Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [164,2,Mod(7,164)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(164, base_ring=CyclotomicField(40))
chi = DirichletCharacter(H, H._module([20, 39]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("164.7");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 164 = 2^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 164.o (of order \(40\), degree \(16\), 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: | \(1.30954659315\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{40}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(-0.156434 - 0.987688i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 164.7 |
Dual form | 164.2.o.a.47.1 |
$q$-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 \(\left(\mathbb{Z}/164\mathbb{Z}\right)^\times\).
\(n\) | \(83\) | \(129\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{39}{40}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.642040 | − | 1.26007i | −0.453990 | − | 0.891007i | ||||
\(3\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(4\) | −1.17557 | + | 1.61803i | −0.587785 | + | 0.809017i | ||||
\(5\) | −0.490920 | − | 3.09954i | −0.219546 | − | 1.38616i | −0.813456 | − | 0.581627i | \(-0.802416\pi\) |
0.593910 | − | 0.804532i | \(-0.297584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) | ||||
0.996917 | + | 0.0784591i | \(0.0250000\pi\) | |||||||
\(8\) | 2.79360 | + | 0.442463i | 0.987688 | + | 0.156434i | ||||
\(9\) | −2.12132 | − | 2.12132i | −0.707107 | − | 0.707107i | ||||
\(10\) | −3.59046 | + | 2.60863i | −1.13540 | + | 0.824920i | ||||
\(11\) | 0 | 0 | 0.972370 | − | 0.233445i | \(-0.0750000\pi\) | ||||
−0.972370 | + | 0.233445i | \(0.925000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.14643 | − | 4.39547i | −1.42736 | − | 1.21908i | −0.937829 | − | 0.347098i | \(-0.887167\pi\) |
−0.489534 | − | 0.871984i | \(-0.662833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.23607 | − | 3.80423i | −0.309017 | − | 0.951057i | ||||
\(17\) | 5.72667 | + | 3.50931i | 1.38892 | + | 0.851132i | 0.997608 | − | 0.0691254i | \(-0.0220209\pi\) |
0.391313 | + | 0.920258i | \(0.372021\pi\) | |||||||
\(18\) | −1.31105 | + | 4.03499i | −0.309017 | + | 0.951057i | ||||
\(19\) | 0 | 0 | 0.760406 | − | 0.649448i | \(-0.225000\pi\) | ||||
−0.760406 | + | 0.649448i | \(0.775000\pi\) | |||||||
\(20\) | 5.59228 | + | 2.84941i | 1.25047 | + | 0.637147i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61089 | + | 1.49817i | −0.922179 | + | 0.299634i | ||||
\(26\) | −2.23440 | + | 9.30694i | −0.438202 | + | 1.82524i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.41386 | − | 3.93042i | 1.19102 | − | 0.729860i | 0.221572 | − | 0.975144i | \(-0.428881\pi\) |
0.969451 | + | 0.245284i | \(0.0788811\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.707107 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.745237 | − | 9.46914i | 0.127807 | − | 1.62394i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.92613 | − | 0.938607i | 0.987688 | − | 0.156434i | ||||
\(37\) | 9.33556 | + | 6.78268i | 1.53476 | + | 1.11507i | 0.953519 | + | 0.301333i | \(0.0974315\pi\) |
0.581238 | + | 0.813733i | \(0.302568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 8.87612i | − | 1.40344i | ||||||
\(41\) | 5.34931 | − | 3.51921i | 0.835422 | − | 0.549609i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.53373 | + | 7.61653i | −0.824920 | + | 1.13540i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.996917 | − | 0.0784591i | \(-0.0250000\pi\) | ||||
−0.996917 | + | 0.0784591i | \(0.975000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.91382 | + | 1.09504i | 0.987688 | + | 0.156434i | ||||
\(50\) | 4.84818 | + | 4.84818i | 0.685636 | + | 0.685636i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.1620 | − | 3.15992i | 1.82524 | − | 0.438202i | ||||
\(53\) | −2.65748 | − | 4.33661i | −0.365033 | − | 0.595679i | 0.616412 | − | 0.787424i | \(-0.288586\pi\) |
−0.981445 | + | 0.191744i | \(0.938586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.07057 | − | 5.55845i | −1.19102 | − | 0.729860i | ||||
\(59\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4730 | − | 5.33625i | −1.34093 | − | 0.683237i | −0.371458 | − | 0.928450i | \(-0.621142\pi\) |
−0.969469 | + | 0.245213i | \(0.921142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.60845 | + | 2.47214i | 0.951057 | + | 0.309017i | ||||
\(65\) | −11.0975 | + | 18.1094i | −1.37647 | + | 2.24620i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.233445 | − | 0.972370i | \(-0.425000\pi\) | ||||
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(68\) | −12.4103 | + | 5.14051i | −1.50497 | + | 0.623378i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.233445 | − | 0.972370i | \(-0.575000\pi\) | ||||
0.233445 | + | 0.972370i | \(0.425000\pi\) | |||||||
\(72\) | −4.98752 | − | 6.86474i | −0.587785 | − | 0.809017i | ||||
\(73\) | −11.6467 | + | 11.6467i | −1.36315 | + | 1.36315i | −0.493275 | + | 0.869874i | \(0.664200\pi\) |
−0.869874 | + | 0.493275i | \(0.835800\pi\) | |||||||
\(74\) | 2.55288 | − | 16.1182i | 0.296766 | − | 1.87371i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(80\) | −11.1846 | + | 5.69882i | −1.25047 | + | 0.637147i | ||||
\(81\) | 9.00000i | 1.00000i | ||||||||
\(82\) | −7.86894 | − | 4.48105i | −0.868979 | − | 0.494849i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.06592 | − | 19.4729i | 0.874872 | − | 2.11213i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.10626 | + | 0.244468i | 0.329262 | + | 0.0259135i | 0.242013 | − | 0.970273i | \(-0.422192\pi\) |
0.0872493 | + | 0.996187i | \(0.472192\pi\) | |||||||
\(90\) | 13.1503 | + | 2.08280i | 1.38616 | + | 0.219546i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7778 | − | 3.78791i | −1.60199 | − | 0.384604i | −0.668644 | − | 0.743583i | \(-0.733125\pi\) |
−0.933346 | + | 0.358979i | \(0.883125\pi\) | |||||||
\(98\) | −3.05911 | − | 9.41498i | −0.309017 | − | 0.951057i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.99634 | − | 9.22179i | 0.299634 | − | 0.922179i | ||||
\(101\) | 10.5767 | − | 9.03332i | 1.05242 | − | 0.898849i | 0.0573794 | − | 0.998352i | \(-0.481726\pi\) |
0.995037 | + | 0.0995037i | \(0.0317255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(104\) | −12.4323 | − | 14.5563i | −1.21908 | − | 1.42736i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.75824 | + | 6.13289i | −0.365033 | + | 0.595679i | ||||
\(107\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.07645 | − | 1.68852i | 0.390453 | − | 0.161731i | −0.178815 | − | 0.983883i | \(-0.557226\pi\) |
0.569269 | + | 0.822152i | \(0.307226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.65648 | + | 9.16186i | 0.626189 | + | 0.861876i | 0.997785 | − | 0.0665190i | \(-0.0211893\pi\) |
−0.371596 | + | 0.928395i | \(0.621189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.18039 | + | 14.9983i | −0.109597 | + | 1.39256i | ||||
\(117\) | 1.59303 | + | 20.2414i | 0.147276 | + | 1.87132i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.80107 | − | 4.99390i | 0.891007 | − | 0.453990i | ||||
\(122\) | 16.6228i | 1.50496i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.216299 | − | 0.424510i | −0.0193463 | − | 0.0379693i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(128\) | −1.76985 | − | 11.1744i | −0.156434 | − | 0.987688i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 29.9442 | + | 2.35666i | 2.62628 | + | 0.206693i | ||||
\(131\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.4453 | + | 12.3375i | 1.23867 | + | 1.05793i | ||||
\(137\) | −1.01149 | − | 2.44196i | −0.0864178 | − | 0.208631i | 0.874763 | − | 0.484552i | \(-0.161017\pi\) |
−0.961180 | + | 0.275921i | \(0.911017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.44789 | + | 10.6921i | −0.453990 | + | 0.891007i | ||||
\(145\) | −15.3312 | − | 17.9505i | −1.27319 | − | 1.49071i | ||||
\(146\) | 22.1534 | + | 7.19808i | 1.83343 | + | 0.595718i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21.9492 | + | 7.13174i | −1.80422 | + | 0.586225i | ||||
\(149\) | 3.77695 | − | 15.7321i | 0.309420 | − | 1.28883i | −0.573462 | − | 0.819232i | \(-0.694400\pi\) |
0.882882 | − | 0.469595i | \(-0.155600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.649448 | − | 0.760406i | \(-0.275000\pi\) | ||||
−0.649448 | + | 0.760406i | \(0.725000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.70373 | − | 19.5925i | −0.380274 | − | 1.58396i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.979805 | − | 12.4496i | 0.0781970 | − | 0.993587i | −0.825217 | − | 0.564816i | \(-0.808947\pi\) |
0.903414 | − | 0.428770i | \(-0.141053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.3619 | + | 10.4345i | 1.13540 | + | 0.824920i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.3407 | − | 5.77836i | 0.891007 | − | 0.453990i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | −0.594283 | + | 12.7925i | −0.0464057 | + | 0.998923i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.13196 | + | 32.4019i | 0.394766 | + | 2.49246i | ||||
\(170\) | −29.7159 | + | 2.33869i | −2.27910 | + | 0.179369i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8667 | + | 10.8667i | 0.826177 | + | 0.826177i | 0.986986 | − | 0.160809i | \(-0.0514102\pi\) |
−0.160809 | + | 0.986986i | \(0.551410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.68629 | − | 4.07107i | −0.126393 | − | 0.305139i | ||||
\(179\) | 0 | 0 | −0.972370 | − | 0.233445i | \(-0.925000\pi\) | ||||
0.972370 | + | 0.233445i | \(0.0750000\pi\) | |||||||
\(180\) | −5.81851 | − | 17.9075i | −0.433686 | − | 1.33475i | ||||
\(181\) | 21.9960 | + | 13.4792i | 1.63495 | + | 1.00190i | 0.965984 | + | 0.258603i | \(0.0832623\pi\) |
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.4402 | − | 32.2658i | 1.20871 | − | 2.37223i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.3129 | + | 14.2862i | −1.67810 | + | 1.02834i | −0.746132 | + | 0.665798i | \(0.768091\pi\) |
−0.931967 | + | 0.362543i | \(0.881909\pi\) | |||||||
\(194\) | 5.35691 | + | 22.3131i | 0.384604 | + | 1.60199i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.89949 | + | 9.89949i | −0.707107 | + | 0.707107i | ||||
\(197\) | −1.70979 | + | 10.7952i | −0.121817 | + | 0.769123i | 0.848839 | + | 0.528651i | \(0.177302\pi\) |
−0.970656 | + | 0.240472i | \(0.922698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.0784591 | − | 0.996917i | \(-0.525000\pi\) | ||||
0.0784591 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(200\) | −13.5439 | + | 2.14514i | −0.957698 | + | 0.151684i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.1733 | − | 7.52762i | −1.27867 | − | 0.529641i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.5340 | − | 14.8528i | −0.945259 | − | 1.03736i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.3600 | + | 25.0113i | −0.718337 | + | 1.73422i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.996917 | − | 0.0784591i | \(-0.0250000\pi\) | ||||
−0.996917 | + | 0.0784591i | \(0.975000\pi\) | |||||||
\(212\) | 10.1408 | + | 0.798101i | 0.696475 | + | 0.0548138i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.74491 | − | 4.05253i | −0.321366 | − | 0.274472i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.0469 | − | 43.2318i | −0.944894 | − | 2.90808i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.9593 | + | 6.60308i | 0.863952 | + | 0.440206i | ||||
\(226\) | 7.27090 | − | 14.2699i | 0.483653 | − | 0.949222i | ||||
\(227\) | 0 | 0 | −0.649448 | − | 0.760406i | \(-0.725000\pi\) | ||||
0.649448 | + | 0.760406i | \(0.275000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.69149 | + | 9.28767i | −0.376104 | + | 0.613747i | −0.983555 | − | 0.180611i | \(-0.942192\pi\) |
0.607450 | + | 0.794358i | \(0.292192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.6569 | − | 8.14214i | 1.29054 | − | 0.534557i | ||||
\(233\) | −9.03430 | + | 10.5778i | −0.591857 | + | 0.692975i | −0.972806 | − | 0.231621i | \(-0.925597\pi\) |
0.380949 | + | 0.924596i | \(0.375597\pi\) | |||||||
\(234\) | 24.4829 | − | 15.0031i | 1.60050 | − | 0.980785i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.0784591 | − | 0.996917i | \(-0.475000\pi\) | ||||
−0.0784591 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.41174 | − | 1.01552i | 0.413016 | − | 0.0654154i | 0.0535313 | − | 0.998566i | \(-0.482952\pi\) |
0.359485 | + | 0.933151i | \(0.382952\pi\) | |||||||
\(242\) | −12.5854 | − | 9.14379i | −0.809017 | − | 0.587785i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.9460 | − | 10.6725i | 1.34093 | − | 0.683237i | ||||
\(245\) | − | 21.9673i | − | 1.40344i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.396041 | + | 0.545104i | −0.0250479 | + | 0.0344754i | ||||
\(251\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | + | 9.40456i | −0.809017 | + | 0.587785i | ||||
\(257\) | 28.0031 | − | 6.72294i | 1.74678 | − | 0.419366i | 0.770776 | − | 0.637106i | \(-0.219869\pi\) |
0.976007 | + | 0.217740i | \(0.0698685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.2558 | − | 39.2449i | −1.00814 | − | 2.43387i | ||||
\(261\) | −21.9435 | − | 5.26817i | −1.35827 | − | 0.326092i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.852640 | − | 0.522499i | \(-0.825000\pi\) | ||||
0.852640 | + | 0.522499i | \(0.175000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.1369 | + | 10.3659i | −0.745564 | + | 0.636772i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.1853 | − | 10.1327i | −1.90140 | − | 0.617802i | −0.959159 | − | 0.282867i | \(-0.908714\pi\) |
−0.942241 | − | 0.334935i | \(-0.891286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(272\) | 6.27165 | − | 26.1233i | 0.380274 | − | 1.58396i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.42763 | + | 2.84239i | −0.146659 | + | 0.171715i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.4675 | + | 26.7947i | 1.16969 | + | 1.60993i | 0.665689 | + | 0.746229i | \(0.268138\pi\) |
0.503997 | + | 0.863706i | \(0.331862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.73077 | + | 21.9915i | 0.103249 | + | 1.31190i | 0.802339 | + | 0.596869i | \(0.203589\pi\) |
−0.699090 | + | 0.715034i | \(0.746411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.9706 | 1.00000 | ||||||||
\(289\) | 12.7617 | + | 25.0462i | 0.750686 | + | 1.47330i | ||||
\(290\) | −12.7757 | + | 30.8434i | −0.750218 | + | 1.81119i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.15326 | − | 32.5364i | −0.301572 | − | 1.90405i | ||||
\(293\) | −33.4778 | + | 2.63476i | −1.95580 | + | 0.153924i | −0.993151 | − | 0.116841i | \(-0.962723\pi\) |
−0.962645 | + | 0.270766i | \(0.912723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 23.0788 | + | 23.0788i | 1.34143 | + | 1.34143i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.2486 | + | 5.34141i | −1.28883 | + | 0.309420i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.3986 | + | 35.0811i | −0.652679 | + | 2.00874i | ||||
\(306\) | −21.6680 | + | 18.5062i | −1.23867 | + | 1.05793i | ||||
\(307\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.522499 | − | 0.852640i | \(-0.325000\pi\) | ||||
−0.522499 | + | 0.852640i | \(0.675000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.75162 | − | 32.2878i | 0.438147 | − | 1.82501i | −0.116834 | − | 0.993152i | \(-0.537274\pi\) |
0.554981 | − | 0.831863i | \(-0.312726\pi\) | |||||||
\(314\) | −16.3165 | + | 6.75851i | −0.920793 | + | 0.381405i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.25670 | + | 34.3916i | 0.463743 | + | 1.93163i | 0.344597 | + | 0.938751i | \(0.388015\pi\) |
0.119145 | + | 0.992877i | \(0.461985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.92736 | − | 24.7964i | 0.219546 | − | 1.38616i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −14.5623 | − | 10.5801i | −0.809017 | − | 0.587785i | ||||
\(325\) | 30.3148 | + | 12.5568i | 1.68156 | + | 0.696526i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.5010 | − | 7.46442i | 0.911114 | − | 0.412154i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.41548 | − | 34.1920i | −0.296766 | − | 1.87371i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.5868 | + | 17.5868i | 0.958014 | + | 0.958014i | 0.999153 | − | 0.0411389i | \(-0.0130986\pi\) |
−0.0411389 | + | 0.999153i | \(0.513099\pi\) | |||||||
\(338\) | 37.5339 | − | 27.2700i | 2.04158 | − | 1.48329i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 22.0257 | + | 35.9426i | 1.19451 | + | 1.94926i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.71597 | − | 20.6696i | 0.361053 | − | 1.11121i | ||||
\(347\) | 0 | 0 | 0.760406 | − | 0.649448i | \(-0.225000\pi\) | ||||
−0.760406 | + | 0.649448i | \(0.775000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.1408 | + | 27.7530i | −0.756942 | + | 1.48558i | 0.113621 | + | 0.993524i | \(0.463755\pi\) |
−0.870563 | + | 0.492057i | \(0.836245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.7198 | − | 11.6061i | 1.90118 | − | 0.617729i | 0.940887 | − | 0.338719i | \(-0.109994\pi\) |
0.960288 | − | 0.279010i | \(-0.0900062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.04718 | + | 4.73864i | −0.214500 | + | 0.251147i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(360\) | −18.8291 | + | 18.8291i | −0.992380 | + | 0.992380i | ||||
\(361\) | 2.97225 | − | 18.7661i | 0.156434 | − | 0.987688i | ||||
\(362\) | 2.86244 | − | 36.3707i | 0.150446 | − | 1.91160i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 41.8172 | + | 30.3820i | 2.18881 | + | 1.59027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.8130 | − | 3.88222i | −0.979365 | − | 0.202100i | ||||
\(370\) | −51.2125 | −2.66241 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0951 | + | 26.2821i | −0.988706 | + | 1.36084i | −0.0567016 | + | 0.998391i | \(0.518058\pi\) |
−0.932005 | + | 0.362446i | \(0.881942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −50.2845 | − | 7.96428i | −2.58978 | − | 0.410181i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.9694 | + | 20.2037i | 1.67810 | + | 1.02834i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24.6768 | − | 21.0760i | 1.25278 | − | 1.06997i | ||||
\(389\) | −2.12456 | − | 1.08252i | −0.107720 | − | 0.0548859i | 0.399300 | − | 0.916820i | \(-0.369253\pi\) |
−0.507020 | + | 0.861934i | \(0.669253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 18.8300 | + | 6.11822i | 0.951057 | + | 0.309017i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.7004 | − | 4.77646i | 0.740598 | − | 0.240635i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.7047 | − | 16.0461i | 0.687818 | − | 0.805332i | −0.301131 | − | 0.953583i | \(-0.597364\pi\) |
0.988950 | + | 0.148251i | \(0.0473643\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.3988 | + | 15.6890i | 0.569938 | + | 0.784452i | ||||
\(401\) | 26.4629 | − | 26.4629i | 1.32150 | − | 1.32150i | 0.408929 | − | 0.912566i | \(-0.365902\pi\) |
0.912566 | − | 0.408929i | \(-0.134098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.18261 | + | 27.7327i | 0.108589 | + | 1.37975i | ||||
\(405\) | 27.8959 | − | 4.41828i | 1.38616 | − | 0.219546i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.1835i | − | 0.602436i | −0.953555 | − | 0.301218i | \(-0.902607\pi\) | ||
0.953555 | − | 0.301218i | \(-0.0973931\pi\) | |||||||
\(410\) | −10.0262 | + | 26.5900i | −0.495159 | + | 1.31318i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 38.1676 | − | 3.00385i | 1.87132 | − | 0.147276i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.6482 | + | 9.51869i | −1.93233 | + | 0.463913i | −0.939842 | + | 0.341609i | \(0.889028\pi\) |
−0.992493 | + | 0.122304i | \(0.960972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.50515 | − | 13.2906i | −0.267354 | − | 0.645449i | ||||
\(425\) | −31.6626 | − | 7.60152i | −1.53586 | − | 0.368728i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7159 | + | 3.80671i | 0.563028 | + | 0.182939i | 0.576683 | − | 0.816968i | \(-0.304347\pi\) |
−0.0136552 | + | 0.999907i | \(0.504347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.06007 | + | 8.58082i | −0.0986596 | + | 0.410947i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.852640 | − | 0.522499i | \(-0.175000\pi\) | ||||
−0.852640 | + | 0.522499i | \(0.825000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.3435 | − | 16.9894i | −0.587785 | − | 0.809017i | ||||
\(442\) | −45.4566 | + | 45.4566i | −2.16215 | + | 2.16215i | ||||
\(443\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.767184 | − | 9.74799i | −0.0363680 | − | 0.462099i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.4188 | − | 19.0658i | 1.76590 | − | 0.899773i | 0.822045 | − | 0.569422i | \(-0.192833\pi\) |
0.943858 | − | 0.330350i | \(-0.107167\pi\) | |||||||
\(450\) | − | 20.5691i | − | 0.969636i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −22.6494 | −1.06534 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.5334 | + | 2.48173i | −1.47507 | + | 0.116091i | −0.790323 | − | 0.612690i | \(-0.790087\pi\) |
−0.684747 | + | 0.728781i | \(0.740087\pi\) | |||||||
\(458\) | 15.3573 | + | 1.20865i | 0.717600 | + | 0.0564764i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.8330 | − | 20.2219i | 1.29631 | − | 0.941825i | 0.296399 | − | 0.955064i | \(-0.404214\pi\) |
0.999912 | + | 0.0132386i | \(0.00421411\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.522499 | − | 0.852640i | \(-0.675000\pi\) | ||||
0.522499 | + | 0.852640i | \(0.325000\pi\) | |||||||
\(464\) | −22.8802 | − | 19.5415i | −1.06219 | − | 0.907192i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.1292 | + | 4.59251i | 0.886143 | + | 0.212744i | ||||
\(467\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(468\) | −34.6240 | − | 21.2176i | −1.60050 | − | 0.980785i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.56198 | + | 14.8367i | −0.163092 | + | 0.679326i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.649448 | − | 0.760406i | \(-0.275000\pi\) | ||||
−0.649448 | + | 0.760406i | \(0.725000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2318 | − | 75.9407i | −0.831297 | − | 3.46260i | ||||
\(482\) | −5.39622 | − | 7.42726i | −0.245791 | − | 0.338302i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.44156 | + | 21.7291i | −0.156434 | + | 0.987688i | ||||
\(485\) | −3.99517 | + | 50.7635i | −0.181411 | + | 2.30505i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(488\) | −26.8963 | − | 19.5413i | −1.21754 | − | 0.884592i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −27.6804 | + | 14.1039i | −1.25047 | + | 0.637147i | ||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 50.5231 | 2.27545 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) | ||||
0.996917 | + | 0.0784591i | \(0.0250000\pi\) | |||||||
\(500\) | 0.941145 | + | 0.149063i | 0.0420893 | + | 0.00666629i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.972370 | − | 0.233445i | \(-0.0750000\pi\) | ||||
−0.972370 | + | 0.233445i | \(0.925000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.1915 | − | 28.3482i | −1.47700 | − | 1.26148i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.7315 | − | 22.5091i | −1.62810 | − | 0.997699i | −0.969464 | − | 0.245235i | \(-0.921135\pi\) |
−0.658633 | − | 0.752464i | \(-0.728865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.1612 | + | 10.2726i | 0.891007 | + | 0.453990i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.4505 | − | 30.9695i | −1.16668 | − | 1.36601i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −39.0147 | + | 45.6803i | −1.71091 | + | 2.00321i | ||||
\(521\) | 10.2780 | − | 6.29837i | 0.450287 | − | 0.275936i | −0.278810 | − | 0.960346i | \(-0.589940\pi\) |
0.729098 | + | 0.684410i | \(0.239940\pi\) | |||||||
\(522\) | 7.45032 | + | 31.0328i | 0.326092 | + | 1.35827i | ||||
\(523\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.6074 | + | 13.5191i | 0.809017 | + | 0.587785i | ||||
\(530\) | 20.8542 | + | 8.63808i | 0.905847 | + | 0.375214i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −42.9984 | − | 5.40132i | −1.86247 | − | 0.233957i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.25422 | + | 45.8014i | 0.312752 | + | 1.97464i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.96802 | − | 0.945242i | −0.256585 | − | 0.0406391i | 0.0268165 | − | 0.999640i | \(-0.491463\pi\) |
−0.283402 | + | 0.959001i | \(0.591463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −36.9439 | + | 8.86945i | −1.58396 | + | 0.380274i | ||||
\(545\) | −7.23486 | − | 11.8062i | −0.309907 | − | 0.505723i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(548\) | 5.14026 | + | 1.23407i | 0.219581 | + | 0.0527168i | ||||
\(549\) | 10.8966 | + | 33.5364i | 0.465058 | + | 1.43130i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.2644 | − | 41.7336i | 0.903436 | − | 1.77309i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.7449 | + | 20.7978i | −0.540020 | + | 0.881233i | −0.999978 | − | 0.00670815i | \(-0.997865\pi\) |
0.459957 | + | 0.887941i | \(0.347865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.5997 | − | 16.3003i | 1.12204 | − | 0.687587i | ||||
\(563\) | 0 | 0 | −0.233445 | − | 0.972370i | \(-0.575000\pi\) | ||||
0.233445 | + | 0.972370i | \(0.425000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.1298 | − | 25.1298i | 1.05722 | − | 1.05722i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.8680 | + | 2.67163i | −0.707143 | + | 0.112001i | −0.499639 | − | 0.866234i | \(-0.666534\pi\) |
−0.207504 | + | 0.978234i | \(0.566534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.8958 | − | 21.3842i | −0.453990 | − | 0.891007i | ||||
\(577\) | −2.20421 | + | 5.32143i | −0.0917624 | + | 0.221534i | −0.963097 | − | 0.269156i | \(-0.913255\pi\) |
0.871334 | + | 0.490690i | \(0.163255\pi\) | |||||||
\(578\) | 23.3665 | − | 32.1613i | 0.971919 | − | 1.33773i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 47.0675 | − | 3.70429i | 1.95437 | − | 0.153812i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −37.6897 | + | 27.3831i | −1.55961 | + | 1.13312i | ||||
\(585\) | 61.9571 | − | 14.8746i | 2.56161 | − | 0.614988i | ||||
\(586\) | 24.8141 | + | 40.4929i | 1.02506 | + | 1.67275i | ||||
\(587\) | 0 | 0 | −0.760406 | − | 0.649448i | \(-0.775000\pi\) | ||||
0.760406 | + | 0.649448i | \(0.225000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.2635 | − | 43.8985i | 0.586225 | − | 1.80422i | ||||
\(593\) | −7.90266 | + | 6.74951i | −0.324524 | + | 0.277169i | −0.796751 | − | 0.604307i | \(-0.793450\pi\) |
0.472228 | + | 0.881477i | \(0.343450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.0151 | + | 24.6055i | 0.860810 | + | 1.00788i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.36889 | − | 0.567014i | 0.0558383 | − | 0.0231290i | −0.354590 | − | 0.935022i | \(-0.615379\pi\) |
0.410428 | + | 0.911893i | \(0.365379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.2903 | − | 27.9273i | −0.824920 | − | 1.13540i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 51.5231 | − | 8.16046i | 2.08611 | − | 0.330407i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 37.2308 | + | 15.4215i | 1.50497 | + | 0.623378i | ||||
\(613\) | 43.7567 | − | 22.2952i | 1.76732 | − | 0.900493i | 0.825474 | − | 0.564440i | \(-0.190908\pi\) |
0.941843 | − | 0.336053i | \(-0.109092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.11219 | + | 10.0332i | 0.205809 | + | 0.403923i | 0.970720 | − | 0.240213i | \(-0.0772172\pi\) |
−0.764911 | + | 0.644136i | \(0.777217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.8209 | + | 15.1273i | −0.832836 | + | 0.605091i | ||||
\(626\) | −45.6619 | + | 10.9624i | −1.82501 | + | 0.438147i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.9921 | + | 16.2207i | 0.757865 | + | 0.647278i | ||||
\(629\) | 29.6592 | + | 71.6036i | 1.18259 | + | 2.85502i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 38.0349 | − | 32.4849i | 1.51056 | − | 1.29014i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.7683 | − | 36.0250i | −1.21908 | − | 1.42736i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −33.7668 | + | 10.9715i | −1.33475 | + | 0.433686i | ||||
\(641\) | −6.16043 | + | 25.6600i | −0.243322 | + | 1.01351i | 0.708220 | + | 0.705992i | \(0.249498\pi\) |
−0.951542 | + | 0.307518i | \(0.900502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.649448 | − | 0.760406i | \(-0.275000\pi\) | ||||
−0.649448 | + | 0.760406i | \(0.725000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | −3.98217 | + | 25.1424i | −0.156434 | + | 0.987688i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.64081 | − | 46.2608i | −0.142804 | − | 1.81450i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.758775 | − | 0.314295i | −0.0296932 | − | 0.0122993i | 0.367787 | − | 0.929910i | \(-0.380115\pi\) |
−0.397481 | + | 0.917611i | \(0.630115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −20.0000 | − | 16.0000i | −0.780869 | − | 0.624695i | ||||
\(657\) | 49.4130 | 1.92778 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.22451 | + | 32.9862i | 0.203210 | + | 1.28302i | 0.852601 | + | 0.522562i | \(0.175024\pi\) |
−0.649391 | + | 0.760454i | \(0.724976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −39.6074 | + | 28.7765i | −1.53476 | + | 1.11507i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.3607 | + | 20.4435i | 1.28596 | + | 0.788037i | 0.986133 | − | 0.165957i | \(-0.0530712\pi\) |
0.299827 | + | 0.953994i | \(0.403071\pi\) | |||||||
\(674\) | 10.8692 | − | 33.4521i | 0.418668 | − | 1.28853i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −58.4604 | − | 29.7871i | −2.24848 | − | 1.14566i | ||||
\(677\) | −14.6107 | + | 28.6751i | −0.561535 | + | 1.10208i | 0.419411 | + | 0.907796i | \(0.362237\pi\) |
−0.980946 | + | 0.194279i | \(0.937763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 31.1490 | − | 50.8306i | 1.19451 | − | 1.94926i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.07241 | + | 4.33398i | −0.270223 | + | 0.165593i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.38490 | + | 33.9989i | −0.205148 | + | 1.29526i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.0784591 | − | 0.996917i | \(-0.525000\pi\) | ||||
0.0784591 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(692\) | −30.3572 | + | 4.80810i | −1.15401 | + | 0.182777i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.9837 | − | 1.38100i | 1.62813 | − | 0.0523091i | ||||
\(698\) | 44.0497 | 1.66731 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9020 | + | 41.1565i | −1.12938 | + | 1.55446i | −0.340142 | + | 0.940374i | \(0.610475\pi\) |
−0.789239 | + | 0.614086i | \(0.789525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −37.5581 | − | 37.5581i | −1.41352 | − | 1.41352i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.01144 | − | 4.91422i | −0.113097 | − | 0.184557i | 0.791083 | − | 0.611708i | \(-0.209517\pi\) |
−0.904180 | + | 0.427151i | \(0.859517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.56948 | + | 2.05735i | 0.321155 | + | 0.0771025i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.649448 | − | 0.760406i | \(-0.725000\pi\) | ||||
0.649448 | + | 0.760406i | \(0.275000\pi\) | |||||||
\(720\) | 35.8150 | + | 11.6370i | 1.33475 | + | 0.433686i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.5549 | + | 8.30330i | −0.951057 | + | 0.309017i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −47.6676 | + | 19.7445i | −1.77155 | + | 0.733800i | ||||
\(725\) | −23.6852 | + | 27.7318i | −0.879646 | + | 1.02993i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.233445 | − | 0.972370i | \(-0.575000\pi\) | ||||
0.233445 | + | 0.972370i | \(0.425000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.0919 | − | 19.0919i | 0.707107 | − | 0.707107i | ||||
\(730\) | 11.4352 | − | 72.1992i | 0.423237 | − | 2.67221i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.2456 | + | 1.93951i | −0.452301 | + | 0.0716374i | −0.378429 | − | 0.925630i | \(-0.623536\pi\) |
−0.0738717 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 7.18680 | + | 26.1983i | 0.264550 | + | 0.964372i | ||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 32.8804 | + | 64.5315i | 1.20871 | + | 2.37223i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −50.6166 | − | 3.98361i | −1.85445 | − | 0.145948i | ||||
\(746\) | 45.3772 | + | 7.18705i | 1.66138 | + | 0.263136i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.760406 | − | 0.649448i | \(-0.775000\pi\) | ||||
0.760406 | + | 0.649448i | \(0.225000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.2490 | + | 68.4755i | 0.810263 | + | 2.49373i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.4931 | − | 34.5844i | 1.47175 | − | 1.25699i | 0.572239 | − | 0.820087i | \(-0.306075\pi\) |
0.899508 | − | 0.436904i | \(-0.143925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.9303 | − | 4.85114i | −0.541222 | − | 0.175854i | 0.0256326 | − | 0.999671i | \(-0.491840\pi\) |
−0.566855 | + | 0.823818i | \(0.691840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −58.4186 | + | 24.1978i | −2.11213 | + | 0.874872i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.6873 | − | 39.4846i | −1.03449 | − | 1.42385i | −0.901523 | − | 0.432731i | \(-0.857550\pi\) |
−0.132966 | − | 0.991121i | \(-0.542450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.29046 | − | 54.5155i | 0.154417 | − | 1.96205i | ||||
\(773\) | −3.78565 | − | 48.1012i | −0.136160 | − | 1.73008i | −0.563609 | − | 0.826042i | \(-0.690588\pi\) |
0.427449 | − | 0.904040i | \(-0.359412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −42.4008 | − | 17.5630i | −1.52210 | − | 0.630475i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.37213i | 0.120897i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.38017 | − | 27.6553i | −0.156434 | − | 0.987688i | ||||
\(785\) | −39.0691 | + | 3.07481i | −1.39444 | + | 0.109745i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(788\) | −15.4570 | − | 15.4570i | −0.550631 | − | 0.550631i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.4431 | + | 73.4962i | 1.08107 | + | 2.60993i | ||||
\(794\) | −29.0182 | − | 6.96666i | −1.02982 | − | 0.247238i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.3832 | + | 53.5001i | −0.615746 | + | 1.89507i | −0.226106 | + | 0.974103i | \(0.572599\pi\) |
−0.389640 | + | 0.920967i | \(0.627401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 12.4509 | − | 24.4363i | 0.440206 | − | 0.863952i | ||||
\(801\) | −6.07077 | − | 7.10796i | −0.214500 | − | 0.251147i | ||||
\(802\) | −50.3355 | − | 16.3550i | −1.77741 | − | 0.577515i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.5439 | − | 20.5557i | 1.18007 | − | 0.723148i | ||||
\(809\) | −13.2567 | − | 55.2181i | −0.466081 | − | 1.94137i | −0.290290 | − | 0.956939i | \(-0.593752\pi\) |
−0.175791 | − | 0.984428i | \(-0.556248\pi\) | |||||||
\(810\) | −23.4776 | − | 32.3142i | −0.824920 | − | 1.13540i | ||||
\(811\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −15.3521 | + | 7.82229i | −0.536774 | + | 0.273500i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 39.9425 | − | 4.43806i | 1.39485 | − | 0.154984i | ||||
\(821\) | −35.4770 | −1.23816 | −0.619078 | − | 0.785330i | \(-0.712493\pi\) | ||||
−0.619078 | + | 0.785330i | \(0.712493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) | ||||
0.996917 | + | 0.0784591i | \(0.0250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0026 | − | 11.0026i | −0.382137 | − | 0.382137i | 0.489735 | − | 0.871872i | \(-0.337094\pi\) |
−0.871872 | + | 0.489735i | \(0.837094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −28.2902 | − | 46.1654i | −0.980785 | − | 1.60050i | ||||
\(833\) | 35.7503 | + | 30.5337i | 1.23867 | + | 1.05793i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.760406 | − | 0.649448i | \(-0.225000\pi\) | ||||
−0.760406 | + | 0.649448i | \(0.775000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5237 | − | 24.5791i | 0.431851 | − | 0.847556i | ||||
\(842\) | 37.4500 | + | 43.8483i | 1.29061 | + | 1.51111i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 97.9119 | − | 31.8135i | 3.36827 | − | 1.09442i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −13.2126 | + | 15.4700i | −0.453723 | + | 0.531242i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.7502 | + | 44.7777i | 0.368728 | + | 1.53586i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.10616 | − | 6.98401i | 0.0378742 | − | 0.239128i | −0.961488 | − | 0.274848i | \(-0.911372\pi\) |
0.999362 | + | 0.0357200i | \(0.0113725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.7470 | − | 32.5106i | −1.52853 | − | 1.11054i | −0.957050 | − | 0.289922i | \(-0.906370\pi\) |
−0.571477 | − | 0.820618i | \(-0.693630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.3470 | − | 39.0164i | 0.963828 | − | 1.32660i | ||||
\(866\) | −2.72530 | − | 17.2069i | −0.0926096 | − | 0.584714i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12.1351 | − | 2.91338i | 0.410947 | − | 0.0986596i | ||||
\(873\) | 25.4343 | + | 41.5051i | 0.860822 | + | 1.40473i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.01180 | + | 6.19167i | 0.0679335 | + | 0.209078i | 0.979260 | − | 0.202606i | \(-0.0649409\pi\) |
−0.911327 | + | 0.411683i | \(0.864941\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3407 | − | 5.77836i | −0.382077 | − | 0.194678i | 0.252394 | − | 0.967624i | \(-0.418782\pi\) |
−0.634471 | + | 0.772947i | \(0.718782\pi\) | |||||||
\(882\) | −13.4828 | + | 26.4615i | −0.453990 | + | 0.891007i | ||||
\(883\) | 0 | 0 | −0.649448 | − | 0.760406i | \(-0.725000\pi\) | ||||
0.649448 | + | 0.760406i | \(0.275000\pi\) | |||||||
\(884\) | 86.4635 | + | 28.0937i | 2.90808 | + | 0.944894i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.233445 | − | 0.972370i | \(-0.425000\pi\) | ||||
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.7906 | + | 7.22530i | −0.395223 | + | 0.242193i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −48.0487 | − | 34.9094i | −1.60341 | − | 1.16494i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −25.9186 | + | 13.2062i | −0.863952 | + | 0.440206i | ||||
\(901\) | − | 34.1602i | − | 1.13804i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.5418 | + | 28.5399i | 0.483653 | + | 0.949222i | ||||
\(905\) | 30.9810 | − | 74.7947i | 1.02984 | − | 2.48626i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.5990 | − | 3.27392i | −1.37975 | − | 0.108589i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 23.3728 | + | 38.1410i | 0.773105 | + | 1.26159i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.33702 | − | 20.1273i | −0.275463 | − | 0.665026i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.852640 | − | 0.522499i | \(-0.825000\pi\) | ||||
0.852640 | + | 0.522499i | \(0.175000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −43.3509 | − | 22.0884i | −1.42769 | − | 0.727442i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −53.2069 | − | 17.2880i | −1.74943 | − | 0.568425i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.93377 | + | 41.3771i | −0.326092 | + | 1.35827i | ||||
\(929\) | 16.9269 | − | 7.01134i | 0.555352 | − | 0.230034i | −0.0873137 | − | 0.996181i | \(-0.527828\pi\) |
0.642666 | + | 0.766146i | \(0.277828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.49480 | − | 27.0528i | −0.212744 | − | 0.886143i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.50578 | + | 57.2514i | −0.147276 | + | 1.87132i | ||||
\(937\) | 4.62031 | + | 58.7067i | 0.150939 | + | 1.91786i | 0.348040 | + | 0.937480i | \(0.386847\pi\) |
−0.197101 | + | 0.980383i | \(0.563153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.51646 | − | 4.84888i | 0.310228 | − | 0.158069i | −0.291944 | − | 0.956435i | \(-0.594302\pi\) |
0.602172 | + | 0.798366i | \(0.294302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 111.132 | − | 8.74628i | 3.60750 | − | 0.283916i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.1618 | + | 12.4688i | −0.555927 | + | 0.403904i | −0.829966 | − | 0.557814i | \(-0.811640\pi\) |
0.274039 | + | 0.961719i | \(0.411640\pi\) | |||||||
\(954\) | 20.9823 | − | 5.03740i | 0.679326 | − | 0.163092i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.57953 | + | 29.4828i | −0.309017 | + | 0.951057i | ||||
\(962\) | −83.9854 | + | 71.7303i | −2.70780 | + | 2.31268i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.89431 | + | 11.5682i | −0.189843 | + | 0.372588i | ||||
\(965\) | 55.7254 | + | 65.2460i | 1.79386 | + | 2.10034i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.522499 | − | 0.852640i | \(-0.325000\pi\) | ||||
−0.522499 | + | 0.852640i | \(0.675000\pi\) | |||||||
\(968\) | 29.5899 | − | 9.61435i | 0.951057 | − | 0.309017i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 66.5307 | − | 27.5579i | 2.13617 | − | 0.884832i | ||||
\(971\) | 0 | 0 | 0.649448 | − | 0.760406i | \(-0.275000\pi\) | ||||
−0.649448 | + | 0.760406i | \(0.725000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.35498 | + | 46.4375i | −0.235427 | + | 1.48643i | ||||
\(977\) | 1.28166 | − | 16.2850i | 0.0410038 | − | 0.521003i | −0.941778 | − | 0.336234i | \(-0.890847\pi\) |
0.982782 | − | 0.184768i | \(-0.0591534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 35.5438 | + | 25.8241i | 1.13540 | + | 0.824920i | ||||
\(981\) | −12.2294 | − | 5.06557i | −0.390453 | − | 0.161731i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.2994 | 1.09287 | ||||||||
\(986\) | −32.4378 | − | 63.6628i | −1.03303 | − | 2.02744i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) | ||||
0.996917 | + | 0.0784591i | \(0.0250000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.7158 | − | 40.7531i | −1.51117 | − | 1.29066i | −0.828589 | − | 0.559857i | \(-0.810856\pi\) |
−0.682585 | − | 0.730807i | \(-0.739144\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 164.2.o.a.7.1 | ✓ | 16 | |
4.3 | odd | 2 | CM | 164.2.o.a.7.1 | ✓ | 16 | |
41.6 | odd | 40 | inner | 164.2.o.a.47.1 | yes | 16 | |
164.47 | even | 40 | inner | 164.2.o.a.47.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.2.o.a.7.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
164.2.o.a.7.1 | ✓ | 16 | 4.3 | odd | 2 | CM | |
164.2.o.a.47.1 | yes | 16 | 41.6 | odd | 40 | inner | |
164.2.o.a.47.1 | yes | 16 | 164.47 | even | 40 | inner |