Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(31,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bl (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: | \(2.68297350792\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.31 |
Dual form | 336.2.bl.a.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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | + | 1.73205i | −1.34164 | + | 0.774597i | −0.987048 | − | 0.160424i | \(-0.948714\pi\) |
−0.354593 | + | 0.935021i | \(0.615380\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | −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 | ||||||||
\(15\) | − | 3.46410i | − | 0.894427i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | − | 3.46410i | −1.45521 | − | 0.840168i | −0.456444 | − | 0.889752i | \(-0.650877\pi\) |
−0.998770 | + | 0.0495842i | \(0.984210\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 1.73205i | 0.436436 | + | 0.377964i | ||||
\(22\) | 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 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 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 | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | − | 1.73205i | 0.522233 | − | 0.301511i | ||||
\(34\) | 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 | ||||||||
\(39\) | −4.50000 | − | 2.59808i | −0.720577 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3923i | 1.62301i | 0.584349 | + | 0.811503i | \(0.301350\pi\) | ||||
−0.584349 | + | 0.811503i | \(0.698650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.73205i | 0.264135i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) | ||||
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | + | 1.73205i | 0.447214 | + | 0.258199i | ||||
\(46\) | 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 | ||||||||
\(51\) | 6.00000 | − | 3.46410i | 0.840168 | − | 0.485071i | ||||
\(52\) | 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 | ||||||||
\(57\) | 7.00000 | 0.927173 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | −2.50000 | + | 0.866025i | −0.314970 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.00000 | − | 15.5885i | −1.11631 | − | 1.93351i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50000 | + | 0.866025i | 0.183254 | + | 0.105802i | 0.588821 | − | 0.808264i | \(-0.299592\pi\) |
−0.405567 | + | 0.914066i | \(0.632926\pi\) | |||||||
\(68\) | 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 | ||||||||
\(75\) | 3.50000 | + | 6.06218i | 0.404145 | + | 0.700000i | ||||
\(76\) | 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 | \(0.673739\pi\) |
−0.999753 | + | 0.0222151i | \(0.992928\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 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 | −0.147073 | − | 0.989126i | \(-0.546985\pi\) |
0.783072 | + | 0.621932i | \(0.213652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5000 | + | 2.59808i | 1.41518 | + | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.50000 | − | 4.33013i | −0.259238 | − | 0.449013i | ||||
\(94\) | 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 | ||||||||
\(99\) | 3.46410i | 0.348155i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | − | 1.73205i | −0.298511 | − | 0.172345i | 0.343263 | − | 0.939239i | \(-0.388468\pi\) |
−0.641774 | + | 0.766894i | \(0.721801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.50000 | − | 4.33013i | −0.246332 | − | 0.426660i | 0.716173 | − | 0.697923i | \(-0.245892\pi\) |
−0.962505 | + | 0.271263i | \(0.912559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.00000 | − | 1.73205i | −0.878310 | − | 0.169031i | ||||
\(106\) | 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 | ||||||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.50000 | − | 2.59808i | 0.416025 | − | 0.240192i | ||||
\(118\) | 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 | ||||||||
\(123\) | −9.00000 | − | 5.19615i | −0.811503 | − | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.5885i | − | 1.38325i | −0.722256 | − | 0.691626i | \(-0.756895\pi\) | ||
0.722256 | − | 0.691626i | \(-0.243105\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.50000 | − | 0.866025i | −0.132068 | − | 0.0762493i | ||||
\(130\) | 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 | ||||||||
\(135\) | −3.00000 | + | 1.73205i | −0.258199 | + | 0.149071i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | − | 10.3923i | 0.512615 | − | 0.887875i | −0.487278 | − | 0.873247i | \(-0.662010\pi\) |
0.999893 | − | 0.0146279i | \(-0.00465636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.00000 | − | 15.5885i | 0.752618 | − | 1.30357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.50000 | − | 4.33013i | 0.453632 | − | 0.357143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | + | 10.3923i | 0.491539 | + | 0.851371i | 0.999953 | − | 0.00974235i | \(-0.00310113\pi\) |
−0.508413 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.00000 | − | 5.19615i | −0.732410 | − | 0.422857i | 0.0868934 | − | 0.996218i | \(-0.472306\pi\) |
−0.819303 | + | 0.573361i | \(0.805639\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.92820i | 0.560112i | ||||||||
\(154\) | 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 | −0.612866 | − | 0.790186i | \(-0.709984\pi\) |
0.377888 | + | 0.925851i | \(0.376650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | + | 10.3923i | −0.467099 | + | 0.809040i | ||||
\(166\) | 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 | ||||||||
\(171\) | −3.50000 | + | 6.06218i | −0.267652 | + | 0.463586i | ||||
\(172\) | 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 | ||||||||
\(189\) | 0.500000 | − | 2.59808i | 0.0363696 | − | 0.188982i | ||||
\(190\) | 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 | ||||||||
\(195\) | 18.0000 | 1.28901 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | + | 13.8564i | −0.567105 | + | 0.982255i | 0.429745 | + | 0.902950i | \(0.358603\pi\) |
−0.996850 | + | 0.0793045i | \(0.974730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.50000 | + | 0.866025i | −0.105802 | + | 0.0610847i | ||||
\(202\) | 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 | \(0.203322\pi\) | ||||
−0.802839 | + | 0.596196i | \(0.796678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.00000 | + | 1.73205i | 0.205557 | + | 0.118678i | ||||
\(214\) | 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 | ||||||||
\(219\) | −7.50000 | + | 4.33013i | −0.506803 | + | 0.292603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | − | 31.1769i | 1.21081 | − | 2.09719i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.00000 | −0.466667 | ||||||||
\(226\) | 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 | ||||||||
\(231\) | −3.00000 | − | 8.66025i | −0.197386 | − | 0.569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.00000 | + | 15.5885i | 0.589610 | + | 1.02123i | 0.994283 | + | 0.106773i | \(0.0340517\pi\) |
−0.404674 | + | 0.914461i | \(0.632615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | − | 10.3923i | −1.17419 | − | 0.677919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 15.5885i | − | 1.01258i | ||||||
\(238\) | 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 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 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 | ||||||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 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 | ||||||||
\(255\) | −12.0000 | + | 20.7846i | −0.751469 | + | 1.30158i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | + | 5.19615i | −0.561405 | + | 0.324127i | −0.753709 | − | 0.657208i | \(-0.771737\pi\) |
0.192304 | + | 0.981335i | \(0.438404\pi\) | |||||||
\(258\) | 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 | ||||||||
\(267\) | 6.92820i | 0.423999i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.0000 | − | 15.5885i | −1.64622 | − | 0.950445i | −0.978556 | − | 0.205982i | \(-0.933961\pi\) |
−0.667663 | − | 0.744463i | \(-0.732705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.00000 | + | 10.3923i | −0.544705 | + | 0.628971i | ||||
\(274\) | 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 | ||||||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.50000 | − | 4.33013i | 0.148610 | − | 0.257399i | −0.782104 | − | 0.623148i | \(-0.785854\pi\) |
0.930714 | + | 0.365748i | \(0.119187\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −21.0000 | + | 12.1244i | −1.24393 | + | 0.718185i | ||||
\(286\) | 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 | ||||||||
\(291\) | 6.00000 | + | 3.46410i | 0.351726 | + | 0.203069i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 20.7846i | − | 1.21425i | −0.794606 | − | 0.607125i | \(-0.792323\pi\) | ||
0.794606 | − | 0.607125i | \(-0.207677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00000 | − | 1.73205i | −0.174078 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.50000 | + | 0.866025i | 0.259376 | + | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.00000 | − | 1.73205i | 0.172345 | − | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0000 | 1.42683 | 0.713413 | − | 0.700744i | \(-0.247149\pi\) | ||||
0.713413 | + | 0.700744i | \(0.247149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.00000 | 0.284440 | ||||||||
\(310\) | 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 | ||||||||
\(315\) | 6.00000 | − | 6.92820i | 0.338062 | − | 0.390360i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6.92820i | − | 0.386695i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 48.4974i | 2.69847i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.5000 | + | 18.1865i | 1.74731 | + | 1.00881i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.50000 | − | 4.33013i | −0.138250 | − | 0.239457i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0000 | − | 5.19615i | 0.826977 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.50000 | − | 4.33013i | 0.412237 | − | 0.238005i | −0.279513 | − | 0.960142i | \(-0.590173\pi\) |
0.691751 | + | 0.722137i | \(0.256840\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.500000 | + | 0.866025i | −0.0273998 | + | 0.0474579i | ||||
\(334\) | 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 | ||||||||
\(339\) | −3.00000 | + | 5.19615i | −0.162938 | + | 0.282216i | ||||
\(340\) | 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 | ||||||||
\(351\) | 5.19615i | 0.277350i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0000 | + | 8.66025i | 0.798369 | + | 0.460939i | 0.842901 | − | 0.538069i | \(-0.180846\pi\) |
−0.0445312 | + | 0.999008i | \(0.514179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | − | 17.3205i | −0.317554 | − | 0.916698i | ||||
\(358\) | 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 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.0000 | −1.57027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5000 | + | 32.0429i | −0.965692 | + | 1.67263i | −0.257948 | + | 0.966159i | \(0.583046\pi\) |
−0.707744 | + | 0.706469i | \(0.750287\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.00000 | − | 5.19615i | 0.468521 | − | 0.270501i | ||||
\(370\) | 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 | ||||||||
\(375\) | −6.00000 | − | 3.46410i | −0.309839 | − | 0.178885i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.1244i | − | 0.622786i | −0.950281 | − | 0.311393i | \(-0.899204\pi\) | ||
0.950281 | − | 0.311393i | \(-0.100796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.5000 | + | 7.79423i | 0.691626 | + | 0.399310i | ||||
\(382\) | 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 | ||||||||
\(387\) | 1.50000 | − | 0.866025i | 0.0762493 | − | 0.0440225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0000 | + | 25.9808i | −0.760530 | + | 1.31728i | 0.182047 | + | 0.983290i | \(0.441728\pi\) |
−0.942578 | + | 0.333987i | \(0.891606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 3.50000 | − | 18.1865i | 0.175219 | − | 0.910465i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | − | 20.7846i | −0.599251 | − | 1.03793i | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.5000 | − | 12.9904i | −1.12080 | − | 0.647097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 3.46410i | − | 0.172133i | ||||||
\(406\) | 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 | ||||||||
\(411\) | 6.00000 | + | 10.3923i | 0.295958 | + | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | − | 10.3923i | 0.883585 | − | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.50000 | + | 4.33013i | −0.122426 | + | 0.212047i | ||||
\(418\) | 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 | ||||||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −42.0000 | + | 24.2487i | −2.03730 | + | 1.17624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.00000 | + | 15.5885i | 0.434524 | + | 0.752618i | ||||
\(430\) | 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 | 0.609503 | − | 0.792784i | \(-0.291369\pi\) |
−0.991322 | + | 0.131453i | \(0.958036\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 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 | ||||||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.0000 | − | 31.1769i | 0.847587 | − | 1.46806i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.00000 | − | 5.19615i | 0.422857 | − | 0.244137i | ||||
\(454\) | 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 | ||||||||
\(459\) | −6.00000 | − | 3.46410i | −0.280056 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.8564i | − | 0.645357i | −0.946509 | − | 0.322679i | \(-0.895417\pi\) | ||
0.946509 | − | 0.322679i | \(-0.104583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1244i | 0.563467i | 0.959493 | + | 0.281733i | \(0.0909093\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.0000 | + | 8.66025i | 0.695608 | + | 0.401610i | ||||
\(466\) | 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 | ||||||||
\(471\) | 12.0000 | − | 6.92820i | 0.552931 | − | 0.319235i | ||||
\(472\) | 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 | 0.718665 | − | 0.695357i | \(-0.244754\pi\) |
−0.242864 | + | 0.970060i | \(0.578087\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.46410i | − | 0.156652i | ||||||
\(490\) | 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 | ||||||||
\(495\) | −6.00000 | − | 10.3923i | −0.269680 | − | 0.467099i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.00000 | − | 1.73205i | −0.403705 | − | 0.0776931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5000 | + | 6.06218i | −0.470045 | + | 0.271380i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.246214 | + | 0.969216i | \(0.420813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.00000 | + | 5.19615i | −0.134030 | + | 0.232147i | ||||
\(502\) | 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 | ||||||||
\(507\) | 7.00000 | − | 12.1244i | 0.310881 | − | 0.538462i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.00000 | + | 1.73205i | −0.132973 | + | 0.0767718i | −0.565011 | − | 0.825084i | \(-0.691128\pi\) |
0.432038 | + | 0.901855i | \(0.357795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0000 | − | 17.3205i | 0.663561 | − | 0.766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.50000 | − | 6.06218i | −0.154529 | − | 0.267652i | ||||
\(514\) | 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 | 0.213546 | − | 0.976933i | \(-0.431499\pi\) |
−0.739276 | + | 0.673403i | \(0.764832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | + | 0.866025i | 0.0218635 | + | 0.0378686i | 0.876750 | − | 0.480946i | \(-0.159707\pi\) |
−0.854887 | + | 0.518815i | \(0.826373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.5000 | − | 6.06218i | 0.763763 | − | 0.264575i | ||||
\(526\) | 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 | ||||||||
\(537\) | 15.0000 | − | 8.66025i | 0.647298 | − | 0.373718i | ||||
\(538\) | 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 | ||||||||
\(543\) | −13.5000 | − | 7.79423i | −0.579340 | − | 0.334482i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 17.3205i | − | 0.741929i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3923i | 0.444343i | 0.975008 | + | 0.222171i | \(0.0713145\pi\) | ||||
−0.975008 | + | 0.222171i | \(0.928686\pi\) | |||||||
\(548\) | 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 | ||||||||
\(555\) | −3.00000 | + | 1.73205i | −0.127343 | + | 0.0735215i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.00000 | + | 15.5885i | −0.381342 | + | 0.660504i | −0.991254 | − | 0.131965i | \(-0.957871\pi\) |
0.609912 | + | 0.792469i | \(0.291205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.00000 | −0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 2.00000 | + | 1.73205i | 0.0839921 | + | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.5000 | − | 12.9904i | −0.941596 | − | 0.543631i | −0.0511355 | − | 0.998692i | \(-0.516284\pi\) |
−0.890460 | + | 0.455061i | \(0.849617\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.46410i | − | 0.144715i | ||||||
\(574\) | 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 | ||||||||
\(579\) | −6.50000 | − | 11.2583i | −0.270131 | − | 0.467880i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.00000 | + | 15.5885i | −0.124461 | + | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.00000 | + | 15.5885i | −0.372104 | + | 0.644503i | ||||
\(586\) | 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 | ||||||||
\(591\) | −6.00000 | + | 10.3923i | −0.246807 | + | 0.427482i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.0000 | + | 19.0526i | −1.35515 | + | 0.782395i | −0.988965 | − | 0.148148i | \(-0.952669\pi\) |
−0.366182 | + | 0.930543i | \(0.619335\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | − | 62.3538i | 0.491952 | − | 2.55626i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.00000 | − | 13.8564i | −0.327418 | − | 0.567105i | ||||
\(598\) | 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 | ||||||||
\(603\) | − | 1.73205i | − | 0.0705346i | ||||||
\(604\) | 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 | \(-0.896291\pi\) |
0.196499 | − | 0.980504i | \(-0.437043\pi\) | |||||||
\(608\) | 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 | ||||||||
\(615\) | 36.0000 | 1.45166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.0000 | −1.69086 | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.5000 | + | 30.3109i | −0.703384 | + | 1.21830i | 0.263887 | + | 0.964554i | \(0.414995\pi\) |
−0.967271 | + | 0.253744i | \(0.918338\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | −21.0000 | − | 12.1244i | −0.838659 | − | 0.484200i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.92820i | 0.276246i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.46410i | 0.137904i | 0.997620 | + | 0.0689519i | \(0.0219655\pi\) | ||||
−0.997620 | + | 0.0689519i | \(0.978035\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.0000 | − | 8.66025i | −0.596196 | − | 0.344214i | ||||
\(634\) | 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 | ||||||||
\(639\) | −3.00000 | + | 1.73205i | −0.118678 | + | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | − | 31.1769i | 0.710957 | − | 1.23141i | −0.253541 | − | 0.967325i | \(-0.581595\pi\) |
0.964498 | − | 0.264089i | \(-0.0850714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.0000 | 1.69575 | 0.847877 | − | 0.530193i | \(-0.177880\pi\) | ||||
0.847877 | + | 0.530193i | \(0.177880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | −12.5000 | + | 4.33013i | −0.489914 | + | 0.169711i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | + | 15.5885i | 0.352197 | + | 0.610023i | 0.986634 | − | 0.162951i | \(-0.0521013\pi\) |
−0.634437 | + | 0.772975i | \(0.718768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 54.0000 | + | 31.1769i | 2.10995 | + | 1.21818i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8.66025i | − | 0.337869i | ||||||
\(658\) | 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 | ||||||||
\(663\) | 18.0000 | + | 31.1769i | 0.699062 | + | 1.21081i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 42.0000 | − | 48.4974i | 1.62869 | − | 1.88065i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | − | 6.92820i | 0.154649 | − | 0.267860i | ||||
\(670\) | 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 | ||||||||
\(675\) | 3.50000 | − | 6.06218i | 0.134715 | − | 0.233333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0000 | − | 17.3205i | 1.15299 | − | 0.665681i | 0.203379 | − | 0.979100i | \(-0.434808\pi\) |
0.949615 | + | 0.313419i | \(0.101474\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.0000 | − | 3.46410i | −0.690777 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.0000 | + | 25.9808i | 0.574801 | + | 0.995585i | ||||
\(682\) | 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 | ||||||||
\(687\) | 1.73205i | 0.0660819i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.50000 | + | 11.2583i | 0.247272 | + | 0.428287i | 0.962768 | − | 0.270330i | \(-0.0871327\pi\) |
−0.715496 | + | 0.698617i | \(0.753799\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.00000 | + | 1.73205i | 0.341882 | + | 0.0657952i | ||||
\(694\) | 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 | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 18.0000 | − | 10.3923i | 0.677919 | − | 0.391397i | ||||
\(706\) | 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 | ||||||||
\(711\) | 13.5000 | + | 7.79423i | 0.506290 | + | 0.292306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.3538i | 2.33190i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.0000 | + | 8.66025i | 0.560185 | + | 0.323423i | ||||
\(718\) | 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 | ||||||||
\(723\) | 12.0000 | − | 6.92820i | 0.446285 | − | 0.257663i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.00000 | −0.0370879 | −0.0185440 | − | 0.999828i | \(-0.505903\pi\) | ||||
−0.0185440 | + | 0.999828i | \(0.505903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | −9.00000 | + | 22.5167i | −0.331970 | + | 0.830540i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.00000 | − | 5.19615i | −0.110506 | − | 0.191403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.5000 | + | 18.1865i | 1.15875 | + | 0.669002i | 0.951003 | − | 0.309181i | \(-0.100055\pi\) |
0.207743 | + | 0.978183i | \(0.433388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.3731i | 1.33620i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 3.00000 | + | 5.19615i | 0.109764 | + | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000 | + | 17.3205i | 0.219235 | + | 0.632878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.5000 | + | 23.3827i | −1.47787 | + | 0.853246i | −0.999687 | − | 0.0250161i | \(-0.992036\pi\) |
−0.478179 | + | 0.878262i | \(0.658703\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000 | − | 20.7846i | 0.437304 | − | 0.757433i | ||||
\(754\) | 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 | 0.154590 | − | 0.987979i | \(-0.450594\pi\) |
0.932910 | + | 0.360111i | \(0.117261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | + | 8.66025i | 0.362024 | + | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.0000 | − | 20.7846i | −0.433861 | − | 0.751469i | ||||
\(766\) | 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 | ||||||||
\(771\) | − | 10.3923i | − | 0.374270i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.0000 | − | 15.5885i | −0.971123 | − | 0.560678i | −0.0715442 | − | 0.997437i | \(-0.522793\pi\) |
−0.899578 | + | 0.436760i | \(0.856126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.5000 | + | 30.3109i | 0.628619 | + | 1.08880i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.500000 | − | 2.59808i | 0.0179374 | − | 0.0932055i | ||||
\(778\) | 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 | −0.928469 | − | 0.371409i | \(-0.878875\pi\) |
0.785885 | + | 0.618373i | \(0.212208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.0000 | + | 13.8564i | −0.854423 | + | 0.493301i | ||||
\(790\) | 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 | \(0.263395\pi\) | ||||
−0.676733 | + | 0.736229i | \(0.736605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 41.5692i | − | 1.47061i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | − | 3.46410i | −0.212000 | − | 0.122398i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0000 | − | 25.9808i | −0.529339 | − | 0.916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.0000 | − | 15.5885i | 0.950445 | − | 0.548740i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.0000 | + | 46.7654i | −0.949269 | + | 1.64418i | −0.202301 | + | 0.979323i | \(0.564842\pi\) |
−0.746968 | + | 0.664860i | \(0.768491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | −4.50000 | − | 12.9904i | −0.157243 | − | 0.453921i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.00000 | + | 5.19615i | 0.104701 | + | 0.181347i | 0.913616 | − | 0.406578i | \(-0.133278\pi\) |
−0.808915 | + | 0.587925i | \(0.799945\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.0000 | − | 8.66025i | −0.522867 | − | 0.301877i | 0.215240 | − | 0.976561i | \(-0.430947\pi\) |
−0.738107 | + | 0.674684i | \(0.764280\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 24.2487i | − | 0.844232i | ||||||
\(826\) | 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 | ||||||||
\(831\) | 8.50000 | + | 14.7224i | 0.294862 | + | 0.510716i | ||||
\(832\) | 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 | ||||||||
\(837\) | −2.50000 | + | 4.33013i | −0.0864126 | + | 0.149671i | ||||
\(838\) | 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 | ||||||||
\(843\) | −6.00000 | + | 10.3923i | −0.206651 | + | 0.357930i | ||||
\(844\) | 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 | ||||||||
\(849\) | 2.50000 | + | 4.33013i | 0.0857998 | + | 0.148610i | ||||
\(850\) | 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 | ||||||||
\(855\) | − | 24.2487i | − | 0.829288i | ||||||
\(856\) | 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 | \(-0.927607\pi\) |
0.291858 | − | 0.956462i | \(-0.405727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.0000 | + | 20.7846i | −0.613438 | + | 0.708338i | ||||
\(862\) | 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 | ||||||||
\(867\) | −31.0000 | −1.05282 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.0000 | 1.83182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.50000 | + | 7.79423i | −0.152477 | + | 0.264097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.00000 | + | 3.46410i | −0.203069 | + | 0.117242i | ||||
\(874\) | 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 | ||||||||
\(879\) | 18.0000 | + | 10.3923i | 0.607125 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 27.7128i | − | 0.933668i | −0.884345 | − | 0.466834i | \(-0.845394\pi\) | ||
0.884345 | − | 0.466834i | \(-0.154606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.1244i | − | 0.408017i | −0.978969 | − | 0.204009i | \(-0.934603\pi\) | ||
0.978969 | − | 0.204009i | \(-0.0653970\pi\) | |||||||
\(884\) | 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 | ||||||||
\(891\) | 3.00000 | − | 1.73205i | 0.100504 | − | 0.0580259i | ||||
\(892\) | 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 | ||||||||
\(903\) | −3.00000 | + | 3.46410i | −0.0998337 | + | 0.115278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.0000 | − | 46.7654i | −0.897510 | − | 1.55453i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5000 | − | 7.79423i | −0.448260 | − | 0.258803i | 0.258835 | − | 0.965922i | \(-0.416661\pi\) |
−0.707095 | + | 0.707118i | \(0.749995\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.46410i | 0.114897i | ||||||||
\(910\) | 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 | −0.475056 | − | 0.879956i | \(-0.657572\pi\) |
0.524536 | + | 0.851388i | \(0.324239\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.5000 | + | 21.6506i | −0.411889 | + | 0.713413i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.0000 | 0.592477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | −0.230159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.50000 | + | 4.33013i | −0.0821108 | + | 0.142220i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | − | 1.73205i | 0.0984268 | − | 0.0568267i | −0.449979 | − | 0.893039i | \(-0.648568\pi\) |
0.548405 | + | 0.836213i | \(0.315235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.00000 | + | 48.4974i | 0.229416 | + | 1.58944i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.00000 | − | 15.5885i | −0.294647 | − | 0.510343i | ||||
\(934\) | 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 | ||||||||
\(939\) | 15.5885i | 0.508710i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.0000 | + | 24.2487i | 1.36916 | + | 0.790485i | 0.990821 | − | 0.135181i | \(-0.0431617\pi\) |
0.378340 | + | 0.925667i | \(0.376495\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.00000 | + | 8.66025i | 0.0975900 | + | 0.281718i | ||||
\(946\) | 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 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 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 | ||||||||
\(963\) | 6.00000 | + | 3.46410i | 0.193347 | + | 0.111629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 45.0333i | − | 1.44967i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.5167i | − | 0.724087i | −0.932161 | − | 0.362043i | \(-0.882079\pi\) | ||
0.932161 | − | 0.362043i | \(-0.117921\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −42.0000 | − | 24.2487i | −1.34923 | − | 0.778981i | ||||
\(970\) | 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 | ||||||||
\(975\) | −31.5000 | + | 18.1865i | −1.00881 | + | 0.582435i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.0000 | + | 46.7654i | −0.863807 | + | 1.49616i | 0.00442082 | + | 0.999990i | \(0.498593\pi\) |
−0.868227 | + | 0.496167i | \(0.834741\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.0000 | −0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.00000 | 0.159638 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | −3.00000 | + | 15.5885i | −0.0954911 | + | 0.496186i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5000 | + | 6.06218i | 0.333543 | + | 0.192571i | 0.657413 | − | 0.753530i | \(-0.271651\pi\) |
−0.323870 | + | 0.946102i | \(0.604984\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.66025i | 0.274825i | ||||||||
\(994\) | 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 | ||||||||
\(999\) | −0.500000 | − | 0.866025i | −0.0158193 | − | 0.0273998i |
(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 | 336.2.bl.a.31.1 | ✓ | 2 | |
3.2 | odd | 2 | 1008.2.cs.n.703.1 | 2 | |||
4.3 | odd | 2 | 336.2.bl.e.31.1 | yes | 2 | ||
7.2 | even | 3 | 2352.2.bl.f.607.1 | 2 | |||
7.3 | odd | 6 | 2352.2.b.a.1567.2 | 2 | |||
7.4 | even | 3 | 2352.2.b.h.1567.1 | 2 | |||
7.5 | odd | 6 | 336.2.bl.e.271.1 | yes | 2 | ||
7.6 | odd | 2 | 2352.2.bl.l.31.1 | 2 | |||
8.3 | odd | 2 | 1344.2.bl.d.703.1 | 2 | |||
8.5 | even | 2 | 1344.2.bl.h.703.1 | 2 | |||
12.11 | even | 2 | 1008.2.cs.m.703.1 | 2 | |||
21.5 | even | 6 | 1008.2.cs.m.271.1 | 2 | |||
21.11 | odd | 6 | 7056.2.b.l.1567.2 | 2 | |||
21.17 | even | 6 | 7056.2.b.a.1567.1 | 2 | |||
28.3 | even | 6 | 2352.2.b.h.1567.2 | 2 | |||
28.11 | odd | 6 | 2352.2.b.a.1567.1 | 2 | |||
28.19 | even | 6 | inner | 336.2.bl.a.271.1 | yes | 2 | |
28.23 | odd | 6 | 2352.2.bl.l.607.1 | 2 | |||
28.27 | even | 2 | 2352.2.bl.f.31.1 | 2 | |||
56.5 | odd | 6 | 1344.2.bl.d.1279.1 | 2 | |||
56.19 | even | 6 | 1344.2.bl.h.1279.1 | 2 | |||
84.11 | even | 6 | 7056.2.b.a.1567.2 | 2 | |||
84.47 | odd | 6 | 1008.2.cs.n.271.1 | 2 | |||
84.59 | odd | 6 | 7056.2.b.l.1567.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bl.a.31.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
336.2.bl.a.271.1 | yes | 2 | 28.19 | even | 6 | inner | |
336.2.bl.e.31.1 | yes | 2 | 4.3 | odd | 2 | ||
336.2.bl.e.271.1 | yes | 2 | 7.5 | odd | 6 | ||
1008.2.cs.m.271.1 | 2 | 21.5 | even | 6 | |||
1008.2.cs.m.703.1 | 2 | 12.11 | even | 2 | |||
1008.2.cs.n.271.1 | 2 | 84.47 | odd | 6 | |||
1008.2.cs.n.703.1 | 2 | 3.2 | odd | 2 | |||
1344.2.bl.d.703.1 | 2 | 8.3 | odd | 2 | |||
1344.2.bl.d.1279.1 | 2 | 56.5 | odd | 6 | |||
1344.2.bl.h.703.1 | 2 | 8.5 | even | 2 | |||
1344.2.bl.h.1279.1 | 2 | 56.19 | even | 6 | |||
2352.2.b.a.1567.1 | 2 | 28.11 | odd | 6 | |||
2352.2.b.a.1567.2 | 2 | 7.3 | odd | 6 | |||
2352.2.b.h.1567.1 | 2 | 7.4 | even | 3 | |||
2352.2.b.h.1567.2 | 2 | 28.3 | even | 6 | |||
2352.2.bl.f.31.1 | 2 | 28.27 | even | 2 | |||
2352.2.bl.f.607.1 | 2 | 7.2 | even | 3 | |||
2352.2.bl.l.31.1 | 2 | 7.6 | odd | 2 | |||
2352.2.bl.l.607.1 | 2 | 28.23 | odd | 6 | |||
7056.2.b.a.1567.1 | 2 | 21.17 | even | 6 | |||
7056.2.b.a.1567.2 | 2 | 84.11 | even | 6 | |||
7056.2.b.l.1567.1 | 2 | 84.59 | odd | 6 | |||
7056.2.b.l.1567.2 | 2 | 21.11 | odd | 6 |