Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(649,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
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: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.649 |
Dual form | 1950.2.f.n.649.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | −4.60555 | −1.74073 | −0.870367 | − | 0.492403i | \(-0.836119\pi\) | ||||
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | 3.60555i | 1.00000i | ||||||||
\(14\) | −4.60555 | −1.23089 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 4.60555i | − 1.11701i | −0.829501 | − | 0.558505i | \(-0.811375\pi\) | ||||
0.829501 | − | 0.558505i | \(-0.188625\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.60555i | 1.05659i | 0.849062 | + | 0.528293i | \(0.177168\pi\) | ||||
−0.849062 | + | 0.528293i | \(0.822832\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.60555i | 1.00501i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.39445i | − 0.290763i | −0.989376 | − | 0.145381i | \(-0.953559\pi\) | ||||
0.989376 | − | 0.145381i | \(-0.0464409\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.60555i | 0.707107i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −4.60555 | −0.870367 | ||||||||
\(29\) | −4.60555 | −0.855229 | −0.427615 | − | 0.903961i | \(-0.640646\pi\) | ||||
−0.427615 | + | 0.903961i | \(0.640646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000i | 1.07763i | 0.842424 | + | 0.538816i | \(0.181128\pi\) | ||||
−0.842424 | + | 0.538816i | \(0.818872\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 4.60555i | − 0.789846i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −9.21110 | −1.51430 | −0.757148 | − | 0.653243i | \(-0.773408\pi\) | ||||
−0.757148 | + | 0.653243i | \(0.773408\pi\) | |||||||
\(38\) | 4.60555i | 0.747119i | ||||||||
\(39\) | 3.60555 | 0.577350 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.21110i | 0.501490i | 0.968053 | + | 0.250745i | \(0.0806756\pi\) | ||||
−0.968053 | + | 0.250745i | \(0.919324\pi\) | |||||||
\(42\) | 4.60555i | 0.710652i | ||||||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 1.39445i | − 0.205600i | ||||||||
\(47\) | −9.21110 | −1.34358 | −0.671789 | − | 0.740743i | \(-0.734474\pi\) | ||||
−0.671789 | + | 0.740743i | \(0.734474\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | 14.2111 | 2.03016 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60555 | −0.644906 | ||||||||
\(52\) | 3.60555i | 0.500000i | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.60555 | −0.615443 | ||||||||
\(57\) | 4.60555 | 0.610020 | ||||||||
\(58\) | −4.60555 | −0.604739 | ||||||||
\(59\) | 9.21110i | 1.19918i | 0.800306 | + | 0.599592i | \(0.204670\pi\) | ||||
−0.800306 | + | 0.599592i | \(0.795330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2111 | −1.43543 | −0.717717 | − | 0.696335i | \(-0.754813\pi\) | ||||
−0.717717 | + | 0.696335i | \(0.754813\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 4.60555 | 0.580245 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.21110 | −0.392299 | −0.196149 | − | 0.980574i | \(-0.562844\pi\) | ||||
−0.196149 | + | 0.980574i | \(0.562844\pi\) | |||||||
\(68\) | − 4.60555i | − 0.558505i | ||||||||
\(69\) | −1.39445 | −0.167872 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.21110i | 1.09316i | 0.837408 | + | 0.546578i | \(0.184070\pi\) | ||||
−0.837408 | + | 0.546578i | \(0.815930\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 1.39445 | 0.163208 | 0.0816039 | − | 0.996665i | \(-0.473996\pi\) | ||||
0.0816039 | + | 0.996665i | \(0.473996\pi\) | |||||||
\(74\) | −9.21110 | −1.07077 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.60555i | 0.528293i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.60555 | 0.408248 | ||||||||
\(79\) | 14.4222 | 1.62262 | 0.811312 | − | 0.584613i | \(-0.198754\pi\) | ||||
0.811312 | + | 0.584613i | \(0.198754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.21110i | 0.354607i | ||||||||
\(83\) | −2.78890 | −0.306121 | −0.153061 | − | 0.988217i | \(-0.548913\pi\) | ||||
−0.153061 | + | 0.988217i | \(0.548913\pi\) | |||||||
\(84\) | 4.60555i | 0.502507i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000i | 0.862662i | ||||||||
\(87\) | 4.60555i | 0.493767i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 15.2111i | − 1.61237i | −0.591661 | − | 0.806187i | \(-0.701528\pi\) | ||||
0.591661 | − | 0.806187i | \(-0.298472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 16.6056i | − 1.74073i | ||||||||
\(92\) | − 1.39445i | − 0.145381i | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | −9.21110 | −0.950053 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | 1.39445 | 0.141585 | 0.0707924 | − | 0.997491i | \(-0.477447\pi\) | ||||
0.0707924 | + | 0.997491i | \(0.477447\pi\) | |||||||
\(98\) | 14.2111 | 1.43554 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.39445 | −0.735775 | −0.367888 | − | 0.929870i | \(-0.619919\pi\) | ||||
−0.367888 | + | 0.929870i | \(0.619919\pi\) | |||||||
\(102\) | −4.60555 | −0.456018 | ||||||||
\(103\) | − 4.00000i | − 0.394132i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) | ||||
0.980390 | − | 0.197066i | \(-0.0631413\pi\) | |||||||
\(104\) | 3.60555i | 0.353553i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000i | 0.582772i | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | − 1.39445i | − 0.133564i | −0.997768 | − | 0.0667820i | \(-0.978727\pi\) | ||||
0.997768 | − | 0.0667820i | \(-0.0212732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.21110i | 0.874279i | ||||||||
\(112\) | −4.60555 | −0.435184 | ||||||||
\(113\) | − 13.8167i | − 1.29976i | −0.760036 | − | 0.649881i | \(-0.774819\pi\) | ||||
0.760036 | − | 0.649881i | \(-0.225181\pi\) | |||||||
\(114\) | 4.60555 | 0.431349 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.60555 | −0.427615 | ||||||||
\(117\) | − 3.60555i | − 0.333333i | ||||||||
\(118\) | 9.21110i | 0.847951i | ||||||||
\(119\) | 21.2111i | 1.94442i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | −11.2111 | −1.01501 | ||||||||
\(123\) | 3.21110 | 0.289535 | ||||||||
\(124\) | 6.00000i | 0.538816i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.60555 | 0.410295 | ||||||||
\(127\) | − 1.21110i | − 0.107468i | −0.998555 | − | 0.0537340i | \(-0.982888\pi\) | ||||
0.998555 | − | 0.0537340i | \(-0.0171123\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.6056 | 1.97506 | 0.987528 | − | 0.157443i | \(-0.0503250\pi\) | ||||
0.987528 | + | 0.157443i | \(0.0503250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 21.2111i | − 1.83924i | ||||||||
\(134\) | −3.21110 | −0.277397 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 4.60555i | − 0.394923i | ||||||||
\(137\) | 3.21110 | 0.274343 | 0.137172 | − | 0.990547i | \(-0.456199\pi\) | ||||
0.137172 | + | 0.990547i | \(0.456199\pi\) | |||||||
\(138\) | −1.39445 | −0.118703 | ||||||||
\(139\) | −17.2111 | −1.45983 | −0.729913 | − | 0.683540i | \(-0.760440\pi\) | ||||
−0.729913 | + | 0.683540i | \(0.760440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.21110i | 0.775715i | ||||||||
\(142\) | 9.21110i | 0.772979i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.39445 | 0.115405 | ||||||||
\(147\) | − 14.2111i | − 1.17211i | ||||||||
\(148\) | −9.21110 | −0.757148 | ||||||||
\(149\) | − 15.2111i | − 1.24614i | −0.782165 | − | 0.623071i | \(-0.785885\pi\) | ||||
0.782165 | − | 0.623071i | \(-0.214115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.00000i | 0.488273i | 0.969741 | + | 0.244137i | \(0.0785045\pi\) | ||||
−0.969741 | + | 0.244137i | \(0.921495\pi\) | |||||||
\(152\) | 4.60555i | 0.373560i | ||||||||
\(153\) | 4.60555i | 0.372337i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.60555 | 0.288675 | ||||||||
\(157\) | − 20.4222i | − 1.62987i | −0.579553 | − | 0.814935i | \(-0.696773\pi\) | ||||
0.579553 | − | 0.814935i | \(-0.303227\pi\) | |||||||
\(158\) | 14.4222 | 1.14737 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.42221i | 0.506141i | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −24.4222 | −1.91289 | −0.956447 | − | 0.291905i | \(-0.905711\pi\) | ||||
−0.956447 | + | 0.291905i | \(0.905711\pi\) | |||||||
\(164\) | 3.21110i | 0.250745i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.78890 | −0.216460 | ||||||||
\(167\) | 9.21110 | 0.712777 | 0.356388 | − | 0.934338i | \(-0.384008\pi\) | ||||
0.356388 | + | 0.934338i | \(0.384008\pi\) | |||||||
\(168\) | 4.60555i | 0.355326i | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 4.60555i | − 0.352195i | ||||||||
\(172\) | 8.00000i | 0.609994i | ||||||||
\(173\) | − 12.4222i | − 0.944443i | −0.881480 | − | 0.472221i | \(-0.843452\pi\) | ||||
0.881480 | − | 0.472221i | \(-0.156548\pi\) | |||||||
\(174\) | 4.60555i | 0.349146i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.21110 | 0.692349 | ||||||||
\(178\) | − 15.2111i | − 1.14012i | ||||||||
\(179\) | 19.8167 | 1.48117 | 0.740583 | − | 0.671965i | \(-0.234549\pi\) | ||||
0.740583 | + | 0.671965i | \(0.234549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.42221 | 0.626018 | 0.313009 | − | 0.949750i | \(-0.398663\pi\) | ||||
0.313009 | + | 0.949750i | \(0.398663\pi\) | |||||||
\(182\) | − 16.6056i | − 1.23089i | ||||||||
\(183\) | 11.2111i | 0.828749i | ||||||||
\(184\) | − 1.39445i | − 0.102800i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.21110 | −0.671789 | ||||||||
\(189\) | − 4.60555i | − 0.335005i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | −7.81665 | −0.562655 | −0.281328 | − | 0.959612i | \(-0.590775\pi\) | ||||
−0.281328 | + | 0.959612i | \(0.590775\pi\) | |||||||
\(194\) | 1.39445 | 0.100116 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.2111 | 1.01508 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.4222 | −1.58947 | −0.794734 | − | 0.606958i | \(-0.792390\pi\) | ||||
−0.794734 | + | 0.606958i | \(0.792390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.21110i | 0.226494i | ||||||||
\(202\) | −7.39445 | −0.520272 | ||||||||
\(203\) | 21.2111 | 1.48873 | ||||||||
\(204\) | −4.60555 | −0.322453 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − 4.00000i | − 0.278693i | ||||||||
\(207\) | 1.39445i | 0.0969209i | ||||||||
\(208\) | 3.60555i | 0.250000i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2111 | −1.18486 | −0.592431 | − | 0.805622i | \(-0.701832\pi\) | ||||
−0.592431 | + | 0.805622i | \(0.701832\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 9.21110 | 0.631134 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | − 27.6333i | − 1.87587i | ||||||||
\(218\) | − 1.39445i | − 0.0944440i | ||||||||
\(219\) | − 1.39445i | − 0.0942281i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.6056 | 1.11701 | ||||||||
\(222\) | 9.21110i | 0.618209i | ||||||||
\(223\) | −1.81665 | −0.121652 | −0.0608261 | − | 0.998148i | \(-0.519373\pi\) | ||||
−0.0608261 | + | 0.998148i | \(0.519373\pi\) | |||||||
\(224\) | −4.60555 | −0.307721 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 13.8167i | − 0.919070i | ||||||||
\(227\) | 24.0000 | 1.59294 | 0.796468 | − | 0.604681i | \(-0.206699\pi\) | ||||
0.796468 | + | 0.604681i | \(0.206699\pi\) | |||||||
\(228\) | 4.60555 | 0.305010 | ||||||||
\(229\) | 19.8167i | 1.30952i | 0.755836 | + | 0.654761i | \(0.227231\pi\) | ||||
−0.755836 | + | 0.654761i | \(0.772769\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.60555 | −0.302369 | ||||||||
\(233\) | − 1.81665i | − 0.119013i | −0.998228 | − | 0.0595065i | \(-0.981047\pi\) | ||||
0.998228 | − | 0.0595065i | \(-0.0189527\pi\) | |||||||
\(234\) | − 3.60555i | − 0.235702i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.21110i | 0.599592i | ||||||||
\(237\) | − 14.4222i | − 0.936823i | ||||||||
\(238\) | 21.2111i | 1.37491i | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 6.42221i | − 0.413691i | −0.978374 | − | 0.206845i | \(-0.933680\pi\) | ||||
0.978374 | − | 0.206845i | \(-0.0663197\pi\) | |||||||
\(242\) | 11.0000 | 0.707107 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −11.2111 | −0.717717 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.21110 | 0.204732 | ||||||||
\(247\) | −16.6056 | −1.05659 | ||||||||
\(248\) | 6.00000i | 0.381000i | ||||||||
\(249\) | 2.78890i | 0.176739i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3944 | −0.845450 | −0.422725 | − | 0.906258i | \(-0.638926\pi\) | ||||
−0.422725 | + | 0.906258i | \(0.638926\pi\) | |||||||
\(252\) | 4.60555 | 0.290122 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 1.21110i | − 0.0759913i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.6056i | 1.78437i | 0.451675 | + | 0.892183i | \(0.350827\pi\) | ||||
−0.451675 | + | 0.892183i | \(0.649173\pi\) | |||||||
\(258\) | 8.00000 | 0.498058 | ||||||||
\(259\) | 42.4222 | 2.63599 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.60555 | 0.285076 | ||||||||
\(262\) | 22.6056 | 1.39658 | ||||||||
\(263\) | − 7.81665i | − 0.481996i | −0.970526 | − | 0.240998i | \(-0.922525\pi\) | ||||
0.970526 | − | 0.240998i | \(-0.0774746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 21.2111i | − 1.30054i | ||||||||
\(267\) | −15.2111 | −0.930904 | ||||||||
\(268\) | −3.21110 | −0.196149 | ||||||||
\(269\) | −25.8167 | −1.57407 | −0.787035 | − | 0.616909i | \(-0.788385\pi\) | ||||
−0.787035 | + | 0.616909i | \(0.788385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 0.422205i | − 0.0256471i | −0.999918 | − | 0.0128236i | \(-0.995918\pi\) | ||||
0.999918 | − | 0.0128236i | \(-0.00408198\pi\) | |||||||
\(272\) | − 4.60555i | − 0.279253i | ||||||||
\(273\) | −16.6056 | −1.00501 | ||||||||
\(274\) | 3.21110 | 0.193990 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.39445 | −0.0839359 | ||||||||
\(277\) | 16.4222i | 0.986715i | 0.869827 | + | 0.493357i | \(0.164230\pi\) | ||||
−0.869827 | + | 0.493357i | \(0.835770\pi\) | |||||||
\(278\) | −17.2111 | −1.03225 | ||||||||
\(279\) | − 6.00000i | − 0.359211i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2111i | 1.62328i | 0.584159 | + | 0.811639i | \(0.301424\pi\) | ||||
−0.584159 | + | 0.811639i | \(0.698576\pi\) | |||||||
\(282\) | 9.21110i | 0.548513i | ||||||||
\(283\) | 10.4222i | 0.619536i | 0.950812 | + | 0.309768i | \(0.100251\pi\) | ||||
−0.950812 | + | 0.309768i | \(0.899749\pi\) | |||||||
\(284\) | 9.21110i | 0.546578i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 14.7889i | − 0.872961i | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −4.21110 | −0.247712 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.39445i | − 0.0817440i | ||||||||
\(292\) | 1.39445 | 0.0816039 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | − 14.2111i | − 0.828808i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.21110 | −0.535384 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 15.2111i | − 0.881156i | ||||||||
\(299\) | 5.02776 | 0.290763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 36.8444i | − 2.12368i | ||||||||
\(302\) | 6.00000i | 0.345261i | ||||||||
\(303\) | 7.39445i | 0.424800i | ||||||||
\(304\) | 4.60555i | 0.264146i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.60555i | 0.263282i | ||||||||
\(307\) | −8.78890 | −0.501609 | −0.250804 | − | 0.968038i | \(-0.580695\pi\) | ||||
−0.250804 | + | 0.968038i | \(0.580695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 3.60555 | 0.204124 | ||||||||
\(313\) | 3.57779i | 0.202229i | 0.994875 | + | 0.101114i | \(0.0322408\pi\) | ||||
−0.994875 | + | 0.101114i | \(0.967759\pi\) | |||||||
\(314\) | − 20.4222i | − 1.15249i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.4222 | 0.811312 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 6.00000 | 0.336463 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.42221i | 0.357895i | ||||||||
\(323\) | 21.2111 | 1.18022 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −24.4222 | −1.35262 | ||||||||
\(327\) | −1.39445 | −0.0771132 | ||||||||
\(328\) | 3.21110i | 0.177303i | ||||||||
\(329\) | 42.4222 | 2.33881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 16.6056i | − 0.912724i | −0.889794 | − | 0.456362i | \(-0.849152\pi\) | ||||
0.889794 | − | 0.456362i | \(-0.150848\pi\) | |||||||
\(332\) | −2.78890 | −0.153061 | ||||||||
\(333\) | 9.21110 | 0.504765 | ||||||||
\(334\) | 9.21110 | 0.504009 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.60555i | 0.251253i | ||||||||
\(337\) | − 13.6333i | − 0.742654i | −0.928502 | − | 0.371327i | \(-0.878903\pi\) | ||||
0.928502 | − | 0.371327i | \(-0.121097\pi\) | |||||||
\(338\) | −13.0000 | −0.707107 | ||||||||
\(339\) | −13.8167 | −0.750418 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − 4.60555i | − 0.249040i | ||||||||
\(343\) | −33.2111 | −1.79323 | ||||||||
\(344\) | 8.00000i | 0.431331i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 12.4222i | − 0.667822i | ||||||||
\(347\) | 27.6333i | 1.48343i | 0.670713 | + | 0.741717i | \(0.265988\pi\) | ||||
−0.670713 | + | 0.741717i | \(0.734012\pi\) | |||||||
\(348\) | 4.60555i | 0.246883i | ||||||||
\(349\) | 7.81665i | 0.418416i | 0.977871 | + | 0.209208i | \(0.0670886\pi\) | ||||
−0.977871 | + | 0.209208i | \(0.932911\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.60555 | −0.192450 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.78890 | 0.467786 | 0.233893 | − | 0.972262i | \(-0.424853\pi\) | ||||
0.233893 | + | 0.972262i | \(0.424853\pi\) | |||||||
\(354\) | 9.21110 | 0.489565 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − 15.2111i | − 0.806187i | ||||||||
\(357\) | 21.2111 | 1.12261 | ||||||||
\(358\) | 19.8167 | 1.04734 | ||||||||
\(359\) | − 15.6333i | − 0.825094i | −0.910936 | − | 0.412547i | \(-0.864639\pi\) | ||||
0.910936 | − | 0.412547i | \(-0.135361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.21110 | −0.116374 | ||||||||
\(362\) | 8.42221 | 0.442661 | ||||||||
\(363\) | − 11.0000i | − 0.577350i | ||||||||
\(364\) | − 16.6056i | − 0.870367i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.2111i | 0.586014i | ||||||||
\(367\) | 19.6333i | 1.02485i | 0.858732 | + | 0.512425i | \(0.171253\pi\) | ||||
−0.858732 | + | 0.512425i | \(0.828747\pi\) | |||||||
\(368\) | − 1.39445i | − 0.0726907i | ||||||||
\(369\) | − 3.21110i | − 0.167163i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 27.6333i | − 1.43465i | ||||||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | − 20.4222i | − 1.05742i | −0.848802 | − | 0.528711i | \(-0.822676\pi\) | ||||
0.848802 | − | 0.528711i | \(-0.177324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.21110 | −0.475026 | ||||||||
\(377\) | − 16.6056i | − 0.855229i | ||||||||
\(378\) | − 4.60555i | − 0.236884i | ||||||||
\(379\) | − 35.0278i | − 1.79925i | −0.436658 | − | 0.899627i | \(-0.643838\pi\) | ||||
0.436658 | − | 0.899627i | \(-0.356162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.21110 | −0.0620467 | ||||||||
\(382\) | −12.0000 | −0.613973 | ||||||||
\(383\) | 27.6333 | 1.41200 | 0.705998 | − | 0.708214i | \(-0.250499\pi\) | ||||
0.705998 | + | 0.708214i | \(0.250499\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.81665 | −0.397857 | ||||||||
\(387\) | − 8.00000i | − 0.406663i | ||||||||
\(388\) | 1.39445 | 0.0707924 | ||||||||
\(389\) | −4.60555 | −0.233511 | −0.116755 | − | 0.993161i | \(-0.537249\pi\) | ||||
−0.116755 | + | 0.993161i | \(0.537249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.42221 | −0.324785 | ||||||||
\(392\) | 14.2111 | 0.717769 | ||||||||
\(393\) | − 22.6056i | − 1.14030i | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.63331 | −0.182350 | −0.0911752 | − | 0.995835i | \(-0.529062\pi\) | ||||
−0.0911752 | + | 0.995835i | \(0.529062\pi\) | |||||||
\(398\) | −22.4222 | −1.12392 | ||||||||
\(399\) | −21.2111 | −1.06188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.78890i | 0.438897i | 0.975624 | + | 0.219448i | \(0.0704257\pi\) | ||||
−0.975624 | + | 0.219448i | \(0.929574\pi\) | |||||||
\(402\) | 3.21110i | 0.160155i | ||||||||
\(403\) | −21.6333 | −1.07763 | ||||||||
\(404\) | −7.39445 | −0.367888 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.2111 | 1.05269 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.60555 | −0.228009 | ||||||||
\(409\) | 14.7889i | 0.731264i | 0.930760 | + | 0.365632i | \(0.119147\pi\) | ||||
−0.930760 | + | 0.365632i | \(0.880853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 3.21110i | − 0.158392i | ||||||||
\(412\) | − 4.00000i | − 0.197066i | ||||||||
\(413\) | − 42.4222i | − 2.08746i | ||||||||
\(414\) | 1.39445i | 0.0685334i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.60555i | 0.176777i | ||||||||
\(417\) | 17.2111i | 0.842831i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.18335 | −0.204370 | −0.102185 | − | 0.994765i | \(-0.532583\pi\) | ||||
−0.102185 | + | 0.994765i | \(0.532583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 19.8167i | − 0.965805i | −0.875674 | − | 0.482902i | \(-0.839583\pi\) | ||||
0.875674 | − | 0.482902i | \(-0.160417\pi\) | |||||||
\(422\) | −17.2111 | −0.837823 | ||||||||
\(423\) | 9.21110 | 0.447859 | ||||||||
\(424\) | 6.00000i | 0.291386i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.21110 | 0.446279 | ||||||||
\(427\) | 51.6333 | 2.49871 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000i | 0.578020i | 0.957326 | + | 0.289010i | \(0.0933260\pi\) | ||||
−0.957326 | + | 0.289010i | \(0.906674\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 19.2111i | 0.923227i | 0.887081 | + | 0.461613i | \(0.152729\pi\) | ||||
−0.887081 | + | 0.461613i | \(0.847271\pi\) | |||||||
\(434\) | − 27.6333i | − 1.32644i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 1.39445i | − 0.0667820i | ||||||||
\(437\) | 6.42221 | 0.307216 | ||||||||
\(438\) | − 1.39445i | − 0.0666293i | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.2111 | −0.676719 | ||||||||
\(442\) | 16.6056 | 0.789846 | ||||||||
\(443\) | 15.6333i | 0.742761i | 0.928481 | + | 0.371380i | \(0.121115\pi\) | ||||
−0.928481 | + | 0.371380i | \(0.878885\pi\) | |||||||
\(444\) | 9.21110i | 0.437140i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.81665 | −0.0860211 | ||||||||
\(447\) | −15.2111 | −0.719460 | ||||||||
\(448\) | −4.60555 | −0.217592 | ||||||||
\(449\) | − 33.6333i | − 1.58725i | −0.608405 | − | 0.793627i | \(-0.708190\pi\) | ||||
0.608405 | − | 0.793627i | \(-0.291810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 13.8167i | − 0.649881i | ||||||||
\(453\) | 6.00000 | 0.281905 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.60555 | 0.215675 | ||||||||
\(457\) | 38.2389 | 1.78874 | 0.894369 | − | 0.447330i | \(-0.147625\pi\) | ||||
0.894369 | + | 0.447330i | \(0.147625\pi\) | |||||||
\(458\) | 19.8167i | 0.925971i | ||||||||
\(459\) | 4.60555 | 0.214969 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 33.6333i | − 1.56646i | −0.621733 | − | 0.783230i | \(-0.713571\pi\) | ||||
0.621733 | − | 0.783230i | \(-0.286429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.3944 | 1.45902 | 0.729512 | − | 0.683968i | \(-0.239747\pi\) | ||||
0.729512 | + | 0.683968i | \(0.239747\pi\) | |||||||
\(464\) | −4.60555 | −0.213807 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − 1.81665i | − 0.0841549i | ||||||||
\(467\) | 30.4222i | 1.40777i | 0.710313 | + | 0.703886i | \(0.248553\pi\) | ||||
−0.710313 | + | 0.703886i | \(0.751447\pi\) | |||||||
\(468\) | − 3.60555i | − 0.166667i | ||||||||
\(469\) | 14.7889 | 0.682888 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.4222 | −0.941006 | ||||||||
\(472\) | 9.21110i | 0.423975i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | − 14.4222i | − 0.662434i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.2111i | 0.972209i | ||||||||
\(477\) | − 6.00000i | − 0.274721i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 5.57779i | − 0.254856i | −0.991848 | − | 0.127428i | \(-0.959328\pi\) | ||||
0.991848 | − | 0.127428i | \(-0.0406722\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 33.2111i | − 1.51430i | ||||||||
\(482\) | − 6.42221i | − 0.292523i | ||||||||
\(483\) | 6.42221 | 0.292220 | ||||||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | −0.972244 | −0.0440566 | −0.0220283 | − | 0.999757i | \(-0.507012\pi\) | ||||
−0.0220283 | + | 0.999757i | \(0.507012\pi\) | |||||||
\(488\) | −11.2111 | −0.507503 | ||||||||
\(489\) | 24.4222i | 1.10441i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.81665 | 0.352761 | 0.176380 | − | 0.984322i | \(-0.443561\pi\) | ||||
0.176380 | + | 0.984322i | \(0.443561\pi\) | |||||||
\(492\) | 3.21110 | 0.144768 | ||||||||
\(493\) | 21.2111i | 0.955300i | ||||||||
\(494\) | −16.6056 | −0.747119 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000i | 0.269408i | ||||||||
\(497\) | − 42.4222i | − 1.90290i | ||||||||
\(498\) | 2.78890i | 0.124973i | ||||||||
\(499\) | − 23.0278i | − 1.03086i | −0.856930 | − | 0.515432i | \(-0.827631\pi\) | ||||
0.856930 | − | 0.515432i | \(-0.172369\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 9.21110i | − 0.411522i | ||||||||
\(502\) | −13.3944 | −0.597824 | ||||||||
\(503\) | 23.4500i | 1.04558i | 0.852461 | + | 0.522791i | \(0.175109\pi\) | ||||
−0.852461 | + | 0.522791i | \(0.824891\pi\) | |||||||
\(504\) | 4.60555 | 0.205148 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.0000i | 0.577350i | ||||||||
\(508\) | − 1.21110i | − 0.0537340i | ||||||||
\(509\) | 33.6333i | 1.49077i | 0.666634 | + | 0.745385i | \(0.267734\pi\) | ||||
−0.666634 | + | 0.745385i | \(0.732266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.42221 | −0.284102 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.60555 | −0.203340 | ||||||||
\(514\) | 28.6056i | 1.26174i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 42.4222 | 1.86392 | ||||||||
\(519\) | −12.4222 | −0.545274 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.6333 | 0.947772 | 0.473886 | − | 0.880586i | \(-0.342851\pi\) | ||||
0.473886 | + | 0.880586i | \(0.342851\pi\) | |||||||
\(522\) | 4.60555 | 0.201580 | ||||||||
\(523\) | 32.8444i | 1.43619i | 0.695947 | + | 0.718093i | \(0.254985\pi\) | ||||
−0.695947 | + | 0.718093i | \(0.745015\pi\) | |||||||
\(524\) | 22.6056 | 0.987528 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − 7.81665i | − 0.340822i | ||||||||
\(527\) | 27.6333 | 1.20373 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.0555 | 0.915457 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 9.21110i | − 0.399728i | ||||||||
\(532\) | − 21.2111i | − 0.919618i | ||||||||
\(533\) | −11.5778 | −0.501490 | ||||||||
\(534\) | −15.2111 | −0.658249 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.21110 | −0.138699 | ||||||||
\(537\) | − 19.8167i | − 0.855152i | ||||||||
\(538\) | −25.8167 | −1.11303 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.97224i | 0.299760i | 0.988704 | + | 0.149880i | \(0.0478888\pi\) | ||||
−0.988704 | + | 0.149880i | \(0.952111\pi\) | |||||||
\(542\) | − 0.422205i | − 0.0181353i | ||||||||
\(543\) | − 8.42221i | − 0.361431i | ||||||||
\(544\) | − 4.60555i | − 0.197461i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.6056 | −0.710652 | ||||||||
\(547\) | − 14.4222i | − 0.616649i | −0.951281 | − | 0.308324i | \(-0.900232\pi\) | ||||
0.951281 | − | 0.308324i | \(-0.0997682\pi\) | |||||||
\(548\) | 3.21110 | 0.137172 | ||||||||
\(549\) | 11.2111 | 0.478478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 21.2111i | − 0.903623i | ||||||||
\(552\) | −1.39445 | −0.0593517 | ||||||||
\(553\) | −66.4222 | −2.82456 | ||||||||
\(554\) | 16.4222i | 0.697713i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2111 | −0.729913 | ||||||||
\(557\) | 11.5778 | 0.490567 | 0.245283 | − | 0.969451i | \(-0.421119\pi\) | ||||
0.245283 | + | 0.969451i | \(0.421119\pi\) | |||||||
\(558\) | − 6.00000i | − 0.254000i | ||||||||
\(559\) | −28.8444 | −1.21999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.2111i | 1.14783i | ||||||||
\(563\) | 34.0555i | 1.43527i | 0.696420 | + | 0.717634i | \(0.254775\pi\) | ||||
−0.696420 | + | 0.717634i | \(0.745225\pi\) | |||||||
\(564\) | 9.21110i | 0.387857i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.4222i | 0.438078i | ||||||||
\(567\) | −4.60555 | −0.193415 | ||||||||
\(568\) | 9.21110i | 0.386489i | ||||||||
\(569\) | −33.6333 | −1.40998 | −0.704991 | − | 0.709216i | \(-0.749049\pi\) | ||||
−0.704991 | + | 0.709216i | \(0.749049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.0555 | −1.25778 | −0.628892 | − | 0.777493i | \(-0.716491\pi\) | ||||
−0.628892 | + | 0.777493i | \(0.716491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000i | 0.501307i | ||||||||
\(574\) | − 14.7889i | − 0.617277i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −37.3944 | −1.55675 | −0.778376 | − | 0.627799i | \(-0.783956\pi\) | ||||
−0.778376 | + | 0.627799i | \(0.783956\pi\) | |||||||
\(578\) | −4.21110 | −0.175159 | ||||||||
\(579\) | 7.81665i | 0.324849i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8444 | 0.532876 | ||||||||
\(582\) | − 1.39445i | − 0.0578018i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.39445 | 0.0577027 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | −6.42221 | −0.265073 | −0.132536 | − | 0.991178i | \(-0.542312\pi\) | ||||
−0.132536 | + | 0.991178i | \(0.542312\pi\) | |||||||
\(588\) | − 14.2111i | − 0.586056i | ||||||||
\(589\) | −27.6333 | −1.13861 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000i | 0.246807i | ||||||||
\(592\) | −9.21110 | −0.378574 | ||||||||
\(593\) | 24.4222 | 1.00290 | 0.501450 | − | 0.865187i | \(-0.332800\pi\) | ||||
0.501450 | + | 0.865187i | \(0.332800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 15.2111i | − 0.623071i | ||||||||
\(597\) | 22.4222i | 0.917680i | ||||||||
\(598\) | 5.02776 | 0.205600 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.63331 | 0.0666240 | 0.0333120 | − | 0.999445i | \(-0.489394\pi\) | ||||
0.0333120 | + | 0.999445i | \(0.489394\pi\) | |||||||
\(602\) | − 36.8444i | − 1.50167i | ||||||||
\(603\) | 3.21110 | 0.130766 | ||||||||
\(604\) | 6.00000i | 0.244137i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.39445i | 0.300379i | ||||||||
\(607\) | − 17.2111i | − 0.698577i | −0.937015 | − | 0.349289i | \(-0.886423\pi\) | ||||
0.937015 | − | 0.349289i | \(-0.113577\pi\) | |||||||
\(608\) | 4.60555i | 0.186780i | ||||||||
\(609\) | − 21.2111i | − 0.859517i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 33.2111i | − 1.34358i | ||||||||
\(612\) | 4.60555i | 0.186168i | ||||||||
\(613\) | 33.2111 | 1.34138 | 0.670692 | − | 0.741736i | \(-0.265997\pi\) | ||||
0.670692 | + | 0.741736i | \(0.265997\pi\) | |||||||
\(614\) | −8.78890 | −0.354691 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4222 | 0.500099 | 0.250050 | − | 0.968233i | \(-0.419553\pi\) | ||||
0.250050 | + | 0.968233i | \(0.419553\pi\) | |||||||
\(618\) | −4.00000 | −0.160904 | ||||||||
\(619\) | − 25.8167i | − 1.03766i | −0.854878 | − | 0.518829i | \(-0.826368\pi\) | ||||
0.854878 | − | 0.518829i | \(-0.173632\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.39445 | 0.0559573 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 70.0555i | 2.80671i | ||||||||
\(624\) | 3.60555 | 0.144338 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.57779i | 0.142997i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 20.4222i | − 0.814935i | ||||||||
\(629\) | 42.4222i | 1.69148i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.21110i | 0.127832i | 0.997955 | + | 0.0639160i | \(0.0203590\pi\) | ||||
−0.997955 | + | 0.0639160i | \(0.979641\pi\) | |||||||
\(632\) | 14.4222 | 0.573685 | ||||||||
\(633\) | 17.2111i | 0.684080i | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 51.2389i | 2.03016i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 9.21110i | − 0.364386i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.422205 | 0.0166761 | 0.00833805 | − | 0.999965i | \(-0.497346\pi\) | ||||
0.00833805 | + | 0.999965i | \(0.497346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.63331 | −0.379901 | −0.189950 | − | 0.981794i | \(-0.560833\pi\) | ||||
−0.189950 | + | 0.981794i | \(0.560833\pi\) | |||||||
\(644\) | 6.42221i | 0.253070i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.2111 | 0.834540 | ||||||||
\(647\) | 34.6056i | 1.36048i | 0.732987 | + | 0.680242i | \(0.238125\pi\) | ||||
−0.732987 | + | 0.680242i | \(0.761875\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.6333 | −1.08303 | ||||||||
\(652\) | −24.4222 | −0.956447 | ||||||||
\(653\) | 39.2111i | 1.53445i | 0.641379 | + | 0.767225i | \(0.278363\pi\) | ||||
−0.641379 | + | 0.767225i | \(0.721637\pi\) | |||||||
\(654\) | −1.39445 | −0.0545273 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.21110i | 0.125372i | ||||||||
\(657\) | −1.39445 | −0.0544026 | ||||||||
\(658\) | 42.4222 | 1.65379 | ||||||||
\(659\) | 26.2389 | 1.02212 | 0.511060 | − | 0.859545i | \(-0.329253\pi\) | ||||
0.511060 | + | 0.859545i | \(0.329253\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.2389i | 1.95407i | 0.213090 | + | 0.977033i | \(0.431647\pi\) | ||||
−0.213090 | + | 0.977033i | \(0.568353\pi\) | |||||||
\(662\) | − 16.6056i | − 0.645393i | ||||||||
\(663\) | − 16.6056i | − 0.644906i | ||||||||
\(664\) | −2.78890 | −0.108230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.21110 | 0.356923 | ||||||||
\(667\) | 6.42221i | 0.248669i | ||||||||
\(668\) | 9.21110 | 0.356388 | ||||||||
\(669\) | 1.81665i | 0.0702359i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.60555i | 0.177663i | ||||||||
\(673\) | − 37.6333i | − 1.45066i | −0.688403 | − | 0.725329i | \(-0.741688\pi\) | ||||
0.688403 | − | 0.725329i | \(-0.258312\pi\) | |||||||
\(674\) | − 13.6333i | − 0.525135i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 28.0555i | 1.07826i | 0.842222 | + | 0.539130i | \(0.181247\pi\) | ||||
−0.842222 | + | 0.539130i | \(0.818753\pi\) | |||||||
\(678\) | −13.8167 | −0.530625 | ||||||||
\(679\) | −6.42221 | −0.246462 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − 24.0000i | − 0.919682i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.21110 | −0.352453 | −0.176227 | − | 0.984350i | \(-0.556389\pi\) | ||||
−0.176227 | + | 0.984350i | \(0.556389\pi\) | |||||||
\(684\) | − 4.60555i | − 0.176098i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −33.2111 | −1.26801 | ||||||||
\(687\) | 19.8167 | 0.756053 | ||||||||
\(688\) | 8.00000i | 0.304997i | ||||||||
\(689\) | −21.6333 | −0.824163 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2389i | 0.769922i | 0.922933 | + | 0.384961i | \(0.125785\pi\) | ||||
−0.922933 | + | 0.384961i | \(0.874215\pi\) | |||||||
\(692\) | − 12.4222i | − 0.472221i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.6333i | 1.04895i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.60555i | 0.174573i | ||||||||
\(697\) | 14.7889 | 0.560169 | ||||||||
\(698\) | 7.81665i | 0.295865i | ||||||||
\(699\) | −1.81665 | −0.0687122 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.0278 | 1.77621 | 0.888107 | − | 0.459637i | \(-0.152020\pi\) | ||||
0.888107 | + | 0.459637i | \(0.152020\pi\) | |||||||
\(702\) | −3.60555 | −0.136083 | ||||||||
\(703\) | − 42.4222i | − 1.59998i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.78890 | 0.330775 | ||||||||
\(707\) | 34.0555 | 1.28079 | ||||||||
\(708\) | 9.21110 | 0.346174 | ||||||||
\(709\) | 1.39445i | 0.0523696i | 0.999657 | + | 0.0261848i | \(0.00833584\pi\) | ||||
−0.999657 | + | 0.0261848i | \(0.991664\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.4222 | −0.540875 | ||||||||
\(712\) | − 15.2111i | − 0.570060i | ||||||||
\(713\) | 8.36669 | 0.313335 | ||||||||
\(714\) | 21.2111 | 0.793806 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.8167 | 0.740583 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 15.6333i | − 0.583430i | ||||||||
\(719\) | 51.6333 | 1.92560 | 0.962799 | − | 0.270220i | \(-0.0870963\pi\) | ||||
0.962799 | + | 0.270220i | \(0.0870963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.4222i | 0.686079i | ||||||||
\(722\) | −2.21110 | −0.0822887 | ||||||||
\(723\) | −6.42221 | −0.238844 | ||||||||
\(724\) | 8.42221 | 0.313009 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − 11.0000i | − 0.408248i | ||||||||
\(727\) | 14.4222i | 0.534890i | 0.963573 | + | 0.267445i | \(0.0861794\pi\) | ||||
−0.963573 | + | 0.267445i | \(0.913821\pi\) | |||||||
\(728\) | − 16.6056i | − 0.615443i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.8444 | 1.36274 | ||||||||
\(732\) | 11.2111i | 0.414374i | ||||||||
\(733\) | 34.0555 | 1.25787 | 0.628935 | − | 0.777458i | \(-0.283491\pi\) | ||||
0.628935 | + | 0.777458i | \(0.283491\pi\) | |||||||
\(734\) | 19.6333i | 0.724679i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 1.39445i | − 0.0514001i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − 3.21110i | − 0.118202i | ||||||||
\(739\) | − 20.2389i | − 0.744498i | −0.928133 | − | 0.372249i | \(-0.878587\pi\) | ||||
0.928133 | − | 0.372249i | \(-0.121413\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.6056i | 0.610020i | ||||||||
\(742\) | − 27.6333i | − 1.01445i | ||||||||
\(743\) | −36.8444 | −1.35169 | −0.675845 | − | 0.737044i | \(-0.736221\pi\) | ||||
−0.675845 | + | 0.737044i | \(0.736221\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − 20.4222i | − 0.747710i | ||||||||
\(747\) | 2.78890 | 0.102040 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4222 | −0.380312 | −0.190156 | − | 0.981754i | \(-0.560899\pi\) | ||||
−0.190156 | + | 0.981754i | \(0.560899\pi\) | |||||||
\(752\) | −9.21110 | −0.335894 | ||||||||
\(753\) | 13.3944i | 0.488121i | ||||||||
\(754\) | − 16.6056i | − 0.604739i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − 4.60555i | − 0.167502i | ||||||||
\(757\) | − 12.7889i | − 0.464820i | −0.972618 | − | 0.232410i | \(-0.925339\pi\) | ||||
0.972618 | − | 0.232410i | \(-0.0746612\pi\) | |||||||
\(758\) | − 35.0278i | − 1.27227i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.6333i | 1.21921i | 0.792707 | + | 0.609603i | \(0.208671\pi\) | ||||
−0.792707 | + | 0.609603i | \(0.791329\pi\) | |||||||
\(762\) | −1.21110 | −0.0438736 | ||||||||
\(763\) | 6.42221i | 0.232499i | ||||||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.6333 | 0.998432 | ||||||||
\(767\) | −33.2111 | −1.19918 | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | 12.8444i | 0.463181i | 0.972813 | + | 0.231591i | \(0.0743930\pi\) | ||||
−0.972813 | + | 0.231591i | \(0.925607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.6056 | 1.03020 | ||||||||
\(772\) | −7.81665 | −0.281328 | ||||||||
\(773\) | −30.0000 | −1.07903 | −0.539513 | − | 0.841978i | \(-0.681391\pi\) | ||||
−0.539513 | + | 0.841978i | \(0.681391\pi\) | |||||||
\(774\) | − 8.00000i | − 0.287554i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.39445 | 0.0500578 | ||||||||
\(777\) | − 42.4222i | − 1.52189i | ||||||||
\(778\) | −4.60555 | −0.165117 | ||||||||
\(779\) | −14.7889 | −0.529867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −6.42221 | −0.229658 | ||||||||
\(783\) | − 4.60555i | − 0.164589i | ||||||||
\(784\) | 14.2111 | 0.507539 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − 22.6056i | − 0.806313i | ||||||||
\(787\) | 49.2666 | 1.75617 | 0.878083 | − | 0.478509i | \(-0.158823\pi\) | ||||
0.878083 | + | 0.478509i | \(0.158823\pi\) | |||||||
\(788\) | −6.00000 | −0.213741 | ||||||||
\(789\) | −7.81665 | −0.278280 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.6333i | 2.26254i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 40.4222i | − 1.43543i | ||||||||
\(794\) | −3.63331 | −0.128941 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.4222 | −0.794734 | ||||||||
\(797\) | 6.00000i | 0.212531i | 0.994338 | + | 0.106265i | \(0.0338893\pi\) | ||||
−0.994338 | + | 0.106265i | \(0.966111\pi\) | |||||||
\(798\) | −21.2111 | −0.750865 | ||||||||
\(799\) | 42.4222i | 1.50079i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.2111i | 0.537458i | ||||||||
\(802\) | 8.78890i | 0.310347i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 3.21110i | 0.113247i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.6333 | −0.762001 | ||||||||
\(807\) | 25.8167i | 0.908789i | ||||||||
\(808\) | −7.39445 | −0.260136 | ||||||||
\(809\) | 6.84441 | 0.240637 | 0.120318 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120318 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.2389i | 1.13206i | 0.824385 | + | 0.566030i | \(0.191521\pi\) | ||||
−0.824385 | + | 0.566030i | \(0.808479\pi\) | |||||||
\(812\) | 21.2111 | 0.744364 | ||||||||
\(813\) | −0.422205 | −0.0148074 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.60555 | −0.161227 | ||||||||
\(817\) | −36.8444 | −1.28902 | ||||||||
\(818\) | 14.7889i | 0.517082i | ||||||||
\(819\) | 16.6056i | 0.580245i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.21110i | − 0.112068i | −0.998429 | − | 0.0560341i | \(-0.982154\pi\) | ||||
0.998429 | − | 0.0560341i | \(-0.0178456\pi\) | |||||||
\(822\) | − 3.21110i | − 0.112000i | ||||||||
\(823\) | − 4.00000i | − 0.139431i | −0.997567 | − | 0.0697156i | \(-0.977791\pi\) | ||||
0.997567 | − | 0.0697156i | \(-0.0222092\pi\) | |||||||
\(824\) | − 4.00000i | − 0.139347i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − 42.4222i | − 1.47606i | ||||||||
\(827\) | −27.6333 | −0.960904 | −0.480452 | − | 0.877021i | \(-0.659527\pi\) | ||||
−0.480452 | + | 0.877021i | \(0.659527\pi\) | |||||||
\(828\) | 1.39445i | 0.0484604i | ||||||||
\(829\) | −46.8444 | −1.62697 | −0.813487 | − | 0.581583i | \(-0.802433\pi\) | ||||
−0.813487 | + | 0.581583i | \(0.802433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.4222 | 0.569680 | ||||||||
\(832\) | 3.60555i | 0.125000i | ||||||||
\(833\) | − 65.4500i | − 2.26771i | ||||||||
\(834\) | 17.2111i | 0.595972i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.00000 | −0.207390 | ||||||||
\(838\) | −4.18335 | −0.144511 | ||||||||
\(839\) | 18.4222i | 0.636005i | 0.948090 | + | 0.318003i | \(0.103012\pi\) | ||||
−0.948090 | + | 0.318003i | \(0.896988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | − 19.8167i | − 0.682927i | ||||||||
\(843\) | 27.2111 | 0.937200 | ||||||||
\(844\) | −17.2111 | −0.592431 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.21110 | 0.316684 | ||||||||
\(847\) | −50.6611 | −1.74073 | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 10.4222 | 0.357689 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.8444i | 0.440301i | ||||||||
\(852\) | 9.21110 | 0.315567 | ||||||||
\(853\) | 14.7889 | 0.506362 | 0.253181 | − | 0.967419i | \(-0.418523\pi\) | ||||
0.253181 | + | 0.967419i | \(0.418523\pi\) | |||||||
\(854\) | 51.6333 | 1.76686 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.0278i | 0.786613i | 0.919407 | + | 0.393307i | \(0.128669\pi\) | ||||
−0.919407 | + | 0.393307i | \(0.871331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.2111 | −0.860192 | −0.430096 | − | 0.902783i | \(-0.641520\pi\) | ||||
−0.430096 | + | 0.902783i | \(0.641520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.7889 | −0.504004 | ||||||||
\(862\) | 12.0000i | 0.408722i | ||||||||
\(863\) | −51.6333 | −1.75762 | −0.878809 | − | 0.477173i | \(-0.841661\pi\) | ||||
−0.878809 | + | 0.477173i | \(0.841661\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.2111i | 0.652820i | ||||||||
\(867\) | 4.21110i | 0.143017i | ||||||||
\(868\) | − 27.6333i | − 0.937936i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 11.5778i | − 0.392299i | ||||||||
\(872\) | − 1.39445i | − 0.0472220i | ||||||||
\(873\) | −1.39445 | −0.0471949 | ||||||||
\(874\) | 6.42221 | 0.217234 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − 1.39445i | − 0.0471141i | ||||||||
\(877\) | −24.8444 | −0.838936 | −0.419468 | − | 0.907770i | \(-0.637783\pi\) | ||||
−0.419468 | + | 0.907770i | \(0.637783\pi\) | |||||||
\(878\) | −8.00000 | −0.269987 | ||||||||
\(879\) | 18.0000i | 0.607125i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.2111 | 1.32106 | 0.660528 | − | 0.750802i | \(-0.270333\pi\) | ||||
0.660528 | + | 0.750802i | \(0.270333\pi\) | |||||||
\(882\) | −14.2111 | −0.478513 | ||||||||
\(883\) | 9.57779i | 0.322318i | 0.986928 | + | 0.161159i | \(0.0515233\pi\) | ||||
−0.986928 | + | 0.161159i | \(0.948477\pi\) | |||||||
\(884\) | 16.6056 | 0.558505 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.6333i | 0.525211i | ||||||||
\(887\) | − 6.97224i | − 0.234105i | −0.993126 | − | 0.117053i | \(-0.962655\pi\) | ||||
0.993126 | − | 0.117053i | \(-0.0373446\pi\) | |||||||
\(888\) | 9.21110i | 0.309104i | ||||||||
\(889\) | 5.57779i | 0.187073i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.81665 | −0.0608261 | ||||||||
\(893\) | − 42.4222i | − 1.41960i | ||||||||
\(894\) | −15.2111 | −0.508735 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.60555 | −0.153861 | ||||||||
\(897\) | − 5.02776i | − 0.167872i | ||||||||
\(898\) | − 33.6333i | − 1.12236i | ||||||||
\(899\) | − 27.6333i | − 0.921622i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.6333 | 0.920599 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.8444 | −1.22611 | ||||||||
\(904\) | − 13.8167i | − 0.459535i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | − 21.5778i | − 0.716479i | −0.933630 | − | 0.358239i | \(-0.883377\pi\) | ||||
0.933630 | − | 0.358239i | \(-0.116623\pi\) | |||||||
\(908\) | 24.0000 | 0.796468 | ||||||||
\(909\) | 7.39445 | 0.245258 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.6333 | −0.915532 | −0.457766 | − | 0.889073i | \(-0.651350\pi\) | ||||
−0.457766 | + | 0.889073i | \(0.651350\pi\) | |||||||
\(912\) | 4.60555 | 0.152505 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 38.2389 | 1.26483 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.8167i | 0.654761i | ||||||||
\(917\) | −104.111 | −3.43805 | ||||||||
\(918\) | 4.60555 | 0.152006 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.78890i | 0.289604i | ||||||||
\(922\) | − 33.6333i | − 1.10765i | ||||||||
\(923\) | −33.2111 | −1.09316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.3944 | 1.03169 | ||||||||
\(927\) | 4.00000i | 0.131377i | ||||||||
\(928\) | −4.60555 | −0.151185 | ||||||||
\(929\) | − 39.2111i | − 1.28647i | −0.765667 | − | 0.643237i | \(-0.777591\pi\) | ||||
0.765667 | − | 0.643237i | \(-0.222409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 65.4500i | 2.14504i | ||||||||
\(932\) | − 1.81665i | − 0.0595065i | ||||||||
\(933\) | − 12.0000i | − 0.392862i | ||||||||
\(934\) | 30.4222i | 0.995445i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − 3.60555i | − 0.117851i | ||||||||
\(937\) | 10.3667i | 0.338665i | 0.985559 | + | 0.169333i | \(0.0541612\pi\) | ||||
−0.985559 | + | 0.169333i | \(0.945839\pi\) | |||||||
\(938\) | 14.7889 | 0.482875 | ||||||||
\(939\) | 3.57779 | 0.116757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 54.0000i | − 1.76035i | −0.474650 | − | 0.880175i | \(-0.657425\pi\) | ||||
0.474650 | − | 0.880175i | \(-0.342575\pi\) | |||||||
\(942\) | −20.4222 | −0.665391 | ||||||||
\(943\) | 4.47772 | 0.145815 | ||||||||
\(944\) | 9.21110i | 0.299796i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.6333 | −0.508014 | −0.254007 | − | 0.967202i | \(-0.581749\pi\) | ||||
−0.254007 | + | 0.967202i | \(0.581749\pi\) | |||||||
\(948\) | − 14.4222i | − 0.468411i | ||||||||
\(949\) | 5.02776i | 0.163208i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000i | 0.583690i | ||||||||
\(952\) | 21.2111i | 0.687456i | ||||||||
\(953\) | − 20.2389i | − 0.655601i | −0.944747 | − | 0.327800i | \(-0.893693\pi\) | ||||
0.944747 | − | 0.327800i | \(-0.106307\pi\) | |||||||
\(954\) | − 6.00000i | − 0.194257i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 5.57779i | − 0.180210i | ||||||||
\(959\) | −14.7889 | −0.477558 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | − 33.2111i | − 1.07077i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 6.42221i | − 0.206845i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.42221 | 0.206631 | ||||||||
\(967\) | −8.23886 | −0.264944 | −0.132472 | − | 0.991187i | \(-0.542291\pi\) | ||||
−0.132472 | + | 0.991187i | \(0.542291\pi\) | |||||||
\(968\) | 11.0000 | 0.353553 | ||||||||
\(969\) | − 21.2111i | − 0.681399i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.0278 | −1.70174 | −0.850871 | − | 0.525375i | \(-0.823925\pi\) | ||||
−0.850871 | + | 0.525375i | \(0.823925\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | 79.2666 | 2.54117 | ||||||||
\(974\) | −0.972244 | −0.0311527 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.2111 | −0.358859 | ||||||||
\(977\) | 18.8444 | 0.602886 | 0.301443 | − | 0.953484i | \(-0.402532\pi\) | ||||
0.301443 | + | 0.953484i | \(0.402532\pi\) | |||||||
\(978\) | 24.4222i | 0.780936i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.39445i | 0.0445213i | ||||||||
\(982\) | 7.81665 | 0.249439 | ||||||||
\(983\) | 42.4222 | 1.35306 | 0.676529 | − | 0.736416i | \(-0.263483\pi\) | ||||
0.676529 | + | 0.736416i | \(0.263483\pi\) | |||||||
\(984\) | 3.21110 | 0.102366 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.2111i | 0.675499i | ||||||||
\(987\) | − 42.4222i | − 1.35031i | ||||||||
\(988\) | −16.6056 | −0.528293 | ||||||||
\(989\) | 11.1556 | 0.354727 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.4222 | −0.712265 | −0.356132 | − | 0.934436i | \(-0.615905\pi\) | ||||
−0.356132 | + | 0.934436i | \(0.615905\pi\) | |||||||
\(992\) | 6.00000i | 0.190500i | ||||||||
\(993\) | −16.6056 | −0.526961 | ||||||||
\(994\) | − 42.4222i | − 1.34555i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.78890i | 0.0883696i | ||||||||
\(997\) | 16.4222i | 0.520096i | 0.965596 | + | 0.260048i | \(0.0837385\pi\) | ||||
−0.965596 | + | 0.260048i | \(0.916262\pi\) | |||||||
\(998\) | − 23.0278i | − 0.728931i | ||||||||
\(999\) | − 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 | 1950.2.f.n.649.1 | 4 | ||
5.2 | odd | 4 | 390.2.b.c.181.3 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.b.k.1351.2 | 4 | |||
5.4 | even | 2 | 1950.2.f.m.649.4 | 4 | |||
13.12 | even | 2 | 1950.2.f.m.649.2 | 4 | |||
15.2 | even | 4 | 1170.2.b.d.181.1 | 4 | |||
20.7 | even | 4 | 3120.2.g.q.961.4 | 4 | |||
65.12 | odd | 4 | 390.2.b.c.181.2 | ✓ | 4 | ||
65.38 | odd | 4 | 1950.2.b.k.1351.3 | 4 | |||
65.47 | even | 4 | 5070.2.a.z.1.1 | 2 | |||
65.57 | even | 4 | 5070.2.a.bf.1.2 | 2 | |||
65.64 | even | 2 | inner | 1950.2.f.n.649.3 | 4 | ||
195.77 | even | 4 | 1170.2.b.d.181.4 | 4 | |||
260.207 | even | 4 | 3120.2.g.q.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.c.181.2 | ✓ | 4 | 65.12 | odd | 4 | ||
390.2.b.c.181.3 | yes | 4 | 5.2 | odd | 4 | ||
1170.2.b.d.181.1 | 4 | 15.2 | even | 4 | |||
1170.2.b.d.181.4 | 4 | 195.77 | even | 4 | |||
1950.2.b.k.1351.2 | 4 | 5.3 | odd | 4 | |||
1950.2.b.k.1351.3 | 4 | 65.38 | odd | 4 | |||
1950.2.f.m.649.2 | 4 | 13.12 | even | 2 | |||
1950.2.f.m.649.4 | 4 | 5.4 | even | 2 | |||
1950.2.f.n.649.1 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.f.n.649.3 | 4 | 65.64 | even | 2 | inner | ||
3120.2.g.q.961.1 | 4 | 260.207 | even | 4 | |||
3120.2.g.q.961.4 | 4 | 20.7 | even | 4 | |||
5070.2.a.z.1.1 | 2 | 65.47 | even | 4 | |||
5070.2.a.bf.1.2 | 2 | 65.57 | even | 4 |