Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(137,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("552.137");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.m (of order \(2\), degree \(1\), 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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} - 2x^{12} + 8x^{10} - 8x^{8} + 32x^{6} - 32x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.8 | ||
Root | \(-0.883519 + 1.10426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.137 |
Dual form | 552.2.m.b.137.6 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.356193 | + | 1.69503i | −0.205648 | + | 0.978626i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.441484 | 0.197438 | 0.0987189 | − | 0.995115i | \(-0.468526\pi\) | ||||
0.0987189 | + | 0.995115i | \(0.468526\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.97556i | 1.50262i | 0.659949 | + | 0.751311i | \(0.270578\pi\) | ||||
−0.659949 | + | 0.751311i | \(0.729422\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.74625 | − | 1.20752i | −0.915418 | − | 0.402505i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.64330 | −1.40001 | −0.700004 | − | 0.714139i | \(-0.746818\pi\) | ||||
−0.700004 | + | 0.714139i | \(0.746818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.73736 | 1.03656 | 0.518278 | − | 0.855212i | \(-0.326573\pi\) | ||||
0.518278 | + | 0.855212i | \(0.326573\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.157254 | + | 0.748329i | −0.0406027 | + | 0.193218i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.441484 | −0.107076 | −0.0535378 | − | 0.998566i | \(-0.517050\pi\) | ||||
−0.0535378 | + | 0.998566i | \(0.517050\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.47890i | 0.568700i | 0.958721 | + | 0.284350i | \(0.0917777\pi\) | ||||
−0.958721 | + | 0.284350i | \(0.908222\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.73870 | − | 1.41607i | −1.47050 | − | 0.309011i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.64330 | − | 1.19990i | −0.968195 | − | 0.250196i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80509 | −0.961018 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.02497 | − | 4.22487i | 0.582156 | − | 0.813077i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.41503i | 1.19124i | 0.803266 | + | 0.595621i | \(0.203094\pi\) | ||||
−0.803266 | + | 0.595621i | \(0.796906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.71239 | 0.846370 | 0.423185 | − | 0.906043i | \(-0.360912\pi\) | ||||
0.423185 | + | 0.906043i | \(0.360912\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.65391 | − | 7.87053i | 0.287909 | − | 1.37008i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.75515i | 0.296674i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.33743i | − | 1.20627i | −0.797640 | − | 0.603133i | \(-0.793919\pi\) | ||
0.797640 | − | 0.603133i | \(-0.206081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.33122 | + | 6.33493i | −0.213166 | + | 1.01440i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.365088i | − | 0.0570172i | −0.999594 | − | 0.0285086i | \(-0.990924\pi\) | ||
0.999594 | − | 0.0285086i | \(-0.00907579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.69067i | 1.17282i | 0.810016 | + | 0.586408i | \(0.199458\pi\) | ||||
−0.810016 | + | 0.586408i | \(0.800542\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.21243 | − | 0.533099i | −0.180738 | − | 0.0794697i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.36509i | 0.344984i | 0.985011 | + | 0.172492i | \(0.0551818\pi\) | ||||
−0.985011 | + | 0.172492i | \(0.944818\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.80509 | −1.25787 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.157254 | − | 0.748329i | 0.0220199 | − | 0.104787i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.70712 | −1.19601 | −0.598007 | − | 0.801491i | \(-0.704041\pi\) | ||||
−0.598007 | + | 0.801491i | \(0.704041\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.04994 | −0.276414 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.20182 | − | 0.882968i | −0.556544 | − | 0.116952i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.20489i | 0.287053i | 0.989647 | + | 0.143526i | \(0.0458441\pi\) | ||||
−0.989647 | + | 0.143526i | \(0.954156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1629i | 1.68533i | 0.538434 | + | 0.842667i | \(0.319016\pi\) | ||||
−0.538434 | + | 0.842667i | \(0.680984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.80055 | − | 10.9179i | 0.604813 | − | 1.37553i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.64998 | 0.204655 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.93337i | 1.09138i | 0.837986 | + | 0.545692i | \(0.183733\pi\) | ||||
−0.837986 | + | 0.545692i | \(0.816267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.68778 | − | 7.44314i | 0.443956 | − | 0.896048i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.22012i | − | 0.975549i | −0.872970 | − | 0.487775i | \(-0.837809\pi\) | ||
0.872970 | − | 0.487775i | \(-0.162191\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9173 | 1.27777 | 0.638885 | − | 0.769302i | \(-0.279396\pi\) | ||||
0.638885 | + | 0.769302i | \(0.279396\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.71154 | − | 8.14477i | 0.197632 | − | 0.940478i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 18.4597i | − | 2.10368i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.02639i | − | 0.227987i | −0.993481 | − | 0.113994i | \(-0.963636\pi\) | ||
0.993481 | − | 0.113994i | \(-0.0363643\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.08381 | + | 6.63229i | 0.675979 | + | 0.736921i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2589 | 1.23583 | 0.617915 | − | 0.786245i | \(-0.287978\pi\) | ||||
0.617915 | + | 0.786245i | \(0.287978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.194908 | −0.0211408 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.8737 | − | 2.28499i | −1.16578 | − | 0.244977i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.3647 | 1.84065 | 0.920327 | − | 0.391149i | \(-0.127922\pi\) | ||||
0.920327 | + | 0.391149i | \(0.127922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.8581i | 1.55755i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.67852 | + | 7.98764i | −0.174054 | + | 0.828279i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.09440i | 0.112283i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.82545i | − | 0.591485i | −0.955268 | − | 0.295742i | \(-0.904433\pi\) | ||
0.955268 | − | 0.295742i | \(-0.0955670\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.7517 | + | 5.60686i | 1.28159 | + | 0.563511i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.04994i | 0.601992i | 0.953625 | + | 0.300996i | \(0.0973191\pi\) | ||||
−0.953625 | + | 0.300996i | \(0.902681\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.3792i | − | 1.21976i | −0.792494 | − | 0.609879i | \(-0.791218\pi\) | ||
0.792494 | − | 0.609879i | \(-0.208782\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.97503 | − | 0.625172i | −0.290333 | − | 0.0610105i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.32879 | 0.418480 | 0.209240 | − | 0.977864i | \(-0.432901\pi\) | ||||
0.209240 | + | 0.977864i | \(0.432901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.17625i | 0.687360i | 0.939087 | + | 0.343680i | \(0.111674\pi\) | ||||
−0.939087 | + | 0.343680i | \(0.888326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.4372 | + | 2.61354i | 1.18048 | + | 0.248067i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.39929 | 0.507923 | 0.253961 | − | 0.967214i | \(-0.418266\pi\) | ||||
0.253961 | + | 0.967214i | \(0.418266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.04994 | − | 0.529737i | −0.191158 | − | 0.0493982i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.2637 | − | 4.51292i | −0.948882 | − | 0.417220i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.75515i | − | 0.160894i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5602 | 0.960022 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.618835 | + | 0.130042i | 0.0557985 | + | 0.0117255i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.32879 | −0.387179 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7473 | 1.21988 | 0.609940 | − | 0.792448i | \(-0.291194\pi\) | ||||
0.609940 | + | 0.792448i | \(0.291194\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.0359 | − | 2.73936i | −1.14775 | − | 0.241187i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7998i | 1.72992i | 0.501840 | + | 0.864960i | \(0.332656\pi\) | ||||
−0.501840 | + | 0.864960i | \(0.667344\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.85504 | −0.854540 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.33548 | − | 1.86521i | 0.114940 | − | 0.160532i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.1529 | 1.03830 | 0.519148 | − | 0.854684i | \(-0.326249\pi\) | ||||
0.519148 | + | 0.854684i | \(0.326249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.8828 | 1.85608 | 0.928038 | − | 0.372486i | \(-0.121495\pi\) | ||||
0.928038 | + | 0.372486i | \(0.121495\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00889 | − | 0.842428i | −0.337610 | − | 0.0709452i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.3537 | −1.45119 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.83214i | 0.235196i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.13631 | − | 14.9249i | 0.258679 | − | 1.23098i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.1107 | 1.40177 | 0.700884 | − | 0.713276i | \(-0.252789\pi\) | ||||
0.700884 | + | 0.713276i | \(0.252789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2726 | −1.48701 | −0.743503 | − | 0.668733i | \(-0.766837\pi\) | ||||
−0.743503 | + | 0.668733i | \(0.766837\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.21243 | + | 0.533099i | 0.0980189 | + | 0.0430985i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.08044 | 0.167105 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.1696i | − | 0.811620i | −0.913957 | − | 0.405810i | \(-0.866989\pi\) | ||
0.913957 | − | 0.405810i | \(-0.133011\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.10141 | − | 14.7588i | 0.245958 | − | 1.17045i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.77028 | − | 18.4597i | 0.375951 | − | 1.45483i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4730 | −1.05529 | −0.527644 | − | 0.849465i | \(-0.676925\pi\) | ||||
−0.527644 | + | 0.849465i | \(0.676925\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.730176 | − | 3.47472i | 0.0568441 | − | 0.270506i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.60020i | 0.433356i | 0.976243 | + | 0.216678i | \(0.0695222\pi\) | ||||
−0.976243 | + | 0.216678i | \(0.930478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.967846 | 0.0744497 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.99332 | − | 6.80770i | 0.228905 | − | 0.520598i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.56024i | 0.118623i | 0.998240 | + | 0.0593114i | \(0.0188905\pi\) | ||||
−0.998240 | + | 0.0593114i | \(0.981110\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 19.1029i | − | 1.44405i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.73736 | − | 0.785367i | −0.280917 | − | 0.0590318i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 15.1952i | − | 1.13574i | −0.823119 | − | 0.567869i | \(-0.807768\pi\) | ||
0.823119 | − | 0.567869i | \(-0.192232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3307i | 0.767879i | 0.923358 | + | 0.383939i | \(0.125433\pi\) | ||||
−0.923358 | + | 0.383939i | \(0.874567\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.3115 | − | 4.68853i | −1.64931 | − | 0.346586i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.23936i | − | 0.238163i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.04994 | 0.149907 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.7962 | + | 12.0260i | 1.22175 | + | 0.874760i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.08044 | 0.150536 | 0.0752678 | − | 0.997163i | \(-0.476019\pi\) | ||||
0.0752678 | + | 0.997163i | \(0.476019\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.77294 | −0.271582 | −0.135791 | − | 0.990738i | \(-0.543358\pi\) | ||||
−0.135791 | + | 0.990738i | \(0.543358\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.587713 | + | 2.79677i | −0.0420870 | + | 0.200281i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.8942i | 1.63115i | 0.578653 | + | 0.815574i | \(0.303578\pi\) | ||||
−0.578653 | + | 0.815574i | \(0.696422\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.1607i | − | 0.720276i | −0.932899 | − | 0.360138i | \(-0.882730\pi\) | ||
0.932899 | − | 0.360138i | \(-0.117270\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.1423 | − | 3.18200i | −1.06806 | − | 0.224441i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −25.5034 | −1.78998 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 0.161181i | − | 0.0112573i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.3028 | + | 8.90209i | 0.785597 | + | 0.618738i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 11.5103i | − | 0.796184i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.3093 | −1.19162 | −0.595810 | − | 0.803126i | \(-0.703169\pi\) | ||||
−0.595810 | + | 0.803126i | \(0.703169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.9334 | + | 2.92795i | 0.954698 | + | 0.200620i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.39531i | 0.231558i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.7344i | 1.27177i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.88866 | + | 18.5051i | −0.262771 | + | 1.25046i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.64998 | −0.110990 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.0705 | −1.14313 | −0.571564 | − | 0.820558i | \(-0.693663\pi\) | ||||
−0.571564 | + | 0.820558i | \(0.693663\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.1960 | + | 5.80222i | 0.879733 | + | 0.386815i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.9824 | −1.65814 | −0.829071 | − | 0.559143i | \(-0.811130\pi\) | ||||
−0.829071 | + | 0.559143i | \(0.811130\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.9355i | − | 0.788720i | −0.918956 | − | 0.394360i | \(-0.870966\pi\) | ||
0.918956 | − | 0.394360i | \(-0.129034\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31.2898 | + | 6.57523i | 2.05872 | + | 0.432618i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.6549i | 1.02559i | 0.858513 | + | 0.512793i | \(0.171389\pi\) | ||||
−0.858513 | + | 0.512793i | \(0.828611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.04415i | 0.0681128i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.43480 | + | 0.721788i | 0.223114 | + | 0.0468852i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.7804i | − | 0.891378i | −0.895188 | − | 0.445689i | \(-0.852959\pi\) | ||
0.895188 | − | 0.445689i | \(-0.147041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.06620i | − | 0.0686799i | −0.999410 | − | 0.0343399i | \(-0.989067\pi\) | ||
0.999410 | − | 0.0343399i | \(-0.0109329\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.4089 | + | 7.94987i | −0.860184 | + | 0.509984i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.88731 | −0.248351 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.26455i | 0.589489i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.01036 | + | 19.0843i | −0.254146 | + | 1.20942i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.49301 | 0.599193 | 0.299597 | − | 0.954066i | \(-0.403148\pi\) | ||||
0.299597 | + | 0.954066i | \(0.403148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.5602 | + | 5.57150i | 1.35548 | + | 0.350277i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0694250 | − | 0.330375i | 0.00434756 | − | 0.0206889i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.51554i | 0.344050i | 0.985093 | + | 0.172025i | \(0.0550310\pi\) | ||||
−0.985093 | + | 0.172025i | \(0.944969\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.1704 | 1.81256 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.74625 | − | 17.6173i | 0.479481 | − | 1.09048i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.5313 | −1.01936 | −0.509681 | − | 0.860364i | \(-0.670236\pi\) | ||||
−0.509681 | + | 0.860364i | \(0.670236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.84405 | −0.236138 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.18519 | + | 29.4337i | −0.378527 | + | 1.80131i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.11474i | 0.189909i | 0.995482 | + | 0.0949547i | \(0.0302706\pi\) | ||||
−0.995482 | + | 0.0949547i | \(0.969729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.1205 | −0.675521 | −0.337760 | − | 0.941232i | \(-0.609669\pi\) | ||||
−0.337760 | + | 0.941232i | \(0.609669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.1849 | − | 5.29235i | −1.52426 | − | 0.320308i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.3115 | 1.34543 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.1676 | 0.971418 | 0.485709 | − | 0.874121i | \(-0.338561\pi\) | ||||
0.485709 | + | 0.874121i | \(0.338561\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.9414 | − | 5.69028i | −0.774782 | − | 0.340668i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.695438 | 0.0414864 | 0.0207432 | − | 0.999785i | \(-0.493397\pi\) | ||||
0.0207432 | + | 0.999785i | \(0.493397\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 24.3147i | − | 1.44536i | −0.691183 | − | 0.722679i | \(-0.742910\pi\) | ||
0.691183 | − | 0.722679i | \(-0.257090\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.85504 | − | 0.389817i | −0.109883 | − | 0.0230907i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.45143 | 0.0856752 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8051 | −0.988535 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.87431 | + | 2.07499i | 0.578843 | + | 0.121638i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.5479 | −0.849897 | −0.424948 | − | 0.905218i | \(-0.639708\pi\) | ||||
−0.424948 | + | 0.905218i | \(0.639708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.973425i | 0.0566750i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.0459 | + | 19.6174i | −0.815023 | + | 1.13831i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.3537 | − | 4.48446i | −1.00359 | − | 0.259343i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.5747 | −1.76230 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.2548 | − | 2.15495i | −0.589125 | − | 0.123799i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.81121i | 0.332749i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.9831 | + | 4.40938i | 1.19369 | + | 0.250841i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.9253i | 0.903042i | 0.892260 | + | 0.451521i | \(0.149118\pi\) | ||||
−0.892260 | + | 0.451521i | \(0.850882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.8112i | 1.62850i | 0.580511 | + | 0.814252i | \(0.302853\pi\) | ||||
−0.580511 | + | 0.814252i | \(0.697147\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.11937 | − | 4.82008i | 0.119413 | − | 0.271581i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 29.6601i | − | 1.66588i | −0.553364 | − | 0.832939i | \(-0.686656\pi\) | ||
0.553364 | − | 0.832939i | \(-0.313344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 29.7869i | − | 1.66775i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.54189 | + | 7.33743i | −0.0860597 | + | 0.409536i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.09440i | − | 0.0608939i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.9583 | −0.996150 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.1640 | − | 2.55613i | −0.672669 | − | 0.141354i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.40255 | −0.518380 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8479 | 0.706182 | 0.353091 | − | 0.935589i | \(-0.385131\pi\) | ||||
0.353091 | + | 0.935589i | \(0.385131\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.86007 | + | 20.1505i | −0.485529 | + | 1.10424i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.94394i | 0.215481i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.5732i | − | 1.01175i | −0.862608 | − | 0.505873i | \(-0.831170\pi\) | ||
0.862608 | − | 0.505873i | \(-0.168830\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.92319 | + | 9.15196i | −0.104453 | + | 0.497066i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.8810 | −1.18492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.17625i | − | 0.387481i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.62810 | − | 3.28603i | 0.0876537 | − | 0.176914i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.0544i | 1.13026i | 0.825001 | + | 0.565131i | \(0.191174\pi\) | ||||
−0.825001 | + | 0.565131i | \(0.808826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.7074 | 0.947854 | 0.473927 | − | 0.880564i | \(-0.342836\pi\) | ||||
0.473927 | + | 0.880564i | \(0.342836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3054 | − | 15.7899i | 0.603438 | − | 0.842800i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.6654i | 0.620885i | 0.950592 | + | 0.310443i | \(0.100477\pi\) | ||||
−0.950592 | + | 0.310443i | \(0.899523\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.62905i | − | 0.192610i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.97503 | + | 0.625172i | 0.157455 | + | 0.0330876i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.67095 | 0.140968 | 0.0704838 | − | 0.997513i | \(-0.477546\pi\) | ||||
0.0704838 | + | 0.997513i | \(0.477546\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.8550 | 0.676581 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.76148 | + | 17.8999i | −0.197427 | + | 0.939502i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.81981 | 0.252280 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.0541i | − | 1.41221i | −0.708107 | − | 0.706105i | \(-0.750451\pi\) | ||
0.708107 | − | 0.706105i | \(-0.249549\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.440849 | + | 1.00262i | −0.0229497 | + | 0.0521945i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 34.6157i | − | 1.79716i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.7145i | − | 0.865444i | −0.901528 | − | 0.432722i | \(-0.857553\pi\) | ||
0.901528 | − | 0.432722i | \(-0.142447\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.54189 | − | 7.33743i | 0.0796227 | − | 0.378903i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.9753i | 1.23479i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.2639i | 1.34908i | 0.738236 | + | 0.674542i | \(0.235659\pi\) | ||||
−0.738236 | + | 0.674542i | \(0.764341\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.89671 | + | 23.3022i | −0.250866 | + | 1.19381i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.0525 | −0.564758 | −0.282379 | − | 0.959303i | \(-0.591124\pi\) | ||||
−0.282379 | + | 0.959303i | \(0.591124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 8.14968i | − | 0.415346i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.28660 | − | 21.1205i | 0.472064 | − | 1.07362i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.1728 | 0.718591 | 0.359296 | − | 0.933224i | \(-0.383017\pi\) | ||||
0.359296 | + | 0.933224i | \(0.383017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.04994 | + | 0.529737i | 0.103670 | + | 0.0267900i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.5613 | − | 7.05257i | −1.69295 | − | 0.355755i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 0.894621i | − | 0.0450133i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.4775 | 1.42925 | 0.714623 | − | 0.699510i | \(-0.246598\pi\) | ||||
0.714623 | + | 0.699510i | \(0.246598\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.51030 | − | 16.7046i | 0.175735 | − | 0.836275i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.05713 | −0.352416 | −0.176208 | − | 0.984353i | \(-0.556383\pi\) | ||||
−0.176208 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.6119 | 0.877310 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.68591 | + | 2.92805i | 0.133464 | + | 0.145496i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.0699i | 1.68878i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.21270 | −0.307198 | −0.153599 | − | 0.988133i | \(-0.549086\pi\) | ||||
−0.153599 | + | 0.988133i | \(0.549086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.32879 | + | 20.5996i | −0.213524 | + | 1.01610i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.76568 | −0.431331 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.97065 | 0.243999 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.79451 | + | 37.0920i | −0.381699 | + | 1.81640i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.9126 | 1.55903 | 0.779516 | − | 0.626382i | \(-0.215465\pi\) | ||||
0.779516 | + | 0.626382i | \(0.215465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.7610i | − | 0.865616i | −0.901486 | − | 0.432808i | \(-0.857523\pi\) | ||
0.901486 | − | 0.432808i | \(-0.142477\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.85588 | − | 6.49513i | 0.138858 | − | 0.315804i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.12137 | 0.102902 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −52.3299 | −2.53242 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.18126 | − | 29.4150i | 0.298434 | − | 1.42017i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1363 | 0.680922 | 0.340461 | − | 0.940259i | \(-0.389417\pi\) | ||||
0.340461 | + | 0.940259i | \(0.389417\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11.8427i | − | 0.569125i | −0.958657 | − | 0.284563i | \(-0.908152\pi\) | ||
0.958657 | − | 0.284563i | \(-0.0918484\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.80055 | − | 1.00879i | −0.230169 | − | 0.0483676i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.97444 | − | 11.5103i | 0.142287 | − | 0.550612i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4880 | −0.500566 | −0.250283 | − | 0.968173i | \(-0.580524\pi\) | ||||
−0.250283 | + | 0.968173i | \(0.580524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 24.1810 | + | 10.6323i | 1.15148 | + | 0.506299i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 25.5294i | − | 1.21294i | −0.795107 | − | 0.606469i | \(-0.792585\pi\) | ||
0.795107 | − | 0.606469i | \(-0.207415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.66624 | 0.363415 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.09473 | + | 29.0032i | −0.288271 | + | 1.37181i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.6308i | − | 1.44556i | −0.691080 | − | 0.722778i | \(-0.742865\pi\) | ||
0.691080 | − | 0.722778i | \(-0.257135\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.69521i | 0.0798245i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.50858 | − | 30.9726i | 0.305800 | − | 1.45522i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.55962i | 0.307520i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.7277i | − | 1.01638i | −0.861245 | − | 0.508189i | \(-0.830315\pi\) | ||
0.861245 | − | 0.508189i | \(-0.169685\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.33548 | + | 1.86521i | −0.0623347 | + | 0.0870608i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.34561i | 0.295544i | 0.989021 | + | 0.147772i | \(0.0472102\pi\) | ||||
−0.989021 | + | 0.147772i | \(0.952790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.2593 | −1.26685 | −0.633424 | − | 0.773805i | \(-0.718351\pi\) | ||||
−0.633424 | + | 0.773805i | \(0.718351\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.741040 | + | 3.52642i | −0.0343649 | + | 0.163534i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.9444 | −0.506448 | −0.253224 | − | 0.967408i | \(-0.581491\pi\) | ||||
−0.253224 | + | 0.967408i | \(0.581491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.5152 | −1.63994 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.2377 | + | 3.62233i | 0.794272 | + | 0.166908i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 35.7101i | − | 1.64195i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 11.9114i | − | 0.546531i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.9119 | + | 10.5140i | 1.09485 | + | 0.481402i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5877 | 0.712222 | 0.356111 | − | 0.934444i | \(-0.384102\pi\) | ||||
0.356111 | + | 0.934444i | \(0.384102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 27.4226i | − | 1.25036i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.5907 | + | 14.6610i | 1.34642 | + | 0.667098i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.57184i | − | 0.116781i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.0333 | 1.40625 | 0.703126 | − | 0.711066i | \(-0.251787\pi\) | ||||
0.703126 | + | 0.711066i | \(0.251787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.79900 | − | 22.8372i | 0.217018 | − | 1.03273i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.77376i | − | 0.0800488i | −0.999199 | − | 0.0400244i | \(-0.987256\pi\) | ||
0.999199 | − | 0.0400244i | \(-0.0127436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.83214i | − | 0.127553i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.62966 | + | 2.47534i | 0.253035 | + | 0.111258i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.6796 | 1.46588 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3376 | −0.776136 | −0.388068 | − | 0.921631i | \(-0.626857\pi\) | ||||
−0.388068 | + | 0.921631i | \(0.626857\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.49251 | − | 1.99475i | −0.424094 | − | 0.0891190i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.6363 | 1.72271 | 0.861355 | − | 0.508004i | \(-0.169617\pi\) | ||||
0.861355 | + | 0.508004i | \(0.169617\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.67095i | 0.118856i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.344740 | + | 1.64053i | −0.0153104 | + | 0.0728584i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8443i | 0.569313i | 0.958630 | + | 0.284657i | \(0.0918796\pi\) | ||||
−0.958630 | + | 0.284657i | \(0.908120\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.4023i | 1.92001i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.4731 | + | 7.49861i | 0.462397 | + | 0.331072i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5.46522i | − | 0.240826i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.9818i | − | 0.482980i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.64465 | − | 0.555747i | −0.116087 | − | 0.0243946i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.7158 | −0.644711 | −0.322355 | − | 0.946619i | \(-0.604475\pi\) | ||||
−0.322355 | + | 0.946619i | \(0.604475\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5910i | 0.769199i | 0.923084 | + | 0.384599i | \(0.125660\pi\) | ||||
−0.923084 | + | 0.384599i | \(0.874340\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.3801 | + | 6.80433i | 1.41318 | + | 0.296966i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.08044 | −0.0906256 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.1205 | + | 11.1430i | 0.874803 | + | 0.484478i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.66244 | − | 6.05519i | 0.115540 | − | 0.262773i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.36446i | − | 0.0591015i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.91109 | 0.0826238 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.7562 | + | 5.41241i | 1.11146 | + | 0.233563i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 40.8847 | 1.76103 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.3120 | −1.00226 | −0.501130 | − | 0.865372i | \(-0.667082\pi\) | ||||
−0.501130 | + | 0.865372i | \(0.667082\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.5109 | − | 3.67974i | −0.751466 | − | 0.157913i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.16820i | 0.135711i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.84785 | 0.207279 | 0.103640 | − | 0.994615i | \(-0.466951\pi\) | ||||
0.103640 | + | 0.994615i | \(0.466951\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.8944 | − | 36.1486i | 0.678356 | − | 1.54279i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.9022 | −0.677459 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.05606 | 0.342578 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.49081 | + | 1.15384i | 0.233072 | + | 0.0489777i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.0971 | −1.27526 | −0.637628 | − | 0.770344i | \(-0.720084\pi\) | ||||
−0.637628 | + | 0.770344i | \(0.720084\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.7428i | 1.21569i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.730176 | + | 3.47472i | −0.0308280 | + | 0.146703i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.4785 | −0.525905 | −0.262952 | − | 0.964809i | \(-0.584696\pi\) | ||||
−0.262952 | + | 0.964809i | \(0.584696\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.38370 | 0.100283 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.3671 | + | 24.1866i | −1.10731 | + | 1.01574i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.8881 | 1.42066 | 0.710332 | − | 0.703867i | \(-0.248545\pi\) | ||||
0.710332 | + | 0.703867i | \(0.248545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10.4454i | − | 0.437124i | −0.975823 | − | 0.218562i | \(-0.929863\pi\) | ||
0.975823 | − | 0.218562i | \(-0.0701367\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.741040 | + | 3.52642i | −0.0309574 | + | 0.147318i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.3115 | + | 5.76563i | 0.930453 | + | 0.240443i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.8428 | −1.57542 | −0.787709 | − | 0.616047i | \(-0.788733\pi\) | ||||
−0.787709 | + | 0.616047i | \(0.788733\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.34389 | − | 6.39524i | 0.0558503 | − | 0.265777i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.7606i | 1.85698i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.4298 | 1.67443 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.53128 | − | 1.99238i | −0.187345 | − | 0.0823749i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.0502i | 0.538639i | 0.963051 | + | 0.269319i | \(0.0867987\pi\) | ||||
−0.963051 | + | 0.269319i | \(0.913201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6816i | 0.481330i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −38.8064 | − | 8.15477i | −1.59628 | − | 0.335442i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.35984i | 0.261167i | 0.991437 | + | 0.130584i | \(0.0416851\pi\) | ||||
−0.991437 | + | 0.130584i | \(0.958315\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.774870i | − | 0.0317666i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.2228 | + | 3.61919i | 0.704881 | + | 0.148124i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 47.3193i | − | 1.93341i | −0.255889 | − | 0.966706i | \(-0.582368\pi\) | ||
0.255889 | − | 0.966706i | \(-0.417632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.5835 | −0.758038 | −0.379019 | − | 0.925389i | \(-0.623738\pi\) | ||||
−0.379019 | + | 0.925389i | \(0.623738\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.7872 | − | 24.5333i | 0.439288 | − | 0.999073i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.66218 | 0.189545 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.91109 | 0.402279 | 0.201139 | − | 0.979563i | \(-0.435536\pi\) | ||||
0.201139 | + | 0.979563i | \(0.435536\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.08412 | − | 43.2290i | 0.368107 | − | 1.75173i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.83918i | 0.357595i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.3480i | 0.660291i | 0.943930 | + | 0.330145i | \(0.107098\pi\) | ||||
−0.943930 | + | 0.330145i | \(0.892902\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.273206 | + | 0.0574114i | 0.0110167 | + | 0.00231505i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.5535 | 1.71314 | 0.856571 | − | 0.516030i | \(-0.172591\pi\) | ||||
0.856571 | + | 0.516030i | \(0.172591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.2505i | 1.29626i | 0.761531 | + | 0.648129i | \(0.224448\pi\) | ||||
−0.761531 | + | 0.648129i | \(0.775552\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.1153 | + | 15.9877i | −0.767070 | + | 0.641564i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 69.0344i | 2.76581i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.1144 | 0.884575 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.5103 | + | 4.09989i | 0.779166 | + | 0.163734i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.23936i | 0.129162i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.3350i | 0.451241i | 0.974215 | + | 0.225621i | \(0.0724409\pi\) | ||||
−0.974215 | + | 0.225621i | \(0.927559\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.16544 | − | 29.3397i | 0.245054 | − | 1.16615i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.06923 | 0.240850 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.9078 | −1.30385 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.92593 | + | 22.5745i | −0.392664 | + | 0.893035i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.47330 | −0.137187 | −0.0685936 | − | 0.997645i | \(-0.521851\pi\) | ||||
−0.0685936 | + | 0.997645i | \(0.521851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.6309i | − | 0.419242i | −0.977783 | − | 0.209621i | \(-0.932777\pi\) | ||
0.977783 | − | 0.209621i | \(-0.0672230\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.75515 | − | 1.20939i | −0.226609 | − | 0.0476195i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.0447i | − | 1.81020i | −0.425195 | − | 0.905102i | \(-0.639794\pi\) | ||
0.425195 | − | 0.905102i | \(-0.360206\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10.2380i | − | 0.401876i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.7553 | − | 6.67306i | −1.24459 | − | 0.261538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.4856i | 0.605997i | 0.952991 | + | 0.302999i | \(0.0979877\pi\) | ||||
−0.952991 | + | 0.302999i | \(0.902012\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.74132i | 0.341552i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.9816 | − | 13.1828i | −1.16969 | − | 0.514310i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.7930 | 0.498344 | 0.249172 | − | 0.968459i | \(-0.419842\pi\) | ||||
0.249172 | + | 0.968459i | \(0.419842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 45.8724i | − | 1.78423i | −0.451809 | − | 0.892115i | \(-0.649221\pi\) | ||
0.451809 | − | 0.892115i | \(-0.350779\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.587713 | − | 2.79677i | 0.0228249 | − | 0.108618i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.35084 | −0.168718 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.69740 | − | 29.7869i | 0.298044 | − | 1.15335i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.08041 | − | 28.9351i | 0.235082 | − | 1.11869i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 61.1192i | − | 2.35948i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4371 | 0.479414 | 0.239707 | − | 0.970845i | \(-0.422949\pi\) | ||||
0.239707 | + | 0.970845i | \(0.422949\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.5353 | + | 20.3009i | −0.559463 | + | 0.781382i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.3329 | −1.47325 | −0.736626 | − | 0.676301i | \(-0.763582\pi\) | ||||
−0.736626 | + | 0.676301i | \(0.763582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.1594 | 0.888778 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.89857 | − | 42.3460i | 0.340994 | − | 1.62270i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.42004i | 0.207392i | 0.994609 | + | 0.103696i | \(0.0330669\pi\) | ||||
−0.994609 | + | 0.103696i | \(0.966933\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.36533 | 0.204999 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.2310 | + | 4.25134i | 0.771862 | + | 0.162199i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.5416 | −1.23974 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.3093 | 1.57148 | 0.785739 | − | 0.618558i | \(-0.212283\pi\) | ||||
0.785739 | + | 0.618558i | \(0.212283\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.2904 | + | 50.6951i | −0.846743 | + | 1.92575i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.66091 | 0.366459 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.161181i | 0.00610515i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.5355 | − | 5.57616i | −1.00366 | − | 0.210910i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.1815 | −1.66871 | −0.834356 | − | 0.551226i | \(-0.814160\pi\) | ||||
−0.834356 | + | 0.551226i | \(0.814160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.1888 | 0.686003 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.76986 | − | 0.371919i | −0.0666569 | − | 0.0140073i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.0519 | −0.904566 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9000i | 0.634694i | 0.948309 | + | 0.317347i | \(0.102792\pi\) | ||||
−0.948309 | + | 0.317347i | \(0.897208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.44690 | + | 5.56499i | −0.0917661 | + | 0.208704i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.8810 | − | 5.65439i | −0.819451 | − | 0.211759i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.66137 | −0.286519 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.3581 | + | 4.90847i | 0.872325 | + | 0.183310i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 3.80409i | − | 0.141869i | −0.997481 | − | 0.0709344i | \(-0.977402\pi\) | ||
0.997481 | − | 0.0709344i | \(-0.0225981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.2143 | 1.83283 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.80724 | + | 0.379773i | 0.0672119 | + | 0.0141239i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 30.8248i | − | 1.14480i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.87165i | 0.217767i | 0.994055 | + | 0.108884i | \(0.0347276\pi\) | ||||
−0.994055 | + | 0.108884i | \(0.965272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.69909 | − | 25.5602i | −0.322188 | − | 0.946676i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.39531i | − | 0.125580i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.6101i | 1.31529i | 0.753329 | + | 0.657644i | \(0.228447\pi\) | ||||
−0.753329 | + | 0.657644i | \(0.771553\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.38463 | − | 6.58911i | 0.0510729 | − | 0.243043i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 41.4803i | − | 1.52795i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.4574 | −1.67218 | −0.836089 | − | 0.548594i | \(-0.815163\pi\) | ||||
−0.836089 | + | 0.548594i | \(0.815163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.7037 | − | 3.29997i | −0.576890 | − | 0.121227i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.83517 | −0.287445 | −0.143722 | − | 0.989618i | \(-0.545907\pi\) | ||||
−0.143722 | + | 0.989618i | \(0.545907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.55413 | 0.276762 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.9199 | − | 13.5954i | −1.13130 | − | 0.497428i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.2094i | 0.628817i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.3284i | 0.522849i | 0.965224 | + | 0.261425i | \(0.0841923\pi\) | ||||
−0.965224 | + | 0.261425i | \(0.915808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.38134 | + | 16.0909i | −0.123223 | + | 0.586386i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.06708 | −0.293591 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.2291i | − | 0.517165i | −0.965989 | − | 0.258582i | \(-0.916745\pi\) | ||
0.965989 | − | 0.258582i | \(-0.0832554\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.1235 | + | 34.5607i | −0.621542 | + | 1.25447i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.2346i | 1.27725i | 0.769517 | + | 0.638627i | \(0.220497\pi\) | ||||
−0.769517 | + | 0.638627i | \(0.779503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.5296 | −1.03284 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.535268 | + | 0.235355i | 0.0193526 | + | 0.00850927i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.24047i | 0.297546i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.5483i | − | 1.17372i | −0.809687 | − | 0.586861i | \(-0.800363\pi\) | ||
0.809687 | − | 0.586861i | \(-0.199637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.34901 | − | 1.96460i | −0.336696 | − | 0.0707533i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.9373 | −1.76015 | −0.880076 | − | 0.474833i | \(-0.842509\pi\) | ||||
−0.880076 | + | 0.474833i | \(0.842509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.6434 | −0.813377 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.3903 | + | 49.4447i | −0.372750 | + | 1.77382i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.905018 | 0.0324256 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.1685i | 1.36578i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.1027 | + | 19.4053i | 0.968571 | + | 0.693489i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.48970i | − | 0.160244i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.40381i | − | 0.192625i | −0.995351 | − | 0.0963126i | \(-0.969295\pi\) | ||
0.995351 | − | 0.0963126i | \(-0.0307048\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.88832 | − | 28.0210i | 0.209630 | − | 0.997573i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.4652i | 0.763215i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.1944i | 1.74694i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.36923 | − | 6.51579i | 0.0485614 | − | 0.231091i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.48235 | 0.123351 | 0.0616755 | − | 0.998096i | \(-0.480356\pi\) | ||||
0.0616755 | + | 0.998096i | \(0.480356\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.04415i | − | 0.0369393i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.6879 | − | 20.9682i | −1.68497 | − | 0.740873i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −50.6922 | −1.78889 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.10600 | − | 8.14968i | 0.0742268 | − | 0.287238i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.27959 | − | 1.10945i | −0.185850 | − | 0.0390545i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.0905i | 1.72593i | 0.505264 | + | 0.862965i | \(0.331395\pi\) | ||||
−0.505264 | + | 0.862965i | \(0.668605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.88343 | 0.171481 | 0.0857403 | − | 0.996318i | \(-0.472674\pi\) | ||||
0.0857403 | + | 0.996318i | \(0.472674\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.96104 | − | 18.8495i | 0.138920 | − | 0.661082i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.94813 | −0.208354 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.0644 | −0.666980 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.9414 | − | 40.8041i | 0.626923 | − | 1.42581i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.82958i | 0.238354i | 0.992873 | + | 0.119177i | \(0.0380256\pi\) | ||||
−0.992873 | + | 0.119177i | \(0.961974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.6674 | −0.894710 | −0.447355 | − | 0.894356i | \(-0.647634\pi\) | ||||
−0.447355 | + | 0.894356i | \(0.647634\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.94720 | + | 37.8186i | −0.276686 | + | 1.31668i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.6227 | 1.79510 | 0.897549 | − | 0.440915i | \(-0.145346\pi\) | ||||
0.897549 | + | 0.440915i | \(0.145346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.4043 | 0.951790 | 0.475895 | − | 0.879502i | \(-0.342124\pi\) | ||||
0.475895 | + | 0.879502i | \(0.342124\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.75880 | + | 27.4046i | −0.199770 | + | 0.950655i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.88731 | 0.134687 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.47240i | 0.0855609i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.2548 | − | 19.9092i | 0.492719 | − | 0.688164i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.8006 | 1.51216 | 0.756082 | − | 0.654477i | \(-0.227111\pi\) | ||||
0.756082 | + | 0.654477i | \(0.227111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.1526 | −0.419056 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.247710 | + | 1.17879i | −0.00853159 | + | 0.0405996i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.427289 | 0.0146992 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.9829i | 1.44255i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.2141 | + | 8.66073i | 1.41447 | + | 0.297235i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.80419 | + | 34.0699i | −0.301804 | + | 1.16790i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.9610 | 0.614974 | 0.307487 | − | 0.951552i | \(-0.400512\pi\) | ||||
0.307487 | + | 0.951552i | \(0.400512\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.32150 | − | 3.00549i | 0.0451944 | − | 0.102786i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 10.2335i | − | 0.349569i | −0.984607 | − | 0.174785i | \(-0.944077\pi\) | ||
0.984607 | − | 0.174785i | \(-0.0559229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.28761 | 0.248650 | 0.124325 | − | 0.992242i | \(-0.460323\pi\) | ||||
0.124325 | + | 0.992242i | \(0.460323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.516989 | + | 2.46022i | −0.0176189 | + | 0.0838440i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 6.04470i | − | 0.205764i | −0.994694 | − | 0.102882i | \(-0.967194\pi\) | ||
0.994694 | − | 0.102882i | \(-0.0328064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.688821i | 0.0234206i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.98586 | − | 28.4851i | 0.203290 | − | 0.967406i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.40916i | 0.319184i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3872i | 1.13128i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.03432 | + | 15.9982i | −0.238076 | + | 0.541456i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 17.2094i | − | 0.581783i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.3592 | 0.721250 | 0.360625 | − | 0.932711i | \(-0.382564\pi\) | ||||
0.360625 | + | 0.932711i | \(0.382564\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.18186 | − | 24.6591i | 0.174780 | − | 0.831731i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.4847 | 0.622766 | 0.311383 | − | 0.950284i | \(-0.399208\pi\) | ||||
0.311383 | + | 0.950284i | \(0.399208\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.5090 | 1.66611 | 0.833056 | − | 0.553189i | \(-0.186589\pi\) | ||||
0.833056 | + | 0.553189i | \(0.186589\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.64998 | − | 0.346727i | −0.0554636 | − | 0.0116551i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 43.8047i | − | 1.47082i | −0.677623 | − | 0.735409i | \(-0.736990\pi\) | ||
0.677623 | − | 0.735409i | \(-0.263010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.6534i | 1.83302i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.2490 | − | 30.7957i | −0.946376 | − | 1.03170i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.86283 | −0.196192 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.70842i | − | 0.224238i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.7825 | − | 27.8177i | 0.460186 | − | 0.928805i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.2301i | 1.00823i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.84405 | 0.128064 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.8905 | − | 51.8251i | 0.362413 | − | 1.72463i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.56086i | 0.151608i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 52.8742i | − | 1.75566i | −0.478972 | − | 0.877830i | \(-0.658990\pi\) | ||
0.478972 | − | 0.877830i | \(-0.341010\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.30540 | − | 16.6147i | 0.242305 | − | 0.551074i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.6671 | −1.47989 | −0.739943 | − | 0.672670i | \(-0.765148\pi\) | ||||
−0.739943 | + | 0.672670i | \(0.765148\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.2787 | −1.73017 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.85017 | − | 2.06991i | −0.325637 | − | 0.0684292i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −78.7155 | −2.59941 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.8812i | 1.51348i | 0.653715 | + | 0.756741i | \(0.273210\pi\) | ||||
−0.653715 | + | 0.756741i | \(0.726790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.42477 | + | 6.78012i | −0.0469478 | + | 0.223413i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 30.7215i | − | 1.01121i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.2570i | 1.15924i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.9481 | + | 33.9964i | −0.490959 | + | 1.11659i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.7554i | 1.66523i | 0.553852 | + | 0.832615i | \(0.313157\pi\) | ||||
−0.553852 | + | 0.832615i | \(0.686843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 21.8270i | − | 0.715350i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.9939 | − | 5.67249i | −0.883741 | − | 0.185709i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.905018 | 0.0295972 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.2908i | 0.564866i | 0.959287 | + | 0.282433i | \(0.0911415\pi\) | ||||
−0.959287 | + | 0.282433i | \(0.908859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.8358 | − | 10.2623i | −1.59370 | − | 0.334899i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.94010 | −0.258840 | −0.129420 | − | 0.991590i | \(-0.541312\pi\) | ||||
−0.129420 | + | 0.991590i | \(0.541312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.438069 | + | 1.69521i | −0.0142655 | + | 0.0552037i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.41528 | + | 5.30927i | 0.241219 | + | 0.172711i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 0.655503i | − | 0.0213010i | −0.999943 | − | 0.0106505i | \(-0.996610\pi\) | ||
0.999943 | − | 0.0106505i | \(-0.00339022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.8018 | 1.32448 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.2748 | + | 10.5647i | 1.63027 | + | 0.342585i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.2530 | 1.69264 | 0.846320 | − | 0.532675i | \(-0.178813\pi\) | ||||
0.846320 | + | 0.532675i | \(0.178813\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.918483 | 0.0297214 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 50.4897 | + | 10.6099i | 1.63210 | + | 0.342969i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.3148i | 1.56017i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.79342 | −0.283659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.8880 | − | 5.22709i | −0.383084 | − | 0.168441i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.66569 | −0.0536205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.7124 | −0.408803 | −0.204401 | − | 0.978887i | \(-0.565525\pi\) | ||||
−0.204401 | + | 0.978887i | \(0.565525\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.85504 | + | 0.389817i | 0.0595923 | + | 0.0125227i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.2842 | 0.586768 | 0.293384 | − | 0.955995i | \(-0.405219\pi\) | ||||
0.293384 | + | 0.955995i | \(0.405219\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 86.9965i | 2.78898i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.39664 | − | 30.4399i | 0.204856 | − | 0.974858i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.18728 | −0.229941 | −0.114971 | − | 0.993369i | \(-0.536677\pi\) | ||||
−0.114971 | + | 0.993369i | \(0.536677\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −80.6295 | −2.57693 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.66544 | − | 19.7078i | 0.276666 | − | 0.629222i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.5704 | −1.07073 | −0.535365 | − | 0.844621i | \(-0.679826\pi\) | ||||
−0.535365 | + | 0.844621i | \(0.679826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1074i | 0.322050i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.34912 | − | 15.9376i | 0.106604 | − | 0.507300i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.22803 | − | 35.7101i | 0.293434 | − | 1.13551i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.30927 | 0.168655 | 0.0843273 | − | 0.996438i | \(-0.473126\pi\) | ||||
0.0843273 | + | 0.996438i | \(0.473126\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.57632 | + | 21.7775i | −0.145225 | + | 0.691088i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.48581i | − | 0.142210i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.89400 | −0.123324 | −0.0616621 | − | 0.998097i | \(-0.519640\pi\) | ||||
−0.0616621 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.9997 | − | 22.1955i | −0.980788 | − | 0.702236i |
(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 | 552.2.m.b.137.8 | yes | 16 | |
3.2 | odd | 2 | inner | 552.2.m.b.137.5 | ✓ | 16 | |
4.3 | odd | 2 | 1104.2.m.e.689.10 | 16 | |||
12.11 | even | 2 | 1104.2.m.e.689.11 | 16 | |||
23.22 | odd | 2 | inner | 552.2.m.b.137.7 | yes | 16 | |
69.68 | even | 2 | inner | 552.2.m.b.137.6 | yes | 16 | |
92.91 | even | 2 | 1104.2.m.e.689.9 | 16 | |||
276.275 | odd | 2 | 1104.2.m.e.689.12 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.m.b.137.5 | ✓ | 16 | 3.2 | odd | 2 | inner | |
552.2.m.b.137.6 | yes | 16 | 69.68 | even | 2 | inner | |
552.2.m.b.137.7 | yes | 16 | 23.22 | odd | 2 | inner | |
552.2.m.b.137.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1104.2.m.e.689.9 | 16 | 92.91 | even | 2 | |||
1104.2.m.e.689.10 | 16 | 4.3 | odd | 2 | |||
1104.2.m.e.689.11 | 16 | 12.11 | even | 2 | |||
1104.2.m.e.689.12 | 16 | 276.275 | odd | 2 |