Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,12,Mod(17,252)]
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, 3, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.17");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.t (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: | \(193.622481501\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(30\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.16 | ||
Character | \(\chi\) | \(=\) | 252.89 |
Dual form | 252.12.t.a.17.16 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 11.5001 | − | 19.9187i | 0.00164575 | − | 0.00285053i | −0.865201 | − | 0.501425i | \(-0.832809\pi\) |
0.866847 | + | 0.498574i | \(0.166143\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9655.86 | − | 43406.1i | −0.217146 | − | 0.976139i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −866549. | + | 500302.i | −1.62231 | + | 0.936640i | −0.636007 | + | 0.771683i | \(0.719415\pi\) |
−0.986301 | + | 0.164957i | \(0.947252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.96677e6i | − | 1.46915i | −0.678530 | − | 0.734573i | \(-0.737383\pi\) | ||
0.678530 | − | 0.734573i | \(-0.262617\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.15075e6 | − | 8.92136e6i | −0.879835 | − | 1.52392i | −0.851521 | − | 0.524321i | \(-0.824319\pi\) |
−0.0283146 | − | 0.999599i | \(-0.509014\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 86620.1 | + | 50010.1i | 0.00802553 | + | 0.00463354i | 0.504007 | − | 0.863699i | \(-0.331858\pi\) |
−0.495982 | + | 0.868333i | \(0.665192\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.11110e7 | − | 2.37355e7i | −1.33185 | − | 0.768944i | −0.346267 | − | 0.938136i | \(-0.612551\pi\) |
−0.985583 | + | 0.169192i | \(0.945884\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.44138e7 | + | 4.22859e7i | 0.499995 | + | 0.866016i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.43463e8i | − | 1.29882i | −0.760437 | − | 0.649412i | \(-0.775015\pi\) | ||
0.760437 | − | 0.649412i | \(-0.224985\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.35624e8 | − | 7.83028e7i | 0.850841 | − | 0.491233i | −0.0100936 | − | 0.999949i | \(-0.503213\pi\) |
0.860934 | + | 0.508716i | \(0.169880\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −975635. | − | 306841.i | −0.00313988 | − | 0.000987504i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.38300e7 | + | 1.45198e8i | −0.198742 | + | 0.344231i | −0.948121 | − | 0.317910i | \(-0.897019\pi\) |
0.749379 | + | 0.662142i | \(0.230352\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.37400e7 | −0.0185215 | −0.00926074 | − | 0.999957i | \(-0.502948\pi\) | ||||
−0.00926074 | + | 0.999957i | \(0.502948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.33366e9 | −1.38346 | −0.691731 | − | 0.722155i | \(-0.743152\pi\) | ||||
−0.691731 | + | 0.722155i | \(0.743152\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.44565e8 | + | 1.28962e9i | −0.473548 | + | 0.820210i | −0.999541 | − | 0.0302790i | \(-0.990360\pi\) |
0.525993 | + | 0.850489i | \(0.323694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.79086e9 | + | 8.38247e8i | −0.905695 | + | 0.423929i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.06369e9 | − | 6.14121e8i | 0.349379 | − | 0.201714i | −0.315032 | − | 0.949081i | \(-0.602015\pi\) |
0.664412 | + | 0.747367i | \(0.268682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.30140e7i | 0.00616591i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.83274e9 | − | 4.90645e9i | −0.515847 | − | 0.893472i | −0.999831 | − | 0.0183957i | \(-0.994144\pi\) |
0.483984 | − | 0.875077i | \(-0.339189\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.76775e9 | + | 5.06206e9i | 1.32915 | + | 0.767385i | 0.985168 | − | 0.171591i | \(-0.0548906\pi\) |
0.343982 | + | 0.938976i | \(0.388224\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.91754e7 | − | 2.26179e7i | −0.00418784 | − | 0.00241785i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.65304e9 | − | 6.32724e9i | −0.330554 | − | 0.572537i | 0.652066 | − | 0.758162i | \(-0.273902\pi\) |
−0.982621 | + | 0.185625i | \(0.940569\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.66198e9i | − | 0.175099i | −0.996160 | − | 0.0875495i | \(-0.972096\pi\) | ||
0.996160 | − | 0.0875495i | \(-0.0279036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.27629e10 | − | 7.36864e9i | 0.720564 | − | 0.416018i | −0.0943965 | − | 0.995535i | \(-0.530092\pi\) |
0.814960 | + | 0.579517i | \(0.196759\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00835e10 | + | 3.27827e10i | 1.26657 | + | 1.38021i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.02751e10 | − | 3.51175e10i | 0.741333 | − | 1.28403i | −0.210555 | − | 0.977582i | \(-0.567527\pi\) |
0.951888 | − | 0.306445i | \(-0.0991395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.35523e9 | −0.232825 | −0.116412 | − | 0.993201i | \(-0.537139\pi\) | ||||
−0.116412 | + | 0.993201i | \(0.537139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.36936e8 | −0.00579197 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.64117e9 | + | 1.49669e10i | −0.164032 | + | 0.284111i | −0.936311 | − | 0.351172i | \(-0.885783\pi\) |
0.772279 | + | 0.635283i | \(0.219117\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.53698e10 | + | 1.89908e10i | −1.43409 | + | 0.319019i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.99227e6 | − | 1.15024e6i | 2.64161e−5 | − | 1.52513e-5i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.68607e11i | 1.99357i | 0.0801314 | + | 0.996784i | \(0.474466\pi\) | ||||
−0.0801314 | + | 0.996784i | \(0.525534\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.09756e10 | − | 5.36513e10i | −0.293259 | − | 0.507940i | 0.681319 | − | 0.731987i | \(-0.261407\pi\) |
−0.974578 | + | 0.224046i | \(0.928073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.28465e10 | − | 4.78315e10i | −0.704157 | − | 0.406545i | 0.104737 | − | 0.994500i | \(-0.466600\pi\) |
−0.808894 | + | 0.587955i | \(0.799933\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.36618e10 | − | 1.36612e10i | −0.163094 | − | 0.0941622i | 0.416232 | − | 0.909259i | \(-0.363351\pi\) |
−0.579325 | + | 0.815096i | \(0.696684\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.56977e10 | + | 1.13792e11i | 0.408983 | + | 0.708378i | 0.994776 | − | 0.102082i | \(-0.0325504\pi\) |
−0.585793 | + | 0.810460i | \(0.699217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.71579e11i | − | 1.38665i | −0.720627 | − | 0.693323i | \(-0.756146\pi\) | ||
0.720627 | − | 0.693323i | \(-0.243854\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.45558e8 | + | 5.45918e8i | −0.00438379 | + | 0.00253098i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.37507e11 | + | 3.09718e11i | −1.29651 | + | 1.18975i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.57949e11 | − | 6.19985e11i | 1.25459 | − | 2.17301i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.24609e9 | 0.00658298 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.05482e10 | 0.0283307 | 0.0141653 | − | 0.999900i | \(-0.495491\pi\) | ||||
0.0141653 | + | 0.999900i | \(0.495491\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.42239e9 | − | 1.11239e10i | 0.0145447 | − | 0.0251922i | −0.858661 | − | 0.512543i | \(-0.828703\pi\) |
0.873206 | + | 0.487351i | \(0.162037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.33435e9 | − | 4.24273e9i | 0.00278027 | − | 0.00884019i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.02534e11 | − | 3.47873e11i | 1.06664 | − | 0.615826i | 0.139379 | − | 0.990239i | \(-0.455489\pi\) |
0.927262 | + | 0.374414i | \(0.122156\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.97459e11i | 1.30355i | 0.758413 | + | 0.651774i | \(0.225975\pi\) | ||||
−0.758413 | + | 0.651774i | \(0.774025\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.83979e11 | + | 1.70430e12i | 1.37606 | + | 2.38341i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.85759e9 | − | 1.64983e9i | −0.00370233 | − | 0.00213754i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.29587e11 | − | 5.36697e11i | −1.03697 | − | 0.598694i | −0.117995 | − | 0.993014i | \(-0.537647\pi\) |
−0.918973 | + | 0.394320i | \(0.870980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.57718e11 | + | 7.92791e11i | 0.474487 | + | 0.821836i | 0.999573 | − | 0.0292131i | \(-0.00930014\pi\) |
−0.525086 | + | 0.851049i | \(0.675967\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.60194e9i | − | 0.00323380i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.28544e12 | + | 7.42150e11i | −1.07549 | + | 0.620932i | −0.929675 | − | 0.368381i | \(-0.879912\pi\) |
−0.145810 | + | 0.989313i | \(0.546579\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.33302e11 | + | 2.01366e12i | −0.461390 | + | 1.46704i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.35055e12 | − | 2.33922e12i | 0.919343 | − | 1.59235i | 0.118929 | − | 0.992903i | \(-0.462054\pi\) |
0.800415 | − | 0.599447i | \(-0.204613\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.89232e12 | −1.72308 | −0.861540 | − | 0.507690i | \(-0.830500\pi\) | ||||
−0.861540 | + | 0.507690i | \(0.830500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.07602e12 | −1.15839 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.79119e11 | − | 1.52268e12i | 0.431315 | − | 0.747059i | −0.565672 | − | 0.824630i | \(-0.691383\pi\) |
0.996987 | + | 0.0775713i | \(0.0247165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.59973e12 | − | 1.46802e12i | 0.736780 | − | 0.676116i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.22049e11 | − | 3.01405e11i | 0.212334 | − | 0.122591i | −0.390062 | − | 0.920789i | \(-0.627546\pi\) |
0.602396 | + | 0.798198i | \(0.294213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.10745e12i | 0.423733i | 0.977299 | + | 0.211867i | \(0.0679542\pi\) | ||||
−0.977299 | + | 0.211867i | \(0.932046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.92810e9 | + | 3.33956e9i | 0.000654161 | + | 0.00113304i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.92675e12 | + | 5.15386e12i | 2.85473 | + | 1.64818i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.83427e9 | + | 5.67782e9i | 0.00279936 | + | 0.00161621i | 0.501399 | − | 0.865216i | \(-0.332819\pi\) |
−0.498600 | + | 0.866832i | \(0.666152\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.19675e8 | + | 5.53693e8i | 8.59297e−5 | + | 0.000148835i | 0.866068 | − | 0.499926i | \(-0.166639\pi\) |
−0.865982 | + | 0.500074i | \(0.833306\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.84901e12i | 0.924240i | 0.886817 | + | 0.462120i | \(0.152911\pi\) | ||||
−0.886817 | + | 0.462120i | \(0.847089\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.47949e12 | + | 1.43153e12i | −0.563209 | + | 0.325169i | −0.754433 | − | 0.656377i | \(-0.772088\pi\) |
0.191223 | + | 0.981547i | \(0.438755\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.22716e12 | + | 1.38526e12i | −1.26783 | + | 0.282034i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.58011e8 | + | 2.73683e8i | −3.04818e−5 | + | 5.27960e-5i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00081e11 | −0.0173598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.29030e12 | −0.706210 | −0.353105 | − | 0.935584i | \(-0.614874\pi\) | ||||
−0.353105 | + | 0.935584i | \(0.614874\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.53371e10 | + | 2.65647e10i | −0.00227684 | + | 0.00394360i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.70839e12 | − | 5.13085e12i | −0.664269 | − | 0.723870i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.75463e13 | + | 1.01303e13i | −2.23886 | + | 1.29261i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.58836e12i | 1.16431i | 0.813079 | + | 0.582154i | \(0.197790\pi\) | ||||
−0.813079 | + | 0.582154i | \(0.802210\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.69186e12 | + | 9.85859e12i | 0.626776 | + | 1.08561i | 0.988195 | + | 0.153204i | \(0.0489590\pi\) |
−0.361419 | + | 0.932403i | \(0.617708\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.47341e13 | + | 8.50676e12i | 1.54607 | + | 0.892625i | 0.998436 | + | 0.0559079i | \(0.0178053\pi\) |
0.547636 | + | 0.836717i | \(0.315528\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.82646e12 | + | 3.94126e12i | 0.651236 | + | 0.375991i | 0.788929 | − | 0.614484i | \(-0.210636\pi\) |
−0.137694 | + | 0.990475i | \(0.543969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.71251e10 | + | 2.96615e10i | 0.00155869 | + | 0.00269973i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.33846e13i | 1.11024i | 0.831770 | + | 0.555120i | \(0.187328\pi\) | ||||
−0.831770 | + | 0.555120i | \(0.812672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.31664e12 | − | 4.22426e12i | 0.579719 | − | 0.334701i | −0.181302 | − | 0.983427i | \(-0.558031\pi\) |
0.761022 | + | 0.648726i | \(0.224698\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.89817e9 | + | 4.53114e10i | −0.000282129 | + | 0.00327939i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.83584e10 | − | 1.70362e11i | 0.00680735 | − | 0.0117907i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.29725e12 | 0.462332 | 0.231166 | − | 0.972914i | \(-0.425746\pi\) | ||||
0.231166 | + | 0.972914i | \(0.425746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.74996e13 | 2.88089 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.17267e13 | + | 2.03112e13i | −0.652442 | + | 1.13006i | 0.330087 | + | 0.943951i | \(0.392922\pi\) |
−0.982529 | + | 0.186112i | \(0.940411\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.11192e12 | + | 2.23672e12i | 0.379174 | + | 0.119251i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.67295e13 | + | 9.65878e12i | −0.819835 | + | 0.473332i | −0.850359 | − | 0.526202i | \(-0.823615\pi\) |
0.0305248 | + | 0.999534i | \(0.490282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.82497e10i | − | 0.00132789i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.54103e12 | − | 1.30615e13i | −0.326433 | − | 0.565398i | 0.655369 | − | 0.755309i | \(-0.272513\pi\) |
−0.981801 | + | 0.189911i | \(0.939180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.01891e13 | − | 5.88268e12i | −0.423453 | − | 0.244481i | 0.273101 | − | 0.961985i | \(-0.411951\pi\) |
−0.696553 | + | 0.717505i | \(0.745284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.23115e13 | − | 2.44286e13i | −1.62229 | − | 0.936630i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.31657e13 | + | 2.28037e13i | 0.485072 | + | 0.840169i | 0.999853 | − | 0.0171528i | \(-0.00546018\pi\) |
−0.514781 | + | 0.857322i | \(0.672127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.63734e13i | 1.91950i | 0.280848 | + | 0.959752i | \(0.409384\pi\) | ||||
−0.280848 | + | 0.959752i | \(0.590616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.45860e12 | − | 1.99683e12i | 0.113260 | − | 0.0653905i | −0.442300 | − | 0.896867i | \(-0.645837\pi\) |
0.555560 | + | 0.831477i | \(0.312504\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.32672e11 | + | 5.96400e11i | 0.00402186 | + | 0.0180795i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.59245e13 | + | 6.22231e13i | −1.04822 | + | 1.81557i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.10431e13 | −0.839833 | −0.419916 | − | 0.907563i | \(-0.637941\pi\) | ||||
−0.419916 | + | 0.907563i | \(0.637941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.30307e11 | −0.00339583 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.66822e13 | + | 8.08559e13i | −1.12969 | + | 1.95668i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.28776e13 | + | 5.78888e13i | 0.300413 | + | 1.35045i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.01659e11 | − | 1.16428e11i | 0.00437491 | − | 0.00252586i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.63806e13i | − | 0.970677i | −0.874326 | − | 0.485339i | \(-0.838696\pi\) | ||
0.874326 | − | 0.485339i | \(-0.161304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.31858e13 | + | 2.28385e13i | 0.256995 | + | 0.445129i | 0.965436 | − | 0.260642i | \(-0.0839342\pi\) |
−0.708440 | + | 0.705771i | \(0.750601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.55233e13 | − | 2.62829e13i | −0.856524 | − | 0.494514i | 0.00632286 | − | 0.999980i | \(-0.497987\pi\) |
−0.862847 | + | 0.505466i | \(0.831321\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.11310e11 | + | 1.79735e11i | 0.00546219 | + | 0.00315360i | 0.502729 | − | 0.864444i | \(-0.332330\pi\) |
−0.497266 | + | 0.867598i | \(0.665663\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.17747e13 | + | 1.24317e14i | 1.21653 | + | 2.10709i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.03036e12i | − | 0.0163070i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.31667e13 | − | 4.80163e13i | 1.27230 | − | 0.734565i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.31670e13 | + | 1.98662e13i | 0.903468 | + | 0.284144i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.49845e13 | − | 7.79155e13i | 0.622314 | − | 1.07788i | −0.366740 | − | 0.930323i | \(-0.619526\pi\) |
0.989054 | − | 0.147555i | \(-0.0471404\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.68040e11 | −0.00217604 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.02721e14 | 1.28734 | 0.643671 | − | 0.765302i | \(-0.277410\pi\) | ||||
0.643671 | + | 0.765302i | \(0.277410\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.83501e13 | + | 1.35706e14i | −0.920217 | + | 1.59386i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.36773e13 | + | 6.96401e13i | 0.610482 | + | 0.792030i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.82475e13 | + | 4.51762e13i | −0.834945 | + | 0.482056i | −0.855543 | − | 0.517732i | \(-0.826776\pi\) |
0.0205975 | + | 0.999788i | \(0.493443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.58170e13i | − | 0.577068i | −0.957470 | − | 0.288534i | \(-0.906832\pi\) | ||
0.957470 | − | 0.288534i | \(-0.0931678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.57547e13 | − | 4.46084e13i | −0.250089 | − | 0.433168i | 0.713461 | − | 0.700695i | \(-0.247127\pi\) |
−0.963550 | + | 0.267528i | \(0.913793\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.30231e10 | − | 3.06129e10i | −0.000499125 | − | 0.000288170i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.18975e14 | + | 6.86904e13i | 1.05302 | + | 0.607963i | 0.923494 | − | 0.383613i | \(-0.125320\pi\) |
0.129528 | + | 0.991576i | \(0.458654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.82401e13 | − | 1.00875e14i | −0.499957 | − | 0.865951i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.38959e11i | − | 0.00273865i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.49247e13 | − | 8.61678e12i | 0.117015 | − | 0.0675588i | −0.440350 | − | 0.897826i | \(-0.645146\pi\) |
0.557365 | + | 0.830267i | \(0.311812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.69274e13 | − | 4.02407e13i | −0.272768 | − | 0.297242i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.23892e13 | + | 1.42702e14i | −0.590842 | + | 1.02337i | 0.403277 | + | 0.915078i | \(0.367871\pi\) |
−0.994119 | + | 0.108291i | \(0.965462\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.82158e14 | −1.90816 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.42928e13 | −0.356637 | −0.178319 | − | 0.983973i | \(-0.557066\pi\) | ||||
−0.178319 | + | 0.983973i | \(0.557066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.51958e13 | − | 7.82815e13i | 0.280224 | − | 0.485362i | −0.691216 | − | 0.722648i | \(-0.742925\pi\) |
0.971440 | + | 0.237286i | \(0.0762580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.98949e11 | − | 2.22220e11i | 0.00601879 | − | 0.00133890i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.78815e13 | − | 1.03239e13i | 0.101785 | − | 0.0587654i | −0.448244 | − | 0.893911i | \(-0.647950\pi\) |
0.550028 | + | 0.835146i | \(0.314617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.89022e14i | 2.70618i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.66329e11 | − | 8.07705e11i | −0.00244010 | − | 0.00422638i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.18023e12 | + | 4.14551e12i | 0.0365419 | + | 0.0210974i | 0.518160 | − | 0.855284i | \(-0.326617\pi\) |
−0.481618 | + | 0.876381i | \(0.659951\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00472e14 | + | 1.73477e14i | 1.44714 | + | 0.835505i | 0.998310 | − | 0.0581144i | \(-0.0185088\pi\) |
0.448826 | + | 0.893619i | \(0.351842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.54003e14 | − | 2.66742e14i | −0.721693 | − | 1.25001i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.67761e14i | − | 0.744599i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.28684e13 | + | 1.32031e13i | −0.0988000 | + | 0.0570422i | −0.548586 | − | 0.836094i | \(-0.684834\pi\) |
0.449786 | + | 0.893136i | \(0.351500\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.85617e14 | + | 1.70334e14i | −0.760139 | + | 0.697552i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.60856e10 | + | 1.66425e11i | −0.000383172 | + | 0.000663674i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.25764e14 | 0.854038 | 0.427019 | − | 0.904243i | \(-0.359564\pi\) | ||||
0.427019 | + | 0.904243i | \(0.359564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.69685e14 | −0.625304 | −0.312652 | − | 0.949868i | \(-0.601217\pi\) | ||||
−0.312652 | + | 0.949868i | \(0.601217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.51499e14 | − | 4.35609e14i | 0.879826 | − | 1.52390i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.35064e14 | − | 4.29453e14i | 0.460455 | − | 1.46407i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.70790e14 | + | 9.86056e13i | −0.553143 | + | 0.319357i | −0.750389 | − | 0.660997i | \(-0.770134\pi\) |
0.197246 | + | 0.980354i | \(0.436800\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.53250e14i | − | 1.11532i | −0.830070 | − | 0.557660i | \(-0.811699\pi\) | ||
0.830070 | − | 0.557660i | \(-0.188301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.37403e12 | − | 4.11194e12i | −0.00712587 | − | 0.0123424i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.31130e14 | + | 1.91178e14i | 0.969267 | + | 0.559607i | 0.899013 | − | 0.437922i | \(-0.144286\pi\) |
0.0702544 | + | 0.997529i | \(0.477619\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.60058e14 | − | 2.65614e14i | −1.28113 | − | 0.739658i | −0.304071 | − | 0.952649i | \(-0.598346\pi\) |
−0.977054 | + | 0.212991i | \(0.931679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.98748e11 | + | 3.44241e11i | 0.000539911 | + | 0.000935154i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.99677e14i | − | 1.03360i | −0.856105 | − | 0.516802i | \(-0.827123\pi\) | ||
0.856105 | − | 0.516802i | \(-0.172877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.19064e13 | − | 6.87416e12i | 0.0300475 | − | 0.0173480i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.03485e11 | + | 1.91885e12i | −0.00145079 | + | 0.00461294i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.82167e14 | − | 3.15522e14i | 0.427493 | − | 0.740440i | −0.569156 | − | 0.822229i | \(-0.692730\pi\) |
0.996650 | + | 0.0817890i | \(0.0260634\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.20414e14 | 0.269354 | 0.134677 | − | 0.990890i | \(-0.457000\pi\) | ||||
0.134677 | + | 0.990890i | \(0.457000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.46137e14 | −1.62976 | −0.814879 | − | 0.579632i | \(-0.803196\pi\) | ||||
−0.814879 | + | 0.579632i | \(0.803196\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.76208e14 | − | 3.05201e14i | 0.367099 | − | 0.635833i | −0.622012 | − | 0.783008i | \(-0.713685\pi\) |
0.989111 | + | 0.147174i | \(0.0470179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.39368e14 | + | 2.19659e14i | −0.487097 | + | 0.446991i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.15568e15 | − | 6.67231e14i | 2.24440 | − | 1.29581i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.88375e12i | 0.00926699i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.84464e14 | + | 6.65910e14i | 0.696642 | + | 1.20662i | 0.969624 | + | 0.244601i | \(0.0786569\pi\) |
−0.272981 | + | 0.962019i | \(0.588010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.85570e14 | + | 1.64874e14i | 0.505726 | + | 0.291981i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.35843e12 | + | 1.93899e12i | 0.00568273 | + | 0.00328092i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.79826e14 | − | 3.11469e14i | −0.297471 | − | 0.515234i | 0.678086 | − | 0.734983i | \(-0.262810\pi\) |
−0.975557 | + | 0.219748i | \(0.929476\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.76622e14i | 0.753748i | 0.926265 | + | 0.376874i | \(0.123001\pi\) | ||||
−0.926265 | + | 0.376874i | \(0.876999\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.27988e15 | + | 7.38941e14i | −1.97930 | + | 1.14275i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.15546e14 | + | 2.57037e13i | −0.170921 | + | 0.0380221i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50175e14 | − | 4.33315e14i | 0.361985 | − | 0.626976i | −0.626303 | − | 0.779580i | \(-0.715433\pi\) |
0.988287 | + | 0.152604i | \(0.0487659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.03031e14 | 1.11201 | 0.556004 | − | 0.831179i | \(-0.312334\pi\) | ||||
0.556004 | + | 0.831179i | \(0.312334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.42488e12 | −0.00193053 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.95221e14 | − | 1.03095e15i | 0.772201 | − | 1.33749i | −0.164153 | − | 0.986435i | \(-0.552489\pi\) |
0.936354 | − | 0.351057i | \(-0.114178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.43081e14 | − | 4.82836e14i | −0.562559 | − | 0.613034i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.90548e12 | + | 1.10013e12i | −0.00231774 | + | 0.00133815i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.49003e15i | − | 1.77418i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.01620e14 | − | 6.95627e14i | −0.458362 | − | 0.793906i | 0.540513 | − | 0.841336i | \(-0.318230\pi\) |
−0.998875 | + | 0.0474299i | \(0.984897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.49100e15 | − | 8.60830e14i | −1.66617 | − | 0.961963i | −0.969675 | − | 0.244400i | \(-0.921409\pi\) |
−0.696494 | − | 0.717563i | \(-0.745258\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.39713e15 | − | 8.06636e14i | −1.49720 | − | 0.864409i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50340e14 | + | 1.12642e15i | 0.682550 | + | 1.18221i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.70234e13i | 0.0272108i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.44224e11 | + | 3.14208e11i | −0.000536824 | + | 0.000309936i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.13249e15 | − | 1.62235e15i | 1.07225 | − | 1.53605i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.42661e14 | − | 1.11312e15i | 0.596207 | − | 1.03266i | −0.397169 | − | 0.917746i | \(-0.630007\pi\) |
0.993375 | − | 0.114914i | \(-0.0366594\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.02211e12 | 0.00269234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.03623e14 | 0.701652 | 0.350826 | − | 0.936441i | \(-0.385901\pi\) | ||||
0.350826 | + | 0.936441i | \(0.385901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.17459e12 | − | 1.24268e13i | 0.00601816 | − | 0.0104238i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.72009e15 | − | 5.40973e14i | −1.41437 | − | 0.444823i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.02951e15 | − | 5.94389e14i | 0.813632 | − | 0.469751i | −0.0345834 | − | 0.999402i | \(-0.511010\pi\) |
0.848216 | + | 0.529651i | \(0.177677\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.62299e15i | 2.03251i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.27949e14 | − | 1.26085e15i | −0.542382 | − | 0.939433i | −0.998767 | − | 0.0496502i | \(-0.984189\pi\) |
0.456385 | − | 0.889782i | \(-0.349144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.40950e12 | − | 3.12318e12i | −0.00395267 | − | 0.00228208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.21721e13 | + | 1.28010e13i | 0.0155843 | + | 0.00899763i | 0.507772 | − | 0.861492i | \(-0.330469\pi\) |
−0.492188 | + | 0.870489i | \(0.663803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.61684e13 | + | 1.66569e14i | 0.0663031 | + | 0.114840i | 0.897271 | − | 0.441480i | \(-0.145546\pi\) |
−0.830968 | + | 0.556320i | \(0.812213\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.31789e15i | − | 1.53787i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.64456e14 | − | 9.49486e13i | 0.107049 | − | 0.0618047i | −0.445520 | − | 0.895272i | \(-0.646981\pi\) |
0.552569 | + | 0.833467i | \(0.313648\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.06770e13 | + | 3.62668e14i | 0.0505569 | + | 0.227269i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.14492e14 | + | 1.06433e15i | −0.377867 | + | 0.654485i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.42436e15 | 1.43578 | 0.717889 | − | 0.696158i | \(-0.245109\pi\) | ||||
0.717889 | + | 0.696158i | \(0.245109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.56637e13 | 0.00910460 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.22737e15 | + | 2.12586e15i | −0.687344 | + | 1.19051i | 0.285350 | + | 0.958423i | \(0.407890\pi\) |
−0.972694 | + | 0.232091i | \(0.925443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.28782e12 | + | 1.02845e13i | 0.00125770 | + | 0.00565377i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.15668e15 | + | 6.67811e14i | −0.612868 | + | 0.353839i | −0.774087 | − | 0.633079i | \(-0.781791\pi\) |
0.161219 | + | 0.986919i | \(0.448457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.83665e15i | − | 1.47569i | −0.674968 | − | 0.737847i | \(-0.735843\pi\) | ||
0.674968 | − | 0.737847i | \(-0.264157\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.23286e12 | − | 1.42597e13i | −0.00412949 | − | 0.00715248i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.80681e15 | − | 1.62051e15i | −1.38253 | − | 0.798206i | −0.390074 | − | 0.920783i | \(-0.627551\pi\) |
−0.992459 | + | 0.122578i | \(0.960884\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.53639e15 | + | 1.46439e15i | 1.20501 | + | 0.695712i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.04479e15 | − | 3.54169e15i | −0.954151 | − | 1.65264i | −0.736299 | − | 0.676656i | \(-0.763428\pi\) |
−0.217852 | − | 0.975982i | \(-0.569905\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.38686e15i | 1.52486i | 0.647072 | + | 0.762429i | \(0.275993\pi\) | ||||
−0.647072 | + | 0.762429i | \(0.724007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.63749e15 | − | 9.45404e14i | 0.724235 | − | 0.418137i | −0.0920746 | − | 0.995752i | \(-0.529350\pi\) |
0.816309 | + | 0.577615i | \(0.196016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.33095e14 | + | 2.30561e14i | 0.312951 | + | 0.0984241i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.19205e15 | + | 2.06470e15i | −0.499984 | + | 0.865997i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.72715e15 | 0.699441 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.26763e15 | 0.902426 | 0.451213 | − | 0.892416i | \(-0.350992\pi\) | ||||
0.451213 | + | 0.892416i | \(0.350992\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.21305e11 | − | 2.10106e11i | 4.66253e−5 | − | 8.07575e-5i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.64864e15 | + | 3.52220e15i | 0.622814 | + | 1.33060i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.95266e14 | + | 3.43677e14i | −0.217266 | + | 0.125439i | −0.604684 | − | 0.796466i | \(-0.706700\pi\) |
0.387418 | + | 0.921904i | \(0.373367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.84301e14i | − | 0.102004i | −0.998699 | − | 0.0510021i | \(-0.983758\pi\) | ||
0.998699 | − | 0.0510021i | \(-0.0162415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.12791e14 | − | 7.14975e14i | −0.143139 | − | 0.247923i | 0.785538 | − | 0.618813i | \(-0.212386\pi\) |
−0.928677 | + | 0.370890i | \(0.879053\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.90941e15 | + | 2.83445e15i | 1.67372 | + | 0.966325i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.68583e14 | + | 5.01477e14i | 0.286279 | + | 0.165283i | 0.636262 | − | 0.771473i | \(-0.280480\pi\) |
−0.349984 | + | 0.936756i | \(0.613813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.47716e11 | − | 2.55851e11i | −4.78740e−5 | − | 8.29202e-5i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.00574e15i | − | 1.56891i | −0.620184 | − | 0.784456i | \(-0.712942\pi\) | ||
0.620184 | − | 0.784456i | \(-0.287058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.10059e15 | − | 1.79013e15i | 0.955732 | − | 0.551792i | 0.0608753 | − | 0.998145i | \(-0.480611\pi\) |
0.894857 | + | 0.446353i | \(0.147277\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.91645e10 | − | 7.53702e10i | −2.06236e−5 | − | 2.24740e-5i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.40515e15 | + | 5.89790e15i | −0.998722 | + | 1.72984i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.01302e16 | −2.87506 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.91527e15 | −1.09315 | −0.546574 | − | 0.837411i | \(-0.684068\pi\) | ||||
−0.546574 | + | 0.837411i | \(0.684068\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.98069e15 | − | 3.43066e15i | 0.535278 | − | 0.927129i | −0.463872 | − | 0.885902i | \(-0.653540\pi\) |
0.999150 | − | 0.0412263i | \(-0.0131265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.31858e15 | − | 1.62805e15i | 1.94600 | − | 0.432895i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.91517e15 | + | 2.26042e15i | −1.00794 | + | 0.581937i | −0.910589 | − | 0.413313i | \(-0.864371\pi\) |
−0.0973548 | + | 0.995250i | \(0.531038\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.60022e13i | − | 0.00405399i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.20783e15 | − | 2.09203e15i | −0.296348 | − | 0.513289i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.19526e15 | − | 2.42213e15i | −1.01305 | − | 0.584883i | −0.100964 | − | 0.994890i | \(-0.532193\pi\) |
−0.912082 | + | 0.410007i | \(0.865526\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.58843e13 | + | 9.17082e12i | 0.00371580 | + | 0.00214532i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.07713e13 | + | 1.22580e14i | 0.0162959 | + | 0.0282253i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.60368e15i | 1.47345i | 0.676190 | + | 0.736727i | \(0.263630\pi\) | ||||
−0.676190 | + | 0.736727i | \(0.736370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.45227e13 | + | 8.38470e12i | −0.00319002 | + | 0.00184176i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.02970e15 | + | 1.86258e15i | −0.432140 | + | 0.396559i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.15278e15 | − | 1.99667e15i | 0.241652 | − | 0.418554i | −0.719533 | − | 0.694459i | \(-0.755644\pi\) |
0.961185 | + | 0.275904i | \(0.0889773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.43421e15 | −1.51092 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.52632e13 | 0.00905863 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.41440e15 | + | 7.64597e15i | −0.856768 | + | 1.48397i | 0.0182271 | + | 0.999834i | \(0.494198\pi\) |
−0.874995 | + | 0.484132i | \(0.839136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.27622e15 | + | 4.05790e15i | −0.243940 | + | 0.775635i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.06646e15 | − | 3.50247e15i | 1.12480 | − | 0.649405i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.62928e15i | 0.845424i | 0.906264 | + | 0.422712i | \(0.138922\pi\) | ||||
−0.906264 | + | 0.422712i | \(0.861078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.86933e15 | + | 1.18980e16i | 1.21722 | + | 2.10829i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.19085e15 | + | 1.26489e15i | 0.382420 | + | 0.220790i | 0.678870 | − | 0.734258i | \(-0.262470\pi\) |
−0.296451 | + | 0.955048i | \(0.595803\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.33107e15 | + | 3.65524e15i | 1.07252 | + | 0.619220i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.96520e15 | + | 6.86792e15i | 0.661790 | + | 1.14625i | 0.980145 | + | 0.198282i | \(0.0635363\pi\) |
−0.318355 | + | 0.947972i | \(0.603130\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.64254e15i | 0.590155i | 0.955473 | + | 0.295078i | \(0.0953455\pi\) | ||||
−0.955473 | + | 0.295078i | \(0.904654\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.13806e13 | + | 1.23441e13i | −0.00341319 | + | 0.00197061i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.64503e14 | + | 1.15898e15i | −0.0565003 | + | 0.179649i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.52341e14 | − | 1.30309e15i | 0.114920 | − | 0.199047i | −0.802828 | − | 0.596211i | \(-0.796672\pi\) |
0.917748 | + | 0.397164i | \(0.130006\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.10551e13 | 0.00312356 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.87442e15 | 0.274056 | 0.137028 | − | 0.990567i | \(-0.456245\pi\) | ||||
0.137028 | + | 0.990567i | \(0.456245\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.27224e14 | − | 1.60600e15i | 0.131695 | − | 0.228102i | −0.792635 | − | 0.609696i | \(-0.791291\pi\) |
0.924330 | + | 0.381594i | \(0.124625\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.30489e15 | − | 3.95044e15i | 0.602667 | − | 0.553045i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.64985e15 | + | 5.57134e15i | −1.31264 | + | 0.757854i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.42059e14i | − | 0.0190491i | −0.999955 | − | 0.00952457i | \(-0.996968\pi\) | ||
0.999955 | − | 0.00952457i | \(-0.00303181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.10209e15 | − | 3.64093e15i | −0.273946 | − | 0.474488i | 0.695923 | − | 0.718117i | \(-0.254996\pi\) |
−0.969869 | + | 0.243628i | \(0.921662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.62221e15 | + | 3.82334e15i | 0.850832 | + | 0.491228i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.19016e12 | − | 6.87140e11i | −0.000148645 | − | 8.58201e-5i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.33179e15 | + | 2.30674e15i | 0.164005 | + | 0.284065i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.41391e13i | 0.00408760i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.77943e15 | + | 4.49146e15i | −0.918516 | + | 0.530306i | −0.883161 | − | 0.469069i | \(-0.844589\pi\) |
−0.0353548 | + | 0.999375i | \(0.511256\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.17882e16 | + | 2.62233e15i | −1.35356 | + | 0.301104i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.95591e15 | − | 1.72441e16i | 1.12740 | − | 1.95272i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.92579e15 | 0.432420 | 0.216210 | − | 0.976347i | \(-0.430630\pi\) | ||||
0.216210 | + | 0.976347i | \(0.430630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.53403e16 | 1.66658 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.37310e15 | + | 1.27706e16i | −0.779317 | + | 1.34982i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.28264e13 | + | 3.57717e13i | 0.00342252 | + | 0.00372960i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.18413e15 | + | 2.41571e15i | −0.424510 | + | 0.245091i | −0.697005 | − | 0.717066i | \(-0.745485\pi\) |
0.272495 | + | 0.962157i | \(0.412151\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.36416e16i | 1.36538i | 0.730710 | + | 0.682688i | \(0.239189\pi\) | ||||
−0.730710 | + | 0.682688i | \(0.760811\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.10627e13 | − | 5.38022e13i | −0.00302603 | − | 0.00524123i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.15521e14 | − | 6.66963e13i | −0.0111030 | − | 0.00641033i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.53119e16 | − | 8.84031e15i | −1.43265 | − | 0.827142i | −0.435330 | − | 0.900271i | \(-0.643368\pi\) |
−0.997322 | + | 0.0731290i | \(0.976702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.63669e15 | + | 4.56689e15i | 0.243423 | + | 0.421620i | 0.961687 | − | 0.274150i | \(-0.0883965\pi\) |
−0.718264 | + | 0.695770i | \(0.755063\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.09486e16i | − | 0.984187i | −0.870542 | − | 0.492093i | \(-0.836232\pi\) | ||
0.870542 | − | 0.492093i | \(-0.163768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.55065e15 | − | 3.20467e15i | 0.492372 | − | 0.284271i | −0.233186 | − | 0.972432i | \(-0.574915\pi\) |
0.725558 | + | 0.688161i | \(0.241582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.67026e16 | + | 1.16593e16i | 1.44290 | + | 1.00722i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.32618e13 | + | 5.76111e13i | −0.00283577 | + | 0.00491169i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.54319e15 | 0.211197 | 0.105599 | − | 0.994409i | \(-0.466324\pi\) | ||||
0.105599 | + | 0.994409i | \(0.466324\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.38105e15 | −0.686942 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.38743e13 | + | 4.13516e13i | −0.00190642 | + | 0.00330202i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.03675e16 | − | 9.55068e15i | −2.39359 | − | 0.752793i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.89267e15 | − | 3.97949e15i | 0.529389 | − | 0.305643i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.26976e15i | 0.551189i | 0.961274 | + | 0.275595i | \(0.0888747\pi\) | ||||
−0.961274 | + | 0.275595i | \(0.911125\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.15105e15 | + | 7.18983e15i | 0.306735 | + | 0.531281i | 0.977646 | − | 0.210257i | \(-0.0674301\pi\) |
−0.670911 | + | 0.741538i | \(0.734097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.49473e16 | + | 8.62980e15i | 1.09043 | + | 0.629562i | 0.933692 | − | 0.358078i | \(-0.116568\pi\) |
0.156741 | + | 0.987640i | \(0.449901\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.34715e16 | − | 1.35513e16i | −1.66910 | − | 0.963655i | −0.968124 | − | 0.250470i | \(-0.919415\pi\) |
−0.700975 | − | 0.713186i | \(-0.747252\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.02198e13 | − | 3.50218e13i | −0.00141968 | − | 0.00245895i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.05747e16i | 2.77745i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.24442e16 | + | 7.18468e15i | −0.841140 | + | 0.485632i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.16879e13 | − | 9.74941e13i | −0.00142947 | − | 0.00642590i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.95332e15 | + | 3.38325e15i | −0.127138 | + | 0.220210i | −0.922567 | − | 0.385838i | \(-0.873912\pi\) |
0.795429 | + | 0.606047i | \(0.207246\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.75839e16 | 1.11622 | 0.558108 | − | 0.829768i | \(-0.311527\pi\) | ||||
0.558108 | + | 0.829768i | \(0.311527\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.16134e16 | 0.728072 | 0.364036 | − | 0.931385i | \(-0.381399\pi\) | ||||
0.364036 | + | 0.931385i | \(0.381399\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.07215e16 | − | 1.85702e16i | 0.655657 | − | 1.13563i | −0.326072 | − | 0.945345i | \(-0.605725\pi\) |
0.981729 | − | 0.190286i | \(-0.0609416\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.01852e14 | − | 4.57856e14i | −0.00615189 | − | 0.0276547i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.28989e14 | + | 7.44716e13i | −0.00760096 | + | 0.00438841i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.38647e13i | − | 0.000807020i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.12335e16 | − | 1.94570e16i | −0.638025 | − | 1.10509i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09576e16 | − | 6.32637e15i | −0.614793 | − | 0.354951i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.20590e13 | + | 1.27358e13i | 0.00120786 | + | 0.000697361i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.24276e15 | + | 5.61662e15i | 0.175418 | + | 0.303833i | 0.940306 | − | 0.340330i | \(-0.110539\pi\) |
−0.764888 | + | 0.644164i | \(0.777206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.22553e15i | 0.0647100i | 0.999476 | + | 0.0323550i | \(0.0103007\pi\) | ||||
−0.999476 | + | 0.0323550i | \(0.989699\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.24022e15 | − | 4.18014e15i | 0.377713 | − | 0.218073i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.44860e14 | − | 1.71360e14i | −0.0277494 | − | 0.00872728i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.10755e15 | + | 1.91833e15i | −0.0557350 | + | 0.0965359i | −0.892547 | − | 0.450955i | \(-0.851084\pi\) |
0.836812 | + | 0.547491i | \(0.184417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.23550e15 | −0.257246 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.18643e15 | −0.397480 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.29966e16 | − | 2.25109e16i | 0.616233 | − | 1.06735i | −0.373934 | − | 0.927455i | \(-0.621991\pi\) |
0.990167 | − | 0.139892i | \(-0.0446754\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.97045e14 | − | 1.69519e13i | −0.00923298 | − | 0.000794320i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.05316e14 | − | 1.18539e14i | 0.00939636 | − | 0.00542499i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.40600e16i | − | 1.54056i | −0.637709 | − | 0.770278i | \(-0.720118\pi\) | ||
0.637709 | − | 0.770278i | \(-0.279882\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.84571e15 | − | 3.19687e15i | −0.0815495 | − | 0.141248i | 0.822366 | − | 0.568959i | \(-0.192654\pi\) |
−0.903916 | + | 0.427711i | \(0.859320\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.64866e14 | + | 3.26125e14i | 0.0246678 | + | 0.0142420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.90002e14 | − | 5.13843e14i | −0.0379723 | − | 0.0219233i | 0.480894 | − | 0.876779i | \(-0.340312\pi\) |
−0.518866 | + | 0.854856i | \(0.673646\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.44924e16 | − | 2.51016e16i | −0.611191 | − | 1.05861i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.38369e15i | − | 0.0570199i | −0.999594 | − | 0.0285099i | \(-0.990924\pi\) | ||
0.999594 | − | 0.0285099i | \(-0.00907623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.26189e11 | − | 1.30590e11i | 9.21411e−6 | − | 5.31977e-6i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.09178e16 | − | 2.27946e16i | −0.832748 | − | 0.907466i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.41596e14 | + | 7.64867e14i | −0.0173799 | + | 0.0301028i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.47051e10 | 5.65677e−7 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.83732e15 | 0.183975 | 0.0919876 | − | 0.995760i | \(-0.470678\pi\) | ||||
0.0919876 | + | 0.995760i | \(0.470678\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.06237e16 | − | 1.84009e16i | 0.394977 | − | 0.684120i | −0.598121 | − | 0.801405i | \(-0.704086\pi\) |
0.993098 | + | 0.117286i | \(0.0374193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.46146e16 | − | 7.70015e15i | 1.27244 | − | 0.283060i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.61786e16 | − | 1.51142e16i | 0.940863 | − | 0.543207i | 0.0506320 | − | 0.998717i | \(-0.483876\pi\) |
0.890231 | + | 0.455510i | \(0.150543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.72928e16i | − | 0.614554i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.62691e16 | + | 2.81790e16i | 0.565353 | + | 0.979221i | 0.997017 | + | 0.0771860i | \(0.0245935\pi\) |
−0.431663 | + | 0.902035i | \(0.642073\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.66672e13 | + | 4.42638e13i | 0.00263457 | + | 0.00152107i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.48280e16 | + | 3.16549e16i | 1.84256 | + | 1.06380i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.82053e15 | − | 1.18135e16i | −0.226680 | − | 0.392621i | 0.730142 | − | 0.683295i | \(-0.239454\pi\) |
−0.956822 | + | 0.290674i | \(0.906120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.58508e13i | 0.00214059i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.41149e15 | + | 3.70168e15i | −0.206127 | + | 0.119008i | −0.599510 | − | 0.800367i | \(-0.704638\pi\) |
0.393383 | + | 0.919375i | \(0.371305\pi\) | |||||||
\(998\) | 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.t.a.89.16 | yes | 60 | |
3.2 | odd | 2 | inner | 252.12.t.a.89.15 | yes | 60 | |
7.3 | odd | 6 | inner | 252.12.t.a.17.15 | ✓ | 60 | |
21.17 | even | 6 | inner | 252.12.t.a.17.16 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.12.t.a.17.15 | ✓ | 60 | 7.3 | odd | 6 | inner | |
252.12.t.a.17.16 | yes | 60 | 21.17 | even | 6 | inner | |
252.12.t.a.89.15 | yes | 60 | 3.2 | odd | 2 | inner | |
252.12.t.a.89.16 | yes | 60 | 1.1 | even | 1 | trivial |