Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(32,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bf (of order \(12\), degree \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 443.2 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.443 |
Dual form | 525.2.bf.c.32.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | 0.448288 | − | 1.67303i | 0.258819 | − | 0.965926i | ||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.189469 | + | 2.63896i | 0.0716124 | + | 0.997433i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.59808 | − | 1.50000i | −0.866025 | − | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0.896575 | + | 3.34607i | 0.258819 | + | 0.965926i | ||||
\(13\) | 4.89898 | + | 4.89898i | 1.35873 | + | 1.35873i | 0.875482 | + | 0.483250i | \(0.160544\pi\) |
0.483250 | + | 0.875482i | \(0.339456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820 | + | 4.00000i | 1.58944 | + | 0.917663i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) |
0.596040 | + | 0.802955i | \(0.296740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.50000 | + | 0.866025i | 0.981981 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.707107 | + | 0.707107i | ||||
\(28\) | −2.96713 | − | 4.38134i | −0.560734 | − | 0.827996i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | − | 6.06218i | −0.628619 | − | 1.08880i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 1.34486 | + | 5.01910i | 0.221094 | + | 0.825135i | 0.983932 | + | 0.178545i | \(0.0571389\pi\) |
−0.762838 | + | 0.646590i | \(0.776194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.3923 | − | 6.00000i | 1.66410 | − | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.57321 | + | 8.57321i | 1.30740 | + | 1.30740i | 0.923283 | + | 0.384120i | \(0.125495\pi\) |
0.384120 | + | 0.923283i | \(0.374505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.707107 | − | 0.707107i | ||||
\(49\) | −6.92820 | + | 1.00000i | −0.989743 | + | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.3843 | − | 3.58630i | −1.85606 | − | 0.497331i | ||||
\(53\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.79796 | − | 9.79796i | 1.29777 | − | 1.29777i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.46618 | − | 7.14042i | 0.436698 | − | 0.899608i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.34607 | + | 0.896575i | 0.408787 | + | 0.109534i | 0.457352 | − | 0.889286i | \(-0.348798\pi\) |
−0.0485648 | + | 0.998820i | \(0.515465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.448288 | + | 1.67303i | −0.0524681 | + | 0.195814i | −0.987185 | − | 0.159579i | \(-0.948986\pi\) |
0.934717 | + | 0.355393i | \(0.115653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.0000 | −1.83533 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.7224 | − | 8.50000i | −1.65640 | − | 0.956325i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) |
−0.682048 | − | 0.731307i | \(-0.738911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | −8.66025 | + | 3.00000i | −0.944911 | + | 0.327327i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | + | 13.8564i | −1.25794 | + | 1.45255i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.7112 | + | 3.13801i | −1.21440 | + | 0.325397i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.67423 | − | 3.67423i | 0.373062 | − | 0.373062i | −0.495529 | − | 0.868591i | \(-0.665026\pi\) |
0.868591 | + | 0.495529i | \(0.165026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0573 | + | 4.03459i | −1.48364 | + | 0.397540i | −0.907584 | − | 0.419871i | \(-0.862075\pi\) |
−0.576055 | + | 0.817411i | \(0.695409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(108\) | 2.68973 | − | 10.0382i | 0.258819 | − | 0.965926i | ||||
\(109\) | 1.73205 | − | 1.00000i | 0.165900 | − | 0.0957826i | −0.414751 | − | 0.909935i | \(-0.636131\pi\) |
0.580651 | + | 0.814152i | \(0.302798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.00000 | 0.854242 | ||||||||
\(112\) | 9.52056 | + | 4.62158i | 0.899608 | + | 0.436698i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.37945 | − | 20.0764i | −0.497331 | − | 1.85606i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.1244 | + | 7.00000i | 1.08880 | + | 0.628619i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9217 | − | 15.9217i | 1.41282 | − | 1.41282i | 0.675038 | − | 0.737783i | \(-0.264127\pi\) |
0.737783 | − | 0.675038i | \(-0.235873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.1865 | − | 10.5000i | 1.60123 | − | 0.924473i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.24316 | + | 19.0411i | −0.801483 | + | 1.65107i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 23.0000i | − | 1.95083i | −0.220366 | − | 0.975417i | \(-0.570725\pi\) | ||
0.220366 | − | 0.975417i | \(-0.429275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.3923 | + | 6.00000i | −0.866025 | + | 0.500000i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.43280 | + | 12.0394i | −0.118175 | + | 0.992993i | ||||
\(148\) | −7.34847 | − | 7.34847i | −0.604040 | − | 0.604040i | ||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.50000 | − | 16.4545i | −0.773099 | − | 1.33905i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
0.162758 | − | 0.986666i | \(-0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.0000 | + | 20.7846i | −0.960769 | + | 1.66410i | ||||
\(157\) | −21.7494 | − | 5.82774i | −1.73579 | − | 0.465104i | −0.754288 | − | 0.656543i | \(-0.772018\pi\) |
−0.981505 | + | 0.191439i | \(0.938685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.4034 | − | 4.93117i | 1.44146 | − | 0.386239i | 0.548417 | − | 0.836205i | \(-0.315231\pi\) |
0.893045 | + | 0.449966i | \(0.148564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.0000i | 2.69231i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.0000 | − | 20.7846i | −0.917663 | − | 1.58944i | ||||
\(172\) | −23.4225 | − | 6.27603i | −1.78595 | − | 0.478543i | ||||
\(173\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.22474 | − | 1.22474i | −0.0905357 | − | 0.0905357i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.3923 | − | 9.00000i | −0.755929 | − | 0.654654i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 13.3843 | + | 3.58630i | 0.965926 | + | 0.258819i | ||||
\(193\) | 3.13801 | − | 11.7112i | 0.225879 | − | 0.842993i | −0.756171 | − | 0.654374i | \(-0.772932\pi\) |
0.982050 | − | 0.188619i | \(-0.0604011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0000 | − | 8.66025i | 0.785714 | − | 0.618590i | ||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7224 | − | 8.50000i | 1.04365 | − | 0.602549i | 0.122782 | − | 0.992434i | \(-0.460818\pi\) |
0.920864 | + | 0.389885i | \(0.127485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.00000 | − | 5.19615i | 0.211604 | − | 0.366508i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 26.7685 | − | 7.17260i | 1.85606 | − | 0.497331i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 29.0000 | 1.99644 | 0.998221 | − | 0.0596196i | \(-0.0189888\pi\) | ||||
0.998221 | + | 0.0596196i | \(0.0189888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.3347 | − | 10.3849i | 1.04099 | − | 0.704976i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.59808 | + | 1.50000i | 0.175562 | + | 0.101361i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4722 | − | 13.4722i | −0.902165 | − | 0.902165i | 0.0934584 | − | 0.995623i | \(-0.470208\pi\) |
−0.995623 | + | 0.0934584i | \(0.970208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(228\) | −7.17260 | + | 26.7685i | −0.475017 | + | 1.77279i | ||||
\(229\) | −19.0526 | − | 11.0000i | −1.25903 | − | 0.726900i | −0.286143 | − | 0.958187i | \(-0.592373\pi\) |
−0.972886 | + | 0.231287i | \(0.925707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.8207 | + | 20.8207i | −1.35245 | + | 1.35245i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.5000 | + | 26.8468i | 0.998443 | + | 1.72935i | 0.547533 | + | 0.836784i | \(0.315567\pi\) |
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0573 | − | 4.03459i | 0.965926 | − | 0.258819i | ||||
\(244\) | 2.00000i | 0.128037i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.3452 | + | 53.5370i | 0.912764 | + | 3.40648i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 1.13681 | + | 15.8338i | 0.0716124 | + | 0.997433i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.9904 | + | 4.50000i | −0.807183 | + | 0.279616i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.69213 | + | 1.79315i | −0.408787 | + | 0.109534i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | − | 24.2487i | 0.850439 | − | 1.47300i | −0.0303728 | − | 0.999539i | \(-0.509669\pi\) |
0.880812 | − | 0.473466i | \(-0.156997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.8028 | + | 26.2880i | 1.07747 | + | 1.59103i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0764 | + | 5.37945i | 1.20627 | + | 0.323220i | 0.805299 | − | 0.592869i | \(-0.202005\pi\) |
0.400975 | + | 0.916089i | \(0.368672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.0000i | 1.25724i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.68973 | + | 10.0382i | −0.159888 | + | 0.596709i | 0.838749 | + | 0.544518i | \(0.183287\pi\) |
−0.998637 | + | 0.0521913i | \(0.983379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.7224 | + | 8.50000i | 0.866025 | + | 0.500000i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.50000 | − | 7.79423i | −0.263795 | − | 0.456906i | ||||
\(292\) | −0.896575 | − | 3.34607i | −0.0524681 | − | 0.195814i | ||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.0000 | + | 24.2487i | −1.21042 | + | 1.39767i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 27.7128 | − | 16.0000i | 1.58944 | − | 0.917663i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.22474 | + | 1.22474i | −0.0698999 | + | 0.0698999i | −0.741192 | − | 0.671293i | \(-0.765739\pi\) |
0.671293 | + | 0.741192i | \(0.265739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.0000i | 1.53598i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.01910 | − | 1.34486i | 0.283696 | − | 0.0760162i | −0.114165 | − | 0.993462i | \(-0.536419\pi\) |
0.397861 | + | 0.917446i | \(0.369753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 34.0000 | 1.91265 | ||||||||
\(317\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −15.5885 | − | 9.00000i | −0.866025 | − | 0.500000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.896575 | − | 3.34607i | −0.0495807 | − | 0.185038i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5000 | − | 26.8468i | 0.851957 | − | 1.47563i | −0.0274825 | − | 0.999622i | \(-0.508749\pi\) |
0.879440 | − | 0.476011i | \(-0.157918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.03459 | − | 15.0573i | 0.221094 | − | 0.825135i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.0000 | − | 13.8564i | 0.654654 | − | 0.755929i | ||||
\(337\) | −25.7196 | + | 25.7196i | −1.40104 | + | 1.40104i | −0.604223 | + | 0.796815i | \(0.706516\pi\) |
−0.796815 | + | 0.604223i | \(0.793484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.95164 | − | 18.0938i | −0.213368 | − | 0.976972i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.0000i | − | 0.749403i | −0.927146 | − | 0.374701i | \(-0.877745\pi\) | ||
0.927146 | − | 0.374701i | \(-0.122255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.0000 | −1.92154 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5000 | + | 38.9711i | 1.18421 | + | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.4722 | + | 13.4722i | 0.707107 | + | 0.707107i | ||||
\(364\) | 6.92820 | − | 36.0000i | 0.363137 | − | 1.88691i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.0573 | − | 4.03459i | −0.785984 | − | 0.210604i | −0.156563 | − | 0.987668i | \(-0.550041\pi\) |
−0.629421 | + | 0.777064i | \(0.716708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 17.1464 | − | 17.1464i | 0.889001 | − | 0.889001i | ||||
\(373\) | −6.69213 | + | 1.79315i | −0.346505 | + | 0.0928458i | −0.427874 | − | 0.903838i | \(-0.640737\pi\) |
0.0813690 | + | 0.996684i | \(0.474071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.5000 | − | 33.7750i | −0.999015 | − | 1.73035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.41404 | − | 35.1337i | −0.478543 | − | 1.78595i | ||||
\(388\) | −2.68973 | + | 10.0382i | −0.136550 | + | 0.509612i | ||||
\(389\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.93117 | − | 18.4034i | −0.247488 | − | 0.923638i | −0.972117 | − | 0.234498i | \(-0.924655\pi\) |
0.724628 | − | 0.689140i | \(-0.242011\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.7128 | + | 24.0000i | 1.38738 | + | 1.20150i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5521 | − | 46.8449i | 0.625262 | − | 2.33351i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.9090 | + | 19.0000i | −1.62724 | + | 0.939490i | −0.642333 | + | 0.766426i | \(0.722033\pi\) |
−0.984911 | + | 0.173064i | \(0.944633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22.0454 | − | 22.0454i | 1.08610 | − | 1.08610i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.4797 | − | 10.3106i | −1.88436 | − | 0.504913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −41.0000 | −1.99822 | −0.999109 | − | 0.0422075i | \(-0.986561\pi\) | ||||
−0.999109 | + | 0.0422075i | \(0.986561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.38014 | + | 1.15539i | 0.115183 | + | 0.0559135i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 5.37945 | + | 20.0764i | 0.258819 | + | 0.965926i | ||||
\(433\) | −15.9217 | − | 15.9217i | −0.765147 | − | 0.765147i | 0.212101 | − | 0.977248i | \(-0.431970\pi\) |
−0.977248 | + | 0.212101i | \(0.931970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | + | 3.46410i | −0.0957826 | + | 0.165900i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2583 | + | 6.50000i | 0.537331 | + | 0.310228i | 0.743996 | − | 0.668184i | \(-0.232928\pi\) |
−0.206666 | + | 0.978412i | \(0.566261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5000 | + | 7.79423i | 0.928571 | + | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(444\) | −15.5885 | + | 9.00000i | −0.739795 | + | 0.427121i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.1117 | + | 1.51575i | −0.997433 | + | 0.0716124i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.7876 | + | 8.51747i | −1.49351 | + | 0.400186i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.62089 | − | 28.4416i | −0.356490 | − | 1.33044i | −0.878599 | − | 0.477561i | \(-0.841521\pi\) |
0.522108 | − | 0.852879i | \(-0.325146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.22474 | − | 1.22474i | −0.0569187 | − | 0.0569187i | 0.678074 | − | 0.734993i | \(-0.262815\pi\) |
−0.734993 | + | 0.678074i | \(0.762815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(468\) | 29.3939 | + | 29.3939i | 1.35873 | + | 1.35873i | ||||
\(469\) | −1.73205 | + | 9.00000i | −0.0799787 | + | 0.415581i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.5000 | + | 33.7750i | −0.898513 | + | 1.55627i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | + | 31.1769i | −0.820729 | + | 1.42154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 22.0000i | − | 1.00000i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.1337 | + | 9.41404i | 1.59206 | + | 0.426591i | 0.942632 | − | 0.333833i | \(-0.108342\pi\) |
0.649427 | + | 0.760424i | \(0.275009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 33.0000i | − | 1.49231i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.0000 | −1.25724 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.7128 | − | 16.0000i | −1.24060 | − | 0.716258i | −0.271380 | − | 0.962472i | \(-0.587480\pi\) |
−0.969216 | + | 0.246214i | \(0.920813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 58.5561 | + | 15.6901i | 2.60057 | + | 0.696821i | ||||
\(508\) | −11.6555 | + | 43.4988i | −0.517128 | + | 1.92995i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.50000 | − | 0.866025i | −0.199068 | − | 0.0383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −40.1528 | + | 10.7589i | −1.77279 | + | 0.475017i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.0000 | + | 36.3731i | −0.924473 | + | 1.60123i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.4416 | + | 7.62089i | −1.24366 | + | 0.333238i | −0.819885 | − | 0.572528i | \(-0.805963\pi\) |
−0.423777 | + | 0.905766i | \(0.639296\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9186 | − | 11.5000i | 0.866025 | − | 0.500000i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.03150 | − | 42.2233i | −0.131432 | − | 1.83061i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0000 | − | 39.8372i | 0.988847 | − | 1.71273i | 0.365444 | − | 0.930834i | \(-0.380917\pi\) |
0.623404 | − | 0.781900i | \(-0.285749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.13801 | − | 11.7112i | 0.134665 | − | 0.502577i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.1464 | − | 17.1464i | 0.733128 | − | 0.733128i | −0.238110 | − | 0.971238i | \(-0.576528\pi\) |
0.971238 | + | 0.238110i | \(0.0765278\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.59808 | + | 1.50000i | −0.110883 | + | 0.0640184i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.6417 | − | 40.4624i | 0.835250 | − | 1.72063i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 23.0000 | + | 39.8372i | 0.975417 | + | 1.68947i | ||||
\(557\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 84.0000i | 3.55282i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.7160 | + | 13.3521i | −0.827996 | + | 0.560734i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | + | 13.8564i | 0.334790 | + | 0.579873i | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.500000 | − | 0.866025i | ||||
\(577\) | −31.7876 | − | 8.51747i | −1.32334 | − | 0.354587i | −0.473109 | − | 0.881004i | \(-0.656868\pi\) |
−0.850227 | + | 0.526417i | \(0.823535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.1865 | − | 10.5000i | −0.755807 | − | 0.436365i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | −9.55772 | − | 22.2856i | −0.394154 | − | 0.919044i | ||||
\(589\) | − | 56.0000i | − | 2.30744i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 20.0764 | + | 5.37945i | 0.825135 | + | 0.221094i | ||||
\(593\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.62089 | − | 28.4416i | −0.311902 | − | 1.16404i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.34847 | − | 7.34847i | −0.299253 | − | 0.299253i | ||||
\(604\) | 32.9090 | + | 19.0000i | 1.33905 | + | 0.773099i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.3106 | + | 38.4797i | 0.418495 | + | 1.56184i | 0.777730 | + | 0.628598i | \(0.216371\pi\) |
−0.359235 | + | 0.933247i | \(0.616962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.5521 | + | 46.8449i | −0.506973 | + | 1.89205i | −0.0584195 | + | 0.998292i | \(0.518606\pi\) |
−0.448553 | + | 0.893756i | \(0.648061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.4352 | + | 24.5000i | −1.70562 | + | 0.984738i | −0.765787 | + | 0.643094i | \(0.777650\pi\) |
−0.939829 | + | 0.341644i | \(0.889016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 48.0000i | − | 1.92154i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 43.4988 | − | 11.6555i | 1.73579 | − | 0.465104i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | −0.0398094 | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199047 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.0003 | − | 48.5179i | 0.516717 | − | 1.92842i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.8401 | − | 29.0421i | −1.53890 | − | 1.15069i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.4722 | − | 13.4722i | −0.531291 | − | 0.531291i | 0.389665 | − | 0.920957i | \(-0.372591\pi\) |
−0.920957 | + | 0.389665i | \(0.872591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5000 | − | 30.3109i | −0.411527 | − | 1.18798i | ||||
\(652\) | −26.9444 | + | 26.9444i | −1.05522 | + | 1.05522i | ||||
\(653\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.67423 | − | 3.67423i | 0.143346 | − | 0.143346i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.50000 | + | 9.52628i | 0.213925 | + | 0.370529i | 0.952940 | − | 0.303160i | \(-0.0980418\pi\) |
−0.739014 | + | 0.673690i | \(0.764708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.5788 | + | 16.5000i | −1.10492 | + | 0.637927i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.5176 | + | 35.5176i | 1.36910 | + | 1.36910i | 0.861722 | + | 0.507381i | \(0.169386\pi\) |
0.507381 | + | 0.861722i | \(0.330614\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −35.0000 | − | 60.6218i | −1.34615 | − | 2.33161i | ||||
\(677\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3923 | + | 9.00000i | 0.398820 | + | 0.345388i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(684\) | 41.5692 | + | 24.0000i | 1.58944 | + | 0.917663i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.9444 | + | 26.9444i | −1.02799 | + | 1.02799i | ||||
\(688\) | 46.8449 | − | 12.5521i | 1.78595 | − | 0.478543i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.5000 | − | 35.5070i | 0.779857 | − | 1.35075i | −0.152167 | − | 0.988355i | \(-0.548625\pi\) |
0.932024 | − | 0.362397i | \(-0.118041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7589 | + | 40.1528i | −0.405780 | + | 1.51439i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.8993 | + | 26.5000i | 1.72379 | + | 0.995228i | 0.910679 | + | 0.413114i | \(0.135559\pi\) |
0.813107 | + | 0.582115i | \(0.197775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.5000 | + | 44.1673i | 0.956325 | + | 1.65640i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5000 | − | 38.9711i | −0.502766 | − | 1.45136i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 51.8640 | − | 13.8969i | 1.92884 | − | 0.516832i | ||||
\(724\) | −12.1244 | + | 7.00000i | −0.450598 | + | 0.260153i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0454 | − | 22.0454i | 0.817619 | − | 0.817619i | −0.168144 | − | 0.985763i | \(-0.553777\pi\) |
0.985763 | + | 0.168144i | \(0.0537772\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3.34607 | + | 0.896575i | 0.123674 | + | 0.0331384i | ||||
\(733\) | −31.7876 | + | 8.51747i | −1.17410 | + | 0.314600i | −0.792585 | − | 0.609762i | \(-0.791265\pi\) |
−0.381518 | + | 0.924362i | \(0.624598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0429 | − | 18.5000i | 1.17872 | − | 0.680534i | 0.223001 | − | 0.974818i | \(-0.428415\pi\) |
0.955718 | + | 0.294285i | \(0.0950814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 96.0000 | 3.52665 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.50000 | − | 9.52628i | 0.200698 | − | 0.347619i | −0.748056 | − | 0.663636i | \(-0.769012\pi\) |
0.948753 | + | 0.316017i | \(0.102346\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 27.0000 | + | 5.19615i | 0.981981 | + | 0.188982i | ||||
\(757\) | −33.0681 | + | 33.0681i | −1.20188 | + | 1.20188i | −0.228287 | + | 0.973594i | \(0.573312\pi\) |
−0.973594 | + | 0.228287i | \(0.926688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.96713 | + | 4.38134i | 0.107417 | + | 0.158615i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −26.7685 | + | 7.17260i | −0.965926 | + | 0.258819i | ||||
\(769\) | − | 49.0000i | − | 1.76699i | −0.468445 | − | 0.883493i | \(-0.655186\pi\) | ||
0.468445 | − | 0.883493i | \(-0.344814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.27603 | + | 23.4225i | 0.225879 | + | 0.842993i | ||||
\(773\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.70522 | + | 23.7506i | 0.0611744 | + | 0.852049i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.3923 | + | 26.0000i | −0.371154 | + | 0.928571i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.1719 | + | 12.1038i | 1.61020 | + | 0.431453i | 0.948103 | − | 0.317962i | \(-0.102999\pi\) |
0.662100 | + | 0.749415i | \(0.269665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.69213 | − | 1.79315i | 0.237645 | − | 0.0636767i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.0000 | + | 29.4449i | −0.602549 | + | 1.04365i | ||||
\(797\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 12.0000i | 0.423207i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0000 | 0.667180 | 0.333590 | − | 0.942718i | \(-0.391740\pi\) | ||||
0.333590 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.2929 | − | 34.2929i | −1.20270 | − | 1.20270i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.1041 | + | 93.6898i | 0.878282 | + | 3.27779i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 51.9615 | − | 18.0000i | 1.81568 | − | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.51747 | − | 31.7876i | 0.296900 | − | 1.10805i | −0.642796 | − | 0.766037i | \(-0.722226\pi\) |
0.939696 | − | 0.342010i | \(-0.111108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.8993 | + | 26.5000i | −1.59415 | + | 0.920383i | −0.601566 | + | 0.798823i | \(0.705456\pi\) |
−0.992584 | + | 0.121560i | \(0.961210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.0000 | − | 31.1769i | 0.624413 | − | 1.08152i | ||||
\(832\) | −39.1918 | + | 39.1918i | −1.35873 | + | 1.35873i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35.1337 | + | 9.41404i | 1.21440 | + | 0.325397i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −50.2295 | + | 29.0000i | −1.72897 | + | 0.998221i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.1815 | − | 12.7093i | −0.899608 | − | 0.436698i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.5885 | + | 9.00000i | 0.534994 | + | 0.308879i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.0681 | + | 33.0681i | 1.13223 | + | 1.13223i | 0.989806 | + | 0.142425i | \(0.0454900\pi\) |
0.142425 | + | 0.989806i | \(0.454510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.4974 | − | 28.0000i | −1.65471 | − | 0.955348i | −0.975097 | − | 0.221777i | \(-0.928814\pi\) |
−0.679613 | − | 0.733571i | \(-0.737852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.8207 | − | 20.8207i | 0.707107 | − | 0.707107i | ||||
\(868\) | −16.1755 | + | 33.3220i | −0.549033 | + | 1.13102i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | + | 20.7846i | 0.406604 | + | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.0573 | + | 4.03459i | −0.509612 | + | 0.136550i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | 1.34486 | + | 5.01910i | 0.0454128 | + | 0.169483i | 0.984908 | − | 0.173080i | \(-0.0553718\pi\) |
−0.939495 | + | 0.342563i | \(0.888705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.6413 | + | 41.6413i | 1.40134 | + | 1.40134i | 0.795855 | + | 0.605487i | \(0.207022\pi\) |
0.605487 | + | 0.795855i | \(0.292978\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.0333 | + | 39.0000i | 1.51037 | + | 1.30802i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.8067 | + | 9.86233i | 1.23238 | + | 0.330215i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.1548 | + | 46.0041i | 1.03677 | + | 1.53092i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.2101 | − | 14.7935i | −1.83322 | − | 0.491210i | −0.834968 | − | 0.550299i | \(-0.814514\pi\) |
−0.998253 | + | 0.0590889i | \(0.981180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −14.3452 | − | 53.5370i | −0.475017 | − | 1.77279i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.0000 | 1.45380 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.866025 | − | 0.500000i | −0.0285675 | − | 0.0164935i | 0.485648 | − | 0.874154i | \(-0.338584\pi\) |
−0.514216 | + | 0.857661i | \(0.671917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50000 | + | 2.59808i | 0.0494267 | + | 0.0856095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 45.1719 | + | 12.1038i | 1.48364 | + | 0.397540i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −52.0000 | − | 20.7846i | −1.70423 | − | 0.681188i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.5176 | − | 35.5176i | 1.16031 | − | 1.16031i | 0.175902 | − | 0.984408i | \(-0.443716\pi\) |
0.984408 | − | 0.175902i | \(-0.0562841\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 9.00000i | − | 0.293704i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(948\) | 15.2418 | − | 56.8831i | 0.495030 | − | 1.84748i | ||||
\(949\) | −10.3923 | + | 6.00000i | −0.337348 | + | 0.194768i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −53.6936 | − | 31.0000i | −1.72935 | − | 0.998443i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.0681 | + | 33.0681i | −1.06340 | + | 1.06340i | −0.0655495 | + | 0.997849i | \(0.520880\pi\) |
−0.997849 | + | 0.0655495i | \(0.979120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.707107 | + | 0.707107i | ||||
\(973\) | 60.6960 | − | 4.35778i | 1.94583 | − | 0.139704i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | − | 3.46410i | −0.0640184 | − | 0.110883i | ||||
\(977\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −78.3837 | − | 78.3837i | −2.49372 | − | 2.49372i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.50000 | − | 14.7224i | −0.270011 | − | 0.467673i | 0.698853 | − | 0.715265i | \(-0.253694\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37.9671 | − | 37.9671i | −1.20485 | − | 1.20485i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.7494 | − | 5.82774i | −0.688811 | − | 0.184566i | −0.102598 | − | 0.994723i | \(-0.532715\pi\) |
−0.586214 | + | 0.810157i | \(0.699382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.3827 | − | 13.5000i | −0.739795 | − | 0.427121i |
(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 | 525.2.bf.c.443.2 | yes | 8 | |
3.2 | odd | 2 | CM | 525.2.bf.c.443.2 | yes | 8 | |
5.2 | odd | 4 | inner | 525.2.bf.c.107.1 | yes | 8 | |
5.3 | odd | 4 | inner | 525.2.bf.c.107.2 | yes | 8 | |
5.4 | even | 2 | inner | 525.2.bf.c.443.1 | yes | 8 | |
7.4 | even | 3 | inner | 525.2.bf.c.368.1 | yes | 8 | |
15.2 | even | 4 | inner | 525.2.bf.c.107.1 | yes | 8 | |
15.8 | even | 4 | inner | 525.2.bf.c.107.2 | yes | 8 | |
15.14 | odd | 2 | inner | 525.2.bf.c.443.1 | yes | 8 | |
21.11 | odd | 6 | inner | 525.2.bf.c.368.1 | yes | 8 | |
35.4 | even | 6 | inner | 525.2.bf.c.368.2 | yes | 8 | |
35.18 | odd | 12 | inner | 525.2.bf.c.32.1 | ✓ | 8 | |
35.32 | odd | 12 | inner | 525.2.bf.c.32.2 | yes | 8 | |
105.32 | even | 12 | inner | 525.2.bf.c.32.2 | yes | 8 | |
105.53 | even | 12 | inner | 525.2.bf.c.32.1 | ✓ | 8 | |
105.74 | odd | 6 | inner | 525.2.bf.c.368.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bf.c.32.1 | ✓ | 8 | 35.18 | odd | 12 | inner | |
525.2.bf.c.32.1 | ✓ | 8 | 105.53 | even | 12 | inner | |
525.2.bf.c.32.2 | yes | 8 | 35.32 | odd | 12 | inner | |
525.2.bf.c.32.2 | yes | 8 | 105.32 | even | 12 | inner | |
525.2.bf.c.107.1 | yes | 8 | 5.2 | odd | 4 | inner | |
525.2.bf.c.107.1 | yes | 8 | 15.2 | even | 4 | inner | |
525.2.bf.c.107.2 | yes | 8 | 5.3 | odd | 4 | inner | |
525.2.bf.c.107.2 | yes | 8 | 15.8 | even | 4 | inner | |
525.2.bf.c.368.1 | yes | 8 | 7.4 | even | 3 | inner | |
525.2.bf.c.368.1 | yes | 8 | 21.11 | odd | 6 | inner | |
525.2.bf.c.368.2 | yes | 8 | 35.4 | even | 6 | inner | |
525.2.bf.c.368.2 | yes | 8 | 105.74 | odd | 6 | inner | |
525.2.bf.c.443.1 | yes | 8 | 5.4 | even | 2 | inner | |
525.2.bf.c.443.1 | yes | 8 | 15.14 | odd | 2 | inner | |
525.2.bf.c.443.2 | yes | 8 | 1.1 | even | 1 | trivial | |
525.2.bf.c.443.2 | yes | 8 | 3.2 | odd | 2 | CM |