Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.865 |
Dual form | 1512.2.s.b.1297.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | − | 1.73205i | −0.208514 | − | 0.361158i | 0.742732 | − | 0.669588i | \(-0.233529\pi\) |
−0.951247 | + | 0.308431i | \(0.900196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.500000 | + | 0.866025i | −0.0898027 | + | 0.155543i | −0.907428 | − | 0.420208i | \(-0.861957\pi\) |
0.817625 | + | 0.575751i | \(0.195290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | + | 5.19615i | −0.169031 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50000 | + | 2.59808i | 0.246598 | + | 0.427121i | 0.962580 | − | 0.270998i | \(-0.0873538\pi\) |
−0.715981 | + | 0.698119i | \(0.754020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | − | 6.92820i | −0.583460 | − | 1.01058i | −0.995066 | − | 0.0992202i | \(-0.968365\pi\) |
0.411606 | − | 0.911362i | \(-0.364968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.00000 | + | 12.1244i | −0.961524 | + | 1.66541i | −0.242846 | + | 0.970065i | \(0.578081\pi\) |
−0.718677 | + | 0.695344i | \(0.755252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | + | 10.3923i | −0.781133 | + | 1.35296i | 0.150148 | + | 0.988663i | \(0.452025\pi\) |
−0.931282 | + | 0.364299i | \(0.881308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.500000 | − | 0.866025i | −0.0640184 | − | 0.110883i | 0.832240 | − | 0.554416i | \(-0.187058\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50000 | + | 2.59808i | −0.183254 | + | 0.317406i | −0.942987 | − | 0.332830i | \(-0.891996\pi\) |
0.759733 | + | 0.650236i | \(0.225330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.00000 | + | 8.66025i | −0.585206 | + | 1.01361i | 0.409644 | + | 0.912245i | \(0.365653\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | − | 0.866025i | −0.0562544 | − | 0.0974355i | 0.836527 | − | 0.547926i | \(-0.184582\pi\) |
−0.892781 | + | 0.450490i | \(0.851249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00000 | + | 1.73205i | 0.106000 | + | 0.183597i | 0.914146 | − | 0.405385i | \(-0.132862\pi\) |
−0.808146 | + | 0.588982i | \(0.799529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | − | 5.19615i | −0.628971 | − | 0.544705i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | + | 6.92820i | −0.410391 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | 0.101535 | 0.0507673 | − | 0.998711i | \(-0.483833\pi\) | ||||
0.0507673 | + | 0.998711i | \(0.483833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.50000 | − | 12.9904i | −0.738997 | − | 1.27998i | −0.952947 | − | 0.303136i | \(-0.901966\pi\) |
0.213950 | − | 0.976845i | \(-0.431367\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | − | 5.19615i | −0.290021 | − | 0.502331i | 0.683793 | − | 0.729676i | \(-0.260329\pi\) |
−0.973814 | + | 0.227345i | \(0.926996\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.50000 | − | 4.33013i | 0.239457 | − | 0.414751i | −0.721102 | − | 0.692829i | \(-0.756364\pi\) |
0.960558 | + | 0.278078i | \(0.0896974\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | + | 3.46410i | −0.186501 | + | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0000 | − | 3.46410i | 0.916698 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0000 | 1.50851 | 0.754253 | − | 0.656584i | \(-0.227999\pi\) | ||||
0.754253 | + | 0.656584i | \(0.227999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | − | 6.92820i | −0.349482 | − | 0.605320i | 0.636676 | − | 0.771132i | \(-0.280309\pi\) |
−0.986157 | + | 0.165812i | \(0.946976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | + | 10.3923i | −0.173422 | + | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00000 | + | 1.73205i | −0.0854358 | + | 0.147979i | −0.905577 | − | 0.424182i | \(-0.860562\pi\) |
0.820141 | + | 0.572161i | \(0.193895\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.0000 | −1.27228 | −0.636142 | − | 0.771572i | \(-0.719471\pi\) | ||||
−0.636142 | + | 0.771572i | \(0.719471\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | + | 6.92820i | 0.332182 | + | 0.575356i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.00000 | + | 12.1244i | 0.573462 | + | 0.993266i | 0.996207 | + | 0.0870170i | \(0.0277334\pi\) |
−0.422744 | + | 0.906249i | \(0.638933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.50000 | − | 14.7224i | 0.691720 | − | 1.19809i | −0.279554 | − | 0.960130i | \(-0.590186\pi\) |
0.971274 | − | 0.237964i | \(-0.0764802\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | − | 15.5885i | 0.718278 | − | 1.24409i | −0.243403 | − | 0.969925i | \(-0.578264\pi\) |
0.961681 | − | 0.274169i | \(-0.0884028\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | + | 5.19615i | −0.0788110 | + | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.50000 | − | 16.4545i | −0.744097 | − | 1.28881i | −0.950615 | − | 0.310372i | \(-0.899546\pi\) |
0.206518 | − | 0.978443i | \(-0.433787\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | −0.464294 | −0.232147 | − | 0.972681i | \(-0.574575\pi\) | ||||
−0.232147 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.00000 | − | 6.92820i | −0.304114 | − | 0.526742i | 0.672949 | − | 0.739689i | \(-0.265027\pi\) |
−0.977064 | + | 0.212947i | \(0.931694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | + | 0.866025i | −0.188982 | + | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.0000 | + | 22.5167i | −0.971666 | + | 1.68297i | −0.281139 | + | 0.959667i | \(0.590712\pi\) |
−0.690526 | + | 0.723307i | \(0.742621\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.00000 | − | 8.66025i | −0.361787 | − | 0.626634i | 0.626468 | − | 0.779447i | \(-0.284500\pi\) |
−0.988255 | + | 0.152813i | \(0.951167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.50000 | − | 7.79423i | 0.323917 | − | 0.561041i | −0.657376 | − | 0.753563i | \(-0.728333\pi\) |
0.981293 | + | 0.192522i | \(0.0616668\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.50000 | + | 4.33013i | −0.177220 | + | 0.306955i | −0.940927 | − | 0.338608i | \(-0.890044\pi\) |
0.763707 | + | 0.645563i | \(0.223377\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | + | 6.92820i | 0.561490 | + | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00000 | + | 13.8564i | 0.558744 | + | 0.967773i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0000 | −1.72107 | −0.860535 | − | 0.509390i | \(-0.829871\pi\) | ||||
−0.860535 | + | 0.509390i | \(0.829871\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.00000 | + | 1.73205i | 0.0681994 | + | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.50000 | − | 0.866025i | 0.169711 | − | 0.0587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0000 | 0.803579 | 0.401790 | − | 0.915732i | \(-0.368388\pi\) | ||||
0.401790 | + | 0.915732i | \(0.368388\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0000 | − | 19.0526i | 0.730096 | − | 1.26456i | −0.226746 | − | 0.973954i | \(-0.572809\pi\) |
0.956842 | − | 0.290609i | \(-0.0938578\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | + | 0.866025i | 0.0330409 | + | 0.0572286i | 0.882073 | − | 0.471113i | \(-0.156147\pi\) |
−0.849032 | + | 0.528341i | \(0.822814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.00000 | + | 13.8564i | 0.524097 | + | 0.907763i | 0.999606 | + | 0.0280525i | \(0.00893057\pi\) |
−0.475509 | + | 0.879711i | \(0.657736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | + | 13.8564i | −0.521862 | + | 0.903892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.0000 | 1.68180 | 0.840900 | − | 0.541190i | \(-0.182026\pi\) | ||||
0.840900 | + | 0.541190i | \(0.182026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | + | 0.866025i | −0.0322078 | + | 0.0557856i | −0.881680 | − | 0.471848i | \(-0.843587\pi\) |
0.849472 | + | 0.527633i | \(0.176921\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.0000 | − | 8.66025i | 0.702764 | − | 0.553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | − | 10.3923i | −0.381771 | − | 0.661247i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.0000 | 0.631194 | 0.315597 | − | 0.948893i | \(-0.397795\pi\) | ||||
0.315597 | + | 0.948893i | \(0.397795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.0000 | − | 25.9808i | −0.935674 | − | 1.62064i | −0.773427 | − | 0.633885i | \(-0.781459\pi\) |
−0.162247 | − | 0.986750i | \(-0.551874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.50000 | − | 7.79423i | 0.0932055 | − | 0.484310i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.0000 | 1.72003 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.50000 | + | 11.2583i | 0.394847 | + | 0.683895i | 0.993082 | − | 0.117426i | \(-0.0374643\pi\) |
−0.598235 | + | 0.801321i | \(0.704131\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5000 | + | 26.8468i | −0.931305 | + | 1.61307i | −0.150210 | + | 0.988654i | \(0.547995\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.5000 | + | 19.9186i | −0.683604 | + | 1.18404i | 0.290269 | + | 0.956945i | \(0.406255\pi\) |
−0.973873 | + | 0.227092i | \(0.927078\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.0000 | + | 13.8564i | 0.944450 | + | 0.817918i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000 | 1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | − | 5.19615i | −0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | + | 1.73205i | 0.115278 | + | 0.0998337i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00000 | + | 1.73205i | −0.0572598 | + | 0.0991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.0000 | −1.31268 | −0.656340 | − | 0.754466i | \(-0.727896\pi\) | ||||
−0.656340 | + | 0.754466i | \(0.727896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000 | − | 5.19615i | 0.170114 | − | 0.294647i | −0.768345 | − | 0.640036i | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.00000 | − | 12.1244i | −0.395663 | − | 0.685309i | 0.597522 | − | 0.801852i | \(-0.296152\pi\) |
−0.993186 | + | 0.116543i | \(0.962819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.0000 | − | 20.7846i | −0.673987 | − | 1.16738i | −0.976764 | − | 0.214318i | \(-0.931247\pi\) |
0.302777 | − | 0.953062i | \(-0.402086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0000 | 0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.50000 | − | 2.59808i | 0.0832050 | − | 0.144115i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00000 | + | 20.7846i | −0.220527 | + | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.00000 | 0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0000 | −1.01705 | −0.508523 | − | 0.861048i | \(-0.669808\pi\) | ||||
−0.508523 | + | 0.861048i | \(0.669808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.00000 | + | 5.19615i | 0.158334 | + | 0.274242i | 0.934268 | − | 0.356572i | \(-0.116054\pi\) |
−0.775934 | + | 0.630814i | \(0.782721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.0000 | 1.04685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | − | 13.8564i | 0.417597 | − | 0.723299i | −0.578101 | − | 0.815966i | \(-0.696206\pi\) |
0.995697 | + | 0.0926670i | \(0.0295392\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.0000 | − | 12.1244i | 1.81711 | − | 0.629465i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0000 | 0.770498 | 0.385249 | − | 0.922813i | \(-0.374116\pi\) | ||||
0.385249 | + | 0.922813i | \(0.374116\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.0000 | − | 25.9808i | −0.766464 | − | 1.32755i | −0.939469 | − | 0.342634i | \(-0.888681\pi\) |
0.173005 | − | 0.984921i | \(-0.444652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0000 | + | 24.2487i | −0.709828 | + | 1.22946i | 0.255092 | + | 0.966917i | \(0.417894\pi\) |
−0.964921 | + | 0.262542i | \(0.915439\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00000 | + | 1.73205i | −0.0503155 | + | 0.0871489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.50000 | − | 11.2583i | −0.326226 | − | 0.565039i | 0.655534 | − | 0.755166i | \(-0.272444\pi\) |
−0.981760 | + | 0.190126i | \(0.939110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50000 | + | 2.59808i | −0.0747203 | + | 0.129419i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5000 | − | 33.7750i | 0.964213 | − | 1.67007i | 0.252498 | − | 0.967597i | \(-0.418748\pi\) |
0.711715 | − | 0.702468i | \(-0.247919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.0000 | − | 10.3923i | 1.47620 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | + | 10.3923i | 0.294528 | + | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.0000 | 0.683945 | 0.341972 | − | 0.939710i | \(-0.388905\pi\) | ||||
0.341972 | + | 0.939710i | \(0.388905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.0000 | −1.85201 | −0.926003 | − | 0.377515i | \(-0.876779\pi\) | ||||
−0.926003 | + | 0.377515i | \(0.876779\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | + | 3.46410i | 0.0970143 | + | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.500000 | + | 2.59808i | −0.0241967 | + | 0.125730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0000 | + | 20.7846i | −0.578020 | + | 1.00116i | 0.417687 | + | 0.908591i | \(0.362841\pi\) |
−0.995706 | + | 0.0925683i | \(0.970492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000 | 0.336399 | 0.168199 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168199 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.00000 | + | 6.92820i | −0.191346 | + | 0.331421i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | + | 20.7846i | 0.572729 | + | 0.991995i | 0.996284 | + | 0.0861252i | \(0.0274485\pi\) |
−0.423556 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.00000 | − | 6.92820i | −0.190046 | − | 0.329169i | 0.755219 | − | 0.655472i | \(-0.227530\pi\) |
−0.945265 | + | 0.326303i | \(0.894197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | − | 3.46410i | 0.0948091 | − | 0.164214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.00000 | + | 15.5885i | −0.140642 | + | 0.730798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | − | 21.6506i | −0.584725 | − | 1.01277i | −0.994910 | − | 0.100771i | \(-0.967869\pi\) |
0.410184 | − | 0.912003i | \(-0.365464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.00000 | − | 5.19615i | −0.138823 | − | 0.240449i | 0.788228 | − | 0.615383i | \(-0.210999\pi\) |
−0.927052 | + | 0.374934i | \(0.877665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.50000 | − | 2.59808i | 0.346318 | − | 0.119968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.00000 | + | 8.66025i | −0.228456 | + | 0.395697i | −0.957351 | − | 0.288929i | \(-0.906701\pi\) |
0.728895 | + | 0.684626i | \(0.240034\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | + | 7.79423i | 0.205182 | + | 0.355386i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.00000 | − | 1.73205i | −0.0454077 | − | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000 | − | 6.92820i | 0.181257 | − | 0.313947i | −0.761052 | − | 0.648691i | \(-0.775317\pi\) |
0.942309 | + | 0.334744i | \(0.108650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | 0.270776 | 0.135388 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135388 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000 | − | 13.8564i | 0.360302 | − | 0.624061i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | + | 10.3923i | 0.538274 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | − | 6.06218i | −0.156682 | − | 0.271380i | 0.776989 | − | 0.629515i | \(-0.216746\pi\) |
−0.933670 | + | 0.358134i | \(0.883413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.0000 | −0.624229 | −0.312115 | − | 0.950044i | \(-0.601037\pi\) | ||||
−0.312115 | + | 0.950044i | \(0.601037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.00000 | − | 5.19615i | −0.132973 | − | 0.230315i | 0.791849 | − | 0.610718i | \(-0.209119\pi\) |
−0.924821 | + | 0.380402i | \(0.875786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.0000 | − | 8.66025i | 1.10593 | − | 0.383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0000 | + | 25.9808i | −0.660979 | + | 1.14485i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | − | 5.19615i | 0.131432 | − | 0.227648i | −0.792797 | − | 0.609486i | \(-0.791376\pi\) |
0.924229 | + | 0.381839i | \(0.124709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5000 | + | 21.6506i | 0.546587 | + | 0.946716i | 0.998505 | + | 0.0546569i | \(0.0174065\pi\) |
−0.451918 | + | 0.892059i | \(0.649260\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.00000 | − | 3.46410i | −0.0871214 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0000 | −1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | + | 10.3923i | −0.259403 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0000 | − | 29.4449i | −0.730887 | − | 1.26593i | −0.956504 | − | 0.291718i | \(-0.905773\pi\) |
0.225617 | − | 0.974216i | \(-0.427560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.00000 | 0.299298 | 0.149649 | − | 0.988739i | \(-0.452186\pi\) | ||||
0.149649 | + | 0.988739i | \(0.452186\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.00000 | + | 13.8564i | 0.340811 | + | 0.590303i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | + | 2.59808i | −0.0212622 | + | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00000 | − | 1.73205i | 0.0423714 | − | 0.0733893i | −0.844062 | − | 0.536246i | \(-0.819842\pi\) |
0.886433 | + | 0.462856i | \(0.153175\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.00000 | −0.126886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.00000 | − | 12.1244i | 0.295015 | − | 0.510981i | −0.679974 | − | 0.733237i | \(-0.738009\pi\) |
0.974988 | + | 0.222256i | \(0.0713421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | − | 10.3923i | −0.252422 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.5000 | + | 23.3827i | −0.562012 | + | 0.973434i | 0.435308 | + | 0.900281i | \(0.356639\pi\) |
−0.997321 | + | 0.0731526i | \(0.976694\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | + | 10.3923i | 0.497844 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.0000 | −1.56843 | −0.784214 | − | 0.620491i | \(-0.786934\pi\) | ||||
−0.784214 | + | 0.620491i | \(0.786934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.0000 | − | 36.3731i | −0.862367 | − | 1.49366i | −0.869638 | − | 0.493689i | \(-0.835648\pi\) |
0.00727173 | − | 0.999974i | \(-0.497685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0000 | − | 13.8564i | −0.655936 | − | 0.568057i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.0000 | + | 34.6410i | −0.817178 | + | 1.41539i | 0.0905757 | + | 0.995890i | \(0.471129\pi\) |
−0.907754 | + | 0.419504i | \(0.862204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.00000 | −0.203954 | −0.101977 | − | 0.994787i | \(-0.532517\pi\) | ||||
−0.101977 | + | 0.994787i | \(0.532517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | − | 19.0526i | 0.447214 | − | 0.774597i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0000 | + | 27.7128i | 0.649420 | + | 1.12483i | 0.983262 | + | 0.182199i | \(0.0583216\pi\) |
−0.333842 | + | 0.942629i | \(0.608345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | − | 20.7846i | −0.485468 | − | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.500000 | + | 0.866025i | −0.0201948 | + | 0.0349784i | −0.875946 | − | 0.482409i | \(-0.839762\pi\) |
0.855751 | + | 0.517387i | \(0.173095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.0000 | 1.44931 | 0.724653 | − | 0.689114i | \(-0.242000\pi\) | ||||
0.724653 | + | 0.689114i | \(0.242000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.5000 | + | 23.3827i | −0.542611 | + | 0.939829i | 0.456142 | + | 0.889907i | \(0.349231\pi\) |
−0.998753 | + | 0.0499226i | \(0.984103\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.00000 | − | 5.19615i | 0.0400642 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.0000 | 1.87104 | 0.935520 | − | 0.353273i | \(-0.114931\pi\) | ||||
0.935520 | + | 0.353273i | \(0.114931\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.0000 | − | 29.4449i | −0.674624 | − | 1.16848i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | + | 20.7846i | 0.118864 | + | 0.823516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.0000 | + | 34.6410i | −0.789953 | + | 1.36824i | 0.136043 | + | 0.990703i | \(0.456562\pi\) |
−0.925995 | + | 0.377535i | \(0.876772\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.0000 | −1.14365 | −0.571824 | − | 0.820376i | \(-0.693764\pi\) | ||||
−0.571824 | + | 0.820376i | \(0.693764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | − | 20.7846i | 0.471769 | − | 0.817127i | −0.527710 | − | 0.849425i | \(-0.676949\pi\) |
0.999478 | + | 0.0322975i | \(0.0102824\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.00000 | − | 12.1244i | −0.273931 | − | 0.474463i | 0.695934 | − | 0.718106i | \(-0.254991\pi\) |
−0.969865 | + | 0.243643i | \(0.921657\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | + | 13.8564i | −0.312586 | + | 0.541415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.0000 | −0.389545 | −0.194772 | − | 0.980848i | \(-0.562397\pi\) | ||||
−0.194772 | + | 0.980848i | \(0.562397\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0000 | − | 19.0526i | 0.427850 | − | 0.741059i | −0.568831 | − | 0.822454i | \(-0.692604\pi\) |
0.996682 | + | 0.0813955i | \(0.0259377\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.0000 | − | 6.92820i | 0.775567 | − | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000 | + | 6.92820i | 0.154881 | + | 0.268261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0000 | −1.00223 | −0.501113 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000 | + | 31.1769i | 0.691796 | + | 1.19823i | 0.971249 | + | 0.238067i | \(0.0765137\pi\) |
−0.279453 | + | 0.960159i | \(0.590153\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | − | 1.73205i | −0.0767530 | − | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.00000 | − | 15.5885i | 0.344375 | − | 0.596476i | −0.640865 | − | 0.767654i | \(-0.721424\pi\) |
0.985240 | + | 0.171178i | \(0.0547574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | 0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.0000 | + | 36.3731i | −0.800036 | + | 1.38570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.50000 | + | 6.06218i | 0.133146 | + | 0.230616i | 0.924888 | − | 0.380240i | \(-0.124159\pi\) |
−0.791742 | + | 0.610856i | \(0.790825\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0000 | + | 25.9808i | 0.568982 | + | 0.985506i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000 | − | 27.7128i | 0.606043 | − | 1.04970i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.0000 | −1.66186 | −0.830929 | − | 0.556379i | \(-0.812190\pi\) | ||||
−0.830929 | + | 0.556379i | \(0.812190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | − | 10.3923i | 0.226294 | − | 0.391953i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −45.0000 | + | 15.5885i | −1.69240 | + | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.50000 | + | 14.7224i | 0.319224 | + | 0.552913i | 0.980326 | − | 0.197383i | \(-0.0632444\pi\) |
−0.661102 | + | 0.750296i | \(0.729911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.00000 | 0.0749006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.00000 | − | 15.5885i | −0.335643 | − | 0.581351i | 0.647965 | − | 0.761670i | \(-0.275620\pi\) |
−0.983608 | + | 0.180319i | \(0.942287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.50000 | + | 38.9711i | −0.279315 | + | 1.45136i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | + | 3.46410i | −0.0742781 | + | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.0000 | 0.853023 | 0.426511 | − | 0.904482i | \(-0.359742\pi\) | ||||
0.426511 | + | 0.904482i | \(0.359742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.00000 | − | 3.46410i | 0.0739727 | − | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.5000 | − | 26.8468i | −0.572506 | − | 0.991609i | −0.996308 | − | 0.0858539i | \(-0.972638\pi\) |
0.423802 | − | 0.905755i | \(-0.360695\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.50000 | + | 16.4545i | −0.349463 | + | 0.605288i | −0.986154 | − | 0.165831i | \(-0.946969\pi\) |
0.636691 | + | 0.771119i | \(0.280303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.0000 | 1.61420 | 0.807102 | − | 0.590412i | \(-0.201035\pi\) | ||||
0.807102 | + | 0.590412i | \(0.201035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.0000 | − | 24.2487i | 0.512920 | − | 0.888404i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.00000 | + | 15.5885i | −0.109618 | + | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0000 | − | 17.3205i | −0.364905 | − | 0.632034i | 0.623856 | − | 0.781540i | \(-0.285565\pi\) |
−0.988761 | + | 0.149505i | \(0.952232\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.0000 | −1.23739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0000 | −0.617876 | −0.308938 | − | 0.951082i | \(-0.599973\pi\) | ||||
−0.308938 | + | 0.951082i | \(0.599973\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0000 | − | 41.5692i | −0.869999 | − | 1.50688i | −0.861996 | − | 0.506915i | \(-0.830786\pi\) |
−0.00800331 | − | 0.999968i | \(-0.502548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.5000 | + | 4.33013i | −0.452530 | + | 0.156761i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.0000 | + | 31.1769i | −0.649942 | + | 1.12573i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.0000 | −0.937584 | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||||
−0.468792 | + | 0.883309i | \(0.655311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.0000 | − | 17.3205i | 0.359675 | − | 0.622975i | −0.628231 | − | 0.778027i | \(-0.716221\pi\) |
0.987906 | + | 0.155051i | \(0.0495542\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.500000 | + | 0.866025i | 0.0179605 | + | 0.0311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0000 | + | 27.7128i | 0.573259 | + | 0.992915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.5000 | + | 32.0429i | −0.659454 | + | 1.14221i | 0.321303 | + | 0.946976i | \(0.395879\pi\) |
−0.980757 | + | 0.195231i | \(0.937454\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | − | 10.3923i | −0.426671 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50000 | − | 2.59808i | −0.0532666 | − | 0.0922604i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.0000 | −0.850124 | −0.425062 | − | 0.905164i | \(-0.639748\pi\) | ||||
−0.425062 | + | 0.905164i | \(0.639748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.0000 | 1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.0000 | − | 3.46410i | 0.352454 | − | 0.122094i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | + | 25.9808i | −0.527372 | + | 0.913435i | 0.472119 | + | 0.881535i | \(0.343489\pi\) |
−0.999491 | + | 0.0319002i | \(0.989844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0000 | 0.421377 | 0.210688 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210688 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.0000 | + | 32.9090i | −0.665541 | + | 1.15275i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | + | 3.46410i | 0.0699711 | + | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | − | 15.5885i | −0.314102 | − | 0.544041i | 0.665144 | − | 0.746715i | \(-0.268370\pi\) |
−0.979246 | + | 0.202674i | \(0.935037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.500000 | − | 0.866025i | 0.0174289 | − | 0.0301877i | −0.857179 | − | 0.515018i | \(-0.827785\pi\) |
0.874608 | + | 0.484830i | \(0.161119\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.0000 | − | 39.8372i | 0.798823 | − | 1.38360i | −0.121560 | − | 0.992584i | \(-0.538790\pi\) |
0.920383 | − | 0.391018i | \(-0.127877\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.0000 | − | 10.3923i | −0.900847 | − | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.00000 | + | 10.3923i | 0.207639 | + | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.0000 | −1.86429 | −0.932144 | − | 0.362089i | \(-0.882064\pi\) | ||||
−0.932144 | + | 0.362089i | \(0.882064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.00000 | + | 6.92820i | 0.137604 | + | 0.238337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.50000 | − | 28.5788i | 0.188982 | − | 0.981981i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.00000 | − | 5.19615i | 0.102839 | − | 0.178122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.00000 | −0.0684787 | −0.0342393 | − | 0.999414i | \(-0.510901\pi\) | ||||
−0.0342393 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0000 | + | 36.3731i | −0.717346 | + | 1.24248i | 0.244701 | + | 0.969599i | \(0.421310\pi\) |
−0.962048 | + | 0.272882i | \(0.912023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.5000 | − | 26.8468i | −0.528853 | − | 0.916001i | −0.999434 | − | 0.0336436i | \(-0.989289\pi\) |
0.470581 | − | 0.882357i | \(-0.344044\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.0000 | − | 17.3205i | −0.340404 | − | 0.589597i | 0.644104 | − | 0.764938i | \(-0.277230\pi\) |
−0.984508 | + | 0.175341i | \(0.943897\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00000 | + | 13.8564i | −0.272008 | + | 0.471132i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.50000 | + | 7.79423i | −0.152477 | + | 0.264097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0000 | + | 20.7846i | 0.811348 | + | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.50000 | − | 14.7224i | −0.287025 | − | 0.497141i | 0.686074 | − | 0.727532i | \(-0.259333\pi\) |
−0.973098 | + | 0.230391i | \(0.925999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.00000 | −0.0673817 | −0.0336909 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.0000 | − | 25.9808i | −0.503651 | − | 0.872349i | −0.999991 | − | 0.00422062i | \(-0.998657\pi\) |
0.496340 | − | 0.868128i | \(-0.334677\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.0000 | − | 29.4449i | −1.14032 | − | 0.987549i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0000 | + | 27.7128i | −0.535420 | + | 0.927374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.0000 | 1.73817 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.00000 | − | 3.46410i | 0.0667037 | − | 0.115534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.0000 | − | 48.4974i | −0.932815 | − | 1.61568i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.00000 | − | 3.46410i | −0.0664822 | − | 0.115151i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.500000 | − | 0.866025i | 0.0166022 | − | 0.0287559i | −0.857605 | − | 0.514309i | \(-0.828048\pi\) |
0.874207 | + | 0.485553i | \(0.161382\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.0000 | −1.45779 | −0.728893 | − | 0.684628i | \(-0.759965\pi\) | ||||
−0.728893 | + | 0.684628i | \(0.759965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | + | 20.7846i | −0.132092 | + | 0.686368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.5000 | + | 35.5070i | 0.676233 | + | 1.17127i | 0.976107 | + | 0.217291i | \(0.0697219\pi\) |
−0.299874 | + | 0.953979i | \(0.596945\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.0000 | −0.592477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | 0.0986394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.00000 | + | 12.1244i | 0.229663 | + | 0.397787i | 0.957708 | − | 0.287742i | \(-0.0929044\pi\) |
−0.728046 | + | 0.685529i | \(0.759571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.0000 | − | 17.3205i | 0.721021 | − | 0.567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0000 | 0.882052 | 0.441026 | − | 0.897494i | \(-0.354615\pi\) | ||||
0.441026 | + | 0.897494i | \(0.354615\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000 | + | 13.8564i | 0.260516 | + | 0.451227i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.0000 | + | 27.7128i | 0.519930 | + | 0.900545i | 0.999732 | + | 0.0231683i | \(0.00737536\pi\) |
−0.479801 | + | 0.877377i | \(0.659291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0000 | + | 25.9808i | −0.486921 | + | 0.843371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.0000 | 0.323932 | 0.161966 | − | 0.986796i | \(-0.448217\pi\) | ||||
0.161966 | + | 0.986796i | \(0.448217\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0000 | + | 17.3205i | −0.323592 | + | 0.560478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.00000 | − | 1.73205i | 0.161458 | − | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | + | 25.9808i | 0.483871 | + | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.0000 | −0.579441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.0000 | 1.06121 | 0.530604 | − | 0.847620i | \(-0.321965\pi\) | ||||
0.530604 | + | 0.847620i | \(0.321965\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | + | 6.92820i | 0.128366 | + | 0.222337i | 0.923044 | − | 0.384695i | \(-0.125693\pi\) |
−0.794678 | + | 0.607032i | \(0.792360\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.0000 | + | 25.9808i | 0.961756 | + | 0.832905i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.0000 | − | 25.9808i | 0.479893 | − | 0.831198i | −0.519841 | − | 0.854263i | \(-0.674009\pi\) |
0.999734 | + | 0.0230645i | \(0.00734232\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.0000 | − | 36.3731i | 0.669796 | − | 1.16012i | −0.308165 | − | 0.951333i | \(-0.599715\pi\) |
0.977961 | − | 0.208788i | \(-0.0669518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0000 | − | 20.7846i | −0.382352 | − | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.00000 | + | 1.73205i | 0.0317982 | + | 0.0550760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5000 | − | 18.1865i | 0.333543 | − | 0.577714i | −0.649660 | − | 0.760224i | \(-0.725089\pi\) |
0.983204 | + | 0.182510i | \(0.0584223\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | 0.317021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.5000 | + | 32.0429i | −0.585901 | + | 1.01481i | 0.408862 | + | 0.912596i | \(0.365926\pi\) |
−0.994762 | + | 0.102214i | \(0.967407\pi\) | |||||||
\(998\) | 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 | 1512.2.s.b.865.1 | ✓ | 2 | |
3.2 | odd | 2 | 1512.2.s.f.865.1 | yes | 2 | ||
7.2 | even | 3 | inner | 1512.2.s.b.1297.1 | yes | 2 | |
21.2 | odd | 6 | 1512.2.s.f.1297.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.b.865.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1512.2.s.b.1297.1 | yes | 2 | 7.2 | even | 3 | inner | |
1512.2.s.f.865.1 | yes | 2 | 3.2 | odd | 2 | ||
1512.2.s.f.1297.1 | yes | 2 | 21.2 | odd | 6 |