Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,8,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("448.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(139.948491417\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1969}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 492 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-21.6867\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | 9.37342 | 0.200435 | 0.100217 | − | 0.994966i | \(-0.468046\pi\) | ||||
0.100217 | + | 0.994966i | \(0.468046\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −462.361 | −1.65419 | −0.827096 | − | 0.562061i | \(-0.810009\pi\) | ||||
−0.827096 | + | 0.562061i | \(0.810009\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2099.14 | −0.959826 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3881.05 | −0.879174 | −0.439587 | − | 0.898200i | \(-0.644875\pi\) | ||||
−0.439587 | + | 0.898200i | \(0.644875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11585.6 | 1.46257 | 0.731284 | − | 0.682073i | \(-0.238922\pi\) | ||||
0.731284 | + | 0.682073i | \(0.238922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4333.90 | −0.331558 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15242.4 | −0.752457 | −0.376229 | − | 0.926527i | \(-0.622779\pi\) | ||||
−0.376229 | + | 0.926527i | \(0.622779\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32461.7 | 1.08576 | 0.542880 | − | 0.839810i | \(-0.317334\pi\) | ||||
0.542880 | + | 0.839810i | \(0.317334\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3215.08 | 0.0757573 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 56146.1 | 0.962215 | 0.481108 | − | 0.876662i | \(-0.340235\pi\) | ||||
0.481108 | + | 0.876662i | \(0.340235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 135652. | 1.73635 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −40175.8 | −0.392818 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26442.0 | 0.201326 | 0.100663 | − | 0.994921i | \(-0.467904\pi\) | ||||
0.100663 | + | 0.994921i | \(0.467904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −45448.2 | −0.274000 | −0.137000 | − | 0.990571i | \(-0.543746\pi\) | ||||
−0.137000 | + | 0.990571i | \(0.543746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −36378.7 | −0.176217 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −158590. | −0.625226 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 555245. | 1.80210 | 0.901049 | − | 0.433717i | \(-0.142798\pi\) | ||||
0.901049 | + | 0.433717i | \(0.142798\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 108596. | 0.293150 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 306385. | 0.694264 | 0.347132 | − | 0.937816i | \(-0.387156\pi\) | ||||
0.347132 | + | 0.937816i | \(0.387156\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −780755. | −1.49753 | −0.748765 | − | 0.662836i | \(-0.769353\pi\) | ||||
−0.748765 | + | 0.662836i | \(0.769353\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 970559. | 1.58774 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −531243. | −0.746364 | −0.373182 | − | 0.927758i | \(-0.621733\pi\) | ||||
−0.373182 | + | 0.927758i | \(0.621733\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −142873. | −0.150819 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 363593. | 0.335467 | 0.167733 | − | 0.985832i | \(-0.446355\pi\) | ||||
0.167733 | + | 0.985832i | \(0.446355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79445e6 | 1.45432 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 304277. | 0.217624 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.14095e6 | 1.35714 | 0.678570 | − | 0.734535i | \(-0.262600\pi\) | ||||
0.678570 | + | 0.734535i | \(0.262600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −888824. | −0.501373 | −0.250687 | − | 0.968068i | \(-0.580656\pi\) | ||||
−0.250687 | + | 0.968068i | \(0.580656\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −720005. | −0.362780 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.35672e6 | −2.41937 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.34541e6 | −1.76510 | −0.882549 | − | 0.470221i | \(-0.844174\pi\) | ||||
−0.882549 | + | 0.470221i | \(0.844174\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 526281. | 0.192862 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 663207. | 0.219910 | 0.109955 | − | 0.993937i | \(-0.464929\pi\) | ||||
0.109955 | + | 0.993937i | \(0.464929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.34202e6 | 0.403765 | 0.201882 | − | 0.979410i | \(-0.435294\pi\) | ||||
0.201882 | + | 0.979410i | \(0.435294\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.27153e6 | 0.348026 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.33120e6 | −0.332297 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.05834e6 | 1.61067 | 0.805337 | − | 0.592818i | \(-0.201984\pi\) | ||||
0.805337 | + | 0.592818i | \(0.201984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.21423e6 | 0.881091 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.60874e6 | −1.26866 | −0.634330 | − | 0.773063i | \(-0.718724\pi\) | ||||
−0.634330 | + | 0.773063i | \(0.718724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.04748e6 | 1.24471 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 247851. | 0.0403528 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.32998e6 | −0.801420 | −0.400710 | − | 0.916205i | \(-0.631237\pi\) | ||||
−0.400710 | + | 0.916205i | \(0.631237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.97385e6 | 0.552799 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −426005. | −0.0549192 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.50090e7 | −1.79606 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.09810e6 | −0.233413 | −0.116707 | − | 0.993166i | \(-0.537234\pi\) | ||||
−0.116707 | + | 0.993166i | \(0.537234\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.14686e6 | 0.843854 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.95538e7 | −1.88845 | −0.944227 | − | 0.329294i | \(-0.893189\pi\) | ||||
−0.944227 | + | 0.329294i | \(0.893189\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.95093e6 | −0.807119 | −0.403560 | − | 0.914953i | \(-0.632227\pi\) | ||||
−0.403560 | + | 0.914953i | \(0.632227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.48653e6 | −0.125317 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.39509e7 | 1.10093 | 0.550466 | − | 0.834858i | \(-0.314450\pi\) | ||||
0.550466 | + | 0.834858i | \(0.314450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.84295e6 | −0.432155 | −0.216077 | − | 0.976376i | \(-0.569326\pi\) | ||||
−0.216077 | + | 0.976376i | \(0.569326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.20454e6 | 0.361203 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.20951e7 | −0.788562 | −0.394281 | − | 0.918990i | \(-0.629006\pi\) | ||||
−0.394281 | + | 0.918990i | \(0.629006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.59598e7 | −1.59169 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.43197e7 | −1.40381 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.22814e6 | −0.284402 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.42462e6 | −0.227053 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.87188e6 | 0.139155 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.65984e7 | −1.21807 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −325760. | −0.0141119 | −0.00705594 | − | 0.999975i | \(-0.502246\pi\) | ||||
−0.00705594 | + | 0.999975i | \(0.502246\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.31834e6 | −0.300157 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.38049e6 | −0.247973 | −0.123986 | − | 0.992284i | \(-0.539568\pi\) | ||||
−0.123986 | + | 0.992284i | \(0.539568\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.11344e7 | 0.410379 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.85757e7 | 0.649796 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.62324e6 | 0.153612 | 0.0768059 | − | 0.997046i | \(-0.475528\pi\) | ||||
0.0768059 | + | 0.997046i | \(0.475528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.55394e7 | 1.12243 | 0.561214 | − | 0.827671i | \(-0.310335\pi\) | ||||
0.561214 | + | 0.827671i | \(0.310335\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.97956e6 | −0.149597 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.49642e7 | −1.28585 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.22257e7 | −0.333032 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.10277e6 | 0.0286336 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.01708e7 | −0.251885 | −0.125943 | − | 0.992038i | \(-0.540196\pi\) | ||||
−0.125943 | + | 0.992038i | \(0.540196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.45272e7 | 0.579735 | 0.289867 | − | 0.957067i | \(-0.406389\pi\) | ||||
0.289867 | + | 0.957067i | \(0.406389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.19959e7 | 0.722228 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.10135e7 | 0.453249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.27379e7 | 0.262693 | 0.131346 | − | 0.991337i | \(-0.458070\pi\) | ||||
0.131346 | + | 0.991337i | \(0.458070\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.40810e6 | 0.0672393 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.92581e7 | 0.363683 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.51531e7 | 1.54008 | 0.770041 | − | 0.637995i | \(-0.220236\pi\) | ||||
0.770041 | + | 0.637995i | \(0.220236\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.68201e7 | 0.291497 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.74260e6 | −0.0621822 | −0.0310911 | − | 0.999517i | \(-0.509898\pi\) | ||||
−0.0310911 | + | 0.999517i | \(0.509898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.14770e7 | 1.13910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.81417e7 | −1.04214 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.26865e7 | 1.06731 | 0.533657 | − | 0.845701i | \(-0.320817\pi\) | ||||
0.533657 | + | 0.845701i | \(0.320817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.65288e7 | 0.656279 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00680e7 | 0.272018 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.02445e8 | −1.33507 | −0.667536 | − | 0.744578i | \(-0.732651\pi\) | ||||
−0.667536 | + | 0.744578i | \(0.732651\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.79161e6 | −0.0600630 | −0.0300315 | − | 0.999549i | \(-0.509561\pi\) | ||||
−0.0300315 | + | 0.999549i | \(0.509561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.33131e6 | −0.100493 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.56723e8 | −2.98102 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.91565e7 | 0.661541 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.37803e7 | −0.148471 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.60173e7 | 0.270175 | 0.135087 | − | 0.990834i | \(-0.456868\pi\) | ||||
0.135087 | + | 0.990834i | \(0.456868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.58326e7 | −0.759286 | −0.379643 | − | 0.925133i | \(-0.623953\pi\) | ||||
−0.379643 | + | 0.925133i | \(0.623953\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.02107e7 | −0.484926 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.19192e8 | −1.11075 | −0.555374 | − | 0.831601i | \(-0.687425\pi\) | ||||
−0.555374 | + | 0.831601i | \(0.687425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.72662e7 | 0.605078 | 0.302539 | − | 0.953137i | \(-0.402166\pi\) | ||||
0.302539 | + | 0.953137i | \(0.402166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.07313e7 | −0.353787 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.06959e6 | 0.0760942 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.41661e8 | −1.14845 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.17858e8 | −0.923559 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.25986e8 | −0.954573 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.32421e8 | −1.70328 | −0.851641 | − | 0.524126i | \(-0.824392\pi\) | ||||
−0.851641 | + | 0.524126i | \(0.824392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.21651e6 | 0.0440776 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.60991e8 | 2.47720 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.55887e7 | −0.103562 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.25793e7 | 0.0809286 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.76592e8 | −1.10052 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.53319e8 | −1.52968 | −0.764840 | − | 0.644221i | \(-0.777182\pi\) | ||||
−0.764840 | + | 0.644221i | \(0.777182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.84753e8 | −1.66659 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.50124e7 | −0.255412 | −0.127706 | − | 0.991812i | \(-0.540761\pi\) | ||||
−0.127706 | + | 0.991812i | \(0.540761\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.86973e8 | −1.02886 | −0.514429 | − | 0.857533i | \(-0.671996\pi\) | ||||
−0.514429 | + | 0.857533i | \(0.671996\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.24779e7 | −0.0666039 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.57588e8 | −1.33408 | −0.667038 | − | 0.745024i | \(-0.732438\pi\) | ||||
−0.667038 | + | 0.745024i | \(0.732438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.45626e8 | 1.23463 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.61607e7 | 0.322835 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.15071e8 | −1.49285 | −0.746425 | − | 0.665469i | \(-0.768231\pi\) | ||||
−0.746425 | + | 0.665469i | \(0.768231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.39900e7 | 0.386516 | 0.193258 | − | 0.981148i | \(-0.438095\pi\) | ||||
0.193258 | + | 0.981148i | \(0.438095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.27366e8 | 0.569419 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.43963e7 | −0.236313 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.76088e8 | 1.58800 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.19464e7 | −0.254284 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.33130e6 | 0.0212802 | 0.0106401 | − | 0.999943i | \(-0.496613\pi\) | ||||
0.0106401 | + | 0.999943i | \(0.496613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.17906e8 | −0.845955 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.60590e7 | 0.249483 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.09942e8 | −0.771495 | −0.385747 | − | 0.922604i | \(-0.626056\pi\) | ||||
−0.385747 | + | 0.922604i | \(0.626056\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.90449e8 | 0.681129 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.55053e7 | −0.193238 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.50805e8 | −0.850143 | −0.425071 | − | 0.905160i | \(-0.639751\pi\) | ||||
−0.425071 | + | 0.905160i | \(0.639751\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.68111e8 | −0.554926 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.99601e7 | −0.160633 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.39197e8 | −1.06248 | −0.531238 | − | 0.847223i | \(-0.678273\pi\) | ||||
−0.531238 | + | 0.847223i | \(0.678273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.59574e7 | 0.231834 | 0.115917 | − | 0.993259i | \(-0.463019\pi\) | ||||
0.115917 | + | 0.993259i | \(0.463019\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.72486e7 | 0.110800 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.26474e8 | −1.52656 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00883e7 | 0.141598 | 0.0707990 | − | 0.997491i | \(-0.477445\pi\) | ||||
0.0707990 | + | 0.997491i | \(0.477445\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.54021e7 | 0.262992 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.41917e8 | 0.919283 | 0.459641 | − | 0.888105i | \(-0.347978\pi\) | ||||
0.459641 | + | 0.888105i | \(0.347978\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.69077e8 | −0.967977 | −0.483988 | − | 0.875074i | \(-0.660812\pi\) | ||||
−0.483988 | + | 0.875074i | \(0.660812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.40686e8 | −0.359993 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.05090e8 | 0.262407 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.78008e8 | −0.433808 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.96664e7 | −0.0467842 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.92780e8 | −1.37676 | −0.688378 | − | 0.725352i | \(-0.741677\pi\) | ||||
−0.688378 | + | 0.725352i | \(0.741677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.89892e8 | −2.24497 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.55924e8 | 0.345355 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.50485e8 | 1.40730 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.67799e8 | −0.566013 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.83286e8 | −0.378512 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.10957e8 | 0.829368 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.43846e8 | 1.86173 | 0.930865 | − | 0.365363i | \(-0.119055\pi\) | ||||
0.930865 | + | 0.365363i | \(0.119055\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.39008e7 | −0.161775 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.64065e8 | −0.309282 | −0.154641 | − | 0.987971i | \(-0.549422\pi\) | ||||
−0.154641 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.46012e8 | 0.637801 | 0.318901 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.32902e8 | 0.600108 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.53240e8 | 1.68072 | 0.840359 | − | 0.542030i | \(-0.182344\pi\) | ||||
0.840359 | + | 0.542030i | \(0.182344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.02623e8 | −0.177001 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.30768e8 | 0.220665 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.94795e8 | −0.816989 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.57161e9 | 2.53953 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.47684e7 | −0.0866189 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.82216e8 | −0.282099 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.24263e8 | −0.339906 | −0.169953 | − | 0.985452i | \(-0.554362\pi\) | ||||
−0.169953 | + | 0.985452i | \(0.554362\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.16554e9 | −1.72970 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.00915e9 | 2.91981 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.56750e8 | 0.507761 | 0.253880 | − | 0.967236i | \(-0.418293\pi\) | ||||
0.253880 | + | 0.967236i | \(0.418293\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.13373e8 | −0.158055 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.76387e8 | 0.240894 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.43332e8 | −0.319030 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.61839e7 | −0.0207936 | −0.0103968 | − | 0.999946i | \(-0.503309\pi\) | ||||
−0.0103968 | + | 0.999946i | \(0.503309\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.07780e8 | −0.261647 | −0.130823 | − | 0.991406i | \(-0.541762\pi\) | ||||
−0.130823 | + | 0.991406i | \(0.541762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.65459e8 | −0.574522 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.31624e9 | −1.59266 | −0.796328 | − | 0.604865i | \(-0.793227\pi\) | ||||
−0.796328 | + | 0.604865i | \(0.793227\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.06641e8 | −0.363773 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.90055e7 | −0.0570041 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.19271e8 | −0.706400 | −0.353200 | − | 0.935548i | \(-0.614906\pi\) | ||||
−0.353200 | + | 0.935548i | \(0.614906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.59893e8 | 0.178877 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.14738e7 | −0.0455093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.20497e8 | −0.667905 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.78628e8 | 0.294235 | 0.147117 | − | 0.989119i | \(-0.453000\pi\) | ||||
0.147117 | + | 0.989119i | \(0.453000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.43146e8 | −0.666373 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.24712e8 | 0.126795 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.65056e8 | 0.164684 | 0.0823420 | − | 0.996604i | \(-0.473760\pi\) | ||||
0.0823420 | + | 0.996604i | \(0.473760\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.49318e8 | −0.244143 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.06345e8 | 0.294453 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.29433e8 | −0.405190 | −0.202595 | − | 0.979263i | \(-0.564937\pi\) | ||||
−0.202595 | + | 0.979263i | \(0.564937\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.05348e6 | −0.00282851 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.34378e9 | 1.22217 | 0.611084 | − | 0.791566i | \(-0.290734\pi\) | ||||
0.611084 | + | 0.791566i | \(0.290734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.15495e8 | 0.549682 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.63891e9 | 1.43737 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.07871e8 | 0.0929139 | 0.0464569 | − | 0.998920i | \(-0.485207\pi\) | ||||
0.0464569 | + | 0.998920i | \(0.485207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.55801e8 | −0.724026 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.98070e7 | −0.0497024 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.26350e9 | −2.66436 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.86525e9 | 1.49613 | 0.748066 | − | 0.663625i | \(-0.230983\pi\) | ||||
0.748066 | + | 0.663625i | \(0.230983\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.04367e8 | 0.0822543 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.94724e6 | 0.00770367 | 0.00385183 | − | 0.999993i | \(-0.498774\pi\) | ||||
0.00385183 | + | 0.999993i | \(0.498774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.26543e8 | −0.400744 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.94850e9 | −1.45749 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.15493e9 | −1.58436 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.76376e8 | −0.633372 | −0.316686 | − | 0.948530i | \(-0.602570\pi\) | ||||
−0.316686 | + | 0.948530i | \(0.602570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.33356e7 | 0.0307892 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.34347e8 | 0.512951 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.05562e9 | 2.09861 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.33126e8 | 0.224974 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.01605e9 | 1.33891 | 0.669457 | − | 0.742851i | \(-0.266527\pi\) | ||||
0.669457 | + | 0.742851i | \(0.266527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.69546e8 | −0.371999 | −0.186000 | − | 0.982550i | \(-0.559552\pi\) | ||||
−0.186000 | + | 0.982550i | \(0.559552\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.11515e9 | 0.716380 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.06767e9 | −1.30653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.04867e8 | −0.189501 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.21468e8 | −0.257730 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.71940e8 | −0.464422 | −0.232211 | − | 0.972665i | \(-0.574596\pi\) | ||||
−0.232211 | + | 0.972665i | \(0.574596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.24002e9 | 0.734043 | 0.367021 | − | 0.930213i | \(-0.380378\pi\) | ||||
0.367021 | + | 0.930213i | \(0.380378\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.14597e8 | −0.0667513 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.82260e9 | 1.04474 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.90621e9 | 1.07534 | 0.537669 | − | 0.843156i | \(-0.319305\pi\) | ||||
0.537669 | + | 0.843156i | \(0.319305\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46962e8 | −0.137118 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.04738e8 | 0.275837 | 0.137919 | − | 0.990444i | \(-0.455959\pi\) | ||||
0.137919 | + | 0.990444i | \(0.455959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.46437e9 | 1.32570 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.53351e7 | −0.0504866 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.02721e9 | −1.05691 | −0.528453 | − | 0.848962i | \(-0.677228\pi\) | ||||
−0.528453 | + | 0.848962i | \(0.677228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.18910e9 | −0.610379 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.29904e8 | 0.116199 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.83735e9 | −0.914435 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.03969e9 | 0.999672 | 0.499836 | − | 0.866120i | \(-0.333394\pi\) | ||||
0.499836 | + | 0.866120i | \(0.333394\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.12375e8 | 0.295579 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.41390e9 | 1.62292 | 0.811461 | − | 0.584406i | \(-0.198673\pi\) | ||||
0.811461 | + | 0.584406i | \(0.198673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.97893e9 | −0.926608 | −0.463304 | − | 0.886199i | \(-0.653336\pi\) | ||||
−0.463304 | + | 0.886199i | \(0.653336\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.96968e8 | 0.0908469 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.86422e9 | −0.847007 | −0.423504 | − | 0.905894i | \(-0.639200\pi\) | ||||
−0.423504 | + | 0.905894i | \(0.639200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.49047e9 | −0.667144 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.19397e8 | 0.0526528 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.03015e9 | 1.31659 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.40351e9 | 1.88526 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.63231e8 | −0.321990 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.71828e9 | 1.54585 | 0.772926 | − | 0.634496i | \(-0.218792\pi\) | ||||
0.772926 | + | 0.634496i | \(0.218792\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.43283e9 | 2.63569 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.80514e8 | 0.0728948 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.70080e8 | 0.386110 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.16341e9 | −0.848767 | −0.424383 | − | 0.905483i | \(-0.639509\pi\) | ||||
−0.424383 | + | 0.905483i | \(0.639509\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.98175e8 | 0.308686 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.37608e8 | −0.0905890 | −0.0452945 | − | 0.998974i | \(-0.514423\pi\) | ||||
−0.0452945 | + | 0.998974i | \(0.514423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.03039e8 | −0.151489 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.76679e9 | −1.39590 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.27480e8 | 0.0831181 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.65166e9 | −0.955358 | −0.477679 | − | 0.878535i | \(-0.658522\pi\) | ||||
−0.477679 | + | 0.878535i | \(0.658522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.50810e7 | −0.0124635 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.15865e9 | 0.756300 | 0.378150 | − | 0.925744i | \(-0.376560\pi\) | ||||
0.378150 | + | 0.925744i | \(0.376560\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.04091e9 | 3.12387 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.69984e8 | 0.228316 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.47831e9 | −0.832998 | −0.416499 | − | 0.909136i | \(-0.636743\pi\) | ||||
−0.416499 | + | 0.909136i | \(0.636743\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.60312e8 | 0.152609 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.30418e9 | −0.426506 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.13856e9 | 1.33513 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.06178e9 | 0.656184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.81321e8 | 0.213927 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.99735e9 | −1.23834 | −0.619170 | − | 0.785257i | \(-0.712531\pi\) | ||||
−0.619170 | + | 0.785257i | \(0.712531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.93132e9 | 1.20166 | 0.600831 | − | 0.799376i | \(-0.294837\pi\) | ||||
0.600831 | + | 0.799376i | \(0.294837\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.36134e8 | 0.131541 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.92739e8 | 0.206173 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.52441e8 | −0.0741421 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.49416e9 | −1.30262 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.54965e9 | 1.01541 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.45037e9 | −1.82115 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.60258e8 | −0.267595 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.56602e8 | −0.125596 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.74766e9 | 0.746057 | 0.373028 | − | 0.927820i | \(-0.378319\pi\) | ||||
0.373028 | + | 0.927820i | \(0.378319\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.49138e7 | −0.0120387 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.70155e9 | 0.714867 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.40581e9 | 0.367258 | 0.183629 | − | 0.982996i | \(-0.441216\pi\) | ||||
0.183629 | + | 0.982996i | \(0.441216\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.86576e9 | 0.481231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.58352e8 | 0.218592 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.42101e9 | 0.608777 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.40637e9 | −0.597500 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.87805e8 | −0.242202 | −0.121101 | − | 0.992640i | \(-0.538643\pi\) | ||||
−0.121101 | + | 0.992640i | \(0.538643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.04550e9 | −2.19024 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.54498e8 | 0.132596 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.88115e9 | −0.444268 | −0.222134 | − | 0.975016i | \(-0.571302\pi\) | ||||
−0.222134 | + | 0.975016i | \(0.571302\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.59231e9 | 1.30443 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.44548e9 | 0.333021 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.88531e9 | −0.884164 | −0.442082 | − | 0.896975i | \(-0.645760\pi\) | ||||
−0.442082 | + | 0.896975i | \(0.645760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.44900e9 | −0.550505 | −0.275253 | − | 0.961372i | \(-0.588762\pi\) | ||||
−0.275253 | + | 0.961372i | \(0.588762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.43871e8 | 0.0541525 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.61636e9 | 1.67074 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.88218e9 | 0.624605 | 0.312303 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312303 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.10811e8 | −0.152188 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.26680e9 | −0.479508 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.41112e9 | −0.294934 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.12445e10 | 2.32217 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.72250e9 | −0.963692 | −0.481846 | − | 0.876256i | \(-0.660034\pi\) | ||||
−0.481846 | + | 0.876256i | \(0.660034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.47533e9 | −0.297499 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.11724e9 | −0.222633 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.23167e8 | 0.0242550 | 0.0121275 | − | 0.999926i | \(-0.496140\pi\) | ||||
0.0121275 | + | 0.999926i | \(0.496140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.41729e9 | 0.470456 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.30514e8 | 0.121279 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.35497e9 | 0.257594 | 0.128797 | − | 0.991671i | \(-0.458888\pi\) | ||||
0.128797 | + | 0.991671i | \(0.458888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.25107e9 | −0.986704 | −0.493352 | − | 0.869830i | \(-0.664228\pi\) | ||||
−0.493352 | + | 0.869830i | \(0.664228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.12161e9 | 1.69419 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.04577e9 | 0.375589 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.99012e9 | 0.905630 | 0.452815 | − | 0.891605i | \(-0.350420\pi\) | ||||
0.452815 | + | 0.891605i | \(0.350420\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.50130e7 | 0.0152519 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.15476e9 | −1.09161 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.46028e9 | 0.431393 | 0.215696 | − | 0.976460i | \(-0.430798\pi\) | ||||
0.215696 | + | 0.976460i | \(0.430798\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.32784e9 | −0.230189 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.93223e9 | −0.331178 | −0.165589 | − | 0.986195i | \(-0.552953\pi\) | ||||
−0.165589 | + | 0.986195i | \(0.552953\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.13699e9 | 1.37894 | 0.689472 | − | 0.724313i | \(-0.257843\pi\) | ||||
0.689472 | + | 0.724313i | \(0.257843\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.25571e9 | −0.377975 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.82818e9 | −0.302908 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.70022e9 | 0.278565 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.18092e9 | −0.191330 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.46326e9 | −1.35600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.83737e9 | 1.40030 | 0.700149 | − | 0.713997i | \(-0.253117\pi\) | ||||
0.700149 | + | 0.713997i | \(0.253117\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.17858e9 | −0.341397 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.50619e8 | 0.0233438 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.36303e9 | 0.208938 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.39216e9 | −0.211075 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.25905e10 | −1.88817 | −0.944086 | − | 0.329700i | \(-0.893052\pi\) | ||||
−0.944086 | + | 0.329700i | \(0.893052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.47578e9 | −0.960625 | −0.480312 | − | 0.877098i | \(-0.659477\pi\) | ||||
−0.480312 | + | 0.877098i | \(0.659477\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.38371e9 | 0.496518 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.69520e9 | 1.26216 | 0.631081 | − | 0.775717i | \(-0.282612\pi\) | ||||
0.631081 | + | 0.775717i | \(0.282612\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.30914e9 | −1.19316 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.46120e8 | −0.0207575 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.87898e9 | 0.545156 | 0.272578 | − | 0.962134i | \(-0.412124\pi\) | ||||
0.272578 | + | 0.962134i | \(0.412124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.95009e9 | 0.410195 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.81708e9 | −0.387544 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.30333e9 | 0.177400 | 0.0887000 | − | 0.996058i | \(-0.471729\pi\) | ||||
0.0887000 | + | 0.996058i | \(0.471729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.85888e9 | −0.923736 | −0.461868 | − | 0.886949i | \(-0.652821\pi\) | ||||
−0.461868 | + | 0.886949i | \(0.652821\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.65527e9 | −0.220583 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.14810e9 | −0.678846 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.48461e9 | 0.193719 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.37446e9 | −0.306601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.44957e9 | 0.440794 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.44953e9 | −0.815596 | −0.407798 | − | 0.913072i | \(-0.633703\pi\) | ||||
−0.407798 | + | 0.913072i | \(0.633703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.44994e9 | −0.682069 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.83027e9 | −0.474426 | −0.237213 | − | 0.971458i | \(-0.576234\pi\) | ||||
−0.237213 | + | 0.971458i | \(0.576234\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.19649e8 | −0.0882219 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.21920e8 | −0.0511936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.97836e9 | 0.237592 | 0.118796 | − | 0.992919i | \(-0.462097\pi\) | ||||
0.118796 | + | 0.992919i | \(0.462097\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.13761e9 | −0.254103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.75258e9 | −0.206219 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.21243e9 | 0.490643 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.00255e10 | −1.15593 | −0.577967 | − | 0.816060i | \(-0.696154\pi\) | ||||
−0.577967 | + | 0.816060i | \(0.696154\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.79437e9 | 0.318947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.64320e10 | −1.85671 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.67005e9 | −0.522404 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.41448e9 | −0.267395 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.21616e9 | −0.133345 | −0.0666727 | − | 0.997775i | \(-0.521238\pi\) | ||||
−0.0666727 | + | 0.997775i | \(0.521238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.80242e10 | 1.95665 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.30235e9 | 0.247463 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.70696e9 | −0.713769 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.04706e10 | −1.10334 | −0.551671 | − | 0.834062i | \(-0.686010\pi\) | ||||
−0.551671 | + | 0.834062i | \(0.686010\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.48164e10 | −1.54597 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.55174e9 | −0.263647 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.07897e10 | 2.12705 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.95330e9 | −0.299219 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.99586e9 | −0.300587 | −0.150294 | − | 0.988641i | \(-0.548022\pi\) | ||||
−0.150294 | + | 0.988641i | \(0.548022\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.07017e9 | −0.305062 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.87273e8 | 0.0774714 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.58692e9 | 0.349573 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.52469e9 | −0.629781 | −0.314890 | − | 0.949128i | \(-0.601968\pi\) | ||||
−0.314890 | + | 0.949128i | \(0.601968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.02267e9 | −0.766960 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.19006e10 | 1.12683 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.19856e10 | 1.12408 | 0.562040 | − | 0.827110i | \(-0.310017\pi\) | ||||
0.562040 | + | 0.827110i | \(0.310017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.09879e8 | −0.0473654 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.68647e10 | 1.55183 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.81843e10 | −1.65746 | −0.828728 | − | 0.559651i | \(-0.810935\pi\) | ||||
−0.828728 | + | 0.559651i | \(0.810935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.52523e9 | 0.318290 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.10111e9 | 0.545692 | 0.272846 | − | 0.962058i | \(-0.412035\pi\) | ||||
0.272846 | + | 0.962058i | \(0.412035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.70257e9 | 0.416667 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.38727e10 | 1.21769 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.78517e9 | 0.416113 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.69384e9 | −0.318228 | −0.159114 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159114 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.99725e7 | 0.00426529 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.13404e10 | −0.958992 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.35894e10 | −1.13858 | −0.569292 | − | 0.822135i | \(-0.692783\pi\) | ||||
−0.569292 | + | 0.822135i | \(0.692783\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.04252e9 | −0.169559 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.79994e10 | 1.48051 | 0.740255 | − | 0.672326i | \(-0.234705\pi\) | ||||
0.740255 | + | 0.672326i | \(0.234705\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00413e9 | −0.163339 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.47936e10 | −1.19470 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.48042e10 | 1.98491 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.41340e10 | 1.12079 | 0.560394 | − | 0.828226i | \(-0.310650\pi\) | ||||
0.560394 | + | 0.828226i | \(0.310650\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.96787e9 | −0.154634 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.39484e9 | 0.575838 | 0.287919 | − | 0.957655i | \(-0.407037\pi\) | ||||
0.287919 | + | 0.957655i | \(0.407037\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.16516e9 | −0.475760 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.78516e9 | 0.136522 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.94581e9 | 0.753805 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.57394e9 | −0.193339 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.06233e9 | −0.0790845 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.88949e9 | −0.434544 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.49146e9 | 0.694099 | 0.347050 | − | 0.937847i | \(-0.387184\pi\) | ||||
0.347050 | + | 0.937847i | \(0.387184\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.35090e9 | −0.170398 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.14863e9 | −0.298049 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.02975e10 | −0.733292 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.57577e9 | −0.111227 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.83350e9 | 0.618057 | 0.309029 | − | 0.951053i | \(-0.399996\pi\) | ||||
0.309029 | + | 0.951053i | \(0.399996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.09742e9 | 0.561607 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.11884e10 | 0.769224 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.20844e9 | −0.354980 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.90420e9 | −0.601602 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.17943e9 | −0.212957 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.15622e9 | 0.408784 | 0.204392 | − | 0.978889i | \(-0.434478\pi\) | ||||
0.204392 | + | 0.978889i | \(0.434478\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.53945e10 | 1.01343 | 0.506715 | − | 0.862114i | \(-0.330860\pi\) | ||||
0.506715 | + | 0.862114i | \(0.330860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.11980e8 | 0.0464677 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.93714e10 | −2.54759 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.53447e10 | −1.62596 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.34167e9 | −0.530590 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.74907e10 | 1.73374 | 0.866871 | − | 0.498532i | \(-0.166128\pi\) | ||||
0.866871 | + | 0.498532i | \(0.166128\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.61300e9 | 0.100864 | 0.0504318 | − | 0.998728i | \(-0.483940\pi\) | ||||
0.0504318 | + | 0.998728i | \(0.483940\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.93486e9 | −0.305975 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.03950e9 | −0.555745 | −0.277872 | − | 0.960618i | \(-0.589629\pi\) | ||||
−0.277872 | + | 0.960618i | \(0.589629\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.46326e10 | −1.50165 | −0.750826 | − | 0.660501i | \(-0.770344\pi\) | ||||
−0.750826 | + | 0.660501i | \(0.770344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.69499e8 | 0.0283812 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.79325e9 | −0.107494 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.73043e9 | 0.102861 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.82592e9 | 0.107632 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.84347e9 | −0.400046 | −0.200023 | − | 0.979791i | \(-0.564102\pi\) | ||||
−0.200023 | + | 0.979791i | \(0.564102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.65507e10 | −0.959468 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.20493e9 | 0.184256 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.30482e10 | −1.88430 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.51764e9 | −0.0858179 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.45952e9 | −0.194016 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.11748e10 | 1.73401 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.54072e10 | −1.95330 | −0.976652 | − | 0.214826i | \(-0.931081\pi\) | ||||
−0.976652 | + | 0.214826i | \(0.931081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.15061e10 | 1.72390 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.87299e10 | −1.01649 | −0.508245 | − | 0.861213i | \(-0.669706\pi\) | ||||
−0.508245 | + | 0.861213i | \(0.669706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.38272e9 | 0.289752 | 0.144876 | − | 0.989450i | \(-0.453722\pi\) | ||||
0.144876 | + | 0.989450i | \(0.453722\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.85054e8 | 0.0525956 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.29444e9 | 0.386326 | 0.193163 | − | 0.981167i | \(-0.438125\pi\) | ||||
0.193163 | + | 0.981167i | \(0.438125\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.36074e10 | −1.76554 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.66854e9 | −0.0869503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.73938e10 | −1.41606 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.03440e10 | −2.58157 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.40421e9 | 0.224036 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.12326e9 | −0.460386 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.05623e10 | −1.52998 | −0.764992 | − | 0.644039i | \(-0.777257\pi\) | ||||
−0.764992 | + | 0.644039i | \(0.777257\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.55637e9 | −0.275950 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.10736e10 | −1.53100 | −0.765500 | − | 0.643436i | \(-0.777508\pi\) | ||||
−0.765500 | + | 0.643436i | \(0.777508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.10432e9 | −0.445026 | −0.222513 | − | 0.974930i | \(-0.571426\pi\) | ||||
−0.222513 | + | 0.974930i | \(0.571426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.27867e9 | −0.449971 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.03417e8 | −0.0242212 | −0.0121106 | − | 0.999927i | \(-0.503855\pi\) | ||||
−0.0121106 | + | 0.999927i | \(0.503855\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.11736e8 | −0.00533379 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.63557e10 | −0.774633 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.72451e10 | −0.810373 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.73665e10 | 2.20846 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.09727e9 | 0.282073 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.20174e9 | −0.0551634 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.54202e9 | −0.252424 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.51019e9 | −0.113449 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.21545e9 | 0.0993557 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.55392e10 | −1.58155 | −0.790774 | − | 0.612108i | \(-0.790322\pi\) | ||||
−0.790774 | + | 0.612108i | \(0.790322\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.10462e10 | 1.81259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.60841e10 | 1.58125 | 0.790627 | − | 0.612299i | \(-0.209755\pi\) | ||||
0.790627 | + | 0.612299i | \(0.209755\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.56488e10 | 1.11537 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.85207e9 | 0.166234 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.18851e9 | −0.0937250 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.06975e9 | −0.300469 | −0.150235 | − | 0.988650i | \(-0.548003\pi\) | ||||
−0.150235 | + | 0.988650i | \(0.548003\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.84706e9 | 0.373156 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.68363e9 | 0.321633 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.53203e10 | 3.12908 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.87892e10 | 0.774694 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.55102e10 | −0.634691 | −0.317345 | − | 0.948310i | \(-0.602791\pi\) | ||||
−0.317345 | + | 0.948310i | \(0.602791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.81909e9 | 0.155109 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.53785e9 | −0.0619910 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.73516e10 | −1.09432 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.61814e10 | −1.43680 | −0.718400 | − | 0.695630i | \(-0.755125\pi\) | ||||
−0.718400 | + | 0.695630i | \(0.755125\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.24331e9 | 0.127838 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.86518e10 | −0.729720 | −0.364860 | − | 0.931062i | \(-0.618883\pi\) | ||||
−0.364860 | + | 0.931062i | \(0.618883\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.72023e10 | 0.668031 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.37146e9 | 0.245600 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.55630e9 | −0.327387 | −0.163693 | − | 0.986511i | \(-0.552341\pi\) | ||||
−0.163693 | + | 0.986511i | \(0.552341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.55481e10 | 0.590533 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.93512e9 | 0.336875 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.92820e8 | −0.0221870 | −0.0110935 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110935 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.20294e10 | −0.446921 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.61924e8 | −0.0354772 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.58577e9 | 0.0580598 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.54471e10 | −0.924924 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.92850e10 | −1.05670 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.50620e10 | 1.25601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.25393e10 | −1.86849 | −0.934247 | − | 0.356626i | \(-0.883927\pi\) | ||||
−0.934247 | + | 0.356626i | \(0.883927\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.63792e9 | −0.163753 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.16576e9 | 0.321293 | 0.160647 | − | 0.987012i | \(-0.448642\pi\) | ||||
0.160647 | + | 0.987012i | \(0.448642\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.21900e10 | 0.424238 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.47314e10 | 0.509011 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.01603e10 | −0.691618 | −0.345809 | − | 0.938305i | \(-0.612396\pi\) | ||||
−0.345809 | + | 0.938305i | \(0.612396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.06859e10 | 0.704588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.22652e10 | 0.414793 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.18989e9 | −0.0399549 | −0.0199775 | − | 0.999800i | \(-0.506359\pi\) | ||||
−0.0199775 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.51097e10 | 1.83739 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.70799e9 | −0.0565425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.38364e10 | −1.44095 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.09986e10 | 0.685382 | 0.342691 | − | 0.939448i | \(-0.388662\pi\) | ||||
0.342691 | + | 0.939448i | \(0.388662\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.10211e9 | −0.0681291 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.11013e10 | −1.00092 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.21657e10 | −1.02792 | −0.513961 | − | 0.857814i | \(-0.671822\pi\) | ||||
−0.513961 | + | 0.857814i | \(0.671822\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.23074e10 | −0.707896 |
(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 | 448.8.a.l.1.2 | 2 | ||
4.3 | odd | 2 | 448.8.a.s.1.1 | 2 | |||
8.3 | odd | 2 | 112.8.a.g.1.2 | 2 | |||
8.5 | even | 2 | 14.8.a.c.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 126.8.a.i.1.1 | 2 | |||
40.13 | odd | 4 | 350.8.c.k.99.1 | 4 | |||
40.29 | even | 2 | 350.8.a.j.1.2 | 2 | |||
40.37 | odd | 4 | 350.8.c.k.99.4 | 4 | |||
56.5 | odd | 6 | 98.8.c.k.67.1 | 4 | |||
56.13 | odd | 2 | 98.8.a.g.1.2 | 2 | |||
56.37 | even | 6 | 98.8.c.g.67.2 | 4 | |||
56.45 | odd | 6 | 98.8.c.k.79.1 | 4 | |||
56.53 | even | 6 | 98.8.c.g.79.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.8.a.c.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
98.8.a.g.1.2 | 2 | 56.13 | odd | 2 | |||
98.8.c.g.67.2 | 4 | 56.37 | even | 6 | |||
98.8.c.g.79.2 | 4 | 56.53 | even | 6 | |||
98.8.c.k.67.1 | 4 | 56.5 | odd | 6 | |||
98.8.c.k.79.1 | 4 | 56.45 | odd | 6 | |||
112.8.a.g.1.2 | 2 | 8.3 | odd | 2 | |||
126.8.a.i.1.1 | 2 | 24.5 | odd | 2 | |||
350.8.a.j.1.2 | 2 | 40.29 | even | 2 | |||
350.8.c.k.99.1 | 4 | 40.13 | odd | 4 | |||
350.8.c.k.99.4 | 4 | 40.37 | odd | 4 | |||
448.8.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
448.8.a.s.1.1 | 2 | 4.3 | odd | 2 |