Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(1,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, 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("76.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.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: | \(23.7412619368\) |
Analytic rank: | \(0\) |
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: | \( x^{6} - 2x^{5} - 8376x^{4} + 135458x^{3} + 16275767x^{2} - 280013424x - 6276171312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-13.7370\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.1 |
$q$-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 | ||||||||
\(3\) | 20.7370 | 0.443427 | 0.221713 | − | 0.975112i | \(-0.428835\pi\) | ||||
0.221713 | + | 0.975112i | \(0.428835\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −501.411 | −1.79390 | −0.896951 | − | 0.442131i | \(-0.854223\pi\) | ||||
−0.896951 | + | 0.442131i | \(0.854223\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1008.02 | −1.11077 | −0.555385 | − | 0.831593i | \(-0.687429\pi\) | ||||
−0.555385 | + | 0.831593i | \(0.687429\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1756.98 | −0.803373 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6783.78 | 1.53673 | 0.768365 | − | 0.640012i | \(-0.221071\pi\) | ||||
0.768365 | + | 0.640012i | \(0.221071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10249.0 | 1.29384 | 0.646919 | − | 0.762559i | \(-0.276057\pi\) | ||||
0.646919 | + | 0.762559i | \(0.276057\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10397.8 | −0.795464 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 27829.3 | 1.37383 | 0.686913 | − | 0.726740i | \(-0.258965\pi\) | ||||
0.686913 | + | 0.726740i | \(0.258965\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −20903.3 | −0.492546 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4350.81 | 0.0745629 | 0.0372815 | − | 0.999305i | \(-0.488130\pi\) | ||||
0.0372815 | + | 0.999305i | \(0.488130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 173288. | 2.21808 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −81786.3 | −0.799664 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −171678. | −1.30714 | −0.653571 | − | 0.756866i | \(-0.726730\pi\) | ||||
−0.653571 | + | 0.756866i | \(0.726730\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −107058. | −0.645438 | −0.322719 | − | 0.946495i | \(-0.604597\pi\) | ||||
−0.322719 | + | 0.946495i | \(0.604597\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 140675. | 0.681427 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 505430. | 1.99261 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 489322. | 1.58814 | 0.794070 | − | 0.607826i | \(-0.207958\pi\) | ||||
0.794070 | + | 0.607826i | \(0.207958\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 212534. | 0.573723 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 25924.1 | 0.0587434 | 0.0293717 | − | 0.999569i | \(-0.490649\pi\) | ||||
0.0293717 | + | 0.999569i | \(0.490649\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 189649. | 0.363757 | 0.181878 | − | 0.983321i | \(-0.441782\pi\) | ||||
0.181878 | + | 0.983321i | \(0.441782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 880966. | 1.44117 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −404901. | −0.568862 | −0.284431 | − | 0.958697i | \(-0.591805\pi\) | ||||
−0.284431 | + | 0.958697i | \(0.591805\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 192554. | 0.233811 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 577098. | 0.609192 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.48333e6 | 1.36859 | 0.684295 | − | 0.729205i | \(-0.260110\pi\) | ||||
0.684295 | + | 0.729205i | \(0.260110\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.40146e6 | −2.75674 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 142235. | 0.101729 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 834818. | 0.529188 | 0.264594 | − | 0.964360i | \(-0.414762\pi\) | ||||
0.264594 | + | 0.964360i | \(0.414762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −344246. | −0.194184 | −0.0970922 | − | 0.995275i | \(-0.530954\pi\) | ||||
−0.0970922 | + | 0.995275i | \(0.530954\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.77106e6 | 0.892363 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.13896e6 | −2.32102 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.08156e6 | 0.845526 | 0.422763 | − | 0.906240i | \(-0.361060\pi\) | ||||
0.422763 | + | 0.906240i | \(0.361060\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 90222.9 | 0.0330632 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.08187e6 | 0.690318 | 0.345159 | − | 0.938544i | \(-0.387825\pi\) | ||||
0.345159 | + | 0.938544i | \(0.387825\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.99207e6 | −0.599342 | −0.299671 | − | 0.954043i | \(-0.596877\pi\) | ||||
−0.299671 | + | 0.954043i | \(0.596877\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.59347e6 | 0.983557 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.83816e6 | −1.70695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.22247e6 | −0.963544 | −0.481772 | − | 0.876297i | \(-0.660007\pi\) | ||||
−0.481772 | + | 0.876297i | \(0.660007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.14650e6 | 0.448780 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.66320e6 | 1.08715 | 0.543574 | − | 0.839361i | \(-0.317071\pi\) | ||||
0.543574 | + | 0.839361i | \(0.317071\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.39539e7 | −2.46451 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.56010e6 | −0.579622 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.04694e7 | 1.57418 | 0.787092 | − | 0.616835i | \(-0.211586\pi\) | ||||
0.787092 | + | 0.616835i | \(0.211586\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.03312e7 | −1.43716 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.22007e6 | −0.286204 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.43918e6 | −0.411549 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.45838e7 | −1.62245 | −0.811223 | − | 0.584738i | \(-0.801198\pi\) | ||||
−0.811223 | + | 0.584738i | \(0.801198\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.19189e7 | −1.23457 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 306934. | 0.0296429 | 0.0148214 | − | 0.999890i | \(-0.495282\pi\) | ||||
0.0148214 | + | 0.999890i | \(0.495282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.57505e7 | 1.42024 | 0.710122 | − | 0.704078i | \(-0.248640\pi\) | ||||
0.710122 | + | 0.704078i | \(0.248640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.04811e7 | 0.883578 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.34511e7 | 1.06148 | 0.530742 | − | 0.847534i | \(-0.321913\pi\) | ||||
0.530742 | + | 0.847534i | \(0.321913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.39015e7 | 1.02818 | 0.514089 | − | 0.857737i | \(-0.328130\pi\) | ||||
0.514089 | + | 0.857737i | \(0.328130\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.01471e7 | 0.704224 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.85824e7 | 1.21151 | 0.605755 | − | 0.795651i | \(-0.292871\pi\) | ||||
0.605755 | + | 0.795651i | \(0.292871\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.18154e6 | −0.133758 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.80073e7 | −1.03943 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.80524e7 | −1.52601 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.65325e7 | 1.36154 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 537588. | 0.0260484 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.77155e7 | −2.18512 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.05149e7 | −1.32190 | −0.660951 | − | 0.750429i | \(-0.729847\pi\) | ||||
−0.660951 | + | 0.750429i | \(0.729847\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.93276e6 | 0.161300 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.28387e7 | 1.66489 | 0.832446 | − | 0.554105i | \(-0.186940\pi\) | ||||
0.832446 | + | 0.554105i | \(0.186940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.91398e6 | −0.254828 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.10085e7 | 1.43452 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.68434e7 | −1.22416 | −0.612079 | − | 0.790797i | \(-0.709667\pi\) | ||||
−0.612079 | + | 0.790797i | \(0.709667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.18263e7 | 1.63681 | 0.818405 | − | 0.574643i | \(-0.194859\pi\) | ||||
0.818405 | + | 0.574643i | \(0.194859\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.39645e6 | −0.252249 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.95270e7 | 1.98828 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.60813e7 | 2.34488 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.99299e6 | 0.103678 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.36079e7 | −1.07997 | −0.539986 | − | 0.841674i | \(-0.681571\pi\) | ||||
−0.539986 | + | 0.841674i | \(0.681571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.26610e7 | 1.00835 | 0.504175 | − | 0.863601i | \(-0.331797\pi\) | ||||
0.504175 | + | 0.863601i | \(0.331797\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.88955e7 | −1.10369 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.36801e7 | 1.15785 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.75145e6 | 0.159858 | 0.0799290 | − | 0.996801i | \(-0.474531\pi\) | ||||
0.0799290 | + | 0.996801i | \(0.474531\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.07599e7 | 0.606870 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.38569e6 | −0.0828223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.13287e7 | −1.29005 | −0.645027 | − | 0.764160i | \(-0.723154\pi\) | ||||
−0.645027 | + | 0.764160i | \(0.723154\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.05361e7 | −1.22241 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.82203e7 | 1.29961 | 0.649803 | − | 0.760102i | \(-0.274851\pi\) | ||||
0.649803 | + | 0.760102i | \(0.274851\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.22936e7 | 0.674017 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.20511e7 | −0.184306 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.48988e7 | −0.806123 | −0.403062 | − | 0.915173i | \(-0.632054\pi\) | ||||
−0.403062 | + | 0.915173i | \(0.632054\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.74677e8 | −2.46378 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.73116e7 | 0.234656 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.47688e7 | −0.974395 | −0.487197 | − | 0.873292i | \(-0.661981\pi\) | ||||
−0.487197 | + | 0.873292i | \(0.661981\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.58486e7 | −0.700063 | −0.350031 | − | 0.936738i | \(-0.613829\pi\) | ||||
−0.350031 | + | 0.936738i | \(0.613829\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.13864e6 | −0.0861066 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.45351e8 | −2.84897 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.88788e8 | 2.11120 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.24419e7 | 0.888243 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.71702e7 | 0.697525 | 0.348763 | − | 0.937211i | \(-0.386602\pi\) | ||||
0.348763 | + | 0.937211i | \(0.386602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.89356e7 | −0.389849 | −0.194925 | − | 0.980818i | \(-0.562446\pi\) | ||||
−0.194925 | + | 0.980818i | \(0.562446\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.06567e8 | −1.02920 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.94584e7 | 0.367712 | 0.183856 | − | 0.982953i | \(-0.441142\pi\) | ||||
0.183856 | + | 0.982953i | \(0.441142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.45572e8 | −1.30946 | −0.654731 | − | 0.755862i | \(-0.727218\pi\) | ||||
−0.654731 | + | 0.755862i | \(0.727218\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.31654e7 | 0.374929 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.73055e8 | 1.45193 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.29986e7 | −0.105380 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.64427e6 | −0.0599018 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.65300e7 | 0.352550 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.82801e8 | −1.33965 | −0.669823 | − | 0.742521i | \(-0.733630\pi\) | ||||
−0.669823 | + | 0.742521i | \(0.733630\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.31717e7 | 0.306105 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.50921e7 | −0.652544 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.07916e8 | 0.716933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.13096e7 | −0.265765 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.85223e8 | 1.77751 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.04726e7 | −0.244396 | −0.122198 | − | 0.992506i | \(-0.538994\pi\) | ||||
−0.122198 | + | 0.992506i | \(0.538994\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.04462e8 | −1.78195 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.37641e8 | −0.781013 | −0.390507 | − | 0.920600i | \(-0.627700\pi\) | ||||
−0.390507 | + | 0.920600i | \(0.627700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.31082e8 | −1.27157 | −0.635787 | − | 0.771865i | \(-0.719324\pi\) | ||||
−0.635787 | + | 0.771865i | \(0.719324\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.41803e8 | −0.756909 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.37486e7 | −0.226579 | −0.113289 | − | 0.993562i | \(-0.536139\pi\) | ||||
−0.113289 | + | 0.993562i | \(0.536139\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.03022e8 | 1.02048 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.75614e7 | −0.427261 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.53555e8 | 1.67519 | 0.837597 | − | 0.546289i | \(-0.183960\pi\) | ||||
0.837597 | + | 0.546289i | \(0.183960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.02396e8 | 0.931411 | 0.465705 | − | 0.884940i | \(-0.345801\pi\) | ||||
0.465705 | + | 0.884940i | \(0.345801\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23379e8 | 0.998665 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.65484e7 | −0.419434 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.02979e7 | 0.296827 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.17438e8 | 0.482070 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.33482e7 | −0.212942 | −0.106471 | − | 0.994316i | \(-0.533955\pi\) | ||||
−0.106471 | + | 0.994316i | \(0.533955\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.95150e7 | 0.114583 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.89363e8 | −1.09283 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.54687e8 | 1.30340 | 0.651702 | − | 0.758475i | \(-0.274055\pi\) | ||||
0.651702 | + | 0.758475i | \(0.274055\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.93245e8 | −1.76406 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.01635e8 | 1.05012 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.73491e8 | 1.60497 | 0.802484 | − | 0.596673i | \(-0.203511\pi\) | ||||
0.802484 | + | 0.596673i | \(0.203511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.43760e8 | −2.45512 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.17104e8 | 0.698036 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.38349e7 | 0.293921 | 0.146961 | − | 0.989142i | \(-0.453051\pi\) | ||||
0.146961 | + | 0.989142i | \(0.453051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.34812e8 | 1.02190 | 0.510950 | − | 0.859610i | \(-0.329294\pi\) | ||||
0.510950 | + | 0.859610i | \(0.329294\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.14238e8 | −0.637274 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.17554e9 | 3.40859 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.19729e8 | −0.338469 | −0.169235 | − | 0.985576i | \(-0.554130\pi\) | ||||
−0.169235 | + | 0.985576i | \(0.554130\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.88099e8 | 0.518527 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.81327e8 | 0.756378 | 0.378189 | − | 0.925728i | \(-0.376547\pi\) | ||||
0.378189 | + | 0.925728i | \(0.376547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.47945e7 | 0.0388016 | 0.0194008 | − | 0.999812i | \(-0.493824\pi\) | ||||
0.0194008 | + | 0.999812i | \(0.493824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.13183e7 | −0.182492 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.61319e7 | −0.0652505 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.64134e8 | 0.887399 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.02425e8 | −0.719436 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.35486e8 | 1.24369 | 0.621845 | − | 0.783141i | \(-0.286384\pi\) | ||||
0.621845 | + | 0.783141i | \(0.286384\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.18587e8 | −0.949310 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.54820e8 | −1.22887 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.45915e7 | 0.0964723 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.91169e8 | −0.404050 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.36490e6 | 0.0131444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.72609e8 | 0.348348 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.23353e8 | −1.03231 | −0.516155 | − | 0.856495i | \(-0.672637\pi\) | ||||
−0.516155 | + | 0.856495i | \(0.672637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.26618e8 | 0.629775 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.01475e8 | −1.32236 | −0.661182 | − | 0.750226i | \(-0.729945\pi\) | ||||
−0.661182 | + | 0.750226i | \(0.729945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.49136e8 | −0.274902 | −0.137451 | − | 0.990509i | \(-0.543891\pi\) | ||||
−0.137451 | + | 0.990509i | \(0.543891\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.88028e8 | −1.60081 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.62409e8 | 0.815302 | 0.407651 | − | 0.913138i | \(-0.366348\pi\) | ||||
0.407651 | + | 0.913138i | \(0.366348\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.16463e9 | −2.00872 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.78935e8 | 0.470690 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.90882e8 | 0.315177 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.77602e9 | 2.86984 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.88275e8 | 0.455921 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.08147e8 | 0.631875 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.78961e8 | 0.574376 | 0.287188 | − | 0.957874i | \(-0.407280\pi\) | ||||
0.287188 | + | 0.957874i | \(0.407280\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.59727e8 | −1.27587 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.04372e9 | −1.51679 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.67178e8 | 0.664933 | 0.332467 | − | 0.943115i | \(-0.392119\pi\) | ||||
0.332467 | + | 0.943115i | \(0.392119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.85343e8 | 0.537216 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.26260e8 | −0.991863 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.36047e8 | 0.851060 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.52387e7 | −0.0593121 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.93105e8 | −1.14749 | −0.573745 | − | 0.819034i | \(-0.694510\pi\) | ||||
−0.573745 | + | 0.819034i | \(0.694510\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.93562e8 | −0.747441 | −0.373720 | − | 0.927541i | \(-0.621918\pi\) | ||||
−0.373720 | + | 0.927541i | \(0.621918\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.38228e8 | −1.03464 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.88892e8 | −0.470563 | −0.235282 | − | 0.971927i | \(-0.575601\pi\) | ||||
−0.235282 | + | 0.971927i | \(0.575601\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.04387e9 | −1.23836 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.81724e8 | −0.676672 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.12699e7 | 0.0927042 | 0.0463521 | − | 0.998925i | \(-0.485240\pi\) | ||||
0.0463521 | + | 0.998925i | \(0.485240\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.50205e8 | 0.603742 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.98846e8 | 1.07516 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.36670e8 | 0.144325 | 0.0721627 | − | 0.997393i | \(-0.477010\pi\) | ||||
0.0721627 | + | 0.997393i | \(0.477010\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.55479e7 | −0.0471929 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.49523e9 | −1.52019 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.53262e8 | 0.152916 | 0.0764581 | − | 0.997073i | \(-0.475639\pi\) | ||||
0.0764581 | + | 0.997073i | \(0.475639\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.89478e8 | −0.968939 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.75953e9 | −1.69123 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.04506e8 | −0.192961 | −0.0964803 | − | 0.995335i | \(-0.530758\pi\) | ||||
−0.0964803 | + | 0.995335i | \(0.530758\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.32789e8 | −0.586167 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.03716e8 | 0.276231 | 0.138115 | − | 0.990416i | \(-0.455896\pi\) | ||||
0.138115 | + | 0.990416i | \(0.455896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.42873e9 | 3.06211 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.33209e8 | −0.292232 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.25621e8 | −0.797278 | −0.398639 | − | 0.917108i | \(-0.630517\pi\) | ||||
−0.398639 | + | 0.917108i | \(0.630517\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.21080e8 | 0.102436 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.88346e8 | 0.738258 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.11719e9 | 1.72850 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.31806e9 | −1.05723 | −0.528615 | − | 0.848862i | \(-0.677289\pi\) | ||||
−0.528615 | + | 0.848862i | \(0.677289\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.43375e8 | −0.112998 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.42599e9 | 1.10436 | 0.552181 | − | 0.833724i | \(-0.313796\pi\) | ||||
0.552181 | + | 0.833724i | \(0.313796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.09724e9 | −0.835092 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.07628e9 | −0.805067 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.31945e9 | 2.44054 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.44675e9 | 1.76831 | 0.884154 | − | 0.467196i | \(-0.154736\pi\) | ||||
0.884154 | + | 0.467196i | \(0.154736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.64022e8 | −0.542825 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.41510e8 | −0.587806 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.83959e9 | −1.95023 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.07472e9 | 0.725805 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.62114e9 | 1.07664 | 0.538320 | − | 0.842740i | \(-0.319059\pi\) | ||||
0.538320 | + | 0.842740i | \(0.319059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.97506e8 | −0.520891 | −0.260445 | − | 0.965489i | \(-0.583869\pi\) | ||||
−0.260445 | + | 0.965489i | \(0.583869\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.11402e8 | 0.457008 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.82248e9 | 3.04726 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.47006e8 | 0.215694 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.44178e9 | 0.881656 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.33983e9 | 0.806085 | 0.403042 | − | 0.915181i | \(-0.367953\pi\) | ||||
0.403042 | + | 0.915181i | \(0.367953\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.49611e9 | −0.885639 | −0.442819 | − | 0.896611i | \(-0.646022\pi\) | ||||
−0.442819 | + | 0.896611i | \(0.646022\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.78507e9 | 1.03978 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.98422e7 | 0.0171059 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.18648e9 | −1.23344 | −0.616721 | − | 0.787182i | \(-0.711539\pi\) | ||||
−0.616721 | + | 0.787182i | \(0.711539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.38312e8 | −0.187838 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.00352e9 | 0.548420 | 0.274210 | − | 0.961670i | \(-0.411584\pi\) | ||||
0.274210 | + | 0.961670i | \(0.411584\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.24945e9 | −2.82393 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.04297e8 | −0.478889 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.07250e9 | −1.08052 | −0.540259 | − | 0.841499i | \(-0.681674\pi\) | ||||
−0.540259 | + | 0.841499i | \(0.681674\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75863e8 | 0.0902728 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.84662e8 | 0.447130 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.18015e9 | 2.57812 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00176e9 | −0.490974 | −0.245487 | − | 0.969400i | \(-0.578948\pi\) | ||||
−0.245487 | + | 0.969400i | \(0.578948\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.27606e9 | −1.09860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.48579e9 | −1.18171 | −0.590856 | − | 0.806777i | \(-0.701210\pi\) | ||||
−0.590856 | + | 0.806777i | \(0.701210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.38703e9 | 0.649459 | 0.324729 | − | 0.945807i | \(-0.394727\pi\) | ||||
0.324729 | + | 0.945807i | \(0.394727\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.11317e9 | 0.513422 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.93622e9 | −1.33407 | −0.667036 | − | 0.745026i | \(-0.732437\pi\) | ||||
−0.667036 | + | 0.745026i | \(0.732437\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.09825e9 | −0.939186 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.60742e8 | 0.0708853 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.28654e9 | 0.558996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.18858e9 | 0.508863 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.60618e9 | −1.09949 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.12696e9 | 0.468526 | 0.234263 | − | 0.972173i | \(-0.424732\pi\) | ||||
0.234263 | + | 0.972173i | \(0.424732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.01506e9 | 2.05480 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.09461e7 | −0.0367256 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.31248e9 | 2.91051 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.17540e9 | 1.63812 | 0.819062 | − | 0.573705i | \(-0.194494\pi\) | ||||
0.819062 | + | 0.573705i | \(0.194494\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.47914e9 | −0.572044 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.34194e9 | 1.27413 | 0.637064 | − | 0.770811i | \(-0.280149\pi\) | ||||
0.637064 | + | 0.770811i | \(0.280149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.77770e9 | −1.79578 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.97628e9 | 2.21469 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.09856e9 | −0.766784 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.98948e9 | −1.43735 | −0.718677 | − | 0.695344i | \(-0.755252\pi\) | ||||
−0.718677 | + | 0.695344i | \(0.755252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.62206e9 | 0.576281 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.47180e9 | −1.56673 | −0.783365 | − | 0.621562i | \(-0.786498\pi\) | ||||
−0.783365 | + | 0.621562i | \(0.786498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.53900e8 | −0.0531764 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.77043e8 | 0.298877 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.36655e9 | 0.795433 | 0.397716 | − | 0.917508i | \(-0.369803\pi\) | ||||
0.397716 | + | 0.917508i | \(0.369803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00804e9 | 0.665732 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.60972e8 | −0.183455 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.89745e9 | −2.54778 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.74676e9 | −0.874186 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.13844e9 | −0.357457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.20799e9 | −0.374222 | −0.187111 | − | 0.982339i | \(-0.559912\pi\) | ||||
−0.187111 | + | 0.982339i | \(0.559912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.99004e9 | 1.21961 | 0.609806 | − | 0.792551i | \(-0.291247\pi\) | ||||
0.609806 | + | 0.792551i | \(0.291247\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.62227e9 | −1.09251 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.97936e9 | −0.886719 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.38590e9 | −0.994440 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.46675e9 | −0.425135 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.65696e8 | 0.0760045 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.74450e9 | −1.90420 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.55048e9 | −0.432073 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.30624e9 | 0.359305 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.43642e8 | 0.147612 | 0.0738061 | − | 0.997273i | \(-0.476485\pi\) | ||||
0.0738061 | + | 0.997273i | \(0.476485\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.15813e9 | −0.310427 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.97034e9 | −1.84445 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.39107e9 | −0.363407 | −0.181704 | − | 0.983353i | \(-0.558161\pi\) | ||||
−0.181704 | + | 0.983353i | \(0.558161\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.04832e8 | 0.156002 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.17754e9 | −0.299879 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.25632e9 | 1.07028 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.08786e9 | −1.26331 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.95293e9 | 0.969229 | 0.484614 | − | 0.874728i | \(-0.338960\pi\) | ||||
0.484614 | + | 0.874728i | \(0.338960\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.94371e9 | 0.470643 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.91491e9 | 0.936163 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.52515e9 | 0.360191 | 0.180096 | − | 0.983649i | \(-0.442359\pi\) | ||||
0.180096 | + | 0.983649i | \(0.442359\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.31740e9 | −2.17333 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.16371e9 | −0.498492 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.48747e9 | 1.24876 | 0.624381 | − | 0.781120i | \(-0.285351\pi\) | ||||
0.624381 | + | 0.781120i | \(0.285351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.93275e9 | 1.78319 | 0.891595 | − | 0.452834i | \(-0.149587\pi\) | ||||
0.891595 | + | 0.452834i | \(0.149587\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.39291e9 | 0.309302 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.53942e8 | 0.165387 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.64252e9 | −0.789380 | −0.394690 | − | 0.918814i | \(-0.629148\pi\) | ||||
−0.394690 | + | 0.918814i | \(0.629148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.07409e8 | −0.172870 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.70860e9 | −1.20757 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.00626e10 | 2.10315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.02903e9 | 1.86464 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.40965e9 | −0.899850 | −0.449925 | − | 0.893066i | \(-0.648549\pi\) | ||||
−0.449925 | + | 0.893066i | \(0.648549\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.34313e8 | −0.148074 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.18250e8 | 0.163053 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.72019e9 | −1.12647 | −0.563235 | − | 0.826297i | \(-0.690443\pi\) | ||||
−0.563235 | + | 0.826297i | \(0.690443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.40658e10 | 2.73750 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.01874e9 | −0.580651 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.46158e9 | 1.79875 | 0.899373 | − | 0.437182i | \(-0.144023\pi\) | ||||
0.899373 | + | 0.437182i | \(0.144023\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.40265e9 | −0.451470 | −0.225735 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225735 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.65725e9 | −0.679273 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.33037e10 | −2.44246 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.03151e9 | −1.27611 | −0.638055 | − | 0.769991i | \(-0.720261\pi\) | ||||
−0.638055 | + | 0.769991i | \(0.720261\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.58864e9 | 0.643827 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.14983e9 | −0.736015 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.30413e9 | −0.579356 | −0.289678 | − | 0.957124i | \(-0.593548\pi\) | ||||
−0.289678 | + | 0.957124i | \(0.593548\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.69552e8 | −0.0467283 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.23310e9 | 0.211349 | 0.105674 | − | 0.994401i | \(-0.466300\pi\) | ||||
0.105674 | + | 0.994401i | \(0.466300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.23102e9 | 1.56434 | 0.782172 | − | 0.623062i | \(-0.214112\pi\) | ||||
0.782172 | + | 0.623062i | \(0.214112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.55837e8 | −0.0596253 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.05533e10 | −1.74856 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.03870e10 | 1.70180 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.64893e8 | 0.156330 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.36175e10 | 2.18183 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.58497e9 | 1.20185 | 0.600926 | − | 0.799304i | \(-0.294799\pi\) | ||||
0.600926 | + | 0.799304i | \(0.294799\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.79075e9 | −0.594035 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.53005e10 | 2.37136 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.97348e9 | 0.302514 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.65779e9 | −0.554582 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00750e10 | −1.51092 | −0.755459 | − | 0.655196i | \(-0.772586\pi\) | ||||
−0.755459 | + | 0.655196i | \(0.772586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.40961e9 | 0.505785 | 0.252892 | − | 0.967494i | \(-0.418618\pi\) | ||||
0.252892 | + | 0.967494i | \(0.418618\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.97193e9 | −0.289356 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.78057e9 | 0.839085 | 0.419542 | − | 0.907736i | \(-0.362191\pi\) | ||||
0.419542 | + | 0.907736i | \(0.362191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.66322e9 | 0.813218 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.23787e9 | 0.317907 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.34746e9 | 0.892080 | 0.446040 | − | 0.895013i | \(-0.352834\pi\) | ||||
0.446040 | + | 0.895013i | \(0.352834\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.14798e10 | −2.98665 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.50002e9 | 0.481495 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.10542e9 | 0.286576 | 0.143288 | − | 0.989681i | \(-0.454232\pi\) | ||||
0.143288 | + | 0.989681i | \(0.454232\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.50157e9 | −0.471583 | −0.235791 | − | 0.971804i | \(-0.575768\pi\) | ||||
−0.235791 | + | 0.971804i | \(0.575768\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.91468e9 | 0.788195 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.46674e9 | 0.457137 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.46940e8 | −0.0974642 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.39282e8 | −0.108372 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.33529e9 | −0.298409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.06704e9 | −0.387852 | −0.193926 | − | 0.981016i | \(-0.562122\pi\) | ||||
−0.193926 | + | 0.981016i | \(0.562122\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.41726e10 | −1.77372 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.07375e10 | −1.32997 | −0.664984 | − | 0.746858i | \(-0.731562\pi\) | ||||
−0.664984 | + | 0.746858i | \(0.731562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.47007e10 | 1.80216 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.85427e9 | −0.346322 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.34679e10 | 1.61743 | 0.808716 | − | 0.588200i | \(-0.200163\pi\) | ||||
0.808716 | + | 0.588200i | \(0.200163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.84737e10 | 2.19602 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.79195e9 | −0.563850 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.52027e10 | 1.77073 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.06634e10 | 1.22948 | 0.614742 | − | 0.788728i | \(-0.289260\pi\) | ||||
0.614742 | + | 0.788728i | \(0.289260\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.20145e10 | 1.37132 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.59862e10 | −2.93627 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.21450e8 | 0.0807033 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.07217e8 | −0.100471 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.21534e10 | −1.33255 | −0.666275 | − | 0.745707i | \(-0.732112\pi\) | ||||
−0.666275 | + | 0.745707i | \(0.732112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.35626e9 | 0.364344 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.21007e9 | 0.452509 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.09394e8 | −0.0329264 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.57486e9 | 0.798202 | 0.399101 | − | 0.916907i | \(-0.369322\pi\) | ||||
0.399101 | + | 0.916907i | \(0.369322\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.41877e9 | 0.774085 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.65790e8 | −0.0481257 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.48616e10 | −3.56678 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.33169e9 | 0.742826 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.12422e9 | −0.815137 | −0.407569 | − | 0.913175i | \(-0.633623\pi\) | ||||
−0.407569 | + | 0.913175i | \(0.633623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.58767e10 | −1.57757 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.19708e9 | 0.413013 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.97497e10 | −2.89934 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.10999e10 | 1.07140 | 0.535698 | − | 0.844410i | \(-0.320049\pi\) | ||||
0.535698 | + | 0.844410i | \(0.320049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.21877e7 | −0.00594508 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.27781e9 | 0.499739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.18891e10 | −1.11502 | −0.557511 | − | 0.830170i | \(-0.688243\pi\) | ||||
−0.557511 | + | 0.830170i | \(0.688243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.00213e9 | −0.185988 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.41208e10 | 1.29935 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.97595e9 | 0.544693 | 0.272346 | − | 0.962199i | \(-0.412200\pi\) | ||||
0.272346 | + | 0.962199i | \(0.412200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.45777e9 | 0.131621 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.33399e8 | −0.0477080 | −0.0238540 | − | 0.999715i | \(-0.507594\pi\) | ||||
−0.0238540 | + | 0.999715i | \(0.507594\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.18654e10 | 1.93736 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.95010e9 | −0.873384 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.35589e10 | −1.17906 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.50180e9 | −0.387834 | −0.193917 | − | 0.981018i | \(-0.562119\pi\) | ||||
−0.193917 | + | 0.981018i | \(0.562119\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.10628e9 | −0.0944244 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.13907e10 | −1.80888 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.89821e10 | −1.59041 | −0.795204 | − | 0.606342i | \(-0.792636\pi\) | ||||
−0.795204 | + | 0.606342i | \(0.792636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.12052e8 | 0.0508092 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.94728e9 | −0.735944 | −0.367972 | − | 0.929837i | \(-0.619948\pi\) | ||||
−0.367972 | + | 0.929837i | \(0.619948\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.40129e10 | −1.14207 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.45167e10 | 1.97992 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.55605e9 | 0.684683 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.75298e10 | 1.39006 | 0.695031 | − | 0.718979i | \(-0.255390\pi\) | ||||
0.695031 | + | 0.718979i | \(0.255390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.35515e9 | 0.577965 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.24048e10 | 0.965963 | 0.482982 | − | 0.875631i | \(-0.339554\pi\) | ||||
0.482982 | + | 0.875631i | \(0.339554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.85519e10 | −1.43163 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.02284e10 | −0.782231 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.77813e8 | 0.0134767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.41229e10 | 1.06083 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.40409e10 | 1.04527 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.88666e9 | −0.286769 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.69738e9 | −0.270385 | −0.135193 | − | 0.990819i | \(-0.543165\pi\) | ||||
−0.135193 | + | 0.990819i | \(0.543165\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.81879e9 | 0.711686 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.87313e10 | −1.34571 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.52818e9 | −0.251243 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.54234e10 | −1.08866 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.67626e10 | −1.17284 | −0.586419 | − | 0.810008i | \(-0.699463\pi\) | ||||
−0.586419 | + | 0.810008i | \(0.699463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.12681e10 | −0.781517 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.83944e10 | −1.26466 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.35138e10 | −0.921027 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.19903e9 | 0.148575 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.94586e9 | 0.130333 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.30672e9 | 0.551582 | 0.275791 | − | 0.961218i | \(-0.411060\pi\) | ||||
0.275791 | + | 0.961218i | \(0.411060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.35615e10 | 0.892757 | 0.446378 | − | 0.894844i | \(-0.352714\pi\) | ||||
0.446378 | + | 0.894844i | \(0.352714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.94300e9 | 0.453138 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.57650e10 | 2.31423 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.30080e9 | 0.0834516 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.81516e10 | 1.15457 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.43086e9 | 0.279439 | 0.139719 | − | 0.990191i | \(-0.455380\pi\) | ||||
0.139719 | + | 0.990191i | \(0.455380\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.75941e10 | 1.10019 | 0.550095 | − | 0.835102i | \(-0.314591\pi\) | ||||
0.550095 | + | 0.835102i | \(0.314591\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.43773e10 | 1.51146 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.61056e9 | −0.590853 | −0.295427 | − | 0.955365i | \(-0.595462\pi\) | ||||
−0.295427 | + | 0.955365i | \(0.595462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.63344e10 | −1.60540 | −0.802699 | − | 0.596384i | \(-0.796604\pi\) | ||||
−0.802699 | + | 0.596384i | \(0.796604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.48282e9 | −0.150086 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.35864e9 | 0.321216 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.92205e10 | −2.33137 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.75590e9 | 0.516133 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.52726e9 | −0.498474 | −0.249237 | − | 0.968443i | \(-0.580180\pi\) | ||||
−0.249237 | + | 0.968443i | \(0.580180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.22236e10 | 0.708618 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.83388e9 | 0.335398 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.12064e10 | −1.20912 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.67452e10 | −1.51236 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.06795e8 | 0.0172057 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.12895e9 | 0.118416 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.87090e10 | −1.03212 | −0.516058 | − | 0.856554i | \(-0.672601\pi\) | ||||
−0.516058 | + | 0.856554i | \(0.672601\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.04255e9 | 0.330627 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.07860e10 | −0.585367 | −0.292684 | − | 0.956209i | \(-0.594548\pi\) | ||||
−0.292684 | + | 0.956209i | \(0.594548\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.42048e9 | −0.291784 | −0.145892 | − | 0.989301i | \(-0.546605\pi\) | ||||
−0.145892 | + | 0.989301i | \(0.546605\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.41897e8 | −0.0289338 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.53103e8 | 0.0345895 | 0.0172947 | − | 0.999850i | \(-0.494495\pi\) | ||||
0.0172947 | + | 0.999850i | \(0.494495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.75268e10 | 1.44611 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.55106e9 | 0.393496 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.86443e10 | −1.48071 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.13339e10 | 1.09397 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.56234e10 | 1.30343 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.80980e10 | 2.42716 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.04507e10 | −0.523174 | −0.261587 | − | 0.965180i | \(-0.584246\pi\) | ||||
−0.261587 | + | 0.965180i | \(0.584246\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.11044e10 | 0.551485 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.20111e8 | −0.0404070 | −0.0202035 | − | 0.999796i | \(-0.506431\pi\) | ||||
−0.0202035 | + | 0.999796i | \(0.506431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.27244e10 | −1.11079 | −0.555393 | − | 0.831588i | \(-0.687432\pi\) | ||||
−0.555393 | + | 0.831588i | \(0.687432\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.68024e9 | −0.420950 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.09428e9 | −0.293217 | −0.146609 | − | 0.989195i | \(-0.546836\pi\) | ||||
−0.146609 | + | 0.989195i | \(0.546836\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.07596e10 | 1.46833 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.45614e10 | 0.689654 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.77722e9 | −0.130506 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.74899e10 | 1.74797 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.24695e8 | 0.0427784 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.83796e10 | 0.843678 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.12802e10 | 1.88021 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.96428e9 | −0.179167 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.80031e10 | 1.25584 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.41819e9 | 0.196616 | 0.0983080 | − | 0.995156i | \(-0.468657\pi\) | ||||
0.0983080 | + | 0.995156i | \(0.468657\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.39276e8 | −0.0238143 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.45414e8 | −0.0414293 | −0.0207146 | − | 0.999785i | \(-0.506594\pi\) | ||||
−0.0207146 | + | 0.999785i | \(0.506594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.84179e10 | 1.67065 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.57939e9 | 0.154467 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.31821e10 | −1.84931 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.00356e10 | −0.426520 | −0.213260 | − | 0.976995i | \(-0.568408\pi\) | ||||
−0.213260 | + | 0.976995i | \(0.568408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.08528e10 | −0.457754 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.13371e10 | 0.893159 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.47934e10 | 3.52262 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.76732e10 | −1.14099 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.51917e10 | 1.44008 | 0.720038 | − | 0.693935i | \(-0.244125\pi\) | ||||
0.720038 | + | 0.693935i | \(0.244125\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.32073e9 | 0.0536400 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.45465e10 | −0.586371 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.46604e10 | −3.78728 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.89212e10 | 0.751381 | 0.375690 | − | 0.926745i | \(-0.377406\pi\) | ||||
0.375690 | + | 0.926745i | \(0.377406\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.09264e9 | −0.121899 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.63328e10 | 0.638995 | 0.319497 | − | 0.947587i | \(-0.396486\pi\) | ||||
0.319497 | + | 0.947587i | \(0.396486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.12791e8 | 0.00438008 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.13373e10 | −1.59342 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.04581e10 | −1.16541 | −0.582704 | − | 0.812684i | \(-0.698005\pi\) | ||||
−0.582704 | + | 0.812684i | \(0.698005\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.04168e10 | −0.775452 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.58898e9 | 0.361527 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.31953e9 | −0.0868110 | −0.0434055 | − | 0.999058i | \(-0.513821\pi\) | ||||
−0.0434055 | + | 0.999058i | \(0.513821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.36799e10 | −1.25129 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.41509e10 | −0.890722 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.71387e10 | 1.35976 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.60511e10 | −0.583410 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.36332e10 | −0.852767 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.95227e10 | 0.699351 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.94483e10 | −0.691653 | −0.345827 | − | 0.938298i | \(-0.612401\pi\) | ||||
−0.345827 | + | 0.938298i | \(0.612401\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.95831e9 | 0.139758 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.73991e10 | −1.66151 | −0.830755 | − | 0.556638i | \(-0.812091\pi\) | ||||
−0.830755 | + | 0.556638i | \(0.812091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.22417e10 | −1.81812 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.68295e10 | 1.27256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.15960e10 | −0.740871 | −0.370436 | − | 0.928858i | \(-0.620792\pi\) | ||||
−0.370436 | + | 0.928858i | \(0.620792\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.10219e10 | 2.41910 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.44245e10 | −0.826009 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.36016e10 | −1.12829 | −0.564147 | − | 0.825674i | \(-0.690795\pi\) | ||||
−0.564147 | + | 0.825674i | \(0.690795\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.97849e10 | −0.659639 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.46376e9 | 0.280190 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.25128e8 | 0.0271228 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.87751e10 | 1.26560 | 0.632799 | − | 0.774316i | \(-0.281906\pi\) | ||||
0.632799 | + | 0.774316i | \(0.281906\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.85852e9 | 0.254694 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.29915e10 | 2.34905 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.57638e9 | −0.210162 | −0.105081 | − | 0.994464i | \(-0.533510\pi\) | ||||
−0.105081 | + | 0.994464i | \(0.533510\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.00199e10 | −1.26998 |
(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 | 76.8.a.b.1.4 | ✓ | 6 | |
4.3 | odd | 2 | 304.8.a.i.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.a.b.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
304.8.a.i.1.3 | 6 | 4.3 | odd | 2 |