Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(143,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.s (of order \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 143.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.143 |
Dual form | 432.2.s.e.287.2 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | + | 0.866025i | −0.670820 | + | 0.387298i | −0.796387 | − | 0.604787i | \(-0.793258\pi\) |
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59808 | + | 1.50000i | 0.981981 | + | 0.566947i | 0.902867 | − | 0.429919i | \(-0.141458\pi\) |
0.0791130 | + | 0.996866i | \(0.474791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59808 | + | 4.50000i | −0.783349 | + | 1.35680i | 0.146631 | + | 0.989191i | \(0.453157\pi\) |
−0.929980 | + | 0.367610i | \(0.880176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.46410i | − | 0.840168i | −0.907485 | − | 0.420084i | \(-0.862001\pi\) | ||
0.907485 | − | 0.420084i | \(-0.137999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.59808 | + | 4.50000i | 0.541736 | + | 0.938315i | 0.998805 | + | 0.0488832i | \(0.0155662\pi\) |
−0.457068 | + | 0.889432i | \(0.651100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.50000 | + | 4.33013i | 1.39272 | + | 0.804084i | 0.993615 | − | 0.112823i | \(-0.0359893\pi\) |
0.399100 | + | 0.916907i | \(0.369323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.59808 | − | 1.50000i | 0.466628 | − | 0.269408i | −0.248199 | − | 0.968709i | \(-0.579839\pi\) |
0.714827 | + | 0.699301i | \(0.246505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.19615 | −0.878310 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | + | 2.59808i | −0.702782 | + | 0.405751i | −0.808383 | − | 0.588657i | \(-0.799657\pi\) |
0.105601 | + | 0.994409i | \(0.466323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.59808 | + | 1.50000i | 0.396203 | + | 0.228748i | 0.684844 | − | 0.728689i | \(-0.259870\pi\) |
−0.288641 | + | 0.957437i | \(0.593204\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.59808 | − | 4.50000i | 0.378968 | − | 0.656392i | −0.611944 | − | 0.790901i | \(-0.709612\pi\) |
0.990912 | + | 0.134509i | \(0.0429456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 1.73205i | 0.142857 | + | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.3923i | − | 1.42749i | −0.700404 | − | 0.713746i | \(-0.746997\pi\) | ||
0.700404 | − | 0.713746i | \(-0.253003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.00000i | − | 1.21356i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.59808 | − | 4.50000i | −0.338241 | − | 0.585850i | 0.645861 | − | 0.763455i | \(-0.276498\pi\) |
−0.984102 | + | 0.177605i | \(0.943165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | − | 6.06218i | 0.448129 | − | 0.776182i | −0.550135 | − | 0.835076i | \(-0.685424\pi\) |
0.998264 | + | 0.0588933i | \(0.0187572\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.50000 | + | 0.866025i | 0.186052 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.79423 | + | 4.50000i | −0.952217 | + | 0.549762i | −0.893769 | − | 0.448528i | \(-0.851948\pi\) |
−0.0584478 | + | 0.998290i | \(0.518615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3923 | 1.23334 | 0.616670 | − | 0.787222i | \(-0.288481\pi\) | ||||
0.616670 | + | 0.787222i | \(0.288481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.5000 | + | 7.79423i | −1.53847 | + | 0.888235i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9904 | − | 7.50000i | −1.46153 | − | 0.843816i | −0.462450 | − | 0.886646i | \(-0.653029\pi\) |
−0.999082 | + | 0.0428296i | \(0.986363\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.59808 | − | 4.50000i | 0.285176 | − | 0.493939i | −0.687476 | − | 0.726207i | \(-0.741281\pi\) |
0.972652 | + | 0.232268i | \(0.0746146\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | + | 5.19615i | 0.325396 | + | 0.563602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.46410i | 0.367194i | 0.983002 | + | 0.183597i | \(0.0587741\pi\) | ||||
−0.983002 | + | 0.183597i | \(0.941226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.00000i | − | 0.314485i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.19615 | − | 9.00000i | −0.533114 | − | 0.923381i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | + | 0.866025i | −0.0507673 | + | 0.0879316i | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50000 | + | 2.59808i | 0.447767 | + | 0.258518i | 0.706887 | − | 0.707327i | \(-0.250099\pi\) |
−0.259120 | + | 0.965845i | \(0.583432\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.79423 | − | 4.50000i | 0.767988 | − | 0.443398i | −0.0641683 | − | 0.997939i | \(-0.520439\pi\) |
0.832156 | + | 0.554541i | \(0.187106\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5000 | − | 6.06218i | 0.987757 | − | 0.570282i | 0.0831539 | − | 0.996537i | \(-0.473501\pi\) |
0.904603 | + | 0.426255i | \(0.140167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.79423 | − | 4.50000i | −0.726816 | − | 0.419627i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.19615 | − | 9.00000i | 0.476331 | − | 0.825029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | − | 13.8564i | −0.727273 | − | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.00000i | − | 0.532414i | −0.963916 | − | 0.266207i | \(-0.914230\pi\) | ||
0.963916 | − | 0.266207i | \(-0.0857705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59808 | − | 4.50000i | −0.226995 | − | 0.393167i | 0.729921 | − | 0.683531i | \(-0.239557\pi\) |
−0.956916 | + | 0.290365i | \(0.906223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.00000 | + | 15.5885i | −0.780399 | + | 1.35169i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50000 | + | 0.866025i | 0.128154 | + | 0.0739895i | 0.562706 | − | 0.826657i | \(-0.309760\pi\) |
−0.434553 | + | 0.900646i | \(0.643094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.59808 | + | 1.50000i | −0.220366 | + | 0.127228i | −0.606120 | − | 0.795373i | \(-0.707275\pi\) |
0.385754 | + | 0.922602i | \(0.373941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.19615 | 0.434524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.0000 | −1.24568 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.50000 | − | 0.866025i | 0.122885 | − | 0.0709476i | −0.437298 | − | 0.899317i | \(-0.644064\pi\) |
0.560182 | + | 0.828369i | \(0.310731\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.79423 | + | 4.50000i | 0.634285 | + | 0.366205i | 0.782410 | − | 0.622764i | \(-0.213990\pi\) |
−0.148124 | + | 0.988969i | \(0.547324\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.59808 | + | 4.50000i | −0.208683 | + | 0.361449i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.500000 | + | 0.866025i | 0.0399043 | + | 0.0691164i | 0.885288 | − | 0.465044i | \(-0.153961\pi\) |
−0.845383 | + | 0.534160i | \(0.820628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.5885i | 1.22854i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000i | 0.469956i | 0.972001 | + | 0.234978i | \(0.0755019\pi\) | ||||
−0.972001 | + | 0.234978i | \(0.924498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.79423 | + | 13.5000i | 0.603136 | + | 1.04466i | 0.992343 | + | 0.123511i | \(0.0394155\pi\) |
−0.389208 | + | 0.921150i | \(0.627251\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.50000 | − | 0.866025i | −0.114043 | − | 0.0658427i | 0.441894 | − | 0.897067i | \(-0.354307\pi\) |
−0.555936 | + | 0.831225i | \(0.687640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.19615 | + | 3.00000i | −0.392792 | + | 0.226779i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.7846 | −1.55351 | −0.776757 | − | 0.629800i | \(-0.783137\pi\) | ||||
−0.776757 | + | 0.629800i | \(0.783137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0000 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | − | 3.46410i | 0.441129 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.5885 | + | 9.00000i | 1.13994 | + | 0.658145i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.79423 | + | 13.5000i | −0.563971 | + | 0.976826i | 0.433174 | + | 0.901310i | \(0.357394\pi\) |
−0.997145 | + | 0.0755154i | \(0.975940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.50000 | + | 16.4545i | 0.683825 | + | 1.18442i | 0.973805 | + | 0.227387i | \(0.0730182\pi\) |
−0.289980 | + | 0.957033i | \(0.593649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.92820i | 0.493614i | 0.969065 | + | 0.246807i | \(0.0793814\pi\) | ||||
−0.969065 | + | 0.246807i | \(0.920619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0000i | 0.850657i | 0.905039 | + | 0.425329i | \(0.139842\pi\) | ||||
−0.905039 | + | 0.425329i | \(0.860158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.9904 | + | 22.5000i | 0.911746 | + | 1.57919i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.0000 | − | 15.5885i | −1.86763 | − | 1.07828i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.59808 | − | 1.50000i | 0.178859 | − | 0.103264i | −0.407898 | − | 0.913028i | \(-0.633738\pi\) |
0.586756 | + | 0.809763i | \(0.300405\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.19615 | −0.354375 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.00000 | 0.610960 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 1.73205i | −0.201802 | + | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9904 | + | 7.50000i | 0.869900 | + | 0.502237i | 0.867315 | − | 0.497760i | \(-0.165844\pi\) |
0.00258516 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.59808 | + | 4.50000i | −0.172440 | + | 0.298675i | −0.939272 | − | 0.343172i | \(-0.888499\pi\) |
0.766832 | + | 0.641848i | \(0.221832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.50000 | − | 16.4545i | −0.627778 | − | 1.08734i | −0.987997 | − | 0.154475i | \(-0.950631\pi\) |
0.360219 | − | 0.932868i | \(-0.382702\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.8564i | 0.907763i | 0.891062 | + | 0.453882i | \(0.149961\pi\) | ||||
−0.891062 | + | 0.453882i | \(0.850039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000i | 0.587095i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.79423 | − | 13.5000i | −0.504167 | − | 0.873242i | −0.999988 | − | 0.00481804i | \(-0.998466\pi\) |
0.495822 | − | 0.868424i | \(-0.334867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | + | 6.06218i | −0.225455 | + | 0.390499i | −0.956456 | − | 0.291877i | \(-0.905720\pi\) |
0.731001 | + | 0.682376i | \(0.239053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | − | 1.73205i | −0.191663 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.19615 | − | 3.00000i | 0.330623 | − | 0.190885i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7846 | 1.31191 | 0.655956 | − | 0.754799i | \(-0.272265\pi\) | ||||
0.655956 | + | 0.754799i | \(0.272265\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.0000 | −1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.5000 | − | 9.52628i | 1.02924 | − | 0.594233i | 0.112474 | − | 0.993655i | \(-0.464122\pi\) |
0.916767 | + | 0.399422i | \(0.130789\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3923 | − | 6.00000i | −0.645746 | − | 0.372822i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.9904 | + | 22.5000i | −0.801021 | + | 1.38741i | 0.117923 | + | 0.993023i | \(0.462376\pi\) |
−0.918945 | + | 0.394387i | \(0.870957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | + | 15.5885i | 0.552866 | + | 0.957591i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.46410i | 0.211210i | 0.994408 | + | 0.105605i | \(0.0336779\pi\) | ||||
−0.994408 | + | 0.105605i | \(0.966322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0000i | 1.09342i | 0.837321 | + | 0.546711i | \(0.184120\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.19615 | − | 9.00000i | −0.313340 | − | 0.542720i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50000 | − | 14.7224i | 0.510716 | − | 0.884585i | −0.489207 | − | 0.872167i | \(-0.662714\pi\) |
0.999923 | − | 0.0124177i | \(-0.00395278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.5000 | − | 6.06218i | −0.626377 | − | 0.361639i | 0.152970 | − | 0.988231i | \(-0.451116\pi\) |
−0.779348 | + | 0.626592i | \(0.784449\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.5788 | − | 16.5000i | 1.69884 | − | 0.980823i | 0.751968 | − | 0.659200i | \(-0.229105\pi\) |
0.946868 | − | 0.321624i | \(-0.104229\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.5885 | −0.920158 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.5000 | − | 9.52628i | 0.963940 | − | 0.556531i | 0.0665568 | − | 0.997783i | \(-0.478799\pi\) |
0.897384 | + | 0.441251i | \(0.145465\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.79423 | + | 4.50000i | 0.453798 | + | 0.262000i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.59808 | − | 4.50000i | 0.150251 | − | 0.260242i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.50000 | + | 7.79423i | 0.259376 | + | 0.449252i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.1244i | 0.694239i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.0000i | − | 1.02731i | −0.857996 | − | 0.513657i | \(-0.828290\pi\) | ||
0.857996 | − | 0.513657i | \(-0.171710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.59808 | + | 4.50000i | 0.147323 | + | 0.255172i | 0.930237 | − | 0.366958i | \(-0.119601\pi\) |
−0.782914 | + | 0.622130i | \(0.786268\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.50000 | + | 9.52628i | −0.310878 | + | 0.538457i | −0.978553 | − | 0.205996i | \(-0.933957\pi\) |
0.667674 | + | 0.744453i | \(0.267290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.5000 | + | 11.2583i | 1.09523 | + | 0.632331i | 0.934964 | − | 0.354743i | \(-0.115432\pi\) |
0.160265 | + | 0.987074i | \(0.448765\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38.9711 | + | 22.5000i | −2.18197 | + | 1.25976i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.7846 | 1.15649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.5000 | − | 7.79423i | 0.744279 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.59808 | − | 1.50000i | −0.142803 | − | 0.0824475i | 0.426896 | − | 0.904301i | \(-0.359607\pi\) |
−0.569699 | + | 0.821853i | \(0.692940\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.79423 | − | 13.5000i | 0.425844 | − | 0.737584i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5000 | − | 26.8468i | −0.844339 | − | 1.46244i | −0.886194 | − | 0.463314i | \(-0.846660\pi\) |
0.0418554 | − | 0.999124i | \(-0.486673\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.5885i | 0.844162i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.0000i | − | 0.809924i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.59808 | + | 4.50000i | 0.139472 | + | 0.241573i | 0.927297 | − | 0.374327i | \(-0.122126\pi\) |
−0.787825 | + | 0.615899i | \(0.788793\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.5000 | + | 30.3109i | −0.936754 | + | 1.62250i | −0.165277 | + | 0.986247i | \(0.552852\pi\) |
−0.771477 | + | 0.636257i | \(0.780482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.5000 | − | 12.9904i | −1.19755 | − | 0.691408i | −0.237545 | − | 0.971377i | \(-0.576343\pi\) |
−0.960009 | + | 0.279968i | \(0.909676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.5885 | + | 9.00000i | −0.827349 | + | 0.477670i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.7846 | −1.09697 | −0.548485 | − | 0.836160i | \(-0.684795\pi\) | ||||
−0.548485 | + | 0.836160i | \(0.684795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | + | 3.46410i | −0.314054 | + | 0.181319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.3827 | − | 13.5000i | −1.22057 | − | 0.704694i | −0.255528 | − | 0.966802i | \(-0.582249\pi\) |
−0.965039 | + | 0.262108i | \(0.915582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.5885 | − | 27.0000i | 0.809312 | − | 1.40177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.50000 | − | 4.33013i | −0.129445 | − | 0.224205i | 0.794017 | − | 0.607896i | \(-0.207986\pi\) |
−0.923462 | + | 0.383691i | \(0.874653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.66025i | − | 0.446026i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.0000i | − | 1.23280i | −0.787434 | − | 0.616399i | \(-0.788591\pi\) | ||
0.787434 | − | 0.616399i | \(-0.211409\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.59808 | − | 4.50000i | −0.132755 | − | 0.229939i | 0.791982 | − | 0.610544i | \(-0.209049\pi\) |
−0.924738 | + | 0.380605i | \(0.875716\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.5000 | − | 23.3827i | 0.688024 | − | 1.19169i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.5000 | − | 7.79423i | −0.684477 | − | 0.395183i | 0.117063 | − | 0.993125i | \(-0.462652\pi\) |
−0.801540 | + | 0.597941i | \(0.795986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.5885 | − | 9.00000i | 0.788342 | − | 0.455150i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.9808 | 1.30723 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.0000 | 1.60603 | 0.803017 | − | 0.595956i | \(-0.203227\pi\) | ||||
0.803017 | + | 0.595956i | \(0.203227\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.50000 | − | 4.33013i | 0.374532 | − | 0.216236i | −0.300904 | − | 0.953654i | \(-0.597289\pi\) |
0.675437 | + | 0.737418i | \(0.263955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.59808 | − | 1.50000i | −0.129419 | − | 0.0747203i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3923 | − | 18.0000i | 0.515127 | − | 0.892227i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50000 | + | 14.7224i | 0.420298 | + | 0.727977i | 0.995968 | − | 0.0897044i | \(-0.0285922\pi\) |
−0.575670 | + | 0.817682i | \(0.695259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 15.5885i | − | 0.767058i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.00000i | 0.441793i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1865 | − | 31.5000i | −0.888470 | − | 1.53888i | −0.841684 | − | 0.539971i | \(-0.818435\pi\) |
−0.0467865 | − | 0.998905i | \(-0.514898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.50000 | − | 9.52628i | 0.268054 | − | 0.464282i | −0.700306 | − | 0.713843i | \(-0.746953\pi\) |
0.968359 | + | 0.249561i | \(0.0802862\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | + | 3.46410i | 0.291043 | + | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.1865 | − | 10.5000i | 0.880108 | − | 0.508131i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7846 | −1.00116 | −0.500580 | − | 0.865690i | \(-0.666880\pi\) | ||||
−0.500580 | + | 0.865690i | \(0.666880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.0000 | 1.53782 | 0.768911 | − | 0.639356i | \(-0.220799\pi\) | ||||
0.768911 | + | 0.639356i | \(0.220799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.0000 | + | 15.5885i | −1.29159 | + | 0.745697i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.3827 | − | 13.5000i | −1.11599 | − | 0.644320i | −0.175619 | − | 0.984458i | \(-0.556193\pi\) |
−0.940375 | + | 0.340138i | \(0.889526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.59808 | − | 4.50000i | 0.123438 | − | 0.213801i | −0.797683 | − | 0.603077i | \(-0.793941\pi\) |
0.921121 | + | 0.389275i | \(0.127275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | − | 5.19615i | −0.142214 | − | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1769i | 1.47133i | 0.677346 | + | 0.735665i | \(0.263130\pi\) | ||||
−0.677346 | + | 0.735665i | \(0.736870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 27.0000i | − | 1.27138i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.59808 | + | 4.50000i | 0.121800 | + | 0.210963i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | + | 21.6506i | −0.584725 | + | 1.01277i | 0.410184 | + | 0.912003i | \(0.365464\pi\) |
−0.994910 | + | 0.100771i | \(0.967869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.50000 | − | 2.59808i | −0.209586 | − | 0.121004i | 0.391533 | − | 0.920164i | \(-0.371945\pi\) |
−0.601119 | + | 0.799160i | \(0.705278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.59808 | − | 1.50000i | 0.120743 | − | 0.0697109i | −0.438412 | − | 0.898774i | \(-0.644459\pi\) |
0.559155 | + | 0.829063i | \(0.311126\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.0000 | −1.24674 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.5000 | + | 7.79423i | −0.620731 | + | 0.358379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.3923 | − | 6.00000i | −0.476832 | − | 0.275299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.79423 | − | 13.5000i | 0.356127 | − | 0.616831i | −0.631183 | − | 0.775634i | \(-0.717430\pi\) |
0.987310 | + | 0.158803i | \(0.0507636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | + | 3.46410i | 0.0911922 | + | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.73205i | − | 0.0786484i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.0000i | 1.35943i | 0.733476 | + | 0.679715i | \(0.237896\pi\) | ||||
−0.733476 | + | 0.679715i | \(0.762104\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.79423 | + | 13.5000i | 0.351749 | + | 0.609246i | 0.986556 | − | 0.163424i | \(-0.0522539\pi\) |
−0.634807 | + | 0.772670i | \(0.718921\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0000 | − | 25.9808i | 0.675566 | − | 1.17011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.0000 | + | 15.5885i | 1.21112 | + | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.3827 | + | 13.5000i | −1.04675 | + | 0.604343i | −0.921739 | − | 0.387812i | \(-0.873231\pi\) |
−0.125014 | + | 0.992155i | \(0.539898\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.1769 | 1.39011 | 0.695055 | − | 0.718957i | \(-0.255380\pi\) | ||||
0.695055 | + | 0.718957i | \(0.255380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.5000 | − | 7.79423i | 0.598377 | − | 0.345473i | −0.170026 | − | 0.985440i | \(-0.554385\pi\) |
0.768403 | + | 0.639966i | \(0.221052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.3923 | + | 6.00000i | 0.459728 | + | 0.265424i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.79423 | + | 13.5000i | −0.343455 | + | 0.594881i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.5000 | + | 23.3827i | 0.593729 | + | 1.02837i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 41.5692i | − | 1.82118i | −0.413310 | − | 0.910590i | \(-0.635627\pi\) | ||
0.413310 | − | 0.910590i | \(-0.364373\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.19615 | − | 9.00000i | −0.226348 | − | 0.392046i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.00000 | + | 3.46410i | −0.0869565 | + | 0.150613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.50000 | + | 2.59808i | 0.194917 | + | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.3923 | −0.447628 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0000 | −0.601907 | −0.300954 | − | 0.953639i | \(-0.597305\pi\) | ||||
−0.300954 | + | 0.953639i | \(0.597305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.00000 | + | 3.46410i | −0.257012 | + | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.79423 | + | 4.50000i | 0.333257 | + | 0.192406i | 0.657286 | − | 0.753641i | \(-0.271704\pi\) |
−0.324029 | + | 0.946047i | \(0.605038\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.9808 | + | 45.0000i | −1.10682 | + | 1.91706i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.5000 | − | 38.9711i | −0.956797 | − | 1.65722i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 45.0333i | − | 1.90812i | −0.299611 | − | 0.954062i | \(-0.596857\pi\) | ||
0.299611 | − | 0.954062i | \(-0.403143\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.00000i | − | 0.126886i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.9904 | + | 22.5000i | 0.547479 | + | 0.948262i | 0.998446 | + | 0.0557214i | \(0.0177458\pi\) |
−0.450967 | + | 0.892541i | \(0.648921\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.5000 | + | 18.1865i | −0.441738 | + | 0.765113i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.5000 | + | 9.52628i | 0.691716 | + | 0.399362i | 0.804255 | − | 0.594285i | \(-0.202565\pi\) |
−0.112539 | + | 0.993647i | \(0.535898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.59808 | − | 1.50000i | 0.108726 | − | 0.0627730i | −0.444651 | − | 0.895704i | \(-0.646672\pi\) |
0.553377 | + | 0.832931i | \(0.313339\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.3923 | −0.433389 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.0000 | −1.66522 | −0.832611 | − | 0.553858i | \(-0.813155\pi\) | ||||
−0.832611 | + | 0.553858i | \(0.813155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5000 | − | 7.79423i | 0.560074 | − | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.7654 | + | 27.0000i | 1.93682 | + | 1.11823i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.79423 | + | 13.5000i | −0.321702 | + | 0.557205i | −0.980839 | − | 0.194818i | \(-0.937588\pi\) |
0.659137 | + | 0.752023i | \(0.270922\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.00000 | + | 15.5885i | 0.370839 | + | 0.642311i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.2487i | 0.995775i | 0.867242 | + | 0.497888i | \(0.165891\pi\) | ||||
−0.867242 | + | 0.497888i | \(0.834109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.0000i | 0.737928i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.9904 | − | 22.5000i | −0.530773 | − | 0.919325i | −0.999355 | − | 0.0359054i | \(-0.988569\pi\) |
0.468583 | − | 0.883420i | \(-0.344765\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.50000 | − | 6.06218i | 0.142768 | − | 0.247281i | −0.785770 | − | 0.618519i | \(-0.787733\pi\) |
0.928538 | + | 0.371237i | \(0.121066\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.0000 | + | 13.8564i | 0.975739 | + | 0.563343i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.59808 | + | 1.50000i | −0.105453 | + | 0.0608831i | −0.551799 | − | 0.833977i | \(-0.686058\pi\) |
0.446346 | + | 0.894860i | \(0.352725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.19615 | −0.210214 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.0000 | 0.807792 | 0.403896 | − | 0.914805i | \(-0.367656\pi\) | ||||
0.403896 | + | 0.914805i | \(0.367656\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.5000 | + | 16.4545i | −1.14737 | + | 0.662433i | −0.948244 | − | 0.317542i | \(-0.897143\pi\) |
−0.199123 | + | 0.979975i | \(0.563809\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.79423 | + | 4.50000i | 0.313276 | + | 0.180870i | 0.648392 | − | 0.761307i | \(-0.275442\pi\) |
−0.335115 | + | 0.942177i | \(0.608775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.19615 | + | 9.00000i | −0.208179 | + | 0.360577i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8564i | 0.552491i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.00000i | − | 0.238856i | −0.992843 | − | 0.119428i | \(-0.961894\pi\) | ||
0.992843 | − | 0.119428i | \(-0.0381061\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.19615 | + | 9.00000i | 0.206203 | + | 0.357154i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | − | 1.73205i | 0.0396214 | − | 0.0686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5000 | + | 6.06218i | 0.414725 | + | 0.239442i | 0.692818 | − | 0.721113i | \(-0.256369\pi\) |
−0.278093 | + | 0.960554i | \(0.589702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.3827 | − | 13.5000i | 0.922123 | − | 0.532388i | 0.0378113 | − | 0.999285i | \(-0.487961\pi\) |
0.884312 | + | 0.466897i | \(0.154628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7846 | 0.817127 | 0.408564 | − | 0.912730i | \(-0.366030\pi\) | ||||
0.408564 | + | 0.912730i | \(0.366030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.0000 | 1.05984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.5000 | + | 18.1865i | −1.23269 | + | 0.711694i | −0.967590 | − | 0.252527i | \(-0.918738\pi\) |
−0.265100 | + | 0.964221i | \(0.585405\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.79423 | + | 4.50000i | 0.304546 | + | 0.175830i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.59808 | + | 4.50000i | −0.101207 | + | 0.175295i | −0.912182 | − | 0.409785i | \(-0.865604\pi\) |
0.810975 | + | 0.585080i | \(0.198937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.500000 | + | 0.866025i | 0.0194477 | + | 0.0336845i | 0.875585 | − | 0.483063i | \(-0.160476\pi\) |
−0.856138 | + | 0.516748i | \(0.827143\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 31.1769i | − | 1.20899i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.0000i | 1.74241i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.1865 | + | 31.5000i | 0.702083 | + | 1.21604i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.50000 | − | 6.06218i | 0.134915 | − | 0.233680i | −0.790650 | − | 0.612268i | \(-0.790257\pi\) |
0.925565 | + | 0.378589i | \(0.123591\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5000 | − | 7.79423i | −0.518847 | − | 0.299557i | 0.217616 | − | 0.976035i | \(-0.430172\pi\) |
−0.736463 | + | 0.676478i | \(0.763505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.59808 | + | 1.50000i | −0.0997050 | + | 0.0575647i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.5692 | −1.59060 | −0.795301 | − | 0.606215i | \(-0.792687\pi\) | ||||
−0.795301 | + | 0.606215i | \(0.792687\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.00000 | −0.114624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.00000 | + | 5.19615i | −0.342873 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.9904 | + | 7.50000i | 0.494177 | + | 0.285313i | 0.726306 | − | 0.687372i | \(-0.241236\pi\) |
−0.232128 | + | 0.972685i | \(0.574569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.59808 | − | 4.50000i | 0.0985506 | − | 0.170695i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | + | 15.5885i | 0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 17.3205i | − | 0.654187i | −0.944992 | − | 0.327093i | \(-0.893931\pi\) | ||
0.944992 | − | 0.327093i | \(-0.106069\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24.0000i | − | 0.905177i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.79423 | + | 13.5000i | 0.293132 | + | 0.507720i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.5000 | − | 25.1147i | 0.544559 | − | 0.943204i | −0.454076 | − | 0.890963i | \(-0.650030\pi\) |
0.998635 | − | 0.0522406i | \(-0.0166363\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.5000 | + | 7.79423i | 0.505579 | + | 0.291896i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.79423 | + | 4.50000i | −0.291488 | + | 0.168290i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.7846 | −0.775135 | −0.387568 | − | 0.921841i | \(-0.626685\pi\) | ||||
−0.387568 | + | 0.921841i | \(0.626685\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.0000 | 1.00553 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.0000 | + | 8.66025i | −0.557086 | + | 0.321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.3827 | − | 13.5000i | −0.867216 | − | 0.500687i | −0.000793791 | − | 1.00000i | \(-0.500253\pi\) |
−0.866422 | + | 0.499312i | \(0.833586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.19615 | − | 9.00000i | 0.192187 | − | 0.332877i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.50000 | − | 11.2583i | −0.240083 | − | 0.415836i | 0.720655 | − | 0.693294i | \(-0.243841\pi\) |
−0.960738 | + | 0.277458i | \(0.910508\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 46.7654i | − | 1.72262i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.0000i | 1.76571i | 0.469647 | + | 0.882854i | \(0.344381\pi\) | ||||
−0.469647 | + | 0.882854i | \(0.655619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.1865 | + | 31.5000i | 0.667199 | + | 1.15562i | 0.978684 | + | 0.205372i | \(0.0658404\pi\) |
−0.311485 | + | 0.950251i | \(0.600826\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.50000 | + | 2.59808i | −0.0549557 | + | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.1865 | − | 10.5000i | 0.663636 | − | 0.383150i | −0.130025 | − | 0.991511i | \(-0.541506\pi\) |
0.793661 | + | 0.608360i | \(0.208172\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.5885 | −0.567322 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.5000 | + | 6.06218i | −0.380625 | + | 0.219754i | −0.678090 | − | 0.734979i | \(-0.737192\pi\) |
0.297465 | + | 0.954733i | \(0.403859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.3923 | + | 6.00000i | 0.376227 | + | 0.217215i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.59808 | + | 4.50000i | −0.0938111 | + | 0.162486i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.5000 | − | 30.3109i | −0.631066 | − | 1.09304i | −0.987334 | − | 0.158655i | \(-0.949284\pi\) |
0.356268 | − | 0.934384i | \(-0.384049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.1051i | 1.37055i | 0.728286 | + | 0.685273i | \(0.240317\pi\) | ||||
−0.728286 | + | 0.685273i | \(0.759683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000i | 0.215526i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.5885 | − | 27.0000i | −0.558514 | − | 0.967375i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | + | 46.7654i | −0.966136 | + | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.50000 | − | 0.866025i | −0.0535373 | − | 0.0309098i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.79423 | − | 4.50000i | 0.277834 | − | 0.160408i | −0.354608 | − | 0.935015i | \(-0.615386\pi\) |
0.632443 | + | 0.774607i | \(0.282052\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.3731 | 1.29328 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.00000 | −0.248577 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.5000 | + | 9.52628i | −0.584460 | + | 0.337438i | −0.762904 | − | 0.646512i | \(-0.776227\pi\) |
0.178444 | + | 0.983950i | \(0.442894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.5885 | − | 9.00000i | −0.551480 | − | 0.318397i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.3923 | + | 18.0000i | −0.366736 | + | 0.635206i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.5000 | − | 23.3827i | −0.475812 | − | 0.824131i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17.3205i | − | 0.608957i | −0.952519 | − | 0.304478i | \(-0.901518\pi\) | ||
0.952519 | − | 0.304478i | \(-0.0984821\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.0000i | − | 1.05344i | −0.850038 | − | 0.526721i | \(-0.823421\pi\) | ||
0.850038 | − | 0.526721i | \(-0.176579\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.19615 | − | 9.00000i | −0.182013 | − | 0.315256i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.00000 | + | 15.5885i | −0.314870 | + | 0.545371i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.50000 | + | 0.866025i | 0.0523504 | + | 0.0302245i | 0.525947 | − | 0.850518i | \(-0.323711\pi\) |
−0.473596 | + | 0.880742i | \(0.657044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.1865 | + | 10.5000i | −0.633943 | + | 0.366007i | −0.782277 | − | 0.622930i | \(-0.785942\pi\) |
0.148335 | + | 0.988937i | \(0.452609\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0000 | 0.555703 | 0.277851 | − | 0.960624i | \(-0.410378\pi\) | ||||
0.277851 | + | 0.960624i | \(0.410378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000 | − | 3.46410i | 0.207888 | − | 0.120024i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.3827 | − | 13.5000i | −0.809191 | − | 0.467187i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.9904 | − | 22.5000i | 0.448478 | − | 0.776786i | −0.549809 | − | 0.835290i | \(-0.685300\pi\) |
0.998287 | + | 0.0585039i | \(0.0186330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0000 | + | 39.8372i | 0.793103 | + | 1.37370i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.7846i | 0.715012i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 48.0000i | − | 1.64930i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.3923 | − | 18.0000i | −0.356244 | − | 0.617032i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.50000 | − | 16.4545i | 0.325274 | − | 0.563391i | −0.656294 | − | 0.754505i | \(-0.727877\pi\) |
0.981568 | + | 0.191115i | \(0.0612102\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.5000 | + | 21.6506i | 1.28098 | + | 0.739572i | 0.977027 | − | 0.213117i | \(-0.0683615\pi\) |
0.303949 | + | 0.952688i | \(0.401695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.3634 | + | 28.5000i | −1.68426 | + | 0.972407i | −0.725485 | + | 0.688238i | \(0.758385\pi\) |
−0.958774 | + | 0.284170i | \(0.908282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.5692 | 1.41503 | 0.707516 | − | 0.706697i | \(-0.249816\pi\) | ||||
0.707516 | + | 0.706697i | \(0.249816\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.00000 | 0.102003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 67.5000 | − | 38.9711i | 2.28978 | − | 1.32201i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.79423 | + | 4.50000i | 0.264097 | + | 0.152477i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.1865 | − | 31.5000i | 0.614817 | − | 1.06489i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.50000 | − | 14.7224i | −0.287025 | − | 0.497141i | 0.686074 | − | 0.727532i | \(-0.259333\pi\) |
−0.973098 | + | 0.230391i | \(0.925999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.3923i | − | 0.350126i | −0.984557 | − | 0.175063i | \(-0.943987\pi\) | ||
0.984557 | − | 0.175063i | \(-0.0560129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.00000i | − | 0.201916i | −0.994891 | − | 0.100958i | \(-0.967809\pi\) | ||
0.994891 | − | 0.100958i | \(-0.0321908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.5788 | − | 49.5000i | −0.959583 | − | 1.66205i | −0.723512 | − | 0.690312i | \(-0.757473\pi\) |
−0.236071 | − | 0.971736i | \(-0.575860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.00000 | − | 15.5885i | 0.301850 | − | 0.522820i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.0000 | + | 15.5885i | 0.903521 | + | 0.521648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.1769 | − | 18.0000i | 1.04213 | − | 0.601674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.9808 | 0.866507 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.0000 | + | 13.8564i | −0.797787 | + | 0.460603i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.59808 | + | 1.50000i | 0.0862677 | + | 0.0498067i | 0.542513 | − | 0.840047i | \(-0.317473\pi\) |
−0.456246 | + | 0.889854i | \(0.650806\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.1865 | − | 31.5000i | 0.602547 | − | 1.04364i | −0.389887 | − | 0.920863i | \(-0.627486\pi\) |
0.992434 | − | 0.122779i | \(-0.0391806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.5000 | + | 23.3827i | 0.446785 | + | 0.773854i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 15.5885i | − | 0.514776i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 54.0000i | − | 1.78130i | −0.454694 | − | 0.890648i | \(-0.650251\pi\) | ||
0.454694 | − | 0.890648i | \(-0.349749\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.19615 | − | 9.00000i | −0.171033 | − | 0.296239i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | − | 6.92820i | 0.131519 | − | 0.227798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.5000 | − | 26.8468i | −1.52562 | − | 0.880815i | −0.999538 | − | 0.0303776i | \(-0.990329\pi\) |
−0.526077 | − | 0.850437i | \(-0.676338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.3923 | + | 6.00000i | −0.340594 | + | 0.196642i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.1769 | −1.01959 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.0000 | −1.30674 | −0.653372 | − | 0.757037i | \(-0.726646\pi\) | ||||
−0.653372 | + | 0.757037i | \(0.726646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5000 | − | 6.06218i | 0.342290 | − | 0.197621i | −0.318994 | − | 0.947757i | \(-0.603345\pi\) |
0.661284 | + | 0.750135i | \(0.270012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.3827 | − | 13.5000i | −0.761445 | − | 0.439620i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.9904 | + | 22.5000i | −0.422131 | + | 0.731152i | −0.996148 | − | 0.0876916i | \(-0.972051\pi\) |
0.574017 | + | 0.818843i | \(0.305384\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | − | 3.46410i | −0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.2487i | 0.785493i | 0.919647 | + | 0.392746i | \(0.128475\pi\) | ||||
−0.919647 | + | 0.392746i | \(0.871525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 27.0000i | − | 0.873699i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.59808 | + | 4.50000i | 0.0838963 | + | 0.145313i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0000 | + | 19.0526i | −0.354839 | + | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.5000 | − | 16.4545i | −0.917447 | − | 0.529689i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3827 | − | 13.5000i | 0.751936 | − | 0.434131i | −0.0744567 | − | 0.997224i | \(-0.523722\pi\) |
0.826393 | + | 0.563094i | \(0.190389\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.1769 | −1.00051 | −0.500257 | − | 0.865877i | \(-0.666761\pi\) | ||||
−0.500257 | + | 0.865877i | \(0.666761\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.00000 | −0.288527 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.5000 | + | 7.79423i | −0.431903 | + | 0.249359i | −0.700157 | − | 0.713989i | \(-0.746887\pi\) |
0.268254 | + | 0.963348i | \(0.413553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.5885 | − | 9.00000i | −0.498209 | − | 0.287641i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.5788 | − | 49.5000i | 0.911523 | − | 1.57880i | 0.0996103 | − | 0.995027i | \(-0.468240\pi\) |
0.811913 | − | 0.583778i | \(-0.198426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | − | 10.3923i | −0.191176 | − | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.5885i | 0.495684i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.0000i | 1.71537i | 0.514178 | + | 0.857683i | \(0.328097\pi\) | ||||
−0.514178 | + | 0.857683i | \(0.671903\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3923 | − | 18.0000i | −0.329458 | − | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.50000 | + | 9.52628i | −0.174187 | + | 0.301700i | −0.939880 | − | 0.341506i | \(-0.889063\pi\) |
0.765693 | + | 0.643206i | \(0.222396\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.s.e.143.2 | 4 | ||
3.2 | odd | 2 | 144.2.s.e.47.1 | ✓ | 4 | ||
4.3 | odd | 2 | inner | 432.2.s.e.143.1 | 4 | ||
8.3 | odd | 2 | 1728.2.s.e.575.1 | 4 | |||
8.5 | even | 2 | 1728.2.s.e.575.2 | 4 | |||
9.2 | odd | 6 | 1296.2.c.f.1295.3 | 4 | |||
9.4 | even | 3 | 144.2.s.e.95.2 | yes | 4 | ||
9.5 | odd | 6 | inner | 432.2.s.e.287.1 | 4 | ||
9.7 | even | 3 | 1296.2.c.f.1295.1 | 4 | |||
12.11 | even | 2 | 144.2.s.e.47.2 | yes | 4 | ||
24.5 | odd | 2 | 576.2.s.e.191.2 | 4 | |||
24.11 | even | 2 | 576.2.s.e.191.1 | 4 | |||
36.7 | odd | 6 | 1296.2.c.f.1295.2 | 4 | |||
36.11 | even | 6 | 1296.2.c.f.1295.4 | 4 | |||
36.23 | even | 6 | inner | 432.2.s.e.287.2 | 4 | ||
36.31 | odd | 6 | 144.2.s.e.95.1 | yes | 4 | ||
72.5 | odd | 6 | 1728.2.s.e.1151.1 | 4 | |||
72.11 | even | 6 | 5184.2.c.f.5183.2 | 4 | |||
72.13 | even | 6 | 576.2.s.e.383.1 | 4 | |||
72.29 | odd | 6 | 5184.2.c.f.5183.1 | 4 | |||
72.43 | odd | 6 | 5184.2.c.f.5183.4 | 4 | |||
72.59 | even | 6 | 1728.2.s.e.1151.2 | 4 | |||
72.61 | even | 6 | 5184.2.c.f.5183.3 | 4 | |||
72.67 | odd | 6 | 576.2.s.e.383.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.s.e.47.1 | ✓ | 4 | 3.2 | odd | 2 | ||
144.2.s.e.47.2 | yes | 4 | 12.11 | even | 2 | ||
144.2.s.e.95.1 | yes | 4 | 36.31 | odd | 6 | ||
144.2.s.e.95.2 | yes | 4 | 9.4 | even | 3 | ||
432.2.s.e.143.1 | 4 | 4.3 | odd | 2 | inner | ||
432.2.s.e.143.2 | 4 | 1.1 | even | 1 | trivial | ||
432.2.s.e.287.1 | 4 | 9.5 | odd | 6 | inner | ||
432.2.s.e.287.2 | 4 | 36.23 | even | 6 | inner | ||
576.2.s.e.191.1 | 4 | 24.11 | even | 2 | |||
576.2.s.e.191.2 | 4 | 24.5 | odd | 2 | |||
576.2.s.e.383.1 | 4 | 72.13 | even | 6 | |||
576.2.s.e.383.2 | 4 | 72.67 | odd | 6 | |||
1296.2.c.f.1295.1 | 4 | 9.7 | even | 3 | |||
1296.2.c.f.1295.2 | 4 | 36.7 | odd | 6 | |||
1296.2.c.f.1295.3 | 4 | 9.2 | odd | 6 | |||
1296.2.c.f.1295.4 | 4 | 36.11 | even | 6 | |||
1728.2.s.e.575.1 | 4 | 8.3 | odd | 2 | |||
1728.2.s.e.575.2 | 4 | 8.5 | even | 2 | |||
1728.2.s.e.1151.1 | 4 | 72.5 | odd | 6 | |||
1728.2.s.e.1151.2 | 4 | 72.59 | even | 6 | |||
5184.2.c.f.5183.1 | 4 | 72.29 | odd | 6 | |||
5184.2.c.f.5183.2 | 4 | 72.11 | even | 6 | |||
5184.2.c.f.5183.3 | 4 | 72.61 | even | 6 | |||
5184.2.c.f.5183.4 | 4 | 72.43 | odd | 6 |