Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,1,Mod(68,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(28))
chi = DirichletCharacter(H, H._module([14, 14, 23]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.68");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.bf (of order \(28\), degree \(12\), 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: | \(0.998629090279\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{28})\) |
Coefficient field: | \(\Q(\zeta_{84})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{84}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{84} - \cdots)\) |
Embedding invariants
Embedding label | 896.2 | ||
Root | \(-0.997204 + 0.0747301i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.896 |
Dual form | 2001.1.bf.c.1034.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times\).
\(n\) | \(553\) | \(668\) | \(1132\) |
\(\chi(n)\) | \(e\left(\frac{19}{28}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.791295 | + | 0.497204i | 0.791295 | + | 0.497204i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(3\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(4\) | −0.0549471 | − | 0.114099i | −0.0549471 | − | 0.114099i | ||||
\(5\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(6\) | −0.173741 | + | 0.918245i | −0.173741 | + | 0.918245i | ||||
\(7\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(8\) | 0.117886 | − | 1.04627i | 0.117886 | − | 1.04627i | ||||
\(9\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(12\) | 0.0861372 | − | 0.0928338i | 0.0861372 | − | 0.0928338i | ||||
\(13\) | 1.49419 | + | 1.19158i | 1.49419 | + | 1.19158i | 0.930874 | + | 0.365341i | \(0.119048\pi\) |
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.534532 | − | 0.670281i | 0.534532 | − | 0.670281i | ||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | −0.918245 | + | 0.173741i | −0.918245 | + | 0.173741i | ||||
\(19\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.974928 | + | 0.222521i | 0.974928 | + | 0.222521i | ||||
\(24\) | 1.01701 | − | 0.272507i | 1.01701 | − | 0.272507i | ||||
\(25\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(26\) | 0.589891 | + | 1.68581i | 0.589891 | + | 1.68581i | ||||
\(27\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.997204 | + | 0.0747301i | 0.997204 | + | 0.0747301i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.275400 | + | 0.438297i | −0.275400 | + | 0.438297i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(32\) | −0.237564 | + | 0.0831272i | −0.237564 | + | 0.0831272i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.117886 | + | 0.0462668i | 0.117886 | + | 0.0462668i | ||||
\(37\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.563320 | + | 1.82624i | −0.563320 | + | 1.82624i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.839789 | − | 0.839789i | −0.839789 | − | 0.839789i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.660818 | + | 0.660818i | 0.660818 | + | 0.660818i | ||||
\(47\) | −1.50641 | + | 0.169732i | −1.50641 | + | 0.169732i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(48\) | 0.819234 | + | 0.252700i | 0.819234 | + | 0.252700i | ||||
\(49\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(50\) | −0.928661 | − | 0.104635i | −0.928661 | − | 0.104635i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0538562 | − | 0.235960i | 0.0538562 | − | 0.235960i | ||||
\(53\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(54\) | −0.497204 | − | 0.791295i | −0.497204 | − | 0.791295i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.751927 | + | 0.554947i | 0.751927 | + | 0.554947i | ||||
\(59\) | − | 1.80194i | − | 1.80194i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||
0.433884 | − | 0.900969i | \(-0.357143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(62\) | −0.435846 | + | 0.209892i | −0.435846 | + | 0.209892i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.06514 | − | 0.243112i | −1.06514 | − | 0.243112i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.149042 | + | 0.988831i | 0.149042 | + | 0.988831i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.848162 | − | 1.06356i | 0.848162 | − | 1.06356i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(72\) | 0.625226 | + | 0.847151i | 0.625226 | + | 0.847151i | ||||
\(73\) | −0.197822 | − | 0.314832i | −0.197822 | − | 0.314832i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.35377 | + | 1.16501i | −1.35377 | + | 1.16501i | ||||
\(79\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(82\) | −0.246975 | − | 1.08207i | −0.246975 | − | 1.08207i | ||||
\(83\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.294755 | + | 0.955573i | 0.294755 | + | 0.955573i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.0281801 | − | 0.123465i | −0.0281801 | − | 0.123465i | ||||
\(93\) | −0.508614 | − | 0.0962349i | −0.508614 | − | 0.0962349i | ||||
\(94\) | −1.27641 | − | 0.614686i | −1.27641 | − | 0.614686i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.164173 | − | 0.190772i | −0.164173 | − | 0.190772i | ||||
\(97\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(98\) | 0.104635 | + | 0.928661i | 0.104635 | + | 0.928661i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0990112 | + | 0.0789588i | 0.0990112 | + | 0.0789588i | ||||
\(101\) | −1.00435 | − | 1.59842i | −1.00435 | − | 1.59842i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(104\) | 1.42285 | − | 1.42285i | 1.42285 | − | 1.42285i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(108\) | 0.126640i | 0.126640i | ||||||||
\(109\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0462668 | − | 0.117886i | −0.0462668 | − | 0.117886i | ||||
\(117\) | −1.90580 | + | 0.142820i | −1.90580 | + | 0.142820i | ||||
\(118\) | 0.895930 | − | 1.42586i | 0.895930 | − | 1.42586i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.474928 | − | 1.08855i | 0.474928 | − | 1.08855i | ||||
\(124\) | 0.0651416 | + | 0.00733969i | 0.0651416 | + | 0.00733969i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.794755 | − | 0.0895474i | 0.794755 | − | 0.0895474i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | −0.543995 | − | 0.543995i | −0.543995 | − | 0.543995i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.49720 | + | 0.940755i | −1.49720 | + | 0.940755i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(138\) | −0.373714 | + | 0.856562i | −0.373714 | + | 0.856562i | ||||
\(139\) | 0.302705 | − | 1.32624i | 0.302705 | − | 1.32624i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.708353 | − | 1.34027i | −0.708353 | − | 1.34027i | ||||
\(142\) | 1.19995 | − | 0.419882i | 1.19995 | − | 0.419882i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.0640678 | + | 0.854925i | 0.0640678 | + | 0.854925i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 0.347483i | − | 0.347483i | ||||||
\(147\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(150\) | −0.241876 | − | 0.902694i | −0.241876 | − | 0.902694i | ||||
\(151\) | −0.974928 | − | 0.222521i | −0.974928 | − | 0.222521i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.239324 | − | 0.0360724i | 0.239324 | − | 0.0360724i | ||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.554947 | − | 0.751927i | 0.554947 | − | 0.751927i | ||||
\(163\) | −0.169732 | − | 1.50641i | −0.169732 | − | 1.50641i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.563320 | − | 0.826239i | \(-0.309524\pi\) | |||||||
\(164\) | −0.0496749 | + | 0.141963i | −0.0496749 | + | 0.141963i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.400969 | + | 0.193096i | 0.400969 | + | 0.193096i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.590232 | + | 2.58597i | 0.590232 | + | 2.58597i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.24698 | −1.24698 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(174\) | −0.241876 | + | 0.902694i | −0.241876 | + | 0.902694i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.67738 | − | 0.658322i | 1.67738 | − | 0.658322i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.162592 | + | 0.712362i | 0.162592 | + | 0.712362i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.347747 | − | 0.993803i | 0.347747 | − | 0.993803i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.354615 | − | 0.329035i | −0.354615 | − | 0.329035i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.102139 | + | 0.162553i | 0.102139 | + | 0.162553i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | −0.162834 | − | 1.08033i | −0.162834 | − | 1.08033i | ||||
\(193\) | 1.85486 | + | 0.649042i | 1.85486 | + | 0.649042i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0549471 | − | 0.114099i | 0.0549471 | − | 0.114099i | ||||
\(197\) | 1.68862 | + | 0.385418i | 1.68862 | + | 0.385418i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(200\) | 0.347747 | + | 0.993803i | 0.347747 | + | 0.993803i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 1.76419i | − | 1.76419i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(208\) | 1.59739 | − | 0.364593i | 1.59739 | − | 0.364593i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.40532 | − | 0.158342i | −1.40532 | − | 0.158342i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.29991 | + | 0.400969i | 1.29991 | + | 0.400969i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.560170 | + | 0.891505i | −0.560170 | + | 0.891505i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.220796 | − | 0.299168i | 0.220796 | − | 0.299168i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.777479 | − | 0.974928i | −0.777479 | − | 0.974928i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.195744 | − | 1.03453i | 0.195744 | − | 1.03453i | ||||
\(233\) | 1.97766i | 1.97766i | 0.149042 | + | 0.988831i | \(0.452381\pi\) | ||||
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(234\) | −1.57906 | − | 0.834559i | −1.57906 | − | 0.834559i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.205599 | + | 0.0990112i | −0.205599 | + | 0.0990112i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.129334 | + | 0.268565i | −0.129334 | + | 0.268565i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(242\) | −0.882094 | − | 0.308658i | −0.882094 | − | 0.308658i | ||||
\(243\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.917038 | − | 0.625226i | 0.917038 | − | 0.625226i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.426109 | + | 0.339811i | 0.426109 | + | 0.339811i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.673409 | + | 0.324297i | 0.673409 | + | 0.324297i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.0831272 | + | 0.364204i | 0.0831272 | + | 0.364204i | ||||
\(257\) | −0.865341 | − | 1.79690i | −0.865341 | − | 1.79690i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.365341 | − | 0.930874i | \(-0.619048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.781831 | + | 0.623490i | −0.781831 | + | 0.623490i | ||||
\(262\) | −1.65248 | −1.65248 | ||||||||
\(263\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.0895474 | + | 0.794755i | −0.0895474 | + | 0.794755i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.559311 | − | 1.59842i | 0.559311 | − | 1.59842i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.781831 | − | 0.623490i | \(-0.214286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.104635 | − | 0.0713389i | 0.104635 | − | 0.0713389i | ||||
\(277\) | −0.914101 | + | 1.14625i | −0.914101 | + | 1.14625i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(278\) | 0.898940 | − | 0.898940i | 0.898940 | − | 0.898940i | ||||
\(279\) | −0.0962349 | − | 0.508614i | −0.0962349 | − | 0.508614i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(282\) | 0.105871 | − | 1.41274i | 0.105871 | − | 1.41274i | ||||
\(283\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(284\) | −0.167955 | − | 0.0383346i | −0.167955 | − | 0.0383346i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.117606 | − | 0.222521i | 0.117606 | − | 0.222521i | ||||
\(289\) | − | 1.00000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.0250522 | + | 0.0398703i | −0.0250522 | + | 0.0398703i | ||||
\(293\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(294\) | −0.826239 | + | 0.436680i | −0.826239 | + | 0.436680i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | ||||
\(300\) | −0.0373278 | + | 0.121014i | −0.0373278 | + | 0.121014i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.660818 | − | 0.660818i | −0.660818 | − | 0.660818i | ||||
\(303\) | 1.12099 | − | 1.51889i | 1.12099 | − | 1.51889i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.467085 | + | 0.467085i | 0.467085 | + | 0.467085i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.98603 | − | 0.223772i | −1.98603 | − | 0.223772i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
−0.988831 | − | 0.149042i | \(-0.952381\pi\) | |||||||
\(312\) | 1.84433 | + | 0.804671i | 1.84433 | + | 0.804671i | ||||
\(313\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.566116 | + | 0.900969i | −0.566116 | + | 0.900969i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.117886 | + | 0.0462668i | −0.117886 | + | 0.0462668i | ||||
\(325\) | −1.86323 | − | 0.425270i | −1.86323 | − | 0.425270i | ||||
\(326\) | 0.614686 | − | 1.27641i | 0.614686 | − | 1.27641i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.977642 | + | 0.779644i | −0.977642 | + | 0.779644i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.29621 | − | 1.29621i | 1.29621 | − | 1.29621i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.930874 | − | 0.365341i | \(-0.119048\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.221277 | + | 0.352160i | 0.221277 | + | 0.352160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(338\) | −0.818709 | + | 2.33973i | −0.818709 | + | 2.33973i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.986729 | − | 0.620003i | −0.986729 | − | 0.620003i | ||||
\(347\) | 1.56366 | 1.56366 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(348\) | 0.0928338 | − | 0.0861372i | 0.0928338 | − | 0.0861372i | ||||
\(349\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.829215 | − | 1.72188i | −0.829215 | − | 1.72188i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.414278 | + | 1.81507i | 0.414278 | + | 1.81507i | 0.563320 | + | 0.826239i | \(0.309524\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(354\) | 1.65462 | + | 0.313071i | 1.65462 | + | 0.313071i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.225531 | + | 0.644530i | −0.225531 | + | 0.644530i | ||||
\(359\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.781831 | + | 0.623490i | 0.781831 | + | 0.623490i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.563320 | − | 0.826239i | −0.563320 | − | 0.826239i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(368\) | 0.670281 | − | 0.534532i | 0.670281 | − | 0.534532i | ||||
\(369\) | 1.18681 | + | 0.0444073i | 1.18681 | + | 0.0444073i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.0169666 | + | 0.0633201i | 0.0169666 | + | 0.0633201i | ||||
\(373\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.59612i | 1.59612i | ||||||||
\(377\) | 1.40097 | + | 1.29991i | 1.40097 | + | 1.29991i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.373714 | + | 0.707101i | 0.373714 | + | 0.707101i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(384\) | 0.307647 | − | 0.705135i | 0.307647 | − | 0.705135i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.14503 | + | 1.43583i | 1.14503 | + | 1.43583i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.891505 | − | 0.560170i | 0.891505 | − | 0.560170i | ||||
\(393\) | −1.42271 | − | 1.05001i | −1.42271 | − | 1.05001i | ||||
\(394\) | 1.14457 | + | 1.14457i | 1.14457 | + | 1.14457i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.185853 | − | 0.233052i | −0.185853 | − | 0.233052i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.190772 | + | 0.835827i | −0.190772 | + | 0.835827i | ||||
\(401\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.933767 | + | 0.326739i | −0.933767 | + | 0.326739i | ||||
\(404\) | −0.127191 | + | 0.202424i | −0.127191 | + | 0.202424i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.392253 | + | 1.12099i | 0.392253 | + | 1.12099i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.933884 | − | 0.0349435i | −0.933884 | − | 0.0349435i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.454019 | − | 0.158868i | −0.454019 | − | 0.158868i | ||||
\(417\) | 1.34515 | − | 0.202749i | 1.34515 | − | 0.202749i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(422\) | −1.03330 | − | 0.824026i | −1.03330 | − | 0.824026i | ||||
\(423\) | 0.988831 | − | 1.14904i | 0.988831 | − | 1.14904i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.829249 | + | 0.963605i | 0.829249 | + | 0.963605i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(432\) | −0.772421 | + | 0.371978i | −0.772421 | + | 0.371978i | ||||
\(433\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.323462 | − | 0.126950i | 0.323462 | − | 0.126950i | ||||
\(439\) | −0.129334 | − | 0.268565i | −0.129334 | − | 0.268565i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.220025 | + | 1.95278i | −0.220025 | + | 1.95278i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.130478 | − | 1.15802i | −0.130478 | − | 1.15802i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.900969 | − | 1.43388i | −0.900969 | − | 1.43388i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(450\) | 0.751927 | − | 0.554947i | 0.751927 | − | 0.554947i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.149042 | − | 0.988831i | −0.149042 | − | 0.988831i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.605443 | + | 1.73026i | 0.605443 | + | 1.73026i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.445042i | − | 0.445042i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(464\) | 0.583127 | − | 0.628462i | 0.583127 | − | 0.628462i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.983301 | + | 1.56491i | −0.983301 | + | 1.56491i | ||||
\(467\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(468\) | 0.121014 | + | 0.209602i | 0.121014 | + | 0.209602i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.88531 | − | 0.212423i | −1.88531 | − | 0.212423i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.235873 | + | 0.148209i | −0.235873 | + | 0.148209i | ||||
\(479\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0789588 | + | 0.0990112i | 0.0789588 | + | 0.0990112i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.902694 | + | 0.241876i | 0.902694 | + | 0.241876i | ||||
\(487\) | 0.414278 | − | 1.81507i | 0.414278 | − | 1.81507i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.563320 | − | 0.826239i | \(-0.309524\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.34027 | − | 0.708353i | 1.34027 | − | 0.708353i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.856144 | − | 1.36254i | 0.856144 | − | 1.36254i | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) |
0.930874 | − | 0.365341i | \(-0.119048\pi\) | |||||||
\(492\) | −0.150298 | + | 0.00562374i | −0.150298 | + | 0.00562374i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.146572 | + | 0.418879i | 0.146572 | + | 0.418879i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.145713 | − | 0.0332580i | −0.145713 | − | 0.0332580i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0332580 | + | 0.443797i | −0.0332580 | + | 0.443797i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.19158 | + | 1.49419i | −2.19158 | + | 1.49419i | ||||
\(508\) | −0.0538867 | − | 0.0857602i | −0.0538867 | − | 0.0857602i | ||||
\(509\) | −0.880843 | − | 0.702449i | −0.880843 | − | 0.702449i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.369398 | + | 1.05568i | −0.369398 | + | 1.05568i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.208685 | − | 1.85213i | 0.208685 | − | 1.85213i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.455573 | − | 1.16078i | −0.455573 | − | 1.16078i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | −0.928661 | + | 0.104635i | −0.928661 | + | 0.104635i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0.189606 | + | 0.119137i | 0.189606 | + | 0.119137i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.900969 | + | 0.433884i | 0.900969 | + | 0.433884i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22563 | + | 1.32091i | 1.22563 | + | 1.32091i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.254132 | − | 2.25548i | −0.254132 | − | 2.25548i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.603718 | + | 0.411608i | −0.603718 | + | 0.411608i | ||||
\(538\) | −0.466014 | + | 0.584363i | −0.466014 | + | 0.584363i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.23137 | − | 0.430874i | −1.23137 | − | 0.430874i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(542\) | 1.23732 | − | 0.986729i | 1.23732 | − | 0.986729i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.78181 | + | 0.858075i | −1.78181 | + | 0.858075i | −0.826239 | + | 0.563320i | \(0.809524\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.05215 | − | 0.0393687i | 1.05215 | − | 0.0393687i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.29324 | + | 0.452525i | −1.29324 | + | 0.452525i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.167955 | + | 0.0383346i | −0.167955 | + | 0.0383346i | ||||
\(557\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(558\) | 0.176734 | − | 0.450312i | 0.176734 | − | 0.450312i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | −0.114001 | + | 0.154466i | −0.114001 | + | 0.154466i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.01278 | − | 1.01278i | −1.01278 | − | 1.01278i | ||||
\(569\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | ||||
\(576\) | 0.946162 | − | 0.546267i | 0.946162 | − | 0.546267i | ||||
\(577\) | 1.73026 | − | 0.605443i | 1.73026 | − | 0.605443i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(578\) | 0.497204 | − | 0.791295i | 0.497204 | − | 0.791295i | ||||
\(579\) | 0.0734787 | + | 1.96376i | 0.0734787 | + | 1.96376i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.352718 | + | 0.169860i | −0.352718 | + | 0.169860i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.807782 | + | 1.67738i | −0.807782 | + | 1.67738i | −0.0747301 | + | 0.997204i | \(0.523810\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(588\) | 0.126286 | + | 0.00946383i | 0.126286 | + | 0.00946383i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.258149 | + | 1.71271i | 0.258149 | + | 1.71271i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.974928 | + | 1.22252i | −0.974928 | + | 1.22252i | 1.00000i | \(0.5\pi\) | ||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.199973 | + | 1.77481i | 0.199973 | + | 1.77481i | ||||
\(599\) | −0.559311 | + | 1.59842i | −0.559311 | + | 1.59842i | 0.222521 | + | 0.974928i | \(0.428571\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(600\) | −0.798059 | + | 0.686785i | −0.798059 | + | 0.686785i | ||||
\(601\) | −0.216299 | + | 1.91970i | −0.216299 | + | 1.91970i | 0.149042 | + | 0.988831i | \(0.452381\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.0281801 | + | 0.123465i | 0.0281801 | + | 0.123465i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.64224 | − | 0.644530i | 1.64224 | − | 0.644530i | ||||
\(607\) | −0.189606 | − | 0.119137i | −0.189606 | − | 0.119137i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.45312 | − | 1.54140i | −2.45312 | − | 1.54140i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(614\) | 0.137366 | + | 0.601839i | 0.137366 | + | 0.601839i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | ||||
\(622\) | −1.46028 | − | 1.16453i | −1.46028 | − | 1.16453i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.922982 | + | 1.35377i | 0.922982 | + | 1.35377i | ||||
\(625\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(634\) | −0.895930 | + | 0.431457i | −0.895930 | + | 0.431457i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.91115i | 1.91115i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.101659 | + | 1.35654i | 0.101659 | + | 1.35654i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.702449 | − | 0.880843i | −0.702449 | − | 0.880843i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(648\) | −1.03453 | − | 0.195744i | −1.03453 | − | 0.195744i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.26292 | − | 1.26292i | −1.26292 | − | 1.26292i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.162553 | + | 0.102139i | −0.162553 | + | 0.102139i | ||||
\(653\) | 1.63575 | − | 1.02781i | 1.63575 | − | 1.02781i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.01179 | + | 0.114001i | −1.01179 | + | 0.114001i | ||||
\(657\) | 0.359154 | + | 0.0962349i | 0.359154 | + | 0.0962349i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(662\) | 1.67017 | − | 0.381206i | 1.67017 | − | 0.381206i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(668\) | − | 0.0563602i | − | 0.0563602i | ||||||
\(669\) | 0.623490 | − | 1.07992i | 0.623490 | − | 1.07992i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.81507 | + | 0.414278i | 1.81507 | + | 0.414278i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 1.00000 | ||||||||
\(676\) | 0.262625 | − | 0.209436i | 0.262625 | − | 0.209436i | ||||
\(677\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.55929 | − | 1.24349i | −1.55929 | − | 1.24349i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
−0.733052 | − | 0.680173i | \(-0.761905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.433884 | + | 1.90097i | 0.433884 | + | 1.90097i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(692\) | 0.0685179 | + | 0.142279i | 0.0685179 | + | 0.142279i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.23732 | + | 0.777459i | 1.23732 | + | 0.777459i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.03453 | − | 0.195744i | 1.03453 | − | 0.195744i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.118267 | + | 0.0743122i | 0.118267 | + | 0.0743122i | ||||
\(699\) | −1.84095 | + | 0.722521i | −1.84095 | + | 0.722521i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(702\) | 0.199973 | − | 1.77481i | 0.199973 | − | 1.77481i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.574643 | + | 1.64224i | −0.574643 | + | 1.64224i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.167281 | − | 0.155214i | −0.167281 | − | 0.155214i | ||||
\(709\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.366025 | + | 0.366025i | −0.366025 | + | 0.366025i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.0723457 | − | 0.0576938i | 0.0723457 | − | 0.0576938i | ||||
\(717\) | −0.297251 | − | 0.0222759i | −0.297251 | − | 0.0222759i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.90097 | + | 0.433884i | 1.90097 | + | 0.433884i | 1.00000 | \(0\) | ||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.308658 | + | 0.882094i | 0.308658 | + | 0.882094i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.930874 | + | 0.365341i | −0.930874 | + | 0.365341i | ||||
\(726\) | −0.0349435 | − | 0.933884i | −0.0349435 | − | 0.933884i | ||||
\(727\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.250105 | + | 0.0281801i | −0.250105 | + | 0.0281801i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.917038 | + | 0.625226i | 0.917038 | + | 0.625226i | ||||
\(739\) | −1.00560 | + | 0.631863i | −1.00560 | + | 0.631863i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(744\) | −0.160646 | + | 0.520801i | −0.160646 | + | 0.520801i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(752\) | −0.691457 | + | 1.10045i | −0.691457 | + | 1.10045i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.462260 | + | 1.72518i | 0.462260 | + | 1.72518i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.636119 | − | 1.32091i | 0.636119 | − | 1.32091i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
0.930874 | − | 0.365341i | \(-0.119048\pi\) | |||||||
\(762\) | −0.0558554 | + | 0.745338i | −0.0558554 | + | 0.745338i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.14715 | − | 2.69244i | 2.14715 | − | 2.69244i | ||||
\(768\) | −0.308658 | + | 0.210440i | −0.308658 | + | 0.210440i | ||||
\(769\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.35654 | − | 1.46200i | 1.35654 | − | 1.46200i | ||||
\(772\) | −0.0278640 | − | 0.247300i | −0.0278640 | − | 0.247300i | ||||
\(773\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0579571 | − | 0.514383i | 0.0579571 | − | 0.514383i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(784\) | 0.857322 | 0.857322 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.603718 | − | 1.53825i | −0.603718 | − | 1.53825i | ||||
\(787\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(788\) | −0.0488093 | − | 0.213848i | −0.0488093 | − | 0.213848i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.0311901 | − | 0.276820i | −0.0311901 | − | 0.276820i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.177970 | − | 0.177970i | 0.177970 | − | 0.177970i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.901341 | − | 0.205725i | −0.901341 | − | 0.205725i | ||||
\(807\) | −0.772532 | + | 0.206999i | −0.772532 | + | 0.206999i | ||||
\(808\) | −1.79077 | + | 0.862390i | −1.79077 | + | 0.862390i | ||||
\(809\) | 0.0739590 | + | 0.211363i | 0.0739590 | + | 0.211363i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.73205i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.69226 | − | 0.0633201i | 1.69226 | − | 0.0633201i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.246975 | + | 1.08207i | −0.246975 | + | 1.08207i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.541044 | + | 0.678448i | 0.541044 | + | 0.678448i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.59908 | + | 0.180173i | −1.59908 | + | 0.180173i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(828\) | 0.104635 | + | 0.0713389i | 0.104635 | + | 0.0713389i | ||||
\(829\) | 0.752407 | + | 0.752407i | 0.752407 | + | 0.752407i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.40097 | − | 0.432142i | −1.40097 | − | 0.432142i | ||||
\(832\) | −1.30184 | − | 1.63246i | −1.30184 | − | 1.63246i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.16522 | + | 0.508380i | 1.16522 | + | 0.508380i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.438297 | − | 0.275400i | 0.438297 | − | 0.275400i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.988831 | + | 0.149042i | 0.988831 | + | 0.149042i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.0591517 | + | 0.169046i | 0.0591517 | + | 0.169046i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.35377 | − | 0.417581i | 1.35377 | − | 0.417581i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.0256762 | − | 0.170350i | −0.0256762 | − | 0.170350i | ||||
\(853\) | 1.33485 | − | 1.33485i | 1.33485 | − | 1.33485i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.900969 | − | 0.433884i | \(-0.142857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.180173 | + | 1.59908i | 0.180173 | + | 1.59908i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.900969 | + | 0.433884i | 0.900969 | + | 0.433884i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(864\) | 0.250105 | + | 0.0281801i | 0.250105 | + | 0.0281801i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.930874 | − | 0.365341i | 0.930874 | − | 0.365341i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0462668 | − | 0.00875416i | −0.0462668 | − | 0.00875416i | ||||
\(877\) | 0.781831 | + | 0.376510i | 0.781831 | + | 0.376510i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(878\) | 0.0311901 | − | 0.276820i | 0.0311901 | − | 0.276820i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(882\) | −0.708353 | − | 0.609587i | −0.708353 | − | 0.609587i | ||||
\(883\) | 1.40881 | + | 1.12349i | 1.40881 | + | 1.12349i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.14503 | + | 1.43583i | −1.14503 | + | 1.43583i | ||||
\(887\) | 0.565533 | − | 0.565533i | 0.565533 | − | 0.565533i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.0685179 | + | 0.142279i | −0.0685179 | + | 0.142279i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | ||||
\(898\) | − | 1.58259i | − | 1.58259i | ||||||
\(899\) | −0.307384 | + | 0.416490i | −0.307384 | + | 0.416490i | ||||
\(900\) | −0.126286 | + | 0.00946383i | −0.126286 | + | 0.00946383i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.373714 | − | 0.856562i | 0.373714 | − | 0.856562i | ||||
\(907\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.82344 | + | 0.488590i | 1.82344 | + | 0.488590i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.264152 | + | 0.605443i | −0.264152 | + | 0.605443i | ||||
\(922\) | −0.381206 | + | 1.67017i | −0.381206 | + | 1.67017i | ||||
\(923\) | 2.53464 | − | 0.578514i | 2.53464 | − | 0.578514i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.221277 | − | 0.352160i | 0.221277 | − | 0.352160i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.243112 | + | 0.0651416i | −0.243112 | + | 0.0651416i | ||||
\(929\) | 1.91115i | 1.91115i | 0.294755 | + | 0.955573i | \(0.404762\pi\) | ||||
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.225649 | − | 0.108667i | 0.225649 | − | 0.108667i | ||||
\(933\) | −0.517276 | − | 1.93050i | −0.517276 | − | 1.93050i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.0752393 | + | 2.01081i | −0.0752393 | + | 2.01081i | ||||
\(937\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.631863 | − | 1.00560i | −0.631863 | − | 1.00560i | ||||
\(944\) | −1.20781 | − | 0.963193i | −1.20781 | − | 0.963193i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.264152 | − | 0.754903i | 0.264152 | − | 0.754903i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0795629 | − | 0.706140i | 0.0795629 | − | 0.706140i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.04551 | − | 0.197822i | −1.04551 | − | 0.197822i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.0377495 | 0.0377495 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.317625 | + | 0.659555i | 0.317625 | + | 0.659555i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.649042 | − | 1.85486i | 0.649042 | − | 1.85486i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(968\) | 0.117886 | + | 1.04627i | 0.117886 | + | 1.04627i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(972\) | −0.0861372 | − | 0.0928338i | −0.0861372 | − | 0.0928338i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.23028 | − | 1.23028i | 1.23028 | − | 1.23028i | ||||
\(975\) | −0.284841 | − | 1.88980i | −0.284841 | − | 1.88980i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(978\) | 1.41274 | + | 0.105871i | 1.41274 | + | 0.105871i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.35492 | − | 0.652497i | 1.35492 | − | 0.652497i | ||||
\(983\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(984\) | −1.08292 | − | 0.625226i | −1.08292 | − | 0.625226i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.52446 | + | 0.347948i | −1.52446 | + | 0.347948i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(992\) | 0.0289907 | − | 0.127017i | 0.0289907 | − | 0.127017i | ||||
\(993\) | 1.68017 | + | 0.733052i | 1.68017 | + | 0.733052i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.68280 | + | 0.189606i | −1.68280 | + | 0.189606i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(998\) | −0.0987659 | − | 0.0987659i | −0.0987659 | − | 0.0987659i | ||||
\(999\) | 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 | 2001.1.bf.c.896.2 | ✓ | 24 | |
3.2 | odd | 2 | 2001.1.bf.d.896.1 | yes | 24 | ||
23.22 | odd | 2 | CM | 2001.1.bf.c.896.2 | ✓ | 24 | |
29.19 | odd | 28 | 2001.1.bf.d.1034.1 | yes | 24 | ||
69.68 | even | 2 | 2001.1.bf.d.896.1 | yes | 24 | ||
87.77 | even | 28 | inner | 2001.1.bf.c.1034.2 | yes | 24 | |
667.367 | even | 28 | 2001.1.bf.d.1034.1 | yes | 24 | ||
2001.1034 | odd | 28 | inner | 2001.1.bf.c.1034.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.1.bf.c.896.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2001.1.bf.c.896.2 | ✓ | 24 | 23.22 | odd | 2 | CM | |
2001.1.bf.c.1034.2 | yes | 24 | 87.77 | even | 28 | inner | |
2001.1.bf.c.1034.2 | yes | 24 | 2001.1034 | odd | 28 | inner | |
2001.1.bf.d.896.1 | yes | 24 | 3.2 | odd | 2 | ||
2001.1.bf.d.896.1 | yes | 24 | 69.68 | even | 2 | ||
2001.1.bf.d.1034.1 | yes | 24 | 29.19 | odd | 28 | ||
2001.1.bf.d.1034.1 | yes | 24 | 667.367 | even | 28 |