Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3997,1,Mod(13,3997)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3997, base_ring=CyclotomicField(570))
chi = DirichletCharacter(H, H._module([285, 352]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3997.13");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3997 = 7 \cdot 571 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3997.cz (of order \(570\), degree \(144\), 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: | \(1.99476285549\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Coefficient field: | \(\Q(\zeta_{570})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{144} - x^{143} + x^{142} + x^{139} - x^{138} + x^{137} - x^{129} + x^{128} - x^{127} + x^{125} - 2 x^{124} + 2 x^{123} - x^{122} + x^{120} - x^{119} + x^{118} + x^{114} - x^{113} + x^{112} - x^{110} + 2 x^{109} - 2 x^{108} + x^{107} - x^{105} + x^{104} - x^{103} - x^{99} + x^{98} - x^{97} + x^{95} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{285}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{285} - \cdots)\) |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(0.868768 + 0.495219i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3997.97 |
Dual form | 3997.1.cz.a.2596.1 |
$q$-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 \(\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times\).
\(n\) | \(1716\) | \(2285\) |
\(\chi(n)\) | \(e\left(\frac{146}{285}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.62671 | + | 1.12794i | 1.62671 | + | 1.12794i | 0.894729 | + | 0.446609i | \(0.147368\pi\) |
0.731980 | + | 0.681326i | \(0.238596\pi\) | |||||||
\(3\) | 0 | 0 | 0.0385714 | − | 0.999256i | \(-0.487719\pi\) | ||||
−0.0385714 | + | 0.999256i | \(0.512281\pi\) | |||||||
\(4\) | 1.02331 | + | 2.73313i | 1.02331 | + | 2.73313i | ||||
\(5\) | 0 | 0 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
0.840168 | + | 0.542326i | \(0.182456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.490424 | + | 0.871484i | 0.490424 | + | 0.871484i | ||||
\(8\) | −0.932234 | + | 3.68131i | −0.932234 | + | 3.68131i | ||||
\(9\) | −0.997024 | − | 0.0770854i | −0.997024 | − | 0.0770854i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.978802 | − | 1.27197i | −0.978802 | − | 1.27197i | −0.962268 | − | 0.272103i | \(-0.912281\pi\) |
−0.0165339 | − | 0.999863i | \(-0.505263\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.528360 | − | 0.849020i | \(-0.677193\pi\) | ||||
0.528360 | + | 0.849020i | \(0.322807\pi\) | |||||||
\(14\) | −0.185201 | + | 1.97082i | −0.185201 | + | 1.97082i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.46795 | + | 3.02024i | −3.46795 | + | 3.02024i | ||||
\(17\) | 0 | 0 | 0.224056 | − | 0.974576i | \(-0.428070\pi\) | ||||
−0.224056 | + | 0.974576i | \(0.571930\pi\) | |||||||
\(18\) | −1.53492 | − | 1.24997i | −1.53492 | − | 1.24997i | ||||
\(19\) | 0 | 0 | −0.938430 | − | 0.345471i | \(-0.887719\pi\) | ||||
0.938430 | + | 0.345471i | \(0.112281\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.157530 | − | 3.17315i | −0.157530 | − | 3.17315i | ||||
\(23\) | −0.252301 | − | 0.0167112i | −0.252301 | − | 0.0167112i | −0.0605901 | − | 0.998163i | \(-0.519298\pi\) |
−0.191711 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.411766 | + | 0.911290i | 0.411766 | + | 0.911290i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.88003 | + | 2.23219i | −1.88003 | + | 2.23219i | ||||
\(29\) | 0.248433 | + | 1.79157i | 0.248433 | + | 1.79157i | 0.546948 | + | 0.837166i | \(0.315789\pi\) |
−0.298515 | + | 0.954405i | \(0.596491\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(32\) | −5.27352 | + | 0.583674i | −5.27352 | + | 0.583674i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.809578 | − | 2.80388i | −0.809578 | − | 2.80388i | ||||
\(37\) | 1.87393 | + | 0.463568i | 1.87393 | + | 0.463568i | 0.999757 | − | 0.0220445i | \(-0.00701754\pi\) |
0.874174 | + | 0.485613i | \(0.161404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.998482 | − | 0.0550878i | \(-0.0175439\pi\) | ||||
−0.998482 | + | 0.0550878i | \(0.982456\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.373713 | − | 1.54723i | 0.373713 | − | 1.54723i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) |
0.775409 | − | 0.631460i | \(-0.217544\pi\) | |||||||
\(44\) | 2.47484 | − | 3.97681i | 2.47484 | − | 3.97681i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.391571 | − | 0.311763i | −0.391571 | − | 0.311763i | ||||
\(47\) | 0 | 0 | −0.191711 | − | 0.981451i | \(-0.561404\pi\) | ||||
0.191711 | + | 0.981451i | \(0.438596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.518970 | + | 0.854793i | −0.518970 | + | 0.854793i | ||||
\(50\) | −0.358053 | + | 1.94685i | −0.358053 | + | 1.94685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.372974 | − | 1.06725i | 0.372974 | − | 1.06725i | −0.592235 | − | 0.805765i | \(-0.701754\pi\) |
0.965209 | − | 0.261480i | \(-0.0842105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.66539 | + | 0.992973i | −3.66539 | + | 0.992973i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.61665 | + | 3.19458i | −1.61665 | + | 3.19458i | ||||
\(59\) | 0 | 0 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.126427 | − | 0.991976i | \(-0.540351\pi\) | ||||
0.126427 | + | 0.991976i | \(0.459649\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.421786 | − | 0.906696i | −0.421786 | − | 0.906696i | ||||
\(64\) | −5.19235 | − | 2.80996i | −5.19235 | − | 2.80996i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.61478 | − | 0.306192i | 1.61478 | − | 0.306192i | 0.701237 | − | 0.712928i | \(-0.252632\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.353856 | + | 0.0752144i | −0.353856 | + | 0.0752144i | −0.381410 | − | 0.924406i | \(-0.624561\pi\) |
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(72\) | 1.21324 | − | 3.59849i | 1.21324 | − | 3.59849i | ||||
\(73\) | 0 | 0 | 0.693336 | − | 0.720615i | \(-0.256140\pi\) | ||||
−0.693336 | + | 0.720615i | \(0.743860\pi\) | |||||||
\(74\) | 2.52547 | + | 2.86776i | 2.52547 | + | 2.86776i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.628472 | − | 1.47681i | 0.628472 | − | 1.47681i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.64652 | − | 0.647707i | 1.64652 | − | 0.647707i | 0.652586 | − | 0.757715i | \(-0.273684\pi\) |
0.993931 | + | 0.110008i | \(0.0350877\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.988116 | + | 0.153712i | 0.988116 | + | 0.153712i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.992658 | − | 0.120958i | \(-0.961404\pi\) | ||||
0.992658 | + | 0.120958i | \(0.0385965\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.35310 | − | 2.09537i | 2.35310 | − | 2.09537i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.59498 | − | 2.41750i | 5.59498 | − | 2.41750i | ||||
\(89\) | 0 | 0 | −0.391577 | − | 0.920146i | \(-0.628070\pi\) | ||||
0.391577 | + | 0.920146i | \(0.371930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.212507 | − | 0.706672i | −0.212507 | − | 0.706672i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.266796 | − | 0.963753i | \(-0.414035\pi\) | ||||
−0.266796 | + | 0.963753i | \(0.585965\pi\) | |||||||
\(98\) | −1.80836 | + | 0.805135i | −1.80836 | + | 0.805135i | ||||
\(99\) | 0.877839 | + | 1.34363i | 0.877839 | + | 1.34363i | ||||
\(100\) | −2.06931 | + | 2.05794i | −2.06931 | + | 2.05794i | ||||
\(101\) | 0 | 0 | 0.834139 | − | 0.551554i | \(-0.185965\pi\) | ||||
−0.834139 | + | 0.551554i | \(0.814035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.81050 | − | 1.31541i | 1.81050 | − | 1.31541i | ||||
\(107\) | −0.174175 | − | 0.151690i | −0.174175 | − | 0.151690i | 0.565270 | − | 0.824906i | \(-0.308772\pi\) |
−0.739446 | + | 0.673216i | \(0.764912\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.922290 | − | 1.59745i | −0.922290 | − | 1.59745i | −0.795863 | − | 0.605477i | \(-0.792982\pi\) |
−0.126427 | − | 0.991976i | \(-0.540351\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.33286 | − | 1.54107i | −4.33286 | − | 1.54107i | ||||
\(113\) | 0.0320799 | − | 0.446962i | 0.0320799 | − | 0.446962i | −0.956036 | − | 0.293250i | \(-0.905263\pi\) |
0.988116 | − | 0.153712i | \(-0.0491228\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.64238 | + | 2.51233i | −4.64238 | + | 2.51233i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.403690 | + | 1.52337i | −0.403690 | + | 1.52337i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.336571 | − | 1.95068i | 0.336571 | − | 1.95068i | ||||
\(127\) | 1.98424 | − | 0.153413i | 1.98424 | − | 0.153413i | 0.984487 | − | 0.175457i | \(-0.0561404\pi\) |
0.999757 | + | 0.0220445i | \(0.00701754\pi\) | |||||||
\(128\) | −2.88128 | − | 5.69356i | −2.88128 | − | 5.69356i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.97215 | + | 1.32328i | 2.97215 | + | 1.32328i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0770492 | − | 0.170520i | 0.0770492 | − | 0.170520i | −0.868768 | − | 0.495219i | \(-0.835088\pi\) |
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.565270 | − | 0.824906i | \(-0.691228\pi\) | ||||
0.565270 | + | 0.824906i | \(0.308772\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.660457 | − | 0.276774i | −0.660457 | − | 0.276774i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.69045 | − | 2.74393i | 3.69045 | − | 2.74393i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.650614 | + | 5.59608i | 0.650614 | + | 5.59608i | ||||
\(149\) | −0.382583 | + | 0.0253405i | −0.382583 | + | 0.0253405i | −0.256156 | − | 0.966635i | \(-0.582456\pi\) |
−0.126427 | + | 0.991976i | \(0.540351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.468021 | − | 1.76613i | −0.468021 | − | 1.76613i | −0.627176 | − | 0.778877i | \(-0.715789\pi\) |
0.159156 | − | 0.987253i | \(-0.449123\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.68809 | − | 1.69347i | 2.68809 | − | 1.69347i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.731980 | − | 0.681326i | \(-0.761404\pi\) | ||||
0.731980 | + | 0.681326i | \(0.238596\pi\) | |||||||
\(158\) | 3.40897 | + | 0.803533i | 3.40897 | + | 0.803533i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.109171 | − | 0.228072i | −0.109171 | − | 0.228072i | ||||
\(162\) | 1.43400 | + | 1.36458i | 1.43400 | + | 1.36458i | ||||
\(163\) | −0.710550 | + | 1.26265i | −0.710550 | + | 1.26265i | 0.245485 | + | 0.969400i | \(0.421053\pi\) |
−0.956036 | + | 0.293250i | \(0.905263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.441671 | + | 0.897177i | −0.441671 | + | 0.897177i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.61122 | − | 0.561887i | 4.61122 | − | 0.561887i | ||||
\(173\) | 0 | 0 | −0.815447 | − | 0.578832i | \(-0.803509\pi\) | ||||
0.815447 | + | 0.578832i | \(0.196491\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.592235 | + | 0.805765i | −0.592235 | + | 0.805765i | ||||
\(176\) | 7.23609 | + | 1.45490i | 7.23609 | + | 1.45490i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.26166 | − | 1.28270i | −1.26166 | − | 1.28270i | −0.942181 | − | 0.335105i | \(-0.891228\pi\) |
−0.319482 | − | 0.947592i | \(-0.603509\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.296723 | − | 0.913218i | 0.296723 | − | 0.913218i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.627284 | + | 0.983642i | −0.627284 | + | 0.983642i | 0.371197 | + | 0.928554i | \(0.378947\pi\) |
−0.998482 | + | 0.0550878i | \(0.982456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.766039 | − | 0.162827i | −0.766039 | − | 0.162827i | −0.191711 | − | 0.981451i | \(-0.561404\pi\) |
−0.574329 | + | 0.818625i | \(0.694737\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.86733 | − | 0.543697i | −2.86733 | − | 0.543697i | ||||
\(197\) | −1.93450 | − | 0.344771i | −1.93450 | − | 0.344771i | −0.934564 | − | 0.355794i | \(-0.884211\pi\) |
−0.999939 | + | 0.0110229i | \(0.996491\pi\) | |||||||
\(198\) | −0.0875416 | + | 3.17585i | −0.0875416 | + | 3.17585i | ||||
\(199\) | 0 | 0 | −0.999939 | − | 0.0110229i | \(-0.996491\pi\) | ||||
0.999939 | + | 0.0110229i | \(0.00350877\pi\) | |||||||
\(200\) | −3.73860 | + | 0.666301i | −3.73860 | + | 0.666301i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.43949 | + | 1.09513i | −1.43949 | + | 1.09513i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.250262 | + | 0.0361102i | 0.250262 | + | 0.0361102i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0948019 | − | 0.0754800i | 0.0948019 | − | 0.0754800i | −0.574329 | − | 0.818625i | \(-0.694737\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(212\) | 3.29859 | − | 0.0727334i | 3.29859 | − | 0.0727334i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.112237 | − | 0.443213i | −0.112237 | − | 0.443213i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.301526 | − | 3.63887i | 0.301526 | − | 3.63887i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.441671 | − | 0.897177i | \(-0.645614\pi\) | ||||
0.441671 | + | 0.897177i | \(0.354386\pi\) | |||||||
\(224\) | −3.09492 | − | 4.30955i | −3.09492 | − | 4.30955i | ||||
\(225\) | −0.340293 | − | 0.940319i | −0.340293 | − | 0.940319i | ||||
\(226\) | 0.556329 | − | 0.690893i | 0.556329 | − | 0.690893i | ||||
\(227\) | 0 | 0 | −0.884667 | − | 0.466224i | \(-0.845614\pi\) | ||||
0.884667 | + | 0.466224i | \(0.154386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.509516 | − | 0.860461i | \(-0.670175\pi\) | ||||
0.509516 | + | 0.860461i | \(0.329825\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.82693 | − | 0.755604i | −6.82693 | − | 0.755604i | ||||
\(233\) | −0.372922 | + | 0.207162i | −0.372922 | + | 0.207162i | −0.660898 | − | 0.750475i | \(-0.729825\pi\) |
0.287976 | + | 0.957638i | \(0.407018\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.435054 | + | 1.80119i | 0.435054 | + | 1.80119i | 0.583317 | + | 0.812244i | \(0.301754\pi\) |
−0.148264 | + | 0.988948i | \(0.547368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.846095 | − | 0.533032i | \(-0.821053\pi\) | ||||
0.846095 | + | 0.533032i | \(0.178947\pi\) | |||||||
\(242\) | −2.37495 | + | 2.02275i | −2.37495 | + | 2.02275i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.480787 | − | 0.876837i | \(-0.659649\pi\) | ||||
0.480787 | + | 0.876837i | \(0.340351\pi\) | |||||||
\(252\) | 2.04650 | − | 2.08062i | 2.04650 | − | 2.08062i | ||||
\(253\) | 0.225696 | + | 0.337275i | 0.225696 | + | 0.337275i | ||||
\(254\) | 3.40083 | + | 1.98854i | 3.40083 | + | 1.98854i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.924040 | − | 6.66370i | 0.924040 | − | 6.66370i | ||||
\(257\) | 0 | 0 | −0.213300 | − | 0.976987i | \(-0.568421\pi\) | ||||
0.213300 | + | 0.976987i | \(0.431579\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.515027 | + | 1.86045i | 0.515027 | + | 1.86045i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.109590 | − | 1.80539i | −0.109590 | − | 1.80539i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.65441 | + | 0.0729943i | 1.65441 | + | 0.0729943i | 0.851919 | − | 0.523673i | \(-0.175439\pi\) |
0.802489 | + | 0.596667i | \(0.203509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.48928 | + | 4.10009i | 2.48928 | + | 4.10009i | ||||
\(269\) | 0 | 0 | 0.340293 | − | 0.940319i | \(-0.389474\pi\) | ||||
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.317672 | − | 0.190480i | 0.317672 | − | 0.190480i | ||||
\(275\) | 0.756094 | − | 1.41572i | 0.756094 | − | 1.41572i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.628136 | − | 1.57129i | −0.628136 | − | 1.57129i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.180881 | − | 0.983505i | \(-0.442105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.35069 | + | 0.789779i | −1.35069 | + | 0.789779i | −0.989750 | − | 0.142811i | \(-0.954386\pi\) |
−0.360939 | + | 0.932589i | \(0.617544\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.999453 | − | 0.0330634i | \(-0.0105263\pi\) | ||||
−0.999453 | + | 0.0330634i | \(0.989474\pi\) | |||||||
\(284\) | −0.567674 | − | 0.890167i | −0.567674 | − | 0.890167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.30283 | − | 0.175425i | 5.30283 | − | 0.175425i | ||||
\(289\) | −0.899598 | − | 0.436719i | −0.899598 | − | 0.436719i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.00551154 | − | 0.999985i | \(-0.498246\pi\) | ||||
−0.00551154 | + | 0.999985i | \(0.501754\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.45348 | + | 6.46637i | −3.45348 | + | 6.46637i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.650934 | − | 0.390307i | −0.650934 | − | 0.390307i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.53167 | − | 0.433114i | 1.53167 | − | 0.433114i | ||||
\(302\) | 1.23075 | − | 3.40088i | 1.23075 | − | 3.40088i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.360939 | − | 0.932589i | \(-0.617544\pi\) | ||||
0.360939 | + | 0.932589i | \(0.382456\pi\) | |||||||
\(308\) | 4.67945 | + | 0.206462i | 4.67945 | + | 0.206462i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.942181 | − | 0.335105i | \(-0.108772\pi\) | ||||
−0.942181 | + | 0.335105i | \(0.891228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.635724 | − | 0.771917i | \(-0.719298\pi\) | ||||
0.635724 | + | 0.771917i | \(0.280702\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.45516 | + | 3.83735i | 3.45516 | + | 3.83735i | ||||
\(317\) | 1.18327 | + | 0.691882i | 1.18327 | + | 0.691882i | 0.959210 | − | 0.282694i | \(-0.0912281\pi\) |
0.224056 | + | 0.974576i | \(0.428070\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.03565 | − | 2.06959i | 2.03565 | − | 2.06959i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0796612 | − | 0.494144i | 0.0796612 | − | 0.494144i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.591031 | + | 2.85795i | 0.591031 | + | 2.85795i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.58005 | + | 1.25251i | −2.58005 | + | 1.25251i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.160640 | + | 1.52838i | 0.160640 | + | 1.52838i | 0.716783 | + | 0.697297i | \(0.245614\pi\) |
−0.556143 | + | 0.831087i | \(0.687719\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.83262 | − | 0.606642i | −1.83262 | − | 0.606642i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.106650 | − | 0.836802i | 0.106650 | − | 0.836802i | −0.846095 | − | 0.533032i | \(-0.821053\pi\) |
0.952745 | − | 0.303771i | \(-0.0982456\pi\) | |||||||
\(338\) | −1.73043 | + | 0.961271i | −1.73043 | + | 0.961271i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.999453 | − | 0.0330634i | −0.999453 | − | 0.0330634i | ||||
\(344\) | 5.34746 | + | 2.81814i | 5.34746 | + | 2.81814i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.286392 | + | 0.398788i | 0.286392 | + | 0.398788i | 0.930586 | − | 0.366074i | \(-0.119298\pi\) |
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.775409 | − | 0.631460i | \(-0.217544\pi\) | ||||
−0.775409 | + | 0.631460i | \(0.782456\pi\) | |||||||
\(350\) | −1.87225 | + | 0.642743i | −1.87225 | + | 0.642743i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.90415 | + | 6.13645i | 5.90415 | + | 6.13645i | ||||
\(353\) | 0 | 0 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.605558 | − | 3.50965i | −0.605558 | − | 3.50965i | ||||
\(359\) | −1.94618 | + | 0.0429130i | −1.94618 | + | 0.0429130i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.968033 | + | 0.250825i | \(0.919298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.761300 | + | 0.648400i | 0.761300 | + | 0.648400i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.0935596 | − | 0.995614i | \(-0.529825\pi\) | ||||
0.0935596 | + | 0.995614i | \(0.470175\pi\) | |||||||
\(368\) | 0.925439 | − | 0.704056i | 0.925439 | − | 0.704056i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.11300 | − | 0.198361i | 1.11300 | − | 0.198361i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0204562 | − | 0.742113i | 0.0204562 | − | 0.742113i | −0.917973 | − | 0.396642i | \(-0.870175\pi\) |
0.938430 | − | 0.345471i | \(-0.112281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.830966 | − | 1.40332i | 0.830966 | − | 1.40332i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.12989 | + | 0.892563i | −2.12989 | + | 0.892563i | ||||
\(383\) | 0 | 0 | 0.851919 | − | 0.523673i | \(-0.175439\pi\) | ||||
−0.851919 | + | 0.523673i | \(0.824561\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.06247 | − | 1.12891i | −1.06247 | − | 1.12891i | ||||
\(387\) | −0.491870 | + | 1.51382i | −0.491870 | + | 1.51382i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.00986267 | − | 0.00492300i | 0.00986267 | − | 0.00492300i | −0.441671 | − | 0.897177i | \(-0.645614\pi\) |
0.451533 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.66296 | − | 2.70736i | −2.66296 | − | 2.70736i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.75800 | − | 2.74284i | −2.75800 | − | 2.74284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.77403 | + | 3.77420i | −2.77403 | + | 3.77420i | ||||
\(397\) | 0 | 0 | −0.874174 | − | 0.485613i | \(-0.838596\pi\) | ||||
0.874174 | + | 0.485613i | \(0.161404\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.18030 | − | 1.91668i | −4.18030 | − | 1.91668i | ||||
\(401\) | −1.25411 | + | 0.209273i | −1.25411 | + | 0.209273i | −0.754107 | − | 0.656752i | \(-0.771930\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.57687 | + | 0.157816i | −3.57687 | + | 0.157816i | ||||
\(407\) | −1.24456 | − | 2.83732i | −1.24456 | − | 2.83732i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.724425 | − | 0.689353i | \(-0.757895\pi\) | ||||
0.724425 | + | 0.689353i | \(0.242105\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.366373 | + | 0.341020i | 0.366373 | + | 0.341020i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.565270 | − | 0.824906i | \(-0.308772\pi\) | ||||
−0.565270 | + | 0.824906i | \(0.691228\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.92132 | + | 0.430577i | 1.92132 | + | 0.430577i | 0.999028 | + | 0.0440782i | \(0.0140351\pi\) |
0.922290 | + | 0.386499i | \(0.126316\pi\) | |||||||
\(422\) | 0.239352 | − | 0.0158536i | 0.239352 | − | 0.0158536i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.58116 | + | 2.36795i | 3.58116 | + | 2.36795i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.236353 | − | 0.631270i | 0.236353 | − | 0.631270i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.06339 | − | 0.326178i | 1.06339 | − | 0.326178i | 0.287976 | − | 0.957638i | \(-0.407018\pi\) |
0.775409 | + | 0.631460i | \(0.217544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.652586 | − | 0.757715i | \(-0.273684\pi\) | ||||
−0.652586 | + | 0.757715i | \(0.726316\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.42227 | − | 4.15543i | 3.42227 | − | 4.15543i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.828009 | − | 0.560715i | \(-0.810526\pi\) | ||||
0.828009 | + | 0.560715i | \(0.189474\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.583317 | − | 0.812244i | 0.583317 | − | 0.812244i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.269579 | − | 0.532702i | −0.269579 | − | 0.532702i | 0.716783 | − | 0.697297i | \(-0.245614\pi\) |
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.0976152 | − | 5.90312i | −0.0976152 | − | 5.90312i | ||||
\(449\) | −0.919097 | + | 1.76755i | −0.919097 | + | 1.76755i | −0.381410 | + | 0.924406i | \(0.624561\pi\) |
−0.537687 | + | 0.843145i | \(0.680702\pi\) | |||||||
\(450\) | 0.507061 | − | 1.91345i | 0.507061 | − | 1.91345i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.25443 | − | 0.369701i | 1.25443 | − | 0.369701i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.05387 | + | 0.680268i | −1.05387 | + | 0.680268i | −0.949339 | − | 0.314254i | \(-0.898246\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.876642 | − | 0.216861i | 0.876642 | − | 0.216861i | 0.224056 | − | 0.974576i | \(-0.428070\pi\) |
0.652586 | + | 0.757715i | \(0.273684\pi\) | |||||||
\(464\) | −6.27254 | − | 5.46276i | −6.27254 | − | 5.46276i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.840301 | − | 0.0836393i | −0.840301 | − | 0.0836393i | ||||
\(467\) | 0 | 0 | 0.952745 | − | 0.303771i | \(-0.0982456\pi\) | ||||
−0.952745 | + | 0.303771i | \(0.901754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.05877 | + | 1.25709i | 1.05877 | + | 1.25709i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.33382 | + | 1.03908i | −2.33382 | + | 1.03908i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.454133 | + | 1.03532i | −0.454133 | + | 1.03532i | ||||
\(478\) | −1.32392 | + | 3.42073i | −1.32392 | + | 3.42073i | ||||
\(479\) | 0 | 0 | −0.287976 | − | 0.957638i | \(-0.592982\pi\) | ||||
0.287976 | + | 0.957638i | \(0.407018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.57668 | + | 0.455539i | −4.57668 | + | 0.455539i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.47566 | − | 1.34349i | −1.47566 | − | 1.34349i | −0.782322 | − | 0.622874i | \(-0.785965\pi\) |
−0.693336 | − | 0.720615i | \(-0.743860\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.84997 | − | 0.266932i | 1.84997 | − | 0.266932i | 0.874174 | − | 0.485613i | \(-0.161404\pi\) |
0.975796 | + | 0.218681i | \(0.0701754\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.239087 | − | 0.271493i | −0.239087 | − | 0.271493i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.422290 | − | 1.25252i | 0.422290 | − | 1.25252i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.922290 | − | 0.386499i | \(-0.126316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.991264 | − | 0.131892i | \(-0.0421053\pi\) | ||||
−0.991264 | + | 0.131892i | \(0.957895\pi\) | |||||||
\(504\) | 3.73103 | − | 0.707471i | 3.73103 | − | 0.707471i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.0132822 | + | 0.803219i | −0.0132822 | + | 0.803219i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.44979 | + | 5.26622i | 2.44979 | + | 5.26622i | ||||
\(509\) | 0 | 0 | −0.592235 | − | 0.805765i | \(-0.701754\pi\) | ||||
0.592235 | + | 0.805765i | \(0.298246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.69756 | − | 5.10291i | 4.69756 | − | 5.10291i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.26066 | + | 3.60732i | −1.26066 | + | 3.60732i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.180881 | − | 0.983505i | \(-0.442105\pi\) | ||||
−0.180881 | + | 0.983505i | \(0.557895\pi\) | |||||||
\(522\) | 1.85809 | − | 3.06046i | 1.85809 | − | 3.06046i | ||||
\(523\) | 0 | 0 | −0.627176 | − | 0.778877i | \(-0.715789\pi\) | ||||
0.627176 | + | 0.778877i | \(0.284211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.60891 | + | 1.98481i | 2.60891 | + | 1.98481i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.927888 | − | 0.123460i | −0.927888 | − | 0.123460i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.378168 | + | 6.22996i | −0.378168 | + | 6.22996i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.59524 | − | 0.176561i | 1.59524 | − | 0.176561i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.86547 | − | 0.686748i | 1.86547 | − | 0.686748i | 0.894729 | − | 0.446609i | \(-0.147368\pi\) |
0.970739 | − | 0.240139i | \(-0.0771930\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.55203 | − | 0.457408i | −1.55203 | − | 0.457408i | −0.609854 | − | 0.792514i | \(-0.708772\pi\) |
−0.942181 | + | 0.335105i | \(0.891228\pi\) | |||||||
\(548\) | 0.544898 | + | 0.0360916i | 0.544898 | + | 0.0360916i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.82679 | − | 1.45015i | 2.82679 | − | 1.45015i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.37196 | + | 1.11726i | 1.37196 | + | 1.11726i | ||||
\(554\) | 0.750518 | − | 3.26453i | 0.750518 | − | 3.26453i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.187074 | − | 1.99074i | 0.187074 | − | 1.99074i | 0.0715891 | − | 0.997434i | \(-0.477193\pi\) |
0.115485 | − | 0.993309i | \(-0.463158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.08800 | − | 0.238750i | −3.08800 | − | 0.238750i | ||||
\(563\) | 0 | 0 | 0.245485 | − | 0.969400i | \(-0.421053\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.350638 | + | 0.936511i | 0.350638 | + | 0.936511i | ||||
\(568\) | 0.0529891 | − | 1.37277i | 0.0529891 | − | 1.37277i | ||||
\(569\) | 1.42787 | + | 0.990062i | 1.42787 | + | 0.990062i | 0.996114 | + | 0.0880708i | \(0.0280702\pi\) |
0.431754 | + | 0.901991i | \(0.357895\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.754107 | + | 0.656752i | −0.754107 | + | 0.656752i | ||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0886600 | − | 0.236800i | −0.0886600 | − | 0.236800i | ||||
\(576\) | 4.96029 | + | 3.20185i | 4.96029 | + | 3.20185i | ||||
\(577\) | 0 | 0 | 0.601081 | − | 0.799188i | \(-0.294737\pi\) | ||||
−0.601081 | + | 0.799188i | \(0.705263\pi\) | |||||||
\(578\) | −0.970793 | − | 1.72510i | −0.970793 | − | 1.72510i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.72257 | + | 0.570211i | −1.72257 | + | 0.570211i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.754107 | − | 0.656752i | \(-0.228070\pi\) | ||||
−0.754107 | + | 0.656752i | \(0.771930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.89879 | + | 4.05209i | −7.89879 | + | 4.05209i | ||||
\(593\) | 0 | 0 | −0.0495838 | − | 0.998770i | \(-0.515789\pi\) | ||||
0.0495838 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.460759 | − | 1.01972i | −0.460759 | − | 1.01972i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.491404 | − | 0.583452i | 0.491404 | − | 0.583452i | −0.461341 | − | 0.887223i | \(-0.652632\pi\) |
0.952745 | + | 0.303771i | \(0.0982456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.938430 | − | 0.345471i | \(-0.112281\pi\) | ||||
−0.938430 | + | 0.345471i | \(0.887719\pi\) | |||||||
\(602\) | 2.98010 | + | 1.02307i | 2.98010 | + | 1.02307i | ||||
\(603\) | −1.63358 | + | 0.180805i | −1.63358 | + | 0.180805i | ||||
\(604\) | 4.34814 | − | 3.08646i | 4.34814 | − | 3.08646i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.277403 | − | 0.960754i | \(-0.589474\pi\) | ||||
0.277403 | + | 0.960754i | \(0.410526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.77383 | + | 0.236016i | 1.77383 | + | 0.236016i | 0.945817 | − | 0.324699i | \(-0.105263\pi\) |
0.828009 | + | 0.560715i | \(0.189474\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.85072 | + | 3.69033i | 4.85072 | + | 3.69033i | ||||
\(617\) | −0.644267 | − | 0.512956i | −0.644267 | − | 0.512956i | 0.245485 | − | 0.969400i | \(-0.421053\pi\) |
−0.889752 | + | 0.456444i | \(0.849123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.627176 | − | 0.778877i | \(-0.715789\pi\) | ||||
0.627176 | + | 0.778877i | \(0.284211\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.660898 | + | 0.750475i | −0.660898 | + | 0.750475i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.986456 | − | 0.255598i | −0.986456 | − | 0.255598i | −0.277403 | − | 0.960754i | \(-0.589474\pi\) |
−0.709053 | + | 0.705155i | \(0.750877\pi\) | |||||||
\(632\) | 0.849470 | + | 6.66515i | 0.849470 | + | 6.66515i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.14443 | + | 2.46014i | 1.14443 | + | 2.46014i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.64578 | − | 1.07054i | 5.64578 | − | 1.07054i | ||||
\(639\) | 0.358601 | − | 0.0477135i | 0.358601 | − | 0.0477135i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.886736 | − | 1.12641i | 0.886736 | − | 1.12641i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.991264 | − | 0.131892i | \(-0.0421053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.319482 | − | 0.947592i | \(-0.396491\pi\) | ||||
−0.319482 | + | 0.947592i | \(0.603509\pi\) | |||||||
\(644\) | 0.511635 | − | 0.531765i | 0.511635 | − | 0.531765i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.00551154 | − | 0.999985i | \(-0.501754\pi\) | ||||
0.00551154 | + | 0.999985i | \(0.498246\pi\) | |||||||
\(648\) | −1.48702 | + | 3.49426i | −1.48702 | + | 3.49426i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.17810 | − | 0.649949i | −4.17810 | − | 0.649949i | ||||
\(653\) | 0.345057 | + | 0.212106i | 0.345057 | + | 0.212106i | 0.685350 | − | 0.728214i | \(-0.259649\pi\) |
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.21337 | − | 0.524280i | 1.21337 | − | 0.524280i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(662\) | −1.46260 | + | 2.66743i | −1.46260 | + | 2.66743i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.29689 | − | 3.05391i | −2.29689 | − | 3.05391i | ||||
\(667\) | −0.0327405 | − | 0.456166i | −0.0327405 | − | 0.456166i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0355007 | − | 0.0421506i | −0.0355007 | − | 0.0421506i | 0.746821 | − | 0.665025i | \(-0.231579\pi\) |
−0.782322 | + | 0.622874i | \(0.785965\pi\) | |||||||
\(674\) | 1.11735 | − | 1.24094i | 1.11735 | − | 1.24094i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.90407 | − | 0.289056i | −2.90407 | − | 0.289056i | ||||
\(677\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.81326 | + | 0.644922i | 1.81326 | + | 0.644922i | 0.997814 | + | 0.0660906i | \(0.0210526\pi\) |
0.815447 | + | 0.578832i | \(0.196491\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.58853 | − | 1.18110i | −1.58853 | − | 1.18110i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.37700 | + | 6.49444i | 3.37700 | + | 6.49444i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.652586 | − | 0.757715i | \(-0.726316\pi\) | ||||
0.652586 | + | 0.757715i | \(0.273684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.740442 | + | 1.42397i | −0.740442 | + | 1.42397i | ||||
\(694\) | 0.0160690 | + | 0.971744i | 0.0160690 | + | 0.971744i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.80830 | − | 0.794112i | −2.80830 | − | 0.794112i | ||||
\(701\) | −1.01353 | + | 1.41130i | −1.01353 | + | 1.41130i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.909007 | + | 0.416782i | \(0.863158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.50811 | + | 9.35489i | 1.50811 | + | 9.35489i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.23905 | + | 1.43866i | −1.23905 | + | 1.43866i | −0.381410 | + | 0.924406i | \(0.624561\pi\) |
−0.857640 | + | 0.514250i | \(0.828070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.69155 | + | 0.518857i | −1.69155 | + | 0.518857i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.21472 | − | 4.76089i | 2.21472 | − | 4.76089i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.21427 | − | 2.12536i | −3.21427 | − | 2.12536i | ||||
\(719\) | 0 | 0 | −0.115485 | − | 0.993309i | \(-0.536842\pi\) | ||||
0.115485 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.507061 | + | 1.91345i | 0.507061 | + | 1.91345i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.53034 | + | 0.964102i | −1.53034 | + | 0.964102i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.768401 | − | 0.639969i | \(-0.778947\pi\) | ||||
0.768401 | + | 0.639969i | \(0.221053\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.973327 | − | 0.229424i | −0.973327 | − | 0.229424i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.724425 | − | 0.689353i | \(-0.757895\pi\) | ||||
0.724425 | + | 0.689353i | \(0.242105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.34027 | − | 0.0591341i | 1.34027 | − | 0.0591341i | ||||
\(737\) | −1.97002 | − | 1.75425i | −1.97002 | − | 1.75425i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.0615498 | + | 0.267723i | 0.0615498 | + | 0.267723i | 0.996114 | − | 0.0880708i | \(-0.0280702\pi\) |
−0.934564 | + | 0.355794i | \(0.884211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.03427 | + | 0.932718i | 2.03427 | + | 0.932718i | ||||
\(743\) | 0.294350 | − | 0.0358672i | 0.294350 | − | 0.0358672i | 0.0275543 | − | 0.999620i | \(-0.491228\pi\) |
0.266796 | + | 0.963753i | \(0.414035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.870331 | − | 1.18413i | 0.870331 | − | 1.18413i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0467753 | − | 0.226183i | 0.0467753 | − | 0.226183i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.454508 | − | 1.51142i | 0.454508 | − | 1.51142i | −0.360939 | − | 0.932589i | \(-0.617544\pi\) |
0.815447 | − | 0.578832i | \(-0.196491\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.65511 | + | 1.12082i | −1.65511 | + | 1.12082i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.846095 | + | 0.533032i | \(0.821053\pi\) | |||||||
\(758\) | 2.93460 | − | 1.34552i | 2.93460 | − | 1.34552i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.0385714 | − | 0.999256i | \(-0.512281\pi\) | ||||
0.0385714 | + | 0.999256i | \(0.487719\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.939842 | − | 1.58719i | 0.939842 | − | 1.58719i | ||||
\(764\) | −3.33033 | − | 0.707883i | −3.33033 | − | 0.707883i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 0.0275543 | − | 0.999620i | \(-0.491228\pi\) | ||||
−0.0275543 | + | 0.999620i | \(0.508772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.338867 | − | 2.26031i | −0.338867 | − | 2.26031i | ||||
\(773\) | 0 | 0 | −0.999757 | − | 0.0220445i | \(-0.992982\pi\) | ||||
0.999757 | + | 0.0220445i | \(0.00701754\pi\) | |||||||
\(774\) | −2.50762 | + | 1.90775i | −2.50762 | + | 1.90775i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.0215965 | + | 0.00311616i | 0.0215965 | + | 0.00311616i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.442025 | + | 0.376473i | 0.442025 | + | 0.376473i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.781920 | − | 4.53180i | −0.781920 | − | 4.53180i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.934564 | − | 0.355794i | \(-0.884211\pi\) | ||||
0.934564 | + | 0.355794i | \(0.115789\pi\) | |||||||
\(788\) | −1.03729 | − | 5.64006i | −1.03729 | − | 5.64006i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.405253 | − | 0.191244i | 0.405253 | − | 0.191244i | ||||
\(792\) | −5.76468 | + | 1.97902i | −5.76468 | + | 1.97902i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.627176 | − | 0.778877i | \(-0.284211\pi\) | ||||
−0.627176 | + | 0.778877i | \(0.715789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2.70335 | − | 4.56537i | −2.70335 | − | 4.56537i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.27611 | − | 1.07412i | −2.27611 | − | 1.07412i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.445781 | + | 0.147564i | 0.445781 | + | 0.147564i | 0.528360 | − | 0.849020i | \(-0.322807\pi\) |
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(812\) | −4.46619 | − | 2.81366i | −4.46619 | − | 2.81366i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.17577 | − | 6.01928i | 1.17577 | − | 6.01928i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.36537 | − | 1.45077i | 1.36537 | − | 1.45077i | 0.618553 | − | 0.785743i | \(-0.287719\pi\) |
0.746821 | − | 0.665025i | \(-0.231579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.779976 | + | 0.792980i | −0.779976 | + | 0.792980i | −0.982493 | − | 0.186298i | \(-0.940351\pi\) |
0.202517 | + | 0.979279i | \(0.435088\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.0906279 | − | 0.653561i | 0.0906279 | − | 0.653561i | −0.889752 | − | 0.456444i | \(-0.849123\pi\) |
0.980380 | − | 0.197117i | \(-0.0631579\pi\) | |||||||
\(828\) | 0.157401 | + | 0.720951i | 0.157401 | + | 0.720951i | ||||
\(829\) | 0 | 0 | −0.635724 | − | 0.771917i | \(-0.719298\pi\) | ||||
0.635724 | + | 0.771917i | \(0.280702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.518970 | − | 0.854793i | \(-0.673684\pi\) | ||||
0.518970 | + | 0.854793i | \(0.326316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.18574 | + | 0.618069i | −2.18574 | + | 0.618069i | ||||
\(842\) | 2.63976 | + | 2.86755i | 2.63976 | + | 2.86755i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.303308 | + | 0.181867i | 0.303308 | + | 0.181867i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.52557 | + | 0.395288i | −1.52557 | + | 0.395288i | ||||
\(848\) | 1.92988 | + | 4.82763i | 1.92988 | + | 4.82763i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.465047 | − | 0.148274i | −0.465047 | − | 0.148274i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.899598 | − | 0.436719i | \(-0.856140\pi\) | ||||
0.899598 | + | 0.436719i | \(0.143860\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.720789 | − | 0.499784i | 0.720789 | − | 0.499784i | ||||
\(857\) | 0 | 0 | 0.821778 | − | 0.569808i | \(-0.192982\pi\) | ||||
−0.821778 | + | 0.569808i | \(0.807018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.999453 | − | 0.0330634i | \(-0.0105263\pi\) | ||||
−0.999453 | + | 0.0330634i | \(0.989474\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.09773 | + | 0.668833i | 2.09773 | + | 0.668833i | ||||
\(863\) | −1.70851 | − | 0.738219i | −1.70851 | − | 0.738219i | −0.999453 | − | 0.0330634i | \(-0.989474\pi\) |
−0.709053 | − | 0.705155i | \(-0.750877\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.43547 | − | 1.46034i | −2.43547 | − | 1.46034i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.74051 | − | 1.90603i | 6.74051 | − | 1.90603i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.55676 | + | 1.21167i | −1.55676 | + | 1.21167i | −0.677282 | + | 0.735724i | \(0.736842\pi\) |
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.0605901 | − | 0.998163i | \(-0.519298\pi\) | ||||
0.0605901 | + | 0.998163i | \(0.480702\pi\) | |||||||
\(882\) | 1.86505 | − | 0.663341i | 1.86505 | − | 0.663341i | ||||
\(883\) | −0.0557755 | − | 0.201479i | −0.0557755 | − | 0.201479i | 0.930586 | − | 0.366074i | \(-0.119298\pi\) |
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.162327 | − | 1.17062i | 0.162327 | − | 1.17062i | ||||
\(887\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.10682 | + | 1.65400i | 1.10682 | + | 1.65400i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.771653 | − | 1.40730i | −0.771653 | − | 1.40730i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.54880 | − | 5.30325i | 3.54880 | − | 5.30325i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.48879 | + | 1.83861i | −3.48879 | + | 1.83861i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 2.22179 | − | 1.89230i | 2.22179 | − | 1.89230i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.61550 | + | 0.534769i | 1.61550 | + | 0.534769i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.741267 | + | 1.85429i | −0.741267 | + | 1.85429i | −0.319482 | + | 0.947592i | \(0.603509\pi\) |
−0.421786 | + | 0.906696i | \(0.638596\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.76047 | − | 0.830786i | −1.76047 | − | 0.830786i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.782322 | − | 0.622874i | \(-0.785965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.48163 | − | 0.0820961i | −2.48163 | − | 0.0820961i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.300595 | + | 0.610607i | 0.300595 | + | 0.610607i | 0.993931 | − | 0.110008i | \(-0.0350877\pi\) |
−0.693336 | + | 0.720615i | \(0.743860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.349175 | + | 1.89858i | 0.349175 | + | 1.89858i | ||||
\(926\) | 1.67065 | + | 0.636024i | 1.67065 | + | 0.636024i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.35581 | − | 9.30289i | −2.35581 | − | 9.30289i | ||||
\(929\) | 0 | 0 | −0.170028 | − | 0.985439i | \(-0.554386\pi\) | ||||
0.170028 | + | 0.985439i | \(0.445614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.947816 | − | 0.807255i | −0.947816 | − | 0.807255i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.868768 | − | 0.495219i | \(-0.835088\pi\) | ||||
0.868768 | + | 0.495219i | \(0.164912\pi\) | |||||||
\(938\) | 0.304388 | + | 3.23915i | 0.304388 | + | 3.23915i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.148264 | − | 0.988948i | \(-0.547368\pi\) | ||||
0.148264 | + | 0.988948i | \(0.452632\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.96847 | − | 0.942111i | −4.96847 | − | 0.942111i | ||||
\(947\) | 1.77680 | + | 0.0980289i | 1.77680 | + | 0.0980289i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.863256 | + | 0.504766i | \(0.168421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.09243 | + | 0.457797i | −1.09243 | + | 0.457797i | −0.857640 | − | 0.514250i | \(-0.828070\pi\) |
−0.234785 | + | 0.972047i | \(0.575439\pi\) | |||||||
\(954\) | −1.90651 | + | 1.17193i | −1.90651 | + | 1.17193i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.47770 | + | 3.03223i | −4.47770 | + | 3.03223i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.186392 | − | 0.0164797i | 0.186392 | − | 0.0164797i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.789141 | + | 0.614213i | 0.789141 | + | 0.614213i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.161964 | + | 0.164665i | 0.161964 | + | 0.164665i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.792565 | + | 1.07832i | −0.792565 | + | 1.07832i | 0.202517 | + | 0.979279i | \(0.435088\pi\) |
−0.995083 | + | 0.0990455i | \(0.968421\pi\) | |||||||
\(968\) | −5.23167 | − | 2.90625i | −5.23167 | − | 2.90625i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.909007 | − | 0.416782i | \(-0.863158\pi\) | ||||
0.909007 | + | 0.416782i | \(0.136842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.885098 | − | 3.84991i | −0.885098 | − | 3.84991i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.03693 | + | 0.0457505i | −1.03693 | + | 0.0457505i | −0.556143 | − | 0.831087i | \(-0.687719\pi\) |
−0.480787 | + | 0.876837i | \(0.659649\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.796405 | + | 1.66379i | 0.796405 | + | 1.66379i | ||||
\(982\) | 3.31045 | + | 1.65243i | 3.31045 | + | 1.65243i | ||||
\(983\) | 0 | 0 | −0.930586 | − | 0.366074i | \(-0.880702\pi\) | ||||
0.930586 | + | 0.366074i | \(0.119298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.120144 | + | 0.384123i | −0.120144 | + | 0.384123i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.499913 | − | 1.88648i | −0.499913 | − | 1.88648i | −0.461341 | − | 0.887223i | \(-0.652632\pi\) |
−0.0385714 | − | 0.999256i | \(-0.512281\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.0826992 | − | 0.711315i | −0.0826992 | − | 0.711315i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.421786 | − | 0.906696i | \(-0.361404\pi\) | ||||
−0.421786 | + | 0.906696i | \(0.638596\pi\) | |||||||
\(998\) | 2.09971 | − | 1.56118i | 2.09971 | − | 1.56118i | ||||
\(999\) | 0 | 0 |
(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 | 3997.1.cz.a.97.1 | ✓ | 144 | |
7.6 | odd | 2 | CM | 3997.1.cz.a.97.1 | ✓ | 144 | |
571.312 | even | 285 | inner | 3997.1.cz.a.2596.1 | yes | 144 | |
3997.2596 | odd | 570 | inner | 3997.1.cz.a.2596.1 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3997.1.cz.a.97.1 | ✓ | 144 | 1.1 | even | 1 | trivial | |
3997.1.cz.a.97.1 | ✓ | 144 | 7.6 | odd | 2 | CM | |
3997.1.cz.a.2596.1 | yes | 144 | 571.312 | even | 285 | inner | |
3997.1.cz.a.2596.1 | yes | 144 | 3997.2596 | odd | 570 | inner |