Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,12,Mod(1,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.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: | \(193.622481501\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 7264685 x^{4} + 1525918007 x^{3} + 9975646206208 x^{2} + 929027169420686 x - 10\!\cdots\!80 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{8}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(290.010\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10562.7 | 1.51161 | 0.755807 | − | 0.654794i | \(-0.227245\pi\) | ||||
0.755807 | + | 0.654794i | \(0.227245\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16807.0 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −487870. | −0.913366 | −0.456683 | − | 0.889630i | \(-0.650963\pi\) | ||||
−0.456683 | + | 0.889630i | \(0.650963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −29411.3 | −0.0219698 | −0.0109849 | − | 0.999940i | \(-0.503497\pi\) | ||||
−0.0109849 | + | 0.999940i | \(0.503497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.33196e6 | 0.398338 | 0.199169 | − | 0.979965i | \(-0.436176\pi\) | ||||
0.199169 | + | 0.979965i | \(0.436176\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94204e6 | −0.179934 | −0.0899671 | − | 0.995945i | \(-0.528676\pi\) | ||||
−0.0899671 | + | 0.995945i | \(0.528676\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.87855e7 | 0.608583 | 0.304291 | − | 0.952579i | \(-0.401580\pi\) | ||||
0.304291 | + | 0.952579i | \(0.401580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.27431e7 | 1.28498 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.99877e7 | 0.180956 | 0.0904780 | − | 0.995898i | \(-0.471161\pi\) | ||||
0.0904780 | + | 0.995898i | \(0.471161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43126e8 | −1.52525 | −0.762625 | − | 0.646841i | \(-0.776090\pi\) | ||||
−0.762625 | + | 0.646841i | \(0.776090\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.77528e8 | −0.571337 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.32206e8 | 1.26174 | 0.630871 | − | 0.775888i | \(-0.282698\pi\) | ||||
0.630871 | + | 0.775888i | \(0.282698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.90556e8 | −1.20047 | −0.600234 | − | 0.799825i | \(-0.704926\pi\) | ||||
−0.600234 | + | 0.799825i | \(0.704926\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.15347e8 | 0.534593 | 0.267297 | − | 0.963614i | \(-0.413870\pi\) | ||||
0.267297 | + | 0.963614i | \(0.413870\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.38113e9 | −1.51442 | −0.757208 | − | 0.653174i | \(-0.773437\pi\) | ||||
−0.757208 | + | 0.653174i | \(0.773437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.82475e8 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.59935e9 | −1.18224 | −0.591122 | − | 0.806582i | \(-0.701315\pi\) | ||||
−0.591122 | + | 0.806582i | \(0.701315\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.15324e9 | −1.38066 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.83221e9 | −0.879953 | −0.439977 | − | 0.898009i | \(-0.645013\pi\) | ||||
−0.439977 | + | 0.898009i | \(0.645013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.98288e9 | 0.452191 | 0.226095 | − | 0.974105i | \(-0.427404\pi\) | ||||
0.226095 | + | 0.974105i | \(0.427404\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.10664e8 | −0.0332098 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.87198e10 | 1.69390 | 0.846952 | − | 0.531669i | \(-0.178435\pi\) | ||||
0.846952 | + | 0.531669i | \(0.178435\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.13149e9 | −0.337538 | −0.168769 | − | 0.985656i | \(-0.553979\pi\) | ||||
−0.168769 | + | 0.985656i | \(0.553979\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.28191e10 | −1.85290 | −0.926449 | − | 0.376421i | \(-0.877155\pi\) | ||||
−0.926449 | + | 0.376421i | \(0.877155\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.19964e9 | 0.345220 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.03185e10 | −0.742920 | −0.371460 | − | 0.928449i | \(-0.621143\pi\) | ||||
−0.371460 | + | 0.928449i | \(0.621143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.70301e10 | −0.474557 | −0.237278 | − | 0.971442i | \(-0.576255\pi\) | ||||
−0.237278 | + | 0.971442i | \(0.576255\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.46318e10 | 0.602133 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.06379e10 | 0.771412 | 0.385706 | − | 0.922622i | \(-0.373958\pi\) | ||||
0.385706 | + | 0.922622i | \(0.373958\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.94316e8 | 0.00830380 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.05133e10 | −0.271991 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.26360e10 | 1.09531 | 0.547653 | − | 0.836706i | \(-0.315522\pi\) | ||||
0.547653 | + | 0.836706i | \(0.315522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.55048e11 | 1.46791 | 0.733953 | − | 0.679200i | \(-0.237673\pi\) | ||||
0.733953 | + | 0.679200i | \(0.237673\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.00875e11 | −0.857393 | −0.428697 | − | 0.903448i | \(-0.641027\pi\) | ||||
−0.428697 | + | 0.903448i | \(0.641027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.05859e11 | 0.729655 | 0.364828 | − | 0.931075i | \(-0.381128\pi\) | ||||
0.364828 | + | 0.931075i | \(0.381128\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.06411e11 | −0.662431 | −0.331215 | − | 0.943555i | \(-0.607459\pi\) | ||||
−0.331215 | + | 0.943555i | \(0.607459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.46301e11 | 0.746990 | 0.373495 | − | 0.927632i | \(-0.378159\pi\) | ||||
0.373495 | + | 0.927632i | \(0.378159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.98426e11 | 0.919942 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.91932e10 | −0.150558 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.72941e10 | −0.165763 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.46980e11 | 0.430778 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.82386e10 | −0.156419 | −0.0782096 | − | 0.996937i | \(-0.524920\pi\) | ||||
−0.0782096 | + | 0.996937i | \(0.524920\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.70533e11 | −0.386203 | −0.193102 | − | 0.981179i | \(-0.561855\pi\) | ||||
−0.193102 | + | 0.981179i | \(0.561855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.26399e10 | 0.0680087 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.50175e11 | −1.15098 | −0.575489 | − | 0.817810i | \(-0.695188\pi\) | ||||
−0.575489 | + | 0.817810i | \(0.695188\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.50597e11 | −1.22695 | −0.613473 | − | 0.789715i | \(-0.710228\pi\) | ||||
−0.613473 | + | 0.789715i | \(0.710228\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.43489e10 | 0.0200664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.11124e11 | 0.273536 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.55556e11 | −0.173525 | −0.0867627 | − | 0.996229i | \(-0.527652\pi\) | ||||
−0.0867627 | + | 0.996229i | \(0.527652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.73262e11 | −0.801592 | −0.400796 | − | 0.916167i | \(-0.631266\pi\) | ||||
−0.400796 | + | 0.916167i | \(0.631266\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.56807e12 | −2.30559 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.08932e11 | −0.258473 | −0.129236 | − | 0.991614i | \(-0.541253\pi\) | ||||
−0.129236 | + | 0.991614i | \(0.541253\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.15728e11 | −0.230023 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.52668e11 | 0.512356 | 0.256178 | − | 0.966630i | \(-0.417537\pi\) | ||||
0.256178 | + | 0.966630i | \(0.417537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.64430e11 | −0.455404 | −0.227702 | − | 0.973731i | \(-0.573121\pi\) | ||||
−0.227702 | + | 0.973731i | \(0.573121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.79130e12 | −0.999517 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.24546e12 | 0.611047 | 0.305524 | − | 0.952185i | \(-0.401169\pi\) | ||||
0.305524 | + | 0.952185i | \(0.401169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.05452e12 | −0.485676 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.51610e11 | −0.102338 | −0.0511690 | − | 0.998690i | \(-0.516295\pi\) | ||||
−0.0511690 | + | 0.998690i | \(0.516295\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.73790e11 | −0.143020 | −0.0715098 | − | 0.997440i | \(-0.522782\pi\) | ||||
−0.0715098 | + | 0.997440i | \(0.522782\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.62155e12 | 1.90727 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.13769e12 | −0.363828 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.55209e12 | 0.726461 | 0.363230 | − | 0.931699i | \(-0.381674\pi\) | ||||
0.363230 | + | 0.931699i | \(0.381674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.17515e12 | 0.853490 | 0.426745 | − | 0.904372i | \(-0.359660\pi\) | ||||
0.426745 | + | 0.904372i | \(0.359660\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.90882e11 | 0.213922 | 0.106961 | − | 0.994263i | \(-0.465888\pi\) | ||||
0.106961 | + | 0.994263i | \(0.465888\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.79997e12 | −1.31745 | −0.658725 | − | 0.752384i | \(-0.728904\pi\) | ||||
−0.658725 | + | 0.752384i | \(0.728904\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.35933e11 | −0.0683950 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.40671e12 | −1.81464 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.47465e11 | 0.164346 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.07644e11 | −0.116483 | −0.0582413 | − | 0.998303i | \(-0.518549\pi\) | ||||
−0.0582413 | + | 0.998303i | \(0.518549\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.44347e12 | 0.808099 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.08621e12 | 0.576491 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.85859e10 | −0.00875139 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.96653e10 | −0.00967370 | −0.00483685 | − | 0.999988i | \(-0.501540\pi\) | ||||
−0.00483685 | + | 0.999988i | \(0.501540\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.07241e13 | −1.18092 | −0.590460 | − | 0.807067i | \(-0.701053\pi\) | ||||
−0.590460 | + | 0.807067i | \(0.701053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.48664e13 | −1.55995 | −0.779974 | − | 0.625812i | \(-0.784768\pi\) | ||||
−0.779974 | + | 0.625812i | \(0.784768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50195e13 | 1.43284 | 0.716421 | − | 0.697668i | \(-0.245779\pi\) | ||||
0.716421 | + | 0.697668i | \(0.245779\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.51512e13 | −2.28921 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.98552e13 | −1.64697 | −0.823486 | − | 0.567336i | \(-0.807974\pi\) | ||||
−0.823486 | + | 0.567336i | \(0.807974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.51467e12 | −0.436944 | −0.218472 | − | 0.975843i | \(-0.570107\pi\) | ||||
−0.218472 | + | 0.975843i | \(0.570107\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.98371e12 | 0.215945 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.71180e10 | 0.00395311 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.70789e11 | 0.0488349 | 0.0244174 | − | 0.999702i | \(-0.492227\pi\) | ||||
0.0244174 | + | 0.999702i | \(0.492227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.16489e12 | −0.555858 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.35879e13 | 0.755996 | 0.377998 | − | 0.925806i | \(-0.376613\pi\) | ||||
0.377998 | + | 0.925806i | \(0.376613\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.94479e12 | −0.476894 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.30882e13 | −1.13145 | −0.565723 | − | 0.824595i | \(-0.691403\pi\) | ||||
−0.565723 | + | 0.824595i | \(0.691403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.80190e13 | −1.78710 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.20663e12 | −0.398532 | −0.199266 | − | 0.979945i | \(-0.563856\pi\) | ||||
−0.199266 | + | 0.979945i | \(0.563856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.03206e12 | 0.126010 | 0.0630052 | − | 0.998013i | \(-0.479932\pi\) | ||||
0.0630052 | + | 0.998013i | \(0.479932\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.06105e13 | −1.17366 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.01089e12 | −0.0740882 | −0.0370441 | − | 0.999314i | \(-0.511794\pi\) | ||||
−0.0370441 | + | 0.999314i | \(0.511794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.74313e13 | −1.27453 | −0.637265 | − | 0.770645i | \(-0.719934\pi\) | ||||
−0.637265 | + | 0.770645i | \(0.719934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.78019e13 | −0.582963 | −0.291482 | − | 0.956576i | \(-0.594148\pi\) | ||||
−0.291482 | + | 0.956576i | \(0.594148\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.49676e13 | 0.453734 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.88339e13 | −0.841327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.73563e13 | 1.01063 | 0.505315 | − | 0.862935i | \(-0.331376\pi\) | ||||
0.505315 | + | 0.862935i | \(0.331376\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.10413e13 | −1.33015 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.52506e11 | −0.0133704 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.66144e12 | −0.202057 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.15074e13 | 0.683538 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.02676e13 | −0.424172 | −0.212086 | − | 0.977251i | \(-0.568026\pi\) | ||||
−0.212086 | + | 0.977251i | \(0.568026\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.66339e13 | −1.29871 | −0.649357 | − | 0.760484i | \(-0.724962\pi\) | ||||
−0.649357 | + | 0.760484i | \(0.724962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.07089e13 | −0.954092 | −0.477046 | − | 0.878878i | \(-0.658293\pi\) | ||||
−0.477046 | + | 0.878878i | \(0.658293\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.79440e13 | 0.665760 | 0.332880 | − | 0.942969i | \(-0.391980\pi\) | ||||
0.332880 | + | 0.942969i | \(0.391980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.75139e12 | −0.165279 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.52876e12 | −0.0716746 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.84536e12 | −0.0282307 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00197e13 | 0.572395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.71251e13 | −0.790266 | −0.395133 | − | 0.918624i | \(-0.629301\pi\) | ||||
−0.395133 | + | 0.918624i | \(0.629301\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.97732e14 | 2.56053 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.13875e13 | −0.894659 | −0.447330 | − | 0.894369i | \(-0.647625\pi\) | ||||
−0.447330 | + | 0.894369i | \(0.647625\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.18614e14 | 1.39311 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.74756e12 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.75474e12 | 0.0293946 | 0.0146973 | − | 0.999892i | \(-0.495322\pi\) | ||||
0.0146973 | + | 0.999892i | \(0.495322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.66638e13 | −0.172279 | −0.0861396 | − | 0.996283i | \(-0.527453\pi\) | ||||
−0.0861396 | + | 0.996283i | \(0.527453\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.35893e14 | −1.31958 | −0.659792 | − | 0.751448i | \(-0.729356\pi\) | ||||
−0.659792 | + | 0.751448i | \(0.729356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.42026e13 | −0.510228 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.49245e14 | 1.32093 | 0.660464 | − | 0.750857i | \(-0.270359\pi\) | ||||
0.660464 | + | 0.750857i | \(0.270359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.12719e14 | −0.967624 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.46660e14 | −2.80087 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.96772e14 | −1.54277 | −0.771384 | − | 0.636370i | \(-0.780435\pi\) | ||||
−0.771384 | + | 0.636370i | \(0.780435\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.04943e13 | 0.446846 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.25191e13 | 0.304920 | 0.152460 | − | 0.988310i | \(-0.451281\pi\) | ||||
0.152460 | + | 0.988310i | \(0.451281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.87863e11 | −0.00397556 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.41365e14 | 1.58547 | 0.792736 | − | 0.609565i | \(-0.208656\pi\) | ||||
0.792736 | + | 0.609565i | \(0.208656\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.74375e14 | 1.08116 | 0.540580 | − | 0.841293i | \(-0.318205\pi\) | ||||
0.540580 | + | 0.841293i | \(0.318205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.66106e13 | 0.521839 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.64981e14 | −1.50831 | −0.754157 | − | 0.656694i | \(-0.771954\pi\) | ||||
−0.754157 | + | 0.656694i | \(0.771954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.38070e13 | 0.242421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.14619e14 | −1.12301 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.99270e12 | −0.0152305 | −0.00761526 | − | 0.999971i | \(-0.502424\pi\) | ||||
−0.00761526 | + | 0.999971i | \(0.502424\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.45178e14 | −0.699210 | −0.349605 | − | 0.936897i | \(-0.613684\pi\) | ||||
−0.349605 | + | 0.936897i | \(0.613684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.15064e12 | 0.0335094 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.59648e14 | −1.15243 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.63187e14 | 0.705028 | 0.352514 | − | 0.935807i | \(-0.385327\pi\) | ||||
0.352514 | + | 0.935807i | \(0.385327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.12149e13 | 0.332591 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.79884e14 | −0.717347 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.42018e13 | −0.242868 | −0.121434 | − | 0.992600i | \(-0.538749\pi\) | ||||
−0.121434 | + | 0.992600i | \(0.538749\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.49920e14 | −0.552471 | −0.276236 | − | 0.961090i | \(-0.589087\pi\) | ||||
−0.276236 | + | 0.961090i | \(0.589087\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.46314e14 | 0.511856 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.01333e13 | −0.170912 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.60524e14 | 0.519895 | 0.259948 | − | 0.965623i | \(-0.416295\pi\) | ||||
0.259948 | + | 0.965623i | \(0.416295\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.26688e13 | 0.292584 | 0.146292 | − | 0.989241i | \(-0.453266\pi\) | ||||
0.146292 | + | 0.989241i | \(0.453266\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.64822e13 | −0.109505 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.60669e14 | 1.05573 | 0.527866 | − | 0.849327i | \(-0.322992\pi\) | ||||
0.527866 | + | 0.849327i | \(0.322992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.41959e14 | 1.23073 | 0.615363 | − | 0.788244i | \(-0.289009\pi\) | ||||
0.615363 | + | 0.788244i | \(0.289009\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.29247e14 | 1.16608 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.20805e14 | −1.60546 | −0.802731 | − | 0.596341i | \(-0.796621\pi\) | ||||
−0.802731 | + | 0.596341i | \(0.796621\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.34476e14 | 1.09647 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.22132e12 | 0.0125521 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.38797e14 | 1.73375 | 0.866874 | − | 0.498528i | \(-0.166126\pi\) | ||||
0.866874 | + | 0.498528i | \(0.166126\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.86457e14 | 1.08815 | 0.544076 | − | 0.839036i | \(-0.316880\pi\) | ||||
0.544076 | + | 0.839036i | \(0.316880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.98986e14 | −0.871490 | −0.435745 | − | 0.900070i | \(-0.643515\pi\) | ||||
−0.435745 | + | 0.900070i | \(0.643515\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.15156e14 | 1.90657 | 0.953284 | − | 0.302077i | \(-0.0976799\pi\) | ||||
0.953284 | + | 0.302077i | \(0.0976799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.14623e14 | −0.640236 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.51423e14 | −0.488279 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.21850e14 | −0.231212 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.92244e13 | 0.143553 | 0.0717767 | − | 0.997421i | \(-0.477133\pi\) | ||||
0.0717767 | + | 0.997421i | \(0.477133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.56529e13 | −0.0277202 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.78489e14 | 1.65568 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.18996e14 | 0.693108 | 0.346554 | − | 0.938030i | \(-0.387352\pi\) | ||||
0.346554 | + | 0.938030i | \(0.387352\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.06855e15 | −1.68984 | −0.844922 | − | 0.534890i | \(-0.820353\pi\) | ||||
−0.844922 | + | 0.534890i | \(0.820353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.66104e13 | 0.0720816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.62450e13 | 0.127577 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.81718e14 | 0.407626 | 0.203813 | − | 0.979010i | \(-0.434667\pi\) | ||||
0.203813 | + | 0.979010i | \(0.434667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.62474e14 | 1.33280 | 0.666400 | − | 0.745594i | \(-0.267834\pi\) | ||||
0.666400 | + | 0.745594i | \(0.267834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.63773e15 | 2.21891 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.47837e14 | −0.451261 | −0.225630 | − | 0.974213i | \(-0.572444\pi\) | ||||
−0.225630 | + | 0.974213i | \(0.572444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.51591e14 | 0.700329 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.06552e15 | −1.29605 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.16168e15 | 1.38322 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.00284e15 | 1.14452 | 0.572260 | − | 0.820072i | \(-0.306067\pi\) | ||||
0.572260 | + | 0.820072i | \(0.306067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.13233e14 | 0.461781 | 0.230891 | − | 0.972980i | \(-0.425836\pi\) | ||||
0.230891 | + | 0.972980i | \(0.425836\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.66958e14 | −0.607565 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.99915e14 | −0.629627 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.61924e13 | 0.0263740 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.11816e15 | 1.10296 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.37811e14 | −0.130481 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.18938e14 | −0.481427 | −0.240714 | − | 0.970596i | \(-0.577381\pi\) | ||||
−0.240714 | + | 0.970596i | \(0.577381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.12399e15 | −1.00134 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.07863e14 | 0.268799 | 0.134399 | − | 0.990927i | \(-0.457090\pi\) | ||||
0.134399 | + | 0.990927i | \(0.457090\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.88169e13 | −0.0325602 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.41493e14 | 0.280797 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.54386e15 | 1.22012 | 0.610061 | − | 0.792354i | \(-0.291145\pi\) | ||||
0.610061 | + | 0.792354i | \(0.291145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.51570e13 | −0.0117449 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.19701e15 | −0.891872 | −0.445936 | − | 0.895065i | \(-0.647129\pi\) | ||||
−0.445936 | + | 0.895065i | \(0.647129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.54533e15 | 1.12916 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.82173e15 | −1.28046 | −0.640231 | − | 0.768182i | \(-0.721161\pi\) | ||||
−0.640231 | + | 0.768182i | \(0.721161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.09310e15 | 0.753639 | 0.376819 | − | 0.926287i | \(-0.377018\pi\) | ||||
0.376819 | + | 0.926287i | \(0.377018\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.17866e15 | 0.782016 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.41570e14 | −0.482709 | −0.241354 | − | 0.970437i | \(-0.577592\pi\) | ||||
−0.241354 | + | 0.970437i | \(0.577592\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.86225e14 | 0.179366 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.75602e15 | 1.07982 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.43620e15 | −0.850561 | −0.425280 | − | 0.905062i | \(-0.639824\pi\) | ||||
−0.425280 | + | 0.905062i | \(0.639824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.72160e14 | 0.274445 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.33066e15 | −0.745189 | −0.372595 | − | 0.927994i | \(-0.621532\pi\) | ||||
−0.372595 | + | 0.927994i | \(0.621532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.13987e14 | −0.227585 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.13669e15 | −1.13212 | −0.566062 | − | 0.824362i | \(-0.691534\pi\) | ||||
−0.566062 | + | 0.824362i | \(0.691534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.37107e14 | 0.435483 | 0.217742 | − | 0.976006i | \(-0.430131\pi\) | ||||
0.217742 | + | 0.976006i | \(0.430131\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.99555e14 | −0.250570 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.23824e15 | −1.59504 | −0.797519 | − | 0.603293i | \(-0.793855\pi\) | ||||
−0.797519 | + | 0.603293i | \(0.793855\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.00322e13 | 0.0332714 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00991e15 | 0.937871 | 0.468935 | − | 0.883232i | \(-0.344638\pi\) | ||||
0.468935 | + | 0.883232i | \(0.344638\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.29759e15 | 1.03444 | 0.517219 | − | 0.855853i | \(-0.326967\pi\) | ||||
0.517219 | + | 0.855853i | \(0.326967\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.32881e15 | −0.587713 | −0.293856 | − | 0.955850i | \(-0.594939\pi\) | ||||
−0.293856 | + | 0.955850i | \(0.594939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.83001e14 | −0.291566 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.51112e15 | −0.633808 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.24108e15 | 0.502600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.69942e15 | −0.676301 | −0.338150 | − | 0.941092i | \(-0.609801\pi\) | ||||
−0.338150 | + | 0.941092i | \(0.609801\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.15158e14 | −0.236446 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.30796e12 | −0.00313854 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.41351e15 | 1.24590 | 0.622949 | − | 0.782262i | \(-0.285934\pi\) | ||||
0.622949 | + | 0.782262i | \(0.285934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.41457e14 | 0.194269 | 0.0971345 | − | 0.995271i | \(-0.469032\pi\) | ||||
0.0971345 | + | 0.995271i | \(0.469032\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.42396e15 | 0.493770 | 0.246885 | − | 0.969045i | \(-0.420593\pi\) | ||||
0.246885 | + | 0.969045i | \(0.420593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.35749e15 | 0.803719 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.53010e15 | 1.16349 | 0.581747 | − | 0.813370i | \(-0.302369\pi\) | ||||
0.581747 | + | 0.813370i | \(0.302369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.80129e15 | −0.583791 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.83382e15 | 1.82845 | 0.914225 | − | 0.405207i | \(-0.132800\pi\) | ||||
0.914225 | + | 0.405207i | \(0.132800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.74739e15 | 0.846861 | 0.423431 | − | 0.905929i | \(-0.360826\pi\) | ||||
0.423431 | + | 0.905929i | \(0.360826\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.44766e14 | 0.102803 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.75478e14 | 0.110127 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.45526e15 | −0.413016 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.72553e15 | −1.04017 | −0.520086 | − | 0.854114i | \(-0.674100\pi\) | ||||
−0.520086 | + | 0.854114i | \(0.674100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.03218e15 | −0.549193 | −0.274597 | − | 0.961559i | \(-0.588544\pi\) | ||||
−0.274597 | + | 0.961559i | \(0.588544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.55693e15 | −0.413986 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.40117e15 | 1.39051 | 0.695255 | − | 0.718763i | \(-0.255291\pi\) | ||||
0.695255 | + | 0.718763i | \(0.255291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.86762e15 | −1.73983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.05862e14 | 0.0259736 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.49176e14 | 0.108464 | 0.0542322 | − | 0.998528i | \(-0.482729\pi\) | ||||
0.0542322 | + | 0.998528i | \(0.482729\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.92836e15 | −1.85467 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.07674e15 | −0.478191 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.88883e15 | 1.53708 | 0.768539 | − | 0.639803i | \(-0.220984\pi\) | ||||
0.768539 | + | 0.639803i | \(0.220984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.03357e15 | −0.227031 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.60589e15 | −0.554817 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.44603e15 | 0.303125 | 0.151562 | − | 0.988448i | \(-0.451570\pi\) | ||||
0.151562 | + | 0.988448i | \(0.451570\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.56723e15 | −0.928241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.51564e14 | 0.0303327 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.17402e15 | −1.19828 | −0.599141 | − | 0.800643i | \(-0.704491\pi\) | ||||
−0.599141 | + | 0.800643i | \(0.704491\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.69541e15 | 0.324064 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.25409e15 | 0.232525 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.67029e15 | −0.670287 | −0.335144 | − | 0.942167i | \(-0.608785\pi\) | ||||
−0.335144 | + | 0.942167i | \(0.608785\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.20177e15 | 0.212949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.92773e15 | −1.03470 | −0.517352 | − | 0.855773i | \(-0.673082\pi\) | ||||
−0.517352 | + | 0.855773i | \(0.673082\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.13282e15 | −1.54715 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.79229e15 | −1.63433 | −0.817165 | − | 0.576403i | \(-0.804456\pi\) | ||||
−0.817165 | + | 0.576403i | \(0.804456\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.62273e15 | 0.910980 | 0.455490 | − | 0.890241i | \(-0.349464\pi\) | ||||
0.455490 | + | 0.890241i | \(0.349464\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.64310e15 | −0.262303 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.77918e15 | −0.275784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.92348e15 | −1.51581 | −0.757904 | − | 0.652366i | \(-0.773777\pi\) | ||||
−0.757904 | + | 0.652366i | \(0.773777\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.16776e15 | −1.21170 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.43579e15 | 0.356134 | 0.178067 | − | 0.984018i | \(-0.443016\pi\) | ||||
0.178067 | + | 0.984018i | \(0.443016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.18798e16 | −1.68731 | −0.843655 | − | 0.536886i | \(-0.819601\pi\) | ||||
−0.843655 | + | 0.536886i | \(0.819601\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.78845e15 | 0.250375 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.42122e14 | 0.0193324 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.87658e15 | 1.19028 | 0.595142 | − | 0.803621i | \(-0.297096\pi\) | ||||
0.595142 | + | 0.803621i | \(0.297096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.63183e15 | 1.12491 | 0.562453 | − | 0.826830i | \(-0.309858\pi\) | ||||
0.562453 | + | 0.826830i | \(0.309858\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.52544e16 | −1.95991 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.72950e15 | 0.216005 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.50350e15 | 0.308296 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.26316e15 | −0.390711 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.60940e16 | −1.90021 | −0.950107 | − | 0.311923i | \(-0.899027\pi\) | ||||
−0.950107 | + | 0.311923i | \(0.899027\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.45888e15 | −0.282336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.77304e13 | −0.00993454 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.12583e15 | 0.124008 | 0.0620042 | − | 0.998076i | \(-0.480251\pi\) | ||||
0.0620042 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.55270e15 | −0.603249 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.60115e16 | 1.69237 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.33495e15 | −0.347705 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.65264e16 | −1.67673 | −0.838363 | − | 0.545112i | \(-0.816487\pi\) | ||||
−0.838363 | + | 0.545112i | \(0.816487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.72460e15 | −0.572968 | −0.286484 | − | 0.958085i | \(-0.592487\pi\) | ||||
−0.286484 | + | 0.958085i | \(0.592487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.95023e15 | 0.774484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.00083e15 | −0.0961916 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.36110e16 | 1.27351 | 0.636756 | − | 0.771066i | \(-0.280276\pi\) | ||||
0.636756 | + | 0.771066i | \(0.280276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.12527e15 | 0.842455 | 0.421228 | − | 0.906955i | \(-0.361599\pi\) | ||||
0.421228 | + | 0.906955i | \(0.361599\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.09672e15 | 0.637936 | 0.318968 | − | 0.947765i | \(-0.396664\pi\) | ||||
0.318968 | + | 0.947765i | \(0.396664\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.15670e15 | 0.634838 | 0.317419 | − | 0.948285i | \(-0.397184\pi\) | ||||
0.317419 | + | 0.948285i | \(0.397184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.58720e14 | 0.0569054 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.07446e15 | −0.688396 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.67038e15 | 0.553937 | 0.276968 | − | 0.960879i | \(-0.410670\pi\) | ||||
0.276968 | + | 0.960879i | \(0.410670\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.18010e16 | −0.967255 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.89210e16 | −1.51089 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.94872e14 | 0.0626525 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.99776e15 | 0.767874 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.37743e16 | −1.04436 | −0.522179 | − | 0.852836i | \(-0.674881\pi\) | ||||
−0.522179 | + | 0.852836i | \(0.674881\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.39602e15 | 0.620410 | 0.310205 | − | 0.950670i | \(-0.399602\pi\) | ||||
0.310205 | + | 0.950670i | \(0.399602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.86860e16 | 1.36318 | 0.681590 | − | 0.731735i | \(-0.261289\pi\) | ||||
0.681590 | + | 0.731735i | \(0.261289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.08199e15 | 0.219165 | 0.109583 | − | 0.993978i | \(-0.465049\pi\) | ||||
0.109583 | + | 0.993978i | \(0.465049\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.31554e16 | 0.923668 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.91278e15 | 0.678558 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.50572e14 | −0.0372147 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.47030e15 | −0.162819 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.60620e16 | 1.04545 | 0.522723 | − | 0.852503i | \(-0.324916\pi\) | ||||
0.522723 | + | 0.852503i | \(0.324916\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.82581e16 | −1.15901 | −0.579507 | − | 0.814967i | \(-0.696755\pi\) | ||||
−0.579507 | + | 0.814967i | \(0.696755\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.43785e15 | −0.528990 | −0.264495 | − | 0.964387i | \(-0.585205\pi\) | ||||
−0.264495 | + | 0.964387i | \(0.585205\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.34139e16 | 1.43184 | 0.715920 | − | 0.698182i | \(-0.246007\pi\) | ||||
0.715920 | + | 0.698182i | \(0.246007\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.78816e14 | 0.0591209 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.62426e15 | 0.272495 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.65769e15 | −0.154696 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.85951e15 | −0.276003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.39354e15 | −0.470933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.94824e15 | −0.216191 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.56483e16 | −1.38745 | −0.693726 | − | 0.720239i | \(-0.744032\pi\) | ||||
−0.693726 | + | 0.720239i | \(0.744032\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.30075e15 | −0.438295 | −0.219147 | − | 0.975692i | \(-0.570328\pi\) | ||||
−0.219147 | + | 0.975692i | \(0.570328\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.30849e15 | 0.433444 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.86615e15 | 0.145971 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.44710e15 | 0.324436 | 0.162218 | − | 0.986755i | \(-0.448135\pi\) | ||||
0.162218 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.50924e14 | 0.00741564 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.33923e16 | 1.62131 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.04782e15 | −0.0496822 | −0.0248411 | − | 0.999691i | \(-0.507908\pi\) | ||||
−0.0248411 | + | 0.999691i | \(0.507908\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.48579e14 | −0.0257049 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.20171e16 | −0.549968 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.72463e16 | 1.23237 | 0.616184 | − | 0.787602i | \(-0.288678\pi\) | ||||
0.616184 | + | 0.787602i | \(0.288678\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.22733e16 | 0.542271 | 0.271136 | − | 0.962541i | \(-0.412601\pi\) | ||||
0.271136 | + | 0.962541i | \(0.412601\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.67295e16 | −0.730583 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.45969e15 | −0.360936 | −0.180468 | − | 0.983581i | \(-0.557761\pi\) | ||||
−0.180468 | + | 0.983581i | \(0.557761\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.65253e14 | 0.0407077 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.57712e16 | −1.88617 | −0.943086 | − | 0.332549i | \(-0.892091\pi\) | ||||
−0.943086 | + | 0.332549i | \(0.892091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.69570e16 | 1.09813 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.09275e16 | 0.435029 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.37015e16 | 1.32639 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.35382e16 | 1.29015 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.46356e16 | −0.556629 | −0.278314 | − | 0.960490i | \(-0.589776\pi\) | ||||
−0.278314 | + | 0.960490i | \(0.589776\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.30470e15 | −0.197222 | −0.0986109 | − | 0.995126i | \(-0.531440\pi\) | ||||
−0.0986109 | + | 0.995126i | \(0.531440\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.26153e16 | 0.463742 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.46828e16 | −0.527701 | −0.263850 | − | 0.964564i | \(-0.584993\pi\) | ||||
−0.263850 | + | 0.964564i | \(0.584993\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.98260e16 | −0.704581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.59170e16 | −1.94312 | −0.971560 | − | 0.236794i | \(-0.923904\pi\) | ||||
−0.971560 | + | 0.236794i | \(0.923904\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.41014e15 | 0.323368 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.68105e15 | 0.325344 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.28712e16 | 0.760122 | 0.380061 | − | 0.924961i | \(-0.375903\pi\) | ||||
0.380061 | + | 0.924961i | \(0.375903\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.12635e16 | −1.99148 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.80843e16 | 0.902901 | 0.451450 | − | 0.892296i | \(-0.350907\pi\) | ||||
0.451450 | + | 0.892296i | \(0.350907\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.12.a.h.1.6 | yes | 6 | |
3.2 | odd | 2 | inner | 252.12.a.h.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.12.a.h.1.1 | ✓ | 6 | 3.2 | odd | 2 | inner | |
252.12.a.h.1.6 | yes | 6 | 1.1 | even | 1 | trivial |