Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,38,Mod(1,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.1");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(34.6856152498\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 134608389910x + 8010664803252592 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{5}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(61215.0\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.1 |
$q$-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 | ||||||||
\(3\) | −2.31760e8 | −0.345378 | −0.172689 | − | 0.984976i | \(-0.555246\pi\) | ||||
−0.172689 | + | 0.984976i | \(0.555246\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.08025e13 | −1.26642 | −0.633211 | − | 0.773979i | \(-0.718263\pi\) | ||||
−0.633211 | + | 0.773979i | \(0.718263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.54986e15 | −1.05605 | −0.528025 | − | 0.849229i | \(-0.677067\pi\) | ||||
−0.528025 | + | 0.849229i | \(0.677067\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.96571e17 | −0.880714 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.61802e19 | 0.877444 | 0.438722 | − | 0.898623i | \(-0.355431\pi\) | ||||
0.438722 | + | 0.898623i | \(0.355431\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.66947e20 | −1.39827 | −0.699134 | − | 0.714991i | \(-0.746431\pi\) | ||||
−0.699134 | + | 0.714991i | \(0.746431\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.50358e21 | 0.437394 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.03513e21 | −0.0350983 | −0.0175492 | − | 0.999846i | \(-0.505586\pi\) | ||||
−0.0175492 | + | 0.999846i | \(0.505586\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44505e22 | 0.0538699 | 0.0269350 | − | 0.999637i | \(-0.491425\pi\) | ||||
0.0269350 | + | 0.999637i | \(0.491425\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.05447e24 | 0.364736 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.30489e25 | −0.838707 | −0.419354 | − | 0.907823i | \(-0.637743\pi\) | ||||
−0.419354 | + | 0.907823i | \(0.637743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.39339e25 | 0.603824 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.96267e26 | 0.649557 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.16791e27 | −1.03050 | −0.515250 | − | 0.857040i | \(-0.672301\pi\) | ||||
−0.515250 | + | 0.857040i | \(0.672301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.59209e27 | 1.69368 | 0.846841 | − | 0.531846i | \(-0.178502\pi\) | ||||
0.846841 | + | 0.531846i | \(0.178502\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.74992e27 | −0.303050 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.91498e28 | 1.33740 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.44956e29 | 1.41093 | 0.705463 | − | 0.708747i | \(-0.250739\pi\) | ||||
0.705463 | + | 0.708747i | \(0.250739\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.31395e29 | 0.482931 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.04384e30 | 1.52101 | 0.760503 | − | 0.649334i | \(-0.224952\pi\) | ||||
0.760503 | + | 0.649334i | \(0.224952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.02175e30 | 1.22056 | 0.610282 | − | 0.792185i | \(-0.291056\pi\) | ||||
0.610282 | + | 0.792185i | \(0.291056\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.28395e30 | 1.11536 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.03340e30 | −0.819134 | −0.409567 | − | 0.912280i | \(-0.634320\pi\) | ||||
−0.409567 | + | 0.912280i | \(0.634320\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.13911e30 | 0.115241 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.71661e29 | 0.0121222 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.24164e32 | −1.56636 | −0.783180 | − | 0.621795i | \(-0.786404\pi\) | ||||
−0.783180 | + | 0.621795i | \(0.786404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.74786e32 | −1.11121 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.66664e30 | −0.0186055 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.71997e32 | −0.645324 | −0.322662 | − | 0.946514i | \(-0.604578\pi\) | ||||
−0.322662 | + | 0.946514i | \(0.604578\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.11074e32 | −0.197621 | −0.0988104 | − | 0.995106i | \(-0.531504\pi\) | ||||
−0.0988104 | + | 0.995106i | \(0.531504\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.80434e33 | 0.930078 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.12443e33 | 1.77080 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.63890e33 | −0.600601 | −0.300300 | − | 0.953845i | \(-0.597087\pi\) | ||||
−0.300300 | + | 0.953845i | \(0.597087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.02422e33 | 0.289671 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.36753e34 | 1.90122 | 0.950610 | − | 0.310388i | \(-0.100459\pi\) | ||||
0.950610 | + | 0.310388i | \(0.100459\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.78227e34 | −1.27726 | −0.638631 | − | 0.769513i | \(-0.720499\pi\) | ||||
−0.638631 | + | 0.769513i | \(0.720499\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.01821e34 | −0.208547 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.36177e34 | −0.926625 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.82842e35 | −1.43210 | −0.716052 | − | 0.698047i | \(-0.754053\pi\) | ||||
−0.716052 | + | 0.698047i | \(0.754053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.33083e35 | 0.656371 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.67857e35 | −0.527223 | −0.263611 | − | 0.964629i | \(-0.584914\pi\) | ||||
−0.263611 | + | 0.964629i | \(0.584914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.19844e34 | 0.0444493 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.70676e35 | 0.355912 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.60208e35 | 0.829183 | 0.414591 | − | 0.910008i | \(-0.363925\pi\) | ||||
0.414591 | + | 0.910008i | \(0.363925\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.57953e36 | 1.47664 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.52778e36 | −0.584960 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.64126e35 | −0.0682220 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.57484e36 | 1.15507 | 0.577535 | − | 0.816366i | \(-0.304015\pi\) | ||||
0.577535 | + | 0.816366i | \(0.304015\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.41661e36 | −0.772778 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.39074e37 | −1.15691 | −0.578455 | − | 0.815714i | \(-0.696344\pi\) | ||||
−0.578455 | + | 0.815714i | \(0.696344\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.01160e37 | −1.16427 | −0.582134 | − | 0.813093i | \(-0.697782\pi\) | ||||
−0.582134 | + | 0.813093i | \(0.697782\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.13909e37 | −0.461910 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.07555e37 | 0.879676 | 0.439838 | − | 0.898077i | \(-0.355036\pi\) | ||||
0.439838 | + | 0.898077i | \(0.355036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.42599e36 | 0.191398 | 0.0956989 | − | 0.995410i | \(-0.469491\pi\) | ||||
0.0956989 | + | 0.995410i | \(0.469491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.35950e37 | −0.487303 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.03827e37 | 0.212476 | 0.106238 | − | 0.994341i | \(-0.466119\pi\) | ||||
0.106238 | + | 0.994341i | \(0.466119\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.40961e38 | 1.06216 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.24835e38 | 1.23147 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.25954e36 | 0.0370656 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.82401e37 | −0.230091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.41919e38 | −0.525322 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.11388e38 | 0.501726 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.39428e39 | −1.67487 | −0.837436 | − | 0.546535i | \(-0.815946\pi\) | ||||
−0.837436 | + | 0.546535i | \(0.815946\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.68559e38 | −0.421556 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.32651e38 | −0.0897827 | −0.0448913 | − | 0.998992i | \(-0.514294\pi\) | ||||
−0.0448913 | + | 0.998992i | \(0.514294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.11246e38 | −0.0568893 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.12017e39 | −0.822613 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.90101e39 | 0.561893 | 0.280947 | − | 0.959723i | \(-0.409352\pi\) | ||||
0.280947 | + | 0.959723i | \(0.409352\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.31029e39 | 1.87863 | 0.939317 | − | 0.343050i | \(-0.111460\pi\) | ||||
0.939317 | + | 0.343050i | \(0.111460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.63006e39 | 0.282911 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.17332e39 | −1.22690 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.26164e40 | 1.30505 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.95760e38 | −0.0398016 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.20198e40 | 1.37679 | 0.688395 | − | 0.725336i | \(-0.258316\pi\) | ||||
0.688395 | + | 0.725336i | \(0.258316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.65159e40 | −1.29549 | −0.647744 | − | 0.761858i | \(-0.724287\pi\) | ||||
−0.647744 | + | 0.761858i | \(0.724287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.07073e38 | 0.0309116 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.12109e40 | −2.14491 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.39401e40 | −0.568830 | −0.284415 | − | 0.958701i | \(-0.591799\pi\) | ||||
−0.284415 | + | 0.958701i | \(0.591799\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.87762e40 | 0.540986 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.93709e40 | 0.885717 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.69475e40 | −1.15098 | −0.575488 | − | 0.817810i | \(-0.695188\pi\) | ||||
−0.575488 | + | 0.817810i | \(0.695188\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.05084e40 | 0.383789 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.54501e40 | 0.344572 | 0.172286 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172286 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.57028e41 | 0.955152 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.69637e39 | −0.0474440 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.12570e41 | 1.62796 | 0.813981 | − | 0.580891i | \(-0.197296\pi\) | ||||
0.813981 | + | 0.580891i | \(0.197296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.99893e41 | −0.637668 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.62140e40 | 0.222881 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.16454e41 | −1.29455 | −0.647276 | − | 0.762256i | \(-0.724092\pi\) | ||||
−0.647276 | + | 0.762256i | \(0.724092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.59766e41 | 0.786110 | 0.393055 | − | 0.919515i | \(-0.371418\pi\) | ||||
0.393055 | + | 0.919515i | \(0.371418\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.89184e40 | 0.0682539 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.56588e42 | −1.78683 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.29288e40 | −0.0307968 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.92987e41 | −0.685965 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.15394e41 | −0.199405 | −0.0997026 | − | 0.995017i | \(-0.531789\pi\) | ||||
−0.0997026 | + | 0.995017i | \(0.531789\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.24569e42 | 0.649532 | 0.324766 | − | 0.945794i | \(-0.394714\pi\) | ||||
0.324766 | + | 0.945794i | \(0.394714\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.41940e42 | −0.611594 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.99627e42 | 1.78246 | 0.891232 | − | 0.453548i | \(-0.149842\pi\) | ||||
0.891232 | + | 0.453548i | \(0.149842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.57820e42 | 0.467069 | 0.233535 | − | 0.972348i | \(-0.424971\pi\) | ||||
0.233535 | + | 0.972348i | \(0.424971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.43350e41 | 0.207434 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.31385e42 | 1.08826 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.12760e43 | −1.92623 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.17484e42 | 0.738661 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.95615e41 | 0.0472679 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.36838e43 | 1.37082 | 0.685410 | − | 0.728158i | \(-0.259623\pi\) | ||||
0.685410 | + | 0.728158i | \(0.259623\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.80458e42 | −0.656640 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.18399e43 | −1.54575 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.99931e43 | −1.78861 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.76579e42 | 0.441138 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.15381e42 | 0.0490769 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.02201e43 | 0.728019 | 0.364010 | − | 0.931395i | \(-0.381408\pi\) | ||||
0.364010 | + | 0.931395i | \(0.381408\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.74229e43 | −0.531796 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.21148e42 | 0.109133 | 0.0545665 | − | 0.998510i | \(-0.482622\pi\) | ||||
0.0545665 | + | 0.998510i | \(0.482622\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.22246e43 | 0.709955 | 0.354977 | − | 0.934875i | \(-0.384489\pi\) | ||||
0.354977 | + | 0.934875i | \(0.384489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.70616e43 | 0.320036 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.32663e43 | 0.212160 | 0.106080 | − | 0.994358i | \(-0.466170\pi\) | ||||
0.106080 | + | 0.994358i | \(0.466170\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.59782e43 | 1.03737 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.23754e43 | 0.494617 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.49078e43 | 0.548622 | 0.274311 | − | 0.961641i | \(-0.411550\pi\) | ||||
0.274311 | + | 0.961641i | \(0.411550\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.31742e44 | −1.12826 | −0.564128 | − | 0.825688i | \(-0.690787\pi\) | ||||
−0.564128 | + | 0.825688i | \(0.690787\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.19219e44 | −0.876254 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.31077e43 | −0.145943 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.38621e43 | −0.0753246 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.89024e43 | 0.182091 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.67421e44 | −0.675842 | −0.337921 | − | 0.941174i | \(-0.609724\pi\) | ||||
−0.337921 | + | 0.941174i | \(0.609724\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.11135e44 | −0.735919 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.09510e42 | −0.0153518 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.88763e44 | 0.492215 | 0.246108 | − | 0.969243i | \(-0.420848\pi\) | ||||
0.246108 | + | 0.969243i | \(0.420848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.59529e44 | −1.49001 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.63161e44 | 0.907576 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.47596e44 | 0.251127 | 0.125564 | − | 0.992086i | \(-0.459926\pi\) | ||||
0.125564 | + | 0.992086i | \(0.459926\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.34128e45 | 1.98367 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.22538e44 | −0.286381 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.36652e44 | 0.825744 | 0.412872 | − | 0.910789i | \(-0.364526\pi\) | ||||
0.412872 | + | 0.910789i | \(0.364526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.39411e44 | 0.233998 | 0.116999 | − | 0.993132i | \(-0.462673\pi\) | ||||
0.116999 | + | 0.993132i | \(0.462673\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.97831e44 | −0.509999 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.10861e44 | 0.529822 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.20053e45 | −0.782522 | −0.391261 | − | 0.920280i | \(-0.627961\pi\) | ||||
−0.391261 | + | 0.920280i | \(0.627961\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.61423e45 | −1.49165 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.31149e45 | 0.655688 | 0.327844 | − | 0.944732i | \(-0.393678\pi\) | ||||
0.327844 | + | 0.944732i | \(0.393678\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.28691e45 | 0.564287 | 0.282143 | − | 0.959372i | \(-0.408955\pi\) | ||||
0.282143 | + | 0.959372i | \(0.408955\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.12138e43 | 0.0235624 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.74931e45 | −1.60626 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.35795e45 | −0.998768 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.52378e45 | −0.398936 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.72231e45 | 0.627894 | 0.313947 | − | 0.949440i | \(-0.398349\pi\) | ||||
0.313947 | + | 0.949440i | \(0.398349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.01849e45 | 0.817252 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.17564e45 | 0.569950 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.39806e45 | 1.17274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.19866e45 | −1.28898 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.22317e45 | 0.399572 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.28012e45 | 0.250271 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.62882e45 | 0.644727 | 0.322364 | − | 0.946616i | \(-0.395523\pi\) | ||||
0.322364 | + | 0.946616i | \(0.395523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.66207e45 | 0.402112 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.44200e46 | 1.86930 | 0.934649 | − | 0.355571i | \(-0.115714\pi\) | ||||
0.934649 | + | 0.355571i | \(0.115714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.81885e46 | −1.23659 | −0.618297 | − | 0.785944i | \(-0.712177\pi\) | ||||
−0.618297 | + | 0.785944i | \(0.712177\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.94914e46 | −1.17787 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.86315e45 | −0.315163 | −0.157581 | − | 0.987506i | \(-0.550370\pi\) | ||||
−0.157581 | + | 0.987506i | \(0.550370\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.88971e46 | −0.904207 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.12789e45 | −0.303821 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.97599e43 | −0.00189074 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.49082e46 | −0.844307 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.18457e45 | −0.0661046 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.20010e46 | 0.865047 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.22607e46 | 0.779572 | 0.389786 | − | 0.920906i | \(-0.372549\pi\) | ||||
0.389786 | + | 0.920906i | \(0.372549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.74854e46 | −1.24262 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.93091e46 | 0.760614 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.79861e46 | −0.311733 | −0.155867 | − | 0.987778i | \(-0.549817\pi\) | ||||
−0.155867 | + | 0.987778i | \(0.549817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.72388e45 | −0.0733845 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.06661e47 | 1.48611 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.47224e46 | 0.934350 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.26691e46 | −0.366846 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.03561e46 | 0.205399 | 0.102700 | − | 0.994712i | \(-0.467252\pi\) | ||||
0.102700 | + | 0.994712i | \(0.467252\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.55636e46 | 0.685555 | 0.342777 | − | 0.939417i | \(-0.388632\pi\) | ||||
0.342777 | + | 0.939417i | \(0.388632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.11273e47 | −0.908255 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.78872e47 | 1.31435 | 0.657176 | − | 0.753737i | \(-0.271751\pi\) | ||||
0.657176 | + | 0.753737i | \(0.271751\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.63777e47 | −2.40775 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.14599e45 | −0.0128016 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.12637e46 | −0.329576 | −0.164788 | − | 0.986329i | \(-0.552694\pi\) | ||||
−0.164788 | + | 0.986329i | \(0.552694\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.05410e47 | −0.997098 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.81329e46 | 0.0794685 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.08579e47 | 1.61755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.59083e47 | −1.64274 | −0.821371 | − | 0.570395i | \(-0.806790\pi\) | ||||
−0.821371 | + | 0.570395i | \(0.806790\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.13955e47 | −1.33957 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.64928e47 | 1.65415 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.54916e47 | −0.410661 | −0.205330 | − | 0.978693i | \(-0.565827\pi\) | ||||
−0.205330 | + | 0.978693i | \(0.565827\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.21672e46 | −0.173285 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.62145e47 | 1.44091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.30180e47 | 0.651516 | 0.325758 | − | 0.945453i | \(-0.394381\pi\) | ||||
0.325758 | + | 0.945453i | \(0.394381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.23138e47 | 0.578464 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.41516e46 | 0.104239 | 0.0521195 | − | 0.998641i | \(-0.483402\pi\) | ||||
0.0521195 | + | 0.998641i | \(0.483402\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.95254e47 | 1.17350 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.01767e47 | −1.07497 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.03221e48 | −1.25806 | −0.629030 | − | 0.777381i | \(-0.716548\pi\) | ||||
−0.629030 | + | 0.777381i | \(0.716548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.65563e46 | 0.0294372 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.07432e46 | 0.0310090 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.97515e48 | 1.81365 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.62836e47 | −0.387082 | −0.193541 | − | 0.981092i | \(-0.561997\pi\) | ||||
−0.193541 | + | 0.981092i | \(0.561997\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.57824e46 | 0.0196483 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.52846e48 | −1.06190 | −0.530949 | − | 0.847404i | \(-0.678164\pi\) | ||||
−0.530949 | + | 0.847404i | \(0.678164\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.73736e48 | −2.36822 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.43763e48 | −0.831243 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.34542e48 | 1.23801 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.46279e47 | −0.215142 | −0.107571 | − | 0.994197i | \(-0.534307\pi\) | ||||
−0.107571 | + | 0.994197i | \(0.534307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.40578e47 | −0.194066 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.69254e48 | 0.681494 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.81327e48 | 0.667686 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.92599e48 | −0.648839 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.73559e48 | 1.76856 | 0.884278 | − | 0.466960i | \(-0.154651\pi\) | ||||
0.884278 | + | 0.466960i | \(0.154651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.64196e48 | −0.463600 | −0.231800 | − | 0.972763i | \(-0.574462\pi\) | ||||
−0.231800 | + | 0.972763i | \(0.574462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.78925e48 | 0.721423 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.94112e46 | −0.0211932 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.60357e47 | 0.208697 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.12601e48 | 0.423745 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.79980e48 | −0.512033 | −0.256017 | − | 0.966672i | \(-0.582410\pi\) | ||||
−0.256017 | + | 0.966672i | \(0.582410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.94771e48 | 0.662704 | 0.331352 | − | 0.943507i | \(-0.392495\pi\) | ||||
0.331352 | + | 0.943507i | \(0.392495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.92397e48 | −0.450735 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.19053e47 | −0.0451811 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.54774e48 | −0.331559 | −0.165780 | − | 0.986163i | \(-0.553014\pi\) | ||||
−0.165780 | + | 0.986163i | \(0.553014\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.48310e47 | −0.101494 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.78938e48 | −0.747070 | −0.373535 | − | 0.927616i | \(-0.621854\pi\) | ||||
−0.373535 | + | 0.927616i | \(0.621854\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.03726e49 | −1.05009 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.10331e48 | −0.475513 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.78360e48 | −0.496182 | −0.248091 | − | 0.968737i | \(-0.579803\pi\) | ||||
−0.248091 | + | 0.968737i | \(0.579803\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.68895e49 | 1.33460 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.14532e48 | 0.447433 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.78653e49 | −1.87005 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.70414e49 | 1.05452 | 0.527260 | − | 0.849704i | \(-0.323219\pi\) | ||||
0.527260 | + | 0.849704i | \(0.323219\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.99428e47 | −0.0227984 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.95615e48 | 0.471687 | 0.235844 | − | 0.971791i | \(-0.424215\pi\) | ||||
0.235844 | + | 0.971791i | \(0.424215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.71924e46 | 0.00375255 | 0.00187627 | − | 0.999998i | \(-0.499403\pi\) | ||||
0.00187627 | + | 0.999998i | \(0.499403\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.65038e49 | 0.740807 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.47410e47 | 0.0392804 | 0.0196402 | − | 0.999807i | \(-0.493748\pi\) | ||||
0.0196402 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.65565e49 | 0.634264 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.54835e48 | 0.196461 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.27123e49 | 1.07098 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.07421e48 | 0.0325279 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.92398e49 | 1.37951 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.93800e49 | −1.28040 | −0.640198 | − | 0.768210i | \(-0.721148\pi\) | ||||
−0.640198 | + | 0.768210i | \(0.721148\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.21823e49 | −1.97285 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.37598e49 | −0.305907 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.10246e49 | −1.46281 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.14970e49 | 0.982871 | 0.491435 | − | 0.870914i | \(-0.336472\pi\) | ||||
0.491435 | + | 0.870914i | \(0.336472\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.24685e49 | 0.397522 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.61978e49 | −0.429792 | −0.214896 | − | 0.976637i | \(-0.568941\pi\) | ||||
−0.214896 | + | 0.976637i | \(0.568941\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.37685e48 | 0.0361688 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.93153e49 | 0.978662 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.53218e50 | −2.00778 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.10414e49 | 0.377643 | 0.188822 | − | 0.982011i | \(-0.439533\pi\) | ||||
0.188822 | + | 0.982011i | \(0.439533\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.05335e49 | −0.119008 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.24708e50 | −1.30884 | −0.654420 | − | 0.756131i | \(-0.727087\pi\) | ||||
−0.654420 | + | 0.756131i | \(0.727087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.50234e50 | 1.46514 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.63927e49 | −0.329888 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.23242e50 | 1.03868 | 0.519338 | − | 0.854569i | \(-0.326178\pi\) | ||||
0.519338 | + | 0.854569i | \(0.326178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.72088e50 | 1.34885 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.79883e48 | 0.0349916 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.17302e50 | 1.47445 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.13802e50 | −0.718745 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.56170e49 | −0.562262 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.52770e50 | −0.836641 | −0.418320 | − | 0.908300i | \(-0.637381\pi\) | ||||
−0.418320 | + | 0.908300i | \(0.637381\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.24295e50 | 1.14430 | 0.572148 | − | 0.820151i | \(-0.306110\pi\) | ||||
0.572148 | + | 0.820151i | \(0.306110\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.63272e49 | 0.220236 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.34157e49 | −0.0594454 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.17889e49 | −0.296570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.47523e50 | 0.568346 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.91799e50 | −2.12677 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.32236e50 | −1.11404 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.42869e50 | 0.447110 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.46113e49 | 0.101117 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.16928e49 | −0.113739 | −0.0568697 | − | 0.998382i | \(-0.518112\pi\) | ||||
−0.0568697 | + | 0.998382i | \(0.518112\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.06555e50 | −0.271505 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.01824e50 | −0.242390 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.87730e50 | −0.640059 | −0.320029 | − | 0.947408i | \(-0.603693\pi\) | ||||
−0.320029 | + | 0.947408i | \(0.603693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.37059e49 | 0.174047 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.85561e49 | −0.0555130 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.31905e50 | 1.51237 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.62909e50 | 0.617131 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.05807e51 | 1.68343 | 0.841715 | − | 0.539922i | \(-0.181546\pi\) | ||||
0.841715 | + | 0.539922i | \(0.181546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.14622e51 | −1.70667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.63157e48 | 0.0106366 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.79551e50 | 1.14777 | 0.573886 | − | 0.818935i | \(-0.305435\pi\) | ||||
0.573886 | + | 0.818935i | \(0.305435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.20183e50 | −0.269084 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.05509e50 | −0.693160 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.05710e50 | 0.327894 | 0.163947 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163947 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.13121e51 | 1.13704 | 0.568521 | − | 0.822668i | \(-0.307516\pi\) | ||||
0.568521 | + | 0.822668i | \(0.307516\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.30957e49 | 0.0688702 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.73292e50 | −0.506431 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.65515e50 | 0.219957 | 0.109978 | − | 0.993934i | \(-0.464922\pi\) | ||||
0.109978 | + | 0.993934i | \(0.464922\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.88701e50 | −0.224334 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.63725e50 | 0.556773 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00900e51 | −1.37439 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.42877e51 | −1.55956 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.35709e51 | −0.818093 | −0.409047 | − | 0.912513i | \(-0.634139\pi\) | ||||
−0.409047 | + | 0.912513i | \(0.634139\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.61180e50 | 0.0912385 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.15793e51 | −0.615624 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.19816e51 | 0.598418 | 0.299209 | − | 0.954188i | \(-0.403277\pi\) | ||||
0.299209 | + | 0.954188i | \(0.403277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.00026e50 | −0.0469407 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.65764e50 | −0.161315 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.71203e51 | 1.53892 | 0.769458 | − | 0.638698i | \(-0.220526\pi\) | ||||
0.769458 | + | 0.638698i | \(0.220526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.98939e49 | 0.0116521 | 0.00582605 | − | 0.999983i | \(-0.498146\pi\) | ||||
0.00582605 | + | 0.999983i | \(0.498146\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.44308e51 | 0.528957 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.45187e50 | 0.291393 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.82791e51 | −0.592875 | −0.296438 | − | 0.955052i | \(-0.595799\pi\) | ||||
−0.296438 | + | 0.955052i | \(0.595799\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.23154e51 | −0.375861 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.98756e51 | 1.14537 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.48635e51 | −0.942654 | −0.471327 | − | 0.881959i | \(-0.656225\pi\) | ||||
−0.471327 | + | 0.881959i | \(0.656225\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.61333e51 | 0.665279 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.90579e51 | 1.65553 | 0.827766 | − | 0.561073i | \(-0.189611\pi\) | ||||
0.827766 | + | 0.561073i | \(0.189611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.48084e51 | 1.46337 | 0.731685 | − | 0.681643i | \(-0.238734\pi\) | ||||
0.731685 | + | 0.681643i | \(0.238734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.56108e51 | −0.544789 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.36881e51 | −0.875658 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.56038e51 | −1.23922 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.16875e49 | −0.0163253 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.95004e50 | −0.0495212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.04373e51 | −1.43154 | −0.715772 | − | 0.698335i | \(-0.753925\pi\) | ||||
−0.715772 | + | 0.698335i | \(0.753925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.17135e51 | −0.473451 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.50617e52 | 2.12109 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.21276e51 | −0.161137 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.33547e52 | −1.67443 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.02640e52 | −1.21463 | −0.607314 | − | 0.794462i | \(-0.707753\pi\) | ||||
−0.607314 | + | 0.794462i | \(0.707753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.12581e52 | 1.25766 | 0.628830 | − | 0.777543i | \(-0.283534\pi\) | ||||
0.628830 | + | 0.777543i | \(0.283534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.06160e51 | 0.533867 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.32899e52 | −1.32370 | −0.661852 | − | 0.749634i | \(-0.730229\pi\) | ||||
−0.661852 | + | 0.749634i | \(0.730229\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.01900e51 | −0.566236 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.95119e51 | 0.617747 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.11156e51 | −0.0933335 | −0.0466668 | − | 0.998911i | \(-0.514860\pi\) | ||||
−0.0466668 | + | 0.998911i | \(0.514860\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.43296e51 | 0.113703 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.49994e52 | 1.12490 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.43589e51 | 0.172694 | 0.0863469 | − | 0.996265i | \(-0.472481\pi\) | ||||
0.0863469 | + | 0.996265i | \(0.472481\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.08839e52 | 1.39986 | 0.699929 | − | 0.714212i | \(-0.253215\pi\) | ||||
0.699929 | + | 0.714212i | \(0.253215\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.67406e50 | −0.0169501 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.20174e51 | 0.0720459 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.52401e52 | 0.864288 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.68620e51 | −0.251442 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.41522e51 | −0.173401 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00239e51 | 0.384540 | 0.192270 | − | 0.981342i | \(-0.438415\pi\) | ||||
0.192270 | + | 0.981342i | \(0.438415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.62278e51 | 0.392218 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.17793e52 | −0.507258 | −0.253629 | − | 0.967302i | \(-0.581624\pi\) | ||||
−0.253629 | + | 0.967302i | \(0.581624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.99146e52 | −1.21981 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.76051e50 | −0.0376922 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.05105e52 | −1.11600 | −0.558002 | − | 0.829840i | \(-0.688432\pi\) | ||||
−0.558002 | + | 0.829840i | \(0.688432\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.05356e52 | −0.711594 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.46836e51 | −0.245203 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.03943e52 | 2.19019 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.38514e52 | −0.408459 | −0.204230 | − | 0.978923i | \(-0.565469\pi\) | ||||
−0.204230 | + | 0.978923i | \(0.565469\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.91947e52 | 0.816091 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.97717e52 | −2.37914 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.12434e51 | −0.0533848 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.07459e51 | −0.0732755 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.94343e52 | −1.11749 | −0.558747 | − | 0.829338i | \(-0.688718\pi\) | ||||
−0.558747 | + | 0.829338i | \(0.688718\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.54425e51 | 0.0760065 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.76087e52 | −0.358285 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.32766e52 | 1.22175 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.70722e52 | 1.22910 | 0.614550 | − | 0.788878i | \(-0.289337\pi\) | ||||
0.614550 | + | 0.788878i | \(0.289337\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.25099e52 | 1.26127 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.60198e52 | −1.42050 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.90946e52 | 1.55377 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.27254e52 | −0.189482 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.50366e52 | −0.212649 | −0.106325 | − | 0.994331i | \(-0.533908\pi\) | ||||
−0.106325 | + | 0.994331i | \(0.533908\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.15249e52 | 1.22952 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.05324e52 | 0.389675 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.13111e52 | −0.622240 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.05250e52 | −0.467021 | −0.233510 | − | 0.972354i | \(-0.575021\pi\) | ||||
−0.233510 | + | 0.972354i | \(0.575021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.22949e52 | −0.353732 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.11451e51 | −0.0428397 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.49902e52 | 0.742303 | 0.371151 | − | 0.928572i | \(-0.378963\pi\) | ||||
0.371151 | + | 0.928572i | \(0.378963\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.35544e51 | 0.0504056 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.88781e52 | −0.526994 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.81728e52 | 0.324962 | 0.162481 | − | 0.986712i | \(-0.448050\pi\) | ||||
0.162481 | + | 0.986712i | \(0.448050\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.21269e51 | 0.0260154 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.98672e53 | −1.53054 | −0.765269 | − | 0.643710i | \(-0.777394\pi\) | ||||
−0.765269 | + | 0.643710i | \(0.777394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.37869e53 | −1.74360 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.65672e52 | 0.464332 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.39933e53 | −0.928982 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.32961e52 | −0.526364 | −0.263182 | − | 0.964746i | \(-0.584772\pi\) | ||||
−0.263182 | + | 0.964746i | \(0.584772\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.88014e52 | 0.233421 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.86438e53 | 1.64063 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.52303e52 | −0.246692 | −0.123346 | − | 0.992364i | \(-0.539363\pi\) | ||||
−0.123346 | + | 0.992364i | \(0.539363\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.89325e52 | 0.254170 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.94307e53 | 0.961329 | 0.480664 | − | 0.876905i | \(-0.340396\pi\) | ||||
0.480664 | + | 0.876905i | \(0.340396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.28869e52 | −0.202126 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.71839e51 | −0.0391471 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.10903e53 | 0.902335 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.45326e53 | −1.00025 | −0.500123 | − | 0.865954i | \(-0.666712\pi\) | ||||
−0.500123 | + | 0.865954i | \(0.666712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.37478e52 | −0.170000 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.97446e52 | −0.0731356 | −0.0365678 | − | 0.999331i | \(-0.511642\pi\) | ||||
−0.0365678 | + | 0.999331i | \(0.511642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.89617e53 | 1.02268 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.52852e53 | 0.514616 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.55223e52 | 0.0819365 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.44874e53 | 1.66821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.29223e53 | −0.669369 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.58612e53 | 0.720379 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.81731e53 | −1.28018 | −0.640091 | − | 0.768299i | \(-0.721103\pi\) | ||||
−0.640091 | + | 0.768299i | \(0.721103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.42069e52 | −0.0867339 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.27383e52 | −0.224385 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.19668e53 | 0.276327 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.10854e53 | −0.685117 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.66157e53 | −0.349575 | −0.174788 | − | 0.984606i | \(-0.555924\pi\) | ||||
−0.174788 | + | 0.984606i | \(0.555924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.43139e52 | 0.0287503 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.80791e53 | −0.730273 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.11980e53 | −1.12073 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.41353e53 | −1.12169 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.70726e53 | −0.285194 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.10187e53 | 1.13325 | 0.566624 | − | 0.823976i | \(-0.308249\pi\) | ||||
0.566624 | + | 0.823976i | \(0.308249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.23793e52 | −0.0798498 | −0.0399249 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399249 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.54858e52 | −0.0808178 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.04727e54 | 1.45762 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.94327e52 | 0.0657516 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.02297e54 | −1.30050 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.36447e54 | 1.65811 | 0.829057 | − | 0.559164i | \(-0.188878\pi\) | ||||
0.829057 | + | 0.559164i | \(0.188878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.74606e53 | −0.551361 | −0.275680 | − | 0.961249i | \(-0.588903\pi\) | ||||
−0.275680 | + | 0.961249i | \(0.588903\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.64749e53 | −0.182989 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.60680e53 | 0.701680 | 0.350840 | − | 0.936435i | \(-0.385896\pi\) | ||||
0.350840 | + | 0.936435i | \(0.385896\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.19800e53 | 0.324803 | 0.162402 | − | 0.986725i | \(-0.448076\pi\) | ||||
0.162402 | + | 0.986725i | \(0.448076\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.78234e53 | 0.270266 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.35336e51 | −0.00404476 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.90974e53 | −0.436374 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.29381e54 | 1.10014 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.08226e54 | 1.69410 | 0.847048 | − | 0.531516i | \(-0.178378\pi\) | ||||
0.847048 | + | 0.531516i | \(0.178378\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.95482e52 | 0.0619305 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.03950e53 | −0.226460 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.69629e54 | −1.20962 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.55982e53 | 0.242988 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.98254e53 | −0.194892 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.89152e54 | −1.18335 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.18441e54 | −1.90753 | −0.953766 | − | 0.300550i | \(-0.902830\pi\) | ||||
−0.953766 | + | 0.300550i | \(0.902830\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.04745e53 | 0.0600841 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.50624e54 | 0.827463 | 0.413732 | − | 0.910399i | \(-0.364225\pi\) | ||||
0.413732 | + | 0.910399i | \(0.364225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.69349e54 | 0.891067 | 0.445533 | − | 0.895265i | \(-0.353014\pi\) | ||||
0.445533 | + | 0.895265i | \(0.353014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.10070e54 | 0.554766 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.71066e52 | 0.0324015 | 0.0162008 | − | 0.999869i | \(-0.494843\pi\) | ||||
0.0162008 | + | 0.999869i | \(0.494843\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.45677e54 | −2.06169 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.78238e53 | 0.344953 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.95842e54 | −1.25659 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.06306e54 | 0.839800 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.60739e54 | −1.01729 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.41677e54 | −0.529848 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.24921e54 | 0.806375 | 0.403187 | − | 0.915117i | \(-0.367902\pi\) | ||||
0.403187 | + | 0.915117i | \(0.367902\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.30921e53 | −0.216861 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.31934e54 | 1.42352 | 0.711759 | − | 0.702423i | \(-0.247899\pi\) | ||||
0.711759 | + | 0.702423i | \(0.247899\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.08099e53 | 0.160574 | 0.0802870 | − | 0.996772i | \(-0.474416\pi\) | ||||
0.0802870 | + | 0.996772i | \(0.474416\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.31325e53 | −0.282261 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.25491e54 | 0.364775 | 0.182388 | − | 0.983227i | \(-0.441617\pi\) | ||||
0.182388 | + | 0.983227i | \(0.441617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.34379e54 | 1.76875 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.15331e54 | 0.575929 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.71970e53 | −0.0441267 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.65923e54 | 1.63945 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.71457e54 | −0.405038 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.69900e54 | −1.74534 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.52689e53 | 0.0549766 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.13188e54 | 0.445184 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.96661e54 | −0.995547 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.42855e54 | −1.62188 | −0.810939 | − | 0.585131i | \(-0.801043\pi\) | ||||
−0.810939 | + | 0.585131i | \(0.801043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.51527e54 | 1.01891 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.47562e54 | 1.50342 | 0.751712 | − | 0.659491i | \(-0.229228\pi\) | ||||
0.751712 | + | 0.659491i | \(0.229228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.71596e54 | −0.462609 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.28440e53 | −0.0864382 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.03545e53 | 0.0948149 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.38417e54 | −0.812423 | −0.406211 | − | 0.913779i | \(-0.633150\pi\) | ||||
−0.406211 | + | 0.913779i | \(0.633150\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.53629e54 | −0.222675 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.90921e55 | −2.65841 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.36849e54 | 0.851950 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.97742e54 | 1.02539 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.45967e54 | −0.921360 | −0.460680 | − | 0.887566i | \(-0.652394\pi\) | ||||
−0.460680 | + | 0.887566i | \(0.652394\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.23024e52 | 0.00620801 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.65957e54 | −0.645615 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.55713e53 | 0.0390018 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.19621e54 | 0.863835 | 0.431917 | − | 0.901913i | \(-0.357837\pi\) | ||||
0.431917 | + | 0.901913i | \(0.357837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.21537e54 | 0.427093 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.20640e53 | −0.0604550 | −0.0302275 | − | 0.999543i | \(-0.509623\pi\) | ||||
−0.0302275 | + | 0.999543i | \(0.509623\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.36210e55 | −1.27568 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.64647e54 | 0.868721 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.79896e54 | 0.675401 | 0.337701 | − | 0.941254i | \(-0.390351\pi\) | ||||
0.337701 | + | 0.941254i | \(0.390351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.14435e55 | 1.78595 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.35884e54 | 0.108850 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.57034e54 | −0.275100 | −0.137550 | − | 0.990495i | \(-0.543923\pi\) | ||||
−0.137550 | + | 0.990495i | \(0.543923\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.40704e54 | 0.252531 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.37959e54 | 0.312293 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.64933e54 | −0.593387 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.83067e55 | 1.86856 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.21968e55 | −0.774743 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.34566e55 | −0.822581 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.24792e54 | −0.308743 | −0.154372 | − | 0.988013i | \(-0.549335\pi\) | ||||
−0.154372 | + | 0.988013i | \(0.549335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.15323e52 | 0.000653022 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.07962e55 | 1.67858 | 0.839288 | − | 0.543688i | \(-0.182972\pi\) | ||||
0.839288 | + | 0.543688i | \(0.182972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.78106e55 | −1.98393 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.77272e54 | 0.291605 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.24607e54 | 0.109238 | 0.0546191 | − | 0.998507i | \(-0.482606\pi\) | ||||
0.0546191 | + | 0.998507i | \(0.482606\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.55364e55 | 0.727562 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.73808e54 | −0.168567 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.49118e55 | −1.51611 | −0.758057 | − | 0.652188i | \(-0.773851\pi\) | ||||
−0.758057 | + | 0.652188i | \(0.773851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.39721e55 | −2.25735 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.41654e54 | −0.298768 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.63817e55 | −1.02370 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.70743e55 | 1.75963 | 0.879815 | − | 0.475317i | \(-0.157667\pi\) | ||||
0.879815 | + | 0.475317i | \(0.157667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.47673e54 | −0.269247 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.70485e55 | −0.591507 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.07899e55 | 0.695012 | 0.347506 | − | 0.937678i | \(-0.387029\pi\) | ||||
0.347506 | + | 0.937678i | \(0.387029\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.84501e55 | 0.916477 |
(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 | 4.38.a.a.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 16.38.a.d.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.38.a.a.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
16.38.a.d.1.2 | 3 | 4.3 | odd | 2 |