Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(289,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 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("1344.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.bk (of order \(6\), degree \(2\), 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.865 |
Dual form | 1344.2.bk.d.289.1 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | −0.680989 | − | 0.732294i | \(-0.738450\pi\) |
0.293691 | + | 0.955901i | \(0.405116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.866025 | + | 0.500000i | 0.261116 | + | 0.150756i | 0.624844 | − | 0.780750i | \(-0.285163\pi\) |
−0.363727 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | − | 3.46410i | 0.485071 | − | 0.840168i | −0.514782 | − | 0.857321i | \(-0.672127\pi\) |
0.999853 | + | 0.0171533i | \(0.00546033\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.866025 | + | 2.50000i | −0.188982 | + | 0.545545i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.00000i | − | 0.185695i | −0.995680 | − | 0.0928477i | \(-0.970403\pi\) | ||
0.995680 | − | 0.0928477i | \(-0.0295970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50000 | − | 4.33013i | 0.449013 | − | 0.777714i | −0.549309 | − | 0.835619i | \(-0.685109\pi\) |
0.998322 | + | 0.0579057i | \(0.0184423\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.73205 | + | 2.00000i | 0.292770 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.92820 | + | 4.00000i | −1.13899 | + | 0.657596i | −0.946180 | − | 0.323640i | \(-0.895093\pi\) |
−0.192809 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | − | 1.73205i | 0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.866025 | − | 0.500000i | −0.129099 | − | 0.0745356i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | − | 6.92820i | −0.583460 | − | 1.01058i | −0.995066 | − | 0.0992202i | \(-0.968365\pi\) |
0.411606 | − | 0.911362i | \(-0.364968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.46410 | + | 2.00000i | −0.485071 | + | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.79423 | − | 4.50000i | −1.07062 | − | 0.618123i | −0.142269 | − | 0.989828i | \(-0.545440\pi\) |
−0.928351 | + | 0.371706i | \(0.878773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.866025 | + | 0.500000i | 0.112747 | + | 0.0650945i | 0.555313 | − | 0.831641i | \(-0.312598\pi\) |
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.92820 | + | 4.00000i | −0.887066 | + | 0.512148i | −0.872982 | − | 0.487753i | \(-0.837817\pi\) |
−0.0140840 | + | 0.999901i | \(0.504483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | − | 1.73205i | 0.251976 | − | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73205 | − | 1.00000i | −0.211604 | − | 0.122169i | 0.390453 | − | 0.920623i | \(-0.372318\pi\) |
−0.602056 | + | 0.798454i | \(0.705652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000i | 0.722315i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.0000 | −1.89885 | −0.949425 | − | 0.313993i | \(-0.898333\pi\) | ||||
−0.949425 | + | 0.313993i | \(0.898333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | − | 5.19615i | 0.351123 | − | 0.608164i | −0.635323 | − | 0.772246i | \(-0.719133\pi\) |
0.986447 | + | 0.164083i | \(0.0524664\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.46410 | − | 2.00000i | 0.400000 | − | 0.230940i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.866025 | − | 2.50000i | 0.0986928 | − | 0.284901i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 15.0000i | − | 1.64646i | −0.567705 | − | 0.823232i | \(-0.692169\pi\) | ||
0.567705 | − | 0.823232i | \(-0.307831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000i | 0.433861i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.500000 | + | 0.866025i | −0.0536056 | + | 0.0928477i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.00000 | + | 6.92820i | 0.423999 | + | 0.734388i | 0.996326 | − | 0.0856373i | \(-0.0272926\pi\) |
−0.572327 | + | 0.820025i | \(0.693959\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.19615 | − | 1.00000i | 0.544705 | − | 0.104828i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.33013 | + | 2.50000i | −0.449013 | + | 0.259238i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0000 | 1.11688 | 0.558440 | − | 0.829545i | \(-0.311400\pi\) | ||||
0.558440 | + | 0.829545i | \(0.311400\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000i | 0.100504i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.1244 | − | 7.00000i | −1.20642 | − | 0.696526i | −0.244443 | − | 0.969664i | \(-0.578605\pi\) |
−0.961975 | + | 0.273138i | \(0.911939\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.500000 | − | 2.59808i | −0.0487950 | − | 0.253546i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9904 | + | 7.50000i | −1.25583 | + | 0.725052i | −0.972261 | − | 0.233900i | \(-0.924851\pi\) |
−0.283567 | + | 0.958952i | \(0.591518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.73205 | − | 1.00000i | −0.165900 | − | 0.0957826i | 0.414751 | − | 0.909935i | \(-0.363869\pi\) |
−0.580651 | + | 0.814152i | \(0.697202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.19615 | + | 3.00000i | 0.484544 | + | 0.279751i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.73205 | + | 1.00000i | −0.160128 | + | 0.0924500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.0000 | − | 3.46410i | −0.916698 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | − | 8.66025i | −0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.73205 | + | 1.00000i | 0.156174 | + | 0.0901670i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 9.00000i | − | 0.804984i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0000 | 1.15356 | 0.576782 | − | 0.816898i | \(-0.304308\pi\) | ||||
0.576782 | + | 0.816898i | \(0.304308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59808 | + | 1.50000i | −0.226995 | + | 0.131056i | −0.609185 | − | 0.793028i | \(-0.708503\pi\) |
0.382190 | + | 0.924084i | \(0.375170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.00000i | − | 0.678551i | −0.940687 | − | 0.339276i | \(-0.889818\pi\) | ||
0.940687 | − | 0.339276i | \(-0.110182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000i | 0.673722i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | + | 1.73205i | −0.0836242 | + | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.500000 | + | 0.866025i | 0.0415227 | + | 0.0719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.92820 | + | 1.00000i | 0.571429 | + | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.66025 | − | 5.00000i | 0.709476 | − | 0.409616i | −0.101391 | − | 0.994847i | \(-0.532329\pi\) |
0.810867 | + | 0.585231i | \(0.198996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000i | 0.401610i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.46410 | + | 2.00000i | 0.276465 | + | 0.159617i | 0.631822 | − | 0.775113i | \(-0.282307\pi\) |
−0.355357 | + | 0.934731i | \(0.615641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.50000 | + | 7.79423i | 0.356873 | + | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | + | 10.3923i | −0.945732 | + | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0526 | + | 11.0000i | −1.49231 | + | 0.861586i | −0.999961 | − | 0.00881059i | \(-0.997195\pi\) |
−0.492350 | + | 0.870397i | \(0.663862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.866025 | + | 0.500000i | 0.0674200 | + | 0.0389249i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.5885 | − | 9.00000i | 1.18517 | − | 0.684257i | 0.227964 | − | 0.973670i | \(-0.426793\pi\) |
0.957205 | + | 0.289412i | \(0.0934598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | + | 3.46410i | 0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.500000 | − | 0.866025i | −0.0375823 | − | 0.0650945i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.3205 | + | 10.0000i | 1.29460 | + | 0.747435i | 0.979465 | − | 0.201613i | \(-0.0646184\pi\) |
0.315130 | + | 0.949048i | \(0.397952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0000i | 1.33793i | 0.743294 | + | 0.668965i | \(0.233262\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | − | 6.92820i | 0.294086 | − | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.46410 | − | 2.00000i | 0.253320 | − | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.59808 | + | 0.500000i | −0.188982 | + | 0.0363696i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.50000 | + | 11.2583i | −0.467880 | + | 0.810392i | −0.999326 | − | 0.0366998i | \(-0.988315\pi\) |
0.531446 | + | 0.847092i | \(0.321649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.00000i | 0.143223i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | + | 6.92820i | −0.283552 | + | 0.491127i | −0.972257 | − | 0.233915i | \(-0.924846\pi\) |
0.688705 | + | 0.725042i | \(0.258180\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | + | 1.73205i | 0.0705346 | + | 0.122169i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.59808 | + | 0.500000i | −0.182349 | + | 0.0350931i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.73205 | − | 1.00000i | 0.120972 | − | 0.0698430i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.0000i | − | 1.10149i | −0.834675 | − | 0.550743i | \(-0.814345\pi\) | ||
0.834675 | − | 0.550743i | \(-0.185655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.8564 | + | 8.00000i | 0.949425 | + | 0.548151i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.00000 | − | 1.73205i | −0.0681994 | − | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5000 | − | 4.33013i | −0.848555 | − | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.19615 | + | 3.00000i | −0.351123 | + | 0.202721i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.92820 | + | 4.00000i | 0.466041 | + | 0.269069i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.0000 | 1.40626 | 0.703132 | − | 0.711059i | \(-0.251784\pi\) | ||||
0.703132 | + | 0.711059i | \(0.251784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.59808 | − | 1.50000i | −0.172440 | − | 0.0995585i | 0.411296 | − | 0.911502i | \(-0.365076\pi\) |
−0.583736 | + | 0.811943i | \(0.698410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.66025 | − | 5.00000i | 0.572286 | − | 0.330409i | −0.185776 | − | 0.982592i | \(-0.559480\pi\) |
0.758062 | + | 0.652183i | \(0.226147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | + | 1.73205i | −0.131590 | + | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0000 | − | 20.7846i | −0.786146 | − | 1.36165i | −0.928312 | − | 0.371802i | \(-0.878740\pi\) |
0.142166 | − | 0.989843i | \(-0.454593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.92820 | + | 4.00000i | 0.451946 | + | 0.260931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.00000i | − | 0.0649570i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.50000 | − | 11.2583i | 0.418702 | − | 0.725213i | −0.577107 | − | 0.816668i | \(-0.695819\pi\) |
0.995809 | + | 0.0914555i | \(0.0291519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.33013 | − | 5.50000i | 0.276642 | − | 0.351382i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.50000 | + | 12.9904i | −0.475293 | + | 0.823232i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.0000i | − | 1.32551i | −0.748837 | − | 0.662754i | \(-0.769387\pi\) | ||
0.748837 | − | 0.662754i | \(-0.230613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00000 | − | 3.46410i | 0.125245 | − | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | + | 10.3923i | 0.374270 | + | 0.648254i | 0.990217 | − | 0.139533i | \(-0.0445601\pi\) |
−0.615948 | + | 0.787787i | \(0.711227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.8564 | + | 16.0000i | 0.860995 | + | 0.994192i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.866025 | − | 0.500000i | 0.0536056 | − | 0.0309492i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.00000 | + | 8.66025i | −0.308313 | + | 0.534014i | −0.977993 | − | 0.208635i | \(-0.933098\pi\) |
0.669680 | + | 0.742650i | \(0.266431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.00000i | − | 0.489592i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1865 | + | 10.5000i | 1.10885 | + | 0.640196i | 0.938532 | − | 0.345192i | \(-0.112186\pi\) |
0.170321 | + | 0.985389i | \(0.445520\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | + | 21.6506i | 0.759321 | + | 1.31518i | 0.943197 | + | 0.332233i | \(0.107802\pi\) |
−0.183876 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.00000 | − | 1.73205i | −0.302614 | − | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.46410 | + | 2.00000i | −0.208893 | + | 0.120605i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.7128 | + | 16.0000i | 1.66510 | + | 0.961347i | 0.970221 | + | 0.242222i | \(0.0778761\pi\) |
0.694881 | + | 0.719125i | \(0.255457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.0526 | − | 11.0000i | −1.13256 | − | 0.653882i | −0.187980 | − | 0.982173i | \(-0.560194\pi\) |
−0.944577 | + | 0.328291i | \(0.893527\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00000 | + | 5.19615i | 0.0590281 | + | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.52628 | − | 5.50000i | −0.558440 | − | 0.322416i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 31.0000i | − | 1.81104i | −0.424304 | − | 0.905520i | \(-0.639481\pi\) | ||
0.424304 | − | 0.905520i | \(-0.360519\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.00000 | −0.0582223 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.500000 | − | 0.866025i | 0.0290129 | − | 0.0502519i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.3923 | − | 6.00000i | 0.601003 | − | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.19615 | − | 1.00000i | 0.299501 | − | 0.0576390i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.00000 | + | 12.1244i | 0.402139 | + | 0.696526i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.00000 | − | 6.92820i | 0.229039 | − | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.0000i | − | 0.799022i | −0.916728 | − | 0.399511i | \(-0.869180\pi\) | ||
0.916728 | − | 0.399511i | \(-0.130820\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000i | 0.455104i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.00000 | + | 12.1244i | −0.396934 | + | 0.687509i | −0.993346 | − | 0.115169i | \(-0.963259\pi\) |
0.596412 | + | 0.802678i | \(0.296592\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50000 | + | 7.79423i | 0.254355 | + | 0.440556i | 0.964720 | − | 0.263278i | \(-0.0848035\pi\) |
−0.710365 | + | 0.703833i | \(0.751470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.866025 | + | 2.50000i | −0.0487950 | + | 0.140859i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.52628 | − | 5.50000i | 0.535049 | − | 0.308911i | −0.208021 | − | 0.978124i | \(-0.566702\pi\) |
0.743070 | + | 0.669214i | \(0.233369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.500000 | − | 0.866025i | 0.0279946 | − | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.0000 | 0.837218 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.92820 | − | 4.00000i | −0.384308 | − | 0.221880i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.00000 | + | 1.73205i | 0.0553001 | + | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | + | 13.8564i | −0.882109 | + | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7846 | + | 12.0000i | −1.14243 | + | 0.659580i | −0.947030 | − | 0.321145i | \(-0.895932\pi\) |
−0.195395 | + | 0.980725i | \(0.562599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.92820 | − | 4.00000i | −0.379663 | − | 0.219199i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.00000 | 0.109272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.0000 | −0.817102 | −0.408551 | − | 0.912735i | \(-0.633966\pi\) | ||||
−0.408551 | + | 0.912735i | \(0.633966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.73205 | − | 1.00000i | −0.0940721 | − | 0.0543125i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.33013 | − | 2.50000i | 0.234490 | − | 0.135383i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.00000 | − | 5.19615i | −0.161515 | − | 0.279751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | + | 12.0000i | 1.11578 | + | 0.644194i | 0.940319 | − | 0.340293i | \(-0.110526\pi\) |
0.175457 | + | 0.984487i | \(0.443860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.0000i | − | 0.749403i | −0.927146 | − | 0.374701i | \(-0.877745\pi\) | ||
0.927146 | − | 0.374701i | \(-0.122255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.8564 | − | 8.00000i | 0.735422 | − | 0.424596i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.92820 | + | 8.00000i | 0.366679 | + | 0.423405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.00000 | − | 5.19615i | −0.158334 | − | 0.274242i | 0.775934 | − | 0.630814i | \(-0.217279\pi\) |
−0.934268 | + | 0.356572i | \(0.883946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.0000i | 0.524864i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000i | 0.314054i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.50000 | − | 2.59808i | 0.0782994 | − | 0.135618i | −0.824217 | − | 0.566274i | \(-0.808384\pi\) |
0.902516 | + | 0.430656i | \(0.141718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | − | 1.73205i | −0.0520579 | − | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.79423 | + | 22.5000i | −0.404656 | + | 1.16814i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.9808 | − | 15.0000i | 1.34523 | − | 0.776671i | 0.357663 | − | 0.933851i | \(-0.383574\pi\) |
0.987570 | + | 0.157180i | \(0.0502403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.50000 | + | 7.79423i | −0.232379 | + | 0.402492i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.00000 | 0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000i | 0.513665i | 0.966456 | + | 0.256833i | \(0.0826790\pi\) | ||||
−0.966456 | + | 0.256833i | \(0.917321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.2583 | − | 6.50000i | −0.576782 | − | 0.333005i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | + | 20.7846i | 0.613171 | + | 1.06204i | 0.990702 | + | 0.136047i | \(0.0434398\pi\) |
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.500000 | + | 2.59808i | 0.0254824 | + | 0.132410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.73205 | + | 1.00000i | −0.0880451 | + | 0.0508329i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.5885 | − | 9.00000i | −0.790366 | − | 0.456318i | 0.0497253 | − | 0.998763i | \(-0.484165\pi\) |
−0.840091 | + | 0.542445i | \(0.817499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000 | 0.151330 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.866025 | − | 0.500000i | −0.0435745 | − | 0.0251577i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.3205 | + | 10.0000i | −0.869291 | + | 0.501886i | −0.867113 | − | 0.498112i | \(-0.834027\pi\) |
−0.00217869 | + | 0.999998i | \(0.500693\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.0000 | − | 24.2487i | −0.699127 | − | 1.21092i | −0.968770 | − | 0.247962i | \(-0.920239\pi\) |
0.269643 | − | 0.962960i | \(-0.413094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.66025 | + | 5.00000i | 0.431398 | + | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.50000 | + | 14.7224i | −0.420298 | + | 0.727977i | −0.995968 | − | 0.0897044i | \(-0.971408\pi\) |
0.575670 | + | 0.817682i | \(0.304741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.19615 | − | 3.00000i | 0.256307 | − | 0.147979i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.866025 | − | 2.50000i | 0.0426143 | − | 0.123017i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.50000 | + | 12.9904i | 0.368161 | + | 0.637673i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | + | 6.92820i | −0.195881 | + | 0.339276i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 28.0000i | − | 1.36789i | −0.729534 | − | 0.683945i | \(-0.760263\pi\) | ||
0.729534 | − | 0.683945i | \(-0.239737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.00000 | − | 6.92820i | 0.194487 | − | 0.336861i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | + | 13.8564i | 0.388057 | + | 0.672134i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.8564 | + | 16.0000i | 0.670559 | + | 0.774294i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.73205 | − | 1.00000i | 0.0836242 | − | 0.0482805i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.00000 | − | 1.73205i | 0.0481683 | − | 0.0834300i | −0.840936 | − | 0.541135i | \(-0.817995\pi\) |
0.889104 | + | 0.457705i | \(0.151328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 1.00000i | − | 0.0479463i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.50000 | − | 7.79423i | −0.214773 | − | 0.371998i | 0.738429 | − | 0.674331i | \(-0.235568\pi\) |
−0.953202 | + | 0.302333i | \(0.902235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.50000 | − | 4.33013i | −0.261905 | − | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.79423 | + | 4.50000i | −0.370315 | + | 0.213801i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.92820 | − | 4.00000i | −0.328428 | − | 0.189618i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.73205 | − | 1.00000i | −0.0815591 | − | 0.0470882i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.33013 | − | 2.50000i | 0.203447 | − | 0.117460i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | + | 3.46410i | −0.187523 | + | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | − | 21.6506i | −0.584725 | − | 1.01277i | −0.994910 | − | 0.100771i | \(-0.967869\pi\) |
0.410184 | − | 0.912003i | \(-0.365464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.46410 | − | 2.00000i | −0.161690 | − | 0.0933520i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0000i | 1.02464i | 0.858794 | + | 0.512321i | \(0.171214\pi\) | ||||
−0.858794 | + | 0.512321i | \(0.828786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.50000 | − | 4.33013i | 0.115935 | − | 0.200805i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.7128 | + | 16.0000i | −1.28240 | + | 0.740392i | −0.977286 | − | 0.211925i | \(-0.932027\pi\) |
−0.305110 | + | 0.952317i | \(0.598693\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.73205 | + | 5.00000i | −0.0799787 | + | 0.230879i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | − | 3.46410i | −0.0921551 | − | 0.159617i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 9.00000i | − | 0.412082i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.00000 | − | 1.73205i | 0.0456912 | − | 0.0791394i | −0.842275 | − | 0.539048i | \(-0.818784\pi\) |
0.887967 | + | 0.459908i | \(0.152118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | − | 13.8564i | −0.364769 | − | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.5885 | − | 3.00000i | 0.709299 | − | 0.136505i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.52628 | + | 5.50000i | −0.432566 | + | 0.249742i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.50000 | + | 6.06218i | −0.158600 | + | 0.274703i | −0.934364 | − | 0.356320i | \(-0.884031\pi\) |
0.775764 | + | 0.631023i | \(0.217365\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.0000 | 0.994874 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00000i | 0.135388i | 0.997706 | + | 0.0676941i | \(0.0215642\pi\) | ||||
−0.997706 | + | 0.0676941i | \(0.978436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.46410 | − | 2.00000i | −0.156015 | − | 0.0900755i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.500000 | − | 0.866025i | −0.0224733 | − | 0.0389249i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | + | 41.5692i | 0.358849 | + | 1.86463i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3205 | + | 10.0000i | −0.775372 | + | 0.447661i | −0.834788 | − | 0.550572i | \(-0.814410\pi\) |
0.0594153 | + | 0.998233i | \(0.481076\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.5885 | + | 9.00000i | 0.696441 | + | 0.402090i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.79423 | − | 4.50000i | −0.346154 | − | 0.199852i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.79423 | + | 4.50000i | −0.345473 | + | 0.199459i | −0.662690 | − | 0.748894i | \(-0.730585\pi\) |
0.317217 | + | 0.948353i | \(0.397252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0000 | − | 5.19615i | −0.663561 | − | 0.229864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.92820 | + | 4.00000i | 0.305293 | + | 0.176261i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.00000i | − | 0.351840i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.0000 | −0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | + | 15.5885i | −0.394297 | + | 0.682943i | −0.993011 | − | 0.118020i | \(-0.962345\pi\) |
0.598714 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.4449 | − | 17.0000i | 1.28753 | − | 0.743358i | 0.309320 | − | 0.950958i | \(-0.399899\pi\) |
0.978214 | + | 0.207600i | \(0.0665652\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.92820 | − | 8.00000i | −0.302372 | − | 0.349149i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.0000 | − | 17.3205i | −0.435607 | − | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.00000i | 0.0433963i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.00000i | − | 0.173259i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.50000 | − | 12.9904i | 0.324253 | − | 0.561623i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.0000 | − | 17.3205i | −0.431532 | − | 0.747435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.92820 | − | 1.00000i | −0.298419 | − | 0.0430730i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.9090 | + | 19.0000i | −1.41487 | + | 0.816874i | −0.995842 | − | 0.0911008i | \(-0.970961\pi\) |
−0.419025 | + | 0.907975i | \(0.637628\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.00000 | − | 15.5885i | 0.386227 | − | 0.668965i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.0000i | − | 0.684111i | −0.939680 | − | 0.342055i | \(-0.888877\pi\) | ||
0.939680 | − | 0.342055i | \(-0.111123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.92820 | − | 4.00000i | −0.295689 | − | 0.170716i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000 | − | 1.73205i | 0.0850487 | − | 0.0736543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.92820 | + | 4.00000i | −0.294086 | + | 0.169791i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.9186 | + | 11.5000i | 0.843978 | + | 0.487271i | 0.858614 | − | 0.512622i | \(-0.171326\pi\) |
−0.0146368 | + | 0.999893i | \(0.504659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.1865 | − | 10.5000i | −0.766471 | − | 0.442522i | 0.0651433 | − | 0.997876i | \(-0.479250\pi\) |
−0.831614 | + | 0.555354i | \(0.812583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.73205 | + | 1.00000i | −0.0728679 | + | 0.0420703i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.50000 | + | 0.866025i | 0.104990 | + | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.0000 | − | 34.6410i | −0.838444 | − | 1.45223i | −0.891196 | − | 0.453619i | \(-0.850133\pi\) |
0.0527519 | − | 0.998608i | \(-0.483201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.3923 | + | 6.00000i | 0.434904 | + | 0.251092i | 0.701434 | − | 0.712735i | \(-0.252544\pi\) |
−0.266529 | + | 0.963827i | \(0.585877\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 8.00000i | − | 0.334205i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000 | 1.00087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50000 | − | 14.7224i | 0.353860 | − | 0.612903i | −0.633062 | − | 0.774101i | \(-0.718202\pi\) |
0.986922 | + | 0.161198i | \(0.0515357\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.2583 | − | 6.50000i | 0.467880 | − | 0.270131i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.9711 | + | 7.50000i | −1.61680 | + | 0.311152i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | − | 1.73205i | 0.0413449 | − | 0.0716115i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 47.0000i | − | 1.93990i | −0.243309 | − | 0.969949i | \(-0.578233\pi\) | ||
0.243309 | − | 0.969949i | \(-0.421767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00000 | + | 15.5885i | −0.370211 | + | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.0000 | + | 19.0526i | 0.451716 | + | 0.782395i | 0.998493 | − | 0.0548835i | \(-0.0174787\pi\) |
−0.546777 | + | 0.837278i | \(0.684145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3923 | − | 2.00000i | 0.426043 | − | 0.0819920i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.92820 | − | 4.00000i | 0.283552 | − | 0.163709i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0000 | − | 25.9808i | 0.612883 | − | 1.06155i | −0.377869 | − | 0.925859i | \(-0.623343\pi\) |
0.990752 | − | 0.135686i | \(-0.0433238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.0000 | 1.01977 | 0.509886 | − | 0.860242i | \(-0.329688\pi\) | ||||
0.509886 | + | 0.860242i | \(0.329688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.00000i | − | 0.0814463i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.66025 | + | 5.00000i | 0.352089 | + | 0.203279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.5000 | − | 38.9711i | −0.913247 | − | 1.58179i | −0.809448 | − | 0.587192i | \(-0.800234\pi\) |
−0.103799 | − | 0.994598i | \(-0.533100\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.50000 | + | 0.866025i | 0.101305 | + | 0.0350931i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.8564 | − | 8.00000i | 0.560570 | − | 0.323645i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.5167 | − | 13.0000i | −0.909439 | − | 0.525065i | −0.0291886 | − | 0.999574i | \(-0.509292\pi\) |
−0.880251 | + | 0.474509i | \(0.842626\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0000 | 0.644136 | 0.322068 | − | 0.946717i | \(-0.395622\pi\) | ||||
0.322068 | + | 0.946717i | \(0.395622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.7128 | − | 16.0000i | −1.11387 | − | 0.643094i | −0.174042 | − | 0.984738i | \(-0.555683\pi\) |
−0.939829 | + | 0.341644i | \(0.889016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.19615 | + | 3.00000i | −0.208514 | + | 0.120386i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.0000 | − | 13.8564i | 0.641026 | − | 0.555145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.0000i | 1.27592i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.00000 | −0.199047 | −0.0995234 | − | 0.995035i | \(-0.531732\pi\) | ||||
−0.0995234 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.00000 | + | 13.8564i | −0.317971 | + | 0.550743i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.2583 | + | 6.50000i | −0.446773 | + | 0.257945i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.19615 | − | 13.0000i | −0.205879 | − | 0.515079i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | − | 13.8564i | −0.316475 | − | 0.548151i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | − | 3.46410i | 0.0789953 | − | 0.136824i | −0.823821 | − | 0.566849i | \(-0.808162\pi\) |
0.902817 | + | 0.430026i | \(0.141495\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0000i | 0.552106i | 0.961142 | + | 0.276053i | \(0.0890266\pi\) | ||||
−0.961142 | + | 0.276053i | \(0.910973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.00000i | 0.0787499i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000 | − | 10.3923i | 0.235884 | − | 0.408564i | −0.723645 | − | 0.690172i | \(-0.757535\pi\) |
0.959529 | + | 0.281609i | \(0.0908680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.500000 | + | 0.866025i | 0.0196267 | + | 0.0339945i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.66025 | + | 10.0000i | 0.339422 | + | 0.391931i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.9904 | + | 7.50000i | −0.508353 | + | 0.293498i | −0.732156 | − | 0.681137i | \(-0.761486\pi\) |
0.223803 | + | 0.974634i | \(0.428153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.50000 | − | 2.59808i | 0.0586098 | − | 0.101515i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.00000i | − | 0.311636i | −0.987786 | − | 0.155818i | \(-0.950199\pi\) | ||
0.987786 | − | 0.155818i | \(-0.0498013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.9808 | + | 15.0000i | 1.01053 | + | 0.583432i | 0.911348 | − | 0.411636i | \(-0.135043\pi\) |
0.0991864 | + | 0.995069i | \(0.468376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.00000 | − | 6.92820i | −0.155347 | − | 0.269069i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.19615 | + | 3.00000i | −0.201196 | + | 0.116160i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.1865 | − | 10.5000i | −0.703132 | − | 0.405953i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.00000 | −0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.0000 | −1.50334 | −0.751670 | − | 0.659540i | \(-0.770751\pi\) | ||||
−0.751670 | + | 0.659540i | \(0.770751\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.46410 | + | 2.00000i | 0.133333 | + | 0.0769800i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.5788 | + | 16.5000i | −1.09837 | + | 0.634147i | −0.935793 | − | 0.352549i | \(-0.885315\pi\) |
−0.162581 | + | 0.986695i | \(0.551982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.50000 | − | 28.5788i | −0.211071 | − | 1.09676i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50000 | + | 2.59808i | 0.0574801 | + | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.2391 | + | 21.5000i | 1.42491 | + | 0.822675i | 0.996713 | − | 0.0810089i | \(-0.0258142\pi\) |
0.428201 | + | 0.903684i | \(0.359148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.00000i | − | 0.229248i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.00000 | − | 15.5885i | 0.342873 | − | 0.593873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.66025 | + | 5.00000i | −0.329452 | + | 0.190209i | −0.655598 | − | 0.755110i | \(-0.727583\pi\) |
0.326146 | + | 0.945319i | \(0.394250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.59808 | − | 0.500000i | 0.0986928 | − | 0.0189934i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | + | 6.92820i | 0.151729 | + | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | + | 6.92820i | −0.151511 | + | 0.262424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0000i | 0.907763i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.0000i | 1.47301i | 0.676432 | + | 0.736505i | \(0.263525\pi\) | ||||
−0.676432 | + | 0.736505i | \(0.736475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.00000 | − | 6.92820i | −0.150649 | − | 0.260931i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.1244 | + | 35.0000i | −0.455983 | + | 1.31631i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.8564 | + | 8.00000i | −0.520388 | + | 0.300446i | −0.737093 | − | 0.675791i | \(-0.763802\pi\) |
0.216705 | + | 0.976237i | \(0.430469\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.500000 | + | 0.866025i | −0.0187515 | + | 0.0324785i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.0000 | −1.12351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.00000i | − | 0.0747958i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.73205 | − | 1.00000i | −0.0646846 | − | 0.0373457i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.0000 | − | 24.2487i | −0.522112 | − | 0.904324i | −0.999669 | − | 0.0257237i | \(-0.991811\pi\) |
0.477557 | − | 0.878601i | \(-0.341522\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | + | 13.8564i | −0.595871 | + | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.2583 | + | 6.50000i | −0.418702 | + | 0.241738i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.46410 | + | 2.00000i | 0.128654 | + | 0.0742781i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.0000 | −0.407967 | −0.203984 | − | 0.978974i | \(-0.565389\pi\) | ||||
−0.203984 | + | 0.978974i | \(0.565389\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.92820 | + | 4.00000i | 0.256249 | + | 0.147945i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.5167 | − | 13.0000i | 0.831672 | − | 0.480166i | −0.0227529 | − | 0.999741i | \(-0.507243\pi\) |
0.854425 | + | 0.519575i | \(0.173910\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.50000 | + | 2.59808i | −0.239756 | + | 0.0958315i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.00000 | − | 1.73205i | −0.0368355 | − | 0.0638009i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.3205 | − | 10.0000i | −0.637145 | − | 0.367856i | 0.146369 | − | 0.989230i | \(-0.453241\pi\) |
−0.783514 | + | 0.621374i | \(0.786575\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.0000 | 1.39408 | 0.697042 | − | 0.717030i | \(-0.254499\pi\) | ||||
0.697042 | + | 0.717030i | \(0.254499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.00000 | + | 8.66025i | −0.183186 | + | 0.317287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.9904 | − | 7.50000i | 0.475293 | − | 0.274411i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.9808 | + | 30.0000i | 0.949316 | + | 1.09618i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5000 | − | 38.9711i | −0.821037 | − | 1.42208i | −0.904911 | − | 0.425601i | \(-0.860063\pi\) |
0.0838743 | − | 0.996476i | \(-0.473271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.5000 | + | 18.1865i | −0.382641 | + | 0.662754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5.00000i | − | 0.181969i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0000i | 1.01768i | 0.860862 | + | 0.508839i | \(0.169925\pi\) | ||||
−0.860862 | + | 0.508839i | \(0.830075\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.00000 | + | 5.19615i | −0.108893 | + | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.73205 | + | 5.00000i | −0.0627044 | + | 0.181012i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.46410 | + | 2.00000i | −0.125245 | + | 0.0723102i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.00000 | + | 1.73205i | −0.0361079 | + | 0.0625407i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.0000 | 1.76699 | 0.883493 | − | 0.468445i | \(-0.155186\pi\) | ||||
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 12.0000i | − | 0.432169i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.7654 | − | 27.0000i | −1.68203 | − | 0.971123i | −0.960307 | − | 0.278944i | \(-0.910016\pi\) |
−0.721726 | − | 0.692179i | \(-0.756651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0000 | + | 17.3205i | 0.359211 | + | 0.622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.00000 | − | 20.7846i | −0.143499 | − | 0.745644i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8564 | − | 8.00000i | −0.495821 | − | 0.286263i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.92820 | − | 4.00000i | −0.246964 | − | 0.142585i | 0.371409 | − | 0.928469i | \(-0.378875\pi\) |
−0.618373 | + | 0.785885i | \(0.712208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.66025 | − | 5.00000i | 0.308313 | − | 0.178005i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.00000 | − | 5.19615i | −0.0355559 | − | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | − | 13.8564i | −0.284088 | − | 0.492055i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.79423 | − | 4.50000i | −0.276433 | − | 0.159599i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.0000i | 1.31061i | 0.755366 | + | 0.655304i | \(0.227459\pi\) | ||||
−0.755366 | + | 0.655304i | \(0.772541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.00000 | + | 6.92820i | −0.141333 | + | 0.244796i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.19615 | − | 3.00000i | 0.183368 | − | 0.105868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.19615 | − | 15.0000i | 0.183140 | − | 0.528681i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.5000 | − | 18.1865i | −0.369618 | − | 0.640196i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.0000 | − | 41.5692i | 0.843795 | − | 1.46150i | −0.0428684 | − | 0.999081i | \(-0.513650\pi\) |
0.886664 | − | 0.462415i | \(-0.153017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000i | 1.05344i | 0.850038 | + | 0.526721i | \(0.176579\pi\) | ||||
−0.850038 | + | 0.526721i | \(0.823421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 25.0000i | − | 0.876788i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.0000 | − | 19.0526i | 0.385313 | − | 0.667382i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.46410 | + | 4.00000i | 0.121046 | + | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.7750 | + | 19.5000i | −1.17876 | + | 0.680555i | −0.955726 | − | 0.294257i | \(-0.904928\pi\) |
−0.223029 | + | 0.974812i | \(0.571594\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | − | 27.7128i | 0.557725 | − | 0.966008i | −0.439961 | − | 0.898017i | \(-0.645008\pi\) |
0.997686 | − | 0.0679910i | \(-0.0216589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.0000i | 0.521601i | 0.965393 | + | 0.260801i | \(0.0839865\pi\) | ||||
−0.965393 | + | 0.260801i | \(0.916014\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.5692 | − | 24.0000i | −1.44376 | − | 0.833554i | −0.445661 | − | 0.895202i | \(-0.647031\pi\) |
−0.998098 | + | 0.0616475i | \(0.980365\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0000 | − | 27.7128i | −0.555034 | − | 0.961347i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00000 | + | 27.7128i | −0.138592 | + | 0.960192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.5885 | − | 9.00000i | 0.539461 | − | 0.311458i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.33013 | − | 2.50000i | −0.149671 | − | 0.0864126i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.0000 | 1.65714 | 0.828572 | − | 0.559883i | \(-0.189154\pi\) | ||||
0.828572 | + | 0.559883i | \(0.189154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.0000 | 0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.5167 | − | 13.0000i | −0.775515 | − | 0.447744i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.79423 | + | 4.50000i | −0.268130 | + | 0.154805i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0000 | + | 17.3205i | −0.687208 | + | 0.595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.0000 | + | 19.0526i | 0.377519 | + | 0.653882i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.5692 | + | 24.0000i | 1.42497 | + | 0.822709i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.00000i | − | 0.205436i | −0.994711 | − | 0.102718i | \(-0.967246\pi\) | ||
0.994711 | − | 0.102718i | \(-0.0327539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.00000 | + | 6.92820i | −0.136637 | + | 0.236663i | −0.926222 | − | 0.376979i | \(-0.876963\pi\) |
0.789584 | + | 0.613642i | \(0.210296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1244 | − | 7.00000i | 0.413678 | − | 0.238837i | −0.278691 | − | 0.960381i | \(-0.589901\pi\) |
0.692369 | + | 0.721544i | \(0.256567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.73205 | − | 5.00000i | 0.0590281 | − | 0.170400i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.0000 | + | 31.1769i | 0.612727 | + | 1.06127i | 0.990779 | + | 0.135490i | \(0.0432609\pi\) |
−0.378052 | + | 0.925785i | \(0.623406\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.00000 | + | 15.5885i | −0.306009 | + | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.00000i | 0.0339227i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | − | 3.46410i | 0.0677674 | − | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.50000 | + | 9.52628i | 0.186147 | + | 0.322416i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.3827 | + | 4.50000i | −0.790479 | + | 0.152128i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.7128 | − | 16.0000i | 0.935795 | − | 0.540282i | 0.0471555 | − | 0.998888i | \(-0.484984\pi\) |
0.888640 | + | 0.458606i | \(0.151651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.5000 | + | 26.8468i | −0.522802 | + | 0.905520i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.00000i | − | 0.201916i | −0.994891 | − | 0.100958i | \(-0.967809\pi\) | ||
0.994891 | − | 0.100958i | \(-0.0321908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.866025 | + | 0.500000i | 0.0291111 | + | 0.0168073i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.00000 | + | 5.19615i | 0.100730 | + | 0.174470i | 0.911986 | − | 0.410222i | \(-0.134549\pi\) |
−0.811256 | + | 0.584692i | \(0.801215\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.50000 | − | 33.7750i | −0.218003 | − | 1.13278i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.866025 | + | 0.500000i | −0.0290129 | + | 0.0167506i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.33013 | − | 2.50000i | −0.144418 | − | 0.0833797i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.1769 | + | 18.0000i | −1.03865 | + | 0.599667i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.00000 | − | 1.73205i | −0.166390 | − | 0.0576390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.00000 | − | 15.5885i | −0.299170 | − | 0.518178i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.5167 | − | 13.0000i | −0.747653 | − | 0.431658i | 0.0771920 | − | 0.997016i | \(-0.475405\pi\) |
−0.824845 | + | 0.565358i | \(0.808738\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 14.0000i | − | 0.464351i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.0000 | −1.06021 | −0.530104 | − | 0.847933i | \(-0.677847\pi\) | ||||
−0.530104 | + | 0.847933i | \(0.677847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.50000 | − | 12.9904i | 0.248214 | − | 0.429919i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.92820 | + | 4.00000i | −0.229039 | + | 0.132236i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.19615 | + | 6.00000i | 0.171592 | + | 0.198137i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000 | + | 34.6410i | 0.659739 | + | 1.14270i | 0.980683 | + | 0.195603i | \(0.0626666\pi\) |
−0.320944 | + | 0.947098i | \(0.604000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.00000 | + | 12.1244i | −0.230658 | + | 0.399511i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 32.0000i | − | 1.05329i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 32.0000i | − | 1.05215i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.00000 | − | 6.92820i | 0.131377 | − | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.0000 | − | 19.0526i | −0.360898 | − | 0.625094i | 0.627211 | − | 0.778850i | \(-0.284197\pi\) |
−0.988109 | + | 0.153755i | \(0.950863\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.1244 | − | 7.00000i | 0.396934 | − | 0.229170i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.00000 | + | 3.46410i | −0.0654070 | + | 0.113288i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.00000 | 0.0326686 | 0.0163343 | − | 0.999867i | \(-0.494800\pi\) | ||||
0.0163343 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 9.00000i | − | 0.293704i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.3109 | + | 17.5000i | 0.988107 | + | 0.570484i | 0.904708 | − | 0.426033i | \(-0.140089\pi\) |
0.0833989 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | + | 10.3923i | 0.195387 | + | 0.338420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | − | 1.73205i | 0.0650600 | − | 0.0563436i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2487 | − | 14.0000i | 0.787977 | − | 0.454939i | −0.0512727 | − | 0.998685i | \(-0.516328\pi\) |
0.839250 | + | 0.543746i | \(0.182994\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.3923 | + | 6.00000i | 0.337348 | + | 0.194768i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.0000 | −0.356699 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.92820 | − | 4.00000i | −0.224191 | − | 0.129437i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.866025 | + | 0.500000i | −0.0279946 | + | 0.0161627i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.0000 | + | 5.19615i | 0.484375 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.9904 | − | 7.50000i | −0.418609 | − | 0.241684i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 13.0000i | − | 0.418485i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.0000 | −0.739630 | −0.369815 | − | 0.929105i | \(-0.620579\pi\) | ||||
−0.369815 | + | 0.929105i | \(0.620579\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.9904 | + | 7.50000i | −0.416881 | + | 0.240686i | −0.693742 | − | 0.720224i | \(-0.744039\pi\) |
0.276861 | + | 0.960910i | \(0.410706\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.7846 | + | 4.00000i | −0.666324 | + | 0.128234i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.00000 | + | 6.92820i | 0.128103 | + | 0.221880i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0000 | − | 36.3731i | 0.671850 | − | 1.16368i | −0.305530 | − | 0.952183i | \(-0.598833\pi\) |
0.977379 | − | 0.211495i | \(-0.0678332\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000i | 0.255681i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.00000i | − | 0.0638551i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.00000 | − | 12.1244i | 0.223265 | − | 0.386707i | −0.732532 | − | 0.680732i | \(-0.761662\pi\) |
0.955798 | + | 0.294025i | \(0.0949950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | + | 15.5885i | 0.286764 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.7846 | − | 4.00000i | 0.661581 | − | 0.127321i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.3923 | − | 6.00000i | 0.330456 | − | 0.190789i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.5000 | + | 37.2391i | −0.682970 | + | 1.18294i | 0.291100 | + | 0.956693i | \(0.405979\pi\) |
−0.974070 | + | 0.226246i | \(0.927355\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.0000 | 0.761617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8.00000i | − | 0.253617i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.73205 | + | 1.00000i | 0.0548546 | + | 0.0316703i | 0.527176 | − | 0.849756i | \(-0.323251\pi\) |
−0.472322 | + | 0.881426i | \(0.656584\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | + | 6.92820i | 0.126554 | + | 0.219199i |
(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 | 1344.2.bk.d.865.1 | yes | 4 | |
4.3 | odd | 2 | 1344.2.bk.e.865.2 | yes | 4 | ||
7.2 | even | 3 | inner | 1344.2.bk.d.289.2 | yes | 4 | |
8.3 | odd | 2 | 1344.2.bk.e.865.1 | yes | 4 | ||
8.5 | even | 2 | inner | 1344.2.bk.d.865.2 | yes | 4 | |
28.23 | odd | 6 | 1344.2.bk.e.289.1 | yes | 4 | ||
56.37 | even | 6 | inner | 1344.2.bk.d.289.1 | ✓ | 4 | |
56.51 | odd | 6 | 1344.2.bk.e.289.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.bk.d.289.1 | ✓ | 4 | 56.37 | even | 6 | inner | |
1344.2.bk.d.289.2 | yes | 4 | 7.2 | even | 3 | inner | |
1344.2.bk.d.865.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1344.2.bk.d.865.2 | yes | 4 | 8.5 | even | 2 | inner | |
1344.2.bk.e.289.1 | yes | 4 | 28.23 | odd | 6 | ||
1344.2.bk.e.289.2 | yes | 4 | 56.51 | odd | 6 | ||
1344.2.bk.e.865.1 | yes | 4 | 8.3 | odd | 2 | ||
1344.2.bk.e.865.2 | yes | 4 | 4.3 | odd | 2 |