Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(17,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.cp (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.24 | ||
Character | \(\chi\) | \(=\) | 2016.17 |
Dual form | 2016.2.cp.b.593.24 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.87230 | − | 1.08097i | 0.837318 | − | 0.483426i | −0.0190339 | − | 0.999819i | \(-0.506059\pi\) |
0.856352 | + | 0.516393i | \(0.172726\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.55958 | − | 0.669737i | −0.967431 | − | 0.253137i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.67157 | + | 2.89525i | −0.503998 | + | 0.872949i | 0.495992 | + | 0.868327i | \(0.334805\pi\) |
−0.999989 | + | 0.00462217i | \(0.998529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.74247 | −0.483274 | −0.241637 | − | 0.970367i | \(-0.577684\pi\) | ||||
−0.241637 | + | 0.970367i | \(0.577684\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.283937 | − | 0.491793i | 0.0688648 | − | 0.119277i | −0.829537 | − | 0.558452i | \(-0.811396\pi\) |
0.898402 | + | 0.439174i | \(0.144729\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.270105 | − | 0.467836i | −0.0619664 | − | 0.107329i | 0.833378 | − | 0.552704i | \(-0.186404\pi\) |
−0.895344 | + | 0.445375i | \(0.853071\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.21616 | + | 3.01155i | −1.08764 | + | 0.627952i | −0.932948 | − | 0.360010i | \(-0.882773\pi\) |
−0.154696 | + | 0.987962i | \(0.549440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.162997 | + | 0.282319i | −0.0325994 | + | 0.0564638i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.77912 | 0.330374 | 0.165187 | − | 0.986262i | \(-0.447177\pi\) | ||||
0.165187 | + | 0.986262i | \(0.447177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.56726 | + | 3.79161i | 1.17952 | + | 0.680993i | 0.955902 | − | 0.293685i | \(-0.0948815\pi\) |
0.223613 | + | 0.974678i | \(0.428215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.51627 | + | 1.51289i | −0.932419 | + | 0.255725i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.60029 | + | 5.54273i | −1.57828 | + | 0.911219i | −0.583177 | + | 0.812345i | \(0.698191\pi\) |
−0.995100 | + | 0.0988741i | \(0.968476\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.77201 | −1.21378 | −0.606892 | − | 0.794785i | \(-0.707584\pi\) | ||||
−0.606892 | + | 0.794785i | \(0.707584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.80152i | 0.274730i | 0.990521 | + | 0.137365i | \(0.0438633\pi\) | ||||
−0.990521 | + | 0.137365i | \(0.956137\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.679499 | + | 1.17693i | 0.0991151 | + | 0.171672i | 0.911319 | − | 0.411702i | \(-0.135065\pi\) |
−0.812204 | + | 0.583374i | \(0.801732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.10291 | + | 3.42849i | 0.871844 | + | 0.489784i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.46832 | − | 2.54321i | 0.201689 | − | 0.349336i | −0.747383 | − | 0.664393i | \(-0.768690\pi\) |
0.949073 | + | 0.315057i | \(0.102023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.22769i | 0.974581i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.84763 | − | 5.68553i | −1.28205 | − | 0.740194i | −0.304830 | − | 0.952407i | \(-0.598599\pi\) |
−0.977223 | + | 0.212213i | \(0.931933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.60858 | + | 9.71434i | 0.718105 | + | 1.24379i | 0.961750 | + | 0.273929i | \(0.0883234\pi\) |
−0.243645 | + | 0.969864i | \(0.578343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.26242 | + | 1.88356i | −0.404654 | + | 0.233627i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7563 | − | 6.21014i | −1.31409 | − | 0.758689i | −0.331317 | − | 0.943519i | \(-0.607493\pi\) |
−0.982770 | + | 0.184830i | \(0.940826\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.79753i | 0.925397i | 0.886516 | + | 0.462698i | \(0.153119\pi\) | ||||
−0.886516 | + | 0.462698i | \(0.846881\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.56066 | + | 4.36515i | 0.884909 | + | 0.510902i | 0.872274 | − | 0.489018i | \(-0.162645\pi\) |
0.0126348 | + | 0.999920i | \(0.495978\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.21757 | − | 6.29110i | 0.708558 | − | 0.716938i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.77913 | + | 8.27770i | 0.537694 | + | 0.931314i | 0.999028 | + | 0.0440870i | \(0.0140379\pi\) |
−0.461333 | + | 0.887227i | \(0.652629\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 15.9958i | − | 1.75577i | −0.478875 | − | 0.877883i | \(-0.658955\pi\) | ||
0.478875 | − | 0.877883i | \(-0.341045\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.22771i | − | 0.133164i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.30930 | + | 10.9280i | 0.668784 | + | 1.15837i | 0.978244 | + | 0.207456i | \(0.0665184\pi\) |
−0.309460 | + | 0.950912i | \(0.600148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.45999 | + | 1.16699i | 0.467534 | + | 0.122334i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.01144 | − | 0.583953i | −0.103771 | − | 0.0599123i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4013i | 1.66530i | 0.553802 | + | 0.832649i | \(0.313177\pi\) | ||||
−0.553802 | + | 0.832649i | \(0.686823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4514 | − | 7.76615i | −1.33846 | − | 0.772761i | −0.351882 | − | 0.936044i | \(-0.614458\pi\) |
−0.986579 | + | 0.163283i | \(0.947792\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.69281 | − | 2.70939i | 0.462396 | − | 0.266964i | −0.250655 | − | 0.968076i | \(-0.580646\pi\) |
0.713051 | + | 0.701112i | \(0.247313\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.85983 | + | 3.22131i | 0.179796 | + | 0.311416i | 0.941811 | − | 0.336144i | \(-0.109123\pi\) |
−0.762014 | + | 0.647560i | \(0.775790\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.72483 | + | 3.30523i | 0.548340 | + | 0.316584i | 0.748452 | − | 0.663189i | \(-0.230797\pi\) |
−0.200112 | + | 0.979773i | \(0.564131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.32161i | − | 0.406543i | −0.979122 | − | 0.203272i | \(-0.934843\pi\) | ||
0.979122 | − | 0.203272i | \(-0.0651575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.51081 | + | 11.2771i | −0.607136 | + | 1.05159i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.05613 | + | 1.06862i | −0.0968154 | + | 0.0979603i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0882982 | − | 0.152937i | −0.00802711 | − | 0.0139034i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5145i | 1.02989i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.96976 | −0.618467 | −0.309233 | − | 0.950986i | \(-0.600072\pi\) | ||||
−0.309233 | + | 0.950986i | \(0.600072\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.62582 | − | 4.40277i | 0.666271 | − | 0.384672i | −0.128391 | − | 0.991724i | \(-0.540981\pi\) |
0.794662 | + | 0.607052i | \(0.207648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.378029 | + | 1.37836i | 0.0327793 | + | 0.119519i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.5256 | − | 8.38635i | −1.24100 | − | 0.716494i | −0.271705 | − | 0.962381i | \(-0.587588\pi\) |
−0.969299 | + | 0.245887i | \(0.920921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3308 | −0.876249 | −0.438124 | − | 0.898914i | \(-0.644357\pi\) | ||||
−0.438124 | + | 0.898914i | \(0.644357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.91266 | − | 5.04487i | 0.243569 | − | 0.421873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.33105 | − | 1.92318i | 0.276628 | − | 0.159711i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.10661 | − | 3.64876i | −0.172580 | − | 0.298918i | 0.766741 | − | 0.641957i | \(-0.221877\pi\) |
−0.939321 | + | 0.343039i | \(0.888544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.10493 | − | 5.37790i | 0.252676 | − | 0.437647i | −0.711586 | − | 0.702599i | \(-0.752023\pi\) |
0.964262 | + | 0.264952i | \(0.0853561\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.3945 | 1.31684 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3210 | − | 17.8764i | 0.823702 | − | 1.42669i | −0.0792057 | − | 0.996858i | \(-0.525238\pi\) |
0.902907 | − | 0.429835i | \(-0.141428\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.3681 | − | 4.21486i | 1.21118 | − | 0.332177i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.56609 | − | 2.05888i | 0.279317 | − | 0.161264i | −0.353797 | − | 0.935322i | \(-0.615110\pi\) |
0.633114 | + | 0.774058i | \(0.281776\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.2654 | −1.02651 | −0.513253 | − | 0.858237i | \(-0.671560\pi\) | ||||
−0.513253 | + | 0.858237i | \(0.671560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.96381 | −0.766447 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.4886 | + | 11.2517i | −1.48169 | + | 0.855453i | −0.999784 | − | 0.0207720i | \(-0.993388\pi\) |
−0.481903 | + | 0.876225i | \(0.660054\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.606283 | − | 0.613453i | 0.0458307 | − | 0.0463727i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.63774 | + | 16.6931i | −0.720358 | + | 1.24770i | 0.240498 | + | 0.970650i | \(0.422689\pi\) |
−0.960856 | + | 0.277048i | \(0.910644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.3500 | −1.66126 | −0.830631 | − | 0.556823i | \(-0.812020\pi\) | ||||
−0.830631 | + | 0.556823i | \(0.812020\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.9831 | + | 20.7553i | −0.881013 | + | 1.52596i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.949241 | + | 1.64413i | 0.0694154 | + | 0.120231i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.69175 | + | 3.28613i | −0.411841 | + | 0.237776i | −0.691580 | − | 0.722300i | \(-0.743085\pi\) |
0.279740 | + | 0.960076i | \(0.409752\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.70334 | − | 6.41438i | 0.266572 | − | 0.461717i | −0.701402 | − | 0.712766i | \(-0.747442\pi\) |
0.967974 | + | 0.251049i | \(0.0807755\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.80322 | 0.128474 | 0.0642371 | − | 0.997935i | \(-0.479539\pi\) | ||||
0.0642371 | + | 0.997935i | \(0.479539\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.72728 | + | 4.46135i | 0.547772 | + | 0.316257i | 0.748223 | − | 0.663447i | \(-0.230907\pi\) |
−0.200451 | + | 0.979704i | \(0.564241\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.55380 | − | 1.19154i | −0.319614 | − | 0.0836299i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.5515 | + | 8.40132i | −1.01632 | + | 0.586774i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.80600 | 0.124924 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3878i | 0.783969i | 0.919972 | + | 0.391985i | \(0.128211\pi\) | ||||
−0.919972 | + | 0.391985i | \(0.871789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.94740 | + | 3.37299i | 0.132811 | + | 0.230036i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.2701 | − | 14.1033i | −0.968715 | − | 0.957393i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.494751 | + | 0.856933i | −0.0332805 | + | 0.0576436i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.90035i | 0.328151i | 0.986448 | + | 0.164076i | \(0.0524641\pi\) | ||||
−0.986448 | + | 0.164076i | \(0.947536\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.4585 | + | 10.6570i | 1.22514 | + | 0.707332i | 0.966008 | − | 0.258511i | \(-0.0832319\pi\) |
0.259127 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.59915 | − | 2.76981i | −0.105675 | − | 0.183034i | 0.808339 | − | 0.588717i | \(-0.200367\pi\) |
−0.914014 | + | 0.405683i | \(0.867034\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.35808 | + | 1.93879i | −0.219995 | + | 0.127014i | −0.605948 | − | 0.795504i | \(-0.707206\pi\) |
0.385953 | + | 0.922518i | \(0.373873\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.54445 | + | 1.46904i | 0.165982 | + | 0.0958295i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.1432i | − | 1.43233i | −0.697933 | − | 0.716163i | \(-0.745897\pi\) | ||
0.697933 | − | 0.716163i | \(-0.254103\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.23397 | + | 3.59918i | 0.401565 | + | 0.231844i | 0.687159 | − | 0.726507i | \(-0.258858\pi\) |
−0.285594 | + | 0.958351i | \(0.592191\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.1326 | − | 0.177912i | 0.966784 | − | 0.0113664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.470650 | + | 0.815190i | 0.0299467 | + | 0.0518693i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.58773i | − | 0.605172i | −0.953122 | − | 0.302586i | \(-0.902150\pi\) | ||
0.953122 | − | 0.302586i | \(-0.0978500\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 20.1361i | − | 1.26595i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.33124 | − | 7.50192i | −0.270175 | − | 0.467957i | 0.698731 | − | 0.715384i | \(-0.253748\pi\) |
−0.968907 | + | 0.247427i | \(0.920415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.2849 | − | 7.75739i | 1.75754 | − | 0.482021i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.39801 | + | 3.11654i | 0.332855 | + | 0.192174i | 0.657108 | − | 0.753796i | \(-0.271780\pi\) |
−0.324253 | + | 0.945970i | \(0.605113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.34886i | − | 0.390007i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.46950 | − | 5.46722i | −0.577366 | − | 0.333342i | 0.182720 | − | 0.983165i | \(-0.441510\pi\) |
−0.760086 | + | 0.649823i | \(0.774843\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.1322 | − | 10.4687i | 1.10145 | − | 0.635925i | 0.164852 | − | 0.986318i | \(-0.447285\pi\) |
0.936603 | + | 0.350393i | \(0.113952\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.544922 | − | 0.943833i | −0.0328600 | − | 0.0569152i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.80313 | + | 2.19574i | 0.228508 | + | 0.131929i | 0.609884 | − | 0.792491i | \(-0.291216\pi\) |
−0.381376 | + | 0.924420i | \(0.624550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.93386i | 0.473295i | 0.971596 | + | 0.236647i | \(0.0760486\pi\) | ||||
−0.971596 | + | 0.236647i | \(0.923951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1600 | + | 26.2580i | −0.901171 | + | 1.56087i | −0.0751951 | + | 0.997169i | \(0.523958\pi\) |
−0.825976 | + | 0.563705i | \(0.809375\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.8931 | + | 5.20520i | 1.17425 | + | 0.307253i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.33876 | + | 14.4432i | 0.490515 | + | 0.849597i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.34894i | − | 0.254068i | −0.991898 | − | 0.127034i | \(-0.959454\pi\) | ||
0.991898 | − | 0.127034i | \(-0.0405457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.5836 | −1.43131 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.08899 | − | 5.24753i | 0.525630 | − | 0.303473i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.20655 | − | 4.61115i | 0.0695442 | − | 0.265782i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.0019 | + | 12.1254i | 1.20256 | + | 0.694300i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.81287 | 0.274685 | 0.137343 | − | 0.990524i | \(-0.456144\pi\) | ||||
0.137343 | + | 0.990524i | \(0.456144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.96879 | − | 6.87414i | 0.225049 | − | 0.389797i | −0.731285 | − | 0.682072i | \(-0.761079\pi\) |
0.956334 | + | 0.292275i | \(0.0944123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.95587 | − | 1.12922i | 0.110552 | − | 0.0638273i | −0.443704 | − | 0.896173i | \(-0.646336\pi\) |
0.554257 | + | 0.832346i | \(0.313003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.72820 | − | 6.45744i | −0.209397 | − | 0.362686i | 0.742128 | − | 0.670258i | \(-0.233817\pi\) |
−0.951525 | + | 0.307572i | \(0.900483\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.97393 | + | 5.15099i | −0.166508 | + | 0.288400i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.306771 | −0.0170692 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.284017 | − | 0.491932i | 0.0157544 | − | 0.0272875i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.951001 | − | 3.46752i | −0.0524304 | − | 0.191171i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.5260 | − | 11.2733i | 1.07325 | − | 0.619639i | 0.144180 | − | 0.989551i | \(-0.453946\pi\) |
0.929067 | + | 0.369912i | \(0.120612\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.8519 | −1.46708 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.9907 | −1.41580 | −0.707901 | − | 0.706312i | \(-0.750358\pi\) | ||||
−0.707901 | + | 0.706312i | \(0.750358\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.9553 | + | 12.6759i | −1.18895 | + | 0.686438i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.3247 | − | 12.8628i | −0.719466 | − | 0.694528i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.86526 | + | 13.6230i | −0.422229 | + | 0.731322i | −0.996157 | − | 0.0875835i | \(-0.972086\pi\) |
0.573928 | + | 0.818906i | \(0.305419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.79135 | 0.0958889 | 0.0479444 | − | 0.998850i | \(-0.484733\pi\) | ||||
0.0479444 | + | 0.998850i | \(0.484733\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0108 | − | 22.5353i | 0.692493 | − | 1.19943i | −0.278526 | − | 0.960429i | \(-0.589846\pi\) |
0.971019 | − | 0.239004i | \(-0.0768210\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.42892 | + | 14.5993i | 0.447361 | + | 0.774851i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.8932 | − | 8.59857i | 0.786031 | − | 0.453815i | −0.0525323 | − | 0.998619i | \(-0.516729\pi\) |
0.838563 | + | 0.544804i | \(0.183396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.35409 | − | 16.2018i | 0.492320 | − | 0.852724i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.8744 | 0.987933 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5047 | − | 6.64226i | −0.600542 | − | 0.346723i | 0.168713 | − | 0.985665i | \(-0.446039\pi\) |
−0.769255 | + | 0.638942i | \(0.779372\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.46157 | + | 5.52616i | −0.283550 | + | 0.286904i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.2609 | − | 18.6259i | 1.67041 | − | 0.964410i | 0.702999 | − | 0.711191i | \(-0.251844\pi\) |
0.967409 | − | 0.253219i | \(-0.0814895\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.10006 | −0.159661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 33.4030i | − | 1.71580i | −0.513821 | − | 0.857898i | \(-0.671770\pi\) | ||
0.513821 | − | 0.857898i | \(-0.328230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.1288 | + | 17.5435i | 0.517556 | + | 0.896433i | 0.999792 | + | 0.0203917i | \(0.00649134\pi\) |
−0.482236 | + | 0.876041i | \(0.660175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.84065 | − | 18.4999i | 0.246702 | − | 0.942840i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.87868 | − | 17.1104i | 0.500869 | − | 0.867530i | −0.499131 | − | 0.866527i | \(-0.666347\pi\) |
0.999999 | − | 0.00100341i | \(-0.000319396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.42036i | 0.172975i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.8959 | + | 10.3322i | 0.900442 | + | 0.519870i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.15364 | + | 10.6584i | 0.308842 | + | 0.534930i | 0.978109 | − | 0.208092i | \(-0.0667252\pi\) |
−0.669267 | + | 0.743022i | \(0.733392\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.5658 | − | 17.0698i | 1.47645 | − | 0.852427i | 0.476801 | − | 0.879011i | \(-0.341796\pi\) |
0.999647 | + | 0.0265843i | \(0.00846305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.4432 | − | 6.60676i | −0.570029 | − | 0.329106i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 37.0603i | − | 1.83701i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.4733 | − | 13.5523i | −1.16068 | − | 0.670119i | −0.209213 | − | 0.977870i | \(-0.567090\pi\) |
−0.951467 | + | 0.307752i | \(0.900423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.3980 | + | 21.1479i | 1.05293 | + | 1.04062i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.2910 | − | 29.9489i | −0.848782 | − | 1.47013i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.84933i | − | 0.334612i | −0.985905 | − | 0.167306i | \(-0.946493\pi\) | ||
0.985905 | − | 0.167306i | \(-0.0535067\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 10.8560i | − | 0.529089i | −0.964374 | − | 0.264544i | \(-0.914778\pi\) | ||
0.964374 | − | 0.264544i | \(-0.0852215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0925617 | + | 0.160322i | 0.00448990 | + | 0.00777674i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.84955 | − | 28.6209i | −0.379866 | − | 1.38506i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5579 | + | 11.2917i | 0.942069 | + | 0.543904i | 0.890608 | − | 0.454771i | \(-0.150279\pi\) |
0.0514606 | + | 0.998675i | \(0.483612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.9522i | 1.63164i | 0.578307 | + | 0.815819i | \(0.303713\pi\) | ||||
−0.578307 | + | 0.815819i | \(0.696287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.81783 | + | 1.62687i | 0.134795 | + | 0.0778239i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.4344 | − | 12.3752i | 1.02301 | − | 0.590634i | 0.108034 | − | 0.994147i | \(-0.465544\pi\) |
0.914974 | + | 0.403513i | \(0.132211\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.24079 | − | 16.0055i | −0.439043 | − | 0.760445i | 0.558573 | − | 0.829455i | \(-0.311349\pi\) |
−0.997616 | + | 0.0690105i | \(0.978016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.6258 | + | 13.6404i | 1.11997 | + | 0.646615i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.4888i | − | 1.43886i | −0.694567 | − | 0.719428i | \(-0.744404\pi\) | ||
0.694567 | − | 0.719428i | \(-0.255596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.9915 | − | 22.5019i | 0.611744 | − | 1.05957i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.61192 | − | 2.63616i | 0.450614 | − | 0.123585i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.2873 | − | 23.0142i | −0.621553 | − | 1.07656i | −0.989197 | − | 0.146594i | \(-0.953169\pi\) |
0.367644 | − | 0.929967i | \(-0.380165\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.26742i | − | 0.0590294i | −0.999564 | − | 0.0295147i | \(-0.990604\pi\) | ||
0.999564 | − | 0.0295147i | \(-0.00939619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.82295 | −0.456511 | −0.228256 | − | 0.973601i | \(-0.573302\pi\) | ||||
−0.228256 | + | 0.973601i | \(0.573302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.5816 | + | 10.7281i | −0.859855 | + | 0.496438i | −0.863964 | − | 0.503554i | \(-0.832025\pi\) |
0.00410868 | + | 0.999992i | \(0.498692\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.3724 | + | 23.0992i | 1.07924 | + | 1.06662i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.21585 | − | 3.01137i | −0.239825 | − | 0.138463i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.176105 | 0.00808027 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.5560 | + | 23.4798i | −0.619391 | + | 1.07282i | 0.370206 | + | 0.928950i | \(0.379287\pi\) |
−0.989597 | + | 0.143867i | \(0.954046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7282 | − | 9.65803i | 0.762740 | − | 0.440368i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.7293 | + | 30.7081i | 0.805047 | + | 1.39438i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.06126 | + | 7.03430i | −0.184033 | + | 0.318755i | −0.943250 | − | 0.332083i | \(-0.892249\pi\) |
0.759217 | + | 0.650837i | \(0.225582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.11572 | 0.275998 | 0.137999 | − | 0.990432i | \(-0.455933\pi\) | ||||
0.137999 | + | 0.990432i | \(0.455933\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.505158 | − | 0.874959i | 0.0227512 | − | 0.0394062i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.22229 | − | 19.9584i | 0.234252 | − | 0.895257i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.4251 | + | 9.48302i | −0.735287 | + | 0.424518i | −0.820353 | − | 0.571857i | \(-0.806223\pi\) |
0.0850663 | + | 0.996375i | \(0.472890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.6249 | 1.09797 | 0.548985 | − | 0.835832i | \(-0.315015\pi\) | ||||
0.548985 | + | 0.835832i | \(0.315015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.5800 | −1.49429 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.66857 | − | 4.42745i | 0.339904 | − | 0.196243i | −0.320326 | − | 0.947307i | \(-0.603792\pi\) |
0.660229 | + | 0.751064i | \(0.270459\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.4286 | − | 16.2366i | −0.726759 | − | 0.718265i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.85756 | − | 10.1456i | 0.258115 | − | 0.447068i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.54332 | −0.199815 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0185 | + | 20.8167i | −0.526540 | + | 0.911995i | 0.472981 | + | 0.881072i | \(0.343178\pi\) |
−0.999522 | + | 0.0309222i | \(0.990156\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.89548 | + | 3.28306i | 0.0828835 | + | 0.143558i | 0.904487 | − | 0.426500i | \(-0.140254\pi\) |
−0.821604 | + | 0.570059i | \(0.806920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.72937 | − | 2.15316i | 0.162454 | − | 0.0937929i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.63889 | − | 11.4989i | 0.288648 | − | 0.499952i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5425 | 0.586589 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.96430 | + | 4.02084i | 0.301093 | + | 0.173836i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.1278 | + | 11.9384i | −0.866964 | + | 0.514225i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.4954 | + | 9.52363i | −0.709193 | + | 0.409453i | −0.810762 | − | 0.585376i | \(-0.800947\pi\) |
0.101569 | + | 0.994828i | \(0.467614\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.2915 | 0.612179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 46.3065i | − | 1.97992i | −0.141342 | − | 0.989961i | \(-0.545142\pi\) | ||
0.141342 | − | 0.989961i | \(-0.454858\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.480550 | − | 0.832337i | −0.0204721 | − | 0.0354587i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.68869 | − | 24.3882i | −0.284432 | − | 1.03709i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.1463 | − | 19.3059i | 0.472283 | − | 0.818019i | −0.527214 | − | 0.849733i | \(-0.676763\pi\) |
0.999497 | + | 0.0317140i | \(0.0100966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.13910i | − | 0.132770i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.42370 | + | 1.39932i | 0.102147 | + | 0.0589745i | 0.550203 | − | 0.835031i | \(-0.314550\pi\) |
−0.448056 | + | 0.894005i | \(0.647884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.67155 | − | 8.09136i | −0.196533 | − | 0.340406i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.6988 | + | 20.6107i | −1.49657 | + | 0.864046i | −0.999992 | − | 0.00394571i | \(-0.998744\pi\) |
−0.496579 | + | 0.867992i | \(0.665411\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3886 | + | 14.0808i | 1.02063 | + | 0.589262i | 0.914287 | − | 0.405068i | \(-0.132752\pi\) |
0.106345 | + | 0.994329i | \(0.466085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.96350i | − | 0.0818834i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.23601 | + | 4.75506i | 0.342870 | + | 0.197956i | 0.661540 | − | 0.749910i | \(-0.269903\pi\) |
−0.318671 | + | 0.947866i | \(0.603236\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.7130 | + | 40.9425i | −0.444449 | + | 1.69858i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.90881 | + | 8.50230i | 0.203302 | + | 0.352129i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 6.47220i | − | 0.267136i | −0.991040 | − | 0.133568i | \(-0.957357\pi\) | ||
0.991040 | − | 0.133568i | \(-0.0426435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.09654i | − | 0.168795i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.5174 | + | 25.1449i | 0.596159 | + | 1.03258i | 0.993382 | + | 0.114855i | \(0.0366404\pi\) |
−0.397224 | + | 0.917722i | \(0.630026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.822243 | + | 3.14243i | −0.0337087 | + | 0.128827i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.06979 | + | 2.34969i | 0.166287 | + | 0.0960058i | 0.580834 | − | 0.814022i | \(-0.302727\pi\) |
−0.414547 | + | 0.910028i | \(0.636060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.3259i | 0.829111i | 0.910024 | + | 0.414555i | \(0.136063\pi\) | ||||
−0.910024 | + | 0.414555i | \(0.863937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.330641 | − | 0.190896i | −0.0134425 | − | 0.00776102i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.3222 | + | 15.1971i | −1.06838 | + | 0.616832i | −0.927740 | − | 0.373228i | \(-0.878251\pi\) |
−0.140645 | + | 0.990060i | \(0.544918\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18400 | − | 2.05076i | −0.0478997 | − | 0.0829647i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.4975 | + | 14.1436i | 0.989444 | + | 0.571256i | 0.905108 | − | 0.425182i | \(-0.139790\pi\) |
0.0843357 | + | 0.996437i | \(0.473123\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 21.3569i | − | 0.859795i | −0.902878 | − | 0.429898i | \(-0.858550\pi\) | ||
0.902878 | − | 0.429898i | \(-0.141450\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6447 | + | 18.4372i | −0.427847 | + | 0.741053i | −0.996682 | − | 0.0813988i | \(-0.974061\pi\) |
0.568834 | + | 0.822452i | \(0.307395\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.83026 | − | 32.1967i | −0.353777 | − | 1.28993i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.6319 | + | 20.1470i | 0.465275 | + | 0.805880i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.29514i | 0.251004i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.31457 | −0.330998 | −0.165499 | − | 0.986210i | \(-0.552923\pi\) | ||||
−0.165499 | + | 0.986210i | \(0.552923\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.0495 | + | 7.53412i | −0.517853 | + | 0.298983i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.6341 | − | 5.97403i | −0.421339 | − | 0.236700i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.98896 | − | 2.88038i | −0.197052 | − | 0.113768i | 0.398228 | − | 0.917287i | \(-0.369625\pi\) |
−0.595280 | + | 0.803519i | \(0.702959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.7692 | −0.740184 | −0.370092 | − | 0.928995i | \(-0.620674\pi\) | ||||
−0.370092 | + | 0.928995i | \(0.620674\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.705648 | + | 1.22222i | −0.0277419 | + | 0.0480503i | −0.879563 | − | 0.475782i | \(-0.842165\pi\) |
0.851821 | + | 0.523833i | \(0.175498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.9220 | − | 19.0075i | 1.29230 | − | 0.746112i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.21537 | − | 5.56919i | −0.125827 | − | 0.217939i | 0.796229 | − | 0.604996i | \(-0.206825\pi\) |
−0.922056 | + | 0.387057i | \(0.873492\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.51855 | − | 16.4866i | 0.371920 | − | 0.644185i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.9229 | −0.620269 | −0.310134 | − | 0.950693i | \(-0.600374\pi\) | ||||
−0.310134 | + | 0.950693i | \(0.600374\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.8309 | + | 23.9557i | −0.537958 | + | 0.931770i | 0.461056 | + | 0.887371i | \(0.347471\pi\) |
−0.999014 | + | 0.0443993i | \(0.985863\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.19776 | + | 2.17207i | 0.0852254 | + | 0.0842293i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.28018 | + | 5.35791i | −0.359330 | + | 0.207459i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.5005 | −1.44769 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8132 | 0.648103 | 0.324052 | − | 0.946039i | \(-0.394955\pi\) | ||||
0.324052 | + | 0.946039i | \(0.394955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.3325 | − | 19.2445i | 1.28107 | − | 0.739626i | 0.304026 | − | 0.952664i | \(-0.401669\pi\) |
0.977044 | + | 0.213037i | \(0.0683356\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.9845 | − | 41.9804i | 0.421548 | − | 1.61106i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.8564 | + | 29.1961i | −0.644991 | + | 1.11716i | 0.339313 | + | 0.940674i | \(0.389806\pi\) |
−0.984304 | + | 0.176483i | \(0.943528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.2616 | −1.38549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.55850 | + | 4.43146i | −0.0974712 | + | 0.168825i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.3070 | + | 28.2445i | 0.620346 | + | 1.07447i | 0.989421 | + | 0.145072i | \(0.0463413\pi\) |
−0.369075 | + | 0.929400i | \(0.620325\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.3424 | + | 11.1673i | −0.733699 | + | 0.423601i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.20676 | + | 3.82222i | −0.0835869 | + | 0.144777i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.4784 | −0.697919 | −0.348959 | − | 0.937138i | \(-0.613465\pi\) | ||||
−0.348959 | + | 0.937138i | \(0.613465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.18618 | + | 2.99424i | 0.195600 | + | 0.112930i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.2286 | + | 28.8870i | 1.09925 | + | 1.08641i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.277961 | − | 0.160481i | 0.0104390 | − | 0.00602697i | −0.494771 | − | 0.869023i | \(-0.664748\pi\) |
0.505210 | + | 0.862996i | \(0.331415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −45.6745 | −1.71053 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 12.5940i | − | 0.470989i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.95557 | + | 12.0474i | 0.259399 | + | 0.449292i | 0.966081 | − | 0.258239i | \(-0.0831422\pi\) |
−0.706682 | + | 0.707531i | \(0.749809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8262 | + | 3.79196i | −0.514914 | + | 0.141220i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.289991 | + | 0.502280i | −0.0107700 | + | 0.0186542i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.1216i | 1.56220i | 0.624403 | + | 0.781102i | \(0.285342\pi\) | ||||
−0.624403 | + | 0.781102i | \(0.714658\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.885977 | + | 0.511519i | 0.0327690 | + | 0.0189192i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.20815 | − | 7.28873i | −0.155432 | − | 0.269215i | 0.777785 | − | 0.628531i | \(-0.216343\pi\) |
−0.933216 | + | 0.359316i | \(0.883010\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.9597 | − | 20.7614i | 1.32459 | − | 0.764755i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.15443 | + | 1.24386i | 0.0792519 | + | 0.0457561i | 0.539102 | − | 0.842240i | \(-0.318764\pi\) |
−0.459850 | + | 0.887996i | \(0.652097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.2694i | 1.00042i | 0.865904 | + | 0.500209i | \(0.166744\pi\) | ||||
−0.865904 | + | 0.500209i | \(0.833256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.88841 | − | 4.55438i | −0.289009 | − | 0.166859i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.60294 | − | 9.49080i | −0.0951094 | − | 0.346786i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7789 | + | 27.3299i | 0.575781 | + | 0.997282i | 0.995956 | + | 0.0898389i | \(0.0286352\pi\) |
−0.420175 | + | 0.907443i | \(0.638031\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 13.4254i | − | 0.488599i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 36.9092i | − | 1.34149i | −0.741689 | − | 0.670744i | \(-0.765975\pi\) | ||
0.741689 | − | 0.670744i | \(-0.234025\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.14893 | + | 15.8464i | 0.331648 | + | 0.574432i | 0.982835 | − | 0.184486i | \(-0.0590619\pi\) |
−0.651187 | + | 0.758917i | \(0.725729\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.4395 | − | 12.2941i | −0.450341 | − | 0.445078i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.1592 | + | 9.90686i | 0.619582 | + | 0.357716i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.09495i | 0.183729i | 0.995772 | + | 0.0918644i | \(0.0292826\pi\) | ||||
−0.995772 | + | 0.0918644i | \(0.970717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.0448 | − | 15.6143i | −0.972735 | − | 0.561609i | −0.0726659 | − | 0.997356i | \(-0.523151\pi\) |
−0.900069 | + | 0.435748i | \(0.856484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.14089 | + | 1.23604i | −0.0769030 | + | 0.0444000i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.09926 | + | 3.63603i | 0.0752138 | + | 0.130274i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.5758 | − | 13.0341i | −0.807825 | − | 0.466398i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 44.6267i | − | 1.59279i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.96558 | − | 17.2609i | 0.355235 | − | 0.615284i | −0.631923 | − | 0.775031i | \(-0.717734\pi\) |
0.987158 | + | 0.159746i | \(0.0510676\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.89434 | + | 11.0615i | −0.102911 | + | 0.393302i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.77276 | − | 16.9269i | −0.347041 | − | 0.601093i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 46.5551i | − | 1.64907i | −0.565813 | − | 0.824534i | \(-0.691438\pi\) | ||
0.565813 | − | 0.824534i | \(-0.308562\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.771739 | 0.0273022 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.2764 | + | 14.5933i | −0.891984 | + | 0.514987i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.2176 | − | 24.5040i | 0.853558 | − | 0.863652i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.1771 | + | 20.3095i | 1.23676 | + | 0.714045i | 0.968431 | − | 0.249282i | \(-0.0801946\pi\) |
0.268331 | + | 0.963327i | \(0.413528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.3104 | 1.52083 | 0.760417 | − | 0.649435i | \(-0.224995\pi\) | ||||
0.760417 | + | 0.649435i | \(0.224995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.45119 | − | 7.70968i | 0.155918 | − | 0.270058i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.842818 | − | 0.486601i | 0.0294865 | − | 0.0170240i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.21375 | − | 2.10228i | −0.0423602 | − | 0.0733699i | 0.844068 | − | 0.536236i | \(-0.180154\pi\) |
−0.886428 | + | 0.462866i | \(0.846821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.90145 | − | 15.4178i | 0.310285 | − | 0.537429i | −0.668139 | − | 0.744036i | \(-0.732909\pi\) |
0.978424 | + | 0.206607i | \(0.0662422\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.3153 | 1.36713 | 0.683564 | − | 0.729890i | \(-0.260429\pi\) | ||||
0.683564 | + | 0.729890i | \(0.260429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.4409 | + | 37.1368i | −0.744675 | + | 1.28981i | 0.205672 | + | 0.978621i | \(0.434062\pi\) |
−0.950346 | + | 0.311194i | \(0.899271\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.41895 | − | 2.02789i | 0.118459 | − | 0.0702623i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.8368 | + | 14.3395i | −0.859512 | + | 0.496239i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.03008 | −0.139134 | −0.0695668 | − | 0.997577i | \(-0.522162\pi\) | ||||
−0.0695668 | + | 0.997577i | \(0.522162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8347 | −0.890853 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.6552 | + | 10.7706i | −0.641759 | + | 0.370520i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.123579 | + | 0.450591i | 0.00424622 | + | 0.0154825i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.3844 | − | 57.8235i | 1.14440 | − | 1.98217i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.89394 | −0.0648474 | −0.0324237 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324237 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.3144 | + | 17.8650i | −0.352333 | + | 0.610258i | −0.986658 | − | 0.162808i | \(-0.947945\pi\) |
0.634325 | + | 0.773066i | \(0.281278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.2260 | + | 43.6928i | 0.860701 | + | 1.49078i | 0.871253 | + | 0.490833i | \(0.163308\pi\) |
−0.0105526 | + | 0.999944i | \(0.503359\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.95161 | + | 1.12676i | −0.0664336 | + | 0.0383554i | −0.532849 | − | 0.846210i | \(-0.678879\pi\) |
0.466415 | + | 0.884566i | \(0.345545\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.3256 | + | 42.1332i | −0.827095 | + | 1.43257i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.9546 | −1.08399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.7425 | + | 10.8210i | 0.635064 | + | 0.366654i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.71169 | − | 29.4723i | 0.260703 | − | 0.996346i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7244 | − | 13.1200i | 0.767350 | − | 0.443029i | −0.0645788 | − | 0.997913i | \(-0.520570\pi\) |
0.831928 | + | 0.554883i | \(0.187237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.9743 | 0.470804 | 0.235402 | − | 0.971898i | \(-0.424359\pi\) | ||||
0.235402 | + | 0.971898i | \(0.424359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0650i | 1.34830i | 0.738596 | + | 0.674148i | \(0.235489\pi\) | ||||
−0.738596 | + | 0.674148i | \(0.764511\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.9798 | − | 39.8022i | −0.771586 | − | 1.33643i | −0.936694 | − | 0.350150i | \(-0.886131\pi\) |
0.165108 | − | 0.986275i | \(-0.447203\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.8397 | + | 4.66791i | 0.598323 | + | 0.156557i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.367073 | − | 0.635788i | 0.0122836 | − | 0.0212758i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.6725i | 1.39296i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.6840 | + | 6.74573i | 0.389682 | + | 0.224983i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.833821 | − | 1.44422i | −0.0277786 | − | 0.0481140i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.8459 | + | 24.1597i | −1.39100 | + | 0.803096i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.32291 | + | 4.80524i | 0.276358 | + | 0.159555i | 0.631773 | − | 0.775153i | \(-0.282327\pi\) |
−0.355416 | + | 0.934708i | \(0.615661\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 55.0751i | − | 1.82472i | −0.409390 | − | 0.912359i | \(-0.634258\pi\) | ||
0.409390 | − | 0.912359i | \(-0.365742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.3117 | + | 26.7381i | 1.53269 | + | 0.884902i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.4676 | + | 6.16195i | −0.741946 | + | 0.203486i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.4392 | + | 18.0812i | 0.344357 | + | 0.596444i | 0.985237 | − | 0.171198i | \(-0.0547636\pi\) |
−0.640880 | + | 0.767641i | \(0.721430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 13.5870i | − | 0.447220i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3.61379i | − | 0.118821i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.3495 | + | 33.5143i | 0.634837 | + | 1.09957i | 0.986550 | + | 0.163462i | \(0.0522660\pi\) |
−0.351713 | + | 0.936108i | \(0.614401\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0444554 | − | 3.78121i | −0.00145697 | − | 0.123924i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.55453 | + | 2.05221i | 0.116245 | + | 0.0671143i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.23597i | 0.0730458i | 0.999333 | + | 0.0365229i | \(0.0116282\pi\) | ||||
−0.999333 | + | 0.0365229i | \(0.988372\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.23966 | + | 4.75717i | 0.268605 | + | 0.155079i | 0.628254 | − | 0.778009i | \(-0.283770\pi\) |
−0.359648 | + | 0.933088i | \(0.617103\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.5400 | − | 23.4058i | 1.32017 | − | 0.762198i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.3346 | − | 33.4885i | −0.628290 | − | 1.08823i | −0.987895 | − | 0.155126i | \(-0.950422\pi\) |
0.359605 | − | 0.933105i | \(-0.382912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.1742 | − | 7.60613i | −0.427653 | − | 0.246906i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.5906i | 1.02332i | 0.859188 | + | 0.511659i | \(0.170969\pi\) | ||||
−0.859188 | + | 0.511659i | \(0.829031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.10444 | + | 12.3053i | −0.229894 | + | 0.398189i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.5627 | + | 31.1938i | 1.01921 | + | 1.00730i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.2526 | + | 22.9542i | 0.427504 | + | 0.740459i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 16.0128i | − | 0.515472i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.1994 | −1.74294 | −0.871468 | − | 0.490452i | \(-0.836832\pi\) | ||||
−0.871468 | + | 0.490452i | \(0.836832\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.92025 | − | 3.41806i | 0.189990 | − | 0.109691i | −0.401988 | − | 0.915645i | \(-0.631681\pi\) |
0.591978 | + | 0.805954i | \(0.298347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.4426 | + | 6.91893i | 0.847710 | + | 0.221811i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.1650 | − | 11.0649i | −0.613144 | − | 0.353999i | 0.161051 | − | 0.986946i | \(-0.448512\pi\) |
−0.774195 | + | 0.632947i | \(0.781845\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.1858 | −1.34826 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.18986 | + | 5.52499i | −0.101741 | + | 0.176220i | −0.912402 | − | 0.409296i | \(-0.865775\pi\) |
0.810661 | + | 0.585515i | \(0.199108\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.37617 | − | 1.94923i | 0.107574 | − | 0.0621077i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.42538 | − | 9.39704i | −0.172517 | − | 0.298808i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.49218 | + | 9.51273i | −0.174465 | + | 0.302182i | −0.939976 | − | 0.341241i | \(-0.889153\pi\) |
0.765511 | + | 0.643423i | \(0.222486\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.2904 | 0.611546 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.65692 | + | 6.33397i | −0.115816 | + | 0.200599i | −0.918106 | − | 0.396336i | \(-0.870282\pi\) |
0.802290 | + | 0.596935i | \(0.203615\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2016.2.cp.b.17.24 | 56 | ||
3.2 | odd | 2 | inner | 2016.2.cp.b.17.6 | 56 | ||
4.3 | odd | 2 | 504.2.ch.b.269.19 | yes | 56 | ||
7.5 | odd | 6 | inner | 2016.2.cp.b.593.23 | 56 | ||
8.3 | odd | 2 | 504.2.ch.b.269.27 | yes | 56 | ||
8.5 | even | 2 | inner | 2016.2.cp.b.17.5 | 56 | ||
12.11 | even | 2 | 504.2.ch.b.269.10 | yes | 56 | ||
21.5 | even | 6 | inner | 2016.2.cp.b.593.5 | 56 | ||
24.5 | odd | 2 | inner | 2016.2.cp.b.17.23 | 56 | ||
24.11 | even | 2 | 504.2.ch.b.269.2 | ✓ | 56 | ||
28.19 | even | 6 | 504.2.ch.b.341.2 | yes | 56 | ||
56.5 | odd | 6 | inner | 2016.2.cp.b.593.6 | 56 | ||
56.19 | even | 6 | 504.2.ch.b.341.10 | yes | 56 | ||
84.47 | odd | 6 | 504.2.ch.b.341.27 | yes | 56 | ||
168.5 | even | 6 | inner | 2016.2.cp.b.593.24 | 56 | ||
168.131 | odd | 6 | 504.2.ch.b.341.19 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.ch.b.269.2 | ✓ | 56 | 24.11 | even | 2 | ||
504.2.ch.b.269.10 | yes | 56 | 12.11 | even | 2 | ||
504.2.ch.b.269.19 | yes | 56 | 4.3 | odd | 2 | ||
504.2.ch.b.269.27 | yes | 56 | 8.3 | odd | 2 | ||
504.2.ch.b.341.2 | yes | 56 | 28.19 | even | 6 | ||
504.2.ch.b.341.10 | yes | 56 | 56.19 | even | 6 | ||
504.2.ch.b.341.19 | yes | 56 | 168.131 | odd | 6 | ||
504.2.ch.b.341.27 | yes | 56 | 84.47 | odd | 6 | ||
2016.2.cp.b.17.5 | 56 | 8.5 | even | 2 | inner | ||
2016.2.cp.b.17.6 | 56 | 3.2 | odd | 2 | inner | ||
2016.2.cp.b.17.23 | 56 | 24.5 | odd | 2 | inner | ||
2016.2.cp.b.17.24 | 56 | 1.1 | even | 1 | trivial | ||
2016.2.cp.b.593.5 | 56 | 21.5 | even | 6 | inner | ||
2016.2.cp.b.593.6 | 56 | 56.5 | odd | 6 | inner | ||
2016.2.cp.b.593.23 | 56 | 7.5 | odd | 6 | inner | ||
2016.2.cp.b.593.24 | 56 | 168.5 | even | 6 | inner |