Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (of order \(2\), degree \(1\), 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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.8 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.c.1471.7 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.67125 | 1.38760 | 0.693801 | − | 0.720167i | \(-0.255935\pi\) | ||||
0.693801 | + | 0.720167i | \(0.255935\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00786 | −0.303882 | −0.151941 | − | 0.988390i | \(-0.548552\pi\) | ||||
−0.151941 | + | 0.988390i | \(0.548552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.593836 | −0.164701 | −0.0823503 | − | 0.996603i | \(-0.526243\pi\) | ||||
−0.0823503 | + | 0.996603i | \(0.526243\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.94819i | 1.44265i | 0.692597 | + | 0.721325i | \(0.256466\pi\) | ||||
−0.692597 | + | 0.721325i | \(0.743534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.286037 | 0.0656214 | 0.0328107 | − | 0.999462i | \(-0.489554\pi\) | ||||
0.0328107 | + | 0.999462i | \(0.489554\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.67125i | 0.801132i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.84988 | + | 3.85723i | −0.594241 | + | 0.804287i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.36715 | −1.18235 | −0.591175 | − | 0.806543i | \(-0.701336\pi\) | ||||
−0.591175 | + | 0.806543i | \(0.701336\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.69759i | − | 0.304895i | −0.988312 | − | 0.152448i | \(-0.951284\pi\) | ||
0.988312 | − | 0.152448i | \(-0.0487156\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.00786i | − | 0.175446i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.67125i | 0.620554i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.8469i | − | 1.78322i | −0.452806 | − | 0.891609i | \(-0.649577\pi\) | ||
0.452806 | − | 0.891609i | \(-0.350423\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.593836i | − | 0.0950899i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.08618 | −1.41902 | −0.709511 | − | 0.704694i | \(-0.751084\pi\) | ||||
−0.709511 | + | 0.704694i | \(0.751084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.53039 | −0.385881 | −0.192941 | − | 0.981210i | \(-0.561802\pi\) | ||||
−0.192941 | + | 0.981210i | \(0.561802\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.21965i | 1.34482i | 0.740177 | + | 0.672412i | \(0.234742\pi\) | ||||
−0.740177 | + | 0.672412i | \(0.765258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.47806 | 0.925437 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.94819 | −0.832914 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.48440i | 1.30278i | 0.758742 | + | 0.651391i | \(0.225814\pi\) | ||||
−0.758742 | + | 0.651391i | \(0.774186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.00786i | − | 0.135900i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.286037i | 0.0378865i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7.46964i | − | 0.972465i | −0.873830 | − | 0.486232i | \(-0.838371\pi\) | ||
0.873830 | − | 0.486232i | \(-0.161629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2566i | 1.31322i | 0.754231 | + | 0.656609i | \(0.228010\pi\) | ||||
−0.754231 | + | 0.656609i | \(0.771990\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.67125 | −0.462534 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.593836i | − | 0.0736563i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.43360 | −0.785990 | −0.392995 | − | 0.919541i | \(-0.628561\pi\) | ||||
−0.392995 | + | 0.919541i | \(0.628561\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.85723 | − | 2.84988i | −0.464356 | − | 0.343085i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.38489i | − | 0.283035i | −0.989936 | − | 0.141517i | \(-0.954802\pi\) | ||
0.989936 | − | 0.141517i | \(-0.0451981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8439 | 1.26919 | 0.634593 | − | 0.772846i | \(-0.281168\pi\) | ||||
0.634593 | + | 0.772846i | \(0.281168\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.70011 | −0.421667 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4756 | −1.51612 | −0.758061 | − | 0.652183i | \(-0.773853\pi\) | ||||
−0.758061 | + | 0.652183i | \(0.773853\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.86819 | −0.205061 | −0.102530 | − | 0.994730i | \(-0.532694\pi\) | ||||
−0.102530 | + | 0.994730i | \(0.532694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.94819 | −0.645172 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 6.36715i | − | 0.682631i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.2439i | − | 1.50985i | −0.655810 | − | 0.754926i | \(-0.727673\pi\) | ||
0.655810 | − | 0.754926i | \(-0.272327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.18012 | −0.228539 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.69759 | 0.176031 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.286037i | 0.0293468i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.822365i | 0.0834985i | 0.999128 | + | 0.0417492i | \(0.0132931\pi\) | ||||
−0.999128 | + | 0.0417492i | \(0.986707\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00786 | 0.101294 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.9340 | 1.78450 | 0.892250 | − | 0.451542i | \(-0.149126\pi\) | ||||
0.892250 | + | 0.451542i | \(0.149126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.71186 | −0.562806 | −0.281403 | − | 0.959590i | \(-0.590800\pi\) | ||||
−0.281403 | + | 0.959590i | \(0.590800\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.67125 | −0.358277 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.528453 | −0.0510875 | −0.0255437 | − | 0.999674i | \(-0.508132\pi\) | ||||
−0.0255437 | + | 0.999674i | \(0.508132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.39885i | − | 0.612898i | −0.951887 | − | 0.306449i | \(-0.900859\pi\) | ||
0.951887 | − | 0.306449i | \(-0.0991410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8469 | 1.02954 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.58160i | 0.619145i | 0.950876 | + | 0.309572i | \(0.100186\pi\) | ||||
−0.950876 | + | 0.309572i | \(0.899814\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.85723 | − | 2.84988i | −0.359688 | − | 0.265752i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.593836 | 0.0549002 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.8373i | 2.00182i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.98421 | −0.907656 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 9.08618i | − | 0.819273i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.3310i | 1.53788i | 0.639324 | + | 0.768938i | \(0.279214\pi\) | ||||
−0.639324 | + | 0.768938i | \(0.720786\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 2.53039i | − | 0.222789i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1819i | 1.58856i | 0.607552 | + | 0.794280i | \(0.292152\pi\) | ||||
−0.607552 | + | 0.794280i | \(0.707848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.05011 | 0.0910563 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.6173i | 1.67602i | 0.545657 | + | 0.838009i | \(0.316280\pi\) | ||||
−0.545657 | + | 0.838009i | \(0.683720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6864i | 0.991224i | 0.868544 | + | 0.495612i | \(0.165056\pi\) | ||||
−0.868544 | + | 0.495612i | \(0.834944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.21965 | −0.776434 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.598506 | 0.0500496 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.36715i | − | 0.528763i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.47806i | 0.534301i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 20.0940i | − | 1.64616i | −0.567922 | − | 0.823082i | \(-0.692253\pi\) | ||
0.567922 | − | 0.823082i | \(-0.307747\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0658i | 1.47017i | 0.677972 | + | 0.735087i | \(0.262859\pi\) | ||||
−0.677972 | + | 0.735087i | \(0.737141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.94819i | − | 0.480883i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.69759 | 0.136353 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.5993i | − | 1.32477i | −0.749164 | − | 0.662384i | \(-0.769545\pi\) | ||
0.749164 | − | 0.662384i | \(-0.230455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.48440 | −0.752162 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.4626 | + | 14.1608i | −0.824569 | + | 1.11603i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.12245i | − | 0.166243i | −0.996539 | − | 0.0831216i | \(-0.973511\pi\) | ||
0.996539 | − | 0.0831216i | \(-0.0264890\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.00786 | 0.0784620 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0048i | 1.23849i | 0.785199 | + | 0.619243i | \(0.212560\pi\) | ||||
−0.785199 | + | 0.619243i | \(0.787440\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6474 | −0.972874 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.286037 | −0.0218738 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.91583 | 0.753887 | 0.376943 | − | 0.926236i | \(-0.376975\pi\) | ||||
0.376943 | + | 0.926236i | \(0.376975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.67125 | −0.277520 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.46964 | 0.561453 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.533246i | − | 0.0398567i | −0.999801 | − | 0.0199284i | \(-0.993656\pi\) | ||
0.999801 | − | 0.0199284i | \(-0.00634381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.19483i | − | 0.0888110i | −0.999014 | − | 0.0444055i | \(-0.985861\pi\) | ||
0.999014 | − | 0.0444055i | \(-0.0141394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.2566 | −0.758187 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8469 | 0.797479 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.99497i | − | 0.438395i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.67125i | − | 0.267044i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.5425 | −0.907545 | −0.453772 | − | 0.891118i | \(-0.649922\pi\) | ||||
−0.453772 | + | 0.891118i | \(0.649922\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.5783 | 1.55324 | 0.776620 | − | 0.629969i | \(-0.216932\pi\) | ||||
0.776620 | + | 0.629969i | \(0.216932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.593836 | 0.0425255 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.21949 | 0.0868848 | 0.0434424 | − | 0.999056i | \(-0.486168\pi\) | ||||
0.0434424 | + | 0.999056i | \(0.486168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5570 | 1.17370 | 0.586848 | − | 0.809697i | \(-0.300368\pi\) | ||||
0.586848 | + | 0.809697i | \(0.300368\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.43360i | − | 0.453791i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.3754 | −1.64063 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 9.08618i | − | 0.634606i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.84988 | − | 3.85723i | 0.198080 | − | 0.268096i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.288286 | −0.0199412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.6512i | − | 1.00863i | −0.863520 | − | 0.504315i | \(-0.831745\pi\) | ||
0.863520 | − | 0.504315i | \(-0.168255\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.38489 | 0.163410 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.53039i | − | 0.172571i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.23226i | − | 0.423073i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.8439i | 0.732765i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.53225i | − | 0.237605i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.18336i | 0.347104i | 0.984825 | + | 0.173552i | \(0.0555244\pi\) | ||||
−0.984825 | + | 0.173552i | \(0.944476\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.09848 | −0.272026 | −0.136013 | − | 0.990707i | \(-0.543429\pi\) | ||||
−0.136013 | + | 0.990707i | \(0.543429\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.06167i | 0.202321i | 0.994870 | + | 0.101160i | \(0.0322555\pi\) | ||||
−0.994870 | + | 0.101160i | \(0.967744\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 3.70011i | − | 0.243450i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.2216 | −1.32476 | −0.662381 | − | 0.749167i | \(-0.730454\pi\) | ||||
−0.662381 | + | 0.749167i | \(0.730454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.21965 | −0.601423 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 13.4756i | − | 0.875334i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.16908i | − | 0.204991i | −0.994733 | − | 0.102495i | \(-0.967317\pi\) | ||
0.994733 | − | 0.102495i | \(-0.0326827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 13.3177i | − | 0.857870i | −0.903335 | − | 0.428935i | \(-0.858889\pi\) | ||
0.903335 | − | 0.428935i | \(-0.141111\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.47806i | 0.413868i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.169859 | −0.0108079 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.86819i | − | 0.118392i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.62068 | −0.544132 | −0.272066 | − | 0.962279i | \(-0.587707\pi\) | ||||
−0.272066 | + | 0.962279i | \(0.587707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.87229 | − | 3.88756i | 0.180579 | − | 0.244409i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 5.94819i | − | 0.372490i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.9596 | 1.43218 | 0.716092 | − | 0.698006i | \(-0.245929\pi\) | ||||
0.716092 | + | 0.698006i | \(0.245929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 39.8216i | − | 2.47440i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.36715 | 0.394117 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.66741 | 0.411130 | 0.205565 | − | 0.978643i | \(-0.434097\pi\) | ||||
0.205565 | + | 0.978643i | \(0.434097\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.48440 | −0.582622 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.2439 | 0.871713 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.78049 | −0.535356 | −0.267678 | − | 0.963508i | \(-0.586256\pi\) | ||||
−0.267678 | + | 0.963508i | \(0.586256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2578i | 0.623117i | 0.950227 | + | 0.311558i | \(0.100851\pi\) | ||||
−0.950227 | + | 0.311558i | \(0.899149\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.18012i | − | 0.131947i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00786 | 0.0607764 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.6778 | −1.12224 | −0.561120 | − | 0.827734i | \(-0.689630\pi\) | ||||
−0.561120 | + | 0.827734i | \(0.689630\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.69759i | 0.101632i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.9324i | − | 1.24872i | −0.781135 | − | 0.624362i | \(-0.785359\pi\) | ||
0.781135 | − | 0.624362i | \(-0.214641\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7104 | −0.814996 | −0.407498 | − | 0.913206i | \(-0.633599\pi\) | ||||
−0.407498 | + | 0.913206i | \(0.633599\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.286037 | −0.0169434 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.3576 | −1.96904 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.3810 | −1.08124 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.822365 | −0.0482079 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10.4892i | − | 0.612786i | −0.951905 | − | 0.306393i | \(-0.900878\pi\) | ||
0.951905 | − | 0.306393i | \(-0.0991222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.46964 | 0.434899 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00786i | 0.0584821i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.69236 | − | 2.29056i | 0.0978718 | − | 0.132467i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.28970 | −0.535449 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.9340i | 1.03028i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.2566 | −0.587289 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.93404i | 0.281600i | 0.990038 | + | 0.140800i | \(0.0449675\pi\) | ||||
−0.990038 | + | 0.140800i | \(0.955033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5.71186i | − | 0.324936i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.34926i | 0.246624i | 0.992368 | + | 0.123312i | \(0.0393515\pi\) | ||||
−0.992368 | + | 0.123312i | \(0.960648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.19385i | 0.293574i | 0.989168 | + | 0.146787i | \(0.0468931\pi\) | ||||
−0.989168 | + | 0.146787i | \(0.953107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 3.67125i | − | 0.206851i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.0034 | 1.06734 | 0.533668 | − | 0.845694i | \(-0.320813\pi\) | ||||
0.533668 | + | 0.845694i | \(0.320813\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.41722 | 0.359295 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 0.528453i | − | 0.0294954i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.70140i | 0.0946686i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.593836 | 0.0329401 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.39885 | 0.353857 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.8476i | 1.86608i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.5124i | 1.12746i | 0.825958 | + | 0.563732i | \(0.190635\pi\) | ||||
−0.825958 | + | 0.563732i | \(0.809365\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.8469i | 0.594406i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 6.43360i | − | 0.351505i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.4104i | − | 0.730512i | −0.930907 | − | 0.365256i | \(-0.880981\pi\) | ||
0.930907 | − | 0.365256i | \(-0.119019\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.58160 | −0.357463 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.71093i | 0.0926523i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.91617 | −0.103464 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.84988 | − | 3.85723i | 0.153432 | − | 0.207666i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 26.1151i | − | 1.40193i | −0.713196 | − | 0.700965i | \(-0.752753\pi\) | ||
0.713196 | − | 0.700965i | \(-0.247247\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.72337 | 0.306365 | 0.153182 | − | 0.988198i | \(-0.451048\pi\) | ||||
0.153182 | + | 0.988198i | \(0.451048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.593836i | 0.0316966i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.2032 | 1.12853 | 0.564267 | − | 0.825592i | \(-0.309159\pi\) | ||||
0.564267 | + | 0.825592i | \(0.309159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.38489 | 0.126577 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.8373 | −1.15575 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.32343 | −0.280960 | −0.140480 | − | 0.990084i | \(-0.544865\pi\) | ||||
−0.140480 | + | 0.990084i | \(0.544865\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9182 | −0.995694 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 9.98421i | − | 0.524035i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.8439i | 0.567597i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.3069 | −1.47761 | −0.738803 | − | 0.673921i | \(-0.764609\pi\) | ||||
−0.738803 | + | 0.673921i | \(0.764609\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.08618 | 0.473008 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.8196i | 1.80774i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.9995i | − | 0.828425i | −0.910180 | − | 0.414212i | \(-0.864057\pi\) | ||
0.910180 | − | 0.414212i | \(-0.135943\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.78105 | 0.194734 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.1655 | 1.65223 | 0.826114 | − | 0.563503i | \(-0.190547\pi\) | ||||
0.826114 | + | 0.563503i | \(0.190547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.3310 | −0.887893 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.8992 | −1.47668 | −0.738339 | − | 0.674430i | \(-0.764389\pi\) | ||||
−0.738339 | + | 0.674430i | \(0.764389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 3.70011i | − | 0.188575i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.53039 | 0.128627 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 17.2346i | − | 0.873831i | −0.899503 | − | 0.436915i | \(-0.856071\pi\) | ||
0.899503 | − | 0.436915i | \(-0.143929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.9435 | − | 16.9516i | −1.16030 | − | 0.857281i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.1819 | −0.917155 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 13.4756i | − | 0.678031i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.6669 | −1.63950 | −0.819751 | − | 0.572719i | \(-0.805888\pi\) | ||||
−0.819751 | + | 0.572719i | \(0.805888\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.05011i | 0.0525714i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.6626i | 1.93072i | 0.260926 | + | 0.965359i | \(0.415972\pi\) | ||||
−0.260926 | + | 0.965359i | \(0.584028\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00809i | 0.0502165i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.9322i | 0.541888i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.5284 | 1.11396 | 0.556978 | − | 0.830527i | \(-0.311961\pi\) | ||||
0.556978 | + | 0.830527i | \(0.311961\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.6173 | −0.967649 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 27.4229i | − | 1.34939i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.86819i | − | 0.0917059i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.6864 | −0.572283 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.3376 | 0.700438 | 0.350219 | − | 0.936668i | \(-0.386107\pi\) | ||||
0.350219 | + | 0.936668i | \(0.386107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.89252i | 0.0922360i | 0.998936 | + | 0.0461180i | \(0.0146850\pi\) | ||||
−0.998936 | + | 0.0461180i | \(0.985315\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 9.21965i | − | 0.448275i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.94819i | − | 0.288530i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.6544i | 1.82222i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.598506i | 0.0288961i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.9441 | −0.768002 | −0.384001 | − | 0.923333i | \(-0.625454\pi\) | ||||
−0.384001 | + | 0.923333i | \(0.625454\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.9290i | 0.573273i | 0.958039 | + | 0.286636i | \(0.0925371\pi\) | ||||
−0.958039 | + | 0.286636i | \(0.907463\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.36715 | 0.305282 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.815170 | + | 1.10331i | −0.0389949 | + | 0.0527784i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.4107i | − | 0.735514i | −0.929922 | − | 0.367757i | \(-0.880126\pi\) | ||
0.929922 | − | 0.367757i | \(-0.119874\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.47806 | −0.308479 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.58510i | 0.455402i | 0.973731 | + | 0.227701i | \(0.0731209\pi\) | ||||
−0.973731 | + | 0.227701i | \(0.926879\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.2439 | 0.675226 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.0940 | 0.950414 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.57007 | −0.451640 | −0.225820 | − | 0.974169i | \(-0.572506\pi\) | ||||
−0.225820 | + | 0.974169i | \(0.572506\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.15762 | 0.431216 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.0658 | −0.848806 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2.18012i | − | 0.102206i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.1216i | 1.26870i | 0.773047 | + | 0.634348i | \(0.218731\pi\) | ||||
−0.773047 | + | 0.634348i | \(0.781269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.94819 | 0.277638 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.2112 | −1.77967 | −0.889837 | − | 0.456278i | \(-0.849182\pi\) | ||||
−0.889837 | + | 0.456278i | \(0.849182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 32.4925i | − | 1.51005i | −0.655694 | − | 0.755027i | \(-0.727624\pi\) | ||
0.655694 | − | 0.755027i | \(-0.272376\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.69759i | 0.0787237i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.9305 | 0.922274 | 0.461137 | − | 0.887329i | \(-0.347442\pi\) | ||||
0.461137 | + | 0.887329i | \(0.347442\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.6193 | −1.09064 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.5993 | 0.764855 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.55029 | 0.117262 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.286037 | −0.0131243 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 9.48440i | − | 0.434261i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.0942 | −1.14658 | −0.573292 | − | 0.819351i | \(-0.694334\pi\) | ||||
−0.573292 | + | 0.819351i | \(0.694334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.44128i | 0.293697i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.1608 | − | 10.4626i | −0.644340 | − | 0.476065i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.822365 | −0.0373417 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.1634i | 1.81998i | 0.414635 | + | 0.909988i | \(0.363909\pi\) | ||||
−0.414635 | + | 0.909988i | \(0.636091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.12245 | 0.0959806 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.1707i | − | 0.865161i | −0.901595 | − | 0.432581i | \(-0.857603\pi\) | ||
0.901595 | − | 0.432581i | \(-0.142397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 37.8731i | − | 1.70572i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00786i | 0.0453001i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.75554i | − | 0.392740i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0542i | 0.629154i | 0.949232 | + | 0.314577i | \(0.101863\pi\) | ||||
−0.949232 | + | 0.314577i | \(0.898137\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.0048 | −0.715040 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.6280 | −1.27646 | −0.638230 | − | 0.769846i | \(-0.720333\pi\) | ||||
−0.638230 | + | 0.769846i | \(0.720333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.9340i | 0.798053i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.6474i | − | 0.561689i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8077 | 0.744989 | 0.372494 | − | 0.928034i | \(-0.378503\pi\) | ||||
0.372494 | + | 0.928034i | \(0.378503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.8108 | 1.76112 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.286037i | − | 0.0126288i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5.71186i | − | 0.251694i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.29214i | − | 0.408668i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.91583i | 0.435257i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.7758i | 0.822585i | 0.911503 | + | 0.411292i | \(0.134923\pi\) | ||||
−0.911503 | + | 0.411292i | \(0.865077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.25654 | −0.0986715 | −0.0493357 | − | 0.998782i | \(-0.515710\pi\) | ||||
−0.0493357 | + | 0.998782i | \(0.515710\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3.67125i | − | 0.160226i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0976 | 0.439857 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.75640 | − | 21.9852i | −0.293756 | − | 0.955880i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.46964i | 0.324155i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.39570 | 0.233714 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.528453i | − | 0.0228470i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.533246 | 0.0230113 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.52900 | −0.281224 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.49190 | −0.193122 | −0.0965608 | − | 0.995327i | \(-0.530784\pi\) | ||||
−0.0965608 | + | 0.995327i | \(0.530784\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.19483 | 0.0512751 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.39885 | 0.274096 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.1115i | 1.62953i | 0.579793 | + | 0.814764i | \(0.303134\pi\) | ||||
−0.579793 | + | 0.814764i | \(0.696866\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 10.2566i | − | 0.437740i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.82124 | −0.0775875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.4722 | −2.10377 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.8469i | 0.460425i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.9889i | 0.677472i | 0.940881 | + | 0.338736i | \(0.109999\pi\) | ||||
−0.940881 | + | 0.338736i | \(0.890001\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.50264 | 0.0635549 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.99497 | 0.253108 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.649938 | 0.0273916 | 0.0136958 | − | 0.999906i | \(-0.495640\pi\) | ||||
0.0136958 | + | 0.999906i | \(0.495640\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.58160 | −0.276890 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.67125 | 0.154178 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.2077i | 1.43406i | 0.697042 | + | 0.717030i | \(0.254499\pi\) | ||||
−0.697042 | + | 0.717030i | \(0.745501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.84324 | −0.286381 | −0.143190 | − | 0.989695i | \(-0.545736\pi\) | ||||
−0.143190 | + | 0.989695i | \(0.545736\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 12.5425i | − | 0.523971i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.84988 | − | 3.85723i | 0.118848 | − | 0.160857i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3607 | 1.22230 | 0.611150 | − | 0.791514i | \(-0.290707\pi\) | ||||
0.611150 | + | 0.791514i | \(0.290707\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.5783i | 0.896764i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.85860 | −0.284543 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9.55898i | − | 0.395892i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.593836i | 0.0245521i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.8191i | 1.31332i | 0.754188 | + | 0.656658i | \(0.228030\pi\) | ||||
−0.754188 | + | 0.656658i | \(0.771970\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.485572i | − | 0.0200077i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.21949i | 0.0501630i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.54885 | 0.309994 | 0.154997 | − | 0.987915i | \(-0.450463\pi\) | ||||
0.154997 | + | 0.987915i | \(0.450463\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.8373 | −0.895242 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.5570i | 0.677634i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0867i | 0.657284i | 0.944455 | + | 0.328642i | \(0.106591\pi\) | ||||
−0.944455 | + | 0.328642i | \(0.893409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.1192 | 0.616723 | 0.308362 | − | 0.951269i | \(-0.400219\pi\) | ||||
0.308362 | + | 0.951269i | \(0.400219\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.43360 | 0.261997 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 9.98421i | − | 0.405916i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 46.4376i | − | 1.88484i | −0.334429 | − | 0.942421i | \(-0.608543\pi\) | ||
0.334429 | − | 0.942421i | \(-0.391457\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 23.3754i | − | 0.947219i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.47496i | − | 0.221493i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.0498i | − | 0.809805i | −0.914360 | − | 0.404903i | \(-0.867305\pi\) | ||
0.914360 | − | 0.404903i | \(-0.132695\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.08618 | 0.366390 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.64661i | − | 0.0662900i | −0.999451 | − | 0.0331450i | \(-0.989448\pi\) | ||
0.999451 | − | 0.0331450i | \(-0.0105523\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.64294 | 0.347389 | 0.173695 | − | 0.984800i | \(-0.444429\pi\) | ||||
0.173695 | + | 0.984800i | \(0.444429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.85723 | + | 2.84988i | 0.154785 | + | 0.114362i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 52.2929i | − | 2.09507i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 0.288286i | − | 0.0115130i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 64.5194 | 2.57256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.8648 | 1.70642 | 0.853209 | − | 0.521569i | \(-0.174653\pi\) | ||||
0.853209 | + | 0.521569i | \(0.174653\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.6512 | 0.582333 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.3310 | −0.687759 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.84691 | −0.152420 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.38489i | 0.0943450i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.3332i | 0.803111i | 0.915835 | + | 0.401556i | \(0.131530\pi\) | ||||
−0.915835 | + | 0.401556i | \(0.868470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.0171 | 1.61756 | 0.808779 | − | 0.588113i | \(-0.200129\pi\) | ||||
0.808779 | + | 0.588113i | \(0.200129\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.53039 | 0.0996341 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.97272i | 0.156184i | 0.996946 | + | 0.0780918i | \(0.0248827\pi\) | ||||
−0.996946 | + | 0.0780918i | \(0.975117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.52838i | 0.295515i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.23226 | 0.244261 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.7527 | 0.812115 | 0.406057 | − | 0.913848i | \(-0.366903\pi\) | ||||
0.406057 | + | 0.913848i | \(0.366903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.1819 | −0.710425 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.8439 | −0.423062 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.5149 | −1.38346 | −0.691732 | − | 0.722155i | \(-0.743152\pi\) | ||||
−0.691732 | + | 0.722155i | \(0.743152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.05928i | 0.235679i | 0.993033 | + | 0.117839i | \(0.0375968\pi\) | ||||
−0.993033 | + | 0.117839i | \(0.962403\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.53225 | 0.137181 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.05011i | 0.0407216i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.1456 | − | 24.5596i | 0.702601 | − | 0.950950i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.18336 | −0.200400 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.3372i | − | 0.399064i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.9256 | 1.84740 | 0.923698 | − | 0.383121i | \(-0.125151\pi\) | ||||
0.923698 | + | 0.383121i | \(0.125151\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.09024i | − | 0.349366i | −0.984625 | − | 0.174683i | \(-0.944110\pi\) | ||
0.984625 | − | 0.174683i | \(-0.0558901\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.01910i | 0.115863i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.09848i | − | 0.157054i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 22.5635i | − | 0.863370i | −0.902024 | − | 0.431685i | \(-0.857919\pi\) | ||
0.902024 | − | 0.431685i | \(-0.142081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.6173 | −0.749538 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.06167 | −0.116810 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5.63218i | − | 0.214569i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.3258i | 1.07756i | 0.842445 | + | 0.538782i | \(0.181115\pi\) | ||||
−0.842445 | + | 0.538782i | \(0.818885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.70011 | 0.140556 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.6864 | −0.443289 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 54.0464i | − | 2.04715i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 20.2216i | − | 0.764851i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9040i | 0.751764i | 0.926667 | + | 0.375882i | \(0.122660\pi\) | ||||
−0.926667 | + | 0.375882i | \(0.877340\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.10261i | − | 0.117017i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 9.21965i | − | 0.347232i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 65.8402 | 2.47617 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.9327i | 1.57482i | 0.616432 | + | 0.787409i | \(0.288578\pi\) | ||||
−0.616432 | + | 0.787409i | \(0.711422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4756 | 0.505374 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.54797 | + | 4.83791i | 0.245224 | + | 0.181181i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.598506i | 0.0223828i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.16908 | 0.118352 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.5808i | 1.66258i | 0.555835 | + | 0.831292i | \(0.312398\pi\) | ||||
−0.555835 | + | 0.831292i | \(0.687602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.9696 | −0.780950 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.3177 | 0.495291 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.36715 | 0.236470 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.26736 | −0.0840916 | −0.0420458 | − | 0.999116i | \(-0.513388\pi\) | ||||
−0.0420458 | + | 0.999116i | \(0.513388\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 15.0513i | − | 0.556691i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 40.9074i | − | 1.51095i | −0.655179 | − | 0.755474i | \(-0.727407\pi\) | ||
0.655179 | − | 0.755474i | \(-0.272593\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.47806 | −0.238947 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.48419 | 0.238848 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9120i | 1.39461i | 0.716773 | + | 0.697307i | \(0.245618\pi\) | ||||
−0.716773 | + | 0.697307i | \(0.754382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.169859i | − | 0.00623993i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.3878 | −1.26157 | −0.630784 | − | 0.775959i | \(-0.717266\pi\) | ||||
−0.630784 | + | 0.775959i | \(0.717266\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.0940 | 0.736187 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.86819 | 0.0683536 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.94008 | −0.0708890 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5273 | 0.566599 | 0.283300 | − | 0.959031i | \(-0.408571\pi\) | ||||
0.283300 | + | 0.959031i | \(0.408571\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 8.62068i | − | 0.314155i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.0658 | −0.657482 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.2158i | 0.771102i | 0.922687 | + | 0.385551i | \(0.125989\pi\) | ||||
−0.922687 | + | 0.385551i | \(0.874011\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.88756 | + | 2.87229i | 0.141109 | + | 0.104257i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.2514 | 1.38661 | 0.693306 | − | 0.720643i | \(-0.256153\pi\) | ||||
0.693306 | + | 0.720643i | \(0.256153\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 23.4918i | − | 0.850459i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.94819 | 0.215057 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.43575i | 0.160165i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.2419i | 0.693880i | 0.937887 | + | 0.346940i | \(0.112779\pi\) | ||||
−0.937887 | + | 0.346940i | \(0.887221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.9596i | 0.826871i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.65019i | 0.131288i | 0.997843 | + | 0.0656441i | \(0.0209102\pi\) | ||||
−0.997843 | + | 0.0656441i | \(0.979090\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.69759i | 0.0609791i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39.8216 | 1.42859 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.59898 | −0.0931182 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.40365i | 0.0860093i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.36715i | 0.227544i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.5993 | 0.592454 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.4135 | −0.620724 | −0.310362 | − | 0.950618i | \(-0.600450\pi\) | ||||
−0.310362 | + | 0.950618i | \(0.600450\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.66741i | 0.237366i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.1627i | 0.859126i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.09072i | − | 0.216288i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 9.48440i | − | 0.336377i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 14.0360i | − | 0.497182i | −0.968609 | − | 0.248591i | \(-0.920033\pi\) | ||
0.968609 | − | 0.248591i | \(-0.0799675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54.8402 | −1.94011 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.2439i | 0.503284i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.9292 | −0.385683 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.1608 | − | 10.4626i | −0.499104 | − | 0.368758i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.78049i | − | 0.309088i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.8470 | 1.36579 | 0.682895 | − | 0.730517i | \(-0.260721\pi\) | ||||
0.682895 | + | 0.730517i | \(0.260721\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.9185i | 0.875005i | 0.899217 | + | 0.437503i | \(0.144137\pi\) | ||||
−0.899217 | + | 0.437503i | \(0.855863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.2578 | −0.359757 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.12245 | 0.0743462 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.723786 | −0.0253221 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.18012 | 0.0761796 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.8088 | −1.35444 | −0.677218 | − | 0.735782i | \(-0.736815\pi\) | ||||
−0.677218 | + | 0.735782i | \(0.736815\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 34.2079i | − | 1.19241i | −0.802832 | − | 0.596205i | \(-0.796674\pi\) | ||
0.802832 | − | 0.596205i | \(-0.203326\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.00786i | 0.0350893i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.8324 | 0.620093 | 0.310046 | − | 0.950721i | \(-0.399655\pi\) | ||||
0.310046 | + | 0.950721i | \(0.399655\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.7454 | −1.62353 | −0.811767 | − | 0.583982i | \(-0.801494\pi\) | ||||
−0.811767 | + | 0.583982i | \(0.801494\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 18.6778i | − | 0.647926i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.5328i | 1.33508i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0048 | −0.553868 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.69759 | −0.0586772 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.7766 | 0.717288 | 0.358644 | − | 0.933474i | \(-0.383239\pi\) | ||||
0.358644 | + | 0.933474i | \(0.383239\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5407 | 0.397954 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.9324 | 0.720951 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 12.6474i | − | 0.435082i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.6545 | −1.25946 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 13.7104i | − | 0.470538i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.8389 | + | 30.9123i | 1.43422 | + | 1.05966i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.2032 | 1.44501 | 0.722505 | − | 0.691365i | \(-0.242990\pi\) | ||||
0.722505 | + | 0.691365i | \(0.242990\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.286037i | − | 0.00978226i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.7045 | 1.35628 | 0.678140 | − | 0.734933i | \(-0.262786\pi\) | ||||
0.678140 | + | 0.734933i | \(0.262786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 36.2534i | − | 1.23695i | −0.785804 | − | 0.618475i | \(-0.787751\pi\) | ||
0.785804 | − | 0.618475i | \(-0.212249\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 33.3576i | − | 1.13682i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.2524i | 0.383035i | 0.981489 | + | 0.191517i | \(0.0613408\pi\) | ||||
−0.981489 | + | 0.191517i | \(0.938659\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.91583i | 0.337148i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 18.3810i | − | 0.624252i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.5816 | 0.460723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.82051 | 0.129453 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.822365i | − | 0.0278328i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.67125i | − | 0.124111i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.2662 | 0.718107 | 0.359054 | − | 0.933317i | \(-0.383100\pi\) | ||||
0.359054 | + | 0.933317i | \(0.383100\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.4892 | 0.353792 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0034i | 1.04453i | 0.852783 | + | 0.522266i | \(0.174913\pi\) | ||||
−0.852783 | + | 0.522266i | \(0.825087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.89744i | 0.333075i | 0.986035 | + | 0.166538i | \(0.0532588\pi\) | ||||
−0.986035 | + | 0.166538i | \(0.946741\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.46964i | 0.251089i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.74918i | 0.125885i | 0.998017 | + | 0.0629425i | \(0.0200485\pi\) | ||||
−0.998017 | + | 0.0629425i | \(0.979952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 63.6263i | 2.13396i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00786 | −0.0337647 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.63716i | 0.0882492i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.533246 | 0.0178245 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.29056 | + | 1.69236i | 0.0764796 | + | 0.0565063i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.8088i | 0.360493i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −56.4151 | −1.87946 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 9.28970i | − | 0.309142i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.19483 | 0.0397175 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.1323 | 1.43218 | 0.716092 | − | 0.698006i | \(-0.245929\pi\) | ||||
0.716092 | + | 0.698006i | \(0.245929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.9340 | −0.594833 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.3897 | 1.83514 | 0.917571 | − | 0.397572i | \(-0.130147\pi\) | ||||
0.917571 | + | 0.397572i | \(0.130147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.88288 | 0.0623143 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 10.2566i | − | 0.339072i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 66.7502i | 2.20429i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.6093 | 1.17464 | 0.587321 | − | 0.809354i | \(-0.300183\pi\) | ||||
0.587321 | + | 0.809354i | \(0.300183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.93404 | −0.162582 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.41624i | 0.0466160i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.8469i | 0.356644i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.71186 | 0.187602 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.762573 | 0.0250192 | 0.0125096 | − | 0.999922i | \(-0.496018\pi\) | ||||
0.0125096 | + | 0.999922i | \(0.496018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.85296 | 0.0607285 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.34926 | −0.142388 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.99497 | 0.196056 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.1175i | − | 1.17991i | −0.807437 | − | 0.589953i | \(-0.799146\pi\) | ||
0.807437 | − | 0.589953i | \(-0.200854\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.19385 | −0.169495 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 7.24509i | − | 0.236183i | −0.993003 | − | 0.118092i | \(-0.962322\pi\) | ||
0.993003 | − | 0.118092i | \(-0.0376777\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.8945 | − | 35.0475i | 0.843241 | − | 1.14130i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.67125 | 0.119426 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 49.1935i | − | 1.59858i | −0.600948 | − | 0.799288i | \(-0.705210\pi\) | ||
0.600948 | − | 0.799288i | \(-0.294790\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.43952 | −0.209036 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.0034i | 0.616227i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 38.7511i | − | 1.25527i | −0.778508 | − | 0.627635i | \(-0.784023\pi\) | ||
0.778508 | − | 0.627635i | \(-0.215977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 12.5425i | − | 0.405866i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.41722i | 0.207439i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 72.0199i | 2.32564i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.1182 | 0.907039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.528453 | 0.0170292 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.5783i | 0.694630i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 28.2388i | − | 0.908099i | −0.890976 | − | 0.454050i | \(-0.849979\pi\) | ||
0.890976 | − | 0.454050i | \(-0.150021\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.70140 | −0.0546569 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.7436 | 0.376869 | 0.188434 | − | 0.982086i | \(-0.439659\pi\) | ||||
0.188434 | + | 0.982086i | \(0.439659\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.9035i | 1.37542i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.593836i | 0.0190180i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 8.60547i | − | 0.275313i | −0.990480 | − | 0.137657i | \(-0.956043\pi\) | ||
0.990480 | − | 0.137657i | \(-0.0439571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.3559i | 0.458817i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.39885i | 0.204299i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.59556 | 0.114680 | 0.0573402 | − | 0.998355i | \(-0.481738\pi\) | ||||
0.0573402 | + | 0.998355i | \(0.481738\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.21949i | 0.0388561i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33.8476 | −1.07738 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.21131 | − | 9.76030i | 0.229306 | − | 0.310359i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 58.4314i | − | 1.85613i | −0.372414 | − | 0.928067i | \(-0.621470\pi\) | ||
0.372414 | − | 0.928067i | \(-0.378530\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.5124 | −0.650942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.5570i | 0.524893i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.1189 | −1.23891 | −0.619454 | − | 0.785033i | \(-0.712646\pi\) | ||||
−0.619454 | + | 0.785033i | \(0.712646\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.8469 | −0.343181 |
(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 | 5520.2.be.c.1471.8 | yes | 32 | |
4.3 | odd | 2 | 5520.2.be.d.1471.7 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.d.1471.8 | yes | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.c.1471.7 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.7 | ✓ | 32 | 92.91 | even | 2 | inner | |
5520.2.be.c.1471.8 | yes | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.d.1471.7 | yes | 32 | 4.3 | odd | 2 | ||
5520.2.be.d.1471.8 | yes | 32 | 23.22 | odd | 2 |