Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,12,Mod(37,252)]
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, 2]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), 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: | \(193.622481501\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{15}\cdot 7^{9} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.8 | ||
Root | \(13166.9 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.37 |
Dual form | 252.12.k.d.109.8 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 6718.22 | − | 11636.3i | 0.961433 | − | 1.66525i | 0.242525 | − | 0.970145i | \(-0.422024\pi\) |
0.718908 | − | 0.695106i | \(-0.244642\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 41445.4 | + | 16112.4i | 0.932045 | + | 0.362344i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 425643. | + | 737235.i | 0.796866 | + | 1.38021i | 0.921647 | + | 0.388028i | \(0.126844\pi\) |
−0.124781 | + | 0.992184i | \(0.539823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.13303e6 | 1.59334 | 0.796669 | − | 0.604416i | \(-0.206593\pi\) | ||||
0.796669 | + | 0.604416i | \(0.206593\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.28105e6 | − | 2.21884e6i | −0.218825 | − | 0.379016i | 0.735624 | − | 0.677390i | \(-0.236889\pi\) |
−0.954449 | + | 0.298374i | \(0.903556\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.87791e6 | − | 1.53770e7i | 0.822557 | − | 1.42471i | −0.0812152 | − | 0.996697i | \(-0.525880\pi\) |
0.903772 | − | 0.428014i | \(-0.140787\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.81716e7 | − | 3.14742e7i | 0.588695 | − | 1.01965i | −0.405708 | − | 0.914003i | \(-0.632975\pi\) |
0.994404 | − | 0.105648i | \(-0.0336915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.58548e7 | − | 1.14064e8i | −1.34871 | − | 2.33603i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −571626. | −0.00517515 | −0.00258757 | − | 0.999997i | \(-0.500824\pi\) | ||||
−0.00258757 | + | 0.999997i | \(0.500824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.07907e8 | + | 1.86901e8i | 0.676956 | + | 1.17252i | 0.975893 | + | 0.218250i | \(0.0700348\pi\) |
−0.298936 | + | 0.954273i | \(0.596632\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.65927e8 | − | 3.74024e8i | 1.49949 | − | 1.20372i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.87524e7 | + | 1.71044e8i | −0.234120 | + | 0.405508i | −0.959017 | − | 0.283350i | \(-0.908554\pi\) |
0.724897 | + | 0.688858i | \(0.241887\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.72342e8 | 0.367116 | 0.183558 | − | 0.983009i | \(-0.441238\pi\) | ||||
0.183558 | + | 0.983009i | \(0.441238\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.11575e9 | 1.15741 | 0.578707 | − | 0.815536i | \(-0.303558\pi\) | ||||
0.578707 | + | 0.815536i | \(0.303558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.98664e8 | + | 6.90506e8i | −0.253553 | + | 0.439167i | −0.964501 | − | 0.264077i | \(-0.914933\pi\) |
0.710949 | + | 0.703244i | \(0.248266\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.45811e9 | + | 1.33557e9i | 0.737414 | + | 0.675441i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.76715e8 | + | 1.17210e9i | 0.222274 | + | 0.384990i | 0.955498 | − | 0.294997i | \(-0.0953188\pi\) |
−0.733224 | + | 0.679987i | \(0.761985\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.14382e10 | 3.06453 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.81442e8 | − | 6.60677e8i | −0.0694613 | − | 0.120310i | 0.829203 | − | 0.558948i | \(-0.188795\pi\) |
−0.898664 | + | 0.438637i | \(0.855461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.04039e9 | + | 3.53405e9i | −0.309313 | + | 0.535746i | −0.978212 | − | 0.207607i | \(-0.933432\pi\) |
0.668899 | + | 0.743353i | \(0.266766\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.43301e10 | − | 2.48205e10i | 1.53189 | − | 2.65331i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.08784e9 | + | 1.88419e9i | 0.0984358 | + | 0.170496i | 0.911037 | − | 0.412324i | \(-0.135283\pi\) |
−0.812602 | + | 0.582820i | \(0.801949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.82655e10 | −1.20147 | −0.600733 | − | 0.799450i | \(-0.705124\pi\) | ||||
−0.600733 | + | 0.799450i | \(0.705124\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.03329e10 | + | 1.78972e10i | 0.583375 | + | 1.01043i | 0.995076 | + | 0.0991158i | \(0.0316014\pi\) |
−0.411701 | + | 0.911319i | \(0.635065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.76230e9 | + | 3.74131e10i | 0.242603 | + | 1.57516i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.28553e10 | + | 2.22661e10i | −0.470039 | + | 0.814132i | −0.999413 | − | 0.0342567i | \(-0.989094\pi\) |
0.529374 | + | 0.848389i | \(0.322427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.36264e10 | −0.379710 | −0.189855 | − | 0.981812i | \(-0.560802\pi\) | ||||
−0.189855 | + | 0.981812i | \(0.560802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.44255e10 | −0.841542 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.18461e9 | + | 8.98001e9i | −0.0984173 | + | 0.170464i | −0.911030 | − | 0.412341i | \(-0.864711\pi\) |
0.812612 | + | 0.582804i | \(0.198045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.84041e10 | + | 3.43682e10i | 1.48506 | + | 0.577336i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.19287e11 | − | 2.06612e11i | −1.58167 | − | 2.73953i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.14522e11 | −1.35408 | −0.677040 | − | 0.735947i | \(-0.736737\pi\) | ||||
−0.677040 | + | 0.735947i | \(0.736737\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.25331e10 | − | 2.17079e10i | −0.118656 | − | 0.205518i | 0.800579 | − | 0.599227i | \(-0.204525\pi\) |
−0.919235 | + | 0.393708i | \(0.871192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.90267e10 | + | 6.75962e10i | −0.331709 | + | 0.574536i | −0.982847 | − | 0.184423i | \(-0.940958\pi\) |
0.651138 | + | 0.758959i | \(0.274292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.14704e11 | − | 1.98672e11i | 0.790617 | − | 1.36939i | −0.134969 | − | 0.990850i | \(-0.543093\pi\) |
0.925585 | − | 0.378539i | \(-0.123573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.04619e11 | + | 1.81206e11i | 0.651278 | + | 1.12805i | 0.982813 | + | 0.184603i | \(0.0591001\pi\) |
−0.331535 | + | 0.943443i | \(0.607567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.19133e11 | 1.11886 | 0.559432 | − | 0.828877i | \(-0.311019\pi\) | ||||
0.559432 | + | 0.828877i | \(0.311019\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.44162e11 | − | 4.22901e11i | −1.13198 | − | 1.96065i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.73427e10 | − | 1.12601e11i | −0.0666205 | − | 0.432549i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.19687e11 | + | 3.80510e11i | −0.769991 | + | 1.33366i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.11363e12 | −3.26390 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.57513e11 | 0.691639 | 0.345819 | − | 0.938301i | \(-0.387601\pi\) | ||||
0.345819 | + | 0.938301i | \(0.387601\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.19906e11 | − | 3.80889e11i | 0.498018 | − | 0.862593i | −0.501979 | − | 0.864880i | \(-0.667394\pi\) |
0.999997 | + | 0.00228653i | \(0.000727827\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.15708e11 | − | 4.94261e11i | 1.28289 | − | 1.02985i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.51907e11 | + | 4.36315e11i | 0.445940 | + | 0.772391i | 0.998117 | − | 0.0613357i | \(-0.0195360\pi\) |
−0.552177 | + | 0.833727i | \(0.686203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.93201e11 | 0.315812 | 0.157906 | − | 0.987454i | \(-0.449526\pi\) | ||||
0.157906 | + | 0.987454i | \(0.449526\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.07907e11 | + | 1.57254e12i | 1.26968 | + | 2.19915i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.84031e9 | + | 6.65161e9i | −0.00497556 | + | 0.00861792i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.50276e10 | + | 6.06696e10i | −0.0390738 | + | 0.0676778i | −0.884901 | − | 0.465779i | \(-0.845774\pi\) |
0.845827 | + | 0.533457i | \(0.179107\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.29667e11 | + | 9.17410e11i | 0.549073 | + | 0.951022i | 0.998338 | + | 0.0576234i | \(0.0183523\pi\) |
−0.449266 | + | 0.893398i | \(0.648314\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.89977e12 | 2.60339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.29713e11 | − | 3.97875e11i | −0.192193 | − | 0.332888i | 0.753784 | − | 0.657123i | \(-0.228227\pi\) |
−0.945977 | + | 0.324234i | \(0.894893\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.26025e12 | − | 1.01167e12i | 0.918154 | − | 0.737049i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.42888e11 | + | 2.47489e11i | −0.0972665 | + | 0.168470i | −0.910552 | − | 0.413394i | \(-0.864343\pi\) |
0.813286 | + | 0.581864i | \(0.197677\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.47522e12 | −0.878850 | −0.439425 | − | 0.898279i | \(-0.644818\pi\) | ||||
−0.439425 | + | 0.898279i | \(0.644818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.75764e12 | 1.53873 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.02485e11 | + | 1.21674e12i | −0.344654 | + | 0.596959i | −0.985291 | − | 0.170886i | \(-0.945337\pi\) |
0.640637 | + | 0.767844i | \(0.278670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.91535e11 | − | 5.78850e12i | −0.410610 | − | 2.66598i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.25836e12 | − | 2.17955e12i | −0.511816 | − | 0.886491i | −0.999906 | − | 0.0136982i | \(-0.995640\pi\) |
0.488090 | − | 0.872793i | \(-0.337694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.11043e12 | −1.19011 | −0.595056 | − | 0.803684i | \(-0.702870\pi\) | ||||
−0.595056 | + | 0.803684i | \(0.702870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.32688e12 | + | 2.29822e12i | 0.450181 | + | 0.779737i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.09054e12 | − | 1.88887e12i | 0.348748 | − | 0.604049i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.63090e11 | − | 9.75301e11i | 0.160286 | − | 0.277623i | −0.774686 | − | 0.632347i | \(-0.782092\pi\) |
0.934971 | + | 0.354724i | \(0.115425\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.08140e12 | − | 1.87305e12i | −0.290685 | − | 0.503482i | 0.683287 | − | 0.730150i | \(-0.260550\pi\) |
−0.973972 | + | 0.226669i | \(0.927217\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.02832e12 | −1.44755 | −0.723773 | − | 0.690038i | \(-0.757594\pi\) | ||||
−0.723773 | + | 0.690038i | \(0.757594\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.43126e12 | − | 2.47901e12i | −0.325106 | − | 0.563100i | 0.656428 | − | 0.754389i | \(-0.272067\pi\) |
−0.981534 | + | 0.191289i | \(0.938733\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.36912e10 | − | 9.21026e9i | −0.00482347 | − | 0.00187518i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.82965e12 | − | 3.16905e12i | 0.352958 | − | 0.611341i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.51153e13 | 2.62187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.22306e12 | −0.530535 | −0.265268 | − | 0.964175i | \(-0.585460\pi\) | ||||
−0.265268 | + | 0.964175i | \(0.585460\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.49582e12 | − | 1.29831e13i | 1.11278 | − | 1.92738i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.46083e12 | + | 9.48480e12i | 0.206097 | + | 1.33813i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.73251e12 | − | 4.73285e12i | −0.348662 | − | 0.603900i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.12361e13 | −1.36440 | −0.682198 | − | 0.731167i | \(-0.738976\pi\) | ||||
−0.682198 | + | 0.731167i | \(0.738976\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.58401e12 | − | 1.31359e13i | −0.835135 | − | 1.44650i | −0.893921 | − | 0.448226i | \(-0.852056\pi\) |
0.0587856 | − | 0.998271i | \(-0.481277\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.82140e12 | + | 3.15476e12i | −0.191122 | + | 0.331033i | −0.945622 | − | 0.325267i | \(-0.894546\pi\) |
0.754500 | + | 0.656300i | \(0.227879\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.03650e12 | + | 1.04555e13i | −0.575874 | + | 0.997443i | 0.420072 | + | 0.907491i | \(0.362005\pi\) |
−0.995946 | + | 0.0899524i | \(0.971328\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.35662e12 | + | 9.27794e12i | 0.487548 | + | 0.844458i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.62209e12 | 0.134551 | 0.0672756 | − | 0.997734i | \(-0.478569\pi\) | ||||
0.0672756 | + | 0.997734i | \(0.478569\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.66226e12 | + | 1.32714e13i | 0.607104 | + | 1.05154i | 0.991715 | + | 0.128456i | \(0.0410022\pi\) |
−0.384611 | + | 0.923079i | \(0.625664\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.53369e13 | − | 7.99435e12i | 1.83375 | − | 0.578588i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.89368e13 | − | 3.27995e13i | 1.31061 | − | 2.27005i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.41336e13 | −0.895461 | −0.447731 | − | 0.894169i | \(-0.647768\pi\) | ||||
−0.447731 | + | 0.894169i | \(0.647768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.09385e13 | 1.87645 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.51915e12 | − | 1.30235e13i | 0.418347 | − | 0.724598i | −0.577427 | − | 0.816443i | \(-0.695943\pi\) |
0.995773 | + | 0.0918448i | \(0.0292764\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.84876e12 | + | 5.49785e12i | −0.365143 | + | 0.293119i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.49881e13 | + | 2.59601e13i | 0.734496 | + | 1.27218i | 0.954944 | + | 0.296786i | \(0.0959147\pi\) |
−0.220448 | + | 0.975399i | \(0.570752\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.81853e13 | 0.854806 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.23799e13 | − | 3.87631e13i | −0.968769 | − | 1.67796i | −0.699127 | − | 0.714997i | \(-0.746428\pi\) |
−0.269642 | − | 0.962961i | \(-0.586905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.30406e12 | − | 9.18689e12i | 0.220433 | − | 0.381801i | −0.734506 | − | 0.678602i | \(-0.762586\pi\) |
0.954940 | + | 0.296800i | \(0.0959196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.60612e13 | − | 9.71009e13i | 2.14948 | − | 3.72300i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.06423e13 | + | 3.57535e13i | 0.760536 | + | 1.31729i | 0.942575 | + | 0.333996i | \(0.108397\pi\) |
−0.182039 | + | 0.983291i | \(0.558270\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.69959e12 | −0.194070 | −0.0970350 | − | 0.995281i | \(-0.530936\pi\) | ||||
−0.0970350 | + | 0.995281i | \(0.530936\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.13160e11 | − | 3.69205e11i | −0.00698041 | − | 0.0120904i | 0.862514 | − | 0.506033i | \(-0.168889\pi\) |
−0.869495 | + | 0.493943i | \(0.835555\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.12873e13 | + | 4.38808e12i | 0.342169 | + | 0.133022i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.38538e13 | − | 2.39954e13i | 0.404231 | − | 0.700149i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.60966e13 | 0.435473 | 0.217737 | − | 0.976008i | \(-0.430133\pi\) | ||||
0.217737 | + | 0.976008i | \(0.430133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.02504e13 | −0.267129 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.87606e13 | − | 6.71353e13i | 0.937991 | − | 1.62465i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.62425e13 | + | 1.79773e13i | 1.07876 | + | 0.419382i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.74155e13 | + | 4.74850e13i | 0.594767 | + | 1.03017i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.67881e13 | −1.18849 | −0.594246 | − | 0.804283i | \(-0.702550\pi\) | ||||
−0.594246 | + | 0.804283i | \(0.702550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.92156e13 | + | 5.06029e13i | 0.569420 | + | 0.986264i | 0.996623 | + | 0.0821088i | \(0.0261655\pi\) |
−0.427203 | + | 0.904156i | \(0.640501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.17860e12 | − | 1.24337e13i | 0.135066 | − | 0.233941i | −0.790557 | − | 0.612389i | \(-0.790209\pi\) |
0.925623 | + | 0.378448i | \(0.123542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.47676e13 | − | 2.55782e13i | 0.259109 | − | 0.448790i | −0.706894 | − | 0.707319i | \(-0.749904\pi\) |
0.966004 | + | 0.258529i | \(0.0832377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.43308e11 | − | 4.21422e11i | −0.00412390 | − | 0.00714281i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.54921e13 | −0.719983 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.40470e14 | − | 2.43301e14i | −2.14895 | − | 3.72208i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.76485e13 | + | 2.21948e13i | −0.395452 | + | 0.317449i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.55541e13 | − | 9.62225e13i | 0.768532 | − | 1.33114i | −0.169827 | − | 0.985474i | \(-0.554321\pi\) |
0.938359 | − | 0.345663i | \(-0.112346\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.92334e13 | 0.378558 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.99428e13 | −1.12720 | −0.563601 | − | 0.826047i | \(-0.690585\pi\) | ||||
−0.563601 | + | 0.826047i | \(0.690585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.18597e13 | + | 1.59106e14i | −1.07889 | + | 1.86869i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.89127e13 | + | 7.88467e13i | 0.442561 | + | 0.896738i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.22864e13 | − | 9.05626e13i | −0.557926 | − | 0.966355i | −0.997669 | − | 0.0682322i | \(-0.978264\pi\) |
0.439744 | − | 0.898123i | \(-0.355069\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.39858e13 | 0.558136 | 0.279068 | − | 0.960271i | \(-0.409975\pi\) | ||||
0.279068 | + | 0.960271i | \(0.409975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.09068e13 | − | 1.88911e13i | −0.105910 | − | 0.183441i | 0.808200 | − | 0.588909i | \(-0.200442\pi\) |
−0.914110 | + | 0.405467i | \(0.867109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.22712e14 | + | 2.12543e14i | −1.15513 | + | 2.00074i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.99484e13 | − | 1.21154e14i | 0.619096 | − | 1.07231i | −0.370555 | − | 0.928811i | \(-0.620832\pi\) |
0.989651 | − | 0.143495i | \(-0.0458343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.93895e13 | − | 1.72148e14i | −0.853200 | − | 1.47779i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.77675e14 | 2.24350 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.60223e13 | − | 2.77514e13i | −0.125621 | − | 0.217581i | 0.796355 | − | 0.604830i | \(-0.206759\pi\) |
−0.921975 | + | 0.387249i | \(0.873426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.16129e12 | + | 5.94818e13i | 0.0676706 | + | 0.439367i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.32722e13 | − | 1.61552e14i | 0.668888 | − | 1.15855i | −0.309327 | − | 0.950956i | \(-0.600104\pi\) |
0.978215 | − | 0.207593i | \(-0.0665629\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.21929e12 | −0.00824576 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.85750e13 | 0.187703 | 0.0938515 | − | 0.995586i | \(-0.470082\pi\) | ||||
0.0938515 | + | 0.995586i | \(0.470082\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.81568e13 | − | 3.14486e13i | 0.112576 | − | 0.194988i | −0.804232 | − | 0.594315i | \(-0.797423\pi\) |
0.916808 | + | 0.399328i | \(0.130756\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.74062e14 | + | 1.84297e14i | 2.85628 | + | 1.11041i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.04933e13 | − | 1.39419e14i | −0.458181 | − | 0.793593i | 0.540684 | − | 0.841226i | \(-0.318165\pi\) |
−0.998865 | + | 0.0476332i | \(0.984832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.31149e13 | −0.515285 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.72730e14 | + | 2.99177e14i | 0.903823 | + | 1.56547i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.79387e14 | − | 3.10707e14i | 0.912940 | − | 1.58126i | 0.103052 | − | 0.994676i | \(-0.467139\pi\) |
0.809889 | − | 0.586583i | \(-0.199527\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.22260e13 | − | 1.42420e14i | 0.396018 | − | 0.685923i | −0.597213 | − | 0.802083i | \(-0.703725\pi\) |
0.993231 | + | 0.116160i | \(0.0370585\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.30169e14 | + | 3.98664e14i | 1.07862 | + | 1.86823i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.68133e14 | −0.746249 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.13369e13 | + | 5.42771e13i | 0.135387 | + | 0.234498i | 0.925745 | − | 0.378148i | \(-0.123439\pi\) |
−0.790358 | + | 0.612645i | \(0.790105\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.16392e12 | − | 3.35280e13i | −0.0211473 | − | 0.137304i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.15452e13 | + | 1.58561e14i | −0.365066 | + | 0.632312i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.23062e13 | −0.311355 | −0.155677 | − | 0.987808i | \(-0.549756\pi\) | ||||
−0.155677 | + | 0.987808i | \(0.549756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.99072e13 | −0.257614 | −0.128807 | − | 0.991670i | \(-0.541115\pi\) | ||||
−0.128807 | + | 0.991670i | \(0.541115\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.68726e14 | + | 2.92243e14i | −0.590261 | + | 1.02236i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.41506e14 | + | 1.13595e14i | −0.482417 | + | 0.387261i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.23307e14 | + | 2.13574e14i | 0.399358 | + | 0.691708i | 0.993647 | − | 0.112544i | \(-0.0358998\pi\) |
−0.594289 | + | 0.804252i | \(0.702566\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.21634e14 | −1.33123 | −0.665614 | − | 0.746296i | \(-0.731830\pi\) | ||||
−0.665614 | + | 0.746296i | \(0.731830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.22652e14 | − | 5.58850e14i | −0.968471 | − | 1.67744i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.27459e13 | + | 7.40380e13i | −0.125124 | + | 0.216720i | −0.921781 | − | 0.387710i | \(-0.873266\pi\) |
0.796658 | + | 0.604431i | \(0.206599\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.86748e14 | − | 4.96662e14i | 0.798509 | − | 1.38306i | −0.122078 | − | 0.992520i | \(-0.538956\pi\) |
0.920587 | − | 0.390537i | \(-0.127711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.96627e13 | + | 1.20659e14i | 0.189243 | + | 0.327779i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.33244e14 | −1.63763 | −0.818815 | − | 0.574057i | \(-0.805369\pi\) | ||||
−0.818815 | + | 0.574057i | \(0.805369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.15920e14 | + | 2.00780e14i | 0.292543 | + | 0.506699i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.93836e14 | − | 7.97803e14i | 2.38920 | − | 1.91793i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.99228e13 | − | 3.45073e13i | 0.0467532 | − | 0.0809788i | −0.841702 | − | 0.539943i | \(-0.818446\pi\) |
0.888455 | + | 0.458964i | \(0.151779\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.47695e14 | −1.89620 | −0.948101 | − | 0.317970i | \(-0.896999\pi\) | ||||
−0.948101 | + | 0.317970i | \(0.896999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.99938e14 | 1.74727 | 0.873636 | − | 0.486579i | \(-0.161756\pi\) | ||||
0.873636 | + | 0.486579i | \(0.161756\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.29125e14 | + | 7.43267e14i | −0.894008 | + | 1.54847i | −0.0589797 | + | 0.998259i | \(0.518785\pi\) |
−0.835028 | + | 0.550207i | \(0.814549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.47270e13 | + | 9.56187e13i | 0.0299685 | + | 0.194577i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.74909e14 | + | 8.22566e14i | 0.922304 | + | 1.59748i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.33861e15 | −4.43755 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.28415e13 | + | 1.08845e14i | 0.113868 | + | 0.197225i | 0.917327 | − | 0.398135i | \(-0.130343\pi\) |
−0.803459 | + | 0.595360i | \(0.797009\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.10642e14 | + | 3.64842e14i | −0.373032 | + | 0.646111i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.69383e14 | + | 1.33261e15i | −1.30186 | + | 2.25488i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.87117e14 | + | 8.43711e14i | 0.805794 | + | 1.39568i | 0.915754 | + | 0.401739i | \(0.131594\pi\) |
−0.109960 | + | 0.993936i | \(0.535072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.14406e15 | −1.80926 | −0.904628 | − | 0.426201i | \(-0.859852\pi\) | ||||
−0.904628 | + | 0.426201i | \(0.859852\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.32281e11 | + | 1.26835e12i | 0.00113245 | + | 0.00196146i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.57021e14 | − | 2.94301e14i | −1.11982 | − | 0.435343i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.44591e14 | − | 1.11646e15i | 0.932677 | − | 1.61544i | 0.153952 | − | 0.988078i | \(-0.450800\pi\) |
0.778725 | − | 0.627366i | \(-0.215867\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.01920e15 | −1.41135 | −0.705677 | − | 0.708534i | \(-0.749357\pi\) | ||||
−0.705677 | + | 0.708534i | \(0.749357\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.36800e14 | −0.456320 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.28883e14 | − | 2.23232e14i | 0.167205 | − | 0.289607i | −0.770231 | − | 0.637765i | \(-0.779859\pi\) |
0.937436 | + | 0.348158i | \(0.113193\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39886e14 | + | 9.08242e14i | 0.177607 | + | 1.15315i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.24379e14 | + | 9.08252e14i | 0.637831 | + | 1.10476i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.78753e14 | −0.808191 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50755e14 | + | 2.61115e14i | 0.172053 | + | 0.298005i | 0.939138 | − | 0.343541i | \(-0.111627\pi\) |
−0.767084 | + | 0.641546i | \(0.778293\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.19275e14 | + | 2.06590e14i | −0.133287 | + | 0.230860i | −0.924942 | − | 0.380109i | \(-0.875887\pi\) |
0.791655 | + | 0.610969i | \(0.209220\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.76468e14 | − | 4.78857e14i | 0.296270 | − | 0.513154i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.84011e14 | − | 3.18716e14i | −0.193124 | − | 0.334501i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.80913e14 | 0.584940 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.54121e15 | − | 2.66945e15i | −1.52025 | − | 2.63315i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.63993e14 | + | 1.64344e15i | −0.344632 | + | 1.55602i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.15031e14 | + | 1.23847e15i | −0.663346 | + | 1.14895i | 0.316385 | + | 0.948631i | \(0.397531\pi\) |
−0.979731 | + | 0.200318i | \(0.935803\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.81142e15 | 2.50464 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.19792e14 | 0.803081 | 0.401540 | − | 0.915841i | \(-0.368475\pi\) | ||||
0.401540 | + | 0.915841i | \(0.368475\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.07484e12 | + | 8.78989e12i | −0.00425686 | + | 0.00737309i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.91553e14 | + | 7.15696e14i | −0.733093 | + | 0.588491i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.08145e14 | + | 8.80133e14i | 0.401591 | + | 0.695576i | 0.993918 | − | 0.110121i | \(-0.0351239\pi\) |
−0.592327 | + | 0.805698i | \(0.701791\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.37992e15 | 1.84415 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.05790e14 | + | 1.04926e15i | 0.451363 | + | 0.781784i | 0.998471 | − | 0.0552782i | \(-0.0176046\pi\) |
−0.547108 | + | 0.837062i | \(0.684271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.47219e15 | − | 2.54990e15i | 1.07571 | − | 1.86319i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.24341e14 | − | 1.25460e15i | 0.509126 | − | 0.881833i | −0.490818 | − | 0.871262i | \(-0.663302\pi\) |
0.999944 | − | 0.0105706i | \(-0.00336477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.13063e14 | − | 3.69036e14i | −0.146896 | − | 0.254431i | 0.783183 | − | 0.621792i | \(-0.213595\pi\) |
−0.930079 | + | 0.367360i | \(0.880262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.78676e15 | −3.17591 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.04431e14 | + | 3.54086e14i | 0.133070 | + | 0.230484i | 0.924859 | − | 0.380311i | \(-0.124183\pi\) |
−0.791788 | + | 0.610795i | \(0.790850\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.64751e14 | − | 2.19554e14i | −0.353907 | − | 0.137586i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.76077e14 | + | 9.97795e14i | −0.354245 | + | 0.613570i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.59585e14 | 0.449849 | 0.224925 | − | 0.974376i | \(-0.427786\pi\) | ||||
0.224925 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.83196e15 | 2.22734 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.64766e15 | + | 2.85384e15i | −0.922715 | + | 1.59819i | −0.127519 | + | 0.991836i | \(0.540701\pi\) |
−0.795196 | + | 0.606353i | \(0.792632\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.42678e15 | − | 5.54676e14i | −0.784354 | − | 0.304927i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.26409e15 | − | 2.18947e15i | −0.669777 | − | 1.16009i | −0.977966 | − | 0.208763i | \(-0.933056\pi\) |
0.308189 | − | 0.951325i | \(-0.400277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.40595e15 | 0.731410 | 0.365705 | − | 0.930731i | \(-0.380828\pi\) | ||||
0.365705 | + | 0.930731i | \(0.380828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.95182e15 | + | 5.11270e15i | 1.48059 | + | 2.56446i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.31451e15 | + | 2.27680e15i | −0.647480 | + | 1.12147i | 0.336242 | + | 0.941776i | \(0.390844\pi\) |
−0.983723 | + | 0.179694i | \(0.942489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.50361e14 | + | 1.47287e15i | −0.403995 | + | 0.699741i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.36386e14 | − | 4.09433e14i | −0.110304 | − | 0.191051i | 0.805589 | − | 0.592475i | \(-0.201849\pi\) |
−0.915893 | + | 0.401423i | \(0.868516\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.41641e14 | −0.288884 | −0.144442 | − | 0.989513i | \(-0.546139\pi\) | ||||
−0.144442 | + | 0.989513i | \(0.546139\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.06581e15 | − | 1.84603e15i | −0.471390 | − | 0.816471i | 0.528074 | − | 0.849198i | \(-0.322914\pi\) |
−0.999464 | + | 0.0327268i | \(0.989581\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.59568e14 | + | 2.88643e14i | −0.153496 | + | 0.123219i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.26605e15 | + | 7.38902e15i | −1.78931 | + | 3.09918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.06027e14 | 0.204925 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.49076e15 | −0.991219 | −0.495609 | − | 0.868545i | \(-0.665055\pi\) | ||||
−0.495609 | + | 0.868545i | \(0.665055\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.73003e15 | − | 2.99650e15i | 0.664964 | − | 1.15175i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.11018e15 | + | 2.84880e15i | 1.17495 | + | 1.07621i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.64178e15 | − | 2.84365e15i | −0.599233 | − | 1.03790i | −0.992934 | − | 0.118664i | \(-0.962139\pi\) |
0.393701 | − | 0.919239i | \(-0.371195\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.94429e15 | 0.697592 | 0.348796 | − | 0.937199i | \(-0.386591\pi\) | ||||
0.348796 | + | 0.937199i | \(0.386591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.24795e14 | + | 5.62562e14i | 0.112625 | + | 0.195073i | 0.916828 | − | 0.399282i | \(-0.130741\pi\) |
−0.804203 | + | 0.594355i | \(0.797407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.24716e14 | − | 5.62425e14i | 0.110703 | − | 0.191743i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.92474e15 | − | 3.33375e15i | 0.634380 | − | 1.09878i | −0.352266 | − | 0.935900i | \(-0.614589\pi\) |
0.986646 | − | 0.162879i | \(-0.0520779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.95476e15 | − | 5.11779e15i | −0.957623 | − | 1.65865i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.40489e15 | −0.440324 | −0.220162 | − | 0.975463i | \(-0.570659\pi\) | ||||
−0.220162 | + | 0.975463i | \(0.570659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.55113e15 | − | 2.68663e15i | −0.478123 | − | 0.828134i | 0.521562 | − | 0.853213i | \(-0.325349\pi\) |
−0.999685 | + | 0.0250796i | \(0.992016\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.61490e15 | − | 1.04851e16i | −0.481533 | − | 3.12647i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.03874e13 | + | 1.79915e13i | −0.00304659 | + | 0.00527684i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.47390e15 | −0.985924 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.65798e15 | −1.30051 | −0.650256 | − | 0.759715i | \(-0.725338\pi\) | ||||
−0.650256 | + | 0.759715i | \(0.725338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.70181e15 | − | 2.94763e15i | 0.459912 | − | 0.796590i | −0.539044 | − | 0.842277i | \(-0.681214\pi\) |
0.998956 | + | 0.0456873i | \(0.0145478\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.74640e15 | − | 1.84522e15i | −1.26206 | − | 0.490642i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.52660e14 | − | 1.47685e15i | −0.219514 | − | 0.380209i | 0.735146 | − | 0.677909i | \(-0.237114\pi\) |
−0.954659 | + | 0.297700i | \(0.903780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.76946e15 | 1.71497 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.44345e15 | + | 2.50013e15i | 0.354157 | + | 0.613419i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.28018e15 | − | 3.94939e15i | 0.550606 | − | 0.953677i | −0.447625 | − | 0.894221i | \(-0.647730\pi\) |
0.998231 | − | 0.0594557i | \(-0.0189365\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.29797e15 | − | 2.24814e15i | 0.303632 | − | 0.525905i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.48884e14 | − | 6.04284e14i | −0.0803341 | − | 0.139143i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.93440e15 | 0.654741 | 0.327371 | − | 0.944896i | \(-0.393837\pi\) | ||||
0.327371 | + | 0.944896i | \(0.393837\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.75343e15 | + | 3.03703e15i | 0.385154 | + | 0.667106i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.69671e14 | − | 1.10163e15i | −0.0361245 | − | 0.234547i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.47790e15 | + | 2.55980e15i | −0.309807 | + | 0.536601i | −0.978320 | − | 0.207099i | \(-0.933598\pi\) |
0.668513 | + | 0.743700i | \(0.266931\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.84339e15 | 1.59408 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.43981e16 | 4.88284 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.47695e15 | + | 2.55816e15i | −0.286654 | + | 0.496499i | −0.973009 | − | 0.230768i | \(-0.925876\pi\) |
0.686355 | + | 0.727266i | \(0.259210\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.70661e15 | + | 2.17273e15i | −0.517347 | + | 0.415301i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.76443e13 | + | 6.52019e13i | 0.00697976 | + | 0.0120893i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.57462e15 | −1.01807 | −0.509033 | − | 0.860747i | \(-0.669997\pi\) | ||||
−0.509033 | + | 0.860747i | \(0.669997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.42932e15 | − | 2.47566e15i | −0.253271 | − | 0.438678i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.84328e15 | + | 8.38880e15i | −0.845410 | + | 1.46429i | 0.0398541 | + | 0.999206i | \(0.487311\pi\) |
−0.885264 | + | 0.465088i | \(0.846023\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.26061e14 | + | 1.60399e15i | −0.156880 | + | 0.271725i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.18308e14 | − | 1.59056e15i | −0.153265 | − | 0.265463i | 0.779161 | − | 0.626824i | \(-0.215646\pi\) |
−0.932426 | + | 0.361361i | \(0.882312\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.66724e13 | −0.00918191 | −0.00459095 | − | 0.999989i | \(-0.501461\pi\) | ||||
−0.00459095 | + | 0.999989i | \(0.501461\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.70646e14 | + | 8.15182e14i | 0.0751337 | + | 0.130135i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.95502e15 | − | 6.38590e15i | 1.23308 | − | 0.989856i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.39714e14 | − | 1.45443e15i | 0.128266 | − | 0.222163i | −0.794739 | − | 0.606952i | \(-0.792392\pi\) |
0.923005 | + | 0.384788i | \(0.125726\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.42337e16 | 2.11159 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.82897e15 | 0.852245 | 0.426122 | − | 0.904666i | \(-0.359879\pi\) | ||||
0.426122 | + | 0.904666i | \(0.359879\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.73179e15 | + | 6.46364e15i | −0.530031 | + | 0.918041i | 0.469355 | + | 0.883009i | \(0.344486\pi\) |
−0.999386 | + | 0.0350311i | \(0.988847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.41632e15 | + | 9.19582e15i | 0.198279 | + | 1.28738i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.13627e14 | − | 1.40924e15i | −0.110675 | − | 0.191695i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.93564e15 | 0.661833 | 0.330917 | − | 0.943660i | \(-0.392642\pi\) | ||||
0.330917 | + | 0.943660i | \(0.392642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.32146e15 | − | 5.75293e15i | −0.432854 | − | 0.749725i | 0.564264 | − | 0.825595i | \(-0.309160\pi\) |
−0.997118 | + | 0.0758695i | \(0.975827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.42124e16 | − | 2.46166e16i | 1.82603 | − | 3.16278i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.41783e15 | − | 4.18780e15i | 0.301974 | − | 0.523034i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.77458e15 | − | 1.34660e16i | −0.957407 | − | 1.65828i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.17305e15 | −0.739123 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.38350e15 | + | 5.86039e15i | 0.399489 | + | 0.691935i | 0.993663 | − | 0.112401i | \(-0.0358542\pi\) |
−0.594174 | + | 0.804337i | \(0.702521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.08206e15 | + | 3.53076e15i | 1.04283 | + | 0.405413i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.35220e15 | + | 7.53822e15i | −0.492840 | + | 0.853624i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.32772e16 | 1.46246 | 0.731232 | − | 0.682129i | \(-0.238946\pi\) | ||||
0.731232 | + | 0.682129i | \(0.238946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.04283e15 | 0.221935 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.79627e15 | + | 1.52356e16i | −0.929743 | + | 1.61036i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.30543e15 | − | 2.14613e16i | −0.344628 | − | 2.23758i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.65847e15 | + | 6.33665e15i | 0.371178 | + | 0.642900i | 0.989747 | − | 0.142831i | \(-0.0456206\pi\) |
−0.618569 | + | 0.785731i | \(0.712287\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.29518e15 | −0.830254 | −0.415127 | − | 0.909763i | \(-0.636263\pi\) | ||||
−0.415127 | + | 0.909763i | \(0.636263\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.91990e15 | + | 3.32537e15i | 0.187030 | + | 0.323946i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.90549e15 | − | 1.71568e16i | 0.952039 | − | 1.64898i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.14344e14 | − | 8.90870e14i | 0.0481245 | − | 0.0833541i | −0.840960 | − | 0.541098i | \(-0.818009\pi\) |
0.889084 | + | 0.457744i | \(0.151342\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.29428e15 | − | 9.16996e15i | −0.488774 | − | 0.846581i | 0.511143 | − | 0.859496i | \(-0.329222\pi\) |
−0.999917 | + | 0.0129147i | \(0.995889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.40430e15 | 0.485802 | 0.242901 | − | 0.970051i | \(-0.421901\pi\) | ||||
0.242901 | + | 0.970051i | \(0.421901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.56988e15 | − | 1.13794e16i | −0.582784 | − | 1.00941i | −0.995148 | − | 0.0983919i | \(-0.968630\pi\) |
0.412364 | − | 0.911019i | \(-0.364703\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.09550e15 | − | 4.94624e15i | 0.0946382 | − | 0.427295i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.91082e15 | + | 1.71660e16i | −0.844956 | + | 1.46351i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.43166e16 | −1.18891 | −0.594455 | − | 0.804129i | \(-0.702632\pi\) | ||||
−0.594455 | + | 0.804129i | \(0.702632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.22002e16 | −0.999973 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.85264e16 | − | 3.20887e16i | 1.47938 | − | 2.56236i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.52359e16 | + | 1.22307e16i | −1.20091 | + | 0.964033i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.58898e15 | + | 6.21630e15i | 0.275651 | + | 0.477441i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.17265e16 | 0.889098 | 0.444549 | − | 0.895755i | \(-0.353364\pi\) | ||||
0.444549 | + | 0.895755i | \(0.353364\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.25484e15 | + | 7.36960e15i | 0.314404 | + | 0.544564i | 0.979311 | − | 0.202362i | \(-0.0648619\pi\) |
−0.664906 | + | 0.746927i | \(0.731529\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.63364e15 | + | 9.75774e15i | −0.410985 | + | 0.711848i | −0.994998 | − | 0.0998972i | \(-0.968149\pi\) |
0.584012 | + | 0.811745i | \(0.301482\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.68765e15 | − | 4.65514e15i | 0.191123 | − | 0.331035i | −0.754500 | − | 0.656300i | \(-0.772120\pi\) |
0.945623 | + | 0.325266i | \(0.105454\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.43890e15 | + | 1.63486e16i | 0.662724 | + | 1.14787i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.18871e16 | −1.49823 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.32039e15 | + | 4.01903e15i | 0.156842 | + | 0.271657i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.61549e16 | − | 1.79433e16i | −3.04210 | − | 1.18265i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.70359e15 | − | 1.68071e16i | 0.631589 | − | 1.09394i | −0.355638 | − | 0.934624i | \(-0.615736\pi\) |
0.987227 | − | 0.159321i | \(-0.0509304\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.05160e16 | 1.30234 | 0.651171 | − | 0.758931i | \(-0.274278\pi\) | ||||
0.651171 | + | 0.758931i | \(0.274278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.29505e16 | −0.811903 | −0.405951 | − | 0.913895i | \(-0.633060\pi\) | ||||
−0.405951 | + | 0.913895i | \(0.633060\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.64435e15 | − | 6.31220e15i | 0.222864 | − | 0.386012i | −0.732812 | − | 0.680431i | \(-0.761793\pi\) |
0.955676 | + | 0.294419i | \(0.0951261\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.06727e16 | + | 4.14916e15i | 0.644638 | + | 0.250611i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.07860e15 | + | 1.22605e16i | 0.417123 | + | 0.722479i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.38158e16 | −1.96831 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.16825e13 | − | 1.06837e14i | −0.00350335 | − | 0.00606798i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.73381e15 | − | 3.00305e15i | 0.0972781 | − | 0.168491i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.08965e16 | + | 3.61939e16i | −1.14421 | + | 1.98184i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.98204e15 | + | 1.20933e16i | 0.377696 | + | 0.654189i | 0.990727 | − | 0.135871i | \(-0.0433831\pi\) |
−0.613031 | + | 0.790059i | \(0.710050\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.74544e16 | 0.921623 | 0.460812 | − | 0.887498i | \(-0.347558\pi\) | ||||
0.460812 | + | 0.887498i | \(0.347558\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.79998e15 | − | 1.00459e16i | −0.302578 | − | 0.524080i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.52511e16 | − | 1.22429e16i | 0.776731 | − | 0.623522i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.96055e15 | + | 1.72522e16i | −0.501242 | + | 0.868177i | 0.498757 | + | 0.866742i | \(0.333790\pi\) |
−0.999999 | + | 0.00143523i | \(0.999543\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.89608e16 | −1.91434 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.60133e16 | 1.26304 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.73858e15 | − | 6.47541e15i | 0.177264 | − | 0.307030i | −0.763679 | − | 0.645597i | \(-0.776609\pi\) |
0.940942 | + | 0.338567i | \(0.109942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.34820e16 | − | 1.05643e16i | 1.56887 | − | 0.495013i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.46529e16 | − | 2.53796e16i | −0.670596 | − | 1.16151i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.31704e16 | 1.04801 | 0.524006 | − | 0.851715i | \(-0.324437\pi\) | ||||
0.524006 | + | 0.851715i | \(0.324437\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.48966e15 | + | 1.12404e16i | 0.286734 | + | 0.496638i | 0.973028 | − | 0.230686i | \(-0.0740971\pi\) |
−0.686294 | + | 0.727324i | \(0.740764\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.94890e15 | − | 8.57174e15i | 0.216120 | − | 0.374330i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.37270e16 | − | 2.37759e16i | 0.585667 | − | 1.01440i | −0.409125 | − | 0.912478i | \(-0.634166\pi\) |
0.994792 | − | 0.101926i | \(-0.0325006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.20404e16 | + | 3.81751e16i | 0.929513 | + | 1.60996i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.34657e15 | 0.179117 | 0.0895583 | − | 0.995982i | \(-0.471454\pi\) | ||||
0.0895583 | + | 0.995982i | \(0.471454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.56592e15 | − | 1.31046e16i | −0.308208 | − | 0.533831i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.41028e15 | + | 2.21421e16i | 0.135765 | + | 0.881487i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.05836e16 | + | 1.83314e16i | −0.416540 | + | 0.721469i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.90604e16 | −1.11790 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.78536e15 | −0.181999 | −0.0909995 | − | 0.995851i | \(-0.529006\pi\) | ||||
−0.0909995 | + | 0.995851i | \(0.529006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.79192e15 | + | 6.56779e15i | −0.140978 | + | 0.244182i | −0.927865 | − | 0.372915i | \(-0.878358\pi\) |
0.786887 | + | 0.617097i | \(0.211692\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00729e15 | + | 3.11293e15i | 0.294350 | + | 0.114432i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.61885e16 | + | 2.80392e16i | 0.581816 | + | 1.00773i | 0.995264 | + | 0.0972072i | \(0.0309909\pi\) |
−0.413448 | + | 0.910528i | \(0.635676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.82717e15 | −0.313701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.83330e15 | − | 8.37152e15i | −0.167957 | − | 0.290911i | 0.769744 | − | 0.638353i | \(-0.220384\pi\) |
−0.937702 | + | 0.347442i | \(0.887050\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.04996e16 | + | 7.01473e16i | −1.39172 | + | 2.41053i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.02749e16 | − | 3.51172e16i | 0.681364 | − | 1.18016i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.36964e16 | + | 4.10434e16i | 0.787549 | + | 1.36407i | 0.927465 | + | 0.373911i | \(0.121984\pi\) |
−0.139916 | + | 0.990163i | \(0.544683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.84619e16 | −1.25027 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.37128e15 | − | 7.57128e15i | −0.140535 | − | 0.243414i | 0.787163 | − | 0.616745i | \(-0.211549\pi\) |
−0.927698 | + | 0.373331i | \(0.878216\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.12.k.d.37.8 | 16 | ||
3.2 | odd | 2 | 84.12.i.b.37.1 | yes | 16 | ||
7.4 | even | 3 | inner | 252.12.k.d.109.8 | 16 | ||
21.11 | odd | 6 | 84.12.i.b.25.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.i.b.25.1 | ✓ | 16 | 21.11 | odd | 6 | ||
84.12.i.b.37.1 | yes | 16 | 3.2 | odd | 2 | ||
252.12.k.d.37.8 | 16 | 1.1 | even | 1 | trivial | ||
252.12.k.d.109.8 | 16 | 7.4 | even | 3 | inner |