Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
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.bc (of order \(6\), degree \(2\), 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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 751.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.751 |
Dual form | 1950.2.bc.e.901.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | 1.31431 | + | 0.758819i | 0.496764 | + | 0.286807i | 0.727376 | − | 0.686239i | \(-0.240740\pi\) |
−0.230612 | + | 0.973046i | \(0.574073\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.45680 | + | 2.57313i | −1.34377 | + | 0.775829i | −0.987359 | − | 0.158499i | \(-0.949335\pi\) |
−0.356415 | + | 0.934328i | \(0.616001\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.08725 | − | 1.86250i | 0.856248 | − | 0.516565i | ||||
\(14\) | −1.51764 | −0.405606 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.39778 | + | 4.15307i | −0.581546 | + | 1.00727i | 0.413750 | + | 0.910391i | \(0.364219\pi\) |
−0.995296 | + | 0.0968774i | \(0.969115\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −1.39778 | − | 0.807007i | −0.320672 | − | 0.185140i | 0.331020 | − | 0.943624i | \(-0.392607\pi\) |
−0.651692 | + | 0.758484i | \(0.725941\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.51764i | − | 0.331176i | ||||||
\(22\) | 2.57313 | − | 4.45680i | 0.548594 | − | 0.950192i | ||||
\(23\) | 2.72122 | + | 4.71329i | 0.567414 | + | 0.982789i | 0.996821 | + | 0.0796783i | \(0.0253893\pi\) |
−0.429407 | + | 0.903111i | \(0.641277\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.74238 | + | 3.15660i | −0.341709 | + | 0.619060i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.31431 | − | 0.758819i | 0.248382 | − | 0.143403i | ||||
\(29\) | −4.93684 | − | 8.55085i | −0.916747 | − | 1.58785i | −0.804323 | − | 0.594193i | \(-0.797472\pi\) |
−0.112425 | − | 0.993660i | \(-0.535862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.88072i | − | 1.77463i | −0.461164 | − | 0.887315i | \(-0.652568\pi\) | ||
0.461164 | − | 0.887315i | \(-0.347432\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 4.45680 | + | 2.57313i | 0.775829 | + | 0.447925i | ||||
\(34\) | − | 4.79555i | − | 0.822431i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −7.56873 | + | 4.36981i | −1.24429 | + | 0.718392i | −0.969965 | − | 0.243245i | \(-0.921788\pi\) |
−0.274326 | + | 0.961637i | \(0.588455\pi\) | |||||||
\(38\) | 1.61401 | 0.261828 | ||||||||
\(39\) | −3.15660 | − | 1.74238i | −0.505460 | − | 0.279005i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.10418 | − | 0.637499i | 0.172444 | − | 0.0995606i | −0.411294 | − | 0.911503i | \(-0.634923\pi\) |
0.583738 | + | 0.811942i | \(0.301590\pi\) | |||||||
\(42\) | 0.758819 | + | 1.31431i | 0.117088 | + | 0.202803i | ||||
\(43\) | 1.18336 | − | 2.04965i | 0.180461 | − | 0.312568i | −0.761576 | − | 0.648075i | \(-0.775574\pi\) |
0.942038 | + | 0.335507i | \(0.108908\pi\) | |||||||
\(44\) | 5.14626i | 0.775829i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.71329 | − | 2.72122i | −0.694937 | − | 0.401222i | ||||
\(47\) | − | 6.84909i | − | 0.999043i | −0.866302 | − | 0.499521i | \(-0.833509\pi\) | ||
0.866302 | − | 0.499521i | \(-0.166491\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −2.34839 | − | 4.06753i | −0.335484 | − | 0.581075i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.79555 | 0.671512 | ||||||||
\(52\) | −0.0693504 | − | 3.60488i | −0.00961716 | − | 0.499908i | ||||
\(53\) | −0.881964 | −0.121147 | −0.0605735 | − | 0.998164i | \(-0.519293\pi\) | ||||
−0.0605735 | + | 0.998164i | \(0.519293\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.758819 | + | 1.31431i | −0.101401 | + | 0.175632i | ||||
\(57\) | 1.61401i | 0.213781i | ||||||||
\(58\) | 8.55085 | + | 4.93684i | 1.12278 | + | 0.648238i | ||||
\(59\) | −8.04354 | − | 4.64394i | −1.04718 | − | 0.604590i | −0.125322 | − | 0.992116i | \(-0.539996\pi\) |
−0.921859 | + | 0.387526i | \(0.873330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24056 | + | 10.8090i | −0.799022 | + | 1.38395i | 0.121232 | + | 0.992624i | \(0.461315\pi\) |
−0.920254 | + | 0.391322i | \(0.872018\pi\) | |||||||
\(62\) | 4.94036 | + | 8.55695i | 0.627426 | + | 1.08673i | ||||
\(63\) | −1.31431 | + | 0.758819i | −0.165588 | + | 0.0956022i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.14626 | −0.633461 | ||||||||
\(67\) | 9.98930 | − | 5.76733i | 1.22039 | − | 0.704591i | 0.255387 | − | 0.966839i | \(-0.417797\pi\) |
0.965001 | + | 0.262248i | \(0.0844638\pi\) | |||||||
\(68\) | 2.39778 | + | 4.15307i | 0.290773 | + | 0.503634i | ||||
\(69\) | 2.72122 | − | 4.71329i | 0.327596 | − | 0.567414i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.7133 | + | 7.91737i | 1.62747 | + | 0.939619i | 0.984845 | + | 0.173437i | \(0.0554874\pi\) |
0.642623 | + | 0.766182i | \(0.277846\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | − | 4.39355i | − | 0.514226i | −0.966381 | − | 0.257113i | \(-0.917229\pi\) | ||
0.966381 | − | 0.257113i | \(-0.0827713\pi\) | |||||||
\(74\) | 4.36981 | − | 7.56873i | 0.507980 | − | 0.879847i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.39778 | + | 0.807007i | −0.160336 | + | 0.0925701i | ||||
\(77\) | −7.81017 | −0.890051 | ||||||||
\(78\) | 3.60488 | − | 0.0693504i | 0.408173 | − | 0.00785238i | ||||
\(79\) | −11.0382 | −1.24189 | −0.620947 | − | 0.783853i | \(-0.713252\pi\) | ||||
−0.620947 | + | 0.783853i | \(0.713252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.637499 | + | 1.10418i | −0.0704000 | + | 0.121936i | ||||
\(83\) | − | 0.979336i | − | 0.107496i | −0.998555 | − | 0.0537480i | \(-0.982883\pi\) | ||
0.998555 | − | 0.0537480i | \(-0.0171168\pi\) | |||||||
\(84\) | −1.31431 | − | 0.758819i | −0.143403 | − | 0.0827939i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.36673i | 0.255211i | ||||||||
\(87\) | −4.93684 | + | 8.55085i | −0.529284 | + | 0.916747i | ||||
\(88\) | −2.57313 | − | 4.45680i | −0.274297 | − | 0.475096i | ||||
\(89\) | −3.54146 | + | 2.04466i | −0.375394 | + | 0.216734i | −0.675812 | − | 0.737074i | \(-0.736207\pi\) |
0.300418 | + | 0.953808i | \(0.402874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.47091 | − | 0.105249i | 0.573507 | − | 0.0110331i | ||||
\(92\) | 5.44244 | 0.567414 | ||||||||
\(93\) | −8.55695 | + | 4.94036i | −0.887315 | + | 0.512291i | ||||
\(94\) | 3.42455 | + | 5.93149i | 0.353215 | + | 0.611786i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −4.95189 | − | 2.85898i | −0.502789 | − | 0.290285i | 0.227076 | − | 0.973877i | \(-0.427083\pi\) |
−0.729864 | + | 0.683592i | \(0.760417\pi\) | |||||||
\(98\) | 4.06753 | + | 2.34839i | 0.410882 | + | 0.237223i | ||||
\(99\) | − | 5.14626i | − | 0.517219i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.92687 | − | 6.80153i | −0.390738 | − | 0.676778i | 0.601809 | − | 0.798640i | \(-0.294447\pi\) |
−0.992547 | + | 0.121862i | \(0.961113\pi\) | |||||||
\(102\) | −4.15307 | + | 2.39778i | −0.411215 | + | 0.237415i | ||||
\(103\) | −3.17449 | −0.312792 | −0.156396 | − | 0.987694i | \(-0.549988\pi\) | ||||
−0.156396 | + | 0.987694i | \(0.549988\pi\) | |||||||
\(104\) | 1.86250 | + | 3.08725i | 0.182633 | + | 0.302729i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.763803 | − | 0.440982i | 0.0741871 | − | 0.0428319i | ||||
\(107\) | −6.87662 | − | 11.9106i | −0.664787 | − | 1.15145i | −0.979343 | − | 0.202207i | \(-0.935189\pi\) |
0.314555 | − | 0.949239i | \(-0.398145\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 16.7895i | 1.60814i | 0.594533 | + | 0.804071i | \(0.297337\pi\) | ||||
−0.594533 | + | 0.804071i | \(0.702663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.56873 | + | 4.36981i | 0.718392 | + | 0.414764i | ||||
\(112\) | − | 1.51764i | − | 0.143403i | ||||||
\(113\) | −4.82843 | + | 8.36308i | −0.454220 | + | 0.786732i | −0.998643 | − | 0.0520785i | \(-0.983415\pi\) |
0.544423 | + | 0.838811i | \(0.316749\pi\) | |||||||
\(114\) | −0.807007 | − | 1.39778i | −0.0755831 | − | 0.130914i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.87367 | −0.916747 | ||||||||
\(117\) | 0.0693504 | + | 3.60488i | 0.00641144 | + | 0.333272i | ||||
\(118\) | 9.28788 | 0.855019 | ||||||||
\(119\) | −6.30286 | + | 3.63896i | −0.577782 | + | 0.333583i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.74202 | − | 13.4096i | 0.703820 | − | 1.21905i | ||||
\(122\) | − | 12.4811i | − | 1.12999i | ||||||
\(123\) | −1.10418 | − | 0.637499i | −0.0995606 | − | 0.0574813i | ||||
\(124\) | −8.55695 | − | 4.94036i | −0.768437 | − | 0.443657i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.758819 | − | 1.31431i | 0.0676010 | − | 0.117088i | ||||
\(127\) | −5.99536 | − | 10.3843i | −0.532002 | − | 0.921454i | −0.999302 | − | 0.0373555i | \(-0.988107\pi\) |
0.467300 | − | 0.884099i | \(-0.345227\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −2.36673 | −0.208379 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.3524 | −1.77820 | −0.889098 | − | 0.457717i | \(-0.848667\pi\) | ||||
−0.889098 | + | 0.457717i | \(0.848667\pi\) | |||||||
\(132\) | 4.45680 | − | 2.57313i | 0.387914 | − | 0.223962i | ||||
\(133\) | −1.22474 | − | 2.12132i | −0.106199 | − | 0.183942i | ||||
\(134\) | −5.76733 | + | 9.98930i | −0.498221 | + | 0.862944i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.15307 | − | 2.39778i | −0.356123 | − | 0.205608i | ||||
\(137\) | 6.82684 | + | 3.94148i | 0.583257 | + | 0.336743i | 0.762427 | − | 0.647075i | \(-0.224008\pi\) |
−0.179170 | + | 0.983818i | \(0.557341\pi\) | |||||||
\(138\) | 5.44244i | 0.463291i | ||||||||
\(139\) | −2.05852 | + | 3.56546i | −0.174601 | + | 0.302419i | −0.940023 | − | 0.341110i | \(-0.889197\pi\) |
0.765422 | + | 0.643529i | \(0.222530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.93149 | + | 3.42455i | −0.499521 | + | 0.288399i | ||||
\(142\) | −15.8347 | −1.32882 | ||||||||
\(143\) | −8.96676 | + | 16.2447i | −0.749838 | + | 1.35845i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.19677 | + | 3.80493i | 0.181806 | + | 0.314898i | ||||
\(147\) | −2.34839 | + | 4.06753i | −0.193692 | + | 0.335484i | ||||
\(148\) | 8.73961i | 0.718392i | ||||||||
\(149\) | −8.00644 | − | 4.62252i | −0.655913 | − | 0.378692i | 0.134805 | − | 0.990872i | \(-0.456959\pi\) |
−0.790718 | + | 0.612180i | \(0.790293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.1479i | − | 1.39548i | −0.716351 | − | 0.697740i | \(-0.754189\pi\) | ||
0.716351 | − | 0.697740i | \(-0.245811\pi\) | |||||||
\(152\) | 0.807007 | − | 1.39778i | 0.0654569 | − | 0.113375i | ||||
\(153\) | −2.39778 | − | 4.15307i | −0.193849 | − | 0.335756i | ||||
\(154\) | 6.76380 | − | 3.90508i | 0.545043 | − | 0.314681i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.08725 | + | 1.86250i | −0.247178 | + | 0.149119i | ||||
\(157\) | −18.2791 | −1.45883 | −0.729415 | − | 0.684072i | \(-0.760207\pi\) | ||||
−0.729415 | + | 0.684072i | \(0.760207\pi\) | |||||||
\(158\) | 9.55936 | − | 5.51910i | 0.760502 | − | 0.439076i | ||||
\(159\) | 0.440982 | + | 0.763803i | 0.0349721 | + | 0.0605735i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.25966i | 0.650952i | ||||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | 1.47555 | + | 0.851911i | 0.115574 | + | 0.0667269i | 0.556673 | − | 0.830732i | \(-0.312078\pi\) |
−0.441098 | + | 0.897459i | \(0.645411\pi\) | |||||||
\(164\) | − | 1.27500i | − | 0.0995606i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.489668 | + | 0.848130i | 0.0380056 | + | 0.0658276i | ||||
\(167\) | −4.61967 | + | 2.66717i | −0.357481 | + | 0.206392i | −0.667975 | − | 0.744184i | \(-0.732839\pi\) |
0.310494 | + | 0.950575i | \(0.399505\pi\) | |||||||
\(168\) | 1.51764 | 0.117088 | ||||||||
\(169\) | 6.06218 | − | 11.5000i | 0.466321 | − | 0.884615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.39778 | − | 0.807007i | 0.106891 | − | 0.0617134i | ||||
\(172\) | −1.18336 | − | 2.04965i | −0.0902307 | − | 0.156284i | ||||
\(173\) | −8.83839 | + | 15.3085i | −0.671971 | + | 1.16389i | 0.305374 | + | 0.952233i | \(0.401219\pi\) |
−0.977344 | + | 0.211655i | \(0.932115\pi\) | |||||||
\(174\) | − | 9.87367i | − | 0.748521i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.45680 | + | 2.57313i | 0.335944 | + | 0.193957i | ||||
\(177\) | 9.28788i | 0.698120i | ||||||||
\(178\) | 2.04466 | − | 3.54146i | 0.153254 | − | 0.265444i | ||||
\(179\) | −10.7700 | − | 18.6542i | −0.804987 | − | 1.39428i | −0.916300 | − | 0.400493i | \(-0.868839\pi\) |
0.111313 | − | 0.993785i | \(-0.464494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.08328 | 0.303507 | 0.151754 | − | 0.988418i | \(-0.451508\pi\) | ||||
0.151754 | + | 0.988418i | \(0.451508\pi\) | |||||||
\(182\) | −4.68532 | + | 2.82660i | −0.347299 | + | 0.209522i | ||||
\(183\) | 12.4811 | 0.922631 | ||||||||
\(184\) | −4.71329 | + | 2.72122i | −0.347469 | + | 0.200611i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.94036 | − | 8.55695i | 0.362245 | − | 0.627426i | ||||
\(187\) | − | 24.6792i | − | 1.80472i | ||||||
\(188\) | −5.93149 | − | 3.42455i | −0.432598 | − | 0.249761i | ||||
\(189\) | 1.31431 | + | 0.758819i | 0.0956022 | + | 0.0551960i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.47822 | − | 11.2206i | 0.468747 | − | 0.811894i | −0.530615 | − | 0.847613i | \(-0.678039\pi\) |
0.999362 | + | 0.0357192i | \(0.0113722\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 7.49706 | − | 4.32843i | 0.539650 | − | 0.311567i | −0.205287 | − | 0.978702i | \(-0.565813\pi\) |
0.744937 | + | 0.667135i | \(0.232479\pi\) | |||||||
\(194\) | 5.71795 | 0.410525 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.69677 | −0.335484 | ||||||||
\(197\) | 3.76574 | − | 2.17415i | 0.268298 | − | 0.154902i | −0.359816 | − | 0.933023i | \(-0.617160\pi\) |
0.628114 | + | 0.778121i | \(0.283827\pi\) | |||||||
\(198\) | 2.57313 | + | 4.45680i | 0.182865 | + | 0.316731i | ||||
\(199\) | −3.73351 | + | 6.46663i | −0.264662 | + | 0.458407i | −0.967475 | − | 0.252967i | \(-0.918594\pi\) |
0.702813 | + | 0.711374i | \(0.251927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.98930 | − | 5.76733i | −0.704591 | − | 0.406796i | ||||
\(202\) | 6.80153 | + | 3.92687i | 0.478554 | + | 0.276293i | ||||
\(203\) | − | 14.9847i | − | 1.05172i | ||||||
\(204\) | 2.39778 | − | 4.15307i | 0.167878 | − | 0.290773i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.74919 | − | 1.58725i | 0.191545 | − | 0.110589i | ||||
\(207\) | −5.44244 | −0.378276 | ||||||||
\(208\) | −3.15660 | − | 1.74238i | −0.218871 | − | 0.120813i | ||||
\(209\) | 8.30614 | 0.574548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.74384 | − | 11.6807i | −0.464265 | − | 0.804131i | 0.534903 | − | 0.844914i | \(-0.320348\pi\) |
−0.999168 | + | 0.0407826i | \(0.987015\pi\) | |||||||
\(212\) | −0.440982 | + | 0.763803i | −0.0302868 | + | 0.0524582i | ||||
\(213\) | − | 15.8347i | − | 1.08498i | ||||||
\(214\) | 11.9106 | + | 6.87662i | 0.814195 | + | 0.470076i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 7.49768 | − | 12.9864i | 0.508976 | − | 0.881571i | ||||
\(218\) | −8.39475 | − | 14.5401i | −0.568564 | − | 0.984782i | ||||
\(219\) | −3.80493 | + | 2.19677i | −0.257113 | + | 0.148444i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.332573 | + | 17.2874i | 0.0223713 | + | 1.16288i | ||||
\(222\) | −8.73961 | −0.586565 | ||||||||
\(223\) | −6.08030 | + | 3.51047i | −0.407167 | + | 0.235078i | −0.689572 | − | 0.724217i | \(-0.742201\pi\) |
0.282405 | + | 0.959295i | \(0.408868\pi\) | |||||||
\(224\) | 0.758819 | + | 1.31431i | 0.0507007 | + | 0.0878162i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 9.65685i | − | 0.642364i | ||||||
\(227\) | −7.44370 | − | 4.29762i | −0.494055 | − | 0.285243i | 0.232200 | − | 0.972668i | \(-0.425408\pi\) |
−0.726255 | + | 0.687425i | \(0.758741\pi\) | |||||||
\(228\) | 1.39778 | + | 0.807007i | 0.0925701 | + | 0.0534454i | ||||
\(229\) | 16.4086i | 1.08431i | 0.840279 | + | 0.542155i | \(0.182391\pi\) | ||||
−0.840279 | + | 0.542155i | \(0.817609\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.90508 | + | 6.76380i | 0.256936 | + | 0.445026i | ||||
\(232\) | 8.55085 | − | 4.93684i | 0.561391 | − | 0.324119i | ||||
\(233\) | −6.94230 | −0.454805 | −0.227403 | − | 0.973801i | \(-0.573023\pi\) | ||||
−0.227403 | + | 0.973801i | \(0.573023\pi\) | |||||||
\(234\) | −1.86250 | − | 3.08725i | −0.121756 | − | 0.201820i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.04354 | + | 4.64394i | −0.523590 | + | 0.302295i | ||||
\(237\) | 5.51910 | + | 9.55936i | 0.358504 | + | 0.620947i | ||||
\(238\) | 3.63896 | − | 6.30286i | 0.235879 | − | 0.408554i | ||||
\(239\) | 18.3056i | 1.18409i | 0.805904 | + | 0.592046i | \(0.201680\pi\) | ||||
−0.805904 | + | 0.592046i | \(0.798320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4906 | + | 7.21147i | 0.804592 | + | 0.464532i | 0.845074 | − | 0.534649i | \(-0.179556\pi\) |
−0.0404822 | + | 0.999180i | \(0.512889\pi\) | |||||||
\(242\) | 15.4840i | 0.995352i | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 6.24056 | + | 10.8090i | 0.399511 | + | 0.691973i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.27500 | 0.0812909 | ||||||||
\(247\) | −5.81834 | + | 0.111932i | −0.370212 | + | 0.00712209i | ||||
\(248\) | 9.88072 | 0.627426 | ||||||||
\(249\) | −0.848130 | + | 0.489668i | −0.0537480 | + | 0.0310314i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.88222 | + | 6.72420i | −0.245044 | + | 0.424428i | −0.962144 | − | 0.272542i | \(-0.912136\pi\) |
0.717100 | + | 0.696970i | \(0.245469\pi\) | |||||||
\(252\) | 1.51764i | 0.0956022i | ||||||||
\(253\) | −24.2558 | − | 14.0041i | −1.52495 | − | 0.880432i | ||||
\(254\) | 10.3843 | + | 5.99536i | 0.651566 | + | 0.376182i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 9.69031 | + | 16.7841i | 0.604465 | + | 1.04696i | 0.992136 | + | 0.125166i | \(0.0399463\pi\) |
−0.387671 | + | 0.921798i | \(0.626720\pi\) | |||||||
\(258\) | 2.04965 | − | 1.18336i | 0.127606 | − | 0.0736731i | ||||
\(259\) | −13.2636 | −0.824158 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.87367 | 0.611165 | ||||||||
\(262\) | 17.6257 | − | 10.1762i | 1.08892 | − | 0.628687i | ||||
\(263\) | 0.946961 | + | 1.64019i | 0.0583921 | + | 0.101138i | 0.893744 | − | 0.448578i | \(-0.148069\pi\) |
−0.835352 | + | 0.549716i | \(0.814736\pi\) | |||||||
\(264\) | −2.57313 | + | 4.45680i | −0.158365 | + | 0.274297i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.12132 | + | 1.22474i | 0.130066 | + | 0.0750939i | ||||
\(267\) | 3.54146 | + | 2.04466i | 0.216734 | + | 0.125131i | ||||
\(268\) | − | 11.5347i | − | 0.704591i | ||||||
\(269\) | 2.30104 | − | 3.98551i | 0.140297 | − | 0.243001i | −0.787312 | − | 0.616555i | \(-0.788528\pi\) |
0.927608 | + | 0.373554i | \(0.121861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.22596 | − | 4.17191i | 0.438946 | − | 0.253426i | −0.264204 | − | 0.964467i | \(-0.585109\pi\) |
0.703150 | + | 0.711041i | \(0.251776\pi\) | |||||||
\(272\) | 4.79555 | 0.290773 | ||||||||
\(273\) | −2.82660 | − | 4.68532i | −0.171074 | − | 0.283569i | ||||
\(274\) | −7.88296 | −0.476227 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.72122 | − | 4.71329i | −0.163798 | − | 0.283707i | ||||
\(277\) | 11.1189 | − | 19.2585i | 0.668068 | − | 1.15713i | −0.310375 | − | 0.950614i | \(-0.600455\pi\) |
0.978444 | − | 0.206514i | \(-0.0662120\pi\) | |||||||
\(278\) | − | 4.11704i | − | 0.246924i | ||||||
\(279\) | 8.55695 | + | 4.94036i | 0.512291 | + | 0.295772i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.0961i | − | 1.19883i | −0.800437 | − | 0.599417i | \(-0.795399\pi\) | ||
0.800437 | − | 0.599417i | \(-0.204601\pi\) | |||||||
\(282\) | 3.42455 | − | 5.93149i | 0.203929 | − | 0.353215i | ||||
\(283\) | −0.359921 | − | 0.623402i | −0.0213951 | − | 0.0370574i | 0.855130 | − | 0.518414i | \(-0.173477\pi\) |
−0.876525 | + | 0.481357i | \(0.840144\pi\) | |||||||
\(284\) | 13.7133 | − | 7.91737i | 0.813734 | − | 0.469810i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.356895 | − | 18.5517i | −0.0211037 | − | 1.09698i | ||||
\(287\) | 1.93498 | 0.114219 | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −2.99867 | − | 5.19386i | −0.176393 | − | 0.305521i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.71795i | 0.335192i | ||||||||
\(292\) | −3.80493 | − | 2.19677i | −0.222666 | − | 0.128557i | ||||
\(293\) | 11.4556 | + | 6.61389i | 0.669243 | + | 0.386388i | 0.795790 | − | 0.605573i | \(-0.207056\pi\) |
−0.126547 | + | 0.991961i | \(0.540389\pi\) | |||||||
\(294\) | − | 4.69677i | − | 0.273921i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.36981 | − | 7.56873i | −0.253990 | − | 0.439923i | ||||
\(297\) | −4.45680 | + | 2.57313i | −0.258610 | + | 0.149308i | ||||
\(298\) | 9.24504 | 0.535551 | ||||||||
\(299\) | 17.1796 | + | 9.48282i | 0.993521 | + | 0.548405i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.11062 | − | 1.79592i | 0.179293 | − | 0.103515i | ||||
\(302\) | 8.57397 | + | 14.8506i | 0.493377 | + | 0.854553i | ||||
\(303\) | −3.92687 | + | 6.80153i | −0.225593 | + | 0.390738i | ||||
\(304\) | 1.61401i | 0.0925701i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.15307 | + | 2.39778i | 0.237415 | + | 0.137072i | ||||
\(307\) | − | 7.85174i | − | 0.448123i | −0.974575 | − | 0.224061i | \(-0.928068\pi\) | ||
0.974575 | − | 0.224061i | \(-0.0719316\pi\) | |||||||
\(308\) | −3.90508 | + | 6.76380i | −0.222513 | + | 0.385403i | ||||
\(309\) | 1.58725 | + | 2.74919i | 0.0902953 | + | 0.156396i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7708 | −0.894278 | −0.447139 | − | 0.894465i | \(-0.647557\pi\) | ||||
−0.447139 | + | 0.894465i | \(0.647557\pi\) | |||||||
\(312\) | 1.74238 | − | 3.15660i | 0.0986430 | − | 0.178707i | ||||
\(313\) | −21.0613 | −1.19045 | −0.595227 | − | 0.803558i | \(-0.702938\pi\) | ||||
−0.595227 | + | 0.803558i | \(0.702938\pi\) | |||||||
\(314\) | 15.8301 | − | 9.13954i | 0.893347 | − | 0.515774i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.51910 | + | 9.55936i | −0.310474 | + | 0.537756i | ||||
\(317\) | 26.4141i | 1.48357i | 0.670640 | + | 0.741783i | \(0.266019\pi\) | ||||
−0.670640 | + | 0.741783i | \(0.733981\pi\) | |||||||
\(318\) | −0.763803 | − | 0.440982i | −0.0428319 | − | 0.0247290i | ||||
\(319\) | 44.0049 | + | 25.4063i | 2.46380 | + | 1.42248i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.87662 | + | 11.9106i | −0.383815 | + | 0.664787i | ||||
\(322\) | −4.12983 | − | 7.15307i | −0.230146 | − | 0.398625i | ||||
\(323\) | 6.70312 | − | 3.87005i | 0.372972 | − | 0.215335i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.70382 | −0.0943660 | ||||||||
\(327\) | 14.5401 | − | 8.39475i | 0.804071 | − | 0.464231i | ||||
\(328\) | 0.637499 | + | 1.10418i | 0.0352000 | + | 0.0609681i | ||||
\(329\) | 5.19722 | − | 9.00185i | 0.286532 | − | 0.496288i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6887 | + | 10.2126i | 0.972260 | + | 0.561335i | 0.899925 | − | 0.436046i | \(-0.143621\pi\) |
0.0723356 | + | 0.997380i | \(0.476955\pi\) | |||||||
\(332\) | −0.848130 | − | 0.489668i | −0.0465472 | − | 0.0268740i | ||||
\(333\) | − | 8.73961i | − | 0.478928i | ||||||
\(334\) | 2.66717 | − | 4.61967i | 0.145941 | − | 0.252777i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.31431 | + | 0.758819i | −0.0717017 | + | 0.0413970i | ||||
\(337\) | 13.1035 | 0.713791 | 0.356895 | − | 0.934144i | \(-0.383835\pi\) | ||||
0.356895 | + | 0.934144i | \(0.383835\pi\) | |||||||
\(338\) | 0.500000 | + | 12.9904i | 0.0271964 | + | 0.706584i | ||||
\(339\) | 9.65685 | 0.524488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.4244 | + | 44.0363i | 1.37681 | + | 2.38470i | ||||
\(342\) | −0.807007 | + | 1.39778i | −0.0436380 | + | 0.0755831i | ||||
\(343\) | − | 17.7515i | − | 0.958489i | ||||||
\(344\) | 2.04965 | + | 1.18336i | 0.110510 | + | 0.0638028i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 17.6768i | − | 0.950310i | ||||||
\(347\) | −8.88027 | + | 15.3811i | −0.476718 | + | 0.825700i | −0.999644 | − | 0.0266782i | \(-0.991507\pi\) |
0.522926 | + | 0.852378i | \(0.324840\pi\) | |||||||
\(348\) | 4.93684 | + | 8.55085i | 0.264642 | + | 0.458374i | ||||
\(349\) | 0.103747 | − | 0.0598981i | 0.00555343 | − | 0.00320627i | −0.497221 | − | 0.867624i | \(-0.665646\pi\) |
0.502774 | + | 0.864418i | \(0.332313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.08725 | − | 1.86250i | 0.164785 | − | 0.0994130i | ||||
\(352\) | −5.14626 | −0.274297 | ||||||||
\(353\) | 6.54057 | − | 3.77620i | 0.348119 | − | 0.200987i | −0.315737 | − | 0.948847i | \(-0.602252\pi\) |
0.663857 | + | 0.747860i | \(0.268918\pi\) | |||||||
\(354\) | −4.64394 | − | 8.04354i | −0.246823 | − | 0.427510i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.08933i | 0.216734i | ||||||||
\(357\) | 6.30286 | + | 3.63896i | 0.333583 | + | 0.192594i | ||||
\(358\) | 18.6542 | + | 10.7700i | 0.985903 | + | 0.569212i | ||||
\(359\) | − | 29.9693i | − | 1.58172i | −0.611997 | − | 0.790860i | \(-0.709634\pi\) | ||
0.611997 | − | 0.790860i | \(-0.290366\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.19748 | − | 14.1984i | −0.431446 | − | 0.747287i | ||||
\(362\) | −3.53622 | + | 2.04164i | −0.185860 | + | 0.107306i | ||||
\(363\) | −15.4840 | −0.812701 | ||||||||
\(364\) | 2.64431 | − | 4.79057i | 0.138599 | − | 0.251094i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.8090 | + | 6.24056i | −0.564994 | + | 0.326199i | ||||
\(367\) | 14.4472 | + | 25.0232i | 0.754136 | + | 1.30620i | 0.945802 | + | 0.324742i | \(0.105278\pi\) |
−0.191666 | + | 0.981460i | \(0.561389\pi\) | |||||||
\(368\) | 2.72122 | − | 4.71329i | 0.141853 | − | 0.245697i | ||||
\(369\) | 1.27500i | 0.0663737i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.15918 | − | 0.669251i | −0.0601814 | − | 0.0347458i | ||||
\(372\) | 9.88072i | 0.512291i | ||||||||
\(373\) | −7.35583 | + | 12.7407i | −0.380870 | + | 0.659687i | −0.991187 | − | 0.132471i | \(-0.957709\pi\) |
0.610317 | + | 0.792158i | \(0.291042\pi\) | |||||||
\(374\) | 12.3396 | + | 21.3728i | 0.638065 | + | 1.10516i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.84909 | 0.353215 | ||||||||
\(377\) | −31.1672 | − | 17.2037i | −1.60519 | − | 0.886036i | ||||
\(378\) | −1.51764 | −0.0780589 | ||||||||
\(379\) | −27.1285 | + | 15.6627i | −1.39350 | + | 0.804537i | −0.993701 | − | 0.112067i | \(-0.964253\pi\) |
−0.399798 | + | 0.916603i | \(0.630920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.99536 | + | 10.3843i | −0.307151 | + | 0.532002i | ||||
\(382\) | 12.9564i | 0.662909i | ||||||||
\(383\) | 9.39410 | + | 5.42368i | 0.480016 | + | 0.277137i | 0.720423 | − | 0.693535i | \(-0.243948\pi\) |
−0.240407 | + | 0.970672i | \(0.577281\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.32843 | + | 7.49706i | −0.220311 | + | 0.381590i | ||||
\(387\) | 1.18336 | + | 2.04965i | 0.0601538 | + | 0.104189i | ||||
\(388\) | −4.95189 | + | 2.85898i | −0.251394 | + | 0.145143i | ||||
\(389\) | −18.2977 | −0.927730 | −0.463865 | − | 0.885906i | \(-0.653538\pi\) | ||||
−0.463865 | + | 0.885906i | \(0.653538\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.0995 | −1.31991 | ||||||||
\(392\) | 4.06753 | − | 2.34839i | 0.205441 | − | 0.118611i | ||||
\(393\) | 10.1762 | + | 17.6257i | 0.513321 | + | 0.889098i | ||||
\(394\) | −2.17415 | + | 3.76574i | −0.109532 | + | 0.189715i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.45680 | − | 2.57313i | −0.223962 | − | 0.129305i | ||||
\(397\) | −0.266438 | − | 0.153828i | −0.0133721 | − | 0.00772041i | 0.493299 | − | 0.869860i | \(-0.335791\pi\) |
−0.506671 | + | 0.862139i | \(0.669124\pi\) | |||||||
\(398\) | − | 7.46702i | − | 0.374288i | ||||||
\(399\) | −1.22474 | + | 2.12132i | −0.0613139 | + | 0.106199i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.89266 | − | 1.09273i | 0.0945149 | − | 0.0545682i | −0.451998 | − | 0.892019i | \(-0.649288\pi\) |
0.546512 | + | 0.837451i | \(0.315955\pi\) | |||||||
\(402\) | 11.5347 | 0.575296 | ||||||||
\(403\) | −18.4029 | − | 30.5042i | −0.916711 | − | 1.51952i | ||||
\(404\) | −7.85374 | −0.390738 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.49233 | + | 12.9771i | 0.371838 | + | 0.644042i | ||||
\(407\) | 22.4882 | − | 38.9507i | 1.11470 | − | 1.93071i | ||||
\(408\) | 4.79555i | 0.237415i | ||||||||
\(409\) | 32.6067 | + | 18.8255i | 1.61230 | + | 0.930860i | 0.988836 | + | 0.149006i | \(0.0476073\pi\) |
0.623461 | + | 0.781855i | \(0.285726\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7.88296i | − | 0.388838i | ||||||
\(412\) | −1.58725 | + | 2.74919i | −0.0781980 | + | 0.135443i | ||||
\(413\) | −7.04782 | − | 12.2072i | −0.346801 | − | 0.600676i | ||||
\(414\) | 4.71329 | − | 2.72122i | 0.231646 | − | 0.133741i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.60488 | − | 0.0693504i | 0.176744 | − | 0.00340018i | ||||
\(417\) | 4.11704 | 0.201612 | ||||||||
\(418\) | −7.19333 | + | 4.15307i | −0.351837 | + | 0.203133i | ||||
\(419\) | −13.5307 | − | 23.4359i | −0.661020 | − | 1.14492i | −0.980348 | − | 0.197276i | \(-0.936790\pi\) |
0.319328 | − | 0.947644i | \(-0.396543\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.9356i | − | 0.581706i | −0.956768 | − | 0.290853i | \(-0.906061\pi\) | ||
0.956768 | − | 0.290853i | \(-0.0939390\pi\) | |||||||
\(422\) | 11.6807 | + | 6.74384i | 0.568607 | + | 0.328285i | ||||
\(423\) | 5.93149 | + | 3.42455i | 0.288399 | + | 0.166507i | ||||
\(424\) | − | 0.881964i | − | 0.0428319i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.91737 | + | 13.7133i | 0.383598 | + | 0.664411i | ||||
\(427\) | −16.4041 | + | 9.47091i | −0.793850 | + | 0.458329i | ||||
\(428\) | −13.7532 | −0.664787 | ||||||||
\(429\) | 18.5517 | − | 0.356895i | 0.895684 | − | 0.0172311i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.9671 | − | 14.9921i | 1.25079 | − | 0.722144i | 0.279523 | − | 0.960139i | \(-0.409824\pi\) |
0.971266 | + | 0.237995i | \(0.0764903\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −10.4971 | + | 18.1814i | −0.504456 | + | 0.873744i | 0.495530 | + | 0.868591i | \(0.334974\pi\) |
−0.999987 | + | 0.00515336i | \(0.998360\pi\) | |||||||
\(434\) | 14.9954i | 0.719800i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.5401 | + | 8.39475i | 0.696346 | + | 0.402036i | ||||
\(437\) | − | 8.78418i | − | 0.420204i | ||||||
\(438\) | 2.19677 | − | 3.80493i | 0.104966 | − | 0.181806i | ||||
\(439\) | 3.65685 | + | 6.33386i | 0.174532 | + | 0.302299i | 0.939999 | − | 0.341176i | \(-0.110825\pi\) |
−0.765467 | + | 0.643475i | \(0.777492\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.69677 | 0.223656 | ||||||||
\(442\) | −8.93173 | − | 14.8051i | −0.424839 | − | 0.704205i | ||||
\(443\) | −12.8231 | −0.609244 | −0.304622 | − | 0.952473i | \(-0.598530\pi\) | ||||
−0.304622 | + | 0.952473i | \(0.598530\pi\) | |||||||
\(444\) | 7.56873 | − | 4.36981i | 0.359196 | − | 0.207382i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.51047 | − | 6.08030i | 0.166225 | − | 0.287911i | ||||
\(447\) | 9.24504i | 0.437276i | ||||||||
\(448\) | −1.31431 | − | 0.758819i | −0.0620955 | − | 0.0358508i | ||||
\(449\) | −2.73315 | − | 1.57798i | −0.128985 | − | 0.0744696i | 0.434119 | − | 0.900855i | \(-0.357060\pi\) |
−0.563104 | + | 0.826386i | \(0.690393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.28074 | + | 5.68240i | −0.154484 | + | 0.267574i | ||||
\(452\) | 4.82843 | + | 8.36308i | 0.227110 | + | 0.393366i | ||||
\(453\) | −14.8506 | + | 8.57397i | −0.697740 | + | 0.402840i | ||||
\(454\) | 8.59524 | 0.403395 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.61401 | −0.0755831 | ||||||||
\(457\) | 0.250578 | − | 0.144671i | 0.0117215 | − | 0.00676743i | −0.494128 | − | 0.869389i | \(-0.664513\pi\) |
0.505849 | + | 0.862622i | \(0.331179\pi\) | |||||||
\(458\) | −8.20429 | − | 14.2102i | −0.383361 | − | 0.664001i | ||||
\(459\) | −2.39778 | + | 4.15307i | −0.111919 | + | 0.193849i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.07799 | − | 1.77708i | −0.143356 | − | 0.0827668i | 0.426606 | − | 0.904437i | \(-0.359709\pi\) |
−0.569963 | + | 0.821671i | \(0.693042\pi\) | |||||||
\(462\) | −6.76380 | − | 3.90508i | −0.314681 | − | 0.181681i | ||||
\(463\) | − | 12.1116i | − | 0.562875i | −0.959580 | − | 0.281438i | \(-0.909189\pi\) | ||
0.959580 | − | 0.281438i | \(-0.0908113\pi\) | |||||||
\(464\) | −4.93684 | + | 8.55085i | −0.229187 | + | 0.396963i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.01221 | − | 3.47115i | 0.278510 | − | 0.160798i | ||||
\(467\) | 29.9323 | 1.38510 | 0.692550 | − | 0.721369i | \(-0.256487\pi\) | ||||
0.692550 | + | 0.721369i | \(0.256487\pi\) | |||||||
\(468\) | 3.15660 | + | 1.74238i | 0.145914 | + | 0.0805417i | ||||
\(469\) | 17.5054 | 0.808326 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.13954 | + | 15.8301i | 0.421128 | + | 0.729415i | ||||
\(472\) | 4.64394 | − | 8.04354i | 0.213755 | − | 0.370234i | ||||
\(473\) | 12.1798i | 0.560029i | ||||||||
\(474\) | −9.55936 | − | 5.51910i | −0.439076 | − | 0.253501i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.27792i | 0.333583i | ||||||||
\(477\) | 0.440982 | − | 0.763803i | 0.0201912 | − | 0.0349721i | ||||
\(478\) | −9.15281 | − | 15.8531i | −0.418640 | − | 0.725106i | ||||
\(479\) | 2.03012 | − | 1.17209i | 0.0927584 | − | 0.0535541i | −0.452903 | − | 0.891560i | \(-0.649612\pi\) |
0.545662 | + | 0.838006i | \(0.316278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.2278 | + | 27.5874i | −0.694326 | + | 1.25788i | ||||
\(482\) | −14.4229 | −0.656947 | ||||||||
\(483\) | 7.15307 | − | 4.12983i | 0.325476 | − | 0.187914i | ||||
\(484\) | −7.74202 | − | 13.4096i | −0.351910 | − | 0.609526i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −3.23354 | − | 1.86689i | −0.146526 | − | 0.0845968i | 0.424945 | − | 0.905219i | \(-0.360294\pi\) |
−0.571471 | + | 0.820623i | \(0.693627\pi\) | |||||||
\(488\) | −10.8090 | − | 6.24056i | −0.489299 | − | 0.282497i | ||||
\(489\) | − | 1.70382i | − | 0.0770495i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.14261 | − | 10.6393i | −0.277212 | − | 0.480145i | 0.693479 | − | 0.720477i | \(-0.256077\pi\) |
−0.970691 | + | 0.240332i | \(0.922744\pi\) | |||||||
\(492\) | −1.10418 | + | 0.637499i | −0.0497803 | + | 0.0287407i | ||||
\(493\) | 47.3497 | 2.13252 | ||||||||
\(494\) | 4.98286 | − | 3.00610i | 0.224189 | − | 0.135251i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.55695 | + | 4.94036i | −0.384219 | + | 0.221829i | ||||
\(497\) | 12.0157 | + | 20.8118i | 0.538978 | + | 0.933537i | ||||
\(498\) | 0.489668 | − | 0.848130i | 0.0219425 | − | 0.0380056i | ||||
\(499\) | 17.8267i | 0.798033i | 0.916944 | + | 0.399016i | \(0.130648\pi\) | ||||
−0.916944 | + | 0.399016i | \(0.869352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.61967 | + | 2.66717i | 0.206392 | + | 0.119160i | ||||
\(502\) | − | 7.76444i | − | 0.346544i | ||||||
\(503\) | 2.78988 | − | 4.83222i | 0.124395 | − | 0.215458i | −0.797101 | − | 0.603845i | \(-0.793634\pi\) |
0.921496 | + | 0.388387i | \(0.126968\pi\) | |||||||
\(504\) | −0.758819 | − | 1.31431i | −0.0338005 | − | 0.0585442i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 28.0082 | 1.24512 | ||||||||
\(507\) | −12.9904 | + | 0.500000i | −0.576923 | + | 0.0222058i | ||||
\(508\) | −11.9907 | −0.532002 | ||||||||
\(509\) | 27.6679 | − | 15.9741i | 1.22636 | − | 0.708039i | 0.260093 | − | 0.965584i | \(-0.416247\pi\) |
0.966266 | + | 0.257545i | \(0.0829134\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.33391 | − | 5.77450i | 0.147483 | − | 0.255449i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.39778 | − | 0.807007i | −0.0617134 | − | 0.0356302i | ||||
\(514\) | −16.7841 | − | 9.69031i | −0.740315 | − | 0.427421i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.18336 | + | 2.04965i | −0.0520947 | + | 0.0902307i | ||||
\(517\) | 17.6236 | + | 30.5250i | 0.775086 | + | 1.34249i | ||||
\(518\) | 11.4866 | − | 6.63179i | 0.504692 | − | 0.291384i | ||||
\(519\) | 17.6768 | 0.775925 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.338338 | −0.0148228 | −0.00741142 | − | 0.999973i | \(-0.502359\pi\) | ||||
−0.00741142 | + | 0.999973i | \(0.502359\pi\) | |||||||
\(522\) | −8.55085 | + | 4.93684i | −0.374261 | + | 0.216079i | ||||
\(523\) | 11.5529 | + | 20.0102i | 0.505174 | + | 0.874986i | 0.999982 | + | 0.00598438i | \(0.00190490\pi\) |
−0.494808 | + | 0.869002i | \(0.664762\pi\) | |||||||
\(524\) | −10.1762 | + | 17.6257i | −0.444549 | + | 0.769981i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.64019 | − | 0.946961i | −0.0715155 | − | 0.0412895i | ||||
\(527\) | 41.0353 | + | 23.6918i | 1.78753 | + | 1.03203i | ||||
\(528\) | − | 5.14626i | − | 0.223962i | ||||||
\(529\) | −3.31008 | + | 5.73324i | −0.143917 | + | 0.249271i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.04354 | − | 4.64394i | 0.349060 | − | 0.201530i | ||||
\(532\) | −2.44949 | −0.106199 | ||||||||
\(533\) | 2.22153 | − | 4.02465i | 0.0962253 | − | 0.174327i | ||||
\(534\) | −4.08933 | −0.176963 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.76733 | + | 9.98930i | 0.249111 | + | 0.431472i | ||||
\(537\) | −10.7700 | + | 18.6542i | −0.464759 | + | 0.804987i | ||||
\(538\) | 4.60207i | 0.198409i | ||||||||
\(539\) | 20.9326 | + | 12.0854i | 0.901629 | + | 0.520556i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.8074i | 1.23853i | 0.785183 | + | 0.619264i | \(0.212569\pi\) | ||||
−0.785183 | + | 0.619264i | \(0.787431\pi\) | |||||||
\(542\) | −4.17191 | + | 7.22596i | −0.179199 | + | 0.310382i | ||||
\(543\) | −2.04164 | − | 3.53622i | −0.0876151 | − | 0.151754i | ||||
\(544\) | −4.15307 | + | 2.39778i | −0.178062 | + | 0.102804i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.79057 | + | 2.64431i | 0.205018 | + | 0.113166i | ||||
\(547\) | 33.4957 | 1.43217 | 0.716086 | − | 0.698013i | \(-0.245932\pi\) | ||||
0.716086 | + | 0.698013i | \(0.245932\pi\) | |||||||
\(548\) | 6.82684 | − | 3.94148i | 0.291628 | − | 0.168372i | ||||
\(549\) | −6.24056 | − | 10.8090i | −0.266341 | − | 0.461315i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.9362i | 0.678907i | ||||||||
\(552\) | 4.71329 | + | 2.72122i | 0.200611 | + | 0.115823i | ||||
\(553\) | −14.5076 | − | 8.37599i | −0.616928 | − | 0.356183i | ||||
\(554\) | 22.2377i | 0.944791i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.05852 | + | 3.56546i | 0.0873007 | + | 0.151209i | ||||
\(557\) | −31.6950 | + | 18.2991i | −1.34296 | + | 0.775358i | −0.987241 | − | 0.159236i | \(-0.949097\pi\) |
−0.355718 | + | 0.934593i | \(0.615764\pi\) | |||||||
\(558\) | −9.88072 | −0.418284 | ||||||||
\(559\) | −0.164134 | − | 8.53179i | −0.00694211 | − | 0.360856i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.3728 | + | 12.3396i | −0.902361 | + | 0.520978i | ||||
\(562\) | 10.0481 | + | 17.4038i | 0.423852 | + | 0.734133i | ||||
\(563\) | 5.18180 | − | 8.97514i | 0.218387 | − | 0.378257i | −0.735928 | − | 0.677060i | \(-0.763254\pi\) |
0.954315 | + | 0.298803i | \(0.0965872\pi\) | |||||||
\(564\) | 6.84909i | 0.288399i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.623402 | + | 0.359921i | 0.0262036 | + | 0.0151286i | ||||
\(567\) | − | 1.51764i | − | 0.0637348i | ||||||
\(568\) | −7.91737 | + | 13.7133i | −0.332206 | + | 0.575397i | ||||
\(569\) | 15.7893 | + | 27.3479i | 0.661923 | + | 1.14648i | 0.980110 | + | 0.198456i | \(0.0635928\pi\) |
−0.318187 | + | 0.948028i | \(0.603074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.7160 | 1.41097 | 0.705485 | − | 0.708725i | \(-0.250729\pi\) | ||||
0.705485 | + | 0.708725i | \(0.250729\pi\) | |||||||
\(572\) | 9.58492 | + | 15.8878i | 0.400766 | + | 0.664302i | ||||
\(573\) | −12.9564 | −0.541263 | ||||||||
\(574\) | −1.67575 | + | 0.967492i | −0.0699443 | + | 0.0403823i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 40.8530i | 1.70073i | 0.526193 | + | 0.850365i | \(0.323619\pi\) | ||||
−0.526193 | + | 0.850365i | \(0.676381\pi\) | |||||||
\(578\) | 5.19386 | + | 2.99867i | 0.216036 | + | 0.124728i | ||||
\(579\) | −7.49706 | − | 4.32843i | −0.311567 | − | 0.179883i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.743139 | − | 1.28715i | 0.0308306 | − | 0.0534001i | ||||
\(582\) | −2.85898 | − | 4.95189i | −0.118508 | − | 0.205263i | ||||
\(583\) | 3.93073 | − | 2.26941i | 0.162794 | − | 0.0939893i | ||||
\(584\) | 4.39355 | 0.181806 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.2278 | −0.546435 | ||||||||
\(587\) | 21.3431 | − | 12.3224i | 0.880924 | − | 0.508602i | 0.00996119 | − | 0.999950i | \(-0.496829\pi\) |
0.870963 | + | 0.491349i | \(0.163496\pi\) | |||||||
\(588\) | 2.34839 | + | 4.06753i | 0.0968459 | + | 0.167742i | ||||
\(589\) | −7.97381 | + | 13.8110i | −0.328555 | + | 0.569074i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.76574 | − | 2.17415i | −0.154902 | − | 0.0894327i | ||||
\(592\) | 7.56873 | + | 4.36981i | 0.311073 | + | 0.179598i | ||||
\(593\) | 21.4887i | 0.882436i | 0.897400 | + | 0.441218i | \(0.145453\pi\) | ||||
−0.897400 | + | 0.441218i | \(0.854547\pi\) | |||||||
\(594\) | 2.57313 | − | 4.45680i | 0.105577 | − | 0.182865i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.00644 | + | 4.62252i | −0.327957 | + | 0.189346i | ||||
\(597\) | 7.46702 | 0.305605 | ||||||||
\(598\) | −19.6194 | + | 0.377435i | −0.802296 | + | 0.0154345i | ||||
\(599\) | −29.1850 | −1.19247 | −0.596233 | − | 0.802812i | \(-0.703337\pi\) | ||||
−0.596233 | + | 0.802812i | \(0.703337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.31925 | − | 5.74910i | −0.135395 | − | 0.234511i | 0.790353 | − | 0.612651i | \(-0.209897\pi\) |
−0.925748 | + | 0.378140i | \(0.876564\pi\) | |||||||
\(602\) | −1.79592 | + | 3.11062i | −0.0731962 | + | 0.126780i | ||||
\(603\) | 11.5347i | 0.469727i | ||||||||
\(604\) | −14.8506 | − | 8.57397i | −0.604260 | − | 0.348870i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 7.85374i | − | 0.319036i | ||||||
\(607\) | 11.7047 | − | 20.2731i | 0.475078 | − | 0.822860i | −0.524514 | − | 0.851402i | \(-0.675753\pi\) |
0.999593 | + | 0.0285420i | \(0.00908643\pi\) | |||||||
\(608\) | −0.807007 | − | 1.39778i | −0.0327285 | − | 0.0566874i | ||||
\(609\) | −12.9771 | + | 7.49233i | −0.525858 | + | 0.303605i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.7564 | − | 21.1448i | −0.516070 | − | 0.855428i | ||||
\(612\) | −4.79555 | −0.193849 | ||||||||
\(613\) | 4.55182 | − | 2.62799i | 0.183846 | − | 0.106144i | −0.405252 | − | 0.914205i | \(-0.632816\pi\) |
0.589099 | + | 0.808061i | \(0.299483\pi\) | |||||||
\(614\) | 3.92587 | + | 6.79981i | 0.158435 | + | 0.274418i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 7.81017i | − | 0.314681i | ||||||
\(617\) | −22.8678 | − | 13.2027i | −0.920622 | − | 0.531522i | −0.0367887 | − | 0.999323i | \(-0.511713\pi\) |
−0.883834 | + | 0.467802i | \(0.845046\pi\) | |||||||
\(618\) | −2.74919 | − | 1.58725i | −0.110589 | − | 0.0638484i | ||||
\(619\) | − | 4.68483i | − | 0.188299i | −0.995558 | − | 0.0941497i | \(-0.969987\pi\) | ||
0.995558 | − | 0.0941497i | \(-0.0300132\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.72122 | + | 4.71329i | 0.109199 | + | 0.189138i | ||||
\(622\) | 13.6579 | − | 7.88538i | 0.547631 | − | 0.316175i | ||||
\(623\) | −6.20612 | −0.248643 | ||||||||
\(624\) | 0.0693504 | + | 3.60488i | 0.00277624 | + | 0.144311i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.2396 | − | 10.5306i | 0.729001 | − | 0.420889i | ||||
\(627\) | −4.15307 | − | 7.19333i | −0.165858 | − | 0.287274i | ||||
\(628\) | −9.13954 | + | 15.8301i | −0.364707 | + | 0.631692i | ||||
\(629\) | − | 41.9113i | − | 1.67111i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.85249 | + | 3.37894i | 0.232984 | + | 0.134513i | 0.611948 | − | 0.790898i | \(-0.290386\pi\) |
−0.378964 | + | 0.925411i | \(0.623720\pi\) | |||||||
\(632\) | − | 11.0382i | − | 0.439076i | ||||||
\(633\) | −6.74384 | + | 11.6807i | −0.268044 | + | 0.464265i | ||||
\(634\) | −13.2071 | − | 22.8753i | −0.524520 | − | 0.908494i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.881964 | 0.0349721 | ||||||||
\(637\) | −14.8258 | − | 8.18358i | −0.587420 | − | 0.324245i | ||||
\(638\) | −50.8125 | −2.01169 | ||||||||
\(639\) | −13.7133 | + | 7.91737i | −0.542489 | + | 0.313206i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.6037 | − | 25.2943i | 0.576810 | − | 0.999064i | −0.419033 | − | 0.907971i | \(-0.637631\pi\) |
0.995842 | − | 0.0910927i | \(-0.0290360\pi\) | |||||||
\(642\) | − | 13.7532i | − | 0.542797i | ||||||
\(643\) | −6.98298 | − | 4.03163i | −0.275382 | − | 0.158992i | 0.355949 | − | 0.934505i | \(-0.384158\pi\) |
−0.631331 | + | 0.775514i | \(0.717491\pi\) | |||||||
\(644\) | 7.15307 | + | 4.12983i | 0.281871 | + | 0.162738i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.87005 | + | 6.70312i | −0.152265 | + | 0.263731i | ||||
\(647\) | −0.360179 | − | 0.623849i | −0.0141601 | − | 0.0245260i | 0.858859 | − | 0.512213i | \(-0.171174\pi\) |
−0.873019 | + | 0.487687i | \(0.837841\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 47.7979 | 1.87623 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.9954 | −0.587714 | ||||||||
\(652\) | 1.47555 | − | 0.851911i | 0.0577871 | − | 0.0333634i | ||||
\(653\) | 13.3367 | + | 23.0998i | 0.521904 | + | 0.903963i | 0.999675 | + | 0.0254795i | \(0.00811125\pi\) |
−0.477772 | + | 0.878484i | \(0.658555\pi\) | |||||||
\(654\) | −8.39475 | + | 14.5401i | −0.328261 | + | 0.568564i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.10418 | − | 0.637499i | −0.0431110 | − | 0.0248901i | ||||
\(657\) | 3.80493 | + | 2.19677i | 0.148444 | + | 0.0857043i | ||||
\(658\) | 10.3944i | 0.405218i | ||||||||
\(659\) | 9.02067 | − | 15.6243i | 0.351396 | − | 0.608635i | −0.635099 | − | 0.772431i | \(-0.719041\pi\) |
0.986494 | + | 0.163796i | \(0.0523739\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5904 | − | 6.11439i | 0.411920 | − | 0.237822i | −0.279694 | − | 0.960089i | \(-0.590233\pi\) |
0.691614 | + | 0.722267i | \(0.256900\pi\) | |||||||
\(662\) | −20.4252 | −0.793847 | ||||||||
\(663\) | 14.8051 | − | 8.93173i | 0.574981 | − | 0.346880i | ||||
\(664\) | 0.979336 | 0.0380056 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.36981 | + | 7.56873i | 0.169327 | + | 0.293282i | ||||
\(667\) | 26.8684 | − | 46.5375i | 1.04035 | − | 1.80194i | ||||
\(668\) | 5.33434i | 0.206392i | ||||||||
\(669\) | 6.08030 | + | 3.51047i | 0.235078 | + | 0.135722i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 64.2311i | − | 2.47962i | ||||||
\(672\) | 0.758819 | − | 1.31431i | 0.0292721 | − | 0.0507007i | ||||
\(673\) | 2.32913 | + | 4.03417i | 0.0897814 | + | 0.155506i | 0.907419 | − | 0.420228i | \(-0.138050\pi\) |
−0.817637 | + | 0.575734i | \(0.804716\pi\) | |||||||
\(674\) | −11.3479 | + | 6.55173i | −0.437106 | + | 0.252363i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.92820 | − | 11.0000i | −0.266469 | − | 0.423077i | ||||
\(677\) | −22.1830 | −0.852561 | −0.426280 | − | 0.904591i | \(-0.640176\pi\) | ||||
−0.426280 | + | 0.904591i | \(0.640176\pi\) | |||||||
\(678\) | −8.36308 | + | 4.82843i | −0.321182 | + | 0.185435i | ||||
\(679\) | −4.33889 | − | 7.51518i | −0.166511 | − | 0.288406i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.59524i | 0.329370i | ||||||||
\(682\) | −44.0363 | − | 25.4244i | −1.68624 | − | 0.973550i | ||||
\(683\) | 10.9766 | + | 6.33735i | 0.420008 | + | 0.242492i | 0.695081 | − | 0.718931i | \(-0.255369\pi\) |
−0.275072 | + | 0.961423i | \(0.588702\pi\) | |||||||
\(684\) | − | 1.61401i | − | 0.0617134i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.87574 | + | 15.3732i | 0.338877 | + | 0.586952i | ||||
\(687\) | 14.2102 | − | 8.20429i | 0.542155 | − | 0.313013i | ||||
\(688\) | −2.36673 | −0.0902307 | ||||||||
\(689\) | −2.72284 | + | 1.64266i | −0.103732 | + | 0.0625803i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.7634 | − | 7.36897i | 0.485544 | − | 0.280329i | −0.237180 | − | 0.971466i | \(-0.576223\pi\) |
0.722724 | + | 0.691137i | \(0.242890\pi\) | |||||||
\(692\) | 8.83839 | + | 15.3085i | 0.335985 | + | 0.581944i | ||||
\(693\) | 3.90508 | − | 6.76380i | 0.148342 | − | 0.256936i | ||||
\(694\) | − | 17.7605i | − | 0.674181i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.55085 | − | 4.93684i | −0.324119 | − | 0.187130i | ||||
\(697\) | 6.11432i | 0.231596i | ||||||||
\(698\) | −0.0598981 | + | 0.103747i | −0.00226718 | + | 0.00392687i | ||||
\(699\) | 3.47115 | + | 6.01221i | 0.131291 | + | 0.227403i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.9252 | 0.979182 | 0.489591 | − | 0.871952i | \(-0.337146\pi\) | ||||
0.489591 | + | 0.871952i | \(0.337146\pi\) | |||||||
\(702\) | −1.74238 | + | 3.15660i | −0.0657620 | + | 0.119138i | ||||
\(703\) | 14.1059 | 0.532013 | ||||||||
\(704\) | 4.45680 | − | 2.57313i | 0.167972 | − | 0.0969786i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.77620 | + | 6.54057i | −0.142119 | + | 0.246158i | ||||
\(707\) | − | 11.9191i | − | 0.448265i | ||||||
\(708\) | 8.04354 | + | 4.64394i | 0.302295 | + | 0.174530i | ||||
\(709\) | −28.0091 | − | 16.1711i | −1.05190 | − | 0.607317i | −0.128722 | − | 0.991681i | \(-0.541087\pi\) |
−0.923182 | + | 0.384364i | \(0.874421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.51910 | − | 9.55936i | 0.206982 | − | 0.358504i | ||||
\(712\) | −2.04466 | − | 3.54146i | −0.0766270 | − | 0.132722i | ||||
\(713\) | 46.5707 | − | 26.8876i | 1.74409 | − | 1.00695i | ||||
\(714\) | −7.27792 | −0.272369 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.5400 | −0.804987 | ||||||||
\(717\) | 15.8531 | − | 9.15281i | 0.592046 | − | 0.341818i | ||||
\(718\) | 14.9847 | + | 25.9542i | 0.559223 | + | 0.968602i | ||||
\(719\) | −6.84506 | + | 11.8560i | −0.255278 | + | 0.442154i | −0.964971 | − | 0.262357i | \(-0.915500\pi\) |
0.709693 | + | 0.704511i | \(0.248834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.17228 | − | 2.40887i | −0.155384 | − | 0.0897108i | ||||
\(722\) | 14.1984 | + | 8.19748i | 0.528412 | + | 0.305079i | ||||
\(723\) | − | 14.4229i | − | 0.536395i | ||||||
\(724\) | 2.04164 | − | 3.53622i | 0.0758769 | − | 0.131423i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.4096 | − | 7.74202i | 0.497676 | − | 0.287333i | ||||
\(727\) | −49.1587 | −1.82319 | −0.911597 | − | 0.411084i | \(-0.865150\pi\) | ||||
−0.911597 | + | 0.411084i | \(0.865150\pi\) | |||||||
\(728\) | 0.105249 | + | 5.47091i | 0.00390078 | + | 0.202765i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.67489 | + | 9.82920i | 0.209893 | + | 0.363546i | ||||
\(732\) | 6.24056 | − | 10.8090i | 0.230658 | − | 0.399511i | ||||
\(733\) | − | 44.9158i | − | 1.65900i | −0.558505 | − | 0.829501i | \(-0.688625\pi\) | ||
0.558505 | − | 0.829501i | \(-0.311375\pi\) | |||||||
\(734\) | −25.0232 | − | 14.4472i | −0.923625 | − | 0.533255i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.44244i | 0.200611i | ||||||||
\(737\) | −29.6802 | + | 51.4076i | −1.09328 | + | 1.89362i | ||||
\(738\) | −0.637499 | − | 1.10418i | −0.0234667 | − | 0.0406454i | ||||
\(739\) | 14.2102 | − | 8.20427i | 0.522731 | − | 0.301799i | −0.215320 | − | 0.976543i | \(-0.569080\pi\) |
0.738051 | + | 0.674745i | \(0.235746\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.00610 | + | 4.98286i | 0.110432 | + | 0.183050i | ||||
\(742\) | 1.33850 | 0.0491379 | ||||||||
\(743\) | −5.73773 | + | 3.31268i | −0.210497 | + | 0.121530i | −0.601542 | − | 0.798841i | \(-0.705447\pi\) |
0.391045 | + | 0.920371i | \(0.372114\pi\) | |||||||
\(744\) | −4.94036 | − | 8.55695i | −0.181122 | − | 0.313713i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 14.7117i | − | 0.538632i | ||||||
\(747\) | 0.848130 | + | 0.489668i | 0.0310314 | + | 0.0179160i | ||||
\(748\) | −21.3728 | − | 12.3396i | −0.781467 | − | 0.451180i | ||||
\(749\) | − | 20.8724i | − | 0.762662i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2807 | + | 35.1271i | 0.740052 | + | 1.28181i | 0.952471 | + | 0.304629i | \(0.0985324\pi\) |
−0.212419 | + | 0.977179i | \(0.568134\pi\) | |||||||
\(752\) | −5.93149 | + | 3.42455i | −0.216299 | + | 0.124880i | ||||
\(753\) | 7.76444 | 0.282952 | ||||||||
\(754\) | 35.5934 | − | 0.684743i | 1.29624 | − | 0.0249369i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.31431 | − | 0.758819i | 0.0478011 | − | 0.0275980i | ||||
\(757\) | 12.1639 | + | 21.0685i | 0.442105 | + | 0.765748i | 0.997845 | − | 0.0656076i | \(-0.0208986\pi\) |
−0.555741 | + | 0.831356i | \(0.687565\pi\) | |||||||
\(758\) | 15.6627 | − | 27.1285i | 0.568893 | − | 0.985352i | ||||
\(759\) | 28.0082i | 1.01663i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.355702 | − | 0.205364i | −0.0128942 | − | 0.00744446i | 0.493539 | − | 0.869724i | \(-0.335703\pi\) |
−0.506433 | + | 0.862279i | \(0.669036\pi\) | |||||||
\(762\) | − | 11.9907i | − | 0.434378i | ||||||
\(763\) | −12.7402 | + | 22.0667i | −0.461226 | + | 0.798867i | ||||
\(764\) | −6.47822 | − | 11.2206i | −0.234374 | − | 0.405947i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.8474 | −0.391931 | ||||||||
\(767\) | −33.4817 | + | 0.644118i | −1.20896 | + | 0.0232578i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −36.0692 | + | 20.8246i | −1.30069 | + | 0.750954i | −0.980522 | − | 0.196407i | \(-0.937073\pi\) |
−0.320168 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.69031 | − | 16.7841i | 0.348988 | − | 0.604465i | ||||
\(772\) | − | 8.65685i | − | 0.311567i | ||||||
\(773\) | −44.8150 | − | 25.8739i | −1.61188 | − | 0.930621i | −0.988934 | − | 0.148358i | \(-0.952601\pi\) |
−0.622949 | − | 0.782262i | \(-0.714066\pi\) | |||||||
\(774\) | −2.04965 | − | 1.18336i | −0.0736731 | − | 0.0425352i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.85898 | − | 4.95189i | 0.102631 | − | 0.177763i | ||||
\(777\) | 6.63179 | + | 11.4866i | 0.237914 | + | 0.412079i | ||||
\(778\) | 15.8463 | − | 9.14884i | 0.568116 | − | 0.328002i | ||||
\(779\) | −2.05786 | −0.0737306 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −81.4898 | −2.91593 | ||||||||
\(782\) | 22.6029 | − | 13.0498i | 0.808276 | − | 0.466659i | ||||
\(783\) | −4.93684 | − | 8.55085i | −0.176428 | − | 0.305582i | ||||
\(784\) | −2.34839 | + | 4.06753i | −0.0838710 | + | 0.145269i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.6257 | − | 10.1762i | −0.628687 | − | 0.362973i | ||||
\(787\) | −14.9066 | − | 8.60630i | −0.531361 | − | 0.306782i | 0.210209 | − | 0.977656i | \(-0.432585\pi\) |
−0.741571 | + | 0.670875i | \(0.765919\pi\) | |||||||
\(788\) | − | 4.34831i | − | 0.154902i | ||||||
\(789\) | 0.946961 | − | 1.64019i | 0.0337127 | − | 0.0583921i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.6921 | + | 7.32780i | −0.451280 | + | 0.260547i | ||||
\(792\) | 5.14626 | 0.182865 | ||||||||
\(793\) | 0.865570 | + | 44.9930i | 0.0307373 | + | 1.59775i | ||||
\(794\) | 0.307656 | 0.0109183 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.73351 | + | 6.46663i | 0.132331 | + | 0.229204i | ||||
\(797\) | 12.3539 | − | 21.3976i | 0.437599 | − | 0.757943i | −0.559905 | − | 0.828557i | \(-0.689162\pi\) |
0.997504 | + | 0.0706135i | \(0.0224957\pi\) | |||||||
\(798\) | − | 2.44949i | − | 0.0867110i | ||||||
\(799\) | 28.4448 | + | 16.4226i | 1.00630 | + | 0.580990i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 4.08933i | − | 0.144489i | ||||||
\(802\) | −1.09273 | + | 1.89266i | −0.0385856 | + | 0.0668322i | ||||
\(803\) | 11.3052 | + | 19.5812i | 0.398951 | + | 0.691004i | ||||
\(804\) | −9.98930 | + | 5.76733i | −0.352296 | + | 0.203398i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 31.1894 | + | 17.2160i | 1.09860 | + | 0.606408i | ||||
\(807\) | −4.60207 | −0.162001 | ||||||||
\(808\) | 6.80153 | − | 3.92687i | 0.239277 | − | 0.138147i | ||||
\(809\) | −12.5285 | − | 21.7001i | −0.440480 | − | 0.762934i | 0.557245 | − | 0.830348i | \(-0.311858\pi\) |
−0.997725 | + | 0.0674144i | \(0.978525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.2387i | − | 1.23740i | −0.785628 | − | 0.618699i | \(-0.787660\pi\) | ||
0.785628 | − | 0.618699i | \(-0.212340\pi\) | |||||||
\(812\) | −12.9771 | − | 7.49233i | −0.455407 | − | 0.262929i | ||||
\(813\) | −7.22596 | − | 4.17191i | −0.253426 | − | 0.146315i | ||||
\(814\) | 44.9764i | 1.57642i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.39778 | − | 4.15307i | −0.0839390 | − | 0.145387i | ||||
\(817\) | −3.30816 | + | 1.90997i | −0.115738 | + | 0.0668213i | ||||
\(818\) | −37.6510 | −1.31644 | ||||||||
\(819\) | −2.64431 | + | 4.79057i | −0.0923996 | + | 0.167396i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.5342 | + | 15.3195i | −0.926049 | + | 0.534655i | −0.885560 | − | 0.464525i | \(-0.846225\pi\) |
−0.0404892 | + | 0.999180i | \(0.512892\pi\) | |||||||
\(822\) | 3.94148 | + | 6.82684i | 0.137475 | + | 0.238113i | ||||
\(823\) | 17.8946 | − | 30.9943i | 0.623765 | − | 1.08039i | −0.365014 | − | 0.931002i | \(-0.618936\pi\) |
0.988778 | − | 0.149390i | \(-0.0477310\pi\) | |||||||
\(824\) | − | 3.17449i | − | 0.110589i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.2072 | + | 7.04782i | 0.424742 | + | 0.245225i | ||||
\(827\) | 7.53716i | 0.262093i | 0.991376 | + | 0.131046i | \(0.0418337\pi\) | ||||
−0.991376 | + | 0.131046i | \(0.958166\pi\) | |||||||
\(828\) | −2.72122 | + | 4.71329i | −0.0945690 | + | 0.163798i | ||||
\(829\) | −25.9628 | − | 44.9688i | −0.901724 | − | 1.56183i | −0.825256 | − | 0.564759i | \(-0.808969\pi\) |
−0.0764677 | − | 0.997072i | \(-0.524364\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.2377 | −0.771419 | ||||||||
\(832\) | −3.08725 | + | 1.86250i | −0.107031 | + | 0.0645706i | ||||
\(833\) | 22.5236 | 0.780398 | ||||||||
\(834\) | −3.56546 | + | 2.05852i | −0.123462 | + | 0.0712807i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.15307 | − | 7.19333i | 0.143637 | − | 0.248787i | ||||
\(837\) | − | 9.88072i | − | 0.341528i | ||||||
\(838\) | 23.4359 | + | 13.5307i | 0.809581 | + | 0.467412i | ||||
\(839\) | 6.72183 | + | 3.88085i | 0.232063 | + | 0.133982i | 0.611524 | − | 0.791226i | \(-0.290557\pi\) |
−0.379460 | + | 0.925208i | \(0.623890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.2447 | + | 59.3135i | −1.18085 | + | 2.04529i | ||||
\(842\) | 5.96780 | + | 10.3365i | 0.205664 | + | 0.356221i | ||||
\(843\) | −17.4038 | + | 10.0481i | −0.599417 | + | 0.346074i | ||||
\(844\) | −13.4877 | −0.464265 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.84909 | −0.235477 | ||||||||
\(847\) | 20.3509 | − | 11.7496i | 0.699264 | − | 0.403720i | ||||
\(848\) | 0.440982 | + | 0.763803i | 0.0151434 | + | 0.0262291i | ||||
\(849\) | −0.359921 | + | 0.623402i | −0.0123525 | + | 0.0213951i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.1924 | − | 23.7824i | −1.41206 | − | 0.815251i | ||||
\(852\) | −13.7133 | − | 7.91737i | −0.469810 | − | 0.271245i | ||||
\(853\) | 13.8072i | 0.472751i | 0.971662 | + | 0.236376i | \(0.0759596\pi\) | ||||
−0.971662 | + | 0.236376i | \(0.924040\pi\) | |||||||
\(854\) | 9.47091 | − | 16.4041i | 0.324088 | − | 0.561337i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.9106 | − | 6.87662i | 0.407098 | − | 0.235038i | ||||
\(857\) | −40.8095 | −1.39403 | −0.697013 | − | 0.717059i | \(-0.745488\pi\) | ||||
−0.697013 | + | 0.717059i | \(0.745488\pi\) | |||||||
\(858\) | −15.8878 | + | 9.58492i | −0.542400 | + | 0.327224i | ||||
\(859\) | 24.7784 | 0.845427 | 0.422713 | − | 0.906263i | \(-0.361078\pi\) | ||||
0.422713 | + | 0.906263i | \(0.361078\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.967492 | − | 1.67575i | −0.0329720 | − | 0.0571093i | ||||
\(862\) | −14.9921 | + | 25.9671i | −0.510633 | + | 0.884442i | ||||
\(863\) | − | 27.0018i | − | 0.919153i | −0.888138 | − | 0.459577i | \(-0.848001\pi\) | ||
0.888138 | − | 0.459577i | \(-0.151999\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 20.9941i | − | 0.713409i | ||||||
\(867\) | −2.99867 | + | 5.19386i | −0.101840 | + | 0.176393i | ||||
\(868\) | −7.49768 | − | 12.9864i | −0.254488 | − | 0.440786i | ||||
\(869\) | 49.1950 | − | 28.4027i | 1.66883 | − | 0.963497i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0978 | − | 36.4102i | 0.680987 | − | 1.23371i | ||||
\(872\) | −16.7895 | −0.568564 | ||||||||
\(873\) | 4.95189 | − | 2.85898i | 0.167596 | − | 0.0967617i | ||||
\(874\) | 4.39209 | + | 7.60732i | 0.148565 | + | 0.257322i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.39355i | 0.148444i | ||||||||
\(877\) | 24.4850 | + | 14.1364i | 0.826799 | + | 0.477352i | 0.852755 | − | 0.522311i | \(-0.174930\pi\) |
−0.0259566 | + | 0.999663i | \(0.508263\pi\) | |||||||
\(878\) | −6.33386 | − | 3.65685i | −0.213757 | − | 0.123413i | ||||
\(879\) | − | 13.2278i | − | 0.446162i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.37195 | − | 16.2327i | −0.315749 | − | 0.546894i | 0.663847 | − | 0.747868i | \(-0.268922\pi\) |
−0.979596 | + | 0.200975i | \(0.935589\pi\) | |||||||
\(882\) | −4.06753 | + | 2.34839i | −0.136961 | + | 0.0790743i | ||||
\(883\) | 54.1400 | 1.82196 | 0.910978 | − | 0.412456i | \(-0.135329\pi\) | ||||
0.910978 | + | 0.412456i | \(0.135329\pi\) | |||||||
\(884\) | 15.1376 | + | 8.35569i | 0.509134 | + | 0.281032i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.1051 | − | 6.41155i | 0.373084 | − | 0.215400i | ||||
\(887\) | −12.4062 | − | 21.4881i | −0.416558 | − | 0.721500i | 0.579032 | − | 0.815305i | \(-0.303431\pi\) |
−0.995591 | + | 0.0938043i | \(0.970097\pi\) | |||||||
\(888\) | −4.36981 | + | 7.56873i | −0.146641 | + | 0.253990i | ||||
\(889\) | − | 18.1976i | − | 0.610327i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.45680 | + | 2.57313i | 0.149308 | + | 0.0862032i | ||||
\(892\) | 7.02093i | 0.235078i | ||||||||
\(893\) | −5.52727 | + | 9.57351i | −0.184963 | + | 0.320365i | ||||
\(894\) | −4.62252 | − | 8.00644i | −0.154600 | − | 0.267776i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.51764 | 0.0507007 | ||||||||
\(897\) | −0.377435 | − | 19.6194i | −0.0126022 | − | 0.655072i | ||||
\(898\) | 3.15597 | 0.105316 | ||||||||
\(899\) | −84.4885 | + | 48.7795i | −2.81785 | + | 1.62689i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.11475 | − | 3.66286i | 0.0704526 | − | 0.122028i | ||||
\(902\) | − | 6.56147i | − | 0.218473i | ||||||
\(903\) | −3.11062 | − | 1.79592i | −0.103515 | − | 0.0597645i | ||||
\(904\) | −8.36308 | − | 4.82843i | −0.278152 | − | 0.160591i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.57397 | − | 14.8506i | 0.284851 | − | 0.493377i | ||||
\(907\) | 7.87598 | + | 13.6416i | 0.261517 | + | 0.452962i | 0.966645 | − | 0.256119i | \(-0.0824438\pi\) |
−0.705128 | + | 0.709080i | \(0.749110\pi\) | |||||||
\(908\) | −7.44370 | + | 4.29762i | −0.247028 | + | 0.142622i | ||||
\(909\) | 7.85374 | 0.260492 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.58458 | −0.185025 | −0.0925126 | − | 0.995712i | \(-0.529490\pi\) | ||||
−0.0925126 | + | 0.995712i | \(0.529490\pi\) | |||||||
\(912\) | 1.39778 | − | 0.807007i | 0.0462850 | − | 0.0267227i | ||||
\(913\) | 2.51996 | + | 4.36470i | 0.0833985 | + | 0.144450i | ||||
\(914\) | −0.144671 | + | 0.250578i | −0.00478530 | + | 0.00828838i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.2102 | + | 8.20429i | 0.469520 | + | 0.271077i | ||||
\(917\) | −26.7494 | − | 15.4438i | −0.883343 | − | 0.509998i | ||||
\(918\) | − | 4.79555i | − | 0.158277i | ||||||
\(919\) | −3.54423 | + | 6.13879i | −0.116913 | + | 0.202500i | −0.918543 | − | 0.395321i | \(-0.870633\pi\) |
0.801630 | + | 0.597821i | \(0.203967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.79981 | + | 3.92587i | −0.224061 | + | 0.129362i | ||||
\(922\) | 3.55416 | 0.117050 | ||||||||
\(923\) | 57.0824 | − | 1.09815i | 1.87889 | − | 0.0361459i | ||||
\(924\) | 7.81017 | 0.256936 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.05582 | + | 10.4890i | 0.199006 | + | 0.344689i | ||||
\(927\) | 1.58725 | − | 2.74919i | 0.0521320 | − | 0.0902953i | ||||
\(928\) | − | 9.87367i | − | 0.324119i | ||||||
\(929\) | 3.64324 | + | 2.10342i | 0.119531 | + | 0.0690111i | 0.558573 | − | 0.829455i | \(-0.311349\pi\) |
−0.439043 | + | 0.898466i | \(0.644682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.58066i | 0.248446i | ||||||||
\(932\) | −3.47115 | + | 6.01221i | −0.113701 | + | 0.196936i | ||||
\(933\) | 7.88538 | + | 13.6579i | 0.258156 | + | 0.447139i | ||||
\(934\) | −25.9221 | + | 14.9661i | −0.848198 | + | 0.489707i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.60488 | + | 0.0693504i | −0.117829 | + | 0.00226679i | ||||
\(937\) | −25.2818 | −0.825920 | −0.412960 | − | 0.910749i | \(-0.635505\pi\) | ||||
−0.412960 | + | 0.910749i | \(0.635505\pi\) | |||||||
\(938\) | −15.1601 | + | 8.75272i | −0.494996 | + | 0.285786i | ||||
\(939\) | 10.5306 | + | 18.2396i | 0.343654 | + | 0.595227i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.2457i | − | 1.37717i | −0.725156 | − | 0.688585i | \(-0.758232\pi\) | ||
0.725156 | − | 0.688585i | \(-0.241768\pi\) | |||||||
\(942\) | −15.8301 | − | 9.13954i | −0.515774 | − | 0.297782i | ||||
\(943\) | 6.00944 | + | 3.46955i | 0.195694 | + | 0.112984i | ||||
\(944\) | 9.28788i | 0.302295i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.08991 | − | 10.5480i | −0.198000 | − | 0.342946i | ||||
\(947\) | 35.7719 | − | 20.6529i | 1.16243 | − | 0.671130i | 0.210546 | − | 0.977584i | \(-0.432476\pi\) |
0.951885 | + | 0.306454i | \(0.0991426\pi\) | |||||||
\(948\) | 11.0382 | 0.358504 | ||||||||
\(949\) | −8.18299 | − | 13.5640i | −0.265631 | − | 0.440305i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.8753 | − | 13.2071i | 0.741783 | − | 0.428268i | ||||
\(952\) | −3.63896 | − | 6.30286i | −0.117939 | − | 0.204277i | ||||
\(953\) | 5.69547 | − | 9.86484i | 0.184494 | − | 0.319553i | −0.758912 | − | 0.651193i | \(-0.774269\pi\) |
0.943406 | + | 0.331640i | \(0.107602\pi\) | |||||||
\(954\) | 0.881964i | 0.0285546i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.8531 | + | 9.15281i | 0.512727 | + | 0.296023i | ||||
\(957\) | − | 50.8125i | − | 1.64254i | ||||||
\(958\) | −1.17209 | + | 2.03012i | −0.0378685 | + | 0.0655901i | ||||
\(959\) | 5.98174 | + | 10.3607i | 0.193160 | + | 0.334564i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −66.6286 | −2.14931 | ||||||||
\(962\) | −0.606095 | − | 31.5053i | −0.0195413 | − | 1.01577i | ||||
\(963\) | 13.7532 | 0.443192 | ||||||||
\(964\) | 12.4906 | − | 7.21147i | 0.402296 | − | 0.232266i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.12983 | + | 7.15307i | −0.132875 | + | 0.230146i | ||||
\(967\) | − | 39.5770i | − | 1.27271i | −0.771396 | − | 0.636355i | \(-0.780441\pi\) | ||
0.771396 | − | 0.636355i | \(-0.219559\pi\) | |||||||
\(968\) | 13.4096 | + | 7.74202i | 0.431000 | + | 0.248838i | ||||
\(969\) | −6.70312 | − | 3.87005i | −0.215335 | − | 0.124324i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.93166 | + | 3.34574i | −0.0619900 | + | 0.107370i | −0.895355 | − | 0.445353i | \(-0.853078\pi\) |
0.833365 | + | 0.552723i | \(0.186411\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −5.41108 | + | 3.12409i | −0.173471 | + | 0.100154i | ||||
\(974\) | 3.73378 | 0.119638 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.4811 | 0.399511 | ||||||||
\(977\) | 34.9993 | − | 20.2068i | 1.11973 | − | 0.646474i | 0.178395 | − | 0.983959i | \(-0.442909\pi\) |
0.941331 | + | 0.337485i | \(0.109576\pi\) | |||||||
\(978\) | 0.851911 | + | 1.47555i | 0.0272411 | + | 0.0471830i | ||||
\(979\) | 10.5224 | − | 18.2253i | 0.336297 | − | 0.582483i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.5401 | − | 8.39475i | −0.464231 | − | 0.268024i | ||||
\(982\) | 10.6393 | + | 6.14261i | 0.339514 | + | 0.196018i | ||||
\(983\) | 15.5229i | 0.495103i | 0.968875 | + | 0.247551i | \(0.0796259\pi\) | ||||
−0.968875 | + | 0.247551i | \(0.920374\pi\) | |||||||
\(984\) | 0.637499 | − | 1.10418i | 0.0203227 | − | 0.0352000i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −41.0061 | + | 23.6749i | −1.30590 | + | 0.753961i | ||||
\(987\) | −10.3944 | −0.330859 | ||||||||
\(988\) | −2.81223 | + | 5.09479i | −0.0894690 | + | 0.162087i | ||||
\(989\) | 12.8808 | 0.409585 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.5010 | + | 32.0447i | 0.587704 | + | 1.01793i | 0.994532 | + | 0.104428i | \(0.0333012\pi\) |
−0.406829 | + | 0.913504i | \(0.633365\pi\) | |||||||
\(992\) | 4.94036 | − | 8.55695i | 0.156857 | − | 0.271684i | ||||
\(993\) | − | 20.4252i | − | 0.648173i | ||||||
\(994\) | −20.8118 | − | 12.0157i | −0.660111 | − | 0.381115i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.979336i | 0.0310314i | ||||||||
\(997\) | −24.0165 | + | 41.5979i | −0.760611 | + | 1.31742i | 0.181925 | + | 0.983312i | \(0.441767\pi\) |
−0.942536 | + | 0.334105i | \(0.891566\pi\) | |||||||
\(998\) | −8.91335 | − | 15.4384i | −0.282147 | − | 0.488693i | ||||
\(999\) | −7.56873 | + | 4.36981i | −0.239464 | + | 0.138255i |
(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.bc.e.751.2 | ✓ | 8 | |
5.2 | odd | 4 | 1950.2.y.i.49.1 | 8 | |||
5.3 | odd | 4 | 1950.2.y.l.49.4 | 8 | |||
5.4 | even | 2 | 1950.2.bc.f.751.3 | yes | 8 | ||
13.4 | even | 6 | inner | 1950.2.bc.e.901.2 | yes | 8 | |
65.4 | even | 6 | 1950.2.bc.f.901.3 | yes | 8 | ||
65.17 | odd | 12 | 1950.2.y.l.199.4 | 8 | |||
65.43 | odd | 12 | 1950.2.y.i.199.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.i.49.1 | 8 | 5.2 | odd | 4 | |||
1950.2.y.i.199.1 | 8 | 65.43 | odd | 12 | |||
1950.2.y.l.49.4 | 8 | 5.3 | odd | 4 | |||
1950.2.y.l.199.4 | 8 | 65.17 | odd | 12 | |||
1950.2.bc.e.751.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1950.2.bc.e.901.2 | yes | 8 | 13.4 | even | 6 | inner | |
1950.2.bc.f.751.3 | yes | 8 | 5.4 | even | 2 | ||
1950.2.bc.f.901.3 | yes | 8 | 65.4 | even | 6 |