0513123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.43526e9 | 1.55286 | 0.776431 | − | 0.630203i | \(-0.217028\pi\) | ||||
0.776431 | + | 0.630203i | \(0.217028\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00511e9 | + | 4.36575e8i | 0.615783 | + | 0.267470i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.71914e9i | 2.19007i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.16788e9 | + | 2.02469e9i | −1.18074 | + | 1.10275i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.58486e8i | − | 0.135473i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.19886e9 | 1.61386 | 0.806929 | − | 0.590649i | \(-0.201128\pi\) | ||||
0.806929 | + | 0.590649i | \(0.201128\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.38841e8 | − | 1.01032e9i | 0.213201 | − | 0.490842i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.99981e9 | −2.25483 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.01035e9 | + | 1.74192e9i | 1.74344 | + | 0.757274i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.78448e9i | − | 0.748072i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.61131e9 | −0.651569 | −0.325785 | − | 0.945444i | \(-0.605628\pi\) | ||||
−0.325785 | + | 0.945444i | \(0.605628\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 5.21746e8i | − | 0.196497i | −0.995162 | − | 0.0982485i | \(-0.968676\pi\) | ||
0.995162 | − | 0.0982485i | \(-0.0313240\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.87443e8 | −0.213611 | −0.106805 | − | 0.994280i | \(-0.534062\pi\) | ||||
−0.106805 | + | 0.994280i | \(0.534062\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.46916e9 | − | 3.38238e9i | 0.515966 | − | 1.18788i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.28192e9i | 0.774241i | 0.922029 | + | 0.387120i | \(0.126530\pi\) | ||||
−0.922029 | + | 0.387120i | \(0.873470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.09708e8 | + | 3.51703e8i | 0.256646 | + | 0.111476i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.24611e9i | − | 0.688398i | −0.938897 | − | 0.344199i | \(-0.888151\pi\) | ||
0.938897 | − | 0.344199i | \(-0.111849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.70089e9 | −1.39352 | −0.696758 | − | 0.717306i | \(-0.745375\pi\) | ||||
−0.696758 | + | 0.717306i | \(0.745375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.60410e9 | − | 3.09589e9i | 0.460050 | − | 0.887893i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.34595e8 | 0.0898943 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.78787e9 | + | 4.11612e9i | −0.465091 | + | 1.07076i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.14963e9i | − | 0.793533i | −0.917920 | − | 0.396767i | \(-0.870132\pi\) | ||
0.917920 | − | 0.396767i | \(-0.129868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.12364e9 | −1.25054 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.30731e9i | 0.528899i | 0.964400 | + | 0.264449i | \(0.0851902\pi\) | ||||
−0.964400 | + | 0.264449i | \(0.914810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00232e7 | −0.00889432 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.43908e9 | + | 4.14586e9i | −0.956600 | + | 0.893414i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.60101e9i | − | 0.334634i | −0.985903 | − | 0.167317i | \(-0.946490\pi\) | ||
0.985903 | − | 0.167317i | \(-0.0535104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.63695e9 | + | 6.07093e9i | −0.518869 | + | 1.19457i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.07288e9i | 1.73275i | 0.499394 | + | 0.866375i | \(0.333556\pi\) | ||||
−0.499394 | + | 0.866375i | \(0.666444\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.37176e9 | −0.810549 | −0.405274 | − | 0.914195i | \(-0.632824\pi\) | ||||
−0.405274 | + | 0.914195i | \(0.632824\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.37830e9 | + | 1.90175e9i | 0.788234 | + | 0.342375i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.47715e9 | −1.27004 | −0.635020 | − | 0.772496i | \(-0.719008\pi\) | ||||
−0.635020 | + | 0.772496i | \(0.719008\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.57348e9 | − | 5.96766e9i | −0.919834 | − | 0.984888i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.81988e9i | 1.41461i | 0.706907 | + | 0.707306i | \(0.250090\pi\) | ||||
−0.706907 | + | 0.707306i | \(0.749910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.19993e7 | −0.0143430 | −0.00717148 | − | 0.999974i | \(-0.502283\pi\) | ||||
−0.00717148 | + | 0.999974i | \(0.502283\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.30535e10i | − | 1.92397i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.82208e9 | −1.12132 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.12709e9 | + | 3.96442e9i | 1.27280 | + | 0.552850i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.23825e9i | 0.303695i | 0.988404 | + | 0.151848i | \(0.0485223\pi\) | ||||
−0.988404 | + | 0.151848i | \(0.951478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.67486e9 | − | 2.01691e9i | 0.729338 | − | 0.259215i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 6.63227e9i | − | 0.829807i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.96413e9 | −0.482927 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.36492e8 | + | 5.44465e8i | −0.0280573 | + | 0.0645950i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.85192e9 | 0.996515 | 0.498258 | − | 0.867029i | \(-0.333973\pi\) | ||||
0.498258 | + | 0.867029i | \(0.333973\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.95199e9 | + | 3.01965e9i | 0.762562 | + | 0.331225i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.13950e10i | 1.21807i | 0.793144 | + | 0.609034i | \(0.208443\pi\) | ||||
−0.793144 | + | 0.609034i | \(0.791557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.46179e9 | −0.673248 | −0.336624 | − | 0.941639i | \(-0.609285\pi\) | ||||
−0.336624 | + | 0.941639i | \(0.609285\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.61882e10i | 1.60310i | 0.597928 | + | 0.801550i | \(0.295991\pi\) | ||||
−0.597928 | + | 0.801550i | \(0.704009\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.04914e10 | −1.01315 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.35578e9 | − | 1.23304e10i | 0.504432 | − | 1.16133i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.77463e9i | − | 0.254915i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.05777e9 | − | 8.93809e8i | −0.179973 | − | 0.0781725i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.01261e9i | − | 0.257134i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.24611e10 | 1.03811 | 0.519055 | − | 0.854741i | \(-0.326284\pi\) | ||||
0.519055 | + | 0.854741i | \(0.326284\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.46153e7 | − | 4.77707e7i | −0.00362833 | − | 0.00388495i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.07049e10 | 0.829971 | 0.414985 | − | 0.909828i | \(-0.363787\pi\) | ||||
0.414985 | + | 0.909828i | \(0.363787\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.47547e9 | + | 3.39691e9i | −0.111720 | + | 0.257208i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.41041e10i | − | 1.04311i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.85171e10 | 1.33782 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.65014e9i | 0.251763i | 0.992045 | + | 0.125881i | \(0.0401759\pi\) | ||||
−0.992045 | + | 0.125881i | \(0.959824\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.48706e10 | 1.00237 | 0.501184 | − | 0.865341i | \(-0.332898\pi\) | ||||
0.501184 | + | 0.865341i | \(0.332898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.61077e9 | + | 7.34578e9i | 0.172005 | + | 0.483960i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.09523e10i | − | 0.705356i | −0.935745 | − | 0.352678i | \(-0.885271\pi\) | ||
0.935745 | − | 0.352678i | \(-0.114729\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.57702e10 | − | 3.63071e10i | 0.970880 | − | 2.23521i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.21546e10i | 0.731748i | 0.930664 | + | 0.365874i | \(0.119230\pi\) | ||||
−0.930664 | + | 0.365874i | \(0.880770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.64633e10 | −0.969367 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.38416e9 | − | 2.77301e9i | −0.367686 | − | 0.159707i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.71742e10 | 1.49793 | 0.748966 | − | 0.662609i | \(-0.230551\pi\) | ||||
0.748966 | + | 0.662609i | \(0.230551\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.55803e10 | − | 1.45512e10i | 0.840372 | − | 0.784863i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.60237e10i | − | 0.845797i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00563e10 | 1.55274 | 0.776372 | − | 0.630275i | \(-0.217058\pi\) | ||||
0.776372 | + | 0.630275i | \(0.217058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.35806e10i | − | 0.672285i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.41230e7 | 0.00116916 | 0.000584581 | − | 1.00000i | \(-0.499814\pi\) | ||||
0.000584581 | 1.00000i | \(0.499814\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.67915e10 | + | 7.29353e9i | 0.796876 | + | 0.346129i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.28273e10i | − | 0.596129i | −0.954546 | − | 0.298065i | \(-0.903659\pi\) | ||
0.954546 | − | 0.298065i | \(-0.0963411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.41896e9 | − | 4.73149e9i | −0.197004 | − | 0.210937i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.34652e10i | 0.588051i | 0.955798 | + | 0.294025i | \(0.0949950\pi\) | ||||
−0.955798 | + | 0.294025i | \(0.905005\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.49981e10 | −2.35310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.86173e10 | + | 4.28618e10i | −0.780454 | + | 1.79680i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.09168e9 | 0.285488 | 0.142744 | − | 0.989760i | \(-0.454408\pi\) | ||||
0.142744 | + | 0.989760i | \(0.454408\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.80767e9 | + | 2.95696e9i | 0.268601 | + | 0.116669i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.60936e10i | − | 0.622409i | −0.950343 | − | 0.311205i | \(-0.899268\pi\) | ||
0.950343 | − | 0.311205i | \(-0.100732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.82570e10 | 0.692165 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.12903e8i | − | 0.00411459i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.45211e10 | 0.518928 | 0.259464 | − | 0.965753i | \(-0.416454\pi\) | ||||
0.259464 | + | 0.965753i | \(0.416454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.24349e10 | − | 2.86283e10i | 0.435789 | − | 1.00330i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.73193e10i | − | 1.62644i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.77999e10 | + | 7.73154e9i | 0.588673 | + | 0.255695i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3.60535e10i | − | 1.16975i | −0.811125 | − | 0.584873i | \(-0.801144\pi\) | ||
0.811125 | − | 0.584873i | \(-0.198856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.78217e9 | −0.279559 | −0.139780 | − | 0.990183i | \(-0.544639\pi\) | ||||
−0.139780 | + | 0.990183i | \(0.544639\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.59578e9 | − | 3.35827e9i | 0.112313 | − | 0.104895i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.19535e10 | 2.46522 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.36470e9 | + | 1.23509e10i | −0.158386 | + | 0.364644i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.58709e10i | 0.749726i | 0.927080 | + | 0.374863i | \(0.122310\pi\) | ||||
−0.927080 | + | 0.374863i | \(0.877690\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.71429e10 | −0.487677 | −0.243838 | − | 0.969816i | \(-0.578407\pi\) | ||||
−0.243838 | + | 0.969816i | \(0.578407\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.03123e10i | − | 0.282767i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.21261e10 | −0.864967 | −0.432483 | − | 0.901642i | \(-0.642363\pi\) | ||||
−0.432483 | + | 0.901642i | \(0.642363\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.64580e10 | + | 4.97437e10i | 1.22830 | + | 1.31518i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.31206e10i | 1.11962i | 0.828621 | + | 0.559810i | \(0.189126\pi\) | ||||
−0.828621 | + | 0.559810i | \(0.810874\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.31575e8 | + | 3.02919e8i | −0.00329567 | + | 0.00758746i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.97995e10i | − | 1.47134i | −0.677341 | − | 0.735669i | \(-0.736868\pi\) | ||
0.677341 | − | 0.735669i | \(-0.263132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.68231e10 | 0.890048 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.04592e10 | + | 8.88662e9i | 0.485844 | + | 0.211030i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.83318e9 | −0.225439 | −0.112720 | − | 0.993627i | \(-0.535956\pi\) | ||||
−0.112720 | + | 0.993627i | \(0.535956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.09149e10 | − | 2.16499e10i | 1.37238 | − | 0.487758i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.36056e9i | − | 0.0301242i | −0.999887 | − | 0.0150621i | \(-0.995205\pi\) | ||
0.999887 | − | 0.0150621i | \(-0.00479460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.49710e10 | 0.978608 | 0.489304 | − | 0.872113i | \(-0.337251\pi\) | ||||
0.489304 | + | 0.872113i | \(0.337251\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.97127e10i | − | 0.624705i | −0.949966 | − | 0.312353i | \(-0.898883\pi\) | ||
0.949966 | − | 0.312353i | \(-0.101117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.43493e10 | −1.12332 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.70186e10 | + | 2.04229e10i | 0.955402 | + | 0.414986i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.11825e10i | − | 0.223407i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.91255e10 | − | 1.78622e10i | 0.369435 | − | 0.345033i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.97953e10i | 1.51578i | 0.652385 | + | 0.757888i | \(0.273769\pi\) | ||||
−0.652385 | + | 0.757888i | \(0.726231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.46146e8 | 0.00273028 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.86122e10 | − | 1.34940e11i | 1.07696 | − | 2.47943i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.05153e10 | −0.720284 | −0.360142 | − | 0.932898i | \(-0.617272\pi\) | ||||
−0.360142 | + | 0.932898i | \(0.617272\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.50866e10 | − | 1.95837e10i | −0.788519 | − | 0.342499i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.34994e10i | 0.232268i | 0.993234 | + | 0.116134i | \(0.0370502\pi\) | ||||
−0.993234 | + | 0.116134i | \(0.962950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.12617e11 | −1.90641 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.46314e10i | 0.895399i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.82581e10 | 0.294478 | 0.147239 | − | 0.989101i | \(-0.452961\pi\) | ||||
0.147239 | + | 0.989101i | \(0.452961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.04351e10 | − | 7.00692e10i | 0.483085 | − | 1.11218i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.00331e10i | 1.09403i | 0.837121 | + | 0.547017i | \(0.184237\pi\) | ||||
−0.837121 | + | 0.547017i | \(0.815763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.46165e10 | + | 1.93795e10i | 0.675249 | + | 0.293299i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.18160e10i | 0.176034i | 0.996119 | + | 0.0880172i | \(0.0280530\pi\) | ||||
−0.996119 | + | 0.0880172i | \(0.971947\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.16852e11 | −3.18039 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.05941e9 | + | 1.14217e10i | 0.0586129 | + | 0.164916i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.49837e9 | 0.118953 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.26239e10 | + | 5.20859e10i | −0.311815 | + | 0.717878i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.02514e11i | 1.39134i | 0.718360 | + | 0.695671i | \(0.244893\pi\) | ||||
−0.718360 | + | 0.695671i | \(0.755107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.79035e10 | −0.372952 | −0.186476 | − | 0.982460i | \(-0.559707\pi\) | ||||
−0.186476 | + | 0.982460i | \(0.559707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.51396e11i | − | 1.96279i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.26097e11 | −1.61020 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.64792e10 | − | 5.27486e10i | 0.710413 | − | 0.663488i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.76654e10i | 0.590601i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.54434e10 | + | 8.15996e10i | −0.426224 | + | 0.981275i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.17566e11i | 1.39292i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.60899e11 | −1.87830 | −0.939149 | − | 0.343509i | \(-0.888384\pi\) | ||||
−0.939149 | + | 0.343509i | \(0.888384\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.86632e10 | + | 1.67937e10i | 0.444732 | + | 0.193173i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.48569e11 | −1.65951 | −0.829754 | − | 0.558129i | \(-0.811519\pi\) | ||||
−0.829754 | + | 0.558129i | \(0.811519\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.13566e10 | + | 9.78177e10i | 1.00566 | + | 1.07678i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.11160e10i | − | 0.229090i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.37835e10 | −0.468177 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.20464e10i | 0.748499i | 0.927328 | + | 0.374250i | \(0.122100\pi\) | ||||
−0.927328 | + | 0.374250i | \(0.877900\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.44752e10 | 0.148244 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.02420e11 | + | 4.44868e10i | 1.03403 | + | 0.449138i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.59816e10i | 0.358135i | 0.983837 | + | 0.179067i | \(0.0573080\pi\) | ||||
−0.983837 | + | 0.179067i | \(0.942692\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.17991e10 | + | 1.72530e11i | −0.114160 | + | 1.66929i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.80528e10i | − | 0.172225i | −0.996285 | − | 0.0861124i | \(-0.972556\pi\) | ||
0.996285 | − | 0.0861124i | \(-0.0274444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.51665e10 | −0.518956 | −0.259478 | − | 0.965749i | \(-0.583551\pi\) | ||||
−0.259478 | + | 0.965749i | \(0.583551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.15563e10 | + | 7.26505e10i | −0.292730 | + | 0.673938i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.58383e11 | −1.42891 | −0.714455 | − | 0.699681i | \(-0.753325\pi\) | ||||
−0.714455 | + | 0.699681i | \(0.753325\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.42694e10 | + | 2.35723e10i | 0.482882 | + | 0.209743i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.22572e11i | − | 1.95328i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.52017e10 | 0.391274 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.05361e10i | − | 0.594100i | −0.954862 | − | 0.297050i | \(-0.903997\pi\) | ||
0.954862 | − | 0.297050i | \(-0.0960027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.83872e10 | 0.235864 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.56022e10 | + | 3.59202e10i | −0.127890 | + | 0.294435i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.16827e10i | 0.579689i | 0.957074 | + | 0.289845i | \(0.0936036\pi\) | ||||
−0.957074 | + | 0.289845i | \(0.906396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.80926e11 | − | 7.85864e10i | −1.42430 | − | 0.618657i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.98040e11i | − | 1.53832i | −0.639057 | − | 0.769159i | \(-0.720675\pi\) | ||
0.639057 | − | 0.769159i | \(-0.279325\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.76093e11 | 1.34972 | 0.674861 | − | 0.737945i | \(-0.264204\pi\) | ||||
0.674861 | + | 0.737945i | \(0.264204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.05852e10 | − | 6.48700e10i | −0.458244 | − | 0.490653i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.53412e11 | 1.13007 | 0.565035 | − | 0.825067i | \(-0.308863\pi\) | ||||
0.565035 | + | 0.825067i | \(0.308863\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.20017e11 | − | 2.76310e11i | 0.872520 | − | 2.00876i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.10007e10i | 0.0789322i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.12547e11 | −0.797062 | −0.398531 | − | 0.917155i | \(-0.630480\pi\) | ||||
−0.398531 | + | 0.917155i | \(0.630480\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.70972e10i | 0.669986i | 0.942221 | + | 0.334993i | \(0.108734\pi\) | ||||
−0.942221 | + | 0.334993i | \(0.891266\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.43396e10 | 0.165787 | 0.0828936 | − | 0.996558i | \(-0.473584\pi\) | ||||
0.0828936 | + | 0.996558i | \(0.473584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.26398e11 | − | 8.04645e10i | 1.52232 | − | 0.541051i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.28275e11i | − | 2.17914i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.34140e9 | + | 1.92040e10i | −0.0539720 | + | 0.124257i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.21192e9i | − | 0.00774232i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.38956e10 | −0.276888 | −0.138444 | − | 0.990370i | \(-0.544210\pi\) | ||||
−0.138444 | + | 0.990370i | \(0.544210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.37657e11 | − | 1.03228e11i | −1.48025 | − | 0.642958i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.52182e11 | −0.924286 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.52067e10 | + | 6.08996e10i | −0.391101 | + | 0.365268i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.27326e11i | 0.754196i | 0.926173 | + | 0.377098i | \(0.123078\pi\) | ||||
−0.926173 | + | 0.377098i | \(0.876922\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.50491e11 | 1.46537 | 0.732686 | − | 0.680567i | \(-0.238266\pi\) | ||||
0.732686 | + | 0.680567i | \(0.238266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.85872e11i | 1.63138i | 0.578491 | + | 0.815689i | \(0.303642\pi\) | ||||
−0.578491 | + | 0.815689i | \(0.696358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.33485e11 | 0.752407 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.71457e11 | + | 1.61345e11i | 2.06816 | + | 0.898322i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.78895e11i | 1.53387i | 0.641726 | + | 0.766934i | \(0.278219\pi\) | ||||
−0.641726 | + | 0.766934i | \(0.721781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.41733e11 | − | 2.58830e11i | −1.29740 | − | 1.38916i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.09719e11i | − | 1.64220i | −0.570784 | − | 0.821100i | \(-0.693361\pi\) | ||
0.570784 | − | 0.821100i | \(-0.306639\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.59385e11 | −1.35875 | −0.679374 | − | 0.733792i | \(-0.737748\pi\) | ||||
−0.679374 | + | 0.733792i | \(0.737748\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.75857e10 | + | 1.32577e11i | −0.298031 | + | 0.686141i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.18556e11 | −2.11471 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.19711e11 | + | 5.19975e10i | 0.597627 | + | 0.259584i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.31185e11i | 1.14043i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.68948e10 | −0.0823557 | −0.0411778 | − | 0.999152i | \(-0.513111\pi\) | ||||
−0.0411778 | + | 0.999152i | \(0.513111\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.66225e11i | 1.26734i | 0.773602 | + | 0.633672i | \(0.218453\pi\) | ||||
−0.773602 | + | 0.633672i | \(0.781547\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.93531e11 | −2.32186 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.68369e10 | + | 3.87627e10i | −0.0782841 | + | 0.180230i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.27073e11i | 1.04348i | 0.853106 | + | 0.521738i | \(0.174716\pi\) | ||||
−0.853106 | + | 0.521738i | \(0.825284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.36436e10 | + | 1.89569e10i | 0.195927 | + | 0.0851022i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.85111e10i | 0.259634i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.55909e11 | −1.56109 | −0.780543 | − | 0.625103i | \(-0.785057\pi\) | ||||
−0.780543 | + | 0.625103i | \(0.785057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.18300e11 | + | 2.03881e11i | −0.946502 | + | 0.883983i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.95265e11 | 1.67478 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.36380e10 | − | 1.69533e11i | 0.308456 | − | 0.710143i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.36766e11i | − | 1.39462i | −0.716769 | − | 0.697311i | \(-0.754380\pi\) | ||
0.716769 | − | 0.697311i | \(-0.245620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.27238e8 | 0.000930379 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2.94409e10i | − | 0.117835i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.37614e11 | 0.940345 | 0.470172 | − | 0.882575i | \(-0.344192\pi\) | ||||
0.470172 | + | 0.882575i | \(0.344192\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.88071e10 | − | 5.22590e10i | −0.190987 | − | 0.204495i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.62685e11i | − | 2.17724i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.24825e10 | + | 1.66873e11i | −0.274256 | + | 0.631407i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.53231e11i | 1.32173i | 0.750504 | + | 0.660866i | \(0.229811\pi\) | ||||
−0.750504 | + | 0.660866i | \(0.770189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.75916e11 | −1.39107 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.49249e11 | + | 1.51699e11i | 1.27815 | + | 0.555174i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.44118e11 | −0.515919 | −0.257960 | − | 0.966156i | \(-0.583050\pi\) | ||||
−0.257960 | + | 0.966156i | \(0.583050\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.19080e11 | + | 1.78242e11i | −0.775699 | + | 0.631103i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.20035e11i | − | 0.420378i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.62582e11 | −0.909596 | −0.454798 | − | 0.890595i | \(-0.650288\pi\) | ||||
−0.454798 | + | 0.890595i | \(0.650288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.53316e11i | − | 0.519657i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.83611e11 | −0.615633 | −0.307816 | − | 0.951446i | \(-0.599598\pi\) | ||||
−0.307816 | + | 0.951446i | \(0.599598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.48585e10 | − | 1.07975e10i | −0.0824522 | − | 0.0358137i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.01511e11i | − | 0.661216i | −0.943768 | − | 0.330608i | \(-0.892746\pi\) | ||
0.943768 | − | 0.330608i | \(-0.107254\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.65656e11 | − | 2.48109e11i | 0.853174 | − | 0.796819i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.66742e11i | 2.11851i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.41725e11 | 1.07428 | 0.537139 | − | 0.843494i | \(-0.319505\pi\) | ||||
0.537139 | + | 0.843494i | \(0.319505\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.01639e11 | + | 2.34000e11i | −0.316142 | + | 0.727839i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.06291e11 | −1.23724 | −0.618620 | − | 0.785690i | \(-0.712308\pi\) | ||||
−0.618620 | + | 0.785690i | \(0.712308\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.80657e11 | + | 1.65341e11i | 1.14701 | + | 0.498211i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.14906e11i | 0.938951i | 0.882946 | + | 0.469475i | \(0.155557\pi\) | ||||
−0.882946 | + | 0.469475i | \(0.844443\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.11270e11 | 0.328308 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.72789e11i | 0.499268i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.34345e11 | −0.670118 | −0.335059 | − | 0.942197i | \(-0.608756\pi\) | ||||
−0.335059 | + | 0.942197i | \(0.608756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.44573e10 | − | 1.71419e11i | 0.210712 | − | 0.485113i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.06053e10i | 0.141735i | 0.997486 | + | 0.0708677i | \(0.0225768\pi\) | ||||
−0.997486 | + | 0.0708677i | \(0.977423\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.97349e9 | + | 1.29156e9i | 0.00815798 | + | 0.00354348i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.41133e10i | 0.201255i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.54112e11 | −0.414220 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.63586e11 | − | 1.64764e11i | 1.23334 | − | 0.438343i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.23463e11 | 1.62522 | 0.812610 | − | 0.582808i | \(-0.198046\pi\) | ||||
0.812610 | + | 0.582808i | \(0.198046\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.16649e10 | + | 1.18946e11i | −0.133318 | + | 0.306931i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.83682e11i | − | 0.469202i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.99257e11 | −0.756748 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4.31198e11i | − | 1.06867i | −0.845273 | − | 0.534335i | \(-0.820562\pi\) | ||
0.845273 | − | 0.534335i | \(-0.179438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.12231e10 | 0.223830 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.91821e11 | − | 3.65940e11i | 0.951826 | − | 0.888955i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 6.11726e11i | − | 1.47128i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.92784e11 | − | 6.74062e11i | 0.690324 | − | 1.58930i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.07535e11i | − | 1.18487i | −0.805617 | − | 0.592437i | \(-0.798166\pi\) | ||
0.805617 | − | 0.592437i | \(-0.201834\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.82026e10 | −0.0420774 | −0.0210387 | − | 0.999779i | \(-0.506697\pi\) | ||||
−0.0210387 | + | 0.999779i | \(0.506697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.24796e11 | + | 1.41078e11i | 0.743445 | + | 0.322921i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.25070e10 | 0.0505160 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.63913e11 | − | 2.82578e11i | −0.586576 | − | 0.628062i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.48913e9i | 0.0208859i | 0.999945 | + | 0.0104430i | \(0.00332416\pi\) | ||||
−0.999945 | + | 0.0104430i | \(0.996676\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.82548e11 | 0.615875 | 0.307937 | − | 0.951407i | \(-0.400361\pi\) | ||||
0.307937 | + | 0.951407i | \(0.400361\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2.73392e10i | − | 0.0584472i | −0.999573 | − | 0.0292236i | \(-0.990697\pi\) | ||
0.999573 | − | 0.0292236i | \(-0.00930348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.56575e11 | −0.754976 | −0.377488 | − | 0.926015i | \(-0.623212\pi\) | ||||
−0.377488 | + | 0.926015i | \(0.623212\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.55509e11 | + | 2.41289e11i | 1.16490 | + | 0.505981i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.26197e12i | 2.62102i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.21499e11 | + | 6.23220e11i | 0.451305 | + | 1.26981i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.47820e11i | − | 0.298323i | −0.988813 | − | 0.149161i | \(-0.952343\pi\) | ||
0.988813 | − | 0.149161i | \(-0.0476574\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.56812e11 | −0.713273 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.84620e11 | − | 6.55266e11i | 0.563579 | − | 1.29750i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.45212e11 | 0.670737 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.83502e9 | + | 2.96884e9i | 0.0131555 | + | 0.00571421i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.50426e9i | − | 0.00858825i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.87703e11 | −0.921212 | −0.460606 | − | 0.887605i | \(-0.652368\pi\) | ||||
−0.460606 | + | 0.887605i | \(0.652368\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.65321e11i | 1.04802i | 0.851711 | + | 0.524012i | \(0.175565\pi\) | ||||
−0.851711 | + | 0.524012i | \(0.824435\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.50163e11 | 1.74512 | 0.872561 | − | 0.488506i | \(-0.162458\pi\) | ||||
0.872561 | + | 0.488506i | \(0.162458\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.21239e11 | + | 9.69799e11i | −0.766508 | + | 1.76469i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.75521e10i | 0.157842i | 0.996881 | + | 0.0789211i | \(0.0251475\pi\) | ||||
−0.996881 | + | 0.0789211i | \(0.974852\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.81135e11 | + | 2.52420e11i | 1.02849 | + | 0.446733i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.23510e11i | − | 0.216583i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.98459e11 | 0.344824 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.50157e11 | − | 5.89067e11i | −0.947174 | − | 1.01416i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.80932e11 | 1.65821 | 0.829107 | − | 0.559090i | \(-0.188849\pi\) | ||||
0.829107 | + | 0.559090i | \(0.188849\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.22289e10 | − | 1.66289e11i | 0.120992 | − | 0.278553i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.03446e12i | 1.71716i | 0.512677 | + | 0.858582i | \(0.328654\pi\) | ||||
−0.512677 | + | 0.858582i | \(0.671346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.29618e11 | 0.377714 | 0.188857 | − | 0.982005i | \(-0.439522\pi\) | ||||
0.188857 | + | 0.982005i | \(0.439522\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 9.73588e11i | − | 1.57283i | −0.617701 | − | 0.786413i | \(-0.711936\pi\) | ||
0.617701 | − | 0.786413i | \(-0.288064\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.07972e11 | −1.45367 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.86695e11 | − | 3.32844e10i | −0.772229 | − | 0.0528117i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.71046e10i | 0.0268972i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.14025e11 | + | 4.92739e11i | −0.330594 | + | 0.761110i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.15218e12i | − | 1.76394i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.85203e11 | 0.736249 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.94512e11 | + | 1.27923e11i | 0.442947 | + | 0.192397i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.17806e11 | 0.912900 | 0.456450 | − | 0.889749i | \(-0.349121\pi\) | ||||
0.456450 | + | 0.889749i | \(0.349121\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.51400e10 | − | 3.28189e10i | 0.0514691 | − | 0.0480694i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 9.19187e11i | − | 1.33454i | −0.744817 | − | 0.667268i | \(-0.767463\pi\) | ||
0.744817 | − | 0.667268i | \(-0.232537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.27860e11 | 0.903607 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.31767e12i | − | 3.27774i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.42778e10 | 0.132174 | 0.0660872 | − | 0.997814i | \(-0.478948\pi\) | ||||
0.0660872 | + | 0.997814i | \(0.478948\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.57646e11 | − | 2.85654e11i | −0.914016 | − | 0.397010i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.99489e11i | − | 0.274860i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.19048e11 | − | 4.48685e11i | −0.567473 | − | 0.607607i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.95905e11i | − | 0.531531i | −0.964038 | − | 0.265765i | \(-0.914375\pi\) | ||
0.964038 | − | 0.265765i | \(-0.0856246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.36623e11 | −0.314962 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.67718e11 | − | 8.46580e11i | 0.485276 | − | 1.11723i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.96530e11 | −0.254959 | −0.127480 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127480 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.80073e11 | + | 2.08523e11i | 0.617512 | + | 0.268221i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 5.42960e9i | − | 0.00692483i | −0.999994 | − | 0.00346242i | \(-0.998898\pi\) | ||
0.999994 | − | 0.00346242i | \(-0.00110212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.46906e12 | 1.85777 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.49964e11i | 0.932482i | 0.884658 | + | 0.466241i | \(0.154392\pi\) | ||||
−0.884658 | + | 0.466241i | \(0.845608\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.91846e11 | 0.976283 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.22396e11 | − | 1.20269e12i | 0.638672 | − | 1.47038i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.34634e11i | 0.163224i | 0.996664 | + | 0.0816119i | \(0.0260068\pi\) | ||||
−0.996664 | + | 0.0816119i | \(0.973993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.79454e11 | + | 3.38561e11i | 0.929271 | + | 0.403636i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.54803e12i | 1.83022i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.96044e11 | 0.816100 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.95808e11 | + | 7.43242e11i | −0.925343 | + | 0.864222i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.09741e12 | 1.25506 | 0.627530 | − | 0.778592i | \(-0.284066\pi\) | ||||
0.627530 | + | 0.778592i | \(0.284066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.95381e10 | + | 2.06139e11i | −0.101558 | + | 0.233811i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 5.97472e11i | − | 0.672111i | −0.941842 | − | 0.336055i | \(-0.890907\pi\) | ||
0.941842 | − | 0.336055i | \(-0.109093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.62500e11 | −1.07386 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.84630e11i | − | 0.202639i | −0.994854 | − | 0.101320i | \(-0.967694\pi\) | ||
0.994854 | − | 0.101320i | \(-0.0323064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.26041e11 | 1.00809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.24037e11 | + | 1.32810e11i | 0.133929 | + | 0.143402i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.79919e11i | − | 0.728187i | −0.931362 | − | 0.364093i | \(-0.881379\pi\) | ||
0.931362 | − | 0.364093i | \(-0.118621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.72176e10 | + | 2.23819e11i | −0.102442 | + | 0.235846i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 4.46127e11i | − | 0.466309i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.10490e11 | 0.736653 | 0.368327 | − | 0.929696i | \(-0.379931\pi\) | ||||
0.368327 | + | 0.929696i | \(0.379931\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.25786e11 | − | 4.02122e11i | −0.952168 | − | 0.413581i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.85789e11 | −0.390453 | −0.195227 | − | 0.980758i | \(-0.562544\pi\) | ||||
−0.195227 | + | 0.980758i | \(0.562544\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.77309e9 | + | 4.98884e9i | 0.00178020 | + | 0.00500884i |
(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 | 300.9.g.h.101.3 | 16 | ||
3.2 | odd | 2 | inner | 300.9.g.h.101.4 | 16 | ||
5.2 | odd | 4 | 60.9.b.a.29.6 | yes | 16 | ||
5.3 | odd | 4 | 60.9.b.a.29.11 | yes | 16 | ||
5.4 | even | 2 | inner | 300.9.g.h.101.14 | 16 | ||
15.2 | even | 4 | 60.9.b.a.29.12 | yes | 16 | ||
15.8 | even | 4 | 60.9.b.a.29.5 | ✓ | 16 | ||
15.14 | odd | 2 | inner | 300.9.g.h.101.13 | 16 | ||
20.3 | even | 4 | 240.9.c.d.209.6 | 16 | |||
20.7 | even | 4 | 240.9.c.d.209.11 | 16 | |||
60.23 | odd | 4 | 240.9.c.d.209.12 | 16 | |||
60.47 | odd | 4 | 240.9.c.d.209.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.9.b.a.29.5 | ✓ | 16 | 15.8 | even | 4 | ||
60.9.b.a.29.6 | yes | 16 | 5.2 | odd | 4 | ||
60.9.b.a.29.11 | yes | 16 | 5.3 | odd | 4 | ||
60.9.b.a.29.12 | yes | 16 | 15.2 | even | 4 | ||
240.9.c.d.209.5 | 16 | 60.47 | odd | 4 | |||
240.9.c.d.209.6 | 16 | 20.3 | even | 4 | |||
240.9.c.d.209.11 | 16 | 20.7 | even | 4 | |||
240.9.c.d.209.12 | 16 | 60.23 | odd | 4 | |||
300.9.g.h.101.3 | 16 | 1.1 | even | 1 | trivial | ||
300.9.g.h.101.4 | 16 | 3.2 | odd | 2 | inner | ||
300.9.g.h.101.13 | 16 | 15.14 | odd | 2 | inner | ||
300.9.g.h.101.14 | 16 | 5.4 | even | 2 | inner |