Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1191,1,Mod(65,1191)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1191, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 17]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1191.65");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1191 = 3 \cdot 397 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1191.z (of order \(66\), degree \(20\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.594386430046\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{66}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{66} - \cdots)\) |
Embedding invariants
Embedding label | 1040.1 | ||
Root | \(-0.786053 + 0.618159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1191.1040 |
Dual form | 1191.1.z.a.560.1 |
$q$-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 \(\left(\mathbb{Z}/1191\mathbb{Z}\right)^\times\).
\(n\) | \(398\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{47}{66}\right)\) |
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 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(3\) | −0.327068 | + | 0.945001i | −0.327068 | + | 0.945001i | ||||
\(4\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(5\) | 0 | 0 | 0.618159 | − | 0.786053i | \(-0.287879\pi\) | ||||
−0.618159 | + | 0.786053i | \(0.712121\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.07068 | + | 1.36148i | 1.07068 | + | 1.36148i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(12\) | −0.580057 | + | 0.814576i | −0.580057 | + | 0.814576i | ||||
\(13\) | 0.184753 | − | 0.0448206i | 0.184753 | − | 0.0448206i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(17\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.65033 | − | 0.850806i | −1.65033 | − | 0.850806i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.63679 | + | 0.566498i | −1.63679 | + | 0.566498i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.235759 | − | 0.971812i | −0.235759 | − | 0.971812i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(28\) | 0.643738 | + | 1.60798i | 0.643738 | + | 1.60798i | ||||
\(29\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.30379 | − | 1.50465i | 1.30379 | − | 1.50465i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.580057 | − | 0.814576i | −0.580057 | − | 0.814576i | ||||
\(37\) | −1.65210 | − | 0.318417i | −1.65210 | − | 0.318417i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0180713 | + | 0.189251i | −0.0180713 | + | 0.189251i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.223734 | + | 1.55610i | −0.223734 | + | 1.55610i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(48\) | −0.786053 | + | 0.618159i | −0.786053 | + | 0.618159i | ||||
\(49\) | −0.471518 | + | 1.94362i | −0.471518 | + | 1.94362i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.189897 | + | 0.00904590i | 0.189897 | + | 0.00904590i | ||||
\(53\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.34378 | − | 1.28129i | 1.34378 | − | 1.28129i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.945001 | − | 0.327068i | \(-0.106061\pi\) | ||||
−0.945001 | + | 0.327068i | \(0.893939\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.83673 | − | 0.445585i | −1.83673 | − | 0.445585i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.73205i | − | 1.73205i | ||||||
\(64\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.88431 | + | 0.363170i | 1.88431 | + | 0.363170i | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) |
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0224357 | − | 0.470984i | 0.0224357 | − | 0.470984i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.995472 | + | 0.0950560i | 0.995472 | + | 0.0950560i | ||||
\(76\) | −1.34378 | − | 1.28129i | −1.34378 | − | 1.28129i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.327068 | − | 0.566498i | −0.327068 | − | 0.566498i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.235759 | + | 0.971812i | 0.235759 | + | 0.971812i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(84\) | −1.73009 | + | 0.0824143i | −1.73009 | + | 0.0824143i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.258835 | + | 0.203550i | 0.258835 | + | 0.203550i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.995472 | + | 1.72421i | 0.995472 | + | 1.72421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0883470 | − | 0.0353688i | −0.0883470 | − | 0.0353688i | 0.327068 | − | 0.945001i | \(-0.393939\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0475819 | − | 0.998867i | 0.0475819 | − | 0.998867i | ||||
\(101\) | 0 | 0 | −0.814576 | − | 0.580057i | \(-0.803030\pi\) | ||||
0.814576 | + | 0.580057i | \(0.196970\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.286053 | + | 0.247866i | 0.286053 | + | 0.247866i | 0.786053 | − | 0.618159i | \(-0.212121\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(108\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(109\) | 0.367833 | + | 1.90850i | 0.367833 | + | 1.90850i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.841254 | − | 1.45709i | 0.841254 | − | 1.45709i | ||||
\(112\) | 0.164642 | + | 1.72421i | 0.164642 | + | 1.72421i | ||||
\(113\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.172932 | − | 0.0789754i | −0.172932 | − | 0.0789754i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.327068 | − | 0.945001i | −0.327068 | − | 0.945001i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.67489 | − | 1.07639i | 1.67489 | − | 1.07639i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0671040 | − | 0.276606i | 0.0671040 | − | 0.276606i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.39734 | − | 0.720381i | −1.39734 | − | 0.720381i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.608625 | − | 3.15784i | −0.608625 | − | 3.15784i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.605495 | − | 0.431171i | −0.605495 | − | 0.431171i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.327068 | − | 0.945001i | −0.327068 | − | 0.945001i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.68251 | − | 1.08128i | −1.68251 | − | 1.08128i | ||||
\(148\) | −1.49547 | − | 0.770969i | −1.49547 | − | 0.770969i | ||||
\(149\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.49547 | − | 0.961081i | 1.49547 | − | 0.961081i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0706575 | + | 0.176494i | −0.0706575 | + | 0.176494i | ||||
\(157\) | − | 1.99773i | − | 1.99773i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.21769 | + | 0.782560i | 1.21769 | + | 0.782560i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.856711 | + | 0.441665i | −0.856711 | + | 0.441665i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.771316 | + | 1.68895i | 0.771316 | + | 1.68895i | ||||
\(172\) | −0.653077 | + | 1.43004i | −0.653077 | + | 1.43004i | ||||
\(173\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.07068 | − | 1.36148i | 1.07068 | − | 1.36148i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.07028 | − | 0.153882i | 1.07028 | − | 0.153882i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.02181 | − | 1.58997i | 1.02181 | − | 1.58997i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.63679 | + | 0.566498i | 1.63679 | + | 0.566498i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(192\) | −0.928368 | + | 0.371662i | −0.928368 | + | 0.371662i | ||||
\(193\) | 0.258195 | − | 0.500828i | 0.258195 | − | 0.500828i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(197\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.80075 | + | 0.258908i | −1.80075 | + | 0.258908i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.959493 | + | 1.66189i | −0.959493 | + | 1.66189i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.179656 | + | 0.0621796i | 0.179656 | + | 0.0621796i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.561767 | − | 1.40323i | −0.561767 | − | 1.40323i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.327068 | − | 0.945001i | \(-0.393939\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.44451 | + | 0.164082i | 3.44451 | + | 0.164082i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.437742 | + | 0.175245i | 0.437742 | + | 0.175245i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.143677 | − | 1.50465i | 0.143677 | − | 1.50465i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.618159 | − | 0.786053i | \(-0.287879\pi\) | ||||
−0.618159 | + | 0.786053i | \(0.712121\pi\) | |||||||
\(228\) | 1.65033 | − | 0.850806i | 1.65033 | − | 0.850806i | ||||
\(229\) | −1.30379 | − | 0.124497i | −1.30379 | − | 0.124497i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.690079 | − | 0.723734i | \(-0.742424\pi\) | ||||
0.690079 | + | 0.723734i | \(0.257576\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.642315 | − | 0.123796i | 0.642315 | − | 0.123796i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.371662 | − | 0.928368i | \(-0.621212\pi\) | ||||
0.371662 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.401872 | + | 1.00383i | −0.401872 | + | 1.00383i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.995472 | − | 0.0950560i | −0.995472 | − | 0.0950560i | ||||
\(244\) | −1.63679 | − | 0.945001i | −1.63679 | − | 0.945001i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.343038 | − | 0.0832201i | −0.343038 | − | 0.0832201i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(252\) | 0.487975 | − | 1.66189i | 0.487975 | − | 1.66189i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(257\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.33536 | − | 2.59023i | −1.33536 | − | 2.59023i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.70566 | + | 0.879330i | 1.70566 | + | 0.879330i | ||||
\(269\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.252989 | + | 1.75958i | −0.252989 | + | 1.75958i | 0.327068 | + | 0.945001i | \(0.393939\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.277011 | + | 0.178024i | −0.277011 | + | 0.178024i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.95496 | + | 0.376789i | −1.95496 | + | 0.376789i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.12424 | + | 0.800570i | −1.12424 | + | 0.800570i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0623191 | − | 0.0719200i | 0.0623191 | − | 0.0719200i | ||||
\(292\) | 0.154218 | − | 0.445585i | 0.154218 | − | 0.445585i | ||||
\(293\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.928368 | + | 0.371662i | 0.928368 | + | 0.371662i | ||||
\(301\) | −2.35816 | + | 1.36148i | −2.35816 | + | 1.36148i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.95496 | − | 0.186677i | 1.95496 | − | 0.186677i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.327793 | + | 0.189251i | −0.327793 | + | 0.189251i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.62731 | + | 0.0775182i | −1.62731 | + | 0.0775182i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.154218 | − | 0.635697i | −0.154218 | − | 0.635697i | ||||
\(317\) | 0 | 0 | 0.945001 | − | 0.327068i | \(-0.106061\pi\) | ||||
−0.945001 | + | 0.327068i | \(0.893939\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.0475819 | + | 0.998867i | −0.0475819 | + | 0.998867i | ||||
\(325\) | −0.0871144 | − | 0.168978i | −0.0871144 | − | 0.168978i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.92384 | − | 0.276606i | −1.92384 | − | 0.276606i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.632425 | + | 1.22673i | 0.632425 | + | 1.22673i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.10181 | + | 1.27155i | 1.10181 | + | 1.27155i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.68323 | − | 0.408346i | −1.68323 | − | 0.408346i | ||||
\(337\) | 0.348311 | + | 1.18624i | 0.348311 | + | 1.18624i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.57553 | + | 0.719520i | −1.57553 | + | 0.719520i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.0950560 | − | 0.995472i | \(-0.530303\pi\) | ||||
0.0950560 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.223734 | − | 0.175946i | 0.223734 | − | 0.175946i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.131192 | − | 0.137591i | 0.131192 | − | 0.137591i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.814576 | − | 0.580057i | \(-0.803030\pi\) | ||||
0.814576 | + | 0.580057i | \(0.196970\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.41967 | + | 1.99365i | 1.41967 | + | 1.99365i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 1.00000 | ||||||||
\(364\) | 0.191003 | + | 0.268227i | 0.191003 | + | 0.268227i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.601300 | + | 1.31666i | 0.601300 | + | 1.31666i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.469383 | + | 1.93482i | 0.469383 | + | 1.93482i | ||||
\(373\) | −0.952418 | + | 0.998867i | −0.952418 | + | 0.998867i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.12424 | − | 1.17907i | −1.12424 | − | 1.17907i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.239446 | + | 0.153882i | 0.239446 | + | 0.153882i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.13779 | − | 1.08488i | 1.13779 | − | 1.08488i | ||||
\(388\) | −0.0748038 | − | 0.0588264i | −0.0748038 | − | 0.0588264i | ||||
\(389\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.00000 | 1.00000 | ||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.18323 | + | 0.457679i | 3.18323 | + | 0.457679i | ||||
\(400\) | 0.327068 | − | 0.945001i | 0.327068 | − | 0.945001i | ||||
\(401\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.173440 | − | 0.336426i | 0.173440 | − | 0.336426i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0552004 | − | 0.0775182i | 0.0552004 | − | 0.0775182i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.204634 | + | 0.318417i | 0.204634 | + | 0.318417i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.605495 | − | 0.431171i | 0.605495 | − | 0.431171i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.34125 | + | 1.40667i | −1.34125 | + | 1.40667i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.35989 | − | 2.97775i | −1.35989 | − | 2.97775i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 1.00000 | 1.00000 | ||||||||
\(433\) | 0.672932 | + | 0.945001i | 0.672932 | + | 0.945001i | 1.00000 | \(0\) | ||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.184753 | + | 1.93482i | −0.184753 | + | 1.93482i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.815816 | + | 0.157236i | −0.815816 | + | 0.157236i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.57211 | − | 1.23632i | 1.57211 | − | 1.23632i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(444\) | 1.21769 | − | 1.16106i | 1.21769 | − | 1.16106i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.327793 | + | 1.70075i | −0.327793 | + | 1.70075i | ||||
\(449\) | 0 | 0 | −0.998867 | − | 0.0475819i | \(-0.984848\pi\) | ||||
0.998867 | + | 0.0475819i | \(0.0151515\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.419102 | + | 1.72756i | 0.419102 | + | 1.72756i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.258195 | − | 0.879330i | −0.258195 | − | 0.879330i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(468\) | −0.143677 | − | 0.124497i | −0.143677 | − | 0.124497i | ||||
\(469\) | 1.52304 | + | 2.95429i | 1.52304 | + | 2.95429i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.88786 | + | 0.653395i | 1.88786 | + | 0.653395i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.437742 | + | 1.80440i | −0.437742 | + | 1.80440i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.319503 | + | 0.0152198i | −0.319503 | + | 0.0152198i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.0475819 | − | 0.998867i | −0.0475819 | − | 0.998867i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.283341 | − | 0.0270558i | 0.283341 | − | 0.0270558i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.13779 | + | 0.894765i | −1.13779 | + | 0.894765i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.814576 | − | 0.580057i | \(-0.196970\pi\) | ||||
−0.814576 | + | 0.580057i | \(0.803030\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.91030 | − | 0.560914i | 1.91030 | − | 0.560914i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.213947 | + | 0.618159i | −0.213947 | + | 0.618159i | 0.786053 | + | 0.618159i | \(0.212121\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.137171 | − | 0.954047i | −0.137171 | − | 0.954047i | ||||
\(508\) | 0.142315 | − | 0.246497i | 0.142315 | − | 0.246497i | ||||
\(509\) | 0 | 0 | −0.0950560 | − | 0.995472i | \(-0.530303\pi\) | ||||
0.0950560 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.665258 | − | 0.473728i | 0.665258 | − | 0.473728i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.84833 | + | 0.176494i | −1.84833 | + | 0.176494i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.13779 | − | 1.08488i | −1.13779 | − | 1.08488i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.936417 | + | 1.45709i | 0.936417 | + | 1.45709i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.327068 | − | 0.945001i | −0.327068 | − | 0.945001i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.305697 | − | 3.20140i | 0.305697 | − | 3.20140i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.154218 | + | 0.445585i | 0.154218 | + | 0.445585i | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.204634 | + | 1.06174i | −0.204634 | + | 1.06174i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.722372 | − | 0.175245i | −0.722372 | − | 0.175245i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.16832 | + | 1.48564i | 1.16832 | + | 1.48564i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.421092 | − | 1.05184i | 0.421092 | − | 1.05184i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.459493 | − | 0.584293i | −0.459493 | − | 0.584293i | ||||
\(557\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0284100 | + | 0.297523i | 0.0284100 | + | 0.297523i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.07068 | + | 1.36148i | −1.07068 | + | 1.36148i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.154861 | − | 1.62177i | 0.154861 | − | 1.62177i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0475819 | − | 0.998867i | −0.0475819 | − | 0.998867i | ||||
\(577\) | −1.50979 | − | 0.0719200i | −1.50979 | − | 0.0719200i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.388835 | + | 0.407799i | 0.388835 | + | 0.407799i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(588\) | −1.30972 | − | 1.51150i | −1.30972 | − | 1.51150i | ||||
\(589\) | −3.43186 | + | 1.37391i | −3.43186 | + | 1.37391i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.21769 | − | 1.16106i | −1.21769 | − | 1.16106i | ||||
\(593\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.344298 | − | 1.78639i | 0.344298 | − | 1.78639i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.833635 | − | 1.61703i | 0.833635 | − | 1.61703i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.786053 | − | 0.618159i | \(-0.212121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(604\) | 1.70566 | − | 0.500828i | 1.70566 | − | 0.500828i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.915415 | + | 1.77566i | −0.915415 | + | 1.77566i | −0.415415 | + | 0.909632i | \(0.636364\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.95949 | + | 0.281733i | −1.95949 | + | 0.281733i | −0.959493 | + | 0.281733i | \(0.909091\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.348311 | + | 0.442913i | −0.348311 | + | 0.442913i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.117519 | + | 0.149438i | −0.117519 | + | 0.149438i | ||||
\(625\) | −0.888835 | + | 0.458227i | −0.888835 | + | 0.458227i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.562827 | − | 1.91681i | 0.562827 | − | 1.91681i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.50979 | − | 0.0719200i | 1.50979 | − | 0.0719200i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.380224i | 0.380224i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.0800569 | + | 0.0514495i | −0.0800569 | + | 0.0514495i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.28165 | + | 3.20140i | −1.28165 | + | 3.20140i | ||||
\(652\) | 0.947890 | + | 1.09392i | 0.947890 | + | 1.09392i | ||||
\(653\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.308779 | + | 0.356349i | −0.308779 | + | 0.356349i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.0950560 | − | 0.995472i | \(-0.469697\pi\) | ||||
−0.0950560 | + | 0.995472i | \(0.530303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.357685 | − | 1.85585i | −0.357685 | − | 1.85585i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.37491 | + | 0.627899i | 1.37491 | + | 0.627899i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.428368 | − | 1.23769i | −0.428368 | − | 1.23769i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.723734 | − | 0.690079i | −0.723734 | − | 0.690079i | ||||
\(676\) | −0.946439 | + | 0.182411i | −0.946439 | + | 0.182411i | ||||
\(677\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0464376 | − | 0.158152i | −0.0464376 | − | 0.158152i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | 0.264241 | + | 1.83784i | 0.264241 | + | 1.83784i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.544078 | − | 1.19136i | 0.544078 | − | 1.19136i | ||||
\(688\) | −1.02951 | + | 1.18812i | −1.02951 | + | 1.18812i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.692609 | + | 0.600149i | 0.692609 | + | 0.600149i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.41089 | − | 1.00469i | 1.41089 | − | 1.00469i | ||||
\(701\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45561 | + | 1.93111i | 2.45561 | + | 1.93111i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.580057 | − | 1.00469i | 0.580057 | − | 1.00469i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0930932 | + | 0.647478i | −0.0930932 | + | 0.647478i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0311940 | + | 0.654843i | −0.0311940 | + | 0.654843i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.817178 | − | 0.708089i | −0.817178 | − | 0.708089i | ||||
\(724\) | 1.07028 | + | 0.153882i | 1.07028 | + | 0.153882i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.462997 | + | 0.0892353i | 0.462997 | + | 0.0892353i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.42837 | − | 1.23769i | 1.42837 | − | 1.23769i | ||||
\(733\) | 1.58323 | + | 0.384087i | 1.58323 | + | 0.384087i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.532475 | + | 1.81344i | 0.532475 | + | 1.81344i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.190840 | − | 0.296952i | 0.190840 | − | 0.296952i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0930932 | − | 0.647478i | 0.0930932 | − | 0.647478i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.41089 | + | 1.00469i | 1.41089 | + | 1.00469i | ||||
\(757\) | −0.0934441 | − | 0.0180099i | −0.0934441 | − | 0.0180099i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.20456 | + | 2.54420i | −2.20456 | + | 2.54420i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(769\) | −0.341254 | − | 1.40667i | −0.341254 | − | 1.40667i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.388835 | − | 0.407799i | 0.388835 | − | 0.407799i | ||||
\(773\) | 0 | 0 | 0.945001 | − | 0.327068i | \(-0.106061\pi\) | ||||
−0.945001 | + | 0.327068i | \(0.893939\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.76962 | − | 0.912303i | −1.76962 | − | 0.912303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.88453 | − | 0.414732i | 2.88453 | − | 0.414732i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.44747 | + | 1.38016i | −1.44747 | + | 1.38016i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.22373 | + | 1.55610i | 1.22373 | + | 1.55610i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.359312 | −0.359312 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.80075 | − | 0.258908i | −1.80075 | − | 0.258908i | ||||
\(797\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.38884 | + | 1.32425i | −1.38884 | + | 1.32425i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.97740 | + | 0.284307i | −1.97740 | + | 0.284307i | −0.981929 | + | 0.189251i | \(0.939394\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.58006 | − | 0.814576i | −1.58006 | − | 0.814576i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.69318 | − | 2.37774i | 1.69318 | − | 2.37774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0776316 | − | 0.320002i | −0.0776316 | − | 0.320002i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.82318 | + | 0.729892i | −1.82318 | + | 0.729892i | −0.841254 | + | 0.540641i | \(0.818182\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.77767 | −1.77767 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.28605 | − | 0.247866i | −1.28605 | − | 0.247866i | ||||
\(832\) | 0.154861 | + | 0.110276i | 0.154861 | + | 0.110276i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.283341 | − | 1.97068i | 0.283341 | − | 1.97068i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.971812 | − | 0.235759i | \(-0.0757576\pi\) | ||||
−0.971812 | + | 0.235759i | \(0.924242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.723734 | − | 0.690079i | 0.723734 | − | 0.690079i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.143677 | − | 1.50465i | −0.143677 | − | 1.50465i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.936417 | − | 1.45709i | 0.936417 | − | 1.45709i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.388835 | − | 1.32425i | −0.388835 | − | 1.32425i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.88786 | + | 0.653395i | −1.88786 | + | 0.653395i | −0.928368 | + | 0.371662i | \(0.878788\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.738471 | − | 1.61703i | 0.738471 | − | 1.61703i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) |
0.786053 | − | 0.618159i | \(-0.212121\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.0475819 | + | 0.998867i | −0.0475819 | + | 0.998867i | ||||
\(868\) | 3.25876 | + | 1.12787i | 3.25876 | + | 1.12787i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.364409 | − | 0.0173589i | 0.364409 | − | 0.0173589i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0475819 | + | 0.0824143i | 0.0475819 | + | 0.0824143i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.370638 | + | 0.291473i | 0.370638 | + | 0.291473i | ||||
\(877\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | 0.786053 | + | 0.618159i | \(0.212121\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.547582 | − | 0.132842i | −0.547582 | − | 0.132842i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.448442 | − | 0.204797i | 0.448442 | − | 0.204797i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.561767 | − | 1.40323i | 0.561767 | − | 1.40323i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.515325 | − | 2.67376i | −0.515325 | − | 2.67376i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.817178 | − | 1.27155i | −0.817178 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(912\) | 1.82318 | − | 0.351390i | 1.82318 | − | 0.351390i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.21590 | − | 0.486774i | −1.21590 | − | 0.486774i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.37491 | + | 0.627899i | 1.37491 | + | 0.627899i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.462997 | + | 1.90850i | −0.462997 | + | 1.90850i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0800569 | + | 1.68060i | 0.0800569 | + | 1.68060i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0716321 | − | 0.371662i | −0.0716321 | − | 0.371662i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.0950560 | − | 0.995472i | \(-0.469697\pi\) | ||||
−0.0950560 | + | 0.995472i | \(0.530303\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.43181 | − | 2.80645i | 2.43181 | − | 2.80645i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.209419 | + | 0.523103i | −0.209419 | + | 0.523103i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.458985 | − | 1.56316i | 0.458985 | − | 1.56316i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(948\) | 0.651174 | + | 0.0621796i | 0.651174 | + | 0.0621796i | ||||
\(949\) | −0.0169647 | − | 0.0880213i | −0.0169647 | − | 0.0880213i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.421801 | − | 2.93369i | −0.421801 | − | 2.93369i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.668404 | + | 0.849945i | −0.668404 | + | 0.849945i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.0688733 | + | 1.44583i | −0.0688733 | + | 1.44583i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −0.928368 | − | 0.371662i | −0.928368 | − | 0.371662i | ||||
\(973\) | −0.0612606 | − | 1.28602i | −0.0612606 | − | 1.28602i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.188177 | − | 0.0270558i | 0.188177 | − | 0.0270558i | ||||
\(976\) | −1.30425 | − | 1.36786i | −1.30425 | − | 1.36786i | ||||
\(977\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.890620 | − | 1.72756i | 0.890620 | − | 1.72756i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.305697 | − | 0.176494i | −0.305697 | − | 0.176494i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.233975 | + | 1.21398i | −0.233975 | + | 1.21398i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.36611 | + | 0.196417i | −1.36611 | + | 0.196417i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.936417 | − | 0.540641i | −0.936417 | − | 0.540641i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.56199 | + | 0.625325i | −1.56199 | + | 0.625325i |
(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 | 1191.1.z.a.1040.1 | yes | 20 | |
3.2 | odd | 2 | CM | 1191.1.z.a.1040.1 | yes | 20 | |
397.163 | even | 66 | inner | 1191.1.z.a.560.1 | ✓ | 20 | |
1191.560 | odd | 66 | inner | 1191.1.z.a.560.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1191.1.z.a.560.1 | ✓ | 20 | 397.163 | even | 66 | inner | |
1191.1.z.a.560.1 | ✓ | 20 | 1191.560 | odd | 66 | inner | |
1191.1.z.a.1040.1 | yes | 20 | 1.1 | even | 1 | trivial | |
1191.1.z.a.1040.1 | yes | 20 | 3.2 | odd | 2 | CM |