Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(64,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.c (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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.5 | ||
Root | \(-0.854638 - 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.64 |
Dual form | 91.2.c.a.64.2 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17009i | 0.827376i | 0.910419 | + | 0.413688i | \(0.135760\pi\) | ||||
−0.910419 | + | 0.413688i | \(0.864240\pi\) | |||||||
\(3\) | 0.539189 | 0.311301 | 0.155650 | − | 0.987812i | \(-0.450253\pi\) | ||||
0.155650 | + | 0.987812i | \(0.450253\pi\) | |||||||
\(4\) | 0.630898 | 0.315449 | ||||||||
\(5\) | − | 0.460811i | − | 0.206081i | −0.994677 | − | 0.103041i | \(-0.967143\pi\) | ||
0.994677 | − | 0.103041i | \(-0.0328571\pi\) | |||||||
\(6\) | 0.630898i | 0.257563i | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 3.07838i | 1.08837i | ||||||||
\(9\) | −2.70928 | −0.903092 | ||||||||
\(10\) | 0.539189 | 0.170506 | ||||||||
\(11\) | 0.829914i | 0.250228i | 0.992142 | + | 0.125114i | \(0.0399297\pi\) | ||||
−0.992142 | + | 0.125114i | \(0.960070\pi\) | |||||||
\(12\) | 0.340173 | 0.0981995 | ||||||||
\(13\) | −2.87936 | − | 2.17009i | −0.798591 | − | 0.601874i | ||||
\(14\) | 1.17009 | 0.312719 | ||||||||
\(15\) | − | 0.248464i | − | 0.0641532i | ||||||
\(16\) | −2.34017 | −0.585043 | ||||||||
\(17\) | 2.87936 | 0.698348 | 0.349174 | − | 0.937058i | \(-0.386462\pi\) | ||||
0.349174 | + | 0.937058i | \(0.386462\pi\) | |||||||
\(18\) | − | 3.17009i | − | 0.747197i | ||||||
\(19\) | − | 4.32684i | − | 0.992646i | −0.868138 | − | 0.496323i | \(-0.834683\pi\) | ||
0.868138 | − | 0.496323i | \(-0.165317\pi\) | |||||||
\(20\) | − | 0.290725i | − | 0.0650080i | ||||||
\(21\) | − | 0.539189i | − | 0.117661i | ||||||
\(22\) | −0.971071 | −0.207033 | ||||||||
\(23\) | −5.04945 | −1.05288 | −0.526441 | − | 0.850211i | \(-0.676474\pi\) | ||||
−0.526441 | + | 0.850211i | \(0.676474\pi\) | |||||||
\(24\) | 1.65983i | 0.338811i | ||||||||
\(25\) | 4.78765 | 0.957531 | ||||||||
\(26\) | 2.53919 | − | 3.36910i | 0.497976 | − | 0.660735i | ||||
\(27\) | −3.07838 | −0.592434 | ||||||||
\(28\) | − | 0.630898i | − | 0.119228i | ||||||
\(29\) | 0.261795 | 0.0486142 | 0.0243071 | − | 0.999705i | \(-0.492262\pi\) | ||||
0.0243071 | + | 0.999705i | \(0.492262\pi\) | |||||||
\(30\) | 0.290725 | 0.0530788 | ||||||||
\(31\) | − | 6.80098i | − | 1.22149i | −0.791826 | − | 0.610746i | \(-0.790869\pi\) | ||
0.791826 | − | 0.610746i | \(-0.209131\pi\) | |||||||
\(32\) | 3.41855i | 0.604320i | ||||||||
\(33\) | 0.447480i | 0.0778963i | ||||||||
\(34\) | 3.36910i | 0.577796i | ||||||||
\(35\) | −0.460811 | −0.0778913 | ||||||||
\(36\) | −1.70928 | −0.284879 | ||||||||
\(37\) | 9.51026i | 1.56348i | 0.623606 | + | 0.781739i | \(0.285667\pi\) | ||||
−0.623606 | + | 0.781739i | \(0.714333\pi\) | |||||||
\(38\) | 5.06278 | 0.821291 | ||||||||
\(39\) | −1.55252 | − | 1.17009i | −0.248602 | − | 0.187364i | ||||
\(40\) | 1.41855 | 0.224293 | ||||||||
\(41\) | 6.68035i | 1.04329i | 0.853161 | + | 0.521647i | \(0.174682\pi\) | ||||
−0.853161 | + | 0.521647i | \(0.825318\pi\) | |||||||
\(42\) | 0.630898 | 0.0973496 | ||||||||
\(43\) | 0.418551 | 0.0638284 | 0.0319142 | − | 0.999491i | \(-0.489840\pi\) | ||||
0.0319142 | + | 0.999491i | \(0.489840\pi\) | |||||||
\(44\) | 0.523590i | 0.0789342i | ||||||||
\(45\) | 1.24846i | 0.186110i | ||||||||
\(46\) | − | 5.90829i | − | 0.871130i | ||||||
\(47\) | 9.24846i | 1.34903i | 0.738262 | + | 0.674514i | \(0.235647\pi\) | ||||
−0.738262 | + | 0.674514i | \(0.764353\pi\) | |||||||
\(48\) | −1.26180 | −0.182124 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 5.60197i | 0.792238i | ||||||||
\(51\) | 1.55252 | 0.217396 | ||||||||
\(52\) | −1.81658 | − | 1.36910i | −0.251915 | − | 0.189860i | ||||
\(53\) | 1.63090 | 0.224021 | 0.112011 | − | 0.993707i | \(-0.464271\pi\) | ||||
0.112011 | + | 0.993707i | \(0.464271\pi\) | |||||||
\(54\) | − | 3.60197i | − | 0.490166i | ||||||
\(55\) | 0.382433 | 0.0515673 | ||||||||
\(56\) | 3.07838 | 0.411366 | ||||||||
\(57\) | − | 2.33299i | − | 0.309011i | ||||||
\(58\) | 0.306323i | 0.0402222i | ||||||||
\(59\) | − | 2.78765i | − | 0.362922i | −0.983398 | − | 0.181461i | \(-0.941917\pi\) | ||
0.983398 | − | 0.181461i | \(-0.0580825\pi\) | |||||||
\(60\) | − | 0.156755i | − | 0.0202370i | ||||||
\(61\) | 7.26180 | 0.929778 | 0.464889 | − | 0.885369i | \(-0.346094\pi\) | ||||
0.464889 | + | 0.885369i | \(0.346094\pi\) | |||||||
\(62\) | 7.95774 | 1.01063 | ||||||||
\(63\) | 2.70928i | 0.341337i | ||||||||
\(64\) | −8.68035 | −1.08504 | ||||||||
\(65\) | −1.00000 | + | 1.32684i | −0.124035 | + | 0.164574i | ||||
\(66\) | −0.523590 | −0.0644495 | ||||||||
\(67\) | 5.07838i | 0.620423i | 0.950668 | + | 0.310211i | \(0.100400\pi\) | ||||
−0.950668 | + | 0.310211i | \(0.899600\pi\) | |||||||
\(68\) | 1.81658 | 0.220293 | ||||||||
\(69\) | −2.72261 | −0.327763 | ||||||||
\(70\) | − | 0.539189i | − | 0.0644454i | ||||||
\(71\) | − | 12.7721i | − | 1.51576i | −0.652392 | − | 0.757882i | \(-0.726234\pi\) | ||
0.652392 | − | 0.757882i | \(-0.273766\pi\) | |||||||
\(72\) | − | 8.34017i | − | 0.982899i | ||||||
\(73\) | 0.353504i | 0.0413745i | 0.999786 | + | 0.0206873i | \(0.00658543\pi\) | ||||
−0.999786 | + | 0.0206873i | \(0.993415\pi\) | |||||||
\(74\) | −11.1278 | −1.29358 | ||||||||
\(75\) | 2.58145 | 0.298080 | ||||||||
\(76\) | − | 2.72979i | − | 0.313129i | ||||||
\(77\) | 0.829914 | 0.0945774 | ||||||||
\(78\) | 1.36910 | − | 1.81658i | 0.155020 | − | 0.205687i | ||||
\(79\) | 2.81658 | 0.316890 | 0.158445 | − | 0.987368i | \(-0.449352\pi\) | ||||
0.158445 | + | 0.987368i | \(0.449352\pi\) | |||||||
\(80\) | 1.07838i | 0.120566i | ||||||||
\(81\) | 6.46800 | 0.718667 | ||||||||
\(82\) | −7.81658 | −0.863197 | ||||||||
\(83\) | − | 10.3763i | − | 1.13895i | −0.822010 | − | 0.569473i | \(-0.807147\pi\) | ||
0.822010 | − | 0.569473i | \(-0.192853\pi\) | |||||||
\(84\) | − | 0.340173i | − | 0.0371159i | ||||||
\(85\) | − | 1.32684i | − | 0.143916i | ||||||
\(86\) | 0.489741i | 0.0528101i | ||||||||
\(87\) | 0.141157 | 0.0151336 | ||||||||
\(88\) | −2.55479 | −0.272341 | ||||||||
\(89\) | 5.43188i | 0.575778i | 0.957664 | + | 0.287889i | \(0.0929535\pi\) | ||||
−0.957664 | + | 0.287889i | \(0.907047\pi\) | |||||||
\(90\) | −1.46081 | −0.153983 | ||||||||
\(91\) | −2.17009 | + | 2.87936i | −0.227487 | + | 0.301839i | ||||
\(92\) | −3.18568 | −0.332131 | ||||||||
\(93\) | − | 3.66701i | − | 0.380252i | ||||||
\(94\) | −10.8215 | −1.11615 | ||||||||
\(95\) | −1.99386 | −0.204565 | ||||||||
\(96\) | 1.84324i | 0.188125i | ||||||||
\(97\) | 12.6092i | 1.28027i | 0.768264 | + | 0.640133i | \(0.221121\pi\) | ||||
−0.768264 | + | 0.640133i | \(0.778879\pi\) | |||||||
\(98\) | − | 1.17009i | − | 0.118197i | ||||||
\(99\) | − | 2.24846i | − | 0.225979i | ||||||
\(100\) | 3.02052 | 0.302052 | ||||||||
\(101\) | −3.64423 | −0.362614 | −0.181307 | − | 0.983427i | \(-0.558033\pi\) | ||||
−0.181307 | + | 0.983427i | \(0.558033\pi\) | |||||||
\(102\) | 1.81658i | 0.179868i | ||||||||
\(103\) | −17.9421 | −1.76789 | −0.883946 | − | 0.467589i | \(-0.845123\pi\) | ||||
−0.883946 | + | 0.467589i | \(0.845123\pi\) | |||||||
\(104\) | 6.68035 | − | 8.86376i | 0.655062 | − | 0.869164i | ||||
\(105\) | −0.248464 | −0.0242476 | ||||||||
\(106\) | 1.90829i | 0.185350i | ||||||||
\(107\) | 2.94441 | 0.284647 | 0.142323 | − | 0.989820i | \(-0.454543\pi\) | ||||
0.142323 | + | 0.989820i | \(0.454543\pi\) | |||||||
\(108\) | −1.94214 | −0.186883 | ||||||||
\(109\) | − | 8.43188i | − | 0.807628i | −0.914841 | − | 0.403814i | \(-0.867684\pi\) | ||
0.914841 | − | 0.403814i | \(-0.132316\pi\) | |||||||
\(110\) | 0.447480i | 0.0426656i | ||||||||
\(111\) | 5.12783i | 0.486712i | ||||||||
\(112\) | 2.34017i | 0.221126i | ||||||||
\(113\) | 12.8082 | 1.20489 | 0.602446 | − | 0.798160i | \(-0.294193\pi\) | ||||
0.602446 | + | 0.798160i | \(0.294193\pi\) | |||||||
\(114\) | 2.72979 | 0.255669 | ||||||||
\(115\) | 2.32684i | 0.216979i | ||||||||
\(116\) | 0.165166 | 0.0153353 | ||||||||
\(117\) | 7.80098 | + | 5.87936i | 0.721201 | + | 0.543547i | ||||
\(118\) | 3.26180 | 0.300273 | ||||||||
\(119\) | − | 2.87936i | − | 0.263951i | ||||||
\(120\) | 0.764867 | 0.0698225 | ||||||||
\(121\) | 10.3112 | 0.937386 | ||||||||
\(122\) | 8.49693i | 0.769276i | ||||||||
\(123\) | 3.60197i | 0.324779i | ||||||||
\(124\) | − | 4.29072i | − | 0.385318i | ||||||
\(125\) | − | 4.51026i | − | 0.403410i | ||||||
\(126\) | −3.17009 | −0.282414 | ||||||||
\(127\) | 13.4680 | 1.19509 | 0.597546 | − | 0.801835i | \(-0.296143\pi\) | ||||
0.597546 | + | 0.801835i | \(0.296143\pi\) | |||||||
\(128\) | − | 3.31965i | − | 0.293419i | ||||||
\(129\) | 0.225678 | 0.0198698 | ||||||||
\(130\) | −1.55252 | − | 1.17009i | −0.136165 | − | 0.102623i | ||||
\(131\) | −14.4391 | −1.26155 | −0.630774 | − | 0.775967i | \(-0.717262\pi\) | ||||
−0.630774 | + | 0.775967i | \(0.717262\pi\) | |||||||
\(132\) | 0.282314i | 0.0245723i | ||||||||
\(133\) | −4.32684 | −0.375185 | ||||||||
\(134\) | −5.94214 | −0.513323 | ||||||||
\(135\) | 1.41855i | 0.122089i | ||||||||
\(136\) | 8.86376i | 0.760061i | ||||||||
\(137\) | 16.4319i | 1.40387i | 0.712241 | + | 0.701935i | \(0.247680\pi\) | ||||
−0.712241 | + | 0.701935i | \(0.752320\pi\) | |||||||
\(138\) | − | 3.18568i | − | 0.271184i | ||||||
\(139\) | 13.2195 | 1.12127 | 0.560633 | − | 0.828064i | \(-0.310558\pi\) | ||||
0.560633 | + | 0.828064i | \(0.310558\pi\) | |||||||
\(140\) | −0.290725 | −0.0245707 | ||||||||
\(141\) | 4.98667i | 0.419953i | ||||||||
\(142\) | 14.9444 | 1.25411 | ||||||||
\(143\) | 1.80098 | − | 2.38962i | 0.150606 | − | 0.199830i | ||||
\(144\) | 6.34017 | 0.528348 | ||||||||
\(145\) | − | 0.120638i | − | 0.0100185i | ||||||
\(146\) | −0.413630 | −0.0342323 | ||||||||
\(147\) | −0.539189 | −0.0444715 | ||||||||
\(148\) | 6.00000i | 0.493197i | ||||||||
\(149\) | − | 20.5041i | − | 1.67976i | −0.542770 | − | 0.839881i | \(-0.682624\pi\) | ||
0.542770 | − | 0.839881i | \(-0.317376\pi\) | |||||||
\(150\) | 3.02052i | 0.246624i | ||||||||
\(151\) | − | 1.59478i | − | 0.129781i | −0.997892 | − | 0.0648907i | \(-0.979330\pi\) | ||
0.997892 | − | 0.0648907i | \(-0.0206699\pi\) | |||||||
\(152\) | 13.3197 | 1.08037 | ||||||||
\(153\) | −7.80098 | −0.630672 | ||||||||
\(154\) | 0.971071i | 0.0782511i | ||||||||
\(155\) | −3.13397 | −0.251726 | ||||||||
\(156\) | −0.979481 | − | 0.738205i | −0.0784212 | − | 0.0591037i | ||||
\(157\) | −8.29791 | −0.662246 | −0.331123 | − | 0.943588i | \(-0.607427\pi\) | ||||
−0.331123 | + | 0.943588i | \(0.607427\pi\) | |||||||
\(158\) | 3.29565i | 0.262187i | ||||||||
\(159\) | 0.879362 | 0.0697379 | ||||||||
\(160\) | 1.57531 | 0.124539 | ||||||||
\(161\) | 5.04945i | 0.397952i | ||||||||
\(162\) | 7.56812i | 0.594608i | ||||||||
\(163\) | 0.398032i | 0.0311763i | 0.999878 | + | 0.0155881i | \(0.00496206\pi\) | ||||
−0.999878 | + | 0.0155881i | \(0.995038\pi\) | |||||||
\(164\) | 4.21461i | 0.329106i | ||||||||
\(165\) | 0.206204 | 0.0160529 | ||||||||
\(166\) | 12.1412 | 0.942337 | ||||||||
\(167\) | − | 23.8710i | − | 1.84719i | −0.383370 | − | 0.923595i | \(-0.625237\pi\) | ||
0.383370 | − | 0.923595i | \(-0.374763\pi\) | |||||||
\(168\) | 1.65983 | 0.128058 | ||||||||
\(169\) | 3.58145 | + | 12.4969i | 0.275496 | + | 0.961302i | ||||
\(170\) | 1.55252 | 0.119073 | ||||||||
\(171\) | 11.7226i | 0.896450i | ||||||||
\(172\) | 0.264063 | 0.0201346 | ||||||||
\(173\) | −25.8999 | −1.96913 | −0.984566 | − | 0.175015i | \(-0.944003\pi\) | ||||
−0.984566 | + | 0.175015i | \(0.944003\pi\) | |||||||
\(174\) | 0.165166i | 0.0125212i | ||||||||
\(175\) | − | 4.78765i | − | 0.361913i | ||||||
\(176\) | − | 1.94214i | − | 0.146394i | ||||||
\(177\) | − | 1.50307i | − | 0.112978i | ||||||
\(178\) | −6.35577 | −0.476385 | ||||||||
\(179\) | −20.6742 | −1.54526 | −0.772631 | − | 0.634855i | \(-0.781060\pi\) | ||||
−0.772631 | + | 0.634855i | \(0.781060\pi\) | |||||||
\(180\) | 0.787653i | 0.0587082i | ||||||||
\(181\) | −15.7165 | −1.16820 | −0.584098 | − | 0.811683i | \(-0.698552\pi\) | ||||
−0.584098 | + | 0.811683i | \(0.698552\pi\) | |||||||
\(182\) | −3.36910 | − | 2.53919i | −0.249734 | − | 0.188217i | ||||
\(183\) | 3.91548 | 0.289441 | ||||||||
\(184\) | − | 15.5441i | − | 1.14593i | ||||||
\(185\) | 4.38243 | 0.322203 | ||||||||
\(186\) | 4.29072 | 0.314611 | ||||||||
\(187\) | 2.38962i | 0.174746i | ||||||||
\(188\) | 5.83483i | 0.425549i | ||||||||
\(189\) | 3.07838i | 0.223919i | ||||||||
\(190\) | − | 2.33299i | − | 0.169253i | ||||||
\(191\) | −16.7877 | −1.21471 | −0.607356 | − | 0.794430i | \(-0.707770\pi\) | ||||
−0.607356 | + | 0.794430i | \(0.707770\pi\) | |||||||
\(192\) | −4.68035 | −0.337775 | ||||||||
\(193\) | − | 20.0144i | − | 1.44067i | −0.693628 | − | 0.720333i | \(-0.743989\pi\) | ||
0.693628 | − | 0.720333i | \(-0.256011\pi\) | |||||||
\(194\) | −14.7538 | −1.05926 | ||||||||
\(195\) | −0.539189 | + | 0.715418i | −0.0386121 | + | 0.0512322i | ||||
\(196\) | −0.630898 | −0.0450641 | ||||||||
\(197\) | − | 17.5174i | − | 1.24807i | −0.781398 | − | 0.624033i | \(-0.785493\pi\) | ||
0.781398 | − | 0.624033i | \(-0.214507\pi\) | |||||||
\(198\) | 2.63090 | 0.186970 | ||||||||
\(199\) | 16.2979 | 1.15533 | 0.577664 | − | 0.816275i | \(-0.303964\pi\) | ||||
0.577664 | + | 0.816275i | \(0.303964\pi\) | |||||||
\(200\) | 14.7382i | 1.04215i | ||||||||
\(201\) | 2.73820i | 0.193138i | ||||||||
\(202\) | − | 4.26406i | − | 0.300018i | ||||||
\(203\) | − | 0.261795i | − | 0.0183744i | ||||||
\(204\) | 0.979481 | 0.0685774 | ||||||||
\(205\) | 3.07838 | 0.215003 | ||||||||
\(206\) | − | 20.9939i | − | 1.46271i | ||||||
\(207\) | 13.6803 | 0.950850 | ||||||||
\(208\) | 6.73820 | + | 5.07838i | 0.467210 | + | 0.352122i | ||||
\(209\) | 3.59090 | 0.248388 | ||||||||
\(210\) | − | 0.290725i | − | 0.0200619i | ||||||
\(211\) | 2.70928 | 0.186514 | 0.0932571 | − | 0.995642i | \(-0.470272\pi\) | ||||
0.0932571 | + | 0.995642i | \(0.470272\pi\) | |||||||
\(212\) | 1.02893 | 0.0706672 | ||||||||
\(213\) | − | 6.88655i | − | 0.471859i | ||||||
\(214\) | 3.44521i | 0.235510i | ||||||||
\(215\) | − | 0.192873i | − | 0.0131538i | ||||||
\(216\) | − | 9.47641i | − | 0.644788i | ||||||
\(217\) | −6.80098 | −0.461681 | ||||||||
\(218\) | 9.86603 | 0.668212 | ||||||||
\(219\) | 0.190605i | 0.0128799i | ||||||||
\(220\) | 0.241276 | 0.0162668 | ||||||||
\(221\) | −8.29072 | − | 6.24846i | −0.557694 | − | 0.420317i | ||||
\(222\) | −6.00000 | −0.402694 | ||||||||
\(223\) | 19.7948i | 1.32556i | 0.748814 | + | 0.662780i | \(0.230624\pi\) | ||||
−0.748814 | + | 0.662780i | \(0.769376\pi\) | |||||||
\(224\) | 3.41855 | 0.228412 | ||||||||
\(225\) | −12.9711 | −0.864738 | ||||||||
\(226\) | 14.9867i | 0.996898i | ||||||||
\(227\) | − | 13.2618i | − | 0.880216i | −0.897945 | − | 0.440108i | \(-0.854940\pi\) | ||
0.897945 | − | 0.440108i | \(-0.145060\pi\) | |||||||
\(228\) | − | 1.47187i | − | 0.0974773i | ||||||
\(229\) | − | 27.8082i | − | 1.83762i | −0.394705 | − | 0.918808i | \(-0.629153\pi\) | ||
0.394705 | − | 0.918808i | \(-0.370847\pi\) | |||||||
\(230\) | −2.72261 | −0.179523 | ||||||||
\(231\) | 0.447480 | 0.0294420 | ||||||||
\(232\) | 0.805905i | 0.0529102i | ||||||||
\(233\) | 13.3668 | 0.875690 | 0.437845 | − | 0.899050i | \(-0.355742\pi\) | ||||
0.437845 | + | 0.899050i | \(0.355742\pi\) | |||||||
\(234\) | −6.87936 | + | 9.12783i | −0.449718 | + | 0.596705i | ||||
\(235\) | 4.26180 | 0.278009 | ||||||||
\(236\) | − | 1.75872i | − | 0.114483i | ||||||
\(237\) | 1.51867 | 0.0986482 | ||||||||
\(238\) | 3.36910 | 0.218386 | ||||||||
\(239\) | 8.70701i | 0.563210i | 0.959530 | + | 0.281605i | \(0.0908667\pi\) | ||||
−0.959530 | + | 0.281605i | \(0.909133\pi\) | |||||||
\(240\) | 0.581449i | 0.0375324i | ||||||||
\(241\) | 16.9311i | 1.09063i | 0.838232 | + | 0.545313i | \(0.183589\pi\) | ||||
−0.838232 | + | 0.545313i | \(0.816411\pi\) | |||||||
\(242\) | 12.0650i | 0.775571i | ||||||||
\(243\) | 12.7226 | 0.816156 | ||||||||
\(244\) | 4.58145 | 0.293297 | ||||||||
\(245\) | 0.460811i | 0.0294401i | ||||||||
\(246\) | −4.21461 | −0.268714 | ||||||||
\(247\) | −9.38962 | + | 12.4585i | −0.597447 | + | 0.792718i | ||||
\(248\) | 20.9360 | 1.32944 | ||||||||
\(249\) | − | 5.59478i | − | 0.354555i | ||||||
\(250\) | 5.27739 | 0.333772 | ||||||||
\(251\) | 8.82150 | 0.556808 | 0.278404 | − | 0.960464i | \(-0.410195\pi\) | ||||
0.278404 | + | 0.960464i | \(0.410195\pi\) | |||||||
\(252\) | 1.70928i | 0.107674i | ||||||||
\(253\) | − | 4.19061i | − | 0.263461i | ||||||
\(254\) | 15.7587i | 0.988790i | ||||||||
\(255\) | − | 0.715418i | − | 0.0448012i | ||||||
\(256\) | −13.4764 | −0.842276 | ||||||||
\(257\) | 13.6442 | 0.851104 | 0.425552 | − | 0.904934i | \(-0.360080\pi\) | ||||
0.425552 | + | 0.904934i | \(0.360080\pi\) | |||||||
\(258\) | 0.264063i | 0.0164398i | ||||||||
\(259\) | 9.51026 | 0.590939 | ||||||||
\(260\) | −0.630898 | + | 0.837101i | −0.0391266 | + | 0.0519148i | ||||
\(261\) | −0.709275 | −0.0439030 | ||||||||
\(262\) | − | 16.8950i | − | 1.04377i | ||||||
\(263\) | −12.1773 | −0.750883 | −0.375441 | − | 0.926846i | \(-0.622509\pi\) | ||||
−0.375441 | + | 0.926846i | \(0.622509\pi\) | |||||||
\(264\) | −1.37751 | −0.0847801 | ||||||||
\(265\) | − | 0.751536i | − | 0.0461665i | ||||||
\(266\) | − | 5.06278i | − | 0.310419i | ||||||
\(267\) | 2.92881i | 0.179240i | ||||||||
\(268\) | 3.20394i | 0.195712i | ||||||||
\(269\) | −11.0472 | −0.673559 | −0.336779 | − | 0.941584i | \(-0.609338\pi\) | ||||
−0.336779 | + | 0.941584i | \(0.609338\pi\) | |||||||
\(270\) | −1.65983 | −0.101014 | ||||||||
\(271\) | 10.9360i | 0.664315i | 0.943224 | + | 0.332157i | \(0.107776\pi\) | ||||
−0.943224 | + | 0.332157i | \(0.892224\pi\) | |||||||
\(272\) | −6.73820 | −0.408564 | ||||||||
\(273\) | −1.17009 | + | 1.55252i | −0.0708169 | + | 0.0939628i | ||||
\(274\) | −19.2267 | −1.16153 | ||||||||
\(275\) | 3.97334i | 0.239601i | ||||||||
\(276\) | −1.71769 | −0.103393 | ||||||||
\(277\) | 26.1194 | 1.56936 | 0.784682 | − | 0.619899i | \(-0.212826\pi\) | ||||
0.784682 | + | 0.619899i | \(0.212826\pi\) | |||||||
\(278\) | 15.4680i | 0.927709i | ||||||||
\(279\) | 18.4257i | 1.10312i | ||||||||
\(280\) | − | 1.41855i | − | 0.0847746i | ||||||
\(281\) | − | 4.80325i | − | 0.286538i | −0.989684 | − | 0.143269i | \(-0.954239\pi\) | ||
0.989684 | − | 0.143269i | \(-0.0457614\pi\) | |||||||
\(282\) | −5.83483 | −0.347459 | ||||||||
\(283\) | −0.979481 | −0.0582241 | −0.0291121 | − | 0.999576i | \(-0.509268\pi\) | ||||
−0.0291121 | + | 0.999576i | \(0.509268\pi\) | |||||||
\(284\) | − | 8.05786i | − | 0.478146i | ||||||
\(285\) | −1.07507 | −0.0636814 | ||||||||
\(286\) | 2.79606 | + | 2.10731i | 0.165335 | + | 0.124608i | ||||
\(287\) | 6.68035 | 0.394328 | ||||||||
\(288\) | − | 9.26180i | − | 0.545757i | ||||||
\(289\) | −8.70928 | −0.512310 | ||||||||
\(290\) | 0.141157 | 0.00828903 | ||||||||
\(291\) | 6.79872i | 0.398548i | ||||||||
\(292\) | 0.223025i | 0.0130515i | ||||||||
\(293\) | 24.3268i | 1.42119i | 0.703602 | + | 0.710595i | \(0.251574\pi\) | ||||
−0.703602 | + | 0.710595i | \(0.748426\pi\) | |||||||
\(294\) | − | 0.630898i | − | 0.0367947i | ||||||
\(295\) | −1.28458 | −0.0747912 | ||||||||
\(296\) | −29.2762 | −1.70164 | ||||||||
\(297\) | − | 2.55479i | − | 0.148244i | ||||||
\(298\) | 23.9916 | 1.38980 | ||||||||
\(299\) | 14.5392 | + | 10.9577i | 0.840823 | + | 0.633702i | ||||
\(300\) | 1.62863 | 0.0940290 | ||||||||
\(301\) | − | 0.418551i | − | 0.0241249i | ||||||
\(302\) | 1.86603 | 0.107378 | ||||||||
\(303\) | −1.96493 | −0.112882 | ||||||||
\(304\) | 10.1256i | 0.580741i | ||||||||
\(305\) | − | 3.34632i | − | 0.191609i | ||||||
\(306\) | − | 9.12783i | − | 0.521803i | ||||||
\(307\) | − | 6.21953i | − | 0.354968i | −0.984124 | − | 0.177484i | \(-0.943204\pi\) | ||
0.984124 | − | 0.177484i | \(-0.0567957\pi\) | |||||||
\(308\) | 0.523590 | 0.0298343 | ||||||||
\(309\) | −9.67420 | −0.550346 | ||||||||
\(310\) | − | 3.66701i | − | 0.208272i | ||||||
\(311\) | 25.1084 | 1.42376 | 0.711882 | − | 0.702299i | \(-0.247843\pi\) | ||||
0.711882 | + | 0.702299i | \(0.247843\pi\) | |||||||
\(312\) | 3.60197 | − | 4.77924i | 0.203921 | − | 0.270571i | ||||
\(313\) | 2.24005 | 0.126615 | 0.0633077 | − | 0.997994i | \(-0.479835\pi\) | ||||
0.0633077 | + | 0.997994i | \(0.479835\pi\) | |||||||
\(314\) | − | 9.70928i | − | 0.547926i | ||||||
\(315\) | 1.24846 | 0.0703430 | ||||||||
\(316\) | 1.77698 | 0.0999627 | ||||||||
\(317\) | 2.89496i | 0.162597i | 0.996690 | + | 0.0812986i | \(0.0259067\pi\) | ||||
−0.996690 | + | 0.0812986i | \(0.974093\pi\) | |||||||
\(318\) | 1.02893i | 0.0576995i | ||||||||
\(319\) | 0.217267i | 0.0121646i | ||||||||
\(320\) | 4.00000i | 0.223607i | ||||||||
\(321\) | 1.58759 | 0.0886108 | ||||||||
\(322\) | −5.90829 | −0.329256 | ||||||||
\(323\) | − | 12.4585i | − | 0.693212i | ||||||
\(324\) | 4.08065 | 0.226703 | ||||||||
\(325\) | −13.7854 | − | 10.3896i | −0.764676 | − | 0.576312i | ||||
\(326\) | −0.465732 | −0.0257945 | ||||||||
\(327\) | − | 4.54638i | − | 0.251415i | ||||||
\(328\) | −20.5646 | −1.13549 | ||||||||
\(329\) | 9.24846 | 0.509884 | ||||||||
\(330\) | 0.241276i | 0.0132818i | ||||||||
\(331\) | 4.25565i | 0.233912i | 0.993137 | + | 0.116956i | \(0.0373136\pi\) | ||||
−0.993137 | + | 0.116956i | \(0.962686\pi\) | |||||||
\(332\) | − | 6.54638i | − | 0.359279i | ||||||
\(333\) | − | 25.7659i | − | 1.41196i | ||||||
\(334\) | 27.9311 | 1.52832 | ||||||||
\(335\) | 2.34017 | 0.127857 | ||||||||
\(336\) | 1.26180i | 0.0688366i | ||||||||
\(337\) | −15.5464 | −0.846865 | −0.423433 | − | 0.905928i | \(-0.639175\pi\) | ||||
−0.423433 | + | 0.905928i | \(0.639175\pi\) | |||||||
\(338\) | −14.6225 | + | 4.19061i | −0.795358 | + | 0.227939i | ||||
\(339\) | 6.90602 | 0.375084 | ||||||||
\(340\) | − | 0.837101i | − | 0.0453982i | ||||||
\(341\) | 5.64423 | 0.305652 | ||||||||
\(342\) | −13.7165 | −0.741701 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 1.28846i | 0.0694690i | ||||||||
\(345\) | 1.25461i | 0.0675458i | ||||||||
\(346\) | − | 30.3051i | − | 1.62921i | ||||||
\(347\) | −20.3812 | −1.09412 | −0.547060 | − | 0.837093i | \(-0.684253\pi\) | ||||
−0.547060 | + | 0.837093i | \(0.684253\pi\) | |||||||
\(348\) | 0.0890557 | 0.00477388 | ||||||||
\(349\) | − | 7.16394i | − | 0.383477i | −0.981446 | − | 0.191739i | \(-0.938587\pi\) | ||
0.981446 | − | 0.191739i | \(-0.0614126\pi\) | |||||||
\(350\) | 5.60197 | 0.299438 | ||||||||
\(351\) | 8.86376 | + | 6.68035i | 0.473113 | + | 0.356570i | ||||
\(352\) | −2.83710 | −0.151218 | ||||||||
\(353\) | 5.38348i | 0.286534i | 0.989684 | + | 0.143267i | \(0.0457607\pi\) | ||||
−0.989684 | + | 0.143267i | \(0.954239\pi\) | |||||||
\(354\) | 1.75872 | 0.0934751 | ||||||||
\(355\) | −5.88550 | −0.312370 | ||||||||
\(356\) | 3.42696i | 0.181629i | ||||||||
\(357\) | − | 1.55252i | − | 0.0821681i | ||||||
\(358\) | − | 24.1906i | − | 1.27851i | ||||||
\(359\) | 15.6937i | 0.828281i | 0.910213 | + | 0.414140i | \(0.135918\pi\) | ||||
−0.910213 | + | 0.414140i | \(0.864082\pi\) | |||||||
\(360\) | −3.84324 | −0.202557 | ||||||||
\(361\) | 0.278438 | 0.0146547 | ||||||||
\(362\) | − | 18.3896i | − | 0.966537i | ||||||
\(363\) | 5.55971 | 0.291809 | ||||||||
\(364\) | −1.36910 | + | 1.81658i | −0.0717605 | + | 0.0952148i | ||||
\(365\) | 0.162899 | 0.00852650 | ||||||||
\(366\) | 4.58145i | 0.239476i | ||||||||
\(367\) | 0.324575 | 0.0169427 | 0.00847133 | − | 0.999964i | \(-0.497303\pi\) | ||||
0.00847133 | + | 0.999964i | \(0.497303\pi\) | |||||||
\(368\) | 11.8166 | 0.615982 | ||||||||
\(369\) | − | 18.0989i | − | 0.942191i | ||||||
\(370\) | 5.12783i | 0.266583i | ||||||||
\(371\) | − | 1.63090i | − | 0.0846720i | ||||||
\(372\) | − | 2.31351i | − | 0.119950i | ||||||
\(373\) | −25.3112 | −1.31057 | −0.655283 | − | 0.755383i | \(-0.727451\pi\) | ||||
−0.655283 | + | 0.755383i | \(0.727451\pi\) | |||||||
\(374\) | −2.79606 | −0.144581 | ||||||||
\(375\) | − | 2.43188i | − | 0.125582i | ||||||
\(376\) | −28.4703 | −1.46824 | ||||||||
\(377\) | −0.753803 | − | 0.568118i | −0.0388228 | − | 0.0292596i | ||||
\(378\) | −3.60197 | −0.185265 | ||||||||
\(379\) | 16.7187i | 0.858784i | 0.903118 | + | 0.429392i | \(0.141272\pi\) | ||||
−0.903118 | + | 0.429392i | \(0.858728\pi\) | |||||||
\(380\) | −1.25792 | −0.0645299 | ||||||||
\(381\) | 7.26180 | 0.372033 | ||||||||
\(382\) | − | 19.6430i | − | 1.00502i | ||||||
\(383\) | − | 13.1629i | − | 0.672593i | −0.941756 | − | 0.336296i | \(-0.890826\pi\) | ||
0.941756 | − | 0.336296i | \(-0.109174\pi\) | |||||||
\(384\) | − | 1.78992i | − | 0.0913415i | ||||||
\(385\) | − | 0.382433i | − | 0.0194906i | ||||||
\(386\) | 23.4186 | 1.19197 | ||||||||
\(387\) | −1.13397 | −0.0576429 | ||||||||
\(388\) | 7.95509i | 0.403858i | ||||||||
\(389\) | 10.0761 | 0.510879 | 0.255440 | − | 0.966825i | \(-0.417780\pi\) | ||||
0.255440 | + | 0.966825i | \(0.417780\pi\) | |||||||
\(390\) | −0.837101 | − | 0.630898i | −0.0423883 | − | 0.0319467i | ||||
\(391\) | −14.5392 | −0.735278 | ||||||||
\(392\) | − | 3.07838i | − | 0.155482i | ||||||
\(393\) | −7.78539 | −0.392721 | ||||||||
\(394\) | 20.4969 | 1.03262 | ||||||||
\(395\) | − | 1.29791i | − | 0.0653051i | ||||||
\(396\) | − | 1.41855i | − | 0.0712849i | ||||||
\(397\) | 8.07119i | 0.405081i | 0.979274 | + | 0.202541i | \(0.0649198\pi\) | ||||
−0.979274 | + | 0.202541i | \(0.935080\pi\) | |||||||
\(398\) | 19.0700i | 0.955891i | ||||||||
\(399\) | −2.33299 | −0.116795 | ||||||||
\(400\) | −11.2039 | −0.560197 | ||||||||
\(401\) | 12.8371i | 0.641054i | 0.947239 | + | 0.320527i | \(0.103860\pi\) | ||||
−0.947239 | + | 0.320527i | \(0.896140\pi\) | |||||||
\(402\) | −3.20394 | −0.159798 | ||||||||
\(403\) | −14.7587 | + | 19.5825i | −0.735184 | + | 0.975474i | ||||
\(404\) | −2.29914 | −0.114386 | ||||||||
\(405\) | − | 2.98053i | − | 0.148104i | ||||||
\(406\) | 0.306323 | 0.0152026 | ||||||||
\(407\) | −7.89269 | −0.391226 | ||||||||
\(408\) | 4.77924i | 0.236608i | ||||||||
\(409\) | 18.7515i | 0.927204i | 0.886044 | + | 0.463602i | \(0.153443\pi\) | ||||
−0.886044 | + | 0.463602i | \(0.846557\pi\) | |||||||
\(410\) | 3.60197i | 0.177889i | ||||||||
\(411\) | 8.85989i | 0.437026i | ||||||||
\(412\) | −11.3197 | −0.557679 | ||||||||
\(413\) | −2.78765 | −0.137171 | ||||||||
\(414\) | 16.0072i | 0.786710i | ||||||||
\(415\) | −4.78151 | −0.234715 | ||||||||
\(416\) | 7.41855 | − | 9.84324i | 0.363724 | − | 0.482605i | ||||
\(417\) | 7.12783 | 0.349051 | ||||||||
\(418\) | 4.20167i | 0.205510i | ||||||||
\(419\) | 23.6319 | 1.15450 | 0.577248 | − | 0.816569i | \(-0.304127\pi\) | ||||
0.577248 | + | 0.816569i | \(0.304127\pi\) | |||||||
\(420\) | −0.156755 | −0.00764888 | ||||||||
\(421\) | 19.4524i | 0.948052i | 0.880511 | + | 0.474026i | \(0.157200\pi\) | ||||
−0.880511 | + | 0.474026i | \(0.842800\pi\) | |||||||
\(422\) | 3.17009i | 0.154317i | ||||||||
\(423\) | − | 25.0566i | − | 1.21830i | ||||||
\(424\) | 5.02052i | 0.243818i | ||||||||
\(425\) | 13.7854 | 0.668689 | ||||||||
\(426\) | 8.05786 | 0.390405 | ||||||||
\(427\) | − | 7.26180i | − | 0.351423i | ||||||
\(428\) | 1.85762 | 0.0897915 | ||||||||
\(429\) | 0.971071 | − | 1.28846i | 0.0468837 | − | 0.0622073i | ||||
\(430\) | 0.225678 | 0.0108832 | ||||||||
\(431\) | 18.0989i | 0.871793i | 0.899997 | + | 0.435897i | \(0.143569\pi\) | ||||
−0.899997 | + | 0.435897i | \(0.856431\pi\) | |||||||
\(432\) | 7.20394 | 0.346600 | ||||||||
\(433\) | −20.5380 | −0.986992 | −0.493496 | − | 0.869748i | \(-0.664281\pi\) | ||||
−0.493496 | + | 0.869748i | \(0.664281\pi\) | |||||||
\(434\) | − | 7.95774i | − | 0.381984i | ||||||
\(435\) | − | 0.0650468i | − | 0.00311875i | ||||||
\(436\) | − | 5.31965i | − | 0.254765i | ||||||
\(437\) | 21.8482i | 1.04514i | ||||||||
\(438\) | −0.223025 | −0.0106565 | ||||||||
\(439\) | 26.9627 | 1.28686 | 0.643429 | − | 0.765506i | \(-0.277511\pi\) | ||||
0.643429 | + | 0.765506i | \(0.277511\pi\) | |||||||
\(440\) | 1.17727i | 0.0561244i | ||||||||
\(441\) | 2.70928 | 0.129013 | ||||||||
\(442\) | 7.31124 | − | 9.70086i | 0.347760 | − | 0.461423i | ||||
\(443\) | 26.4101 | 1.25478 | 0.627392 | − | 0.778704i | \(-0.284122\pi\) | ||||
0.627392 | + | 0.778704i | \(0.284122\pi\) | |||||||
\(444\) | 3.23513i | 0.153533i | ||||||||
\(445\) | 2.50307 | 0.118657 | ||||||||
\(446\) | −23.1617 | −1.09674 | ||||||||
\(447\) | − | 11.0556i | − | 0.522912i | ||||||
\(448\) | 8.68035i | 0.410108i | ||||||||
\(449\) | 31.4329i | 1.48341i | 0.670725 | + | 0.741706i | \(0.265983\pi\) | ||||
−0.670725 | + | 0.741706i | \(0.734017\pi\) | |||||||
\(450\) | − | 15.1773i | − | 0.715464i | ||||||
\(451\) | −5.54411 | −0.261062 | ||||||||
\(452\) | 8.08065 | 0.380082 | ||||||||
\(453\) | − | 0.859888i | − | 0.0404011i | ||||||
\(454\) | 15.5174 | 0.728270 | ||||||||
\(455\) | 1.32684 | + | 1.00000i | 0.0622033 | + | 0.0468807i | ||||
\(456\) | 7.18181 | 0.336319 | ||||||||
\(457\) | − | 18.0650i | − | 0.845047i | −0.906352 | − | 0.422524i | \(-0.861144\pi\) | ||
0.906352 | − | 0.422524i | \(-0.138856\pi\) | |||||||
\(458\) | 32.5380 | 1.52040 | ||||||||
\(459\) | −8.86376 | −0.413725 | ||||||||
\(460\) | 1.46800i | 0.0684458i | ||||||||
\(461\) | − | 23.0784i | − | 1.07487i | −0.843306 | − | 0.537434i | \(-0.819394\pi\) | ||
0.843306 | − | 0.537434i | \(-0.180606\pi\) | |||||||
\(462\) | 0.523590i | 0.0243596i | ||||||||
\(463\) | 4.54760i | 0.211345i | 0.994401 | + | 0.105672i | \(0.0336995\pi\) | ||||
−0.994401 | + | 0.105672i | \(0.966301\pi\) | |||||||
\(464\) | −0.612646 | −0.0284414 | ||||||||
\(465\) | −1.68980 | −0.0783627 | ||||||||
\(466\) | 15.6404i | 0.724525i | ||||||||
\(467\) | −37.8154 | −1.74989 | −0.874943 | − | 0.484226i | \(-0.839101\pi\) | ||||
−0.874943 | + | 0.484226i | \(0.839101\pi\) | |||||||
\(468\) | 4.92162 | + | 3.70928i | 0.227502 | + | 0.171461i | ||||
\(469\) | 5.07838 | 0.234498 | ||||||||
\(470\) | 4.98667i | 0.230018i | ||||||||
\(471\) | −4.47414 | −0.206158 | ||||||||
\(472\) | 8.58145 | 0.394993 | ||||||||
\(473\) | 0.347361i | 0.0159717i | ||||||||
\(474\) | 1.77698i | 0.0816192i | ||||||||
\(475\) | − | 20.7154i | − | 0.950489i | ||||||
\(476\) | − | 1.81658i | − | 0.0832629i | ||||||
\(477\) | −4.41855 | −0.202312 | ||||||||
\(478\) | −10.1880 | −0.465986 | ||||||||
\(479\) | 9.24005i | 0.422189i | 0.977466 | + | 0.211094i | \(0.0677028\pi\) | ||||
−0.977466 | + | 0.211094i | \(0.932297\pi\) | |||||||
\(480\) | 0.849388 | 0.0387691 | ||||||||
\(481\) | 20.6381 | − | 27.3835i | 0.941016 | − | 1.24858i | ||||
\(482\) | −19.8108 | −0.902358 | ||||||||
\(483\) | 2.72261i | 0.123883i | ||||||||
\(484\) | 6.50534 | 0.295697 | ||||||||
\(485\) | 5.81044 | 0.263838 | ||||||||
\(486\) | 14.8865i | 0.675268i | ||||||||
\(487\) | 13.6598i | 0.618986i | 0.950902 | + | 0.309493i | \(0.100159\pi\) | ||||
−0.950902 | + | 0.309493i | \(0.899841\pi\) | |||||||
\(488\) | 22.3545i | 1.01194i | ||||||||
\(489\) | 0.214614i | 0.00970519i | ||||||||
\(490\) | −0.539189 | −0.0243581 | ||||||||
\(491\) | 29.6514 | 1.33815 | 0.669075 | − | 0.743195i | \(-0.266691\pi\) | ||||
0.669075 | + | 0.743195i | \(0.266691\pi\) | |||||||
\(492\) | 2.27247i | 0.102451i | ||||||||
\(493\) | 0.753803 | 0.0339496 | ||||||||
\(494\) | −14.5776 | − | 10.9867i | −0.655876 | − | 0.494314i | ||||
\(495\) | −1.03612 | −0.0465700 | ||||||||
\(496\) | 15.9155i | 0.714626i | ||||||||
\(497\) | −12.7721 | −0.572905 | ||||||||
\(498\) | 6.54638 | 0.293350 | ||||||||
\(499\) | − | 35.5246i | − | 1.59030i | −0.606412 | − | 0.795151i | \(-0.707392\pi\) | ||
0.606412 | − | 0.795151i | \(-0.292608\pi\) | |||||||
\(500\) | − | 2.84551i | − | 0.127255i | ||||||
\(501\) | − | 12.8710i | − | 0.575032i | ||||||
\(502\) | 10.3219i | 0.460690i | ||||||||
\(503\) | 34.4124 | 1.53437 | 0.767187 | − | 0.641424i | \(-0.221656\pi\) | ||||
0.767187 | + | 0.641424i | \(0.221656\pi\) | |||||||
\(504\) | −8.34017 | −0.371501 | ||||||||
\(505\) | 1.67930i | 0.0747279i | ||||||||
\(506\) | 4.90337 | 0.217981 | ||||||||
\(507\) | 1.93108 | + | 6.73820i | 0.0857622 | + | 0.299254i | ||||
\(508\) | 8.49693 | 0.376990 | ||||||||
\(509\) | − | 11.1184i | − | 0.492813i | −0.969167 | − | 0.246407i | \(-0.920750\pi\) | ||
0.969167 | − | 0.246407i | \(-0.0792498\pi\) | |||||||
\(510\) | 0.837101 | 0.0370675 | ||||||||
\(511\) | 0.353504 | 0.0156381 | ||||||||
\(512\) | − | 22.4079i | − | 0.990297i | ||||||
\(513\) | 13.3197i | 0.588077i | ||||||||
\(514\) | 15.9649i | 0.704183i | ||||||||
\(515\) | 8.26794i | 0.364329i | ||||||||
\(516\) | 0.142380 | 0.00626791 | ||||||||
\(517\) | −7.67543 | −0.337565 | ||||||||
\(518\) | 11.1278i | 0.488929i | ||||||||
\(519\) | −13.9649 | −0.612992 | ||||||||
\(520\) | −4.08452 | − | 3.07838i | −0.179118 | − | 0.134996i | ||||
\(521\) | −17.8888 | −0.783723 | −0.391862 | − | 0.920024i | \(-0.628169\pi\) | ||||
−0.391862 | + | 0.920024i | \(0.628169\pi\) | |||||||
\(522\) | − | 0.829914i | − | 0.0363243i | ||||||
\(523\) | −23.9877 | −1.04891 | −0.524455 | − | 0.851438i | \(-0.675731\pi\) | ||||
−0.524455 | + | 0.851438i | \(0.675731\pi\) | |||||||
\(524\) | −9.10957 | −0.397954 | ||||||||
\(525\) | − | 2.58145i | − | 0.112664i | ||||||
\(526\) | − | 14.2485i | − | 0.621263i | ||||||
\(527\) | − | 19.5825i | − | 0.853027i | ||||||
\(528\) | − | 1.04718i | − | 0.0455727i | ||||||
\(529\) | 2.49693 | 0.108562 | ||||||||
\(530\) | 0.879362 | 0.0381970 | ||||||||
\(531\) | 7.55252i | 0.327751i | ||||||||
\(532\) | −2.72979 | −0.118352 | ||||||||
\(533\) | 14.4969 | − | 19.2351i | 0.627932 | − | 0.833166i | ||||
\(534\) | −3.42696 | −0.148299 | ||||||||
\(535\) | − | 1.35682i | − | 0.0586603i | ||||||
\(536\) | −15.6332 | −0.675250 | ||||||||
\(537\) | −11.1473 | −0.481042 | ||||||||
\(538\) | − | 12.9262i | − | 0.557286i | ||||||
\(539\) | − | 0.829914i | − | 0.0357469i | ||||||
\(540\) | 0.894960i | 0.0385130i | ||||||||
\(541\) | − | 19.4114i | − | 0.834560i | −0.908778 | − | 0.417280i | \(-0.862983\pi\) | ||
0.908778 | − | 0.417280i | \(-0.137017\pi\) | |||||||
\(542\) | −12.7961 | −0.549638 | ||||||||
\(543\) | −8.47414 | −0.363660 | ||||||||
\(544\) | 9.84324i | 0.422026i | ||||||||
\(545\) | −3.88550 | −0.166437 | ||||||||
\(546\) | −1.81658 | − | 1.36910i | −0.0777426 | − | 0.0585922i | ||||
\(547\) | −1.81432 | −0.0775745 | −0.0387873 | − | 0.999247i | \(-0.512349\pi\) | ||||
−0.0387873 | + | 0.999247i | \(0.512349\pi\) | |||||||
\(548\) | 10.3668i | 0.442849i | ||||||||
\(549\) | −19.6742 | −0.839675 | ||||||||
\(550\) | −4.64915 | −0.198240 | ||||||||
\(551\) | − | 1.13275i | − | 0.0482566i | ||||||
\(552\) | − | 8.38121i | − | 0.356728i | ||||||
\(553\) | − | 2.81658i | − | 0.119773i | ||||||
\(554\) | 30.5620i | 1.29845i | ||||||||
\(555\) | 2.36296 | 0.100302 | ||||||||
\(556\) | 8.34017 | 0.353702 | ||||||||
\(557\) | 23.4186i | 0.992276i | 0.868244 | + | 0.496138i | \(0.165249\pi\) | ||||
−0.868244 | + | 0.496138i | \(0.834751\pi\) | |||||||
\(558\) | −21.5597 | −0.912695 | ||||||||
\(559\) | −1.20516 | − | 0.908291i | −0.0509728 | − | 0.0384166i | ||||
\(560\) | 1.07838 | 0.0455698 | ||||||||
\(561\) | 1.28846i | 0.0543987i | ||||||||
\(562\) | 5.62022 | 0.237075 | ||||||||
\(563\) | −26.6947 | −1.12505 | −0.562524 | − | 0.826781i | \(-0.690170\pi\) | ||||
−0.562524 | + | 0.826781i | \(0.690170\pi\) | |||||||
\(564\) | 3.14608i | 0.132474i | ||||||||
\(565\) | − | 5.90215i | − | 0.248305i | ||||||
\(566\) | − | 1.14608i | − | 0.0481732i | ||||||
\(567\) | − | 6.46800i | − | 0.271630i | ||||||
\(568\) | 39.3172 | 1.64971 | ||||||||
\(569\) | 26.5897 | 1.11470 | 0.557349 | − | 0.830279i | \(-0.311819\pi\) | ||||
0.557349 | + | 0.830279i | \(0.311819\pi\) | |||||||
\(570\) | − | 1.25792i | − | 0.0526885i | ||||||
\(571\) | 3.43310 | 0.143671 | 0.0718355 | − | 0.997416i | \(-0.477114\pi\) | ||||
0.0718355 | + | 0.997416i | \(0.477114\pi\) | |||||||
\(572\) | 1.13624 | − | 1.50761i | 0.0475084 | − | 0.0630362i | ||||
\(573\) | −9.05172 | −0.378141 | ||||||||
\(574\) | 7.81658i | 0.326258i | ||||||||
\(575\) | −24.1750 | −1.00817 | ||||||||
\(576\) | 23.5174 | 0.979894 | ||||||||
\(577\) | − | 30.4657i | − | 1.26831i | −0.773208 | − | 0.634153i | \(-0.781349\pi\) | ||
0.773208 | − | 0.634153i | \(-0.218651\pi\) | |||||||
\(578\) | − | 10.1906i | − | 0.423873i | ||||||
\(579\) | − | 10.7915i | − | 0.448481i | ||||||
\(580\) | − | 0.0761103i | − | 0.00316031i | ||||||
\(581\) | −10.3763 | −0.430481 | ||||||||
\(582\) | −7.95509 | −0.329749 | ||||||||
\(583\) | 1.35350i | 0.0560564i | ||||||||
\(584\) | −1.08822 | −0.0450308 | ||||||||
\(585\) | 2.70928 | − | 3.59478i | 0.112015 | − | 0.148626i | ||||
\(586\) | −28.4645 | −1.17586 | ||||||||
\(587\) | − | 26.2606i | − | 1.08389i | −0.840414 | − | 0.541945i | \(-0.817688\pi\) | ||
0.840414 | − | 0.541945i | \(-0.182312\pi\) | |||||||
\(588\) | −0.340173 | −0.0140285 | ||||||||
\(589\) | −29.4268 | −1.21251 | ||||||||
\(590\) | − | 1.50307i | − | 0.0618805i | ||||||
\(591\) | − | 9.44521i | − | 0.388524i | ||||||
\(592\) | − | 22.2557i | − | 0.914702i | ||||||
\(593\) | 40.8420i | 1.67718i | 0.544762 | + | 0.838590i | \(0.316620\pi\) | ||||
−0.544762 | + | 0.838590i | \(0.683380\pi\) | |||||||
\(594\) | 2.98932 | 0.122653 | ||||||||
\(595\) | −1.32684 | −0.0543952 | ||||||||
\(596\) | − | 12.9360i | − | 0.529879i | ||||||
\(597\) | 8.78765 | 0.359655 | ||||||||
\(598\) | −12.8215 | + | 17.0121i | −0.524310 | + | 0.695677i | ||||
\(599\) | −27.3545 | −1.11768 | −0.558838 | − | 0.829277i | \(-0.688753\pi\) | ||||
−0.558838 | + | 0.829277i | \(0.688753\pi\) | |||||||
\(600\) | 7.94668i | 0.324422i | ||||||||
\(601\) | 25.4908 | 1.03979 | 0.519895 | − | 0.854230i | \(-0.325971\pi\) | ||||
0.519895 | + | 0.854230i | \(0.325971\pi\) | |||||||
\(602\) | 0.489741 | 0.0199603 | ||||||||
\(603\) | − | 13.7587i | − | 0.560299i | ||||||
\(604\) | − | 1.00614i | − | 0.0409394i | ||||||
\(605\) | − | 4.75154i | − | 0.193177i | ||||||
\(606\) | − | 2.29914i | − | 0.0933960i | ||||||
\(607\) | 19.9311 | 0.808977 | 0.404489 | − | 0.914543i | \(-0.367449\pi\) | ||||
0.404489 | + | 0.914543i | \(0.367449\pi\) | |||||||
\(608\) | 14.7915 | 0.599876 | ||||||||
\(609\) | − | 0.141157i | − | 0.00571997i | ||||||
\(610\) | 3.91548 | 0.158533 | ||||||||
\(611\) | 20.0700 | − | 26.6297i | 0.811944 | − | 1.07732i | ||||
\(612\) | −4.92162 | −0.198945 | ||||||||
\(613\) | − | 22.7214i | − | 0.917708i | −0.888512 | − | 0.458854i | \(-0.848260\pi\) | ||
0.888512 | − | 0.458854i | \(-0.151740\pi\) | |||||||
\(614\) | 7.27739 | 0.293692 | ||||||||
\(615\) | 1.65983 | 0.0669307 | ||||||||
\(616\) | 2.55479i | 0.102935i | ||||||||
\(617\) | 14.3545i | 0.577892i | 0.957345 | + | 0.288946i | \(0.0933049\pi\) | ||||
−0.957345 | + | 0.288946i | \(0.906695\pi\) | |||||||
\(618\) | − | 11.3197i | − | 0.455343i | ||||||
\(619\) | 27.9832i | 1.12474i | 0.826886 | + | 0.562369i | \(0.190110\pi\) | ||||
−0.826886 | + | 0.562369i | \(0.809890\pi\) | |||||||
\(620\) | −1.97721 | −0.0794068 | ||||||||
\(621\) | 15.5441 | 0.623764 | ||||||||
\(622\) | 29.3789i | 1.17799i | ||||||||
\(623\) | 5.43188 | 0.217624 | ||||||||
\(624\) | 3.63317 | + | 2.73820i | 0.145443 | + | 0.109616i | ||||
\(625\) | 21.8599 | 0.874396 | ||||||||
\(626\) | 2.62106i | 0.104758i | ||||||||
\(627\) | 1.93618 | 0.0773234 | ||||||||
\(628\) | −5.23513 | −0.208905 | ||||||||
\(629\) | 27.3835i | 1.09185i | ||||||||
\(630\) | 1.46081i | 0.0582001i | ||||||||
\(631\) | − | 21.4186i | − | 0.852659i | −0.904568 | − | 0.426330i | \(-0.859806\pi\) | ||
0.904568 | − | 0.426330i | \(-0.140194\pi\) | |||||||
\(632\) | 8.67050i | 0.344894i | ||||||||
\(633\) | 1.46081 | 0.0580620 | ||||||||
\(634\) | −3.38735 | −0.134529 | ||||||||
\(635\) | − | 6.20620i | − | 0.246286i | ||||||
\(636\) | 0.554787 | 0.0219987 | ||||||||
\(637\) | 2.87936 | + | 2.17009i | 0.114084 | + | 0.0859820i | ||||
\(638\) | −0.254222 | −0.0100647 | ||||||||
\(639\) | 34.6030i | 1.36887i | ||||||||
\(640\) | −1.52973 | −0.0604680 | ||||||||
\(641\) | 37.9360 | 1.49838 | 0.749191 | − | 0.662354i | \(-0.230443\pi\) | ||||
0.749191 | + | 0.662354i | \(0.230443\pi\) | |||||||
\(642\) | 1.85762i | 0.0733144i | ||||||||
\(643\) | − | 36.2122i | − | 1.42807i | −0.700111 | − | 0.714034i | \(-0.746866\pi\) | ||
0.700111 | − | 0.714034i | \(-0.253134\pi\) | |||||||
\(644\) | 3.18568i | 0.125534i | ||||||||
\(645\) | − | 0.103995i | − | 0.00409479i | ||||||
\(646\) | 14.5776 | 0.573547 | ||||||||
\(647\) | −42.7948 | −1.68244 | −0.841219 | − | 0.540694i | \(-0.818162\pi\) | ||||
−0.841219 | + | 0.540694i | \(0.818162\pi\) | |||||||
\(648\) | 19.9109i | 0.782176i | ||||||||
\(649\) | 2.31351 | 0.0908132 | ||||||||
\(650\) | 12.1568 | − | 16.1301i | 0.476827 | − | 0.632674i | ||||
\(651\) | −3.66701 | −0.143722 | ||||||||
\(652\) | 0.251117i | 0.00983451i | ||||||||
\(653\) | 5.54864 | 0.217135 | 0.108568 | − | 0.994089i | \(-0.465374\pi\) | ||||
0.108568 | + | 0.994089i | \(0.465374\pi\) | |||||||
\(654\) | 5.31965 | 0.208015 | ||||||||
\(655\) | 6.65368i | 0.259981i | ||||||||
\(656\) | − | 15.6332i | − | 0.610373i | ||||||
\(657\) | − | 0.957740i | − | 0.0373650i | ||||||
\(658\) | 10.8215i | 0.421866i | ||||||||
\(659\) | −23.1529 | −0.901908 | −0.450954 | − | 0.892547i | \(-0.648916\pi\) | ||||
−0.450954 | + | 0.892547i | \(0.648916\pi\) | |||||||
\(660\) | 0.130094 | 0.00506388 | ||||||||
\(661\) | 47.2544i | 1.83798i | 0.394276 | + | 0.918992i | \(0.370995\pi\) | ||||
−0.394276 | + | 0.918992i | \(0.629005\pi\) | |||||||
\(662\) | −4.97948 | −0.193533 | ||||||||
\(663\) | −4.47027 | − | 3.36910i | −0.173611 | − | 0.130845i | ||||
\(664\) | 31.9421 | 1.23960 | ||||||||
\(665\) | 1.99386i | 0.0773185i | ||||||||
\(666\) | 30.1483 | 1.16822 | ||||||||
\(667\) | −1.32192 | −0.0511850 | ||||||||
\(668\) | − | 15.0601i | − | 0.582694i | ||||||
\(669\) | 10.6732i | 0.412648i | ||||||||
\(670\) | 2.73820i | 0.105786i | ||||||||
\(671\) | 6.02666i | 0.232657i | ||||||||
\(672\) | 1.84324 | 0.0711047 | ||||||||
\(673\) | 3.42082 | 0.131863 | 0.0659314 | − | 0.997824i | \(-0.478998\pi\) | ||||
0.0659314 | + | 0.997824i | \(0.478998\pi\) | |||||||
\(674\) | − | 18.1906i | − | 0.700676i | ||||||
\(675\) | −14.7382 | −0.567274 | ||||||||
\(676\) | 2.25953 | + | 7.88428i | 0.0869049 | + | 0.303242i | ||||
\(677\) | 10.6959 | 0.411079 | 0.205539 | − | 0.978649i | \(-0.434105\pi\) | ||||
0.205539 | + | 0.978649i | \(0.434105\pi\) | |||||||
\(678\) | 8.08065i | 0.310335i | ||||||||
\(679\) | 12.6092 | 0.483895 | ||||||||
\(680\) | 4.08452 | 0.156634 | ||||||||
\(681\) | − | 7.15061i | − | 0.274012i | ||||||
\(682\) | 6.60424i | 0.252889i | ||||||||
\(683\) | 6.59583i | 0.252382i | 0.992006 | + | 0.126191i | \(0.0402753\pi\) | ||||
−0.992006 | + | 0.126191i | \(0.959725\pi\) | |||||||
\(684\) | 7.39576i | 0.282784i | ||||||||
\(685\) | 7.57199 | 0.289311 | ||||||||
\(686\) | −1.17009 | −0.0446741 | ||||||||
\(687\) | − | 14.9939i | − | 0.572051i | ||||||
\(688\) | −0.979481 | −0.0373424 | ||||||||
\(689\) | −4.69594 | − | 3.53919i | −0.178901 | − | 0.134832i | ||||
\(690\) | −1.46800 | −0.0558858 | ||||||||
\(691\) | 49.4729i | 1.88204i | 0.338353 | + | 0.941019i | \(0.390130\pi\) | ||||
−0.338353 | + | 0.941019i | \(0.609870\pi\) | |||||||
\(692\) | −16.3402 | −0.621160 | ||||||||
\(693\) | −2.24846 | −0.0854121 | ||||||||
\(694\) | − | 23.8478i | − | 0.905249i | ||||||
\(695\) | − | 6.09171i | − | 0.231072i | ||||||
\(696\) | 0.434535i | 0.0164710i | ||||||||
\(697\) | 19.2351i | 0.728583i | ||||||||
\(698\) | 8.38243 | 0.317280 | ||||||||
\(699\) | 7.20725 | 0.272603 | ||||||||
\(700\) | − | 3.02052i | − | 0.114165i | ||||||
\(701\) | −20.8166 | −0.786231 | −0.393116 | − | 0.919489i | \(-0.628603\pi\) | ||||
−0.393116 | + | 0.919489i | \(0.628603\pi\) | |||||||
\(702\) | −7.81658 | + | 10.3714i | −0.295018 | + | 0.391442i | ||||
\(703\) | 41.1494 | 1.55198 | ||||||||
\(704\) | − | 7.20394i | − | 0.271509i | ||||||
\(705\) | 2.29791 | 0.0865444 | ||||||||
\(706\) | −6.29914 | −0.237071 | ||||||||
\(707\) | 3.64423i | 0.137055i | ||||||||
\(708\) | − | 0.948284i | − | 0.0356387i | ||||||
\(709\) | 5.95386i | 0.223602i | 0.993731 | + | 0.111801i | \(0.0356619\pi\) | ||||
−0.993731 | + | 0.111801i | \(0.964338\pi\) | |||||||
\(710\) | − | 6.88655i | − | 0.258448i | ||||||
\(711\) | −7.63090 | −0.286181 | ||||||||
\(712\) | −16.7214 | −0.626660 | ||||||||
\(713\) | 34.3412i | 1.28609i | ||||||||
\(714\) | 1.81658 | 0.0679839 | ||||||||
\(715\) | −1.10116 | − | 0.829914i | −0.0411812 | − | 0.0310370i | ||||
\(716\) | −13.0433 | −0.487451 | ||||||||
\(717\) | 4.69472i | 0.175328i | ||||||||
\(718\) | −18.3630 | −0.685300 | ||||||||
\(719\) | 1.68980 | 0.0630190 | 0.0315095 | − | 0.999503i | \(-0.489969\pi\) | ||||
0.0315095 | + | 0.999503i | \(0.489969\pi\) | |||||||
\(720\) | − | 2.92162i | − | 0.108882i | ||||||
\(721\) | 17.9421i | 0.668200i | ||||||||
\(722\) | 0.325797i | 0.0121249i | ||||||||
\(723\) | 9.12905i | 0.339513i | ||||||||
\(724\) | −9.91548 | −0.368506 | ||||||||
\(725\) | 1.25338 | 0.0465495 | ||||||||
\(726\) | 6.50534i | 0.241436i | ||||||||
\(727\) | −14.0722 | −0.521910 | −0.260955 | − | 0.965351i | \(-0.584037\pi\) | ||||
−0.260955 | + | 0.965351i | \(0.584037\pi\) | |||||||
\(728\) | −8.86376 | − | 6.68035i | −0.328513 | − | 0.247590i | ||||
\(729\) | −12.5441 | −0.464597 | ||||||||
\(730\) | 0.190605i | 0.00705462i | ||||||||
\(731\) | 1.20516 | 0.0445744 | ||||||||
\(732\) | 2.47027 | 0.0913037 | ||||||||
\(733\) | 10.9311i | 0.403749i | 0.979411 | + | 0.201874i | \(0.0647032\pi\) | ||||
−0.979411 | + | 0.201874i | \(0.935297\pi\) | |||||||
\(734\) | 0.379780i | 0.0140179i | ||||||||
\(735\) | 0.248464i | 0.00916474i | ||||||||
\(736\) | − | 17.2618i | − | 0.636278i | ||||||
\(737\) | −4.21461 | −0.155247 | ||||||||
\(738\) | 21.1773 | 0.779546 | ||||||||
\(739\) | − | 3.17009i | − | 0.116614i | −0.998299 | − | 0.0583068i | \(-0.981430\pi\) | ||
0.998299 | − | 0.0583068i | \(-0.0185701\pi\) | |||||||
\(740\) | 2.76487 | 0.101639 | ||||||||
\(741\) | −5.06278 | + | 6.71751i | −0.185986 | + | 0.246774i | ||||
\(742\) | 1.90829 | 0.0700556 | ||||||||
\(743\) | − | 9.73206i | − | 0.357035i | −0.983937 | − | 0.178517i | \(-0.942870\pi\) | ||
0.983937 | − | 0.178517i | \(-0.0571301\pi\) | |||||||
\(744\) | 11.2885 | 0.413855 | ||||||||
\(745\) | −9.44852 | −0.346167 | ||||||||
\(746\) | − | 29.6163i | − | 1.08433i | ||||||
\(747\) | 28.1122i | 1.02857i | ||||||||
\(748\) | 1.50761i | 0.0551235i | ||||||||
\(749\) | − | 2.94441i | − | 0.107586i | ||||||
\(750\) | 2.84551 | 0.103903 | ||||||||
\(751\) | −7.77924 | −0.283869 | −0.141934 | − | 0.989876i | \(-0.545332\pi\) | ||||
−0.141934 | + | 0.989876i | \(0.545332\pi\) | |||||||
\(752\) | − | 21.6430i | − | 0.789239i | ||||||
\(753\) | 4.75646 | 0.173335 | ||||||||
\(754\) | 0.664748 | − | 0.882015i | 0.0242087 | − | 0.0321211i | ||||
\(755\) | −0.734892 | −0.0267455 | ||||||||
\(756\) | 1.94214i | 0.0706350i | ||||||||
\(757\) | 10.8576 | 0.394627 | 0.197313 | − | 0.980340i | \(-0.436778\pi\) | ||||
0.197313 | + | 0.980340i | \(0.436778\pi\) | |||||||
\(758\) | −19.5624 | −0.710537 | ||||||||
\(759\) | − | 2.25953i | − | 0.0820157i | ||||||
\(760\) | − | 6.13784i | − | 0.222643i | ||||||
\(761\) | 1.82150i | 0.0660294i | 0.999455 | + | 0.0330147i | \(0.0105108\pi\) | ||||
−0.999455 | + | 0.0330147i | \(0.989489\pi\) | |||||||
\(762\) | 8.49693i | 0.307811i | ||||||||
\(763\) | −8.43188 | −0.305255 | ||||||||
\(764\) | −10.5913 | −0.383179 | ||||||||
\(765\) | 3.59478i | 0.129970i | ||||||||
\(766\) | 15.4017 | 0.556487 | ||||||||
\(767\) | −6.04945 | + | 8.02666i | −0.218433 | + | 0.289826i | ||||
\(768\) | −7.26633 | −0.262201 | ||||||||
\(769\) | − | 39.7948i | − | 1.43504i | −0.696539 | − | 0.717519i | \(-0.745277\pi\) | ||
0.696539 | − | 0.717519i | \(-0.254723\pi\) | |||||||
\(770\) | 0.447480 | 0.0161261 | ||||||||
\(771\) | 7.35682 | 0.264949 | ||||||||
\(772\) | − | 12.6270i | − | 0.454456i | ||||||
\(773\) | − | 18.3135i | − | 0.658691i | −0.944209 | − | 0.329346i | \(-0.893172\pi\) | ||
0.944209 | − | 0.329346i | \(-0.106828\pi\) | |||||||
\(774\) | − | 1.32684i | − | 0.0476924i | ||||||
\(775\) | − | 32.5608i | − | 1.16962i | ||||||
\(776\) | −38.8157 | −1.39340 | ||||||||
\(777\) | 5.12783 | 0.183960 | ||||||||
\(778\) | 11.7899i | 0.422689i | ||||||||
\(779\) | 28.9048 | 1.03562 | ||||||||
\(780\) | −0.340173 | + | 0.451356i | −0.0121801 | + | 0.0161611i | ||||
\(781\) | 10.5997 | 0.379287 | ||||||||
\(782\) | − | 17.0121i | − | 0.608352i | ||||||
\(783\) | −0.805905 | −0.0288007 | ||||||||
\(784\) | 2.34017 | 0.0835776 | ||||||||
\(785\) | 3.82377i | 0.136476i | ||||||||
\(786\) | − | 9.10957i | − | 0.324928i | ||||||
\(787\) | − | 26.2606i | − | 0.936088i | −0.883705 | − | 0.468044i | \(-0.844959\pi\) | ||
0.883705 | − | 0.468044i | \(-0.155041\pi\) | |||||||
\(788\) | − | 11.0517i | − | 0.393701i | ||||||
\(789\) | −6.56585 | −0.233750 | ||||||||
\(790\) | 1.51867 | 0.0540319 | ||||||||
\(791\) | − | 12.8082i | − | 0.455406i | ||||||
\(792\) | 6.92162 | 0.245949 | ||||||||
\(793\) | −20.9093 | − | 15.7587i | −0.742512 | − | 0.559609i | ||||
\(794\) | −9.44399 | −0.335155 | ||||||||
\(795\) | − | 0.405220i | − | 0.0143717i | ||||||
\(796\) | 10.2823 | 0.364447 | ||||||||
\(797\) | 44.0677 | 1.56096 | 0.780479 | − | 0.625182i | \(-0.214975\pi\) | ||||
0.780479 | + | 0.625182i | \(0.214975\pi\) | |||||||
\(798\) | − | 2.72979i | − | 0.0966337i | ||||||
\(799\) | 26.6297i | 0.942090i | ||||||||
\(800\) | 16.3668i | 0.578655i | ||||||||
\(801\) | − | 14.7165i | − | 0.519981i | ||||||
\(802\) | −15.0205 | −0.530393 | ||||||||
\(803\) | −0.293378 | −0.0103531 | ||||||||
\(804\) | 1.72753i | 0.0609252i | ||||||||
\(805\) | 2.32684 | 0.0820104 | ||||||||
\(806\) | −22.9132 | − | 17.2690i | −0.807083 | − | 0.608274i | ||||
\(807\) | −5.95652 | −0.209679 | ||||||||
\(808\) | − | 11.2183i | − | 0.394659i | ||||||
\(809\) | −8.07838 | −0.284021 | −0.142010 | − | 0.989865i | \(-0.545357\pi\) | ||||
−0.142010 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(810\) | 3.48747 | 0.122537 | ||||||||
\(811\) | 38.0098i | 1.33471i | 0.744742 | + | 0.667353i | \(0.232573\pi\) | ||||
−0.744742 | + | 0.667353i | \(0.767427\pi\) | |||||||
\(812\) | − | 0.165166i | − | 0.00579619i | ||||||
\(813\) | 5.89657i | 0.206802i | ||||||||
\(814\) | − | 9.23513i | − | 0.323691i | ||||||
\(815\) | 0.183417 | 0.00642483 | ||||||||
\(816\) | −3.63317 | −0.127186 | ||||||||
\(817\) | − | 1.81100i | − | 0.0633590i | ||||||
\(818\) | −21.9409 | −0.767146 | ||||||||
\(819\) | 5.87936 | − | 7.80098i | 0.205442 | − | 0.272588i | ||||
\(820\) | 1.94214 | 0.0678225 | ||||||||
\(821\) | 13.7542i | 0.480025i | 0.970770 | + | 0.240012i | \(0.0771515\pi\) | ||||
−0.970770 | + | 0.240012i | \(0.922849\pi\) | |||||||
\(822\) | −10.3668 | −0.361585 | ||||||||
\(823\) | −9.91935 | −0.345767 | −0.172883 | − | 0.984942i | \(-0.555308\pi\) | ||||
−0.172883 | + | 0.984942i | \(0.555308\pi\) | |||||||
\(824\) | − | 55.2327i | − | 1.92412i | ||||||
\(825\) | 2.14238i | 0.0745881i | ||||||||
\(826\) | − | 3.26180i | − | 0.113492i | ||||||
\(827\) | 3.77101i | 0.131131i | 0.997848 | + | 0.0655654i | \(0.0208851\pi\) | ||||
−0.997848 | + | 0.0655654i | \(0.979115\pi\) | |||||||
\(828\) | 8.63090 | 0.299944 | ||||||||
\(829\) | 11.5187 | 0.400060 | 0.200030 | − | 0.979790i | \(-0.435896\pi\) | ||||
0.200030 | + | 0.979790i | \(0.435896\pi\) | |||||||
\(830\) | − | 5.59478i | − | 0.194198i | ||||||
\(831\) | 14.0833 | 0.488544 | ||||||||
\(832\) | 24.9939 | + | 18.8371i | 0.866506 | + | 0.653059i | ||||
\(833\) | −2.87936 | −0.0997640 | ||||||||
\(834\) | 8.34017i | 0.288797i | ||||||||
\(835\) | −11.0000 | −0.380671 | ||||||||
\(836\) | 2.26549 | 0.0783537 | ||||||||
\(837\) | 20.9360i | 0.723654i | ||||||||
\(838\) | 27.6514i | 0.955202i | ||||||||
\(839\) | − | 43.6475i | − | 1.50688i | −0.657516 | − | 0.753440i | \(-0.728393\pi\) | ||
0.657516 | − | 0.753440i | \(-0.271607\pi\) | |||||||
\(840\) | − | 0.764867i | − | 0.0263904i | ||||||
\(841\) | −28.9315 | −0.997637 | ||||||||
\(842\) | −22.7610 | −0.784396 | ||||||||
\(843\) | − | 2.58986i | − | 0.0891995i | ||||||
\(844\) | 1.70928 | 0.0588357 | ||||||||
\(845\) | 5.75872 | − | 1.65037i | 0.198106 | − | 0.0567745i | ||||
\(846\) | 29.3184 | 1.00799 | ||||||||
\(847\) | − | 10.3112i | − | 0.354299i | ||||||
\(848\) | −3.81658 | −0.131062 | ||||||||
\(849\) | −0.528125 | −0.0181252 | ||||||||
\(850\) | 16.1301i | 0.553258i | ||||||||
\(851\) | − | 48.0216i | − | 1.64616i | ||||||
\(852\) | − | 4.34471i | − | 0.148847i | ||||||
\(853\) | − | 10.0940i | − | 0.345611i | −0.984956 | − | 0.172806i | \(-0.944717\pi\) | ||
0.984956 | − | 0.172806i | \(-0.0552832\pi\) | |||||||
\(854\) | 8.49693 | 0.290759 | ||||||||
\(855\) | 5.40191 | 0.184741 | ||||||||
\(856\) | 9.06400i | 0.309801i | ||||||||
\(857\) | 24.0267 | 0.820735 | 0.410368 | − | 0.911920i | \(-0.365400\pi\) | ||||
0.410368 | + | 0.911920i | \(0.365400\pi\) | |||||||
\(858\) | 1.50761 | + | 1.13624i | 0.0514688 | + | 0.0387905i | ||||
\(859\) | −1.65983 | −0.0566326 | −0.0283163 | − | 0.999599i | \(-0.509015\pi\) | ||||
−0.0283163 | + | 0.999599i | \(0.509015\pi\) | |||||||
\(860\) | − | 0.121683i | − | 0.00414936i | ||||||
\(861\) | 3.60197 | 0.122755 | ||||||||
\(862\) | −21.1773 | −0.721301 | ||||||||
\(863\) | 28.6270i | 0.974475i | 0.873269 | + | 0.487238i | \(0.161995\pi\) | ||||
−0.873269 | + | 0.487238i | \(0.838005\pi\) | |||||||
\(864\) | − | 10.5236i | − | 0.358020i | ||||||
\(865\) | 11.9350i | 0.405801i | ||||||||
\(866\) | − | 24.0312i | − | 0.816613i | ||||||
\(867\) | −4.69594 | −0.159483 | ||||||||
\(868\) | −4.29072 | −0.145637 | ||||||||
\(869\) | 2.33752i | 0.0792949i | ||||||||
\(870\) | 0.0761103 | 0.00258038 | ||||||||
\(871\) | 11.0205 | − | 14.6225i | 0.373416 | − | 0.495464i | ||||
\(872\) | 25.9565 | 0.878999 | ||||||||
\(873\) | − | 34.1617i | − | 1.15620i | ||||||
\(874\) | −25.5642 | −0.864723 | ||||||||
\(875\) | −4.51026 | −0.152475 | ||||||||
\(876\) | 0.120252i | 0.00406296i | ||||||||
\(877\) | 40.8587i | 1.37970i | 0.723953 | + | 0.689850i | \(0.242323\pi\) | ||||
−0.723953 | + | 0.689850i | \(0.757677\pi\) | |||||||
\(878\) | 31.5486i | 1.06472i | ||||||||
\(879\) | 13.1168i | 0.442417i | ||||||||
\(880\) | −0.894960 | −0.0301691 | ||||||||
\(881\) | −48.5835 | −1.63682 | −0.818411 | − | 0.574634i | \(-0.805144\pi\) | ||||
−0.818411 | + | 0.574634i | \(0.805144\pi\) | |||||||
\(882\) | 3.17009i | 0.106742i | ||||||||
\(883\) | 49.2456 | 1.65725 | 0.828624 | − | 0.559806i | \(-0.189124\pi\) | ||||
0.828624 | + | 0.559806i | \(0.189124\pi\) | |||||||
\(884\) | −5.23060 | − | 3.94214i | −0.175924 | − | 0.132589i | ||||
\(885\) | −0.692632 | −0.0232826 | ||||||||
\(886\) | 30.9021i | 1.03818i | ||||||||
\(887\) | −13.1773 | −0.442450 | −0.221225 | − | 0.975223i | \(-0.571005\pi\) | ||||
−0.221225 | + | 0.975223i | \(0.571005\pi\) | |||||||
\(888\) | −15.7854 | −0.529723 | ||||||||
\(889\) | − | 13.4680i | − | 0.451702i | ||||||
\(890\) | 2.92881i | 0.0981739i | ||||||||
\(891\) | 5.36788i | 0.179831i | ||||||||
\(892\) | 12.4885i | 0.418147i | ||||||||
\(893\) | 40.0166 | 1.33911 | ||||||||
\(894\) | 12.9360 | 0.432644 | ||||||||
\(895\) | 9.52690i | 0.318449i | ||||||||
\(896\) | −3.31965 | −0.110902 | ||||||||
\(897\) | 7.83937 | + | 5.90829i | 0.261749 | + | 0.197272i | ||||
\(898\) | −36.7792 | −1.22734 | ||||||||
\(899\) | − | 1.78047i | − | 0.0593818i | ||||||
\(900\) | −8.18342 | −0.272781 | ||||||||
\(901\) | 4.69594 | 0.156445 | ||||||||
\(902\) | − | 6.48709i | − | 0.215996i | ||||||
\(903\) | − | 0.225678i | − | 0.00751009i | ||||||
\(904\) | 39.4284i | 1.31137i | ||||||||
\(905\) | 7.24232i | 0.240743i | ||||||||
\(906\) | 1.00614 | 0.0334269 | ||||||||
\(907\) | −15.3051 | −0.508198 | −0.254099 | − | 0.967178i | \(-0.581779\pi\) | ||||
−0.254099 | + | 0.967178i | \(0.581779\pi\) | |||||||
\(908\) | − | 8.36683i | − | 0.277663i | ||||||
\(909\) | 9.87322 | 0.327474 | ||||||||
\(910\) | −1.17009 | + | 1.55252i | −0.0387880 | + | 0.0514655i | ||||
\(911\) | −5.07223 | −0.168051 | −0.0840253 | − | 0.996464i | \(-0.526778\pi\) | ||||
−0.0840253 | + | 0.996464i | \(0.526778\pi\) | |||||||
\(912\) | 5.45959i | 0.180785i | ||||||||
\(913\) | 8.61142 | 0.284997 | ||||||||
\(914\) | 21.1377 | 0.699172 | ||||||||
\(915\) | − | 1.80430i | − | 0.0596482i | ||||||
\(916\) | − | 17.5441i | − | 0.579674i | ||||||
\(917\) | 14.4391i | 0.476820i | ||||||||
\(918\) | − | 10.3714i | − | 0.342306i | ||||||
\(919\) | −46.3689 | −1.52957 | −0.764785 | − | 0.644286i | \(-0.777155\pi\) | ||||
−0.764785 | + | 0.644286i | \(0.777155\pi\) | |||||||
\(920\) | −7.16290 | −0.236154 | ||||||||
\(921\) | − | 3.35350i | − | 0.110502i | ||||||
\(922\) | 27.0037 | 0.889319 | ||||||||
\(923\) | −27.7165 | + | 36.7754i | −0.912299 | + | 1.21048i | ||||
\(924\) | 0.282314 | 0.00928745 | ||||||||
\(925\) | 45.5318i | 1.49708i | ||||||||
\(926\) | −5.32108 | −0.174862 | ||||||||
\(927\) | 48.6102 | 1.59657 | ||||||||
\(928\) | 0.894960i | 0.0293785i | ||||||||
\(929\) | 23.4547i | 0.769523i | 0.923016 | + | 0.384761i | \(0.125716\pi\) | ||||
−0.923016 | + | 0.384761i | \(0.874284\pi\) | |||||||
\(930\) | − | 1.97721i | − | 0.0648354i | ||||||
\(931\) | 4.32684i | 0.141807i | ||||||||
\(932\) | 8.43310 | 0.276236 | ||||||||
\(933\) | 13.5381 | 0.443219 | ||||||||
\(934\) | − | 44.2472i | − | 1.44781i | ||||||
\(935\) | 1.10116 | 0.0360119 | ||||||||
\(936\) | −18.0989 | + | 24.0144i | −0.591581 | + | 0.784934i | ||||
\(937\) | −18.0156 | −0.588544 | −0.294272 | − | 0.955722i | \(-0.595077\pi\) | ||||
−0.294272 | + | 0.955722i | \(0.595077\pi\) | |||||||
\(938\) | 5.94214i | 0.194018i | ||||||||
\(939\) | 1.20781 | 0.0394155 | ||||||||
\(940\) | 2.68876 | 0.0876976 | ||||||||
\(941\) | 31.7805i | 1.03601i | 0.855377 | + | 0.518007i | \(0.173326\pi\) | ||||
−0.855377 | + | 0.518007i | \(0.826674\pi\) | |||||||
\(942\) | − | 5.23513i | − | 0.170570i | ||||||
\(943\) | − | 33.7321i | − | 1.09847i | ||||||
\(944\) | 6.52359i | 0.212325i | ||||||||
\(945\) | 1.41855 | 0.0461455 | ||||||||
\(946\) | −0.406442 | −0.0132146 | ||||||||
\(947\) | − | 46.3812i | − | 1.50719i | −0.657341 | − | 0.753593i | \(-0.728319\pi\) | ||
0.657341 | − | 0.753593i | \(-0.271681\pi\) | |||||||
\(948\) | 0.958125 | 0.0311185 | ||||||||
\(949\) | 0.767134 | − | 1.01787i | 0.0249022 | − | 0.0330413i | ||||
\(950\) | 24.2388 | 0.786412 | ||||||||
\(951\) | 1.56093i | 0.0506166i | ||||||||
\(952\) | 8.86376 | 0.287276 | ||||||||
\(953\) | 27.2511 | 0.882750 | 0.441375 | − | 0.897323i | \(-0.354491\pi\) | ||||
0.441375 | + | 0.897323i | \(0.354491\pi\) | |||||||
\(954\) | − | 5.17009i | − | 0.167388i | ||||||
\(955\) | 7.73594i | 0.250329i | ||||||||
\(956\) | 5.49323i | 0.177664i | ||||||||
\(957\) | 0.117148i | 0.00378686i | ||||||||
\(958\) | −10.8117 | −0.349309 | ||||||||
\(959\) | 16.4319 | 0.530613 | ||||||||
\(960\) | 2.15676i | 0.0696090i | ||||||||
\(961\) | −15.2534 | −0.492045 | ||||||||
\(962\) | 32.0410 | + | 24.1483i | 1.03304 | + | 0.778574i | ||||
\(963\) | −7.97721 | −0.257062 | ||||||||
\(964\) | 10.6818i | 0.344037i | ||||||||
\(965\) | −9.22285 | −0.296894 | ||||||||
\(966\) | −3.18568 | −0.102498 | ||||||||
\(967\) | 9.77045i | 0.314196i | 0.987583 | + | 0.157098i | \(0.0502139\pi\) | ||||
−0.987583 | + | 0.157098i | \(0.949786\pi\) | |||||||
\(968\) | 31.7419i | 1.02022i | ||||||||
\(969\) | − | 6.71751i | − | 0.215797i | ||||||
\(970\) | 6.79872i | 0.218294i | ||||||||
\(971\) | −13.9856 | −0.448820 | −0.224410 | − | 0.974495i | \(-0.572045\pi\) | ||||
−0.224410 | + | 0.974495i | \(0.572045\pi\) | |||||||
\(972\) | 8.02666 | 0.257455 | ||||||||
\(973\) | − | 13.2195i | − | 0.423799i | ||||||
\(974\) | −15.9832 | −0.512134 | ||||||||
\(975\) | −7.43293 | − | 5.60197i | −0.238044 | − | 0.179407i | ||||
\(976\) | −16.9939 | −0.543960 | ||||||||
\(977\) | − | 54.7454i | − | 1.75146i | −0.482801 | − | 0.875730i | \(-0.660381\pi\) | ||
0.482801 | − | 0.875730i | \(-0.339619\pi\) | |||||||
\(978\) | −0.251117 | −0.00802985 | ||||||||
\(979\) | −4.50799 | −0.144076 | ||||||||
\(980\) | 0.290725i | 0.00928686i | ||||||||
\(981\) | 22.8443i | 0.729362i | ||||||||
\(982\) | 34.6947i | 1.10715i | ||||||||
\(983\) | − | 0.0399930i | − | 0.00127558i | −1.00000 | 0.000637789i | \(-0.999797\pi\) | |||
1.00000 | 0.000637789i | \(-0.000203015\pi\) | ||||||||
\(984\) | −11.0882 | −0.353480 | ||||||||
\(985\) | −8.07223 | −0.257203 | ||||||||
\(986\) | 0.882015i | 0.0280891i | ||||||||
\(987\) | 4.98667 | 0.158727 | ||||||||
\(988\) | −5.92389 | + | 7.86007i | −0.188464 | + | 0.250062i | ||||
\(989\) | −2.11345 | −0.0672038 | ||||||||
\(990\) | − | 1.21235i | − | 0.0385309i | ||||||
\(991\) | 53.9481 | 1.71372 | 0.856859 | − | 0.515551i | \(-0.172413\pi\) | ||||
0.856859 | + | 0.515551i | \(0.172413\pi\) | |||||||
\(992\) | 23.2495 | 0.738173 | ||||||||
\(993\) | 2.29460i | 0.0728169i | ||||||||
\(994\) | − | 14.9444i | − | 0.474008i | ||||||
\(995\) | − | 7.51026i | − | 0.238091i | ||||||
\(996\) | − | 3.52973i | − | 0.111844i | ||||||
\(997\) | 42.0554 | 1.33191 | 0.665954 | − | 0.745993i | \(-0.268025\pi\) | ||||
0.665954 | + | 0.745993i | \(0.268025\pi\) | |||||||
\(998\) | 41.5669 | 1.31578 | ||||||||
\(999\) | − | 29.2762i | − | 0.926257i |
(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 | 91.2.c.a.64.5 | yes | 6 | |
3.2 | odd | 2 | 819.2.c.b.64.2 | 6 | |||
4.3 | odd | 2 | 1456.2.k.c.337.3 | 6 | |||
7.2 | even | 3 | 637.2.r.e.116.5 | 12 | |||
7.3 | odd | 6 | 637.2.r.d.324.2 | 12 | |||
7.4 | even | 3 | 637.2.r.e.324.2 | 12 | |||
7.5 | odd | 6 | 637.2.r.d.116.5 | 12 | |||
7.6 | odd | 2 | 637.2.c.d.246.5 | 6 | |||
13.5 | odd | 4 | 1183.2.a.h.1.3 | 3 | |||
13.8 | odd | 4 | 1183.2.a.j.1.1 | 3 | |||
13.12 | even | 2 | inner | 91.2.c.a.64.2 | ✓ | 6 | |
39.38 | odd | 2 | 819.2.c.b.64.5 | 6 | |||
52.51 | odd | 2 | 1456.2.k.c.337.4 | 6 | |||
91.12 | odd | 6 | 637.2.r.d.116.2 | 12 | |||
91.25 | even | 6 | 637.2.r.e.324.5 | 12 | |||
91.34 | even | 4 | 8281.2.a.bi.1.1 | 3 | |||
91.38 | odd | 6 | 637.2.r.d.324.5 | 12 | |||
91.51 | even | 6 | 637.2.r.e.116.2 | 12 | |||
91.83 | even | 4 | 8281.2.a.be.1.3 | 3 | |||
91.90 | odd | 2 | 637.2.c.d.246.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.c.a.64.2 | ✓ | 6 | 13.12 | even | 2 | inner | |
91.2.c.a.64.5 | yes | 6 | 1.1 | even | 1 | trivial | |
637.2.c.d.246.2 | 6 | 91.90 | odd | 2 | |||
637.2.c.d.246.5 | 6 | 7.6 | odd | 2 | |||
637.2.r.d.116.2 | 12 | 91.12 | odd | 6 | |||
637.2.r.d.116.5 | 12 | 7.5 | odd | 6 | |||
637.2.r.d.324.2 | 12 | 7.3 | odd | 6 | |||
637.2.r.d.324.5 | 12 | 91.38 | odd | 6 | |||
637.2.r.e.116.2 | 12 | 91.51 | even | 6 | |||
637.2.r.e.116.5 | 12 | 7.2 | even | 3 | |||
637.2.r.e.324.2 | 12 | 7.4 | even | 3 | |||
637.2.r.e.324.5 | 12 | 91.25 | even | 6 | |||
819.2.c.b.64.2 | 6 | 3.2 | odd | 2 | |||
819.2.c.b.64.5 | 6 | 39.38 | odd | 2 | |||
1183.2.a.h.1.3 | 3 | 13.5 | odd | 4 | |||
1183.2.a.j.1.1 | 3 | 13.8 | odd | 4 | |||
1456.2.k.c.337.3 | 6 | 4.3 | odd | 2 | |||
1456.2.k.c.337.4 | 6 | 52.51 | odd | 2 | |||
8281.2.a.be.1.3 | 3 | 91.83 | even | 4 | |||
8281.2.a.bi.1.1 | 3 | 91.34 | even | 4 |