Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,14,Mod(1,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.a (trivial) |
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: | yes |
Analytic conductor: | \(90.0739803196\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 82385347x^{2} + 61134548293x + 1123635148704894 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{4}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3608.22\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16831.3 | −0.481741 | −0.240870 | − | 0.970557i | \(-0.577433\pi\) | ||||
−0.240870 | + | 0.970557i | \(0.577433\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 117649. | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.93891e6 | 1.18097 | 0.590485 | − | 0.807049i | \(-0.298937\pi\) | ||||
0.590485 | + | 0.807049i | \(0.298937\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.45397e6 | −0.255927 | −0.127963 | − | 0.991779i | \(-0.540844\pi\) | ||||
−0.127963 | + | 0.991779i | \(0.540844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.22700e7 | −0.278133 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.47755e8 | 1.48465 | 0.742325 | − | 0.670040i | \(-0.233723\pi\) | ||||
0.742325 | + | 0.670040i | \(0.233723\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.83966e8 | −1.38474 | −0.692370 | − | 0.721542i | \(-0.743433\pi\) | ||||
−0.692370 | + | 0.721542i | \(0.743433\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.57661e7 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.85997e8 | −0.261984 | −0.130992 | − | 0.991383i | \(-0.541816\pi\) | ||||
−0.130992 | + | 0.991383i | \(0.541816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.37410e8 | −0.767926 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.72179e9 | 0.849704 | 0.424852 | − | 0.905263i | \(-0.360326\pi\) | ||||
0.424852 | + | 0.905263i | \(0.360326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.54365e9 | −0.312390 | −0.156195 | − | 0.987726i | \(-0.549923\pi\) | ||||
−0.156195 | + | 0.987726i | \(0.549923\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.05846e9 | 0.681833 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.98019e9 | −0.182081 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.53182e9 | 0.226302 | 0.113151 | − | 0.993578i | \(-0.463906\pi\) | ||||
0.113151 | + | 0.993578i | \(0.463906\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.24695e9 | −0.147759 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.36893e10 | −0.450075 | −0.225037 | − | 0.974350i | \(-0.572250\pi\) | ||||
−0.225037 | + | 0.974350i | \(0.572250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.67546e10 | 1.36917 | 0.684583 | − | 0.728935i | \(-0.259984\pi\) | ||||
0.684583 | + | 0.728935i | \(0.259984\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.94486e9 | −0.160580 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.36999e11 | 1.85388 | 0.926942 | − | 0.375206i | \(-0.122428\pi\) | ||||
0.926942 | + | 0.375206i | \(0.122428\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.38413e10 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.07713e11 | 0.857163 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.64179e11 | −1.01747 | −0.508737 | − | 0.860922i | \(-0.669887\pi\) | ||||
−0.508737 | + | 0.860922i | \(0.669887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.16791e11 | −0.568921 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.07011e11 | −0.799480 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.52920e11 | −0.780629 | −0.390315 | − | 0.920682i | \(-0.627634\pi\) | ||||
−0.390315 | + | 0.920682i | \(0.627634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.46331e11 | 1.10921 | 0.554604 | − | 0.832115i | \(-0.312870\pi\) | ||||
0.554604 | + | 0.832115i | \(0.312870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.25235e10 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.49663e10 | 0.123290 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.09315e11 | 0.417748 | 0.208874 | − | 0.977943i | \(-0.433020\pi\) | ||||
0.208874 | + | 0.977943i | \(0.433020\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.35592e11 | −0.151257 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.19400e12 | −1.10618 | −0.553089 | − | 0.833122i | \(-0.686551\pi\) | ||||
−0.553089 | + | 0.833122i | \(0.686551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.11420e11 | 0.472870 | 0.236435 | − | 0.971647i | \(-0.424021\pi\) | ||||
0.236435 | + | 0.971647i | \(0.424021\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.83372e11 | −0.443362 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.16356e11 | 0.446364 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.09740e11 | 0.421057 | 0.210529 | − | 0.977588i | \(-0.432481\pi\) | ||||
0.210529 | + | 0.977588i | \(0.432481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.61316e12 | 1.54879 | 0.774393 | − | 0.632705i | \(-0.218056\pi\) | ||||
0.774393 | + | 0.632705i | \(0.218056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.48691e12 | −0.715217 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.98418e12 | 0.490577 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.09449e11 | 0.129988 | 0.0649938 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649938 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.24005e11 | −0.0967312 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.12532e12 | −0.180358 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.77953e12 | 0.667086 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.78760e12 | 0.583581 | 0.291791 | − | 0.956482i | \(-0.405749\pi\) | ||||
0.291791 | + | 0.956482i | \(0.405749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.68762e12 | 0.393656 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.25982e12 | 0.211828 | 0.105914 | − | 0.994375i | \(-0.466223\pi\) | ||||
0.105914 | + | 0.994375i | \(0.466223\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.39271e13 | 1.97446 | 0.987228 | − | 0.159315i | \(-0.0509286\pi\) | ||||
0.987228 | + | 0.159315i | \(0.0509286\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.44356e12 | −0.105124 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.26412e12 | 0.145849 | 0.0729246 | − | 0.997337i | \(-0.476767\pi\) | ||||
0.0729246 | + | 0.997337i | \(0.476767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.91471e12 | 0.394913 | 0.197457 | − | 0.980312i | \(-0.436732\pi\) | ||||
0.197457 | + | 0.980312i | \(0.436732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.57470e12 | 0.130655 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.43824e12 | 0.426463 | 0.213231 | − | 0.977002i | \(-0.431601\pi\) | ||||
0.213231 | + | 0.977002i | \(0.431601\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.13058e12 | 0.126208 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.36702e12 | −0.0853089 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.73832e13 | 0.561145 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.36257e13 | 0.394689 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.97946e12 | −0.259851 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.63239e13 | 0.851682 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.60092e13 | 1.81895 | 0.909475 | − | 0.415759i | \(-0.136484\pi\) | ||||
0.909475 | + | 0.415759i | \(0.136484\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.13741e13 | 0.790489 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.87204e13 | 1.36089 | 0.680447 | − | 0.732798i | \(-0.261786\pi\) | ||||
0.680447 | + | 0.732798i | \(0.261786\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.34083e13 | −0.523383 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.52080e12 | −0.0927110 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.33454e13 | −0.430876 | −0.215438 | − | 0.976518i | \(-0.569118\pi\) | ||||
−0.215438 | + | 0.976518i | \(0.569118\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.53503e14 | −1.80518 | −0.902590 | − | 0.430501i | \(-0.858337\pi\) | ||||
−0.902590 | + | 0.430501i | \(0.858337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.98725e13 | 1.07034 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.09057e13 | −0.302242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.58113e13 | −0.409337 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00903e13 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.63817e13 | 0.197511 | 0.0987555 | − | 0.995112i | \(-0.468514\pi\) | ||||
0.0987555 | + | 0.995112i | \(0.468514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.66799e14 | 1.83161 | 0.915807 | − | 0.401619i | \(-0.131552\pi\) | ||||
0.915807 | + | 0.401619i | \(0.131552\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.85231e13 | 0.494883 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.59816e13 | 0.150491 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.58874e14 | 0.846651 | 0.423326 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423326 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.19686e14 | −0.587439 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18824e13 | −0.0990207 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.93423e14 | 0.807770 | 0.403885 | − | 0.914810i | \(-0.367660\pi\) | ||||
0.403885 | + | 0.914810i | \(0.367660\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.51407e13 | −0.328467 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.76411e14 | 0.986049 | 0.493024 | − | 0.870015i | \(-0.335891\pi\) | ||||
0.493024 | + | 0.870015i | \(0.335891\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.83037e14 | −0.934501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.50911e14 | −0.461580 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.59234e14 | 0.451582 | 0.225791 | − | 0.974176i | \(-0.427503\pi\) | ||||
0.225791 | + | 0.974176i | \(0.427503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.10285e14 | −0.290249 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.84379e14 | −0.450696 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.61147e14 | −1.04784 | −0.523920 | − | 0.851767i | \(-0.675531\pi\) | ||||
−0.523920 | + | 0.851767i | \(0.675531\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.48584e14 | 0.525489 | 0.262744 | − | 0.964866i | \(-0.415372\pi\) | ||||
0.262744 | + | 0.964866i | \(0.415372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.25375e14 | 0.640401 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.94452e13 | −0.109019 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.02526e15 | 1.75333 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.55796e13 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.10794e14 | −0.761252 | −0.380626 | − | 0.924729i | \(-0.624292\pi\) | ||||
−0.380626 | + | 0.924729i | \(0.624292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00056e15 | −1.39354 | −0.696772 | − | 0.717293i | \(-0.745381\pi\) | ||||
−0.696772 | + | 0.717293i | \(0.745381\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.46504e13 | 0.0711817 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.67569e14 | −0.326141 | −0.163071 | − | 0.986614i | \(-0.552140\pi\) | ||||
−0.163071 | + | 0.986614i | \(0.552140\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.05437e15 | −1.20350 | −0.601752 | − | 0.798683i | \(-0.705530\pi\) | ||||
−0.601752 | + | 0.798683i | \(0.705530\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.25490e14 | 0.241187 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.20216e14 | 0.321158 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.30408e14 | 0.216819 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.88464e13 | −0.0873280 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.97042e15 | −1.63534 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.25130e14 | −0.409667 | −0.204834 | − | 0.978797i | \(-0.565665\pi\) | ||||
−0.204834 | + | 0.978797i | \(0.565665\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.70425e14 | −0.638652 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.55256e14 | −0.659583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.81609e14 | −0.118072 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.45726e14 | 0.273011 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.58097e14 | −0.379962 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.63699e15 | −1.43591 | −0.717954 | − | 0.696091i | \(-0.754921\pi\) | ||||
−0.717954 | + | 0.696091i | \(0.754921\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.98178e14 | −0.255975 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.56101e15 | −1.24235 | −0.621174 | − | 0.783673i | \(-0.713344\pi\) | ||||
−0.621174 | + | 0.783673i | \(0.713344\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.08889e14 | −0.324824 | −0.162412 | − | 0.986723i | \(-0.551927\pi\) | ||||
−0.162412 | + | 0.986723i | \(0.551927\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.95123e14 | 0.257709 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.38574e15 | −0.567371 | −0.283685 | − | 0.958917i | \(-0.591557\pi\) | ||||
−0.283685 | + | 0.958917i | \(0.591557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.30588e15 | −0.893091 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.63200e14 | 0.243098 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.39521e15 | 0.831298 | 0.415649 | − | 0.909525i | \(-0.363554\pi\) | ||||
0.415649 | + | 0.909525i | \(0.363554\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.70784e15 | 1.87655 | 0.938277 | − | 0.345884i | \(-0.112421\pi\) | ||||
0.938277 | + | 0.345884i | \(0.112421\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.32967e14 | −0.0688201 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.26478e15 | 0.354392 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.36300e15 | 0.894192 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.51633e15 | −0.887587 | −0.443793 | − | 0.896129i | \(-0.646368\pi\) | ||||
−0.443793 | + | 0.896129i | \(0.646368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.29062e15 | −0.309395 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.81296e15 | −0.412930 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.00438e15 | −0.650413 | −0.325207 | − | 0.945643i | \(-0.605434\pi\) | ||||
−0.325207 | + | 0.945643i | \(0.605434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.15515e14 | 0.0855339 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.44647e15 | 0.283235 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.74031e15 | 1.06960 | 0.534802 | − | 0.844978i | \(-0.320386\pi\) | ||||
0.534802 | + | 0.844978i | \(0.320386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.76334e15 | 0.490159 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.44288e14 | 0.0750484 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.09531e15 | −0.337177 | −0.168589 | − | 0.985686i | \(-0.553921\pi\) | ||||
−0.168589 | + | 0.985686i | \(0.553921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.34576e15 | 0.359735 | 0.179868 | − | 0.983691i | \(-0.442433\pi\) | ||||
0.179868 | + | 0.983691i | \(0.442433\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.82000e14 | −0.0558478 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.50460e15 | −0.906897 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.04986e16 | −1.39641 | −0.698207 | − | 0.715896i | \(-0.746018\pi\) | ||||
−0.698207 | + | 0.715896i | \(0.746018\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.20357e14 | −0.104130 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.61452e15 | 1.16503 | 0.582514 | − | 0.812820i | \(-0.302069\pi\) | ||||
0.582514 | + | 0.812820i | \(0.302069\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.42693e15 | 1.09083 | 0.545417 | − | 0.838165i | \(-0.316371\pi\) | ||||
0.545417 | + | 0.838165i | \(0.316371\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.48428e15 | 0.385142 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.61053e15 | −0.170112 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.19270e16 | 1.20419 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.49016e15 | 0.336931 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.67428e15 | −0.800928 | −0.400464 | − | 0.916312i | \(-0.631151\pi\) | ||||
−0.400464 | + | 0.916312i | \(0.631151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.25698e15 | 0.376061 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.68827e15 | 0.227278 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.28426e14 | 0.0670488 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.67713e15 | 0.517496 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.64741e15 | 0.122299 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.51234e15 | −0.534350 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.33933e15 | −0.363988 | −0.181994 | − | 0.983300i | \(-0.558255\pi\) | ||||
−0.181994 | + | 0.983300i | \(0.558255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.74428e16 | 1.13995 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.23775e16 | −0.775694 | −0.387847 | − | 0.921724i | \(-0.626781\pi\) | ||||
−0.387847 | + | 0.921724i | \(0.626781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.38517e15 | 0.263601 | 0.131801 | − | 0.991276i | \(-0.457924\pi\) | ||||
0.131801 | + | 0.991276i | \(0.457924\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.05235e15 | −0.0606936 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.07503e16 | 1.70202 | 0.851009 | − | 0.525151i | \(-0.175991\pi\) | ||||
0.851009 | + | 0.525151i | \(0.175991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.88862e16 | 1.00347 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.65054e15 | 0.0842061 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.19574e16 | −2.05586 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.17520e15 | 0.196533 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.04082e15 | 0.228003 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.61178e16 | 0.700702 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.42644e16 | 1.43206 | 0.716031 | − | 0.698069i | \(-0.245957\pi\) | ||||
0.716031 | + | 0.698069i | \(0.245957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.87695e15 | 0.0754338 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.20618e15 | −0.201246 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.09364e16 | 1.15047 | 0.575235 | − | 0.817988i | \(-0.304910\pi\) | ||||
0.575235 | + | 0.817988i | \(0.304910\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.88048e15 | 0.246218 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.07112e16 | −0.368923 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.62841e15 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.28219e15 | 0.0728665 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.87720e16 | −1.49979 | −0.749893 | − | 0.661560i | \(-0.769895\pi\) | ||||
−0.749893 | + | 0.661560i | \(0.769895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.38981e16 | 0.411709 | 0.205854 | − | 0.978583i | \(-0.434003\pi\) | ||||
0.205854 | + | 0.978583i | \(0.434003\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.72556e15 | −0.0492531 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.92853e15 | −0.190593 | −0.0952963 | − | 0.995449i | \(-0.530380\pi\) | ||||
−0.0952963 | + | 0.995449i | \(0.530380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00966e16 | 0.532891 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.26724e16 | 0.323977 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.74394e16 | −0.429950 | −0.214975 | − | 0.976620i | \(-0.568967\pi\) | ||||
−0.214975 | + | 0.976620i | \(0.568967\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.85839e16 | 0.917506 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.93315e15 | 0.227874 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.02910e16 | −0.227801 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.69229e16 | −0.788799 | −0.394400 | − | 0.918939i | \(-0.629047\pi\) | ||||
−0.394400 | + | 0.918939i | \(0.629047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.27503e15 | −0.150025 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.93154e16 | −0.384569 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.45077e16 | −1.04797 | −0.523987 | − | 0.851726i | \(-0.675556\pi\) | ||||
−0.523987 | + | 0.851726i | \(0.675556\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.64801e16 | 0.491719 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.21228e16 | −0.217462 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.91684e16 | −0.678860 | −0.339430 | − | 0.940631i | \(-0.610234\pi\) | ||||
−0.339430 | + | 0.940631i | \(0.610234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.27007e16 | 1.05017 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.62532e16 | −0.425002 | −0.212501 | − | 0.977161i | \(-0.568161\pi\) | ||||
−0.212501 | + | 0.977161i | \(0.568161\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.37403e16 | −0.215032 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.01617e16 | 0.456389 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.96900e16 | −0.727104 | −0.363552 | − | 0.931574i | \(-0.618436\pi\) | ||||
−0.363552 | + | 0.931574i | \(0.618436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.74820e16 | −0.388955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.73872e16 | 0.785712 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.53121e16 | −0.202840 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.27542e16 | 0.419884 | 0.209942 | − | 0.977714i | \(-0.432673\pi\) | ||||
0.209942 | + | 0.977714i | \(0.432673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.43547e16 | −0.302175 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.23550e17 | −1.48390 | −0.741952 | − | 0.670453i | \(-0.766100\pi\) | ||||
−0.741952 | + | 0.670453i | \(0.766100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.87536e15 | 0.0799490 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.75366e15 | −0.0535267 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.45070e16 | 0.267255 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.64479e16 | −0.913172 | −0.456586 | − | 0.889679i | \(-0.650928\pi\) | ||||
−0.456586 | + | 0.889679i | \(0.650928\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.43088e16 | −0.248766 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.97558e16 | −0.295050 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.76457e16 | −0.746113 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.11904e17 | −1.04222 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.56678e17 | −1.41454 | −0.707270 | − | 0.706943i | \(-0.750074\pi\) | ||||
−0.707270 | + | 0.706943i | \(0.750074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.72013e16 | 0.500694 | 0.250347 | − | 0.968156i | \(-0.419455\pi\) | ||||
0.250347 | + | 0.968156i | \(0.419455\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.28071e16 | 0.617961 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.38507e17 | −1.14010 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.25104e16 | 0.419241 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.25303e16 | −0.174499 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.14881e17 | −1.61471 | −0.807356 | − | 0.590065i | \(-0.799102\pi\) | ||||
−0.807356 | + | 0.590065i | \(0.799102\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.21444e17 | 0.885534 | 0.442767 | − | 0.896637i | \(-0.353997\pi\) | ||||
0.442767 | + | 0.896637i | \(0.353997\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.33965e16 | −0.236331 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.28169e16 | 0.362780 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.61040e16 | 0.240733 | 0.120367 | − | 0.992730i | \(-0.461593\pi\) | ||||
0.120367 | + | 0.992730i | \(0.461593\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.35583e15 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.88387e16 | −0.621302 | −0.310651 | − | 0.950524i | \(-0.600547\pi\) | ||||
−0.310651 | + | 0.950524i | \(0.600547\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.02578e16 | −0.0626203 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.92322e16 | 0.114033 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.02823e16 | −0.232013 | −0.116007 | − | 0.993248i | \(-0.537009\pi\) | ||||
−0.116007 | + | 0.993248i | \(0.537009\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.49885e16 | −0.531525 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.94496e17 | 1.05748 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.81971e15 | 0.0465994 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.76202e17 | 1.41831 | 0.709155 | − | 0.705053i | \(-0.249077\pi\) | ||||
0.709155 | + | 0.705053i | \(0.249077\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.72433e16 | 0.285721 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.05459e16 | −0.245262 | −0.122631 | − | 0.992452i | \(-0.539133\pi\) | ||||
−0.122631 | + | 0.992452i | \(0.539133\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.46280e16 | −0.446420 | −0.223210 | − | 0.974770i | \(-0.571653\pi\) | ||||
−0.223210 | + | 0.974770i | \(0.571653\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.89406e16 | 0.0868860 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.37692e17 | −1.06037 | −0.530183 | − | 0.847883i | \(-0.677877\pi\) | ||||
−0.530183 | + | 0.847883i | \(0.677877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.63906e16 | 0.157894 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.15819e17 | 0.488814 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.93815e17 | 1.61694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.66193e17 | 1.06338 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.72512e16 | −0.339158 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.43070e16 | −0.281092 | −0.140546 | − | 0.990074i | \(-0.544886\pi\) | ||||
−0.140546 | + | 0.990074i | \(0.544886\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.57306e16 | −0.0579166 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.59522e16 | −0.0571696 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.05816e16 | −0.281135 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.37729e17 | −0.467828 | −0.233914 | − | 0.972257i | \(-0.575153\pi\) | ||||
−0.233914 | + | 0.972257i | \(0.575153\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.41005e17 | 0.466366 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.05407e16 | 0.227201 | 0.113601 | − | 0.993527i | \(-0.463762\pi\) | ||||
0.113601 | + | 0.993527i | \(0.463762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.02158e17 | 1.26151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.20675e16 | −0.189640 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.40473e17 | −0.418096 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.27709e17 | −1.24021 | −0.620104 | − | 0.784519i | \(-0.712910\pi\) | ||||
−0.620104 | + | 0.784519i | \(0.712910\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.01504e17 | 0.569296 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.29978e17 | 1.73434 | 0.867168 | − | 0.498015i | \(-0.165938\pi\) | ||||
0.867168 | + | 0.498015i | \(0.165938\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.80357e16 | −0.102046 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.06334e17 | −0.539535 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.92905e17 | 1.76607 | 0.883036 | − | 0.469306i | \(-0.155496\pi\) | ||||
0.883036 | + | 0.469306i | \(0.155496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.19330e16 | 0.178728 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.10014e17 | −0.266493 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.02724e17 | −0.951176 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.50626e17 | 2.18938 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.16082e17 | 0.260721 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.21528e17 | 0.485269 | 0.242635 | − | 0.970118i | \(-0.421988\pi\) | ||||
0.242635 | + | 0.970118i | \(0.421988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.36297e16 | −0.200057 | −0.100028 | − | 0.994985i | \(-0.531893\pi\) | ||||
−0.100028 | + | 0.994985i | \(0.531893\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.03980e16 | −0.167575 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.28082e17 | −0.463790 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.69441e17 | −0.931364 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.34412e17 | −0.260210 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.09716e16 | 0.115186 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.81081e16 | −0.0702615 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.36176e17 | −0.604971 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.60434e16 | 0.168710 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.32047e17 | 1.25533 | 0.627663 | − | 0.778485i | \(-0.284012\pi\) | ||||
0.627663 | + | 0.778485i | \(0.284012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.81218e17 | 0.303391 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.16384e17 | −0.190246 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.71808e17 | −0.753092 | −0.376546 | − | 0.926398i | \(-0.622888\pi\) | ||||
−0.376546 | + | 0.926398i | \(0.622888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.37198e17 | 0.369736 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.72897e17 | −1.17662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.07030e17 | 0.159145 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.33356e16 | −0.0629420 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.34214e17 | 0.899864 | 0.449932 | − | 0.893063i | \(-0.351448\pi\) | ||||
0.449932 | + | 0.893063i | \(0.351448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.52784e17 | −0.350406 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.47413e17 | 1.01228 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.00992e18 | 1.33654 | 0.668268 | − | 0.743920i | \(-0.267036\pi\) | ||||
0.668268 | + | 0.743920i | \(0.267036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.58858e17 | −0.205444 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.32276e16 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.07390e18 | 1.32659 | 0.663294 | − | 0.748359i | \(-0.269158\pi\) | ||||
0.663294 | + | 0.748359i | \(0.269158\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.95807e17 | −0.236425 | −0.118212 | − | 0.992988i | \(-0.537716\pi\) | ||||
−0.118212 | + | 0.992988i | \(0.537716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.72369e17 | −0.439509 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.74355e17 | 0.201184 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.07321e17 | 0.685134 | 0.342567 | − | 0.939493i | \(-0.388704\pi\) | ||||
0.342567 | + | 0.939493i | \(0.388704\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.29408e17 | −0.804563 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.42734e17 | 0.585386 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.13922e18 | −1.20161 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.98402e16 | 0.0410968 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.47840e17 | 0.855394 | 0.427697 | − | 0.903922i | \(-0.359325\pi\) | ||||
0.427697 | + | 0.903922i | \(0.359325\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.38344e17 | 0.432579 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.95058e17 | −0.188298 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.22479e17 | −0.210104 | −0.105052 | − | 0.994467i | \(-0.533501\pi\) | ||||
−0.105052 | + | 0.994467i | \(0.533501\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.92583e17 | −0.270326 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.68635e17 | −0.694843 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.76625e17 | −0.333146 | −0.166573 | − | 0.986029i | \(-0.553270\pi\) | ||||
−0.166573 | + | 0.986029i | \(0.553270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.20495e18 | −1.04300 | −0.521502 | − | 0.853250i | \(-0.674628\pi\) | ||||
−0.521502 | + | 0.853250i | \(0.674628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.64383e17 | 0.139249 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.29339e17 | −0.190138 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.96571e17 | −0.240659 | −0.120329 | − | 0.992734i | \(-0.538395\pi\) | ||||
−0.120329 | + | 0.992734i | \(0.538395\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.33437e17 | 0.185421 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.10191e17 | −0.474458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.29072e18 | −0.982516 | −0.491258 | − | 0.871014i | \(-0.663463\pi\) | ||||
−0.491258 | + | 0.871014i | \(0.663463\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.67968e17 | 0.125181 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.10503e18 | 0.806342 | 0.403171 | − | 0.915125i | \(-0.367908\pi\) | ||||
0.403171 | + | 0.915125i | \(0.367908\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.91510e18 | 1.36836 | 0.684182 | − | 0.729312i | \(-0.260160\pi\) | ||||
0.684182 | + | 0.729312i | \(0.260160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.20590e16 | −0.0504189 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.17010e16 | 0.0491307 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.32919e17 | 0.357636 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.43643e18 | −0.944162 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.21844e17 | 0.335979 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.01471e18 | −1.27064 | −0.635319 | − | 0.772249i | \(-0.719132\pi\) | ||||
−0.635319 | + | 0.772249i | \(0.719132\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.82820e17 | −0.236522 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.44765e18 | −0.876262 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.16487e16 | −0.0365610 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.34540e17 | −0.368726 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.59723e17 | −0.375651 | −0.187825 | − | 0.982202i | \(-0.560144\pi\) | ||||
−0.187825 | + | 0.982202i | \(0.560144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.35094e17 | 0.0753812 | 0.0376906 | − | 0.999289i | \(-0.488000\pi\) | ||||
0.0376906 | + | 0.999289i | \(0.488000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.96381e17 | −0.380811 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.90976e17 | −0.155948 | −0.0779740 | − | 0.996955i | \(-0.524845\pi\) | ||||
−0.0779740 | + | 0.996955i | \(0.524845\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.75499e18 | −0.921899 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.32393e17 | −0.0681691 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.89972e18 | −0.958856 | −0.479428 | − | 0.877581i | \(-0.659156\pi\) | ||||
−0.479428 | + | 0.877581i | \(0.659156\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.32497e18 | −0.655598 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.24934e17 | 0.157623 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.04869e18 | 0.498760 | 0.249380 | − | 0.968406i | \(-0.419773\pi\) | ||||
0.249380 | + | 0.968406i | \(0.419773\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.01488e18 | −1.40592 | −0.702960 | − | 0.711229i | \(-0.748139\pi\) | ||||
−0.702960 | + | 0.711229i | \(0.748139\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.79753e17 | −0.219371 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.62307e17 | 0.252135 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.06245e17 | −0.222609 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.92236e18 | −0.829022 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.09705e18 | 1.30994 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.84669e18 | −0.766118 | −0.383059 | − | 0.923724i | \(-0.625129\pi\) | ||||
−0.383059 | + | 0.923724i | \(0.625129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.63172e17 | −0.147787 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.40006e18 | 1.35725 | 0.678625 | − | 0.734485i | \(-0.262576\pi\) | ||||
0.678625 | + | 0.734485i | \(0.262576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.63256e17 | 0.220573 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.86698e18 | −0.717270 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.24420e18 | −1.59978 | −0.799892 | − | 0.600144i | \(-0.795110\pi\) | ||||
−0.799892 | + | 0.600144i | \(0.795110\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.61248e17 | 0.207571 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.16780e17 | −0.187537 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.31247e17 | 0.260399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.79035e18 | 0.975104 | 0.487552 | − | 0.873094i | \(-0.337890\pi\) | ||||
0.487552 | + | 0.873094i | \(0.337890\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.33845e17 | 0.148788 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.58366e18 | 0.869629 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.02266e18 | −0.668204 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.01020e18 | −0.327572 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.02202e18 | 1.28020 | 0.640100 | − | 0.768292i | \(-0.278893\pi\) | ||||
0.640100 | + | 0.768292i | \(0.278893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.00292e18 | −0.313369 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.68099e18 | −0.515626 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.65865e17 | 0.0800636 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.08042e18 | 0.615106 | 0.307553 | − | 0.951531i | \(-0.400490\pi\) | ||||
0.307553 | + | 0.951531i | \(0.400490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.83473e17 | 0.140352 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.87114e17 | 0.0818412 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.20184e17 | 0.145602 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.74611e18 | 0.479950 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.69620e18 | −0.727805 | −0.363902 | − | 0.931437i | \(-0.618556\pi\) | ||||
−0.363902 | + | 0.931437i | \(0.618556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.81499e18 | 0.746274 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.16102e18 | 1.08343 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.55143e18 | −0.652510 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.74015e17 | 0.0688335 | 0.0344168 | − | 0.999408i | \(-0.489043\pi\) | ||||
0.0344168 | + | 0.999408i | \(0.489043\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.38578e18 | 2.03273 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.01229e18 | −0.717334 | −0.358667 | − | 0.933466i | \(-0.616769\pi\) | ||||
−0.358667 | + | 0.933466i | \(0.616769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.69833e17 | −0.0397333 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.14631e18 | 0.493348 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.42884e18 | −1.45192 | −0.725962 | − | 0.687734i | \(-0.758605\pi\) | ||||
−0.725962 | + | 0.687734i | \(0.758605\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.22023e17 | 0.204608 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.02122e18 | 1.74909 | 0.874547 | − | 0.484941i | \(-0.161159\pi\) | ||||
0.874547 | + | 0.484941i | \(0.161159\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.44038e17 | −0.0951491 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.45162e18 | 0.516262 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.66371e17 | 0.0551258 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.93658e18 | −1.20747 | −0.603735 | − | 0.797185i | \(-0.706322\pi\) | ||||
−0.603735 | + | 0.797185i | \(0.706322\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.56341e18 | −0.512448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.49058e18 | −0.882363 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.79758e18 | 1.89232 | 0.946162 | − | 0.323694i | \(-0.104925\pi\) | ||||
0.946162 | + | 0.323694i | \(0.104925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.40859e17 | −0.178629 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.70979e18 | −0.505750 | −0.252875 | − | 0.967499i | \(-0.581376\pi\) | ||||
−0.252875 | + | 0.967499i | \(0.581376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.13508e17 | 0.149263 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.32165e18 | −0.238406 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.12650e18 | 0.199784 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.54004e18 | 0.791660 | 0.395830 | − | 0.918324i | \(-0.370457\pi\) | ||||
0.395830 | + | 0.918324i | \(0.370457\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.19019e18 | −0.375516 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.58635e18 | 0.941805 | 0.470903 | − | 0.882185i | \(-0.343928\pi\) | ||||
0.470903 | + | 0.882185i | \(0.343928\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.44703e18 | 0.239892 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.02911e17 | 0.0493830 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.88729e18 | 0.623237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.28505e18 | −1.30636 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.05448e18 | 0.163526 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.67406e18 | −0.407866 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03749e19 | 1.55649 | 0.778245 | − | 0.627961i | \(-0.216110\pi\) | ||||
0.778245 | + | 0.627961i | \(0.216110\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.18468e18 | 0.617536 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.11040e18 | 0.161188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.98794e18 | −0.283876 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.01448e18 | 0.282993 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.33254e18 | 1.28980 | 0.644898 | − | 0.764269i | \(-0.276900\pi\) | ||||
0.644898 | + | 0.764269i | \(0.276900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.02423e19 | 2.75237 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.23886e17 | 0.0433292 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.24259e18 | 0.558445 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.68309e17 | 0.0477023 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.52748e18 | −0.194670 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.39047e19 | −1.74380 | −0.871901 | − | 0.489683i | \(-0.837112\pi\) | ||||
−0.871901 | + | 0.489683i | \(0.837112\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.49833e19 | 1.84915 | 0.924575 | − | 0.381000i | \(-0.124420\pi\) | ||||
0.924575 | + | 0.381000i | \(0.124420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.71006e18 | 0.207693 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.25556e18 | −0.389136 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.61164e19 | −1.89594 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.78478e17 | −0.0322437 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.20542e19 | −1.37375 | −0.686875 | − | 0.726776i | \(-0.741018\pi\) | ||||
−0.686875 | + | 0.726776i | \(0.741018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.02391e18 | −0.114859 | −0.0574293 | − | 0.998350i | \(-0.518290\pi\) | ||||
−0.0574293 | + | 0.998350i | \(0.518290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.74185e18 | −0.523597 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.67445e19 | −1.82006 | −0.910031 | − | 0.414541i | \(-0.863942\pi\) | ||||
−0.910031 | + | 0.414541i | \(0.863942\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.52152e18 | 0.269809 | 0.134905 | − | 0.990859i | \(-0.456927\pi\) | ||||
0.134905 | + | 0.990859i | \(0.456927\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.65350e18 | −0.806220 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.04512e18 | 0.212093 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.65237e18 | −0.475020 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.98040e17 | −0.0601195 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.56609e18 | 0.352971 | 0.176486 | − | 0.984303i | \(-0.443527\pi\) | ||||
0.176486 | + | 0.984303i | \(0.443527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.85249e18 | −0.278003 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.00899e18 | 0.672630 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.76389e18 | 0.450187 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.60305e18 | 0.149178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.87223e18 | 0.629793 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.56908e17 | −0.0592874 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.52869e18 | −0.224764 | −0.112382 | − | 0.993665i | \(-0.535848\pi\) | ||||
−0.112382 | + | 0.993665i | \(0.535848\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.54004e18 | 0.222362 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.19030e18 | 0.275078 | 0.137539 | − | 0.990496i | \(-0.456081\pi\) | ||||
0.137539 | + | 0.990496i | \(0.456081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.28369e16 | 0.00363800 | 0.00181900 | − | 0.999998i | \(-0.499421\pi\) | ||||
0.00181900 | + | 0.999998i | \(0.499421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.17407e18 | −0.0982144 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.85927e18 | −0.153205 | −0.0766024 | − | 0.997062i | \(-0.524407\pi\) | ||||
−0.0766024 | + | 0.997062i | \(0.524407\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.68012e18 | −0.217546 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.69476e18 | 0.695238 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.31260e18 | 0.497256 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.37768e18 | −0.106913 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.54433e18 | 0.194527 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.27347e18 | 0.321905 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.55182e18 | −0.708906 | −0.354453 | − | 0.935074i | \(-0.615333\pi\) | ||||
−0.354453 | + | 0.935074i | \(0.615333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.32355e18 | −0.462416 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.90258e18 | 0.353249 | 0.176625 | − | 0.984278i | \(-0.443482\pi\) | ||||
0.176625 | + | 0.984278i | \(0.443482\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.98079e18 | −0.353634 | −0.176817 | − | 0.984244i | \(-0.556580\pi\) | ||||
−0.176817 | + | 0.984244i | \(0.556580\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.10334e18 | 0.217119 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.07352e19 | −1.42957 | −0.714783 | − | 0.699346i | \(-0.753475\pi\) | ||||
−0.714783 | + | 0.699346i | \(0.753475\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.01189e19 | 0.687498 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.95975e18 | 0.131219 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.89032e19 | −2.56715 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.76172e18 | 0.504787 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.03922e17 | 0.0387106 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.20148e18 | −0.265439 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.42582e19 | −1.51059 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.86762e18 | 0.298777 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.18401e18 | −0.253149 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.23785e19 | −0.738278 | −0.369139 | − | 0.929374i | \(-0.620347\pi\) | ||||
−0.369139 | + | 0.929374i | \(0.620347\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.20096e18 | 0.0706095 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.80820e18 | −0.452565 | −0.226283 | − | 0.974062i | \(-0.572657\pi\) | ||||
−0.226283 | + | 0.974062i | \(0.572657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.20103e19 | 1.82907 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.47649e18 | −0.308507 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.26138e18 | 0.514369 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.07890e19 | 1.68595 | 0.842976 | − | 0.537951i | \(-0.180802\pi\) | ||||
0.842976 | + | 0.537951i | \(0.180802\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.89237e18 | −0.210149 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.31804e18 | 0.283100 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.31076e18 | −0.173783 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.27158e19 | 0.658152 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.09891e19 | −1.58164 | −0.790818 | − | 0.612052i | \(-0.790344\pi\) | ||||
−0.790818 | + | 0.612052i | \(0.790344\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.93046e18 | −0.197820 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.02320e18 | −0.447847 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.72565e19 | −0.844649 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.88022e17 | −0.0380392 | −0.0190196 | − | 0.999819i | \(-0.506054\pi\) | ||||
−0.0190196 | + | 0.999819i | \(0.506054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.19679e18 | 0.152190 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.68836e19 | −1.26228 | −0.631138 | − | 0.775670i | \(-0.717412\pi\) | ||||
−0.631138 | + | 0.775670i | \(0.717412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.54616e18 | 0.117912 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.67166e17 | −0.0350415 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.38940e19 | −1.52703 | −0.763517 | − | 0.645788i | \(-0.776529\pi\) | ||||
−0.763517 | + | 0.645788i | \(0.776529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.72325e18 | −0.121020 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.24170e19 | 0.982660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.38566e19 | −0.599173 | −0.299586 | − | 0.954069i | \(-0.596849\pi\) | ||||
−0.299586 | + | 0.954069i | \(0.596849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.59734e18 | 0.366726 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.37681e19 | 0.579356 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.92305e18 | −0.162856 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.20347e19 | −0.902413 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.20324e18 | 0.0486164 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.68408e19 | 0.671327 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.82197e17 | −0.0386302 | −0.0193151 | − | 0.999813i | \(-0.506149\pi\) | ||||
−0.0193151 | + | 0.999813i | \(0.506149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.05870e19 | −1.18695 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.82100e19 | −0.697244 | −0.348622 | − | 0.937263i | \(-0.613350\pi\) | ||||
−0.348622 | + | 0.937263i | \(0.613350\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.80595e19 | −0.682294 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.04372e18 | 0.113468 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.75890e19 | −0.647035 | −0.323517 | − | 0.946222i | \(-0.604865\pi\) | ||||
−0.323517 | + | 0.946222i | \(0.604865\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.22891e18 | 0.153511 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.67476e18 | 0.131638 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.61488e19 | 1.63141 | 0.815705 | − | 0.578469i | \(-0.196349\pi\) | ||||
0.815705 | + | 0.578469i | \(0.196349\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.50354e18 | 0.157115 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.17499e19 | 0.404550 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.05562e19 | −0.358700 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.99245e19 | −1.33894 | −0.669470 | − | 0.742839i | \(-0.733479\pi\) | ||||
−0.669470 | + | 0.742839i | \(0.733479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.49788e19 | 0.826801 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.77464e19 | 0.579777 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.94762e18 | 0.127296 | 0.0636482 | − | 0.997972i | \(-0.479726\pi\) | ||||
0.0636482 | + | 0.997972i | \(0.479726\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.36830e18 | 0.0435518 |
(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 | 84.14.a.d.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.14.a.d.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial |