Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [704,2,Mod(63,704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(704, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("704.63");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 704.u (of order \(10\), degree \(4\), 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: | \(5.62146830230\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 44) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 447.2 | ||
Root | \(1.40958 - 0.114404i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 704.447 |
Dual form | 704.2.u.c.63.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/704\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(321\) | \(639\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.704424 | − | 0.228881i | −0.406700 | − | 0.132145i | 0.0985210 | − | 0.995135i | \(-0.468589\pi\) |
−0.505221 | + | 0.862990i | \(0.668589\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.09089 | + | 0.792578i | −0.487861 | + | 0.354452i | −0.804361 | − | 0.594141i | \(-0.797492\pi\) |
0.316500 | + | 0.948592i | \(0.397492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.503194 | + | 1.54867i | 0.190189 | + | 0.585343i | 0.999999 | − | 0.00134995i | \(-0.000429701\pi\) |
−0.809810 | + | 0.586693i | \(0.800430\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.98322 | − | 1.44090i | −0.661075 | − | 0.480299i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.29726 | + | 0.357912i | 0.994160 | + | 0.107915i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.09089 | − | 2.87786i | 0.579909 | − | 0.798176i | −0.413777 | − | 0.910378i | \(-0.635791\pi\) |
0.993685 | + | 0.112203i | \(0.0357906\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.949856 | − | 0.308627i | 0.245252 | − | 0.0796871i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.0411247 | − | 0.0566033i | −0.00997420 | − | 0.0137283i | 0.804001 | − | 0.594628i | \(-0.202701\pi\) |
−0.813975 | + | 0.580900i | \(0.802701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.45716 | + | 7.56236i | −0.563711 | + | 1.73493i | 0.108038 | + | 0.994147i | \(0.465543\pi\) |
−0.671749 | + | 0.740778i | \(0.734457\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.20609i | − | 0.263191i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.30988i | 1.10719i | 0.832787 | + | 0.553593i | \(0.186744\pi\) | ||||
−0.832787 | + | 0.553593i | \(0.813256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.983224 | + | 3.02605i | −0.196645 | + | 0.605210i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.37331 | + | 3.26658i | 0.456744 | + | 0.628654i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.74364 | + | 1.21638i | −0.695177 | + | 0.225877i | −0.635228 | − | 0.772325i | \(-0.719094\pi\) |
−0.0599489 | + | 0.998201i | \(0.519094\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.17121 | + | 2.98842i | −0.389961 | + | 0.536735i | −0.958189 | − | 0.286136i | \(-0.907629\pi\) |
0.568228 | + | 0.822871i | \(0.307629\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.24075 | − | 1.00680i | −0.390064 | − | 0.175262i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.77637 | − | 1.29061i | −0.300262 | − | 0.218153i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.12561 | + | 6.54194i | 0.349448 | + | 1.07549i | 0.959159 | + | 0.282866i | \(0.0912852\pi\) |
−0.609712 | + | 0.792623i | \(0.708715\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.13156 | + | 1.54867i | −0.341323 | + | 0.247986i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.50305 | + | 1.78805i | 0.859432 | + | 0.279246i | 0.705391 | − | 0.708818i | \(-0.250771\pi\) |
0.154041 | + | 0.988065i | \(0.450771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.89516 | −0.289009 | −0.144505 | − | 0.989504i | \(-0.546159\pi\) | ||||
−0.144505 | + | 0.989504i | \(0.546159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.30550 | 0.492755 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.32545 | + | 3.03002i | 1.36026 | + | 0.441974i | 0.896129 | − | 0.443794i | \(-0.146368\pi\) |
0.464128 | + | 0.885768i | \(0.346368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.51794 | − | 2.55593i | 0.502563 | − | 0.365133i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0160138 | + | 0.0492854i | 0.00224238 | + | 0.00690134i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.14518 | − | 2.28511i | −0.432023 | − | 0.313883i | 0.350434 | − | 0.936587i | \(-0.386034\pi\) |
−0.782457 | + | 0.622704i | \(0.786034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.88062 | + | 2.22289i | −0.523262 | + | 0.299734i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.46177 | − | 4.76471i | 0.458522 | − | 0.631102i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.62366 | − | 1.50232i | 0.601950 | − | 0.195585i | 0.00783982 | − | 0.999969i | \(-0.497504\pi\) |
0.594110 | + | 0.804384i | \(0.297504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.791173 | − | 1.08896i | −0.101299 | − | 0.139427i | 0.755358 | − | 0.655312i | \(-0.227463\pi\) |
−0.856657 | + | 0.515886i | \(0.827463\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.23353 | − | 3.79641i | 0.155410 | − | 0.478303i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.79662i | 0.594948i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.91303i | 0.600223i | 0.953904 | + | 0.300111i | \(0.0970238\pi\) | ||||
−0.953904 | + | 0.300111i | \(0.902976\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.21533 | − | 3.74041i | 0.146309 | − | 0.450292i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.10014 | − | 5.64335i | −0.486597 | − | 0.669743i | 0.493159 | − | 0.869939i | \(-0.335842\pi\) |
−0.979756 | + | 0.200196i | \(0.935842\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.62677 | + | 3.12793i | −1.12673 | + | 0.366096i | −0.812332 | − | 0.583195i | \(-0.801802\pi\) |
−0.314397 | + | 0.949292i | \(0.601802\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.38521 | − | 1.90658i | 0.159951 | − | 0.220153i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.10487 | + | 5.28646i | 0.125912 | + | 0.602449i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.85779 | + | 3.52939i | 0.546544 | + | 0.397088i | 0.826510 | − | 0.562923i | \(-0.190323\pi\) |
−0.279966 | + | 0.960010i | \(0.590323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.34841 | + | 4.14999i | 0.149824 | + | 0.461110i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.92211 | + | 2.12304i | −0.320744 | + | 0.233034i | −0.736493 | − | 0.676446i | \(-0.763519\pi\) |
0.415749 | + | 0.909479i | \(0.363519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0897250 | + | 0.0291534i | 0.00973205 | + | 0.00316213i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.91552 | 0.312576 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.39711 | −0.572093 | −0.286046 | − | 0.958216i | \(-0.592341\pi\) | ||||
−0.286046 | + | 0.958216i | \(0.592341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.50899 | + | 1.78998i | 0.577499 | + | 0.187641i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.21345 | − | 1.60816i | 0.229524 | − | 0.166759i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.31327 | − | 10.1972i | −0.339934 | − | 1.04621i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.92705 | − | 4.30625i | −0.601801 | − | 0.437234i | 0.244717 | − | 0.969595i | \(-0.421305\pi\) |
−0.846518 | + | 0.532361i | \(0.821305\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.02348 | − | 5.46083i | −0.605383 | − | 0.548834i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.62667 | − | 7.74445i | 0.559875 | − | 0.770602i | −0.431436 | − | 0.902144i | \(-0.641993\pi\) |
0.991311 | + | 0.131542i | \(0.0419928\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.81631 | + | 3.18951i | −0.967230 | + | 0.314272i | −0.749697 | − | 0.661781i | \(-0.769801\pi\) |
−0.217533 | + | 0.976053i | \(0.569801\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.955923 | + | 1.31571i | 0.0932885 | + | 0.128401i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.42303 | − | 10.5350i | 0.330917 | − | 1.01846i | −0.637782 | − | 0.770217i | \(-0.720148\pi\) |
0.968699 | − | 0.248240i | \(-0.0798522\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.95933i | 0.858149i | 0.903269 | + | 0.429074i | \(0.141160\pi\) | ||||
−0.903269 | + | 0.429074i | \(0.858840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.09482i | − | 0.483579i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.40631 | − | 10.4836i | 0.320439 | − | 0.986210i | −0.653018 | − | 0.757342i | \(-0.726498\pi\) |
0.973457 | − | 0.228868i | \(-0.0735025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.20849 | − | 5.79249i | −0.392444 | − | 0.540153i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.29341 | + | 2.69469i | −0.766726 | + | 0.249124i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0669662 | − | 0.0921710i | 0.00613878 | − | 0.00844931i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7438 | + | 2.36026i | 0.976709 | + | 0.214569i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.46723 | − | 2.51909i | −0.312630 | − | 0.227139i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.40921 | − | 10.4925i | −0.304929 | − | 0.938474i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.32668 | − | 6.04969i | 0.738874 | − | 0.536823i | −0.153485 | − | 0.988151i | \(-0.549050\pi\) |
0.892358 | + | 0.451328i | \(0.149050\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.33500 | + | 0.433767i | 0.117540 | + | 0.0381910i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.86768 | −0.163180 | −0.0815901 | − | 0.996666i | \(-0.526000\pi\) | ||||
−0.0815901 | + | 0.996666i | \(0.526000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9480 | −1.12274 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.17804 | − | 1.68245i | −0.445655 | − | 0.144802i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.01489 | − | 0.737362i | 0.0867080 | − | 0.0629971i | −0.543587 | − | 0.839353i | \(-0.682934\pi\) |
0.630295 | + | 0.776356i | \(0.282934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.94407 | − | 5.98323i | −0.164894 | − | 0.507491i | 0.834135 | − | 0.551561i | \(-0.185968\pi\) |
−0.999028 | + | 0.0440698i | \(0.985968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.87556 | − | 4.26884i | −0.494811 | − | 0.359501i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.92422 | − | 8.74070i | 0.662657 | − | 0.730934i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.11982 | − | 4.29407i | 0.259087 | − | 0.356603i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.06313 | + | 0.995271i | −0.252643 | + | 0.0820886i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0839 | + | 13.8792i | 0.826102 | + | 1.13703i | 0.988636 | + | 0.150329i | \(0.0480332\pi\) |
−0.162534 | + | 0.986703i | \(0.551967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.75712 | + | 11.5632i | −0.305750 | + | 0.941002i | 0.673646 | + | 0.739054i | \(0.264727\pi\) |
−0.979396 | + | 0.201948i | \(0.935273\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.171513i | 0.0138660i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.98089i | − | 0.400074i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.63833 | − | 5.04225i | 0.130753 | − | 0.402415i | −0.864153 | − | 0.503230i | \(-0.832145\pi\) |
0.994905 | + | 0.100815i | \(0.0321449\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.69252 | + | 2.32956i | 0.134226 | + | 0.184746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.22325 | + | 2.67190i | −0.648083 | + | 0.210575i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.91168 | + | 8.13673i | −0.463039 | + | 0.637318i | −0.975135 | − | 0.221610i | \(-0.928869\pi\) |
0.512097 | + | 0.858928i | \(0.328869\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.24238 | − | 0.677657i | 0.252419 | − | 0.0527555i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.7237 | − | 12.8770i | −1.37150 | − | 0.996451i | −0.997618 | − | 0.0689735i | \(-0.978028\pi\) |
−0.373879 | − | 0.927478i | \(-0.621972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.106946 | + | 0.329146i | 0.00822661 | + | 0.0253189i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.7697 | − | 11.4573i | 1.20594 | − | 0.876165i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2531 | + | 3.65635i | 0.855557 | + | 0.277987i | 0.703772 | − | 0.710426i | \(-0.251498\pi\) |
0.151785 | + | 0.988413i | \(0.451498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.18111 | −0.391655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.60087 | −0.270658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.887979 | − | 0.288522i | −0.0663707 | − | 0.0215651i | 0.275643 | − | 0.961260i | \(-0.411109\pi\) |
−0.342014 | + | 0.939695i | \(0.611109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.2414 | − | 11.0736i | 1.13289 | − | 0.823091i | 0.146775 | − | 0.989170i | \(-0.453111\pi\) |
0.986113 | + | 0.166079i | \(0.0531106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.308080 | + | 0.948172i | 0.0227739 | + | 0.0700909i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.50380 | − | 5.45183i | −0.551691 | − | 0.400827i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.115340 | − | 0.201355i | −0.00843447 | − | 0.0147245i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.86463 | + | 5.31920i | −0.281110 | + | 0.386915i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.4435 | − | 6.31757i | 1.40688 | − | 0.457124i | 0.495472 | − | 0.868624i | \(-0.334995\pi\) |
0.911410 | + | 0.411500i | \(0.134995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.1927 | + | 14.0291i | 0.733690 | + | 1.00984i | 0.998957 | + | 0.0456628i | \(0.0145400\pi\) |
−0.265267 | + | 0.964175i | \(0.585460\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.09786 | − | 3.37886i | 0.0786192 | − | 0.241965i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.49133i | 0.248747i | 0.992235 | + | 0.124374i | \(0.0396921\pi\) | ||||
−0.992235 | + | 0.124374i | \(0.960308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.2660i | − | 0.798625i | −0.916815 | − | 0.399313i | \(-0.869249\pi\) | ||
0.916815 | − | 0.399313i | \(-0.130751\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.12450 | − | 3.46086i | 0.0793162 | − | 0.244110i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.76755 | − | 5.18559i | −0.264430 | − | 0.363957i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.42039 | + | 2.41103i | −0.518262 | + | 0.168394i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.65098 | − | 10.5307i | 0.531780 | − | 0.731932i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.8086 | + | 24.0556i | −0.747643 | + | 1.66396i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.21909 | + | 1.61227i | 0.152769 | + | 0.110993i | 0.661544 | − | 0.749906i | \(-0.269902\pi\) |
−0.508775 | + | 0.860899i | \(0.669902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.59658 | + | 4.91376i | 0.109396 | + | 0.336685i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.06741 | − | 1.50206i | 0.140996 | − | 0.102440i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.72061 | − | 1.85874i | −0.388341 | − | 0.126180i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.49726 | 0.506618 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.248884 | −0.0167417 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.5646 | − | 7.33167i | −1.51103 | − | 0.490965i | −0.567821 | − | 0.823152i | \(-0.692213\pi\) |
−0.943213 | + | 0.332187i | \(0.892213\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.31018 | − | 4.58462i | 0.420679 | − | 0.305641i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.247473 | − | 0.761643i | −0.0164254 | − | 0.0505520i | 0.942508 | − | 0.334184i | \(-0.108461\pi\) |
−0.958933 | + | 0.283632i | \(0.908461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.0839 | − | 13.8652i | −1.26110 | − | 0.916241i | −0.262286 | − | 0.964990i | \(-0.584476\pi\) |
−0.998811 | + | 0.0487497i | \(0.984476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.431676 | − | 3.97680i | 0.0284022 | − | 0.261654i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.2812 | − | 14.1509i | 0.673547 | − | 0.927058i | −0.326287 | − | 0.945271i | \(-0.605798\pi\) |
0.999834 | + | 0.0182127i | \(0.00579761\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.5746 | + | 4.08572i | −0.820274 | + | 0.266523i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.61413 | − | 3.59805i | −0.169806 | − | 0.233718i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.06577 | + | 6.35778i | −0.133623 | + | 0.411251i | −0.995373 | − | 0.0960826i | \(-0.969369\pi\) |
0.861750 | + | 0.507333i | \(0.169369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.28655i | 0.276121i | 0.990424 | + | 0.138061i | \(0.0440868\pi\) | ||||
−0.990424 | + | 0.138061i | \(0.955913\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.3451i | − | 0.984391i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.81191 | + | 5.57648i | −0.115759 | + | 0.356268i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.6258 | + | 22.8834i | 1.05787 | + | 1.45604i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.54433 | − | 0.826703i | 0.161240 | − | 0.0523902i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.87878 | − | 3.96230i | 0.181707 | − | 0.250098i | −0.708441 | − | 0.705770i | \(-0.750601\pi\) |
0.890148 | + | 0.455672i | \(0.150601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.90047 | + | 17.5080i | −0.119482 | + | 1.10072i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0565318 | − | 0.0410728i | −0.00354016 | − | 0.00257208i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.82696 | − | 11.7782i | −0.238719 | − | 0.734702i | −0.996606 | − | 0.0823161i | \(-0.973768\pi\) |
0.757887 | − | 0.652386i | \(-0.226232\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.06173 | + | 6.58373i | −0.563068 | + | 0.409093i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.17716 | + | 2.98184i | 0.568052 | + | 0.184571i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.9489 | −1.04511 | −0.522556 | − | 0.852605i | \(-0.675021\pi\) | ||||
−0.522556 | + | 0.852605i | \(0.675021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.24217 | 0.322024 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.80186 | + | 1.23530i | 0.232670 | + | 0.0755990i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.19947 | − | 2.32455i | 0.195075 | − | 0.141730i | −0.485960 | − | 0.873981i | \(-0.661530\pi\) |
0.681035 | + | 0.732251i | \(0.261530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.33528 | + | 22.5757i | 0.445587 | + | 1.37137i | 0.881839 | + | 0.471550i | \(0.156305\pi\) |
−0.436252 | + | 0.899824i | \(0.643695\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.47097 | − | 2.52181i | −0.210073 | − | 0.152627i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.32500 | + | 9.62576i | −0.260807 | + | 0.580455i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.82329 | − | 12.1442i | 0.530140 | − | 0.729675i | −0.457012 | − | 0.889461i | \(-0.651080\pi\) |
0.987152 | + | 0.159786i | \(0.0510803\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.61200 | − | 2.79821i | 0.515587 | − | 0.167524i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.37468 | + | 4.64485i | 0.201317 | + | 0.277089i | 0.897724 | − | 0.440558i | \(-0.145219\pi\) |
−0.696408 | + | 0.717647i | \(0.745219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.45938 | + | 10.6469i | −0.205639 | + | 0.632890i | 0.794048 | + | 0.607855i | \(0.207970\pi\) |
−0.999687 | + | 0.0250353i | \(0.992030\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.94150i | 0.470414i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.42215i | 0.556172i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.25178 | − | 16.1633i | 0.308928 | − | 0.950783i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.18954 | + | 4.39002i | 0.186974 | + | 0.257348i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.04336 | + | 1.63869i | −0.294636 | + | 0.0957331i | −0.452605 | − | 0.891711i | \(-0.649505\pi\) |
0.157969 | + | 0.987444i | \(0.449505\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.85320 | + | 5.30348i | −0.224342 | + | 0.308780i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.65627 | + | 11.6202i | 0.386236 | + | 0.674272i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.2811 | + | 11.1024i | 0.883729 | + | 0.642066i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.953632 | − | 2.93498i | −0.0549664 | − | 0.169169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.73613 | + | 4.16754i | −0.329532 | + | 0.239419i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.72617 | + | 0.560865i | 0.0988400 | + | 0.0321150i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.27014 | 0.129564 | 0.0647820 | − | 0.997899i | \(-0.479365\pi\) | ||||
0.0647820 | + | 0.997899i | \(0.479365\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.64487 | 0.434901 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1795 | + | 6.23180i | 1.08757 | + | 0.353373i | 0.797307 | − | 0.603574i | \(-0.206257\pi\) |
0.290263 | + | 0.956947i | \(0.406257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.24741 | + | 0.906296i | −0.0705078 | + | 0.0512269i | −0.622481 | − | 0.782635i | \(-0.713875\pi\) |
0.551973 | + | 0.833862i | \(0.313875\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.66331 | + | 5.11913i | 0.0937168 | + | 0.288431i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.6418 | − | 9.91136i | −0.766201 | − | 0.556678i | 0.134605 | − | 0.990899i | \(-0.457023\pi\) |
−0.900806 | + | 0.434222i | \(0.857023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.7791 | + | 2.67083i | −0.715492 | + | 0.149538i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.82253 | + | 6.63765i | −0.269167 | + | 0.370477i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.529105 | − | 0.171917i | 0.0294402 | − | 0.00956569i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.65275 | + | 9.15673i | 0.369028 | + | 0.507924i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.05062 | − | 6.31117i | 0.113400 | − | 0.349009i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.9667i | 0.880275i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.9735i | 1.86735i | 0.358115 | + | 0.933677i | \(0.383419\pi\) | ||||
−0.358115 | + | 0.933677i | \(0.616581\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.21071 | − | 16.0369i | 0.285545 | − | 0.878818i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.89396 | − | 5.35958i | −0.212750 | − | 0.292825i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.2590 | + | 5.28286i | −0.885683 | + | 0.287776i | −0.716315 | − | 0.697777i | \(-0.754173\pi\) |
−0.169368 | + | 0.985553i | \(0.554173\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.79898 | + | 6.60523i | −0.260645 | + | 0.358747i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.22863 | + | 9.07647i | −0.445605 | + | 0.491518i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.9502 | + | 10.8619i | 0.807232 | + | 0.586489i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.63877 | + | 5.04362i | 0.0882284 | + | 0.271539i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.02180 | − | 1.46893i | 0.108536 | − | 0.0788561i | −0.532193 | − | 0.846623i | \(-0.678632\pi\) |
0.640729 | + | 0.767767i | \(0.278632\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.66811 | + | 2.16660i | 0.356936 | + | 0.115975i | 0.481995 | − | 0.876174i | \(-0.339912\pi\) |
−0.125060 | + | 0.992149i | \(0.539912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.3631 | 0.766646 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.9431 | 0.955017 | 0.477509 | − | 0.878627i | \(-0.341540\pi\) | ||||
0.477509 | + | 0.878627i | \(0.341540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.94560 | + | 2.90660i | 0.474783 | + | 0.154266i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0682688 | + | 0.0496002i | −0.00361317 | + | 0.00262512i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.99112 | − | 9.20572i | −0.157865 | − | 0.485859i | 0.840575 | − | 0.541696i | \(-0.182217\pi\) |
−0.998440 | + | 0.0558363i | \(0.982217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.7804 | − | 25.9960i | −1.88318 | − | 1.36821i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.02797 | − | 4.12168i | −0.368873 | − | 0.216332i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.02262 | − | 11.0422i | 0.419923 | − | 0.577975i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.4325 | + | 9.56319i | −1.53636 | + | 0.499194i | −0.950370 | − | 0.311122i | \(-0.899295\pi\) |
−0.585992 | + | 0.810317i | \(0.699295\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.33739 | − | 11.4754i | −0.434027 | − | 0.597387i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.95624 | − | 6.02070i | 0.101563 | − | 0.312579i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.92658i | − | 0.255088i | −0.991833 | − | 0.127544i | \(-0.959291\pi\) | ||
0.991833 | − | 0.127544i | \(-0.0407095\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.17145i | 0.421972i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.32696 | + | 13.3170i | −0.222850 | + | 0.685861i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.36592 | + | 3.25642i | 0.121529 | + | 0.167271i | 0.865447 | − | 0.501000i | \(-0.167035\pi\) |
−0.743918 | + | 0.668271i | \(0.767035\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.25018 | + | 2.35573i | −0.371438 | + | 0.120688i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.04690 | + | 9.69922i | −0.360080 | + | 0.495607i | −0.950171 | − | 0.311729i | \(-0.899092\pi\) |
0.590091 | + | 0.807337i | \(0.299092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.39523 | − | 4.89125i | −0.274966 | − | 0.249281i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.75853 | + | 2.73073i | 0.191057 | + | 0.138811i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.24498 | − | 13.0647i | −0.215229 | − | 0.662407i | −0.999137 | − | 0.0415304i | \(-0.986777\pi\) |
0.783908 | − | 0.620877i | \(-0.213223\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.300556 | − | 0.218367i | 0.0151998 | − | 0.0110433i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.31564 | + | 0.427478i | 0.0663654 | + | 0.0215634i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.09663 | −0.407386 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.1547 | 0.610027 | 0.305014 | − | 0.952348i | \(-0.401339\pi\) | ||||
0.305014 | + | 0.952348i | \(0.401339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.12092 | + | 2.96357i | 0.456617 | + | 0.148364i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.2839 | − | 16.9167i | 1.16274 | − | 0.844782i | 0.172620 | − | 0.984989i | \(-0.444777\pi\) |
0.990122 | + | 0.140207i | \(0.0447768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.06049 | + | 12.4969i | 0.202267 | + | 0.622515i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.76016 | − | 3.45846i | −0.236534 | − | 0.171852i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.66723 | + | 22.3312i | 0.231346 | + | 1.10692i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.1416 | − | 15.3351i | 0.550917 | − | 0.758272i | −0.439219 | − | 0.898380i | \(-0.644745\pi\) |
0.990136 | + | 0.140108i | \(0.0447449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.883682 | + | 0.287126i | −0.0435888 | + | 0.0141629i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.65320 | + | 6.40457i | 0.228969 | + | 0.315149i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.50503 | − | 4.63200i | 0.0738790 | − | 0.227376i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.65970i | 0.228186i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 15.3705i | − | 0.750898i | −0.926843 | − | 0.375449i | \(-0.877488\pi\) | ||
0.926843 | − | 0.375449i | \(-0.122512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.97047 | + | 18.3752i | −0.290983 | + | 0.895553i | 0.693558 | + | 0.720400i | \(0.256042\pi\) |
−0.984541 | + | 0.175153i | \(0.943958\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.1285 | − | 19.4462i | −0.686952 | − | 0.945508i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.211719 | − | 0.0687918i | 0.0102699 | − | 0.00333689i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.28832 | − | 1.77322i | 0.0623463 | − | 0.0858123i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.58260 | + | 4.34345i | −0.366091 | + | 0.209704i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.9276 | + | 15.9313i | 1.05621 | + | 0.767385i | 0.973384 | − | 0.229179i | \(-0.0736040\pi\) |
0.0828305 | + | 0.996564i | \(0.473604\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.34612 | + | 4.14294i | 0.0646905 | + | 0.199097i | 0.978177 | − | 0.207771i | \(-0.0666209\pi\) |
−0.913487 | + | 0.406868i | \(0.866621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.18051 | + | 2.31078i | −0.152494 | + | 0.110793i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −40.1552 | − | 13.0472i | −1.92088 | − | 0.624133i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0996 | 1.15021 | 0.575105 | − | 0.818080i | \(-0.304961\pi\) | ||||
0.575105 | + | 0.818080i | \(0.304961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.6597 | −0.507605 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.9169 | − | 7.12124i | −1.04130 | − | 0.338340i | −0.262054 | − | 0.965053i | \(-0.584400\pi\) |
−0.779250 | + | 0.626713i | \(0.784400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.88765 | − | 4.27763i | 0.279102 | − | 0.202779i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.92662 | − | 12.0849i | −0.185723 | − | 0.571595i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.05281 | + | 2.21800i | 0.144071 | + | 0.104674i | 0.657486 | − | 0.753467i | \(-0.271620\pi\) |
−0.513415 | + | 0.858140i | \(0.671620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.5050 | + | 7.86527i | 0.824278 | + | 0.370361i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.29321 | − | 7.28548i | 0.248697 | − | 0.342302i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.42839 | + | 2.41363i | −0.348248 | + | 0.113153i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7236 | + | 28.5236i | 0.969409 | + | 1.33428i | 0.942345 | + | 0.334644i | \(0.108616\pi\) |
0.0270646 | + | 0.999634i | \(0.491384\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0872976 | − | 0.268674i | 0.00407470 | − | 0.0125406i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.5074i | 1.79347i | 0.442571 | + | 0.896734i | \(0.354067\pi\) | ||||
−0.442571 | + | 0.896734i | \(0.645933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.7672i | 0.500394i | 0.968195 | + | 0.250197i | \(0.0804954\pi\) | ||||
−0.968195 | + | 0.250197i | \(0.919505\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.14003 | + | 3.50866i | −0.0528677 | + | 0.162710i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.1553 | + | 16.7304i | 0.562481 | + | 0.774189i | 0.991639 | − | 0.129040i | \(-0.0411897\pi\) |
−0.429158 | + | 0.903229i | \(0.641190\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.60867 | + | 2.47221i | −0.351336 | + | 0.114156i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.30815 | + | 3.17690i | −0.106354 | + | 0.146384i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.24883 | − | 0.678301i | −0.287321 | − | 0.0311883i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.4682 | − | 14.8710i | −0.939144 | − | 0.682328i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.94499 | + | 9.06375i | 0.134842 | + | 0.415001i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.23398 | + | 6.70888i | −0.421911 | + | 0.306536i | −0.778406 | − | 0.627761i | \(-0.783972\pi\) |
0.356495 | + | 0.934297i | \(0.383972\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.2712 | + | 7.56128i | 1.06108 | + | 0.344765i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.40421 | 0.291401 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.87880 | 0.448573 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.80894 | + | 1.23760i | 0.172600 | + | 0.0560810i | 0.394042 | − | 0.919092i | \(-0.371076\pi\) |
−0.221442 | + | 0.975173i | \(0.571076\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.02668 | − | 4.37864i | 0.272536 | − | 0.198009i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.45914 | + | 10.6461i | 0.156109 | + | 0.480454i | 0.998272 | − | 0.0587698i | \(-0.0187178\pi\) |
−0.842163 | + | 0.539223i | \(0.818718\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.222807 | + | 0.161879i | 0.0100347 | + | 0.00729066i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.8991 | + | 1.18308i | 0.489877 | + | 0.0531755i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.67654 | − | 9.18946i | 0.299484 | − | 0.412204i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.4389 | − | 12.1646i | 1.67599 | − | 0.544564i | 0.691867 | − | 0.722025i | \(-0.256789\pi\) |
0.984128 | + | 0.177462i | \(0.0567886\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.53767 | + | 13.1275i | 0.426112 | + | 0.586492i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.97544 | − | 18.3905i | 0.266432 | − | 0.819993i | −0.724928 | − | 0.688824i | \(-0.758127\pi\) |
0.991360 | − | 0.131168i | \(-0.0418729\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.9079i | 0.574395i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 0.256336i | − | 0.0113843i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.2867 | − | 40.8921i | 0.588920 | − | 1.81251i | 0.00599915 | − | 0.999982i | \(-0.498090\pi\) |
0.582921 | − | 0.812529i | \(-0.301910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.68826 | − | 13.3347i | −0.428583 | − | 0.589895i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.5347 | + | 9.92132i | −1.34814 | + | 0.438037i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.18058 | − | 11.2596i | 0.360479 | − | 0.496157i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.6639 | + | 13.3285i | 1.30462 | + | 0.586185i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.09009 | − | 5.15125i | −0.311220 | − | 0.226115i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.55221 | − | 14.0103i | −0.199436 | − | 0.613801i | −0.999896 | − | 0.0144150i | \(-0.995411\pi\) |
0.800460 | − | 0.599386i | \(-0.204589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.7270 | + | 23.7776i | −1.43105 | + | 1.03972i | −0.441234 | + | 0.897392i | \(0.645459\pi\) |
−0.989819 | + | 0.142329i | \(0.954541\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.64970 | + | 1.18586i | 0.159286 | + | 0.0517552i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.258445 | 0.0112580 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.19479 | −0.225860 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.3344 | − | 3.68278i | −0.491873 | − | 0.159819i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.6520 | − | 12.0984i | 0.721280 | − | 0.524040i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.61566 | + | 14.2055i | 0.199552 | + | 0.614159i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.559477 | + | 0.406484i | 0.0241432 | + | 0.0175411i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.5144 | − | 7.16845i | 0.539031 | − | 0.308767i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.83661 | − | 13.5389i | 0.422909 | − | 0.582084i | −0.543399 | − | 0.839475i | \(-0.682863\pi\) |
0.966307 | + | 0.257391i | \(0.0828627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.2710 | + | 4.31200i | −0.569512 | + | 0.185046i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.10097 | − | 9.77365i | −0.304172 | − | 0.418657i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.87078 | + | 8.83536i | −0.122746 | + | 0.377773i | −0.993484 | − | 0.113975i | \(-0.963642\pi\) |
0.870738 | + | 0.491747i | \(0.163642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.29964i | 0.140825i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 31.2996i | − | 1.33341i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.02146 | + | 9.29909i | −0.128485 | + | 0.395437i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.03804 | + | 5.55788i | 0.171405 | + | 0.235919i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.6129 | + | 4.09818i | −0.534425 | + | 0.173645i | −0.563782 | − | 0.825924i | \(-0.690654\pi\) |
0.0293567 | + | 0.999569i | \(0.490654\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.96257 | + | 5.45401i | −0.167599 | + | 0.230680i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0351618 | + | 0.168238i | 0.00148453 | + | 0.00710302i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0155 | − | 13.8156i | −0.801408 | − | 0.582257i | 0.109919 | − | 0.993941i | \(-0.464941\pi\) |
−0.911327 | + | 0.411684i | \(0.864941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.59312 | + | 14.1362i | 0.193234 | + | 0.594713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.74846 | + | 4.17650i | −0.241413 | + | 0.175396i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.2494 | − | 3.98008i | −0.513523 | − | 0.166854i | 0.0407811 | − | 0.999168i | \(-0.487015\pi\) |
−0.554304 | + | 0.832315i | \(0.687015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4261 | −0.854806 | −0.427403 | − | 0.904061i | \(-0.640571\pi\) | ||||
−0.427403 | + | 0.904061i | \(0.640571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.1424 | −0.632585 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0680 | − | 5.22080i | −0.670080 | − | 0.217722i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.53777 | + | 4.02342i | −0.230540 | + | 0.167497i | −0.697058 | − | 0.717014i | \(-0.745508\pi\) |
0.466518 | + | 0.884512i | \(0.345508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.96902 | − | 12.2154i | −0.164947 | − | 0.507654i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.75828 | − | 3.45709i | −0.197407 | − | 0.143424i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.55259 | − | 8.66028i | −0.395628 | − | 0.358672i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.91144 | − | 9.51278i | 0.285753 | − | 0.393305i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.607533 | − | 0.197399i | 0.0250756 | − | 0.00814754i | −0.296452 | − | 0.955048i | \(-0.595804\pi\) |
0.321528 | + | 0.946900i | \(0.395804\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.2645 | − | 23.7625i | −0.711370 | − | 0.979117i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.799100 | − | 2.45938i | 0.0328706 | − | 0.101165i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.0480i | 0.700077i | 0.936735 | + | 0.350039i | \(0.113832\pi\) | ||||
−0.936735 | + | 0.350039i | \(0.886168\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.153624i | 0.00629799i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.57858 | + | 7.93604i | −0.105534 | + | 0.324801i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.16656 | − | 1.60564i | −0.0476645 | − | 0.0656045i | 0.784519 | − | 0.620104i | \(-0.212910\pi\) |
−0.832184 | + | 0.554500i | \(0.812910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.6571 | − | 5.08729i | 0.638665 | − | 0.207515i | 0.0282553 | − | 0.999601i | \(-0.491005\pi\) |
0.610410 | + | 0.792086i | \(0.291005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.07917 | − | 9.74365i | 0.288286 | − | 0.396792i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.5910 | + | 5.94052i | −0.552552 | + | 0.241516i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.2353 | − | 16.8814i | −0.943091 | − | 0.685196i | 0.00607141 | − | 0.999982i | \(-0.498067\pi\) |
−0.949163 | + | 0.314786i | \(0.898067\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.46707 | + | 4.51518i | 0.0594487 | + | 0.182964i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.2185 | − | 20.5019i | 1.14160 | − | 0.829419i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.32812 | − | 2.05613i | −0.255590 | − | 0.0830464i | 0.178419 | − | 0.983955i | \(-0.442902\pi\) |
−0.434010 | + | 0.900908i | \(0.642902\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.77894 | 0.233029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.8948 | −0.720416 | −0.360208 | − | 0.932872i | \(-0.617294\pi\) | ||||
−0.360208 | + | 0.932872i | \(0.617294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.1005 | − | 7.18088i | −0.888293 | − | 0.288624i | −0.170897 | − | 0.985289i | \(-0.554666\pi\) |
−0.717397 | + | 0.696665i | \(0.754666\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.3452 | + | 12.6020i | −0.696037 | + | 0.505700i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.71579 | − | 8.35835i | −0.108806 | − | 0.334870i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.835407 | − | 0.606959i | −0.0334163 | − | 0.0242784i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.1197 | − | 14.4715i | 0.523950 | − | 0.577935i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.282881 | − | 0.389352i | 0.0112792 | − | 0.0155245i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.0545 | − | 14.3142i | 1.75378 | − | 0.569838i | 0.757255 | − | 0.653119i | \(-0.226540\pi\) |
0.996526 | + | 0.0832806i | \(0.0265398\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.19417 | − | 1.64363i | −0.0474639 | − | 0.0653284i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.28864 | + | 13.1991i | −0.170190 | + | 0.523790i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 15.4683i | − | 0.612877i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.0999i | 0.676462i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.39773 | − | 25.8456i | 0.331691 | − | 1.02084i | −0.636639 | − | 0.771162i | \(-0.719676\pi\) |
0.968329 | − | 0.249676i | \(-0.0803242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.2352 | − | 25.0987i | −0.719128 | − | 0.989794i | −0.999552 | − | 0.0299182i | \(-0.990475\pi\) |
0.280425 | − | 0.959876i | \(-0.409525\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.80013 | + | 0.584897i | −0.0708800 | + | 0.0230303i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.7877 | − | 34.1173i | 0.974505 | − | 1.34129i | 0.0347664 | − | 0.999395i | \(-0.488931\pi\) |
0.939738 | − | 0.341895i | \(-0.111069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.7831 | − | 3.29867i | 0.619541 | − | 0.129484i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.60431 | + | 2.61868i | 0.141264 | + | 0.102634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.25077 | + | 3.84947i | 0.0489464 | + | 0.150641i | 0.972542 | − | 0.232726i | \(-0.0747644\pi\) |
−0.923596 | + | 0.383367i | \(0.874764\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.03744 | − | 1.48028i | 0.0796093 | − | 0.0578395i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.5991 | + | 7.66780i | 0.920687 | + | 0.299149i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.46292 | 0.251760 | 0.125880 | − | 0.992045i | \(-0.459825\pi\) | ||||
0.125880 | + | 0.992045i | \(0.459825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.6232 | −1.03552 | −0.517761 | − | 0.855525i | \(-0.673234\pi\) | ||||
−0.517761 | + | 0.855525i | \(0.673234\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.175320 | + | 0.0569648i | 0.00680885 | + | 0.00221233i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.1249 | − | 10.2623i | 0.547740 | − | 0.397956i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.45884 | − | 19.8783i | −0.250087 | − | 0.769690i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.2169 | + | 10.3292i | 0.549659 | + | 0.399350i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.21895 | − | 3.87374i | −0.0856616 | − | 0.149544i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.89033 | + | 6.73096i | −0.188508 | + | 0.259460i | −0.892802 | − | 0.450449i | \(-0.851264\pi\) |
0.704294 | + | 0.709909i | \(0.251264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.2183 | + | 3.96998i | −0.470284 | + | 0.152805i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.97132 | + | 12.3480i | 0.344796 | + | 0.474571i | 0.945834 | − | 0.324649i | \(-0.105246\pi\) |
−0.601039 | + | 0.799220i | \(0.705246\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.68652 | − | 11.3459i | 0.141476 | − | 0.435417i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.593162i | 0.0227300i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 32.9156i | − | 1.25948i | −0.776806 | − | 0.629740i | \(-0.783161\pi\) | ||
0.776806 | − | 0.629740i | \(-0.216839\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.522718 | + | 1.60876i | −0.0199720 | + | 0.0614676i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2696 | + | 14.1349i | 0.391811 | + | 0.539282i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.1524 | + | 4.27349i | −0.501068 | + | 0.162807i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.7545 | − | 36.8244i | 1.01779 | − | 1.40087i | 0.104047 | − | 0.994572i | \(-0.466821\pi\) |
0.913742 | − | 0.406294i | \(-0.133179\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.42604 | − | 12.0762i | 0.206118 | − | 0.458739i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.86294 | + | 4.98622i | 0.260326 | + | 0.189138i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.125102 | − | 0.385024i | −0.00473857 | − | 0.0145838i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.4812 | + | 7.61507i | −0.396437 | + | 0.288028i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.6330 | + | 15.4769i | 1.79907 | + | 0.584555i | 0.999864 | − | 0.0164975i | \(-0.00525154\pi\) |
0.799210 | + | 0.601052i | \(0.205252\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.6955 | −2.06288 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.79298 | 0.368825 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.8249 | + | 4.81691i | 0.557548 | + | 0.181158i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.87556 | + | 4.99539i | −0.258217 | + | 0.187606i | −0.709361 | − | 0.704846i | \(-0.751016\pi\) |
0.451144 | + | 0.892451i | \(0.351016\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.54860 | − | 13.9991i | −0.170586 | − | 0.525009i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.8681 | − | 11.5289i | −0.594266 | − | 0.431759i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.71677 | + | 15.8157i | −0.0642036 | + | 0.591474i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.91036 | − | 4.00576i | 0.108689 | − | 0.149598i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.94019 | − | 2.25500i | 0.258825 | − | 0.0840974i | −0.176730 | − | 0.984259i | \(-0.556552\pi\) |
0.435555 | + | 0.900162i | \(0.356552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.87901 | − | 13.5973i | −0.367914 | − | 0.506390i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.981112 | − | 3.01955i | 0.0364879 | − | 0.112298i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 12.5244i | − | 0.465146i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.85004i | 0.0686140i | 0.999411 | + | 0.0343070i | \(0.0109224\pi\) | ||||
−0.999411 | + | 0.0343070i | \(0.989078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.533026 | − | 1.64049i | 0.0197417 | − | 0.0607587i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0779378 | + | 0.107272i | 0.00288264 | + | 0.00396761i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.9690 | + | 5.83849i | −0.663701 | + | 0.215650i | −0.621446 | − | 0.783457i | \(-0.713454\pi\) |
−0.0422555 | + | 0.999107i | \(0.513454\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.55271 | − | 3.51350i | 0.0941580 | − | 0.129597i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.75843 | + | 16.1995i | −0.0647728 | + | 0.596717i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.7166 | + | 9.23916i | 0.467788 | + | 0.339868i | 0.796579 | − | 0.604535i | \(-0.206641\pi\) |
−0.328791 | + | 0.944403i | \(0.606641\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.47402 | − | 19.9250i | −0.237829 | − | 0.731963i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.69746 | + | 3.41290i | −0.172333 | + | 0.125207i | −0.670608 | − | 0.741812i | \(-0.733967\pi\) |
0.498275 | + | 0.867019i | \(0.333967\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.0008 | − | 7.14848i | −0.806045 | − | 0.261900i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.85428 | 0.323961 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0377 | 0.659083 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.85643 | − | 0.928110i | −0.104233 | − | 0.0338672i | 0.256436 | − | 0.966561i | \(-0.417452\pi\) |
−0.360669 | + | 0.932694i | \(0.617452\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.93478 | + | 2.13224i | −0.106949 | + | 0.0777033i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.06615 | − | 15.5920i | −0.184376 | − | 0.567451i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.1049 | − | 15.3336i | −0.767071 | − | 0.557310i | 0.134000 | − | 0.990981i | \(-0.457218\pi\) |
−0.901071 | + | 0.433672i | \(0.857218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.34600 | − | 11.8981i | 0.194047 | − | 0.431874i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.7813 | + | 25.8502i | −0.680820 | + | 0.937068i | −0.999943 | − | 0.0106450i | \(-0.996612\pi\) |
0.319123 | + | 0.947713i | \(0.396612\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.8751 | + | 4.50828i | −0.502311 | + | 0.163211i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.135938 | − | 0.187102i | −0.00491484 | − | 0.00676470i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.34410 | − | 16.4474i | 0.192964 | − | 0.593883i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 22.3560i | − | 0.806176i | −0.915161 | − | 0.403088i | \(-0.867937\pi\) | ||
0.915161 | − | 0.403088i | \(-0.132063\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.17275i | 0.330348i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.56889 | + | 4.82855i | −0.0564291 | + | 0.173671i | −0.975299 | − | 0.220891i | \(-0.929104\pi\) |
0.918869 | + | 0.394562i | \(0.129104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.90832 | − | 9.50848i | −0.248154 | − | 0.341555i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.89020 | − | 2.56368i | 0.283059 | − | 0.0919715i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.0438 | + | 37.2225i | −0.968943 | + | 1.33364i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4994 | − | 20.0751i | −0.411480 | − | 0.718343i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.8582 | − | 9.34206i | −0.459516 | − | 0.333858i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.20914 | + | 6.79904i | 0.0788476 | + | 0.242668i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.38155 | − | 1.73029i | 0.0848930 | − | 0.0616783i | −0.544529 | − | 0.838742i | \(-0.683292\pi\) |
0.629422 | + | 0.777064i | \(0.283292\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.9392 | + | 3.87928i | 0.425046 | + | 0.138106i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.9496 | 0.638215 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.78812 | −0.170031 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.69271 | − | 1.19983i | −0.130967 | − | 0.0425537i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.06111 | − | 4.40365i | 0.214695 | − | 0.155985i | −0.475240 | − | 0.879856i | \(-0.657639\pi\) |
0.689936 | + | 0.723871i | \(0.257639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.211997 | − | 0.652460i | −0.00749992 | − | 0.0230824i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.7037 | + | 7.77668i | 0.378196 | + | 0.274775i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.8615 | + | 6.86804i | −1.15966 | + | 0.242368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.85298 | − | 9.43231i | 0.241536 | − | 0.332445i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.78583 | + | 0.905170i | −0.0980658 | + | 0.0318635i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.4091 | + | 32.2199i | 0.823022 | + | 1.13279i | 0.989182 | + | 0.146694i | \(0.0468631\pi\) |
−0.166160 | + | 0.986099i | \(0.553137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.1790 | − | 40.5607i | 0.462777 | − | 1.42428i | −0.398981 | − | 0.916959i | \(-0.630636\pi\) |
0.861757 | − | 0.507321i | \(-0.169364\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 17.5818i | − | 0.616619i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 13.5617i | − | 0.475047i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.65671 | − | 14.3319i | 0.162918 | − | 0.501409i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.34638 | − | 11.4878i | −0.291646 | − | 0.401416i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3658 | − | 5.96742i | 0.640972 | − | 0.208264i | 0.0295426 | − | 0.999564i | \(-0.490595\pi\) |
0.611429 | + | 0.791299i | \(0.290595\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.83041 | − | 8.02487i | 0.203235 | − | 0.279729i | −0.695218 | − | 0.718799i | \(-0.744692\pi\) |
0.898453 | + | 0.439070i | \(0.144692\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.24979 | − | 5.79071i | 0.182774 | − | 0.201607i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.2981 | + | 25.6455i | 1.22743 | + | 0.891783i | 0.996695 | − | 0.0812332i | \(-0.0258859\pi\) |
0.230738 | + | 0.973016i | \(0.425886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.69871 | + | 26.7719i | 0.302119 | + | 0.929826i | 0.980737 | + | 0.195335i | \(0.0625793\pi\) |
−0.678618 | + | 0.734491i | \(0.737421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.99492 | + | 6.53519i | −0.312030 | + | 0.226703i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.289348 | − | 0.0940150i | −0.0100253 | − | 0.00325743i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.5406 | 1.02229 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.9149 | −0.515533 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.2421 | − | 10.8010i | −1.14764 | − | 0.372892i | −0.327388 | − | 0.944890i | \(-0.606169\pi\) |
−0.820255 | + | 0.571998i | \(0.806169\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9262 | + | 7.93837i | −0.376767 | + | 0.273737i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.31409 | − | 4.04435i | −0.0452596 | − | 0.139295i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.377540 | − | 0.274299i | −0.0129878 | − | 0.00943617i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.75095 | + | 17.8263i | 0.0601634 | + | 0.612518i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.87374 | − | 6.70812i | 0.167266 | − | 0.230222i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.7369 | + | 11.2867i | −1.19077 | + | 0.386903i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.9973 | + | 22.0183i | 0.547736 | + | 0.753894i | 0.989703 | − | 0.143138i | \(-0.0457191\pi\) |
−0.441967 | + | 0.897031i | \(0.645719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.12215 | + | 24.9974i | −0.277772 | + | 0.854893i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 37.5541i | − | 1.28282i | −0.767197 | − | 0.641412i | \(-0.778349\pi\) | ||
0.767197 | − | 0.641412i | \(-0.221651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.50293i | 0.153638i | 0.997045 | + | 0.0768190i | \(0.0244764\pi\) | ||||
−0.997045 | + | 0.0768190i | \(0.975524\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.15655 | − | 6.63719i | 0.0734952 | − | 0.226195i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.6014 | + | 14.5915i | 0.360875 | + | 0.496702i | 0.950392 | − | 0.311054i | \(-0.100682\pi\) |
−0.589517 | + | 0.807756i | \(0.700682\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.1738 | + | 4.93028i | −0.515926 | + | 0.167634i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.39896 | + | 10.1838i | −0.251282 | + | 0.345860i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.7542 | + | 13.3760i | 0.500501 | + | 0.453749i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.1390 | + | 10.2726i | 0.479083 | + | 0.348074i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.54980 | + | 17.0805i | 0.187832 | + | 0.578089i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.5339 | − | 10.5595i | 0.491335 | − | 0.356976i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.9541 | + | 4.20903i | 0.437428 | + | 0.142129i | 0.519449 | − | 0.854502i | \(-0.326137\pi\) |
−0.0820206 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.92773 | 0.132479 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.44549 | 0.183463 | 0.0917317 | − | 0.995784i | \(-0.470760\pi\) | ||||
0.0917317 | + | 0.995784i | \(0.470760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.8480 | + | 8.72345i | 0.903508 | + | 0.293568i | 0.723684 | − | 0.690131i | \(-0.242447\pi\) |
0.179824 | + | 0.983699i | \(0.442447\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.92816 | − | 2.85397i | 0.132044 | − | 0.0959352i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.1145 | + | 40.3623i | 0.440342 | + | 1.35523i | 0.887512 | + | 0.460784i | \(0.152432\pi\) |
−0.447171 | + | 0.894449i | \(0.647568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.5589 | + | 9.85113i | 0.454751 | + | 0.330396i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.96073 | + | 14.1662i | 0.0991883 | + | 0.474586i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.8283 | + | 63.0772i | −1.53358 | + | 2.11080i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.19736 | − | 0.389047i | 0.0400234 | − | 0.0130044i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.22325 | − | 11.3183i | −0.274566 | − | 0.377908i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.49318 | − | 13.8286i | 0.149856 | − | 0.461209i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.272002i | 0.00906169i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.28574i | 0.0760646i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.85008 | + | 24.1601i | −0.260946 | + | 0.803108i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.3902 | − | 28.0647i | −0.677046 | − | 0.931873i | 0.322848 | − | 0.946451i | \(-0.395360\pi\) |
−0.999894 | + | 0.0145776i | \(0.995360\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.3179 | + | 7.25153i | −0.740238 | + | 0.240518i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.4380 | + | 24.0014i | −0.577748 | + | 0.795202i | −0.993446 | − | 0.114300i | \(-0.963537\pi\) |
0.415698 | + | 0.909503i | \(0.363537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3948 | + | 5.95434i | −0.344018 | + | 0.197060i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.08758 | − | 0.790174i | −0.0359543 | − | 0.0261224i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.939807 | − | 2.89243i | −0.0310352 | − | 0.0955164i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.4823 | − | 12.7016i | 0.576687 | − | 0.418988i | −0.260841 | − | 0.965382i | \(-0.584000\pi\) |
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.59915 | − | 0.519594i | −0.0526936 | − | 0.0171212i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.8137 | −0.816754 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.8862 | −0.719614 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.0637 | + | 7.81877i | 0.790356 | + | 0.256802i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.2024 | + | 27.7557i | −1.25338 | + | 0.910635i | −0.998413 | − | 0.0563145i | \(-0.982065\pi\) |
−0.254968 | + | 0.966949i | \(0.582065\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.6848 | + | 32.8843i | 0.350179 | + | 1.07774i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.0842 | − | 8.77967i | −0.395618 | − | 0.287433i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.285412 | + | 0.128240i | 0.00933397 | + | 0.00419390i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.2659 | − | 37.5283i | 0.890738 | − | 1.22600i | −0.0825914 | − | 0.996583i | \(-0.526320\pi\) |
0.973329 | − | 0.229412i | \(-0.0736804\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.08614 | − | 0.352908i | 0.0354449 | − | 0.0115167i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.1708 | − | 31.8919i | −0.755347 | − | 1.03965i | −0.997587 | − | 0.0694293i | \(-0.977882\pi\) |
0.242240 | − | 0.970216i | \(-0.422118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.49432 | + | 29.2205i | −0.309178 | + | 0.951551i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 8.86568i | − | 0.288401i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.9488i | 0.810725i | 0.914156 | + | 0.405363i | \(0.132855\pi\) | ||||
−0.914156 | + | 0.405363i | \(0.867145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.1268 | + | 34.2447i | −0.361190 | + | 1.11163i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.34110 | + | 10.1042i | 0.238052 | + | 0.327650i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.9090 | − | 12.6423i | 1.26039 | − | 0.409524i | 0.398754 | − | 0.917058i | \(-0.369443\pi\) |
0.861632 | + | 0.507534i | \(0.169443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.2035 | + | 22.3023i | −0.524334 | + | 0.721684i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.61321 | + | 1.04350i | 0.310751 | + | 0.0337316i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.65262 | + | 1.20070i | 0.0533658 | + | 0.0387725i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.36305 | + | 16.5058i | 0.173002 | + | 0.532445i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.9685 | + | 15.9610i | −0.707925 | + | 0.514337i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.2383 | − | 7.22567i | −0.715877 | − | 0.232603i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.6696 | 0.761164 | 0.380582 | − | 0.924747i | \(-0.375724\pi\) | ||||
0.380582 | + | 0.924747i | \(0.375724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.412063 | −0.0132374 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.2925 | + | 16.6659i | 1.64606 | + | 0.534836i | 0.977880 | − | 0.209168i | \(-0.0670755\pi\) |
0.668176 | + | 0.744004i | \(0.267076\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.28781 | − | 6.02145i | 0.265695 | − | 0.193039i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.59056 | − | 7.97291i | −0.0829642 | − | 0.255338i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.76321 | + | 5.64030i | 0.248367 | + | 0.180449i | 0.705003 | − | 0.709204i | \(-0.250946\pi\) |
−0.456636 | + | 0.889654i | \(0.650946\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.7957 | − | 1.93169i | −0.568752 | − | 0.0617371i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.9095 | − | 17.7684i | 0.412168 | − | 0.567300i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.5747 | + | 10.9091i | −1.07087 | + | 0.347945i | −0.790824 | − | 0.612043i | \(-0.790348\pi\) |
−0.280041 | + | 0.959988i | \(0.590348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.76715 | − | 3.80866i | −0.0881688 | − | 0.121354i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.65449 | − | 11.2474i | 0.116324 | − | 0.358007i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10.0631i | − | 0.319987i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 17.8021i | − | 0.565502i | −0.959193 | − | 0.282751i | \(-0.908753\pi\) | ||
0.959193 | − | 0.282751i | \(-0.0912471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.77591 | − | 23.9318i | 0.246761 | − | 0.759452i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.92918 | + | 12.2900i | 0.283074 | + | 0.389618i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.8586 | − | 19.4492i | 1.89574 | − | 0.615963i | 0.922596 | − | 0.385766i | \(-0.126063\pi\) |
0.973144 | − | 0.230197i | \(-0.0739370\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.3251 | + | 22.4695i | −0.516503 | + | 0.710905i |
(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 | 704.2.u.c.447.2 | 16 | ||
4.3 | odd | 2 | inner | 704.2.u.c.447.3 | 16 | ||
8.3 | odd | 2 | 44.2.g.a.7.3 | yes | 16 | ||
8.5 | even | 2 | 44.2.g.a.7.1 | ✓ | 16 | ||
11.8 | odd | 10 | inner | 704.2.u.c.63.3 | 16 | ||
24.5 | odd | 2 | 396.2.r.a.271.4 | 16 | |||
24.11 | even | 2 | 396.2.r.a.271.2 | 16 | |||
44.19 | even | 10 | inner | 704.2.u.c.63.2 | 16 | ||
88.3 | odd | 10 | 484.2.g.i.239.4 | 16 | |||
88.5 | even | 10 | 484.2.c.d.483.13 | 16 | |||
88.13 | odd | 10 | 484.2.g.j.215.1 | 16 | |||
88.19 | even | 10 | 44.2.g.a.19.1 | yes | 16 | ||
88.21 | odd | 2 | 484.2.g.i.403.4 | 16 | |||
88.27 | odd | 10 | 484.2.c.d.483.3 | 16 | |||
88.29 | odd | 10 | 484.2.g.f.475.3 | 16 | |||
88.35 | even | 10 | 484.2.g.j.215.2 | 16 | |||
88.37 | even | 10 | 484.2.g.j.475.2 | 16 | |||
88.43 | even | 2 | 484.2.g.i.403.2 | 16 | |||
88.51 | even | 10 | 484.2.g.f.475.4 | 16 | |||
88.53 | even | 10 | 484.2.g.f.215.4 | 16 | |||
88.59 | odd | 10 | 484.2.g.j.475.1 | 16 | |||
88.61 | odd | 10 | 484.2.c.d.483.4 | 16 | |||
88.69 | even | 10 | 484.2.g.i.239.2 | 16 | |||
88.75 | odd | 10 | 484.2.g.f.215.3 | 16 | |||
88.83 | even | 10 | 484.2.c.d.483.14 | 16 | |||
88.85 | odd | 10 | 44.2.g.a.19.3 | yes | 16 | ||
264.107 | odd | 10 | 396.2.r.a.19.4 | 16 | |||
264.173 | even | 10 | 396.2.r.a.19.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
44.2.g.a.7.1 | ✓ | 16 | 8.5 | even | 2 | ||
44.2.g.a.7.3 | yes | 16 | 8.3 | odd | 2 | ||
44.2.g.a.19.1 | yes | 16 | 88.19 | even | 10 | ||
44.2.g.a.19.3 | yes | 16 | 88.85 | odd | 10 | ||
396.2.r.a.19.2 | 16 | 264.173 | even | 10 | |||
396.2.r.a.19.4 | 16 | 264.107 | odd | 10 | |||
396.2.r.a.271.2 | 16 | 24.11 | even | 2 | |||
396.2.r.a.271.4 | 16 | 24.5 | odd | 2 | |||
484.2.c.d.483.3 | 16 | 88.27 | odd | 10 | |||
484.2.c.d.483.4 | 16 | 88.61 | odd | 10 | |||
484.2.c.d.483.13 | 16 | 88.5 | even | 10 | |||
484.2.c.d.483.14 | 16 | 88.83 | even | 10 | |||
484.2.g.f.215.3 | 16 | 88.75 | odd | 10 | |||
484.2.g.f.215.4 | 16 | 88.53 | even | 10 | |||
484.2.g.f.475.3 | 16 | 88.29 | odd | 10 | |||
484.2.g.f.475.4 | 16 | 88.51 | even | 10 | |||
484.2.g.i.239.2 | 16 | 88.69 | even | 10 | |||
484.2.g.i.239.4 | 16 | 88.3 | odd | 10 | |||
484.2.g.i.403.2 | 16 | 88.43 | even | 2 | |||
484.2.g.i.403.4 | 16 | 88.21 | odd | 2 | |||
484.2.g.j.215.1 | 16 | 88.13 | odd | 10 | |||
484.2.g.j.215.2 | 16 | 88.35 | even | 10 | |||
484.2.g.j.475.1 | 16 | 88.59 | odd | 10 | |||
484.2.g.j.475.2 | 16 | 88.37 | even | 10 | |||
704.2.u.c.63.2 | 16 | 44.19 | even | 10 | inner | ||
704.2.u.c.63.3 | 16 | 11.8 | odd | 10 | inner | ||
704.2.u.c.447.2 | 16 | 1.1 | even | 1 | trivial | ||
704.2.u.c.447.3 | 16 | 4.3 | odd | 2 | inner |