Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,12,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), 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: | \(193.622481501\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{15}\cdot 7^{9} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.3 | ||
Root | \(-6748.51 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.37 |
Dual form | 252.12.k.d.109.3 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3239.51 | + | 5610.99i | −0.463600 | + | 0.802979i | −0.999137 | − | 0.0415326i | \(-0.986776\pi\) |
0.535537 | + | 0.844512i | \(0.320109\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −44011.6 | + | 6348.37i | −0.989757 | + | 0.142766i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −153860. | − | 266493.i | −0.288048 | − | 0.498914i | 0.685296 | − | 0.728265i | \(-0.259673\pi\) |
−0.973344 | + | 0.229351i | \(0.926340\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 584277. | 0.436446 | 0.218223 | − | 0.975899i | \(-0.429974\pi\) | ||||
0.218223 | + | 0.975899i | \(0.429974\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.72018e6 | − | 8.17558e6i | −0.806286 | − | 1.39653i | −0.915419 | − | 0.402501i | \(-0.868141\pi\) |
0.109134 | − | 0.994027i | \(-0.465192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.44479e6 | − | 1.46268e7i | 0.782427 | − | 1.35520i | −0.148097 | − | 0.988973i | \(-0.547315\pi\) |
0.930524 | − | 0.366231i | \(-0.119352\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.59358e7 | + | 2.76016e7i | −0.516262 | + | 0.894193i | 0.483559 | + | 0.875312i | \(0.339344\pi\) |
−0.999822 | + | 0.0188811i | \(0.993990\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.42527e6 | + | 5.93275e6i | 0.0701496 | + | 0.121503i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.08011e8 | 0.977864 | 0.488932 | − | 0.872322i | \(-0.337387\pi\) | ||||
0.488932 | + | 0.872322i | \(0.337387\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25482e8 | + | 2.17341e8i | 0.787210 | + | 1.36349i | 0.927670 | + | 0.373402i | \(0.121809\pi\) |
−0.140459 | + | 0.990086i | \(0.544858\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.06955e8 | − | 2.67514e8i | 0.344214 | − | 0.860940i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.03798e7 | − | 1.39222e8i | 0.190563 | − | 0.330064i | −0.754874 | − | 0.655870i | \(-0.772302\pi\) |
0.945437 | + | 0.325805i | \(0.105635\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.43424e8 | 0.732534 | 0.366267 | − | 0.930510i | \(-0.380636\pi\) | ||||
0.366267 | + | 0.930510i | \(0.380636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35306e8 | 0.244094 | 0.122047 | − | 0.992524i | \(-0.461054\pi\) | ||||
0.122047 | + | 0.992524i | \(0.461054\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.31156e8 | + | 7.46784e8i | −0.274218 | + | 0.474960i | −0.969938 | − | 0.243354i | \(-0.921752\pi\) |
0.695719 | + | 0.718314i | \(0.255086\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.89672e9 | − | 5.58805e8i | 0.959236 | − | 0.282606i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.83924e9 | + | 3.18566e9i | 0.604117 | + | 1.04636i | 0.992190 | + | 0.124733i | \(0.0398075\pi\) |
−0.388073 | + | 0.921629i | \(0.626859\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.99372e9 | 0.534156 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.91162e9 | + | 3.31102e9i | 0.348109 | + | 0.602943i | 0.985914 | − | 0.167255i | \(-0.0534905\pi\) |
−0.637804 | + | 0.770198i | \(0.720157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.30312e9 | + | 3.98912e9i | −0.349142 | + | 0.604732i | −0.986097 | − | 0.166169i | \(-0.946860\pi\) |
0.636955 | + | 0.770901i | \(0.280194\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.89277e9 | + | 3.27837e9i | −0.202336 | + | 0.350457i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.21035e8 | + | 1.59528e9i | 0.0833422 | + | 0.144353i | 0.904684 | − | 0.426084i | \(-0.140107\pi\) |
−0.821341 | + | 0.570437i | \(0.806774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.51591e10 | −0.997131 | −0.498566 | − | 0.866852i | \(-0.666140\pi\) | ||||
−0.498566 | + | 0.866852i | \(0.666140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.51263e10 | − | 2.61995e10i | −0.853997 | − | 1.47917i | −0.877573 | − | 0.479444i | \(-0.840838\pi\) |
0.0235759 | − | 0.999722i | \(-0.492495\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.46341e9 | + | 1.07520e10i | 0.356325 | + | 0.452680i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.74865e10 | − | 3.02876e10i | 0.639374 | − | 1.10743i | −0.346197 | − | 0.938162i | \(-0.612527\pi\) |
0.985570 | − | 0.169266i | \(-0.0541396\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.03419e10 | −0.566842 | −0.283421 | − | 0.958996i | \(-0.591469\pi\) | ||||
−0.283421 | + | 0.958996i | \(0.591469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.11641e10 | 1.49518 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.42219e10 | + | 7.65945e10i | −0.839444 | + | 1.45396i | 0.0509155 | + | 0.998703i | \(0.483786\pi\) |
−0.890360 | + | 0.455257i | \(0.849547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.57150e10 | + | 3.70921e9i | −0.431975 | + | 0.0623094i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.47139e10 | + | 9.47672e10i | 0.725467 | + | 1.25655i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.58828e10 | −1.13370 | −0.566848 | − | 0.823823i | \(-0.691837\pi\) | ||||
−0.566848 | + | 0.823823i | \(0.691837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.02124e10 | − | 1.38932e11i | −0.759406 | − | 1.31533i | −0.943154 | − | 0.332357i | \(-0.892156\pi\) |
0.183748 | − | 0.982973i | \(-0.441177\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.76095e10 | − | 1.17103e11i | 0.574650 | − | 0.995322i | −0.421430 | − | 0.906861i | \(-0.638472\pi\) |
0.996080 | − | 0.0884613i | \(-0.0281950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.11930e10 | + | 7.13484e10i | −0.283931 | + | 0.491783i | −0.972349 | − | 0.233531i | \(-0.924972\pi\) |
0.688418 | + | 0.725314i | \(0.258305\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.13457e11 | − | 1.96514e11i | −0.706295 | − | 1.22334i | −0.966222 | − | 0.257711i | \(-0.917032\pi\) |
0.259927 | − | 0.965628i | \(-0.416301\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.73656e11 | 0.886661 | 0.443331 | − | 0.896358i | \(-0.353797\pi\) | ||||
0.443331 | + | 0.896358i | \(0.353797\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.03248e11 | − | 1.78831e11i | −0.478679 | − | 0.829096i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.59644e11 | + | 3.29855e11i | 0.997403 | + | 1.26711i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.53103e10 | − | 1.65082e11i | 0.334057 | − | 0.578603i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.60743e11 | −1.05729 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.34602e11 | 1.43585 | 0.717926 | − | 0.696119i | \(-0.245091\pi\) | ||||
0.717926 | + | 0.696119i | \(0.245091\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.15277e9 | + | 3.72871e9i | −0.00487535 | + | 0.00844435i | −0.868453 | − | 0.495772i | \(-0.834885\pi\) |
0.863577 | + | 0.504216i | \(0.168219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.78813e11 | + | 6.97360e11i | −0.580936 | + | 1.45303i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.72967e11 | − | 4.72793e11i | −0.483222 | − | 0.836966i | 0.516592 | − | 0.856232i | \(-0.327200\pi\) |
−0.999814 | + | 0.0192659i | \(0.993867\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.98706e11 | −0.324811 | −0.162405 | − | 0.986724i | \(-0.551925\pi\) | ||||
−0.162405 | + | 0.986724i | \(0.551925\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.98965e10 | − | 1.55705e11i | −0.125717 | − | 0.217749i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.49902e11 | + | 6.06048e11i | −0.453338 | + | 0.785205i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.06132e11 | + | 7.03441e11i | −0.453047 | + | 0.784700i | −0.998574 | − | 0.0533936i | \(-0.982996\pi\) |
0.545527 | + | 0.838093i | \(0.316330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.00195e10 | + | 1.21277e11i | 0.0725848 | + | 0.125721i | 0.900033 | − | 0.435821i | \(-0.143542\pi\) |
−0.827449 | + | 0.561541i | \(0.810209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.62599e12 | −1.45980 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.58436e11 | + | 1.48686e12i | 0.718224 | + | 1.24400i | 0.961703 | + | 0.274094i | \(0.0883780\pi\) |
−0.243479 | + | 0.969906i | \(0.578289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.26135e11 | − | 1.31596e12i | 0.383314 | − | 0.958737i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.32301e11 | + | 7.48767e11i | −0.294276 | + | 0.509701i | −0.974816 | − | 0.223010i | \(-0.928412\pi\) |
0.680540 | + | 0.732711i | \(0.261745\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.19947e12 | 1.31032 | 0.655160 | − | 0.755490i | \(-0.272601\pi\) | ||||
0.655160 | + | 0.755490i | \(0.272601\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.45078e12 | −0.809515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.03725e11 | − | 6.99272e11i | 0.198076 | − | 0.343078i | −0.749828 | − | 0.661632i | \(-0.769864\pi\) |
0.947905 | + | 0.318554i | \(0.103197\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.88415e11 | − | 2.39365e11i | −0.0867774 | − | 0.110243i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.33293e12 | − | 2.30870e12i | −0.542145 | − | 0.939022i | −0.998781 | − | 0.0493684i | \(-0.984279\pi\) |
0.456636 | − | 0.889654i | \(-0.349054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.78597e11 | 0.374431 | 0.187216 | − | 0.982319i | \(-0.440054\pi\) | ||||
0.187216 | + | 0.982319i | \(0.440054\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.20782e11 | + | 9.02021e11i | 0.176690 | + | 0.306036i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.45249e12 | + | 2.51578e12i | −0.464498 | + | 0.804534i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.05977e10 | + | 5.29968e10i | −0.00870975 | + | 0.0150857i | −0.870347 | − | 0.492438i | \(-0.836106\pi\) |
0.861638 | + | 0.507524i | \(0.169439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.45854e11 | − | 7.72242e11i | −0.119847 | − | 0.207581i | 0.799860 | − | 0.600187i | \(-0.204907\pi\) |
−0.919707 | + | 0.392605i | \(0.871574\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.84992e12 | −0.444211 | −0.222105 | − | 0.975023i | \(-0.571293\pi\) | ||||
−0.222105 | + | 0.975023i | \(0.571293\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.14607e12 | − | 1.98506e12i | −0.260328 | − | 0.450901i | 0.706001 | − | 0.708210i | \(-0.250497\pi\) |
−0.966329 | + | 0.257310i | \(0.917164\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.75374e12 | + | 6.85693e11i | −0.967847 | + | 0.139605i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.76043e12 | + | 3.04915e12i | −0.339603 | + | 0.588210i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.19725e12 | −0.901506 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.84826e12 | −0.633449 | −0.316724 | − | 0.948518i | \(-0.602583\pi\) | ||||
−0.316724 | + | 0.948518i | \(0.602583\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.62276e11 | + | 1.32030e12i | −0.113162 | + | 0.196002i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.90241e12 | − | 8.76891e12i | −0.973806 | − | 1.23714i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.75789e12 | − | 4.77680e12i | −0.351900 | − | 0.609509i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00191e13 | 1.21661 | 0.608303 | − | 0.793705i | \(-0.291850\pi\) | ||||
0.608303 | + | 0.793705i | \(0.291850\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.22157e12 | + | 5.57992e12i | 0.354752 | + | 0.614449i | 0.987075 | − | 0.160256i | \(-0.0512320\pi\) |
−0.632323 | + | 0.774704i | \(0.717899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.43324e12 | + | 1.46068e13i | −0.884911 | + | 1.53271i | −0.0390952 | + | 0.999235i | \(0.512448\pi\) |
−0.845816 | + | 0.533475i | \(0.820886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.37785e12 | + | 1.27788e13i | −0.703837 | + | 1.21908i | 0.263273 | + | 0.964721i | \(0.415198\pi\) |
−0.967110 | + | 0.254360i | \(0.918135\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.79346e12 | − | 4.83842e12i | −0.254255 | − | 0.440383i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.22602e13 | −1.84646 | −0.923231 | − | 0.384247i | \(-0.874461\pi\) | ||||
−0.923231 | + | 0.384247i | \(0.874461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.59484e12 | − | 9.69055e12i | −0.443296 | − | 0.767812i | 0.554636 | − | 0.832093i | \(-0.312858\pi\) |
−0.997932 | + | 0.0642818i | \(0.979524\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00900e12 | + | 1.24527e13i | −0.217775 | + | 0.901263i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.93409e12 | − | 8.54610e12i | 0.341487 | − | 0.591473i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.65870e13 | −1.68447 | −0.842237 | − | 0.539107i | \(-0.818762\pi\) | ||||
−0.842237 | + | 0.539107i | \(0.818762\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.80749e12 | 0.594833 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.80530e12 | + | 1.52512e13i | −0.489905 | + | 0.848541i | −0.999933 | − | 0.0116173i | \(-0.996302\pi\) |
0.510027 | + | 0.860158i | \(0.329635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.65382e12 | + | 6.63767e12i | −0.141489 | + | 0.353889i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.38995e12 | + | 1.62639e13i | 0.460158 | + | 0.797016i | 0.998968 | − | 0.0454104i | \(-0.0144596\pi\) |
−0.538811 | + | 0.842427i | \(0.681126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.38329e13 | −1.12028 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.02550e13 | + | 1.77621e13i | 0.443912 | + | 0.768878i | 0.997976 | − | 0.0635960i | \(-0.0202569\pi\) |
−0.554064 | + | 0.832474i | \(0.686924\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.99679e13 | − | 3.45854e13i | 0.829853 | − | 1.43735i | −0.0683002 | − | 0.997665i | \(-0.521758\pi\) |
0.898153 | − | 0.439683i | \(-0.144909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.05402e12 | − | 1.82562e12i | 0.0404129 | − | 0.0699972i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.57932e12 | + | 1.48598e13i | 0.316092 | + | 0.547488i | 0.979669 | − | 0.200620i | \(-0.0642957\pi\) |
−0.663577 | + | 0.748108i | \(0.730962\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.74808e12 | 0.0935718 | 0.0467859 | − | 0.998905i | \(-0.485102\pi\) | ||||
0.0467859 | + | 0.998905i | \(0.485102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.50503e12 | − | 1.12670e13i | −0.213022 | − | 0.368965i | 0.739637 | − | 0.673006i | \(-0.234997\pi\) |
−0.952659 | + | 0.304041i | \(0.901664\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.39170e13 | + | 3.44986e12i | −0.725030 | + | 0.104581i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.74242e13 | + | 4.75001e13i | −0.800194 | + | 1.38598i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.21317e13 | −0.328208 | −0.164104 | − | 0.986443i | \(-0.552473\pi\) | ||||
−0.164104 | + | 0.986443i | \(0.552473\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.47708e13 | −0.645534 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.31091e12 | + | 1.61270e13i | −0.225320 | + | 0.390266i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.03562e13 | + | 1.49381e12i | −0.241594 | + | 0.0348482i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.49219e13 | − | 2.58455e13i | −0.323725 | − | 0.560708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.49166e13 | 0.521467 | 0.260734 | − | 0.965411i | \(-0.416036\pi\) | ||||
0.260734 | + | 0.965411i | \(0.416036\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.40293e13 | − | 4.16199e13i | −0.468337 | − | 0.811184i | 0.531008 | − | 0.847367i | \(-0.321813\pi\) |
−0.999345 | + | 0.0361830i | \(0.988480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.23518e13 | + | 3.87144e13i | −0.420550 | + | 0.728415i | −0.995993 | − | 0.0894273i | \(-0.971496\pi\) |
0.575443 | + | 0.817842i | \(0.304830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.52513e13 | + | 4.37365e13i | −0.443055 | + | 0.767394i | −0.997914 | − | 0.0645502i | \(-0.979439\pi\) |
0.554859 | + | 0.831944i | \(0.312772\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.66185e13 | − | 2.87841e13i | −0.281672 | − | 0.487870i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.59444e14 | −2.52344 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00131e12 | + | 3.46637e12i | 0.0306165 | + | 0.0530293i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.42350e13 | − | 3.56043e13i | 0.203601 | − | 0.509243i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.47976e13 | + | 9.49122e13i | −0.758067 | + | 1.31301i | 0.185769 | + | 0.982594i | \(0.440523\pi\) |
−0.943835 | + | 0.330416i | \(0.892811\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.19348e13 | −0.154550 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.51104e13 | 0.815992 | 0.407996 | − | 0.912984i | \(-0.366228\pi\) | ||||
0.407996 | + | 0.912984i | \(0.366228\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.86131e13 | − | 6.68799e13i | 0.453509 | − | 0.785500i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.99304e13 | + | 3.66350e13i | −0.909064 | + | 0.416657i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.58107e13 | − | 2.73849e13i | −0.168709 | − | 0.292212i | 0.769257 | − | 0.638939i | \(-0.220626\pi\) |
−0.937966 | + | 0.346727i | \(0.887293\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.82337e14 | −1.88510 | −0.942549 | − | 0.334068i | \(-0.891578\pi\) | ||||
−0.942549 | + | 0.334068i | \(0.891578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.26328e13 | − | 9.11627e13i | −0.511088 | − | 0.885230i | −0.999917 | − | 0.0128510i | \(-0.995909\pi\) |
0.488829 | − | 0.872379i | \(-0.337424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.91080e13 | − | 8.50575e13i | 0.462270 | − | 0.800676i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.42748e13 | + | 1.11327e14i | −0.568881 | + | 0.985330i | 0.427796 | + | 0.903875i | \(0.359290\pi\) |
−0.996677 | + | 0.0814552i | \(0.974043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.43838e13 | − | 1.46157e14i | −0.724385 | − | 1.25467i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.96007e14 | 1.58365 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.45396e13 | + | 1.63747e14i | 0.741225 | + | 1.28384i | 0.951938 | + | 0.306292i | \(0.0990884\pi\) |
−0.210712 | + | 0.977548i | \(0.567578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.01172e14 | − | 1.28530e14i | −0.747313 | − | 0.949396i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.09656e14 | + | 1.89929e14i | −0.786381 | + | 1.36205i | 0.141790 | + | 0.989897i | \(0.454714\pi\) |
−0.928171 | + | 0.372155i | \(0.878619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.31082e13 | 0.426784 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.98932e13 | 0.327737 | 0.163869 | − | 0.986482i | \(-0.447603\pi\) | ||||
0.163869 | + | 0.986482i | \(0.447603\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.22245e14 | + | 2.11734e14i | −0.757945 | + | 1.31280i | 0.185952 | + | 0.982559i | \(0.440463\pi\) |
−0.943897 | + | 0.330240i | \(0.892870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.77467e13 | + | 1.26569e13i | −0.528685 | + | 0.0762591i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.42290e13 | − | 2.46453e13i | −0.0809937 | − | 0.140285i | 0.822683 | − | 0.568500i | \(-0.192476\pi\) |
−0.903677 | + | 0.428215i | \(0.859143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.00879e14 | 1.66502 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.13295e14 | + | 1.96233e14i | 0.592828 | + | 1.02681i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.53607e13 | − | 9.58875e13i | 0.281743 | − | 0.487994i | −0.690071 | − | 0.723742i | \(-0.742421\pi\) |
0.971814 | + | 0.235748i | \(0.0757540\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.25564e13 | − | 3.90688e13i | 0.108636 | − | 0.188164i | −0.806582 | − | 0.591123i | \(-0.798685\pi\) |
0.915218 | + | 0.402959i | \(0.132018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.33160e13 | + | 1.26987e14i | 0.343574 | + | 0.595088i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.94688e13 | −0.219565 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.07447e13 | + | 1.86104e13i | 0.0464213 | + | 0.0804041i | 0.888302 | − | 0.459259i | \(-0.151885\pi\) |
−0.841881 | + | 0.539663i | \(0.818552\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.05153e14 | − | 1.33588e14i | −0.430623 | − | 0.547069i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.58977e13 | − | 1.14138e14i | 0.262788 | − | 0.455163i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.15127e14 | 1.57038 | 0.785189 | − | 0.619256i | \(-0.212566\pi\) | ||||
0.785189 | + | 0.619256i | \(0.212566\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.01947e14 | 0.375683 | 0.187842 | − | 0.982199i | \(-0.439851\pi\) | ||||
0.187842 | + | 0.982199i | \(0.439851\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.23358e13 | − | 5.60072e13i | 0.113121 | − | 0.195932i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.60396e13 | − | 1.90189e14i | 0.259231 | − | 0.648383i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.54120e13 | + | 7.86560e13i | 0.147077 | + | 0.254746i | 0.930146 | − | 0.367190i | \(-0.119680\pi\) |
−0.783069 | + | 0.621935i | \(0.786347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.65109e14 | 0.837029 | 0.418515 | − | 0.908210i | \(-0.362551\pi\) | ||||
0.418515 | + | 0.908210i | \(0.362551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.69149e14 | + | 4.66179e14i | 0.807875 | + | 1.39928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.01623e13 | − | 1.56166e14i | 0.263919 | − | 0.457121i | −0.703361 | − | 0.710833i | \(-0.748318\pi\) |
0.967280 | + | 0.253712i | \(0.0816516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.03229e14 | − | 1.78798e14i | 0.287463 | − | 0.497901i | −0.685740 | − | 0.727846i | \(-0.740521\pi\) |
0.973203 | + | 0.229946i | \(0.0738548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.86514e14 | − | 4.96257e14i | −0.778333 | − | 1.34811i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.98661e14 | −0.772366 | −0.386183 | − | 0.922422i | \(-0.626207\pi\) | ||||
−0.386183 | + | 0.922422i | \(0.626207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.36110e13 | − | 1.44819e14i | −0.211005 | − | 0.365471i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.24915e13 | − | 1.56302e14i | 0.150231 | − | 0.375753i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.32118e13 | − | 5.75245e13i | 0.0779386 | − | 0.134994i | −0.824422 | − | 0.565976i | \(-0.808500\pi\) |
0.902360 | + | 0.430982i | \(0.141833\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.90622e13 | 0.154485 | 0.0772424 | − | 0.997012i | \(-0.475388\pi\) | ||||
0.0772424 | + | 0.997012i | \(0.475388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.06831e14 | −0.451772 | −0.225886 | − | 0.974154i | \(-0.572528\pi\) | ||||
−0.225886 | + | 0.974154i | \(0.572528\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.93370e14 | + | 6.81337e14i | −0.819518 | + | 1.41945i | 0.0865201 | + | 0.996250i | \(0.472425\pi\) |
−0.906038 | + | 0.423196i | \(0.860908\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.06637e13 | − | 6.43638e13i | −0.103097 | − | 0.130976i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.62041e13 | − | 6.27074e13i | −0.0703108 | − | 0.121782i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.15703e14 | 0.219548 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.50604e13 | + | 1.12688e14i | 0.117889 | + | 0.204189i | 0.918931 | − | 0.394419i | \(-0.129054\pi\) |
−0.801042 | + | 0.598608i | \(0.795721\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.69641e13 | − | 8.13441e13i | 0.0831702 | − | 0.144055i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.10613e14 | − | 5.37997e14i | 0.525581 | − | 0.910334i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.32294e13 | − | 5.75550e13i | −0.0549684 | − | 0.0952081i | 0.837232 | − | 0.546848i | \(-0.184172\pi\) |
−0.892200 | + | 0.451640i | \(0.850839\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.37328e13 | 0.0375320 | 0.0187660 | − | 0.999824i | \(-0.494026\pi\) | ||||
0.0187660 | + | 0.999824i | \(0.494026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.09830e14 | − | 8.83052e14i | −0.788438 | − | 1.36561i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.67177e14 | − | 9.62356e13i | 0.986917 | − | 0.142356i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.56733e14 | + | 7.91084e14i | −0.660859 | + | 1.14464i | 0.319531 | + | 0.947576i | \(0.396475\pi\) |
−0.980390 | + | 0.197066i | \(0.936859\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.77391e12 | 0.00661075 | 0.00330537 | − | 0.999995i | \(-0.498948\pi\) | ||||
0.00330537 | + | 0.999995i | \(0.498948\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.03939e15 | 1.40824 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.48244e14 | − | 1.12279e15i | 0.840990 | − | 1.45664i | −0.0480692 | − | 0.998844i | \(-0.515307\pi\) |
0.889059 | − | 0.457793i | \(-0.151360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.32056e14 | + | 1.05705e15i | 1.05642 | + | 1.34209i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.38043e14 | + | 7.58712e14i | 0.532815 | + | 0.922863i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.65350e14 | 0.315952 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.33019e14 | + | 4.03600e14i | 0.265940 | + | 0.460621i | 0.967809 | − | 0.251684i | \(-0.0809844\pi\) |
−0.701870 | + | 0.712305i | \(0.747651\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.61957e14 | − | 1.14654e15i | 0.739725 | − | 1.28124i | −0.212894 | − | 0.977075i | \(-0.568289\pi\) |
0.952619 | − | 0.304166i | \(-0.0983777\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.18459e15 | − | 2.05177e15i | 1.26943 | − | 2.19872i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.14938e13 | − | 5.45489e13i | −0.0330536 | − | 0.0572505i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.17510e14 | 0.319711 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.66890e14 | − | 4.62267e14i | −0.263261 | − | 0.455982i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.40746e14 | − | 4.19485e14i | −0.417302 | − | 0.397172i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.67334e14 | + | 1.50227e15i | −0.804639 | + | 1.39368i | 0.111895 | + | 0.993720i | \(0.464308\pi\) |
−0.916534 | + | 0.399956i | \(0.869025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.47018e15 | 1.30975 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.77536e15 | 1.55009 | 0.775043 | − | 0.631908i | \(-0.217728\pi\) | ||||
0.775043 | + | 0.631908i | \(0.217728\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.12129e14 | − | 1.57985e15i | 0.765108 | − | 1.32521i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.77334e14 | + | 1.44402e15i | −0.474722 | + | 1.18736i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.78568e14 | − | 1.00211e15i | −0.457247 | − | 0.791975i | 0.541567 | − | 0.840657i | \(-0.317831\pi\) |
−0.998814 | + | 0.0486825i | \(0.984498\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.37484e14 | 0.106534 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.74197e13 | + | 6.48129e13i | 0.0278808 | + | 0.0482909i | 0.879629 | − | 0.475660i | \(-0.157791\pi\) |
−0.851748 | + | 0.523951i | \(0.824457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.62559e14 | + | 9.74380e14i | −0.411056 | + | 0.711971i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.17284e14 | + | 1.24237e15i | −0.504166 | + | 0.873242i | 0.495822 | + | 0.868424i | \(0.334867\pi\) |
−0.999988 | + | 0.00481770i | \(0.998466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.10440e14 | + | 8.84108e14i | 0.351922 | + | 0.609546i | 0.986586 | − | 0.163242i | \(-0.0521950\pi\) |
−0.634665 | + | 0.772788i | \(0.718862\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.18338e14 | −0.144862 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.42848e14 | + | 5.93830e14i | 0.223169 | + | 0.386540i | 0.955769 | − | 0.294120i | \(-0.0950264\pi\) |
−0.732599 | + | 0.680660i | \(0.761693\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.95281e14 | − | 1.29138e14i | 0.561036 | − | 0.0809255i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.65970e14 | − | 9.80288e14i | 0.348029 | − | 0.602805i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.45428e15 | 1.45350 | 0.726749 | − | 0.686903i | \(-0.241030\pi\) | ||||
0.726749 | + | 0.686903i | \(0.241030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.23866e15 | 2.46374 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.66959e14 | + | 2.89182e14i | −0.0934995 | + | 0.161946i | −0.908981 | − | 0.416837i | \(-0.863139\pi\) |
0.815482 | + | 0.578783i | \(0.196472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.69193e15 | + | 3.88293e14i | −1.47986 | + | 0.213460i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.76178e14 | + | 3.05148e14i | 0.0933476 | + | 0.161683i | 0.908918 | − | 0.416975i | \(-0.136910\pi\) |
−0.815570 | + | 0.578658i | \(0.803577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.86713e15 | −0.971327 | −0.485663 | − | 0.874146i | \(-0.661422\pi\) | ||||
−0.485663 | + | 0.874146i | \(0.661422\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.17516e14 | + | 1.06957e15i | 0.309738 | + | 0.536481i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.87189e14 | − | 3.24221e14i | 0.0922025 | − | 0.159699i | −0.816235 | − | 0.577720i | \(-0.803943\pi\) |
0.908438 | + | 0.418020i | \(0.137276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.51914e14 | + | 4.36328e14i | −0.119681 | + | 0.207294i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.64601e14 | + | 2.85097e14i | 0.0768067 | + | 0.133033i | 0.901871 | − | 0.432006i | \(-0.142194\pi\) |
−0.825064 | + | 0.565040i | \(0.808861\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.23369e15 | −1.90612 | −0.953061 | − | 0.302777i | \(-0.902086\pi\) | ||||
−0.953061 | + | 0.302777i | \(0.902086\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.66928e15 | − | 2.89129e15i | −0.738298 | − | 1.27877i | −0.953261 | − | 0.302148i | \(-0.902296\pi\) |
0.214963 | − | 0.976622i | \(-0.431037\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.46003e15 | − | 3.65179e15i | 0.623270 | − | 1.55891i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00138e15 | − | 1.73444e15i | 0.420008 | − | 0.727476i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.51763e15 | −0.614592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.53088e14 | −0.299698 | −0.149849 | − | 0.988709i | \(-0.547879\pi\) | ||||
−0.149849 | + | 0.988709i | \(0.547879\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.73185e15 | + | 2.99964e15i | −0.665662 | + | 1.15296i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.10821e15 | − | 3.26497e14i | 0.418654 | − | 0.123342i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.70022e14 | + | 1.33372e15i | 0.281050 | + | 0.486793i | 0.971644 | − | 0.236450i | \(-0.0759840\pi\) |
−0.690594 | + | 0.723243i | \(0.742651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.35931e15 | −1.56407 | −0.782037 | − | 0.623232i | \(-0.785819\pi\) | ||||
−0.782037 | + | 0.623232i | \(0.785819\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.90014e15 | + | 3.29114e15i | 0.658890 | + | 1.14123i | 0.980903 | + | 0.194496i | \(0.0623070\pi\) |
−0.322014 | + | 0.946735i | \(0.604360\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.88242e14 | − | 1.01887e15i | 0.200544 | − | 0.347353i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.23183e15 | − | 2.13359e15i | 0.406001 | − | 0.703215i | −0.588436 | − | 0.808544i | \(-0.700256\pi\) |
0.994437 | + | 0.105329i | \(0.0335896\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.39478e13 | − | 2.41583e13i | −0.00452043 | − | 0.00782961i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.32943e15 | −1.35694 | −0.678471 | − | 0.734627i | \(-0.737357\pi\) | ||||
−0.678471 | + | 0.734627i | \(0.737357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.08449e15 | − | 1.87839e15i | −0.334284 | − | 0.578998i | 0.649063 | − | 0.760735i | \(-0.275161\pi\) |
−0.983347 | + | 0.181737i | \(0.941828\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.00967e15 | − | 3.82352e15i | −0.897427 | − | 1.14010i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.72124e15 | + | 2.98127e15i | −0.504834 | + | 0.874399i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.41743e15 | 0.402279 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.47908e13 | 0.0236737 | 0.0118368 | − | 0.999930i | \(-0.496232\pi\) | ||||
0.0118368 | + | 0.999930i | \(0.496232\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.98941e15 | + | 5.17782e15i | −0.807883 | + | 1.39929i | 0.106445 | + | 0.994319i | \(0.466053\pi\) |
−0.914328 | + | 0.404976i | \(0.867280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.21996e15 | − | 6.08700e14i | 1.12208 | − | 0.161853i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.50741e15 | + | 2.61091e15i | 0.388077 | + | 0.672169i | 0.992191 | − | 0.124729i | \(-0.0398062\pi\) |
−0.604114 | + | 0.796898i | \(0.706473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.53711e15 | 0.896088 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.07463e15 | + | 1.86131e15i | 0.263664 | + | 0.456680i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.26172e15 | − | 2.18537e15i | 0.304673 | − | 0.527710i | −0.672515 | − | 0.740083i | \(-0.734786\pi\) |
0.977189 | + | 0.212374i | \(0.0681194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.43710e14 | − | 1.11494e15i | 0.150582 | − | 0.260816i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.56506e15 | − | 4.44281e15i | −0.590632 | − | 1.02300i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.09678e15 | −1.36035 | −0.680176 | − | 0.733049i | \(-0.738097\pi\) | ||||
−0.680176 | + | 0.733049i | \(0.738097\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.35758e15 | − | 2.35140e15i | −0.298203 | − | 0.516502i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.41227e15 | + | 5.60541e15i | 0.939411 | + | 1.19344i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.01210e15 | − | 5.21711e15i | 0.631415 | − | 1.09364i | −0.355848 | − | 0.934544i | \(-0.615808\pi\) |
0.987263 | − | 0.159099i | \(-0.0508589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.99860e15 | −1.62563 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.16488e15 | 0.233130 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.19170e13 | − | 1.24564e14i | 0.0139580 | − | 0.0241759i | −0.858962 | − | 0.512039i | \(-0.828890\pi\) |
0.872920 | + | 0.487863i | \(0.162224\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.23219e15 | + | 5.58311e15i | −0.426665 | + | 1.06717i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.69967e14 | + | 6.40801e14i | 0.0685968 | + | 0.118813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.32629e15 | −1.52059 | −0.760295 | − | 0.649578i | \(-0.774946\pi\) | ||||
−0.760295 | + | 0.649578i | \(0.774946\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.11069e15 | − | 1.92377e15i | −0.196810 | − | 0.340884i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.34131e15 | + | 2.32322e15i | −0.234131 | + | 0.405526i | −0.959020 | − | 0.283339i | \(-0.908558\pi\) |
0.724889 | + | 0.688866i | \(0.241891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.83420e14 | − | 4.90898e14i | 0.0480131 | − | 0.0831611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.12901e15 | + | 7.15166e15i | 0.689131 | + | 1.19361i | 0.972119 | + | 0.234486i | \(0.0753408\pi\) |
−0.282989 | + | 0.959123i | \(0.591326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.41601e15 | −0.391435 | −0.195718 | − | 0.980660i | \(-0.562704\pi\) | ||||
−0.195718 | + | 0.980660i | \(0.562704\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.63133e15 | − | 4.55760e15i | −0.420065 | − | 0.727574i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.36003e15 | − | 3.40167e15i | 0.210813 | − | 0.527281i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.49081e15 | + | 9.51036e15i | −0.838719 | + | 1.45270i | 0.0522466 | + | 0.998634i | \(0.483362\pi\) |
−0.890966 | + | 0.454070i | \(0.849972\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.07314e14 | −0.134601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.46816e15 | −0.507075 | −0.253537 | − | 0.967326i | \(-0.581594\pi\) | ||||
−0.253537 | + | 0.967326i | \(0.581594\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.37973e15 | + | 5.85386e15i | −0.480028 | + | 0.831432i | −0.999738 | − | 0.0229104i | \(-0.992707\pi\) |
0.519710 | + | 0.854343i | \(0.326040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.24098e15 | + | 7.92862e15i | 0.873711 | + | 1.10997i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.11692e15 | + | 1.93455e15i | 0.151931 | + | 0.263152i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.71762e15 | −1.16897 | −0.584485 | − | 0.811405i | \(-0.698703\pi\) | ||||
−0.584485 | + | 0.811405i | \(0.698703\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.98343e15 | + | 3.43541e15i | 0.258482 | + | 0.447704i | 0.965835 | − | 0.259156i | \(-0.0834444\pi\) |
−0.707354 | + | 0.706860i | \(0.750111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.59618e14 | + | 1.48890e15i | −0.110445 | + | 0.191296i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.58910e15 | − | 7.94856e15i | 0.573155 | − | 0.992733i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.33237e15 | + | 4.03979e15i | 0.287222 | + | 0.497482i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.11236e16 | −1.33188 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.39520e14 | + | 7.61272e14i | 0.0518941 | + | 0.0898832i | 0.890806 | − | 0.454385i | \(-0.150141\pi\) |
−0.838911 | + | 0.544268i | \(0.816808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.64288e15 | + | 1.10243e15i | −0.877579 | + | 0.126585i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.34566e15 | + | 2.33075e15i | −0.152382 | + | 0.263933i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.25139e16 | −1.37839 | −0.689193 | − | 0.724578i | \(-0.742035\pi\) | ||||
−0.689193 | + | 0.724578i | \(0.742035\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.14053e15 | 0.884393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.65464e15 | + | 8.06208e15i | −0.491984 | + | 0.852141i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.67941e15 | + | 7.21519e15i | 0.592142 | + | 0.752264i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.81136e15 | − | 1.00656e16i | −0.589605 | − | 1.02123i | −0.994284 | − | 0.106767i | \(-0.965950\pi\) |
0.404679 | − | 0.914459i | \(-0.367383\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.78327e15 | −0.478752 | −0.239376 | − | 0.970927i | \(-0.576943\pi\) | ||||
−0.239376 | + | 0.970927i | \(0.576943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.80088e15 | − | 4.85127e15i | −0.272853 | − | 0.472595i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.98711e15 | − | 3.44178e15i | 0.190986 | − | 0.330797i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.45650e15 | − | 7.71888e15i | 0.416971 | − | 0.722216i | −0.578662 | − | 0.815568i | \(-0.696425\pi\) |
0.995633 | + | 0.0933519i | \(0.0297582\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.97971e15 | − | 1.03572e16i | −0.552054 | − | 0.956185i | −0.998126 | − | 0.0611881i | \(-0.980511\pi\) |
0.446073 | − | 0.894997i | \(-0.352822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.33380e16 | 1.19897 | 0.599486 | − | 0.800385i | \(-0.295372\pi\) | ||||
0.599486 | + | 0.800385i | \(0.295372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.19823e15 | − | 1.59318e16i | −0.815933 | − | 1.41324i | −0.908656 | − | 0.417545i | \(-0.862891\pi\) |
0.0927232 | − | 0.995692i | \(-0.470443\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.35214e16 | − | 1.28692e16i | −1.16809 | − | 1.11174i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.12519e15 | + | 1.23412e16i | −0.607465 | + | 1.05216i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.68002e15 | 0.803869 | 0.401935 | − | 0.915668i | \(-0.368338\pi\) | ||||
0.401935 | + | 0.915668i | \(0.368338\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.34159e14 | −0.0437817 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.69981e15 | − | 8.14032e15i | 0.375291 | − | 0.650024i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.14676e15 | + | 7.87061e15i | −0.248030 | + | 0.620368i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.56183e15 | + | 4.43722e15i | 0.196761 | + | 0.340799i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.53181e15 | 0.343599 | 0.171800 | − | 0.985132i | \(-0.445042\pi\) | ||||
0.171800 | + | 0.985132i | \(0.445042\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.76035e15 | − | 8.24516e15i | −0.351758 | − | 0.609263i | 0.634800 | − | 0.772677i | \(-0.281083\pi\) |
−0.986558 | + | 0.163414i | \(0.947749\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.08779e15 | + | 1.22764e16i | −0.517069 | + | 0.895589i | 0.482735 | + | 0.875767i | \(0.339643\pi\) |
−0.999804 | + | 0.0198225i | \(0.993690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.72665e15 | + | 1.16509e16i | −0.478343 | + | 0.828515i | −0.999692 | − | 0.0248291i | \(-0.992096\pi\) |
0.521348 | + | 0.853344i | \(0.325429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.61574e15 | + | 4.53059e15i | 0.183656 | + | 0.318102i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.07619e16 | −0.736681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.38139e14 | + | 9.32084e14i | 0.0363743 | + | 0.0630022i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.58769e16 | − | 2.29013e15i | 1.04646 | − | 0.150944i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.63403e14 | − | 1.49546e15i | 0.0561973 | − | 0.0973366i | −0.836558 | − | 0.547878i | \(-0.815436\pi\) |
0.892755 | + | 0.450542i | \(0.148769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.12123e16 | 1.98134 | 0.990670 | − | 0.136285i | \(-0.0435163\pi\) | ||||
0.990670 | + | 0.136285i | \(0.0435163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.18187e14 | −0.0324865 | −0.0162432 | − | 0.999868i | \(-0.505171\pi\) | ||||
−0.0162432 | + | 0.999868i | \(0.505171\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.54428e15 | + | 1.65312e16i | −0.583664 | + | 1.01094i | 0.411376 | + | 0.911466i | \(0.365048\pi\) |
−0.995041 | + | 0.0994704i | \(0.968285\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.35287e16 | + | 3.39385e15i | −1.42114 | + | 0.204990i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.28204e15 | + | 1.26129e16i | 0.429112 | + | 0.743243i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.72721e16 | 1.00535 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.35534e16 | + | 2.34751e16i | 0.769785 | + | 1.33331i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.73631e16 | − | 3.00737e16i | 0.974183 | − | 1.68733i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.17017e15 | + | 5.49090e15i | −0.173586 | + | 0.300660i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.47127e15 | − | 1.29406e16i | −0.404161 | − | 0.700028i | 0.590062 | − | 0.807358i | \(-0.299103\pi\) |
−0.994223 | + | 0.107330i | \(0.965770\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.17361e16 | −1.14770 | −0.573852 | − | 0.818959i | \(-0.694552\pi\) | ||||
−0.573852 | + | 0.818959i | \(0.694552\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.12980e15 | + | 5.42097e15i | 0.163278 | + | 0.282805i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.10758e13 | − | 1.77773e14i | 0.00361985 | − | 0.00905388i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.69066e16 | − | 2.92831e16i | 0.850787 | − | 1.47361i | −0.0297130 | − | 0.999558i | \(-0.509459\pi\) |
0.880500 | − | 0.474047i | \(-0.157207\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.85710e15 | −0.435194 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.10129e15 | 0.0534716 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.17628e15 | − | 1.41617e16i | 0.387676 | − | 0.671475i | −0.604460 | − | 0.796635i | \(-0.706611\pi\) |
0.992137 | + | 0.125160i | \(0.0399445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.84390e15 | − | 3.24620e16i | 0.367543 | − | 1.52108i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.41069e15 | − | 1.62998e16i | −0.430683 | − | 0.745964i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.22063e15 | 0.190902 | 0.0954508 | − | 0.995434i | \(-0.469571\pi\) | ||||
0.0954508 | + | 0.995434i | \(0.469571\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.69807e16 | − | 2.94115e16i | −0.750262 | − | 1.29949i | −0.947695 | − | 0.319176i | \(-0.896594\pi\) |
0.197433 | − | 0.980316i | \(-0.436739\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.65989e15 | + | 1.49994e16i | −0.378180 | + | 0.655027i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.89987e16 | + | 3.29068e16i | −0.810588 | + | 1.40398i | 0.101865 | + | 0.994798i | \(0.467519\pi\) |
−0.912453 | + | 0.409181i | \(0.865814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.83793e15 | − | 1.53077e16i | −0.372723 | − | 0.645575i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.34699e16 | 0.967163 | 0.483582 | − | 0.875299i | \(-0.339336\pi\) | ||||
0.483582 | + | 0.875299i | \(0.339336\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.98243e14 | − | 3.43367e14i | −0.00807568 | − | 0.0139875i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.50152e16 | + | 1.90755e16i | 0.597762 | + | 0.759405i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.87870e16 | + | 3.25401e16i | −0.739401 | + | 1.28068i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.77739e15 | 0.222245 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.48719e16 | 1.32627 | 0.663133 | − | 0.748502i | \(-0.269227\pi\) | ||||
0.663133 | + | 0.748502i | \(0.269227\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.10378e16 | − | 1.91180e16i | 0.410371 | − | 0.710783i | −0.584559 | − | 0.811351i | \(-0.698733\pi\) |
0.994930 | + | 0.100568i | \(0.0320659\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.74540e15 | − | 1.26146e15i | 0.321484 | − | 0.0463718i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.07614e16 | + | 3.59598e16i | 0.746168 | + | 1.29240i | 0.949647 | + | 0.313322i | \(0.101442\pi\) |
−0.203479 | + | 0.979079i | \(0.565225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.72158e16 | 0.967201 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.25256e14 | + | 1.60259e15i | 0.0321527 | + | 0.0556902i | 0.881654 | − | 0.471896i | \(-0.156430\pi\) |
−0.849501 | + | 0.527587i | \(0.823097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.99283e15 | − | 1.03799e16i | 0.205936 | − | 0.356692i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.74979e15 | + | 6.49483e15i | −0.126017 | + | 0.218267i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.85376e16 | + | 4.94286e16i | 0.948447 | + | 1.64276i | 0.748698 | + | 0.662911i | \(0.230679\pi\) |
0.199748 | + | 0.979847i | \(0.435988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.48508e16 | 0.482752 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.99297e16 | + | 3.45192e16i | 0.640733 | + | 1.10978i | 0.985269 | + | 0.171009i | \(0.0547028\pi\) |
−0.344536 | + | 0.938773i | \(0.611964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.12.k.d.37.3 | 16 | ||
3.2 | odd | 2 | 84.12.i.b.37.6 | yes | 16 | ||
7.4 | even | 3 | inner | 252.12.k.d.109.3 | 16 | ||
21.11 | odd | 6 | 84.12.i.b.25.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.i.b.25.6 | ✓ | 16 | 21.11 | odd | 6 | ||
84.12.i.b.37.6 | yes | 16 | 3.2 | odd | 2 | ||
252.12.k.d.37.3 | 16 | 1.1 | even | 1 | trivial | ||
252.12.k.d.109.3 | 16 | 7.4 | even | 3 | inner |