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 | 107.2 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.107 |
Dual form | 525.2.bf.b.368.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 1.67303 | + | 0.448288i | 0.965926 | + | 0.258819i | ||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.19067 | − | 1.48356i | −0.827996 | − | 0.560734i | ||||
\(8\) | 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 | \(0.333333\pi\) | |||||||
\(12\) | 3.34607 | − | 0.896575i | 0.965926 | − | 0.258819i | ||||
\(13\) | 1.22474 | − | 1.22474i | 0.339683 | − | 0.339683i | −0.516565 | − | 0.856248i | \(-0.672790\pi\) |
0.856248 | + | 0.516565i | \(0.172790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.06218 | + | 3.50000i | 1.39076 | + | 0.802955i | 0.993399 | − | 0.114708i | \(-0.0365932\pi\) |
0.397360 | + | 0.917663i | \(0.369927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | − | 3.46410i | −0.654654 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.707107 | + | 0.707107i | ||||
\(28\) | −5.27792 | − | 0.378937i | −0.997433 | − | 0.0716124i | ||||
\(29\) | 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 | ||||||||
\(37\) | −11.7112 | + | 3.13801i | −1.92531 | + | 0.515886i | −0.941382 | + | 0.337342i | \(0.890472\pi\) |
−0.983932 | + | 0.178545i | \(0.942861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.59808 | − | 1.50000i | 0.416025 | − | 0.240192i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.57321 | + | 8.57321i | −1.30740 | + | 1.30740i | −0.384120 | + | 0.923283i | \(0.625495\pi\) |
−0.923283 | + | 0.384120i | \(0.874505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.707107 | − | 0.707107i | ||||
\(49\) | 2.59808 | + | 6.50000i | 0.371154 | + | 0.928571i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.896575 | − | 3.34607i | 0.124333 | − | 0.464016i | ||||
\(53\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.57321 | + | 8.57321i | 1.13555 | + | 1.13555i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00000 | + | 12.1244i | −0.896258 | + | 1.55236i | −0.0640184 | + | 0.997949i | \(0.520392\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.46618 | − | 7.14042i | −0.436698 | − | 0.899608i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.13801 | − | 11.7112i | 0.383369 | − | 1.43075i | −0.457352 | − | 0.889286i | \(-0.651202\pi\) |
0.840721 | − | 0.541468i | \(-0.182131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.0573 | + | 4.03459i | 1.76232 | + | 0.472213i | 0.987185 | − | 0.159579i | \(-0.0510137\pi\) |
0.775138 | + | 0.631792i | \(0.217680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.0000 | 1.60591 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.2583 | − | 6.50000i | −1.26666 | − | 0.731307i | −0.292306 | − | 0.956325i | \(-0.594423\pi\) |
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | −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 | ||||||||
\(91\) | −4.50000 | + | 0.866025i | −0.471728 | + | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.13801 | − | 11.7112i | −0.325397 | − | 1.21440i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.79796 | − | 9.79796i | −0.994832 | − | 0.994832i | 0.00515471 | − | 0.999987i | \(-0.498359\pi\) |
−0.999987 | + | 0.00515471i | \(0.998359\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 4.93117 | + | 18.4034i | 0.485882 | + | 1.81334i | 0.576055 | + | 0.817411i | \(0.304591\pi\) |
−0.0901732 | + | 0.995926i | \(0.528742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(108\) | 10.0382 | + | 2.68973i | 0.965926 | + | 0.258819i | ||||
\(109\) | −14.7224 | + | 8.50000i | −1.41015 | + | 0.814152i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) |
−0.414751 | + | 0.909935i | \(0.636131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.0000 | −1.99323 | ||||||||
\(112\) | −9.52056 | + | 4.62158i | −0.899608 | + | 0.436698i | ||||
\(113\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.01910 | − | 1.34486i | 0.464016 | − | 0.124333i | ||||
\(118\) | 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 | ||||||||
\(127\) | 8.57321 | + | 8.57321i | 0.760750 | + | 0.760750i | 0.976458 | − | 0.215708i | \(-0.0692060\pi\) |
−0.215708 | + | 0.976458i | \(0.569206\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | −8.08776 | − | 16.6610i | −0.701298 | − | 1.44469i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.00000i | − | 0.593732i | −0.954919 | − | 0.296866i | \(-0.904058\pi\) | ||
0.954919 | − | 0.296866i | \(-0.0959415\pi\) | |||||||
\(140\) | 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 | ||||
\(148\) | −17.1464 | + | 17.1464i | −1.40943 | + | 1.40943i | ||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | − | 3.46410i | −0.162758 | − | 0.281905i | 0.773099 | − | 0.634285i | \(-0.218706\pi\) |
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | 5.37945 | − | 20.0764i | 0.429327 | − | 1.60227i | −0.324961 | − | 0.945727i | \(-0.605351\pi\) |
0.754288 | − | 0.656543i | \(-0.227982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.27603 | − | 23.4225i | −0.491576 | − | 1.83459i | −0.548417 | − | 0.836205i | \(-0.684769\pi\) |
0.0568404 | − | 0.998383i | \(-0.481897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0000i | 0.769231i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5000 | + | 18.1865i | 0.802955 | + | 1.39076i | ||||
\(172\) | −6.27603 | + | 23.4225i | −0.478543 | + | 1.78595i | ||||
\(173\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(174\) | 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 | ||||||||
\(183\) | −17.1464 | + | 17.1464i | −1.26750 | + | 1.26750i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.59808 | − | 13.5000i | −0.188982 | − | 0.981981i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 3.58630 | − | 13.3843i | 0.258819 | − | 0.965926i | ||||
\(193\) | 11.7112 | + | 3.13801i | 0.842993 | + | 0.225879i | 0.654374 | − | 0.756171i | \(-0.272932\pi\) |
0.188619 | + | 0.982050i | \(0.439599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0000 | + | 8.66025i | 0.785714 | + | 0.618590i | ||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.2487 | − | 14.0000i | 1.71895 | − | 0.992434i | 0.798082 | − | 0.602549i | \(-0.205848\pi\) |
0.920864 | − | 0.389885i | \(-0.127485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5000 | − | 18.1865i | 0.740613 | − | 1.28278i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.79315 | − | 6.69213i | −0.124333 | − | 0.464016i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.32628 | + | 18.4727i | −0.0900338 | + | 1.25401i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.3827 | + | 13.5000i | 1.58006 | + | 0.912245i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.34847 | − | 7.34847i | 0.492090 | − | 0.492090i | −0.416874 | − | 0.908964i | \(-0.636874\pi\) |
0.908964 | + | 0.416874i | \(0.136874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(228\) | 23.4225 | + | 6.27603i | 1.55119 | + | 0.415640i | ||||
\(229\) | 6.06218 | + | 3.50000i | 0.400600 | + | 0.231287i | 0.686743 | − | 0.726900i | \(-0.259040\pi\) |
−0.286143 | + | 0.958187i | \(0.592373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.9217 | − | 15.9217i | −1.03422 | − | 1.03422i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.03459 | + | 15.0573i | 0.258819 | + | 0.965926i | ||||
\(244\) | 28.0000i | 1.79252i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.7112 | − | 3.13801i | 0.745168 | − | 0.199667i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −13.1440 | − | 8.90138i | −0.827996 | − | 0.560734i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.3109 | + | 10.5000i | 1.88343 | + | 0.652438i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.27603 | − | 23.4225i | −0.383369 | − | 1.43075i | ||||
\(269\) | 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 | ||||||||
\(273\) | −7.91688 | − | 0.568406i | −0.479151 | − | 0.0344015i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.13801 | − | 11.7112i | 0.188545 | − | 0.703660i | −0.805299 | − | 0.592869i | \(-0.797995\pi\) |
0.993844 | − | 0.110790i | \(-0.0353382\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 21.0000i | − | 1.25724i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.7876 | + | 8.51747i | 1.88958 | + | 0.506311i | 0.998637 | + | 0.0521913i | \(0.0166205\pi\) |
0.890941 | + | 0.454120i | \(0.150046\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | −12.0000 | − | 20.7846i | −0.703452 | − | 1.21842i | ||||
\(292\) | 30.1146 | − | 8.06918i | 1.76232 | − | 0.472213i | ||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.5000 | − | 6.06218i | 1.81563 | − | 0.349418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 24.2487 | − | 14.0000i | 1.39076 | − | 0.802955i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.22474 | + | 1.22474i | 0.0698999 | + | 0.0698999i | 0.741192 | − | 0.671293i | \(-0.234261\pi\) |
−0.671293 | + | 0.741192i | \(0.734261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 33.0000i | 1.87730i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.34486 | + | 5.01910i | 0.0760162 | + | 0.283696i | 0.993462 | − | 0.114165i | \(-0.0364192\pi\) |
−0.917446 | + | 0.397861i | \(0.869753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.0000 | −1.46261 | ||||||||
\(317\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −28.4416 | + | 7.62089i | −1.57282 | + | 0.421436i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | − | 0.866025i | 0.0274825 | − | 0.0476011i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) |
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −35.1337 | − | 9.41404i | −1.92531 | − | 0.515886i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −18.0000 | + | 3.46410i | −0.981981 | + | 0.188982i | ||||
\(337\) | 25.7196 | + | 25.7196i | 1.40104 | + | 1.40104i | 0.796815 | + | 0.604223i | \(0.206516\pi\) |
0.604223 | + | 0.796815i | \(0.293484\pi\) | |||||||
\(338\) | 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 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000i | 0.749403i | 0.927146 | + | 0.374701i | \(0.122255\pi\) | ||||
−0.927146 | + | 0.374701i | \(0.877745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | 0.480384 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(354\) | 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 | ||||||||
\(361\) | 15.0000 | + | 25.9808i | 0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.4722 | + | 13.4722i | −0.707107 | + | 0.707107i | ||||
\(364\) | −6.92820 | + | 6.00000i | −0.363137 | + | 0.314485i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.03459 | + | 15.0573i | −0.210604 | + | 0.785984i | 0.777064 | + | 0.629421i | \(0.216708\pi\) |
−0.987668 | + | 0.156563i | \(0.949959\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −17.1464 | − | 17.1464i | −0.889001 | − | 0.889001i | ||||
\(373\) | 9.41404 | + | 35.1337i | 0.487441 | + | 1.81915i | 0.568810 | + | 0.822469i | \(0.307404\pi\) |
−0.0813690 | + | 0.996684i | \(0.525929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 37.0000i | − | 1.90056i | −0.311393 | − | 0.950281i | \(-0.600796\pi\) | ||
0.311393 | − | 0.950281i | \(-0.399204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.5000 | + | 18.1865i | 0.537931 | + | 0.931724i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −35.1337 | + | 9.41404i | −1.78595 | + | 0.478543i | ||||
\(388\) | −26.7685 | − | 7.17260i | −1.35897 | − | 0.364134i | ||||
\(389\) | 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 | ||||||||
\(397\) | −18.4034 | + | 4.93117i | −0.923638 | + | 0.247488i | −0.689140 | − | 0.724628i | \(-0.742011\pi\) |
−0.234498 | + | 0.972117i | \(0.575345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.06218 | − | 31.5000i | −0.303488 | − | 1.57697i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.7112 | − | 3.13801i | −0.583378 | − | 0.156316i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.06218 | + | 3.50000i | −0.299755 | + | 0.173064i | −0.642333 | − | 0.766426i | \(-0.722033\pi\) |
0.342578 | + | 0.939490i | \(0.388700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.9444 | + | 26.9444i | 1.32745 | + | 1.32745i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.13801 | − | 11.7112i | 0.153669 | − | 0.573501i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.3220 | − | 16.1755i | 1.61256 | − | 0.782788i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 20.0764 | − | 5.37945i | 0.965926 | − | 0.258819i | ||||
\(433\) | 15.9217 | − | 15.9217i | 0.765147 | − | 0.765147i | −0.212101 | − | 0.977248i | \(-0.568030\pi\) |
0.977248 | + | 0.212101i | \(0.0680304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.0000 | + | 29.4449i | −0.814152 | + | 1.41015i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.2487 | − | 14.0000i | −1.15733 | − | 0.668184i | −0.206666 | − | 0.978412i | \(-0.566261\pi\) |
−0.950662 | + | 0.310228i | \(0.899595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(444\) | −36.3731 | + | 21.0000i | −1.72619 | + | 0.996616i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.8685 | + | 17.5254i | −0.560734 | + | 0.827996i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.79315 | − | 6.69213i | −0.0842496 | − | 0.314424i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7112 | + | 3.13801i | −0.547828 | + | 0.146790i | −0.522108 | − | 0.852879i | \(-0.674854\pi\) |
−0.0257197 | + | 0.999669i | \(0.508188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7196 | − | 25.7196i | 1.19529 | − | 1.19529i | 0.219733 | − | 0.975560i | \(-0.429481\pi\) |
0.975560 | − | 0.219733i | \(-0.0705187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(468\) | 7.34847 | − | 7.34847i | 0.339683 | − | 0.339683i | ||||
\(469\) | −24.2487 | + | 21.0000i | −1.11970 | + | 0.969690i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | − | 31.1769i | 0.829396 | − | 1.43656i | ||||
\(472\) | 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 | ||||||||
\(481\) | −10.5000 | + | 18.1865i | −0.478759 | + | 0.829235i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000i | 1.00000i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.41404 | − | 35.1337i | 0.426591 | − | 1.59206i | −0.333833 | − | 0.942632i | \(-0.608342\pi\) |
0.760424 | − | 0.649427i | \(-0.224991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 42.0000i | − | 1.89931i | ||||||
\(490\) | 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 | ||||||||
\(499\) | −37.2391 | − | 21.5000i | −1.66705 | − | 0.962472i | −0.969216 | − | 0.246214i | \(-0.920813\pi\) |
−0.697835 | − | 0.716258i | \(-0.745853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.48288 | + | 16.7303i | −0.199092 | + | 0.743020i | ||||
\(508\) | 23.4225 | + | 6.27603i | 1.03920 | + | 0.278454i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.0000 | − | 31.1769i | −1.19441 | − | 1.37919i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.41404 | + | 35.1337i | 0.415640 | + | 1.55119i | ||||
\(514\) | 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 | ||||||||
\(523\) | −7.62089 | − | 28.4416i | −0.333238 | − | 1.24366i | −0.905766 | − | 0.423777i | \(-0.860704\pi\) |
0.572528 | − | 0.819885i | \(-0.305963\pi\) | |||||||
\(524\) | 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 | ||||||||
\(532\) | −30.6694 | − | 20.7699i | −1.32969 | − | 0.900489i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.5000 | + | 25.1147i | −0.623404 | + | 1.07977i | 0.365444 | + | 0.930834i | \(0.380917\pi\) |
−0.988847 | + | 0.148933i | \(0.952416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.7112 | + | 3.13801i | 0.502577 | + | 0.134665i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.1464 | − | 17.1464i | −0.733128 | − | 0.733128i | 0.238110 | − | 0.971238i | \(-0.423472\pi\) |
−0.971238 | + | 0.238110i | \(0.923472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36.3731 | + | 21.0000i | −1.55236 | + | 0.896258i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.0201 | + | 30.9418i | 0.638721 | + | 1.31578i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.00000 | − | 12.1244i | −0.296866 | − | 0.514187i | ||||
\(557\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.0000i | 0.888205i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.70522 | − | 23.7506i | 0.0716124 | − | 0.997433i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.5000 | + | 26.8468i | 0.648655 | + | 1.12350i | 0.983444 | + | 0.181210i | \(0.0580014\pi\) |
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.500000 | − | 0.866025i | ||||
\(577\) | −8.51747 | + | 31.7876i | −0.354587 | + | 1.32334i | 0.526417 | + | 0.850227i | \(0.323535\pi\) |
−0.881004 | + | 0.473109i | \(0.843132\pi\) | |||||||
\(578\) | 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 | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | 14.5211 | + | 19.4201i | 0.598839 | + | 0.800869i | ||||
\(589\) | − | 49.0000i | − | 2.01901i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.5521 | + | 46.8449i | −0.515886 | + | 1.92531i | ||||
\(593\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 46.8449 | − | 12.5521i | 1.91723 | − | 0.513721i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 49.0000 | 1.99875 | 0.999376 | − | 0.0353259i | \(-0.0112469\pi\) | ||||
0.999376 | + | 0.0353259i | \(0.0112469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.7196 | − | 25.7196i | 1.04738 | − | 1.04738i | ||||
\(604\) | −6.92820 | − | 4.00000i | −0.281905 | − | 0.162758i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.01910 | − | 1.34486i | 0.203719 | − | 0.0545863i | −0.155517 | − | 0.987833i | \(-0.549704\pi\) |
0.359235 | + | 0.933247i | \(0.383038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.8449 | − | 12.5521i | −1.89205 | − | 0.506973i | −0.998292 | − | 0.0584195i | \(-0.981394\pi\) |
−0.893756 | − | 0.448553i | \(-0.851939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.4352 | − | 24.5000i | 1.70562 | − | 0.984738i | 0.765787 | − | 0.643094i | \(-0.222350\pi\) |
0.939829 | − | 0.341644i | \(-0.110984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 12.0000i | − | 0.480384i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.7589 | − | 40.1528i | −0.429327 | − | 1.60227i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.0000 | 1.75161 | 0.875806 | − | 0.482663i | \(-0.160330\pi\) | ||||
0.875806 | + | 0.482663i | \(0.160330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.7685 | − | 7.17260i | −1.06395 | − | 0.285085i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.1428 | + | 4.77886i | 0.441495 | + | 0.189345i | ||||
\(638\) | 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 | ||||||||
\(643\) | −35.5176 | + | 35.5176i | −1.40068 | + | 1.40068i | −0.602739 | + | 0.797938i | \(0.705924\pi\) |
−0.797938 | + | 0.602739i | \(0.794076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5000 | + | 30.3109i | −0.411527 | + | 1.18798i | ||||
\(652\) | −34.2929 | − | 34.2929i | −1.34301 | − | 1.34301i | ||||
\(653\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.0681 | + | 33.0681i | 1.29011 | + | 1.29011i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.5000 | − | 42.4352i | −0.952940 | − | 1.65054i | −0.739014 | − | 0.673690i | \(-0.764708\pi\) |
−0.213925 | − | 0.976850i | \(-0.568625\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.5885 | − | 9.00000i | 0.602685 | − | 0.347960i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.7196 | − | 25.7196i | 0.991419 | − | 0.991419i | −0.00854415 | − | 0.999963i | \(-0.502720\pi\) |
0.999963 | + | 0.00854415i | \(0.00271972\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.0000 | + | 17.3205i | 0.384615 | + | 0.666173i | ||||
\(677\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.92820 | + | 36.0000i | 0.265880 | + | 1.38155i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(684\) | 36.3731 | + | 21.0000i | 1.39076 | + | 0.802955i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.57321 | + | 8.57321i | 0.327089 | + | 0.327089i | ||||
\(688\) | 12.5521 | + | 46.8449i | 0.478543 | + | 1.78595i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.5000 | + | 42.4352i | −0.932024 | + | 1.61431i | −0.152167 | + | 0.988355i | \(0.548625\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | 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 | ||||||||
\(703\) | −81.9786 | − | 21.9661i | −3.09188 | − | 0.828467i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0526 | + | 11.0000i | 0.715534 | + | 0.413114i | 0.813107 | − | 0.582115i | \(-0.197775\pi\) |
−0.0975728 | + | 0.995228i | \(0.531108\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.5000 | − | 33.7750i | −0.731307 | − | 1.26666i | ||||
\(712\) | 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 | ||||||||
\(721\) | 16.5000 | − | 47.6314i | 0.614492 | − | 1.77389i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.27603 | − | 23.4225i | −0.233408 | − | 0.871091i | ||||
\(724\) | 12.1244 | − | 7.00000i | 0.450598 | − | 0.260153i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.9217 | − | 15.9217i | −0.590503 | − | 0.590503i | 0.347265 | − | 0.937767i | \(-0.387111\pi\) |
−0.937767 | + | 0.347265i | \(0.887111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −12.5521 | + | 46.8449i | −0.463937 | + | 1.73144i | ||||
\(733\) | 13.8969 | + | 51.8640i | 0.513294 | + | 1.91564i | 0.381518 | + | 0.924362i | \(0.375402\pi\) |
0.131777 | + | 0.991279i | \(0.457932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.8993 | − | 26.5000i | 1.68843 | − | 0.974818i | 0.732717 | − | 0.680534i | \(-0.238252\pi\) |
0.955718 | − | 0.294285i | \(-0.0950814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.0000 | 0.771454 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.5000 | − | 35.5070i | 0.748056 | − | 1.29567i | −0.200698 | − | 0.979653i | \(-0.564321\pi\) |
0.948753 | − | 0.316017i | \(-0.102346\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.0000 | − | 20.7846i | −0.654654 | − | 0.755929i | ||||
\(757\) | −34.2929 | − | 34.2929i | −1.24640 | − | 1.24640i | −0.957301 | − | 0.289095i | \(-0.906646\pi\) |
−0.289095 | − | 0.957301i | \(-0.593354\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 44.8623 | + | 3.22097i | 1.62412 | + | 0.116607i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −7.17260 | − | 26.7685i | −0.258819 | − | 0.965926i | ||||
\(769\) | 49.0000i | 1.76699i | 0.468445 | + | 0.883493i | \(0.344814\pi\) | ||||
−0.468445 | + | 0.883493i | \(0.655186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.4225 | − | 6.27603i | 0.842993 | − | 0.225879i | ||||
\(773\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 46.0041 | + | 31.1548i | 1.65039 | + | 1.11767i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.7128 | + | 4.00000i | 0.989743 | + | 0.142857i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.896575 | − | 3.34607i | 0.0319595 | − | 0.119274i | −0.948103 | − | 0.317962i | \(-0.897001\pi\) |
0.980063 | + | 0.198688i | \(0.0636681\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.27603 | + | 23.4225i | 0.222868 | + | 0.831756i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.0000 | − | 48.4974i | 0.992434 | − | 1.71895i | ||||
\(797\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 42.0000i | − | 1.48123i | ||||||
\(805\) | 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 | ||||||||
\(811\) | −56.0000 | −1.96643 | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||||
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.2929 | − | 34.2929i | 1.20270 | − | 1.20270i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −81.9786 | + | 21.9661i | −2.86807 | + | 0.768497i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.9904 | − | 4.50000i | −0.453921 | − | 0.157243i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.4225 | + | 6.27603i | 0.816456 | + | 0.218769i | 0.642796 | − | 0.766037i | \(-0.277774\pi\) |
0.173659 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.06218 | + | 3.50000i | −0.210548 | + | 0.121560i | −0.601566 | − | 0.798823i | \(-0.705456\pi\) |
0.391018 | + | 0.920383i | \(0.372123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5000 | − | 18.1865i | 0.364241 | − | 0.630884i | ||||
\(832\) | −9.79796 | − | 9.79796i | −0.339683 | − | 0.339683i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.41404 | − | 35.1337i | 0.325397 | − | 1.21440i | ||||
\(838\) | 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 | ||||||||
\(844\) | −27.7128 | + | 16.0000i | −0.953914 | + | 0.550743i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.1815 | − | 12.7093i | 0.899608 | − | 0.436698i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.3634 | + | 28.5000i | 1.69415 | + | 0.978117i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.0681 | + | 33.0681i | −1.13223 | + | 1.13223i | −0.142425 | + | 0.989806i | \(0.545490\pi\) |
−0.989806 | + | 0.142425i | \(0.954510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.4974 | + | 28.0000i | 1.65471 | + | 0.955348i | 0.975097 | + | 0.221777i | \(0.0711857\pi\) |
0.679613 | + | 0.733571i | \(0.262148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | −10.5000 | − | 18.1865i | −0.355779 | − | 0.616227i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.7589 | − | 40.1528i | −0.364134 | − | 1.35897i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 54.0000 | 1.82449 | ||||||||
\(877\) | 46.8449 | − | 12.5521i | 1.58184 | − | 0.423853i | 0.642345 | − | 0.766415i | \(-0.277962\pi\) |
0.939495 | + | 0.342563i | \(0.111295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.7196 | − | 25.7196i | 0.865535 | − | 0.865535i | −0.126439 | − | 0.991974i | \(-0.540355\pi\) |
0.991974 | + | 0.126439i | \(0.0403549\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.06218 | − | 31.5000i | −0.203319 | − | 1.05648i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.37945 | − | 20.0764i | 0.180117 | − | 0.672207i | ||||
\(893\) | 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 | ||||||||
\(903\) | 55.4181 | + | 3.97884i | 1.84420 | + | 0.132408i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.13801 | − | 11.7112i | 0.104196 | − | 0.388865i | −0.894057 | − | 0.447954i | \(-0.852153\pi\) |
0.998253 | + | 0.0590889i | \(0.0188195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 46.8449 | − | 12.5521i | 1.55119 | − | 0.415640i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.866025 | + | 0.500000i | 0.0285675 | + | 0.0164935i | 0.514216 | − | 0.857661i | \(-0.328083\pi\) |
−0.485648 | + | 0.874154i | \(0.661416\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | −14.7935 | + | 55.2101i | −0.485882 | + | 1.81334i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | + | 48.4974i | −0.229416 | + | 1.58944i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.5176 | − | 35.5176i | −1.16031 | − | 1.16031i | −0.984408 | − | 0.175902i | \(-0.943716\pi\) |
−0.175902 | − | 0.984408i | \(-0.556284\pi\) | |||||||
\(938\) | 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 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(948\) | −43.4988 | − | 11.6555i | −1.41278 | − | 0.378552i | ||||
\(949\) | 23.3827 | − | 13.5000i | 0.759034 | − | 0.438229i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(954\) | 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 | ||||||||
\(964\) | −24.2487 | − | 14.0000i | −0.780998 | − | 0.450910i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.57321 | + | 8.57321i | 0.275696 | + | 0.275696i | 0.831388 | − | 0.555692i | \(-0.187547\pi\) |
−0.555692 | + | 0.831388i | \(0.687547\pi\) | |||||||
\(968\) | 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 | ||||
\(973\) | −10.3849 | + | 15.3347i | −0.332926 | + | 0.491608i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.0000 | + | 48.4974i | 0.896258 | + | 1.55236i | ||||
\(977\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.0000 | −1.62830 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.1464 | − | 17.1464i | 0.545501 | − | 0.545501i | ||||
\(989\) | 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 | ||||||||
\(993\) | 1.22474 | − | 1.22474i | 0.0388661 | − | 0.0388661i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3106 | + | 38.4797i | −0.326541 | + | 1.21867i | 0.586214 | + | 0.810157i | \(0.300618\pi\) |
−0.912754 | + | 0.408509i | \(0.866049\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −54.5596 | − | 31.5000i | −1.72619 | − | 0.996616i |
(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.b.107.2 | yes | 8 | |
3.2 | odd | 2 | CM | 525.2.bf.b.107.2 | yes | 8 | |
5.2 | odd | 4 | inner | 525.2.bf.b.443.2 | yes | 8 | |
5.3 | odd | 4 | inner | 525.2.bf.b.443.1 | yes | 8 | |
5.4 | even | 2 | inner | 525.2.bf.b.107.1 | yes | 8 | |
7.4 | even | 3 | inner | 525.2.bf.b.32.1 | ✓ | 8 | |
15.2 | even | 4 | inner | 525.2.bf.b.443.2 | yes | 8 | |
15.8 | even | 4 | inner | 525.2.bf.b.443.1 | yes | 8 | |
15.14 | odd | 2 | inner | 525.2.bf.b.107.1 | yes | 8 | |
21.11 | odd | 6 | inner | 525.2.bf.b.32.1 | ✓ | 8 | |
35.4 | even | 6 | inner | 525.2.bf.b.32.2 | yes | 8 | |
35.18 | odd | 12 | inner | 525.2.bf.b.368.2 | yes | 8 | |
35.32 | odd | 12 | inner | 525.2.bf.b.368.1 | yes | 8 | |
105.32 | even | 12 | inner | 525.2.bf.b.368.1 | yes | 8 | |
105.53 | even | 12 | inner | 525.2.bf.b.368.2 | yes | 8 | |
105.74 | odd | 6 | inner | 525.2.bf.b.32.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bf.b.32.1 | ✓ | 8 | 7.4 | even | 3 | inner | |
525.2.bf.b.32.1 | ✓ | 8 | 21.11 | odd | 6 | inner | |
525.2.bf.b.32.2 | yes | 8 | 35.4 | even | 6 | inner | |
525.2.bf.b.32.2 | yes | 8 | 105.74 | odd | 6 | inner | |
525.2.bf.b.107.1 | yes | 8 | 5.4 | even | 2 | inner | |
525.2.bf.b.107.1 | yes | 8 | 15.14 | odd | 2 | inner | |
525.2.bf.b.107.2 | yes | 8 | 1.1 | even | 1 | trivial | |
525.2.bf.b.107.2 | yes | 8 | 3.2 | odd | 2 | CM | |
525.2.bf.b.368.1 | yes | 8 | 35.32 | odd | 12 | inner | |
525.2.bf.b.368.1 | yes | 8 | 105.32 | even | 12 | inner | |
525.2.bf.b.368.2 | yes | 8 | 35.18 | odd | 12 | inner | |
525.2.bf.b.368.2 | yes | 8 | 105.53 | even | 12 | inner | |
525.2.bf.b.443.1 | yes | 8 | 5.3 | odd | 4 | inner | |
525.2.bf.b.443.1 | yes | 8 | 15.8 | even | 4 | inner | |
525.2.bf.b.443.2 | yes | 8 | 5.2 | odd | 4 | inner | |
525.2.bf.b.443.2 | yes | 8 | 15.2 | even | 4 | inner |