Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(129,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.3 | ||
Root | \(0.403032 + 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.129 |
Dual form | 1280.2.f.i.129.4 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.806063 | −0.465381 | −0.232690 | − | 0.972551i | \(-0.574753\pi\) | ||||
−0.232690 | + | 0.972551i | \(0.574753\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.67513 | − | 1.48119i | −0.749141 | − | 0.662410i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.15633i | 0.815014i | 0.913202 | + | 0.407507i | \(0.133602\pi\) | ||||
−0.913202 | + | 0.407507i | \(0.866398\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.35026 | −0.783421 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.387873i | 0.116948i | 0.998289 | + | 0.0584741i | \(0.0186235\pi\) | ||||
−0.998289 | + | 0.0584741i | \(0.981377\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.962389 | 0.266919 | 0.133459 | − | 0.991054i | \(-0.457391\pi\) | ||||
0.133459 | + | 0.991054i | \(0.457391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.35026 | + | 1.19394i | 0.348636 | + | 0.308273i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.61213i | − | 0.390998i | −0.980704 | − | 0.195499i | \(-0.937367\pi\) | ||
0.980704 | − | 0.195499i | \(-0.0626327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.31265i | − | 1.44822i | −0.689684 | − | 0.724111i | \(-0.742250\pi\) | ||
0.689684 | − | 0.724111i | \(-0.257750\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.73813i | − | 0.379292i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.15633i | 1.28368i | 0.766838 | + | 0.641841i | \(0.221829\pi\) | ||||
−0.766838 | + | 0.641841i | \(0.778171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.612127 | + | 4.96239i | 0.122425 | + | 0.992478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.31265 | 0.829970 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.92478 | 1.78254 | 0.891271 | − | 0.453470i | \(-0.149814\pi\) | ||||
0.891271 | + | 0.453470i | \(0.149814\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.312650i | − | 0.0544254i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.19394 | − | 3.61213i | 0.539874 | − | 0.610561i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.57452 | −1.08084 | −0.540422 | − | 0.841394i | \(-0.681735\pi\) | ||||
−0.540422 | + | 0.841394i | \(0.681735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.775746 | −0.124219 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.57452 | −0.714419 | −0.357210 | − | 0.934024i | \(-0.616272\pi\) | ||||
−0.357210 | + | 0.934024i | \(0.616272\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.5066 | 1.75474 | 0.877369 | − | 0.479816i | \(-0.159297\pi\) | ||||
0.877369 | + | 0.479816i | \(0.159297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.93700 | + | 3.48119i | 0.586893 | + | 0.518946i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.54420i | 0.662839i | 0.943483 | + | 0.331420i | \(0.107528\pi\) | ||||
−0.943483 | + | 0.331420i | \(0.892472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.35026 | 0.335752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.29948i | 0.181963i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.96239 | 1.23108 | 0.615539 | − | 0.788106i | \(-0.288938\pi\) | ||||
0.615539 | + | 0.788106i | \(0.288938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.574515 | − | 0.649738i | 0.0774677 | − | 0.0876107i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.08840i | 0.673975i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.31265i | − | 0.821837i | −0.911672 | − | 0.410919i | \(-0.865208\pi\) | ||
0.911672 | − | 0.410919i | \(-0.134792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.261865i | − | 0.0335284i | −0.999859 | − | 0.0167642i | \(-0.994664\pi\) | ||
0.999859 | − | 0.0167642i | \(-0.00533646\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5.06793i | − | 0.638499i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.61213 | − | 1.42548i | −0.199960 | − | 0.176810i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.89446 | 1.20880 | 0.604400 | − | 0.796681i | \(-0.293413\pi\) | ||||
0.604400 | + | 0.796681i | \(0.293413\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4.96239i | − | 0.597401i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7005 | 1.26992 | 0.634959 | − | 0.772546i | \(-0.281017\pi\) | ||||
0.634959 | + | 0.772546i | \(0.281017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.0884i | − | 1.53188i | −0.642911 | − | 0.765940i | \(-0.722274\pi\) | ||
0.642911 | − | 0.765940i | \(-0.277726\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.493413 | − | 4.00000i | −0.0569744 | − | 0.461880i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.836381 | −0.0953144 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.92478 | 0.216554 | 0.108277 | − | 0.994121i | \(-0.465467\pi\) | ||||
0.108277 | + | 0.994121i | \(0.465467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.57452 | 0.397168 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.88129 | −0.316262 | −0.158131 | − | 0.987418i | \(-0.550547\pi\) | ||||
−0.158131 | + | 0.987418i | \(0.550547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.38787 | + | 2.70052i | −0.259001 | + | 0.292913i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.61213i | − | 0.172838i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6253 | 1.12628 | 0.563140 | − | 0.826362i | \(-0.309593\pi\) | ||||
0.563140 | + | 0.826362i | \(0.309593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.07522i | 0.217542i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.00000 | −0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.35026 | + | 10.5745i | −0.959317 | + | 1.08492i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.61213i | − | 0.975964i | −0.872854 | − | 0.487982i | \(-0.837733\pi\) | ||
0.872854 | − | 0.487982i | \(-0.162267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.911603i | − | 0.0916196i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4010i | 1.13445i | 0.823564 | + | 0.567223i | \(0.191982\pi\) | ||||
−0.823564 | + | 0.567223i | \(0.808018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9321i | 1.07717i | 0.842572 | + | 0.538585i | \(0.181041\pi\) | ||||
−0.842572 | + | 0.538585i | \(0.818959\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.57452 | + | 2.91160i | −0.251247 | + | 0.284143i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.0435 | −1.06761 | −0.533807 | − | 0.845606i | \(-0.679239\pi\) | ||||
−0.533807 | + | 0.845606i | \(0.679239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.03761i | − | 0.482516i | −0.970461 | − | 0.241258i | \(-0.922440\pi\) | ||
0.970461 | − | 0.241258i | \(-0.0775599\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.29948 | 0.503004 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.8496i | 1.86729i | 0.358201 | + | 0.933645i | \(0.383390\pi\) | ||||
−0.358201 | + | 0.933645i | \(0.616610\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.11871 | − | 10.3127i | 0.850324 | − | 0.961660i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.26187 | −0.209110 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.47627 | 0.318669 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8496 | 0.986323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.68735 | 0.332477 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.32487 | − | 9.21933i | 0.565713 | − | 0.824602i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7685i | 1.04428i | 0.852859 | + | 0.522141i | \(0.174866\pi\) | ||||
−0.852859 | + | 0.522141i | \(0.825134\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.27504 | −0.816622 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0884i | 1.31828i | 0.752021 | + | 0.659140i | \(0.229079\pi\) | ||||
−0.752021 | + | 0.659140i | \(0.770921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.6121 | 1.18032 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.22425 | − | 6.38787i | −0.621765 | − | 0.549781i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.5501i | − | 1.58484i | −0.609976 | − | 0.792420i | \(-0.708821\pi\) | ||
0.609976 | − | 0.792420i | \(-0.291179\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.61213i | − | 0.645652i | −0.946458 | − | 0.322826i | \(-0.895367\pi\) | ||
0.946458 | − | 0.322826i | \(-0.104633\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 3.66291i | − | 0.308473i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.373285i | 0.0312156i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.96239 | − | 3.35026i | 0.246013 | − | 0.278224i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.89446 | −0.156252 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6629i | 1.11931i | 0.828726 | + | 0.559655i | \(0.189066\pi\) | ||||
−0.828726 | + | 0.559655i | \(0.810934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.2243 | 1.23893 | 0.619466 | − | 0.785023i | \(-0.287349\pi\) | ||||
0.619466 | + | 0.785023i | \(0.287349\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.78892i | 0.306316i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6253 | − | 14.7005i | −1.33538 | − | 1.18077i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.42548 | 0.113766 | 0.0568830 | − | 0.998381i | \(-0.481884\pi\) | ||||
0.0568830 | + | 0.998381i | \(0.481884\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.22425 | −0.572921 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.2750 | −1.04622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.80606 | −0.689744 | −0.344872 | − | 0.938650i | \(-0.612078\pi\) | ||||
−0.344872 | + | 0.938650i | \(0.612078\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.463096 | + | 0.523730i | −0.0360520 | + | 0.0407723i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 10.4690i | − | 0.810114i | −0.914292 | − | 0.405057i | \(-0.867252\pi\) | ||
0.914292 | − | 0.405057i | \(-0.132748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0738 | −0.928754 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.8364i | 1.13457i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.9756 | −1.51871 | −0.759357 | − | 0.650674i | \(-0.774486\pi\) | ||||
−0.759357 | + | 0.650674i | \(0.774486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.7005 | + | 1.31994i | −0.808884 | + | 0.0997784i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.08840i | 0.382467i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2374i | 0.914668i | 0.889295 | + | 0.457334i | \(0.151196\pi\) | ||||
−0.889295 | + | 0.457334i | \(0.848804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.8496i | − | 1.02943i | −0.857362 | − | 0.514715i | \(-0.827898\pi\) | ||
0.857362 | − | 0.514715i | \(-0.172102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.211080i | 0.0156035i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.0132 | + | 9.73813i | 0.809705 | + | 0.715962i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.625301 | 0.0457265 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.29948i | 0.676437i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.84955 | −0.278544 | −0.139272 | − | 0.990254i | \(-0.544476\pi\) | ||||
−0.139272 | + | 0.990254i | \(0.544476\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.61213i | 0.691896i | 0.938254 | + | 0.345948i | \(0.112443\pi\) | ||||
−0.938254 | + | 0.345948i | \(0.887557\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.29948 | + | 1.14903i | 0.0930574 | + | 0.0822838i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.58769 | 0.683095 | 0.341547 | − | 0.939865i | \(-0.389049\pi\) | ||||
0.341547 | + | 0.939865i | \(0.389049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.29948 | −0.375670 | −0.187835 | − | 0.982201i | \(-0.560147\pi\) | ||||
−0.187835 | + | 0.982201i | \(0.560147\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.97556 | −0.562553 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.31265 | −0.302689 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.66291 | + | 6.77575i | 0.535201 | + | 0.473239i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 14.4690i | − | 1.00566i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.44851 | 0.169367 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0884i | 1.03873i | 0.854553 | + | 0.519364i | \(0.173831\pi\) | ||||
−0.854553 | + | 0.519364i | \(0.826169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.62530 | −0.590996 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.2750 | − | 17.0435i | −1.31455 | − | 1.16236i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.4010i | 1.45280i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5501i | 0.712908i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.55149i | − | 0.104365i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.5296i | − | 1.50869i | −0.656476 | − | 0.754347i | \(-0.727954\pi\) | ||
0.656476 | − | 0.754347i | \(-0.272046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.43866 | − | 11.6629i | −0.0959106 | − | 0.777527i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.35756 | −0.156476 | −0.0782382 | − | 0.996935i | \(-0.524929\pi\) | ||||
−0.0782382 | + | 0.996935i | \(0.524929\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.55149i | − | 0.234689i | −0.993091 | − | 0.117345i | \(-0.962562\pi\) | ||
0.993091 | − | 0.117345i | \(-0.0374382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.674176 | 0.0443575 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.0884i | − | 0.857449i | −0.903435 | − | 0.428725i | \(-0.858963\pi\) | ||
0.903435 | − | 0.428725i | \(-0.141037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.73084 | − | 7.61213i | 0.439072 | − | 0.496560i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.55149 | −0.100780 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3258 | −0.991345 | −0.495673 | − | 0.868509i | \(-0.665078\pi\) | ||||
−0.495673 | + | 0.868509i | \(0.665078\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.12601 | 0.136948 | 0.0684741 | − | 0.997653i | \(-0.478187\pi\) | ||||
0.0684741 | + | 0.997653i | \(0.478187\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.8192 | −1.01480 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.93700 | − | 3.48119i | −0.251525 | − | 0.222405i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.07522i | − | 0.386557i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.32250 | 0.147182 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.6859i | 1.68440i | 0.539164 | + | 0.842201i | \(0.318740\pi\) | ||||
−0.539164 | + | 0.842201i | \(0.681260\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.38787 | −0.150124 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.92478 | − | 2.17679i | 0.120534 | − | 0.136316i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5.40105i | − | 0.336908i | −0.985710 | − | 0.168454i | \(-0.946123\pi\) | ||
0.985710 | − | 0.168454i | \(-0.0538775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 14.1768i | − | 0.880903i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 4.70052i | − | 0.290955i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 14.4690i | − | 0.892195i | −0.894984 | − | 0.446098i | \(-0.852813\pi\) | ||
0.894984 | − | 0.446098i | \(-0.147187\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0132 | − | 13.2750i | −0.922252 | − | 0.815479i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.56467 | −0.524149 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 28.1114i | − | 1.71398i | −0.515330 | − | 0.856992i | \(-0.672331\pi\) | ||
0.515330 | − | 0.856992i | \(-0.327669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.8773 | 1.51119 | 0.755595 | − | 0.655039i | \(-0.227348\pi\) | ||||
0.755595 | + | 0.655039i | \(0.227348\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.67276i | − | 0.101240i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.92478 | + | 0.237428i | −0.116068 | + | 0.0143174i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.9756 | −1.20022 | −0.600108 | − | 0.799919i | \(-0.704876\pi\) | ||||
−0.600108 | + | 0.799919i | \(0.704876\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.3258 | −1.39648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4993 | 0.864955 | 0.432478 | − | 0.901645i | \(-0.357639\pi\) | ||||
0.432478 | + | 0.901645i | \(0.357639\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.80606 | 0.523466 | 0.261733 | − | 0.965140i | \(-0.415706\pi\) | ||||
0.261733 | + | 0.965140i | \(0.415706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.53690 | − | 8.52373i | 0.446448 | − | 0.504902i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.86414i | − | 0.582262i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4010 | 0.847120 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.74798i | 0.454195i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.35026 | −0.195724 | −0.0978622 | − | 0.995200i | \(-0.531200\pi\) | ||||
−0.0978622 | + | 0.995200i | \(0.531200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.35026 | + | 10.5745i | −0.544393 | + | 0.615672i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.67276i | 0.0970634i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.92478i | 0.342639i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.8119i | 1.43014i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.18997i | − | 0.527950i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.387873 | + | 0.438658i | −0.0222096 | + | 0.0251175i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.95509 | −0.111583 | −0.0557916 | − | 0.998442i | \(-0.517768\pi\) | ||||
−0.0557916 | + | 0.998442i | \(0.517768\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 8.81194i | − | 0.501294i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.77575 | 0.497627 | 0.248813 | − | 0.968551i | \(-0.419959\pi\) | ||||
0.248813 | + | 0.968551i | \(0.419959\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.5501i | 1.04851i | 0.851561 | + | 0.524256i | \(0.175657\pi\) | ||||
−0.851561 | + | 0.524256i | \(0.824343\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.50659 | + | 8.48944i | −0.422948 | + | 0.478326i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.58769 | 0.538498 | 0.269249 | − | 0.963071i | \(-0.413224\pi\) | ||||
0.269249 | + | 0.963071i | \(0.413224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.775746 | −0.0434335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.90175 | 0.496847 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.1768 | −0.566252 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.589104 | + | 4.77575i | 0.0326776 | + | 0.264911i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.06063i | 0.224554i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.79877 | −0.540224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.0884i | 1.26905i | 0.772901 | + | 0.634527i | \(0.218805\pi\) | ||||
−0.772901 | + | 0.634527i | \(0.781195\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.4518 | 0.846755 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.5745 | − | 14.6556i | −0.905563 | − | 0.800722i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.77575i | − | 0.260151i | −0.991504 | − | 0.130076i | \(-0.958478\pi\) | ||
0.991504 | − | 0.130076i | \(-0.0415220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 16.0000i | − | 0.869001i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.84955i | 0.208465i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1622i | 1.08866i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.35026 | + | 8.31265i | −0.395725 | + | 0.447538i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.89446 | −0.101700 | −0.0508500 | − | 0.998706i | \(-0.516193\pi\) | ||||
−0.0508500 | + | 0.998706i | \(0.516193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.4010i | 1.68086i | 0.541921 | + | 0.840430i | \(0.317697\pi\) | ||||
−0.541921 | + | 0.840430i | \(0.682303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.15045 | 0.221534 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.7757i | − | 0.679984i | −0.940428 | − | 0.339992i | \(-0.889576\pi\) | ||
0.940428 | − | 0.339992i | \(-0.110424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.9248 | − | 15.8496i | −0.951348 | − | 0.841207i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.80209 | −0.148303 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.4749 | −0.869510 | −0.434755 | − | 0.900549i | \(-0.643165\pi\) | ||||
−0.434755 | + | 0.900549i | \(0.643165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −20.8496 | −1.09734 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.74543 | −0.459016 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.3865 | + | 21.9248i | −1.01473 | + | 1.14760i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0957i | 0.526991i | 0.964661 | + | 0.263495i | \(0.0848754\pi\) | ||||
−0.964661 | + | 0.263495i | \(0.915125\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.7513 | 0.559691 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.3258i | 1.00335i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.82653 | 0.353464 | 0.176732 | − | 0.984259i | \(-0.443447\pi\) | ||||
0.176732 | + | 0.984259i | \(0.443447\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.09825 | + | 7.43136i | −0.263272 | + | 0.383754i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.92478i | 0.0991311i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.4617i | − | 0.999679i | −0.866118 | − | 0.499840i | \(-0.833392\pi\) | ||
0.866118 | − | 0.499840i | \(-0.166608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 9.48612i | − | 0.485989i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.90431i | − | 0.301696i | −0.988557 | − | 0.150848i | \(-0.951800\pi\) | ||
0.988557 | − | 0.150848i | \(-0.0482004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.40105 | + | 1.23884i | 0.0714040 | + | 0.0631372i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.0435 | −1.37470 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 14.1866i | − | 0.719291i | −0.933089 | − | 0.359646i | \(-0.882898\pi\) | ||
0.933089 | − | 0.359646i | \(-0.117102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.92478 | 0.501918 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.1622i | − | 0.613502i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.22425 | − | 2.85097i | −0.162230 | − | 0.143448i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1866 | 1.41465 | 0.707324 | − | 0.706890i | \(-0.249902\pi\) | ||||
0.707324 | + | 0.706890i | \(0.249902\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.9722 | −0.549299 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.62530 | 0.330852 | 0.165426 | − | 0.986222i | \(-0.447100\pi\) | ||||
0.165426 | + | 0.986222i | \(0.447100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.55149 | 0.475794 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.98778 | − | 5.29455i | −0.297535 | − | 0.263088i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.55008i | − | 0.126403i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.6761 | 0.626792 | 0.313396 | − | 0.949623i | \(-0.398533\pi\) | ||||
0.313396 | + | 0.949623i | \(0.398533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.9525i | 0.737554i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.6121 | 0.669809 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.82653 | + | 4.26774i | 0.236925 | + | 0.209495i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.13586i | 0.300474i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.8364i | 0.724805i | 0.932022 | + | 0.362402i | \(0.118043\pi\) | ||||
−0.932022 | + | 0.362402i | \(0.881957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.261865i | 0.0127625i | 0.999980 | + | 0.00638126i | \(0.00203123\pi\) | ||||
−0.999980 | + | 0.00638126i | \(0.997969\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 10.6801i | − | 0.519282i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | − | 0.986826i | 0.388057 | − | 0.0478681i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.564666 | 0.0273261 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 0.300891i | − | 0.0145272i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.52373 | 0.217900 | 0.108950 | − | 0.994047i | \(-0.465251\pi\) | ||||
0.108950 | + | 0.994047i | \(0.465251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.6385i | − | 0.751537i | −0.926714 | − | 0.375769i | \(-0.877379\pi\) | ||
0.926714 | − | 0.375769i | \(-0.122621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.38787 | + | 2.70052i | −0.114490 | + | 0.129480i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38.8627 | 1.85906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.3272 | −0.492892 | −0.246446 | − | 0.969156i | \(-0.579263\pi\) | ||||
−0.246446 | + | 0.969156i | \(0.579263\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.52373 | −0.263035 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.1939 | −0.721886 | −0.360943 | − | 0.932588i | \(-0.617545\pi\) | ||||
−0.360943 | + | 0.932588i | \(0.617545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.7988 | − | 15.7381i | −0.843743 | − | 0.746059i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 11.0132i | − | 0.520905i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.6761 | −1.16454 | −0.582268 | − | 0.812997i | \(-0.697835\pi\) | ||||
−0.582268 | + | 0.812997i | \(0.697835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.77433i | − | 0.0835500i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.2717 | −0.576575 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.07381 | − | 3.47627i | 0.144102 | − | 0.162970i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.37328i | 0.391686i | 0.980635 | + | 0.195843i | \(0.0627443\pi\) | ||||
−0.980635 | + | 0.195843i | \(0.937256\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 6.95254i | − | 0.324517i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8.29806i | − | 0.386479i | −0.981152 | − | 0.193240i | \(-0.938101\pi\) | ||
0.981152 | − | 0.193240i | \(-0.0618995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.4676i | 1.83421i | 0.398642 | + | 0.917107i | \(0.369482\pi\) | ||||
−0.398642 | + | 0.917107i | \(0.630518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.4010 | + | 11.8496i | 0.621459 | + | 0.549510i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.41819 | 0.111901 | 0.0559503 | − | 0.998434i | \(-0.482181\pi\) | ||||
0.0559503 | + | 0.998434i | \(0.482181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.3357i | 0.985190i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.14903 | −0.0529446 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.46310i | 0.205213i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.3258 | − | 3.86414i | 1.43733 | − | 0.177299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.0640 | −0.964452 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.44851 | 0.294640 | 0.147320 | − | 0.989089i | \(-0.452935\pi\) | ||||
0.147320 | + | 0.989089i | \(0.452935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.32724 | −0.288497 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.7005 | 0.486891 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.2374 | + | 16.1016i | −0.646488 | + | 0.731135i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.3331i | 0.558867i | 0.960165 | + | 0.279433i | \(0.0901466\pi\) | ||||
−0.960165 | + | 0.279433i | \(0.909853\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.09825 | 0.320994 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.3127i | − | 0.645921i | −0.946412 | − | 0.322960i | \(-0.895322\pi\) | ||
0.946412 | − | 0.322960i | \(-0.104678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.22425 | 0.145213 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.35026 | + | 1.52705i | −0.0606898 | + | 0.0686360i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.0738i | 1.03500i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 14.0606i | − | 0.629440i | −0.949184 | − | 0.314720i | \(-0.898089\pi\) | ||
0.949184 | − | 0.314720i | \(-0.101911\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.43866i | 0.377011i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 31.8700i | − | 1.42101i | −0.703690 | − | 0.710507i | \(-0.748466\pi\) | ||
0.703690 | − | 0.710507i | \(-0.251534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.8872 | − | 19.0982i | 0.751469 | − | 0.849861i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.73226 | 0.432225 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.0000i | 1.15243i | 0.817298 | + | 0.576215i | \(0.195471\pi\) | ||||
−0.817298 | + | 0.576215i | \(0.804529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.2228 | 1.24850 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 27.2243i | − | 1.20198i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.1925 | − | 18.3127i | 0.713528 | − | 0.806952i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.76257 | −0.0775178 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.1016 | 0.706780 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.4010 | 0.849975 | 0.424988 | − | 0.905199i | \(-0.360278\pi\) | ||||
0.424988 | + | 0.905199i | \(0.360278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.75860 | 0.339260 | 0.169630 | − | 0.985508i | \(-0.445743\pi\) | ||||
0.169630 | + | 0.985508i | \(0.445743\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.62530 | − | 1.06396i | 0.376439 | − | 0.0464350i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.0000i | − | 0.696971i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.9003 | −0.647841 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.8364i | 0.643844i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.40246 | −0.190692 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.4993 | + | 16.3576i | 0.799794 | + | 0.707199i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.86414i | − | 0.425669i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.911603i | 0.0392655i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 25.8496i | − | 1.11136i | −0.831397 | − | 0.555680i | \(-0.812458\pi\) | ||
0.831397 | − | 0.555680i | \(-0.187542\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1636i | 0.479077i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.46168 | + | 8.43866i | −0.319623 | + | 0.361472i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.2677 | 1.63621 | 0.818105 | − | 0.575068i | \(-0.195025\pi\) | ||||
0.818105 | + | 0.575068i | \(0.195025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.615452i | 0.0262668i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6253 | 0.537856 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.15045i | 0.176495i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.87732 | − | 7.84955i | −0.376821 | − | 0.333195i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.5271 | −1.59007 | −0.795036 | − | 0.606562i | \(-0.792548\pi\) | ||||
−0.795036 | + | 0.606562i | \(0.792548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0738 | 0.468372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.504032 | −0.0212802 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.6688 | 1.84042 | 0.920210 | − | 0.391425i | \(-0.128018\pi\) | ||||
0.920210 | + | 0.391425i | \(0.128018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.4010 | − | 33.2506i | 1.23691 | − | 1.39886i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.70782i | 0.323698i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.42407 | −0.353155 | −0.176578 | − | 0.984287i | \(-0.556503\pi\) | ||||
−0.176578 | + | 0.984287i | \(0.556503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.8627i | − | 1.04047i | −0.854022 | − | 0.520236i | \(-0.825844\pi\) | ||
0.854022 | − | 0.520236i | \(-0.174156\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.10299 | 0.129629 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.5501 | + | 3.76845i | −1.27403 | + | 0.157155i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0263i | 0.583924i | 0.956430 | + | 0.291962i | \(0.0943082\pi\) | ||||
−0.956430 | + | 0.291962i | \(0.905692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 7.74798i | − | 0.321995i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 6.21299i | − | 0.257758i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.47627i | 0.143972i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.78892 | + | 3.35026i | 0.156653 | + | 0.138516i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.5804 | 1.42729 | 0.713643 | − | 0.700510i | \(-0.247044\pi\) | ||||
0.713643 | + | 0.700510i | \(0.247044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 62.6516i | − | 2.58152i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.72829 | −0.317899 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.00000i | − | 0.328521i | −0.986417 | − | 0.164260i | \(-0.947476\pi\) | ||
0.986417 | − | 0.164260i | \(-0.0525237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.82321 | − | 5.14903i | −0.238728 | − | 0.211090i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.27171 | 0.174830 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.3996 | 1.73240 | 0.866201 | − | 0.499696i | \(-0.166555\pi\) | ||||
0.866201 | + | 0.499696i | \(0.166555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.75131 | −0.112228 | −0.0561141 | − | 0.998424i | \(-0.517871\pi\) | ||||
−0.0561141 | + | 0.998424i | \(0.517871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.2546 | −0.946999 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.1744 | − | 16.0703i | −0.738895 | − | 0.653351i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.7948i | 1.53404i | 0.641621 | + | 0.767022i | \(0.278262\pi\) | ||||
−0.641621 | + | 0.767022i | \(0.721738\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.47627 | 0.140866 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.37328i | 0.176924i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.7659 | −0.757947 | −0.378974 | − | 0.925407i | \(-0.623723\pi\) | ||||
−0.378974 | + | 0.925407i | \(0.623723\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.17679 | − | 5.46168i | −0.249072 | − | 0.220236i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.6107i | − | 0.749239i | −0.927179 | − | 0.374620i | \(-0.877773\pi\) | ||
0.927179 | − | 0.374620i | \(-0.122227\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19.2097i | − | 0.772102i | −0.922478 | − | 0.386051i | \(-0.873839\pi\) | ||
0.922478 | − | 0.386051i | \(-0.126161\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.5501i | 1.06542i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.9116i | 0.917934i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | + | 6.07522i | −0.970024 | + | 0.243009i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.97365 | −0.0788201 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.5990i | 0.422608i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.0263 | 1.03609 | 0.518046 | − | 0.855353i | \(-0.326659\pi\) | ||||
0.518046 | + | 0.855353i | \(0.326659\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 12.1622i | − | 0.483404i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.4314 | − | 19.7137i | 0.691743 | − | 0.782314i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.26187 | 0.0896184 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.1490 | −0.994880 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1735 | 0.441325 | 0.220663 | − | 0.975350i | \(-0.429178\pi\) | ||||
0.220663 | + | 0.975350i | \(0.429178\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.1451 | 1.38599 | 0.692993 | − | 0.720944i | \(-0.256292\pi\) | ||||
0.692993 | + | 0.720944i | \(0.256292\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.5369 | + | 13.7381i | 0.611765 | + | 0.540939i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.93207i | 0.272528i | 0.990673 | + | 0.136264i | \(0.0435095\pi\) | ||||
−0.990673 | + | 0.136264i | \(0.956490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.44851 | 0.0961123 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 17.2506i | − | 0.676104i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.7381 | 1.16374 | 0.581872 | − | 0.813281i | \(-0.302321\pi\) | ||||
0.581872 | + | 0.813281i | \(0.302321\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3488 | − | 25.2750i | 0.873242 | − | 0.987577i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.7612i | 1.20011i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.3879i | 0.950017i | 0.879981 | + | 0.475008i | \(0.157555\pi\) | ||||
−0.879981 | + | 0.475008i | \(0.842445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1378i | 1.32781i | 0.747819 | + | 0.663903i | \(0.231101\pi\) | ||||
−0.747819 | + | 0.663903i | \(0.768899\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.25060i | 0.0485693i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.8021 | − | 20.1622i | −0.884227 | − | 0.781857i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.3127 | −0.476748 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.1603i | 0.702118i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.101570 | 0.00392108 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.6385i | 0.911196i | 0.890186 | + | 0.455598i | \(0.150575\pi\) | ||||
−0.890186 | + | 0.455598i | \(0.849425\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.63989 | + | 21.4010i | 0.101609 | + | 0.823727i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.88717 | −0.110963 | −0.0554814 | − | 0.998460i | \(-0.517669\pi\) | ||||
−0.0554814 | + | 0.998460i | \(0.517669\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7269 | 0.795424 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.90034 | 0.0728212 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.7440 | −0.525900 | −0.262950 | − | 0.964809i | \(-0.584695\pi\) | ||||
−0.262950 | + | 0.964809i | \(0.584695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.4763 | + | 31.0738i | −1.04981 | + | 1.18727i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.86273i | 0.109220i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.62530 | 0.328598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31.5633i | − | 1.20072i | −0.799729 | − | 0.600361i | \(-0.795023\pi\) | ||
0.799729 | − | 0.600361i | \(-0.204977\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.96571 | 0.0746713 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.2750 | + | 12.7513i | −0.427687 | + | 0.483685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.37470i | 0.279337i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5501i | 0.399041i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.8397i | − | 0.900413i | −0.892924 | − | 0.450207i | \(-0.851350\pi\) | ||
0.892924 | − | 0.450207i | \(-0.148650\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.5026i | 1.56530i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.42548 | + | 6.13586i | −0.204336 | + | 0.231090i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.5844 | −0.924590 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 21.8496i | − | 0.820577i | −0.911956 | − | 0.410289i | \(-0.865428\pi\) | ||
0.911956 | − | 0.410289i | \(-0.134572\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.52373 | −0.169653 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 61.1002i | 2.28822i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.552907 | − | 0.625301i | 0.0206776 | − | 0.0233849i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.3536 | 0.461353 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.9248 | 1.26518 | 0.632590 | − | 0.774487i | \(-0.281992\pi\) | ||||
0.632590 | + | 0.774487i | \(0.281992\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.5731 | −0.877908 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.71370 | −0.0637331 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.92478 | + | 1.22425i | −0.368597 | + | 0.0454676i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.78163i | 0.103165i | 0.998669 | + | 0.0515824i | \(0.0164265\pi\) | ||||
−0.998669 | + | 0.0515824i | \(0.983574\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.02776 | 0.0751023 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 18.5501i | − | 0.686099i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.90175 | −0.181050 | −0.0905252 | − | 0.995894i | \(-0.528855\pi\) | ||||
−0.0905252 | + | 0.995894i | \(0.528855\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.17347 | + | 2.80606i | 0.117055 | + | 0.103503i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.83780i | 0.141367i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 25.9102i | − | 0.953122i | −0.879141 | − | 0.476561i | \(-0.841883\pi\) | ||
0.879141 | − | 0.476561i | \(-0.158117\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.89701i | 0.179896i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 9.06793i | − | 0.332670i | −0.986069 | − | 0.166335i | \(-0.946807\pi\) | ||
0.986069 | − | 0.166335i | \(-0.0531933\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.2374 | − | 22.8872i | 0.741442 | − | 0.838521i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.77178 | 0.247766 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 23.8134i | − | 0.870121i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.8496 | −0.432396 | −0.216198 | − | 0.976349i | \(-0.569366\pi\) | ||||
−0.216198 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 21.5106i | − | 0.783888i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.5026 | − | 22.5501i | −0.928135 | − | 0.820681i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.05079 | 0.0745371 | 0.0372685 | − | 0.999305i | \(-0.488134\pi\) | ||||
0.0372685 | + | 0.999305i | \(0.488134\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.92478 | 0.0698650 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.0738 | −0.908925 | −0.454462 | − | 0.890766i | \(-0.650169\pi\) | ||||
−0.454462 | + | 0.890766i | \(0.650169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8627 | 0.393257 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.61213 | − | 6.34694i | 0.202907 | − | 0.229474i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.07522i | − | 0.219364i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.7466 | 0.531775 | 0.265887 | − | 0.964004i | \(-0.414335\pi\) | ||||
0.265887 | + | 0.964004i | \(0.414335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.35359i | 0.156791i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.8872 | −0.391584 | −0.195792 | − | 0.980645i | \(-0.562728\pi\) | ||||
−0.195792 | + | 0.980645i | \(0.562728\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.07522 | + | 49.2506i | 0.218228 | + | 1.76913i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.4274i | 0.409955i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.8773i | 1.03464i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.15045i | 0.148515i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.62530i | 0.308243i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.38787 | − | 2.11142i | −0.0852268 | − | 0.0753598i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.8178 | 1.31241 | 0.656207 | − | 0.754581i | \(-0.272160\pi\) | ||||
0.656207 | + | 0.754581i | \(0.272160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.6629i | 0.415211i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.8021 | −1.52187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.252016i | − | 0.00894935i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.1016 | + | 10.7005i | 0.429198 | + | 0.379508i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.8119 | 0.453822 | 0.226911 | − | 0.973915i | \(-0.427137\pi\) | ||||
0.226911 | + | 0.973915i | \(0.427137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.32582 | 0.259169 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.9722 | −0.882351 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.07664 | 0.179151 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.2374 | + | 19.6629i | 0.783766 | + | 0.693027i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.6596i | 0.797655i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.2981 | 0.573009 | 0.286505 | − | 0.958079i | \(-0.407507\pi\) | ||||
0.286505 | + | 0.958079i | \(0.407507\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.21108i | − | 0.0776415i | −0.999246 | − | 0.0388208i | \(-0.987640\pi\) | ||
0.999246 | − | 0.0388208i | \(-0.0123601\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.0527 | −0.703279 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.7513 | + | 13.0435i | 0.516716 | + | 0.456894i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 72.6371i | − | 2.54125i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 4.87732i | − | 0.170427i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 50.6615i | − | 1.76810i | −0.467394 | − | 0.884049i | \(-0.654807\pi\) | ||
0.467394 | − | 0.884049i | \(-0.345193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 0.917483i | − | 0.0319814i | −0.999872 | − | 0.0159907i | \(-0.994910\pi\) | ||
0.999872 | − | 0.0159907i | \(-0.00509022\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.55149 | − | 0.191382i | 0.0540160 | − | 0.00666305i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.5198 | −0.365808 | −0.182904 | − | 0.983131i | \(-0.558550\pi\) | ||||
−0.182904 | + | 0.983131i | \(0.558550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.6907i | 1.34378i | 0.740650 | + | 0.671891i | \(0.234518\pi\) | ||||
−0.740650 | + | 0.671891i | \(0.765482\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.1016 | 0.558557 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.78892i | − | 0.131278i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.5066 | + | 17.5369i | −0.536628 | + | 0.606890i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42.8021 | 1.47946 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.0263 | −0.346148 | −0.173074 | − | 0.984909i | \(-0.555370\pi\) | ||||
−0.173074 | + | 0.984909i | \(0.555370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.6873 | −0.402534 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.2252 | + | 17.8837i | 0.695768 | + | 0.615216i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.3952i | 0.803867i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.09825 | −0.243611 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 40.4749i | − | 1.38746i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.5388 | −1.69618 | −0.848088 | − | 0.529855i | \(-0.822246\pi\) | ||||
−0.848088 | + | 0.529855i | \(0.822246\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.9756 | − | 24.8529i | 0.751548 | − | 0.849951i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 43.4763i | − | 1.48512i | −0.669779 | − | 0.742561i | \(-0.733611\pi\) | ||
0.669779 | − | 0.742561i | \(-0.266389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 23.5633i | − | 0.803968i | −0.915647 | − | 0.401984i | \(-0.868321\pi\) | ||
0.915647 | − | 0.401984i | \(-0.131679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.95112i | 0.270974i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 13.3317i | − | 0.453816i | −0.973916 | − | 0.226908i | \(-0.927138\pi\) | ||
0.973916 | − | 0.226908i | \(-0.0728617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.4617 | + | 29.5877i | 1.13773 | + | 1.00601i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.6082 | −0.394234 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.746569i | 0.0253256i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.52232 | 0.322651 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.5910i | 0.764590i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.8799 | + | 13.6385i | 0.672062 | + | 0.461065i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.6483 | −0.460871 | −0.230436 | − | 0.973088i | \(-0.574015\pi\) | ||||
−0.230436 | + | 0.973088i | \(0.574015\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.70052 | 0.0910864 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.3028 | 0.549255 | 0.274628 | − | 0.961551i | \(-0.411445\pi\) | ||||
0.274628 | + | 0.961551i | \(0.411445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5818 | −0.457064 | −0.228532 | − | 0.973536i | \(-0.573393\pi\) | ||||
−0.228532 | + | 0.973536i | \(0.573393\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.53690 | − | 8.52373i | 0.253350 | − | 0.286522i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.0797i | 1.24501i | 0.782614 | + | 0.622507i | \(0.213886\pi\) | ||||
−0.782614 | + | 0.622507i | \(0.786114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.3766 | −0.851104 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.38646i | 0.0464481i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.6859 | 0.959938 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.1260 | − | 20.4993i | 0.605886 | − | 0.685216i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 4.77575i | − | 0.159458i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.8496i | 0.662020i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.4485i | − | 0.481350i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 20.0000i | − | 0.665558i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.5139 | + | 23.1998i | −0.681904 | + | 0.771188i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.7294 | 1.18638 | 0.593188 | − | 0.805064i | \(-0.297869\pi\) | ||||
0.593188 | + | 0.805064i | \(0.297869\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 26.7954i | − | 0.888749i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5237 | −0.679982 | −0.339991 | − | 0.940429i | \(-0.610424\pi\) | ||||
−0.339991 | + | 0.940429i | \(0.610424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.11757i | − | 0.0369863i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.312650 | − | 0.353586i | 0.0103359 | − | 0.0116892i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.5355 | −1.07442 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.9986 | −0.692679 | −0.346340 | − | 0.938109i | \(-0.612576\pi\) | ||||
−0.346340 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.57593 | 0.0519287 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.2981 | 0.338965 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.02444 | − | 32.6253i | −0.132323 | − | 1.07271i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 25.6932i | − | 0.843876i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.5271 | 1.03437 | 0.517185 | − | 0.855874i | \(-0.326980\pi\) | ||||
0.517185 | + | 0.855874i | \(0.326980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 14.8364i | − | 0.486243i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.07381 | −0.231586 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.04746 | − | 0.926192i | −0.0342556 | − | 0.0302897i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.8641i | 0.583596i | 0.956480 | + | 0.291798i | \(0.0942535\pi\) | ||||
−0.956480 | + | 0.291798i | \(0.905746\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 14.9525i | − | 0.487958i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.5487i | 1.48484i | 0.669933 | + | 0.742422i | \(0.266323\pi\) | ||||
−0.669933 | + | 0.742422i | \(0.733677\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 28.1622i | − | 0.917088i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.7743 | − | 15.5778i | 0.448079 | − | 0.506747i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.2057 | −1.40400 | −0.701998 | − | 0.712179i | \(-0.747709\pi\) | ||||
−0.701998 | + | 0.712179i | \(0.747709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.5961i | − | 0.408887i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.72829 | −0.250607 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.9722i | 0.355426i | 0.984082 | + | 0.177713i | \(0.0568698\pi\) | ||||
−0.984082 | + | 0.177713i | \(0.943130\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.44851 | + | 5.70194i | 0.208669 | + | 0.184510i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.625301 | 0.0202131 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.0000 | 1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.5012 | 2.17746 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.9551 | 0.836391 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.2374 | − | 16.1016i | 0.458319 | − | 0.518328i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 44.1417i | − | 1.41950i | −0.704452 | − | 0.709751i | \(-0.748807\pi\) | ||
0.704452 | − | 0.709751i | \(-0.251193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.20314 | 0.263523 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.1886i | 0.647881i | 0.946077 | + | 0.323941i | \(0.105008\pi\) | ||||
−0.946077 | + | 0.323941i | \(0.894992\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.4142 | 0.526216 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.474855 | − | 3.84955i | −0.0152075 | − | 0.123284i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.73340i | − | 0.0554562i | −0.999616 | − | 0.0277281i | \(-0.991173\pi\) | ||
0.999616 | − | 0.0277281i | \(-0.00882727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.12127i | 0.131716i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.8397i | 0.378013i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.0059i | 0.446718i | 0.974736 | + | 0.223359i | \(0.0717023\pi\) | ||||
−0.974736 | + | 0.223359i | \(0.928298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0606 | − | 14.2012i | −0.511734 | − | 0.452489i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.89843 | 0.251410 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 70.8383i | 2.25253i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.8021 | −1.35965 | −0.679827 | − | 0.733373i | \(-0.737945\pi\) | ||||
−0.679827 | + | 0.733373i | \(0.737945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 18.6107i | − | 0.590593i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.87732 | + | 7.84955i | 0.281430 | + | 0.248848i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.8872 | −1.35825 | −0.679125 | − | 0.734023i | \(-0.737641\pi\) | ||||
−0.679125 | + | 0.734023i | \(0.737641\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.3536 | −0.897068 |
(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 | 1280.2.f.i.129.3 | 6 | ||
4.3 | odd | 2 | 1280.2.f.k.129.3 | 6 | |||
5.4 | even | 2 | 1280.2.f.l.129.3 | 6 | |||
8.3 | odd | 2 | 1280.2.f.j.129.4 | 6 | |||
8.5 | even | 2 | 1280.2.f.l.129.4 | 6 | |||
16.3 | odd | 4 | 640.2.c.c.129.4 | yes | 6 | ||
16.5 | even | 4 | 640.2.c.a.129.4 | yes | 6 | ||
16.11 | odd | 4 | 640.2.c.b.129.3 | yes | 6 | ||
16.13 | even | 4 | 640.2.c.d.129.3 | yes | 6 | ||
20.19 | odd | 2 | 1280.2.f.j.129.3 | 6 | |||
40.19 | odd | 2 | 1280.2.f.k.129.4 | 6 | |||
40.29 | even | 2 | inner | 1280.2.f.i.129.4 | 6 | ||
80.3 | even | 4 | 3200.2.a.bo.1.2 | 3 | |||
80.13 | odd | 4 | 3200.2.a.bv.1.2 | 3 | |||
80.19 | odd | 4 | 640.2.c.c.129.3 | yes | 6 | ||
80.27 | even | 4 | 3200.2.a.br.1.2 | 3 | |||
80.29 | even | 4 | 640.2.c.d.129.4 | yes | 6 | ||
80.37 | odd | 4 | 3200.2.a.bs.1.2 | 3 | |||
80.43 | even | 4 | 3200.2.a.bt.1.2 | 3 | |||
80.53 | odd | 4 | 3200.2.a.bq.1.2 | 3 | |||
80.59 | odd | 4 | 640.2.c.b.129.4 | yes | 6 | ||
80.67 | even | 4 | 3200.2.a.bu.1.2 | 3 | |||
80.69 | even | 4 | 640.2.c.a.129.3 | ✓ | 6 | ||
80.77 | odd | 4 | 3200.2.a.bp.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.c.a.129.3 | ✓ | 6 | 80.69 | even | 4 | ||
640.2.c.a.129.4 | yes | 6 | 16.5 | even | 4 | ||
640.2.c.b.129.3 | yes | 6 | 16.11 | odd | 4 | ||
640.2.c.b.129.4 | yes | 6 | 80.59 | odd | 4 | ||
640.2.c.c.129.3 | yes | 6 | 80.19 | odd | 4 | ||
640.2.c.c.129.4 | yes | 6 | 16.3 | odd | 4 | ||
640.2.c.d.129.3 | yes | 6 | 16.13 | even | 4 | ||
640.2.c.d.129.4 | yes | 6 | 80.29 | even | 4 | ||
1280.2.f.i.129.3 | 6 | 1.1 | even | 1 | trivial | ||
1280.2.f.i.129.4 | 6 | 40.29 | even | 2 | inner | ||
1280.2.f.j.129.3 | 6 | 20.19 | odd | 2 | |||
1280.2.f.j.129.4 | 6 | 8.3 | odd | 2 | |||
1280.2.f.k.129.3 | 6 | 4.3 | odd | 2 | |||
1280.2.f.k.129.4 | 6 | 40.19 | odd | 2 | |||
1280.2.f.l.129.3 | 6 | 5.4 | even | 2 | |||
1280.2.f.l.129.4 | 6 | 8.5 | even | 2 | |||
3200.2.a.bo.1.2 | 3 | 80.3 | even | 4 | |||
3200.2.a.bp.1.2 | 3 | 80.77 | odd | 4 | |||
3200.2.a.bq.1.2 | 3 | 80.53 | odd | 4 | |||
3200.2.a.br.1.2 | 3 | 80.27 | even | 4 | |||
3200.2.a.bs.1.2 | 3 | 80.37 | odd | 4 | |||
3200.2.a.bt.1.2 | 3 | 80.43 | even | 4 | |||
3200.2.a.bu.1.2 | 3 | 80.67 | even | 4 | |||
3200.2.a.bv.1.2 | 3 | 80.13 | odd | 4 |