Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(961,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.q (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: | \(18.7808145554\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.961 |
Dual form | 2352.2.q.p.1537.1 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 6.92820i | 0.917663 | − | 1.58944i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.0000 | −1.85695 | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||||
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | + | 1.73205i | −0.174078 | + | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 5.19615i | −0.493197 | + | 0.854242i | −0.999969 | − | 0.00783774i | \(-0.997505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | − | 3.46410i | −0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | − | 6.92820i | 0.583460 | − | 1.01058i | −0.411606 | − | 0.911362i | \(-0.635032\pi\) |
0.995066 | − | 0.0992202i | \(-0.0316348\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | − | 5.19615i | 0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | − | 1.73205i | −0.137361 | − | 0.237915i | 0.789136 | − | 0.614218i | \(-0.210529\pi\) |
−0.926497 | + | 0.376303i | \(0.877195\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.00000 | 1.05963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | − | 3.46410i | −0.260378 | − | 0.450988i | 0.705965 | − | 0.708247i | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | − | 6.92820i | 0.496139 | − | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | − | 6.92820i | −0.488678 | − | 0.846415i | 0.511237 | − | 0.859440i | \(-0.329187\pi\) |
−0.999915 | + | 0.0130248i | \(0.995854\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | − | 3.46410i | −0.234082 | − | 0.405442i | 0.724923 | − | 0.688830i | \(-0.241875\pi\) |
−0.959006 | + | 0.283387i | \(0.908542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.00000 | − | 8.66025i | −0.536056 | − | 0.928477i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.00000 | − | 12.1244i | 0.741999 | − | 1.28518i | −0.209585 | − | 0.977790i | \(-0.567211\pi\) |
0.951584 | − | 0.307389i | \(-0.0994552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | + | 3.46410i | −0.207390 | + | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.00000 | + | 13.8564i | 0.820783 | + | 1.42164i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000 | 0.406138 | 0.203069 | − | 0.979164i | \(-0.434908\pi\) | ||||
0.203069 | + | 0.979164i | \(0.434908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00000 | + | 8.66025i | 0.497519 | + | 0.861727i | 0.999996 | − | 0.00286291i | \(-0.000911295\pi\) |
−0.502477 | + | 0.864590i | \(0.667578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.00000 | + | 12.1244i | −0.676716 | + | 1.17211i | 0.299249 | + | 0.954175i | \(0.403264\pi\) |
−0.975964 | + | 0.217931i | \(0.930069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | − | 8.66025i | −0.478913 | − | 0.829502i | 0.520794 | − | 0.853682i | \(-0.325636\pi\) |
−0.999708 | + | 0.0241802i | \(0.992302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.00000 | − | 10.3923i | −0.559503 | − | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | − | 3.46410i | 0.184900 | − | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00000 | − | 5.19615i | −0.270501 | − | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | − | 3.46410i | −0.176090 | − | 0.304997i | ||||
\(130\) | 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 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | − | 1.73205i | 0.0860663 | − | 0.149071i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000 | + | 8.66025i | 0.427179 | + | 0.739895i | 0.996621 | − | 0.0821359i | \(-0.0261741\pi\) |
−0.569442 | + | 0.822031i | \(0.692841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | − | 6.92820i | −0.334497 | − | 0.579365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | − | 17.3205i | 0.830455 | − | 1.43839i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.00000 | + | 1.73205i | −0.0819232 | + | 0.141895i | −0.904076 | − | 0.427372i | \(-0.859440\pi\) |
0.822153 | + | 0.569267i | \(0.192773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.00000 | + | 13.8564i | 0.638470 | + | 1.10586i | 0.985769 | + | 0.168107i | \(0.0537655\pi\) |
−0.347299 | + | 0.937754i | \(0.612901\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.00000 | − | 1.73205i | 0.0793052 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | − | 20.7846i | 0.939913 | − | 1.62798i | 0.174282 | − | 0.984696i | \(-0.444240\pi\) |
0.765631 | − | 0.643280i | \(-0.222427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00000 | − | 3.46410i | −0.155700 | − | 0.269680i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | + | 6.92820i | 0.305888 | + | 0.529813i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.00000 | − | 1.73205i | 0.0760286 | − | 0.131685i | −0.825505 | − | 0.564396i | \(-0.809109\pi\) |
0.901533 | + | 0.432710i | \(0.142443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00000 | − | 3.46410i | 0.150329 | − | 0.260378i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | + | 5.19615i | 0.224231 | + | 0.388379i | 0.956088 | − | 0.293079i | \(-0.0946798\pi\) |
−0.731858 | + | 0.681457i | \(0.761346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | − | 10.3923i | −0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | − | 10.3923i | 0.438763 | − | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | + | 8.66025i | 0.359908 | + | 0.623379i | 0.987945 | − | 0.154805i | \(-0.0494748\pi\) |
−0.628037 | + | 0.778183i | \(0.716141\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.00000 | 0.572892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | − | 6.92820i | −0.283552 | − | 0.491127i | 0.688705 | − | 0.725042i | \(-0.258180\pi\) |
−0.972257 | + | 0.233915i | \(0.924846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | − | 6.92820i | 0.282138 | − | 0.488678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | − | 10.3923i | 0.419058 | − | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.00000 | − | 5.19615i | −0.208514 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.00000 | + | 8.66025i | 0.342594 | + | 0.593391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | − | 6.92820i | 0.272798 | − | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | + | 20.7846i | 0.807207 | + | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.00000 | + | 3.46410i | 0.132745 | + | 0.229920i | 0.924734 | − | 0.380615i | \(-0.124288\pi\) |
−0.791989 | + | 0.610535i | \(0.790954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | + | 17.3205i | −0.660819 | + | 1.14457i | 0.319582 | + | 0.947559i | \(0.396457\pi\) |
−0.980401 | + | 0.197013i | \(0.936876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.00000 | + | 12.1244i | −0.458585 | + | 0.794293i | −0.998886 | − | 0.0471787i | \(-0.984977\pi\) |
0.540301 | + | 0.841472i | \(0.318310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | + | 13.8564i | 0.521862 | + | 0.903892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000 | 0.259828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0000 | −1.16432 | −0.582162 | − | 0.813073i | \(-0.697793\pi\) | ||||
−0.582162 | + | 0.813073i | \(0.697793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | − | 24.2487i | −0.901819 | − | 1.56200i | −0.825131 | − | 0.564942i | \(-0.808899\pi\) |
−0.0766885 | − | 0.997055i | \(-0.524435\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.0000 | + | 27.7128i | −1.01806 | + | 1.76332i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.0000 | 1.76734 | 0.883672 | − | 0.468106i | \(-0.155064\pi\) | ||||
0.883672 | + | 0.468106i | \(0.155064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.00000 | + | 10.3923i | 0.375735 | + | 0.650791i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.00000 | + | 8.66025i | −0.311891 | + | 0.540212i | −0.978772 | − | 0.204953i | \(-0.934296\pi\) |
0.666880 | + | 0.745165i | \(0.267629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | − | 8.66025i | 0.309492 | − | 0.536056i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0000 | + | 22.5167i | 0.801614 | + | 1.38844i | 0.918553 | + | 0.395298i | \(0.129359\pi\) |
−0.116939 | + | 0.993139i | \(0.537308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.0000 | 0.856786 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.00000 | − | 1.73205i | −0.0609711 | − | 0.105605i | 0.833929 | − | 0.551872i | \(-0.186086\pi\) |
−0.894900 | + | 0.446267i | \(0.852753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00000 | + | 3.46410i | −0.121491 | + | 0.210429i | −0.920356 | − | 0.391082i | \(-0.872101\pi\) |
0.798865 | + | 0.601511i | \(0.205434\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | − | 8.66025i | −0.300421 | − | 0.520344i | 0.675810 | − | 0.737075i | \(-0.263794\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | + | 13.8564i | 0.475551 | + | 0.823678i | 0.999608 | − | 0.0280052i | \(-0.00891551\pi\) |
−0.524057 | + | 0.851683i | \(0.675582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.00000 | + | 13.8564i | −0.473879 | + | 0.820783i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000 | + | 3.46410i | 0.117242 | + | 0.203069i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | − | 1.73205i | −0.0580259 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000 | − | 20.7846i | 0.693978 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.00000 | + | 8.66025i | −0.287242 | + | 0.497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | + | 13.8564i | 0.458079 | + | 0.793416i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | + | 13.8564i | 0.453638 | + | 0.785725i | 0.998609 | − | 0.0527306i | \(-0.0167924\pi\) |
−0.544970 | + | 0.838455i | \(0.683459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0000 | + | 20.7846i | −0.678280 | + | 1.17482i | 0.297218 | + | 0.954810i | \(0.403941\pi\) |
−0.975499 | + | 0.220006i | \(0.929392\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0000 | − | 17.3205i | −0.559893 | − | 0.969762i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0000 | −0.781404 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −48.0000 | −2.67079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | − | 3.46410i | −0.110940 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.00000 | − | 8.66025i | 0.276501 | − | 0.478913i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | − | 5.19615i | −0.164399 | − | 0.284747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.0000 | 0.874173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.00000 | − | 12.1244i | −0.380188 | − | 0.658505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | + | 6.92820i | −0.216612 | + | 0.375183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | − | 10.3923i | 0.323029 | − | 0.559503i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00000 | − | 15.5885i | −0.483145 | − | 0.836832i | 0.516667 | − | 0.856186i | \(-0.327172\pi\) |
−0.999813 | + | 0.0193540i | \(0.993839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | − | 5.19615i | −0.159674 | − | 0.276563i | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0000 | + | 17.3205i | −0.530745 | + | 0.919277i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.0000 | − | 19.0526i | 0.580558 | − | 1.00556i | −0.414855 | − | 0.909887i | \(-0.636168\pi\) |
0.995413 | − | 0.0956683i | \(-0.0304988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5000 | − | 38.9711i | −1.18421 | − | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | + | 13.8564i | 0.417597 | + | 0.723299i | 0.995697 | − | 0.0926670i | \(-0.0295392\pi\) |
−0.578101 | + | 0.815966i | \(0.696206\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0000 | − | 22.5167i | 0.673114 | − | 1.16587i | −0.303902 | − | 0.952703i | \(-0.598289\pi\) |
0.977016 | − | 0.213165i | \(-0.0683772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | − | 10.3923i | −0.309839 | − | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.0000 | 2.06010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.0000 | 1.84920 | 0.924598 | − | 0.380945i | \(-0.124401\pi\) | ||||
0.924598 | + | 0.380945i | \(0.124401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.00000 | + | 3.46410i | 0.102463 | + | 0.177471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000 | − | 3.46410i | 0.101666 | − | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.00000 | + | 15.5885i | 0.456318 | + | 0.790366i | 0.998763 | − | 0.0497253i | \(-0.0158346\pi\) |
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000 | 1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | + | 6.92820i | 0.201262 | + | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0000 | + | 27.7128i | −0.803017 | + | 1.39087i | 0.114605 | + | 0.993411i | \(0.463440\pi\) |
−0.917622 | + | 0.397455i | \(0.869893\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | + | 25.9808i | −0.749064 | + | 1.29742i | 0.199207 | + | 0.979957i | \(0.436163\pi\) |
−0.948272 | + | 0.317460i | \(0.897170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | − | 13.8564i | −0.398508 | − | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.0000 | −0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | − | 10.3923i | −0.296681 | − | 0.513866i | 0.678694 | − | 0.734422i | \(-0.262546\pi\) |
−0.975375 | + | 0.220555i | \(0.929213\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.00000 | + | 8.66025i | −0.246632 | + | 0.427179i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | − | 20.7846i | 0.589057 | − | 1.02028i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | − | 10.3923i | −0.293821 | − | 0.508913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.00000 | 0.195413 | 0.0977064 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977064 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.00000 | + | 6.92820i | 0.194487 | + | 0.336861i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | − | 6.92820i | 0.193122 | − | 0.334497i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.00000 | − | 1.73205i | −0.0481683 | − | 0.0834300i | 0.840936 | − | 0.541135i | \(-0.182005\pi\) |
−0.889104 | + | 0.457705i | \(0.848672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.0000 | 1.53782 | 0.768911 | − | 0.639356i | \(-0.220799\pi\) | ||||
0.768911 | + | 0.639356i | \(0.220799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.0000 | 0.958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.0000 | + | 41.5692i | 1.14808 | + | 1.98853i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | + | 20.7846i | −0.572729 | + | 0.991995i | 0.423556 | + | 0.905870i | \(0.360782\pi\) |
−0.996284 | + | 0.0861252i | \(0.972552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.00000 | + | 15.5885i | −0.427603 | + | 0.740630i | −0.996660 | − | 0.0816684i | \(-0.973975\pi\) |
0.569057 | + | 0.822298i | \(0.307309\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0000 | + | 24.2487i | 0.663664 | + | 1.14950i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.00000 | −0.0945968 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00000 | − | 6.92820i | 0.187936 | − | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0000 | − | 19.0526i | 0.514558 | − | 0.891241i | −0.485299 | − | 0.874348i | \(-0.661289\pi\) |
0.999857 | − | 0.0168929i | \(-0.00537742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.00000 | + | 5.19615i | 0.140028 | + | 0.242536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.00000 | − | 6.92820i | −0.185496 | − | 0.321288i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0000 | + | 17.3205i | −0.462745 | + | 0.801498i | −0.999097 | − | 0.0424970i | \(-0.986469\pi\) |
0.536352 | + | 0.843995i | \(0.319802\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.00000 | + | 13.8564i | −0.368621 | + | 0.638470i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.00000 | − | 6.92820i | −0.183920 | − | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | 0.367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | − | 20.7846i | 0.547153 | − | 0.947697i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.00000 | + | 6.92820i | −0.181631 | + | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | + | 13.8564i | 0.362515 | + | 0.627894i | 0.988374 | − | 0.152042i | \(-0.0485850\pi\) |
−0.625859 | + | 0.779936i | \(0.715252\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0000 | 1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.0000 | + | 51.9615i | 1.35113 | + | 2.34023i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | − | 3.46410i | 0.0898933 | − | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0000 | + | 31.1769i | −0.805791 | + | 1.39567i | 0.109965 | + | 0.993935i | \(0.464926\pi\) |
−0.915756 | + | 0.401735i | \(0.868407\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.00000 | − | 13.8564i | −0.357414 | − | 0.619059i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.0000 | −0.889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.50000 | + | 2.59808i | 0.0666173 | + | 0.115385i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.00000 | + | 8.66025i | −0.221621 | + | 0.383859i | −0.955300 | − | 0.295637i | \(-0.904468\pi\) |
0.733679 | + | 0.679496i | \(0.237801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | + | 6.92820i | −0.176604 | + | 0.305888i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.00000 | − | 6.92820i | −0.176261 | − | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | 0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.00000 | 0.0877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0000 | − | 19.0526i | −0.481919 | − | 0.834708i | 0.517866 | − | 0.855462i | \(-0.326727\pi\) |
−0.999785 | + | 0.0207541i | \(0.993393\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.00000 | + | 3.46410i | −0.0874539 | + | 0.151475i | −0.906434 | − | 0.422347i | \(-0.861206\pi\) |
0.818980 | + | 0.573822i | \(0.194540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | − | 20.7846i | 0.522728 | − | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | 1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.0000 | − | 24.2487i | −0.605273 | − | 1.04836i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.00000 | + | 5.19615i | −0.129460 | + | 0.224231i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0000 | + | 29.4449i | −0.730887 | + | 1.26593i | 0.225617 | + | 0.974216i | \(0.427560\pi\) |
−0.956504 | + | 0.291718i | \(0.905773\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.0000 | − | 17.3205i | −0.429141 | − | 0.743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.0000 | 0.856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | −0.684111 | −0.342055 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342055 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.00000 | + | 6.92820i | 0.170716 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.0000 | + | 69.2820i | −1.70406 | + | 2.95151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.00000 | − | 10.3923i | 0.254686 | − | 0.441129i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.00000 | + | 5.19615i | 0.127114 | + | 0.220168i | 0.922557 | − | 0.385860i | \(-0.126095\pi\) |
−0.795443 | + | 0.606028i | \(0.792762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.00000 | + | 3.46410i | 0.0842900 | + | 0.145994i | 0.905088 | − | 0.425223i | \(-0.139804\pi\) |
−0.820798 | + | 0.571218i | \(0.806471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000 | − | 24.2487i | 0.588984 | − | 1.02015i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.00000 | + | 6.92820i | 0.166522 | + | 0.288425i | 0.937195 | − | 0.348806i | \(-0.113413\pi\) |
−0.770673 | + | 0.637231i | \(0.780080\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.00000 | + | 8.66025i | −0.207793 | + | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | − | 3.46410i | 0.0828315 | − | 0.143468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.00000 | + | 6.92820i | 0.165380 | + | 0.286446i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.00000 | 0.165098 | 0.0825488 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825488 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0000 | 1.31854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.00000 | + | 5.19615i | −0.123195 | + | 0.213380i | −0.921026 | − | 0.389501i | \(-0.872647\pi\) |
0.797831 | + | 0.602881i | \(0.205981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.00000 | − | 6.92820i | 0.163709 | − | 0.283552i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0000 | + | 25.9808i | 0.612883 | + | 1.06155i | 0.990752 | + | 0.135686i | \(0.0433238\pi\) |
−0.377869 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.00000 | 0.326327 | 0.163163 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163163 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | + | 12.1244i | 0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0000 | − | 20.7846i | 0.487065 | − | 0.843621i | −0.512824 | − | 0.858494i | \(-0.671401\pi\) |
0.999889 | + | 0.0148722i | \(0.00473415\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.0000 | + | 27.7128i | −0.647291 | + | 1.12114i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0000 | − | 22.5167i | −0.525065 | − | 0.909439i | −0.999574 | − | 0.0291886i | \(-0.990708\pi\) |
0.474509 | − | 0.880251i | \(-0.342626\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | 0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00000 | + | 3.46410i | 0.0803868 | + | 0.139234i | 0.903416 | − | 0.428765i | \(-0.141051\pi\) |
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | − | 5.19615i | 0.120386 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.00000 | + | 13.8564i | 0.319489 | + | 0.553372i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.0000 | 1.43541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0000 | −0.477712 | −0.238856 | − | 0.971055i | \(-0.576772\pi\) | ||||
−0.238856 | + | 0.971055i | \(0.576772\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.00000 | + | 3.46410i | 0.0794929 | + | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | + | 6.92820i | −0.158735 | + | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.00000 | + | 8.66025i | −0.197797 | + | 0.342594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0000 | + | 22.5167i | 0.513469 | + | 0.889355i | 0.999878 | + | 0.0156233i | \(0.00497325\pi\) |
−0.486409 | + | 0.873731i | \(0.661693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | − | 41.5692i | −0.943537 | − | 1.63425i | −0.758654 | − | 0.651494i | \(-0.774142\pi\) |
−0.184884 | − | 0.982760i | \(-0.559191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | − | 6.92820i | 0.157014 | − | 0.271956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.0000 | − | 29.4449i | 0.665261 | − | 1.15227i | −0.313953 | − | 0.949439i | \(-0.601653\pi\) |
0.979214 | − | 0.202828i | \(-0.0650132\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0000 | − | 20.7846i | −0.468879 | − | 0.812122i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.0000 | 0.545363 | 0.272681 | − | 0.962104i | \(-0.412090\pi\) | ||||
0.272681 | + | 0.962104i | \(0.412090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.00000 | − | 6.92820i | −0.155582 | − | 0.269476i | 0.777689 | − | 0.628649i | \(-0.216392\pi\) |
−0.933271 | + | 0.359174i | \(0.883059\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.0000 | + | 20.7846i | −0.466041 | + | 0.807207i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.0000 | − | 51.9615i | 1.16160 | − | 2.01196i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | + | 6.92820i | 0.154649 | + | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.0000 | 0.617673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0000 | −0.848038 | −0.424019 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424019 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.0000 | + | 25.9808i | −0.576497 | + | 0.998522i | 0.419380 | + | 0.907811i | \(0.362247\pi\) |
−0.995877 | + | 0.0907112i | \(0.971086\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.00000 | + | 3.46410i | −0.0766402 | + | 0.132745i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.0000 | + | 19.0526i | 0.420903 | + | 0.729026i | 0.996028 | − | 0.0890398i | \(-0.0283798\pi\) |
−0.575125 | + | 0.818066i | \(0.695047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.0000 | −0.764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.0000 | −0.763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00000 | + | 6.92820i | 0.152388 | + | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0000 | + | 17.3205i | −0.380418 | + | 0.658903i | −0.991122 | − | 0.132956i | \(-0.957553\pi\) |
0.610704 | + | 0.791859i | \(0.290887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0000 | − | 20.7846i | 0.455186 | − | 0.788405i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | + | 31.1769i | 0.681799 | + | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.0000 | −0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.0000 | −1.88847 | −0.944237 | − | 0.329267i | \(-0.893198\pi\) | ||||
−0.944237 | + | 0.329267i | \(0.893198\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | + | 41.5692i | 0.905177 | + | 1.56781i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | + | 13.8564i | −0.301297 | + | 0.521862i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.00000 | − | 12.1244i | 0.262891 | − | 0.455340i | −0.704118 | − | 0.710083i | \(-0.748658\pi\) |
0.967009 | + | 0.254743i | \(0.0819909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00000 | + | 3.46410i | 0.0750059 | + | 0.129914i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.0000 | −0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000 | 0.598366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.00000 | − | 15.5885i | −0.336111 | − | 0.582162i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | − | 41.5692i | 0.895049 | − | 1.55027i | 0.0613050 | − | 0.998119i | \(-0.480474\pi\) |
0.833744 | − | 0.552151i | \(-0.186193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.0000 | − | 24.2487i | 0.520666 | − | 0.901819i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.00000 | − | 8.66025i | −0.185695 | − | 0.321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.0000 | −1.63187 | −0.815935 | − | 0.578144i | \(-0.803777\pi\) | ||||
−0.815935 | + | 0.578144i | \(0.803777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.00000 | + | 3.46410i | −0.0738717 | + | 0.127950i | −0.900595 | − | 0.434659i | \(-0.856869\pi\) |
0.826723 | + | 0.562609i | \(0.190202\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.00000 | − | 13.8564i | 0.294684 | − | 0.510407i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | + | 34.6410i | 0.735712 | + | 1.27429i | 0.954410 | + | 0.298498i | \(0.0964856\pi\) |
−0.218698 | + | 0.975793i | \(0.570181\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.0000 | −1.17555 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | 0.660356 | 0.330178 | − | 0.943919i | \(-0.392891\pi\) | ||||
0.330178 | + | 0.943919i | \(0.392891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | − | 3.46410i | −0.0732743 | − | 0.126915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0000 | + | 41.5692i | −0.875772 | + | 1.51688i | −0.0198348 | + | 0.999803i | \(0.506314\pi\) |
−0.855938 | + | 0.517079i | \(0.827019\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.0000 | + | 24.2487i | 0.510188 | + | 0.883672i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.508839 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.00000 | − | 10.3923i | −0.217786 | − | 0.377217i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.0000 | − | 19.0526i | 0.398750 | − | 0.690655i | −0.594822 | − | 0.803857i | \(-0.702778\pi\) |
0.993572 | + | 0.113203i | \(0.0361109\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.00000 | + | 10.3923i | −0.216930 | + | 0.375735i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.00000 | + | 13.8564i | 0.288863 | + | 0.500326i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.0000 | 1.15395 | 0.576975 | − | 0.816762i | \(-0.304233\pi\) | ||||
0.576975 | + | 0.816762i | \(0.304233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.0000 | −0.360141 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.00000 | − | 5.19615i | −0.107903 | − | 0.186893i | 0.807018 | − | 0.590527i | \(-0.201080\pi\) |
−0.914920 | + | 0.403634i | \(0.867747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | + | 3.46410i | −0.0718421 | + | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.0000 | + | 41.5692i | −0.859889 | + | 1.48937i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | + | 17.3205i | 0.357828 | + | 0.619777i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.0000 | 0.357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.0000 | −1.14213 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.00000 | + | 3.46410i | 0.0712923 | + | 0.123482i | 0.899468 | − | 0.436987i | \(-0.143954\pi\) |
−0.828176 | + | 0.560469i | \(0.810621\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.0000 | + | 22.5167i | −0.462812 | + | 0.801614i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0000 | + | 27.7128i | −0.568177 | + | 0.984111i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.00000 | + | 3.46410i | 0.0709327 | + | 0.122859i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.0000 | −1.69812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.00000 | + | 12.1244i | 0.247333 | + | 0.428393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.00000 | − | 6.92820i | 0.141157 | − | 0.244491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.00000 | − | 1.73205i | 0.0352017 | − | 0.0609711i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.00000 | + | 5.19615i | 0.105474 | + | 0.182687i | 0.913932 | − | 0.405868i | \(-0.133031\pi\) |
−0.808458 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.00000 | −0.140286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0000 | + | 41.5692i | 0.840683 | + | 1.45611i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | + | 27.7128i | −0.559769 | + | 0.969549i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.00000 | + | 1.73205i | −0.0349002 | + | 0.0604490i | −0.882948 | − | 0.469471i | \(-0.844445\pi\) |
0.848048 | + | 0.529920i | \(0.177778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.0000 | − | 38.1051i | −0.766872 | − | 1.32826i | −0.939251 | − | 0.343230i | \(-0.888479\pi\) |
0.172379 | − | 0.985031i | \(-0.444854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.00000 | −0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.0000 | 1.04320 | 0.521601 | − | 0.853189i | \(-0.325335\pi\) | ||||
0.521601 | + | 0.853189i | \(0.325335\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.00000 | − | 3.46410i | −0.0694629 | − | 0.120313i | 0.829202 | − | 0.558949i | \(-0.188795\pi\) |
−0.898665 | + | 0.438636i | \(0.855462\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.00000 | − | 8.66025i | 0.173448 | − | 0.300421i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | − | 27.7128i | 0.553703 | − | 0.959041i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | − | 3.46410i | −0.0691301 | − | 0.119737i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 71.0000 | 2.44828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.00000 | + | 5.19615i | 0.103325 | + | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | + | 5.19615i | −0.103203 | + | 0.178753i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.00000 | + | 13.8564i | −0.274559 | + | 0.475551i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.0000 | − | 31.1769i | −0.617032 | − | 1.06873i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.0000 | −0.547830 | −0.273915 | − | 0.961754i | \(-0.588319\pi\) | ||||
−0.273915 | + | 0.961754i | \(0.588319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.0000 | −0.547188 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0000 | − | 36.3731i | −0.717346 | − | 1.24248i | −0.962048 | − | 0.272882i | \(-0.912023\pi\) |
0.244701 | − | 0.969599i | \(-0.421310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0000 | − | 41.5692i | 0.818869 | − | 1.41832i | −0.0876464 | − | 0.996152i | \(-0.527935\pi\) |
0.906516 | − | 0.422172i | \(-0.138732\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.00000 | − | 15.5885i | 0.306364 | − | 0.530637i | −0.671200 | − | 0.741276i | \(-0.734221\pi\) |
0.977564 | + | 0.210639i | \(0.0675543\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | + | 3.46410i | 0.0680020 | + | 0.117783i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.0000 | −0.645274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | + | 27.7128i | 0.542139 | + | 0.939013i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.00000 | + | 3.46410i | −0.0676897 | + | 0.117242i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.00000 | + | 15.5885i | −0.303908 | + | 0.526385i | −0.977018 | − | 0.213158i | \(-0.931625\pi\) |
0.673109 | + | 0.739543i | \(0.264958\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.00000 | − | 15.5885i | −0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.0000 | −1.14549 | −0.572745 | − | 0.819734i | \(-0.694121\pi\) | ||||
−0.572745 | + | 0.819734i | \(0.694121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | + | 6.92820i | 0.134459 | + | 0.232889i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0000 | − | 41.5692i | 0.805841 | − | 1.39576i | −0.109881 | − | 0.993945i | \(-0.535047\pi\) |
0.915722 | − | 0.401813i | \(-0.131620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.0000 | − | 55.4256i | −1.07084 | − | 1.85475i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000 | 0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.0000 | − | 34.6410i | −0.667037 | − | 1.15534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.00000 | + | 10.3923i | −0.199889 | + | 0.346218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.0000 | − | 34.6410i | 0.664822 | − | 1.15151i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0000 | + | 24.2487i | 0.464862 | + | 0.805165i | 0.999195 | − | 0.0401089i | \(-0.0127705\pi\) |
−0.534333 | + | 0.845274i | \(0.679437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.0000 | 1.65657 | 0.828287 | − | 0.560304i | \(-0.189316\pi\) | ||||
0.828287 | + | 0.560304i | \(0.189316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | − | 20.7846i | −0.397142 | − | 0.687870i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.00000 | + | 13.8564i | −0.264472 | + | 0.458079i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0000 | − | 20.7846i | 0.395843 | − | 0.685621i | −0.597365 | − | 0.801970i | \(-0.703786\pi\) |
0.993208 | + | 0.116348i | \(0.0371189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.00000 | − | 13.8564i | −0.263609 | − | 0.456584i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.0000 | −1.31662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.00000 | − | 3.46410i | −0.0656886 | − | 0.113776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | + | 13.8564i | −0.261908 | + | 0.453638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | + | 20.7846i | 0.392442 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.0000 | −0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.00000 | − | 15.5885i | −0.293392 | − | 0.508169i | 0.681218 | − | 0.732081i | \(-0.261451\pi\) |
−0.974609 | + | 0.223912i | \(0.928117\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000 | − | 31.1769i | 0.586161 | − | 1.01526i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.0000 | + | 39.8372i | −0.747400 | + | 1.29453i | 0.201666 | + | 0.979454i | \(0.435365\pi\) |
−0.949065 | + | 0.315080i | \(0.897969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | + | 13.8564i | 0.259691 | + | 0.449798i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.0000 | 1.36051 | 0.680257 | − | 0.732974i | \(-0.261868\pi\) | ||||
0.680257 | + | 0.732974i | \(0.261868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.00000 | + | 10.3923i | 0.194155 | + | 0.336287i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.0000 | − | 17.3205i | 0.323254 | − | 0.559893i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.00000 | − | 12.1244i | −0.225572 | − | 0.390702i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.0000 | −0.643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.00000 | −0.128631 | −0.0643157 | − | 0.997930i | \(-0.520486\pi\) | ||||
−0.0643157 | + | 0.997930i | \(0.520486\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0000 | − | 41.5692i | −0.770991 | − | 1.33540i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.0000 | − | 17.3205i | 0.320915 | − | 0.555842i | −0.659762 | − | 0.751475i | \(-0.729343\pi\) |
0.980677 | + | 0.195633i | \(0.0626762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00000 | − | 3.46410i | 0.0640513 | − | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.0000 | − | 32.9090i | −0.607864 | − | 1.05285i | −0.991592 | − | 0.129405i | \(-0.958693\pi\) |
0.383728 | − | 0.923446i | \(-0.374640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.0000 | 0.894884 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.00000 | − | 13.8564i | −0.255160 | − | 0.441951i | 0.709779 | − | 0.704425i | \(-0.248795\pi\) |
−0.964939 | + | 0.262474i | \(0.915462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | − | 10.3923i | 0.191176 | − | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | − | 20.7846i | 0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | + | 27.7128i | 0.508257 | + | 0.880327i | 0.999954 | + | 0.00956046i | \(0.00304324\pi\) |
−0.491698 | + | 0.870766i | \(0.663623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.00000 | − | 6.92820i | −0.126681 | − | 0.219418i | 0.795708 | − | 0.605681i | \(-0.207099\pi\) |
−0.922389 | + | 0.386263i | \(0.873766\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.00000 | − | 5.19615i | 0.0949158 | − | 0.164399i |
(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 | 2352.2.q.p.961.1 | 2 | ||
4.3 | odd | 2 | 588.2.i.a.373.1 | 2 | |||
7.2 | even | 3 | 2352.2.a.j.1.1 | 1 | |||
7.3 | odd | 6 | 2352.2.q.k.1537.1 | 2 | |||
7.4 | even | 3 | inner | 2352.2.q.p.1537.1 | 2 | ||
7.5 | odd | 6 | 2352.2.a.p.1.1 | 1 | |||
7.6 | odd | 2 | 2352.2.q.k.961.1 | 2 | |||
12.11 | even | 2 | 1764.2.k.i.1549.1 | 2 | |||
21.2 | odd | 6 | 7056.2.a.n.1.1 | 1 | |||
21.5 | even | 6 | 7056.2.a.bu.1.1 | 1 | |||
28.3 | even | 6 | 588.2.i.g.361.1 | 2 | |||
28.11 | odd | 6 | 588.2.i.a.361.1 | 2 | |||
28.19 | even | 6 | 588.2.a.b.1.1 | ✓ | 1 | ||
28.23 | odd | 6 | 588.2.a.e.1.1 | yes | 1 | ||
28.27 | even | 2 | 588.2.i.g.373.1 | 2 | |||
56.5 | odd | 6 | 9408.2.a.bf.1.1 | 1 | |||
56.19 | even | 6 | 9408.2.a.cu.1.1 | 1 | |||
56.37 | even | 6 | 9408.2.a.ca.1.1 | 1 | |||
56.51 | odd | 6 | 9408.2.a.l.1.1 | 1 | |||
84.11 | even | 6 | 1764.2.k.i.361.1 | 2 | |||
84.23 | even | 6 | 1764.2.a.b.1.1 | 1 | |||
84.47 | odd | 6 | 1764.2.a.i.1.1 | 1 | |||
84.59 | odd | 6 | 1764.2.k.c.361.1 | 2 | |||
84.83 | odd | 2 | 1764.2.k.c.1549.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.2.a.b.1.1 | ✓ | 1 | 28.19 | even | 6 | ||
588.2.a.e.1.1 | yes | 1 | 28.23 | odd | 6 | ||
588.2.i.a.361.1 | 2 | 28.11 | odd | 6 | |||
588.2.i.a.373.1 | 2 | 4.3 | odd | 2 | |||
588.2.i.g.361.1 | 2 | 28.3 | even | 6 | |||
588.2.i.g.373.1 | 2 | 28.27 | even | 2 | |||
1764.2.a.b.1.1 | 1 | 84.23 | even | 6 | |||
1764.2.a.i.1.1 | 1 | 84.47 | odd | 6 | |||
1764.2.k.c.361.1 | 2 | 84.59 | odd | 6 | |||
1764.2.k.c.1549.1 | 2 | 84.83 | odd | 2 | |||
1764.2.k.i.361.1 | 2 | 84.11 | even | 6 | |||
1764.2.k.i.1549.1 | 2 | 12.11 | even | 2 | |||
2352.2.a.j.1.1 | 1 | 7.2 | even | 3 | |||
2352.2.a.p.1.1 | 1 | 7.5 | odd | 6 | |||
2352.2.q.k.961.1 | 2 | 7.6 | odd | 2 | |||
2352.2.q.k.1537.1 | 2 | 7.3 | odd | 6 | |||
2352.2.q.p.961.1 | 2 | 1.1 | even | 1 | trivial | ||
2352.2.q.p.1537.1 | 2 | 7.4 | even | 3 | inner | ||
7056.2.a.n.1.1 | 1 | 21.2 | odd | 6 | |||
7056.2.a.bu.1.1 | 1 | 21.5 | even | 6 | |||
9408.2.a.l.1.1 | 1 | 56.51 | odd | 6 | |||
9408.2.a.bf.1.1 | 1 | 56.5 | odd | 6 | |||
9408.2.a.ca.1.1 | 1 | 56.37 | even | 6 | |||
9408.2.a.cu.1.1 | 1 | 56.19 | even | 6 |