Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(881,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 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("1680.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.2 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.881 |
Dual form | 1680.2.f.g.881.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.68614 | + | 0.396143i | −0.973494 | + | 0.228714i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.68614 | − | 1.33591i | 0.895380 | − | 0.445302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.792287i | 0.238884i | 0.992841 | + | 0.119442i | \(0.0381105\pi\) | ||||
−0.992841 | + | 0.119442i | \(0.961890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.84096i | 1.61999i | 0.586436 | + | 0.809996i | \(0.300531\pi\) | ||||
−0.586436 | + | 0.809996i | \(0.699469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.68614 | + | 0.396143i | −0.435360 | + | 0.102284i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.37228 | −0.332827 | −0.166414 | − | 0.986056i | \(-0.553219\pi\) | ||||
−0.166414 | + | 0.986056i | \(0.553219\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.68614 | + | 3.71277i | −0.586164 | + | 0.810192i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.87953i | 0.391909i | 0.980613 | + | 0.195954i | \(0.0627804\pi\) | ||||
−0.980613 | + | 0.195954i | \(0.937220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | + | 3.31662i | −0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.25639i | − | 0.790392i | −0.918597 | − | 0.395196i | \(-0.870677\pi\) | ||
0.918597 | − | 0.395196i | \(-0.129323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.313859 | − | 1.33591i | −0.0546359 | − | 0.232552i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | − | 1.73205i | 0.338062 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.74456 | 0.780001 | 0.390001 | − | 0.920815i | \(-0.372475\pi\) | ||||
0.390001 | + | 0.920815i | \(0.372475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.31386 | − | 9.84868i | −0.370514 | − | 1.57705i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.74456 | 1.02854 | 0.514268 | − | 0.857629i | \(-0.328064\pi\) | ||||
0.514268 | + | 0.857629i | \(0.328064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.68614 | − | 1.33591i | 0.400426 | − | 0.199145i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.37228 | 1.07536 | 0.537679 | − | 0.843150i | \(-0.319301\pi\) | ||||
0.537679 | + | 0.843150i | \(0.319301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.31386 | − | 0.543620i | 0.324005 | − | 0.0761221i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.51278i | 1.16932i | 0.811278 | + | 0.584660i | \(0.198772\pi\) | ||||
−0.811278 | + | 0.584660i | \(0.801228\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.792287i | 0.106832i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.37228 | − | 5.84096i | −0.181763 | − | 0.773654i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.74456 | −0.357312 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.05842 | − | 7.32435i | 0.385325 | − | 0.922781i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.84096i | 0.724482i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.74456 | 0.823979 | 0.411990 | − | 0.911188i | \(-0.364834\pi\) | ||||
0.411990 | + | 0.911188i | \(0.364834\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.744563 | − | 3.16915i | −0.0896348 | − | 0.381521i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5615i | 1.60945i | 0.593649 | + | 0.804724i | \(0.297687\pi\) | ||||
−0.593649 | + | 0.804724i | \(0.702313\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.68614 | + | 0.396143i | −0.194699 | + | 0.0457427i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.37228 | + | 1.58457i | 0.156386 | + | 0.180579i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.37228 | −0.379411 | −0.189706 | − | 0.981841i | \(-0.560753\pi\) | ||||
−0.189706 | + | 0.981841i | \(0.560753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.43070 | − | 7.17687i | 0.603411 | − | 0.797430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.48913 | −0.602510 | −0.301255 | − | 0.953544i | \(-0.597406\pi\) | ||||
−0.301255 | + | 0.953544i | \(0.597406\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.37228 | −0.148845 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.68614 | + | 7.17687i | 0.180773 | + | 0.769441i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.25544 | 0.345076 | 0.172538 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172538 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.1168 | + | 11.6819i | 1.06053 | + | 1.22460i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.37228 | + | 5.84096i | 0.142299 | + | 0.605680i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.46410i | 0.355409i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.08724i | − | 0.110393i | −0.998476 | − | 0.0551963i | \(-0.982422\pi\) | ||
0.998476 | − | 0.0551963i | \(-0.0175785\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.05842 | + | 2.12819i | 0.106375 | + | 0.213892i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2333i | 1.59951i | 0.600326 | + | 0.799756i | \(0.295038\pi\) | ||||
−0.600326 | + | 0.799756i | \(0.704962\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.68614 | + | 3.71277i | −0.262140 | + | 0.362329i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.63325i | 0.641260i | 0.947204 | + | 0.320630i | \(0.103895\pi\) | ||||
−0.947204 | + | 0.320630i | \(0.896105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.116844 | 0.0111916 | 0.00559581 | − | 0.999984i | \(-0.498219\pi\) | ||||
0.00559581 | + | 0.999984i | \(0.498219\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | + | 1.87953i | −0.759326 | + | 0.178397i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.0974i | − | 0.949879i | −0.880018 | − | 0.474939i | \(-0.842470\pi\) | ||
0.880018 | − | 0.474939i | \(-0.157530\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.87953i | 0.175267i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.80298 | + | 15.6896i | 0.721386 | + | 1.45051i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.74456 | + | 2.37686i | −0.251594 | + | 0.217886i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3723 | 0.942935 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.1168 | − | 2.37686i | 0.912205 | − | 0.214314i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.7446 | −0.953426 | −0.476713 | − | 0.879059i | \(-0.658172\pi\) | ||||
−0.476713 | + | 0.879059i | \(0.658172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.3723 | + | 2.67181i | −1.00127 | + | 0.235240i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4891 | 1.52803 | 0.764016 | − | 0.645197i | \(-0.223225\pi\) | ||||
0.764016 | + | 0.645197i | \(0.223225\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | + | 6.92820i | 0.520266 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.00000 | + | 3.31662i | −0.344265 | + | 0.285450i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.2665i | 1.13343i | 0.823913 | + | 0.566717i | \(0.191787\pi\) | ||||
−0.823913 | + | 0.566717i | \(0.808213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.28962i | 0.109384i | 0.998503 | + | 0.0546921i | \(0.0174177\pi\) | ||||
−0.998503 | + | 0.0546921i | \(0.982582\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.4307 | + | 2.92048i | −1.04685 | + | 0.245949i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.62772 | −0.386989 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.25639i | − | 0.353474i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.05842 | + | 12.0781i | 0.0872972 | + | 0.996182i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.0974i | − | 0.827207i | −0.910457 | − | 0.413604i | \(-0.864270\pi\) | ||
0.910457 | − | 0.413604i | \(-0.135730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.37228 | −0.274432 | −0.137216 | − | 0.990541i | \(-0.543816\pi\) | ||||
−0.137216 | + | 0.990541i | \(0.543816\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.68614 | + | 1.83324i | −0.298007 | + | 0.148209i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.46410i | − | 0.278243i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.37228 | − | 14.3537i | −0.267439 | − | 1.13833i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.25544 | + | 3.75906i | 0.256564 | + | 0.296255i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.313859 | − | 1.33591i | −0.0244339 | − | 0.104000i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.1168 | 1.71145 | 0.855726 | − | 0.517429i | \(-0.173111\pi\) | ||||
0.855726 | + | 0.517429i | \(0.173111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.1168 | −1.62437 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.62772 | + | 9.30506i | 0.353890 | + | 0.711576i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.1168 | 1.22534 | 0.612670 | − | 0.790338i | \(-0.290095\pi\) | ||||
0.612670 | + | 0.790338i | \(0.290095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 1.73205i | 0.151186 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.62772 | − | 1.08724i | 0.347841 | − | 0.0817220i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.63325i | 0.495792i | 0.968787 | + | 0.247896i | \(0.0797392\pi\) | ||||
−0.968787 | + | 0.247896i | \(0.920261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.6101i | − | 1.38328i | −0.722242 | − | 0.691640i | \(-0.756889\pi\) | ||
0.722242 | − | 0.691640i | \(-0.243111\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.74456 | − | 11.6819i | −0.202884 | − | 0.863553i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.74456 | 0.348827 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.08724i | − | 0.0795069i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.25544 | + | 13.5615i | −0.164059 | + | 0.986451i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.6434i | − | 1.13191i | −0.824435 | − | 0.565957i | \(-0.808507\pi\) | ||
0.824435 | − | 0.565957i | \(-0.191493\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.2337 | 1.60042 | 0.800208 | − | 0.599723i | \(-0.204722\pi\) | ||||
0.800208 | + | 0.599723i | \(0.204722\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.31386 | − | 9.84868i | −0.165699 | − | 0.705279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3692i | 1.59374i | 0.604152 | + | 0.796869i | \(0.293512\pi\) | ||||
−0.604152 | + | 0.796869i | \(0.706488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.9715i | − | 0.919528i | −0.888041 | − | 0.459764i | \(-0.847934\pi\) | ||
0.888041 | − | 0.459764i | \(-0.152066\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3723 | + | 2.67181i | −0.802139 | + | 0.188455i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.37228 | − | 8.51278i | −0.517433 | − | 0.597480i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.51087 | + | 5.04868i | 0.174518 | + | 0.350907i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.74456 | −0.189845 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.11684 | −0.421101 | −0.210550 | − | 0.977583i | \(-0.567526\pi\) | ||||
−0.210550 | + | 0.977583i | \(0.567526\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.37228 | − | 22.8665i | −0.368103 | − | 1.56679i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.74456 | 0.459975 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | − | 6.92820i | −0.407307 | − | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.74456 | − | 11.6819i | −0.185460 | − | 0.789391i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.01544i | − | 0.539177i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.9870i | − | 1.40539i | −0.711490 | − | 0.702696i | \(-0.751979\pi\) | ||
0.711490 | − | 0.702696i | \(-0.248021\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.68614 | − | 1.33591i | 0.179076 | − | 0.0890605i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.6060 | 1.03580 | 0.517902 | − | 0.855440i | \(-0.326713\pi\) | ||||
0.517902 | + | 0.855440i | \(0.326713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.75372i | − | 0.314135i | −0.987588 | − | 0.157067i | \(-0.949796\pi\) | ||
0.987588 | − | 0.157067i | \(-0.0502040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.94158 | − | 2.12819i | −0.193542 | − | 0.140025i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.75906i | 0.246264i | 0.992390 | + | 0.123132i | \(0.0392938\pi\) | ||||
−0.992390 | + | 0.123132i | \(0.960706\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.37228 | 0.480915 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.68614 | − | 1.33591i | 0.369355 | − | 0.0867765i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.6434i | − | 1.01188i | −0.862567 | − | 0.505942i | \(-0.831145\pi\) | ||
0.862567 | − | 0.505942i | \(-0.168855\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.3639i | 1.50500i | 0.658593 | + | 0.752499i | \(0.271152\pi\) | ||||
−0.658593 | + | 0.752499i | \(0.728848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.31386 | + | 14.2525i | −0.405034 | + | 0.914302i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | − | 6.92820i | 0.0638877 | − | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.2337 | −1.28744 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.25544 | − | 2.17448i | 0.586540 | − | 0.137802i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.4891 | −1.10390 | −0.551952 | − | 0.833876i | \(-0.686117\pi\) | ||||
−0.551952 | + | 0.833876i | \(0.686117\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.48913 | −0.0936205 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.31386 | − | 0.543620i | 0.144899 | − | 0.0340428i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4891 | 1.46521 | 0.732606 | − | 0.680653i | \(-0.238304\pi\) | ||||
0.732606 | + | 0.680653i | \(0.238304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.48913 | − | 8.21782i | 0.589626 | − | 0.510631i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.68614 | − | 11.4333i | −0.351963 | − | 0.707701i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5615i | 0.836235i | 0.908393 | + | 0.418118i | \(0.137310\pi\) | ||||
−0.908393 | + | 0.418118i | \(0.862690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.51278i | 0.522936i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.48913 | + | 1.28962i | −0.335929 | + | 0.0789235i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.74456 | −0.533165 | −0.266583 | − | 0.963812i | \(-0.585895\pi\) | ||||
−0.266583 | + | 0.963812i | \(0.585895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.1460i | − | 0.920056i | −0.887905 | − | 0.460028i | \(-0.847839\pi\) | ||
0.887905 | − | 0.460028i | \(-0.152161\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.6861 | − | 15.6896i | −1.31250 | − | 0.949581i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.792287i | 0.0477767i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.23369 | −0.374546 | −0.187273 | − | 0.982308i | \(-0.559965\pi\) | ||||
−0.187273 | + | 0.982308i | \(0.559965\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.62772 | − | 9.30506i | −0.277054 | − | 0.557080i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.84630i | 0.289106i | 0.989497 | + | 0.144553i | \(0.0461744\pi\) | ||||
−0.989497 | + | 0.144553i | \(0.953826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.30506i | 0.553129i | 0.960995 | + | 0.276564i | \(0.0891959\pi\) | ||||
−0.960995 | + | 0.276564i | \(0.910804\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.37228 | − | 5.84096i | −0.0812869 | − | 0.345989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | + | 10.3923i | −0.708338 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1168 | −0.889226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.430703 | + | 1.83324i | 0.0252483 | + | 0.107466i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.1168 | −1.64260 | −0.821302 | − | 0.570494i | \(-0.806752\pi\) | ||||
−0.821302 | + | 0.570494i | \(0.806752\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.74456 | −0.159795 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.62772 | − | 3.16915i | −0.152476 | − | 0.183893i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.9783 | −0.634889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.4891 | − | 11.6819i | 0.777500 | − | 0.673335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1168 | + | 2.37686i | −0.581198 | + | 0.136547i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.92820i | 0.396708i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.13058i | 0.406964i | 0.979079 | + | 0.203482i | \(0.0652258\pi\) | ||||
−0.979079 | + | 0.203482i | \(0.934774\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.43070 | − | 27.3716i | −0.365830 | − | 1.55711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.2337 | −1.14735 | −0.573674 | − | 0.819084i | \(-0.694482\pi\) | ||||
−0.573674 | + | 0.819084i | \(0.694482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.4511i | − | 1.38206i | −0.722827 | − | 0.691029i | \(-0.757158\pi\) | ||
0.722827 | − | 0.691029i | \(-0.242842\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.05842 | − | 7.32435i | 0.172323 | − | 0.412680i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.51278i | 0.478125i | 0.971004 | + | 0.239063i | \(0.0768401\pi\) | ||||
−0.971004 | + | 0.239063i | \(0.923160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.37228 | 0.188812 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.62772 | − | 11.1846i | −0.146665 | − | 0.624263i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.75372i | − | 0.264504i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.84096i | 0.323998i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.197015 | + | 0.0462870i | −0.0108950 | + | 0.00255968i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.7446 | − | 12.7692i | 0.812894 | − | 0.703987i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.7446 | − | 6.33830i | 0.698398 | − | 0.347336i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.74456 | 0.368495 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.2337 | −0.993252 | −0.496626 | − | 0.867965i | \(-0.665428\pi\) | ||||
−0.496626 | + | 0.867965i | \(0.665428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.00000 | + | 17.0256i | 0.217250 | + | 0.924701i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.74456 | 0.148626 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.744563 | − | 3.16915i | −0.0400859 | − | 0.170621i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3152i | 0.983210i | 0.870818 | + | 0.491605i | \(0.163590\pi\) | ||||
−0.870818 | + | 0.491605i | \(0.836410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.75372i | 0.254461i | 0.991873 | + | 0.127230i | \(0.0406088\pi\) | ||||
−0.991873 | + | 0.127230i | \(0.959391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.3723 | − | 23.3639i | −1.03402 | − | 1.24707i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.88316 | 0.419578 | 0.209789 | − | 0.977747i | \(-0.432722\pi\) | ||||
0.209789 | + | 0.977747i | \(0.432722\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.5615i | 0.719767i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.68614 | − | 5.09496i | 0.195091 | − | 0.269654i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.80240i | − | 0.517351i | −0.965964 | − | 0.258675i | \(-0.916714\pi\) | ||
0.965964 | − | 0.258675i | \(-0.0832860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.4891 | + | 4.10891i | −0.917941 | + | 0.215662i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.92820i | 0.362639i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 25.3360i | − | 1.32253i | −0.750154 | − | 0.661263i | \(-0.770021\pi\) | ||
0.750154 | − | 0.661263i | \(-0.229979\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.1168 | + | 8.01544i | −0.839009 | + | 0.417267i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.7446 | + | 17.0256i | 0.765500 | + | 0.883923i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.7446 | −1.28122 | −0.640612 | − | 0.767864i | \(-0.721319\pi\) | ||||
−0.640612 | + | 0.767864i | \(0.721319\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.68614 | + | 0.396143i | −0.0870719 | + | 0.0204568i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.8614 | 1.28043 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.48913 | −0.0764912 | −0.0382456 | − | 0.999268i | \(-0.512177\pi\) | ||||
−0.0382456 | + | 0.999268i | \(0.512177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.1168 | − | 4.25639i | 0.928154 | − | 0.218061i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.4891 | 0.893653 | 0.446826 | − | 0.894621i | \(-0.352554\pi\) | ||||
0.446826 | + | 0.894621i | \(0.352554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.37228 | + | 1.58457i | 0.0699379 | + | 0.0807574i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.1168 | − | 9.01011i | 0.920931 | − | 0.458010i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 13.7638i | − | 0.697854i | −0.937150 | − | 0.348927i | \(-0.886546\pi\) | ||
0.937150 | − | 0.348927i | \(-0.113454\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.57924i | − | 0.130438i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.4891 | + | 6.92820i | −1.48753 | + | 0.349482i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.37228 | −0.169678 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.66648i | 0.184015i | 0.995758 | + | 0.0920077i | \(0.0293284\pi\) | ||||
−0.995758 | + | 0.0920077i | \(0.970672\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.8614 | − | 9.30506i | −0.643876 | − | 0.465836i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.67181i | 0.133424i | 0.997772 | + | 0.0667120i | \(0.0212509\pi\) | ||||
−0.997772 | + | 0.0667120i | \(0.978749\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.2337 | 1.00791 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.43070 | − | 7.17687i | 0.269854 | − | 0.356622i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.75906i | 0.186329i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 35.0458i | − | 1.73290i | −0.499262 | − | 0.866451i | \(-0.666396\pi\) | ||
0.499262 | − | 0.866451i | \(-0.333604\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.25544 | − | 22.3692i | −0.259232 | − | 1.10339i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.48913 | + | 4.75372i | −0.270102 | + | 0.233915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.48913 | −0.269451 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.510875 | − | 2.17448i | −0.0250176 | − | 0.106485i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.74456 | 0.134081 | 0.0670403 | − | 0.997750i | \(-0.478644\pi\) | ||||
0.0670403 | + | 0.997750i | \(0.478644\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.6060 | −1.24796 | −0.623979 | − | 0.781441i | \(-0.714485\pi\) | ||||
−0.623979 | + | 0.781441i | \(0.714485\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.8030 | − | 9.84868i | 0.962854 | − | 0.478859i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.37228 | −0.0665654 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | + | 13.8564i | 0.580721 | + | 0.670559i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.80298 | − | 1.83324i | 0.376732 | − | 0.0885097i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 31.6742i | − | 1.52569i | −0.646579 | − | 0.762847i | \(-0.723801\pi\) | ||
0.646579 | − | 0.762847i | \(-0.276199\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.57924i | − | 0.123950i | −0.998078 | − | 0.0619752i | \(-0.980260\pi\) | ||
0.998078 | − | 0.0619752i | \(-0.0197400\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.68614 | + | 7.17687i | 0.0808443 | + | 0.344105i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.51087 | −0.311457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.28962i | − | 0.0615502i | −0.999526 | − | 0.0307751i | \(-0.990202\pi\) | ||
0.999526 | − | 0.0307751i | \(-0.00979757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.56930 | − | 19.9460i | −0.312824 | − | 0.949811i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.63325i | 0.315155i | 0.987507 | + | 0.157578i | \(0.0503684\pi\) | ||||
−0.987507 | + | 0.157578i | \(0.949632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.25544 | 0.154323 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.00000 | + | 17.0256i | 0.189194 | + | 0.805281i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.2101i | 1.33132i | 0.746256 | + | 0.665660i | \(0.231850\pi\) | ||||
−0.746256 | + | 0.665660i | \(0.768150\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.75372i | − | 0.223844i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.68614 | − | 1.33591i | 0.267158 | − | 0.0627664i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.1168 | + | 11.6819i | 0.474285 | + | 0.547657i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.9783 | −1.54266 | −0.771329 | − | 0.636437i | \(-0.780408\pi\) | ||||
−0.771329 | + | 0.636437i | \(0.780408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.48913 | − | 4.55134i | 0.256210 | − | 0.212438i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.74456 | −0.407275 | −0.203637 | − | 0.979046i | \(-0.565276\pi\) | ||||
−0.203637 | + | 0.979046i | \(0.565276\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.4674 | −1.69478 | −0.847391 | − | 0.530969i | \(-0.821828\pi\) | ||||
−0.847391 | + | 0.530969i | \(0.821828\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.37228 | + | 5.84096i | 0.0636380 | + | 0.270868i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.8832 | 0.642436 | 0.321218 | − | 0.947005i | \(-0.395908\pi\) | ||||
0.321218 | + | 0.947005i | \(0.395908\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4891 | − | 11.6819i | 0.622870 | − | 0.539421i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.34363i | 0.245700i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.46410i | 0.158944i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.3723 | + | 22.8665i | 0.520701 | + | 1.04699i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.5109 | −0.845783 | −0.422892 | − | 0.906180i | \(-0.638985\pi\) | ||||
−0.422892 | + | 0.906180i | \(0.638985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7128i | 1.26360i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.97825 | − | 5.04868i | −0.317521 | − | 0.229723i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.08724i | − | 0.0493691i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.5109 | −0.657550 | −0.328775 | − | 0.944408i | \(-0.606636\pi\) | ||||
−0.328775 | + | 0.944408i | \(0.606636\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.4891 | − | 3.16915i | 0.609999 | − | 0.143314i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.8896i | − | 0.491442i | −0.969341 | − | 0.245721i | \(-0.920975\pi\) | ||
0.969341 | − | 0.245721i | \(-0.0790248\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.84096i | 0.263064i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.05842 | + | 2.12819i | 0.0475725 | + | 0.0956552i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.4891 | + | 27.1229i | 1.05363 | + | 1.21663i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.3505 | 0.463353 | 0.231677 | − | 0.972793i | \(-0.425579\pi\) | ||||
0.231677 | + | 0.972793i | \(0.425579\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −37.2921 | + | 8.76144i | −1.66609 | + | 0.391432i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.6060 | 1.23089 | 0.615445 | − | 0.788180i | \(-0.288976\pi\) | ||||
0.615445 | + | 0.788180i | \(0.288976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.6060 | − | 8.36530i | 1.58132 | − | 0.371516i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.2337 | −1.69468 | −0.847339 | − | 0.531052i | \(-0.821797\pi\) | ||||
−0.847339 | + | 0.531052i | \(0.821797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 13.8564i | 0.530849 | + | 0.612971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.4891 | − | 13.8564i | −0.507257 | − | 0.611775i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.2333i | 0.715323i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.84096i | 0.256885i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.1753 | + | 6.38458i | −1.19286 | + | 0.280252i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4674 | 1.51004 | 0.755022 | − | 0.655700i | \(-0.227626\pi\) | ||||
0.755022 | + | 0.655700i | \(0.227626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 10.3923i | − | 0.454424i | −0.973845 | − | 0.227212i | \(-0.927039\pi\) | ||
0.973845 | − | 0.227212i | \(-0.0729610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.68614 | + | 3.71277i | −0.117233 | + | 0.162038i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.75372i | 0.207075i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4674 | 0.846408 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.37228 | + | 3.66648i | −0.319930 | + | 0.159112i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 35.0458i | − | 1.51800i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.63325i | 0.286780i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.62772 | − | 11.1846i | −0.113394 | − | 0.482651i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.48913 | + | 0.792287i | 0.236433 | + | 0.0341262i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6277 | 0.800868 | 0.400434 | − | 0.916326i | \(-0.368859\pi\) | ||||
0.400434 | + | 0.916326i | \(0.368859\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.37228 | + | 31.3793i | 0.316375 | + | 1.34661i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.116844 | 0.00500505 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.9783 | −1.83762 | −0.918809 | − | 0.394703i | \(-0.870847\pi\) | ||||
−0.918809 | + | 0.394703i | \(0.870847\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.25544 | + | 18.6101i | 0.395012 | + | 0.794261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.7446 | 0.628139 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.74456 | + | 5.84096i | −0.286808 | + | 0.248383i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.00000 | + | 1.87953i | −0.339581 | + | 0.0797815i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 30.8820i | − | 1.30851i | −0.756274 | − | 0.654255i | \(-0.772982\pi\) | ||
0.756274 | − | 0.654255i | \(-0.227018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.3947i | 1.66622i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.430703 | + | 1.83324i | 0.0181843 | + | 0.0773995i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.48913 | −0.231339 | −0.115670 | − | 0.993288i | \(-0.536901\pi\) | ||||
−0.115670 | + | 0.993288i | \(0.536901\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10.0974i | − | 0.424799i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.56930 | − | 23.7600i | −0.0659043 | − | 0.997826i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.6873i | 0.448033i | 0.974585 | + | 0.224017i | \(0.0719170\pi\) | ||||
−0.974585 | + | 0.224017i | \(0.928083\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.19702 | + | 26.3769i | 0.258884 | + | 1.10191i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.87953i | 0.0783817i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 12.7692i | − | 0.531587i | −0.964030 | − | 0.265794i | \(-0.914366\pi\) | ||
0.964030 | − | 0.265794i | \(-0.0856340\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −37.4891 | + | 8.80773i | −1.55799 | + | 0.366037i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9783 | + | 9.50744i | −0.455455 | + | 0.394435i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.74456 | −0.279331 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.80298 | + | 15.6896i | 0.322614 | + | 0.648687i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.48913 | 0.226560 | 0.113280 | − | 0.993563i | \(-0.463864\pi\) | ||||
0.113280 | + | 0.993563i | \(0.463864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.86141 | − | 37.7176i | −0.364510 | − | 1.55149i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.37228 | −0.0563528 | −0.0281764 | − | 0.999603i | \(-0.508970\pi\) | ||||
−0.0281764 | + | 0.999603i | \(0.508970\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.74456 | + | 2.37686i | −0.112516 | + | 0.0974418i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.13859 | + | 21.8719i | 0.210309 | + | 0.895155i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.78695i | − | 0.0730129i | −0.999333 | − | 0.0365065i | \(-0.988377\pi\) | ||
0.999333 | − | 0.0365065i | \(-0.0116230\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.17448i | 0.0886989i | 0.999016 | + | 0.0443495i | \(0.0141215\pi\) | ||||
−0.999016 | + | 0.0443495i | \(0.985878\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.1168 | − | 9.01011i | 0.737775 | − | 0.366920i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3723 | 0.421693 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 20.9870i | − | 0.851836i | −0.904762 | − | 0.425918i | \(-0.859951\pi\) | ||
0.904762 | − | 0.425918i | \(-0.140049\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.8030 | + | 11.4333i | 0.640369 | + | 0.463299i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 43.0612i | 1.74207i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.51087 | −0.182193 | −0.0910963 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910963 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.1168 | − | 2.37686i | 0.407951 | − | 0.0958443i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 37.8102i | − | 1.52218i | −0.648646 | − | 0.761090i | \(-0.724665\pi\) | ||
0.648646 | − | 0.761090i | \(-0.275335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.28962i | 0.0518342i | 0.999664 | + | 0.0259171i | \(0.00825060\pi\) | ||||
−0.999664 | + | 0.0259171i | \(0.991749\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.23369 | − | 7.51811i | −0.250149 | − | 0.301691i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.51087 | − | 5.63858i | 0.260853 | − | 0.225905i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.62772 | − | 1.08724i | 0.184813 | − | 0.0434202i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.51087 | −0.259606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.88316 | 0.234205 | 0.117102 | − | 0.993120i | \(-0.462639\pi\) | ||||
0.117102 | + | 0.993120i | \(0.462639\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.3139 | − | 2.42315i | 0.409939 | − | 0.0963115i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.7446 | −0.426385 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 40.4674 | + | 5.84096i | 1.60338 | + | 0.231427i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.1168 | + | 36.4280i | 0.716691 | + | 1.44107i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.7021i | 1.17316i | 0.809890 | + | 0.586582i | \(0.199527\pi\) | ||||
−0.809890 | + | 0.586582i | \(0.800473\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 39.5971i | − | 1.56156i | −0.624807 | − | 0.780779i | \(-0.714822\pi\) | ||
0.624807 | − | 0.780779i | \(-0.285178\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.3723 | + | 2.67181i | −0.447783 | + | 0.105203i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.17448i | − | 0.0853559i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.8614 | + | 9.30506i | 0.504078 | + | 0.364694i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 33.0564i | − | 1.29360i | −0.762660 | − | 0.646799i | \(-0.776107\pi\) | ||
0.762660 | − | 0.646799i | \(-0.223893\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.4891 | 0.683357 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.25544 | + | 18.6101i | 0.361089 | + | 0.726050i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 20.3971i | − | 0.794558i | −0.917698 | − | 0.397279i | \(-0.869955\pi\) | ||
0.917698 | − | 0.397279i | \(-0.130045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.92820i | − | 0.269476i | −0.990881 | − | 0.134738i | \(-0.956981\pi\) | ||
0.990881 | − | 0.134738i | \(-0.0430193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.17527 | + | 13.5152i | 0.123317 | + | 0.524886i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.00000 | + | 6.92820i | 0.232670 | + | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | 0.309761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.31386 | + | 35.3870i | 0.321432 | + | 1.36814i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.48913 | −0.211905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.2337 | 0.857046 | 0.428523 | − | 0.903531i | \(-0.359034\pi\) | ||||
0.428523 | + | 0.903531i | \(0.359034\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | + | 3.31662i | −0.153960 | + | 0.127657i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6060 | 0.830385 | 0.415192 | − | 0.909734i | \(-0.363714\pi\) | ||||
0.415192 | + | 0.909734i | \(0.363714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.88316 | − | 2.17448i | −0.0722689 | − | 0.0834489i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.3139 | + | 6.18220i | −1.00835 | + | 0.236903i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 51.7764i | − | 1.98117i | −0.136906 | − | 0.990584i | \(-0.543716\pi\) | ||
0.136906 | − | 0.990584i | \(-0.456284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2665i | 0.506887i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.88316 | + | 8.01544i | 0.0718469 | + | 0.305808i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −49.7228 | −1.89429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.5099i | 1.46498i | 0.680775 | + | 0.732492i | \(0.261643\pi\) | ||||
−0.680775 | + | 0.732492i | \(0.738357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.80298 | + | 2.42315i | 0.220437 | + | 0.0920478i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.28962i | 0.0489181i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.23369 | 0.311873 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.48913 | − | 6.33830i | −0.0563239 | − | 0.239736i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 45.8256i | − | 1.73081i | −0.501074 | − | 0.865405i | \(-0.667061\pi\) | ||
0.501074 | − | 0.865405i | \(-0.332939\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.4356i | 0.619882i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.4307 | + | 2.92048i | −0.468167 | + | 0.109992i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | − | 10.3923i | 0.451306 | − | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.1168 | 0.905727 | 0.452864 | − | 0.891580i | \(-0.350402\pi\) | ||||
0.452864 | + | 0.891580i | \(0.350402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.05842 | + | 4.50506i | −0.339717 | + | 0.168953i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.51087 | 0.243834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.62772 | −0.173067 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.19702 | + | 26.3769i | 0.231432 | + | 0.985064i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.4674 | −1.50918 | −0.754589 | − | 0.656197i | \(-0.772164\pi\) | ||||
−0.754589 | + | 0.656197i | \(0.772164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.1168 | + | 32.4665i | 1.04713 | + | 1.20912i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.25544 | − | 39.3947i | −0.344213 | − | 1.46511i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 4.25639i | − | 0.158078i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.46410i | − | 0.128476i | −0.997935 | − | 0.0642382i | \(-0.979538\pi\) | ||
0.997935 | − | 0.0642382i | \(-0.0204617\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.25544 | −0.342325 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 10.1899i | − | 0.376373i | −0.982133 | − | 0.188187i | \(-0.939739\pi\) | ||
0.982133 | − | 0.188187i | \(-0.0602610\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.05842 | + | 12.0781i | 0.0390405 | + | 0.445506i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.34363i | 0.196835i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.62772 | 0.317376 | 0.158688 | − | 0.987329i | \(-0.449274\pi\) | ||||
0.158688 | + | 0.987329i | \(0.449274\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.1168 | − | 8.01544i | 1.25331 | − | 0.294455i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.9253i | 1.35466i | 0.735680 | + | 0.677329i | \(0.236863\pi\) | ||||
−0.735680 | + | 0.677329i | \(0.763137\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 10.0974i | − | 0.369938i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.7446 | + | 7.33296i | −0.539475 | + | 0.268299i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.4891 | + | 13.2665i | 0.419804 | + | 0.484747i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.3505 | 0.815582 | 0.407791 | − | 0.913075i | \(-0.366299\pi\) | ||||
0.407791 | + | 0.913075i | \(0.366299\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.4891 | − | 6.92820i | 1.07464 | − | 0.252478i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.37228 | −0.122730 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −54.2337 | −1.97116 | −0.985578 | − | 0.169219i | \(-0.945875\pi\) | ||||
−0.985578 | + | 0.169219i | \(0.945875\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.51087 | − | 0.589907i | 0.0911390 | − | 0.0214123i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.2337 | −0.950970 | −0.475485 | − | 0.879724i | \(-0.657727\pi\) | ||||
−0.475485 | + | 0.879724i | \(0.657727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.233688 | − | 0.202380i | 0.00846007 | − | 0.00732664i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.68614 | + | 1.83324i | −0.133273 | + | 0.0662810i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 16.0309i | − | 0.578842i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.1894i | 0.764108i | 0.924140 | + | 0.382054i | \(0.124783\pi\) | ||||
−0.924140 | + | 0.382054i | \(0.875217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.6060 | + | 9.30506i | −1.42637 | + | 0.335114i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.6277 | −1.67708 | −0.838541 | − | 0.544838i | \(-0.816591\pi\) | ||||
−0.838541 | + | 0.544838i | \(0.816591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.46410i | − | 0.124434i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.7446 | + | 17.6155i | −0.457209 | + | 0.631951i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 20.7846i | − | 0.744686i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7446 | −0.384471 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1168 | + | 17.0256i | 0.504495 | + | 0.608444i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.5253i | 1.65845i | 0.558916 | + | 0.829224i | \(0.311217\pi\) | ||||
−0.558916 | + | 0.829224i | \(0.688783\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.37228 | − | 22.8665i | −0.191258 | − | 0.814070i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.4891 | − | 20.1947i | −0.621842 | − | 0.718041i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.4674 | −1.43704 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.37228 | − | 14.3537i | −0.119602 | − | 0.509075i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.8614 | −1.51823 | −0.759114 | − | 0.650957i | \(-0.774368\pi\) | ||||
−0.759114 | + | 0.650957i | \(0.774368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.1168 | −0.357908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.74456 | − | 4.34896i | 0.308974 | − | 0.153663i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.48913 | −0.193707 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.25544 | + | 3.75906i | 0.114739 | + | 0.132489i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.7446 | − | 3.46410i | 0.519033 | − | 0.121942i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 36.7229i | − | 1.29111i | −0.763714 | − | 0.645555i | \(-0.776626\pi\) | ||
0.763714 | − | 0.645555i | \(-0.223374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.28962i | 0.0452847i | 0.999744 | + | 0.0226423i | \(0.00720790\pi\) | ||||
−0.999744 | + | 0.0226423i | \(0.992792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.00000 | + | 25.5383i | 0.210429 | + | 0.895668i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | −0.280228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.3639i | 0.817398i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 42.7812 | + | 17.8641i | 1.49490 | + | 0.624223i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7745i | 0.410933i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.2337 | 1.68132 | 0.840660 | − | 0.541563i | \(-0.182167\pi\) | ||||
0.840660 | + | 0.541563i | \(0.182167\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.313859 | − | 1.33591i | −0.0109272 | − | 0.0465103i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.3152i | 0.636881i | 0.947943 | + | 0.318441i | \(0.103159\pi\) | ||||
−0.947943 | + | 0.318441i | \(0.896841\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.4665i | 1.12761i | 0.825908 | + | 0.563805i | \(0.190663\pi\) | ||||
−0.825908 | + | 0.563805i | \(0.809337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5109 | − | 2.46943i | 0.364618 | − | 0.0856637i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.37228 | + | 9.50744i | −0.0475467 | + | 0.329413i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.1168 | 0.765385 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.4891 | + | 13.8564i | 0.397122 | + | 0.478947i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.4891 | 1.84665 | 0.923325 | − | 0.384020i | \(-0.125461\pi\) | ||||
0.923325 | + | 0.384020i | \(0.125461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8832 | 0.375281 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.91983 | − | 8.17154i | −0.0661224 | − | 0.281443i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.1168 | −0.726442 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.7446 | − | 17.9653i | 0.712792 | − | 0.617296i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.68614 | − | 15.6896i | −0.126508 | − | 0.538467i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.91754i | 0.305689i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 46.7277i | − | 1.59993i | −0.600049 | − | 0.799963i | \(-0.704852\pi\) | ||
0.600049 | − | 0.799963i | \(-0.295148\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.62772 | + | 9.30506i | 0.158265 | + | 0.318226i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.4674 | −0.767471 | −0.383735 | − | 0.923443i | \(-0.625363\pi\) | ||||
−0.383735 | + | 0.923443i | \(0.625363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 45.4381i | − | 1.55033i | −0.631760 | − | 0.775164i | \(-0.717667\pi\) | ||
0.631760 | − | 0.775164i | \(-0.282333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.1168 | − | 22.2766i | 0.549261 | − | 0.759185i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 28.0078i | − | 0.953395i | −0.879067 | − | 0.476698i | \(-0.841834\pi\) | ||
0.879067 | − | 0.476698i | \(-0.158166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.1168 | 0.547989 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.4891 | − | 5.98844i | 0.865656 | − | 0.203378i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.67181i | − | 0.0906351i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.3947i | 1.33484i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.45245 | − | 2.92048i | −0.0491581 | − | 0.0988433i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.00000 | − | 1.73205i | 0.0676123 | − | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.4674 | 1.02881 | 0.514405 | − | 0.857547i | \(-0.328013\pi\) | ||||
0.514405 | + | 0.857547i | \(0.328013\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47.4090 | − | 11.1383i | 1.59906 | − | 0.375686i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.23369 | −0.0752549 | −0.0376274 | − | 0.999292i | \(-0.511980\pi\) | ||||
−0.0376274 | + | 0.999292i | \(0.511980\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.5109 | −0.892162 | −0.446081 | − | 0.894993i | \(-0.647181\pi\) | ||||
−0.446081 | + | 0.894993i | \(0.647181\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.62772 | − | 1.08724i | 0.155559 | − | 0.0365472i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.4891 | −1.39307 | −0.696534 | − | 0.717524i | \(-0.745276\pi\) | ||||
−0.696534 | + | 0.717524i | \(0.745276\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.4891 | + | 18.6101i | −0.720722 | + | 0.624164i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.68614 | + | 4.30268i | 0.190493 | + | 0.144145i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.5383i | 0.854608i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.63325i | 0.221725i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.5109 | − | 4.34896i | 0.618060 | − | 0.145208i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.7446 | −0.491759 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 11.6819i | − | 0.389181i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.1168 | + | 25.0410i | −0.602891 | + | 0.833312i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18.6101i | − | 0.618622i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.00000 | −0.265636 | −0.132818 | − | 0.991140i | \(-0.542403\pi\) | ||||
−0.132818 | + | 0.991140i | \(0.542403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.1168 | − | 8.01544i | 0.534562 | − | 0.265855i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 23.6588i | − | 0.783851i | −0.919997 | − | 0.391926i | \(-0.871809\pi\) | ||
0.919997 | − | 0.391926i | \(-0.128191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.34896i | − | 0.143930i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.74456 | − | 11.6819i | −0.0907324 | − | 0.386193i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34.9783 | − | 30.2921i | 1.15508 | − | 1.00033i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.3723 | 0.375137 | 0.187568 | − | 0.982252i | \(-0.439939\pi\) | ||||
0.187568 | + | 0.982252i | \(0.439939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.82473 | − | 12.0232i | −0.0930782 | − | 0.396177i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −79.2119 | −2.60729 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.74456 | 0.156000 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.6861 | + | 43.6048i | 0.712266 | + | 1.43217i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.02175 | 0.230376 | 0.115188 | − | 0.993344i | \(-0.463253\pi\) | ||||
0.115188 | + | 0.993344i | \(0.463253\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0000 | + | 3.46410i | 0.786568 | + | 0.113531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.1168 | − | 8.01544i | 1.11694 | − | 0.262414i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.08724i | − | 0.0355566i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 49.9894i | − | 1.63308i | −0.577287 | − | 0.816542i | \(-0.695888\pi\) | ||
0.577287 | − | 0.816542i | \(-0.304112\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.68614 | + | 41.2280i | 0.316095 | + | 1.34542i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.2554 | −0.888502 | −0.444251 | − | 0.895902i | \(-0.646530\pi\) | ||||
−0.444251 | + | 0.895902i | \(0.646530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 11.2772i | − | 0.367235i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.25544 | + | 13.5615i | −0.0733694 | + | 0.441154i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.2025i | 1.56637i | 0.621789 | + | 0.783185i | \(0.286406\pi\) | ||||
−0.621789 | + | 0.783185i | \(0.713594\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.4674 | −1.31363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.37228 | − | 14.3537i | −0.109354 | − | 0.465452i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.8048i | 1.25701i | 0.777805 | + | 0.628506i | \(0.216333\pi\) | ||||
−0.777805 | + | 0.628506i | \(0.783667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 15.6434i | − | 0.506207i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.68614 | + | 1.33591i | −0.183807 | + | 0.0431838i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.9783 | + | 26.5330i | 0.742006 | + | 0.856795i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.86141 | + | 17.8178i | 0.285555 | + | 0.574172i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.2337 | 0.715728 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2337 | 0.779303 | 0.389651 | − | 0.920962i | \(-0.372595\pi\) | ||||
0.389651 | + | 0.920962i | \(0.372595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.88316 | + | 8.01544i | 0.0604957 | + | 0.257493i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.2119 | 1.38674 | 0.693369 | − | 0.720583i | \(-0.256126\pi\) | ||||
0.693369 | + | 0.720583i | \(0.256126\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.23369 | + | 2.57924i | 0.0716087 | + | 0.0826867i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.31386 | − | 9.84868i | −0.0741028 | − | 0.315410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.8048i | 1.24148i | 0.784018 | + | 0.620738i | \(0.213167\pi\) | ||||
−0.784018 | + | 0.620738i | \(0.786833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.57924i | 0.0824329i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.313859 | − | 0.156093i | 0.0100208 | − | 0.00498366i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.1386 | −0.355266 | −0.177633 | − | 0.984097i | \(-0.556844\pi\) | ||||
−0.177633 | + | 0.984097i | \(0.556844\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.3692i | 0.712741i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.8030 | + | 27.3716i | −0.630336 | + | 0.871247i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.6766i | 0.403092i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.51087 | −0.0797606 | −0.0398803 | − | 0.999204i | \(-0.512698\pi\) | ||||
−0.0398803 | + | 0.999204i | \(0.512698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.74456 | + | 1.58457i | −0.214032 | + | 0.0502849i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 12.9715i | − | 0.411226i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 21.8719i | − | 0.692688i | −0.938107 | − | 0.346344i | \(-0.887423\pi\) | ||
0.938107 | − | 0.346344i | \(-0.112577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.9783 | + | 15.7359i | −0.600445 | + | 0.497863i |
(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 | 1680.2.f.g.881.2 | 4 | ||
3.2 | odd | 2 | 1680.2.f.h.881.4 | 4 | |||
4.3 | odd | 2 | 105.2.b.d.41.1 | yes | 4 | ||
7.6 | odd | 2 | 1680.2.f.h.881.3 | 4 | |||
12.11 | even | 2 | 105.2.b.c.41.4 | yes | 4 | ||
20.3 | even | 4 | 525.2.g.d.524.2 | 8 | |||
20.7 | even | 4 | 525.2.g.d.524.7 | 8 | |||
20.19 | odd | 2 | 525.2.b.e.251.4 | 4 | |||
21.20 | even | 2 | inner | 1680.2.f.g.881.1 | 4 | ||
28.3 | even | 6 | 735.2.s.i.656.2 | 4 | |||
28.11 | odd | 6 | 735.2.s.j.656.2 | 4 | |||
28.19 | even | 6 | 735.2.s.h.521.1 | 4 | |||
28.23 | odd | 6 | 735.2.s.g.521.1 | 4 | |||
28.27 | even | 2 | 105.2.b.c.41.1 | ✓ | 4 | ||
60.23 | odd | 4 | 525.2.g.e.524.7 | 8 | |||
60.47 | odd | 4 | 525.2.g.e.524.2 | 8 | |||
60.59 | even | 2 | 525.2.b.g.251.1 | 4 | |||
84.11 | even | 6 | 735.2.s.h.656.1 | 4 | |||
84.23 | even | 6 | 735.2.s.i.521.2 | 4 | |||
84.47 | odd | 6 | 735.2.s.j.521.2 | 4 | |||
84.59 | odd | 6 | 735.2.s.g.656.1 | 4 | |||
84.83 | odd | 2 | 105.2.b.d.41.4 | yes | 4 | ||
140.27 | odd | 4 | 525.2.g.e.524.8 | 8 | |||
140.83 | odd | 4 | 525.2.g.e.524.1 | 8 | |||
140.139 | even | 2 | 525.2.b.g.251.4 | 4 | |||
420.83 | even | 4 | 525.2.g.d.524.8 | 8 | |||
420.167 | even | 4 | 525.2.g.d.524.1 | 8 | |||
420.419 | odd | 2 | 525.2.b.e.251.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.b.c.41.1 | ✓ | 4 | 28.27 | even | 2 | ||
105.2.b.c.41.4 | yes | 4 | 12.11 | even | 2 | ||
105.2.b.d.41.1 | yes | 4 | 4.3 | odd | 2 | ||
105.2.b.d.41.4 | yes | 4 | 84.83 | odd | 2 | ||
525.2.b.e.251.1 | 4 | 420.419 | odd | 2 | |||
525.2.b.e.251.4 | 4 | 20.19 | odd | 2 | |||
525.2.b.g.251.1 | 4 | 60.59 | even | 2 | |||
525.2.b.g.251.4 | 4 | 140.139 | even | 2 | |||
525.2.g.d.524.1 | 8 | 420.167 | even | 4 | |||
525.2.g.d.524.2 | 8 | 20.3 | even | 4 | |||
525.2.g.d.524.7 | 8 | 20.7 | even | 4 | |||
525.2.g.d.524.8 | 8 | 420.83 | even | 4 | |||
525.2.g.e.524.1 | 8 | 140.83 | odd | 4 | |||
525.2.g.e.524.2 | 8 | 60.47 | odd | 4 | |||
525.2.g.e.524.7 | 8 | 60.23 | odd | 4 | |||
525.2.g.e.524.8 | 8 | 140.27 | odd | 4 | |||
735.2.s.g.521.1 | 4 | 28.23 | odd | 6 | |||
735.2.s.g.656.1 | 4 | 84.59 | odd | 6 | |||
735.2.s.h.521.1 | 4 | 28.19 | even | 6 | |||
735.2.s.h.656.1 | 4 | 84.11 | even | 6 | |||
735.2.s.i.521.2 | 4 | 84.23 | even | 6 | |||
735.2.s.i.656.2 | 4 | 28.3 | even | 6 | |||
735.2.s.j.521.2 | 4 | 84.47 | odd | 6 | |||
735.2.s.j.656.2 | 4 | 28.11 | odd | 6 | |||
1680.2.f.g.881.1 | 4 | 21.20 | even | 2 | inner | ||
1680.2.f.g.881.2 | 4 | 1.1 | even | 1 | trivial | ||
1680.2.f.h.881.3 | 4 | 7.6 | odd | 2 | |||
1680.2.f.h.881.4 | 4 | 3.2 | odd | 2 |