Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 13062x^{6} + 45211107x^{4} + 45928424926x^{2} + 852972309225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(-53.8781i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.10.d.b.193.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 81.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 473.533i | − 0.338833i | −0.985545 | − | 0.169416i | \(-0.945812\pi\) | ||||
0.985545 | − | 0.169416i | \(-0.0541882\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 574.939 | 0.0905067 | 0.0452534 | − | 0.998976i | \(-0.485590\pi\) | ||||
0.0452534 | + | 0.998976i | \(0.485590\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 72774.7i | 1.49869i | 0.662177 | + | 0.749347i | \(0.269633\pi\) | ||||
−0.662177 | + | 0.749347i | \(0.730367\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14829.2i | 0.144003i | 0.997405 | + | 0.0720016i | \(0.0229387\pi\) | ||||
−0.997405 | + | 0.0720016i | \(0.977061\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −38356.2 | −0.195625 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 109932. | 0.319229 | 0.159614 | − | 0.987179i | \(-0.448975\pi\) | ||||
0.159614 | + | 0.987179i | \(0.448975\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 497573.i | − 0.875922i | −0.898994 | − | 0.437961i | \(-0.855701\pi\) | ||||
0.898994 | − | 0.437961i | \(-0.144299\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 46570.1i | − 0.0522541i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 104764. | 0.0780614 | 0.0390307 | − | 0.999238i | \(-0.487573\pi\) | ||||
0.0390307 | + | 0.999238i | \(0.487573\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.72889e6 | 0.885192 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.06390e6i | 1.85461i | 0.374301 | + | 0.927307i | \(0.377883\pi\) | ||||
−0.374301 | + | 0.927307i | \(0.622117\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.30578e6 | 0.448426 | 0.224213 | − | 0.974540i | \(-0.428019\pi\) | ||||
0.224213 | + | 0.974540i | \(0.428019\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.89475e6 | 0.865272 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 272253.i | − 0.0306666i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.20960e6i | − 0.456979i | −0.973546 | − | 0.228490i | \(-0.926621\pi\) | ||||
0.973546 | − | 0.228490i | \(-0.0733787\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.20116e6 | 0.0831402 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.08234e7 | −0.598185 | −0.299092 | − | 0.954224i | \(-0.596684\pi\) | ||||
−0.299092 | + | 0.954224i | \(0.596684\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.04081e7i | − 0.910319i | −0.890410 | − | 0.455160i | \(-0.849582\pi\) | ||||
0.890410 | − | 0.455160i | \(-0.150418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.10685e6i | 0.112944i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.47476e7 | −1.03869 | −0.519343 | − | 0.854566i | \(-0.673823\pi\) | ||||
−0.519343 | + | 0.854566i | \(0.673823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.00231e7 | −0.991809 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 8.90445e6i | − 0.184307i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.34226e7i | − 1.62634i | −0.582028 | − | 0.813169i | \(-0.697741\pi\) | ||||
0.582028 | − | 0.813169i | \(-0.302259\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.44612e7 | 0.507807 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.03034e7 | −0.505714 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.04786e7i | 0.972102i | 0.873930 | + | 0.486051i | \(0.161563\pi\) | ||||
−0.873930 | + | 0.486051i | \(0.838437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00269e7i | 0.185195i | 0.995704 | + | 0.0925976i | \(0.0295170\pi\) | ||||
−0.995704 | + | 0.0925976i | \(0.970483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.77218e6 | −0.0301689 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.02210e6 | 0.0487930 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.09151e8i | − 0.661745i | −0.943676 | − | 0.330872i | \(-0.892657\pi\) | ||||
0.943676 | − | 0.330872i | \(-0.107343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 8.48588e6i | − 0.0450688i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.65931e8 | −1.24196 | −0.620978 | − | 0.783828i | \(-0.713264\pi\) | ||||
−0.620978 | + | 0.783828i | \(0.713264\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.05525e7 | 0.208348 | 0.104174 | − | 0.994559i | \(-0.466780\pi\) | ||||
0.104174 | + | 0.994559i | \(0.466780\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.40040e8i | − 0.511066i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.18410e7i | 0.135642i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.24238e7 | 0.0358865 | 0.0179433 | − | 0.999839i | \(-0.494288\pi\) | ||||
0.0179433 | + | 0.999839i | \(0.494288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.72920e8i | 0.631225i | 0.948888 | + | 0.315613i | \(0.102210\pi\) | ||||
−0.948888 | + | 0.315613i | \(0.897790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5.20562e7i | − 0.108165i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.72176e8 | 1.07076 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.70637e8 | −0.457227 | −0.228613 | − | 0.973517i | \(-0.573419\pi\) | ||||
−0.228613 | + | 0.973517i | \(0.573419\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.52588e6i | 0.0130333i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1.86768e8i | − 0.258899i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.35617e8 | −0.296791 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.06136e8 | −0.465799 | −0.232899 | − | 0.972501i | \(-0.574821\pi\) | ||||
−0.232899 | + | 0.972501i | \(0.574821\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 4.77475e8i | − 0.499565i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 3.58458e8i | − 0.342762i | −0.985205 | − | 0.171381i | \(-0.945177\pi\) | ||||
0.985205 | − | 0.171381i | \(-0.0548229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.12727e8 | −0.273777 | −0.136889 | − | 0.990586i | \(-0.543710\pi\) | ||||
−0.136889 | + | 0.990586i | \(0.543710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.20525e7 | −0.0177054 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.28960e8i | 0.685125i | 0.939495 | + | 0.342562i | \(0.111295\pi\) | ||||
−0.939495 | + | 0.342562i | \(0.888705\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.54301e9i | − 1.04701i | −0.852024 | − | 0.523503i | \(-0.824625\pi\) | ||||
0.852024 | − | 0.523503i | \(-0.175375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.21977e8 | −0.263837 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.98385e8 | −0.345245 | −0.172623 | − | 0.984988i | \(-0.555224\pi\) | ||||
−0.172623 | + | 0.984988i | \(0.555224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.96092e7i | − 0.0264498i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 9.72942e7i | − 0.0480010i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.32039e7 | 0.0288924 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.93820e9 | −1.24609 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.76693e8i | 0.345362i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.74356e9i | − 0.638765i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.52986e9 | 0.862940 | 0.431470 | − | 0.902127i | \(-0.357995\pi\) | ||||
0.431470 | + | 0.902127i | \(0.357995\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.65305e9 | −0.525573 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.70203e8i | − 0.0504948i | −0.999681 | − | 0.0252474i | \(-0.991963\pi\) | ||||
0.999681 | − | 0.0252474i | \(-0.00803734\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.86074e8i | − 0.0792768i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.51655e8 | 0.0652084 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.59035e9 | 0.628226 | 0.314113 | − | 0.949386i | \(-0.398293\pi\) | ||||
0.314113 | + | 0.949386i | \(0.398293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.75040e9i | 0.624928i | 0.949930 | + | 0.312464i | \(0.101154\pi\) | ||||
−0.949930 | + | 0.312464i | \(0.898846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.81456e9i | 0.599686i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.07919e9 | −0.215817 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.34499e9 | 0.628404 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.24187e9i | 0.572621i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.97566e9i | − 0.494590i | −0.968940 | − | 0.247295i | \(-0.920458\pi\) | ||||
0.968940 | − | 0.247295i | \(-0.0795416\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.10799e10 | −1.73435 | −0.867177 | − | 0.498000i | \(-0.834068\pi\) | ||||
−0.867177 | + | 0.498000i | \(0.834068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.21261e8 | −0.106410 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.09186e9i | − 0.151941i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.20320e10i | 1.58048i | 0.612797 | + | 0.790240i | \(0.290044\pi\) | ||||
−0.612797 | + | 0.790240i | \(0.709956\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.56723e9 | −0.938966 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.02329e7 | 0.00706508 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.21499e9i | 0.134812i | 0.997726 | + | 0.0674062i | \(0.0214724\pi\) | ||||
−0.997726 | + | 0.0674062i | \(0.978528\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 2.79136e9i | − 0.293182i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.01298e10 | 1.00780 | 0.503902 | − | 0.863761i | \(-0.331897\pi\) | ||||
0.503902 | + | 0.863761i | \(0.331897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.03846e10 | 0.979263 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.26458e9i | 0.291974i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.12366e10i | 0.953738i | 0.878974 | + | 0.476869i | \(0.158228\pi\) | ||||
−0.878974 | + | 0.476869i | \(0.841772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.94008e8 | 0.0801159 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.32877e9 | 0.561244 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.72939e9i | − 0.271518i | −0.990742 | − | 0.135759i | \(-0.956653\pi\) | ||||
0.990742 | − | 0.135759i | \(-0.0433473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.47052e10i | − 1.01840i | −0.860649 | − | 0.509198i | \(-0.829942\pi\) | ||||
0.860649 | − | 0.509198i | \(-0.170058\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.62218e9 | 0.106922 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.46692e9 | −0.154839 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00023e9i | 0.478426i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.05546e8i | 0.0174180i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.16788e10 | −1.17865 | −0.589325 | − | 0.807896i | \(-0.700606\pi\) | ||||
−0.589325 | + | 0.807896i | \(0.700606\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.45321e10 | −1.27270 | −0.636350 | − | 0.771400i | \(-0.719557\pi\) | ||||
−0.636350 | + | 0.771400i | \(0.719557\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 5.68790e8i | − 0.0281706i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.44518e10i | − 0.683632i | −0.939767 | − | 0.341816i | \(-0.888958\pi\) | ||||
0.939767 | − | 0.341816i | \(-0.111042\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.71655e10 | −1.22794 | −0.613972 | − | 0.789328i | \(-0.710429\pi\) | ||||
−0.613972 | + | 0.789328i | \(0.710429\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.84122e9 | −0.382058 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.06132e9i | 0.167855i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.12522e9i | 0.202684i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.87356e8 | −0.0260205 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.62107e10 | 1.31274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.52449e10i | 1.22412i | 0.790810 | + | 0.612062i | \(0.209660\pi\) | ||||
−0.790810 | + | 0.612062i | \(0.790340\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.15404e10i | 0.717044i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.66389e9 | −0.308446 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.32568e9 | 0.0405855 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 4.09475e9i | − 0.120290i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.63019e9i | 0.0459699i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.45878e10 | −0.395019 | −0.197510 | − | 0.980301i | \(-0.563285\pi\) | ||||
−0.197510 | + | 0.980301i | \(0.563285\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.13433e10 | −0.295064 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.30500e10i | 1.57605i | 0.615646 | + | 0.788023i | \(0.288895\pi\) | ||||
−0.615646 | + | 0.788023i | \(0.711105\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.91705e10i | 1.18153i | 0.806843 | + | 0.590765i | \(0.201174\pi\) | ||||
−0.806843 | + | 0.590765i | \(0.798826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.38912e9 | 0.0783129 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.30380e10 | 0.734366 | 0.367183 | − | 0.930149i | \(-0.380322\pi\) | ||||
0.367183 | + | 0.930149i | \(0.380322\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.64541e10i | 0.351941i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.00633e9i | − 0.0207191i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.33801e10 | −1.45475 | −0.727374 | − | 0.686241i | \(-0.759260\pi\) | ||||
−0.727374 | + | 0.686241i | \(0.759260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.53816e10 | 1.05752 | 0.528760 | − | 0.848771i | \(-0.322657\pi\) | ||||
0.528760 | + | 0.848771i | \(0.322657\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3.48678e9i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.89522e10i | 0.336057i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.37860e9 | 0.126136 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.21065e10 | 0.364438 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.51298e10i | 1.51281i | 0.654103 | + | 0.756406i | \(0.273046\pi\) | ||||
−0.654103 | + | 0.756406i | \(0.726954\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.62416e9i | 0.116990i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.21655e9 | −0.0624492 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.82111e10 | −0.832351 | −0.416176 | − | 0.909284i | \(-0.636630\pi\) | ||||
−0.416176 | + | 0.909284i | \(0.636630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.99520e9i | − 0.0413597i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 4.63463e10i | − 0.618205i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.26131e11 | −1.62563 | −0.812814 | − | 0.582524i | \(-0.802065\pi\) | ||||
−0.812814 | + | 0.582524i | \(0.802065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.42387e10 | −0.551056 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.19216e10i | 0.263980i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.23726e10i | 0.144071i | 0.997402 | + | 0.0720356i | \(0.0229495\pi\) | ||||
−0.997402 | + | 0.0720356i | \(0.977050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.40678e10 | −0.721569 | −0.360785 | − | 0.932649i | \(-0.617491\pi\) | ||||
−0.360785 | + | 0.932649i | \(0.617491\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.90596e8 | 0.00752475 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.25820e11i | 1.32663i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.56675e11i | − 1.59897i | −0.600688 | − | 0.799484i | \(-0.705107\pi\) | ||||
0.600688 | − | 0.799484i | \(-0.294893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.51282e10 | −0.149475 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.55568e10 | −0.914288 | −0.457144 | − | 0.889393i | \(-0.651128\pi\) | ||||
−0.457144 | + | 0.889393i | \(0.651128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.99388e10i | 0.740830i | 0.928866 | + | 0.370415i | \(0.120785\pi\) | ||||
−0.928866 | + | 0.370415i | \(0.879215\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.90850e10i | 0.171352i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.22278e9 | −0.0541397 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06503e11 | −0.898093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.28970e10i | 0.268929i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 9.87325e10i | − 0.782629i | −0.920257 | − | 0.391315i | \(-0.872020\pi\) | ||||
0.920257 | − | 0.391315i | \(-0.127980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.28446e10 | 0.329380 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.86754e10 | −0.288424 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.55356e9i | 0.0112411i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.17334e10i | − 0.0823900i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.90351e10 | −0.197894 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.48340e9 | 0.0627502 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.01628e11i | 1.29547i | 0.761864 | + | 0.647737i | \(0.224284\pi\) | ||||
−0.761864 | + | 0.647737i | \(0.775716\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.53309e10i | 0.158065i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.25577e11 | −0.761182 | −0.380591 | − | 0.924744i | \(-0.624279\pi\) | ||||
−0.380591 | + | 0.924744i | \(0.624279\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.72056e10 | 0.572455 | 0.286228 | − | 0.958162i | \(-0.407599\pi\) | ||||
0.286228 | + | 0.958162i | \(0.407599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.78625e9i | 0.0102222i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.24299e10i | − 0.180376i | −0.995925 | − | 0.0901880i | \(-0.971253\pi\) | ||||
0.995925 | − | 0.0901880i | \(-0.0287468\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.14073e11 | −2.77950 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.52457e10 | 0.395557 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.46989e10i | − 0.279620i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.56380e10i | 0.127470i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.24984e11 | −0.604490 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.99778e10 | −0.0940081 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.13971e11i | 0.979781i | 0.871784 | + | 0.489890i | \(0.162963\pi\) | ||||
−0.871784 | + | 0.489890i | \(0.837037\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.41802e10i | 0.152326i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.16865e10 | −0.224221 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.67278e11 | −0.706489 | −0.353244 | − | 0.935531i | \(-0.614922\pi\) | ||||
−0.353244 | + | 0.935531i | \(0.614922\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.84692e10i | 0.199328i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.67802e11i | 0.672053i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.62117e10 | −0.180272 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.01834e9 | −0.0152708 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.93452e11i | 0.716293i | 0.933665 | + | 0.358146i | \(0.116591\pi\) | ||||
−0.933665 | + | 0.358146i | \(0.883409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.79870e11i | − 0.649000i | −0.945886 | − | 0.324500i | \(-0.894804\pi\) | ||||
0.945886 | − | 0.324500i | \(-0.105196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.88083e9 | −0.0277134 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.13154e11 | 0.730646 | 0.365323 | − | 0.930881i | \(-0.380959\pi\) | ||||
0.365323 | + | 0.930881i | \(0.380959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.25927e11i | 0.420815i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 5.11952e9i | − 0.0166810i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.85269e11 | 0.588677 | 0.294339 | − | 0.955701i | \(-0.404901\pi\) | ||||
0.294339 | + | 0.955701i | \(0.404901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.51089e10 | 0.232760 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.37995e11i | 0.719428i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.39383e10i | − 0.0705952i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.99652e11 | −1.14997 | −0.574983 | − | 0.818166i | \(-0.694991\pi\) | ||||
−0.574983 | + | 0.818166i | \(0.694991\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.10122e10 | 0.199395 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 5.37123e10i | − 0.147194i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.17540e11i | 0.849394i | 0.905335 | + | 0.424697i | \(0.139619\pi\) | ||||
−0.905335 | + | 0.424697i | \(0.860381\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.41228e11 | −0.368791 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.04752e11 | −0.267070 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.10387e11i | 0.523771i | 0.965099 | + | 0.261886i | \(0.0843443\pi\) | ||||
−0.965099 | + | 0.261886i | \(0.915656\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2.04919e11i | − 0.498219i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.26458e11 | −1.48764 | −0.743819 | − | 0.668381i | \(-0.766988\pi\) | ||||
−0.743819 | + | 0.668381i | \(0.766988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.98131e10 | 0.0459599 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.33897e11i | 0.303440i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.71840e11i | 1.04477i | 0.852709 | + | 0.522386i | \(0.174958\pi\) | ||||
−0.852709 | + | 0.522386i | \(0.825042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.15169e10 | 0.0249194 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.37864e10 | −0.0291532 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 5.88307e9i | − 0.0121595i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.08614e11i | − 0.825573i | −0.910828 | − | 0.412786i | \(-0.864556\pi\) | ||||
0.910828 | − | 0.412786i | \(-0.135444\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.31720e10 | −0.0457705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.75227e11 | −0.917807 | −0.458903 | − | 0.888486i | \(-0.651758\pi\) | ||||
−0.458903 | + | 0.888486i | \(0.651758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.41928e10i | 0.0645747i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2.03840e10i | − 0.0376481i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.79127e11 | 0.684872 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.47969e11 | 0.261466 | 0.130733 | − | 0.991418i | \(-0.458267\pi\) | ||||
0.130733 | + | 0.991418i | \(0.458267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.09818e11i | − 0.362706i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.20197e10i | 0.0879818i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.29237e11 | 0.213880 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.22783e11 | 0.360802 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.99050e11i | 1.42502i | 0.701663 | + | 0.712509i | \(0.252441\pi\) | ||||
−0.701663 | + | 0.712509i | \(0.747559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 9.67201e10i | − 0.150054i | −0.997182 | − | 0.0750269i | \(-0.976096\pi\) | ||||
0.997182 | − | 0.0750269i | \(-0.0239043\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.27979e11 | 0.346229 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.90060e11 | 0.282579 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.15143e10i | 0.0167614i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.74143e10i | 0.124602i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.91630e11 | −0.686263 | −0.343131 | − | 0.939287i | \(-0.611488\pi\) | ||||
−0.343131 | + | 0.939287i | \(0.611488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.39033e10 | −0.0326786 | −0.0163393 | − | 0.999867i | \(-0.505201\pi\) | ||||
−0.0163393 | + | 0.999867i | \(0.505201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.70944e11i | − 0.362809i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5.21277e10i | − 0.0683757i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.29279e11 | 1.06564 | 0.532820 | − | 0.846229i | \(-0.321132\pi\) | ||||
0.532820 | + | 0.846229i | \(0.321132\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.62591e11 | 0.330603 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.71843e11i | 0.705440i | 0.935729 | + | 0.352720i | \(0.114743\pi\) | ||||
−0.935729 | + | 0.352720i | \(0.885257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.28155e11i | 0.154923i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.41028e11 | −0.285551 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.02914e12 | 1.19500 | 0.597500 | − | 0.801869i | \(-0.296161\pi\) | ||||
0.597500 | + | 0.801869i | \(0.296161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 7.87668e11i | − 0.896496i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.97468e11i | 1.00133i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.03728e9 | 0.00441609 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.44956e11 | −0.798928 | −0.399464 | − | 0.916749i | \(-0.630804\pi\) | ||||
−0.399464 | + | 0.916749i | \(0.630804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.84221e10i | 0.0614356i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.35785e11i | 0.140023i | 0.997546 | + | 0.0700115i | \(0.0223036\pi\) | ||||
−0.997546 | + | 0.0700115i | \(0.977696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.39280e10 | −0.0646512 | −0.0323256 | − | 0.999477i | \(-0.510291\pi\) | ||||
−0.0323256 | + | 0.999477i | \(0.510291\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.84409e10 | −0.0877233 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.08293e11i | − 0.786399i | −0.919453 | − | 0.393199i | \(-0.871368\pi\) | ||||
0.919453 | − | 0.393199i | \(-0.128632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.27551e10i | − 0.0598923i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.74591e11 | 0.912491 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.48519e12 | 1.36429 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 8.60250e11i | − 0.775360i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.12946e11i | 0.542112i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.38621e12 | −1.20315 | −0.601573 | − | 0.798818i | \(-0.705459\pi\) | ||||
−0.601573 | + | 0.798818i | \(0.705459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.72540e10 | 0.0658064 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.87886e9i | − 0.00407903i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.92319e11i | 0.157828i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.20417e11 | 0.0970078 | 0.0485039 | − | 0.998823i | \(-0.484555\pi\) | ||||
0.0485039 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.84146e10 | 0.0778340 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.43283e11i | − 0.111257i | −0.998452 | − | 0.0556287i | \(-0.982284\pi\) | ||||
0.998452 | − | 0.0556287i | \(-0.0177163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.76545e11i | 0.592046i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.26100e11 | −0.169269 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.52894e11 | −0.112405 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.93465e12i | 1.39685i | 0.715683 | + | 0.698426i | \(0.246116\pi\) | ||||
−0.715683 | + | 0.698426i | \(0.753884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 8.20513e11i | − 0.581856i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.14780e12 | 1.49602 | 0.748010 | − | 0.663687i | \(-0.231009\pi\) | ||||
0.748010 | + | 0.663687i | \(0.231009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.69742e11 | −0.116139 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 8.41152e11i | − 0.565378i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.93770e10i | 0.0326058i | 0.999867 | + | 0.0163029i | \(0.00518961\pi\) | ||||
−0.999867 | + | 0.0163029i | \(0.994810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.90646e10 | 0.0188569 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.64431e11 | 0.168571 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.48086e11i | 0.0927646i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.52875e12i | − 1.55667i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.10168e11 | 0.550641 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.06642e12 | −1.82331 | −0.911657 | − | 0.410951i | \(-0.865197\pi\) | ||||
−0.911657 | + | 0.410951i | \(0.865197\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.36512e12i | − 0.797836i | −0.916987 | − | 0.398918i | \(-0.869386\pi\) | ||||
0.916987 | − | 0.398918i | \(-0.130614\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 8.05146e10i | − 0.0462549i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.53478e11 | 0.143150 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.79018e12 | −0.993906 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.93630e11i | − 0.324034i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.60502e11i | − 0.0861405i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.39893e11 | 0.232143 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.02081e11 | −0.156761 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.91266e12i | − 1.48642i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 2.34837e12i | − 1.17863i | −0.807902 | − | 0.589317i | \(-0.799397\pi\) | ||||
0.807902 | − | 0.589317i | \(-0.200603\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.19112e12 | −0.587971 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.30666e11 | −0.354760 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.90038e12i | − 1.86279i | −0.364007 | − | 0.931396i | \(-0.618592\pi\) | ||||
0.364007 | − | 0.931396i | \(-0.381408\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.31397e11i | − 0.0617317i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.51481e12 | 1.62450 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.14292e9 | 0.00324797 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.99820e11i | 0.0893966i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9.85631e11i | − 0.433876i | −0.976185 | − | 0.216938i | \(-0.930393\pi\) | ||||
0.976185 | − | 0.216938i | \(-0.0696070\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.02635e11 | 0.131089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.48019e11 | 0.276220 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 3.71992e12i | − 1.56044i | −0.625508 | − | 0.780218i | \(-0.715108\pi\) | ||||
0.625508 | − | 0.780218i | \(-0.284892\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.83355e11i | 0.116980i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.47493e10 | 0.0100563 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.34608e12 | 0.938293 | 0.469146 | − | 0.883120i | \(-0.344562\pi\) | ||||
0.469146 | + | 0.883120i | \(0.344562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.58941e12i | 0.625710i | 0.949801 | + | 0.312855i | \(0.101285\pi\) | ||||
−0.949801 | + | 0.312855i | \(0.898715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.75598e12i | 0.680493i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.81125e11 | 0.0690994 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.20772e12 | −1.58036 | −0.790179 | − | 0.612876i | \(-0.790013\pi\) | ||||
−0.790179 | + | 0.612876i | \(0.790013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.98710e12i | 0.734794i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.56913e11i | 0.0571302i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.79880e12 | 2.43738 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.60720e10 | −0.0162643 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.63748e12i | − 0.569252i | −0.958639 | − | 0.284626i | \(-0.908131\pi\) | ||||
0.958639 | − | 0.284626i | \(-0.0918694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.14729e12i | − 0.392786i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.17059e12 | −0.394695 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.53148e12 | 1.83694 | 0.918471 | − | 0.395489i | \(-0.129425\pi\) | ||||
0.918471 | + | 0.395489i | \(0.129425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.99292e10i | − 0.00978967i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.20040e12i | 0.708954i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.16661e12 | 1.32240 | 0.661199 | − | 0.750211i | \(-0.270048\pi\) | ||||
0.661199 | + | 0.750211i | \(0.270048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.90464e12 | −0.908149 | −0.454075 | − | 0.890964i | \(-0.650030\pi\) | ||||
−0.454075 | + | 0.890964i | \(0.650030\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.16139e11i | 0.220582i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.39134e12i | 0.422214i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.66728e12 | −1.39545 | −0.697726 | − | 0.716365i | \(-0.745805\pi\) | ||||
−0.697726 | + | 0.716365i | \(0.745805\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.28967e11 | 0.0969112 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 5.15278e11i | − 0.149574i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.12221e11i | 0.0893078i | 0.999003 | + | 0.0446539i | \(0.0142185\pi\) | ||||
−0.999003 | + | 0.0446539i | \(0.985781\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.15143e11 | 0.117020 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.59628e12 | 0.999011 | 0.499505 | − | 0.866311i | \(-0.333515\pi\) | ||||
0.499505 | + | 0.866311i | \(0.333515\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4.85670e12i | − 1.32964i | −0.747004 | − | 0.664819i | \(-0.768509\pi\) | ||||
0.747004 | − | 0.664819i | \(-0.231491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.56758e10i | 0.0150229i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.55600e11 | −0.0413821 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.55111e12 | 0.668758 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.93307e12i | − 0.757911i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 5.72699e11i | − 0.145881i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.19329e12 | 1.55521 | 0.777606 | − | 0.628752i | \(-0.216434\pi\) | ||||
0.777606 | + | 0.628752i | \(0.216434\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.85484e12 | 0.706748 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.19797e12i | − 0.292392i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5.93509e11i | − 0.142824i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.74477e12 | 0.413985 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.96307e12 | −1.39511 | −0.697555 | − | 0.716531i | \(-0.745729\pi\) | ||||
−0.697555 | + | 0.716531i | \(0.745729\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7.48485e11i | − 0.172677i | −0.996266 | − | 0.0863383i | \(-0.972483\pi\) | ||||
0.996266 | − | 0.0863383i | \(-0.0275166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.82775e11i | 0.178081i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.21646e12 | 1.17032 | 0.585162 | − | 0.810916i | \(-0.301031\pi\) | ||||
0.585162 | + | 0.810916i | \(0.301031\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.58455e12 | −1.45688 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1.07380e11i | − 0.0234321i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.05968e12i | 1.08896i | 0.838772 | + | 0.544482i | \(0.183274\pi\) | ||||
−0.838772 | + | 0.544482i | \(0.816726\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.05967e10 | −0.0171093 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.31675e11 | −0.0694494 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.64097e12i | − 0.338936i | −0.985536 | − | 0.169468i | \(-0.945795\pi\) | ||||
0.985536 | − | 0.169468i | \(-0.0542049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 9.39337e12i | − 1.91388i | −0.290284 | − | 0.956941i | \(-0.593750\pi\) | ||||
0.290284 | − | 0.956941i | \(-0.406250\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.32046e11 | 0.0265408 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.35466e11 | −0.0268616 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.40042e11i | 0.144774i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.18161e12i | 0.228065i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.45745e12 | −0.277551 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.84794e11 | 0.128674 | 0.0643372 | − | 0.997928i | \(-0.479507\pi\) | ||||
0.0643372 | + | 0.997928i | \(0.479507\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.18804e11i | 0.170355i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.15344e12i | − 0.393988i | −0.980405 | − | 0.196994i | \(-0.936882\pi\) | ||||
0.980405 | − | 0.196994i | \(-0.0631180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.33503e11 | −0.0421579 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.10705e12 | 0.909930 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.32483e12i | 0.584623i | 0.956323 | + | 0.292311i | \(0.0944244\pi\) | ||||
−0.956323 | + | 0.292311i | \(0.905576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.22662e12i | − 0.212863i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.98281e12 | 0.682157 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.38538e12 | 0.234198 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.50122e12i | − 0.250491i | −0.992126 | − | 0.125246i | \(-0.960028\pi\) | ||||
0.992126 | − | 0.125246i | \(-0.0399719\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.74519e11i | − 0.0452140i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.30241e12 | 0.211746 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.18983e12 | −0.190958 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 2.67608e12i | − 0.423987i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.02156e12i | 0.472607i | 0.971679 | + | 0.236304i | \(0.0759360\pi\) | ||||
−0.971679 | + | 0.236304i | \(0.924064\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.59215e12 | −0.400278 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.33279e12 | 0.203193 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.06092e11i | − 0.0310223i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 3.67440e12i | − 0.546108i | −0.961999 | − | 0.273054i | \(-0.911966\pi\) | ||||
0.961999 | − | 0.273054i | \(-0.0880337\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.15124e10 | −0.0119622 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.41563e11 | 0.0350047 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.11031e11i | 0.0731257i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.94379e12i | 0.839899i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.45558e12 | −1.31950 | −0.659748 | − | 0.751487i | \(-0.729337\pi\) | ||||
−0.659748 | + | 0.751487i | \(0.729337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.79799e11 | −0.0247787 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 4.48591e12i | − 0.610560i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.22127e13i | 1.64169i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44431e13 | 1.91760 | 0.958798 | − | 0.284090i | \(-0.0916913\pi\) | ||||
0.958798 | + | 0.284090i | \(0.0916913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2.24349e12i | − 0.290600i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.09211e12i | 0.523576i | 0.965125 | + | 0.261788i | \(0.0843121\pi\) | ||||
−0.965125 | + | 0.261788i | \(0.915688\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.53513e12 | 0.194023 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.94342e12 | 0.991753 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 9.48921e12i | − 1.17039i | −0.810893 | − | 0.585195i | \(-0.801018\pi\) | ||||
0.810893 | − | 0.585195i | \(-0.198982\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 5.97666e11i | − 0.0728244i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.23279e12 | −0.268781 | −0.134390 | − | 0.990928i | \(-0.542908\pi\) | ||||
−0.134390 | + | 0.990928i | \(0.542908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.40907e12 | −0.167583 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.79063e12i | − 0.210408i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.34095e11i | 0.0620084i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.33252e13 | −1.52860 | −0.764298 | − | 0.644863i | \(-0.776914\pi\) | ||||
−0.764298 | + | 0.644863i | \(0.776914\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.70552e12 | 0.873422 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.24667e12i | 0.587656i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 2.46238e12i | − 0.272536i | −0.990672 | − | 0.136268i | \(-0.956489\pi\) | ||||
0.990672 | − | 0.136268i | \(-0.0435108\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.17557e11 | 0.0675443 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.93783e12 | 0.857968 | 0.428984 | − | 0.903312i | \(-0.358872\pi\) | ||||
0.428984 | + | 0.903312i | \(0.358872\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.87137e11i | − 0.0947611i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.41541e11i | 0.0360550i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.34172e12 | −0.139986 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.58369e13 | −1.63305 | −0.816527 | − | 0.577307i | \(-0.804104\pi\) | ||||
−0.816527 | + | 0.577307i | \(0.804104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.71510e12i | 0.480558i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.21012e13i | 1.21904i | 0.792769 | + | 0.609522i | \(0.208639\pi\) | ||||
−0.792769 | + | 0.609522i | \(0.791361\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.98645e12 | 0.396943 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.42611e11 | −0.0238790 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.38542e12i | 0.523963i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.93530e13i | − 1.86131i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.75405e12 | −0.356921 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.69754e12 | 0.535518 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.64934e13i | 1.53258i | 0.642495 | + | 0.766290i | \(0.277899\pi\) | ||||
−0.642495 | + | 0.766290i | \(0.722101\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.02166e13i | 0.938557i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.44035e11 | −0.0312470 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.96983e11 | −0.0266687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.58333e12i | 0.318152i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9.14539e12i | − 0.802860i | −0.915890 | − | 0.401430i | \(-0.868513\pi\) | ||||
0.915890 | − | 0.401430i | \(-0.131487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.81986e12 | −0.331579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.77565e12 | 0.152409 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.67894e12i | 0.312250i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.85223e10i | − 0.00239388i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.00218e12 | 0.0831796 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.10523e12 | 0.0907160 | 0.0453580 | − | 0.998971i | \(-0.485557\pi\) | ||||
0.0453580 | + | 0.998971i | \(0.485557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 5.17595e12i | − 0.420142i | −0.977686 | − | 0.210071i | \(-0.932631\pi\) | ||||
0.977686 | − | 0.210071i | \(-0.0673695\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.18949e12i | 0.416598i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.75340e11 | 0.0456789 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01545e13 | −0.797369 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 5.59383e10i | − 0.00434442i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.06367e13i | 0.817076i | 0.912741 | + | 0.408538i | \(0.133961\pi\) | ||||
−0.912741 | + | 0.408538i | \(0.866039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.89127e13 | −1.43699 | −0.718495 | − | 0.695532i | \(-0.755169\pi\) | ||||
−0.718495 | + | 0.695532i | \(0.755169\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.01914e13 | 0.765932 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.62866e11i | 0.0492777i | 0.999696 | + | 0.0246389i | \(0.00784359\pi\) | ||||
−0.999696 | + | 0.0246389i | \(0.992156\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 2.27273e13i | − 1.67129i | −0.549267 | − | 0.835647i | \(-0.685093\pi\) | ||||
0.549267 | − | 0.835647i | \(-0.314907\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.26906e13 | −0.923164 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.39979e12 | −0.316614 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 4.79679e12i | − 0.341477i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.22539e12i | 0.0862996i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.12551e12 | −0.148093 | −0.0740463 | − | 0.997255i | \(-0.523591\pi\) | ||||
−0.0740463 | + | 0.997255i | \(0.523591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.53916e13 | −2.43960 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.74010e12i | 0.527865i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 4.91745e12i | − 0.331806i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.68929e12 | −0.112779 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.47504e12 | 0.427718 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 5.45778e11i | − 0.0356724i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.52949e13i | − 1.63592i | −0.575276 | − | 0.817960i | \(-0.695105\pi\) | ||||
0.575276 | − | 0.817960i | \(-0.304895\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.54588e12 | 0.0989303 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.42903e12 | 0.153822 | 0.0769112 | − | 0.997038i | \(-0.475494\pi\) | ||||
0.0769112 | + | 0.997038i | \(0.475494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.92636e13i | 1.83383i | 0.399083 | + | 0.916915i | \(0.369329\pi\) | ||||
−0.399083 | + | 0.916915i | \(0.630671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.04046e11i | 0.0312576i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.25262e13 | −0.768724 | −0.384362 | − | 0.923182i | \(-0.625579\pi\) | ||||
−0.384362 | + | 0.923182i | \(0.625579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.32092e12 | 0.323157 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.62674e12i | 0.518514i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.04136e11i | 0.0537830i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.61862e12 | 0.0952933 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.66466e12 | 0.155266 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.00244e12i | − 0.0578125i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.98911e11i | 0.0398955i | 0.999801 | + | 0.0199477i | \(0.00634998\pi\) | ||||
−0.999801 | + | 0.0199477i | \(0.993650\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.99733e12 | −0.451851 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.80581e13 | −1.00991 | −0.504953 | − | 0.863147i | \(-0.668490\pi\) | ||||
−0.504953 | + | 0.863147i | \(0.668490\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.54103e13i | 1.40665i | 0.710867 | + | 0.703326i | \(0.248303\pi\) | ||||
−0.710867 | + | 0.703326i | \(0.751697\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 3.47041e12i | − 0.190168i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.87381e12 | 0.155884 | 0.0779421 | − | 0.996958i | \(-0.475165\pi\) | ||||
0.0779421 | + | 0.996958i | \(0.475165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.45452e12 | 0.0781019 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.13271e12i | 0.166522i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.72895e13i | 0.909809i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.76599e12 | −0.0919993 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.25839e11 | 0.00649004 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.62878e13i | 0.831657i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.02701e13i | − 0.519174i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.50405e11 | −0.0475679 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.96339e12 | −0.345066 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.81693e10i | 0.00481662i | 0.999997 | + | 0.00240831i | \(0.000766590\pi\) | ||||
−0.999997 | + | 0.00240831i | \(0.999233\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.35185e12i | 0.114254i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.70352e12 | −0.178148 | −0.0890741 | − | 0.996025i | \(-0.528391\pi\) | ||||
−0.0890741 | + | 0.996025i | \(0.528391\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.98617e13 | −0.946014 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 7.68156e11i | − 0.0362288i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 9.78564e10i | − 0.00457012i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.79299e13 | −1.75413 | −0.877066 | − | 0.480370i | \(-0.840502\pi\) | ||||
−0.877066 | + | 0.480370i | \(0.840502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.63319e13 | 0.747942 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.94354e12i | − 0.178846i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 9.00683e12i | − 0.404515i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.05180e12 | 0.0912591 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.49219e13 | 1.53825 | 0.769124 | − | 0.639099i | \(-0.220693\pi\) | ||||
0.769124 | + | 0.639099i | \(0.220693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.99144e13i | 0.868747i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.01717e13i | 0.439468i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.78837e12 | 0.162106 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.39866e13 | −1.01658 | −0.508288 | − | 0.861187i | \(-0.669722\pi\) | ||||
−0.508288 | + | 0.861187i | \(0.669722\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 7.87365e12i | − 0.330507i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 8.10164e12i | − 0.336837i | −0.985716 | − | 0.168418i | \(-0.946134\pi\) | ||||
0.985716 | − | 0.168418i | \(-0.0538660\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.13390e12 | −0.0466951 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.44686e11 | 0.00590180 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.66583e12i | 0.0673061i | 0.999434 | + | 0.0336531i | \(0.0107141\pi\) | ||||
−0.999434 | + | 0.0336531i | \(0.989286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.49652e11i | 0.0300028i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.62682e12 | −0.104140 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.98680e13 | 1.56569 | 0.782846 | − | 0.622215i | \(-0.213767\pi\) | ||||
0.782846 | + | 0.622215i | \(0.213767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.02656e13i | 0.399365i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.16399e13i | 1.60475i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.48929e12 | 0.0568587 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.11230e13 | −0.798914 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 6.09490e12i | − 0.228375i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.16167e13i | 0.431232i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.53153e13 | −1.29880 | −0.649402 | − | 0.760446i | \(-0.724981\pi\) | ||||
−0.649402 | + | 0.760446i | \(0.724981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.43061e12 | −0.161438 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.43725e13i | 0.879862i | 0.898032 | + | 0.439931i | \(0.144997\pi\) | ||||
−0.898032 | + | 0.439931i | \(0.855003\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.58132e12i | 0.0565602i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.07668e12 | 0.0735951 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.11200e13 | 1.09273 | 0.546366 | − | 0.837546i | \(-0.316011\pi\) | ||||
0.546366 | + | 0.837546i | \(0.316011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.96955e13i | − 0.685243i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.01237e13i | 0.349002i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.69352e13 | −0.920088 | −0.460044 | − | 0.887896i | \(-0.652166\pi\) | ||||
−0.460044 | + | 0.887896i | \(0.652166\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.84338e12 | −0.231637 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.61820e12i | 0.0542756i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2.13803e12i | − 0.0710608i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.56596e13 | 1.17448 | 0.587240 | − | 0.809413i | \(-0.300215\pi\) | ||||
0.587240 | + | 0.809413i | \(0.300215\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.73317e13 | 0.565677 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.28638e13i | 0.416068i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.95731e13i | − 1.26844i | −0.773151 | − | 0.634222i | \(-0.781320\pi\) | ||||
0.773151 | − | 0.634222i | \(-0.218680\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.76859e12 | 0.0879457 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.10.d.b.193.2 | yes | 8 | |
4.3 | odd | 2 | 384.10.d.a.193.6 | yes | 8 | ||
8.3 | odd | 2 | 384.10.d.a.193.3 | ✓ | 8 | ||
8.5 | even | 2 | inner | 384.10.d.b.193.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.d.a.193.3 | ✓ | 8 | 8.3 | odd | 2 | ||
384.10.d.a.193.6 | yes | 8 | 4.3 | odd | 2 | ||
384.10.d.b.193.2 | yes | 8 | 1.1 | even | 1 | trivial | |
384.10.d.b.193.7 | yes | 8 | 8.5 | even | 2 | inner |