Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(181,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("390.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.b (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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.3 | ||
Root | \(-2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.181 |
Dual form | 390.2.b.c.181.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | − 4.60555i | − 1.74073i | −0.492403 | − | 0.870367i | \(-0.663881\pi\) | ||||
0.492403 | − | 0.870367i | \(-0.336119\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.60555 | 1.00000 | ||||||||
\(14\) | 4.60555 | 1.23089 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.60555 | 1.11701 | 0.558505 | − | 0.829501i | \(-0.311375\pi\) | ||||
0.558505 | + | 0.829501i | \(0.311375\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − 4.60555i | − 1.05659i | −0.849062 | − | 0.528293i | \(-0.822832\pi\) | ||||
0.849062 | − | 0.528293i | \(-0.177168\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 4.60555i | 1.00501i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.39445 | −0.290763 | −0.145381 | − | 0.989376i | \(-0.546441\pi\) | ||||
−0.145381 | + | 0.989376i | \(0.546441\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.60555i | 0.707107i | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.60555i | 0.870367i | ||||||||
\(29\) | 4.60555 | 0.855229 | 0.427615 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427615 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 6.00000i | 1.07763i | 0.842424 | + | 0.538816i | \(0.181128\pi\) | ||||
−0.842424 | + | 0.538816i | \(0.818872\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.60555i | 0.789846i | ||||||||
\(35\) | 4.60555 | 0.778480 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 9.21110i | − 1.51430i | −0.653243 | − | 0.757148i | \(-0.726592\pi\) | ||||
0.653243 | − | 0.757148i | \(-0.273408\pi\) | |||||||
\(38\) | 4.60555 | 0.747119 | ||||||||
\(39\) | −3.60555 | −0.577350 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 3.21110i | 0.501490i | 0.968053 | + | 0.250745i | \(0.0806756\pi\) | ||||
−0.968053 | + | 0.250745i | \(0.919324\pi\) | |||||||
\(42\) | −4.60555 | −0.710652 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | − 1.39445i | − 0.205600i | ||||||||
\(47\) | − 9.21110i | − 1.34358i | −0.740743 | − | 0.671789i | \(-0.765526\pi\) | ||||
0.740743 | − | 0.671789i | \(-0.234474\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −14.2111 | −2.03016 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | −4.60555 | −0.644906 | ||||||||
\(52\) | −3.60555 | −0.500000 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.60555 | −0.615443 | ||||||||
\(57\) | 4.60555i | 0.610020i | ||||||||
\(58\) | 4.60555i | 0.604739i | ||||||||
\(59\) | − 9.21110i | − 1.19918i | −0.800306 | − | 0.599592i | \(-0.795330\pi\) | ||||
0.800306 | − | 0.599592i | \(-0.204670\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −11.2111 | −1.43543 | −0.717717 | − | 0.696335i | \(-0.754813\pi\) | ||||
−0.717717 | + | 0.696335i | \(0.754813\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | − 4.60555i | − 0.580245i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.60555i | 0.447214i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.21110i | − 0.392299i | −0.980574 | − | 0.196149i | \(-0.937156\pi\) | ||||
0.980574 | − | 0.196149i | \(-0.0628437\pi\) | |||||||
\(68\) | −4.60555 | −0.558505 | ||||||||
\(69\) | 1.39445 | 0.167872 | ||||||||
\(70\) | 4.60555i | 0.550469i | ||||||||
\(71\) | 9.21110i | 1.09316i | 0.837408 | + | 0.546578i | \(0.184070\pi\) | ||||
−0.837408 | + | 0.546578i | \(0.815930\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 1.39445i | − 0.163208i | −0.996665 | − | 0.0816039i | \(-0.973996\pi\) | ||||
0.996665 | − | 0.0816039i | \(-0.0260043\pi\) | |||||||
\(74\) | 9.21110 | 1.07077 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 4.60555i | 0.528293i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − 3.60555i | − 0.408248i | ||||||||
\(79\) | −14.4222 | −1.62262 | −0.811312 | − | 0.584613i | \(-0.801246\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.21110 | −0.354607 | ||||||||
\(83\) | 2.78890i | 0.306121i | 0.988217 | + | 0.153061i | \(0.0489130\pi\) | ||||
−0.988217 | + | 0.153061i | \(0.951087\pi\) | |||||||
\(84\) | − 4.60555i | − 0.502507i | ||||||||
\(85\) | 4.60555i | 0.499542i | ||||||||
\(86\) | 8.00000i | 0.862662i | ||||||||
\(87\) | −4.60555 | −0.493767 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.2111i | 1.61237i | 0.591661 | + | 0.806187i | \(0.298472\pi\) | ||||
−0.591661 | + | 0.806187i | \(0.701528\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | − 16.6056i | − 1.74073i | ||||||||
\(92\) | 1.39445 | 0.145381 | ||||||||
\(93\) | − 6.00000i | − 0.622171i | ||||||||
\(94\) | 9.21110 | 0.950053 | ||||||||
\(95\) | 4.60555 | 0.472520 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | 1.39445i | 0.141585i | 0.997491 | + | 0.0707924i | \(0.0225528\pi\) | ||||
−0.997491 | + | 0.0707924i | \(0.977447\pi\) | |||||||
\(98\) | − 14.2111i | − 1.43554i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −7.39445 | −0.735775 | −0.367888 | − | 0.929870i | \(-0.619919\pi\) | ||||
−0.367888 | + | 0.929870i | \(0.619919\pi\) | |||||||
\(102\) | − 4.60555i | − 0.456018i | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | − 3.60555i | − 0.353553i | ||||||||
\(105\) | −4.60555 | −0.449456 | ||||||||
\(106\) | 6.00000i | 0.582772i | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 1.39445i | 0.133564i | 0.997768 | + | 0.0667820i | \(0.0212732\pi\) | ||||
−0.997768 | + | 0.0667820i | \(0.978727\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.21110i | 0.874279i | ||||||||
\(112\) | − 4.60555i | − 0.435184i | ||||||||
\(113\) | −13.8167 | −1.29976 | −0.649881 | − | 0.760036i | \(-0.725181\pi\) | ||||
−0.649881 | + | 0.760036i | \(0.725181\pi\) | |||||||
\(114\) | −4.60555 | −0.431349 | ||||||||
\(115\) | − 1.39445i | − 0.130033i | ||||||||
\(116\) | −4.60555 | −0.427615 | ||||||||
\(117\) | 3.60555 | 0.333333 | ||||||||
\(118\) | 9.21110 | 0.847951 | ||||||||
\(119\) | − 21.2111i | − 1.94442i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | − 11.2111i | − 1.01501i | ||||||||
\(123\) | − 3.21110i | − 0.289535i | ||||||||
\(124\) | − 6.00000i | − 0.538816i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 4.60555 | 0.410295 | ||||||||
\(127\) | 1.21110 | 0.107468 | 0.0537340 | − | 0.998555i | \(-0.482888\pi\) | ||||
0.0537340 | + | 0.998555i | \(0.482888\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | −3.60555 | −0.316228 | ||||||||
\(131\) | 22.6056 | 1.97506 | 0.987528 | − | 0.157443i | \(-0.0503250\pi\) | ||||
0.987528 | + | 0.157443i | \(0.0503250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.2111 | −1.83924 | ||||||||
\(134\) | 3.21110 | 0.277397 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | − 4.60555i | − 0.394923i | ||||||||
\(137\) | 3.21110i | 0.274343i | 0.990547 | + | 0.137172i | \(0.0438011\pi\) | ||||
−0.990547 | + | 0.137172i | \(0.956199\pi\) | |||||||
\(138\) | 1.39445i | 0.118703i | ||||||||
\(139\) | 17.2111 | 1.45983 | 0.729913 | − | 0.683540i | \(-0.239560\pi\) | ||||
0.729913 | + | 0.683540i | \(0.239560\pi\) | |||||||
\(140\) | −4.60555 | −0.389240 | ||||||||
\(141\) | 9.21110i | 0.775715i | ||||||||
\(142\) | −9.21110 | −0.772979 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.60555i | 0.382470i | ||||||||
\(146\) | 1.39445 | 0.115405 | ||||||||
\(147\) | 14.2111 | 1.17211 | ||||||||
\(148\) | 9.21110i | 0.757148i | ||||||||
\(149\) | 15.2111i | 1.24614i | 0.782165 | + | 0.623071i | \(0.214115\pi\) | ||||
−0.782165 | + | 0.623071i | \(0.785885\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 6.00000i | 0.488273i | 0.969741 | + | 0.244137i | \(0.0785045\pi\) | ||||
−0.969741 | + | 0.244137i | \(0.921495\pi\) | |||||||
\(152\) | −4.60555 | −0.373560 | ||||||||
\(153\) | 4.60555 | 0.372337 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 3.60555 | 0.288675 | ||||||||
\(157\) | 20.4222 | 1.62987 | 0.814935 | − | 0.579553i | \(-0.196773\pi\) | ||||
0.814935 | + | 0.579553i | \(0.196773\pi\) | |||||||
\(158\) | − 14.4222i | − 1.14737i | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 6.42221i | 0.506141i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 24.4222i | 1.91289i | 0.291905 | + | 0.956447i | \(0.405711\pi\) | ||||
−0.291905 | + | 0.956447i | \(0.594289\pi\) | |||||||
\(164\) | − 3.21110i | − 0.250745i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.78890 | −0.216460 | ||||||||
\(167\) | 9.21110i | 0.712777i | 0.934338 | + | 0.356388i | \(0.115992\pi\) | ||||
−0.934338 | + | 0.356388i | \(0.884008\pi\) | |||||||
\(168\) | 4.60555 | 0.355326 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | −4.60555 | −0.353230 | ||||||||
\(171\) | − 4.60555i | − 0.352195i | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | −12.4222 | −0.944443 | −0.472221 | − | 0.881480i | \(-0.656548\pi\) | ||||
−0.472221 | + | 0.881480i | \(0.656548\pi\) | |||||||
\(174\) | − 4.60555i | − 0.349146i | ||||||||
\(175\) | 4.60555i | 0.348147i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.21110i | 0.692349i | ||||||||
\(178\) | −15.2111 | −1.14012 | ||||||||
\(179\) | −19.8167 | −1.48117 | −0.740583 | − | 0.671965i | \(-0.765451\pi\) | ||||
−0.740583 | + | 0.671965i | \(0.765451\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | 8.42221 | 0.626018 | 0.313009 | − | 0.949750i | \(-0.398663\pi\) | ||||
0.313009 | + | 0.949750i | \(0.398663\pi\) | |||||||
\(182\) | 16.6056 | 1.23089 | ||||||||
\(183\) | 11.2111 | 0.828749 | ||||||||
\(184\) | 1.39445i | 0.102800i | ||||||||
\(185\) | 9.21110 | 0.677214 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.21110i | 0.671789i | ||||||||
\(189\) | 4.60555i | 0.335005i | ||||||||
\(190\) | 4.60555i | 0.334122i | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 7.81665i | 0.562655i | 0.959612 | + | 0.281328i | \(0.0907747\pi\) | ||||
−0.959612 | + | 0.281328i | \(0.909225\pi\) | |||||||
\(194\) | −1.39445 | −0.100116 | ||||||||
\(195\) | − 3.60555i | − 0.258199i | ||||||||
\(196\) | 14.2111 | 1.01508 | ||||||||
\(197\) | − 6.00000i | − 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4222 | 1.58947 | 0.794734 | − | 0.606958i | \(-0.207610\pi\) | ||||
0.794734 | + | 0.606958i | \(0.207610\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 3.21110i | 0.226494i | ||||||||
\(202\) | − 7.39445i | − 0.520272i | ||||||||
\(203\) | − 21.2111i | − 1.48873i | ||||||||
\(204\) | 4.60555 | 0.322453 | ||||||||
\(205\) | −3.21110 | −0.224273 | ||||||||
\(206\) | − 4.00000i | − 0.278693i | ||||||||
\(207\) | −1.39445 | −0.0969209 | ||||||||
\(208\) | 3.60555 | 0.250000 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | − 4.60555i | − 0.317813i | ||||||||
\(211\) | −17.2111 | −1.18486 | −0.592431 | − | 0.805622i | \(-0.701832\pi\) | ||||
−0.592431 | + | 0.805622i | \(0.701832\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | − 9.21110i | − 0.631134i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000i | 0.545595i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 27.6333 | 1.87587 | ||||||||
\(218\) | −1.39445 | −0.0944440 | ||||||||
\(219\) | 1.39445i | 0.0942281i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.6056 | 1.11701 | ||||||||
\(222\) | −9.21110 | −0.618209 | ||||||||
\(223\) | 1.81665i | 0.121652i | 0.998148 | + | 0.0608261i | \(0.0193735\pi\) | ||||
−0.998148 | + | 0.0608261i | \(0.980627\pi\) | |||||||
\(224\) | 4.60555 | 0.307721 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 13.8167i | − 0.919070i | ||||||||
\(227\) | 24.0000i | 1.59294i | 0.604681 | + | 0.796468i | \(0.293301\pi\) | ||||
−0.604681 | + | 0.796468i | \(0.706699\pi\) | |||||||
\(228\) | − 4.60555i | − 0.305010i | ||||||||
\(229\) | − 19.8167i | − 1.30952i | −0.755836 | − | 0.654761i | \(-0.772769\pi\) | ||||
0.755836 | − | 0.654761i | \(-0.227231\pi\) | |||||||
\(230\) | 1.39445 | 0.0919472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 4.60555i | − 0.302369i | ||||||||
\(233\) | −1.81665 | −0.119013 | −0.0595065 | − | 0.998228i | \(-0.518953\pi\) | ||||
−0.0595065 | + | 0.998228i | \(0.518953\pi\) | |||||||
\(234\) | 3.60555i | 0.235702i | ||||||||
\(235\) | 9.21110 | 0.600866 | ||||||||
\(236\) | 9.21110i | 0.599592i | ||||||||
\(237\) | 14.4222 | 0.936823 | ||||||||
\(238\) | 21.2111 | 1.37491 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | − 6.42221i | − 0.413691i | −0.978374 | − | 0.206845i | \(-0.933680\pi\) | ||||
0.978374 | − | 0.206845i | \(-0.0663197\pi\) | |||||||
\(242\) | 11.0000i | 0.707107i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.2111 | 0.717717 | ||||||||
\(245\) | − 14.2111i | − 0.907914i | ||||||||
\(246\) | 3.21110 | 0.204732 | ||||||||
\(247\) | − 16.6056i | − 1.05659i | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | − 2.78890i | − 0.176739i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −13.3944 | −0.845450 | −0.422725 | − | 0.906258i | \(-0.638926\pi\) | ||||
−0.422725 | + | 0.906258i | \(0.638926\pi\) | |||||||
\(252\) | 4.60555i | 0.290122i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.21110i | 0.0759913i | ||||||||
\(255\) | − 4.60555i | − 0.288411i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.6056 | −1.78437 | −0.892183 | − | 0.451675i | \(-0.850827\pi\) | ||||
−0.892183 | + | 0.451675i | \(0.850827\pi\) | |||||||
\(258\) | − 8.00000i | − 0.498058i | ||||||||
\(259\) | −42.4222 | −2.63599 | ||||||||
\(260\) | − 3.60555i | − 0.223607i | ||||||||
\(261\) | 4.60555 | 0.285076 | ||||||||
\(262\) | 22.6056i | 1.39658i | ||||||||
\(263\) | −7.81665 | −0.481996 | −0.240998 | − | 0.970526i | \(-0.577475\pi\) | ||||
−0.240998 | + | 0.970526i | \(0.577475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000i | 0.368577i | ||||||||
\(266\) | − 21.2111i | − 1.30054i | ||||||||
\(267\) | − 15.2111i | − 0.930904i | ||||||||
\(268\) | 3.21110i | 0.196149i | ||||||||
\(269\) | 25.8167 | 1.57407 | 0.787035 | − | 0.616909i | \(-0.211615\pi\) | ||||
0.787035 | + | 0.616909i | \(0.211615\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 0.422205i | − 0.0256471i | −0.999918 | − | 0.0128236i | \(-0.995918\pi\) | ||||
0.999918 | − | 0.0128236i | \(-0.00408198\pi\) | |||||||
\(272\) | 4.60555 | 0.279253 | ||||||||
\(273\) | 16.6056i | 1.00501i | ||||||||
\(274\) | −3.21110 | −0.193990 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.39445 | −0.0839359 | ||||||||
\(277\) | −16.4222 | −0.986715 | −0.493357 | − | 0.869827i | \(-0.664230\pi\) | ||||
−0.493357 | + | 0.869827i | \(0.664230\pi\) | |||||||
\(278\) | 17.2111i | 1.03225i | ||||||||
\(279\) | 6.00000i | 0.359211i | ||||||||
\(280\) | − 4.60555i | − 0.275234i | ||||||||
\(281\) | 27.2111i | 1.62328i | 0.584159 | + | 0.811639i | \(0.301424\pi\) | ||||
−0.584159 | + | 0.811639i | \(0.698576\pi\) | |||||||
\(282\) | −9.21110 | −0.548513 | ||||||||
\(283\) | 10.4222 | 0.619536 | 0.309768 | − | 0.950812i | \(-0.399749\pi\) | ||||
0.309768 | + | 0.950812i | \(0.399749\pi\) | |||||||
\(284\) | − 9.21110i | − 0.546578i | ||||||||
\(285\) | −4.60555 | −0.272809 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7889 | 0.872961 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 4.21110 | 0.247712 | ||||||||
\(290\) | −4.60555 | −0.270447 | ||||||||
\(291\) | − 1.39445i | − 0.0817440i | ||||||||
\(292\) | 1.39445i | 0.0816039i | ||||||||
\(293\) | 18.0000i | 1.05157i | 0.850617 | + | 0.525786i | \(0.176229\pi\) | ||||
−0.850617 | + | 0.525786i | \(0.823771\pi\) | |||||||
\(294\) | 14.2111i | 0.828808i | ||||||||
\(295\) | 9.21110 | 0.536291 | ||||||||
\(296\) | −9.21110 | −0.535384 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.2111 | −0.881156 | ||||||||
\(299\) | −5.02776 | −0.290763 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | − 36.8444i | − 2.12368i | ||||||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | 7.39445 | 0.424800 | ||||||||
\(304\) | − 4.60555i | − 0.264146i | ||||||||
\(305\) | − 11.2111i | − 0.641946i | ||||||||
\(306\) | 4.60555i | 0.263282i | ||||||||
\(307\) | − 8.78890i | − 0.501609i | −0.968038 | − | 0.250804i | \(-0.919305\pi\) | ||||
0.968038 | − | 0.250804i | \(-0.0806951\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | − 6.00000i | − 0.340777i | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 3.60555i | 0.204124i | ||||||||
\(313\) | 3.57779 | 0.202229 | 0.101114 | − | 0.994875i | \(-0.467759\pi\) | ||||
0.101114 | + | 0.994875i | \(0.467759\pi\) | |||||||
\(314\) | 20.4222i | 1.15249i | ||||||||
\(315\) | 4.60555 | 0.259493 | ||||||||
\(316\) | 14.4222 | 0.811312 | ||||||||
\(317\) | − 18.0000i | − 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | − 6.00000i | − 0.336463i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.42221 | −0.357895 | ||||||||
\(323\) | − 21.2111i | − 1.18022i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −3.60555 | −0.200000 | ||||||||
\(326\) | −24.4222 | −1.35262 | ||||||||
\(327\) | − 1.39445i | − 0.0771132i | ||||||||
\(328\) | 3.21110 | 0.177303 | ||||||||
\(329\) | −42.4222 | −2.33881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 16.6056i | − 0.912724i | −0.889794 | − | 0.456362i | \(-0.849152\pi\) | ||||
0.889794 | − | 0.456362i | \(-0.150848\pi\) | |||||||
\(332\) | − 2.78890i | − 0.153061i | ||||||||
\(333\) | − 9.21110i | − 0.504765i | ||||||||
\(334\) | −9.21110 | −0.504009 | ||||||||
\(335\) | 3.21110 | 0.175441 | ||||||||
\(336\) | 4.60555i | 0.251253i | ||||||||
\(337\) | 13.6333 | 0.742654 | 0.371327 | − | 0.928502i | \(-0.378903\pi\) | ||||
0.371327 | + | 0.928502i | \(0.378903\pi\) | |||||||
\(338\) | 13.0000i | 0.707107i | ||||||||
\(339\) | 13.8167 | 0.750418 | ||||||||
\(340\) | − 4.60555i | − 0.249771i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.60555 | 0.249040 | ||||||||
\(343\) | 33.2111i | 1.79323i | ||||||||
\(344\) | − 8.00000i | − 0.431331i | ||||||||
\(345\) | 1.39445i | 0.0750746i | ||||||||
\(346\) | − 12.4222i | − 0.667822i | ||||||||
\(347\) | −27.6333 | −1.48343 | −0.741717 | − | 0.670713i | \(-0.765988\pi\) | ||||
−0.741717 | + | 0.670713i | \(0.765988\pi\) | |||||||
\(348\) | 4.60555 | 0.246883 | ||||||||
\(349\) | − 7.81665i | − 0.418416i | −0.977871 | − | 0.209208i | \(-0.932911\pi\) | ||||
0.977871 | − | 0.209208i | \(-0.0670886\pi\) | |||||||
\(350\) | −4.60555 | −0.246177 | ||||||||
\(351\) | −3.60555 | −0.192450 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 8.78890i | − 0.467786i | −0.972262 | − | 0.233893i | \(-0.924853\pi\) | ||||
0.972262 | − | 0.233893i | \(-0.0751465\pi\) | |||||||
\(354\) | −9.21110 | −0.489565 | ||||||||
\(355\) | −9.21110 | −0.488875 | ||||||||
\(356\) | − 15.2111i | − 0.806187i | ||||||||
\(357\) | 21.2111i | 1.12261i | ||||||||
\(358\) | − 19.8167i | − 1.04734i | ||||||||
\(359\) | 15.6333i | 0.825094i | 0.910936 | + | 0.412547i | \(0.135361\pi\) | ||||
−0.910936 | + | 0.412547i | \(0.864639\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −2.21110 | −0.116374 | ||||||||
\(362\) | 8.42221i | 0.442661i | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | 16.6056i | 0.870367i | ||||||||
\(365\) | 1.39445 | 0.0729888 | ||||||||
\(366\) | 11.2111i | 0.586014i | ||||||||
\(367\) | −19.6333 | −1.02485 | −0.512425 | − | 0.858732i | \(-0.671253\pi\) | ||||
−0.512425 | + | 0.858732i | \(0.671253\pi\) | |||||||
\(368\) | −1.39445 | −0.0726907 | ||||||||
\(369\) | 3.21110i | 0.167163i | ||||||||
\(370\) | 9.21110i | 0.478862i | ||||||||
\(371\) | − 27.6333i | − 1.43465i | ||||||||
\(372\) | 6.00000i | 0.311086i | ||||||||
\(373\) | −20.4222 | −1.05742 | −0.528711 | − | 0.848802i | \(-0.677324\pi\) | ||||
−0.528711 | + | 0.848802i | \(0.677324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | −9.21110 | −0.475026 | ||||||||
\(377\) | 16.6056 | 0.855229 | ||||||||
\(378\) | −4.60555 | −0.236884 | ||||||||
\(379\) | 35.0278i | 1.79925i | 0.436658 | + | 0.899627i | \(0.356162\pi\) | ||||
−0.436658 | + | 0.899627i | \(0.643838\pi\) | |||||||
\(380\) | −4.60555 | −0.236260 | ||||||||
\(381\) | −1.21110 | −0.0620467 | ||||||||
\(382\) | − 12.0000i | − 0.613973i | ||||||||
\(383\) | − 27.6333i | − 1.41200i | −0.708214 | − | 0.705998i | \(-0.750499\pi\) | ||||
0.708214 | − | 0.705998i | \(-0.249501\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.81665 | −0.397857 | ||||||||
\(387\) | 8.00000 | 0.406663 | ||||||||
\(388\) | − 1.39445i | − 0.0707924i | ||||||||
\(389\) | 4.60555 | 0.233511 | 0.116755 | − | 0.993161i | \(-0.462751\pi\) | ||||
0.116755 | + | 0.993161i | \(0.462751\pi\) | |||||||
\(390\) | 3.60555 | 0.182574 | ||||||||
\(391\) | −6.42221 | −0.324785 | ||||||||
\(392\) | 14.2111i | 0.717769i | ||||||||
\(393\) | −22.6056 | −1.14030 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | − 14.4222i | − 0.725660i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.63331i | − 0.182350i | −0.995835 | − | 0.0911752i | \(-0.970938\pi\) | ||||
0.995835 | − | 0.0911752i | \(-0.0290623\pi\) | |||||||
\(398\) | 22.4222i | 1.12392i | ||||||||
\(399\) | 21.2111 | 1.06188 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 8.78890i | 0.438897i | 0.975624 | + | 0.219448i | \(0.0704257\pi\) | ||||
−0.975624 | + | 0.219448i | \(0.929574\pi\) | |||||||
\(402\) | −3.21110 | −0.160155 | ||||||||
\(403\) | 21.6333i | 1.07763i | ||||||||
\(404\) | 7.39445 | 0.367888 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 21.2111 | 1.05269 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.60555i | 0.228009i | ||||||||
\(409\) | − 14.7889i | − 0.731264i | −0.930760 | − | 0.365632i | \(-0.880853\pi\) | ||||
0.930760 | − | 0.365632i | \(-0.119147\pi\) | |||||||
\(410\) | − 3.21110i | − 0.158585i | ||||||||
\(411\) | − 3.21110i | − 0.158392i | ||||||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | −42.4222 | −2.08746 | ||||||||
\(414\) | − 1.39445i | − 0.0685334i | ||||||||
\(415\) | −2.78890 | −0.136902 | ||||||||
\(416\) | 3.60555i | 0.176777i | ||||||||
\(417\) | −17.2111 | −0.842831 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.18335 | 0.204370 | 0.102185 | − | 0.994765i | \(-0.467417\pi\) | ||||
0.102185 | + | 0.994765i | \(0.467417\pi\) | |||||||
\(420\) | 4.60555 | 0.224728 | ||||||||
\(421\) | − 19.8167i | − 0.965805i | −0.875674 | − | 0.482902i | \(-0.839583\pi\) | ||||
0.875674 | − | 0.482902i | \(-0.160417\pi\) | |||||||
\(422\) | − 17.2111i | − 0.837823i | ||||||||
\(423\) | − 9.21110i | − 0.447859i | ||||||||
\(424\) | − 6.00000i | − 0.291386i | ||||||||
\(425\) | −4.60555 | −0.223402 | ||||||||
\(426\) | 9.21110 | 0.446279 | ||||||||
\(427\) | 51.6333i | 2.49871i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 12.0000i | 0.578020i | 0.957326 | + | 0.289010i | \(0.0933260\pi\) | ||||
−0.957326 | + | 0.289010i | \(0.906674\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 19.2111 | 0.923227 | 0.461613 | − | 0.887081i | \(-0.347271\pi\) | ||||
0.461613 | + | 0.887081i | \(0.347271\pi\) | |||||||
\(434\) | 27.6333i | 1.32644i | ||||||||
\(435\) | − 4.60555i | − 0.220819i | ||||||||
\(436\) | − 1.39445i | − 0.0667820i | ||||||||
\(437\) | 6.42221i | 0.307216i | ||||||||
\(438\) | −1.39445 | −0.0666293 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.2111 | −0.676719 | ||||||||
\(442\) | 16.6056i | 0.789846i | ||||||||
\(443\) | 15.6333 | 0.742761 | 0.371380 | − | 0.928481i | \(-0.378885\pi\) | ||||
0.371380 | + | 0.928481i | \(0.378885\pi\) | |||||||
\(444\) | − 9.21110i | − 0.437140i | ||||||||
\(445\) | −15.2111 | −0.721075 | ||||||||
\(446\) | −1.81665 | −0.0860211 | ||||||||
\(447\) | − 15.2111i | − 0.719460i | ||||||||
\(448\) | 4.60555i | 0.217592i | ||||||||
\(449\) | 33.6333i | 1.58725i | 0.608405 | + | 0.793627i | \(0.291810\pi\) | ||||
−0.608405 | + | 0.793627i | \(0.708190\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 13.8167 | 0.649881 | ||||||||
\(453\) | − 6.00000i | − 0.281905i | ||||||||
\(454\) | −24.0000 | −1.12638 | ||||||||
\(455\) | 16.6056 | 0.778480 | ||||||||
\(456\) | 4.60555 | 0.215675 | ||||||||
\(457\) | 38.2389i | 1.78874i | 0.447330 | + | 0.894369i | \(0.352375\pi\) | ||||
−0.447330 | + | 0.894369i | \(0.647625\pi\) | |||||||
\(458\) | 19.8167 | 0.925971 | ||||||||
\(459\) | −4.60555 | −0.214969 | ||||||||
\(460\) | 1.39445i | 0.0650165i | ||||||||
\(461\) | − 33.6333i | − 1.56646i | −0.621733 | − | 0.783230i | \(-0.713571\pi\) | ||||
0.621733 | − | 0.783230i | \(-0.286429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 31.3944i | − 1.45902i | −0.683968 | − | 0.729512i | \(-0.739747\pi\) | ||||
0.683968 | − | 0.729512i | \(-0.260253\pi\) | |||||||
\(464\) | 4.60555 | 0.213807 | ||||||||
\(465\) | 6.00000 | 0.278243 | ||||||||
\(466\) | − 1.81665i | − 0.0841549i | ||||||||
\(467\) | −30.4222 | −1.40777 | −0.703886 | − | 0.710313i | \(-0.748553\pi\) | ||||
−0.703886 | + | 0.710313i | \(0.748553\pi\) | |||||||
\(468\) | −3.60555 | −0.166667 | ||||||||
\(469\) | −14.7889 | −0.682888 | ||||||||
\(470\) | 9.21110i | 0.424876i | ||||||||
\(471\) | −20.4222 | −0.941006 | ||||||||
\(472\) | −9.21110 | −0.423975 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 14.4222i | 0.662434i | ||||||||
\(475\) | 4.60555i | 0.211317i | ||||||||
\(476\) | 21.2111i | 0.972209i | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.57779i | 0.254856i | 0.991848 | + | 0.127428i | \(0.0406722\pi\) | ||||
−0.991848 | + | 0.127428i | \(0.959328\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | − 33.2111i | − 1.51430i | ||||||||
\(482\) | 6.42221 | 0.292523 | ||||||||
\(483\) | − 6.42221i | − 0.292220i | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | −1.39445 | −0.0633187 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | − 0.972244i | − 0.0440566i | −0.999757 | − | 0.0220283i | \(-0.992988\pi\) | ||||
0.999757 | − | 0.0220283i | \(-0.00701239\pi\) | |||||||
\(488\) | 11.2111i | 0.507503i | ||||||||
\(489\) | − 24.4222i | − 1.10441i | ||||||||
\(490\) | 14.2111 | 0.641992 | ||||||||
\(491\) | 7.81665 | 0.352761 | 0.176380 | − | 0.984322i | \(-0.443561\pi\) | ||||
0.176380 | + | 0.984322i | \(0.443561\pi\) | |||||||
\(492\) | 3.21110i | 0.144768i | ||||||||
\(493\) | 21.2111 | 0.955300 | ||||||||
\(494\) | 16.6056 | 0.747119 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000i | 0.269408i | ||||||||
\(497\) | 42.4222 | 1.90290 | ||||||||
\(498\) | 2.78890 | 0.124973 | ||||||||
\(499\) | 23.0278i | 1.03086i | 0.856930 | + | 0.515432i | \(0.172369\pi\) | ||||
−0.856930 | + | 0.515432i | \(0.827631\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | − 9.21110i | − 0.411522i | ||||||||
\(502\) | − 13.3944i | − 0.597824i | ||||||||
\(503\) | 23.4500 | 1.04558 | 0.522791 | − | 0.852461i | \(-0.324891\pi\) | ||||
0.522791 | + | 0.852461i | \(0.324891\pi\) | |||||||
\(504\) | −4.60555 | −0.205148 | ||||||||
\(505\) | − 7.39445i | − 0.329049i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | −1.21110 | −0.0537340 | ||||||||
\(509\) | − 33.6333i | − 1.49077i | −0.666634 | − | 0.745385i | \(-0.732266\pi\) | ||||
0.666634 | − | 0.745385i | \(-0.267734\pi\) | |||||||
\(510\) | 4.60555 | 0.203937 | ||||||||
\(511\) | −6.42221 | −0.284102 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 4.60555i | 0.203340i | ||||||||
\(514\) | − 28.6056i | − 1.26174i | ||||||||
\(515\) | − 4.00000i | − 0.176261i | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 42.4222i | − 1.86392i | ||||||||
\(519\) | 12.4222 | 0.545274 | ||||||||
\(520\) | 3.60555 | 0.158114 | ||||||||
\(521\) | 21.6333 | 0.947772 | 0.473886 | − | 0.880586i | \(-0.342851\pi\) | ||||
0.473886 | + | 0.880586i | \(0.342851\pi\) | |||||||
\(522\) | 4.60555i | 0.201580i | ||||||||
\(523\) | 32.8444 | 1.43619 | 0.718093 | − | 0.695947i | \(-0.245015\pi\) | ||||
0.718093 | + | 0.695947i | \(0.245015\pi\) | |||||||
\(524\) | −22.6056 | −0.987528 | ||||||||
\(525\) | − 4.60555i | − 0.201003i | ||||||||
\(526\) | − 7.81665i | − 0.340822i | ||||||||
\(527\) | 27.6333i | 1.20373i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0555 | −0.915457 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | − 9.21110i | − 0.399728i | ||||||||
\(532\) | 21.2111 | 0.919618 | ||||||||
\(533\) | 11.5778i | 0.501490i | ||||||||
\(534\) | 15.2111 | 0.658249 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.21110 | −0.138699 | ||||||||
\(537\) | 19.8167 | 0.855152 | ||||||||
\(538\) | 25.8167i | 1.11303i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 6.97224i | 0.299760i | 0.988704 | + | 0.149880i | \(0.0478888\pi\) | ||||
−0.988704 | + | 0.149880i | \(0.952111\pi\) | |||||||
\(542\) | 0.422205 | 0.0181353 | ||||||||
\(543\) | −8.42221 | −0.361431 | ||||||||
\(544\) | 4.60555i | 0.197461i | ||||||||
\(545\) | −1.39445 | −0.0597316 | ||||||||
\(546\) | −16.6056 | −0.710652 | ||||||||
\(547\) | 14.4222 | 0.616649 | 0.308324 | − | 0.951281i | \(-0.400232\pi\) | ||||
0.308324 | + | 0.951281i | \(0.400232\pi\) | |||||||
\(548\) | − 3.21110i | − 0.137172i | ||||||||
\(549\) | −11.2111 | −0.478478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 21.2111i | − 0.903623i | ||||||||
\(552\) | − 1.39445i | − 0.0593517i | ||||||||
\(553\) | 66.4222i | 2.82456i | ||||||||
\(554\) | − 16.4222i | − 0.697713i | ||||||||
\(555\) | −9.21110 | −0.390990 | ||||||||
\(556\) | −17.2111 | −0.729913 | ||||||||
\(557\) | 11.5778i | 0.490567i | 0.969451 | + | 0.245283i | \(0.0788810\pi\) | ||||
−0.969451 | + | 0.245283i | \(0.921119\pi\) | |||||||
\(558\) | −6.00000 | −0.254000 | ||||||||
\(559\) | 28.8444 | 1.21999 | ||||||||
\(560\) | 4.60555 | 0.194620 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.2111 | −1.14783 | ||||||||
\(563\) | 34.0555 | 1.43527 | 0.717634 | − | 0.696420i | \(-0.245225\pi\) | ||||
0.717634 | + | 0.696420i | \(0.245225\pi\) | |||||||
\(564\) | − 9.21110i | − 0.387857i | ||||||||
\(565\) | − 13.8167i | − 0.581271i | ||||||||
\(566\) | 10.4222i | 0.438078i | ||||||||
\(567\) | − 4.60555i | − 0.193415i | ||||||||
\(568\) | 9.21110 | 0.386489 | ||||||||
\(569\) | 33.6333 | 1.40998 | 0.704991 | − | 0.709216i | \(-0.250951\pi\) | ||||
0.704991 | + | 0.709216i | \(0.250951\pi\) | |||||||
\(570\) | − 4.60555i | − 0.192905i | ||||||||
\(571\) | −30.0555 | −1.25778 | −0.628892 | − | 0.777493i | \(-0.716491\pi\) | ||||
−0.628892 | + | 0.777493i | \(0.716491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 14.7889i | 0.617277i | ||||||||
\(575\) | 1.39445 | 0.0581525 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 37.3944i | − 1.55675i | −0.627799 | − | 0.778376i | \(-0.716044\pi\) | ||||
0.627799 | − | 0.778376i | \(-0.283956\pi\) | |||||||
\(578\) | 4.21110i | 0.175159i | ||||||||
\(579\) | − 7.81665i | − 0.324849i | ||||||||
\(580\) | − 4.60555i | − 0.191235i | ||||||||
\(581\) | 12.8444 | 0.532876 | ||||||||
\(582\) | 1.39445 | 0.0578018 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.39445 | −0.0577027 | ||||||||
\(585\) | 3.60555i | 0.149071i | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | − 6.42221i | − 0.265073i | −0.991178 | − | 0.132536i | \(-0.957688\pi\) | ||||
0.991178 | − | 0.132536i | \(-0.0423121\pi\) | |||||||
\(588\) | −14.2111 | −0.586056 | ||||||||
\(589\) | 27.6333 | 1.13861 | ||||||||
\(590\) | 9.21110i | 0.379215i | ||||||||
\(591\) | 6.00000i | 0.246807i | ||||||||
\(592\) | − 9.21110i | − 0.378574i | ||||||||
\(593\) | − 24.4222i | − 1.00290i | −0.865187 | − | 0.501450i | \(-0.832800\pi\) | ||||
0.865187 | − | 0.501450i | \(-0.167200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.2111 | 0.869570 | ||||||||
\(596\) | − 15.2111i | − 0.623071i | ||||||||
\(597\) | −22.4222 | −0.917680 | ||||||||
\(598\) | − 5.02776i | − 0.205600i | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | 1.63331 | 0.0666240 | 0.0333120 | − | 0.999445i | \(-0.489394\pi\) | ||||
0.0333120 | + | 0.999445i | \(0.489394\pi\) | |||||||
\(602\) | 36.8444 | 1.50167 | ||||||||
\(603\) | − 3.21110i | − 0.130766i | ||||||||
\(604\) | − 6.00000i | − 0.244137i | ||||||||
\(605\) | 11.0000i | 0.447214i | ||||||||
\(606\) | 7.39445i | 0.300379i | ||||||||
\(607\) | 17.2111 | 0.698577 | 0.349289 | − | 0.937015i | \(-0.386423\pi\) | ||||
0.349289 | + | 0.937015i | \(0.386423\pi\) | |||||||
\(608\) | 4.60555 | 0.186780 | ||||||||
\(609\) | 21.2111i | 0.859517i | ||||||||
\(610\) | 11.2111 | 0.453924 | ||||||||
\(611\) | − 33.2111i | − 1.34358i | ||||||||
\(612\) | −4.60555 | −0.186168 | ||||||||
\(613\) | − 33.2111i | − 1.34138i | −0.741736 | − | 0.670692i | \(-0.765997\pi\) | ||||
0.741736 | − | 0.670692i | \(-0.234003\pi\) | |||||||
\(614\) | 8.78890 | 0.354691 | ||||||||
\(615\) | 3.21110 | 0.129484 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4222i | 0.500099i | 0.968233 | + | 0.250050i | \(0.0804469\pi\) | ||||
−0.968233 | + | 0.250050i | \(0.919553\pi\) | |||||||
\(618\) | 4.00000i | 0.160904i | ||||||||
\(619\) | 25.8167i | 1.03766i | 0.854878 | + | 0.518829i | \(0.173632\pi\) | ||||
−0.854878 | + | 0.518829i | \(0.826368\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | 1.39445 | 0.0559573 | ||||||||
\(622\) | 12.0000i | 0.481156i | ||||||||
\(623\) | 70.0555 | 2.80671 | ||||||||
\(624\) | −3.60555 | −0.144338 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.57779i | 0.142997i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.4222 | −0.814935 | ||||||||
\(629\) | − 42.4222i | − 1.69148i | ||||||||
\(630\) | 4.60555i | 0.183490i | ||||||||
\(631\) | 3.21110i | 0.127832i | 0.997955 | + | 0.0639160i | \(0.0203590\pi\) | ||||
−0.997955 | + | 0.0639160i | \(0.979641\pi\) | |||||||
\(632\) | 14.4222i | 0.573685i | ||||||||
\(633\) | 17.2111 | 0.684080 | ||||||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | 1.21110i | 0.0480611i | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | −51.2389 | −2.03016 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.21110i | 0.364386i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 0.422205 | 0.0166761 | 0.00833805 | − | 0.999965i | \(-0.497346\pi\) | ||||
0.00833805 | + | 0.999965i | \(0.497346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.63331i | 0.379901i | 0.981794 | + | 0.189950i | \(0.0608327\pi\) | ||||
−0.981794 | + | 0.189950i | \(0.939167\pi\) | |||||||
\(644\) | − 6.42221i | − 0.253070i | ||||||||
\(645\) | − 8.00000i | − 0.315000i | ||||||||
\(646\) | 21.2111 | 0.834540 | ||||||||
\(647\) | −34.6056 | −1.36048 | −0.680242 | − | 0.732987i | \(-0.738125\pi\) | ||||
−0.680242 | + | 0.732987i | \(0.738125\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 3.60555i | − 0.141421i | ||||||||
\(651\) | −27.6333 | −1.08303 | ||||||||
\(652\) | − 24.4222i | − 0.956447i | ||||||||
\(653\) | 39.2111 | 1.53445 | 0.767225 | − | 0.641379i | \(-0.221637\pi\) | ||||
0.767225 | + | 0.641379i | \(0.221637\pi\) | |||||||
\(654\) | 1.39445 | 0.0545273 | ||||||||
\(655\) | 22.6056i | 0.883272i | ||||||||
\(656\) | 3.21110i | 0.125372i | ||||||||
\(657\) | − 1.39445i | − 0.0544026i | ||||||||
\(658\) | − 42.4222i | − 1.65379i | ||||||||
\(659\) | −26.2389 | −1.02212 | −0.511060 | − | 0.859545i | \(-0.670747\pi\) | ||||
−0.511060 | + | 0.859545i | \(0.670747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.2389i | 1.95407i | 0.213090 | + | 0.977033i | \(0.431647\pi\) | ||||
−0.213090 | + | 0.977033i | \(0.568353\pi\) | |||||||
\(662\) | 16.6056 | 0.645393 | ||||||||
\(663\) | −16.6056 | −0.644906 | ||||||||
\(664\) | 2.78890 | 0.108230 | ||||||||
\(665\) | − 21.2111i | − 0.822531i | ||||||||
\(666\) | 9.21110 | 0.356923 | ||||||||
\(667\) | −6.42221 | −0.248669 | ||||||||
\(668\) | − 9.21110i | − 0.356388i | ||||||||
\(669\) | − 1.81665i | − 0.0702359i | ||||||||
\(670\) | 3.21110i | 0.124056i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.60555 | −0.177663 | ||||||||
\(673\) | −37.6333 | −1.45066 | −0.725329 | − | 0.688403i | \(-0.758312\pi\) | ||||
−0.725329 | + | 0.688403i | \(0.758312\pi\) | |||||||
\(674\) | 13.6333i | 0.525135i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −28.0555 | −1.07826 | −0.539130 | − | 0.842222i | \(-0.681247\pi\) | ||||
−0.539130 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(678\) | 13.8167i | 0.530625i | ||||||||
\(679\) | 6.42221 | 0.246462 | ||||||||
\(680\) | 4.60555 | 0.176615 | ||||||||
\(681\) | − 24.0000i | − 0.919682i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.21110i | 0.352453i | 0.984350 | + | 0.176227i | \(0.0563891\pi\) | ||||
−0.984350 | + | 0.176227i | \(0.943611\pi\) | |||||||
\(684\) | 4.60555i | 0.176098i | ||||||||
\(685\) | −3.21110 | −0.122690 | ||||||||
\(686\) | −33.2111 | −1.26801 | ||||||||
\(687\) | 19.8167i | 0.756053i | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | 21.6333 | 0.824163 | ||||||||
\(690\) | −1.39445 | −0.0530858 | ||||||||
\(691\) | 20.2389i | 0.769922i | 0.922933 | + | 0.384961i | \(0.125785\pi\) | ||||
−0.922933 | + | 0.384961i | \(0.874215\pi\) | |||||||
\(692\) | 12.4222 | 0.472221 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − 27.6333i | − 1.04895i | ||||||||
\(695\) | 17.2111i | 0.652854i | ||||||||
\(696\) | 4.60555i | 0.174573i | ||||||||
\(697\) | 14.7889i | 0.560169i | ||||||||
\(698\) | 7.81665 | 0.295865 | ||||||||
\(699\) | 1.81665 | 0.0687122 | ||||||||
\(700\) | − 4.60555i | − 0.174073i | ||||||||
\(701\) | 47.0278 | 1.77621 | 0.888107 | − | 0.459637i | \(-0.152020\pi\) | ||||
0.888107 | + | 0.459637i | \(0.152020\pi\) | |||||||
\(702\) | − 3.60555i | − 0.136083i | ||||||||
\(703\) | −42.4222 | −1.59998 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.21110 | −0.346910 | ||||||||
\(706\) | 8.78890 | 0.330775 | ||||||||
\(707\) | 34.0555i | 1.28079i | ||||||||
\(708\) | − 9.21110i | − 0.346174i | ||||||||
\(709\) | − 1.39445i | − 0.0523696i | −0.999657 | − | 0.0261848i | \(-0.991664\pi\) | ||||
0.999657 | − | 0.0261848i | \(-0.00833584\pi\) | |||||||
\(710\) | − 9.21110i | − 0.345687i | ||||||||
\(711\) | −14.4222 | −0.540875 | ||||||||
\(712\) | 15.2111 | 0.570060 | ||||||||
\(713\) | − 8.36669i | − 0.313335i | ||||||||
\(714\) | −21.2111 | −0.793806 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.8167 | 0.740583 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.6333 | −0.583430 | ||||||||
\(719\) | −51.6333 | −1.92560 | −0.962799 | − | 0.270220i | \(-0.912904\pi\) | ||||
−0.962799 | + | 0.270220i | \(0.912904\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 18.4222i | 0.686079i | ||||||||
\(722\) | − 2.21110i | − 0.0822887i | ||||||||
\(723\) | 6.42221i | 0.238844i | ||||||||
\(724\) | −8.42221 | −0.313009 | ||||||||
\(725\) | −4.60555 | −0.171046 | ||||||||
\(726\) | − 11.0000i | − 0.408248i | ||||||||
\(727\) | −14.4222 | −0.534890 | −0.267445 | − | 0.963573i | \(-0.586179\pi\) | ||||
−0.267445 | + | 0.963573i | \(0.586179\pi\) | |||||||
\(728\) | −16.6056 | −0.615443 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.39445i | 0.0516109i | ||||||||
\(731\) | 36.8444 | 1.36274 | ||||||||
\(732\) | −11.2111 | −0.414374 | ||||||||
\(733\) | − 34.0555i | − 1.25787i | −0.777458 | − | 0.628935i | \(-0.783491\pi\) | ||||
0.777458 | − | 0.628935i | \(-0.216509\pi\) | |||||||
\(734\) | − 19.6333i | − 0.724679i | ||||||||
\(735\) | 14.2111i | 0.524184i | ||||||||
\(736\) | − 1.39445i | − 0.0514001i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.21110 | −0.118202 | ||||||||
\(739\) | 20.2389i | 0.744498i | 0.928133 | + | 0.372249i | \(0.121413\pi\) | ||||
−0.928133 | + | 0.372249i | \(0.878587\pi\) | |||||||
\(740\) | −9.21110 | −0.338607 | ||||||||
\(741\) | 16.6056i | 0.610020i | ||||||||
\(742\) | 27.6333 | 1.01445 | ||||||||
\(743\) | 36.8444i | 1.35169i | 0.737044 | + | 0.675845i | \(0.236221\pi\) | ||||
−0.737044 | + | 0.675845i | \(0.763779\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | −15.2111 | −0.557292 | ||||||||
\(746\) | − 20.4222i | − 0.747710i | ||||||||
\(747\) | 2.78890i | 0.102040i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −10.4222 | −0.380312 | −0.190156 | − | 0.981754i | \(-0.560899\pi\) | ||||
−0.190156 | + | 0.981754i | \(0.560899\pi\) | |||||||
\(752\) | − 9.21110i | − 0.335894i | ||||||||
\(753\) | 13.3944 | 0.488121 | ||||||||
\(754\) | 16.6056i | 0.604739i | ||||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | − 4.60555i | − 0.167502i | ||||||||
\(757\) | 12.7889 | 0.464820 | 0.232410 | − | 0.972618i | \(-0.425339\pi\) | ||||
0.232410 | + | 0.972618i | \(0.425339\pi\) | |||||||
\(758\) | −35.0278 | −1.27227 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − 4.60555i | − 0.167061i | ||||||||
\(761\) | 33.6333i | 1.21921i | 0.792707 | + | 0.609603i | \(0.208671\pi\) | ||||
−0.792707 | + | 0.609603i | \(0.791329\pi\) | |||||||
\(762\) | − 1.21110i | − 0.0438736i | ||||||||
\(763\) | 6.42221 | 0.232499 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 4.60555i | 0.166514i | ||||||||
\(766\) | 27.6333 | 0.998432 | ||||||||
\(767\) | − 33.2111i | − 1.19918i | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | − 12.8444i | − 0.463181i | −0.972813 | − | 0.231591i | \(-0.925607\pi\) | ||||
0.972813 | − | 0.231591i | \(-0.0743930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.6056 | 1.03020 | ||||||||
\(772\) | − 7.81665i | − 0.281328i | ||||||||
\(773\) | 30.0000i | 1.07903i | 0.841978 | + | 0.539513i | \(0.181391\pi\) | ||||
−0.841978 | + | 0.539513i | \(0.818609\pi\) | |||||||
\(774\) | 8.00000i | 0.287554i | ||||||||
\(775\) | − 6.00000i | − 0.215526i | ||||||||
\(776\) | 1.39445 | 0.0500578 | ||||||||
\(777\) | 42.4222 | 1.52189 | ||||||||
\(778\) | 4.60555i | 0.165117i | ||||||||
\(779\) | 14.7889 | 0.529867 | ||||||||
\(780\) | 3.60555i | 0.129099i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 6.42221i | − 0.229658i | ||||||||
\(783\) | −4.60555 | −0.164589 | ||||||||
\(784\) | −14.2111 | −0.507539 | ||||||||
\(785\) | 20.4222i | 0.728900i | ||||||||
\(786\) | − 22.6056i | − 0.806313i | ||||||||
\(787\) | 49.2666i | 1.75617i | 0.478509 | + | 0.878083i | \(0.341177\pi\) | ||||
−0.478509 | + | 0.878083i | \(0.658823\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | 7.81665 | 0.278280 | ||||||||
\(790\) | 14.4222 | 0.513119 | ||||||||
\(791\) | 63.6333i | 2.26254i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.4222 | −1.43543 | ||||||||
\(794\) | 3.63331 | 0.128941 | ||||||||
\(795\) | − 6.00000i | − 0.212798i | ||||||||
\(796\) | −22.4222 | −0.794734 | ||||||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | 21.2111i | 0.750865i | ||||||||
\(799\) | − 42.4222i | − 1.50079i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 15.2111i | 0.537458i | ||||||||
\(802\) | −8.78890 | −0.310347 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − 3.21110i | − 0.113247i | ||||||||
\(805\) | −6.42221 | −0.226353 | ||||||||
\(806\) | −21.6333 | −0.762001 | ||||||||
\(807\) | −25.8167 | −0.908789 | ||||||||
\(808\) | 7.39445i | 0.260136i | ||||||||
\(809\) | −6.84441 | −0.240637 | −0.120318 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120318 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 32.2389i | 1.13206i | 0.824385 | + | 0.566030i | \(0.191521\pi\) | ||||
−0.824385 | + | 0.566030i | \(0.808479\pi\) | |||||||
\(812\) | 21.2111i | 0.744364i | ||||||||
\(813\) | 0.422205i | 0.0148074i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.4222 | −0.855473 | ||||||||
\(816\) | −4.60555 | −0.161227 | ||||||||
\(817\) | − 36.8444i | − 1.28902i | ||||||||
\(818\) | 14.7889 | 0.517082 | ||||||||
\(819\) | − 16.6056i | − 0.580245i | ||||||||
\(820\) | 3.21110 | 0.112137 | ||||||||
\(821\) | − 3.21110i | − 0.112068i | −0.998429 | − | 0.0560341i | \(-0.982154\pi\) | ||||
0.998429 | − | 0.0560341i | \(-0.0178456\pi\) | |||||||
\(822\) | 3.21110 | 0.112000 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | 4.00000i | 0.139347i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − 42.4222i | − 1.47606i | ||||||||
\(827\) | − 27.6333i | − 0.960904i | −0.877021 | − | 0.480452i | \(-0.840473\pi\) | ||||
0.877021 | − | 0.480452i | \(-0.159527\pi\) | |||||||
\(828\) | 1.39445 | 0.0484604 | ||||||||
\(829\) | 46.8444 | 1.62697 | 0.813487 | − | 0.581583i | \(-0.197567\pi\) | ||||
0.813487 | + | 0.581583i | \(0.197567\pi\) | |||||||
\(830\) | − 2.78890i | − 0.0968040i | ||||||||
\(831\) | 16.4222 | 0.569680 | ||||||||
\(832\) | −3.60555 | −0.125000 | ||||||||
\(833\) | −65.4500 | −2.26771 | ||||||||
\(834\) | − 17.2111i | − 0.595972i | ||||||||
\(835\) | −9.21110 | −0.318763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.00000i | − 0.207390i | ||||||||
\(838\) | 4.18335i | 0.144511i | ||||||||
\(839\) | − 18.4222i | − 0.636005i | −0.948090 | − | 0.318003i | \(-0.896988\pi\) | ||||
0.948090 | − | 0.318003i | \(-0.103012\pi\) | |||||||
\(840\) | 4.60555i | 0.158907i | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | 19.8167 | 0.682927 | ||||||||
\(843\) | − 27.2111i | − 0.937200i | ||||||||
\(844\) | 17.2111 | 0.592431 | ||||||||
\(845\) | 13.0000i | 0.447214i | ||||||||
\(846\) | 9.21110 | 0.316684 | ||||||||
\(847\) | − 50.6611i | − 1.74073i | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | −10.4222 | −0.357689 | ||||||||
\(850\) | − 4.60555i | − 0.157969i | ||||||||
\(851\) | 12.8444i | 0.440301i | ||||||||
\(852\) | 9.21110i | 0.315567i | ||||||||
\(853\) | − 14.7889i | − 0.506362i | −0.967419 | − | 0.253181i | \(-0.918523\pi\) | ||||
0.967419 | − | 0.253181i | \(-0.0814769\pi\) | |||||||
\(854\) | −51.6333 | −1.76686 | ||||||||
\(855\) | 4.60555 | 0.157507 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.0278 | −0.786613 | −0.393307 | − | 0.919407i | \(-0.628669\pi\) | ||||
−0.393307 | + | 0.919407i | \(0.628669\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.2111 | 0.860192 | 0.430096 | − | 0.902783i | \(-0.358480\pi\) | ||||
0.430096 | + | 0.902783i | \(0.358480\pi\) | |||||||
\(860\) | − 8.00000i | − 0.272798i | ||||||||
\(861\) | −14.7889 | −0.504004 | ||||||||
\(862\) | −12.0000 | −0.408722 | ||||||||
\(863\) | 51.6333i | 1.75762i | 0.477173 | + | 0.878809i | \(0.341661\pi\) | ||||
−0.477173 | + | 0.878809i | \(0.658339\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | − 12.4222i | − 0.422368i | ||||||||
\(866\) | 19.2111i | 0.652820i | ||||||||
\(867\) | −4.21110 | −0.143017 | ||||||||
\(868\) | −27.6333 | −0.937936 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.60555 | 0.156143 | ||||||||
\(871\) | − 11.5778i | − 0.392299i | ||||||||
\(872\) | 1.39445 | 0.0472220 | ||||||||
\(873\) | 1.39445i | 0.0471949i | ||||||||
\(874\) | −6.42221 | −0.217234 | ||||||||
\(875\) | −4.60555 | −0.155696 | ||||||||
\(876\) | − 1.39445i | − 0.0471141i | ||||||||
\(877\) | − 24.8444i | − 0.838936i | −0.907770 | − | 0.419468i | \(-0.862217\pi\) | ||||
0.907770 | − | 0.419468i | \(-0.137783\pi\) | |||||||
\(878\) | 8.00000i | 0.269987i | ||||||||
\(879\) | − 18.0000i | − 0.607125i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.2111 | 1.32106 | 0.660528 | − | 0.750802i | \(-0.270333\pi\) | ||||
0.660528 | + | 0.750802i | \(0.270333\pi\) | |||||||
\(882\) | − 14.2111i | − 0.478513i | ||||||||
\(883\) | 9.57779 | 0.322318 | 0.161159 | − | 0.986928i | \(-0.448477\pi\) | ||||
0.161159 | + | 0.986928i | \(0.448477\pi\) | |||||||
\(884\) | −16.6056 | −0.558505 | ||||||||
\(885\) | −9.21110 | −0.309628 | ||||||||
\(886\) | 15.6333i | 0.525211i | ||||||||
\(887\) | 6.97224 | 0.234105 | 0.117053 | − | 0.993126i | \(-0.462655\pi\) | ||||
0.117053 | + | 0.993126i | \(0.462655\pi\) | |||||||
\(888\) | 9.21110 | 0.309104 | ||||||||
\(889\) | − 5.57779i | − 0.187073i | ||||||||
\(890\) | − 15.2111i | − 0.509877i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 1.81665i | − 0.0608261i | ||||||||
\(893\) | −42.4222 | −1.41960 | ||||||||
\(894\) | 15.2111 | 0.508735 | ||||||||
\(895\) | − 19.8167i | − 0.662398i | ||||||||
\(896\) | −4.60555 | −0.153861 | ||||||||
\(897\) | 5.02776 | 0.167872 | ||||||||
\(898\) | −33.6333 | −1.12236 | ||||||||
\(899\) | 27.6333i | 0.921622i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 27.6333 | 0.920599 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.8444i | 1.22611i | ||||||||
\(904\) | 13.8167i | 0.459535i | ||||||||
\(905\) | 8.42221i | 0.279964i | ||||||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | 21.5778 | 0.716479 | 0.358239 | − | 0.933630i | \(-0.383377\pi\) | ||||
0.358239 | + | 0.933630i | \(0.383377\pi\) | |||||||
\(908\) | − 24.0000i | − 0.796468i | ||||||||
\(909\) | −7.39445 | −0.245258 | ||||||||
\(910\) | 16.6056i | 0.550469i | ||||||||
\(911\) | −27.6333 | −0.915532 | −0.457766 | − | 0.889073i | \(-0.651350\pi\) | ||||
−0.457766 | + | 0.889073i | \(0.651350\pi\) | |||||||
\(912\) | 4.60555i | 0.152505i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −38.2389 | −1.26483 | ||||||||
\(915\) | 11.2111i | 0.370628i | ||||||||
\(916\) | 19.8167i | 0.654761i | ||||||||
\(917\) | − 104.111i | − 3.43805i | ||||||||
\(918\) | − 4.60555i | − 0.152006i | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | −1.39445 | −0.0459736 | ||||||||
\(921\) | 8.78890i | 0.289604i | ||||||||
\(922\) | 33.6333 | 1.10765 | ||||||||
\(923\) | 33.2111i | 1.09316i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.21110i | 0.302859i | ||||||||
\(926\) | 31.3944 | 1.03169 | ||||||||
\(927\) | −4.00000 | −0.131377 | ||||||||
\(928\) | 4.60555i | 0.151185i | ||||||||
\(929\) | 39.2111i | 1.28647i | 0.765667 | + | 0.643237i | \(0.222409\pi\) | ||||
−0.765667 | + | 0.643237i | \(0.777591\pi\) | |||||||
\(930\) | 6.00000i | 0.196748i | ||||||||
\(931\) | 65.4500i | 2.14504i | ||||||||
\(932\) | 1.81665 | 0.0595065 | ||||||||
\(933\) | −12.0000 | −0.392862 | ||||||||
\(934\) | − 30.4222i | − 0.995445i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − 3.60555i | − 0.117851i | ||||||||
\(937\) | −10.3667 | −0.338665 | −0.169333 | − | 0.985559i | \(-0.554161\pi\) | ||||
−0.169333 | + | 0.985559i | \(0.554161\pi\) | |||||||
\(938\) | − 14.7889i | − 0.482875i | ||||||||
\(939\) | −3.57779 | −0.116757 | ||||||||
\(940\) | −9.21110 | −0.300433 | ||||||||
\(941\) | − 54.0000i | − 1.76035i | −0.474650 | − | 0.880175i | \(-0.657425\pi\) | ||||
0.474650 | − | 0.880175i | \(-0.342575\pi\) | |||||||
\(942\) | − 20.4222i | − 0.665391i | ||||||||
\(943\) | − 4.47772i | − 0.145815i | ||||||||
\(944\) | − 9.21110i | − 0.299796i | ||||||||
\(945\) | −4.60555 | −0.149819 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 15.6333i | − 0.508014i | −0.967202 | − | 0.254007i | \(-0.918251\pi\) | ||||
0.967202 | − | 0.254007i | \(-0.0817487\pi\) | |||||||
\(948\) | −14.4222 | −0.468411 | ||||||||
\(949\) | − 5.02776i | − 0.163208i | ||||||||
\(950\) | −4.60555 | −0.149424 | ||||||||
\(951\) | 18.0000i | 0.583690i | ||||||||
\(952\) | −21.2111 | −0.687456 | ||||||||
\(953\) | −20.2389 | −0.655601 | −0.327800 | − | 0.944747i | \(-0.606307\pi\) | ||||
−0.327800 | + | 0.944747i | \(0.606307\pi\) | |||||||
\(954\) | 6.00000i | 0.194257i | ||||||||
\(955\) | − 12.0000i | − 0.388311i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.57779 | −0.180210 | ||||||||
\(959\) | 14.7889 | 0.477558 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | 33.2111 | 1.07077 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.42221i | 0.206845i | ||||||||
\(965\) | −7.81665 | −0.251627 | ||||||||
\(966\) | 6.42221 | 0.206631 | ||||||||
\(967\) | − 8.23886i | − 0.264944i | −0.991187 | − | 0.132472i | \(-0.957709\pi\) | ||||
0.991187 | − | 0.132472i | \(-0.0422914\pi\) | |||||||
\(968\) | − 11.0000i | − 0.353553i | ||||||||
\(969\) | 21.2111i | 0.681399i | ||||||||
\(970\) | − 1.39445i | − 0.0447731i | ||||||||
\(971\) | −53.0278 | −1.70174 | −0.850871 | − | 0.525375i | \(-0.823925\pi\) | ||||
−0.850871 | + | 0.525375i | \(0.823925\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − 79.2666i | − 2.54117i | ||||||||
\(974\) | 0.972244 | 0.0311527 | ||||||||
\(975\) | 3.60555 | 0.115470 | ||||||||
\(976\) | −11.2111 | −0.358859 | ||||||||
\(977\) | 18.8444i | 0.602886i | 0.953484 | + | 0.301443i | \(0.0974683\pi\) | ||||
−0.953484 | + | 0.301443i | \(0.902532\pi\) | |||||||
\(978\) | 24.4222 | 0.780936 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.2111i | 0.453957i | ||||||||
\(981\) | 1.39445i | 0.0445213i | ||||||||
\(982\) | 7.81665i | 0.249439i | ||||||||
\(983\) | − 42.4222i | − 1.35306i | −0.736416 | − | 0.676529i | \(-0.763483\pi\) | ||||
0.736416 | − | 0.676529i | \(-0.236517\pi\) | |||||||
\(984\) | −3.21110 | −0.102366 | ||||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | 21.2111i | 0.675499i | ||||||||
\(987\) | 42.4222 | 1.35031 | ||||||||
\(988\) | 16.6056i | 0.528293i | ||||||||
\(989\) | −11.1556 | −0.354727 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.4222 | −0.712265 | −0.356132 | − | 0.934436i | \(-0.615905\pi\) | ||||
−0.356132 | + | 0.934436i | \(0.615905\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | 16.6056i | 0.526961i | ||||||||
\(994\) | 42.4222i | 1.34555i | ||||||||
\(995\) | 22.4222i | 0.710832i | ||||||||
\(996\) | 2.78890i | 0.0883696i | ||||||||
\(997\) | −16.4222 | −0.520096 | −0.260048 | − | 0.965596i | \(-0.583738\pi\) | ||||
−0.260048 | + | 0.965596i | \(0.583738\pi\) | |||||||
\(998\) | −23.0278 | −0.728931 | ||||||||
\(999\) | 9.21110i | 0.291426i |
(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 | 390.2.b.c.181.3 | yes | 4 | |
3.2 | odd | 2 | 1170.2.b.d.181.1 | 4 | |||
4.3 | odd | 2 | 3120.2.g.q.961.4 | 4 | |||
5.2 | odd | 4 | 1950.2.f.m.649.4 | 4 | |||
5.3 | odd | 4 | 1950.2.f.n.649.1 | 4 | |||
5.4 | even | 2 | 1950.2.b.k.1351.2 | 4 | |||
13.5 | odd | 4 | 5070.2.a.bf.1.2 | 2 | |||
13.8 | odd | 4 | 5070.2.a.z.1.1 | 2 | |||
13.12 | even | 2 | inner | 390.2.b.c.181.2 | ✓ | 4 | |
39.38 | odd | 2 | 1170.2.b.d.181.4 | 4 | |||
52.51 | odd | 2 | 3120.2.g.q.961.1 | 4 | |||
65.12 | odd | 4 | 1950.2.f.n.649.3 | 4 | |||
65.38 | odd | 4 | 1950.2.f.m.649.2 | 4 | |||
65.64 | even | 2 | 1950.2.b.k.1351.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.c.181.2 | ✓ | 4 | 13.12 | even | 2 | inner | |
390.2.b.c.181.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1170.2.b.d.181.1 | 4 | 3.2 | odd | 2 | |||
1170.2.b.d.181.4 | 4 | 39.38 | odd | 2 | |||
1950.2.b.k.1351.2 | 4 | 5.4 | even | 2 | |||
1950.2.b.k.1351.3 | 4 | 65.64 | even | 2 | |||
1950.2.f.m.649.2 | 4 | 65.38 | odd | 4 | |||
1950.2.f.m.649.4 | 4 | 5.2 | odd | 4 | |||
1950.2.f.n.649.1 | 4 | 5.3 | odd | 4 | |||
1950.2.f.n.649.3 | 4 | 65.12 | odd | 4 | |||
3120.2.g.q.961.1 | 4 | 52.51 | odd | 2 | |||
3120.2.g.q.961.4 | 4 | 4.3 | odd | 2 | |||
5070.2.a.z.1.1 | 2 | 13.8 | odd | 4 | |||
5070.2.a.bf.1.2 | 2 | 13.5 | odd | 4 |