Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} - 1751639 x^{18} + 15765036 x^{17} + 1288400424989 x^{16} - 10307560742020 x^{15} + \cdots + 51\!\cdots\!63 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{36}\cdot 3^{26}\cdot 7^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.8 | ||
Root | \(-356.003 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.73 |
Dual form | 252.9.z.e.145.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 534.755 | − | 308.741i | 0.855608 | − | 0.493985i | −0.00693126 | − | 0.999976i | \(-0.502206\pi\) |
0.862539 | + | 0.505991i | \(0.168873\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −750.736 | − | 2280.61i | −0.312676 | − | 0.949860i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10012.2 | + | 17341.6i | −0.683844 | + | 1.18445i | 0.289955 | + | 0.957040i | \(0.406360\pi\) |
−0.973799 | + | 0.227412i | \(0.926974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 54961.3i | − | 1.92435i | −0.272439 | − | 0.962173i | \(-0.587830\pi\) | ||
0.272439 | − | 0.962173i | \(-0.412170\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82287.8 | + | 47508.9i | 0.985235 | + | 0.568826i | 0.903847 | − | 0.427857i | \(-0.140731\pi\) |
0.0813884 | + | 0.996682i | \(0.474065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 50039.8 | − | 28890.5i | 0.383974 | − | 0.221687i | −0.295572 | − | 0.955320i | \(-0.595510\pi\) |
0.679546 | + | 0.733633i | \(0.262177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −210993. | − | 365450.i | −0.753974 | − | 1.30592i | −0.945883 | − | 0.324508i | \(-0.894801\pi\) |
0.191909 | − | 0.981413i | \(-0.438532\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4670.69 | + | 8089.87i | −0.0119570 | + | 0.0207101i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.09995e6 | −1.55517 | −0.777587 | − | 0.628775i | \(-0.783557\pi\) | ||||
−0.777587 | + | 0.628775i | \(0.783557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 189251. | + | 109264.i | 0.204924 | + | 0.118313i | 0.598950 | − | 0.800786i | \(-0.295585\pi\) |
−0.394026 | + | 0.919099i | \(0.628918\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.10558e6 | − | 987786.i | −0.736745 | − | 0.658250i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −770458. | − | 1.33447e6i | −0.411095 | − | 0.712038i | 0.583915 | − | 0.811815i | \(-0.301520\pi\) |
−0.995010 | + | 0.0997774i | \(0.968187\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 376213.i | 0.133137i | 0.997782 | + | 0.0665685i | \(0.0212051\pi\) | ||||
−0.997782 | + | 0.0665685i | \(0.978795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.37356e6 | 0.401768 | 0.200884 | − | 0.979615i | \(-0.435619\pi\) | ||||
0.200884 | + | 0.979615i | \(0.435619\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.15852e6 | − | 2.97827e6i | 1.05714 | − | 0.610342i | 0.132503 | − | 0.991183i | \(-0.457699\pi\) |
0.924641 | + | 0.380841i | \(0.124365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.63759e6 | + | 3.42428e6i | −0.804467 | + | 0.593997i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.64313e6 | + | 1.15062e7i | −0.841917 | + | 1.45824i | 0.0463546 | + | 0.998925i | \(0.485240\pi\) |
−0.888272 | + | 0.459318i | \(0.848094\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.23646e7i | 1.35124i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.54090e7 | + | 8.89642e6i | 1.27165 | + | 0.734188i | 0.975298 | − | 0.220891i | \(-0.0708966\pi\) |
0.296352 | + | 0.955079i | \(0.404230\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.14563e6 | + | 1.23878e6i | −0.154966 | + | 0.0894696i | −0.575478 | − | 0.817817i | \(-0.695184\pi\) |
0.420512 | + | 0.907287i | \(0.361851\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.69688e7 | − | 2.93908e7i | −0.950599 | − | 1.64649i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.01117e7 | − | 1.75139e7i | 0.501791 | − | 0.869128i | −0.498207 | − | 0.867058i | \(-0.666008\pi\) |
0.999998 | − | 0.00206964i | \(-0.000658786\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.39469e7 | 0.548836 | 0.274418 | − | 0.961610i | \(-0.411515\pi\) | ||||
0.274418 | + | 0.961610i | \(0.411515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.95536e7 | − | 1.12893e7i | −0.688551 | − | 0.397535i | 0.114518 | − | 0.993421i | \(-0.463468\pi\) |
−0.803069 | + | 0.595886i | \(0.796801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.70659e7 | + | 9.81492e6i | 1.33888 | + | 0.279205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.41314e7 | − | 5.91174e7i | −0.876286 | − | 1.51777i | −0.855386 | − | 0.517991i | \(-0.826680\pi\) |
−0.0209000 | − | 0.999782i | \(-0.506653\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.02081e7i | 0.425807i | 0.977073 | + | 0.212904i | \(0.0682920\pi\) | ||||
−0.977073 | + | 0.212904i | \(0.931708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.86717e7 | 1.12397 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.57842e7 | + | 4.95275e7i | −1.36725 | + | 0.789381i | −0.990576 | − | 0.136966i | \(-0.956265\pi\) |
−0.376672 | + | 0.926347i | \(0.622932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.25345e8 | + | 4.12614e7i | −1.82786 | + | 0.601698i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.78394e7 | − | 3.08987e7i | 0.219021 | − | 0.379355i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.53229e8i | 1.73083i | 0.501054 | + | 0.865416i | \(0.332946\pi\) | ||||
−0.501054 | + | 0.865416i | \(0.667054\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 200235. | + | 115606.i | 0.00192422 | + | 0.00111095i | 0.500962 | − | 0.865469i | \(-0.332980\pi\) |
−0.499038 | + | 0.866580i | \(0.666313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.48173e7 | + | 3.16488e7i | −0.487045 | + | 0.281195i | −0.723348 | − | 0.690484i | \(-0.757398\pi\) |
0.236303 | + | 0.971679i | \(0.424064\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.28012e7 | − | 1.43416e8i | −0.631686 | − | 1.09411i | −0.987207 | − | 0.159445i | \(-0.949030\pi\) |
0.355520 | − | 0.934669i | \(-0.384304\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.08987e7 | + | 8.81591e7i | −0.360579 | + | 0.624541i | −0.988056 | − | 0.154094i | \(-0.950754\pi\) |
0.627477 | + | 0.778635i | \(0.284088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.67939e7 | −0.532323 | −0.266161 | − | 0.963928i | \(-0.585755\pi\) | ||||
−0.266161 | + | 0.963928i | \(0.585755\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.25659e8 | − | 1.30284e8i | −1.29021 | − | 0.744904i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.65730e7 | − | 2.23333e8i | 0.232245 | − | 1.11369i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.33071e7 | − | 1.61613e8i | −0.435284 | − | 0.753935i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.46972e8i | 1.01160i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.20685e8 | −1.23272 | −0.616359 | − | 0.787465i | \(-0.711393\pi\) | ||||
−0.616359 | + | 0.787465i | \(0.711393\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.24550e8 | + | 1.87379e8i | −1.10204 | + | 0.636261i | −0.936755 | − | 0.349985i | \(-0.886187\pi\) |
−0.165281 | + | 0.986246i | \(0.552853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.03455e8 | − | 9.24324e7i | −0.330631 | − | 0.295405i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.06158e8 | − | 3.57076e8i | 0.585218 | − | 1.01363i | −0.409630 | − | 0.912252i | \(-0.634342\pi\) |
0.994848 | − | 0.101376i | \(-0.0323244\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.48791e8i | − | 0.398581i | −0.979940 | − | 0.199290i | \(-0.936136\pi\) | ||
0.979940 | − | 0.199290i | \(-0.0638637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.53114e8 | + | 5.50281e8i | 2.27930 | + | 1.31595i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.88201e8 | + | 3.39598e8i | −1.33062 | + | 0.768234i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.14977e8 | + | 1.99146e8i | 0.233274 | + | 0.404043i | 0.958770 | − | 0.284184i | \(-0.0917227\pi\) |
−0.725495 | + | 0.688227i | \(0.758389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.26244e8 | + | 3.91866e8i | −0.435180 | + | 0.753754i | −0.997310 | − | 0.0732946i | \(-0.976649\pi\) |
0.562130 | + | 0.827049i | \(0.309982\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.34937e8 | 0.233779 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.79759e8 | − | 3.34724e8i | −0.954221 | − | 0.550920i | −0.0598315 | − | 0.998208i | \(-0.519056\pi\) |
−0.894390 | + | 0.447289i | \(0.852390\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.75051e8 | + | 7.55549e8i | −1.00469 | + | 1.12450i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.39051e8 | + | 2.40844e8i | 0.196981 | + | 0.341182i | 0.947548 | − | 0.319613i | \(-0.103553\pi\) |
−0.750567 | + | 0.660794i | \(0.770220\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.45736e9i | − | 1.87370i | −0.349726 | − | 0.936852i | \(-0.613725\pi\) | ||
0.349726 | − | 0.936852i | \(-0.386275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.20501e9 | −2.70311 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.14202e8 | − | 2.39140e8i | 0.462411 | − | 0.266973i | −0.250647 | − | 0.968079i | \(-0.580643\pi\) |
0.713057 | + | 0.701106i | \(0.247310\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.19563e7 | + | 4.57868e6i | 0.0234103 | + | 0.00488189i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.13555e8 | + | 1.96683e8i | −0.110610 | + | 0.191582i | −0.916016 | − | 0.401141i | \(-0.868614\pi\) |
0.805407 | + | 0.592723i | \(0.201947\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.37679e9i | − | 1.28278i | −0.767214 | − | 0.641391i | \(-0.778358\pi\) | ||
0.767214 | − | 0.641391i | \(-0.221642\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.24013e8 | − | 4.75744e8i | −0.703472 | − | 0.406150i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.64776e9 | + | 9.51333e8i | −1.34749 | + | 0.777976i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.38320e8 | − | 7.59193e8i | −0.329350 | − | 0.570451i | 0.653033 | − | 0.757330i | \(-0.273496\pi\) |
−0.982383 | + | 0.186878i | \(0.940163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.10859e9 | + | 1.92013e9i | −0.798987 | + | 1.38389i | 0.121289 | + | 0.992617i | \(0.461297\pi\) |
−0.920276 | + | 0.391270i | \(0.872036\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.18728e9 | −1.45224 | −0.726120 | − | 0.687568i | \(-0.758678\pi\) | ||||
−0.726120 | + | 0.687568i | \(0.758678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.49294e8 | + | 2.59400e8i | 0.286496 | + | 0.165408i | 0.636360 | − | 0.771392i | \(-0.280439\pi\) |
−0.349865 | + | 0.936800i | \(0.613772\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.25769e8 | + | 2.50855e9i | 0.486266 | + | 1.47720i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.16152e8 | + | 2.01182e8i | 0.0657677 | + | 0.113913i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.15703e9i | 0.606398i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.03664e9 | −1.53201 | −0.766007 | − | 0.642832i | \(-0.777759\pi\) | ||||
−0.766007 | + | 0.642832i | \(0.777759\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.34520e8 | − | 4.24075e8i | 0.343755 | − | 0.198467i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.07112e8 | − | 5.13637e8i | 0.0483057 | − | 0.231642i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.61115e9 | − | 4.52264e9i | 1.09462 | − | 1.89593i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.79756e8i | − | 0.113125i | −0.998399 | − | 0.0565627i | \(-0.981986\pi\) | ||
0.998399 | − | 0.0565627i | \(-0.0180141\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.15376e8 | + | 4.13023e8i | 0.269421 | + | 0.155550i | 0.628624 | − | 0.777709i | \(-0.283618\pi\) |
−0.359204 | + | 0.933259i | \(0.616952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.66627e8 | − | 3.27142e8i | 0.206042 | − | 0.118958i | −0.393429 | − | 0.919355i | \(-0.628711\pi\) |
0.599471 | + | 0.800397i | \(0.295378\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.62310e8 | + | 1.32036e9i | 0.258647 | + | 0.447990i | 0.965880 | − | 0.258991i | \(-0.0833899\pi\) |
−0.707232 | + | 0.706981i | \(0.750057\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.83903e9 | − | 3.18529e9i | 0.603000 | − | 1.04443i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.51914e9 | −1.69153 | −0.845766 | − | 0.533554i | \(-0.820856\pi\) | ||||
−0.845766 | + | 0.533554i | \(0.820856\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.81695e9 | − | 2.20372e9i | −1.13148 | − | 0.653262i | −0.187176 | − | 0.982326i | \(-0.559933\pi\) |
−0.944308 | + | 0.329064i | \(0.893267\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.42276e9 | + | 3.26296e9i | −0.394882 | + | 0.905624i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.58786e9 | − | 2.75025e9i | −0.426603 | − | 0.738898i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.04730e8i | 0.0263862i | 0.999913 | + | 0.0131931i | \(0.00419962\pi\) | ||||
−0.999913 | + | 0.0131931i | \(0.995800\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.44997e9 | 2.06240 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.67321e9 | − | 2.69808e9i | 1.07123 | − | 0.618474i | 0.142712 | − | 0.989764i | \(-0.454418\pi\) |
0.928517 | + | 0.371290i | \(0.121084\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.46501e9 | + | 2.75895e9i | −0.547796 | + | 0.613120i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.70883e8 | − | 1.50841e9i | 0.182027 | − | 0.315281i | −0.760543 | − | 0.649287i | \(-0.775067\pi\) |
0.942571 | + | 0.334006i | \(0.108401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.20402e9i | 1.66358i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.49563e9 | + | 3.75025e9i | 1.24054 | + | 0.716228i | 0.969205 | − | 0.246256i | \(-0.0792004\pi\) |
0.271338 | + | 0.962484i | \(0.412534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.43383e9 | − | 8.27820e8i | 0.265839 | − | 0.153482i | −0.361156 | − | 0.932505i | \(-0.617618\pi\) |
0.626995 | + | 0.779023i | \(0.284284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.35273e7 | − | 1.61994e8i | −0.0163534 | − | 0.0283249i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.86228e9 | + | 3.22556e9i | −0.316320 | + | 0.547881i | −0.979717 | − | 0.200386i | \(-0.935781\pi\) |
0.663398 | + | 0.748267i | \(0.269114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.25218e9 | 0.682003 | 0.341001 | − | 0.940063i | \(-0.389234\pi\) | ||||
0.341001 | + | 0.940063i | \(0.389234\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.99908e9 | + | 4.04092e9i | 1.09118 | + | 0.629991i | 0.933890 | − | 0.357561i | \(-0.116392\pi\) |
0.157288 | + | 0.987553i | \(0.449725\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.57997e8 | − | 2.82437e8i | 0.126461 | − | 0.0416288i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.02631e9 | + | 1.77762e9i | 0.147125 | + | 0.254829i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.36774e9i | − | 0.592634i | −0.955090 | − | 0.296317i | \(-0.904241\pi\) | ||
0.955090 | − | 0.296317i | \(-0.0957585\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.09867e10 | 1.45071 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.00856e10 | + | 1.15964e10i | −2.51304 | + | 1.45091i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.03118e9 | − | 3.13257e9i | −0.125623 | − | 0.381623i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.64925e8 | + | 1.32489e9i | −0.0883933 | + | 0.153102i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.92930e9i | − | 0.329769i | −0.986313 | − | 0.164885i | \(-0.947275\pi\) | ||
0.986313 | − | 0.164885i | \(-0.0527252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.82421e9 | + | 2.78526e9i | 0.515685 | + | 0.297731i | 0.735167 | − | 0.677886i | \(-0.237104\pi\) |
−0.219482 | + | 0.975616i | \(0.570437\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.24818e10 | − | 7.20638e9i | 1.30047 | − | 0.750827i | 0.319985 | − | 0.947422i | \(-0.396322\pi\) |
0.980485 | + | 0.196596i | \(0.0629886\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.13011e9 | − | 1.40818e10i | −0.805118 | − | 1.39451i | −0.916211 | − | 0.400695i | \(-0.868769\pi\) |
0.111093 | − | 0.993810i | \(-0.464565\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.10128e10 | − | 1.90748e10i | 1.06350 | − | 1.84203i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.49023e9 | 0.504406 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.44629e8 | + | 2.56707e8i | 0.0398533 | + | 0.0230093i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.06650e10 | − | 9.52870e9i | −0.910283 | − | 0.813299i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.42352e9 | − | 4.19767e9i | −0.201899 | − | 0.349700i | 0.747241 | − | 0.664553i | \(-0.231378\pi\) |
−0.949140 | + | 0.314853i | \(0.898045\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.24875e10i | − | 0.991510i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.83740e10 | 1.42457 | 0.712284 | − | 0.701891i | \(-0.247661\pi\) | ||||
0.712284 | + | 0.701891i | \(0.247661\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.78962e9 | + | 2.18794e9i | −0.280271 | + | 0.161815i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.12911e10 | + | 8.00583e9i | 0.815752 | + | 0.578402i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.52534e9 | − | 2.64197e9i | 0.105208 | − | 0.182226i | −0.808615 | − | 0.588338i | \(-0.799782\pi\) |
0.913823 | + | 0.406112i | \(0.133116\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.05312e8i | 0.00709863i | 0.999994 | + | 0.00354932i | \(0.00112978\pi\) | ||||
−0.999994 | + | 0.00354932i | \(0.998870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.12157e10 | + | 6.47541e9i | 0.722319 | + | 0.417031i | 0.815606 | − | 0.578608i | \(-0.196404\pi\) |
−0.0932863 | + | 0.995639i | \(0.529737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.45815e9 | − | 4.30596e9i | 0.469589 | − | 0.271117i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.07794e9 | + | 5.33115e9i | 0.185303 | + | 0.320954i | 0.943679 | − | 0.330864i | \(-0.107340\pi\) |
−0.758376 | + | 0.651818i | \(0.774007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.82246e9 | + | 1.18168e10i | −0.401709 | + | 0.695781i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.39419e10 | −0.785506 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.46136e10 | + | 1.42107e10i | 1.35679 | + | 0.783341i | 0.989189 | − | 0.146644i | \(-0.0468473\pi\) |
0.367597 | + | 0.929985i | \(0.380181\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.12285e10 | + | 6.51227e9i | 1.64837 | + | 0.343745i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.55292e10 | + | 2.68973e10i | 0.802256 | + | 1.38955i | 0.918128 | + | 0.396285i | \(0.129701\pi\) |
−0.115871 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.04544e10i | 2.99269i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.09851e10 | −1.01708 | −0.508538 | − | 0.861040i | \(-0.669814\pi\) | ||||
−0.508538 | + | 0.861040i | \(0.669814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.52677e10 | − | 1.45883e10i | 1.17428 | − | 0.677968i | 0.219592 | − | 0.975592i | \(-0.429527\pi\) |
0.954683 | + | 0.297623i | \(0.0961939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.81990e10 | − | 9.28258e9i | 1.28348 | − | 0.422499i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.52716e9 | + | 2.64512e9i | −0.0666940 | + | 0.115517i | −0.897444 | − | 0.441128i | \(-0.854578\pi\) |
0.830750 | + | 0.556645i | \(0.187912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.00961e10i | − | 1.71552i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.65039e10 | − | 2.10755e10i | −1.49951 | − | 0.865745i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.03949e10 | + | 1.17750e10i | −0.821029 | + | 0.474022i | −0.850771 | − | 0.525536i | \(-0.823865\pi\) |
0.0297420 | + | 0.999558i | \(0.490531\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.64589e9 | + | 6.31487e9i | 0.141002 | + | 0.244223i | 0.927874 | − | 0.372893i | \(-0.121634\pi\) |
−0.786872 | + | 0.617116i | \(0.788301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00530e9 | − | 1.04015e10i | 0.227674 | − | 0.394344i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.08558e10 | 1.12450 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.53566e9 | − | 3.19602e9i | −0.197823 | − | 0.114213i | 0.397817 | − | 0.917465i | \(-0.369768\pi\) |
−0.595640 | + | 0.803252i | \(0.703101\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.72116e9 | − | 4.18209e10i | 0.299760 | − | 1.43745i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.23906e9 | + | 1.08064e10i | 0.210342 | + | 0.364324i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 2.79463e10i | − | 0.906710i | −0.891330 | − | 0.453355i | \(-0.850227\pi\) | ||
0.891330 | − | 0.453355i | \(-0.149773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.37743e10 | −0.438471 | −0.219236 | − | 0.975672i | \(-0.570356\pi\) | ||||
−0.219236 | + | 0.975672i | \(0.570356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.68681e8 | + | 4.43798e8i | −0.0235608 | + | 0.0136028i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.43598e9 | + | 3.96336e9i | 0.133438 | + | 0.119221i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.39670e10 | + | 4.15121e10i | −0.694553 | + | 1.20300i | 0.275778 | + | 0.961221i | \(0.411064\pi\) |
−0.970331 | + | 0.241780i | \(0.922269\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.89618e10i | − | 0.539421i | −0.962941 | − | 0.269710i | \(-0.913072\pi\) | ||
0.962941 | − | 0.269710i | \(-0.0869280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.11161e10 | − | 1.21914e10i | −0.579012 | − | 0.334293i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.80396e10 | − | 1.04152e10i | 0.485701 | − | 0.280420i | −0.237088 | − | 0.971488i | \(-0.576193\pi\) |
0.722789 | + | 0.691068i | \(0.242860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.13390e9 | − | 3.69603e9i | −0.0554064 | − | 0.0959667i | 0.836992 | − | 0.547215i | \(-0.184312\pi\) |
−0.892398 | + | 0.451249i | \(0.850979\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.05823e10 | + | 5.29702e10i | −0.779885 | + | 1.35080i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.76647e10 | −0.434631 | −0.217315 | − | 0.976101i | \(-0.569730\pi\) | ||||
−0.217315 | + | 0.976101i | \(0.569730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.52413e9 | − | 3.76671e9i | −0.157694 | − | 0.0910449i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.42900e10 | + | 6.07640e10i | −1.26670 | + | 1.41775i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.32670e9 | − | 1.61543e10i | −0.213827 | − | 0.370360i | 0.739082 | − | 0.673616i | \(-0.235260\pi\) |
−0.952909 | + | 0.303256i | \(0.901926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 5.34641e10i | − | 1.18375i | −0.806031 | − | 0.591873i | \(-0.798389\pi\) | ||
0.806031 | − | 0.591873i | \(-0.201611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.51355e9 | 0.207023 | 0.103511 | − | 0.994628i | \(-0.466992\pi\) | ||||
0.103511 | + | 0.994628i | \(0.466992\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.06656e10 | − | 2.92518e10i | 1.06524 | − | 0.615014i | 0.138360 | − | 0.990382i | \(-0.455817\pi\) |
0.926876 | + | 0.375368i | \(0.122484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.75336e10 | − | 9.91246e9i | −0.982448 | − | 0.204876i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.37523e10 | + | 2.38197e10i | −0.274746 | + | 0.475874i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.39754e8i | 0.0106028i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.27318e10 | − | 3.62182e10i | −1.19164 | − | 0.687995i | −0.232963 | − | 0.972486i | \(-0.574842\pi\) |
−0.958679 | + | 0.284491i | \(0.908175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.33443e10 | + | 4.23454e10i | −1.37021 | + | 0.791089i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.73082e10 | + | 8.19401e10i | 0.855006 | + | 1.48091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.05514e10 | − | 3.55961e10i | 0.365364 | − | 0.632829i | −0.623471 | − | 0.781847i | \(-0.714278\pi\) |
0.988834 | + | 0.149018i | \(0.0476112\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.94153e10 | 1.19434 | 0.597171 | − | 0.802114i | \(-0.296291\pi\) | ||||
0.597171 | + | 0.802114i | \(0.296291\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.05121e10 | − | 5.22572e10i | −1.53221 | − | 0.884623i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.04704e10 | − | 3.18074e10i | −0.171608 | − | 0.521318i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.72460e10 | − | 8.18325e10i | −0.762014 | − | 1.31985i | −0.941811 | − | 0.336143i | \(-0.890877\pi\) |
0.179797 | − | 0.983704i | \(-0.442456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.86742e10i | − | 0.291722i | −0.989305 | − | 0.145861i | \(-0.953405\pi\) | ||
0.989305 | − | 0.145861i | \(-0.0465952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.42769e8 | 0.00219517 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.20450e10 | − | 6.95417e9i | 0.179446 | − | 0.103603i | −0.407586 | − | 0.913167i | \(-0.633629\pi\) |
0.587033 | + | 0.809563i | \(0.300296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.10669e10 | + | 5.30696e10i | −0.162309 | + | 0.778327i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.95426e10 | + | 3.38487e10i | −0.277813 | + | 0.481186i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.19276e11i | 1.66951i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.08781e10 | − | 1.20540e10i | −0.283361 | − | 0.163598i | 0.351583 | − | 0.936157i | \(-0.385643\pi\) |
−0.634944 | + | 0.772558i | \(0.718977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.64362e10 | + | 3.83570e10i | −0.887970 | + | 0.512670i | −0.873278 | − | 0.487222i | \(-0.838010\pi\) |
−0.0146920 | + | 0.999892i | \(0.504677\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.03820e10 | + | 1.79822e10i | 0.134599 | + | 0.233132i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.98804e10 | + | 8.63953e10i | −0.636953 | + | 1.10323i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.06772e10 | 0.256202 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.85567e10 | − | 5.11282e10i | −1.08095 | − | 0.624088i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.29500e10 | − | 1.14707e11i | −0.153432 | − | 1.35905i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.11688e10 | + | 1.93448e10i | 0.130381 | + | 0.225827i | 0.923824 | − | 0.382818i | \(-0.125046\pi\) |
−0.793442 | + | 0.608646i | \(0.791713\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.28580e10i | 0.712483i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.84774e10 | 0.318091 | 0.159045 | − | 0.987271i | \(-0.449158\pi\) | ||||
0.159045 | + | 0.987271i | \(0.449158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.50411e10 | + | 3.17780e10i | −0.597146 | + | 0.344763i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.09200e11 | + | 1.22222e11i | −1.16768 | + | 1.30692i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.68470e10 | − | 8.11414e10i | 0.486700 | − | 0.842989i | −0.513183 | − | 0.858279i | \(-0.671534\pi\) |
0.999883 | + | 0.0152903i | \(0.00486723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.54928e10i | − | 0.773140i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.08714e11 | + | 6.27658e10i | 1.08206 | + | 0.624726i | 0.931450 | − | 0.363868i | \(-0.118544\pi\) |
0.150606 | + | 0.988594i | \(0.451877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.64134e10 | + | 2.67968e10i | −0.455460 | + | 0.262960i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.82494e10 | + | 1.00891e11i | 0.555702 | + | 0.962504i | 0.997849 | + | 0.0655615i | \(0.0208839\pi\) |
−0.442146 | + | 0.896943i | \(0.645783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.72065e10 | − | 4.71230e10i | 0.255934 | − | 0.443290i | −0.709215 | − | 0.704992i | \(-0.750950\pi\) |
0.965149 | + | 0.261702i | \(0.0842837\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.94192e9 | 0.0360609 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.45186e10 | + | 1.99293e10i | 0.311422 | + | 0.179800i | 0.647563 | − | 0.762012i | \(-0.275788\pi\) |
−0.336141 | + | 0.941812i | \(0.609122\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.60868e10 | − | 1.51709e10i | 0.404457 | − | 0.133140i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.33024e11 | − | 2.30405e11i | −1.15148 | − | 1.99442i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.67244e11i | 1.40863i | 0.709887 | + | 0.704315i | \(0.248746\pi\) | ||||
−0.709887 | + | 0.704315i | \(0.751254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.26268e10 | 0.104914 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.76644e10 | − | 1.01985e10i | 0.142850 | − | 0.0824745i | −0.426872 | − | 0.904312i | \(-0.640384\pi\) |
0.569722 | + | 0.821838i | \(0.307051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.40470e10 | − | 1.33808e11i | −0.351438 | − | 1.06761i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.56266e9 | + | 6.17071e9i | −0.0276737 | + | 0.0479323i | −0.879531 | − | 0.475842i | \(-0.842143\pi\) |
0.851857 | + | 0.523775i | \(0.175477\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.24623e10i | − | 0.0955217i | −0.998859 | − | 0.0477608i | \(-0.984791\pi\) | ||
0.998859 | − | 0.0477608i | \(-0.0152085\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.97928e10 | − | 5.76154e10i | −0.744865 | − | 0.430048i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.63526e10 | − | 1.52147e10i | 0.194119 | − | 0.112075i | −0.399790 | − | 0.916607i | \(-0.630917\pi\) |
0.593909 | + | 0.804532i | \(0.297584\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.63690e11 | − | 2.83519e11i | −1.17451 | − | 2.03431i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.49181e10 | − | 2.58389e10i | 0.105650 | − | 0.182992i | −0.808353 | − | 0.588698i | \(-0.799641\pi\) |
0.914004 | + | 0.405706i | \(0.132974\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.31729e11 | −0.908951 | −0.454476 | − | 0.890759i | \(-0.650173\pi\) | ||||
−0.454476 | + | 0.890759i | \(0.650173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.67672e10 | − | 5.58686e10i | −0.659121 | − | 0.380544i | 0.132821 | − | 0.991140i | \(-0.457597\pi\) |
−0.791942 | + | 0.610596i | \(0.790930\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.77354e11 | + | 1.58459e11i | 1.17731 | + | 1.05187i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.44258e10 | + | 1.28909e11i | 0.487757 | + | 0.844820i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.46414e11i | − | 0.935366i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.70388e11 | 1.07479 | 0.537394 | − | 0.843331i | \(-0.319409\pi\) | ||||
0.537394 | + | 0.843331i | \(0.319409\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.71488e11 | + | 9.90086e10i | −1.05472 | + | 0.608945i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.88203e11 | + | 2.54888e11i | 1.14306 | + | 1.54807i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.05906e10 | − | 5.29845e10i | 0.181199 | − | 0.313846i | −0.761090 | − | 0.648646i | \(-0.775335\pi\) |
0.942289 | + | 0.334800i | \(0.108669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.91845e11i | − | 1.70730i | −0.520851 | − | 0.853648i | \(-0.674385\pi\) | ||
0.520851 | − | 0.853648i | \(-0.325615\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.80122e10 | − | 2.19463e10i | −0.216923 | − | 0.125241i | 0.387602 | − | 0.921827i | \(-0.373304\pi\) |
−0.604525 | + | 0.796586i | \(0.706637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.08556e11 | + | 1.78145e11i | −1.73922 | + | 1.00414i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.29185e11 | − | 2.23754e11i | −0.710490 | − | 1.23060i | −0.964674 | − | 0.263448i | \(-0.915140\pi\) |
0.254184 | − | 0.967156i | \(-0.418193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.15703e11 | + | 2.00404e11i | −0.628607 | + | 1.08878i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.43842e10 | −0.129291 | −0.0646453 | − | 0.997908i | \(-0.520592\pi\) | ||||
−0.0646453 | + | 0.997908i | \(0.520592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.99492e11 | + | 1.15177e11i | 1.04501 | + | 0.603335i | 0.921247 | − | 0.388977i | \(-0.127171\pi\) |
0.123760 | + | 0.992312i | \(0.460505\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.38606e10 | − | 1.74879e10i | −0.428816 | − | 0.0894236i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.32081e11 | + | 4.01975e11i | 1.17256 | + | 2.03093i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.96115e10i | − | 0.244733i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.55818e11 | −1.24701 | −0.623505 | − | 0.781819i | \(-0.714292\pi\) | ||||
−0.623505 | + | 0.781819i | \(0.714292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.09308e11 | + | 6.31087e10i | −0.520350 | + | 0.300424i | −0.737078 | − | 0.675808i | \(-0.763795\pi\) |
0.216728 | + | 0.976232i | \(0.430462\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.49457e11 | − | 1.15035e11i | 1.64405 | − | 0.541190i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.14943e11 | + | 1.99087e11i | −0.528201 | + | 0.914871i | 0.471258 | + | 0.881995i | \(0.343800\pi\) |
−0.999459 | + | 0.0328759i | \(0.989533\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.54597e11i | − | 1.15636i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.32397e11 | + | 3.65115e11i | 2.80616 | + | 1.62014i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.36193e11 | − | 1.94101e11i | 1.47461 | − | 0.851364i | 0.475016 | − | 0.879977i | \(-0.342442\pi\) |
0.999591 | + | 0.0286128i | \(0.00910899\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.59377e10 | − | 7.95665e10i | −0.196893 | − | 0.341029i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.78735e10 | + | 3.09578e10i | −0.0757317 | + | 0.131171i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.95053e11 | 1.22188 | 0.610938 | − | 0.791678i | \(-0.290792\pi\) | ||||
0.610938 | + | 0.791678i | \(0.290792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.71072e10 | − | 4.45179e10i | −0.315699 | − | 0.182269i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.13328e8 | − | 5.43447e8i | 0.000453587 | − | 0.00217510i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.30909e11 | − | 2.26742e11i | −0.518067 | − | 0.897318i | −0.999780 | − | 0.0209890i | \(-0.993318\pi\) |
0.481713 | − | 0.876329i | \(-0.340015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.22158e10i | − | 0.356818i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.79576e11 | 2.60024 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.38996e11 | − | 1.95719e11i | 1.26847 | − | 0.732349i | 0.293769 | − | 0.955877i | \(-0.405091\pi\) |
0.974698 | + | 0.223527i | \(0.0717572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.13332e11 | + | 1.01257e11i | 0.419384 | + | 0.374701i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.13750e9 | − | 8.89841e9i | 0.0185952 | − | 0.0322078i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.07684e11i | − | 1.45944i | −0.683747 | − | 0.729719i | \(-0.739651\pi\) | ||
0.683747 | − | 0.729719i | \(-0.260349\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.13028e11 | + | 6.52565e10i | 0.395835 | + | 0.228536i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.12013e11 | + | 6.46709e10i | −0.388020 | + | 0.224023i | −0.681302 | − | 0.732003i | \(-0.738586\pi\) |
0.293282 | + | 0.956026i | \(0.405252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.02479e11 | + | 3.50704e11i | 0.686294 | + | 1.18870i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.78609e11 | − | 3.09359e11i | 0.598859 | − | 1.03725i | −0.394130 | − | 0.919055i | \(-0.628954\pi\) |
0.992990 | − | 0.118200i | \(-0.0377125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.59095e11 | −1.83455 | −0.917277 | − | 0.398249i | \(-0.869618\pi\) | ||||
−0.917277 | + | 0.398249i | \(0.869618\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.22969e11 | + | 7.09964e10i | 0.399183 | + | 0.230468i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.64914e11 | + | 2.96505e11i | −0.841741 | + | 0.942117i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.22661e10 | + | 1.59810e11i | 0.290056 | + | 0.502392i | 0.973823 | − | 0.227309i | \(-0.0729926\pi\) |
−0.683766 | + | 0.729701i | \(0.739659\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.79403e11i | 0.859890i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.72832e11 | 1.43987 | 0.719935 | − | 0.694041i | \(-0.244171\pi\) | ||||
0.719935 | + | 0.694041i | \(0.244171\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.50188e11 | + | 8.67112e10i | −0.447813 | + | 0.258545i | −0.706906 | − | 0.707307i | \(-0.749910\pi\) |
0.259093 | + | 0.965852i | \(0.416576\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.39268e11 | + | 4.98960e10i | 0.705971 | + | 0.147220i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.88958e11 | − | 8.46900e11i | 1.41283 | − | 2.44710i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.96725e9i | 0.00562542i | 0.999996 | + | 0.00281271i | \(0.000895314\pi\) | ||||
−0.999996 | + | 0.00281271i | \(0.999105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.82266e11 | − | 2.20701e11i | −1.07065 | − | 0.618141i | −0.142292 | − | 0.989825i | \(-0.545447\pi\) |
−0.928359 | + | 0.371684i | \(0.878780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.76787e9 | + | 1.02068e9i | −0.00490052 | + | 0.00282932i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.08690e10 | + | 1.88257e10i | 0.0295148 | + | 0.0511211i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.39638e11 | + | 2.41860e11i | −0.375318 | + | 0.650070i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.13372e11 | −1.08859 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.79181e10 | + | 5.65331e10i | 0.255249 | + | 0.147368i | 0.622165 | − | 0.782886i | \(-0.286253\pi\) |
−0.366916 | + | 0.930254i | \(0.619586\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.51593e10 | + | 1.97943e11i | 0.166445 | + | 0.505632i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.80850e10 | + | 1.17927e11i | 0.172170 | + | 0.298208i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4.98251e11i | − | 1.23485i | −0.786629 | − | 0.617426i | \(-0.788175\pi\) | ||
0.786629 | − | 0.617426i | \(-0.211825\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.65978e11 | 1.38871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.91548e11 | − | 2.26060e11i | 0.941723 | − | 0.543704i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.27718e11 | + | 6.12449e11i | −0.304136 | + | 1.45843i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.12731e11 | − | 3.68460e11i | 0.496634 | − | 0.860195i | −0.503359 | − | 0.864077i | \(-0.667903\pi\) |
0.999992 | + | 0.00388285i | \(0.00123595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.55952e11i | − | 1.05399i | −0.849869 | − | 0.526994i | \(-0.823319\pi\) | ||
0.849869 | − | 0.526994i | \(-0.176681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.48717e11 | + | 8.58617e10i | 0.337077 | + | 0.194612i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.87329e10 | − | 3.96830e10i | 0.154268 | − | 0.0890668i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.14025e11 | + | 3.70703e11i | 0.471078 | + | 0.815931i | 0.999453 | − | 0.0330806i | \(-0.0105318\pi\) |
−0.528375 | + | 0.849011i | \(0.677198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.99516e10 | − | 6.91983e10i | 0.0870834 | − | 0.150833i | −0.819194 | − | 0.573517i | \(-0.805579\pi\) |
0.906277 | + | 0.422684i | \(0.138912\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.92333e11 | −0.411180 | −0.205590 | − | 0.978638i | \(-0.565911\pi\) | ||||
−0.205590 | + | 0.978638i | \(0.565911\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.70459e10 | + | 2.71620e10i | 0.0996102 | + | 0.0575100i | 0.548978 | − | 0.835837i | \(-0.315017\pi\) |
−0.449367 | + | 0.893347i | \(0.648351\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.44301e11 | + | 6.14494e10i | −1.13047 | + | 0.127625i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.49947e11 | − | 7.79330e11i | −0.925582 | − | 1.60316i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.14519e11i | 0.231116i | 0.993301 | + | 0.115558i | \(0.0368655\pi\) | ||||
−0.993301 | + | 0.115558i | \(0.963134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.09634e11 | 1.41857 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.17914e12 | + | 6.80776e11i | −2.31280 | + | 1.33530i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.98527e11 | + | 3.34126e11i | −0.580029 | + | 0.649197i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.25122e11 | + | 5.63128e11i | −0.619910 | + | 1.07372i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.52816e11i | 0.477538i | 0.971076 | + | 0.238769i | \(0.0767439\pi\) | ||||
−0.971076 | + | 0.238769i | \(0.923256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.35338e11 | − | 3.66813e11i | −1.17783 | − | 0.680019i | −0.222317 | − | 0.974975i | \(-0.571362\pi\) |
−0.955511 | + | 0.294955i | \(0.904695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.41286e11 | + | 3.70246e11i | −1.17782 | + | 0.680015i | −0.955509 | − | 0.294961i | \(-0.904693\pi\) |
−0.222311 | + | 0.974976i | \(0.571360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.45339e11 | + | 2.51735e11i | 0.262024 | + | 0.453838i | 0.966780 | − | 0.255612i | \(-0.0822769\pi\) |
−0.704756 | + | 0.709450i | \(0.748944\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.47664e11 | − | 2.55762e11i | 0.263761 | − | 0.456848i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.36692e12 | 2.39697 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.62586e11 | − | 5.55749e11i | −1.67250 | − | 0.965620i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.63247e11 | − | 1.85411e11i | 0.960875 | − | 0.316302i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.36290e10 | + | 5.82471e10i | 0.0568480 | + | 0.0984636i | 0.893049 | − | 0.449960i | \(-0.148562\pi\) |
−0.836201 | + | 0.548423i | \(0.815228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.59947e10i | 0.0763491i | 0.999271 | + | 0.0381746i | \(0.0121543\pi\) | ||||
−0.999271 | + | 0.0381746i | \(0.987846\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.12554e12 | 1.85147 | 0.925736 | − | 0.378170i | \(-0.123446\pi\) | ||||
0.925736 | + | 0.378170i | \(0.123446\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.90077e11 | − | 5.71621e11i | 1.59946 | − | 0.923451i | 0.607874 | − | 0.794033i | \(-0.292023\pi\) |
0.991590 | − | 0.129418i | \(-0.0413108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.40750e11 | + | 7.31358e11i | 0.385442 | + | 1.17091i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.72088e11 | − | 2.98065e11i | 0.270610 | − | 0.468711i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.40236e11i | 0.218558i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.08166e11 | − | 1.20185e11i | −0.318692 | − | 0.183997i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09330e12 | + | 6.31216e11i | −1.65897 | + | 0.957808i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.25071e11 | − | 7.36244e11i | −0.633676 | − | 1.09756i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.51450e9 | − | 4.35525e9i | 0.00371555 | − | 0.00643552i | −0.864162 | − | 0.503214i | \(-0.832151\pi\) |
0.867877 | + | 0.496779i | \(0.165484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.16880e12 | −1.69695 | −0.848473 | − | 0.529239i | \(-0.822477\pi\) | ||||
−0.848473 | + | 0.529239i | \(0.822477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.50440e11 | − | 2.02327e11i | −0.504348 | − | 0.291185i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.70990e11 | + | 5.99500e11i | 0.948940 | + | 0.847836i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.25808e11 | − | 7.37520e11i | −0.596968 | − | 1.03398i | −0.993266 | − | 0.115857i | \(-0.963038\pi\) |
0.396297 | − | 0.918122i | \(-0.370295\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 7.66537e11i | − | 1.05615i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.43943e10 | 0.0196618 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.58747e11 | − | 2.07123e11i | 0.481643 | − | 0.278077i | −0.239458 | − | 0.970907i | \(-0.576970\pi\) |
0.721101 | + | 0.692830i | \(0.243636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.33135e11 | + | 3.05333e11i | −0.177213 | + | 0.406420i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.87431e11 | + | 1.01746e12i | −0.768617 | + | 1.33128i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.30071e12i | − | 1.68741i | −0.536808 | − | 0.843705i | \(-0.680370\pi\) | ||
0.536808 | − | 0.843705i | \(-0.319630\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.76943e11 | + | 4.48568e11i | 0.990902 | + | 0.572098i | 0.905544 | − | 0.424253i | \(-0.139463\pi\) |
0.0853583 | + | 0.996350i | \(0.472796\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.37487e11 | − | 7.93783e10i | 0.173866 | − | 0.100382i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.01806e11 | + | 1.76333e11i | 0.126582 | + | 0.219247i | 0.922350 | − | 0.386355i | \(-0.126266\pi\) |
−0.795768 | + | 0.605602i | \(0.792933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.20474e11 | + | 1.07469e12i | −0.764995 | + | 1.32501i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.36718e11 | 1.13563 | 0.567815 | − | 0.823156i | \(-0.307789\pi\) | ||||
0.567815 | + | 0.823156i | \(0.307789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.68788e11 | − | 2.70655e11i | −0.563589 | − | 0.325388i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.69122e11 | − | 2.02097e11i | −1.14579 | − | 0.238938i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.02568e11 | − | 6.97269e11i | −0.472004 | − | 0.817535i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.36906e12i | 1.57875i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.50527e11 | −0.743976 | −0.371988 | − | 0.928237i | \(-0.621324\pi\) | ||||
−0.371988 | + | 0.928237i | \(0.621324\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.75548e11 | − | 2.74558e11i | 0.534955 | − | 0.308856i | −0.208077 | − | 0.978112i | \(-0.566720\pi\) |
0.743032 | + | 0.669256i | \(0.233387\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.39334e11 | + | 1.11702e11i | −0.378596 | + | 0.124627i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.65868e11 | + | 8.06907e11i | −0.511310 | + | 0.885616i | 0.488604 | + | 0.872506i | \(0.337506\pi\) |
−0.999914 | + | 0.0131097i | \(0.995827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.98351e12i | − | 2.15925i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.03641e11 | + | 3.48512e11i | 0.646494 | + | 0.373254i | 0.787112 | − | 0.616810i | \(-0.211575\pi\) |
−0.140618 | + | 0.990064i | \(0.544909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.16966e12 | + | 6.75301e11i | −1.24255 | + | 0.717386i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.89812e11 | − | 5.01969e11i | −0.302922 | − | 0.524677i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.15650e11 | + | 1.23954e12i | −0.742004 | + | 1.28519i | 0.209577 | + | 0.977792i | \(0.432791\pi\) |
−0.951581 | + | 0.307397i | \(0.900542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.20349e11 | 0.326837 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.42004e12 | − | 8.19863e11i | −1.43721 | − | 0.829776i | −0.439558 | − | 0.898214i | \(-0.644865\pi\) |
−0.997655 | + | 0.0684384i | \(0.978198\pi\) | |||||||
\(998\) | 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 | 252.9.z.e.73.8 | yes | 20 | |
3.2 | odd | 2 | inner | 252.9.z.e.73.3 | ✓ | 20 | |
7.5 | odd | 6 | inner | 252.9.z.e.145.8 | yes | 20 | |
21.5 | even | 6 | inner | 252.9.z.e.145.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.z.e.73.3 | ✓ | 20 | 3.2 | odd | 2 | inner | |
252.9.z.e.73.8 | yes | 20 | 1.1 | even | 1 | trivial | |
252.9.z.e.145.3 | yes | 20 | 21.5 | even | 6 | inner | |
252.9.z.e.145.8 | yes | 20 | 7.5 | odd | 6 | inner |