Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,8,Mod(1,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.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: | \(79.9705665239\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 163x^{4} + 4820x^{2} - 15296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{27} \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.89807\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.1 |
$q$-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 | ||||||||
\(3\) | 76.9497 | 1.64544 | 0.822721 | − | 0.568446i | \(-0.192455\pi\) | ||||
0.822721 | + | 0.568446i | \(0.192455\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −338.443 | −1.21085 | −0.605425 | − | 0.795903i | \(-0.706997\pi\) | ||||
−0.605425 | + | 0.795903i | \(0.706997\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −438.996 | −0.483746 | −0.241873 | − | 0.970308i | \(-0.577762\pi\) | ||||
−0.241873 | + | 0.970308i | \(0.577762\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3734.25 | 1.70748 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1966.58 | 0.445489 | 0.222744 | − | 0.974877i | \(-0.428498\pi\) | ||||
0.222744 | + | 0.974877i | \(0.428498\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2210.98 | −0.279115 | −0.139557 | − | 0.990214i | \(-0.544568\pi\) | ||||
−0.139557 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −26043.0 | −1.99238 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12114.9 | −0.598064 | −0.299032 | − | 0.954243i | \(-0.596664\pi\) | ||||
−0.299032 | + | 0.954243i | \(0.596664\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32872.2 | 1.09949 | 0.549744 | − | 0.835333i | \(-0.314725\pi\) | ||||
0.549744 | + | 0.835333i | \(0.314725\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33780.6 | −0.795976 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19605.1 | 0.335986 | 0.167993 | − | 0.985788i | \(-0.446271\pi\) | ||||
0.167993 | + | 0.985788i | \(0.446271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 36418.4 | 0.466155 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 119060. | 1.16411 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −160689. | −1.22347 | −0.611735 | − | 0.791063i | \(-0.709528\pi\) | ||||
−0.611735 | + | 0.791063i | \(0.709528\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 229270. | 1.38224 | 0.691118 | − | 0.722742i | \(-0.257119\pi\) | ||||
0.691118 | + | 0.722742i | \(0.257119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 151328. | 0.733026 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 148575. | 0.585744 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −496284. | −1.61074 | −0.805368 | − | 0.592775i | \(-0.798032\pi\) | ||||
−0.805368 | + | 0.592775i | \(0.798032\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −170134. | −0.459267 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −599971. | −1.35952 | −0.679762 | − | 0.733433i | \(-0.737917\pi\) | ||||
−0.679762 | + | 0.733433i | \(0.737917\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −88346.0 | −0.169452 | −0.0847262 | − | 0.996404i | \(-0.527002\pi\) | ||||
−0.0847262 | + | 0.996404i | \(0.527002\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.26383e6 | −2.06750 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −820344. | −1.15253 | −0.576267 | − | 0.817262i | \(-0.695491\pi\) | ||||
−0.576267 | + | 0.817262i | \(0.695491\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −630825. | −0.765989 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −932236. | −0.984080 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.53717e6 | −1.41826 | −0.709131 | − | 0.705077i | \(-0.750913\pi\) | ||||
−0.709131 | + | 0.705077i | \(0.750913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −665574. | −0.539420 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.52950e6 | 1.80914 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.82480e6 | −1.15673 | −0.578367 | − | 0.815776i | \(-0.696310\pi\) | ||||
−0.578367 | + | 0.815776i | \(0.696310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 484582. | 0.273346 | 0.136673 | − | 0.990616i | \(-0.456359\pi\) | ||||
0.136673 | + | 0.990616i | \(0.456359\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.63932e6 | −0.825986 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 748290. | 0.337966 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −79878.2 | −0.0324464 | −0.0162232 | − | 0.999868i | \(-0.505164\pi\) | ||||
−0.0162232 | + | 0.999868i | \(0.505164\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.50860e6 | 0.552845 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.27078e6 | 0.421373 | 0.210686 | − | 0.977554i | \(-0.432430\pi\) | ||||
0.210686 | + | 0.977554i | \(0.432430\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.70820e6 | −1.11566 | −0.557832 | − | 0.829954i | \(-0.688367\pi\) | ||||
−0.557832 | + | 0.829954i | \(0.688367\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.80238e6 | 0.767031 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −863321. | −0.215504 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.55846e6 | 0.583827 | 0.291914 | − | 0.956445i | \(-0.405708\pi\) | ||||
0.291914 | + | 0.956445i | \(0.405708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 994857. | 0.208000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.53414e6 | 0.294505 | 0.147252 | − | 0.989099i | \(-0.452957\pi\) | ||||
0.147252 | + | 0.989099i | \(0.452957\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.10019e6 | 0.724166 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.23650e7 | −2.01315 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.99492e6 | −0.299958 | −0.149979 | − | 0.988689i | \(-0.547921\pi\) | ||||
−0.149979 | + | 0.988689i | \(0.547921\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 970612. | 0.135021 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.76423e7 | 2.27439 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.11253e7 | −1.33131 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −28917.7 | −0.00321708 | −0.00160854 | − | 0.999999i | \(-0.500512\pi\) | ||||
−0.00160854 | + | 0.999999i | \(0.500512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.34370e6 | 0.760662 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.68077e7 | 1.62324 | 0.811622 | − | 0.584182i | \(-0.198585\pi\) | ||||
0.811622 | + | 0.584182i | \(0.198585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.27746e7 | −1.15191 | −0.575953 | − | 0.817483i | \(-0.695369\pi\) | ||||
−0.575953 | + | 0.817483i | \(0.695369\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.14328e7 | 0.963807 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.35610e7 | 1.07016 | 0.535078 | − | 0.844803i | \(-0.320282\pi\) | ||||
0.535078 | + | 0.844803i | \(0.320282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.74206e6 | −0.350731 | −0.175366 | − | 0.984503i | \(-0.556111\pi\) | ||||
−0.175366 | + | 0.984503i | \(0.556111\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.81889e7 | −2.65037 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.06832e6 | −0.526028 | −0.263014 | − | 0.964792i | \(-0.584717\pi\) | ||||
−0.263014 | + | 0.964792i | \(0.584717\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.63520e6 | −0.406828 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.25635e6 | −0.476582 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.31839e6 | 0.289311 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.56197e7 | −0.801540 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.61676e7 | −2.23702 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.41153e7 | 0.646405 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.12410e7 | 0.486960 | 0.243480 | − | 0.969906i | \(-0.421711\pi\) | ||||
0.243480 | + | 0.969906i | \(0.421711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.79820e6 | −0.278824 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.81527e6 | −0.342599 | −0.171299 | − | 0.985219i | \(-0.554797\pi\) | ||||
−0.171299 | + | 0.985219i | \(0.554797\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.44308e7 | −0.531874 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.02951e7 | −1.40956 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.33729e7 | 1.10885 | 0.554424 | − | 0.832234i | \(-0.312939\pi\) | ||||
0.554424 | + | 0.832234i | \(0.312939\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.68161e7 | 1.47857 | 0.739287 | − | 0.673391i | \(-0.235163\pi\) | ||||
0.739287 | + | 0.673391i | \(0.235163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.31252e7 | −1.89643 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.34806e6 | −0.124343 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.43840e7 | 1.48144 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.85418e7 | −1.26039 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.83709e7 | −0.950277 | −0.475139 | − | 0.879911i | \(-0.657602\pi\) | ||||
−0.475139 | + | 0.879911i | \(0.657602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.17648e7 | −1.69626 | −0.848130 | − | 0.529788i | \(-0.822271\pi\) | ||||
−0.848130 | + | 0.529788i | \(0.822271\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.52400e7 | −1.02118 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.75948e7 | −1.67368 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.03778e7 | −0.832710 | −0.416355 | − | 0.909202i | \(-0.636693\pi\) | ||||
−0.416355 | + | 0.909202i | \(0.636693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.18285e8 | −2.33367 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.60656e6 | −0.162532 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.84512e7 | 1.78059 | 0.890296 | − | 0.455383i | \(-0.150498\pi\) | ||||
0.890296 | + | 0.455383i | \(0.150498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.12157e7 | −0.887584 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.24811e7 | −0.705810 | −0.352905 | − | 0.935659i | \(-0.614806\pi\) | ||||
−0.352905 | + | 0.935659i | \(0.614806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.78601e7 | −0.922095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.22753e8 | 1.87735 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.65257e7 | 0.389498 | 0.194749 | − | 0.980853i | \(-0.437611\pi\) | ||||
0.194749 | + | 0.980853i | \(0.437611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.59875e7 | −0.225501 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.40418e8 | −1.90334 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.42148e7 | −0.315570 | −0.157785 | − | 0.987474i | \(-0.550435\pi\) | ||||
−0.157785 | + | 0.987474i | \(0.550435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.78961e7 | 0.349679 | 0.174839 | − | 0.984597i | \(-0.444059\pi\) | ||||
0.174839 | + | 0.984597i | \(0.444059\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.72884e7 | 0.449775 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.67964e8 | 1.95036 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.38249e7 | −0.266431 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.22671e7 | −0.563135 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.67596e7 | −0.174039 | −0.0870195 | − | 0.996207i | \(-0.527734\pi\) | ||||
−0.0870195 | + | 0.996207i | \(0.527734\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.75008e7 | 0.876116 | 0.438058 | − | 0.898947i | \(-0.355667\pi\) | ||||
0.438058 | + | 0.898947i | \(0.355667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.75806e7 | 0.556103 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.56239e7 | 0.238789 | 0.119394 | − | 0.992847i | \(-0.461905\pi\) | ||||
0.119394 | + | 0.992847i | \(0.461905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.31884e7 | 0.478444 | 0.239222 | − | 0.970965i | \(-0.423108\pi\) | ||||
0.239222 | + | 0.970965i | \(0.423108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.14660e6 | −0.0533886 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.05419e7 | 0.591849 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.03056e8 | 1.64618 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.32103e7 | 0.573688 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.46457e7 | 0.489810 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.01165e7 | −0.147423 | −0.0737114 | − | 0.997280i | \(-0.523484\pi\) | ||||
−0.0737114 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.77862e7 | 0.693344 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.99001e7 | 0.205181 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.00649e8 | −0.668651 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.85345e8 | −1.83576 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.67858e7 | 0.166929 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.67012e8 | 1.00851 | 0.504254 | − | 0.863555i | \(-0.331768\pi\) | ||||
0.504254 | + | 0.863555i | \(0.331768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.35995e8 | 0.795949 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.37308e8 | −0.779122 | −0.389561 | − | 0.921001i | \(-0.627373\pi\) | ||||
−0.389561 | + | 0.921001i | \(0.627373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.67935e8 | 1.47436 | 0.737182 | − | 0.675694i | \(-0.236156\pi\) | ||||
0.737182 | + | 0.675694i | \(0.236156\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.64322e7 | −0.354599 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.98032e8 | −1.02563 | −0.512815 | − | 0.858499i | \(-0.671397\pi\) | ||||
−0.512815 | + | 0.858499i | \(0.671397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.77639e8 | 1.39554 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.96873e8 | 0.960654 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.22277e7 | −0.389606 | −0.194803 | − | 0.980842i | \(-0.562407\pi\) | ||||
−0.194803 | + | 0.980842i | \(0.562407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.70650e8 | −1.24551 | −0.622757 | − | 0.782415i | \(-0.713988\pi\) | ||||
−0.622757 | + | 0.782415i | \(0.713988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.83831e8 | −0.821860 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.13498e8 | 0.927498 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.26797e7 | −0.306884 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.18052e8 | 0.484591 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.90747e8 | −1.16053 | −0.580266 | − | 0.814427i | \(-0.697051\pi\) | ||||
−0.580266 | + | 0.814427i | \(0.697051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.85549e7 | 0.149678 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.15508e8 | 1.19157 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.36047e7 | 0.160239 | 0.0801193 | − | 0.996785i | \(-0.474470\pi\) | ||||
0.0801193 | + | 0.996785i | \(0.474470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.17867e8 | 0.779188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00053e8 | −2.08905 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.27678e8 | 1.44968 | 0.724840 | − | 0.688917i | \(-0.241914\pi\) | ||||
0.724840 | + | 0.688917i | \(0.241914\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.20244e8 | 1.71730 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.53509e8 | −0.493564 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.26134e7 | −0.258772 | −0.129386 | − | 0.991594i | \(-0.541301\pi\) | ||||
−0.129386 | + | 0.991594i | \(0.541301\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.15189e7 | −0.187766 | −0.0938829 | − | 0.995583i | \(-0.529928\pi\) | ||||
−0.0938829 | + | 0.995583i | \(0.529928\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.46883e7 | 0.222169 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.16196e7 | 0.207667 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.39237e7 | −0.124171 | −0.0620854 | − | 0.998071i | \(-0.519775\pi\) | ||||
−0.0620854 | + | 0.998071i | \(0.519775\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.56153e8 | 2.36013 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.80931e8 | −1.56190 | −0.780948 | − | 0.624596i | \(-0.785264\pi\) | ||||
−0.780948 | + | 0.624596i | \(0.785264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.03790e8 | 1.58356 | 0.791778 | − | 0.610810i | \(-0.209156\pi\) | ||||
0.791778 | + | 0.610810i | \(0.209156\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.56091e8 | −2.19060 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.63385e8 | 0.657665 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.63568e8 | −0.642319 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.22520e6 | −0.00529352 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.10504e8 | 0.256649 | 0.128325 | − | 0.991732i | \(-0.459040\pi\) | ||||
0.128325 | + | 0.991732i | \(0.459040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.17591e8 | 1.40063 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.34142e8 | 0.518599 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.33464e7 | −0.0937787 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.87836e7 | 0.0819719 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.29335e9 | 2.67095 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.64003e8 | −0.330981 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.03386e8 | 1.38742 | 0.693712 | − | 0.720252i | \(-0.255974\pi\) | ||||
0.693712 | + | 0.720252i | \(0.255974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.83002e8 | −1.89539 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.61240e8 | −1.62354 | −0.811769 | − | 0.583978i | \(-0.801495\pi\) | ||||
−0.811769 | + | 0.583978i | \(0.801495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.42056e8 | −0.446181 | −0.223090 | − | 0.974798i | \(-0.571615\pi\) | ||||
−0.223090 | + | 0.974798i | \(0.571615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.54817e8 | 1.00014 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.38362e8 | 0.949221 | 0.474610 | − | 0.880196i | \(-0.342589\pi\) | ||||
0.474610 | + | 0.880196i | \(0.342589\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.16007e8 | −0.545042 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.04351e9 | 1.76088 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.98242e8 | −0.657565 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.05203e7 | −0.130111 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.64900e8 | −0.577108 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.60128e8 | 0.557534 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.05054e9 | −1.59226 | −0.796131 | − | 0.605124i | \(-0.793123\pi\) | ||||
−0.796131 | + | 0.605124i | \(0.793123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.85325e9 | −2.75029 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.70342e7 | 0.0392877 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.04579e8 | −0.291177 | −0.145589 | − | 0.989345i | \(-0.546508\pi\) | ||||
−0.145589 | + | 0.989345i | \(0.546508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.20855e8 | −0.865548 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.50878e8 | 0.615770 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.38462e8 | 0.854291 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.10576e8 | −0.669412 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.28852e8 | 0.807970 | 0.403985 | − | 0.914766i | \(-0.367625\pi\) | ||||
0.403985 | + | 0.914766i | \(0.367625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.86717e8 | 1.24252 | 0.621260 | − | 0.783604i | \(-0.286621\pi\) | ||||
0.621260 | + | 0.783604i | \(0.286621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.63240e8 | −0.324921 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.59732e8 | 0.677281 | 0.338641 | − | 0.940916i | \(-0.390033\pi\) | ||||
0.338641 | + | 0.940916i | \(0.390033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.30087e8 | −0.510219 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.09248e8 | 0.476045 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.42390e8 | 0.162424 | 0.0812119 | − | 0.996697i | \(-0.474121\pi\) | ||||
0.0812119 | + | 0.996697i | \(0.474121\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.86707e8 | 0.208875 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.20193e9 | −1.31889 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.25501e9 | 1.35090 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.13452e8 | −0.753414 | −0.376707 | − | 0.926333i | \(-0.622944\pi\) | ||||
−0.376707 | + | 0.926333i | \(0.622944\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.24044e9 | −2.32136 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.74812e8 | 0.686079 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.14729e8 | 0.413794 | 0.206897 | − | 0.978363i | \(-0.433664\pi\) | ||||
0.206897 | + | 0.978363i | \(0.433664\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.08617e9 | 1.06362 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.55280e8 | 0.341489 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.23625e8 | 0.116646 | 0.0583229 | − | 0.998298i | \(-0.481425\pi\) | ||||
0.0583229 | + | 0.998298i | \(0.481425\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.64994e8 | 0.801264 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.35784e9 | 1.23496 | 0.617480 | − | 0.786586i | \(-0.288154\pi\) | ||||
0.617480 | + | 0.786586i | \(0.288154\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.92184e8 | 0.260942 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.29906e8 | −0.289336 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00573e9 | 0.866281 | 0.433141 | − | 0.901326i | \(-0.357405\pi\) | ||||
0.433141 | + | 0.901326i | \(0.357405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.37513e8 | −0.200941 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.78332e8 | −0.563726 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.65893e8 | −0.706927 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.30080e8 | 0.184549 | 0.0922747 | − | 0.995734i | \(-0.470586\pi\) | ||||
0.0922747 | + | 0.995734i | \(0.470586\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.11044e9 | −0.875167 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.24791e9 | −0.966446 | −0.483223 | − | 0.875497i | \(-0.660534\pi\) | ||||
−0.483223 | + | 0.875497i | \(0.660534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.06912e8 | −0.385802 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.36702e8 | −0.251857 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.75982e8 | −0.717565 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.79923e9 | 1.30033 | 0.650166 | − | 0.759792i | \(-0.274699\pi\) | ||||
0.650166 | + | 0.759792i | \(0.274699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.56803e9 | 1.82454 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.01081e8 | 0.559566 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.19219e8 | −0.356601 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.60248e9 | 2.43291 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.66870e8 | −0.177235 | −0.0886177 | − | 0.996066i | \(-0.528245\pi\) | ||||
−0.0886177 | + | 0.996066i | \(0.528245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.70575e9 | 1.76726 | 0.883630 | − | 0.468185i | \(-0.155092\pi\) | ||||
0.883630 | + | 0.468185i | \(0.155092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.06337e9 | −1.96792 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.41204e8 | −0.278791 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.12730e8 | −0.132230 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.34582e8 | −0.204598 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.78455e9 | −1.07364 | −0.536820 | − | 0.843697i | \(-0.680374\pi\) | ||||
−0.536820 | + | 0.843697i | \(0.680374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.21276e9 | 0.717905 | 0.358953 | − | 0.933356i | \(-0.383134\pi\) | ||||
0.358953 | + | 0.933356i | \(0.383134\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.18483e9 | 2.43762 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.44461e8 | 0.369413 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.76141e9 | −0.993654 | −0.496827 | − | 0.867850i | \(-0.665502\pi\) | ||||
−0.496827 | + | 0.867850i | \(0.665502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.35566e9 | −1.30791 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.06208e8 | 0.440590 | 0.220295 | − | 0.975433i | \(-0.429298\pi\) | ||||
0.220295 | + | 0.975433i | \(0.429298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.75166e8 | 0.363204 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.95263e9 | −1.56363 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.85913e8 | 0.305472 | 0.152736 | − | 0.988267i | \(-0.451192\pi\) | ||||
0.152736 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.17989e9 | −0.605653 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.52228e9 | −2.79110 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.28496e8 | −0.163490 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.52640e8 | −0.270854 | −0.135427 | − | 0.990787i | \(-0.543241\pi\) | ||||
−0.135427 | + | 0.990787i | \(0.543241\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.44240e9 | −0.696213 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.74101e9 | −0.827652 | −0.413826 | − | 0.910356i | \(-0.635808\pi\) | ||||
−0.413826 | + | 0.910356i | \(0.635808\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.84431e9 | 1.33181 | 0.665906 | − | 0.746035i | \(-0.268045\pi\) | ||||
0.665906 | + | 0.746035i | \(0.268045\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.97090e9 | −2.75394 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.63130e9 | −0.741183 | −0.370592 | − | 0.928796i | \(-0.620845\pi\) | ||||
−0.370592 | + | 0.928796i | \(0.620845\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.50662e7 | 0.0156958 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.10706e9 | −1.37018 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.73739e8 | −0.0754891 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.19715e9 | 0.512532 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.74018e9 | −2.42165 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.69345e9 | −1.53553 | −0.767765 | − | 0.640732i | \(-0.778631\pi\) | ||||
−0.767765 | + | 0.640732i | \(0.778631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.09727e9 | 0.449580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.62272e8 | −0.267437 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.78697e6 | 0.00389540 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.57153e9 | 0.616554 | 0.308277 | − | 0.951297i | \(-0.400248\pi\) | ||||
0.308277 | + | 0.951297i | \(0.400248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.57578e9 | 2.92986 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.63493e9 | 0.623323 | 0.311662 | − | 0.950193i | \(-0.399114\pi\) | ||||
0.311662 | + | 0.950193i | \(0.399114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.94673e9 | 0.731713 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.48542e9 | −0.921047 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.57868e8 | −0.203838 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.86870e8 | −0.247470 | −0.123735 | − | 0.992315i | \(-0.539487\pi\) | ||||
−0.123735 | + | 0.992315i | \(0.539487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.26890e9 | −1.16137 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.33472e9 | 0.817990 | 0.408995 | − | 0.912537i | \(-0.365879\pi\) | ||||
0.408995 | + | 0.912537i | \(0.365879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.68845e9 | −1.96550 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.45231e9 | −1.51725 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.21342e8 | 0.208842 | 0.104421 | − | 0.994533i | \(-0.466701\pi\) | ||||
0.104421 | + | 0.994533i | \(0.466701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.62789e9 | 0.539699 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.91378e9 | 1.27993 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.32347e9 | 1.39478 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.61327e9 | −0.513441 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.04114e9 | 0.640896 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.65562e9 | 0.512897 | 0.256448 | − | 0.966558i | \(-0.417448\pi\) | ||||
0.256448 | + | 0.966558i | \(0.417448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.42671e9 | −1.35309 | −0.676543 | − | 0.736403i | \(-0.736523\pi\) | ||||
−0.676543 | + | 0.736403i | \(0.736523\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.23024e9 | −0.371049 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.77758e9 | −0.826665 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.02047e9 | −0.887113 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.81427e9 | −1.97510 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.32652e9 | 0.379463 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.58961e9 | −1.29580 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.86332e9 | −0.519252 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.24057e9 | −0.341240 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.71878e9 | −1.00974 | −0.504871 | − | 0.863195i | \(-0.668460\pi\) | ||||
−0.504871 | + | 0.863195i | \(0.668460\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.14660e9 | 0.575376 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.60492e9 | 0.424683 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.20749e9 | −0.837934 | −0.418967 | − | 0.908002i | \(-0.637608\pi\) | ||||
−0.418967 | + | 0.908002i | \(0.637608\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.80955e9 | 0.466732 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.28219e9 | −1.34519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.12316e9 | −0.282424 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.29247e10 | 3.20920 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.80739e9 | 1.17873 | 0.589367 | − | 0.807865i | \(-0.299377\pi\) | ||||
0.589367 | + | 0.807865i | \(0.299377\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.95331e8 | 0.0472967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.83332e9 | −0.438397 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.77127e9 | 0.890653 | 0.445326 | − | 0.895368i | \(-0.353088\pi\) | ||||
0.445326 | + | 0.895368i | \(0.353088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.73066e9 | 0.636940 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.36739e8 | −0.100619 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.09341e9 | −0.476388 | −0.238194 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238194 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.86085e9 | −1.54224 | −0.771119 | − | 0.636691i | \(-0.780303\pi\) | ||||
−0.771119 | + | 0.636691i | \(0.780303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.28965e9 | −0.286371 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.13986e8 | 0.156622 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.70742e9 | 1.23687 | 0.618435 | − | 0.785836i | \(-0.287767\pi\) | ||||
0.618435 | + | 0.785836i | \(0.287767\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.73316e9 | 1.44160 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.73483e8 | −0.142466 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.02297e9 | −0.631820 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.79430e9 | 0.577069 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.56510e9 | 0.319380 | 0.159690 | − | 0.987167i | \(-0.448951\pi\) | ||||
0.159690 | + | 0.987167i | \(0.448951\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.53661e9 | 1.51975 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.97175e9 | 0.392913 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.78410e9 | −0.548268 | −0.274134 | − | 0.961692i | \(-0.588391\pi\) | ||||
−0.274134 | + | 0.961692i | \(0.588391\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.79997e9 | −0.350312 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.09283e9 | 0.787251 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.18885e9 | 1.17657 | 0.588283 | − | 0.808655i | \(-0.299804\pi\) | ||||
0.588283 | + | 0.808655i | \(0.299804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.42206e9 | 0.455118 | 0.227559 | − | 0.973764i | \(-0.426926\pi\) | ||||
0.227559 | + | 0.973764i | \(0.426926\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.98285e8 | −0.0554014 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.28639e9 | 0.970544 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.62465e9 | 0.839302 | 0.419651 | − | 0.907686i | \(-0.362152\pi\) | ||||
0.419651 | + | 0.907686i | \(0.362152\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.42817e9 | 0.973852 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.81376e9 | 0.321689 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.45433e9 | 0.956378 | 0.478189 | − | 0.878257i | \(-0.341293\pi\) | ||||
0.478189 | + | 0.878257i | \(0.341293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.56251e10 | 2.70869 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.32837e9 | 0.399074 | 0.199537 | − | 0.979890i | \(-0.436056\pi\) | ||||
0.199537 | + | 0.979890i | \(0.436056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.58626e9 | 1.62455 | 0.812273 | − | 0.583278i | \(-0.198230\pi\) | ||||
0.812273 | + | 0.583278i | \(0.198230\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.33419e9 | 0.391125 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.75763e8 | 0.145104 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.62240e9 | −1.24885 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.97446e9 | 0.805953 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.01242e9 | 0.963324 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.18616e10 | 1.87949 | 0.939747 | − | 0.341870i | \(-0.111060\pi\) | ||||
0.939747 | + | 0.341870i | \(0.111060\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.54796e9 | −0.242576 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.80445e9 | −0.589635 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.39474e9 | 0.213799 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.74542e9 | 0.719484 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.06130e8 | −0.0159161 | −0.00795805 | − | 0.999968i | \(-0.502533\pi\) | ||||
−0.00795805 | + | 0.999968i | \(0.502533\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.19289e9 | −0.325296 | −0.162648 | − | 0.986684i | \(-0.552004\pi\) | ||||
−0.162648 | + | 0.986684i | \(0.552004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.30080e9 | 0.337614 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.23914e9 | −0.615337 | −0.307668 | − | 0.951494i | \(-0.599549\pi\) | ||||
−0.307668 | + | 0.951494i | \(0.599549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.58862e9 | −0.515312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.74489e9 | −1.10023 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.93257e9 | −1.39594 | −0.697968 | − | 0.716129i | \(-0.745912\pi\) | ||||
−0.697968 | + | 0.716129i | \(0.745912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.98346e9 | 0.414836 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.38474e10 | −1.90497 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.36634e10 | −1.85977 | −0.929884 | − | 0.367852i | \(-0.880093\pi\) | ||||
−0.929884 | + | 0.367852i | \(0.880093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.03765e10 | −1.39747 | −0.698737 | − | 0.715378i | \(-0.746254\pi\) | ||||
−0.698737 | + | 0.715378i | \(0.746254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.06115e9 | 0.274671 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.88398e9 | 0.644019 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.15032e9 | −0.411069 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.28515e10 | 1.65944 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.52968e8 | 0.121773 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.70776e9 | 0.595336 | 0.297668 | − | 0.954669i | \(-0.403791\pi\) | ||||
0.297668 | + | 0.954669i | \(0.403791\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.33599e9 | 0.542657 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.55050e9 | −1.18295 | −0.591474 | − | 0.806324i | \(-0.701454\pi\) | ||||
−0.591474 | + | 0.806324i | \(0.701454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.26947e7 | 0.00155625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.05658e10 | −1.28200 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.06442e10 | 1.27832 | 0.639161 | − | 0.769073i | \(-0.279282\pi\) | ||||
0.639161 | + | 0.769073i | \(0.279282\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.12948e10 | −1.34265 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.06175e10 | 2.42598 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.39865e9 | 0.395858 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.41537e9 | 0.970287 | 0.485143 | − | 0.874435i | \(-0.338767\pi\) | ||||
0.485143 | + | 0.874435i | \(0.338767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.22386e9 | −0.367967 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.58445e10 | −1.79033 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.26858e9 | 0.813083 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.52385e10 | −1.68761 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.95355e9 | −0.981707 | −0.490854 | − | 0.871242i | \(-0.663315\pi\) | ||||
−0.490854 | + | 0.871242i | \(0.663315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.63139e10 | −1.77099 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.13643e10 | 2.29629 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.37853e9 | −0.785239 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.11796e9 | 0.855431 | 0.427716 | − | 0.903913i | \(-0.359318\pi\) | ||||
0.427716 | + | 0.903913i | \(0.359318\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.55395e9 | 0.996872 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.49486e9 | 0.464412 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.47157e9 | 0.150560 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.32739e9 | −0.641073 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.54339e8 | −0.0957528 | −0.0478764 | − | 0.998853i | \(-0.515245\pi\) | ||||
−0.0478764 | + | 0.998853i | \(0.515245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.60800e9 | 0.557231 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.08264e10 | −2.04942 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.85203e9 | −0.570327 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.75084e10 | 1.68996 | 0.844979 | − | 0.534799i | \(-0.179613\pi\) | ||||
0.844979 | + | 0.534799i | \(0.179613\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.63215e10 | −1.56032 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.07030e9 | 0.101343 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.16062e10 | −1.08849 | −0.544247 | − | 0.838925i | \(-0.683185\pi\) | ||||
−0.544247 | + | 0.838925i | \(0.683185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.64286e10 | 1.52614 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.57087e8 | −0.0144545 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.74800e9 | 0.432768 | 0.216384 | − | 0.976308i | \(-0.430574\pi\) | ||||
0.216384 | + | 0.976308i | \(0.430574\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.59268e9 | −0.504959 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.35857e9 | −0.389837 | −0.194918 | − | 0.980819i | \(-0.562444\pi\) | ||||
−0.194918 | + | 0.980819i | \(0.562444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.29864e10 | 1.15064 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.72888e9 | 0.502860 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.95321e9 | −0.517684 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.10987e9 | 0.526371 | 0.263186 | − | 0.964745i | \(-0.415227\pi\) | ||||
0.263186 | + | 0.964745i | \(0.415227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.23729e10 | −1.90959 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.42883e10 | 2.05391 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.29472e10 | −1.92262 | −0.961312 | − | 0.275460i | \(-0.911170\pi\) | ||||
−0.961312 | + | 0.275460i | \(0.911170\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.96679e9 | 0.246286 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.15151e9 | −0.588236 | −0.294118 | − | 0.955769i | \(-0.595026\pi\) | ||||
−0.294118 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.08175e9 | 0.169665 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.53111e10 | 1.23650 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.03460e9 | 0.322862 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.85381e10 | −1.47002 | −0.735011 | − | 0.678055i | \(-0.762823\pi\) | ||||
−0.735011 | + | 0.678055i | \(0.762823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.35537e9 | 0.263663 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.25535e9 | −0.642846 | −0.321423 | − | 0.946936i | \(-0.604161\pi\) | ||||
−0.321423 | + | 0.946936i | \(0.604161\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.34966e9 | 0.644336 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.67648e10 | 1.28211 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.97223e10 | −1.49478 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.49909e9 | 0.187717 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.91317e10 | −1.42425 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.36656e10 | 1.00829 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.53185e9 | 0.112023 | 0.0560113 | − | 0.998430i | \(-0.482162\pi\) | ||||
0.0560113 | + | 0.998430i | \(0.482162\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.29097e10 | 2.38536 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.54196e9 | 0.254464 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.07140e9 | −0.0762950 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.00326e10 | 2.82572 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.78553e9 | 0.194896 | 0.0974480 | − | 0.995241i | \(-0.468932\pi\) | ||||
0.0974480 | + | 0.995241i | \(0.468932\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.93837e9 | 0.689289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.44954e9 | −0.512172 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.29247e9 | −0.497016 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.91283e9 | 0.196802 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.35708e9 | −0.425794 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.17657e10 | −0.781267 | −0.390634 | − | 0.920546i | \(-0.627744\pi\) | ||||
−0.390634 | + | 0.920546i | \(0.627744\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.29491e9 | 0.414397 | 0.207198 | − | 0.978299i | \(-0.433565\pi\) | ||||
0.207198 | + | 0.978299i | \(0.433565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.73386e9 | −0.308957 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.33201e10 | −2.15603 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.90413e9 | −0.186311 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.62451e9 | 0.230545 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.27400e9 | 0.269546 | 0.134773 | − | 0.990876i | \(-0.456969\pi\) | ||||
0.134773 | + | 0.990876i | \(0.456969\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.16411e9 | −0.197858 | −0.0989288 | − | 0.995095i | \(-0.531542\pi\) | ||||
−0.0989288 | + | 0.995095i | \(0.531542\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.51111e9 | 0.341704 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.47251e9 | −0.213488 | −0.106744 | − | 0.994287i | \(-0.534043\pi\) | ||||
−0.106744 | + | 0.994287i | \(0.534043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.21388e9 | 0.317848 | 0.158924 | − | 0.987291i | \(-0.449197\pi\) | ||||
0.158924 | + | 0.987291i | \(0.449197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.37991e9 | −0.204316 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.64237e9 | 0.458111 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.43774e10 | 0.854629 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.72970e10 | 1.60908 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.48652e10 | −1.45353 | −0.726766 | − | 0.686885i | \(-0.758977\pi\) | ||||
−0.726766 | + | 0.686885i | \(0.758977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.57107e9 | 0.496877 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.47024e10 | −2.57001 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.95823e10 | 1.11652 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.85701e9 | 0.387742 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.64614e10 | 2.60565 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.72969e9 | −0.541185 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.01930e10 | −1.66565 | −0.832826 | − | 0.553536i | \(-0.813278\pi\) | ||||
−0.832826 | + | 0.553536i | \(0.813278\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.15448e10 | −2.27319 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.57761e10 | −1.39889 | −0.699446 | − | 0.714685i | \(-0.746570\pi\) | ||||
−0.699446 | + | 0.714685i | \(0.746570\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.77848e10 | 1.49565 | 0.747827 | − | 0.663894i | \(-0.231097\pi\) | ||||
0.747827 | + | 0.663894i | \(0.231097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.02674e10 | 1.08215 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.02990e10 | −1.60469 | −0.802344 | − | 0.596862i | \(-0.796414\pi\) | ||||
−0.802344 | + | 0.596862i | \(0.796414\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.97743e9 | −0.471624 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.02815e10 | −1.05690 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.03142e9 | 0.260089 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.76609e8 | 0.00905627 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.07986e8 | −0.00549309 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.19656e9 | −0.312696 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.37410e9 | 0.118850 | 0.0594252 | − | 0.998233i | \(-0.481073\pi\) | ||||
0.0594252 | + | 0.998233i | \(0.481073\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.50323e9 | 0.422302 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.28058e10 | −1.61635 | −0.808175 | − | 0.588942i | \(-0.799544\pi\) | ||||
−0.808175 | + | 0.588942i | \(0.799544\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.14967e10 | 1.05078 | 0.525388 | − | 0.850863i | \(-0.323920\pi\) | ||||
0.525388 | + | 0.850863i | \(0.323920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.75234e10 | 2.30466 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.50080e10 | −0.722089 | −0.361045 | − | 0.932549i | \(-0.617580\pi\) | ||||
−0.361045 | + | 0.932549i | \(0.617580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.93477e9 | −0.235565 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.95647e9 | 0.0926617 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.69665e10 | −1.26720 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.19532e9 | 0.382107 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.33549e9 | −0.154307 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.68412e10 | −1.69112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.86226e10 | 0.848212 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.98438e9 | 0.134880 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.44124e9 | −0.423408 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.57906e10 | −0.702704 | −0.351352 | − | 0.936243i | \(-0.614278\pi\) | ||||
−0.351352 | + | 0.936243i | \(0.614278\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.27643e10 | 2.77165 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.82128e9 | 0.298917 | 0.149459 | − | 0.988768i | \(-0.452247\pi\) | ||||
0.149459 | + | 0.988768i | \(0.452247\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.01701e9 | 0.131199 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.26200e10 | −0.544609 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.86987e9 | 0.165731 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.08588e10 | −0.461506 | −0.230753 | − | 0.973012i | \(-0.574119\pi\) | ||||
−0.230753 | + | 0.973012i | \(0.574119\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.41253e10 | 2.28293 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.80967e9 | −0.117611 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.80739e10 | −0.750853 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.77036e10 | −1.96685 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.99248e9 | −0.122455 | −0.0612275 | − | 0.998124i | \(-0.519502\pi\) | ||||
−0.0612275 | + | 0.998124i | \(0.519502\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.07366e10 | −0.842197 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.62721e10 | −2.67144 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.06335e9 | 0.322608 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.39333e10 | −0.950417 | −0.475208 | − | 0.879873i | \(-0.657627\pi\) | ||||
−0.475208 | + | 0.879873i | \(0.657627\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.86261e10 | −0.734164 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.17291e10 | −1.24135 | −0.620675 | − | 0.784068i | \(-0.713141\pi\) | ||||
−0.620675 | + | 0.784068i | \(0.713141\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.17625e10 | −0.456781 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.76894e10 | 0.681871 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.13161e10 | 1.58086 | 0.790431 | − | 0.612551i | \(-0.209857\pi\) | ||||
0.790431 | + | 0.612551i | \(0.209857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.19876e9 | 0.311399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.14268e10 | 1.56189 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.31993e10 | 1.61678 | 0.808390 | − | 0.588647i | \(-0.200339\pi\) | ||||
0.808390 | + | 0.588647i | \(0.200339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.67216e9 | 0.210735 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.43167e10 | −0.896835 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.46506e10 | −0.536401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.50523e10 | 0.910574 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.06400e10 | 1.82727 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.96140e10 | −1.06084 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.99318e9 | 0.248703 | 0.124352 | − | 0.992238i | \(-0.460315\pi\) | ||||
0.124352 | + | 0.992238i | \(0.460315\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.06446e10 | −1.08198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.48357e9 | 0.297380 | 0.148690 | − | 0.988884i | \(-0.452494\pi\) | ||||
0.148690 | + | 0.988884i | \(0.452494\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.05521e10 | −0.715255 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.19601e9 | −0.214090 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.72197e10 | −0.590739 | −0.295370 | − | 0.955383i | \(-0.595443\pi\) | ||||
−0.295370 | + | 0.955383i | \(0.595443\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.92317e9 | −0.133628 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.77081e10 | −0.598866 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.76267e10 | −1.26345 | −0.631725 | − | 0.775192i | \(-0.717653\pi\) | ||||
−0.631725 | + | 0.775192i | \(0.717653\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.67222e9 | −0.289137 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.77117e10 | 0.917389 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.73203e9 | −0.0569336 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.13036e9 | 0.102173 | 0.0510866 | − | 0.998694i | \(-0.483732\pi\) | ||||
0.0510866 | + | 0.998694i | \(0.483732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.08387e10 | −2.61997 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.80012e10 | −0.579323 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.67605e9 | 0.0535617 | 0.0267808 | − | 0.999641i | \(-0.491474\pi\) | ||||
0.0267808 | + | 0.999641i | \(0.491474\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.90878e10 | −1.87508 |
(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 | 256.8.a.q.1.6 | 6 | ||
4.3 | odd | 2 | 256.8.a.r.1.1 | 6 | |||
8.3 | odd | 2 | 256.8.a.r.1.6 | 6 | |||
8.5 | even | 2 | inner | 256.8.a.q.1.1 | 6 | ||
16.3 | odd | 4 | 8.8.b.a.5.6 | yes | 6 | ||
16.5 | even | 4 | 32.8.b.a.17.1 | 6 | |||
16.11 | odd | 4 | 8.8.b.a.5.5 | ✓ | 6 | ||
16.13 | even | 4 | 32.8.b.a.17.6 | 6 | |||
48.5 | odd | 4 | 288.8.d.b.145.6 | 6 | |||
48.11 | even | 4 | 72.8.d.b.37.2 | 6 | |||
48.29 | odd | 4 | 288.8.d.b.145.1 | 6 | |||
48.35 | even | 4 | 72.8.d.b.37.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.b.a.5.5 | ✓ | 6 | 16.11 | odd | 4 | ||
8.8.b.a.5.6 | yes | 6 | 16.3 | odd | 4 | ||
32.8.b.a.17.1 | 6 | 16.5 | even | 4 | |||
32.8.b.a.17.6 | 6 | 16.13 | even | 4 | |||
72.8.d.b.37.1 | 6 | 48.35 | even | 4 | |||
72.8.d.b.37.2 | 6 | 48.11 | even | 4 | |||
256.8.a.q.1.1 | 6 | 8.5 | even | 2 | inner | ||
256.8.a.q.1.6 | 6 | 1.1 | even | 1 | trivial | ||
256.8.a.r.1.1 | 6 | 4.3 | odd | 2 | |||
256.8.a.r.1.6 | 6 | 8.3 | odd | 2 | |||
288.8.d.b.145.1 | 6 | 48.29 | odd | 4 | |||
288.8.d.b.145.6 | 6 | 48.5 | odd | 4 |