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 | 271.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.271 |
Dual form | 336.2.bl.c.31.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | 1.50000 | + | 0.866025i | 0.670820 | + | 0.387298i | 0.796387 | − | 0.604787i | \(-0.206742\pi\) |
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 1.50000 | − | 0.866025i | 0.452267 | − | 0.261116i | −0.256520 | − | 0.966539i | \(-0.582576\pi\) |
0.708787 | + | 0.705422i | \(0.249243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | − | 1.73205i | 0.727607 | − | 0.420084i | −0.0899392 | − | 0.995947i | \(-0.528667\pi\) |
0.817546 | + | 0.575863i | \(0.195334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | − | 1.73205i | 0.229416 | − | 0.397360i | −0.728219 | − | 0.685344i | \(-0.759652\pi\) |
0.957635 | + | 0.287984i | \(0.0929851\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50000 | + | 0.866025i | −0.545545 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00000 | 1.67126 | 0.835629 | − | 0.549294i | \(-0.185103\pi\) | ||||
0.835629 | + | 0.549294i | \(0.185103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | − | 0.866025i | −0.261116 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | − | 3.46410i | 0.507093 | − | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | + | 8.66025i | −0.821995 | + | 1.42374i | 0.0821995 | + | 0.996616i | \(0.473806\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.3923i | − | 1.62301i | −0.584349 | − | 0.811503i | \(-0.698650\pi\) | ||
0.584349 | − | 0.811503i | \(-0.301350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410i | 0.528271i | 0.964486 | + | 0.264135i | \(0.0850865\pi\) | ||||
−0.964486 | + | 0.264135i | \(0.914913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | + | 0.866025i | −0.223607 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | + | 10.3923i | −0.875190 | + | 1.51587i | −0.0186297 | + | 0.999826i | \(0.505930\pi\) |
−0.856560 | + | 0.516047i | \(0.827403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | − | 1.73205i | −0.420084 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | + | 7.79423i | 0.618123 | + | 1.07062i | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | + | 1.73205i | 0.251976 | + | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0000 | + | 6.92820i | −1.46603 | + | 0.846415i | −0.999279 | − | 0.0379722i | \(-0.987910\pi\) |
−0.466755 | + | 0.884387i | \(0.654577\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8564i | 1.64445i | 0.569160 | + | 0.822226i | \(0.307268\pi\) | ||||
−0.569160 | + | 0.822226i | \(0.692732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | + | 3.46410i | −0.702247 | + | 0.405442i | −0.808184 | − | 0.588930i | \(-0.799549\pi\) |
0.105937 | + | 0.994373i | \(0.466216\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | + | 1.73205i | −0.115470 | + | 0.200000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.50000 | − | 4.33013i | −0.170941 | − | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50000 | + | 2.59808i | 0.506290 | + | 0.292306i | 0.731307 | − | 0.682048i | \(-0.238911\pi\) |
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00000 | 0.329293 | 0.164646 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164646 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.50000 | − | 7.79423i | −0.482451 | − | 0.835629i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | − | 1.73205i | −0.317999 | − | 0.183597i | 0.332501 | − | 0.943103i | \(-0.392107\pi\) |
−0.650500 | + | 0.759506i | \(0.725441\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.50000 | + | 4.33013i | −0.259238 | + | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | − | 1.73205i | 0.307794 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 19.0526i | − | 1.93449i | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||
0.253837 | − | 0.967247i | \(-0.418307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.73205i | 0.174078i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0000 | + | 6.92820i | −1.19404 | + | 0.689382i | −0.959221 | − | 0.282656i | \(-0.908784\pi\) |
−0.234823 | + | 0.972038i | \(0.575451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.50000 | − | 0.866025i | −0.439155 | − | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5000 | − | 6.06218i | −1.01507 | − | 0.586053i | −0.102400 | − | 0.994743i | \(-0.532652\pi\) |
−0.912673 | + | 0.408690i | \(0.865986\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | + | 3.46410i | 0.191565 | + | 0.331801i | 0.945769 | − | 0.324840i | \(-0.105310\pi\) |
−0.754204 | + | 0.656640i | \(0.771977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0000 | 0.949158 | ||||||||
\(112\) | 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 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | − | 8.66025i | −0.275010 | − | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | + | 6.92820i | −0.363636 | + | 0.629837i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.00000 | + | 5.19615i | −0.811503 | + | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.19615i | 0.461084i | 0.973062 | + | 0.230542i | \(0.0740499\pi\) | ||||
−0.973062 | + | 0.230542i | \(0.925950\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.00000 | − | 1.73205i | 0.264135 | − | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50000 | − | 7.79423i | 0.393167 | − | 0.680985i | −0.599699 | − | 0.800226i | \(-0.704713\pi\) |
0.992865 | + | 0.119241i | \(0.0380462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | − | 3.46410i | −0.346844 | − | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.50000 | + | 0.866025i | 0.129099 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.5000 | + | 7.79423i | 1.12111 | + | 0.647275i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | + | 6.92820i | 0.0824786 | + | 0.571429i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.50000 | − | 2.59808i | 0.366205 | − | 0.211428i | −0.305594 | − | 0.952162i | \(-0.598855\pi\) |
0.671799 | + | 0.740733i | \(0.265522\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.46410i | 0.280056i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.66025i | − | 0.695608i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | − | 3.46410i | 0.478852 | − | 0.276465i | −0.241086 | − | 0.970504i | \(-0.577504\pi\) |
0.719938 | + | 0.694038i | \(0.244170\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.50000 | − | 7.79423i | 0.356873 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | − | 6.92820i | −0.939913 | − | 0.542659i | −0.0499796 | − | 0.998750i | \(-0.515916\pi\) |
−0.889933 | + | 0.456091i | \(0.849249\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.50000 | − | 2.59808i | −0.116775 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.00000 | + | 1.73205i | −0.377964 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.50000 | − | 7.79423i | 0.338241 | − | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.0000 | − | 12.1244i | 1.56961 | − | 0.906217i | 0.573400 | − | 0.819275i | \(-0.305624\pi\) |
0.996213 | − | 0.0869415i | \(-0.0277093\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3923i | 0.772454i | 0.922404 | + | 0.386227i | \(0.126222\pi\) | ||||
−0.922404 | + | 0.386227i | \(0.873778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.0000 | + | 8.66025i | −1.10282 | + | 0.636715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | − | 5.19615i | 0.219382 | − | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.500000 | − | 2.59808i | 0.0363696 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | − | 6.92820i | −0.868290 | − | 0.501307i | −0.00151007 | − | 0.999999i | \(-0.500481\pi\) |
−0.866779 | + | 0.498692i | \(0.833814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.50000 | + | 4.33013i | 0.179954 | + | 0.311689i | 0.941865 | − | 0.335993i | \(-0.109072\pi\) |
−0.761911 | + | 0.647682i | \(0.775738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | − | 13.8564i | −0.567105 | − | 0.982255i | −0.996850 | − | 0.0793045i | \(-0.974730\pi\) |
0.429745 | − | 0.902950i | \(-0.358603\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | + | 6.92820i | 0.846415 | + | 0.488678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.50000 | − | 23.3827i | 0.315838 | − | 1.64114i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | − | 15.5885i | 0.628587 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.46410i | − | 0.239617i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.92820i | − | 0.476957i | −0.971148 | − | 0.238479i | \(-0.923351\pi\) | ||
0.971148 | − | 0.238479i | \(-0.0766487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | − | 6.92820i | 0.822226 | − | 0.474713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | + | 5.19615i | −0.204598 | + | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5000 | + | 4.33013i | −0.848555 | + | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | + | 3.46410i | 0.405442 | + | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0000 | 1.27233 | 0.636167 | − | 0.771551i | \(-0.280519\pi\) | ||||
0.636167 | + | 0.771551i | \(0.280519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5000 | + | 18.1865i | 0.696909 | + | 1.20708i | 0.969533 | + | 0.244962i | \(0.0787754\pi\) |
−0.272623 | + | 0.962121i | \(0.587891\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.00000 | − | 1.73205i | −0.198246 | − | 0.114457i | 0.397591 | − | 0.917563i | \(-0.369846\pi\) |
−0.595837 | + | 0.803105i | \(0.703180\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | + | 3.46410i | −0.197386 | + | 0.227921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | + | 10.3923i | −1.17419 | + | 0.677919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.19615i | − | 0.337526i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.92820i | 0.448148i | 0.974572 | + | 0.224074i | \(0.0719358\pi\) | ||||
−0.974572 | + | 0.224074i | \(0.928064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5000 | − | 11.2583i | 1.25611 | − | 0.725213i | 0.283790 | − | 0.958886i | \(-0.408408\pi\) |
0.972315 | + | 0.233674i | \(0.0750747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.50000 | − | 9.52628i | −0.479157 | − | 0.608612i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.50000 | − | 2.59808i | −0.0950586 | − | 0.164646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | − | 5.19615i | −0.187867 | − | 0.325396i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | − | 5.19615i | −0.561405 | − | 0.324127i | 0.192304 | − | 0.981335i | \(-0.438404\pi\) |
−0.753709 | + | 0.657208i | \(0.771737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0000 | + | 17.3205i | 1.24274 | + | 1.07624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.50000 | + | 7.79423i | −0.278543 | + | 0.482451i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0000 | − | 8.66025i | 0.924940 | − | 0.534014i | 0.0397320 | − | 0.999210i | \(-0.487350\pi\) |
0.885208 | + | 0.465196i | \(0.154016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.5885i | 0.957591i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.46410i | 0.212000i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.5000 | + | 7.79423i | −0.823110 | + | 0.475223i | −0.851488 | − | 0.524375i | \(-0.824299\pi\) |
0.0283781 | + | 0.999597i | \(0.490966\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50000 | + | 9.52628i | −0.334101 | + | 0.578680i | −0.983312 | − | 0.181928i | \(-0.941766\pi\) |
0.649211 | + | 0.760609i | \(0.275099\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.00000 | − | 1.73205i | −0.180907 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0000 | − | 24.2487i | −0.841178 | − | 1.45696i | −0.888899 | − | 0.458103i | \(-0.848529\pi\) |
0.0477206 | − | 0.998861i | \(-0.484804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.00000 | + | 12.1244i | 0.416107 | + | 0.720718i | 0.995544 | − | 0.0942988i | \(-0.0300609\pi\) |
−0.579437 | + | 0.815017i | \(0.696728\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 1.73205i | −0.177705 | − | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.0000 | − | 5.19615i | −1.59376 | − | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.50000 | + | 4.33013i | −0.147059 | + | 0.254713i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.5000 | + | 9.52628i | −0.967247 | + | 0.558440i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.19615i | 0.303562i | 0.988414 | + | 0.151781i | \(0.0485009\pi\) | ||||
−0.988414 | + | 0.151781i | \(0.951499\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5885i | 0.907595i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.50000 | − | 0.866025i | 0.0870388 | − | 0.0502519i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.00000 | + | 1.73205i | 0.518751 | + | 0.0998337i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | + | 6.92820i | 0.689382 | + | 0.398015i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.00000 | + | 15.5885i | 0.510343 | + | 0.883940i | 0.999928 | + | 0.0119847i | \(0.00381495\pi\) |
−0.489585 | + | 0.871956i | \(0.662852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.50000 | − | 2.59808i | −0.254355 | − | 0.146852i | 0.367402 | − | 0.930062i | \(-0.380247\pi\) |
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.50000 | + | 4.33013i | 0.0845154 | + | 0.243975i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.5000 | − | 18.1865i | 0.589739 | − | 1.02146i | −0.404528 | − | 0.914526i | \(-0.632564\pi\) |
0.994266 | − | 0.106932i | \(-0.0341026\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5000 | − | 7.79423i | 0.755855 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.1244i | 0.676716i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.92820i | − | 0.385496i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | − | 3.46410i | 0.110600 | − | 0.191565i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.0000 | + | 20.7846i | 1.32316 | + | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | + | 6.92820i | 0.659580 | + | 0.380808i | 0.792117 | − | 0.610370i | \(-0.208979\pi\) |
−0.132537 | + | 0.991178i | \(0.542312\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.00000 | − | 8.66025i | −0.273998 | − | 0.474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.0000 | −1.31126 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | −0.0544735 | −0.0272367 | − | 0.999629i | \(-0.508671\pi\) | ||||
−0.0272367 | + | 0.999629i | \(0.508671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.50000 | − | 4.33013i | −0.406148 | − | 0.234490i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0000 | + | 8.66025i | −0.805242 | + | 0.464907i | −0.845301 | − | 0.534291i | \(-0.820579\pi\) |
0.0400587 | + | 0.999197i | \(0.487246\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.92820i | − | 0.370858i | −0.982658 | − | 0.185429i | \(-0.940632\pi\) | ||
0.982658 | − | 0.185429i | \(-0.0593675\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000 | − | 3.46410i | 0.319348 | − | 0.184376i | −0.331754 | − | 0.943366i | \(-0.607640\pi\) |
0.651102 | + | 0.758990i | \(0.274307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | + | 20.7846i | −0.636894 | + | 1.10313i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | + | 6.92820i | −0.317554 | + | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | + | 13.8564i | 1.26667 | + | 0.731313i | 0.974357 | − | 0.225009i | \(-0.0722411\pi\) |
0.292315 | + | 0.956322i | \(0.405574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.00000 | 0.419891 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0000 | −0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.50000 | − | 16.4545i | −0.495896 | − | 0.858917i | 0.504093 | − | 0.863649i | \(-0.331827\pi\) |
−0.999989 | + | 0.00473247i | \(0.998494\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.00000 | + | 5.19615i | 0.468521 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.5000 | − | 7.79423i | 1.16814 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | + | 1.73205i | −0.0517780 | + | 0.0896822i | −0.890753 | − | 0.454488i | \(-0.849822\pi\) |
0.838975 | + | 0.544170i | \(0.183156\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5000 | + | 6.06218i | −0.542218 | + | 0.313050i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.2487i | − | 1.24557i | −0.782392 | − | 0.622786i | \(-0.786001\pi\) | ||
0.782392 | − | 0.622786i | \(-0.213999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.50000 | − | 2.59808i | 0.230542 | − | 0.133103i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.00000 | + | 15.5885i | −0.459879 | + | 0.796533i | −0.998954 | − | 0.0457244i | \(-0.985440\pi\) |
0.539076 | + | 0.842257i | \(0.318774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.50000 | − | 7.79423i | 0.0764471 | − | 0.397231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | − | 1.73205i | −0.152499 | − | 0.0880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.00000 | −0.453990 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.50000 | + | 7.79423i | 0.226420 | + | 0.392170i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0000 | − | 10.3923i | −0.903394 | − | 0.521575i | −0.0250943 | − | 0.999685i | \(-0.507989\pi\) |
−0.878300 | + | 0.478110i | \(0.841322\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.00000 | + | 5.19615i | −0.0500626 | + | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.73205i | − | 0.0860663i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.3205i | 0.858546i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5000 | + | 11.2583i | −0.964213 | + | 0.556689i | −0.897467 | − | 0.441081i | \(-0.854595\pi\) |
−0.0667458 | + | 0.997770i | \(0.521262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | − | 10.3923i | 0.295958 | − | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.5000 | − | 7.79423i | 1.10715 | − | 0.383529i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.50000 | + | 2.59808i | 0.220896 | + | 0.127535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.00000 | − | 12.1244i | −0.342791 | − | 0.593732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | − | 10.3923i | −0.291730 | − | 0.505291i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | − | 3.46410i | −0.291043 | − | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.0000 | − | 19.0526i | 1.58955 | − | 0.917729i | 0.596174 | − | 0.802855i | \(-0.296687\pi\) |
0.993380 | − | 0.114874i | \(-0.0366465\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 15.5885i | − | 0.747409i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5000 | − | 25.1147i | 0.692047 | − | 1.19866i | −0.279119 | − | 0.960257i | \(-0.590042\pi\) |
0.971166 | − | 0.238404i | \(-0.0766244\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5000 | + | 6.06218i | 0.498870 | + | 0.288023i | 0.728247 | − | 0.685315i | \(-0.240335\pi\) |
−0.229377 | + | 0.973338i | \(0.573669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | − | 5.19615i | −0.142214 | − | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.50000 | − | 2.59808i | −0.211428 | − | 0.122068i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5000 | − | 26.8468i | 0.725059 | − | 1.25584i | −0.233890 | − | 0.972263i | \(-0.575146\pi\) |
0.958950 | − | 0.283577i | \(-0.0915211\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.00000 | − | 1.73205i | 0.140028 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.92820i | − | 0.322679i | −0.986899 | − | 0.161339i | \(-0.948419\pi\) | ||
0.986899 | − | 0.161339i | \(-0.0515813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 38.1051i | − | 1.77090i | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||
0.464739 | − | 0.885448i | \(-0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.50000 | + | 4.33013i | −0.347804 | + | 0.200805i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.00000 | + | 10.3923i | −0.277647 | + | 0.480899i | −0.970799 | − | 0.239892i | \(-0.922888\pi\) |
0.693153 | + | 0.720791i | \(0.256221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | + | 34.6410i | 0.554109 | + | 1.59957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00000 | − | 3.46410i | −0.276465 | − | 0.159617i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | + | 5.19615i | 0.137940 | + | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | −0.412082 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.00000 | − | 5.19615i | −0.137073 | − | 0.237418i | 0.789314 | − | 0.613990i | \(-0.210436\pi\) |
−0.926388 | + | 0.376571i | \(0.877103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.5000 | − | 28.5788i | 0.749226 | − | 1.29770i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.50000 | + | 4.33013i | −0.339857 | + | 0.196217i | −0.660209 | − | 0.751082i | \(-0.729532\pi\) |
0.320352 | + | 0.947299i | \(0.396199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.8564i | 0.626608i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 25.9808i | − | 1.17250i | −0.810132 | − | 0.586248i | \(-0.800605\pi\) | ||
0.810132 | − | 0.586248i | \(-0.199395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0000 | − | 15.5885i | 1.21602 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.50000 | + | 2.59808i | −0.0674200 | + | 0.116775i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36.0000 | + | 6.92820i | 1.61482 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.00000 | + | 1.73205i | 0.134298 | + | 0.0775372i | 0.565644 | − | 0.824650i | \(-0.308628\pi\) |
−0.431346 | + | 0.902187i | \(0.641961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 10.3923i | 0.268060 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0000 | −1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.50000 | − | 11.2583i | −0.288675 | − | 0.500000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.5000 | + | 16.4545i | 1.26324 | + | 0.729332i | 0.973700 | − | 0.227834i | \(-0.0731643\pi\) |
0.289540 | + | 0.957166i | \(0.406498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 17.3205i | 0.265424 | + | 0.766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | − | 1.73205i | 0.0441511 | − | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.00000 | − | 3.46410i | 0.264392 | − | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.7846i | 0.914106i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.0000 | − | 19.0526i | 1.44576 | − | 0.834708i | 0.447532 | − | 0.894268i | \(-0.352303\pi\) |
0.998225 | + | 0.0595604i | \(0.0189699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0000 | − | 24.2487i | 0.612177 | − | 1.06032i | −0.378695 | − | 0.925521i | \(-0.623627\pi\) |
0.990873 | − | 0.134801i | \(-0.0430394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.00000 | + | 3.46410i | 0.174574 | + | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0000 | − | 8.66025i | −0.653410 | − | 0.377247i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.00000 | −0.390567 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.5000 | − | 18.1865i | −0.453955 | − | 0.786272i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.0000 | − | 12.1244i | −0.906217 | − | 0.523205i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0000 | + | 1.73205i | −0.516877 | + | 0.0746047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0000 | + | 19.0526i | −0.472927 | + | 0.819133i | −0.999520 | − | 0.0309841i | \(-0.990136\pi\) |
0.526593 | + | 0.850118i | \(0.323469\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.00000 | − | 5.19615i | 0.386227 | − | 0.222988i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.92820i | 0.296772i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.3923i | − | 0.444343i | −0.975008 | − | 0.222171i | \(-0.928686\pi\) | ||
0.975008 | − | 0.222171i | \(-0.0713145\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.00000 | − | 10.3923i | 0.382719 | − | 0.441926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.0000 | + | 8.66025i | 0.636715 | + | 0.367607i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.5000 | + | 23.3827i | 0.572013 | + | 0.990756i | 0.996359 | + | 0.0852559i | \(0.0271708\pi\) |
−0.424346 | + | 0.905500i | \(0.639496\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.5000 | + | 38.9711i | 0.948262 | + | 1.64244i | 0.749085 | + | 0.662474i | \(0.230494\pi\) |
0.199177 | + | 0.979963i | \(0.436173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | + | 5.19615i | 0.378633 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.50000 | + | 0.866025i | −0.104990 | + | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.0000 | + | 10.3923i | −0.753277 | + | 0.434904i | −0.826877 | − | 0.562383i | \(-0.809885\pi\) |
0.0736000 | + | 0.997288i | \(0.476551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8564i | 0.578860i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.50000 | + | 0.866025i | −0.0624458 | + | 0.0360531i | −0.530898 | − | 0.847436i | \(-0.678145\pi\) |
0.468452 | + | 0.883489i | \(0.344812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.50000 | − | 4.33013i | 0.103896 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.50000 | − | 7.79423i | 0.0622305 | − | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5000 | + | 7.79423i | 0.559113 | + | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.0000 | −1.36206 | −0.681028 | − | 0.732257i | \(-0.738467\pi\) | ||||
−0.681028 | + | 0.732257i | \(0.738467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0000 | −0.412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.0000 | − | 13.8564i | −0.985562 | − | 0.569014i | −0.0816172 | − | 0.996664i | \(-0.526008\pi\) |
−0.903945 | + | 0.427649i | \(0.859342\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00000 | − | 15.5885i | 0.122988 | − | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.00000 | + | 13.8564i | −0.327418 | + | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | − | 13.8564i | 0.980613 | − | 0.566157i | 0.0781581 | − | 0.996941i | \(-0.475096\pi\) |
0.902455 | + | 0.430784i | \(0.141763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.5885i | − | 0.635866i | −0.948113 | − | 0.317933i | \(-0.897011\pi\) | ||
0.948113 | − | 0.317933i | \(-0.102989\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 13.8564i | − | 0.564276i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.0000 | + | 6.92820i | −0.487869 | + | 0.281672i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.50000 | + | 16.4545i | −0.385593 | + | 0.667867i | −0.991851 | − | 0.127401i | \(-0.959336\pi\) |
0.606258 | + | 0.795268i | \(0.292670\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.5000 | + | 7.79423i | −0.911746 | + | 0.315838i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | + | 3.46410i | 0.0807792 | + | 0.139914i | 0.903585 | − | 0.428409i | \(-0.140926\pi\) |
−0.822806 | + | 0.568323i | \(0.807592\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0000 | −0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000 | 0.483102 | 0.241551 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241551 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000 | + | 24.2487i | 0.562708 | + | 0.974638i | 0.997259 | + | 0.0739910i | \(0.0235736\pi\) |
−0.434551 | + | 0.900647i | \(0.643093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | + | 6.92820i | −0.240385 | + | 0.277573i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.00000 | + | 1.73205i | −0.119808 | + | 0.0691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.6410i | 1.38123i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.9090i | 1.31009i | 0.755592 | + | 0.655043i | \(0.227349\pi\) | ||||
−0.755592 | + | 0.655043i | \(0.772651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.00000 | + | 3.46410i | −0.238479 | + | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.50000 | + | 7.79423i | −0.178577 | + | 0.309305i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | − | 6.92820i | −0.474713 | − | 0.274075i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0000 | − | 31.1769i | −0.710957 | − | 1.23141i | −0.964498 | − | 0.264089i | \(-0.914929\pi\) |
0.253541 | − | 0.967325i | \(-0.418405\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.0000 | 0.630978 | 0.315489 | − | 0.948929i | \(-0.397831\pi\) | ||||
0.315489 | + | 0.948929i | \(0.397831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | + | 7.79423i | 0.529921 | + | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0000 | + | 8.66025i | 0.391931 | + | 0.339422i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5000 | − | 23.3827i | 0.528296 | − | 0.915035i | −0.471160 | − | 0.882048i | \(-0.656165\pi\) |
0.999456 | − | 0.0329874i | \(-0.0105021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.5000 | − | 7.79423i | 0.527489 | − | 0.304546i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.92820i | − | 0.270295i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3923i | 0.404827i | 0.979300 | + | 0.202413i | \(0.0648785\pi\) | ||||
−0.979300 | + | 0.202413i | \(0.935122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.00000 | − | 1.73205i | 0.116686 | − | 0.0673690i | −0.440521 | − | 0.897742i | \(-0.645206\pi\) |
0.557207 | + | 0.830373i | \(0.311873\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.00000 | − | 8.66025i | −0.116335 | − | 0.335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.50000 | − | 16.4545i | −0.367291 | − | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.0000 | −1.34915 | −0.674575 | − | 0.738206i | \(-0.735673\pi\) | ||||
−0.674575 | + | 0.738206i | \(0.735673\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | − | 1.73205i | −0.0384900 | − | 0.0666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.5000 | + | 14.7224i | 0.980045 | + | 0.565829i | 0.902284 | − | 0.431143i | \(-0.141890\pi\) |
0.0777610 | + | 0.996972i | \(0.475223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.5000 | − | 9.52628i | −1.89964 | − | 0.365585i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5000 | − | 18.1865i | 0.402361 | − | 0.696909i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.5000 | + | 12.9904i | −0.860939 | + | 0.497063i | −0.864326 | − | 0.502931i | \(-0.832255\pi\) |
0.00338791 | + | 0.999994i | \(0.498922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7846i | 0.794139i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.46410i | 0.132164i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0000 | − | 19.0526i | 0.418460 | − | 0.724793i | −0.577325 | − | 0.816514i | \(-0.695903\pi\) |
0.995785 | + | 0.0917209i | \(0.0292368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.50000 | + | 0.866025i | 0.170941 | + | 0.0328976i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.0000 | + | 12.1244i | 0.796575 | + | 0.459903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | − | 31.1769i | −0.681799 | − | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.0000 | 0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.0000 | −1.69963 | −0.849813 | − | 0.527084i | \(-0.823285\pi\) | ||||
−0.849813 | + | 0.527084i | \(0.823285\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0000 | + | 17.3205i | 0.377157 | + | 0.653255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.0000 | + | 10.3923i | 0.677919 | + | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | + | 34.6410i | 0.451306 | + | 1.30281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.50000 | + | 2.59808i | −0.168763 | + | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.00000 | − | 3.46410i | 0.224074 | − | 0.129369i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.00000 | + | 15.5885i | −0.335643 | + | 0.581351i | −0.983608 | − | 0.180319i | \(-0.942287\pi\) |
0.647965 | + | 0.761670i | \(0.275620\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | − | 6.92820i | −0.297936 | − | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.5000 | − | 11.2583i | −0.725213 | − | 0.418702i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.00000 | − | 15.5885i | −0.334252 | − | 0.578941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.0000 | −1.37225 | −0.686127 | − | 0.727482i | \(-0.740691\pi\) | ||||
−0.686127 | + | 0.727482i | \(0.740691\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | + | 10.3923i | 0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.00000 | − | 5.19615i | −0.332423 | − | 0.191924i | 0.324494 | − | 0.945888i | \(-0.394806\pi\) |
−0.656916 | + | 0.753964i | \(0.728139\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.50000 | + | 11.2583i | −0.165985 | + | 0.415270i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | + | 20.7846i | −0.442026 | + | 0.765611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.00000 | − | 5.19615i | 0.331070 | − | 0.191144i | −0.325246 | − | 0.945629i | \(-0.605447\pi\) |
0.656316 | + | 0.754486i | \(0.272114\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.8564i | − | 0.508342i | −0.967159 | − | 0.254171i | \(-0.918197\pi\) | ||
0.967159 | − | 0.254171i | \(-0.0818026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.00000 | + | 5.19615i | −0.329734 | + | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50000 | + | 2.59808i | −0.0548821 | + | 0.0950586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.0000 | + | 24.2487i | −0.767323 | + | 0.886029i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.50000 | + | 2.59808i | 0.164207 | + | 0.0948051i | 0.579852 | − | 0.814722i | \(-0.303111\pi\) |
−0.415644 | + | 0.909527i | \(0.636444\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.50000 | + | 12.9904i | 0.273315 | + | 0.473396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.00000 | 0.327544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.00000 | −0.145382 | −0.0726912 | − | 0.997354i | \(-0.523159\pi\) | ||||
−0.0726912 | + | 0.997354i | \(0.523159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.0000 | − | 24.2487i | −1.52250 | − | 0.879015i | −0.999646 | − | 0.0265919i | \(-0.991535\pi\) |
−0.522852 | − | 0.852423i | \(-0.675132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | − | 3.46410i | 0.362024 | − | 0.125409i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.00000 | + | 5.19615i | −0.108465 | + | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.0526i | 0.687053i | 0.939143 | + | 0.343526i | \(0.111621\pi\) | ||||
−0.939143 | + | 0.343526i | \(0.888379\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3923i | 0.374270i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.00000 | + | 8.66025i | −0.179605 | + | 0.311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.00000 | − | 25.9808i | 0.179374 | − | 0.932055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.0000 | − | 10.3923i | −0.644917 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | + | 20.7846i | 0.429394 | + | 0.743732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0000 | 0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0000 | + | 24.2487i | 0.499046 | + | 0.864373i | 0.999999 | − | 0.00110111i | \(-0.000350496\pi\) |
−0.500953 | + | 0.865474i | \(0.667017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.0000 | − | 8.66025i | −0.534014 | − | 0.308313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.00000 | − | 15.5885i | 0.106668 | − | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.5000 | − | 7.79423i | 0.478796 | − | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.19615i | 0.184057i | 0.995756 | + | 0.0920286i | \(0.0293351\pi\) | ||||
−0.995756 | + | 0.0920286i | \(0.970665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.5692i | 1.47061i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | − | 1.73205i | 0.106000 | − | 0.0611990i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.00000 | + | 10.3923i | −0.211735 | + | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.5000 | + | 7.79423i | 0.475223 | + | 0.274370i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.0000 | 0.385787 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | − | 20.7846i | −0.420342 | − | 0.728053i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | + | 3.46410i | 0.209913 | + | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.50000 | + | 2.59808i | −0.0523504 | + | 0.0906735i | −0.891013 | − | 0.453978i | \(-0.850005\pi\) |
0.838663 | + | 0.544651i | \(0.183338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.0000 | + | 19.0526i | −1.15031 | + | 0.664130i | −0.948962 | − | 0.315390i | \(-0.897865\pi\) |
−0.201345 | + | 0.979520i | \(0.564531\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.46410i | 0.120605i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.8372i | 1.38527i | 0.721286 | + | 0.692637i | \(0.243551\pi\) | ||||
−0.721286 | + | 0.692637i | \(0.756449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.0000 | + | 8.66025i | −0.520972 | + | 0.300783i | −0.737332 | − | 0.675530i | \(-0.763915\pi\) |
0.216361 | + | 0.976314i | \(0.430581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.0000 | + | 24.2487i | −0.485655 | + | 0.841178i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.0000 | + | 3.46410i | −0.831551 | + | 0.120024i | ||||
\(834\) | 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 | ||||||||
\(839\) | 30.0000 | 1.03572 | 0.517858 | − | 0.855467i | \(-0.326730\pi\) | ||||
0.517858 | + | 0.855467i | \(0.326730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000 | + | 20.7846i | 0.413302 | + | 0.715860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.5000 | + | 11.2583i | 0.670820 | + | 0.387298i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.0000 | + | 13.8564i | 0.549767 | + | 0.476112i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.00000 | − | 12.1244i | 0.240239 | − | 0.416107i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 48.4974i | − | 1.66052i | −0.557376 | − | 0.830260i | \(-0.688192\pi\) | ||
0.557376 | − | 0.830260i | \(-0.311808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.46410i | 0.118470i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.00000 | − | 12.1244i | 0.238837 | − | 0.413678i | −0.721544 | − | 0.692369i | \(-0.756567\pi\) |
0.960381 | + | 0.278691i | \(0.0899005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.00000 | + | 25.9808i | 0.306719 | + | 0.885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0000 | − | 15.5885i | −0.919091 | − | 0.530637i | −0.0357458 | − | 0.999361i | \(-0.511381\pi\) |
−0.883345 | + | 0.468724i | \(0.844714\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.00000 | 0.169809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.00000 | 0.305304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.5000 | + | 9.52628i | 0.558440 | + | 0.322416i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.5000 | − | 6.06218i | −1.06489 | − | 0.204939i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.0000 | + | 27.7128i | −0.540282 | + | 0.935795i | 0.458606 | + | 0.888640i | \(0.348349\pi\) |
−0.998888 | + | 0.0471555i | \(0.984984\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.50000 | − | 2.59808i | 0.151781 | − | 0.0876309i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.8564i | − | 0.466834i | −0.972377 | − | 0.233417i | \(-0.925009\pi\) | ||
0.972377 | − | 0.233417i | \(-0.0749907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.2487i | − | 0.816034i | −0.912974 | − | 0.408017i | \(-0.866220\pi\) | ||
0.912974 | − | 0.408017i | \(-0.133780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5000 | − | 7.79423i | 0.453798 | − | 0.262000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0000 | − | 41.5692i | 0.805841 | − | 1.39576i | −0.109881 | − | 0.993945i | \(-0.535047\pi\) |
0.915722 | − | 0.401813i | \(-0.131620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.5000 | + | 2.59808i | 0.452775 | + | 0.0871367i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 0.866025i | −0.0502519 | − | 0.0290129i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0000 | + | 20.7846i | 0.401565 | + | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.0000 | 1.40391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.5000 | − | 38.9711i | −0.750417 | − | 1.29976i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0000 | + | 15.5885i | 0.899500 | + | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.00000 | − | 8.66025i | −0.0998337 | − | 0.288195i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.00000 | + | 15.5885i | −0.299170 | + | 0.518178i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.0000 | − | 10.3923i | 0.597680 | − | 0.345071i | −0.170448 | − | 0.985367i | \(-0.554522\pi\) |
0.768128 | + | 0.640296i | \(0.221188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 13.8564i | − | 0.459588i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 41.5692i | − | 1.37725i | −0.725118 | − | 0.688625i | \(-0.758215\pi\) | ||
0.725118 | − | 0.688625i | \(-0.241785\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.50000 | − | 2.59808i | 0.148928 | − | 0.0859838i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.0000 | − | 15.5885i | −0.594412 | − | 0.514776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.0000 | + | 8.66025i | 0.494804 | + | 0.285675i | 0.726565 | − | 0.687097i | \(-0.241115\pi\) |
−0.231761 | + | 0.972773i | \(0.574449\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | + | 17.3205i | 0.329511 | + | 0.570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0000 | 0.657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00000 | + | 3.46410i | 0.0656886 | + | 0.113776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.0000 | − | 8.66025i | −0.492134 | − | 0.284134i | 0.233325 | − | 0.972399i | \(-0.425039\pi\) |
−0.725459 | + | 0.688265i | \(0.758373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0000 | + | 8.66025i | −0.360510 | + | 0.283828i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.00000 | − | 15.5885i | 0.294647 | − | 0.510343i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.00000 | − | 5.19615i | 0.294331 | − | 0.169932i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.0526i | − | 0.622420i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) | ||
0.950341 | − | 0.311210i | \(-0.100734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.19615i | 0.169570i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.5000 | + | 19.9186i | −1.12467 | + | 0.649327i | −0.942588 | − | 0.333957i | \(-0.891616\pi\) |
−0.182079 | + | 0.983284i | \(0.558283\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.00000 | − | 3.46410i | 0.0975900 | − | 0.112687i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.0000 | − | 19.0526i | −1.07236 | − | 0.619125i | −0.143532 | − | 0.989646i | \(-0.545846\pi\) |
−0.928824 | + | 0.370521i | \(0.879179\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.0000 | −0.680972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0000 | − | 20.7846i | −0.388311 | − | 0.672574i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.5000 | − | 7.79423i | −0.436393 | − | 0.251952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.0000 | − | 10.3923i | 0.968751 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5000 | − | 6.06218i | 0.338358 | − | 0.195351i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.66025i | 0.278783i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39.8372i | − | 1.28108i | −0.767926 | − | 0.640538i | \(-0.778711\pi\) | ||
0.767926 | − | 0.640538i | \(-0.221289\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.00000 | + | 3.46410i | −0.192748 | + | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5000 | − | 28.5788i | 0.529510 | − | 0.917139i | −0.469897 | − | 0.882721i | \(-0.655709\pi\) |
0.999408 | − | 0.0344175i | \(-0.0109576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.00000 | − | 36.3731i | 0.224410 | − | 1.16607i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | + | 15.5885i | 0.287936 | + | 0.498719i | 0.973317 | − | 0.229465i | \(-0.0736978\pi\) |
−0.685381 | + | 0.728184i | \(0.740364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.00000 | − | 15.5885i | −0.287055 | − | 0.497195i | 0.686050 | − | 0.727554i | \(-0.259343\pi\) |
−0.973106 | + | 0.230360i | \(0.926010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | − | 5.19615i | −0.286764 | − | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | − | 31.1769i | 0.190982 | − | 0.992372i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5000 | − | 6.06218i | 0.333543 | − | 0.192571i | −0.323870 | − | 0.946102i | \(-0.604984\pi\) |
0.657413 | + | 0.753530i | \(0.271651\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.8564i | − | 0.439720i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 27.7128i | − | 0.878555i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.0000 | − | 13.8564i | 0.760088 | − | 0.438837i | −0.0692396 | − | 0.997600i | \(-0.522057\pi\) |
0.829327 | + | 0.558763i | \(0.188724\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.00000 | + | 8.66025i | −0.158193 | + | 0.273998i |
(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.c.271.1 | yes | 2 | |
3.2 | odd | 2 | 1008.2.cs.e.271.1 | 2 | |||
4.3 | odd | 2 | 336.2.bl.g.271.1 | yes | 2 | ||
7.2 | even | 3 | 2352.2.b.g.1567.1 | 2 | |||
7.3 | odd | 6 | 336.2.bl.g.31.1 | yes | 2 | ||
7.4 | even | 3 | 2352.2.bl.b.31.1 | 2 | |||
7.5 | odd | 6 | 2352.2.b.c.1567.2 | 2 | |||
7.6 | odd | 2 | 2352.2.bl.h.607.1 | 2 | |||
8.3 | odd | 2 | 1344.2.bl.b.1279.1 | 2 | |||
8.5 | even | 2 | 1344.2.bl.f.1279.1 | 2 | |||
12.11 | even | 2 | 1008.2.cs.d.271.1 | 2 | |||
21.2 | odd | 6 | 7056.2.b.e.1567.2 | 2 | |||
21.5 | even | 6 | 7056.2.b.i.1567.1 | 2 | |||
21.17 | even | 6 | 1008.2.cs.d.703.1 | 2 | |||
28.3 | even | 6 | inner | 336.2.bl.c.31.1 | ✓ | 2 | |
28.11 | odd | 6 | 2352.2.bl.h.31.1 | 2 | |||
28.19 | even | 6 | 2352.2.b.g.1567.2 | 2 | |||
28.23 | odd | 6 | 2352.2.b.c.1567.1 | 2 | |||
28.27 | even | 2 | 2352.2.bl.b.607.1 | 2 | |||
56.3 | even | 6 | 1344.2.bl.f.703.1 | 2 | |||
56.45 | odd | 6 | 1344.2.bl.b.703.1 | 2 | |||
84.23 | even | 6 | 7056.2.b.i.1567.2 | 2 | |||
84.47 | odd | 6 | 7056.2.b.e.1567.1 | 2 | |||
84.59 | odd | 6 | 1008.2.cs.e.703.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bl.c.31.1 | ✓ | 2 | 28.3 | even | 6 | inner | |
336.2.bl.c.271.1 | yes | 2 | 1.1 | even | 1 | trivial | |
336.2.bl.g.31.1 | yes | 2 | 7.3 | odd | 6 | ||
336.2.bl.g.271.1 | yes | 2 | 4.3 | odd | 2 | ||
1008.2.cs.d.271.1 | 2 | 12.11 | even | 2 | |||
1008.2.cs.d.703.1 | 2 | 21.17 | even | 6 | |||
1008.2.cs.e.271.1 | 2 | 3.2 | odd | 2 | |||
1008.2.cs.e.703.1 | 2 | 84.59 | odd | 6 | |||
1344.2.bl.b.703.1 | 2 | 56.45 | odd | 6 | |||
1344.2.bl.b.1279.1 | 2 | 8.3 | odd | 2 | |||
1344.2.bl.f.703.1 | 2 | 56.3 | even | 6 | |||
1344.2.bl.f.1279.1 | 2 | 8.5 | even | 2 | |||
2352.2.b.c.1567.1 | 2 | 28.23 | odd | 6 | |||
2352.2.b.c.1567.2 | 2 | 7.5 | odd | 6 | |||
2352.2.b.g.1567.1 | 2 | 7.2 | even | 3 | |||
2352.2.b.g.1567.2 | 2 | 28.19 | even | 6 | |||
2352.2.bl.b.31.1 | 2 | 7.4 | even | 3 | |||
2352.2.bl.b.607.1 | 2 | 28.27 | even | 2 | |||
2352.2.bl.h.31.1 | 2 | 28.11 | odd | 6 | |||
2352.2.bl.h.607.1 | 2 | 7.6 | odd | 2 | |||
7056.2.b.e.1567.1 | 2 | 84.47 | odd | 6 | |||
7056.2.b.e.1567.2 | 2 | 21.2 | odd | 6 | |||
7056.2.b.i.1567.1 | 2 | 21.5 | even | 6 | |||
7056.2.b.i.1567.2 | 2 | 84.23 | even | 6 |