Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(569,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.q (of order \(6\), degree \(2\), not 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: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.31116960000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} - 8x^{4} + 9x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 949.3 | ||
Root | \(-1.62968 - 0.586627i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.949 |
Dual form | 980.2.q.i.569.3 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.01607 | + | 0.586627i | 0.586627 | + | 0.338689i | 0.763763 | − | 0.645497i | \(-0.223350\pi\) |
−0.177136 | + | 0.984186i | \(0.556683\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.93649 | + | 1.11803i | −0.866025 | + | 0.500000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.811738 | − | 1.40597i | −0.270579 | − | 0.468657i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.31174 | + | 5.73610i | −0.998526 | + | 1.72950i | −0.452267 | + | 0.891883i | \(0.649385\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.64539i | − | 1.56575i | −0.622179 | − | 0.782875i | \(-0.713753\pi\) | ||
0.622179 | − | 0.782875i | \(-0.286247\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.62348 | −0.677378 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.92119 | − | 3.99595i | −1.67863 | − | 0.969160i | −0.962533 | − | 0.271163i | \(-0.912592\pi\) |
−0.716101 | − | 0.697997i | \(-0.754075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.42451i | − | 1.04395i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.623475 | 0.115776 | 0.0578882 | − | 0.998323i | \(-0.481563\pi\) | ||||
0.0578882 | + | 0.998323i | \(0.481563\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.72990 | + | 3.88551i | −1.17153 | + | 0.676380i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.31174 | − | 5.73610i | 0.530302 | − | 0.918511i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.14385 | + | 1.81510i | 0.468657 | + | 0.270579i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.7942 | + | 6.23202i | −1.57449 | + | 0.909033i | −0.578884 | + | 0.815410i | \(0.696511\pi\) |
−0.995608 | + | 0.0936230i | \(0.970155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.68826 | − | 8.12031i | −0.656488 | − | 1.13707i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.8105i | − | 1.99705i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.31174 | + | 10.9323i | 0.782875 | + | 1.35598i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6190 | − | 6.70820i | −1.35990 | − | 0.785136i | −0.370286 | − | 0.928918i | \(-0.620740\pi\) |
−0.989609 | + | 0.143782i | \(0.954074\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.08034 | − | 2.93313i | 0.586627 | − | 0.338689i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.93521 | + | 13.7442i | 0.892781 | + | 1.54634i | 0.836527 | + | 0.547926i | \(0.184582\pi\) |
0.0562544 | + | 0.998416i | \(0.482084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.746951 | − | 1.29376i | 0.0829945 | − | 0.143751i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.94427i | − | 0.981761i | −0.871227 | − | 0.490881i | \(-0.836675\pi\) | ||
0.871227 | − | 0.490881i | \(-0.163325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.8704 | 1.93832 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.633493 | + | 0.365747i | 0.0679176 | + | 0.0392122i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.6849i | 1.28796i | 0.765043 | + | 0.643979i | \(0.222718\pi\) | ||||
−0.765043 | + | 0.643979i | \(0.777282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.7530 | 1.08072 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.72990 | − | 3.88551i | 0.663117 | − | 0.382851i | −0.130347 | − | 0.991468i | \(-0.541609\pi\) |
0.793463 | + | 0.608618i | \(0.208276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.93521 | + | 8.54804i | −0.472708 | + | 0.818754i | −0.999512 | − | 0.0312328i | \(-0.990057\pi\) |
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.93725 | + | 4.58258i | −0.733799 | + | 0.423659i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.4352 | − | 28.4666i | −1.49411 | − | 2.58787i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.06479 | + | 10.5045i | 0.521974 | + | 0.904085i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.6235 | −1.23152 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 32.3825 | + | 18.6961i | 2.70796 | + | 1.56344i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.20735 | + | 0.697067i | −0.100265 | + | 0.0578882i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9352 | + | 20.6724i | −0.971274 | + | 1.68230i | −0.279554 | + | 0.960130i | \(0.590186\pi\) |
−0.691720 | + | 0.722166i | \(0.743147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.9746i | 1.04894i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6190 | − | 6.70820i | −0.927293 | − | 0.535373i | −0.0413387 | − | 0.999145i | \(-0.513162\pi\) |
−0.885954 | + | 0.463772i | \(0.846496\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.68826 | − | 15.0485i | 0.676380 | − | 1.17153i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.42451i | 0.419761i | 0.977727 | + | 0.209881i | \(0.0673075\pi\) | ||||
−0.977727 | + | 0.209881i | \(0.932692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.8704 | −1.45157 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.0176 | − | 7.51571i | 0.989709 | − | 0.571409i | 0.0845218 | − | 0.996422i | \(-0.473064\pi\) |
0.905187 | + | 0.425013i | \(0.139730\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | − | 20.7846i | 0.896922 | − | 1.55351i | 0.0655145 | − | 0.997852i | \(-0.479131\pi\) |
0.831408 | − | 0.555663i | \(-0.187536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 45.8423 | − | 26.4671i | 3.35232 | − | 1.93546i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.31174 | − | 16.1284i | −0.673774 | − | 1.16701i | −0.976826 | − | 0.214036i | \(-0.931339\pi\) |
0.303052 | − | 0.952974i | \(-0.401994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.8105i | 1.06060i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.87043 | 0.266451 | 0.133226 | − | 0.991086i | \(-0.457467\pi\) | ||||
0.133226 | + | 0.991086i | \(0.457467\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.1928 | − | 7.03952i | −0.835438 | − | 0.482340i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.87043 | − | 13.6320i | −0.531834 | − | 0.921164i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.5587 | + | 39.0728i | −1.51746 | + | 2.62832i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.8501i | 1.46319i | 0.681740 | + | 0.731594i | \(0.261223\pi\) | ||||
−0.681740 | + | 0.731594i | \(0.738777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.11738 | −0.541158 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.5401 | + | 10.7042i | 1.23055 | + | 0.710460i | 0.967145 | − | 0.254225i | \(-0.0818204\pi\) |
0.263407 | + | 0.964685i | \(0.415154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9352 | − | 24.1365i | 0.909033 | − | 1.57449i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.6200i | 1.20950i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1174 | 1.36597 | 0.682985 | − | 0.730433i | \(-0.260682\pi\) | ||||
0.682985 | + | 0.730433i | \(0.260682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.5754 | + | 7.26040i | −0.806711 | + | 0.465755i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.24695 | − | 9.08799i | 0.332512 | − | 0.575928i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.1576 | + | 10.4833i | 1.13707 | + | 0.656488i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.87298 | + | 2.23607i | −0.241590 | + | 0.139482i | −0.615907 | − | 0.787819i | \(-0.711210\pi\) |
0.374317 | + | 0.927301i | \(0.377877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.506098 | − | 0.876588i | −0.0313267 | − | 0.0542595i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5587 | + | 28.6805i | 0.998526 | + | 1.72950i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.3765 | 0.678667 | 0.339333 | − | 0.940666i | \(-0.389799\pi\) | ||||
0.339333 | + | 0.940666i | \(0.389799\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5080 | − | 9.53090i | −0.981299 | − | 0.566553i | −0.0786368 | − | 0.996903i | \(-0.525057\pi\) |
−0.902662 | + | 0.430350i | \(0.858390\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.4352 | + | 40.5910i | 1.37854 | + | 2.38770i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.44131 | + | 12.8887i | −0.436217 | + | 0.755551i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.9200i | 1.92320i | 0.274446 | + | 0.961602i | \(0.411505\pi\) | ||||
−0.274446 | + | 0.961602i | \(0.588495\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.1155 | + | 17.9646i | 1.80551 | + | 1.04241i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 33.1408i | − | 1.89145i | −0.324971 | − | 0.945724i | \(-0.605355\pi\) | ||
0.324971 | − | 0.945724i | \(-0.394645\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.11738 | 0.518669 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.5417 | − | 17.6332i | 1.72632 | − | 0.996689i | 0.822507 | − | 0.568755i | \(-0.192575\pi\) |
0.903810 | − | 0.427934i | \(-0.140759\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.06479 | + | 3.57632i | −0.115606 | + | 0.200235i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.4453 | − | 14.1135i | −1.35598 | − | 0.782875i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.0290 | + | 5.79026i | −0.554606 | + | 0.320202i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.6235 | −1.63456 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.27163 | − | 3.04357i | −0.280580 | − | 0.161993i | 0.353106 | − | 0.935583i | \(-0.385126\pi\) |
−0.633686 | + | 0.773590i | \(0.718459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.2379 | − | 13.4164i | 1.23334 | − | 0.712069i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.0000 | − | 31.1769i | −0.950004 | − | 1.64545i | −0.745409 | − | 0.666608i | \(-0.767746\pi\) |
−0.204595 | − | 0.978847i | \(-0.565588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 38.5654i | − | 2.02416i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.0000 | 1.57027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.633493 | − | 0.365747i | −0.0330681 | − | 0.0190919i | 0.483375 | − | 0.875413i | \(-0.339411\pi\) |
−0.516443 | + | 0.856322i | \(0.672744\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.55869 | + | 11.3600i | −0.338689 | + | 0.586627i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.51976i | − | 0.181277i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.9839 | + | 17.8885i | −1.58320 | + | 0.914062i | −0.588813 | + | 0.808269i | \(0.700405\pi\) |
−0.994388 | + | 0.105793i | \(0.966262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.3117 | − | 21.3246i | 0.624230 | − | 1.08120i | −0.364459 | − | 0.931219i | \(-0.618746\pi\) |
0.988689 | − | 0.149979i | \(-0.0479205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.7329 | − | 17.7437i | −1.54634 | − | 0.892781i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.0819 | + | 9.86222i | −0.857314 | + | 0.494971i | −0.863112 | − | 0.505013i | \(-0.831488\pi\) |
0.00579782 | + | 0.999983i | \(0.498154\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.5587 | − | 33.8766i | −0.976714 | − | 1.69172i | −0.674158 | − | 0.738587i | \(-0.735493\pi\) |
−0.302556 | − | 0.953131i | \(-0.597840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.34047i | 0.165989i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.0000 | + | 17.3205i | 0.490881 | + | 0.850230i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.8704 | −1.65074 | −0.825372 | − | 0.564590i | \(-0.809034\pi\) | ||||
−0.825372 | + | 0.564590i | \(0.809034\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.5241 | + | 10.1175i | 0.852049 | + | 0.491931i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.6059 | + | 19.9797i | −1.67863 | + | 0.969160i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.9352 | + | 37.9929i | 1.05904 | + | 1.83431i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.1822 | − | 29.7604i | 0.827636 | − | 1.43351i | −0.0722525 | − | 0.997386i | \(-0.523019\pi\) |
0.899888 | − | 0.436121i | \(-0.143648\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 40.2492i | − | 1.93425i | −0.254293 | − | 0.967127i | \(-0.581843\pi\) | ||
0.254293 | − | 0.967127i | \(-0.418157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.63567 | −0.0784245 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.03952i | 0.332958i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.3643 | −1.90491 | −0.952455 | − | 0.304679i | \(-0.901451\pi\) | ||||
−0.952455 | + | 0.304679i | \(0.901451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.2540 | + | 14.0030i | −1.13955 | + | 0.657920i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.6761 | + | 37.5440i | −1.01175 | + | 1.75241i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.4437 | + | 7.18439i | −0.575827 | + | 0.332454i | −0.759473 | − | 0.650538i | \(-0.774543\pi\) |
0.183646 | + | 0.982992i | \(0.441210\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.87043 | − | 13.6320i | −0.362650 | − | 0.628128i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.1822 | − | 24.5642i | −0.643979 | − | 1.11540i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.11738 | −0.411461 | −0.205731 | − | 0.978609i | \(-0.565957\pi\) | ||||
−0.205731 | + | 0.978609i | \(0.565957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.31519 | − | 2.49138i | −0.194346 | − | 0.112206i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.8232 | + | 12.0223i | −0.935933 | + | 0.540361i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9352 | − | 31.0647i | −0.802890 | − | 1.39065i | −0.917706 | − | 0.397260i | \(-0.869961\pi\) |
0.114816 | − | 0.993387i | \(-0.463372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.18216 | + | 5.51167i | −0.142169 | + | 0.246243i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.61501i | 0.0720099i | 0.999352 | + | 0.0360049i | \(0.0114632\pi\) | ||||
−0.999352 | + | 0.0360049i | \(0.988537\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.1736 | − | 11.0699i | −0.851531 | − | 0.491632i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.68826 | + | 15.0485i | −0.382851 | + | 0.663117i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 82.5552i | − | 3.63077i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.6357 | 0.774120 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.2379 | − | 13.4164i | 1.01612 | − | 0.586659i | 0.103144 | − | 0.994666i | \(-0.467110\pi\) |
0.912978 | + | 0.408008i | \(0.133776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.3856 | − | 14.0790i | 1.05232 | − | 0.607556i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.06479 | + | 5.30837i | 0.131765 | + | 0.228225i | 0.924357 | − | 0.381528i | \(-0.124602\pi\) |
−0.792592 | + | 0.609753i | \(0.791269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 22.0709i | − | 0.945415i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 62.1052 | 2.62208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.7298 | − | 22.3607i | −1.63227 | − | 0.942390i | −0.983392 | − | 0.181496i | \(-0.941906\pi\) |
−0.648876 | − | 0.760894i | \(-0.724761\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 21.8501i | − | 0.912800i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.3198 | − | 23.2786i | −1.67853 | − | 0.969102i | −0.962597 | − | 0.270936i | \(-0.912667\pi\) |
−0.715936 | − | 0.698165i | \(-0.754000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.2470 | − | 17.7482i | 0.423659 | − | 0.733799i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.94427i | − | 0.369170i | −0.982817 | − | 0.184585i | \(-0.940906\pi\) | ||
0.982817 | − | 0.184585i | \(-0.0590940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.2555 | + | 20.9321i | −1.48883 | + | 0.859579i | −0.999919 | − | 0.0127518i | \(-0.995941\pi\) |
−0.488916 | + | 0.872331i | \(0.662608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.5587 | − | 39.0728i | 0.921723 | − | 1.59647i | 0.124975 | − | 0.992160i | \(-0.460115\pi\) |
0.796748 | − | 0.604311i | \(-0.206552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 63.6533 | + | 36.7503i | 2.58787 | + | 1.49411i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.0191 | + | 14.4448i | −1.01549 | + | 0.586296i | −0.912796 | − | 0.408416i | \(-0.866081\pi\) |
−0.102699 | + | 0.994712i | \(0.532748\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.1822 | + | 60.9373i | 1.42332 | + | 2.46526i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.12957 | 0.323633 | 0.161817 | − | 0.986821i | \(-0.448265\pi\) | ||||
0.161817 | + | 0.986821i | \(0.448265\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.93261 | + | 2.27050i | 0.156307 | + | 0.0902441i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.74085 | + | 16.8717i | 0.385342 | + | 0.667432i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.1804i | 1.58456i | 0.610158 | + | 0.792279i | \(0.291106\pi\) | ||||
−0.610158 | + | 0.792279i | \(0.708894\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.4919 | + | 8.94427i | 0.609051 | + | 0.351636i | 0.772594 | − | 0.634901i | \(-0.218959\pi\) |
−0.163543 | + | 0.986536i | \(0.552292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.7812i | 0.849766i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.6235 | −1.19292 | −0.596461 | − | 0.802642i | \(-0.703427\pi\) | ||||
−0.596461 | + | 0.802642i | \(0.703427\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −45.8423 | + | 26.4671i | −1.78037 | + | 1.02790i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.8178 | + | 22.2011i | −0.495566 | + | 0.858346i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.4888 | − | 13.5613i | −0.904085 | − | 0.521974i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.3167 | − | 9.42046i | 0.627102 | − | 0.362058i | −0.152527 | − | 0.988299i | \(-0.548741\pi\) |
0.779629 | + | 0.626242i | \(0.215408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.5587 | + | 21.7523i | 0.481250 | + | 0.833549i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 52.3643 | 1.97777 | 0.988887 | − | 0.148671i | \(-0.0474996\pi\) | ||||
0.988887 | + | 0.148671i | \(0.0474996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 28.3182 | − | 16.3495i | 1.06653 | − | 0.615759i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.8056 | − | 39.5005i | −0.856484 | − | 1.48347i | −0.875262 | − | 0.483650i | \(-0.839311\pi\) |
0.0187779 | − | 0.999824i | \(-0.494022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.8826 | − | 22.3134i | 0.483136 | − | 0.836816i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −83.6113 | −3.12688 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.4567 | + | 12.3880i | 0.801315 | + | 0.462639i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.55869 | − | 2.69973i | 0.0578882 | − | 0.100265i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 53.6656i | 1.99035i | 0.0981255 | + | 0.995174i | \(0.468715\pi\) | ||||
−0.0981255 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.5183 | −0.796974 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.4162 | − | 26.7984i | 1.71442 | − | 0.989821i | 0.786051 | − | 0.618161i | \(-0.212122\pi\) |
0.928369 | − | 0.371660i | \(-0.121211\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.8056 | − | 44.6967i | 0.949276 | − | 1.64419i | 0.202321 | − | 0.979319i | \(-0.435152\pi\) |
0.746955 | − | 0.664875i | \(-0.231515\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.6190 | − | 6.70820i | −0.425685 | − | 0.245770i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.5754 | + | 7.26040i | −0.460109 | + | 0.265644i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.8056 | + | 34.3044i | 0.722718 | + | 1.25178i | 0.959906 | + | 0.280321i | \(0.0904408\pi\) |
−0.237188 | + | 0.971464i | \(0.576226\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 53.3759i | − | 1.94255i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.5061 | − | 25.1253i | −0.524469 | − | 0.908407i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.24695 | −0.188964 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.7023 | + | 23.4995i | 1.46396 | + | 0.845218i | 0.999191 | − | 0.0402129i | \(-0.0128036\pi\) |
0.464770 | + | 0.885431i | \(0.346137\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.7409 | − | 68.8332i | 1.42204 | − | 2.46304i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.38205i | − | 0.120865i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0000 | 1.07075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.2570 | − | 27.8612i | −1.72018 | − | 0.993145i | −0.918535 | − | 0.395340i | \(-0.870627\pi\) |
−0.801642 | − | 0.597804i | \(-0.796040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.8247i | 1.23355i | 0.787138 | + | 0.616777i | \(0.211562\pi\) | ||||
−0.787138 | + | 0.616777i | \(0.788438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 99.6113 | 3.52399 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 76.9578 | − | 44.4316i | 2.71578 | − | 1.56796i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.18216 | + | 14.1719i | −0.287670 | + | 0.498258i | −0.973253 | − | 0.229736i | \(-0.926214\pi\) |
0.685583 | + | 0.727994i | \(0.259547\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.6883 | + | 20.2447i | 0.407923 | + | 0.706544i | 0.994657 | − | 0.103236i | \(-0.0329198\pi\) |
−0.586734 | + | 0.809780i | \(0.699586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38.8551i | 1.35276i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.06479 | − | 10.5045i | −0.209881 | − | 0.363524i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6113 | −0.986596 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.5593 | + | 6.67378i | 0.398124 | + | 0.229857i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.5424 | − | 21.0978i | 1.25710 | − | 0.725786i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.1822 | − | 19.3681i | −0.383771 | − | 0.664711i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 40.2492i | − | 1.37811i | −0.724710 | − | 0.689054i | \(-0.758026\pi\) | ||
0.724710 | − | 0.689054i | \(-0.241974\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.6028 | + | 24.5967i | 1.45528 | + | 0.840209i | 0.998774 | − | 0.0495090i | \(-0.0157656\pi\) |
0.456511 | + | 0.889718i | \(0.349099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.8056 | + | 29.1082i | −0.571409 | + | 0.989709i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 54.9909i | 1.86759i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −105.117 | −3.56586 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.8346 | − | 10.2968i | 0.603610 | − | 0.348495i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.3117 | + | 33.4489i | −0.651369 | + | 1.12820i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.9839 | + | 17.8885i | −1.04034 | + | 0.600639i | −0.919929 | − | 0.392086i | \(-0.871754\pi\) |
−0.120408 | + | 0.992725i | \(0.538420\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.94741 | + | 8.56917i | 0.165744 | + | 0.287078i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53.6656i | 1.79384i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.3052 | + | 29.6211i | 1.69795 | + | 0.980315i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.8056 | − | 27.3762i | −0.521380 | − | 0.903057i | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) |
0.478311 | − | 0.878191i | \(-0.341249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.4413 | − | 33.6733i | 0.640613 | − | 1.10957i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.7447i | 2.22984i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.9258 | − | 6.30803i | −0.358851 | − | 0.207183i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −59.1822 | + | 102.507i | −1.93546 | + | 3.35232i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.3455i | 1.61205i | 0.591883 | + | 0.806024i | \(0.298385\pi\) | ||||
−0.591883 | + | 0.806024i | \(0.701615\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.3765 | 1.35027 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.8704 | + | 65.5935i | −1.22933 | + | 2.12926i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.0642 | + | 20.8217i | 1.16701 | + | 0.673774i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.19593 | + | 2.42252i | −0.135635 | + | 0.0783089i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.5587 | − | 28.6805i | −0.530302 | − | 0.918511i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.0244 | 0.511620 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.0834 | − | 16.7913i | −0.927616 | − | 0.535559i | −0.0415592 | − | 0.999136i | \(-0.513233\pi\) |
−0.886057 | + | 0.463577i | \(0.846566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.0000 | − | 45.0333i | 0.825917 | − | 1.43053i | −0.0752991 | − | 0.997161i | \(-0.523991\pi\) |
0.901216 | − | 0.433370i | \(-0.142676\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.38603i | − | 0.297857i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.2524 | + | 7.07395i | 0.388039 | + | 0.224034i | 0.681310 | − | 0.731995i | \(-0.261411\pi\) |
−0.293271 | + | 0.956029i | \(0.594744\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 980.2.q.i.949.3 | 8 | ||
5.4 | even | 2 | inner | 980.2.q.i.949.2 | 8 | ||
7.2 | even | 3 | inner | 980.2.q.i.569.2 | 8 | ||
7.3 | odd | 6 | 980.2.e.d.589.3 | yes | 4 | ||
7.4 | even | 3 | 980.2.e.d.589.2 | ✓ | 4 | ||
7.5 | odd | 6 | inner | 980.2.q.i.569.3 | 8 | ||
7.6 | odd | 2 | inner | 980.2.q.i.949.2 | 8 | ||
35.3 | even | 12 | 4900.2.a.bj.1.2 | 4 | |||
35.4 | even | 6 | 980.2.e.d.589.3 | yes | 4 | ||
35.9 | even | 6 | inner | 980.2.q.i.569.3 | 8 | ||
35.17 | even | 12 | 4900.2.a.bj.1.3 | 4 | |||
35.18 | odd | 12 | 4900.2.a.bj.1.3 | 4 | |||
35.19 | odd | 6 | inner | 980.2.q.i.569.2 | 8 | ||
35.24 | odd | 6 | 980.2.e.d.589.2 | ✓ | 4 | ||
35.32 | odd | 12 | 4900.2.a.bj.1.2 | 4 | |||
35.34 | odd | 2 | CM | 980.2.q.i.949.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.e.d.589.2 | ✓ | 4 | 7.4 | even | 3 | ||
980.2.e.d.589.2 | ✓ | 4 | 35.24 | odd | 6 | ||
980.2.e.d.589.3 | yes | 4 | 7.3 | odd | 6 | ||
980.2.e.d.589.3 | yes | 4 | 35.4 | even | 6 | ||
980.2.q.i.569.2 | 8 | 7.2 | even | 3 | inner | ||
980.2.q.i.569.2 | 8 | 35.19 | odd | 6 | inner | ||
980.2.q.i.569.3 | 8 | 7.5 | odd | 6 | inner | ||
980.2.q.i.569.3 | 8 | 35.9 | even | 6 | inner | ||
980.2.q.i.949.2 | 8 | 5.4 | even | 2 | inner | ||
980.2.q.i.949.2 | 8 | 7.6 | odd | 2 | inner | ||
980.2.q.i.949.3 | 8 | 1.1 | even | 1 | trivial | ||
980.2.q.i.949.3 | 8 | 35.34 | odd | 2 | CM | ||
4900.2.a.bj.1.2 | 4 | 35.3 | even | 12 | |||
4900.2.a.bj.1.2 | 4 | 35.32 | odd | 12 | |||
4900.2.a.bj.1.3 | 4 | 35.17 | even | 12 | |||
4900.2.a.bj.1.3 | 4 | 35.18 | odd | 12 |