Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7628 x^{10} + 22070097 x^{8} - 30593373916 x^{6} + 21405948373596 x^{4} + \cdots + 90\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{57}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.3 | ||
Root | \(-49.2636 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.e.193.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 27.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 8.99895i | − 0.0321956i | −0.999870 | − | 0.0160978i | \(-0.994876\pi\) | ||||
0.999870 | − | 0.0160978i | \(-0.00512432\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −616.197 | −0.679011 | −0.339505 | − | 0.940604i | \(-0.610260\pi\) | ||||
−0.339505 | + | 0.940604i | \(0.610260\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3035.60i | 0.687655i | 0.939033 | + | 0.343828i | \(0.111724\pi\) | ||||
−0.939033 | + | 0.343828i | \(0.888276\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 12272.8i | − 1.54932i | −0.632377 | − | 0.774660i | \(-0.717921\pi\) | ||||
0.632377 | − | 0.774660i | \(-0.282079\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −242.972 | −0.0185882 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −35454.2 | −1.75024 | −0.875118 | − | 0.483909i | \(-0.839217\pi\) | ||||
−0.875118 | + | 0.483909i | \(0.839217\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 46835.6i | − 1.56653i | −0.621689 | − | 0.783264i | \(-0.713553\pi\) | ||||
0.621689 | − | 0.783264i | \(-0.286447\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16637.3i | 0.392027i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 89833.4 | 1.53954 | 0.769769 | − | 0.638323i | \(-0.220371\pi\) | ||||
0.769769 | + | 0.638323i | \(0.220371\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 78044.0 | 0.998963 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 113126.i | 0.861333i | 0.902511 | + | 0.430666i | \(0.141721\pi\) | ||||
−0.902511 | + | 0.430666i | \(0.858279\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −246616. | −1.48681 | −0.743403 | − | 0.668843i | \(-0.766790\pi\) | ||||
−0.743403 | + | 0.668843i | \(0.766790\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 81961.3 | 0.397018 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5545.13i | 0.0218612i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 383887.i | − 1.24594i | −0.782245 | − | 0.622970i | \(-0.785926\pi\) | ||||
0.782245 | − | 0.622970i | \(-0.214074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −331365. | −0.894501 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 63822.4 | 0.144620 | 0.0723102 | − | 0.997382i | \(-0.476963\pi\) | ||||
0.0723102 | + | 0.997382i | \(0.476963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 697052.i | − 1.33698i | −0.743720 | − | 0.668491i | \(-0.766940\pi\) | ||||
0.743720 | − | 0.668491i | \(-0.233060\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6560.24i | 0.0107319i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −66539.5 | −0.0934840 | −0.0467420 | − | 0.998907i | \(-0.514884\pi\) | ||||
−0.0467420 | + | 0.998907i | \(0.514884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −443844. | −0.538944 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 957264.i | 1.01050i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.02190e6i | 0.942851i | 0.881906 | + | 0.471426i | \(0.156260\pi\) | ||||
−0.881906 | + | 0.471426i | \(0.843740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 27317.3 | 0.0221395 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.26456e6 | −0.904435 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.66944e6i | 1.05825i | 0.848544 | + | 0.529125i | \(0.177480\pi\) | ||||
−0.848544 | + | 0.529125i | \(0.822520\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.94570e6i | 1.09754i | 0.835972 | + | 0.548772i | \(0.184905\pi\) | ||||
−0.835972 | + | 0.548772i | \(0.815095\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 449208. | 0.226337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −110442. | −0.0498814 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 50973.1i | − 0.0207052i | −0.999946 | − | 0.0103526i | \(-0.996705\pi\) | ||||
0.999946 | − | 0.0103526i | \(-0.00329539\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.42550e6i | − 0.888852i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.04161e6 | −1.67173 | −0.835863 | − | 0.548938i | \(-0.815032\pi\) | ||||
−0.835863 | + | 0.548938i | \(0.815032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.82121e6 | 1.75139 | 0.875696 | − | 0.482863i | \(-0.160403\pi\) | ||||
0.875696 | + | 0.482863i | \(0.160403\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 2.10719e6i | − 0.576752i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.87053e6i | − 0.466925i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.30931e6 | −0.526972 | −0.263486 | − | 0.964663i | \(-0.584872\pi\) | ||||
−0.263486 | + | 0.964663i | \(0.584872\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.20768e6i | − 0.615768i | −0.951424 | − | 0.307884i | \(-0.900379\pi\) | ||||
0.951424 | − | 0.307884i | \(-0.0996209\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 319051.i | 0.0563500i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.05441e6 | 0.497291 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.21504e6 | −0.784138 | −0.392069 | − | 0.919936i | \(-0.628240\pi\) | ||||
−0.392069 | + | 0.919936i | \(0.628240\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.56246e6i | 1.05201i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.65862e6i | 0.858408i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −421471. | −0.0504354 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.08632e6 | −0.343352 | −0.171676 | − | 0.985153i | \(-0.554918\pi\) | ||||
−0.171676 | + | 0.985153i | \(0.554918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 2.21296e6i | − 0.229218i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44652e7i | 1.39701i | 0.715604 | + | 0.698507i | \(0.246152\pi\) | ||||
−0.715604 | + | 0.698507i | \(0.753848\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.89906e6 | −0.171241 | −0.0856205 | − | 0.996328i | \(-0.527287\pi\) | ||||
−0.0856205 | + | 0.996328i | \(0.527287\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 149719. | 0.0126216 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.54233e7i | − 1.21712i | −0.793506 | − | 0.608562i | \(-0.791747\pi\) | ||||
0.793506 | − | 0.608562i | \(-0.208253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.59792e6i | 0.487994i | 0.969776 | + | 0.243997i | \(0.0784587\pi\) | ||||
−0.969776 | + | 0.243997i | \(0.921541\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.03650e7 | −0.719344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.66038e6 | −0.369038 | −0.184519 | − | 0.982829i | \(-0.559073\pi\) | ||||
−0.184519 | + | 0.982829i | \(0.559073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 808407.i | − 0.0495664i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.94686e6i | 0.516440i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.18468e7 | 1.18843 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.02723e7 | 0.527130 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.72321e6i | − 0.0834967i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.40536e6i | − 0.0643579i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.21577e7 | 0.526669 | 0.263334 | − | 0.964705i | \(-0.415178\pi\) | ||||
0.263334 | + | 0.964705i | \(0.415178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.88204e7 | −0.771907 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.25216e7i | 1.26393i | 0.774997 | + | 0.631965i | \(0.217751\pi\) | ||||
−0.774997 | + | 0.631965i | \(0.782249\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.88599e7i | 1.06369i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 177126. | 0.00619605 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.34472e7 | 1.44358 | 0.721789 | − | 0.692114i | \(-0.243320\pi\) | ||||
0.721789 | + | 0.692114i | \(0.243320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.11016e6i | 0.0666444i | 0.999445 | + | 0.0333222i | \(0.0106088\pi\) | ||||
−0.999445 | + | 0.0333222i | \(0.989391\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.79657e6i | 0.0539730i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.72553e7 | 1.06540 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.01802e6 | 0.0277312 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.19838e7i | 0.311160i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.58625e7i | 0.888156i | 0.895988 | + | 0.444078i | \(0.146469\pi\) | ||||
−0.895988 | + | 0.444078i | \(0.853531\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.80703e6 | 0.184530 | 0.0922649 | − | 0.995734i | \(-0.470589\pi\) | ||||
0.0922649 | + | 0.995734i | \(0.470589\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.58461e7 | 0.583412 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.21928e6i | 0.0478687i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.98173e7i | 1.64607i | 0.567991 | + | 0.823035i | \(0.307721\pi\) | ||||
−0.567991 | + | 0.823035i | \(0.692279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.75913e7 | 0.544355 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.53551e7 | −1.04536 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.10447e7i | − 0.742336i | −0.928566 | − | 0.371168i | \(-0.878957\pi\) | ||||
0.928566 | − | 0.371168i | \(-0.121043\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 737566.i | − 0.0127822i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.79088e7 | −1.46058 | −0.730289 | − | 0.683139i | \(-0.760614\pi\) | ||||
−0.730289 | + | 0.683139i | \(0.760614\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.78727e7 | −1.40040 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.41431e7i | 0.522176i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.29158e8i | 1.89653i | 0.317478 | + | 0.948266i | \(0.397164\pi\) | ||||
−0.317478 | + | 0.948266i | \(0.602836\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.80905e7 | −0.678307 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.50749e7 | 0.610981 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.13096e7i | 0.147388i | 0.997281 | + | 0.0736941i | \(0.0234789\pi\) | ||||
−0.997281 | + | 0.0736941i | \(0.976521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.01595e8i | 1.27349i | 0.771074 | + | 0.636746i | \(0.219720\pi\) | ||||
−0.771074 | + | 0.636746i | \(0.780280\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.25340e7 | 0.633668 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.45458e6 | −0.0401139 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.07625e8i | − 1.20356i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.21286e7i | − 0.130676i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.54258e7 | 0.264032 | 0.132016 | − | 0.991248i | \(-0.457855\pi\) | ||||
0.132016 | + | 0.991248i | \(0.457855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.01605e7 | 0.101734 | 0.0508668 | − | 0.998705i | \(-0.483802\pi\) | ||||
0.0508668 | + | 0.998705i | \(0.483802\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.98194e6i | 0.0287990i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.94284e7i | 0.553812i | 0.960897 | + | 0.276906i | \(0.0893091\pi\) | ||||
−0.960897 | + | 0.276906i | \(0.910691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.32802e8 | 1.19459 | 0.597293 | − | 0.802023i | \(-0.296243\pi\) | ||||
0.597293 | + | 0.802023i | \(0.296243\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.37627e6 | −0.0119541 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 6.97082e7i | − 0.584854i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 574335.i | − 0.00465615i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.54885e7 | −0.513179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.42174e8 | 1.07723 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.57624e8i | 1.88798i | 0.329971 | + | 0.943991i | \(0.392961\pi\) | ||||
−0.329971 | + | 0.943991i | \(0.607039\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.36123e8i | 0.965171i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.27274e6 | −0.0430450 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.51964e8 | 1.00956 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1.57173e8i | − 1.01117i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.35122e8i | 2.71168i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.96405e8 | −1.18600 | −0.593002 | − | 0.805201i | \(-0.702057\pi\) | ||||
−0.593002 | + | 0.805201i | \(0.702057\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.68941e7 | −0.332988 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.67364e7i | − 0.492165i | −0.969249 | − | 0.246082i | \(-0.920857\pi\) | ||||
0.969249 | − | 0.246082i | \(-0.0791434\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.22165e8i | 0.672237i | 0.941820 | + | 0.336118i | \(0.109114\pi\) | ||||
−0.941820 | + | 0.336118i | \(0.890886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.05044e7 | −0.269580 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.39072e7 | −0.279191 | −0.139595 | − | 0.990209i | \(-0.544580\pi\) | ||||
−0.139595 | + | 0.990209i | \(0.544580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 598786.i | 0.00300978i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.23514e7i | 0.304247i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.90175e7 | 0.137489 | 0.0687443 | − | 0.997634i | \(-0.478101\pi\) | ||||
0.0687443 | + | 0.997634i | \(0.478101\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.43173e8 | −1.57926 | −0.789630 | − | 0.613583i | \(-0.789728\pi\) | ||||
−0.789630 | + | 0.613583i | \(0.789728\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.43489e7i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.99413e6i | 0.0173517i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.74803e8 | −2.42705 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.66072e7 | −0.355514 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.87903e8i | 0.750025i | 0.927020 | + | 0.375012i | \(0.122362\pi\) | ||||
−0.927020 | + | 0.375012i | \(0.877638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.72699e8i | 1.05867i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.61438e6 | 0.0325337 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.70210e7 | 0.209541 | 0.104770 | − | 0.994496i | \(-0.466589\pi\) | ||||
0.104770 | + | 0.994496i | \(0.466589\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.36550e8i | 0.846007i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 8.24692e7i | − 0.287111i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.54738e8 | 0.863474 | 0.431737 | − | 0.902000i | \(-0.357901\pi\) | ||||
0.431737 | + | 0.902000i | \(0.357901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.19604e6 | 0.0303557 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.40806e8i | 0.452722i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 6.31643e8i | − 1.97851i | −0.146193 | − | 0.989256i | \(-0.546702\pi\) | ||||
0.146193 | − | 0.989256i | \(-0.453298\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.74328e8 | 0.837293 | 0.418646 | − | 0.908149i | \(-0.362505\pi\) | ||||
0.418646 | + | 0.908149i | \(0.362505\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.04186e8 | 0.607376 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.36911e8i | 0.686943i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.83552e8i | 1.08429i | 0.840285 | + | 0.542145i | \(0.182388\pi\) | ||||
−0.840285 | + | 0.542145i | \(0.817612\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.79783e8 | 0.495602 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.03791e8 | −1.08564 | −0.542819 | − | 0.839850i | \(-0.682643\pi\) | ||||
−0.542819 | + | 0.839850i | \(0.682643\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.57245e8i | − 1.19921i | −0.800295 | − | 0.599607i | \(-0.795324\pi\) | ||||
0.800295 | − | 0.599607i | \(-0.204676\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.13797e7i | 0.0291189i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.93272e7 | −0.0981989 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.46664e8 | 2.06333 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.33306e7i | 0.198234i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.48249e8i | 1.73784i | 0.494953 | + | 0.868920i | \(0.335185\pi\) | ||||
−0.494953 | + | 0.868920i | \(0.664815\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.50232e7 | 0.0340711 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.97498e7 | −0.132339 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.10251e9i | − 2.38524i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.29522e8i | 0.907826i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.90561e8 | 0.806566 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.75093e7 | 0.0353362 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4.34755e7i | − 0.0857551i | −0.999080 | − | 0.0428775i | \(-0.986347\pi\) | ||||
0.999080 | − | 0.0428775i | \(-0.0136525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.12746e7i | 0.0988661i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.82116e8 | −0.343310 | −0.171655 | − | 0.985157i | \(-0.554911\pi\) | ||||
−0.171655 | + | 0.985157i | \(0.554911\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.21850e7 | 0.0961923 | 0.0480961 | − | 0.998843i | \(-0.484685\pi\) | ||||
0.0480961 | + | 0.998843i | \(0.484685\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 4.04240e6i | − 0.00728706i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6.76984e7i | − 0.119363i | −0.998217 | − | 0.0596816i | \(-0.980991\pi\) | ||||
0.998217 | − | 0.0596816i | \(-0.0190086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.43407e8 | −0.592300 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.16430e8 | −0.702707 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.66052e9i | 2.74179i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 9.57817e8i | − 1.54771i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.78144e8 | 0.281743 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.10015e7 | 0.0634767 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 7.97772e8i | − 1.20915i | −0.796548 | − | 0.604576i | \(-0.793343\pi\) | ||||
0.796548 | − | 0.604576i | \(-0.206657\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.79854e8i | 0.415314i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −458704. | −0.000666617 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.52453e7 | 0.0216986 | 0.0108493 | − | 0.999941i | \(-0.496546\pi\) | ||||
0.0108493 | + | 0.999941i | \(0.496546\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.52830e8i | 0.213064i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7.48627e8i | − 1.02241i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.80960e8 | 1.04496 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.18270e7 | −0.0286172 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.45017e8i | − 0.571773i | −0.958263 | − | 0.285887i | \(-0.907712\pi\) | ||||
0.958263 | − | 0.285887i | \(-0.0922881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.38196e9i | − 1.74023i | −0.492846 | − | 0.870117i | \(-0.664043\pi\) | ||||
0.492846 | − | 0.870117i | \(-0.335957\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.41565e8 | 0.298167 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.14032e8 | −0.379981 | −0.189991 | − | 0.981786i | \(-0.560846\pi\) | ||||
−0.189991 | + | 0.981786i | \(0.560846\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.53692e7i | 0.0538223i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 5.89864e8i | − 0.686140i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.14356e9 | 1.30445 | 0.652224 | − | 0.758027i | \(-0.273836\pi\) | ||||
0.652224 | + | 0.758027i | \(0.273836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.29970e9 | −1.45401 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.77351e8i | − 0.304339i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.23848e7i | − 0.0563872i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.40602e9 | −1.48478 | −0.742388 | − | 0.669970i | \(-0.766307\pi\) | ||||
−0.742388 | + | 0.669970i | \(0.766307\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.65266e7 | −0.0482068 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6.29693e8i | − 0.640206i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3.92421e8i | − 0.391536i | −0.980650 | − | 0.195768i | \(-0.937280\pi\) | ||||
0.980650 | − | 0.195768i | \(-0.0627199\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.79447e7 | −0.0371571 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.38838e9 | 1.33448 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.58729e8i | 0.621541i | 0.950485 | + | 0.310770i | \(0.100587\pi\) | ||||
−0.950485 | + | 0.310770i | \(0.899413\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3.28257e8i | − 0.304072i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.37352e9 | 1.24923 | 0.624613 | − | 0.780935i | \(-0.285257\pi\) | ||||
0.624613 | + | 0.780935i | \(0.285257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.68328e7 | −0.0150330 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.08151e8i | 0.445661i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 5.75082e7i | − 0.0495343i | −0.999693 | − | 0.0247671i | \(-0.992116\pi\) | ||||
0.999693 | − | 0.0247671i | \(-0.00788443\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.18497e9 | −2.69456 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.78085e8 | 0.729730 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.07814e7i | 0.0169662i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.45178e8i | − 0.357082i | −0.983933 | − | 0.178541i | \(-0.942862\pi\) | ||||
0.983933 | − | 0.178541i | \(-0.0571376\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.79219e8 | 0.614121 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.79495e8 | 0.603682 | 0.301841 | − | 0.953358i | \(-0.402399\pi\) | ||||
0.301841 | + | 0.953358i | \(0.402399\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.02666e9i | 2.30354i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 4.78241e6i | − 0.00357729i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.16533e9 | 0.856778 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.35057e9 | 0.976077 | 0.488039 | − | 0.872822i | \(-0.337712\pi\) | ||||
0.488039 | + | 0.872822i | \(0.337712\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.17307e9i | − 0.833450i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.02870e9i | − 0.718564i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.88657e7 | −0.0198250 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.69743e7 | 0.0384772 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.86568e8i | 0.389556i | 0.980847 | + | 0.194778i | \(0.0623986\pi\) | ||||
−0.980847 | + | 0.194778i | \(0.937601\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.31673e9i | − 0.860021i | −0.902824 | − | 0.430011i | \(-0.858510\pi\) | ||||
0.902824 | − | 0.430011i | \(-0.141490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.85073e7 | 0.0311613 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.76699e9 | −1.74842 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.19894e9i | − 0.745245i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1.00589e9i | − 0.615108i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.97794e8 | −0.359651 | −0.179825 | − | 0.983699i | \(-0.557553\pi\) | ||||
−0.179825 | + | 0.983699i | \(0.557553\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.45917e9 | −0.863769 | −0.431884 | − | 0.901929i | \(-0.642151\pi\) | ||||
−0.431884 | + | 0.901929i | \(0.642151\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.74865e7i | − 0.0160106i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.20740e9i | − 2.41173i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.42889e9 | −0.806069 | −0.403035 | − | 0.915185i | \(-0.632045\pi\) | ||||
−0.403035 | + | 0.915185i | \(0.632045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.23562e8 | 0.179648 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 3.28479e9i | − 1.79512i | −0.440887 | − | 0.897562i | \(-0.645336\pi\) | ||||
0.440887 | − | 0.897562i | \(-0.354664\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.69299e7i | 0.0252458i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.68289e8 | 0.512777 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.38143e8 | −0.436974 | −0.218487 | − | 0.975840i | \(-0.570112\pi\) | ||||
−0.218487 | + | 0.975840i | \(0.570112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.93740e8i | 0.0994491i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 2.10790e8i | − 0.106538i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.80542e7 | 0.0338700 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.45042e9 | 0.710865 | 0.355432 | − | 0.934702i | \(-0.384334\pi\) | ||||
0.355432 | + | 0.934702i | \(0.384334\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 6.97846e8i | − 0.336833i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.19272e9i | − 0.567001i | −0.958972 | − | 0.283500i | \(-0.908504\pi\) | ||||
0.958972 | − | 0.283500i | \(-0.0914957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.74225e9 | −0.815786 | −0.407893 | − | 0.913030i | \(-0.633736\pi\) | ||||
−0.407893 | + | 0.913030i | \(0.633736\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.99206e7 | 0.0276370 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.77787e9i | 1.26213i | 0.775732 | + | 0.631063i | \(0.217381\pi\) | ||||
−0.775732 | + | 0.631063i | \(0.782619\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.14095e7i | 0.0140590i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.15507e9 | 0.950359 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.11598e9 | 0.919383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3.65524e9i | − 1.56490i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 7.44966e8i | − 0.314284i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.35409e9 | −1.39444 | −0.697221 | − | 0.716857i | \(-0.745580\pi\) | ||||
−0.697221 | + | 0.716857i | \(0.745580\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.71136e9 | −1.93036 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.49459e9i | 0.603540i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.77736e7i | 0.0110544i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.25553e9 | −1.27723 | −0.638617 | − | 0.769525i | \(-0.720493\pi\) | ||||
−0.638617 | + | 0.769525i | \(0.720493\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.10821e9 | −0.428588 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.37036e9i | 0.522457i | 0.965277 | + | 0.261228i | \(0.0841276\pi\) | ||||
−0.965277 | + | 0.261228i | \(0.915872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.01081e9i | − 1.50754i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.99143e7 | −0.00737984 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.10663e9 | 1.13512 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 6.61371e7i | − 0.0238283i | −0.999929 | − | 0.0119142i | \(-0.996208\pi\) | ||||
0.999929 | − | 0.0119142i | \(-0.00379249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.37354e9i | 0.843265i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.57092e8 | −0.300289 | −0.150145 | − | 0.988664i | \(-0.547974\pi\) | ||||
−0.150145 | + | 0.988664i | \(0.547974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.30172e8 | 0.0449777 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.37256e9i | 0.808519i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 9.83151e8i | − 0.330452i | −0.986256 | − | 0.165226i | \(-0.947165\pi\) | ||||
0.986256 | − | 0.165226i | \(-0.0528353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.58702e9 | −1.18921 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.21864e8 | 0.301478 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.70895e7i | 0.00551322i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.01988e8i | − 0.0642848i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.48727e9 | 1.09496 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.95745e7 | −0.0122598 | −0.00612990 | − | 0.999981i | \(-0.501951\pi\) | ||||
−0.00612990 | + | 0.999981i | \(0.501951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.92926e9i | − 0.895370i | −0.894191 | − | 0.447685i | \(-0.852249\pi\) | ||||
0.894191 | − | 0.447685i | \(-0.147751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.29844e9i | 0.391621i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.74356e9 | 2.60226 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.66521e9 | 1.37018 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.21702e9i | − 0.352750i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.83279e8i | − 0.224064i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.38794e8 | −0.0391861 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.05360e8 | 0.0850947 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.34733e9i | − 0.370608i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.59458e9i | − 0.976018i | −0.872839 | − | 0.488009i | \(-0.837723\pi\) | ||||
0.872839 | − | 0.488009i | \(-0.162277\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.74306e9 | 0.735250 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.93744e7 | 0.0157113 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.96194e9i | 0.773786i | 0.922125 | + | 0.386893i | \(0.126452\pi\) | ||||
−0.922125 | + | 0.386893i | \(0.873548\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.41842e9i | − 0.365848i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.29834e9 | 1.34930 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.42299e9 | 0.357820 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.32737e7i | 0.0231598i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.16328e9i | 0.775611i | 0.921741 | + | 0.387805i | \(0.126767\pi\) | ||||
−0.921741 | + | 0.387805i | \(0.873233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.55477e9 | −2.07142 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.90588e9 | −0.694876 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.08736e9i | 0.729135i | 0.931177 | + | 0.364567i | \(0.118783\pi\) | ||||
−0.931177 | + | 0.364567i | \(0.881217\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.09375e7i | 0.0118814i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.27473e8 | −0.0754457 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.45313e9 | −1.24095 | −0.620473 | − | 0.784228i | \(-0.713059\pi\) | ||||
−0.620473 | + | 0.784228i | \(0.713059\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.86211e9i | 1.09294i | 0.837477 | + | 0.546472i | \(0.184030\pi\) | ||||
−0.837477 | + | 0.546472i | \(0.815970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 6.86495e8i | − 0.152439i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.01096e9 | 1.53794 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.41178e8 | −0.0305950 | −0.0152975 | − | 0.999883i | \(-0.504870\pi\) | ||||
−0.0152975 | + | 0.999883i | \(0.504870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 2.74333e8i | − 0.0587359i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.97656e9i | 0.418113i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.10209e9 | −0.648357 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.05124e7 | 0.0166271 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.79450e9i | − 0.570257i | −0.958489 | − | 0.285128i | \(-0.907964\pi\) | ||||
0.958489 | − | 0.285128i | \(-0.0920363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.15504e10i | 2.32912i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.60457e9 | 0.319743 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.71016e9 | −1.51835 | −0.759175 | − | 0.650887i | \(-0.774397\pi\) | ||||
−0.759175 | + | 0.650887i | \(0.774397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.96598e8i | − 0.0382623i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.58565e9i | − 0.689695i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.24833e9 | −0.427432 | −0.213716 | − | 0.976896i | \(-0.568557\pi\) | ||||
−0.213716 | + | 0.976896i | \(0.568557\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.75844e9 | 0.330421 | 0.165210 | − | 0.986258i | \(-0.447170\pi\) | ||||
0.165210 | + | 0.986258i | \(0.447170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.71594e7i | 0.00690173i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 9.24397e7i | − 0.0169713i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.78653e9 | −0.324227 | −0.162114 | − | 0.986772i | \(-0.551831\pi\) | ||||
−0.162114 | + | 0.986772i | \(0.551831\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.88212e9 | −0.337666 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.16625e8i | 0.144837i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.12242e9i | 0.898180i | 0.893487 | + | 0.449090i | \(0.148252\pi\) | ||||
−0.893487 | + | 0.449090i | \(0.851748\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.55070e7 | −0.00268823 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.14822e8 | −0.0539594 | −0.0269797 | − | 0.999636i | \(-0.508589\pi\) | ||||
−0.0269797 | + | 0.999636i | \(0.508589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4.60016e9i | − 0.779572i | −0.920906 | − | 0.389786i | \(-0.872549\pi\) | ||||
0.920906 | − | 0.389786i | \(-0.127451\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.76819e9i | 0.296284i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.21349e9 | 0.532438 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.08454e9 | 0.996891 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.83870e9i | − 0.621940i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.36104e10i | 2.18069i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.57151e9 | −1.51662 | −0.758312 | − | 0.651892i | \(-0.773976\pi\) | ||||
−0.758312 | + | 0.651892i | \(0.773976\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.95585e9 | 1.09003 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.09406e8i | − 0.0169564i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.44720e9i | 0.834998i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.67533e9 | 0.557242 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.32428e10 | 1.98598 | 0.992992 | − | 0.118182i | \(-0.0377066\pi\) | ||||
0.992992 | + | 0.118182i | \(0.0377066\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.68707e8i | 0.0991967i | 0.998769 | + | 0.0495984i | \(0.0157941\pi\) | ||||
−0.998769 | + | 0.0495984i | \(0.984206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.69364e8i | 0.0248520i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.36051e9 | 0.923266 | 0.461633 | − | 0.887071i | \(-0.347264\pi\) | ||||
0.461633 | + | 0.887071i | \(0.347264\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.06776e9 | −0.727712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 4.10302e9i | − 0.582868i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.19579e9i | − 0.308599i | −0.988024 | − | 0.154299i | \(-0.950688\pi\) | ||||
0.988024 | − | 0.154299i | \(-0.0493121\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.92661e8 | 0.0406930 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.24366e9 | −0.583797 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 8.29618e9i | − 1.12922i | −0.825357 | − | 0.564611i | \(-0.809026\pi\) | ||||
0.825357 | − | 0.564611i | \(-0.190974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.60145e9i | − 0.889067i | −0.895762 | − | 0.444533i | \(-0.853370\pi\) | ||||
0.895762 | − | 0.444533i | \(-0.146630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.17483e10 | 1.56559 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.59709e8 | 0.0342462 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.01625e10i | 1.32605i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.30294e9i | 0.684740i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.90639e9 | −0.754733 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.92354e9 | −0.875539 | −0.437769 | − | 0.899087i | \(-0.644231\pi\) | ||||
−0.437769 | + | 0.899087i | \(0.644231\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.53614e9i | 0.192251i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.27425e8i | − 0.0281694i | −0.999901 | − | 0.0140847i | \(-0.995517\pi\) | ||||
0.999901 | − | 0.0140847i | \(-0.00448344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.90178e9 | 0.233140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.34188e9 | −0.284152 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.09687e9i | 0.251825i | 0.992041 | + | 0.125913i | \(0.0401859\pi\) | ||||
−0.992041 | + | 0.125913i | \(0.959814\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 3.90980e8i | − 0.0464769i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.29845e9 | 0.388116 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.25416e10 | 1.46078 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 6.49885e8i | − 0.0749313i | −0.999298 | − | 0.0374656i | \(-0.988072\pi\) | ||||
0.999298 | − | 0.0374656i | \(-0.0119285\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.36362e9i | 0.155642i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.89892e7 | 0.00214566 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.26277e9 | −0.253120 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.45549e9i | 0.161191i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.22103e10i | 1.33879i | 0.742907 | + | 0.669394i | \(0.233446\pi\) | ||||
−0.742907 | + | 0.669394i | \(0.766554\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.79796e10 | −1.95180 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.61672e7 | 0.00173770 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 8.91344e9i | − 0.948587i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.06693e10i | 1.12428i | 0.827041 | + | 0.562141i | \(0.190022\pi\) | ||||
−0.827041 | + | 0.562141i | \(0.809978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.68349e9 | 0.175657 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.21543e10 | −2.28899 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 3.35259e8i | − 0.0343012i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 7.83471e8i | − 0.0793791i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.40260e9 | −0.441731 | −0.220866 | − | 0.975304i | \(-0.570888\pi\) | ||||
−0.220866 | + | 0.975304i | \(0.570888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.17019e9 | 0.116275 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.26568e9i | 0.911786i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.82884e9i | 0.860440i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.63117e10 | −1.57445 | −0.787225 | − | 0.616666i | \(-0.788483\pi\) | ||||
−0.787225 | + | 0.616666i | \(0.788483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.47134e10i | 2.34004i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.33690e10i | 1.25382i | 0.779091 | + | 0.626911i | \(0.215681\pi\) | ||||
−0.779091 | + | 0.626911i | \(0.784319\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.07842e8 | 0.0100180 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.54734e8 | 0.0142380 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.52697e10i | − 1.39180i | −0.718141 | − | 0.695898i | \(-0.755007\pi\) | ||||
0.718141 | − | 0.695898i | \(-0.244993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.55197e10i | 1.40126i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.40139e9 | 0.125342 | 0.0626712 | − | 0.998034i | \(-0.480038\pi\) | ||||
0.0626712 | + | 0.998034i | \(0.480038\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.22725e8 | 0.0285947 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.33840e9i | 0.205256i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.50382e9i | 0.826441i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.12628e9 | −0.527785 | −0.263893 | − | 0.964552i | \(-0.585006\pi\) | ||||
−0.263893 | + | 0.964552i | \(0.585006\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.07338e9 | 0.433027 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 7.02551e7i | − 0.00594106i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.54406e10i | 1.29369i | 0.762623 | + | 0.646844i | \(0.223911\pi\) | ||||
−0.762623 | + | 0.646844i | \(0.776089\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.36286e9 | 0.611224 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.10270e9 | 0.419714 | 0.209857 | − | 0.977732i | \(-0.432700\pi\) | ||||
0.209857 | + | 0.977732i | \(0.432700\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.06562e9i | − 0.331353i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2.32588e8i | − 0.0187833i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.04887e10 | 1.63957 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.19721e9 | −0.570718 | −0.285359 | − | 0.958421i | \(-0.592113\pi\) | ||||
−0.285359 | + | 0.958421i | \(0.592113\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.53957e9i | − 0.120978i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.39957e10i | − 1.08985i | −0.838486 | − | 0.544924i | \(-0.816559\pi\) | ||||
0.838486 | − | 0.544924i | \(-0.183441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.92469e10 | −1.48527 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.38686e9 | 0.488443 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 2.98916e9i | − 0.226552i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.53043e10i | − 1.14957i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.22667e9 | −0.165764 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.18272e8 | 0.0529963 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.50580e10i | − 1.10117i | −0.834778 | − | 0.550587i | \(-0.814404\pi\) | ||||
0.834778 | − | 0.550587i | \(-0.185596\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 6.87794e9i | − 0.498527i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.48791e9 | 0.250581 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.38792e10 | 1.70045 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 2.48293e8i | − 0.0175259i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 5.06926e9i | − 0.354683i | −0.984149 | − | 0.177342i | \(-0.943250\pi\) | ||||
0.984149 | − | 0.177342i | \(-0.0567498\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.35911e9 | 0.163619 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.80176e9 | 0.261379 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.76709e10i | 1.20435i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.98138e8i | 0.0336561i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.70544e10 | −1.14229 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.19545e9 | 0.344988 | 0.172494 | − | 0.985011i | \(-0.444818\pi\) | ||||
0.172494 | + | 0.985011i | \(0.444818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.10691e10i | 1.38699i | 0.720461 | + | 0.693496i | \(0.243930\pi\) | ||||
−0.720461 | + | 0.693496i | \(0.756070\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.40685e9i | − 0.483411i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.69360e8 | −0.0239000 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.26468e10 | −2.09442 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 5.51303e9i | − 0.350669i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.98065e9i | 0.377179i | 0.982056 | + | 0.188590i | \(0.0603916\pi\) | ||||
−0.982056 | + | 0.188590i | \(0.939608\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.62100e9 | 0.476554 | 0.238277 | − | 0.971197i | \(-0.423417\pi\) | ||||
0.238277 | + | 0.971197i | \(0.423417\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.39659e9 | 0.396606 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.30836e10i | − 0.804373i | −0.915558 | − | 0.402187i | \(-0.868250\pi\) | ||||
0.915558 | − | 0.402187i | \(-0.131750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.21207e9i | 0.317738i | 0.987300 | + | 0.158869i | \(0.0507848\pi\) | ||||
−0.987300 | + | 0.158869i | \(0.949215\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.03559e10 | 0.626015 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.57361e10 | 0.943280 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.91087e8i | 0.0470242i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4.85413e9i | − 0.286136i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.15426e9 | 0.535126 | 0.267563 | − | 0.963540i | \(-0.413782\pi\) | ||||
0.267563 | + | 0.963540i | \(0.413782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.45229e9 | 0.258106 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.09024e10i | 0.626793i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.90763e8i | 0.0450866i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.32975e9 | −0.357927 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.23456e10 | −0.692367 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3.44859e10i | − 1.91817i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.58918e10i | 0.876699i | 0.898805 | + | 0.438349i | \(0.144437\pi\) | ||||
−0.898805 | + | 0.438349i | \(0.855563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.07252e8 | 0.0168118 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.04443e10 | −1.65224 | −0.826120 | − | 0.563495i | \(-0.809457\pi\) | ||||
−0.826120 | + | 0.563495i | \(0.809457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.79263e10i | 0.964971i | 0.875904 | + | 0.482486i | \(0.160266\pi\) | ||||
−0.875904 | + | 0.482486i | \(0.839734\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.06183e9i | 0.0566952i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.12123e9 | −0.377153 | −0.188576 | − | 0.982059i | \(-0.560387\pi\) | ||||
−0.188576 | + | 0.982059i | \(0.560387\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.16229e9 | 0.0610600 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.28599e10i | − 1.19126i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 7.01015e9i | − 0.362375i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.25582e8 | −0.0320790 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.24993e9 | 0.114451 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.65978e8i | 0.0436997i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 5.49211e8i | − 0.0274942i | −0.999906 | − | 0.0137471i | \(-0.995624\pi\) | ||||
0.999906 | − | 0.0137471i | \(-0.00437597\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.02027e10 | 1.00334 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.12382e10 | 1.04641 | 0.523205 | − | 0.852207i | \(-0.324736\pi\) | ||||
0.523205 | + | 0.852207i | \(0.324736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.26798e10i | − 1.10861i | −0.832315 | − | 0.554303i | \(-0.812985\pi\) | ||||
0.832315 | − | 0.554303i | \(-0.187015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 4.05627e8i | − 0.0196709i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.09480e10 | 1.00788 | 0.503942 | − | 0.863737i | \(-0.331883\pi\) | ||||
0.503942 | + | 0.863737i | \(0.331883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.49153e9 | −0.357614 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.61324e9i | 0.0764062i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.11642e9i | 0.146445i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.01775e8 | 0.00474526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.97677e10 | −1.37712 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 2.78987e10i | − 1.28064i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.62307e10i | − 1.65021i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.15971e10 | 0.524133 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.14246e8 | 0.0410009 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.65970e10i | 1.18361i | 0.806083 | + | 0.591803i | \(0.201584\pi\) | ||||
−0.806083 | + | 0.591803i | \(0.798416\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 1.05452e10i | − 0.465671i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.28193e10 | −0.561760 | −0.280880 | − | 0.959743i | \(-0.590626\pi\) | ||||
−0.280880 | + | 0.959743i | \(0.590626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.73723e9 | 0.423436 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 4.72751e8i | − 0.0204013i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2.00398e10i | − 0.858222i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.23675e10 | 1.37564 | 0.687820 | − | 0.725881i | \(-0.258568\pi\) | ||||
0.687820 | + | 0.725881i | \(0.258568\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.17384e9 | −0.0495107 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.18746e10i | 2.59004i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2.99601e10i | − 1.24465i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.38441e9 | 0.0570804 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.31144e10 | −0.536653 | −0.268327 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268327 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.07877e10i | 0.844271i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.91713e9i | 0.198210i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.68513e8 | −0.0387494 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.21245e10 | 1.27570 | 0.637849 | − | 0.770161i | \(-0.279824\pi\) | ||||
0.637849 | + | 0.770161i | \(0.279824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.40899e9i | − 0.0555366i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.15677e10i | 0.452566i | 0.974062 | + | 0.226283i | \(0.0726574\pi\) | ||||
−0.974062 | + | 0.226283i | \(0.927343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.73338e9 | 0.222649 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.09145e8 | −0.00420719 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.21746e10i | 0.465833i | 0.972497 | + | 0.232916i | \(0.0748269\pi\) | ||||
−0.972497 | + | 0.232916i | \(0.925173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 7.14425e10i | − 2.71347i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.82786e9 | −0.0689144 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.00590e10 | −0.750730 | −0.375365 | − | 0.926877i | \(-0.622483\pi\) | ||||
−0.375365 | + | 0.926877i | \(0.622483\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2.28805e8i | − 0.00850069i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.27199e9i | 0.341965i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.67721e10 | −0.980205 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.33066e10 | 1.21059 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.12436e10i | 0.405708i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 9.14338e7i | − 0.00327538i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.05520e10 | −1.08654 | −0.543271 | − | 0.839558i | \(-0.682814\pi\) | ||||
−0.543271 | + | 0.839558i | \(0.682814\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.48340e10 | 1.58298 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 4.05142e10i | − 1.42017i | −0.704117 | − | 0.710084i | \(-0.748657\pi\) | ||||
0.704117 | − | 0.710084i | \(-0.251343\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.30028e9i | − 0.0452523i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.58611e10 | −0.893574 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.00689e10 | 0.688483 | 0.344242 | − | 0.938881i | \(-0.388136\pi\) | ||||
0.344242 | + | 0.938881i | \(0.388136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.58308e10i | − 0.539216i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 4.80988e9i | − 0.162665i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.88669e10 | −1.30510 | −0.652548 | − | 0.757748i | \(-0.726300\pi\) | ||||
−0.652548 | + | 0.757748i | \(0.726300\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.34794e8 | 0.0178303 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.10704e9i | − 0.0366483i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 6.26186e10i | − 2.05834i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.43097e10 | 1.44624 | 0.723122 | − | 0.690721i | \(-0.242707\pi\) | ||||
0.723122 | + | 0.690721i | \(0.242707\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.15398e10 | −0.698104 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.19508e9i | − 0.0384605i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.67500e10i | 1.17442i | 0.809433 | + | 0.587212i | \(0.199774\pi\) | ||||
−0.809433 | + | 0.587212i | \(0.800226\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.55605e9 | 0.239781 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.8.d.e.193.3 | ✓ | 12 | |
4.3 | odd | 2 | inner | 384.8.d.e.193.9 | yes | 12 | |
8.3 | odd | 2 | inner | 384.8.d.e.193.4 | yes | 12 | |
8.5 | even | 2 | inner | 384.8.d.e.193.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.e.193.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
384.8.d.e.193.4 | yes | 12 | 8.3 | odd | 2 | inner | |
384.8.d.e.193.9 | yes | 12 | 4.3 | odd | 2 | inner | |
384.8.d.e.193.10 | yes | 12 | 8.5 | even | 2 | inner |