Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(190,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, 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("567.190");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.f (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: | \(4.52751779461\) |
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 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 190.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.190 |
Dual form | 567.2.f.d.379.1 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | − | 5.19615i | −0.904534 | − | 1.56670i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 3.00000 | + | 5.19615i | 0.670820 | + | 1.16190i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | −12.0000 | −1.80907 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.50000 | − | 7.79423i | −0.656392 | − | 1.13691i | −0.981543 | − | 0.191243i | \(-0.938748\pi\) |
0.325150 | − | 0.945662i | \(-0.394585\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | − | 6.92820i | −0.554700 | − | 0.960769i | ||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.0000 | 2.42712 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.50000 | + | 7.79423i | −0.585850 | + | 1.01472i | 0.408919 | + | 0.912571i | \(0.365906\pi\) |
−0.994769 | + | 0.102151i | \(0.967427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 6.00000 | + | 10.3923i | 0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 3.00000 | − | 5.19615i | 0.363803 | − | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | −3.00000 | + | 5.19615i | −0.341882 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 12.0000 | 1.34164 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.50000 | − | 2.59808i | −0.164646 | − | 0.285176i | 0.771883 | − | 0.635764i | \(-0.219315\pi\) |
−0.936530 | + | 0.350588i | \(0.885982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | + | 7.79423i | −0.488094 | + | 0.845403i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | −6.00000 | − | 10.3923i | −0.625543 | − | 1.08347i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | + | 8.66025i | 0.507673 | + | 0.879316i | 0.999961 | + | 0.00888289i | \(0.00282755\pi\) |
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.00000 | −0.800000 | ||||||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | + | 12.1244i | −0.689730 | + | 1.19465i | 0.282194 | + | 0.959357i | \(0.408938\pi\) |
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0000 | 1.05361 | 0.526804 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | + | 3.46410i | −0.188982 | + | 0.327327i | ||||
\(113\) | 6.00000 | − | 10.3923i | 0.564433 | − | 0.977626i | −0.432670 | − | 0.901553i | \(-0.642428\pi\) |
0.997102 | − | 0.0760733i | \(-0.0242383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.00000 | + | 15.5885i | 0.839254 | + | 1.45363i | ||||
\(116\) | 12.0000 | 1.11417 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.50000 | − | 2.59808i | −0.137505 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.00000 | − | 6.92820i | −0.359211 | − | 0.622171i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | − | 1.73205i | −0.0867110 | − | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0000 | − | 19.0526i | 0.933008 | − | 1.61602i | 0.154859 | − | 0.987937i | \(-0.450508\pi\) |
0.778148 | − | 0.628080i | \(-0.216159\pi\) | |||||||
\(140\) | 3.00000 | − | 5.19615i | 0.253546 | − | 0.439155i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.0000 | −2.00698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.0000 | −1.49482 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.00000 | + | 12.1244i | −0.575396 | + | 0.996616i | ||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.50000 | + | 16.4545i | 0.773099 | + | 1.33905i | 0.935857 | + | 0.352381i | \(0.114628\pi\) |
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | + | 10.3923i | 0.481932 | + | 0.834730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | + | 12.1244i | −0.558661 | + | 0.967629i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.00000 | −0.548282 | −0.274141 | − | 0.961689i | \(-0.588394\pi\) | ||||
−0.274141 | + | 0.961689i | \(0.588394\pi\) | |||||||
\(164\) | −3.00000 | − | 5.19615i | −0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.50000 | − | 2.59808i | 0.116073 | − | 0.201045i | −0.802135 | − | 0.597143i | \(-0.796303\pi\) |
0.918208 | + | 0.396098i | \(0.129636\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 9.00000 | + | 15.5885i | 0.684257 | + | 1.18517i | 0.973670 | + | 0.227964i | \(0.0732068\pi\) |
−0.289412 | + | 0.957205i | \(0.593460\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 3.46410i | −0.151186 | + | 0.261861i | ||||
\(176\) | −12.0000 | + | 20.7846i | −0.904534 | + | 1.56670i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.5000 | − | 18.1865i | 0.771975 | − | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | − | 15.5885i | −0.658145 | − | 1.13994i | ||||
\(188\) | −18.0000 | −1.31278 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | − | 15.5885i | −0.651217 | − | 1.12794i | −0.982828 | − | 0.184525i | \(-0.940925\pi\) |
0.331611 | − | 0.943416i | \(-0.392408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50000 | − | 11.2583i | 0.467880 | − | 0.810392i | −0.531446 | − | 0.847092i | \(-0.678351\pi\) |
0.999326 | + | 0.0366998i | \(0.0116845\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 1.73205i | 0.0714286 | + | 0.123718i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000 | − | 5.19615i | 0.210559 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | + | 7.79423i | 0.314294 | + | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.0000 | −1.10940 | ||||||||
\(209\) | −6.00000 | − | 10.3923i | −0.415029 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | −6.00000 | + | 10.3923i | −0.412082 | + | 0.713746i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | −0.204598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 18.0000 | − | 31.1769i | 1.21356 | − | 2.10195i | ||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | + | 10.3923i | 0.398234 | + | 0.689761i | 0.993508 | − | 0.113761i | \(-0.0362899\pi\) |
−0.595274 | + | 0.803523i | \(0.702957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | − | 3.46410i | 0.132164 | − | 0.228914i | −0.792347 | − | 0.610071i | \(-0.791141\pi\) |
0.924510 | + | 0.381157i | \(0.124474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0000 | 1.57229 | 0.786146 | − | 0.618041i | \(-0.212073\pi\) | ||||
0.786146 | + | 0.618041i | \(0.212073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.0000 | 1.76129 | ||||||||
\(236\) | 9.00000 | + | 15.5885i | 0.585850 | + | 1.01472i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | − | 10.3923i | 0.388108 | − | 0.672222i | −0.604087 | − | 0.796918i | \(-0.706462\pi\) |
0.992195 | + | 0.124696i | \(0.0397955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00000 | − | 6.92820i | −0.257663 | − | 0.446285i | 0.707953 | − | 0.706260i | \(-0.249619\pi\) |
−0.965615 | + | 0.259975i | \(0.916286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | − | 6.92820i | 0.254514 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.0000 | 1.70422 | 0.852112 | − | 0.523359i | \(-0.175321\pi\) | ||||
0.852112 | + | 0.523359i | \(0.175321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.0000 | −2.26330 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 3.00000 | − | 5.19615i | 0.187135 | − | 0.324127i | −0.757159 | − | 0.653231i | \(-0.773413\pi\) |
0.944294 | + | 0.329104i | \(0.106747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.50000 | + | 6.06218i | 0.217479 | + | 0.376685i | ||||
\(260\) | 24.0000 | 1.48842 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | − | 15.5885i | 0.552866 | − | 0.957591i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | 3.00000 | 0.182913 | 0.0914566 | − | 0.995809i | \(-0.470848\pi\) | ||||
0.0914566 | + | 0.995809i | \(0.470848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | −6.00000 | − | 10.3923i | −0.363803 | − | 0.630126i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.0000 | + | 20.7846i | −0.723627 | + | 1.25336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.50000 | − | 14.7224i | −0.510716 | − | 0.884585i | −0.999923 | − | 0.0124177i | \(-0.996047\pi\) |
0.489207 | − | 0.872167i | \(-0.337286\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0000 | − | 25.9808i | −0.894825 | − | 1.54988i | −0.834021 | − | 0.551733i | \(-0.813967\pi\) |
−0.0608039 | − | 0.998150i | \(-0.519366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.00000 | + | 12.1244i | −0.416107 | + | 0.720718i | −0.995544 | − | 0.0942988i | \(-0.969939\pi\) |
0.579437 | + | 0.815017i | \(0.303272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.00000 | −0.177084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | −16.5000 | + | 28.5788i | −0.963940 | + | 1.66959i | −0.251505 | + | 0.967856i | \(0.580925\pi\) |
−0.712436 | + | 0.701737i | \(0.752408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.5000 | − | 23.3827i | −0.786000 | − | 1.36139i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | − | 20.7846i | −0.693978 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | − | 0.866025i | 0.0288195 | − | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | − | 6.92820i | −0.229416 | − | 0.397360i | ||||
\(305\) | −30.0000 | −1.71780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | 6.00000 | + | 10.3923i | 0.341882 | + | 0.592157i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.50000 | + | 7.79423i | −0.255172 | + | 0.441970i | −0.964942 | − | 0.262463i | \(-0.915465\pi\) |
0.709771 | + | 0.704433i | \(0.248799\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | − | 6.92820i | −0.226093 | − | 0.391605i | 0.730554 | − | 0.682855i | \(-0.239262\pi\) |
−0.956647 | + | 0.291250i | \(0.905929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −9.00000 | − | 15.5885i | −0.505490 | − | 0.875535i | −0.999980 | − | 0.00635137i | \(-0.997978\pi\) |
0.494489 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | − | 31.1769i | 1.00781 | − | 1.74557i | ||||
\(320\) | 12.0000 | − | 20.7846i | 0.670820 | − | 1.16190i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0000 | −0.887520 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.50000 | + | 7.79423i | −0.248093 | + | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | + | 0.866025i | 0.0274825 | + | 0.0476011i | 0.879440 | − | 0.476011i | \(-0.157918\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.00000 | + | 10.3923i | 0.327815 | + | 0.567792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.50000 | − | 11.2583i | 0.354078 | − | 0.613280i | −0.632882 | − | 0.774248i | \(-0.718128\pi\) |
0.986960 | + | 0.160968i | \(0.0514616\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.00000 | + | 15.5885i | 0.488094 | + | 0.845403i | ||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.00000 | − | 6.92820i | −0.214115 | − | 0.370858i | 0.738883 | − | 0.673833i | \(-0.235353\pi\) |
−0.952998 | + | 0.302975i | \(0.902020\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5000 | + | 18.1865i | 0.558859 | + | 0.967972i | 0.997592 | + | 0.0693543i | \(0.0220939\pi\) |
−0.438733 | + | 0.898617i | \(0.644573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | − | 10.3923i | 0.317999 | − | 0.550791i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00000 | + | 6.92820i | −0.209657 | + | 0.363137i | ||||
\(365\) | −3.00000 | + | 5.19615i | −0.157027 | + | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00000 | + | 8.66025i | 0.260998 | + | 0.452062i | 0.966507 | − | 0.256639i | \(-0.0826151\pi\) |
−0.705509 | + | 0.708700i | \(0.749282\pi\) | |||||||
\(368\) | −24.0000 | −1.25109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | + | 5.19615i | 0.155752 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5000 | + | 19.9186i | −0.595447 | + | 1.03135i | 0.398036 | + | 0.917370i | \(0.369692\pi\) |
−0.993484 | + | 0.113975i | \(0.963641\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0000 | 1.48963 | 0.744815 | − | 0.667271i | \(-0.232538\pi\) | ||||
0.744815 | + | 0.667271i | \(0.232538\pi\) | |||||||
\(380\) | 6.00000 | + | 10.3923i | 0.307794 | + | 0.533114i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.50000 | − | 12.9904i | 0.383232 | − | 0.663777i | −0.608290 | − | 0.793715i | \(-0.708144\pi\) |
0.991522 | + | 0.129937i | \(0.0414776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.00000 | − | 15.5885i | −0.458682 | − | 0.794461i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.0000 | 1.01535 | ||||||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | − | 15.5885i | 0.455150 | − | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.00000 | −0.150946 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | + | 13.8564i | −0.400000 | + | 0.692820i | ||||
\(401\) | −6.00000 | + | 10.3923i | −0.299626 | + | 0.518967i | −0.976050 | − | 0.217545i | \(-0.930195\pi\) |
0.676425 | + | 0.736512i | \(0.263528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | − | 13.8564i | −0.398508 | − | 0.690237i | ||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.0000 | + | 36.3731i | 1.04093 | + | 1.80295i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00000 | − | 3.46410i | 0.0988936 | − | 0.171289i | −0.812333 | − | 0.583193i | \(-0.801803\pi\) |
0.911227 | + | 0.411905i | \(0.135136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.0000 | + | 24.2487i | 0.689730 | + | 1.19465i | ||||
\(413\) | 9.00000 | 0.442861 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.00000 | 0.441793 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.5000 | − | 18.1865i | 0.512959 | − | 0.888470i | −0.486928 | − | 0.873442i | \(-0.661883\pi\) |
0.999887 | − | 0.0150285i | \(-0.00478389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.00000 | − | 8.66025i | 0.241967 | − | 0.419099i | ||||
\(428\) | 6.00000 | − | 10.3923i | 0.290021 | − | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0000 | − | 19.0526i | 0.526804 | − | 0.912452i | ||||
\(437\) | 6.00000 | − | 10.3923i | 0.287019 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | + | 24.2487i | 0.668184 | + | 1.15733i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.00000 | − | 15.5885i | −0.427603 | − | 0.740630i | 0.569057 | − | 0.822298i | \(-0.307309\pi\) |
−0.996660 | + | 0.0816684i | \(0.973975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.00000 | + | 6.92820i | 0.188982 | + | 0.327327i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | −12.0000 | − | 20.7846i | −0.564433 | − | 0.977626i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | − | 10.3923i | 0.281284 | − | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0000 | − | 22.5167i | −0.608114 | − | 1.05328i | −0.991551 | − | 0.129718i | \(-0.958593\pi\) |
0.383437 | − | 0.923567i | \(-0.374740\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 36.0000 | 1.67851 | ||||||||
\(461\) | 7.50000 | + | 12.9904i | 0.349310 | + | 0.605022i | 0.986127 | − | 0.165992i | \(-0.0530827\pi\) |
−0.636817 | + | 0.771015i | \(0.719749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.50000 | + | 4.33013i | −0.116185 | + | 0.201238i | −0.918253 | − | 0.395995i | \(-0.870400\pi\) |
0.802068 | + | 0.597233i | \(0.203733\pi\) | |||||||
\(464\) | 12.0000 | − | 20.7846i | 0.557086 | − | 0.964901i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.0000 | 1.11059 | 0.555294 | − | 0.831654i | \(-0.312606\pi\) | ||||
0.555294 | + | 0.831654i | \(0.312606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 5.19615i | 0.137940 | − | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | − | 6.92820i | −0.183533 | − | 0.317888i | ||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.5000 | + | 18.1865i | 0.479757 | + | 0.830964i | 0.999730 | − | 0.0232187i | \(-0.00739140\pi\) |
−0.519973 | + | 0.854183i | \(0.674058\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.0000 | + | 24.2487i | −0.638345 | + | 1.10565i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.0000 | + | 43.3013i | 1.13636 | + | 1.96824i | ||||
\(485\) | −30.0000 | −1.36223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | + | 20.7846i | −0.541552 | + | 0.937996i | 0.457263 | + | 0.889332i | \(0.348830\pi\) |
−0.998815 | + | 0.0486647i | \(0.984503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 15.5885i | 0.405340 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.0000 | −0.718421 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.50000 | + | 4.33013i | −0.111915 | + | 0.193843i | −0.916542 | − | 0.399937i | \(-0.869032\pi\) |
0.804627 | + | 0.593780i | \(0.202365\pi\) | |||||||
\(500\) | −3.00000 | + | 5.19615i | −0.134164 | + | 0.232379i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.0000 | −1.20387 | −0.601935 | − | 0.798545i | \(-0.705603\pi\) | ||||
−0.601935 | + | 0.798545i | \(0.705603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.00000 | + | 12.1244i | −0.310575 | + | 0.537931i | ||||
\(509\) | −19.5000 | + | 33.7750i | −0.864322 | + | 1.49705i | 0.00339621 | + | 0.999994i | \(0.498919\pi\) |
−0.867719 | + | 0.497056i | \(0.834414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00000 | − | 1.73205i | −0.0442374 | − | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.0000 | − | 36.3731i | −0.925371 | − | 1.60279i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.0000 | + | 46.7654i | −1.18746 | + | 2.05674i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.0000 | 1.70862 | 0.854311 | − | 0.519763i | \(-0.173980\pi\) | ||||
0.854311 | + | 0.519763i | \(0.173980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0000 | −0.699631 | −0.349816 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349816 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(524\) | 12.0000 | + | 20.7846i | 0.524222 | + | 0.907980i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.00000 | −0.173422 | ||||||||
\(533\) | −6.00000 | − | 10.3923i | −0.259889 | − | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | + | 15.5885i | −0.389104 | + | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.0000 | −1.84871 | −0.924357 | − | 0.381528i | \(-0.875398\pi\) | ||||
−0.924357 | + | 0.381528i | \(0.875398\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.5000 | + | 28.5788i | −0.706782 | + | 1.22418i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.500000 | + | 0.866025i | 0.0213785 | + | 0.0370286i | 0.876517 | − | 0.481371i | \(-0.159861\pi\) |
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 24.0000 | 1.02523 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | + | 10.3923i | 0.255609 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.500000 | − | 0.866025i | 0.0212622 | − | 0.0368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.0000 | − | 38.1051i | −0.933008 | − | 1.61602i | ||||
\(557\) | 12.0000 | 0.508456 | 0.254228 | − | 0.967144i | \(-0.418179\pi\) | ||||
0.254228 | + | 0.967144i | \(0.418179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | −6.00000 | − | 10.3923i | −0.253546 | − | 0.439155i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | + | 31.1769i | 0.757266 | + | 1.31162i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00000 | + | 15.5885i | 0.377300 | + | 0.653502i | 0.990668 | − | 0.136295i | \(-0.0435194\pi\) |
−0.613369 | + | 0.789797i | \(0.710186\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.5000 | + | 19.9186i | −0.481260 | + | 0.833567i | −0.999769 | − | 0.0215055i | \(-0.993154\pi\) |
0.518509 | + | 0.855072i | \(0.326487\pi\) | |||||||
\(572\) | −24.0000 | + | 41.5692i | −1.00349 | + | 1.73810i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.0000 | −1.00087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.0000 | −0.666089 | −0.333044 | − | 0.942911i | \(-0.608076\pi\) | ||||
−0.333044 | + | 0.942911i | \(0.608076\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18.0000 | + | 31.1769i | −0.747409 | + | 1.29455i | ||||
\(581\) | −1.50000 | + | 2.59808i | −0.0622305 | + | 0.107786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | + | 31.1769i | 0.745484 | + | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.00000 | − | 10.3923i | −0.247647 | − | 0.428936i | 0.715226 | − | 0.698893i | \(-0.246324\pi\) |
−0.962872 | + | 0.269957i | \(0.912990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | − | 6.92820i | 0.164817 | − | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.0000 | + | 24.2487i | 0.575396 | + | 0.996616i | ||||
\(593\) | 15.0000 | 0.615976 | 0.307988 | − | 0.951390i | \(-0.400344\pi\) | ||||
0.307988 | + | 0.951390i | \(0.400344\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.00000 | 0.368964 | ||||||||
\(596\) | −6.00000 | − | 10.3923i | −0.245770 | − | 0.425685i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.00000 | + | 15.5885i | −0.367730 | + | 0.636927i | −0.989210 | − | 0.146503i | \(-0.953198\pi\) |
0.621480 | + | 0.783430i | \(0.286532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.00000 | − | 6.92820i | −0.163163 | − | 0.282607i | 0.772838 | − | 0.634603i | \(-0.218836\pi\) |
−0.936002 | + | 0.351996i | \(0.885503\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 38.0000 | 1.54620 | ||||||||
\(605\) | −37.5000 | − | 64.9519i | −1.52459 | − | 2.64067i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0000 | − | 34.6410i | 0.811775 | − | 1.40604i | −0.0998457 | − | 0.995003i | \(-0.531835\pi\) |
0.911621 | − | 0.411033i | \(-0.134832\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.0000 | −1.45640 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.0000 | −1.37325 | −0.686624 | − | 0.727013i | \(-0.740908\pi\) | ||||
−0.686624 | + | 0.727013i | \(0.740908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000 | − | 25.9808i | 0.603877 | − | 1.04595i | −0.388351 | − | 0.921512i | \(-0.626955\pi\) |
0.992228 | − | 0.124434i | \(-0.0397116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.00000 | + | 8.66025i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(620\) | 24.0000 | 0.963863 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.00000 | − | 5.19615i | −0.120192 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | + | 24.2487i | 0.558661 | + | 0.967629i | ||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.00000 | −0.278666 | −0.139333 | − | 0.990246i | \(-0.544496\pi\) | ||||
−0.139333 | + | 0.990246i | \(0.544496\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.5000 | − | 18.1865i | 0.416680 | − | 0.721711i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | + | 3.46410i | 0.0792429 | + | 0.137253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | + | 25.9808i | 0.592464 | + | 1.02618i | 0.993899 | + | 0.110291i | \(0.0351782\pi\) |
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00000 | + | 12.1244i | −0.276053 | + | 0.478138i | −0.970400 | − | 0.241502i | \(-0.922360\pi\) |
0.694347 | + | 0.719640i | \(0.255693\pi\) | |||||||
\(644\) | −6.00000 | + | 10.3923i | −0.236433 | + | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.0000 | 2.11969 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.00000 | + | 12.1244i | −0.274141 | + | 0.474826i | ||||
\(653\) | 12.0000 | − | 20.7846i | 0.469596 | − | 0.813365i | −0.529799 | − | 0.848123i | \(-0.677733\pi\) |
0.999396 | + | 0.0347583i | \(0.0110661\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | − | 31.1769i | −0.703318 | − | 1.21818i | ||||
\(656\) | −12.0000 | −0.468521 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | + | 20.7846i | 0.467454 | + | 0.809653i | 0.999309 | − | 0.0371821i | \(-0.0118382\pi\) |
−0.531855 | + | 0.846836i | \(0.678505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.00000 | 0.232670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.0000 | 1.39393 | ||||||||
\(668\) | −3.00000 | − | 5.19615i | −0.116073 | − | 0.201045i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.0000 | − | 51.9615i | 1.15814 | − | 2.00595i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0000 | − | 22.5167i | −0.501113 | − | 0.867953i | −0.999999 | − | 0.00128586i | \(-0.999591\pi\) |
0.498886 | − | 0.866668i | \(-0.333743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | −0.230769 | ||||||||
\(677\) | 9.00000 | + | 15.5885i | 0.345898 | + | 0.599113i | 0.985517 | − | 0.169580i | \(-0.0542410\pi\) |
−0.639618 | + | 0.768693i | \(0.720908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00000 | − | 8.66025i | 0.191882 | − | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.0000 | −1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | −12.0000 | + | 20.7846i | −0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0000 | − | 38.1051i | −0.836919 | − | 1.44959i | −0.892458 | − | 0.451130i | \(-0.851021\pi\) |
0.0555386 | − | 0.998457i | \(-0.482312\pi\) | |||||||
\(692\) | 36.0000 | 1.36851 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.0000 | + | 57.1577i | 1.25176 | + | 2.16811i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.50000 | − | 7.79423i | 0.170450 | − | 0.295227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.00000 | + | 6.92820i | 0.151186 | + | 0.261861i | ||||
\(701\) | 36.0000 | 1.35970 | 0.679851 | − | 0.733351i | \(-0.262045\pi\) | ||||
0.679851 | + | 0.733351i | \(0.262045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | 24.0000 | + | 41.5692i | 0.904534 | + | 1.56670i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.00000 | + | 5.19615i | −0.112827 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.500000 | + | 0.866025i | 0.0187779 | + | 0.0325243i | 0.875262 | − | 0.483650i | \(-0.160689\pi\) |
−0.856484 | + | 0.516174i | \(0.827356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.0000 | − | 20.7846i | −0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | − | 62.3538i | 1.34632 | − | 2.33190i | ||||
\(716\) | 12.0000 | − | 20.7846i | 0.448461 | − | 0.776757i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.0000 | 1.23069 | 0.615346 | − | 0.788257i | \(-0.289016\pi\) | ||||
0.615346 | + | 0.788257i | \(0.289016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0000 | 0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.0000 | − | 34.6410i | 0.743294 | − | 1.28742i | ||||
\(725\) | 12.0000 | − | 20.7846i | 0.445669 | − | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.00000 | + | 8.66025i | 0.185440 | + | 0.321191i | 0.943725 | − | 0.330732i | \(-0.107296\pi\) |
−0.758285 | + | 0.651923i | \(0.773962\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.50000 | + | 2.59808i | 0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.0000 | + | 27.7128i | −0.590973 | + | 1.02360i | 0.403128 | + | 0.915144i | \(0.367923\pi\) |
−0.994102 | + | 0.108453i | \(0.965410\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.0000 | −0.884051 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | −21.0000 | − | 36.3731i | −0.771975 | − | 1.33710i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.00000 | + | 5.19615i | −0.110059 | + | 0.190628i | −0.915794 | − | 0.401648i | \(-0.868437\pi\) |
0.805735 | + | 0.592277i | \(0.201771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −36.0000 | −1.31629 | ||||||||
\(749\) | −3.00000 | − | 5.19615i | −0.109618 | − | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | − | 3.46410i | 0.0729810 | − | 0.126407i | −0.827225 | − | 0.561870i | \(-0.810082\pi\) |
0.900207 | + | 0.435463i | \(0.143415\pi\) | |||||||
\(752\) | −18.0000 | + | 31.1769i | −0.656392 | + | 1.13691i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −57.0000 | −2.07444 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.0000 | 1.70824 | 0.854122 | − | 0.520073i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520073i | \(0.174095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.5000 | − | 44.1673i | 0.924374 | − | 1.60106i | 0.131810 | − | 0.991275i | \(-0.457921\pi\) |
0.792564 | − | 0.609788i | \(-0.208745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.50000 | − | 9.52628i | −0.199113 | − | 0.344874i | ||||
\(764\) | −36.0000 | −1.30243 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.0000 | + | 31.1769i | 0.649942 | + | 1.12573i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0000 | − | 34.6410i | 0.721218 | − | 1.24919i | −0.239293 | − | 0.970947i | \(-0.576916\pi\) |
0.960512 | − | 0.278240i | \(-0.0897509\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.0000 | − | 22.5167i | −0.467880 | − | 0.810392i | ||||
\(773\) | 21.0000 | 0.755318 | 0.377659 | − | 0.925945i | \(-0.376729\pi\) | ||||
0.377659 | + | 0.925945i | \(0.376729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0000 | −0.574737 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.00000 | − | 5.19615i | 0.107486 | − | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | −21.0000 | − | 36.3731i | −0.749522 | − | 1.29821i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.00000 | + | 12.1244i | −0.249523 | + | 0.432187i | −0.963394 | − | 0.268091i | \(-0.913607\pi\) |
0.713871 | + | 0.700278i | \(0.246941\pi\) | |||||||
\(788\) | −18.0000 | + | 31.1769i | −0.641223 | + | 1.11063i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.0000 | 1.42044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.0000 | − | 34.6410i | 0.708881 | − | 1.22782i | ||||
\(797\) | −3.00000 | + | 5.19615i | −0.106265 | + | 0.184057i | −0.914255 | − | 0.405140i | \(-0.867223\pi\) |
0.807989 | + | 0.589197i | \(0.200556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.5000 | − | 23.3827i | −0.477596 | − | 0.827220i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.00000 | − | 10.3923i | −0.211735 | − | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.00000 | − | 15.5885i | 0.317208 | − | 0.549421i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.0000 | −1.82597 | −0.912983 | − | 0.407997i | \(-0.866228\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | −6.00000 | − | 10.3923i | −0.210559 | − | 0.364698i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5000 | − | 18.1865i | 0.367799 | − | 0.637046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.00000 | + | 1.73205i | 0.0349856 | + | 0.0605968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.0000 | 0.628587 | ||||||||
\(821\) | 18.0000 | + | 31.1769i | 0.628204 | + | 1.08808i | 0.987912 | + | 0.155017i | \(0.0495431\pi\) |
−0.359708 | + | 0.933065i | \(0.617124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.50000 | + | 4.33013i | −0.0871445 | + | 0.150939i | −0.906303 | − | 0.422628i | \(-0.861108\pi\) |
0.819159 | + | 0.573567i | \(0.194441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000 | 0.0694629 | 0.0347314 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347314 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.0000 | + | 27.7128i | −0.554700 | + | 0.960769i | ||||
\(833\) | −1.50000 | + | 2.59808i | −0.0519719 | + | 0.0900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.50000 | + | 7.79423i | 0.155729 | + | 0.269730i | ||||
\(836\) | −24.0000 | −0.830057 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.5000 | − | 18.1865i | −0.362500 | − | 0.627869i | 0.625871 | − | 0.779926i | \(-0.284743\pi\) |
−0.988372 | + | 0.152057i | \(0.951410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000 | 0.859010 | ||||||||
\(848\) | 12.0000 | + | 20.7846i | 0.412082 | + | 0.713746i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.0000 | + | 36.3731i | −0.719871 | + | 1.24685i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | − | 38.1051i | −0.753266 | − | 1.30469i | −0.946232 | − | 0.323489i | \(-0.895144\pi\) |
0.192966 | − | 0.981205i | \(-0.438189\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.50000 | + | 2.59808i | 0.0512390 | + | 0.0887486i | 0.890507 | − | 0.454969i | \(-0.150350\pi\) |
−0.839268 | + | 0.543718i | \(0.817016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0000 | − | 19.0526i | 0.375315 | − | 0.650065i | −0.615059 | − | 0.788481i | \(-0.710868\pi\) |
0.990374 | + | 0.138416i | \(0.0442012\pi\) | |||||||
\(860\) | −3.00000 | + | 5.19615i | −0.102299 | + | 0.177187i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000 | 0.204242 | 0.102121 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −54.0000 | −1.83606 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.00000 | + | 6.92820i | −0.135769 | + | 0.235159i | ||||
\(869\) | 3.00000 | − | 5.19615i | 0.101768 | − | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | − | 13.8564i | −0.271070 | − | 0.469506i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.50000 | + | 2.59808i | 0.0507093 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5000 | − | 26.8468i | 0.523398 | − | 0.906552i | −0.476231 | − | 0.879320i | \(-0.657998\pi\) |
0.999629 | − | 0.0272316i | \(-0.00866915\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −36.0000 | − | 62.3538i | −1.21356 | − | 2.10195i | ||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.00000 | −0.235569 | −0.117784 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(884\) | −12.0000 | − | 20.7846i | −0.403604 | − | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.5000 | + | 18.1865i | −0.352555 | + | 0.610644i | −0.986696 | − | 0.162573i | \(-0.948021\pi\) |
0.634141 | + | 0.773217i | \(0.281354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.50000 | + | 6.06218i | 0.117386 | + | 0.203319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | −9.00000 | − | 15.5885i | −0.301174 | − | 0.521648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.0000 | + | 31.1769i | −0.601674 | + | 1.04213i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.0000 | 0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | −0.599667 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.0000 | + | 51.9615i | −0.997234 | + | 1.72726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5000 | + | 47.6314i | 0.913123 | + | 1.58157i | 0.809627 | + | 0.586945i | \(0.199669\pi\) |
0.103495 | + | 0.994630i | \(0.466997\pi\) | |||||||
\(908\) | 24.0000 | 0.796468 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | − | 25.9808i | −0.496972 | − | 0.860781i | 0.503022 | − | 0.864274i | \(-0.332222\pi\) |
−0.999994 | + | 0.00349271i | \(0.998888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.00000 | + | 15.5885i | −0.297857 | + | 0.515903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00000 | − | 6.92820i | −0.132164 | − | 0.228914i | ||||
\(917\) | 12.0000 | 0.396275 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.0000 | 0.956622 | 0.478311 | − | 0.878191i | \(-0.341249\pi\) | ||||
0.478311 | + | 0.878191i | \(0.341249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | + | 24.2487i | 0.460317 | + | 0.797293i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.5000 | + | 23.3827i | 0.442921 | + | 0.767161i | 0.997905 | − | 0.0646999i | \(-0.0206090\pi\) |
−0.554984 | + | 0.831861i | \(0.687276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | + | 1.73205i | −0.0327737 | + | 0.0567657i | ||||
\(932\) | 24.0000 | − | 41.5692i | 0.786146 | − | 1.36165i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 54.0000 | 1.76599 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 27.0000 | − | 46.7654i | 0.880643 | − | 1.52532i | ||||
\(941\) | −13.5000 | + | 23.3827i | −0.440087 | + | 0.762254i | −0.997695 | − | 0.0678506i | \(-0.978386\pi\) |
0.557608 | + | 0.830104i | \(0.311719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | − | 15.5885i | −0.293080 | − | 0.507630i | ||||
\(944\) | 36.0000 | 1.17170 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.0000 | − | 31.1769i | −0.584921 | − | 1.01311i | −0.994885 | − | 0.101012i | \(-0.967792\pi\) |
0.409964 | − | 0.912102i | \(-0.365541\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | − | 6.92820i | 0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.0000 | 1.74923 | 0.874616 | − | 0.484817i | \(-0.161114\pi\) | ||||
0.874616 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.0000 | 1.74740 | ||||||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | − | 10.3923i | 0.193750 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.0000 | −0.515325 | ||||||||
\(965\) | 19.5000 | + | 33.7750i | 0.627727 | + | 1.08726i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000 | − | 34.6410i | 0.643157 | − | 1.11398i | −0.341567 | − | 0.939857i | \(-0.610958\pi\) |
0.984724 | − | 0.174123i | \(-0.0557089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.0000 | −0.673922 | −0.336961 | − | 0.941519i | \(-0.609399\pi\) | ||||
−0.336961 | + | 0.941519i | \(0.609399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.0000 | −0.705288 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.0000 | − | 34.6410i | 0.640184 | − | 1.10883i | ||||
\(977\) | 18.0000 | − | 31.1769i | 0.575871 | − | 0.997438i | −0.420075 | − | 0.907489i | \(-0.637996\pi\) |
0.995946 | − | 0.0899487i | \(-0.0286703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.0000 | − | 31.1769i | −0.575282 | − | 0.996419i | ||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.50000 | + | 2.59808i | 0.0478426 | + | 0.0828658i | 0.888955 | − | 0.457995i | \(-0.151432\pi\) |
−0.841112 | + | 0.540860i | \(0.818099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0000 | − | 46.7654i | 0.860292 | − | 1.49007i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.00000 | − | 13.8564i | −0.254514 | − | 0.440831i | ||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0000 | 1.49300 | 0.746502 | − | 0.665383i | \(-0.231732\pi\) | ||||
0.746502 | + | 0.665383i | \(0.231732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.0000 | + | 51.9615i | −0.951064 | + | 1.64729i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | + | 8.66025i | 0.158352 | + | 0.274273i | 0.934274 | − | 0.356555i | \(-0.116049\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | 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 | 567.2.f.d.190.1 | 2 | ||
3.2 | odd | 2 | 567.2.f.e.190.1 | 2 | |||
9.2 | odd | 6 | 567.2.f.e.379.1 | 2 | |||
9.4 | even | 3 | 189.2.a.c.1.1 | yes | 1 | ||
9.5 | odd | 6 | 189.2.a.b.1.1 | ✓ | 1 | ||
9.7 | even | 3 | inner | 567.2.f.d.379.1 | 2 | ||
36.23 | even | 6 | 3024.2.a.f.1.1 | 1 | |||
36.31 | odd | 6 | 3024.2.a.y.1.1 | 1 | |||
45.4 | even | 6 | 4725.2.a.k.1.1 | 1 | |||
45.14 | odd | 6 | 4725.2.a.i.1.1 | 1 | |||
63.13 | odd | 6 | 1323.2.a.h.1.1 | 1 | |||
63.41 | even | 6 | 1323.2.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.a.b.1.1 | ✓ | 1 | 9.5 | odd | 6 | ||
189.2.a.c.1.1 | yes | 1 | 9.4 | even | 3 | ||
567.2.f.d.190.1 | 2 | 1.1 | even | 1 | trivial | ||
567.2.f.d.379.1 | 2 | 9.7 | even | 3 | inner | ||
567.2.f.e.190.1 | 2 | 3.2 | odd | 2 | |||
567.2.f.e.379.1 | 2 | 9.2 | odd | 6 | |||
1323.2.a.h.1.1 | 1 | 63.13 | odd | 6 | |||
1323.2.a.l.1.1 | 1 | 63.41 | even | 6 | |||
3024.2.a.f.1.1 | 1 | 36.23 | even | 6 | |||
3024.2.a.y.1.1 | 1 | 36.31 | odd | 6 | |||
4725.2.a.i.1.1 | 1 | 45.14 | odd | 6 | |||
4725.2.a.k.1.1 | 1 | 45.4 | even | 6 |