Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(271,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cs (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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.703 |
Dual form | 1008.2.cs.m.271.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 1.73205i | 1.34164 | − | 0.774597i | 0.354593 | − | 0.935021i | \(-0.384620\pi\) |
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | − | 1.73205i | −0.904534 | − | 0.522233i | −0.0258656 | − | 0.999665i | \(-0.508234\pi\) |
−0.878668 | + | 0.477432i | \(0.841568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.19615i | 1.44115i | 0.693375 | + | 0.720577i | \(0.256123\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | + | 3.46410i | 1.45521 | + | 0.840168i | 0.998770 | − | 0.0495842i | \(-0.0157896\pi\) |
0.456444 | + | 0.889752i | \(0.349123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.50000 | − | 6.06218i | 0.700000 | − | 1.21244i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 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 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | + | 8.66025i | 0.507093 | + | 1.46385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.500000 | − | 0.866025i | −0.0821995 | − | 0.142374i | 0.821995 | − | 0.569495i | \(-0.192861\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.3923i | − | 1.62301i | −0.584349 | − | 0.811503i | \(-0.698650\pi\) | ||
0.584349 | − | 0.811503i | \(-0.301350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.73205i | − | 0.264135i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) | ||
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | −1.61808 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.00000 | + | 15.5885i | 1.11631 | + | 1.93351i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50000 | − | 0.866025i | −0.183254 | − | 0.105802i | 0.405567 | − | 0.914066i | \(-0.367074\pi\) |
−0.588821 | + | 0.808264i | \(0.700408\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.46410i | − | 0.411113i | −0.978645 | − | 0.205557i | \(-0.934100\pi\) | ||
0.978645 | − | 0.205557i | \(-0.0659005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.50000 | + | 4.33013i | 0.877809 | + | 0.506803i | 0.869935 | − | 0.493166i | \(-0.164160\pi\) |
0.00787336 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | − | 6.92820i | 0.683763 | − | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5000 | − | 7.79423i | 1.51887 | − | 0.876919i | 0.519115 | − | 0.854704i | \(-0.326261\pi\) |
0.999753 | − | 0.0222151i | \(-0.00707187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.0000 | 2.60317 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | + | 3.46410i | −0.635999 | + | 0.367194i | −0.783072 | − | 0.621932i | \(-0.786348\pi\) |
0.147073 | + | 0.989126i | \(0.453015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.5000 | − | 2.59808i | −1.41518 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.0000 | + | 12.1244i | 2.15455 | + | 1.24393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.92820i | − | 0.703452i | −0.936103 | − | 0.351726i | \(-0.885595\pi\) | ||
0.936103 | − | 0.351726i | \(-0.114405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 1.73205i | 0.298511 | + | 0.172345i | 0.641774 | − | 0.766894i | \(-0.278199\pi\) |
−0.343263 | + | 0.939239i | \(0.611532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.50000 | + | 4.33013i | 0.246332 | + | 0.426660i | 0.962505 | − | 0.271263i | \(-0.0874412\pi\) |
−0.716173 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | + | 3.46410i | −0.580042 | + | 0.334887i | −0.761150 | − | 0.648576i | \(-0.775365\pi\) |
0.181108 | + | 0.983463i | \(0.442032\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | + | 4.33013i | −0.239457 | + | 0.414751i | −0.960558 | − | 0.278078i | \(-0.910303\pi\) |
0.721102 | + | 0.692829i | \(0.243636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.0000 | + | 13.8564i | −1.10004 | + | 1.27021i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.5885i | 1.38325i | 0.722256 | + | 0.691626i | \(0.243105\pi\) | ||||
−0.722256 | + | 0.691626i | \(0.756895\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | − | 15.5885i | −0.786334 | − | 1.36197i | −0.928199 | − | 0.372084i | \(-0.878643\pi\) |
0.141865 | − | 0.989886i | \(-0.454690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5000 | + | 6.06218i | −1.51744 | + | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.00000 | − | 15.5885i | 0.752618 | − | 1.30357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | − | 10.3923i | −0.491539 | − | 0.851371i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.00000 | + | 5.19615i | 0.732410 | + | 0.422857i | 0.819303 | − | 0.573361i | \(-0.194361\pi\) |
−0.0868934 | + | 0.996218i | \(0.527694\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 17.3205i | − | 1.39122i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0000 | − | 6.92820i | −0.957704 | − | 0.552931i | −0.0622385 | − | 0.998061i | \(-0.519824\pi\) |
−0.895466 | + | 0.445130i | \(0.853157\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.00000 | − | 1.73205i | 0.234978 | − | 0.135665i | −0.377888 | − | 0.925851i | \(-0.623350\pi\) |
0.612866 | + | 0.790186i | \(0.290016\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | 0.464294 | 0.232147 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232147 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.0000 | −1.07692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.0000 | + | 12.1244i | 1.05830 | + | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.0000 | − | 8.66025i | −1.12115 | − | 0.647298i | −0.179458 | − | 0.983766i | \(-0.557434\pi\) |
−0.941695 | + | 0.336468i | \(0.890768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5885i | 1.15868i | 0.815086 | + | 0.579340i | \(0.196690\pi\) | ||||
−0.815086 | + | 0.579340i | \(0.803310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | − | 1.73205i | −0.220564 | − | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | − | 20.7846i | −0.877527 | − | 1.51992i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 1.73205i | −0.217072 | + | 0.125327i | −0.604594 | − | 0.796534i | \(-0.706665\pi\) |
0.387522 | + | 0.921861i | \(0.373331\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | − | 13.8564i | 0.567105 | − | 0.982255i | −0.429745 | − | 0.902950i | \(-0.641397\pi\) |
0.996850 | − | 0.0793045i | \(-0.0252700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0000 | − | 31.1769i | −1.25717 | − | 2.17749i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 24.2487i | − | 1.67732i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.3205i | − | 1.19239i | −0.802839 | − | 0.596196i | \(-0.796678\pi\) | ||
0.802839 | − | 0.596196i | \(-0.203322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | − | 5.19615i | −0.204598 | − | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | + | 8.66025i | 0.678844 | + | 0.587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0000 | + | 31.1769i | −1.21081 | + | 2.09719i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0000 | − | 25.9808i | 0.995585 | − | 1.72440i | 0.416503 | − | 0.909134i | \(-0.363255\pi\) |
0.579082 | − | 0.815270i | \(-0.303411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.50000 | − | 0.866025i | 0.0991228 | − | 0.0572286i | −0.449619 | − | 0.893220i | \(-0.648440\pi\) |
0.548742 | + | 0.835992i | \(0.315107\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | − | 15.5885i | −0.589610 | − | 1.02123i | −0.994283 | − | 0.106773i | \(-0.965948\pi\) |
0.404674 | − | 0.914461i | \(-0.367385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0000 | + | 10.3923i | 1.17419 | + | 0.677919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 17.3205i | − | 1.12037i | −0.828367 | − | 0.560185i | \(-0.810730\pi\) | ||
0.828367 | − | 0.560185i | \(-0.189270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0000 | − | 6.92820i | −0.772988 | − | 0.446285i | 0.0609515 | − | 0.998141i | \(-0.480586\pi\) |
−0.833939 | + | 0.551856i | \(0.813920\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.0000 | + | 3.46410i | −1.53330 | + | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.5000 | + | 18.1865i | −2.00430 | + | 1.15718i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.00000 | − | 5.19615i | 0.561405 | − | 0.324127i | −0.192304 | − | 0.981335i | \(-0.561596\pi\) |
0.753709 | + | 0.657208i | \(0.228263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50000 | − | 0.866025i | 0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.0000 | + | 13.8564i | 1.47990 | + | 0.854423i | 0.999741 | − | 0.0227570i | \(-0.00724440\pi\) |
0.480162 | + | 0.877180i | \(0.340578\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.0000 | + | 15.5885i | 1.64622 | + | 0.950445i | 0.978556 | + | 0.205982i | \(0.0660387\pi\) |
0.667663 | + | 0.744463i | \(0.267295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.0000 | + | 12.1244i | −1.26635 | + | 0.731126i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50000 | − | 14.7224i | 0.510716 | − | 0.884585i | −0.489207 | − | 0.872167i | \(-0.662714\pi\) |
0.999923 | − | 0.0124177i | \(-0.00395278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.50000 | + | 4.33013i | −0.148610 | + | 0.257399i | −0.930714 | − | 0.365748i | \(-0.880813\pi\) |
0.782104 | + | 0.623148i | \(0.214146\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.0000 | + | 5.19615i | 1.59376 | + | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5000 | + | 26.8468i | 0.911765 | + | 1.57922i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.7846i | 1.21425i | 0.794606 | + | 0.607125i | \(0.207677\pi\) | ||||
−0.794606 | + | 0.607125i | \(0.792323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.50000 | + | 0.866025i | 0.259376 | + | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.0000 | −1.42683 | −0.713413 | − | 0.700744i | \(-0.752851\pi\) | ||||
−0.713413 | + | 0.700744i | \(0.752851\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00000 | + | 15.5885i | −0.510343 | + | 0.883940i | 0.489585 | + | 0.871956i | \(0.337148\pi\) |
−0.999928 | + | 0.0119847i | \(0.996185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5000 | − | 7.79423i | 0.763065 | − | 0.440556i | −0.0673300 | − | 0.997731i | \(-0.521448\pi\) |
0.830395 | + | 0.557175i | \(0.188115\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | − | 10.3923i | −0.336994 | − | 0.583690i | 0.646872 | − | 0.762598i | \(-0.276077\pi\) |
−0.983866 | + | 0.178908i | \(0.942743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 48.4974i | 2.69847i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.5000 | + | 18.1865i | 1.74731 | + | 1.00881i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.0000 | + | 5.19615i | −0.826977 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.50000 | + | 4.33013i | −0.412237 | + | 0.238005i | −0.691751 | − | 0.722137i | \(-0.743160\pi\) |
0.279513 | + | 0.960142i | \(0.409827\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0000 | −1.03500 | −0.517498 | − | 0.855684i | \(-0.673136\pi\) | ||||
−0.517498 | + | 0.855684i | \(0.673136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.0000 | + | 8.66025i | −0.812296 | + | 0.468979i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.0000 | + | 17.3205i | 1.61048 | + | 0.929814i | 0.989258 | + | 0.146183i | \(0.0466988\pi\) |
0.621227 | + | 0.783631i | \(0.286635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.8564i | − | 0.741716i | −0.928689 | − | 0.370858i | \(-0.879064\pi\) | ||
0.928689 | − | 0.370858i | \(-0.120936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0000 | − | 8.66025i | −0.798369 | − | 0.460939i | 0.0445312 | − | 0.999008i | \(-0.485821\pi\) |
−0.842901 | + | 0.538069i | \(0.819154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | − | 10.3923i | −0.318447 | − | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | − | 3.46410i | 0.316668 | − | 0.182828i | −0.333238 | − | 0.942843i | \(-0.608141\pi\) |
0.649906 | + | 0.760014i | \(0.274808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.0000 | 1.57027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.5000 | − | 32.0429i | 0.965692 | − | 1.67263i | 0.257948 | − | 0.966159i | \(-0.416954\pi\) |
0.707744 | − | 0.706469i | \(-0.249713\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | − | 9.52628i | −0.284779 | − | 0.493252i | 0.687776 | − | 0.725923i | \(-0.258587\pi\) |
−0.972556 | + | 0.232671i | \(0.925254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1244i | 0.622786i | 0.950281 | + | 0.311393i | \(0.100796\pi\) | ||||
−0.950281 | + | 0.311393i | \(0.899204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0000 | − | 31.1769i | −0.919757 | − | 1.59307i | −0.799783 | − | 0.600289i | \(-0.795052\pi\) |
−0.119974 | − | 0.992777i | \(-0.538281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | − | 31.1769i | 0.305788 | − | 1.58892i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.0000 | − | 46.7654i | 1.35852 | − | 2.35302i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.50000 | − | 2.59808i | 0.225849 | − | 0.130394i | −0.382807 | − | 0.923828i | \(-0.625043\pi\) |
0.608655 | + | 0.793435i | \(0.291709\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | + | 20.7846i | 0.599251 | + | 1.03793i | 0.992932 | + | 0.118686i | \(0.0378683\pi\) |
−0.393680 | + | 0.919247i | \(0.628798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.5000 | + | 12.9904i | 1.12080 | + | 0.647097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.46410i | 0.171709i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5000 | + | 9.52628i | 0.815872 | + | 0.471044i | 0.848991 | − | 0.528407i | \(-0.177211\pi\) |
−0.0331186 | + | 0.999451i | \(0.510544\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | + | 10.3923i | −0.883585 | + | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0000 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.0000 | −1.41337 | −0.706687 | − | 0.707527i | \(-0.749811\pi\) | ||||
−0.706687 | + | 0.707527i | \(0.749811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 42.0000 | − | 24.2487i | 2.03730 | − | 1.17624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | + | 8.66025i | 0.722525 | + | 0.417150i | 0.815681 | − | 0.578502i | \(-0.196362\pi\) |
−0.0931566 | + | 0.995651i | \(0.529696\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.4449i | − | 1.41503i | −0.706698 | − | 0.707515i | \(-0.749816\pi\) | ||
0.706698 | − | 0.707515i | \(-0.250184\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | + | 13.8564i | 0.381819 | + | 0.661330i | 0.991322 | − | 0.131453i | \(-0.0419644\pi\) |
−0.609503 | + | 0.792784i | \(0.708631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00000 | − | 3.46410i | 0.285069 | − | 0.164584i | −0.350647 | − | 0.936508i | \(-0.614038\pi\) |
0.635716 | + | 0.771923i | \(0.280705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | + | 20.7846i | −0.568855 | + | 0.985285i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | + | 31.1769i | −0.847587 | + | 1.46806i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −45.0000 | + | 15.5885i | −2.10963 | + | 0.730798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50000 | − | 4.33013i | −0.116945 | − | 0.202555i | 0.801611 | − | 0.597847i | \(-0.203977\pi\) |
−0.918556 | + | 0.395292i | \(0.870643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8564i | 0.645357i | 0.946509 | + | 0.322679i | \(0.104583\pi\) | ||||
−0.946509 | + | 0.322679i | \(0.895417\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.1244i | − | 0.563467i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||
0.959493 | − | 0.281733i | \(-0.0909093\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.00000 | + | 5.19615i | 0.138823 | + | 0.240449i | 0.927052 | − | 0.374934i | \(-0.122335\pi\) |
−0.788228 | + | 0.615383i | \(0.789001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.00000 | − | 3.46410i | 0.138527 | − | 0.159957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00000 | + | 5.19615i | −0.137940 | + | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 49.0000 | 2.24827 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.0000 | + | 20.7846i | −0.548294 | + | 0.949673i | 0.450098 | + | 0.892979i | \(0.351389\pi\) |
−0.998392 | + | 0.0566937i | \(0.981944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | − | 2.59808i | 0.205182 | − | 0.118462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.0000 | − | 20.7846i | −0.544892 | − | 0.943781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.5000 | − | 6.06218i | −0.475800 | − | 0.274703i | 0.242864 | − | 0.970060i | \(-0.421913\pi\) |
−0.718665 | + | 0.695357i | \(0.755246\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.7846i | − | 0.937996i | −0.883199 | − | 0.468998i | \(-0.844615\pi\) | ||
0.883199 | − | 0.468998i | \(-0.155385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.00000 | + | 1.73205i | 0.403705 | + | 0.0776931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.5000 | − | 6.06218i | 0.470045 | − | 0.271380i | −0.246214 | − | 0.969216i | \(-0.579187\pi\) |
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.0000 | −1.33763 | −0.668817 | − | 0.743427i | \(-0.733199\pi\) | ||||
−0.668817 | + | 0.743427i | \(0.733199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | − | 1.73205i | 0.132973 | − | 0.0767718i | −0.432038 | − | 0.901855i | \(-0.642205\pi\) |
0.565011 | + | 0.825084i | \(0.308872\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0000 | + | 17.3205i | −0.663561 | + | 0.766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.0000 | + | 8.66025i | 0.660979 | + | 0.381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20.7846i | − | 0.914106i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | + | 6.92820i | 0.525730 | + | 0.303530i | 0.739276 | − | 0.673403i | \(-0.235168\pi\) |
−0.213546 | + | 0.976933i | \(0.568501\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.500000 | − | 0.866025i | −0.0218635 | − | 0.0378686i | 0.854887 | − | 0.518815i | \(-0.173627\pi\) |
−0.876750 | + | 0.480946i | \(0.840293\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.0000 | − | 17.3205i | 1.30682 | − | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 54.0000 | 2.33900 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | + | 20.7846i | −0.518805 | + | 0.898597i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.0000 | + | 19.0526i | 0.646096 | + | 0.820652i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5000 | + | 35.5070i | 0.881364 | + | 1.52657i | 0.849825 | + | 0.527064i | \(0.176707\pi\) |
0.0315385 | + | 0.999503i | \(0.489959\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.3205i | 0.741929i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.3923i | − | 0.444343i | −0.975008 | − | 0.222171i | \(-0.928686\pi\) | ||
0.975008 | − | 0.222171i | \(-0.0713145\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.5000 | + | 38.9711i | 0.574078 | + | 1.65722i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.00000 | − | 15.5885i | 0.381342 | − | 0.660504i | −0.609912 | − | 0.792469i | \(-0.708795\pi\) |
0.991254 | + | 0.131965i | \(0.0421286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.00000 | 0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.00000 | + | 15.5885i | −0.379305 | + | 0.656975i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) |
0.611656 | + | 0.791123i | \(0.290503\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | + | 10.3923i | −0.757266 | + | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.5000 | + | 12.9904i | 0.941596 | + | 0.543631i | 0.890460 | − | 0.455061i | \(-0.150383\pi\) |
0.0511355 | + | 0.998692i | \(0.483716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.50000 | − | 0.866025i | −0.0624458 | − | 0.0360531i | 0.468452 | − | 0.883489i | \(-0.344812\pi\) |
−0.530898 | + | 0.847436i | \(0.678145\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.00000 | − | 15.5885i | 0.124461 | − | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.0000 | 1.44215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.0000 | − | 19.0526i | 1.35515 | − | 0.782395i | 0.366182 | − | 0.930543i | \(-0.380665\pi\) |
0.988965 | + | 0.148148i | \(0.0473313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | + | 62.3538i | −0.491952 | + | 2.55626i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | + | 3.46410i | 0.245153 | + | 0.141539i | 0.617543 | − | 0.786537i | \(-0.288128\pi\) |
−0.372390 | + | 0.928076i | \(0.621461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.9808i | − | 1.05978i | −0.848067 | − | 0.529889i | \(-0.822234\pi\) | ||
0.848067 | − | 0.529889i | \(-0.177766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.00000 | + | 1.73205i | 0.121967 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.5000 | + | 32.0429i | 0.750892 | + | 1.30058i | 0.947391 | + | 0.320079i | \(0.103709\pi\) |
−0.196499 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.0000 | + | 15.5885i | −1.09230 | + | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | − | 19.0526i | 0.444286 | − | 0.769526i | −0.553716 | − | 0.832705i | \(-0.686791\pi\) |
0.998002 | + | 0.0631797i | \(0.0201241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000 | 1.69086 | 0.845428 | − | 0.534089i | \(-0.179345\pi\) | ||||
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.5000 | − | 30.3109i | 0.703384 | − | 1.21830i | −0.263887 | − | 0.964554i | \(-0.585005\pi\) |
0.967271 | − | 0.253744i | \(-0.0816620\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | − | 17.3205i | −0.240385 | − | 0.693932i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.92820i | − | 0.276246i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.46410i | − | 0.137904i | −0.997620 | − | 0.0689519i | \(-0.978035\pi\) | ||
0.997620 | − | 0.0689519i | \(-0.0219655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.0000 | + | 46.7654i | 1.07146 | + | 1.85583i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.5000 | − | 33.7750i | 0.534889 | − | 1.33821i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0000 | + | 31.1769i | −0.710957 | + | 1.23141i | 0.253541 | + | 0.967325i | \(0.418405\pi\) |
−0.964498 | + | 0.264089i | \(0.914929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.0000 | −1.69575 | −0.847877 | − | 0.530193i | \(-0.822120\pi\) | ||||
−0.847877 | + | 0.530193i | \(0.822120\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.00000 | − | 15.5885i | 0.353827 | − | 0.612845i | −0.633090 | − | 0.774078i | \(-0.718214\pi\) |
0.986916 | + | 0.161233i | \(0.0515470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.00000 | − | 15.5885i | −0.352197 | − | 0.610023i | 0.634437 | − | 0.772975i | \(-0.281232\pi\) |
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −54.0000 | − | 31.1769i | −2.10995 | − | 1.21818i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.7846i | 0.809653i | 0.914393 | + | 0.404827i | \(0.132668\pi\) | ||||
−0.914393 | + | 0.404827i | \(0.867332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.5000 | + | 9.52628i | 0.641776 | + | 0.370529i | 0.785298 | − | 0.619118i | \(-0.212510\pi\) |
−0.143523 | + | 0.989647i | \(0.545843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −42.0000 | + | 48.4974i | −1.62869 | + | 1.88065i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | 0.0385472 | 0.0192736 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192736 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.0000 | + | 17.3205i | −1.15299 | + | 0.665681i | −0.949615 | − | 0.313419i | \(-0.898526\pi\) |
−0.203379 | + | 0.979100i | \(0.565192\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.0000 | + | 3.46410i | 0.690777 | + | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.0000 | − | 20.7846i | −1.37750 | − | 0.795301i | −0.385643 | − | 0.922648i | \(-0.626021\pi\) |
−0.991858 | + | 0.127347i | \(0.959354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.5692i | 1.58828i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.50000 | − | 11.2583i | −0.247272 | − | 0.428287i | 0.715496 | − | 0.698617i | \(-0.246201\pi\) |
−0.962768 | + | 0.270330i | \(0.912867\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.0000 | + | 8.66025i | −0.568982 | + | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.0000 | − | 62.3538i | 1.36360 | − | 2.36182i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.50000 | − | 6.06218i | 0.132005 | − | 0.228639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | + | 6.92820i | −0.225653 | + | 0.260562i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 62.3538i | − | 2.33190i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.00000 | + | 15.5885i | 0.335643 | + | 0.581351i | 0.983608 | − | 0.180319i | \(-0.0577130\pi\) |
−0.647965 | + | 0.761670i | \(0.724380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5000 | + | 4.33013i | −0.465524 | + | 0.161262i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.00000 | 0.0370879 | 0.0185440 | − | 0.999828i | \(-0.494097\pi\) | ||||
0.0185440 | + | 0.999828i | \(0.494097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.5000 | + | 18.1865i | −1.16348 | + | 0.671735i | −0.952135 | − | 0.305677i | \(-0.901117\pi\) |
−0.211344 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.00000 | + | 5.19615i | 0.110506 | + | 0.191403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.5000 | − | 18.1865i | −1.15875 | − | 0.669002i | −0.207743 | − | 0.978183i | \(-0.566612\pi\) |
−0.951003 | + | 0.309181i | \(0.899945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.46410i | 0.127086i | 0.997979 | + | 0.0635428i | \(0.0202399\pi\) | ||||
−0.997979 | + | 0.0635428i | \(0.979760\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.0000 | − | 20.7846i | −1.31894 | − | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | − | 17.3205i | −0.219235 | − | 0.632878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.5000 | − | 23.3827i | 1.47787 | − | 0.853246i | 0.478179 | − | 0.878262i | \(-0.341297\pi\) |
0.999687 | + | 0.0250161i | \(0.00796370\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.0000 | 1.31017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | + | 17.3205i | −1.08750 | + | 0.627868i | −0.932910 | − | 0.360111i | \(-0.882739\pi\) |
−0.154590 | + | 0.987979i | \(0.549406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | − | 8.66025i | −0.362024 | − | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 29.4449i | − | 1.06181i | −0.847432 | − | 0.530904i | \(-0.821852\pi\) | ||
0.847432 | − | 0.530904i | \(-0.178148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.0000 | + | 15.5885i | 0.971123 | + | 0.560678i | 0.899578 | − | 0.436760i | \(-0.143874\pi\) |
0.0715442 | + | 0.997437i | \(0.477207\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5000 | − | 30.3109i | −0.628619 | − | 1.08880i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 63.0000 | − | 36.3731i | 2.25721 | − | 1.30320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | + | 10.3923i | −0.214697 | + | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.0000 | −1.71319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00000 | − | 6.92820i | 0.142585 | − | 0.246964i | −0.785885 | − | 0.618373i | \(-0.787792\pi\) |
0.928469 | + | 0.371409i | \(0.121125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.00000 | − | 15.5885i | 0.106668 | − | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 41.5692i | − | 1.47246i | −0.676733 | − | 0.736229i | \(-0.736605\pi\) | ||
0.676733 | − | 0.736229i | \(-0.263395\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.5692i | 1.47061i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0000 | − | 25.9808i | −0.529339 | − | 0.916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.0000 | − | 46.7654i | 0.949269 | − | 1.64418i | 0.202301 | − | 0.979323i | \(-0.435158\pi\) |
0.746968 | − | 0.664860i | \(-0.231509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | − | 10.3923i | 0.210171 | − | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5000 | − | 6.06218i | 0.367348 | − | 0.212089i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00000 | − | 5.19615i | −0.104701 | − | 0.181347i | 0.808915 | − | 0.587925i | \(-0.200055\pi\) |
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0000 | + | 8.66025i | 0.522867 | + | 0.301877i | 0.738107 | − | 0.674684i | \(-0.235720\pi\) |
−0.215240 | + | 0.976561i | \(0.569053\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.3205i | 0.602293i | 0.953578 | + | 0.301147i | \(0.0973693\pi\) | ||||
−0.953578 | + | 0.301147i | \(0.902631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.5000 | − | 11.2583i | −0.677263 | − | 0.391018i | 0.121560 | − | 0.992584i | \(-0.461210\pi\) |
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.0000 | − | 38.1051i | −1.03944 | − | 1.32026i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | − | 10.3923i | 0.622916 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −42.0000 | + | 24.2487i | −1.44484 | + | 0.834181i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.50000 | + | 0.866025i | −0.0859010 | + | 0.0297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.73205i | 0.0593043i | 0.999560 | + | 0.0296521i | \(0.00943995\pi\) | ||||
−0.999560 | + | 0.0296521i | \(0.990560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | + | 34.6410i | 0.682391 | + | 1.18194i | 0.974249 | + | 0.225475i | \(0.0723932\pi\) |
−0.291858 | + | 0.956462i | \(0.594273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0000 | + | 15.5885i | −0.919091 | + | 0.530637i | −0.883345 | − | 0.468724i | \(-0.844714\pi\) |
−0.0357458 | + | 0.999361i | \(0.511381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −54.0000 | −1.83182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.50000 | − | 7.79423i | 0.152477 | − | 0.264097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.0000 | + | 3.46410i | 0.608511 | + | 0.117108i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0000 | + | 19.0526i | 0.371444 | + | 0.643359i | 0.989788 | − | 0.142548i | \(-0.0455296\pi\) |
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.7128i | 0.933668i | 0.884345 | + | 0.466834i | \(0.154606\pi\) | ||||
−0.884345 | + | 0.466834i | \(0.845394\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.1244i | 0.408017i | 0.978969 | + | 0.204009i | \(0.0653970\pi\) | ||||
−0.978969 | + | 0.204009i | \(0.934603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0000 | + | 25.9808i | 0.503651 | + | 0.872349i | 0.999991 | + | 0.00422062i | \(0.00134347\pi\) |
−0.496340 | + | 0.868128i | \(0.665323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.5000 | − | 7.79423i | −1.35833 | − | 0.261410i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.0000 | + | 36.3731i | −0.702738 | + | 1.21718i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −60.0000 | −2.00558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.0000 | + | 46.7654i | 0.897510 | + | 1.55453i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.5000 | + | 7.79423i | 0.448260 | + | 0.258803i | 0.707095 | − | 0.707118i | \(-0.250005\pi\) |
−0.258835 | + | 0.965922i | \(0.583339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 20.7846i | − | 0.688625i | −0.938855 | − | 0.344312i | \(-0.888112\pi\) | ||
0.938855 | − | 0.344312i | \(-0.111888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | + | 10.3923i | 0.595713 | + | 0.343935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.0000 | − | 15.5885i | 1.48603 | − | 0.514776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.50000 | + | 0.866025i | −0.0494804 | + | 0.0285675i | −0.524536 | − | 0.851388i | \(-0.675761\pi\) |
0.475056 | + | 0.879956i | \(0.342428\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.0000 | 0.592477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | −0.230159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.00000 | + | 1.73205i | −0.0984268 | + | 0.0568267i | −0.548405 | − | 0.836213i | \(-0.684765\pi\) |
0.449979 | + | 0.893039i | \(0.351432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | − | 48.4974i | −0.229416 | − | 1.58944i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −72.0000 | − | 41.5692i | −2.35465 | − | 1.35946i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4449i | 0.961922i | 0.876742 | + | 0.480961i | \(0.159712\pi\) | ||||
−0.876742 | + | 0.480961i | \(0.840288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0000 | − | 24.2487i | −1.36916 | − | 0.790485i | −0.378340 | − | 0.925667i | \(-0.623505\pi\) |
−0.990821 | + | 0.135181i | \(0.956838\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.0000 | + | 8.66025i | −0.487435 | + | 0.281420i | −0.723510 | − | 0.690314i | \(-0.757472\pi\) |
0.236075 | + | 0.971735i | \(0.424139\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.5000 | + | 38.9711i | −0.730381 | + | 1.26506i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.00000 | + | 10.3923i | −0.194155 | + | 0.336287i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.0000 | − | 20.7846i | −0.775000 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.0333i | 1.44967i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5167i | 0.724087i | 0.932161 | + | 0.362043i | \(0.117921\pi\) | ||||
−0.932161 | + | 0.362043i | \(0.882079\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.00000 | − | 10.3923i | −0.192549 | − | 0.333505i | 0.753545 | − | 0.657396i | \(-0.228342\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50000 | − | 12.9904i | 0.0801463 | − | 0.416452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0000 | − | 46.7654i | 0.863807 | − | 1.49616i | −0.00442082 | − | 0.999990i | \(-0.501407\pi\) |
0.868227 | − | 0.496167i | \(-0.165259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000 | 0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | + | 20.7846i | −1.14706 | + | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.5000 | − | 6.06218i | −0.333543 | − | 0.192571i | 0.323870 | − | 0.946102i | \(-0.395016\pi\) |
−0.657413 | + | 0.753530i | \(0.728349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 55.4256i | − | 1.75711i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.5000 | + | 21.6506i | 1.18764 | + | 0.685682i | 0.957769 | − | 0.287539i | \(-0.0928372\pi\) |
0.229868 | + | 0.973222i | \(0.426171\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.2.cs.m.703.1 | 2 | ||
3.2 | odd | 2 | 336.2.bl.e.31.1 | yes | 2 | ||
4.3 | odd | 2 | 1008.2.cs.n.703.1 | 2 | |||
7.3 | odd | 6 | 7056.2.b.l.1567.1 | 2 | |||
7.4 | even | 3 | 7056.2.b.a.1567.2 | 2 | |||
7.5 | odd | 6 | 1008.2.cs.n.271.1 | 2 | |||
12.11 | even | 2 | 336.2.bl.a.31.1 | ✓ | 2 | ||
21.2 | odd | 6 | 2352.2.bl.l.607.1 | 2 | |||
21.5 | even | 6 | 336.2.bl.a.271.1 | yes | 2 | ||
21.11 | odd | 6 | 2352.2.b.a.1567.1 | 2 | |||
21.17 | even | 6 | 2352.2.b.h.1567.2 | 2 | |||
21.20 | even | 2 | 2352.2.bl.f.31.1 | 2 | |||
24.5 | odd | 2 | 1344.2.bl.d.703.1 | 2 | |||
24.11 | even | 2 | 1344.2.bl.h.703.1 | 2 | |||
28.3 | even | 6 | 7056.2.b.a.1567.1 | 2 | |||
28.11 | odd | 6 | 7056.2.b.l.1567.2 | 2 | |||
28.19 | even | 6 | inner | 1008.2.cs.m.271.1 | 2 | ||
84.11 | even | 6 | 2352.2.b.h.1567.1 | 2 | |||
84.23 | even | 6 | 2352.2.bl.f.607.1 | 2 | |||
84.47 | odd | 6 | 336.2.bl.e.271.1 | yes | 2 | ||
84.59 | odd | 6 | 2352.2.b.a.1567.2 | 2 | |||
84.83 | odd | 2 | 2352.2.bl.l.31.1 | 2 | |||
168.5 | even | 6 | 1344.2.bl.h.1279.1 | 2 | |||
168.131 | odd | 6 | 1344.2.bl.d.1279.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bl.a.31.1 | ✓ | 2 | 12.11 | even | 2 | ||
336.2.bl.a.271.1 | yes | 2 | 21.5 | even | 6 | ||
336.2.bl.e.31.1 | yes | 2 | 3.2 | odd | 2 | ||
336.2.bl.e.271.1 | yes | 2 | 84.47 | odd | 6 | ||
1008.2.cs.m.271.1 | 2 | 28.19 | even | 6 | inner | ||
1008.2.cs.m.703.1 | 2 | 1.1 | even | 1 | trivial | ||
1008.2.cs.n.271.1 | 2 | 7.5 | odd | 6 | |||
1008.2.cs.n.703.1 | 2 | 4.3 | odd | 2 | |||
1344.2.bl.d.703.1 | 2 | 24.5 | odd | 2 | |||
1344.2.bl.d.1279.1 | 2 | 168.131 | odd | 6 | |||
1344.2.bl.h.703.1 | 2 | 24.11 | even | 2 | |||
1344.2.bl.h.1279.1 | 2 | 168.5 | even | 6 | |||
2352.2.b.a.1567.1 | 2 | 21.11 | odd | 6 | |||
2352.2.b.a.1567.2 | 2 | 84.59 | odd | 6 | |||
2352.2.b.h.1567.1 | 2 | 84.11 | even | 6 | |||
2352.2.b.h.1567.2 | 2 | 21.17 | even | 6 | |||
2352.2.bl.f.31.1 | 2 | 21.20 | even | 2 | |||
2352.2.bl.f.607.1 | 2 | 84.23 | even | 6 | |||
2352.2.bl.l.31.1 | 2 | 84.83 | odd | 2 | |||
2352.2.bl.l.607.1 | 2 | 21.2 | odd | 6 | |||
7056.2.b.a.1567.1 | 2 | 28.3 | even | 6 | |||
7056.2.b.a.1567.2 | 2 | 7.4 | even | 3 | |||
7056.2.b.l.1567.1 | 2 | 7.3 | odd | 6 | |||
7056.2.b.l.1567.2 | 2 | 28.11 | odd | 6 |