Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,9,Mod(127,384)]
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([1, 0, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.127");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(156.433386263\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.13 | ||
Character | \(\chi\) | \(=\) | 384.127 |
Dual form | 384.9.g.a.127.14 |
$q$-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 | ||||||||
\(3\) | − 46.7654i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −441.863 | −0.706981 | −0.353490 | − | 0.935438i | \(-0.615005\pi\) | ||||
−0.353490 | + | 0.935438i | \(0.615005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 408.575i | 0.170169i | 0.996374 | + | 0.0850843i | \(0.0271160\pi\) | ||||
−0.996374 | + | 0.0850843i | \(0.972884\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2187.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 13982.3i | − 0.955010i | −0.878629 | − | 0.477505i | \(-0.841541\pi\) | ||||
0.878629 | − | 0.477505i | \(-0.158459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50503.9 | 1.76828 | 0.884141 | − | 0.467220i | \(-0.154745\pi\) | ||||
0.884141 | + | 0.467220i | \(0.154745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20663.9i | 0.408175i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 29394.2 | 0.351938 | 0.175969 | − | 0.984396i | \(-0.443694\pi\) | ||||
0.175969 | + | 0.984396i | \(0.443694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 465.954i | 0.00357543i | 0.999998 | + | 0.00178772i | \(0.000569048\pi\) | ||||
−0.999998 | + | 0.00178772i | \(0.999431\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 19107.2 | 0.0982469 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 349779.i | 1.24992i | 0.780657 | + | 0.624960i | \(0.214885\pi\) | ||||
−0.780657 | + | 0.624960i | \(0.785115\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −195382. | −0.500178 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 413282. | 0.584325 | 0.292163 | − | 0.956369i | \(-0.405625\pi\) | ||||
0.292163 | + | 0.956369i | \(0.405625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 291268.i | − 0.315388i | −0.987488 | − | 0.157694i | \(-0.949594\pi\) | ||||
0.987488 | − | 0.157694i | \(-0.0504060\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −653888. | −0.551375 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 180534.i | − 0.120306i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.18340e6 | −1.69857 | −0.849286 | − | 0.527933i | \(-0.822967\pi\) | ||||
−0.849286 | + | 0.527933i | \(0.822967\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 2.36183e6i | − 1.02092i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.90588e6 | −1.38224 | −0.691121 | − | 0.722739i | \(-0.742883\pi\) | ||||
−0.691121 | + | 0.722739i | \(0.742883\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.13172e6i | 1.50103i | 0.660853 | + | 0.750515i | \(0.270195\pi\) | ||||
−0.660853 | + | 0.750515i | \(0.729805\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 966354. | 0.235660 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 3.80555e6i | − 0.779878i | −0.920841 | − | 0.389939i | \(-0.872496\pi\) | ||||
0.920841 | − | 0.389939i | \(-0.127504\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.59787e6 | 0.971043 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1.37463e6i | − 0.203191i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.21515e6 | −0.154002 | −0.0770009 | − | 0.997031i | \(-0.524534\pi\) | ||||
−0.0770009 | + | 0.997031i | \(0.524534\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.17826e6i | 0.675174i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21790.5 | 0.00206428 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5.53322e6i | − 0.456636i | −0.973587 | − | 0.228318i | \(-0.926677\pi\) | ||||
0.973587 | − | 0.228318i | \(-0.0733226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.14915e6 | 0.588563 | 0.294282 | − | 0.955719i | \(-0.404920\pi\) | ||||
0.294282 | + | 0.955719i | \(0.404920\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 893553.i | − 0.0567229i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.23158e7 | −1.25014 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.31597e7i | 1.14930i | 0.818399 | + | 0.574651i | \(0.194862\pi\) | ||||
−0.818399 | + | 0.574651i | \(0.805138\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.63575e7 | 0.721641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.37847e7i | 0.542454i | 0.962515 | + | 0.271227i | \(0.0874294\pi\) | ||||
−0.962515 | + | 0.271227i | \(0.912571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.32192e6 | 0.187403 | 0.0937015 | − | 0.995600i | \(-0.470130\pi\) | ||||
0.0937015 | + | 0.995600i | \(0.470130\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.13712e6i | 0.288778i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.71282e6 | 0.162513 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.42382e7i | 0.879026i | 0.898236 | + | 0.439513i | \(0.144849\pi\) | ||||
−0.898236 | + | 0.439513i | \(0.855151\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.71409e7i | 0.571889i | 0.958246 | + | 0.285944i | \(0.0923072\pi\) | ||||
−0.958246 | + | 0.285944i | \(0.907693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.29882e7 | −0.248813 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.93273e7i | − 0.337360i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.90336e7 | −0.622126 | −0.311063 | − | 0.950389i | \(-0.600685\pi\) | ||||
−0.311063 | + | 0.950389i | \(0.600685\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.06346e7i | 0.300906i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.36212e7 | −0.182089 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 205888.i | − 0.00252776i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.04636e6 | 0.0457065 | 0.0228533 | − | 0.999739i | \(-0.492725\pi\) | ||||
0.0228533 | + | 0.999739i | \(0.492725\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.05793e7i | 0.318337i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.48664e7 | 0.623353 | 0.311677 | − | 0.950188i | \(-0.399109\pi\) | ||||
0.311677 | + | 0.950188i | \(0.399109\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.83327e7i | − 0.607127i | −0.952811 | − | 0.303564i | \(-0.901823\pi\) | ||||
0.952811 | − | 0.303564i | \(-0.0981765\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.44274e6 | −0.0694587 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.79487e8i | − 1.36930i | −0.728873 | − | 0.684649i | \(-0.759956\pi\) | ||||
0.728873 | − | 0.684649i | \(-0.240044\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.24660e8 | 1.59155 | 0.795773 | − | 0.605595i | \(-0.207065\pi\) | ||||
0.795773 | + | 0.605595i | \(0.207065\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.48873e8i | 0.980671i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.25134e8 | 1.38079 | 0.690394 | − | 0.723433i | \(-0.257437\pi\) | ||||
0.690394 | + | 0.723433i | \(0.257437\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.54554e8i | − 0.883669i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.10452e8 | −0.589427 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.20097e7i | 0.0598888i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.88541e7 | 0.0879558 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.82660e8i | 0.798038i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.58935e8 | 1.06060 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.32041e7i | 0.127637i | 0.997962 | + | 0.0638186i | \(0.0203279\pi\) | ||||
−0.997962 | + | 0.0638186i | \(0.979672\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.39987e8 | 0.866620 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.31550e8i | 1.80492i | 0.430770 | + | 0.902462i | \(0.358242\pi\) | ||||
−0.430770 | + | 0.902462i | \(0.641758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −190377. | −0.000608426 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 4.51919e7i | − 0.136058i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.91221e8 | −0.542816 | −0.271408 | − | 0.962464i | \(-0.587489\pi\) | ||||
−0.271408 | + | 0.962464i | \(0.587489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.01862e8i | 0.272868i | 0.990649 | + | 0.136434i | \(0.0435642\pi\) | ||||
−0.990649 | + | 0.136434i | \(0.956436\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.77968e8 | −0.450263 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 7.06161e8i | − 1.68873i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.82614e8 | −0.413106 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.61786e8i | − 0.560632i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.93975e7 | 0.100221 | 0.0501107 | − | 0.998744i | \(-0.484043\pi\) | ||||
0.0501107 | + | 0.998744i | \(0.484043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2.93879e8i | − 0.565275i | −0.959227 | − | 0.282638i | \(-0.908791\pi\) | ||||
0.959227 | − | 0.282638i | \(-0.0912094\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.42851e7 | −0.117313 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.28700e8i | 0.222973i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.27912e8 | −0.704297 | −0.352149 | − | 0.935944i | \(-0.614549\pi\) | ||||
−0.352149 | + | 0.935944i | \(0.614549\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.68268e7i | 0.0889129i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.42911e8 | −0.212697 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.09427e9i | 1.55015i | 0.631868 | + | 0.775076i | \(0.282288\pi\) | ||||
−0.631868 | + | 0.775076i | \(0.717712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.88929e8 | 0.389812 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.34025e9i | − 1.72313i | −0.507645 | − | 0.861566i | \(-0.669484\pi\) | ||||
0.507645 | − | 0.861566i | \(-0.330516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.73491e9 | 2.12682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1.01904e6i | − 0.00119181i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.73349e8 | 0.193524 | 0.0967622 | − | 0.995308i | \(-0.469151\pi\) | ||||
0.0967622 | + | 0.995308i | \(0.469151\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 7.98283e7i | − 0.0851147i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.58763e8 | −0.263639 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.20920e9i | − 1.17784i | −0.808190 | − | 0.588922i | \(-0.799553\pi\) | ||||
0.808190 | − | 0.588922i | \(-0.200447\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.73459e8 | −0.534304 | −0.267152 | − | 0.963654i | \(-0.586083\pi\) | ||||
−0.267152 | + | 0.963654i | \(0.586083\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 3.81098e8i | − 0.339807i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.40662e9 | 1.20086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.10999e8i | − 0.336104i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.17874e7 | −0.0327490 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.78981e8i | 0.359903i | 0.983676 | + | 0.179951i | \(0.0575940\pi\) | ||||
−0.983676 | + | 0.179951i | \(0.942406\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.06454e9 | 0.767240 | 0.383620 | − | 0.923491i | \(-0.374677\pi\) | ||||
0.383620 | + | 0.923491i | \(0.374677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.04361e9i | 0.721769i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.13527e9 | 1.41771 | 0.708857 | − | 0.705352i | \(-0.249211\pi\) | ||||
0.708857 | + | 0.705352i | \(0.249211\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 4.15711e8i | − 0.265081i | −0.991178 | − | 0.132541i | \(-0.957686\pi\) | ||||
0.991178 | − | 0.132541i | \(-0.0423135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.08307e9 | 0.663550 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.68857e8i | 0.0994338i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.72587e9 | 0.977218 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 7.64966e8i | − 0.416640i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.51511e6 | 0.00341457 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.72862e9i | 1.88113i | 0.339616 | + | 0.940564i | \(0.389703\pi\) | ||||
−0.339616 | + | 0.940564i | \(0.610297\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.44645e8 | 0.313186 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 2.26752e9i | − 1.06120i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.19005e8 | 0.0536692 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2.48881e8i | − 0.108197i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.48452e9 | 0.622325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.27642e9i | − 0.920518i | −0.887785 | − | 0.460259i | \(-0.847756\pi\) | ||||
0.887785 | − | 0.460259i | \(-0.152244\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.27301e8 | 0.166726 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.52411e9i | 0.574003i | 0.957930 | + | 0.287002i | \(0.0926585\pi\) | ||||
−0.957930 | + | 0.287002i | \(0.907342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.01820e9 | 1.09750 | 0.548752 | − | 0.835985i | \(-0.315103\pi\) | ||||
0.548752 | + | 0.835985i | \(0.315103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 2.67162e8i | − 0.0938268i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.97441e8 | 0.168779 | 0.0843895 | − | 0.996433i | \(-0.473106\pi\) | ||||
0.0843895 | + | 0.996433i | \(0.473106\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.68153e9i | 0.551358i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.60116e9 | 0.507506 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.57621e9i | 0.483083i | 0.970390 | + | 0.241542i | \(0.0776531\pi\) | ||||
−0.970390 | + | 0.241542i | \(0.922347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.54224e9 | 0.457176 | 0.228588 | − | 0.973523i | \(-0.426589\pi\) | ||||
0.228588 | + | 0.973523i | \(0.426589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.23677e8i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.47349e9 | −0.686508 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.35325e7i | 0.00632237i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.26925e9 | 0.330180 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.80796e9i | 1.21134i | 0.795716 | + | 0.605670i | \(0.207095\pi\) | ||||
−0.795716 | + | 0.605670i | \(0.792905\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.89071e9 | 1.19369 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.07398e8i | 0.143652i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.68574e9 | 0.844874 | 0.422437 | − | 0.906392i | \(-0.361175\pi\) | ||||
0.422437 | + | 0.906392i | \(0.361175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.30066e9i | − 0.289044i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.03848e8 | −0.194775 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 6.14029e8i | − 0.128341i | −0.997939 | − | 0.0641706i | \(-0.979560\pi\) | ||||
0.997939 | − | 0.0641706i | \(-0.0204402\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.36929e8 | 0.108876 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.82542e9i | 0.359185i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.98817e9 | 0.952647 | 0.476324 | − | 0.879270i | \(-0.341969\pi\) | ||||
0.476324 | + | 0.879270i | \(0.341969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 8.07780e9i | − 1.49767i | −0.662757 | − | 0.748834i | \(-0.730614\pi\) | ||||
0.662757 | − | 0.748834i | \(-0.269386\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.64986e8 | 0.173728 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.73189e9i | 0.477675i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.79514e9 | 1.49391 | 0.746954 | − | 0.664876i | \(-0.231516\pi\) | ||||
0.746954 | + | 0.664876i | \(0.231516\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.37002e8i | 0.105129i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.07423e10 | 1.72294 | 0.861470 | − | 0.507809i | \(-0.169544\pi\) | ||||
0.861470 | + | 0.507809i | \(0.169544\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.36710e9i | − 0.524941i | −0.964940 | − | 0.262470i | \(-0.915463\pi\) | ||||
0.964940 | − | 0.262470i | \(-0.0845372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.62841e6 | −0.00145940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.59585e9i | − 0.235214i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.11174e9 | −0.876140 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.89230e8i | − 0.0263887i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.84802e9 | −0.250747 | −0.125373 | − | 0.992110i | \(-0.540013\pi\) | ||||
−0.125373 | + | 0.992110i | \(0.540013\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.44493e9i | 0.322833i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.43005e9 | 0.183792 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.76652e10i | 2.21021i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.09669e9 | −0.255428 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 3.03350e9i | − 0.359893i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.60081e9 | −0.416103 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.29789e10i | 1.46112i | 0.682850 | + | 0.730559i | \(0.260740\pi\) | ||||
−0.682850 | + | 0.730559i | \(0.739260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.19560e9 | −0.350525 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 5.34433e9i | − 0.571283i | −0.958336 | − | 0.285642i | \(-0.907793\pi\) | ||||
0.958336 | − | 0.285642i | \(-0.0922067\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.08796e9 | 0.113354 | 0.0566770 | − | 0.998393i | \(-0.481949\pi\) | ||||
0.0566770 | + | 0.998393i | \(0.481949\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.94828e8i | 0.0401020i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.02228e10 | 1.01236 | 0.506179 | − | 0.862429i | \(-0.331058\pi\) | ||||
0.506179 | + | 0.862429i | \(0.331058\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 5.77863e9i | − 0.558036i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.39378e9 | −0.790565 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.36963e7i | 0.00125833i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.86756e9 | −0.884456 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.05063e10i | − 0.918880i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.55485e9 | 0.132711 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.62844e10i | 1.35662i | 0.734775 | + | 0.678311i | \(0.237288\pi\) | ||||
−0.734775 | + | 0.678311i | \(0.762712\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.96209e9 | 0.566191 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.02334e10i | − 0.812534i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.25820e9 | 0.252614 | 0.126307 | − | 0.991991i | \(-0.459688\pi\) | ||||
0.126307 | + | 0.991991i | \(0.459688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.05285e10i | − 0.797199i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.07259e9 | −0.301199 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.64250e9i | 0.335410i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.22779e9 | −0.510186 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.87548e10i | − 1.29358i | −0.762666 | − | 0.646792i | \(-0.776110\pi\) | ||||
0.762666 | − | 0.646792i | \(-0.223890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.34804e10 | 1.58272 | 0.791361 | − | 0.611349i | \(-0.209373\pi\) | ||||
0.791361 | + | 0.611349i | \(0.209373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.16533e9i | 0.340306i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.78231e10 | 1.14785 | 0.573924 | − | 0.818909i | \(-0.305420\pi\) | ||||
0.573924 | + | 0.818909i | \(0.305420\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6.09093e9i | − 0.383504i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.61640e8 | 0.0345768 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 1.24594e9i | − 0.0750099i | −0.999296 | − | 0.0375049i | \(-0.988059\pi\) | ||||
0.999296 | − | 0.0375049i | \(-0.0119410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.69833e10 | 0.999987 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 8.81719e8i | − 0.0507813i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.35156e9 | −0.132490 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.96071e10i | 1.08081i | 0.841406 | + | 0.540404i | \(0.181729\pi\) | ||||
−0.841406 | + | 0.540404i | \(0.818271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.54217e9 | 0.460747 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 4.96479e8i | − 0.0262063i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.68736e10 | −0.871711 | −0.435856 | − | 0.900017i | \(-0.643554\pi\) | ||||
−0.435856 | + | 0.900017i | \(0.643554\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 1.21092e10i | − 0.612336i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.08723e10 | 1.03325 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.18982e10i | − 0.576664i | −0.957530 | − | 0.288332i | \(-0.906899\pi\) | ||||
0.957530 | − | 0.288332i | \(-0.0931007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.55280e9 | 0.0736913 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.40923e10i | − 0.654918i | −0.944865 | − | 0.327459i | \(-0.893808\pi\) | ||||
0.944865 | − | 0.327459i | \(-0.106192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.52428e9 | −0.114893 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.12231e10i | − 0.500344i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.26952e10 | −1.42786 | −0.713931 | − | 0.700216i | \(-0.753087\pi\) | ||||
−0.713931 | + | 0.700216i | \(0.753087\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.02815e10i | 0.439894i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.48581e10 | 1.04207 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.51286e10i | − 0.621455i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.03713e10 | 0.820080 | 0.410040 | − | 0.912068i | \(-0.365515\pi\) | ||||
0.410040 | + | 0.912068i | \(0.365515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.90305e6i | 0 0.000351275i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.79872e10 | −1.85587 | −0.927937 | − | 0.372738i | \(-0.878419\pi\) | ||||
−0.927937 | + | 0.372738i | \(0.878419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.47101e10i | − 0.557695i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.11342e9 | −0.0785534 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.45112e10i | 1.62215i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.04253e9 | −0.215936 | −0.107968 | − | 0.994154i | \(-0.534434\pi\) | ||||
−0.107968 | + | 0.994154i | \(0.534434\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.94252e9i | 0.313395i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.26074e9 | 0.0777051 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1.19925e10i | − 0.404314i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.76361e9 | 0.157540 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1.14993e10i | − 0.373092i | −0.982446 | − | 0.186546i | \(-0.940271\pi\) | ||||
0.982446 | − | 0.186546i | \(-0.0597294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.21975e10 | −0.388278 | −0.194139 | − | 0.980974i | \(-0.562191\pi\) | ||||
−0.194139 | + | 0.980974i | \(0.562191\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.32275e9i | 0.259959i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.74310e9 | −0.176032 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.32954e9i | 0.100155i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.30239e10 | −0.974987 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.23665e10i | − 0.358376i | −0.983815 | − | 0.179188i | \(-0.942653\pi\) | ||||
0.983815 | − | 0.179188i | \(-0.0573470\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.82670e10 | −1.65757 | −0.828784 | − | 0.559569i | \(-0.810967\pi\) | ||||
−0.828784 | + | 0.559569i | \(0.810967\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.54001e9i | 0.238507i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.62981e8 | −0.00446900 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 1.31028e10i | − 0.352781i | −0.984320 | − | 0.176390i | \(-0.943558\pi\) | ||||
0.984320 | − | 0.176390i | \(-0.0564421\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.22425e10 | −0.323681 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8.18524e9i | − 0.212528i | −0.994338 | − | 0.106264i | \(-0.966111\pi\) | ||||
0.994338 | − | 0.106264i | \(-0.0338889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.72475e10 | 0.439831 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2.31009e9i | − 0.0578628i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.39174e10 | −1.08057 | −0.540283 | − | 0.841483i | \(-0.681683\pi\) | ||||
−0.540283 | + | 0.841483i | \(0.681683\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.46133e10i | 1.32005i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.37433e10 | −0.326362 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 9.11767e9i | − 0.212735i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.38106e10 | 0.545890 | 0.272945 | − | 0.962030i | \(-0.412002\pi\) | ||||
0.272945 | + | 0.962030i | \(0.412002\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.00632e9i | 0.0677305i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.88807e10 | −0.860855 | −0.430427 | − | 0.902625i | \(-0.641637\pi\) | ||||
−0.430427 | + | 0.902625i | \(0.641637\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.69790e10i | 1.23991i | 0.784636 | + | 0.619957i | \(0.212850\pi\) | ||||
−0.784636 | + | 0.619957i | \(0.787150\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.01872e9 | 0.128734 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.00144e10i | − 1.68229i | −0.540810 | − | 0.841145i | \(-0.681882\pi\) | ||||
0.540810 | − | 0.841145i | \(-0.318118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.46248e9 | −0.195575 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.00115e10i | 0.406626i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.17533e10 | 1.43350 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 9.10391e7i | − 0.00178835i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.65753e9 | 0.0513339 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.14708e10i | 1.73756i | 0.495196 | + | 0.868781i | \(0.335096\pi\) | ||||
−0.495196 | + | 0.868781i | \(0.664904\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.60774e11 | −3.00355 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.68328e9i | 0.122801i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.78794e9 | −0.0323136 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.68484e10i | 1.54400i | 0.635625 | + | 0.771998i | \(0.280742\pi\) | ||||
−0.635625 | + | 0.771998i | \(0.719258\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.11740e10 | 0.894981 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 3.57345e9i | − 0.0614840i | −0.999527 | − | 0.0307420i | \(-0.990213\pi\) | ||||
0.999527 | − | 0.0307420i | \(-0.00978702\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.21481e10 | 0.205646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 1.35119e10i | − 0.225058i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.63207e9 | −0.0923086 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 5.59047e10i | − 0.901666i | −0.892608 | − | 0.450833i | \(-0.851127\pi\) | ||||
0.892608 | − | 0.450833i | \(-0.148873\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.26771e10 | −0.994851 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.08704e11i | − 1.69814i | −0.528281 | − | 0.849070i | \(-0.677163\pi\) | ||||
0.528281 | − | 0.849070i | \(-0.322837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.86620e10 | −0.440699 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 8.11338e10i | − 1.22792i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.50653e10 | 0.671384 | 0.335692 | − | 0.941972i | \(-0.391030\pi\) | ||||
0.335692 | + | 0.941972i | \(0.391030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.17440e9i | 0.0318901i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.76558e7 | −0.000688092 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.01937e10i | 0.429227i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.32104e10 | −0.744791 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 8.10671e9i | − 0.111731i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.35453e11 | −1.83839 | −0.919197 | − | 0.393798i | \(-0.871161\pi\) | ||||
−0.919197 | + | 0.393798i | \(0.871161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.21536e10i | − 0.162442i | −0.996696 | − | 0.0812210i | \(-0.974118\pi\) | ||||
0.996696 | − | 0.0812210i | \(-0.0258820\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.73320e9 | −0.0491410 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 8.56158e9i | − 0.110997i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.40342e10 | −0.562299 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.21012e10i | 0.152212i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.97262e11 | −2.44419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.93086e10i | 0.968067i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.65489e10 | −0.680028 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 7.82711e10i | − 0.927355i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.14285e10 | 0.717102 | 0.358551 | − | 0.933510i | \(-0.383271\pi\) | ||||
0.358551 | + | 0.933510i | \(0.383271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.68180e10i | 0.308480i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.92688e10 | −1.12519 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.48785e11i | 1.66192i | 0.556333 | + | 0.830960i | \(0.312208\pi\) | ||||
−0.556333 | + | 0.830960i | \(0.687792\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.78222e10 | −0.196188 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.92570e8i | 0.00208921i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.39888e10 | −0.149583 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 6.57813e10i | − 0.693315i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.18006e11 | 1.22598 | 0.612990 | − | 0.790091i | \(-0.289967\pi\) | ||||
0.612990 | + | 0.790091i | \(0.289967\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.59172e11i | 2.65424i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.92205e10 | −0.194050 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.93137e10i | − 0.590366i | −0.955441 | − | 0.295183i | \(-0.904619\pi\) | ||||
0.955441 | − | 0.295183i | \(-0.0953807\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.94783e10 | −0.976191 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.95420e9i | 0.0189076i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.68389e11 | 1.60644 | 0.803219 | − | 0.595683i | \(-0.203119\pi\) | ||||
0.803219 | + | 0.595683i | \(0.203119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.53680e10i | 0.614923i | 0.951561 | + | 0.307461i | \(0.0994795\pi\) | ||||
−0.951561 | + | 0.307461i | \(0.900521\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.23997e10 | 0.207790 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 6.83405e10i | − 0.625183i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.36475e10 | 0.213345 | 0.106672 | − | 0.994294i | \(-0.465980\pi\) | ||||
0.106672 | + | 0.994294i | \(0.465980\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4.97834e10i | − 0.442966i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.10891e10 | −0.0973175 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.69906e10i | 0.147073i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.88046e10 | 0.416714 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4.51763e10i | − 0.380503i | −0.981735 | − | 0.190251i | \(-0.939070\pi\) | ||||
0.981735 | − | 0.190251i | \(-0.0609303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.35717e8 | 0.00112765 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 9.98569e10i | − 0.818518i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.02734e10 | −0.568293 | −0.284146 | − | 0.958781i | \(-0.591710\pi\) | ||||
−0.284146 | + | 0.958781i | \(0.591710\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 5.30666e9i | − 0.0423402i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.94409e10 | −0.153045 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.40943e11i | 1.09480i | 0.836870 | + | 0.547401i | \(0.184383\pi\) | ||||
−0.836870 | + | 0.547401i | \(0.815617\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.64830e10 | −0.662877 | −0.331439 | − | 0.943477i | \(-0.607534\pi\) | ||||
−0.331439 | + | 0.943477i | \(0.607534\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5.06503e10i | − 0.383101i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.33093e9 | −0.0621830 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.73522e11i | 1.27820i | 0.769124 | + | 0.639100i | \(0.220693\pi\) | ||||
−0.769124 | + | 0.639100i | \(0.779307\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.89664e9 | 0.0574081 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.92195e11i | − 1.37904i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.35596e11 | 0.960296 | 0.480148 | − | 0.877187i | \(-0.340583\pi\) | ||||
0.480148 | + | 0.877187i | \(0.340583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 8.07107e10i | − 0.564197i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.78273e11 | 1.23011 | 0.615056 | − | 0.788484i | \(-0.289133\pi\) | ||||
0.615056 | + | 0.788484i | \(0.289133\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.47992e10i | 0.168917i | 0.996427 | + | 0.0844587i | \(0.0269161\pi\) | ||||
−0.996427 | + | 0.0844587i | \(0.973084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.57739e10 | −0.240547 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.59482e10i | − 0.105866i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.80925e10 | −0.249643 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.04681e8i | − 0.00197140i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.35734e10 | −0.597792 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1.32553e11i | − 0.836125i | −0.908418 | − | 0.418063i | \(-0.862709\pi\) | ||||
0.908418 | − | 0.418063i | \(-0.137291\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.74370e11 | 1.08607 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.46717e10i | − 0.0902370i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.82714e11 | 1.71708 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 3.01471e10i | − 0.180818i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.12454e11 | 1.25844 | 0.629221 | − | 0.777226i | \(-0.283374\pi\) | ||||
0.629221 | + | 0.777226i | \(0.283374\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.56248e11i | − 1.49905i | −0.661976 | − | 0.749525i | \(-0.730282\pi\) | ||||
0.661976 | − | 0.749525i | \(-0.269718\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.06041e11 | −0.612684 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.86616e10i | 0.448896i | 0.974486 | + | 0.224448i | \(0.0720579\pi\) | ||||
−0.974486 | + | 0.224448i | \(0.927942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.73672e10 | −0.436092 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 5.56529e9i | − 0.0309859i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.88198e11 | −1.58503 | −0.792517 | − | 0.609850i | \(-0.791230\pi\) | ||||
−0.792517 | + | 0.609850i | \(0.791230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 2.34872e11i | − 1.27605i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.16390e10 | −0.0624677 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.93182e11i | 1.02430i | 0.858897 | + | 0.512148i | \(0.171150\pi\) | ||||
−0.858897 | + | 0.512148i | \(0.828850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.68528e10 | 0.140664 | 0.0703322 | − | 0.997524i | \(-0.477594\pi\) | ||||
0.0703322 | + | 0.997524i | \(0.477594\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 6.94242e10i | − 0.359300i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.41205e7 | 0.000430146 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.44557e11i | 0.730359i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.06458e11 | −0.531462 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1.13944e11i | − 0.562084i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.05859e11 | −1.49094 | −0.745471 | − | 0.666538i | \(-0.767776\pi\) | ||||
−0.745471 | + | 0.666538i | \(0.767776\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.99829e10i | − 0.0962594i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.23521e11 | −1.54010 | −0.770049 | − | 0.637985i | \(-0.779768\pi\) | ||||
−0.770049 | + | 0.637985i | \(0.779768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.65324e9i | 0.00777782i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.12758e10 | 0.331401 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 4.95194e10i | − 0.227558i | −0.993506 | − | 0.113779i | \(-0.963704\pi\) | ||||
0.993506 | − | 0.113779i | \(-0.0362956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.44934e10 | 0.383761 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 1.41147e11i | − 0.633645i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.13697e10 | −0.272318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.65642e11i | 1.60378i | 0.597473 | + | 0.801889i | \(0.296172\pi\) | ||||
−0.597473 | + | 0.801889i | \(0.703828\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.24939e10 | −0.0541709 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 4.50090e10i | − 0.192912i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.14810e11 | −0.486463 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 2.32630e10i | − 0.0974445i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.67029e10 | 0.317643 | 0.158822 | − | 0.987307i | \(-0.449230\pi\) | ||||
0.158822 | + | 0.987307i | \(0.449230\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.48332e9i | − 0.00607313i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.86375e10 | 0.318327 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.65028e10i | 0.106075i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.43119e11 | 1.75362 | 0.876810 | − | 0.480838i | \(-0.159667\pi\) | ||||
0.876810 | + | 0.480838i | \(0.159667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 7.48788e10i | − 0.293009i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.01879e11 | 0.394210 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.12026e11i | 1.19390i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.37120e10 | 0.278908 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 4.36762e11i | − 1.63429i | −0.576432 | − | 0.817145i | \(-0.695556\pi\) | ||||
0.576432 | − | 0.817145i | \(-0.304444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.79190e10 | 0.103314 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 7.21234e10i | − 0.263951i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.07480e10 | −0.292267 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.38158e10i | 0.300046i | 0.988682 | + | 0.150023i | \(0.0479348\pi\) | ||||
−0.988682 | + | 0.150023i | \(0.952065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.50843e11i | 0.528270i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.84254e11 | 0.984670 | 0.492335 | − | 0.870406i | \(-0.336144\pi\) | ||||
0.492335 | + | 0.870406i | \(0.336144\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.15674e11i | 0.396356i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.23826e11 | 1.09759 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.39738e10i | 0.214499i | 0.994232 | + | 0.107249i | \(0.0342043\pi\) | ||||
−0.994232 | + | 0.107249i | \(0.965796\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.10051e9 | 0.00365022 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.03461e10i | 0.0339485i | 0.999856 | + | 0.0169742i | \(0.00540333\pi\) | ||||
−0.999856 | + | 0.0169742i | \(0.994597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.18269e10 | −0.0708546 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 5.93571e10i | − 0.190630i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.33339e10 | 0.233012 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.76822e11i | 1.81335i | 0.421829 | + | 0.906675i | \(0.361388\pi\) | ||||
−0.421829 | + | 0.906675i | \(0.638612\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.24846e11 | 0.699368 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.29854e11i | 0.399639i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.41065e11 | 0.429572 | 0.214786 | − | 0.976661i | \(-0.431095\pi\) | ||||
0.214786 | + | 0.976661i | \(0.431095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 2.28716e11i | − 0.689175i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.67327e11 | 0.498917 | 0.249458 | − | 0.968386i | \(-0.419747\pi\) | ||||
0.249458 | + | 0.968386i | \(0.419747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.17903e10i | 0.270831i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.84052e10 | 0.0829378 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2.79449e11i | − 0.807461i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.61655e11 | −0.748211 | −0.374105 | − | 0.927386i | \(-0.622050\pi\) | ||||
−0.374105 | + | 0.927386i | \(0.622050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.72365e11i | − 0.487788i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.07979e11 | 0.862587 | 0.431293 | − | 0.902212i | \(-0.358057\pi\) | ||||
0.431293 | + | 0.902212i | \(0.358057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.69085e10i | 0.157750i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.08257e10 | −0.166879 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.81996e9i | − 0.00494211i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.92741e11 | 0.518049 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.22688e10i | 0.112453i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.89078e11 | 0.497924 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.37562e11i | 1.14062i | 0.821430 | + | 0.570309i | \(0.193177\pi\) | ||||
−0.821430 | + | 0.570309i | \(0.806823\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.87153e10 | −0.0740978 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.19841e10i | 0.234967i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.11564e11 | 1.04075 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 2.51097e10i | − 0.0628597i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.55263e11 | 1.12831 | 0.564156 | − | 0.825668i | \(-0.309202\pi\) | ||||
0.564156 | + | 0.825668i | \(0.309202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1.11861e11i | − 0.274469i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.53665e10 | 0.207375 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.44127e10i | − 0.178972i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.31470e10 | 0.150373 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.33274e11i | − 0.550011i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.41357e11 | 1.49729 | 0.748645 | − | 0.662972i | \(-0.230705\pi\) | ||||
0.748645 | + | 0.662972i | \(0.230705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.10975e11i | 1.18118i | 0.806971 | + | 0.590591i | \(0.201105\pi\) | ||||
−0.806971 | + | 0.590591i | \(0.798895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.77761e11 | −0.864680 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 4.83517e11i | − 1.09593i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.39115e9 | −0.00536683 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 4.51279e10i | − 0.100302i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.83695e11 | 1.72494 | 0.862470 | − | 0.506107i | \(-0.168916\pi\) | ||||
0.862470 | + | 0.506107i | \(0.168916\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 6.34964e10i | − 0.138404i | −0.997603 | − | 0.0692022i | \(-0.977955\pi\) | ||||
0.997603 | − | 0.0692022i | \(-0.0220454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.27758e11 | 0.275786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.17395e11i | 1.31990i | 0.751309 | + | 0.659950i | \(0.229423\pi\) | ||||
−0.751309 | + | 0.659950i | \(0.770577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.04138e10 | −0.0643951 | −0.0321975 | − | 0.999482i | \(-0.510251\pi\) | ||||
−0.0321975 | + | 0.999482i | \(0.510251\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 4.11308e11i | − 0.862508i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.64545e11 | 0.341747 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.92205e11i | 1.21822i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.97896e10 | 0.0606965 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 2.99185e11i | − 0.603799i | −0.953340 | − | 0.301900i | \(-0.902379\pi\) | ||||
0.953340 | − | 0.301900i | \(-0.0976207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.29444e11 | −0.658564 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 5.02365e11i | − 0.994740i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.66593e11 | −1.50362 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.70331e9i | 0.0149673i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.57464e11 | −0.303075 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.11348e12i | − 2.12308i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.03892e11 | 1.70734 | 0.853671 | − | 0.520813i | \(-0.174371\pi\) | ||||
0.853671 | + | 0.520813i | \(0.174371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.50276e8i | 0 0.000842587i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.61813e11 | −1.41229 | −0.706147 | − | 0.708066i | \(-0.749568\pi\) | ||||
−0.706147 | + | 0.708066i | \(0.749568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.60448e11i | 1.39668i | 0.715766 | + | 0.698340i | \(0.246078\pi\) | ||||
−0.715766 | + | 0.698340i | \(0.753922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.46303e10 | −0.135801 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.15102e11i | 0.207510i | 0.994603 | + | 0.103755i | \(0.0330858\pi\) | ||||
−0.994603 | + | 0.103755i | \(0.966914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.65963e10 | −0.136818 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.85818e11i | 0.505840i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.78728e11 | 0.839479 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.16966e12i | 2.03229i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.84940e9 | −0.0152355 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.05794e11i | 0.180480i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.65540e11 | 0.279837 | 0.139919 | − | 0.990163i | \(-0.455316\pi\) | ||||
0.139919 | + | 0.990163i | \(0.455316\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.64232e10i | 0.144769i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.92925e11 | 1.15022 | 0.575112 | − | 0.818075i | \(-0.304958\pi\) | ||||
0.575112 | + | 0.818075i | \(0.304958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.72114e11i | 1.27010i | 0.772470 | + | 0.635051i | \(0.219021\pi\) | ||||
−0.772470 | + | 0.635051i | \(0.780979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.14338e11 | 0.186388 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 8.83378e11i | − 1.42709i | −0.700608 | − | 0.713546i | \(-0.747088\pi\) | ||||
0.700608 | − | 0.713546i | \(-0.252912\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.35664e10 | −0.0217198 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 6.68769e10i | − 0.106112i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.77321e9 | 0.00278840 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.34302e11i | 0.832712i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.26119e11 | 1.27607 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.20376e11i | − 0.184289i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.57183e10 | −0.0541990 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.80527e10i | 0.147472i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.53390e11 | 0.377742 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.20277e12i | − 1.77727i | −0.458619 | − | 0.888633i | \(-0.651656\pi\) | ||||
0.458619 | − | 0.888633i | \(-0.348344\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.41863e11 | −0.207784 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 8.65949e10i | − 0.125724i | −0.998022 | − | 0.0628621i | \(-0.979977\pi\) | ||||
0.998022 | − | 0.0628621i | \(-0.0200228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.79492e11 | 0.546159 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.68393e11i | 0.240237i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.17178e11 | −0.307141 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.89815e11i | 0.266114i | 0.991108 | + | 0.133057i | \(0.0424793\pi\) | ||||
−0.991108 | + | 0.133057i | \(0.957521\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.06964e11 | 0.843577 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.96179e11i | 0.959211i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.21979e11 | 0.849589 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.49444e11i | 0.202376i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.56926e11 | −0.479198 | −0.239599 | − | 0.970872i | \(-0.577016\pi\) | ||||
−0.239599 | + | 0.970872i | \(0.577016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.60835e9i | 0.00347190i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.49929e11 | −0.329831 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.81605e11i | 0.237619i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.40006e12 | −1.81631 | −0.908154 | − | 0.418636i | \(-0.862508\pi\) | ||||
−0.908154 | + | 0.418636i | \(0.862508\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 5.08790e10i | − 0.0654450i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.26018e10 | −0.118103 | −0.0590515 | − | 0.998255i | \(-0.518808\pi\) | ||||
−0.0590515 | + | 0.998255i | \(0.518808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.36620e12i | − 1.72769i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.84643e10 | 0.0231529 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.03974e12i | − 1.29278i | −0.763007 | − | 0.646390i | \(-0.776278\pi\) | ||||
0.763007 | − | 0.646390i | \(-0.223722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.68778e11 | 0.331381 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 4.78074e11i | − 0.584485i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.29369e12 | −1.56841 | −0.784205 | − | 0.620501i | \(-0.786929\pi\) | ||||
−0.784205 | + | 0.620501i | \(0.786929\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2.11644e11i | − 0.254444i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.70240e11 | −0.322182 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 7.81280e10i | − 0.0923703i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.68054e11 | 0.900530 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.92538e11i | 0.456433i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.70379e11 | −0.542424 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.49704e12i | − 1.71209i | −0.516902 | − | 0.856045i | \(-0.672915\pi\) | ||||
0.516902 | − | 0.856045i | \(-0.327085\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.40514e8 | 0.000726497 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.15769e11i | − 0.242724i | −0.992608 | − | 0.121362i | \(-0.961274\pi\) | ||||
0.992608 | − | 0.121362i | \(-0.0387261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.16182e10 | −0.0464336 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.61460e11i | 0.510641i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.51586e11 | 1.04441 | 0.522203 | − | 0.852821i | \(-0.325110\pi\) | ||||
0.522203 | + | 0.852821i | \(0.325110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.45780e11i | 0.594137i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.91331e11 | −0.530515 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 5.22888e11i | − 0.560009i | −0.959999 | − | 0.280004i | \(-0.909664\pi\) | ||||
0.959999 | − | 0.280004i | \(-0.0903359\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.43499e11 | −1.00230 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 7.27133e10i | − 0.0766206i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.79497e12 | −1.87617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.96171e11i | 0.514443i | 0.966352 | + | 0.257221i | \(0.0828070\pi\) | ||||
−0.966352 | + | 0.257221i | \(0.917193\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.61544e11 | 0.783246 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.83687e11i | 0.187407i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.07659e11 | 0.412588 | 0.206294 | − | 0.978490i | \(-0.433860\pi\) | ||||
0.206294 | + | 0.978490i | \(0.433860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 3.25585e11i | − 0.326890i |
(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 | 384.9.g.a.127.13 | ✓ | 32 | |
4.3 | odd | 2 | inner | 384.9.g.a.127.14 | yes | 32 | |
8.3 | odd | 2 | 384.9.g.b.127.19 | yes | 32 | ||
8.5 | even | 2 | 384.9.g.b.127.20 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.9.g.a.127.13 | ✓ | 32 | 1.1 | even | 1 | trivial | |
384.9.g.a.127.14 | yes | 32 | 4.3 | odd | 2 | inner | |
384.9.g.b.127.19 | yes | 32 | 8.3 | odd | 2 | ||
384.9.g.b.127.20 | yes | 32 | 8.5 | even | 2 |