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: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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.h.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 | 0.354593 | − | 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 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 1.73205i | 0.904534 | + | 0.522233i | 0.878668 | − | 0.477432i | \(-0.158432\pi\) |
0.0258656 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.73205i | − | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) | ||
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.46410i | − | 0.894427i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 1.73205i | 0.436436 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.00000 | + | 3.46410i | −1.25109 | + | 0.722315i | −0.971325 | − | 0.237754i | \(-0.923589\pi\) |
−0.279761 | + | 0.960070i | \(0.590255\pi\) | |||||||
\(24\) | 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 | −0.549309 | − | 0.835619i | \(-0.685109\pi\) |
0.998322 | + | 0.0579057i | \(0.0184423\pi\) | |||||||
\(32\) | 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 | ||||||||
\(37\) | 5.50000 | + | 9.52628i | 0.904194 | + | 1.56611i | 0.821995 | + | 0.569495i | \(0.192861\pi\) |
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.50000 | − | 0.866025i | −0.240192 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.46410i | − | 0.541002i | −0.962720 | − | 0.270501i | \(-0.912811\pi\) | ||
0.962720 | − | 0.270501i | \(-0.0871893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.66025i | − | 1.32068i | −0.750968 | − | 0.660338i | \(-0.770413\pi\) | ||
0.750968 | − | 0.660338i | \(-0.229587\pi\) | |||||||
\(44\) | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | + | 10.3923i | −0.824163 | + | 1.42749i | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.0000 | 1.61808 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.00000 | −0.662266 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | + | 10.3923i | −0.781133 | + | 1.35296i | 0.150148 | + | 0.988663i | \(0.452025\pi\) |
−0.931282 | + | 0.364299i | \(0.881308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | + | 6.92820i | −1.53644 | + | 0.887066i | −0.537400 | + | 0.843328i | \(0.680593\pi\) |
−0.999043 | + | 0.0437377i | \(0.986073\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.50000 | − | 0.866025i | 0.314970 | − | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.50000 | − | 4.33013i | −0.916271 | − | 0.529009i | −0.0338274 | − | 0.999428i | \(-0.510770\pi\) |
−0.882443 | + | 0.470418i | \(0.844103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92820i | 0.834058i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.46410i | − | 0.411113i | −0.978645 | − | 0.205557i | \(-0.934100\pi\) | ||
0.978645 | − | 0.205557i | \(-0.0659005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.50000 | − | 2.59808i | −0.526685 | − | 0.304082i | 0.212980 | − | 0.977056i | \(-0.431683\pi\) |
−0.739666 | + | 0.672975i | \(0.765016\pi\) | |||||||
\(74\) | 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 | ||||||||
\(79\) | −10.5000 | + | 6.06218i | −1.18134 | + | 0.682048i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.0000 | 1.97576 | 0.987878 | − | 0.155230i | \(-0.0496119\pi\) | ||||
0.987878 | + | 0.155230i | \(0.0496119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 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 | ||||||||
\(91\) | 4.50000 | + | 0.866025i | 0.471728 | + | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.50000 | − | 4.33013i | −0.259238 | − | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.0000 | − | 8.66025i | −1.53897 | − | 0.888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820i | 0.703452i | 0.936103 | + | 0.351726i | \(0.114405\pi\) | ||||
−0.936103 | + | 0.351726i | \(0.885595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | + | 5.19615i | 0.895533 | + | 0.517036i | 0.875748 | − | 0.482768i | \(-0.160368\pi\) |
0.0197851 | + | 0.999804i | \(0.493702\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | 9.00000 | + | 1.73205i | 0.878310 | + | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.50000 | − | 6.06218i | 0.335239 | − | 0.580651i | −0.648292 | − | 0.761392i | \(-0.724516\pi\) |
0.983531 | + | 0.180741i | \(0.0578495\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.0000 | 1.04407 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0000 | + | 20.7846i | −1.11901 | + | 1.93817i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.50000 | + | 0.866025i | −0.138675 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00000 | − | 1.73205i | −0.270501 | − | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.1244i | − | 1.07586i | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||
0.842989 | − | 0.537931i | \(-0.180794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.50000 | − | 4.33013i | −0.660338 | − | 0.381246i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.5000 | − | 4.33013i | 1.08389 | − | 0.375470i | ||||
\(134\) | 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 | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.00000 | 0.593732 | 0.296866 | − | 0.954919i | \(-0.404058\pi\) | ||||
0.296866 | + | 0.954919i | \(0.404058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | − | 5.19615i | 0.250873 | − | 0.434524i | ||||
\(144\) | 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 | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | − | 1.73205i | −0.244137 | − | 0.140952i | 0.372940 | − | 0.927855i | \(-0.378350\pi\) |
−0.617076 | + | 0.786903i | \(0.711683\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 17.3205i | − | 1.39122i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | + | 10.3923i | 0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | − | 17.3205i | −0.472866 | − | 1.36505i | ||||
\(162\) | 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 | ||||||||
\(165\) | 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 | ||||||||
\(169\) | 10.0000 | 0.769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.50000 | + | 4.33013i | −0.191180 | + | 0.331133i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000 | − | 3.46410i | 0.456172 | − | 0.263371i | −0.254262 | − | 0.967135i | \(-0.581832\pi\) |
0.710433 | + | 0.703765i | \(0.248499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.0000 | + | 12.1244i | 1.05830 | + | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | + | 10.3923i | 0.450988 | + | 0.781133i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.00000 | + | 5.19615i | 0.672692 | + | 0.388379i | 0.797096 | − | 0.603853i | \(-0.206369\pi\) |
−0.124404 | + | 0.992232i | \(0.539702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.19615i | − | 0.386227i | −0.981176 | − | 0.193113i | \(-0.938141\pi\) | ||
0.981176 | − | 0.193113i | \(-0.0618586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.8564i | 1.02430i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.0000 | + | 19.0526i | 2.42621 | + | 1.40077i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.500000 | − | 2.59808i | 0.0363696 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.0000 | + | 8.66025i | −1.08536 | + | 0.626634i | −0.932338 | − | 0.361588i | \(-0.882235\pi\) |
−0.153024 | + | 0.988222i | \(0.548901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | − | 9.52628i | 0.395899 | − | 0.685717i | −0.597317 | − | 0.802005i | \(-0.703766\pi\) |
0.993215 | + | 0.116289i | \(0.0370998\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.00000 | −0.429669 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.0000 | 1.70993 | 0.854965 | − | 0.518686i | \(-0.173579\pi\) | ||||
0.854965 | + | 0.518686i | \(0.173579\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | −7.50000 | + | 4.33013i | −0.529009 | + | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | − | 10.3923i | −0.419058 | − | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | + | 3.46410i | 0.417029 | + | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 17.3205i | − | 1.19808i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.46410i | − | 0.238479i | −0.992866 | − | 0.119239i | \(-0.961954\pi\) | ||
0.992866 | − | 0.119239i | \(-0.0380456\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | − | 1.73205i | −0.205557 | − | 0.118678i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.0000 | − | 25.9808i | −1.02299 | − | 1.77187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | + | 8.66025i | 0.678844 | + | 0.587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.50000 | + | 2.59808i | −0.304082 | + | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.00000 | −0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.00000 | − | 15.5885i | 0.597351 | − | 1.03464i | −0.395860 | − | 0.918311i | \(-0.629553\pi\) |
0.993210 | − | 0.116331i | \(-0.0371134\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.50000 | − | 4.33013i | 0.495614 | − | 0.286143i | −0.231287 | − | 0.972886i | \(-0.574293\pi\) |
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00000 | + | 8.66025i | 0.197386 | + | 0.569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0000 | + | 10.3923i | 1.17419 | + | 0.677919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.1244i | 0.787562i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 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 | ||||||||
\(247\) | −7.50000 | + | 4.33013i | −0.477214 | + | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.00000 | − | 15.5885i | 0.570352 | − | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.0000 | −1.50887 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.0000 | + | 8.66025i | −0.935674 | + | 0.540212i | −0.888602 | − | 0.458680i | \(-0.848323\pi\) |
−0.0470726 | + | 0.998891i | \(0.514989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.5000 | + | 9.52628i | −1.70877 | + | 0.591934i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | − | 6.92820i | −0.739952 | − | 0.427211i | 0.0821001 | − | 0.996624i | \(-0.473837\pi\) |
−0.822052 | + | 0.569413i | \(0.807171\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.5692i | 2.55358i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.92820i | − | 0.423999i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0000 | − | 8.66025i | −0.914566 | − | 0.528025i | −0.0326687 | − | 0.999466i | \(-0.510401\pi\) |
−0.881897 | + | 0.471441i | \(0.843734\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | + | 6.92820i | 0.242983 | + | 0.420858i | 0.961563 | − | 0.274586i | \(-0.0885408\pi\) |
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.00000 | − | 3.46410i | 0.181568 | − | 0.209657i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.0000 | − | 12.1244i | 1.26635 | − | 0.731126i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.50000 | + | 16.4545i | −0.570800 | + | 0.988654i | 0.425684 | + | 0.904872i | \(0.360033\pi\) |
−0.996484 | + | 0.0837823i | \(0.973300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.00000 | −0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.50000 | − | 6.06218i | 0.208053 | − | 0.360359i | −0.743048 | − | 0.669238i | \(-0.766621\pi\) |
0.951101 | + | 0.308879i | \(0.0999539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.0000 | + | 8.66025i | −0.888523 | + | 0.512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.00000 | + | 1.73205i | 0.531253 | + | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.50000 | − | 14.7224i | −0.500000 | − | 0.866025i | ||||
\(290\) | 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 | ||||||||
\(295\) | 41.5692i | 2.42025i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00000 | − | 1.73205i | −0.174078 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.5000 | + | 4.33013i | 1.29688 | + | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | − | 5.19615i | 0.517036 | − | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.0000 | + | 41.5692i | −1.37424 | + | 2.38025i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0000 | 0.627803 | 0.313902 | − | 0.949456i | \(-0.398364\pi\) | ||||
0.313902 | + | 0.949456i | \(0.398364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.00000 | 0.284440 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.00000 | − | 15.5885i | 0.510343 | − | 0.883940i | −0.489585 | − | 0.871956i | \(-0.662852\pi\) |
0.999928 | − | 0.0119847i | \(-0.00381495\pi\) | |||||||
\(312\) | 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 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.5000 | − | 6.06218i | −0.582435 | − | 0.336269i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.50000 | − | 6.06218i | −0.193550 | − | 0.335239i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.0000 | + | 5.19615i | −0.826977 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5000 | + | 7.79423i | −0.742027 | + | 0.428410i | −0.822806 | − | 0.568323i | \(-0.807593\pi\) |
0.0807788 | + | 0.996732i | \(0.474259\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.50000 | − | 9.52628i | 0.301398 | − | 0.522037i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.0000 | −1.63908 | ||||||||
\(336\) | 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 | ||||||||
\(345\) | 12.0000 | + | 20.7846i | 0.646058 | + | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0000 | + | 13.8564i | 1.28839 | + | 0.743851i | 0.978367 | − | 0.206879i | \(-0.0663306\pi\) |
0.310021 | + | 0.950730i | \(0.399664\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.8564i | − | 0.741716i | −0.928689 | − | 0.370858i | \(-0.879064\pi\) | ||
0.928689 | − | 0.370858i | \(-0.120936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.73205i | 0.0924500i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.0000 | + | 12.1244i | 1.11772 | + | 0.645314i | 0.940817 | − | 0.338914i | \(-0.110060\pi\) |
0.176900 | + | 0.984229i | \(0.443393\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | − | 10.3923i | −0.318447 | − | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.0000 | − | 10.3923i | 0.950004 | − | 0.548485i | 0.0569216 | − | 0.998379i | \(-0.481871\pi\) |
0.893082 | + | 0.449894i | \(0.148538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.0000 | −0.942163 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.50000 | + | 9.52628i | −0.287098 | + | 0.497268i | −0.973116 | − | 0.230317i | \(-0.926024\pi\) |
0.686018 | + | 0.727585i | \(0.259357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.00000 | + | 1.73205i | −0.156174 | + | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | − | 20.7846i | −1.24602 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.500000 | + | 0.866025i | 0.0258890 | + | 0.0448411i | 0.878680 | − | 0.477412i | \(-0.158425\pi\) |
−0.852791 | + | 0.522253i | \(0.825092\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | − | 3.46410i | −0.309839 | − | 0.178885i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.66025i | − | 0.444847i | −0.974950 | − | 0.222424i | \(-0.928603\pi\) | ||
0.974950 | − | 0.222424i | \(-0.0713968\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5000 | − | 6.06218i | −0.537931 | − | 0.310575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | + | 20.7846i | 0.613171 | + | 1.06204i | 0.990702 | + | 0.136047i | \(0.0434398\pi\) |
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | + | 31.1769i | −0.305788 | + | 1.58892i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.50000 | + | 4.33013i | −0.381246 | + | 0.220113i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.0000 | + | 36.3731i | −1.05662 | + | 1.83013i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.50000 | + | 0.866025i | −0.0752828 | + | 0.0434646i | −0.537169 | − | 0.843475i | \(-0.680506\pi\) |
0.461886 | + | 0.886939i | \(0.347173\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.50000 | − | 12.9904i | 0.125157 | − | 0.650332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | − | 10.3923i | −0.299626 | − | 0.518967i | 0.676425 | − | 0.736512i | \(-0.263528\pi\) |
−0.976050 | + | 0.217545i | \(0.930195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.50000 | − | 4.33013i | −0.373602 | − | 0.215699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.46410i | 0.172133i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.1051i | 1.88880i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5000 | − | 11.2583i | −0.964213 | − | 0.556689i | −0.0667458 | − | 0.997770i | \(-0.521262\pi\) |
−0.897467 | + | 0.441081i | \(0.854595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | + | 10.3923i | 0.295958 | + | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | − | 20.7846i | −1.18096 | − | 1.02274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 54.0000 | − | 31.1769i | 2.65076 | − | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.50000 | − | 6.06218i | 0.171396 | − | 0.296866i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | 0.293119 | 0.146560 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146560 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.00000 | 0.341159 | 0.170580 | − | 0.985344i | \(-0.445436\pi\) | ||||
0.170580 | + | 0.985344i | \(0.445436\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0000 | − | 34.6410i | −0.580721 | − | 1.67640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00000 | − | 5.19615i | −0.144841 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.0000 | − | 12.1244i | −1.01153 | − | 0.584010i | −0.0998939 | − | 0.994998i | \(-0.531850\pi\) |
−0.911641 | + | 0.410988i | \(0.865184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.73205i | − | 0.0832370i | −0.999134 | − | 0.0416185i | \(-0.986749\pi\) | ||
0.999134 | − | 0.0416185i | \(-0.0132514\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.0000 | + | 17.3205i | 1.43509 | + | 0.828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | − | 6.92820i | −0.190910 | − | 0.330665i | 0.754642 | − | 0.656136i | \(-0.227810\pi\) |
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0000 | + | 6.92820i | −0.570137 | + | 0.329169i | −0.757204 | − | 0.653178i | \(-0.773435\pi\) |
0.187067 | + | 0.982347i | \(0.440102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | − | 20.7846i | 0.568855 | − | 0.985285i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | − | 10.3923i | 0.282529 | − | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.00000 | + | 1.73205i | −0.140952 | + | 0.0813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.0000 | − | 5.19615i | 0.703211 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.50000 | + | 16.4545i | 0.444391 | + | 0.769708i | 0.998010 | − | 0.0630623i | \(-0.0200867\pi\) |
−0.553618 | + | 0.832771i | \(0.686753\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.8564i | − | 0.645357i | −0.946509 | − | 0.322679i | \(-0.895417\pi\) | ||
0.946509 | − | 0.322679i | \(-0.104583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5885i | 0.724457i | 0.932089 | + | 0.362229i | \(0.117984\pi\) | ||||
−0.932089 | + | 0.362229i | \(0.882016\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.0000 | − | 8.66025i | −0.695608 | − | 0.401610i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.0000 | + | 25.9808i | 0.694117 | + | 1.20225i | 0.970477 | + | 0.241192i | \(0.0775384\pi\) |
−0.276360 | + | 0.961054i | \(0.589128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.0000 | − | 17.3205i | 0.692636 | − | 0.799787i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.0000 | − | 25.9808i | 0.689701 | − | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.0000 | −1.60591 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.5000 | − | 9.52628i | 0.752335 | − | 0.434361i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.0000 | − | 3.46410i | −0.819028 | − | 0.157622i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0000 | + | 20.7846i | 0.544892 | + | 0.943781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.5000 | − | 12.9904i | −1.01957 | − | 0.588650i | −0.105592 | − | 0.994410i | \(-0.533674\pi\) |
−0.913980 | + | 0.405759i | \(0.867007\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.46410i | − | 0.156652i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.6410i | 1.56333i | 0.623700 | + | 0.781664i | \(0.285629\pi\) | ||||
−0.623700 | + | 0.781664i | \(0.714371\pi\) | |||||||
\(492\) | 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 | ||||||||
\(499\) | 28.5000 | − | 16.4545i | 1.27584 | − | 0.736604i | 0.299755 | − | 0.954016i | \(-0.403095\pi\) |
0.976080 | + | 0.217412i | \(0.0697616\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.00000 | − | 5.19615i | 0.134030 | − | 0.232147i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | − | 8.66025i | 0.222058 | − | 0.384615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.0000 | − | 15.5885i | 1.19675 | − | 0.690946i | 0.236924 | − | 0.971528i | \(-0.423861\pi\) |
0.959830 | + | 0.280582i | \(0.0905275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.00000 | − | 10.3923i | 0.398137 | − | 0.459728i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.50000 | + | 4.33013i | 0.110378 | + | 0.191180i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.0000 | + | 8.66025i | 0.660979 | + | 0.381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.7846i | 0.914106i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.92820i | − | 0.304114i | ||||||
\(520\) | 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 | ||||||||
\(523\) | 5.50000 | + | 9.52628i | 0.240498 | + | 0.416555i | 0.960856 | − | 0.277047i | \(-0.0893559\pi\) |
−0.720358 | + | 0.693602i | \(0.756023\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.5000 | − | 6.06218i | 0.763763 | − | 0.264575i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5000 | − | 21.6506i | 0.543478 | − | 0.941332i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.00000 | −0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.00000 | − | 5.19615i | 0.388379 | − | 0.224231i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.0000 | − | 19.0526i | −0.646096 | − | 0.820652i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.50000 | + | 4.33013i | 0.107483 | + | 0.186167i | 0.914750 | − | 0.404020i | \(-0.132387\pi\) |
−0.807267 | + | 0.590187i | \(0.799054\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.50000 | − | 2.59808i | −0.193113 | − | 0.111494i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 24.2487i | − | 1.03870i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.46410i | 0.148114i | 0.997254 | + | 0.0740571i | \(0.0235947\pi\) | ||||
−0.997254 | + | 0.0740571i | \(0.976405\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.0000 | + | 6.92820i | 0.512148 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.5000 | − | 30.3109i | −0.446505 | − | 1.28895i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.0000 | − | 19.0526i | 1.40077 | − | 0.808736i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0000 | + | 36.3731i | −0.889799 | + | 1.54118i | −0.0496855 | + | 0.998765i | \(0.515822\pi\) |
−0.840113 | + | 0.542411i | \(0.817511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.0000 | −0.634432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.00000 | − | 5.19615i | 0.126435 | − | 0.218992i | −0.795858 | − | 0.605483i | \(-0.792980\pi\) |
0.922293 | + | 0.386492i | \(0.126313\pi\) | |||||||
\(564\) | 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 | ||||||||
\(569\) | −21.0000 | − | 36.3731i | −0.880366 | − | 1.52484i | −0.850935 | − | 0.525271i | \(-0.823964\pi\) |
−0.0294311 | − | 0.999567i | \(-0.509370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.5000 | + | 23.3827i | 1.69487 | + | 0.978535i | 0.950477 | + | 0.310796i | \(0.100596\pi\) |
0.744396 | + | 0.667739i | \(0.232738\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3205i | 0.723575i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 48.4974i | 2.02248i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5000 | + | 6.06218i | 0.437121 | + | 0.252372i | 0.702376 | − | 0.711807i | \(-0.252123\pi\) |
−0.265255 | + | 0.964178i | \(0.585456\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.50000 | − | 9.52628i | −0.228572 | − | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.00000 | + | 46.7654i | −0.373383 | + | 1.94015i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0000 | + | 20.7846i | −1.49097 | + | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.00000 | + | 5.19615i | −0.124035 | + | 0.214834i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.0000 | −1.03011 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.0000 | − | 20.7846i | 0.493614 | − | 0.854965i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.00000 | − | 1.73205i | 0.123195 | − | 0.0711268i | −0.437136 | − | 0.899395i | \(-0.644007\pi\) |
0.560331 | + | 0.828269i | \(0.310674\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.00000 | − | 13.8564i | −0.327418 | − | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.0000 | + | 24.2487i | 1.71607 | + | 0.990775i | 0.925794 | + | 0.378030i | \(0.123398\pi\) |
0.790280 | + | 0.612746i | \(0.209935\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.8372i | − | 1.62499i | −0.582967 | − | 0.812496i | \(-0.698108\pi\) | ||
0.582967 | − | 0.812496i | \(-0.301892\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.66025i | 0.352673i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.00000 | + | 1.73205i | 0.121967 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.50000 | + | 11.2583i | 0.263827 | + | 0.456962i | 0.967256 | − | 0.253804i | \(-0.0816819\pi\) |
−0.703429 | + | 0.710766i | \(0.748349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00000 | − | 5.19615i | 0.364101 | − | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.0000 | −0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.500000 | + | 0.866025i | −0.0200967 | + | 0.0348085i | −0.875899 | − | 0.482495i | \(-0.839731\pi\) |
0.855802 | + | 0.517303i | \(0.173064\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.00000 | − | 3.46410i | 0.240772 | − | 0.139010i | ||||
\(622\) | 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 | ||||||||
\(627\) | −15.0000 | − | 8.66025i | −0.599042 | − | 0.345857i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.46410i | − | 0.137904i | −0.997620 | − | 0.0689519i | \(-0.978035\pi\) | ||
0.997620 | − | 0.0689519i | \(-0.0219655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.00000 | − | 1.73205i | −0.119239 | − | 0.0688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.0000 | − | 36.3731i | −0.833360 | − | 1.44342i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.50000 | + | 11.2583i | −0.178296 | + | 0.446071i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | + | 1.73205i | −0.118678 | + | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0000 | + | 20.7846i | −0.473972 | + | 0.820943i | −0.999556 | − | 0.0297987i | \(-0.990513\pi\) |
0.525584 | + | 0.850741i | \(0.323847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.0000 | −1.22252 | −0.611260 | − | 0.791430i | \(-0.709337\pi\) | ||||
−0.611260 | + | 0.791430i | \(0.709337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.0000 | −1.18125 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0000 | − | 25.9808i | 0.589711 | − | 1.02141i | −0.404559 | − | 0.914512i | \(-0.632575\pi\) |
0.994270 | − | 0.106897i | \(-0.0340916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0000 | + | 20.7846i | −1.41312 | + | 0.815867i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.5000 | − | 4.33013i | 0.489914 | − | 0.169711i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.00000 | − | 5.19615i | −0.117399 | − | 0.203341i | 0.801337 | − | 0.598213i | \(-0.204122\pi\) |
−0.918736 | + | 0.394872i | \(0.870789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | − | 10.3923i | −0.703318 | − | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.19615i | 0.202721i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13.8564i | − | 0.539769i | −0.962893 | − | 0.269884i | \(-0.913014\pi\) | ||
0.962893 | − | 0.269884i | \(-0.0869855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.5000 | + | 12.9904i | 0.875149 | + | 0.505267i | 0.869056 | − | 0.494714i | \(-0.164727\pi\) |
0.00609283 | + | 0.999981i | \(0.498061\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.0000 | − | 34.6410i | 1.16335 | − | 1.34332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.0000 | −1.85302 | ||||||||
\(672\) | 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 | ||||||||
\(677\) | −6.00000 | + | 3.46410i | −0.230599 | + | 0.133136i | −0.610848 | − | 0.791748i | \(-0.709171\pi\) |
0.380250 | + | 0.924884i | \(0.375838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.0000 | − | 3.46410i | −0.690777 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | − | 15.5885i | −0.344881 | − | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | − | 3.46410i | −0.229584 | − | 0.132550i | 0.380796 | − | 0.924659i | \(-0.375650\pi\) |
−0.610380 | + | 0.792109i | \(0.708983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.5692i | 1.58828i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 8.66025i | − | 0.330409i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | + | 10.3923i | 0.685745 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.5000 | + | 19.9186i | 0.437481 | + | 0.757739i | 0.997494 | − | 0.0707446i | \(-0.0225375\pi\) |
−0.560014 | + | 0.828483i | \(0.689204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.00000 | + | 1.73205i | 0.341882 | + | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.0000 | − | 12.1244i | 0.796575 | − | 0.459903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.5000 | − | 47.6314i | 1.03718 | − | 1.79645i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.0000 | − | 10.3923i | 0.677919 | − | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.0000 | + | 20.7846i | −0.676960 | + | 0.781686i | ||||
\(708\) | 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 | ||||||||
\(711\) | 10.5000 | + | 6.06218i | 0.393781 | + | 0.227349i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34.6410i | 1.29732i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 20.7846i | − | 0.777300i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.00000 | − | 5.19615i | −0.336111 | − | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.0000 | + | 25.9808i | 0.559406 | + | 0.968919i | 0.997546 | + | 0.0700124i | \(0.0223039\pi\) |
−0.438141 | + | 0.898906i | \(0.644363\pi\) | |||||||
\(720\) | 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 | ||||||||
\(727\) | −23.0000 | −0.853023 | −0.426511 | − | 0.904482i | \(-0.640258\pi\) | ||||
−0.426511 | + | 0.904482i | \(0.640258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.5000 | + | 14.7224i | −0.941864 | + | 0.543785i | −0.890544 | − | 0.454897i | \(-0.849676\pi\) |
−0.0513199 | + | 0.998682i | \(0.516343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.00000 | + | 22.5167i | −0.331970 | + | 0.830540i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.0000 | − | 25.9808i | −0.552532 | − | 0.957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.5000 | + | 26.8468i | 1.71053 | + | 0.987575i | 0.933839 | + | 0.357693i | \(0.116437\pi\) |
0.776691 | + | 0.629882i | \(0.216897\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.66025i | 0.318142i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.46410i | − | 0.127086i | −0.997979 | − | 0.0635428i | \(-0.979760\pi\) | ||
0.997979 | − | 0.0635428i | \(-0.0202399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.0000 | − | 20.7846i | −1.31894 | − | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.00000 | − | 15.5885i | −0.329293 | − | 0.570352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.50000 | − | 2.59808i | 0.164207 | − | 0.0948051i | −0.415644 | − | 0.909527i | \(-0.636444\pi\) |
0.579852 | + | 0.814722i | \(0.303111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.0000 | + | 20.7846i | −0.435572 | + | 0.754434i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.0000 | + | 20.7846i | −1.30500 | + | 0.753442i | −0.981257 | − | 0.192704i | \(-0.938274\pi\) |
−0.323742 | + | 0.946145i | \(0.604941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | + | 12.1244i | 0.506834 | + | 0.438931i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.0000 | + | 10.3923i | 0.649942 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 15.5885i | − | 0.562134i | −0.959688 | − | 0.281067i | \(-0.909312\pi\) | ||
0.959688 | − | 0.281067i | \(-0.0906883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.3205i | 0.623783i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.0000 | − | 22.5167i | −1.40273 | − | 0.809868i | −0.408060 | − | 0.912955i | \(-0.633795\pi\) |
−0.994672 | + | 0.103087i | \(0.967128\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5000 | − | 30.3109i | −0.628619 | − | 1.08880i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.50000 | + | 28.5788i | −0.197311 | + | 1.02526i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.0000 | + | 8.66025i | −0.537431 | + | 0.310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | − | 10.3923i | 0.214697 | − | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.00000 | + | 13.8564i | −0.285169 | + | 0.493928i | −0.972650 | − | 0.232275i | \(-0.925383\pi\) |
0.687481 | + | 0.726202i | \(0.258716\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.0000 | + | 6.92820i | −0.427211 | + | 0.246651i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.00000 | − | 15.5885i | 0.106668 | − | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | + | 20.7846i | 0.426132 | + | 0.738083i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36.0000 | + | 20.7846i | 1.27679 | + | 0.737154i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.6410i | 1.22705i | 0.789676 | + | 0.613524i | \(0.210249\pi\) | ||||
−0.789676 | + | 0.613524i | \(0.789751\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | − | 3.46410i | −0.212000 | − | 0.122398i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.00000 | − | 15.5885i | −0.317603 | − | 0.550105i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.0000 | − | 41.5692i | −1.69178 | − | 1.46512i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.0000 | + | 8.66025i | −0.528025 | + | 0.304855i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | + | 15.5885i | −0.316423 | + | 0.548061i | −0.979739 | − | 0.200279i | \(-0.935815\pi\) |
0.663316 | + | 0.748340i | \(0.269149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.0000 | 1.40459 | 0.702295 | − | 0.711886i | \(-0.252159\pi\) | ||||
0.702295 | + | 0.711886i | \(0.252159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | 0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | − | 10.3923i | 0.210171 | − | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.5000 | + | 21.6506i | −1.31196 | + | 0.757460i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.50000 | − | 4.33013i | −0.0524142 | − | 0.151307i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.00000 | + | 1.73205i | 0.104573 | + | 0.0603755i | 0.551375 | − | 0.834258i | \(-0.314104\pi\) |
−0.446801 | + | 0.894633i | \(0.647437\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 24.2487i | − | 0.844232i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 38.1051i | − | 1.32504i | −0.749042 | − | 0.662522i | \(-0.769486\pi\) | ||
0.749042 | − | 0.662522i | \(-0.230514\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.5000 | + | 12.9904i | 0.781457 | + | 0.451175i | 0.836947 | − | 0.547285i | \(-0.184339\pi\) |
−0.0554892 | + | 0.998459i | \(0.517672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.50000 | + | 16.4545i | 0.329551 | + | 0.570800i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 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 | ||||||||
\(839\) | 48.0000 | 1.65714 | 0.828572 | − | 0.559883i | \(-0.189154\pi\) | ||||
0.828572 | + | 0.559883i | \(0.189154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.0000 | − | 17.3205i | 1.03203 | − | 0.595844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.50000 | + | 0.866025i | −0.0859010 | + | 0.0297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.50000 | − | 6.06218i | −0.120120 | − | 0.208053i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −66.0000 | − | 38.1051i | −2.26245 | − | 1.30623i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.19615i | − | 0.177913i | −0.996036 | − | 0.0889564i | \(-0.971647\pi\) | ||
0.996036 | − | 0.0889564i | \(-0.0283532\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.3205i | 0.592349i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0000 | + | 6.92820i | 0.409912 | + | 0.236663i | 0.690752 | − | 0.723092i | \(-0.257280\pi\) |
−0.280840 | + | 0.959755i | \(0.590613\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.0000 | − | 27.7128i | −0.545913 | − | 0.945549i | −0.998549 | − | 0.0538535i | \(-0.982850\pi\) |
0.452636 | − | 0.891695i | \(-0.350484\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.00000 | − | 6.92820i | 0.204479 | − | 0.236113i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.00000 | + | 5.19615i | −0.306364 | + | 0.176879i | −0.645298 | − | 0.763931i | \(-0.723267\pi\) |
0.338935 | + | 0.940810i | \(0.389933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | − | 20.7846i | 0.408012 | − | 0.706698i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.0000 | −1.42475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.50000 | + | 12.9904i | −0.254128 | + | 0.440162i | ||||
\(872\) | 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 | ||||||||
\(877\) | −1.00000 | − | 1.73205i | −0.0337676 | − | 0.0584872i | 0.848648 | − | 0.528958i | \(-0.177417\pi\) |
−0.882415 | + | 0.470471i | \(0.844084\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.0000 | − | 10.3923i | −0.607125 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.92820i | 0.233417i | 0.993166 | + | 0.116709i | \(0.0372343\pi\) | ||||
−0.993166 | + | 0.116709i | \(0.962766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.7654i | 1.57378i | 0.617093 | + | 0.786890i | \(0.288310\pi\) | ||||
−0.617093 | + | 0.786890i | \(0.711690\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.0000 | + | 20.7846i | 1.21013 | + | 0.698667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.00000 | + | 15.5885i | 0.302190 | + | 0.523409i | 0.976632 | − | 0.214919i | \(-0.0689488\pi\) |
−0.674441 | + | 0.738328i | \(0.735615\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.5000 | + | 6.06218i | 1.05648 | + | 0.203319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | + | 1.73205i | −0.100504 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.0000 | − | 25.9808i | 0.501956 | − | 0.869413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0000 | 1.20335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.0000 | − | 17.3205i | 0.499169 | − | 0.576390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.00000 | − | 15.5885i | −0.299170 | − | 0.518178i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.5000 | − | 16.4545i | −0.946327 | − | 0.546362i | −0.0543890 | − | 0.998520i | \(-0.517321\pi\) |
−0.891938 | + | 0.452158i | \(0.850654\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 10.3923i | − | 0.344691i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 41.5692i | − | 1.37725i | −0.725118 | − | 0.688625i | \(-0.758215\pi\) | ||
0.725118 | − | 0.688625i | \(-0.241785\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.0000 | + | 31.1769i | 1.78714 | + | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.0000 | + | 41.5692i | 0.793416 | + | 1.37424i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.0000 | − | 5.19615i | 0.495344 | − | 0.171592i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.5000 | + | 21.6506i | −1.23701 | + | 0.714189i | −0.968482 | − | 0.249083i | \(-0.919871\pi\) |
−0.268529 | + | 0.963272i | \(0.586537\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.50000 | − | 9.52628i | 0.181231 | − | 0.313902i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.00000 | −0.197492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 77.0000 | 2.53174 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.50000 | − | 4.33013i | 0.0821108 | − | 0.142220i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | − | 5.19615i | 0.295280 | − | 0.170480i | −0.345040 | − | 0.938588i | \(-0.612135\pi\) |
0.640321 | + | 0.768108i | \(0.278801\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | + | 34.6410i | 0.163868 | + | 1.13531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.00000 | − | 15.5885i | −0.294647 | − | 0.510343i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 53.6936i | − | 1.75409i | −0.480406 | − | 0.877046i | \(-0.659511\pi\) | ||
0.480406 | − | 0.877046i | \(-0.340489\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 15.5885i | − | 0.508710i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | − | 6.92820i | −0.391189 | − | 0.225853i | 0.291486 | − | 0.956575i | \(-0.405850\pi\) |
−0.682675 | + | 0.730722i | \(0.739184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.0000 | + | 20.7846i | 0.390774 | + | 0.676840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.00000 | − | 8.66025i | −0.0975900 | − | 0.281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.0000 | − | 22.5167i | 1.26733 | − | 0.731693i | 0.292848 | − | 0.956159i | \(-0.405397\pi\) |
0.974482 | + | 0.224466i | \(0.0720637\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.50000 | + | 7.79423i | −0.146076 | + | 0.253011i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0000 | 0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.0000 | + | 51.9615i | −0.970777 | + | 1.68144i | ||||
\(956\) | 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 | ||||||||
\(965\) | − | 38.1051i | − | 1.22665i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.66025i | 0.278495i | 0.990258 | + | 0.139247i | \(0.0444684\pi\) | ||||
−0.990258 | + | 0.139247i | \(0.955532\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0000 | − | 41.5692i | −0.770197 | − | 1.33402i | −0.937455 | − | 0.348107i | \(-0.886825\pi\) |
0.167258 | − | 0.985913i | \(-0.446509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.50000 | + | 18.1865i | −0.112205 | + | 0.583033i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.5000 | + | 6.06218i | −0.336269 | + | 0.194145i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0000 | − | 36.3731i | 0.671850 | − | 1.16368i | −0.305530 | − | 0.952183i | \(-0.598833\pi\) |
0.977379 | − | 0.211495i | \(-0.0678332\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000 | 0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.00000 | −0.223493 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.00000 | − | 10.3923i | 0.191370 | − | 0.331463i | −0.754334 | − | 0.656490i | \(-0.772040\pi\) |
0.945705 | + | 0.325027i | \(0.105374\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.0000 | − | 41.5692i | 2.29411 | − | 1.32451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.00000 | + | 15.5885i | −0.0954911 | + | 0.496186i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.0000 | + | 51.9615i | 0.953945 | + | 1.65228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.5000 | − | 19.9186i | −1.09593 | − | 0.632735i | −0.160780 | − | 0.986990i | \(-0.551401\pi\) |
−0.935149 | + | 0.354256i | \(0.884734\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.5885i | 0.494685i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 55.4256i | − | 1.75711i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.5000 | − | 9.52628i | −0.522560 | − | 0.301700i | 0.215421 | − | 0.976521i | \(-0.430888\pi\) |
−0.737982 | + | 0.674821i | \(0.764221\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.50000 | − | 9.52628i | −0.174012 | − | 0.301398i |
(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.h.31.1 | yes | 2 | |
3.2 | odd | 2 | 1008.2.cs.a.703.1 | 2 | |||
4.3 | odd | 2 | 336.2.bl.d.31.1 | ✓ | 2 | ||
7.2 | even | 3 | 2352.2.bl.g.607.1 | 2 | |||
7.3 | odd | 6 | 2352.2.b.e.1567.1 | 2 | |||
7.4 | even | 3 | 2352.2.b.d.1567.2 | 2 | |||
7.5 | odd | 6 | 336.2.bl.d.271.1 | yes | 2 | ||
7.6 | odd | 2 | 2352.2.bl.a.31.1 | 2 | |||
8.3 | odd | 2 | 1344.2.bl.e.703.1 | 2 | |||
8.5 | even | 2 | 1344.2.bl.a.703.1 | 2 | |||
12.11 | even | 2 | 1008.2.cs.b.703.1 | 2 | |||
21.5 | even | 6 | 1008.2.cs.b.271.1 | 2 | |||
21.11 | odd | 6 | 7056.2.b.k.1567.1 | 2 | |||
21.17 | even | 6 | 7056.2.b.d.1567.2 | 2 | |||
28.3 | even | 6 | 2352.2.b.d.1567.1 | 2 | |||
28.11 | odd | 6 | 2352.2.b.e.1567.2 | 2 | |||
28.19 | even | 6 | inner | 336.2.bl.h.271.1 | yes | 2 | |
28.23 | odd | 6 | 2352.2.bl.a.607.1 | 2 | |||
28.27 | even | 2 | 2352.2.bl.g.31.1 | 2 | |||
56.5 | odd | 6 | 1344.2.bl.e.1279.1 | 2 | |||
56.19 | even | 6 | 1344.2.bl.a.1279.1 | 2 | |||
84.11 | even | 6 | 7056.2.b.d.1567.1 | 2 | |||
84.47 | odd | 6 | 1008.2.cs.a.271.1 | 2 | |||
84.59 | odd | 6 | 7056.2.b.k.1567.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bl.d.31.1 | ✓ | 2 | 4.3 | odd | 2 | ||
336.2.bl.d.271.1 | yes | 2 | 7.5 | odd | 6 | ||
336.2.bl.h.31.1 | yes | 2 | 1.1 | even | 1 | trivial | |
336.2.bl.h.271.1 | yes | 2 | 28.19 | even | 6 | inner | |
1008.2.cs.a.271.1 | 2 | 84.47 | odd | 6 | |||
1008.2.cs.a.703.1 | 2 | 3.2 | odd | 2 | |||
1008.2.cs.b.271.1 | 2 | 21.5 | even | 6 | |||
1008.2.cs.b.703.1 | 2 | 12.11 | even | 2 | |||
1344.2.bl.a.703.1 | 2 | 8.5 | even | 2 | |||
1344.2.bl.a.1279.1 | 2 | 56.19 | even | 6 | |||
1344.2.bl.e.703.1 | 2 | 8.3 | odd | 2 | |||
1344.2.bl.e.1279.1 | 2 | 56.5 | odd | 6 | |||
2352.2.b.d.1567.1 | 2 | 28.3 | even | 6 | |||
2352.2.b.d.1567.2 | 2 | 7.4 | even | 3 | |||
2352.2.b.e.1567.1 | 2 | 7.3 | odd | 6 | |||
2352.2.b.e.1567.2 | 2 | 28.11 | odd | 6 | |||
2352.2.bl.a.31.1 | 2 | 7.6 | odd | 2 | |||
2352.2.bl.a.607.1 | 2 | 28.23 | odd | 6 | |||
2352.2.bl.g.31.1 | 2 | 28.27 | even | 2 | |||
2352.2.bl.g.607.1 | 2 | 7.2 | even | 3 | |||
7056.2.b.d.1567.1 | 2 | 84.11 | even | 6 | |||
7056.2.b.d.1567.2 | 2 | 21.17 | even | 6 | |||
7056.2.b.k.1567.1 | 2 | 21.11 | odd | 6 | |||
7056.2.b.k.1567.2 | 2 | 84.59 | odd | 6 |