Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,16,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.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: | \(68.4928824480\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{22}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 22 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.69042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-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 | ||||||||
\(3\) | −2187.00 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 161936. | 0.926978 | 0.463489 | − | 0.886103i | \(-0.346597\pi\) | ||||
0.463489 | + | 0.886103i | \(0.346597\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.16834e6 | 0.995156 | 0.497578 | − | 0.867419i | \(-0.334223\pi\) | ||||
0.497578 | + | 0.867419i | \(0.334223\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.78297e6 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.16723e8 | 1.80597 | 0.902984 | − | 0.429673i | \(-0.141371\pi\) | ||||
0.902984 | + | 0.429673i | \(0.141371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37971.5 | 0.000167835 0 | 8.39175e−5 | − | 1.00000i | \(-0.499973\pi\) | ||||
8.39175e−5 | 1.00000i | \(0.499973\pi\) | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.54155e8 | −0.535191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.72730e8 | 0.574944 | 0.287472 | − | 0.957789i | \(-0.407185\pi\) | ||||
0.287472 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00231e9 | 1.79717 | 0.898585 | − | 0.438800i | \(-0.144596\pi\) | ||||
0.898585 | + | 0.438800i | \(0.144596\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.74215e9 | −0.574554 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.18197e10 | −1.33626 | −0.668128 | − | 0.744047i | \(-0.732904\pi\) | ||||
−0.668128 | + | 0.744047i | \(0.732904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.29419e9 | −0.140712 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.04604e10 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.93511e10 | −0.315965 | −0.157983 | − | 0.987442i | \(-0.550499\pi\) | ||||
−0.157983 | + | 0.987442i | \(0.550499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25467e10 | 0.0819059 | 0.0409529 | − | 0.999161i | \(-0.486961\pi\) | ||||
0.0409529 | + | 0.999161i | \(0.486961\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.55273e11 | −1.04268 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.51133e11 | 0.922488 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.88911e11 | −1.19303 | −0.596514 | − | 0.802603i | \(-0.703448\pi\) | ||||
−0.596514 | + | 0.802603i | \(0.703448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.30437e7 | −9.68996e−5 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.62373e11 | −0.370778 | −0.185389 | − | 0.982665i | \(-0.559354\pi\) | ||||
−0.185389 | + | 0.982665i | \(0.559354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.44271e12 | 0.809404 | 0.404702 | − | 0.914449i | \(-0.367375\pi\) | ||||
0.404702 | + | 0.914449i | \(0.367375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.74537e11 | 0.308993 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.53547e12 | 1.88167 | 0.940833 | − | 0.338869i | \(-0.110044\pi\) | ||||
0.940833 | + | 0.338869i | \(0.110044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.58786e10 | −0.00966361 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.12736e12 | −0.331944 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.75320e12 | −0.789661 | −0.394831 | − | 0.918754i | \(-0.629197\pi\) | ||||
−0.394831 | + | 0.918754i | \(0.629197\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.89017e13 | 1.67409 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.53140e13 | −1.03760 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.52767e13 | −0.799173 | −0.399586 | − | 0.916696i | \(-0.630846\pi\) | ||||
−0.399586 | + | 0.916696i | \(0.630846\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.29878e13 | 1.34394 | 0.671970 | − | 0.740578i | \(-0.265448\pi\) | ||||
0.671970 | + | 0.740578i | \(0.265448\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.03711e13 | 0.331719 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.14897e9 | 0.000155579 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.34942e13 | 0.272010 | 0.136005 | − | 0.990708i | \(-0.456574\pi\) | ||||
0.136005 | + | 0.990708i | \(0.456574\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.77196e13 | 0.771487 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.28420e13 | −0.298055 | −0.149028 | − | 0.988833i | \(-0.547614\pi\) | ||||
−0.149028 | + | 0.988833i | \(0.547614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.39181e13 | 0.783122 | 0.391561 | − | 0.920152i | \(-0.371935\pi\) | ||||
0.391561 | + | 0.920152i | \(0.371935\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.39140e12 | 0.0812401 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.53094e14 | 1.79722 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.69104e14 | −0.990719 | −0.495360 | − | 0.868688i | \(-0.664964\pi\) | ||||
−0.495360 | + | 0.868688i | \(0.664964\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.28768e13 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.62044e14 | 1.05996 | 0.529979 | − | 0.848011i | \(-0.322200\pi\) | ||||
0.529979 | + | 0.848011i | \(0.322200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.57520e14 | 0.532960 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.41909e13 | 0.182423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.04120e14 | −0.249523 | −0.124761 | − | 0.992187i | \(-0.539817\pi\) | ||||
−0.124761 | + | 0.992187i | \(0.539817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.23350e10 | 0.000167022 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.74395e13 | −0.0472884 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.13393e15 | 1.66594 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.54015e15 | 1.93542 | 0.967708 | − | 0.252075i | \(-0.0811129\pi\) | ||||
0.967708 | + | 0.252075i | \(0.0811129\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.58281e14 | 0.601990 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.55394e15 | 1.44220 | 0.721098 | − | 0.692833i | \(-0.243638\pi\) | ||||
0.721098 | + | 0.692833i | \(0.243638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.61833e15 | 1.29654 | 0.648272 | − | 0.761409i | \(-0.275492\pi\) | ||||
0.648272 | + | 0.761409i | \(0.275492\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.67927e14 | −0.532599 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.51910e14 | 0.573083 | 0.286542 | − | 0.958068i | \(-0.407494\pi\) | ||||
0.286542 | + | 0.958068i | \(0.407494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.25626e15 | −1.70616 | −0.853080 | − | 0.521780i | \(-0.825268\pi\) | ||||
−0.853080 | + | 0.521780i | \(0.825268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.50665e15 | 0.688795 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.65429e15 | −1.46122 | −0.730609 | − | 0.682797i | \(-0.760764\pi\) | ||||
−0.730609 | + | 0.682797i | \(0.760764\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.53340e15 | −1.23868 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.81616e11 | 5.59450e−5 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.10921e15 | 0.572159 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.44694e15 | 2.26152 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.01121e15 | 0.214069 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.63729e15 | −1.05741 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.04466e15 | −0.507004 | −0.253502 | − | 0.967335i | \(-0.581582\pi\) | ||||
−0.253502 | + | 0.967335i | \(0.581582\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.15521e15 | −0.467310 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.78722e15 | −0.499788 | −0.249894 | − | 0.968273i | \(-0.580396\pi\) | ||||
−0.249894 | + | 0.968273i | \(0.580396\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.51834e16 | 1.78847 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.69391e15 | −0.178397 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.26867e15 | 0.496932 | 0.248466 | − | 0.968641i | \(-0.420074\pi\) | ||||
0.248466 | + | 0.968641i | \(0.420074\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.57574e16 | −1.33313 | −0.666567 | − | 0.745445i | \(-0.732237\pi\) | ||||
−0.666567 | + | 0.745445i | \(0.732237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.42931e16 | −1.08638 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.43214e12 | 0.000303105 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.75301e15 | −0.292893 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00336e14 | 0.00557929 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.55866e15 | 0.128563 | 0.0642816 | − | 0.997932i | \(-0.479524\pi\) | ||||
0.0642816 | + | 0.997932i | \(0.479524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.68525e16 | −1.22084 | −0.610418 | − | 0.792080i | \(-0.708998\pi\) | ||||
−0.610418 | + | 0.792080i | \(0.708998\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.65254e15 | 0.191648 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.03176e15 | 0.0759249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.03910e16 | −0.352703 | −0.176351 | − | 0.984327i | \(-0.556430\pi\) | ||||
−0.176351 | + | 0.984327i | \(0.556430\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.47693e16 | 0.455911 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.73124e16 | −1.32978 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.68200e16 | −1.71198 | −0.855992 | − | 0.516989i | \(-0.827053\pi\) | ||||
−0.855992 | + | 0.516989i | \(0.827053\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.13379e16 | −0.966538 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.21466e16 | 0.259467 | 0.129733 | − | 0.991549i | \(-0.458588\pi\) | ||||
0.129733 | + | 0.991549i | \(0.458588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.11859e16 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.34918e16 | 0.599057 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.31211e16 | 0.215092 | 0.107546 | − | 0.994200i | \(-0.465701\pi\) | ||||
0.107546 | + | 0.994200i | \(0.465701\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.31125e15 | −0.140031 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.34102e16 | 0.461403 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.25282e17 | 1.59034 | 0.795169 | − | 0.606388i | \(-0.207382\pi\) | ||||
0.795169 | + | 0.606388i | \(0.207382\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.85627e15 | 0.0917545 | 0.0458772 | − | 0.998947i | \(-0.485392\pi\) | ||||
0.0458772 | + | 0.998947i | \(0.485392\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.21444e16 | −0.775924 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.11560e17 | −1.10591 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.13540e17 | 1.03833 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.26816e16 | −0.191518 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.13840e16 | −0.556994 | −0.278497 | − | 0.960437i | \(-0.589836\pi\) | ||||
−0.278497 | + | 0.960437i | \(0.589836\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.04593e17 | 0.754782 | 0.377391 | − | 0.926054i | \(-0.376821\pi\) | ||||
0.377391 | + | 0.926054i | \(0.376821\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.34478e13 | −8.98238e−5 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.07387e17 | 1.28317 | 0.641584 | − | 0.767052i | \(-0.278277\pi\) | ||||
0.641584 | + | 0.767052i | \(0.278277\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.52600e17 | 1.44889 | 0.724443 | − | 0.689334i | \(-0.242097\pi\) | ||||
0.724443 | + | 0.689334i | \(0.242097\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.95118e16 | −0.157045 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.36431e16 | −0.314435 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.48750e16 | −0.343703 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.04363e17 | −0.445418 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.17328e17 | 3.24563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.07629e17 | −1.50711 | −0.753557 | − | 0.657383i | \(-0.771664\pi\) | ||||
−0.753557 | + | 0.657383i | \(0.771664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.99555e16 | 0.172082 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.33627e17 | 0.750300 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.72054e16 | 0.0815092 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.61659e17 | −0.452135 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.69360e13 | 9.64957e−5 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.57353e17 | 0.628410 | 0.314205 | − | 0.949355i | \(-0.398262\pi\) | ||||
0.314205 | + | 0.949355i | \(0.398262\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.05390e16 | −0.0469040 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.41239e17 | 1.58403 | 0.792017 | − | 0.610500i | \(-0.209031\pi\) | ||||
0.792017 | + | 0.610500i | \(0.209031\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.40714e17 | −1.08194 | −0.540968 | − | 0.841043i | \(-0.681942\pi\) | ||||
−0.540968 | + | 0.841043i | \(0.681942\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.53517e17 | −1.03763 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.34981e17 | 0.764365 | 0.382182 | − | 0.924087i | \(-0.375173\pi\) | ||||
0.382182 | + | 0.924087i | \(0.375173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.05833e18 | 1.74426 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.69830e17 | 0.571992 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.12267e17 | −1.03433 | −0.517164 | − | 0.855886i | \(-0.673012\pi\) | ||||
−0.517164 | + | 0.855886i | \(0.673012\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.08573e16 | −0.0148113 | −0.00740567 | − | 0.999973i | \(-0.502357\pi\) | ||||
−0.00740567 | + | 0.999973i | \(0.502357\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.00315e16 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.42941e15 | −0.00895795 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.65888e14 | 0.000301628 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.73091e17 | −0.611967 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.97060e17 | 0.499869 | 0.249934 | − | 0.968263i | \(-0.419591\pi\) | ||||
0.249934 | + | 0.968263i | \(0.419591\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.54685e18 | −2.41324 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.44497e17 | −0.307705 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.81572e17 | 0.237187 | 0.118594 | − | 0.992943i | \(-0.462161\pi\) | ||||
0.118594 | + | 0.992943i | \(0.462161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.49379e18 | −1.18725 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.40385e17 | −0.105322 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.25206e18 | 1.59556 | 0.797779 | − | 0.602950i | \(-0.206008\pi\) | ||||
0.797779 | + | 0.602950i | \(0.206008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.09359e18 | −0.731998 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.27711e17 | 0.144062 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.99999e17 | 0.538394 | 0.269197 | − | 0.963085i | \(-0.413242\pi\) | ||||
0.269197 | + | 0.963085i | \(0.413242\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.90226e17 | 0.277413 | 0.138707 | − | 0.990334i | \(-0.455706\pi\) | ||||
0.138707 | + | 0.990334i | \(0.455706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.80067e14 | −9.64303e−5 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.01230e17 | −0.254122 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.65132e17 | 0.319381 | 0.159691 | − | 0.987167i | \(-0.448950\pi\) | ||||
0.159691 | + | 0.987167i | \(0.448950\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00102e16 | 0.0273020 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.52418e18 | 1.08849 | 0.544244 | − | 0.838927i | \(-0.316817\pi\) | ||||
0.544244 | + | 0.838927i | \(0.316817\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.36532e18 | −1.78492 | −0.892458 | − | 0.451130i | \(-0.851021\pi\) | ||||
−0.892458 | + | 0.451130i | \(0.851021\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.47990e18 | −0.961829 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.00258e18 | −0.368982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.91622e18 | −0.669440 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.36830e18 | −1.11741 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.59279e18 | −0.817073 | −0.408536 | − | 0.912742i | \(-0.633961\pi\) | ||||
−0.408536 | + | 0.912742i | \(0.633961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.47386e18 | −0.740815 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.22096e18 | −0.347559 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.28526e14 | −0.000224270 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.12828e18 | 0.805484 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.39847e18 | −0.832652 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.34193e18 | 1.24580 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.08485e18 | −1.12912 | −0.564560 | − | 0.825392i | \(-0.690954\pi\) | ||||
−0.564560 | + | 0.825392i | \(0.690954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.53928e18 | −0.748560 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.67003e18 | 1.34408 | 0.672040 | − | 0.740515i | \(-0.265418\pi\) | ||||
0.672040 | + | 0.740515i | \(0.265418\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.20097e18 | 1.57501 | 0.787504 | − | 0.616310i | \(-0.211373\pi\) | ||||
0.787504 | + | 0.616310i | \(0.211373\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.67946e18 | 0.307496 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.92096e18 | −1.55764 | −0.778820 | − | 0.627248i | \(-0.784181\pi\) | ||||
−0.778820 | + | 0.627248i | \(0.784181\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.42594e18 | −0.570624 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.08183e18 | −0.330870 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.81135e18 | 1.03327 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.63057e14 | −2.36164e−5 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.12143e18 | 0.985052 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.41711e19 | 1.87255 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.45337e19 | 1.83513 | 0.917564 | − | 0.397588i | \(-0.130153\pi\) | ||||
0.917564 | + | 0.397588i | \(0.130153\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.29504e18 | −0.397676 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.18520e18 | 0.252148 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.35321e18 | 0.149328 | 0.0746641 | − | 0.997209i | \(-0.476212\pi\) | ||||
0.0746641 | + | 0.997209i | \(0.476212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.99193e18 | 0.843634 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.46448e18 | 0.147919 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.03938e19 | −1.00477 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.72754e18 | 0.715152 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45477e19 | 1.28921 | 0.644603 | − | 0.764518i | \(-0.277023\pi\) | ||||
0.644603 | + | 0.764518i | \(0.277023\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00760e19 | −1.70407 | −0.852034 | − | 0.523486i | \(-0.824631\pi\) | ||||
−0.852034 | + | 0.523486i | \(0.824631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.97195e14 | −3.22999e−5 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.21308e18 | −0.717951 | −0.358975 | − | 0.933347i | \(-0.616874\pi\) | ||||
−0.358975 | + | 0.933347i | \(0.616874\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.69896e18 | −0.276291 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.61283e18 | −0.330336 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.20098e19 | 0.824758 | 0.412379 | − | 0.911012i | \(-0.364698\pi\) | ||||
0.412379 | + | 0.911012i | \(0.364698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.38512e19 | 2.22982 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.06605e19 | −1.30569 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.19700e19 | 0.725936 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.49016e18 | 0.144955 | 0.0724773 | − | 0.997370i | \(-0.476910\pi\) | ||||
0.0724773 | + | 0.997370i | \(0.476910\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.21152e18 | −0.123593 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.46432e19 | −0.785836 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.29030e19 | −1.69597 | −0.847987 | − | 0.530017i | \(-0.822186\pi\) | ||||
−0.847987 | + | 0.530017i | \(0.822186\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.23288e19 | 0.610499 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.11451e15 | −5.30301e−5 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.89533e19 | 0.866743 | 0.433372 | − | 0.901215i | \(-0.357324\pi\) | ||||
0.433372 | + | 0.901215i | \(0.357324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.65868e18 | 0.292719 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.02672e18 | 0.127933 | 0.0639663 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639663 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.09851e19 | 1.66598 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.90043e18 | 0.269801 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.09103e18 | 0.153890 | 0.0769451 | − | 0.997035i | \(-0.475483\pi\) | ||||
0.0769451 | + | 0.997035i | \(0.475483\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.12247e19 | −0.768272 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.28265e18 | 0.288553 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.73841e19 | −0.918375 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.49752e18 | −0.306677 | −0.153339 | − | 0.988174i | \(-0.549003\pi\) | ||||
−0.153339 | + | 0.988174i | \(0.549003\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.32060e19 | −1.03257 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.20346e19 | 0.659967 | 0.329983 | − | 0.943987i | \(-0.392957\pi\) | ||||
0.329983 | + | 0.943987i | \(0.392957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.76415e14 | 1.37467e−5 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.70458e18 | 0.102998 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.04116e19 | −2.15457 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.54538e19 | −1.43221 | −0.716105 | − | 0.697993i | \(-0.754077\pi\) | ||||
−0.716105 | + | 0.697993i | \(0.754077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.15226e19 | −0.286904 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.31251e19 | −0.795302 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.24345e19 | 0.982558 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.44615e19 | 0.769686 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.94382e19 | −0.418843 | −0.209422 | − | 0.977825i | \(-0.567158\pi\) | ||||
−0.209422 | + | 0.977825i | \(0.567158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.88886e19 | −0.392722 | −0.196361 | − | 0.980532i | \(-0.562912\pi\) | ||||
−0.196361 | + | 0.980532i | \(0.562912\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.12589e19 | 0.627222 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.17709e18 | −0.0809015 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.15287e19 | 1.33743 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.69308e15 | −0.000174998 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00494e18 | −0.104696 | −0.0523479 | − | 0.998629i | \(-0.516670\pi\) | ||||
−0.0523479 | + | 0.998629i | \(0.516670\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.07741e19 | −0.518235 | −0.259118 | − | 0.965846i | \(-0.583432\pi\) | ||||
−0.259118 | + | 0.965846i | \(0.583432\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.03948e19 | 0.169102 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.52788e20 | −2.40148 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.66145e19 | 0.708006 | 0.354003 | − | 0.935244i | \(-0.384820\pi\) | ||||
0.354003 | + | 0.935244i | \(0.384820\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.19436e17 | −0.00322120 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.79254e19 | −1.38953 | −0.694764 | − | 0.719238i | \(-0.744491\pi\) | ||||
−0.694764 | + | 0.719238i | \(0.744491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.68608e19 | −0.231302 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.59580e18 | −0.0742260 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.72775e19 | −0.221633 | −0.110816 | − | 0.993841i | \(-0.535347\pi\) | ||||
−0.110816 | + | 0.993841i | \(0.535347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.39695e19 | −0.669613 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.87264e19 | 0.704850 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.33330e16 | 0.000154826 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.42260e19 | 0.496942 | 0.248471 | − | 0.968639i | \(-0.420072\pi\) | ||||
0.248471 | + | 0.968639i | \(0.420072\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.01751e19 | −0.110648 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.68186e20 | −1.77024 | −0.885120 | − | 0.465364i | \(-0.845924\pi\) | ||||
−0.885120 | + | 0.465364i | \(0.845924\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.67287e19 | 0.476131 | 0.238065 | − | 0.971249i | \(-0.423487\pi\) | ||||
0.238065 | + | 0.971249i | \(0.423487\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.44346e18 | −0.0438353 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.35648e20 | 1.29579 | 0.647897 | − | 0.761728i | \(-0.275649\pi\) | ||||
0.647897 | + | 0.761728i | \(0.275649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.92599e19 | 0.270693 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.27251e19 | 0.203633 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.68397e20 | 1.46176 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.00692e19 | −0.252883 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.23004e19 | −0.263220 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.70533e19 | −0.213650 | −0.106825 | − | 0.994278i | \(-0.534068\pi\) | ||||
−0.106825 | + | 0.994278i | \(0.534068\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.61590e16 | −0.000200232 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.03472e20 | 0.767751 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.49406e20 | 1.79409 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.46030e19 | −0.450594 | −0.225297 | − | 0.974290i | \(-0.572335\pi\) | ||||
−0.225297 | + | 0.974290i | \(0.572335\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.46135e20 | 0.988414 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.06362e20 | −1.35369 | −0.676845 | − | 0.736125i | \(-0.736653\pi\) | ||||
−0.676845 | + | 0.736125i | \(0.736653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.85507e19 | −0.181662 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.04060e19 | 0.558031 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.95292e19 | −0.296612 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.81301e19 | −0.570227 | −0.285114 | − | 0.958494i | \(-0.592031\pi\) | ||||
−0.285114 | + | 0.958494i | \(0.592031\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.65646e19 | −0.149803 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.13875e19 | −0.117058 | −0.0585290 | − | 0.998286i | \(-0.518641\pi\) | ||||
−0.0585290 | + | 0.998286i | \(0.518641\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.51640e20 | 1.33688 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.11944e20 | 0.577350 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.92005e20 | −0.961455 | −0.480728 | − | 0.876870i | \(-0.659627\pi\) | ||||
−0.480728 | + | 0.876870i | \(0.659627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.60279e20 | 0.779328 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.32466e19 | −0.345865 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.62066e20 | 1.20187 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.62838e20 | 3.39823 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.86958e19 | −0.124183 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.29054e20 | −0.542612 | −0.271306 | − | 0.962493i | \(-0.587455\pi\) | ||||
−0.271306 | + | 0.962493i | \(0.587455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.30149e19 | −0.216588 | −0.108294 | − | 0.994119i | \(-0.534539\pi\) | ||||
−0.108294 | + | 0.994119i | \(0.534539\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.03637e19 | 0.0808467 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.22045e19 | 0.0470913 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.09463e20 | 0.785579 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.30682e19 | −0.266391 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.75570e16 | −6.22295e−5 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.54149e20 | 0.531235 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.73991e20 | −0.918182 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.35507e18 | −0.0174522 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.68157e20 | −0.533009 | −0.266504 | − | 0.963834i | \(-0.585869\pi\) | ||||
−0.266504 | + | 0.963834i | \(0.585869\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.71817e19 | −0.0529745 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.27306e20 | −1.58157 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.54065e20 | −0.449572 | −0.224786 | − | 0.974408i | \(-0.572168\pi\) | ||||
−0.224786 | + | 0.974408i | \(0.572168\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.57780e20 | 0.447980 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.05525e20 | −0.567843 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.66674e20 | −0.985921 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.43981e20 | 0.638498 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.37962e20 | 0.606168 | 0.303084 | − | 0.952964i | \(-0.401984\pi\) | ||||
0.303084 | + | 0.952964i | \(0.401984\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.47818e16 | 0.000135846 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.48311e20 | −0.599480 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.11320e20 | 0.966867 | 0.483433 | − | 0.875381i | \(-0.339390\pi\) | ||||
0.483433 | + | 0.875381i | \(0.339390\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.91763e20 | −1.35452 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.96046e19 | 0.110573 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.48215e20 | −1.19017 | −0.595084 | − | 0.803663i | \(-0.702881\pi\) | ||||
−0.595084 | + | 0.803663i | \(0.702881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.42478e19 | −0.178151 | −0.0890754 | − | 0.996025i | \(-0.528391\pi\) | ||||
−0.0890754 | + | 0.996025i | \(0.528391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.56117e20 | 0.321581 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.36979e19 | 0.188027 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.78619e20 | −1.13129 | −0.565645 | − | 0.824649i | \(-0.691373\pi\) | ||||
−0.565645 | + | 0.824649i | \(0.691373\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.28744e20 | −0.435773 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.68200e20 | 1.05482 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.88252e20 | −1.42610 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.94103e16 | 5.18598e−5 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.85378e20 | 0.318620 | 0.159310 | − | 0.987229i | \(-0.449073\pi\) | ||||
0.159310 | + | 0.987229i | \(0.449073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.78555e19 | 0.147199 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.53554e20 | −0.740838 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.85659e20 | 0.773431 | 0.386716 | − | 0.922199i | \(-0.373610\pi\) | ||||
0.386716 | + | 0.922199i | \(0.373610\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.41557e20 | 0.530379 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.52435e20 | −0.836515 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.12745e20 | −0.461838 | −0.230919 | − | 0.972973i | \(-0.574173\pi\) | ||||
−0.230919 | + | 0.972973i | \(0.574173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.20401e20 | −0.173409 | −0.0867047 | − | 0.996234i | \(-0.527634\pi\) | ||||
−0.0867047 | + | 0.996234i | \(0.527634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.45422e19 | 0.0906701 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.52980e21 | 2.09638 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.42029e20 | −0.858301 | −0.429151 | − | 0.903233i | \(-0.641187\pi\) | ||||
−0.429151 | + | 0.903233i | \(0.641187\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.39187e20 | 0.181539 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.48161e17 | 0.000315810 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.95059e19 | −0.0738935 | −0.0369467 | − | 0.999317i | \(-0.511763\pi\) | ||||
−0.0369467 | + | 0.999317i | \(0.511763\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.63752e20 | 0.198437 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.36774e20 | 0.161758 | 0.0808790 | − | 0.996724i | \(-0.474227\pi\) | ||||
0.0808790 | + | 0.996724i | \(0.474227\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.06727e20 | −0.469486 | −0.234743 | − | 0.972057i | \(-0.575425\pi\) | ||||
−0.234743 | + | 0.972057i | \(0.575425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.28241e20 | 0.257162 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.25768e20 | −0.248314 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.81834e20 | −0.839488 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.78750e21 | −1.87387 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.70125e20 | −0.685924 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.51198e21 | 1.51122 | 0.755609 | − | 0.655023i | \(-0.227341\pi\) | ||||
0.755609 | + | 0.655023i | \(0.227341\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.91484e20 | 0.870133 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.93042e20 | −0.469982 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.74208e15 | −1.62189e−6 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.09253e20 | −0.0993518 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.19317e21 | −1.05990 | −0.529952 | − | 0.848028i | \(-0.677790\pi\) | ||||
−0.529952 | + | 0.848028i | \(0.677790\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.81273e19 | −0.0244088 | −0.0122044 | − | 0.999926i | \(-0.503885\pi\) | ||||
−0.0122044 | + | 0.999926i | \(0.503885\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.10943e20 | −0.433186 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.11423e20 | 0.423641 | 0.211821 | − | 0.977309i | \(-0.432061\pi\) | ||||
0.211821 | + | 0.977309i | \(0.432061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.78314e21 | −1.44328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.94981e19 | −0.0470593 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.75704e21 | 1.35810 | 0.679052 | − | 0.734090i | \(-0.262391\pi\) | ||||
0.679052 | + | 0.734090i | \(0.262391\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.13289e20 | −0.463293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.53548e20 | 0.261041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.07640e21 | −0.776842 | −0.388421 | − | 0.921482i | \(-0.626979\pi\) | ||||
−0.388421 | + | 0.921482i | \(0.626979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.39157e21 | 0.981734 | 0.490867 | − | 0.871235i | \(-0.336680\pi\) | ||||
0.490867 | + | 0.871235i | \(0.336680\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.07791e16 | −5.57118e−5 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.45874e21 | 1.65787 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.40432e20 | 0.422210 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.62832e20 | −0.362813 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.85043e21 | 2.42711 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.31402e21 | −0.810004 | −0.405002 | − | 0.914316i | \(-0.632729\pi\) | ||||
−0.405002 | + | 0.914316i | \(0.632729\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.49188e19 | 0.0270800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.68867e21 | 0.995700 | 0.497850 | − | 0.867263i | \(-0.334123\pi\) | ||||
0.497850 | + | 0.867263i | \(0.334123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.33956e21 | 1.92604 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.62109e21 | −0.914542 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.76934e21 | 1.52835 | 0.764173 | − | 0.645011i | \(-0.223147\pi\) | ||||
0.764173 | + | 0.645011i | \(0.223147\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.53190e20 | 0.460645 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.18254e21 | 0.624656 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.56429e17 | −0.000132533 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.59811e21 | 1.31393 | 0.656965 | − | 0.753921i | \(-0.271840\pi\) | ||||
0.656965 | + | 0.753921i | \(0.271840\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.21054e21 | 0.599074 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.55170e21 | −1.23579 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.49764e20 | −0.213176 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.51303e20 | −0.441306 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.28826e21 | −1.03901 | −0.519506 | − | 0.854467i | \(-0.673884\pi\) | ||||
−0.519506 | + | 0.854467i | \(0.673884\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.82397e21 | −2.14407 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.31457e21 | −1.00705 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.36947e21 | 1.43521 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.16499e21 | 0.485819 | 0.242909 | − | 0.970049i | \(-0.421898\pi\) | ||||
0.242909 | + | 0.970049i | \(0.421898\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.08819e20 | −0.330240 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.73764e20 | −0.109447 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.17724e17 | 0.000280971 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.55773e21 | 0.597170 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.72261e20 | −0.214846 | −0.107423 | − | 0.994213i | \(-0.534260\pi\) | ||||
−0.107423 | + | 0.994213i | \(0.534260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.50908e21 | 1.29026 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.37449e19 | 0.00855133 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.26039e20 | 0.0444601 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.31038e21 | 0.798316 | 0.399158 | − | 0.916882i | \(-0.369303\pi\) | ||||
0.399158 | + | 0.916882i | \(0.369303\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.09419e20 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.40337e21 | 0.465362 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.17298e21 | −0.705954 | −0.352977 | − | 0.935632i | \(-0.614831\pi\) | ||||
−0.352977 | + | 0.935632i | \(0.614831\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.62481e19 | 0.00517187 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.57508e21 | 0.491242 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.25136e21 | −1.91048 | −0.955238 | − | 0.295839i | \(-0.904401\pi\) | ||||
−0.955238 | + | 0.295839i | \(0.904401\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.81497e17 | −0.000174145 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.54644e21 | −0.453856 | −0.226928 | − | 0.973912i | \(-0.572868\pi\) | ||||
−0.226928 | + | 0.973912i | \(0.572868\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.14341e20 | 0.119175 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.25335e21 | 0.353319 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.06406e21 | 0.570307 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.82569e21 | −1.30695 | −0.653476 | − | 0.756947i | \(-0.726690\pi\) | ||||
−0.653476 | + | 0.756947i | \(0.726690\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.08707e21 | −0.288599 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.34839e21 | −1.13169 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.08704e21 | 0.532490 | 0.266245 | − | 0.963905i | \(-0.414217\pi\) | ||||
0.266245 | + | 0.963905i | \(0.414217\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.56996e21 | 1.39328 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.97877e21 | −0.975807 | −0.487903 | − | 0.872898i | \(-0.662238\pi\) | ||||
−0.487903 | + | 0.872898i | \(0.662238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.06066e21 | −1.69790 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.53415e20 | 0.177653 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.80081e17 | −0.000134129 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.34029e21 | 1.21092 | 0.605462 | − | 0.795874i | \(-0.292988\pi\) | ||||
0.605462 | + | 0.795874i | \(0.292988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.15799e20 | −0.136940 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.44754e21 | −1.62430 | −0.812150 | − | 0.583448i | \(-0.801703\pi\) | ||||
−0.812150 | + | 0.583448i | \(0.801703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.38777e19 | −0.0115251 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.26692e21 | 0.685459 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.23768e21 | −0.666351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.66618e21 | −0.538279 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.07023e20 | 0.0608076 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.68268e21 | −0.326948 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.01188e21 | 0.383522 | 0.191761 | − | 0.981442i | \(-0.438580\pi\) | ||||
0.191761 | + | 0.981442i | \(0.438580\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.92526e21 | −0.921195 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.92373e21 | −1.45414 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.25260e18 | 0.000225560 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.39168e21 | 0.422620 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.58422e21 | −1.48855 | −0.744275 | − | 0.667873i | \(-0.767205\pi\) | ||||
−0.744275 | + | 0.667873i | \(0.767205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.35725e21 | 1.08185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.98004e20 | −0.0831742 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.62792e21 | 1.41429 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.66160e21 | −1.23268 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.96830e21 | −0.310842 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.80336e19 | −0.0151971 | −0.00759856 | − | 0.999971i | \(-0.502419\pi\) | ||||
−0.00759856 | + | 0.999971i | \(0.502419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.63811e21 | 1.16233 | 0.581165 | − | 0.813786i | \(-0.302597\pi\) | ||||
0.581165 | + | 0.813786i | \(0.302597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.07213e21 | −0.160165 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.08206e22 | −1.58697 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.01023e22 | 1.45464 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.93806e17 | 5.56740e−5 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.24216e20 | 0.114411 | 0.0572054 | − | 0.998362i | \(-0.481781\pi\) | ||||
0.0572054 | + | 0.998362i | \(0.481781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.59084e21 | −0.216835 | −0.108417 | − | 0.994105i | \(-0.534578\pi\) | ||||
−0.108417 | + | 0.994105i | \(0.534578\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.09619e21 | 0.146717 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.33001e20 | 0.109485 | 0.0547424 | − | 0.998501i | \(-0.482566\pi\) | ||||
0.0547424 | + | 0.998501i | \(0.482566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.94770e20 | 0.128400 | 0.0641998 | − | 0.997937i | \(-0.479551\pi\) | ||||
0.0641998 | + | 0.997937i | \(0.479551\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.45464e21 | −0.184395 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.46275e19 | −0.00555603 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.96698e21 | 0.240520 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.31242e20 | −0.0157628 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.65119e21 | 0.548718 | 0.274359 | − | 0.961627i | \(-0.411534\pi\) | ||||
0.274359 | + | 0.961627i | \(0.411534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.76770e21 | −0.900166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.52039e21 | −0.628439 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.28886e21 | −0.926978 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.04842e22 | 2.25057 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.54696e21 | 1.03052 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.50318e22 | 1.59419 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.26300e21 | 0.965237 | 0.482619 | − | 0.875831i | \(-0.339686\pi\) | ||||
0.482619 | + | 0.875831i | \(0.339686\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.42354e21 | 0.555312 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.37621e21 | 0.540904 | 0.270452 | − | 0.962733i | \(-0.412827\pi\) | ||||
0.270452 | + | 0.962733i | \(0.412827\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.13208e22 | −1.11925 | −0.559627 | − | 0.828745i | \(-0.689056\pi\) | ||||
−0.559627 | + | 0.828745i | \(0.689056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.19264e21 | 0.213032 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.84122e22 | −1.75802 | −0.879011 | − | 0.476802i | \(-0.841796\pi\) | ||||
−0.879011 | + | 0.476802i | \(0.841796\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.12478e21 | 0.199386 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.19077e21 | 0.386501 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.97383e22 | −1.78921 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.12394e17 | 4.56529e−5 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.36648e21 | 0.645139 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.22235e22 | −1.05229 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.24428e22 | −1.05298 | −0.526492 | − | 0.850180i | \(-0.676493\pi\) | ||||
−0.526492 | + | 0.850180i | \(0.676493\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.67044e21 | 0.471737 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.76504e22 | 1.44356 | 0.721780 | − | 0.692122i | \(-0.243324\pi\) | ||||
0.721780 | + | 0.692122i | \(0.243324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.50057e21 | −0.442285 | −0.221143 | − | 0.975241i | \(-0.570979\pi\) | ||||
−0.221143 | + | 0.975241i | \(0.570979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.41033e21 | 0.427710 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.45506e21 | −0.501734 | −0.250867 | − | 0.968022i | \(-0.580716\pi\) | ||||
−0.250867 | + | 0.968022i | \(0.580716\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.60186e21 | −0.504548 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.67024e21 | 0.200663 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.57633e22 | 3.38167 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.02876e22 | 1.47421 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.81199e18 | 0.000129483 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.68258e20 | −0.0258794 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.56904e21 | −0.454011 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.84155e21 | −0.465046 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.27222e21 | 0.0850544 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.01966e22 | 0.670504 | 0.335252 | − | 0.942129i | \(-0.391179\pi\) | ||||
0.335252 | + | 0.942129i | \(0.391179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.43245e21 | 0.480732 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.59652e22 | −1.01575 | −0.507873 | − | 0.861432i | \(-0.669568\pi\) | ||||
−0.507873 | + | 0.861432i | \(0.669568\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.05865e22 | 1.91425 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.16828e22 | −0.719264 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.21197e21 | −0.497368 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.79447e21 | 0.404845 | 0.202423 | − | 0.979298i | \(-0.435119\pi\) | ||||
0.202423 | + | 0.979298i | \(0.435119\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.11206e22 | 0.651898 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.67346e17 | −5.00241e−5 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.95832e21 | 0.167873 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.74041e21 | 0.432181 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.30089e22 | −1.26409 | −0.632044 | − | 0.774933i | \(-0.717784\pi\) | ||||
−0.632044 | + | 0.774933i | \(0.717784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.21256e20 | −0.0173671 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.45874e22 | −0.776005 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.83862e22 | 0.962509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.54775e21 | −0.388840 | −0.194420 | − | 0.980918i | \(-0.562282\pi\) | ||||
−0.194420 | + | 0.980918i | \(0.562282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.79355e22 | −0.909331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.93039e22 | −0.963216 | −0.481608 | − | 0.876387i | \(-0.659947\pi\) | ||||
−0.481608 | + | 0.876387i | \(0.659947\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.00888e22 | 0.495454 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.67297e21 | −0.177533 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.44024e22 | 0.685187 | 0.342593 | − | 0.939484i | \(-0.388695\pi\) | ||||
0.342593 | + | 0.939484i | \(0.388695\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.80678e18 | 0.000131435 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.95101e22 | 0.899303 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.65091e22 | 0.749077 | 0.374539 | − | 0.927211i | \(-0.377801\pi\) | ||||
0.374539 | + | 0.927211i | \(0.377801\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.15597e22 | −0.516321 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.49253e21 | 0.329450 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.14243e22 | 0.494525 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.33078e22 | −0.993291 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.55296e21 | 0.191028 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.69374e22 | 0.699666 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.85951e22 | −0.756311 | −0.378155 | − | 0.925742i | \(-0.623442\pi\) | ||||
−0.378155 | + | 0.925742i | \(0.623442\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.48964e22 | −0.596560 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.84934e22 | 1.51790 | 0.758948 | − | 0.651151i | \(-0.225714\pi\) | ||||
0.758948 | + | 0.651151i | \(0.225714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.41674e22 | −1.32668 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.56605e17 | 1.36349e−5 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.69863e21 | −0.289870 | −0.144935 | − | 0.989441i | \(-0.546297\pi\) | ||||
−0.144935 | + | 0.989441i | \(0.546297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.21532e22 | −0.450630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.55746e22 | −0.568720 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.45537e22 | −1.24263 | −0.621316 | − | 0.783560i | \(-0.713402\pi\) | ||||
−0.621316 | + | 0.783560i | \(0.713402\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.35834e22 | 1.18947 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.09922e22 | −1.08112 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.14795e22 | −1.08157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.38548e22 | −1.14569 | −0.572846 | − | 0.819663i | \(-0.694161\pi\) | ||||
−0.572846 | + | 0.819663i | \(0.694161\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.17852e22 | −1.05951 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.09050e22 | 1.34309 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.03253e22 | −0.980826 | −0.490413 | − | 0.871490i | \(-0.663154\pi\) | ||||
−0.490413 | + | 0.871490i | \(0.663154\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.20626e21 | 0.229598 |
(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 | 48.16.a.h.1.2 | 2 | ||
3.2 | odd | 2 | 144.16.a.u.1.1 | 2 | |||
4.3 | odd | 2 | 24.16.a.c.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 72.16.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.16.a.c.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
48.16.a.h.1.2 | 2 | 1.1 | even | 1 | trivial | ||
72.16.a.f.1.1 | 2 | 12.11 | even | 2 | |||
144.16.a.u.1.1 | 2 | 3.2 | odd | 2 |