Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), 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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 30 x^{10} - 53 x^{9} + 798 x^{8} - 1096 x^{7} + 4060 x^{6} - 915 x^{5} + 10392 x^{4} - 7038 x^{3} + 4869 x^{2} - 675 x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.1 | ||
Root | \(-2.64313 + 4.57803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.841 |
Dual form | 4020.2.q.j.3781.1 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.33998 | + | 4.05297i | −0.884430 | + | 1.53188i | −0.0380644 | + | 0.999275i | \(0.512119\pi\) |
−0.846366 | + | 0.532602i | \(0.821214\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.04957 | − | 3.54996i | 0.617968 | − | 1.07035i | −0.371888 | − | 0.928278i | \(-0.621289\pi\) |
0.989856 | − | 0.142075i | \(-0.0453773\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.405657 | + | 0.702619i | 0.0983864 | + | 0.170410i | 0.911017 | − | 0.412369i | \(-0.135299\pi\) |
−0.812631 | + | 0.582779i | \(0.801965\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.42209 | − | 2.46313i | −0.326250 | − | 0.565081i | 0.655515 | − | 0.755182i | \(-0.272452\pi\) |
−0.981764 | + | 0.190101i | \(0.939118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.33998 | + | 4.05297i | −0.510626 | + | 0.884430i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.18790 | + | 3.78956i | 0.456209 | + | 0.790178i | 0.998757 | − | 0.0498475i | \(-0.0158735\pi\) |
−0.542548 | + | 0.840025i | \(0.682540\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.40150 | + | 7.62362i | −0.817338 | + | 1.41567i | 0.0902986 | + | 0.995915i | \(0.471218\pi\) |
−0.907637 | + | 0.419756i | \(0.862115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.131676 | − | 0.228069i | 0.0236496 | − | 0.0409624i | −0.853958 | − | 0.520341i | \(-0.825805\pi\) |
0.877608 | + | 0.479379i | \(0.159138\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.04957 | − | 3.54996i | 0.356784 | − | 0.617968i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.33998 | − | 4.05297i | 0.395529 | − | 0.685077i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.572659 | − | 0.991874i | −0.0941445 | − | 0.163063i | 0.815107 | − | 0.579311i | \(-0.196678\pi\) |
−0.909251 | + | 0.416248i | \(0.863345\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.81958 | + | 3.15160i | −0.284170 | + | 0.492198i | −0.972408 | − | 0.233288i | \(-0.925051\pi\) |
0.688237 | + | 0.725486i | \(0.258385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.155822 | −0.0237627 | −0.0118813 | − | 0.999929i | \(-0.503782\pi\) | ||||
−0.0118813 | + | 0.999929i | \(0.503782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.69187 | + | 2.93041i | −0.246785 | + | 0.427445i | −0.962632 | − | 0.270813i | \(-0.912708\pi\) |
0.715847 | + | 0.698257i | \(0.246041\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.45103 | − | 12.9056i | −1.06443 | − | 1.84365i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.405657 | + | 0.702619i | 0.0568034 | + | 0.0983864i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.736649 | −0.101187 | −0.0505933 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505933 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.04957 | + | 3.54996i | −0.276364 | + | 0.478676i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.42209 | − | 2.46313i | −0.188360 | − | 0.326250i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.35790 | 0.437162 | 0.218581 | − | 0.975819i | \(-0.429857\pi\) | ||||
0.218581 | + | 0.975819i | \(0.429857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.373303 | + | 0.646580i | 0.0477966 | + | 0.0827861i | 0.888934 | − | 0.458035i | \(-0.151447\pi\) |
−0.841137 | + | 0.540822i | \(0.818113\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.33998 | + | 4.05297i | −0.294810 | + | 0.510626i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.500000 | − | 0.866025i | −0.0620174 | − | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.03665 | − | 1.55314i | −0.981833 | − | 0.189746i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.18790 | + | 3.78956i | 0.263393 | + | 0.456209i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60329 | − | 2.77699i | 0.190276 | − | 0.329568i | −0.755066 | − | 0.655649i | \(-0.772395\pi\) |
0.945342 | + | 0.326082i | \(0.105728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.76087 | + | 8.24608i | 0.557218 | + | 0.965130i | 0.997727 | + | 0.0673821i | \(0.0214646\pi\) |
−0.440509 | + | 0.897748i | \(0.645202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.59191 | + | 16.6137i | 1.09310 | + | 1.89330i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.82437 | + | 10.0881i | −0.655293 | + | 1.13500i | 0.326527 | + | 0.945188i | \(0.394122\pi\) |
−0.981820 | + | 0.189813i | \(0.939212\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.18900 | + | 10.7197i | 0.679331 | + | 1.17664i | 0.975183 | + | 0.221402i | \(0.0710632\pi\) |
−0.295852 | + | 0.955234i | \(0.595603\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.405657 | − | 0.702619i | −0.0439997 | − | 0.0762097i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.40150 | + | 7.62362i | −0.471890 | + | 0.817338i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.1087 | −1.38952 | −0.694761 | − | 0.719241i | \(-0.744490\pi\) | ||||
−0.694761 | + | 0.719241i | \(0.744490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.67996 | −0.490593 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.131676 | − | 0.228069i | 0.0136541 | − | 0.0236496i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.42209 | + | 2.46313i | 0.145903 | + | 0.252712i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.60393 | − | 16.6345i | −0.975131 | − | 1.68898i | −0.679501 | − | 0.733675i | \(-0.737804\pi\) |
−0.295631 | − | 0.955302i | \(-0.595530\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.04957 | − | 3.54996i | 0.205989 | − | 0.356784i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00397 | + | 1.73893i | −0.0998989 | + | 0.173030i | −0.911643 | − | 0.410984i | \(-0.865185\pi\) |
0.811744 | + | 0.584014i | \(0.198519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.39205 | − | 9.33931i | 0.531295 | − | 0.920229i | −0.468038 | − | 0.883708i | \(-0.655039\pi\) |
0.999333 | − | 0.0365212i | \(-0.0116276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.33998 | − | 4.05297i | 0.228359 | − | 0.395529i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.27630 | −0.703426 | −0.351713 | − | 0.936108i | \(-0.614401\pi\) | ||||
−0.351713 | + | 0.936108i | \(0.614401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.59298 | −0.918840 | −0.459420 | − | 0.888219i | \(-0.651943\pi\) | ||||
−0.459420 | + | 0.888219i | \(0.651943\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.572659 | − | 0.991874i | −0.0543544 | − | 0.0941445i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.13168 | − | 1.96012i | 0.106459 | − | 0.184393i | −0.807874 | − | 0.589355i | \(-0.799382\pi\) |
0.914333 | + | 0.404962i | \(0.132715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.18790 | − | 3.78956i | −0.204023 | − | 0.353378i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.79692 | −0.348063 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.90146 | − | 5.02548i | −0.263769 | − | 0.456862i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.81958 | + | 3.15160i | −0.164066 | + | 0.284170i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.47244 | + | 6.01444i | −0.308129 | + | 0.533695i | −0.977953 | − | 0.208825i | \(-0.933036\pi\) |
0.669824 | + | 0.742520i | \(0.266370\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.155822 | −0.0137194 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3695 | −1.51758 | −0.758791 | − | 0.651334i | \(-0.774210\pi\) | ||||
−0.758791 | + | 0.651334i | \(0.774210\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.3106 | 1.15418 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9359 | 1.10519 | 0.552595 | − | 0.833450i | \(-0.313638\pi\) | ||||
0.552595 | + | 0.833450i | \(0.313638\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.1973 | −1.71311 | −0.856555 | − | 0.516055i | \(-0.827400\pi\) | ||||
−0.856555 | + | 0.516055i | \(0.827400\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.69187 | + | 2.93041i | −0.142482 | + | 0.246785i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.09914 | 0.342787 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.40150 | − | 7.62362i | 0.365525 | − | 0.633107i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.45103 | − | 12.9056i | −0.614551 | − | 1.06443i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.1440 | −1.89603 | −0.948013 | − | 0.318231i | \(-0.896911\pi\) | ||||
−0.948013 | + | 0.318231i | \(0.896911\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.32638 | + | 10.9576i | 0.514833 | + | 0.891717i | 0.999852 | + | 0.0172135i | \(0.00547950\pi\) |
−0.485019 | + | 0.874504i | \(0.661187\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.405657 | + | 0.702619i | 0.0327955 | + | 0.0568034i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.131676 | + | 0.228069i | −0.0105764 | + | 0.0183189i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.72579 | − | 2.98916i | −0.137733 | − | 0.238561i | 0.788905 | − | 0.614515i | \(-0.210648\pi\) |
−0.926638 | + | 0.375954i | \(0.877315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.736649 | −0.0584201 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.4786 | −1.61394 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3321 | + | 17.8958i | −0.809275 | + | 1.40170i | 0.104092 | + | 0.994568i | \(0.466806\pi\) |
−0.913367 | + | 0.407137i | \(0.866527\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.04957 | + | 3.54996i | −0.159559 | + | 0.276364i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.4986 | + | 21.6483i | −0.967173 | + | 1.67519i | −0.263513 | + | 0.964656i | \(0.584881\pi\) |
−0.703660 | + | 0.710537i | \(0.748452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.42209 | − | 2.46313i | −0.108750 | − | 0.188360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.90917 | + | 10.2350i | 0.449266 | + | 0.778151i | 0.998338 | − | 0.0576233i | \(-0.0183522\pi\) |
−0.549072 | + | 0.835775i | \(0.685019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.33998 | + | 4.05297i | −0.176886 | + | 0.306376i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.35790 | 0.252396 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.1659 | −0.984063 | −0.492032 | − | 0.870577i | \(-0.663746\pi\) | ||||
−0.492032 | + | 0.870577i | \(0.663746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.319852 | + | 0.553999i | −0.0237744 | + | 0.0411785i | −0.877668 | − | 0.479269i | \(-0.840902\pi\) |
0.853893 | + | 0.520448i | \(0.174235\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.373303 | + | 0.646580i | 0.0275954 | + | 0.0477966i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.572659 | + | 0.991874i | 0.0421027 | + | 0.0729240i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.32569 | 0.243199 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.33998 | + | 4.05297i | −0.170209 | + | 0.294810i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.19598 | − | 14.1959i | −0.593040 | − | 1.02718i | −0.993820 | − | 0.111002i | \(-0.964594\pi\) |
0.400780 | − | 0.916174i | \(-0.368739\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.88217 | 0.711334 | 0.355667 | − | 0.934613i | \(-0.384254\pi\) | ||||
0.355667 | + | 0.934613i | \(0.384254\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.500000 | − | 0.866025i | −0.0358057 | − | 0.0620174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.30338 | + | 2.25751i | −0.0928617 | + | 0.160841i | −0.908714 | − | 0.417419i | \(-0.862935\pi\) |
0.815852 | + | 0.578260i | \(0.196268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.81017 | − | 16.9917i | −0.695424 | − | 1.20451i | −0.970037 | − | 0.242956i | \(-0.921883\pi\) |
0.274613 | − | 0.961555i | \(-0.411450\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.03665 | − | 1.55314i | −0.566862 | − | 0.109550i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.5989 | − | 35.6783i | −1.44576 | − | 2.50412i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.81958 | − | 3.15160i | 0.127085 | − | 0.220117i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.18790 | + | 3.78956i | 0.152070 | + | 0.263393i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6587 | −0.806447 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.30716 | + | 9.19227i | 0.365360 | + | 0.632822i | 0.988834 | − | 0.149022i | \(-0.0476126\pi\) |
−0.623474 | + | 0.781844i | \(0.714279\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.60329 | − | 2.77699i | 0.109856 | − | 0.190276i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.155822 | 0.0106270 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.616237 | + | 1.06735i | 0.0418329 | + | 0.0724567i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.76087 | + | 8.24608i | 0.321710 | + | 0.557218i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.405657 | + | 0.702619i | −0.0272875 | + | 0.0472633i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.92598 | 0.530763 | 0.265382 | − | 0.964143i | \(-0.414502\pi\) | ||||
0.265382 | + | 0.964143i | \(0.414502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.84617 | + | 10.1259i | −0.388024 | + | 0.672077i | −0.992184 | − | 0.124786i | \(-0.960176\pi\) |
0.604160 | + | 0.796863i | \(0.293509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1270 | + | 21.0045i | 0.801374 | + | 1.38802i | 0.918712 | + | 0.394928i | \(0.129230\pi\) |
−0.117339 | + | 0.993092i | \(0.537436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.59191 | + | 16.6137i | 0.631101 | + | 1.09310i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.42684 | + | 2.47137i | −0.0934756 | + | 0.161905i | −0.908971 | − | 0.416859i | \(-0.863131\pi\) |
0.815496 | + | 0.578763i | \(0.196464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.69187 | − | 2.93041i | 0.110366 | − | 0.191159i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.82437 | + | 10.0881i | −0.378334 | + | 0.655293i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.17038 | − | 2.02715i | 0.0757053 | − | 0.131125i | −0.825687 | − | 0.564128i | \(-0.809213\pi\) |
0.901393 | + | 0.433002i | \(0.142546\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.784474 | −0.0505324 | −0.0252662 | − | 0.999681i | \(-0.508043\pi\) | ||||
−0.0252662 | + | 0.999681i | \(0.508043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.45103 | + | 12.9056i | 0.476029 | + | 0.824506i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.42209 | − | 2.46313i | 0.0904854 | − | 0.156725i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.18900 | + | 10.7197i | 0.392212 | + | 0.679331i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.7408 | + | 23.7998i | 0.867311 | + | 1.50223i | 0.864734 | + | 0.502231i | \(0.167487\pi\) |
0.00257757 | + | 0.999997i | \(0.499180\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.9370 | 1.12769 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.405657 | − | 0.702619i | −0.0254032 | − | 0.0439997i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.3528 | − | 19.6637i | 0.708169 | − | 1.22658i | −0.257366 | − | 0.966314i | \(-0.582855\pi\) |
0.965536 | − | 0.260271i | \(-0.0838119\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.36004 | 0.333057 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.40150 | + | 7.62362i | −0.272446 | + | 0.471890i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.16533 | 0.256845 | 0.128423 | − | 0.991720i | \(-0.459009\pi\) | ||||
0.128423 | + | 0.991720i | \(0.459009\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.736649 | 0.0452520 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.1087 | −0.802241 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.9014 | −0.969527 | −0.484764 | − | 0.874645i | \(-0.661094\pi\) | ||||
−0.484764 | + | 0.874645i | \(0.661094\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.3621 | 1.66213 | 0.831065 | − | 0.556175i | \(-0.187732\pi\) | ||||
0.831065 | + | 0.556175i | \(0.187732\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.67996 | −0.283244 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.04957 | − | 3.54996i | 0.123594 | − | 0.214070i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3919 | −0.804640 | −0.402320 | − | 0.915499i | \(-0.631796\pi\) | ||||
−0.402320 | + | 0.915499i | \(0.631796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.131676 | − | 0.228069i | 0.00788321 | − | 0.0136541i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4785 | + | 21.6133i | 0.744402 | + | 1.28934i | 0.950474 | + | 0.310806i | \(0.100599\pi\) |
−0.206071 | + | 0.978537i | \(0.566068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.580906 | −0.0345313 | −0.0172656 | − | 0.999851i | \(-0.505496\pi\) | ||||
−0.0172656 | + | 0.999851i | \(0.505496\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.42209 | + | 2.46313i | 0.0842373 | + | 0.145903i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.51556 | − | 14.7494i | −0.502658 | − | 0.870629i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17088 | − | 14.1524i | 0.480640 | − | 0.832493i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.60393 | − | 16.6345i | −0.562992 | − | 0.975131i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.08517 | −0.530761 | −0.265381 | − | 0.964144i | \(-0.585498\pi\) | ||||
−0.265381 | + | 0.964144i | \(0.585498\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.35790 | −0.195505 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.04957 | − | 3.54996i | 0.118928 | − | 0.205989i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.18790 | + | 3.78956i | −0.126530 | + | 0.219156i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.364621 | − | 0.631542i | 0.0210164 | − | 0.0364015i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.00397 | + | 1.73893i | −0.0576767 | + | 0.0998989i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.373303 | − | 0.646580i | −0.0213753 | − | 0.0370231i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.85294 | + | 11.8696i | 0.391118 | + | 0.677437i | 0.992597 | − | 0.121452i | \(-0.0387550\pi\) |
−0.601479 | + | 0.798889i | \(0.705422\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.39205 | − | 9.33931i | 0.306743 | − | 0.531295i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.5669 | 0.655901 | 0.327950 | − | 0.944695i | \(-0.393642\pi\) | ||||
0.327950 | + | 0.944695i | \(0.393642\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6871 | 0.830163 | 0.415081 | − | 0.909784i | \(-0.363753\pi\) | ||||
0.415081 | + | 0.909784i | \(0.363753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.33998 | − | 4.05297i | 0.131843 | − | 0.228359i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.18470 | + | 3.78401i | 0.122705 | + | 0.212531i | 0.920834 | − | 0.389956i | \(-0.127510\pi\) |
−0.798128 | + | 0.602487i | \(0.794176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0424 | + | 31.2503i | 1.01018 | + | 1.74968i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.27630 | −0.406123 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.15376 | − | 1.99837i | 0.0641970 | − | 0.111192i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.59298 | −0.530493 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.91791 | − | 13.7142i | −0.436529 | − | 0.756090i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.15199 | − | 8.92351i | 0.283179 | − | 0.490480i | −0.688987 | − | 0.724774i | \(-0.741944\pi\) |
0.972166 | + | 0.234293i | \(0.0752776\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.572659 | − | 0.991874i | −0.0313815 | − | 0.0543544i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.03665 | + | 1.55314i | 0.439089 | + | 0.0848572i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.87626 | + | 3.24978i | 0.102207 | + | 0.177027i | 0.912593 | − | 0.408868i | \(-0.134076\pi\) |
−0.810387 | + | 0.585895i | \(0.800743\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.13168 | − | 1.96012i | 0.0614642 | − | 0.106459i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.539756 | − | 0.934885i | −0.0292294 | − | 0.0506269i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 36.9813 | 1.99681 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.18790 | − | 3.78956i | −0.117793 | − | 0.204023i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.308623 | + | 0.534551i | −0.0165678 | + | 0.0286962i | −0.874190 | − | 0.485583i | \(-0.838607\pi\) |
0.857623 | + | 0.514279i | \(0.171941\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.1107 | 1.02297 | 0.511485 | − | 0.859292i | \(-0.329095\pi\) | ||||
0.511485 | + | 0.859292i | \(0.329095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.500000 | + | 0.866025i | 0.0266880 | + | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.37455 | − | 9.30900i | −0.286059 | − | 0.495468i | 0.686807 | − | 0.726840i | \(-0.259012\pi\) |
−0.972865 | + | 0.231372i | \(0.925679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.60329 | + | 2.77699i | −0.0850940 | + | 0.147387i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.79692 | −0.200954 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.3998 | 0.548880 | 0.274440 | − | 0.961604i | \(-0.411508\pi\) | ||||
0.274440 | + | 0.961604i | \(0.411508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.45533 | − | 9.44890i | 0.287122 | − | 0.497311i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.90146 | − | 5.02548i | −0.152287 | − | 0.263769i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.76087 | − | 8.24608i | −0.249196 | − | 0.431619i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.99567 | + | 15.5810i | −0.469570 | + | 0.813319i | −0.999395 | − | 0.0347879i | \(-0.988924\pi\) |
0.529825 | + | 0.848107i | \(0.322258\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.81958 | + | 3.15160i | −0.0947235 | + | 0.164066i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.72375 | − | 2.98561i | 0.0894924 | − | 0.155005i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.92391 | − | 8.52846i | 0.254950 | − | 0.441587i | −0.709932 | − | 0.704271i | \(-0.751274\pi\) |
0.964882 | + | 0.262683i | \(0.0846075\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.80300 | −0.453378 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7497 | + | 29.0113i | 0.860374 | + | 1.49021i | 0.871568 | + | 0.490275i | \(0.163104\pi\) |
−0.0111935 | + | 0.999937i | \(0.503563\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.47244 | + | 6.01444i | −0.177898 | + | 0.308129i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.55000 | − | 11.3449i | −0.334690 | − | 0.579699i | 0.648736 | − | 0.761014i | \(-0.275298\pi\) |
−0.983425 | + | 0.181315i | \(0.941965\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.59191 | − | 16.6137i | −0.488849 | − | 0.846711i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.155822 | −0.00792088 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.20799 | + | 3.82436i | 0.111950 | + | 0.193903i | 0.916556 | − | 0.399906i | \(-0.130957\pi\) |
−0.804607 | + | 0.593808i | \(0.797624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.77508 | + | 3.07452i | −0.0897695 | + | 0.155485i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.3695 | −0.876176 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.82437 | − | 10.0881i | 0.293056 | − | 0.507588i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9026 | 1.09926 | 0.549631 | − | 0.835408i | \(-0.314768\pi\) | ||||
0.549631 | + | 0.835408i | \(0.314768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.3106 | 0.666366 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.5467 | −0.876239 | −0.438120 | − | 0.898917i | \(-0.644355\pi\) | ||||
−0.438120 | + | 0.898917i | \(0.644355\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.263351 | 0.0131185 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.69481 | −0.232713 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.41748 | − | 9.38335i | 0.267877 | − | 0.463977i | −0.700436 | − | 0.713715i | \(-0.747011\pi\) |
0.968313 | + | 0.249738i | \(0.0803445\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.9359 | 0.638082 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.85743 | + | 13.6095i | −0.386639 | + | 0.669678i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.18900 | − | 10.7197i | −0.303806 | − | 0.526207i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.1973 | −0.989065 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.9375 | + | 32.8007i | 0.925158 | + | 1.60242i | 0.791308 | + | 0.611418i | \(0.209401\pi\) |
0.133850 | + | 0.991002i | \(0.457266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.30128 | + | 5.71799i | 0.160895 | + | 0.278678i | 0.935190 | − | 0.354147i | \(-0.115229\pi\) |
−0.774295 | + | 0.632825i | \(0.781895\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.69187 | + | 2.93041i | −0.0822618 | + | 0.142482i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.405657 | + | 0.702619i | 0.0196773 | + | 0.0340820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.49409 | −0.169091 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.09914 | 0.197908 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.84252 | − | 13.5836i | 0.377761 | − | 0.654301i | −0.612975 | − | 0.790102i | \(-0.710027\pi\) |
0.990736 | + | 0.135801i | \(0.0433607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.41965 | − | 11.1192i | 0.308509 | − | 0.534353i | −0.669528 | − | 0.742787i | \(-0.733503\pi\) |
0.978036 | + | 0.208434i | \(0.0668367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.40150 | − | 7.62362i | 0.211036 | − | 0.365525i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.22278 | − | 10.7782i | 0.297676 | − | 0.515590i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7785 | − | 30.7932i | −0.848519 | − | 1.46968i | −0.882530 | − | 0.470257i | \(-0.844161\pi\) |
0.0340103 | − | 0.999421i | \(-0.489172\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.45103 | − | 12.9056i | −0.354811 | − | 0.614551i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.25994 | − | 14.3066i | 0.392442 | − | 0.679729i | −0.600329 | − | 0.799753i | \(-0.704964\pi\) |
0.992771 | + | 0.120024i | \(0.0382971\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1087 | 0.621413 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.1440 | −1.09467 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.80900 | + | 6.59738i | −0.179758 | + | 0.311349i | −0.941797 | − | 0.336181i | \(-0.890865\pi\) |
0.762040 | + | 0.647530i | \(0.224198\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.45870 | + | 12.9188i | 0.351216 | + | 0.608325i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.32638 | + | 10.9576i | 0.297239 | + | 0.514833i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.67996 | 0.219400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.66587 | + | 2.88537i | −0.0779260 | + | 0.134972i | −0.902355 | − | 0.430994i | \(-0.858163\pi\) |
0.824429 | + | 0.565966i | \(0.191496\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.405657 | + | 0.702619i | 0.0189345 | + | 0.0327955i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8604 | 0.645544 | 0.322772 | − | 0.946477i | \(-0.395385\pi\) | ||||
0.322772 | + | 0.946477i | \(0.395385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.46192 | − | 12.9244i | −0.346785 | − | 0.600649i | 0.638891 | − | 0.769297i | \(-0.279393\pi\) |
−0.985676 | + | 0.168648i | \(0.946060\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.131676 | + | 0.228069i | −0.00610631 | + | 0.0105764i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.86736 | + | 6.69846i | 0.178960 | + | 0.309968i | 0.941525 | − | 0.336944i | \(-0.109393\pi\) |
−0.762565 | + | 0.646912i | \(0.776060\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.1004 | − | 28.9380i | 1.15903 | − | 1.33623i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.72579 | − | 2.98916i | −0.0795204 | − | 0.137733i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.319368 | + | 0.553162i | −0.0146846 | + | 0.0254344i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.42209 | − | 2.46313i | −0.0652499 | − | 0.113016i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.736649 | −0.0337288 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.447058 | − | 0.774327i | −0.0204266 | − | 0.0353799i | 0.855631 | − | 0.517586i | \(-0.173169\pi\) |
−0.876058 | + | 0.482206i | \(0.839836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.572659 | − | 0.991874i | 0.0261110 | − | 0.0452256i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.4786 | −0.931809 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.60393 | + | 16.6345i | 0.436092 | + | 0.755334i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.67507 | + | 6.36541i | 0.166533 | + | 0.288444i | 0.937199 | − | 0.348796i | \(-0.113409\pi\) |
−0.770665 | + | 0.637240i | \(0.780076\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.3321 | + | 17.8958i | −0.467235 | + | 0.809275i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0899 | −0.861516 | −0.430758 | − | 0.902467i | \(-0.641754\pi\) | ||||
−0.430758 | + | 0.902467i | \(0.641754\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.14200 | −0.321660 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.04957 | + | 3.54996i | −0.0921212 | + | 0.159559i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.50335 | + | 12.9962i | 0.336571 | + | 0.582959i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.47567 | + | 6.02004i | 0.155593 | + | 0.269494i | 0.933275 | − | 0.359164i | \(-0.116938\pi\) |
−0.777682 | + | 0.628658i | \(0.783605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.4986 | + | 21.6483i | −0.558398 | + | 0.967173i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.11221 | − | 5.39050i | 0.138767 | − | 0.240351i | −0.788263 | − | 0.615338i | \(-0.789020\pi\) |
0.927030 | + | 0.374987i | \(0.122353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.00397 | − | 1.73893i | 0.0446762 | − | 0.0773814i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.49202 | 0.376402 | 0.188201 | − | 0.982131i | \(-0.439734\pi\) | ||||
0.188201 | + | 0.982131i | \(0.439734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.5614 | −1.97128 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.42209 | − | 2.46313i | −0.0627868 | − | 0.108750i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.39205 | + | 9.33931i | −0.237602 | + | 0.411539i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.93523 | + | 12.0122i | 0.305011 | + | 0.528294i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.90917 | + | 10.2350i | 0.259384 | + | 0.449266i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.7233 | −0.601229 | −0.300615 | − | 0.953746i | \(-0.597192\pi\) | ||||
−0.300615 | + | 0.953746i | \(0.597192\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.0672 | − | 19.1690i | −0.483935 | − | 0.838201i | 0.515894 | − | 0.856652i | \(-0.327460\pi\) |
−0.999830 | + | 0.0184516i | \(0.994126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.33998 | + | 4.05297i | −0.102125 | + | 0.176886i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.213661 | 0.00930720 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.92616 | − | 3.33621i | 0.0837463 | − | 0.145053i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.35790 | 0.145721 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.63916 | −0.157629 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.27630 | 0.314582 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.1659 | −0.568149 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −61.0856 | −2.63114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9506 | −0.556790 | −0.278395 | − | 0.960467i | \(-0.589802\pi\) | ||||
−0.278395 | + | 0.960467i | \(0.589802\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.319852 | + | 0.553999i | −0.0137262 | + | 0.0237744i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.59298 | 0.410918 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.02003 | − | 5.23084i | 0.129127 | − | 0.223655i | −0.794212 | − | 0.607641i | \(-0.792116\pi\) |
0.923339 | + | 0.383987i | \(0.125449\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.373303 | + | 0.646580i | 0.0159322 | + | 0.0275954i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.0373 | 1.06662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.2579 | − | 47.2120i | −1.15912 | − | 2.00766i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.572659 | + | 0.991874i | 0.0243080 | + | 0.0421027i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.77286 | + | 15.1950i | −0.371718 | + | 0.643835i | −0.989830 | − | 0.142256i | \(-0.954565\pi\) |
0.618112 | + | 0.786090i | \(0.287898\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0779111 | − | 0.134946i | −0.00329529 | − | 0.00570760i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.32569 | 0.140411 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.35200 | 0.267705 | 0.133853 | − | 0.991001i | \(-0.457265\pi\) | ||||
0.133853 | + | 0.991001i | \(0.457265\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.13168 | + | 1.96012i | −0.0476099 | + | 0.0824628i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.33998 | + | 4.05297i | −0.0982700 | + | 0.170209i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.8063 | − | 18.7171i | 0.453026 | − | 0.784663i | −0.545547 | − | 0.838080i | \(-0.683678\pi\) |
0.998572 | + | 0.0534170i | \(0.0170113\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1088 | − | 19.2410i | 0.464889 | − | 0.805212i | −0.534307 | − | 0.845290i | \(-0.679427\pi\) |
0.999197 | + | 0.0400783i | \(0.0127608\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.19598 | − | 14.1959i | −0.342392 | − | 0.593040i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.18790 | + | 3.78956i | 0.0912418 | + | 0.158036i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.02464 | − | 5.23883i | 0.125917 | − | 0.218095i | −0.796174 | − | 0.605068i | \(-0.793146\pi\) |
0.922091 | + | 0.386973i | \(0.126479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.88217 | 0.410689 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −57.9286 | −2.40328 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.50981 | + | 2.61507i | −0.0625300 | + | 0.108305i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | − | 0.866025i | −0.0206725 | − | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.1727 | + | 38.4042i | 0.915164 | + | 1.58511i | 0.806661 | + | 0.591014i | \(0.201272\pi\) |
0.108502 | + | 0.994096i | \(0.465395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.749017 | −0.0308627 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.30338 | + | 2.25751i | −0.0536137 | + | 0.0928617i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.1509 | − | 31.4383i | −0.745369 | − | 1.29102i | −0.950022 | − | 0.312183i | \(-0.898940\pi\) |
0.204653 | − | 0.978835i | \(-0.434393\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.79692 | 0.155659 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.81017 | − | 16.9917i | −0.401504 | − | 0.695424i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.1631 | + | 19.3350i | −0.456110 | + | 0.790006i | −0.998751 | − | 0.0499585i | \(-0.984091\pi\) |
0.542641 | + | 0.839965i | \(0.317424\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3273 | − | 19.6195i | −0.462052 | − | 0.800297i | 0.537011 | − | 0.843575i | \(-0.319553\pi\) |
−0.999063 | + | 0.0432779i | \(0.986220\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.03665 | − | 1.55314i | −0.327278 | − | 0.0632488i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.90146 | + | 5.02548i | 0.117961 | + | 0.204315i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.378766 | − | 0.656041i | 0.0153736 | − | 0.0266279i | −0.858236 | − | 0.513255i | \(-0.828440\pi\) |
0.873610 | + | 0.486627i | \(0.161773\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.5989 | − | 35.6783i | −0.834708 | − | 1.44576i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.38375 | −0.136892 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.3625 | − | 23.1445i | −0.539706 | − | 0.934799i | −0.998920 | − | 0.0464728i | \(-0.985202\pi\) |
0.459213 | − | 0.888326i | \(-0.348131\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.81958 | − | 3.15160i | 0.0733725 | − | 0.127085i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.14925 | 0.0865256 | 0.0432628 | − | 0.999064i | \(-0.486225\pi\) | ||||
0.0432628 | + | 0.999064i | \(0.486225\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.592777 | − | 1.02672i | −0.0238257 | − | 0.0412674i | 0.853867 | − | 0.520492i | \(-0.174251\pi\) |
−0.877692 | + | 0.479224i | \(0.840918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.18790 | + | 3.78956i | 0.0877975 | + | 0.152070i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.6742 | − | 53.1292i | 1.22893 | − | 2.12858i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.6587 | −0.465603 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.464606 | − | 0.804722i | 0.0185251 | − | 0.0320864i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.64522 | + | 6.31371i | 0.145114 | + | 0.251345i | 0.929415 | − | 0.369035i | \(-0.120312\pi\) |
−0.784301 | + | 0.620380i | \(0.786978\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.30716 | + | 9.19227i | 0.210941 | + | 0.365360i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.47244 | − | 6.01444i | 0.137800 | − | 0.238676i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.45103 | − | 12.9056i | 0.295221 | − | 0.511337i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.60329 | − | 2.77699i | 0.0634253 | − | 0.109856i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.0975 | − | 24.4176i | 0.556817 | − | 0.964435i | −0.440943 | − | 0.897535i | \(-0.645356\pi\) |
0.997760 | − | 0.0669002i | \(-0.0213109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.0318 | 1.61814 | 0.809069 | − | 0.587714i | \(-0.199972\pi\) | ||||
0.809069 | + | 0.587714i | \(0.199972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.155822 | 0.00613549 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.6239 | + | 42.6498i | 0.968064 | + | 1.67674i | 0.701149 | + | 0.713015i | \(0.252671\pi\) |
0.266915 | + | 0.963720i | \(0.413996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.88225 | − | 11.9204i | 0.270152 | − | 0.467917i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.616237 | + | 1.06735i | 0.0241522 | + | 0.0418329i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.95225 | − | 17.2378i | −0.389462 | − | 0.674567i | 0.602915 | − | 0.797805i | \(-0.294006\pi\) |
−0.992377 | + | 0.123238i | \(0.960672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.3695 | 0.678683 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.76087 | + | 8.24608i | 0.185739 | + | 0.321710i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.6665 | + | 20.2070i | −0.454462 | + | 0.787151i | −0.998657 | − | 0.0518074i | \(-0.983502\pi\) |
0.544195 | + | 0.838959i | \(0.316835\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.67541 | −0.142957 | −0.0714784 | − | 0.997442i | \(-0.522772\pi\) | ||||
−0.0714784 | + | 0.997442i | \(0.522772\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.405657 | + | 0.702619i | −0.0157544 | + | 0.0272875i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.3106 | −0.516165 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.5202 | −1.49151 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.92598 | 0.306436 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.06044 | 0.118147 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0122 | −0.848509 | −0.424254 | − | 0.905543i | \(-0.639464\pi\) | ||||
−0.424254 | + | 0.905543i | \(0.639464\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.43919 | − | 7.68890i | 0.170612 | − | 0.295508i | −0.768022 | − | 0.640423i | \(-0.778759\pi\) |
0.938634 | + | 0.344915i | \(0.112092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 89.8921 | 3.44974 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.84617 | + | 10.1259i | −0.224026 | + | 0.388024i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.5061 | + | 19.9292i | 0.440269 | + | 0.762569i | 0.997709 | − | 0.0676485i | \(-0.0215496\pi\) |
−0.557440 | + | 0.830217i | \(0.688216\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.9359 | −0.494256 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.1270 | + | 21.0045i | 0.462673 | + | 0.801374i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.368324 | − | 0.637957i | −0.0140320 | − | 0.0243042i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.9060 | + | 34.4783i | −0.757261 | + | 1.31162i | 0.186981 | + | 0.982364i | \(0.440130\pi\) |
−0.944242 | + | 0.329252i | \(0.893204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.59191 | + | 16.6137i | 0.364366 | + | 0.631101i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.1973 | 0.766126 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.95250 | −0.111834 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.42684 | + | 2.47137i | −0.0539682 | + | 0.0934756i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.60794 | − | 11.4453i | 0.249579 | − | 0.432283i | −0.713830 | − | 0.700319i | \(-0.753041\pi\) |
0.963409 | + | 0.268036i | \(0.0863746\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.62874 | + | 2.82107i | −0.0614292 | + | 0.106399i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.69187 | − | 2.93041i | 0.0637197 | − | 0.110366i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.69855 | − | 8.13813i | −0.176707 | − | 0.306066i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.34170 | − | 2.32389i | −0.0503885 | − | 0.0872754i | 0.839731 | − | 0.543003i | \(-0.182713\pi\) |
−0.890120 | + | 0.455727i | \(0.849379\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.82437 | + | 10.0881i | −0.218431 | + | 0.378334i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.15237 | 0.0431567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.09914 | −0.153299 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.17038 | − | 2.02715i | 0.0437085 | − | 0.0757053i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.9485 | − | 27.6236i | −0.594777 | − | 1.03018i | −0.993578 | − | 0.113147i | \(-0.963907\pi\) |
0.398801 | − | 0.917038i | \(-0.369426\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.2346 | + | 43.7076i | 0.939786 | + | 1.62776i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.784474 | −0.0291749 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.40150 | + | 7.62362i | −0.163468 | + | 0.283134i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.3166 | − | 17.8689i | −0.382622 | − | 0.662721i | 0.608814 | − | 0.793313i | \(-0.291646\pi\) |
−0.991436 | + | 0.130592i | \(0.958312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0632104 | − | 0.109484i | −0.00233792 | − | 0.00404940i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.89664 | + | 8.48123i | −0.180862 | + | 0.313262i | −0.942174 | − | 0.335123i | \(-0.891222\pi\) |
0.761313 | + | 0.648385i | \(0.224555\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.45103 | + | 12.9056i | 0.274835 | + | 0.476029i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.9852 | + | 25.3465i | −0.809837 | + | 0.933650i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.2101 | + | 21.1486i | 0.449157 | + | 0.777962i | 0.998331 | − | 0.0577452i | \(-0.0183911\pi\) |
−0.549175 | + | 0.835708i | \(0.685058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.42209 | − | 2.46313i | 0.0522417 | − | 0.0904854i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.0989 | + | 33.0803i | 0.700671 | + | 1.21360i | 0.968231 | + | 0.250057i | \(0.0804493\pi\) |
−0.267560 | + | 0.963541i | \(0.586217\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.1440 | 0.847929 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.18900 | + | 10.7197i | 0.226444 | + | 0.392212i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.0264 | − | 29.4906i | 0.622131 | − | 1.07756i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.2739 | −1.46962 | −0.734808 | − | 0.678276i | \(-0.762728\pi\) | ||||
−0.734808 | + | 0.678276i | \(0.762728\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.7408 | + | 23.7998i | 0.500742 | + | 0.867311i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.32638 | − | 10.9576i | −0.230240 | − | 0.398788i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.86526 | − | 15.3551i | 0.322213 | − | 0.558090i | −0.658731 | − | 0.752379i | \(-0.728906\pi\) |
0.980944 | + | 0.194288i | \(0.0622398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.9370 | 0.651073 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.44137 | −0.197250 | −0.0986248 | − | 0.995125i | \(-0.531444\pi\) | ||||
−0.0986248 | + | 0.995125i | \(0.531444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.4474 | − | 38.8800i | 0.812650 | − | 1.40755i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.405657 | − | 0.702619i | −0.0146666 | − | 0.0254032i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.67895 | + | 2.90803i | 0.0606234 | + | 0.105003i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.36334 | + | 5.82547i | −0.121285 | + | 0.210072i | −0.920275 | − | 0.391273i | \(-0.872035\pi\) |
0.798990 | + | 0.601345i | \(0.205368\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.3528 | − | 19.6637i | 0.408862 | − | 0.708169i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.87223 | − | 8.43895i | 0.175242 | − | 0.303528i | −0.765003 | − | 0.644027i | \(-0.777263\pi\) |
0.940245 | + | 0.340499i | \(0.110596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.131676 | − | 0.228069i | 0.00472993 | − | 0.00819247i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.36004 | 0.192291 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3504 | 0.370842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.57212 | − | 11.3832i | −0.235169 | − | 0.407324i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.40150 | + | 7.62362i | −0.157297 | + | 0.272446i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.72579 | + | 2.98916i | 0.0615962 | + | 0.106688i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.519118 | − | 0.899139i | −0.0185046 | − | 0.0320509i | 0.856625 | − | 0.515940i | \(-0.172557\pi\) |
−0.875129 | + | 0.483889i | \(0.839224\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.16533 | 0.148290 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.29620 | + | 9.17329i | 0.188311 | + | 0.326165i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.373303 | + | 0.646580i | −0.0132564 | + | 0.0229607i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.736649 | 0.0261262 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.17411 | + | 8.96183i | −0.183276 | + | 0.317444i | −0.942994 | − | 0.332809i | \(-0.892004\pi\) |
0.759718 | + | 0.650253i | \(0.225337\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.74529 | −0.0971212 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.1087 | −0.463174 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.0310 | 1.37737 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.4786 | 0.721776 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.9014 | −0.559757 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.6926 | −0.657198 | −0.328599 | − | 0.944470i | \(-0.606576\pi\) | ||||
−0.328599 | + | 0.944470i | \(0.606576\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.10449 | − | 1.91303i | 0.0387839 | − | 0.0671757i | −0.845982 | − | 0.533212i | \(-0.820985\pi\) |
0.884766 | + | 0.466036i | \(0.154318\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.3621 | 0.959631 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.3321 | − | 17.8958i | 0.361919 | − | 0.626861i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.221593 | + | 0.383810i | 0.00775255 | + | 0.0134278i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.67996 | −0.163531 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.9988 | + | 32.9069i | 0.663063 | + | 1.14846i | 0.979806 | + | 0.199948i | \(0.0640774\pi\) |
−0.316743 | + | 0.948511i | \(0.602589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.8384 | + | 37.8252i | 0.761239 | + | 1.31851i | 0.942212 | + | 0.335017i | \(0.108742\pi\) |
−0.180973 | + | 0.983488i | \(0.557925\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.04957 | − | 3.54996i | 0.0713568 | − | 0.123594i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.5786 | − | 46.0355i | −0.924230 | − | 1.60081i | −0.792796 | − | 0.609488i | \(-0.791375\pi\) |
−0.131434 | − | 0.991325i | \(-0.541958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.1302 | 1.15066 | 0.575329 | − | 0.817922i | \(-0.304874\pi\) | ||||
0.575329 | + | 0.817922i | \(0.304874\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.3919 | −0.464559 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.04513 | − | 10.4705i | 0.209451 | − | 0.362780i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.4986 | − | 21.6483i | 0.432533 | − | 0.749169i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.131676 | − | 0.228069i | 0.00455137 | − | 0.00788321i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.42532 | + | 11.1290i | −0.221827 | + | 0.384215i | −0.955363 | − | 0.295436i | \(-0.904535\pi\) |
0.733536 | + | 0.679651i | \(0.237869\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2464 | − | 41.9960i | −0.836083 | − | 1.44814i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.4785 | + | 21.6133i | 0.429781 | + | 0.744402i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.1575 | 0.933142 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.580906 | −0.0199366 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.50584 | − | 4.34025i | 0.0858992 | − | 0.148782i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.53454 | + | 7.85406i | 0.155260 | + | 0.268918i | 0.933154 | − | 0.359478i | \(-0.117045\pi\) |
−0.777894 | + | 0.628396i | \(0.783712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.42209 | + | 2.46313i | 0.0486344 | + | 0.0842373i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.5338 | 1.35045 | 0.675225 | − | 0.737612i | \(-0.264047\pi\) | ||||
0.675225 | + | 0.737612i | \(0.264047\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.1474 | + | 43.5566i | −0.858019 | + | 1.48613i | 0.0157966 | + | 0.999875i | \(0.494972\pi\) |
−0.873816 | + | 0.486257i | \(0.838362\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.51556 | − | 14.7494i | −0.290210 | − | 0.502658i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.5929 | 0.769071 | 0.384535 | − | 0.923110i | \(-0.374362\pi\) | ||||
0.384535 | + | 0.923110i | \(0.374362\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.90917 | − | 10.2350i | −0.200918 | − | 0.348000i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.17088 | − | 14.1524i | 0.277498 | − | 0.480640i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.8749 | + | 41.3525i | 0.809900 | + | 1.40279i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.67327 | − | 7.73651i | −0.0905801 | − | 0.262142i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.60393 | − | 16.6345i | −0.325044 | − | 0.562992i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.33998 | − | 4.05297i | 0.0791058 | − | 0.137015i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3198 | − | 38.6590i | −0.753686 | − | 1.30542i | −0.946025 | − | 0.324093i | \(-0.894941\pi\) |
0.192340 | − | 0.981328i | \(-0.438392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.08517 | −0.306435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0804 | + | 24.3880i | 0.474381 | + | 0.821652i | 0.999570 | − | 0.0293338i | \(-0.00933858\pi\) |
−0.525189 | + | 0.850986i | \(0.676005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.97646 | + | 15.5477i | −0.302082 | + | 0.523221i | −0.976607 | − | 0.215030i | \(-0.931015\pi\) |
0.674526 | + | 0.738252i | \(0.264348\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.35790 | −0.112875 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.68575 | − | 4.65186i | −0.0901787 | − | 0.156194i | 0.817408 | − | 0.576060i | \(-0.195410\pi\) |
−0.907586 | + | 0.419866i | \(0.862077\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.2509 | − | 28.1474i | −0.545037 | − | 0.944033i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.04957 | − | 3.54996i | 0.0686631 | − | 0.118928i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.62398 | 0.322054 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.1659 | 0.440086 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.18790 | + | 3.78956i | −0.0730519 | + | 0.126530i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.15914 | + | 2.00769i | 0.0386595 | + | 0.0669602i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.298827 | − | 0.517584i | −0.00995537 | − | 0.0172432i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.364621 | − | 0.631542i | 0.0121338 | − | 0.0210164i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.319852 | − | 0.553999i | 0.0106322 | − | 0.0184156i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.52227 | + | 7.83279i | −0.150159 | + | 0.260084i | −0.931286 | − | 0.364289i | \(-0.881312\pi\) |
0.781127 | + | 0.624373i | \(0.214645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.00397 | + | 1.73893i | −0.0332996 | + | 0.0576767i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.3846 | −1.56992 | −0.784960 | − | 0.619546i | \(-0.787317\pi\) | ||||
−0.784960 | + | 0.619546i | \(0.787317\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.7391 | 1.67922 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.373303 | − | 0.646580i | −0.0123410 | − | 0.0213753i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.6443 | − | 70.3981i | 1.34219 | − | 2.32475i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9197 | + | 22.3775i | 0.426180 | + | 0.738166i | 0.996530 | − | 0.0832362i | \(-0.0265256\pi\) |
−0.570350 | + | 0.821402i | \(0.693192\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.85294 | + | 11.8696i | 0.225812 | + | 0.391118i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.20659 | 0.105546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.572659 | − | 0.991874i | −0.0188289 | − | 0.0326126i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.39205 | − | 9.33931i | 0.177098 | − | 0.306743i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.2162 | 1.61473 | 0.807366 | − | 0.590051i | \(-0.200892\pi\) | ||||
0.807366 | + | 0.590051i | \(0.200892\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.1921 | + | 36.7057i | −0.694542 | + | 1.20298i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.5669 | 0.378684 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.32569 | −0.108762 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.17439 | 0.169040 | 0.0845200 | − | 0.996422i | \(-0.473064\pi\) | ||||
0.0845200 | + | 0.996422i | \(0.473064\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.6871 | 0.479295 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.6020 | −0.802003 | −0.401002 | − | 0.916077i | \(-0.631338\pi\) | ||||
−0.401002 | + | 0.916077i | \(0.631338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.9242 | −0.518565 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.33998 | − | 4.05297i | 0.0761196 | − | 0.131843i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.3406 | −0.595990 | −0.297995 | − | 0.954567i | \(-0.596318\pi\) | ||||
−0.297995 | + | 0.954567i | \(0.596318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.76087 | + | 8.24608i | −0.154545 | + | 0.267679i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.18470 | + | 3.78401i | 0.0708438 | + | 0.122705i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0193 | 0.583702 | 0.291851 | − | 0.956464i | \(-0.405729\pi\) | ||||
0.291851 | + | 0.956464i | \(0.405729\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.19598 | + | 14.1959i | 0.265216 | + | 0.459367i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.0424 | + | 31.2503i | 0.583226 | + | 1.01018i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.2698 | + | 52.4289i | −0.977463 | + | 1.69302i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4653 | + | 26.7867i | 0.498881 | + | 0.864088i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.27630 | −0.234475 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.88217 | −0.318118 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.2202 | − | 45.4148i | 0.843186 | − | 1.46044i | −0.0440006 | − | 0.999032i | \(-0.514010\pi\) |
0.887187 | − | 0.461410i | \(-0.152656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.15376 | − | 1.99837i | 0.0370642 | − | 0.0641970i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.268358 | + | 0.464809i | −0.00861201 | + | 0.0149164i | −0.870299 | − | 0.492523i | \(-0.836075\pi\) |
0.861687 | + | 0.507440i | \(0.169408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.2613 | − | 81.8589i | 1.51513 | − | 2.62428i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | + | 0.866025i | 0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.05815 | + | 3.56482i | 0.0658460 | + | 0.114049i | 0.897069 | − | 0.441891i | \(-0.145692\pi\) |
−0.831223 | + | 0.555939i | \(0.812359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.8672 | + | 46.5354i | −0.858680 | + | 1.48728i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.59298 | −0.306280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.1266 | 1.08847 | 0.544235 | − | 0.838933i | \(-0.316820\pi\) | ||||
0.544235 | + | 0.838933i | \(0.316820\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.30338 | − | 2.25751i | 0.0415290 | − | 0.0719303i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.91791 | − | 13.7142i | −0.252030 | − | 0.436529i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.340924 | − | 0.590497i | −0.0108407 | − | 0.0187767i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.8833 | 1.23517 | 0.617584 | − | 0.786505i | \(-0.288112\pi\) | ||||
0.617584 | + | 0.786505i | \(0.288112\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.15199 | − | 8.92351i | 0.163493 | − | 0.283179i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.81017 | + | 16.9917i | 0.311003 | + | 0.538673i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.2131 | −1.05187 | −0.525935 | − | 0.850525i | \(-0.676284\pi\) | ||||
−0.525935 | + | 0.850525i | \(0.676284\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.572659 | − | 0.991874i | −0.0181181 | − | 0.0313815i |
(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 | 4020.2.q.j.841.1 | ✓ | 12 | |
67.29 | even | 3 | inner | 4020.2.q.j.3781.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.j.841.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
4020.2.q.j.3781.1 | yes | 12 | 67.29 | even | 3 | inner |