Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(79,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.e (of order \(3\), degree \(2\), not 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.79 |
Dual form | 637.2.e.e.508.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(3\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | −3.00000 | − | 5.19615i | −0.948683 | − | 1.64317i | ||||
\(11\) | 3.00000 | + | 5.19615i | 0.904534 | + | 1.56670i | 0.821541 | + | 0.570149i | \(0.193114\pi\) |
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −2.00000 | − | 3.46410i | −0.485071 | − | 0.840168i | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | −3.00000 | − | 5.19615i | −0.707107 | − | 1.22474i | ||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | −6.00000 | −1.34164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.0000 | 2.55841 | ||||||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | −1.00000 | + | 1.73205i | −0.196116 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 2.59808i | 0.269408 | + | 0.466628i | 0.968709 | − | 0.248199i | \(-0.0798387\pi\) |
−0.699301 | + | 0.714827i | \(0.746505\pi\) | |||||||
\(32\) | −4.00000 | − | 6.92820i | −0.707107 | − | 1.22474i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.00000 | −1.37199 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −1.00000 | ||||||||
\(37\) | 2.00000 | − | 3.46410i | 0.328798 | − | 0.569495i | −0.653476 | − | 0.756948i | \(-0.726690\pi\) |
0.982274 | + | 0.187453i | \(0.0600231\pi\) | |||||||
\(38\) | 5.00000 | + | 8.66025i | 0.811107 | + | 1.40488i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 6.00000 | − | 10.3923i | 0.904534 | − | 1.56670i | ||||
\(45\) | −4.50000 | − | 7.79423i | −0.670820 | − | 1.16190i | ||||
\(46\) | 3.00000 | + | 5.19615i | 0.442326 | + | 0.766131i | ||||
\(47\) | −3.50000 | + | 6.06218i | −0.510527 | + | 0.884260i | 0.489398 | + | 0.872060i | \(0.337217\pi\) |
−0.999926 | + | 0.0121990i | \(0.996117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.00000 | −1.13137 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | + | 1.73205i | 0.138675 | + | 0.240192i | ||||
\(53\) | 4.50000 | + | 7.79423i | 0.618123 | + | 1.07062i | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.0000 | 2.42712 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | + | 8.66025i | −0.656532 | + | 1.13715i | ||||
\(59\) | −4.00000 | − | 6.92820i | −0.520756 | − | 0.901975i | −0.999709 | − | 0.0241347i | \(-0.992317\pi\) |
0.478953 | − | 0.877841i | \(-0.341016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | − | 8.66025i | 0.640184 | − | 1.10883i | −0.345207 | − | 0.938527i | \(-0.612191\pi\) |
0.985391 | − | 0.170305i | \(-0.0544754\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −1.50000 | + | 2.59808i | −0.186052 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00000 | + | 5.19615i | 0.366508 | + | 0.634811i | 0.989017 | − | 0.147802i | \(-0.0472198\pi\) |
−0.622509 | + | 0.782613i | \(0.713886\pi\) | |||||||
\(68\) | −4.00000 | + | 6.92820i | −0.485071 | + | 0.840168i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.50000 | + | 11.2583i | 0.760767 | + | 1.31769i | 0.942455 | + | 0.334332i | \(0.108511\pi\) |
−0.181688 | + | 0.983356i | \(0.558156\pi\) | |||||||
\(74\) | −4.00000 | − | 6.92820i | −0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.0000 | 1.14708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.50000 | + | 2.59808i | −0.168763 | + | 0.292306i | −0.937985 | − | 0.346675i | \(-0.887311\pi\) |
0.769222 | + | 0.638982i | \(0.220644\pi\) | |||||||
\(80\) | −6.00000 | − | 10.3923i | −0.670820 | − | 1.16190i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −6.00000 | + | 10.3923i | −0.662589 | + | 1.14764i | ||||
\(83\) | 15.0000 | 1.64646 | 0.823232 | − | 0.567705i | \(-0.192169\pi\) | ||||
0.823232 | + | 0.567705i | \(0.192169\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | −1.30158 | ||||||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | + | 2.59808i | −0.159000 | + | 0.275396i | −0.934508 | − | 0.355942i | \(-0.884160\pi\) |
0.775509 | + | 0.631337i | \(0.217494\pi\) | |||||||
\(90\) | −18.0000 | −1.89737 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.00000 | + | 12.1244i | 0.721995 | + | 1.25053i | ||||
\(95\) | 7.50000 | + | 12.9904i | 0.769484 | + | 1.33278i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.0000 | 1.80907 | ||||||||
\(100\) | −4.00000 | + | 6.92820i | −0.400000 | + | 0.692820i | ||||
\(101\) | 7.00000 | + | 12.1244i | 0.696526 | + | 1.20642i | 0.969664 | + | 0.244443i | \(0.0786053\pi\) |
−0.273138 | + | 0.961975i | \(0.588061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.0000 | 1.74831 | ||||||||
\(107\) | 2.00000 | − | 3.46410i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 18.0000 | − | 31.1769i | 1.71623 | − | 2.97260i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | −0.282216 | −0.141108 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141108 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | + | 7.79423i | 0.419627 | + | 0.726816i | ||||
\(116\) | 5.00000 | + | 8.66025i | 0.464238 | + | 0.804084i | ||||
\(117\) | −1.50000 | + | 2.59808i | −0.138675 | + | 0.240192i | ||||
\(118\) | −16.0000 | −1.47292 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | −10.0000 | − | 17.3205i | −0.905357 | − | 1.56813i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.00000 | − | 5.19615i | 0.269408 | − | 0.466628i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.00000 | + | 5.19615i | 0.263117 | + | 0.455733i | ||||
\(131\) | −4.00000 | + | 6.92820i | −0.349482 | + | 0.605320i | −0.986157 | − | 0.165812i | \(-0.946976\pi\) |
0.636676 | + | 0.771132i | \(0.280309\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | − | 3.46410i | −0.170872 | − | 0.295958i | 0.767853 | − | 0.640626i | \(-0.221325\pi\) |
−0.938725 | + | 0.344668i | \(0.887992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.0000 | −1.52674 | −0.763370 | − | 0.645961i | \(-0.776457\pi\) | ||||
−0.763370 | + | 0.645961i | \(0.776457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.00000 | + | 13.8564i | −0.671345 | + | 1.16280i | ||||
\(143\) | −3.00000 | − | 5.19615i | −0.250873 | − | 0.434524i | ||||
\(144\) | −6.00000 | − | 10.3923i | −0.500000 | − | 0.866025i | ||||
\(145\) | −7.50000 | + | 12.9904i | −0.622841 | + | 1.07879i | ||||
\(146\) | 26.0000 | 2.15178 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.00000 | −0.657596 | ||||||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.00000 | 0.722897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.00000 | + | 6.92820i | 0.319235 | + | 0.552931i | 0.980329 | − | 0.197372i | \(-0.0632408\pi\) |
−0.661094 | + | 0.750303i | \(0.729907\pi\) | |||||||
\(158\) | 3.00000 | + | 5.19615i | 0.238667 | + | 0.413384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −24.0000 | −1.89737 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −18.0000 | −1.41421 | ||||||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | 6.00000 | + | 10.3923i | 0.468521 | + | 0.811503i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0000 | − | 25.9808i | 1.16423 | − | 2.01650i | ||||
\(167\) | 5.00000 | 0.386912 | 0.193456 | − | 0.981109i | \(-0.438030\pi\) | ||||
0.193456 | + | 0.981109i | \(0.438030\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −12.0000 | + | 20.7846i | −0.920358 | + | 1.59411i | ||||
\(171\) | 7.50000 | + | 12.9904i | 0.573539 | + | 0.993399i | ||||
\(172\) | 1.00000 | + | 1.73205i | 0.0762493 | + | 0.132068i | ||||
\(173\) | 4.00000 | − | 6.92820i | 0.304114 | − | 0.526742i | −0.672949 | − | 0.739689i | \(-0.734973\pi\) |
0.977064 | + | 0.212947i | \(0.0683062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.0000 | 1.80907 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | −11.5000 | − | 19.9186i | −0.859550 | − | 1.48878i | −0.872358 | − | 0.488867i | \(-0.837410\pi\) |
0.0128080 | − | 0.999918i | \(-0.495923\pi\) | |||||||
\(180\) | −9.00000 | + | 15.5885i | −0.670820 | + | 1.16190i | ||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | − | 10.3923i | −0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0000 | − | 20.7846i | 0.877527 | − | 1.51992i | ||||
\(188\) | 14.0000 | 1.02105 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 30.0000 | 2.17643 | ||||||||
\(191\) | 4.00000 | − | 6.92820i | 0.289430 | − | 0.501307i | −0.684244 | − | 0.729253i | \(-0.739868\pi\) |
0.973674 | + | 0.227946i | \(0.0732010\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | − | 19.0526i | −0.791797 | − | 1.37143i | −0.924853 | − | 0.380325i | \(-0.875812\pi\) |
0.133056 | − | 0.991109i | \(-0.457521\pi\) | |||||||
\(194\) | 7.00000 | − | 12.1244i | 0.502571 | − | 0.870478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 18.0000 | − | 31.1769i | 1.27920 | − | 2.21565i | ||||
\(199\) | −2.00000 | − | 3.46410i | −0.141776 | − | 0.245564i | 0.786389 | − | 0.617731i | \(-0.211948\pi\) |
−0.928166 | + | 0.372168i | \(0.878615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 28.0000 | 1.97007 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | + | 15.5885i | −0.628587 | + | 1.08875i | ||||
\(206\) | −4.00000 | − | 6.92820i | −0.278693 | − | 0.482711i | ||||
\(207\) | 4.50000 | + | 7.79423i | 0.312772 | + | 0.541736i | ||||
\(208\) | −2.00000 | + | 3.46410i | −0.138675 | + | 0.240192i | ||||
\(209\) | −30.0000 | −2.07514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | −0.344214 | −0.172107 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172107 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(212\) | 9.00000 | − | 15.5885i | 0.618123 | − | 1.07062i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.00000 | − | 6.92820i | −0.273434 | − | 0.473602i | ||||
\(215\) | −1.50000 | + | 2.59808i | −0.102299 | + | 0.177187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.00000 | 0.270914 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.0000 | − | 31.1769i | −1.21356 | − | 2.10195i | ||||
\(221\) | 2.00000 | + | 3.46410i | 0.134535 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0000 | 1.00447 | 0.502237 | − | 0.864730i | \(-0.332510\pi\) | ||||
0.502237 | + | 0.864730i | \(0.332510\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0000 | −0.800000 | ||||||||
\(226\) | −3.00000 | + | 5.19615i | −0.199557 | + | 0.345643i | ||||
\(227\) | −10.0000 | − | 17.3205i | −0.663723 | − | 1.14960i | −0.979630 | − | 0.200812i | \(-0.935642\pi\) |
0.315906 | − | 0.948790i | \(-0.397691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 18.0000 | 1.18688 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.50000 | + | 12.9904i | −0.491341 | + | 0.851028i | −0.999950 | − | 0.00996947i | \(-0.996827\pi\) |
0.508609 | + | 0.860998i | \(0.330160\pi\) | |||||||
\(234\) | 3.00000 | + | 5.19615i | 0.196116 | + | 0.339683i | ||||
\(235\) | 10.5000 | + | 18.1865i | 0.684944 | + | 1.18636i | ||||
\(236\) | −8.00000 | + | 13.8564i | −0.520756 | + | 0.901975i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50000 | + | 14.7224i | 0.547533 | + | 0.948355i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 25.0000 | + | 43.3013i | 1.60706 | + | 2.78351i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.0000 | −1.28037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.50000 | − | 4.33013i | 0.159071 | − | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.00000 | − | 5.19615i | 0.189737 | − | 0.328634i | ||||
\(251\) | −26.0000 | −1.64111 | −0.820553 | − | 0.571571i | \(-0.806334\pi\) | ||||
−0.820553 | + | 0.571571i | \(0.806334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | −4.00000 | + | 6.92820i | −0.250982 | + | 0.434714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 1.00000 | − | 1.73205i | 0.0623783 | − | 0.108042i | −0.833150 | − | 0.553047i | \(-0.813465\pi\) |
0.895528 | + | 0.445005i | \(0.146798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | −7.50000 | + | 12.9904i | −0.464238 | + | 0.804084i | ||||
\(262\) | 8.00000 | + | 13.8564i | 0.494242 | + | 0.856052i | ||||
\(263\) | 7.50000 | + | 12.9904i | 0.462470 | + | 0.801021i | 0.999083 | − | 0.0428069i | \(-0.0136300\pi\) |
−0.536614 | + | 0.843828i | \(0.680297\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.0000 | 1.65860 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.00000 | − | 10.3923i | 0.366508 | − | 0.634811i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | −16.0000 | −0.970143 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.00000 | −0.483298 | ||||||||
\(275\) | 12.0000 | − | 20.7846i | 0.723627 | − | 1.25336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.500000 | − | 0.866025i | −0.0300421 | − | 0.0520344i | 0.850613 | − | 0.525792i | \(-0.176231\pi\) |
−0.880656 | + | 0.473757i | \(0.842897\pi\) | |||||||
\(278\) | −18.0000 | + | 31.1769i | −1.07957 | + | 1.86987i | ||||
\(279\) | 9.00000 | 0.538816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.0000 | −1.78965 | −0.894825 | − | 0.446417i | \(-0.852700\pi\) | ||||
−0.894825 | + | 0.446417i | \(0.852700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00000 | − | 13.8564i | −0.475551 | − | 0.823678i | 0.524057 | − | 0.851683i | \(-0.324418\pi\) |
−0.999608 | + | 0.0280052i | \(0.991084\pi\) | |||||||
\(284\) | 8.00000 | + | 13.8564i | 0.474713 | + | 0.822226i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −24.0000 | −1.41421 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 15.0000 | + | 25.9808i | 0.880830 | + | 1.52564i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.0000 | − | 22.5167i | 0.760767 | − | 1.31769i | ||||
\(293\) | −19.0000 | −1.10999 | −0.554996 | − | 0.831853i | \(-0.687280\pi\) | ||||
−0.554996 | + | 0.831853i | \(0.687280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | −1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.0000 | − | 31.1769i | −1.04271 | − | 1.80603i | ||||
\(299\) | 1.50000 | − | 2.59808i | 0.0867472 | − | 0.150251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.0000 | + | 17.3205i | 0.573539 | + | 0.993399i | ||||
\(305\) | −15.0000 | − | 25.9808i | −0.858898 | − | 1.48765i | ||||
\(306\) | −12.0000 | + | 20.7846i | −0.685994 | + | 1.18818i | ||||
\(307\) | −33.0000 | −1.88341 | −0.941705 | − | 0.336440i | \(-0.890777\pi\) | ||||
−0.941705 | + | 0.336440i | \(0.890777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | − | 15.5885i | 0.511166 | − | 0.885365i | ||||
\(311\) | 3.00000 | + | 5.19615i | 0.170114 | + | 0.294647i | 0.938460 | − | 0.345389i | \(-0.112253\pi\) |
−0.768345 | + | 0.640036i | \(0.778920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0000 | + | 19.0526i | −0.621757 | + | 1.07691i | 0.367402 | + | 0.930062i | \(0.380247\pi\) |
−0.989158 | + | 0.146852i | \(0.953086\pi\) | |||||||
\(314\) | 16.0000 | 0.902932 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | 0.337526 | ||||||||
\(317\) | 12.0000 | − | 20.7846i | 0.673987 | − | 1.16738i | −0.302777 | − | 0.953062i | \(-0.597914\pi\) |
0.976764 | − | 0.214318i | \(-0.0687530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0000 | − | 25.9808i | −0.839839 | − | 1.45464i | ||||
\(320\) | −12.0000 | + | 20.7846i | −0.670820 | + | 1.16190i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.0000 | 1.11283 | ||||||||
\(324\) | −9.00000 | + | 15.5885i | −0.500000 | + | 0.866025i | ||||
\(325\) | 2.00000 | + | 3.46410i | 0.110940 | + | 0.192154i | ||||
\(326\) | −4.00000 | − | 6.92820i | −0.221540 | − | 0.383718i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0000 | + | 19.0526i | −0.604615 | + | 1.04722i | 0.387498 | + | 0.921871i | \(0.373340\pi\) |
−0.992112 | + | 0.125353i | \(0.959994\pi\) | |||||||
\(332\) | −15.0000 | − | 25.9808i | −0.823232 | − | 1.42588i | ||||
\(333\) | −6.00000 | − | 10.3923i | −0.328798 | − | 0.569495i | ||||
\(334\) | 5.00000 | − | 8.66025i | 0.273588 | − | 0.473868i | ||||
\(335\) | 18.0000 | 0.983445 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0000 | 0.926049 | 0.463025 | − | 0.886345i | \(-0.346764\pi\) | ||||
0.463025 | + | 0.886345i | \(0.346764\pi\) | |||||||
\(338\) | 1.00000 | − | 1.73205i | 0.0543928 | − | 0.0942111i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.0000 | + | 20.7846i | 0.650791 | + | 1.12720i | ||||
\(341\) | −9.00000 | + | 15.5885i | −0.487377 | + | 0.844162i | ||||
\(342\) | 30.0000 | 1.62221 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.00000 | − | 13.8564i | −0.430083 | − | 0.744925i | ||||
\(347\) | 16.0000 | + | 27.7128i | 0.858925 | + | 1.48770i | 0.872955 | + | 0.487800i | \(0.162201\pi\) |
−0.0140303 | + | 0.999902i | \(0.504466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0000 | 0.588817 | 0.294408 | − | 0.955680i | \(-0.404877\pi\) | ||||
0.294408 | + | 0.955680i | \(0.404877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.0000 | − | 41.5692i | 1.27920 | − | 2.21565i | ||||
\(353\) | 5.00000 | + | 8.66025i | 0.266123 | + | 0.460939i | 0.967857 | − | 0.251500i | \(-0.0809239\pi\) |
−0.701734 | + | 0.712439i | \(0.747591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | + | 20.7846i | −0.636894 | + | 1.10313i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −46.0000 | −2.43118 | ||||||||
\(359\) | −10.0000 | + | 17.3205i | −0.527780 | + | 0.914141i | 0.471696 | + | 0.881761i | \(0.343642\pi\) |
−0.999476 | + | 0.0323801i | \(0.989691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 14.0000 | − | 24.2487i | 0.735824 | − | 1.27448i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.0000 | 2.04135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.00000 | − | 12.1244i | −0.365397 | − | 0.632886i | 0.623443 | − | 0.781869i | \(-0.285733\pi\) |
−0.988840 | + | 0.148983i | \(0.952400\pi\) | |||||||
\(368\) | 6.00000 | + | 10.3923i | 0.312772 | + | 0.541736i | ||||
\(369\) | −9.00000 | + | 15.5885i | −0.468521 | + | 0.811503i | ||||
\(370\) | −24.0000 | −1.24770 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0000 | + | 25.9808i | −0.776671 | + | 1.34523i | 0.157180 | + | 0.987570i | \(0.449760\pi\) |
−0.933851 | + | 0.357663i | \(0.883574\pi\) | |||||||
\(374\) | −24.0000 | − | 41.5692i | −1.24101 | − | 2.14949i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.00000 | 0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.00000 | −0.308199 | −0.154100 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(380\) | 15.0000 | − | 25.9808i | 0.769484 | − | 1.33278i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.00000 | − | 13.8564i | −0.409316 | − | 0.708955i | ||||
\(383\) | 18.0000 | − | 31.1769i | 0.919757 | − | 1.59307i | 0.119974 | − | 0.992777i | \(-0.461719\pi\) |
0.799783 | − | 0.600289i | \(-0.204948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −44.0000 | −2.23954 | ||||||||
\(387\) | −1.50000 | + | 2.59808i | −0.0762493 | + | 0.132068i | ||||
\(388\) | −7.00000 | − | 12.1244i | −0.355371 | − | 0.615521i | ||||
\(389\) | −15.0000 | − | 25.9808i | −0.760530 | − | 1.31728i | −0.942578 | − | 0.333987i | \(-0.891606\pi\) |
0.182047 | − | 0.983290i | \(-0.441728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.00000 | − | 3.46410i | 0.100759 | − | 0.174519i | ||||
\(395\) | 4.50000 | + | 7.79423i | 0.226420 | + | 0.392170i | ||||
\(396\) | −18.0000 | − | 31.1769i | −0.904534 | − | 1.56670i | ||||
\(397\) | 6.50000 | − | 11.2583i | 0.326226 | − | 0.565039i | −0.655534 | − | 0.755166i | \(-0.727556\pi\) |
0.981760 | + | 0.190126i | \(0.0608897\pi\) | |||||||
\(398\) | −8.00000 | −0.401004 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.0000 | −0.800000 | ||||||||
\(401\) | 16.0000 | − | 27.7128i | 0.799002 | − | 1.38391i | −0.121265 | − | 0.992620i | \(-0.538695\pi\) |
0.920267 | − | 0.391292i | \(-0.127972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50000 | − | 2.59808i | −0.0747203 | − | 0.129419i | ||||
\(404\) | 14.0000 | − | 24.2487i | 0.696526 | − | 1.20642i | ||||
\(405\) | −27.0000 | −1.34164 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.50000 | + | 11.2583i | 0.321404 | + | 0.556689i | 0.980778 | − | 0.195127i | \(-0.0625118\pi\) |
−0.659374 | + | 0.751815i | \(0.729178\pi\) | |||||||
\(410\) | 18.0000 | + | 31.1769i | 0.888957 | + | 1.53972i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.0000 | 0.884652 | ||||||||
\(415\) | 22.5000 | − | 38.9711i | 1.10448 | − | 1.91302i | ||||
\(416\) | 4.00000 | + | 6.92820i | 0.196116 | + | 0.339683i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −30.0000 | + | 51.9615i | −1.46735 | + | 2.54152i | ||||
\(419\) | −10.0000 | −0.488532 | −0.244266 | − | 0.969708i | \(-0.578547\pi\) | ||||
−0.244266 | + | 0.969708i | \(0.578547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0000 | −0.584844 | −0.292422 | − | 0.956289i | \(-0.594461\pi\) | ||||
−0.292422 | + | 0.956289i | \(0.594461\pi\) | |||||||
\(422\) | −5.00000 | + | 8.66025i | −0.243396 | + | 0.421575i | ||||
\(423\) | 10.5000 | + | 18.1865i | 0.510527 | + | 0.884260i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.00000 | + | 13.8564i | −0.388057 | + | 0.672134i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.00000 | −0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.00000 | + | 5.19615i | 0.144673 | + | 0.250581i | ||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.0000 | 0.576683 | 0.288342 | − | 0.957528i | \(-0.406896\pi\) | ||||
0.288342 | + | 0.957528i | \(0.406896\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | − | 3.46410i | 0.0957826 | − | 0.165900i | ||||
\(437\) | −7.50000 | − | 12.9904i | −0.358774 | − | 0.621414i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.0000 | − | 19.0526i | 0.525001 | − | 0.909329i | −0.474575 | − | 0.880215i | \(-0.657398\pi\) |
0.999576 | − | 0.0291138i | \(-0.00926853\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.00000 | 0.380521 | ||||||||
\(443\) | −9.50000 | + | 16.4545i | −0.451359 | + | 0.781776i | −0.998471 | − | 0.0552833i | \(-0.982394\pi\) |
0.547112 | + | 0.837059i | \(0.315727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.50000 | + | 7.79423i | 0.213320 | + | 0.369482i | ||||
\(446\) | 15.0000 | − | 25.9808i | 0.710271 | − | 1.23022i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.0000 | 1.69895 | 0.849473 | − | 0.527633i | \(-0.176920\pi\) | ||||
0.849473 | + | 0.527633i | \(0.176920\pi\) | |||||||
\(450\) | −12.0000 | + | 20.7846i | −0.565685 | + | 0.979796i | ||||
\(451\) | −18.0000 | − | 31.1769i | −0.847587 | − | 1.46806i | ||||
\(452\) | 3.00000 | + | 5.19615i | 0.141108 | + | 0.244406i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −40.0000 | −1.87729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(458\) | 14.0000 | + | 24.2487i | 0.654177 | + | 1.13307i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.00000 | − | 15.5885i | 0.419627 | − | 0.726816i | ||||
\(461\) | −22.0000 | −1.02464 | −0.512321 | − | 0.858794i | \(-0.671214\pi\) | ||||
−0.512321 | + | 0.858794i | \(0.671214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | −10.0000 | + | 17.3205i | −0.464238 | + | 0.804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.0000 | + | 25.9808i | 0.694862 | + | 1.20354i | ||||
\(467\) | 11.0000 | − | 19.0526i | 0.509019 | − | 0.881647i | −0.490926 | − | 0.871201i | \(-0.663342\pi\) |
0.999945 | − | 0.0104461i | \(-0.00332515\pi\) | |||||||
\(468\) | 6.00000 | 0.277350 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 42.0000 | 1.93732 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00000 | − | 5.19615i | −0.137940 | − | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.0000 | 0.917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.0000 | 1.23625 | ||||||||
\(478\) | −4.00000 | + | 6.92820i | −0.182956 | + | 0.316889i | ||||
\(479\) | 5.50000 | + | 9.52628i | 0.251301 | + | 0.435267i | 0.963884 | − | 0.266321i | \(-0.0858081\pi\) |
−0.712583 | + | 0.701588i | \(0.752475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | + | 3.46410i | −0.0911922 | + | 0.157949i | ||||
\(482\) | 34.0000 | 1.54866 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 50.0000 | 2.27273 | ||||||||
\(485\) | 10.5000 | − | 18.1865i | 0.476780 | − | 0.825808i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0000 | + | 22.5167i | 0.589086 | + | 1.02033i | 0.994352 | + | 0.106129i | \(0.0338455\pi\) |
−0.405266 | + | 0.914199i | \(0.632821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0000 | + | 17.3205i | 0.450377 | + | 0.780076i | ||||
\(494\) | −5.00000 | − | 8.66025i | −0.224961 | − | 0.389643i | ||||
\(495\) | 27.0000 | − | 46.7654i | 1.21356 | − | 2.10195i | ||||
\(496\) | 12.0000 | 0.538816 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.00000 | − | 13.8564i | 0.358129 | − | 0.620298i | −0.629519 | − | 0.776985i | \(-0.716748\pi\) |
0.987648 | + | 0.156687i | \(0.0500814\pi\) | |||||||
\(500\) | −3.00000 | − | 5.19615i | −0.134164 | − | 0.232379i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.0000 | + | 45.0333i | −1.16044 | + | 2.00994i | ||||
\(503\) | 2.00000 | 0.0891756 | 0.0445878 | − | 0.999005i | \(-0.485803\pi\) | ||||
0.0445878 | + | 0.999005i | \(0.485803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.0000 | 1.86898 | ||||||||
\(506\) | −18.0000 | + | 31.1769i | −0.800198 | + | 1.38598i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.00000 | + | 6.92820i | 0.177471 | + | 0.307389i | ||||
\(509\) | 9.50000 | − | 16.4545i | 0.421080 | − | 0.729332i | −0.574965 | − | 0.818178i | \(-0.694984\pi\) |
0.996045 | + | 0.0888457i | \(0.0283178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −32.0000 | −1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.00000 | − | 3.46410i | −0.0882162 | − | 0.152795i | ||||
\(515\) | −6.00000 | − | 10.3923i | −0.264392 | − | 0.457940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.0000 | −1.84716 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.0000 | − | 34.6410i | −0.876216 | − | 1.51765i | −0.855462 | − | 0.517866i | \(-0.826727\pi\) |
−0.0207541 | − | 0.999785i | \(-0.506607\pi\) | |||||||
\(522\) | 15.0000 | + | 25.9808i | 0.656532 | + | 1.13715i | ||||
\(523\) | −5.00000 | + | 8.66025i | −0.218635 | + | 0.378686i | −0.954391 | − | 0.298560i | \(-0.903494\pi\) |
0.735756 | + | 0.677247i | \(0.236827\pi\) | |||||||
\(524\) | 16.0000 | 0.698963 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30.0000 | 1.30806 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 27.0000 | − | 46.7654i | 1.17281 | − | 2.03136i | ||||
\(531\) | −24.0000 | −1.04151 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | 0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | − | 10.3923i | −0.259403 | − | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | − | 34.6410i | 0.859867 | − | 1.48933i | −0.0121878 | − | 0.999926i | \(-0.503880\pi\) |
0.872055 | − | 0.489408i | \(-0.162787\pi\) | |||||||
\(542\) | 8.00000 | + | 13.8564i | 0.343629 | + | 0.595184i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.0000 | + | 27.7128i | −0.685994 | + | 1.18818i | ||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.00000 | −0.299298 | −0.149649 | − | 0.988739i | \(-0.547814\pi\) | ||||
−0.149649 | + | 0.988739i | \(0.547814\pi\) | |||||||
\(548\) | −4.00000 | + | 6.92820i | −0.170872 | + | 0.295958i | ||||
\(549\) | −15.0000 | − | 25.9808i | −0.640184 | − | 1.10883i | ||||
\(550\) | −24.0000 | − | 41.5692i | −1.02336 | − | 1.77252i | ||||
\(551\) | 12.5000 | − | 21.6506i | 0.532518 | − | 0.922348i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.0000 | + | 31.1769i | 0.763370 | + | 1.32220i | ||||
\(557\) | 6.00000 | + | 10.3923i | 0.254228 | + | 0.440336i | 0.964686 | − | 0.263404i | \(-0.0848453\pi\) |
−0.710457 | + | 0.703740i | \(0.751512\pi\) | |||||||
\(558\) | 9.00000 | − | 15.5885i | 0.381000 | − | 0.659912i | ||||
\(559\) | 1.00000 | 0.0422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.0000 | + | 51.9615i | −1.26547 | + | 2.19186i | ||||
\(563\) | −2.00000 | − | 3.46410i | −0.0842900 | − | 0.145994i | 0.820798 | − | 0.571218i | \(-0.193529\pi\) |
−0.905088 | + | 0.425223i | \(0.860196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.50000 | + | 7.79423i | −0.189316 | + | 0.327906i | ||||
\(566\) | −32.0000 | −1.34506 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.50000 | + | 6.06218i | −0.146728 | + | 0.254140i | −0.930016 | − | 0.367519i | \(-0.880207\pi\) |
0.783289 | + | 0.621658i | \(0.213541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.50000 | + | 14.7224i | 0.355714 | + | 0.616115i | 0.987240 | − | 0.159240i | \(-0.0509044\pi\) |
−0.631526 | + | 0.775355i | \(0.717571\pi\) | |||||||
\(572\) | −6.00000 | + | 10.3923i | −0.250873 | + | 0.434524i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | −12.0000 | + | 20.7846i | −0.500000 | + | 0.866025i | ||||
\(577\) | −1.00000 | − | 1.73205i | −0.0416305 | − | 0.0721062i | 0.844459 | − | 0.535620i | \(-0.179922\pi\) |
−0.886090 | + | 0.463513i | \(0.846589\pi\) | |||||||
\(578\) | −1.00000 | − | 1.73205i | −0.0415945 | − | 0.0720438i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 30.0000 | 1.24568 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.0000 | + | 46.7654i | −1.11823 | + | 1.93682i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.50000 | + | 7.79423i | 0.186052 | + | 0.322252i | ||||
\(586\) | −19.0000 | + | 32.9090i | −0.784883 | + | 1.35946i | ||||
\(587\) | 39.0000 | 1.60970 | 0.804851 | − | 0.593477i | \(-0.202245\pi\) | ||||
0.804851 | + | 0.593477i | \(0.202245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.0000 | −0.618064 | ||||||||
\(590\) | −24.0000 | + | 41.5692i | −0.988064 | + | 1.71138i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.00000 | − | 13.8564i | −0.328798 | − | 0.569495i | ||||
\(593\) | 13.5000 | − | 23.3827i | 0.554379 | − | 0.960212i | −0.443573 | − | 0.896238i | \(-0.646289\pi\) |
0.997952 | − | 0.0639736i | \(-0.0203773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −36.0000 | −1.47462 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | −5.50000 | − | 9.52628i | −0.224724 | − | 0.389233i | 0.731513 | − | 0.681828i | \(-0.238815\pi\) |
−0.956237 | + | 0.292595i | \(0.905481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.0000 | 0.733017 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 37.5000 | + | 64.9519i | 1.52459 | + | 2.64067i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.00000 | + | 1.73205i | −0.0405887 | + | 0.0703018i | −0.885606 | − | 0.464437i | \(-0.846257\pi\) |
0.845017 | + | 0.534739i | \(0.179590\pi\) | |||||||
\(608\) | 40.0000 | 1.62221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −60.0000 | −2.42933 | ||||||||
\(611\) | 3.50000 | − | 6.06218i | 0.141595 | − | 0.245249i | ||||
\(612\) | 12.0000 | + | 20.7846i | 0.485071 | + | 0.840168i | ||||
\(613\) | −4.00000 | − | 6.92820i | −0.161558 | − | 0.279827i | 0.773869 | − | 0.633345i | \(-0.218319\pi\) |
−0.935428 | + | 0.353518i | \(0.884985\pi\) | |||||||
\(614\) | −33.0000 | + | 57.1577i | −1.33177 | + | 2.30670i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | − | 17.3205i | −0.401934 | − | 0.696170i | 0.592025 | − | 0.805919i | \(-0.298329\pi\) |
−0.993959 | + | 0.109749i | \(0.964995\pi\) | |||||||
\(620\) | −9.00000 | − | 15.5885i | −0.361449 | − | 0.626048i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 22.0000 | + | 38.1051i | 0.879297 | + | 1.52299i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.00000 | − | 13.8564i | 0.319235 | − | 0.552931i | ||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0000 | 0.875806 | 0.437903 | − | 0.899022i | \(-0.355721\pi\) | ||||
0.437903 | + | 0.899022i | \(0.355721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.0000 | − | 41.5692i | −0.953162 | − | 1.65092i | ||||
\(635\) | −6.00000 | + | 10.3923i | −0.238103 | + | 0.412406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −60.0000 | −2.37542 | ||||||||
\(639\) | −12.0000 | + | 20.7846i | −0.474713 | + | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | − | 7.79423i | −0.177739 | − | 0.307854i | 0.763367 | − | 0.645966i | \(-0.223545\pi\) |
−0.941106 | + | 0.338112i | \(0.890212\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.00000 | 0.315489 | 0.157745 | − | 0.987480i | \(-0.449578\pi\) | ||||
0.157745 | + | 0.987480i | \(0.449578\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.0000 | − | 34.6410i | 0.786889 | − | 1.36293i | ||||
\(647\) | −9.00000 | − | 15.5885i | −0.353827 | − | 0.612845i | 0.633090 | − | 0.774078i | \(-0.281786\pi\) |
−0.986916 | + | 0.161233i | \(0.948453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | − | 41.5692i | 0.942082 | − | 1.63173i | ||||
\(650\) | 8.00000 | 0.313786 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | + | 20.7846i | 0.468879 | + | 0.812122i | ||||
\(656\) | −12.0000 | + | 20.7846i | −0.468521 | + | 0.811503i | ||||
\(657\) | 39.0000 | 1.52153 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0000 | 0.662226 | 0.331113 | − | 0.943591i | \(-0.392576\pi\) | ||||
0.331113 | + | 0.943591i | \(0.392576\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.5000 | + | 28.5788i | 0.641776 | + | 1.11159i | 0.985036 | + | 0.172348i | \(0.0551353\pi\) |
−0.343261 | + | 0.939240i | \(0.611531\pi\) | |||||||
\(662\) | 22.0000 | + | 38.1051i | 0.855054 | + | 1.48100i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.0000 | −0.929981 | ||||||||
\(667\) | 7.50000 | − | 12.9904i | 0.290401 | − | 0.502990i | ||||
\(668\) | −5.00000 | − | 8.66025i | −0.193456 | − | 0.335075i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.0000 | − | 31.1769i | 0.695401 | − | 1.20447i | ||||
\(671\) | 60.0000 | 2.31627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | 0.0385472 | 0.0192736 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192736 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(674\) | 17.0000 | − | 29.4449i | 0.654816 | − | 1.13417i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.00000 | − | 1.73205i | −0.0384615 | − | 0.0666173i | ||||
\(677\) | −11.0000 | + | 19.0526i | −0.422764 | + | 0.732249i | −0.996209 | − | 0.0869952i | \(-0.972274\pi\) |
0.573444 | + | 0.819244i | \(0.305607\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.0000 | + | 31.1769i | 0.689256 | + | 1.19383i | ||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | 15.0000 | − | 25.9808i | 0.573539 | − | 0.993399i | ||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00000 | + | 3.46410i | −0.0762493 | + | 0.132068i | ||||
\(689\) | −4.50000 | − | 7.79423i | −0.171436 | − | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.50000 | + | 9.52628i | −0.209230 | + | 0.362397i | −0.951472 | − | 0.307735i | \(-0.900429\pi\) |
0.742242 | + | 0.670132i | \(0.233762\pi\) | |||||||
\(692\) | −16.0000 | −0.608229 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 64.0000 | 2.42941 | ||||||||
\(695\) | −27.0000 | + | 46.7654i | −1.02417 | + | 1.77391i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0000 | + | 20.7846i | 0.454532 | + | 0.787273i | ||||
\(698\) | 11.0000 | − | 19.0526i | 0.416356 | − | 0.721150i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0000 | + | 17.3205i | 0.377157 | + | 0.653255i | ||||
\(704\) | −24.0000 | − | 41.5692i | −0.904534 | − | 1.56670i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.0000 | 0.752710 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 24.0000 | + | 41.5692i | 0.900704 | + | 1.56007i | ||||
\(711\) | 4.50000 | + | 7.79423i | 0.168763 | + | 0.292306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.00000 | −0.337053 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | −23.0000 | + | 39.8372i | −0.859550 | + | 1.48878i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.0000 | + | 34.6410i | 0.746393 | + | 1.29279i | ||||
\(719\) | −9.00000 | + | 15.5885i | −0.335643 | + | 0.581351i | −0.983608 | − | 0.180319i | \(-0.942287\pi\) |
0.647965 | + | 0.761670i | \(0.275620\pi\) | |||||||
\(720\) | −36.0000 | −1.34164 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.0000 | −0.446594 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.0000 | − | 24.2487i | −0.520306 | − | 0.901196i | ||||
\(725\) | 10.0000 | + | 17.3205i | 0.371391 | + | 0.643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.0000 | 1.70605 | 0.853023 | − | 0.521874i | \(-0.174767\pi\) | ||||
0.853023 | + | 0.521874i | \(0.174767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 39.0000 | − | 67.5500i | 1.44345 | − | 2.50014i | ||||
\(731\) | 2.00000 | + | 3.46410i | 0.0739727 | + | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.5000 | + | 44.1673i | −0.941864 | + | 1.63136i | −0.179952 | + | 0.983675i | \(0.557594\pi\) |
−0.761912 | + | 0.647681i | \(0.775739\pi\) | |||||||
\(734\) | −28.0000 | −1.03350 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.0000 | 0.884652 | ||||||||
\(737\) | −18.0000 | + | 31.1769i | −0.663039 | + | 1.14842i | ||||
\(738\) | 18.0000 | + | 31.1769i | 0.662589 | + | 1.14764i | ||||
\(739\) | 13.0000 | + | 22.5167i | 0.478213 | + | 0.828289i | 0.999688 | − | 0.0249776i | \(-0.00795146\pi\) |
−0.521475 | + | 0.853266i | \(0.674618\pi\) | |||||||
\(740\) | −12.0000 | + | 20.7846i | −0.441129 | + | 0.764057i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.0000 | − | 46.7654i | −0.989203 | − | 1.71335i | ||||
\(746\) | 30.0000 | + | 51.9615i | 1.09838 | + | 1.90245i | ||||
\(747\) | 22.5000 | − | 38.9711i | 0.823232 | − | 1.42588i | ||||
\(748\) | −48.0000 | −1.75505 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.50000 | − | 14.7224i | 0.310169 | − | 0.537229i | −0.668229 | − | 0.743955i | \(-0.732948\pi\) |
0.978399 | + | 0.206726i | \(0.0662809\pi\) | |||||||
\(752\) | 14.0000 | + | 24.2487i | 0.510527 | + | 0.884260i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.00000 | − | 8.66025i | 0.182089 | − | 0.315388i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | −0.545184 | −0.272592 | − | 0.962130i | \(-0.587881\pi\) | ||||
−0.272592 | + | 0.962130i | \(0.587881\pi\) | |||||||
\(758\) | −6.00000 | + | 10.3923i | −0.217930 | + | 0.377466i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.50000 | + | 7.79423i | −0.163125 | + | 0.282541i | −0.935988 | − | 0.352032i | \(-0.885491\pi\) |
0.772863 | + | 0.634573i | \(0.218824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | −18.0000 | + | 31.1769i | −0.650791 | + | 1.12720i | ||||
\(766\) | −36.0000 | − | 62.3538i | −1.30073 | − | 2.25294i | ||||
\(767\) | 4.00000 | + | 6.92820i | 0.144432 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.0000 | −1.26213 | −0.631066 | − | 0.775729i | \(-0.717382\pi\) | ||||
−0.631066 | + | 0.775729i | \(0.717382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.0000 | + | 38.1051i | −0.791797 | + | 1.37143i | ||||
\(773\) | −27.0000 | − | 46.7654i | −0.971123 | − | 1.68203i | −0.692179 | − | 0.721726i | \(-0.743349\pi\) |
−0.278944 | − | 0.960307i | \(-0.589984\pi\) | |||||||
\(774\) | 3.00000 | + | 5.19615i | 0.107833 | + | 0.186772i | ||||
\(775\) | 6.00000 | − | 10.3923i | 0.215526 | − | 0.373303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −60.0000 | −2.15110 | ||||||||
\(779\) | 15.0000 | − | 25.9808i | 0.537431 | − | 0.930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0000 | − | 41.5692i | −0.858788 | − | 1.48746i | ||||
\(782\) | 12.0000 | − | 20.7846i | 0.429119 | − | 0.743256i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.0000 | 0.856597 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.5000 | − | 32.0429i | −0.659454 | − | 1.14221i | −0.980757 | − | 0.195231i | \(-0.937454\pi\) |
0.321303 | − | 0.946976i | \(-0.395879\pi\) | |||||||
\(788\) | −2.00000 | − | 3.46410i | −0.0712470 | − | 0.123404i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.0000 | 0.640411 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.00000 | + | 8.66025i | −0.177555 | + | 0.307535i | ||||
\(794\) | −13.0000 | − | 22.5167i | −0.461353 | − | 0.799086i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.00000 | + | 6.92820i | −0.141776 | + | 0.245564i | ||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.0000 | 0.990569 | ||||||||
\(800\) | −16.0000 | + | 27.7128i | −0.565685 | + | 0.979796i | ||||
\(801\) | 4.50000 | + | 7.79423i | 0.159000 | + | 0.275396i | ||||
\(802\) | −32.0000 | − | 55.4256i | −1.12996 | − | 1.95715i | ||||
\(803\) | −39.0000 | + | 67.5500i | −1.37628 | + | 2.38379i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.00000 | −0.211341 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.5000 | + | 26.8468i | 0.544951 | + | 0.943883i | 0.998610 | + | 0.0527074i | \(0.0167851\pi\) |
−0.453659 | + | 0.891175i | \(0.649882\pi\) | |||||||
\(810\) | −27.0000 | + | 46.7654i | −0.948683 | + | 1.64317i | ||||
\(811\) | −52.0000 | −1.82597 | −0.912983 | − | 0.407997i | \(-0.866228\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.0000 | − | 41.5692i | 0.841200 | − | 1.45700i | ||||
\(815\) | −6.00000 | − | 10.3923i | −0.210171 | − | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.50000 | − | 4.33013i | 0.0874639 | − | 0.151492i | ||||
\(818\) | 26.0000 | 0.909069 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 36.0000 | 1.25717 | ||||||||
\(821\) | 3.00000 | − | 5.19615i | 0.104701 | − | 0.181347i | −0.808915 | − | 0.587925i | \(-0.799945\pi\) |
0.913616 | + | 0.406578i | \(0.133278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | + | 27.7128i | 0.557725 | + | 0.966008i | 0.997686 | + | 0.0679910i | \(0.0216589\pi\) |
−0.439961 | + | 0.898017i | \(0.645008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.00000 | 0.139094 | 0.0695468 | − | 0.997579i | \(-0.477845\pi\) | ||||
0.0695468 | + | 0.997579i | \(0.477845\pi\) | |||||||
\(828\) | 9.00000 | − | 15.5885i | 0.312772 | − | 0.541736i | ||||
\(829\) | 5.00000 | + | 8.66025i | 0.173657 | + | 0.300783i | 0.939696 | − | 0.342012i | \(-0.111108\pi\) |
−0.766039 | + | 0.642795i | \(0.777775\pi\) | |||||||
\(830\) | −45.0000 | − | 77.9423i | −1.56197 | − | 2.70542i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.00000 | 0.277350 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.50000 | − | 12.9904i | 0.259548 | − | 0.449551i | ||||
\(836\) | 30.0000 | + | 51.9615i | 1.03757 | + | 1.79713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.0000 | + | 17.3205i | −0.345444 | + | 0.598327i | ||||
\(839\) | −8.00000 | −0.276191 | −0.138095 | − | 0.990419i | \(-0.544098\pi\) | ||||
−0.138095 | + | 0.990419i | \(0.544098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | −12.0000 | + | 20.7846i | −0.413547 | + | 0.716285i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.00000 | + | 8.66025i | 0.172107 | + | 0.298098i | ||||
\(845\) | 1.50000 | − | 2.59808i | 0.0516016 | − | 0.0893765i | ||||
\(846\) | 42.0000 | 1.44399 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 36.0000 | 1.23625 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.0000 | + | 27.7128i | 0.548795 | + | 0.950542i | ||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.0000 | 1.54077 | 0.770385 | − | 0.637579i | \(-0.220064\pi\) | ||||
0.770385 | + | 0.637579i | \(0.220064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 45.0000 | 1.53897 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | + | 5.19615i | 0.102478 | + | 0.177497i | 0.912705 | − | 0.408619i | \(-0.133990\pi\) |
−0.810227 | + | 0.586116i | \(0.800656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.00000 | − | 1.73205i | 0.0341196 | − | 0.0590968i | −0.848461 | − | 0.529257i | \(-0.822471\pi\) |
0.882581 | + | 0.470160i | \(0.155804\pi\) | |||||||
\(860\) | 6.00000 | 0.204598 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.0000 | −0.408722 | ||||||||
\(863\) | 16.0000 | − | 27.7128i | 0.544646 | − | 0.943355i | −0.453983 | − | 0.891010i | \(-0.649997\pi\) |
0.998629 | − | 0.0523446i | \(-0.0166694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | − | 20.7846i | −0.408012 | − | 0.706698i | ||||
\(866\) | 12.0000 | − | 20.7846i | 0.407777 | − | 0.706290i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.0000 | −0.610608 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00000 | − | 5.19615i | −0.101651 | − | 0.176065i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.5000 | − | 18.1865i | 0.355371 | − | 0.615521i | ||||
\(874\) | −30.0000 | −1.01477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(878\) | −22.0000 | − | 38.1051i | −0.742464 | − | 1.28599i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 36.0000 | − | 62.3538i | 1.21356 | − | 2.10195i | ||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 4.00000 | − | 6.92820i | 0.134535 | − | 0.233021i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.0000 | + | 32.9090i | 0.638317 | + | 1.10560i | ||||
\(887\) | 6.00000 | − | 10.3923i | 0.201460 | − | 0.348939i | −0.747539 | − | 0.664218i | \(-0.768765\pi\) |
0.948999 | + | 0.315279i | \(0.102098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 27.0000 | − | 46.7654i | 0.904534 | − | 1.56670i | ||||
\(892\) | −15.0000 | − | 25.9808i | −0.502237 | − | 0.869900i | ||||
\(893\) | −17.5000 | − | 30.3109i | −0.585615 | − | 1.01432i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −69.0000 | −2.30642 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.0000 | − | 62.3538i | 1.20134 | − | 2.08077i | ||||
\(899\) | −7.50000 | − | 12.9904i | −0.250139 | − | 0.433253i | ||||
\(900\) | 12.0000 | + | 20.7846i | 0.400000 | + | 0.692820i | ||||
\(901\) | 18.0000 | − | 31.1769i | 0.599667 | − | 1.03865i | ||||
\(902\) | −72.0000 | −2.39734 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0000 | − | 36.3731i | 0.698064 | − | 1.20908i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.50000 | − | 6.06218i | −0.116216 | − | 0.201291i | 0.802049 | − | 0.597258i | \(-0.203743\pi\) |
−0.918265 | + | 0.395966i | \(0.870410\pi\) | |||||||
\(908\) | −20.0000 | + | 34.6410i | −0.663723 | + | 1.14960i | ||||
\(909\) | 42.0000 | 1.39305 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | −0.496972 | −0.248486 | − | 0.968635i | \(-0.579933\pi\) | ||||
−0.248486 | + | 0.968635i | \(0.579933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.0000 | + | 77.9423i | 1.48928 | + | 2.57951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.0000 | 0.925146 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00000 | + | 6.92820i | −0.131948 | + | 0.228540i | −0.924427 | − | 0.381358i | \(-0.875456\pi\) |
0.792480 | + | 0.609898i | \(0.208790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.0000 | + | 38.1051i | −0.724531 | + | 1.25493i | ||||
\(923\) | 8.00000 | 0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | −0.526077 | ||||||||
\(926\) | −14.0000 | + | 24.2487i | −0.460069 | + | 0.796862i | ||||
\(927\) | −6.00000 | − | 10.3923i | −0.197066 | − | 0.341328i | ||||
\(928\) | 20.0000 | + | 34.6410i | 0.656532 | + | 1.13715i | ||||
\(929\) | −2.50000 | + | 4.33013i | −0.0820223 | + | 0.142067i | −0.904118 | − | 0.427282i | \(-0.859471\pi\) |
0.822096 | + | 0.569349i | \(0.192805\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 30.0000 | 0.982683 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.0000 | − | 38.1051i | −0.719862 | − | 1.24684i | ||||
\(935\) | −36.0000 | − | 62.3538i | −1.17733 | − | 2.03919i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.00000 | −0.261349 | −0.130674 | − | 0.991425i | \(-0.541714\pi\) | ||||
−0.130674 | + | 0.991425i | \(0.541714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.0000 | − | 36.3731i | 0.684944 | − | 1.18636i | ||||
\(941\) | −27.5000 | − | 47.6314i | −0.896474 | − | 1.55274i | −0.831969 | − | 0.554822i | \(-0.812786\pi\) |
−0.0645052 | − | 0.997917i | \(-0.520547\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | − | 15.5885i | 0.293080 | − | 0.507630i | ||||
\(944\) | −32.0000 | −1.04151 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 9.00000 | − | 15.5885i | 0.292461 | − | 0.506557i | −0.681930 | − | 0.731417i | \(-0.738859\pi\) |
0.974391 | + | 0.224860i | \(0.0721926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.50000 | − | 11.2583i | −0.210999 | − | 0.365461i | ||||
\(950\) | 20.0000 | − | 34.6410i | 0.648886 | − | 1.12390i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.0000 | −1.26333 | −0.631667 | − | 0.775240i | \(-0.717629\pi\) | ||||
−0.631667 | + | 0.775240i | \(0.717629\pi\) | |||||||
\(954\) | 27.0000 | − | 46.7654i | 0.874157 | − | 1.51408i | ||||
\(955\) | −12.0000 | − | 20.7846i | −0.388311 | − | 0.672574i | ||||
\(956\) | 4.00000 | + | 6.92820i | 0.129369 | + | 0.224074i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.0000 | 0.710788 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 4.00000 | + | 6.92820i | 0.128965 | + | 0.223374i | ||||
\(963\) | −6.00000 | − | 10.3923i | −0.193347 | − | 0.334887i | ||||
\(964\) | 17.0000 | − | 29.4449i | 0.547533 | − | 0.948355i | ||||
\(965\) | −66.0000 | −2.12462 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.0000 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.0000 | − | 36.3731i | −0.674269 | − | 1.16787i | ||||
\(971\) | −19.0000 | + | 32.9090i | −0.609739 | + | 1.05610i | 0.381544 | + | 0.924351i | \(0.375392\pi\) |
−0.991283 | + | 0.131748i | \(0.957941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 52.0000 | 1.66619 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.0000 | − | 34.6410i | −0.640184 | − | 1.10883i | ||||
\(977\) | −5.00000 | − | 8.66025i | −0.159964 | − | 0.277066i | 0.774891 | − | 0.632094i | \(-0.217805\pi\) |
−0.934856 | + | 0.355028i | \(0.884471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | −12.0000 | + | 20.7846i | −0.382935 | + | 0.663264i | ||||
\(983\) | −8.50000 | − | 14.7224i | −0.271108 | − | 0.469573i | 0.698038 | − | 0.716061i | \(-0.254057\pi\) |
−0.969146 | + | 0.246488i | \(0.920723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | − | 5.19615i | 0.0955879 | − | 0.165563i | ||||
\(986\) | 40.0000 | 1.27386 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.0000 | −0.318142 | ||||||||
\(989\) | 1.50000 | − | 2.59808i | 0.0476972 | − | 0.0826140i | ||||
\(990\) | −54.0000 | − | 93.5307i | −1.71623 | − | 2.97260i | ||||
\(991\) | −2.00000 | − | 3.46410i | −0.0635321 | − | 0.110041i | 0.832510 | − | 0.554010i | \(-0.186903\pi\) |
−0.896042 | + | 0.443969i | \(0.853570\pi\) | |||||||
\(992\) | 12.0000 | − | 20.7846i | 0.381000 | − | 0.659912i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0000 | −0.380426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0000 | + | 24.2487i | 0.443384 | + | 0.767964i | 0.997938 | − | 0.0641836i | \(-0.0204443\pi\) |
−0.554554 | + | 0.832148i | \(0.687111\pi\) | |||||||
\(998\) | −16.0000 | − | 27.7128i | −0.506471 | − | 0.877234i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.e.e.79.1 | 2 | ||
7.2 | even | 3 | 91.2.a.a.1.1 | ✓ | 1 | ||
7.3 | odd | 6 | 637.2.e.d.508.1 | 2 | |||
7.4 | even | 3 | inner | 637.2.e.e.508.1 | 2 | ||
7.5 | odd | 6 | 637.2.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 637.2.e.d.79.1 | 2 | |||
21.2 | odd | 6 | 819.2.a.f.1.1 | 1 | |||
21.5 | even | 6 | 5733.2.a.l.1.1 | 1 | |||
28.23 | odd | 6 | 1456.2.a.g.1.1 | 1 | |||
35.9 | even | 6 | 2275.2.a.h.1.1 | 1 | |||
56.37 | even | 6 | 5824.2.a.s.1.1 | 1 | |||
56.51 | odd | 6 | 5824.2.a.t.1.1 | 1 | |||
91.12 | odd | 6 | 8281.2.a.l.1.1 | 1 | |||
91.44 | odd | 12 | 1183.2.c.b.337.2 | 2 | |||
91.51 | even | 6 | 1183.2.a.b.1.1 | 1 | |||
91.86 | odd | 12 | 1183.2.c.b.337.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.a.1.1 | ✓ | 1 | 7.2 | even | 3 | ||
637.2.a.a.1.1 | 1 | 7.5 | odd | 6 | |||
637.2.e.d.79.1 | 2 | 7.6 | odd | 2 | |||
637.2.e.d.508.1 | 2 | 7.3 | odd | 6 | |||
637.2.e.e.79.1 | 2 | 1.1 | even | 1 | trivial | ||
637.2.e.e.508.1 | 2 | 7.4 | even | 3 | inner | ||
819.2.a.f.1.1 | 1 | 21.2 | odd | 6 | |||
1183.2.a.b.1.1 | 1 | 91.51 | even | 6 | |||
1183.2.c.b.337.1 | 2 | 91.86 | odd | 12 | |||
1183.2.c.b.337.2 | 2 | 91.44 | odd | 12 | |||
1456.2.a.g.1.1 | 1 | 28.23 | odd | 6 | |||
2275.2.a.h.1.1 | 1 | 35.9 | even | 6 | |||
5733.2.a.l.1.1 | 1 | 21.5 | even | 6 | |||
5824.2.a.s.1.1 | 1 | 56.37 | even | 6 | |||
5824.2.a.t.1.1 | 1 | 56.51 | odd | 6 | |||
8281.2.a.l.1.1 | 1 | 91.12 | odd | 6 |