Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [943,1,Mod(367,943)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(943, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("943.367");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 943 = 23 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 943.n (of order \(20\), degree \(8\), 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: | \(0.470618306913\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{20})\) |
Coefficient field: | \(\Q(\zeta_{60})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{60}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{60} - \cdots)\) |
Embedding invariants
Embedding label | 781.1 | ||
Root | \(0.406737 + 0.913545i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 943.781 |
Dual form | 943.1.n.b.390.1 |
$q$-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 \(\left(\mathbb{Z}/943\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(534\) |
\(\chi(n)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.86055 | + | 0.604528i | −1.86055 | + | 0.604528i | −0.866025 | + | 0.500000i | \(0.833333\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(3\) | −0.506809 | + | 0.506809i | −0.506809 | + | 0.506809i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(4\) | 2.28716 | − | 1.66172i | 2.28716 | − | 1.66172i | ||||
\(5\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(6\) | 0.636561 | − | 1.24932i | 0.636561 | − | 1.24932i | ||||
\(7\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(8\) | −2.10094 | + | 2.89169i | −2.10094 | + | 2.89169i | ||||
\(9\) | 0.486290i | 0.486290i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(12\) | −0.316980 | + | 2.00133i | −0.316980 | + | 2.00133i | ||||
\(13\) | −1.38488 | − | 0.705634i | −1.38488 | − | 0.705634i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.28716 | − | 3.96149i | 1.28716 | − | 3.96149i | ||||
\(17\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(18\) | −0.293976 | − | 0.904765i | −0.293976 | − | 0.904765i | ||||
\(19\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(24\) | −0.400762 | − | 2.53031i | −0.400762 | − | 2.53031i | ||||
\(25\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(26\) | 3.00322 | + | 0.475663i | 3.00322 | + | 0.475663i | ||||
\(27\) | −0.753265 | − | 0.753265i | −0.753265 | − | 0.753265i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.292088 | + | 1.84417i | −0.292088 | + | 1.84417i | 0.207912 | + | 0.978148i | \(0.433333\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.658114 | + | 0.478148i | 0.658114 | + | 0.478148i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(32\) | 4.57433i | 4.57433i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.808078 | + | 1.11222i | 0.808078 | + | 1.11222i | ||||
\(37\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.05949 | − | 0.344250i | 1.05949 | − | 0.344250i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.14988 | − | 1.58268i | −1.14988 | − | 1.58268i | ||||
\(47\) | 0.0475201 | − | 0.0932634i | 0.0475201 | − | 0.0932634i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(48\) | 1.35537 | + | 2.66006i | 1.35537 | + | 2.66006i | ||||
\(49\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(50\) | − | 1.95630i | − | 1.95630i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.34003 | + | 0.687393i | −4.34003 | + | 0.687393i | ||||
\(53\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(54\) | 1.85685 | + | 0.946115i | 1.85685 | + | 0.946115i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.571411 | − | 3.60775i | −0.571411 | − | 3.60775i | ||||
\(59\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(62\) | −1.51351 | − | 0.491768i | −1.51351 | − | 0.491768i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.47815 | − | 4.54927i | −1.47815 | − | 4.54927i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.638616 | − | 0.325391i | −0.638616 | − | 0.325391i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.07587 | + | 0.170401i | −1.07587 | + | 0.170401i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(72\) | −1.40620 | − | 1.02166i | −1.40620 | − | 1.02166i | ||||
\(73\) | 1.98904i | 1.98904i | 0.104528 | + | 0.994522i | \(0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.325391 | − | 0.638616i | −0.325391 | − | 0.638616i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.76313 | + | 1.28099i | −1.76313 | + | 1.28099i | ||||
\(79\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.277233 | 0.277233 | ||||||||
\(82\) | 1.94558 | − | 0.204489i | 1.94558 | − | 0.204489i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.786610 | − | 1.08268i | −0.786610 | − | 1.08268i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.28716 | + | 1.66172i | 2.28716 | + | 1.66172i | ||||
\(93\) | −0.575867 | + | 0.0912084i | −0.575867 | + | 0.0912084i | ||||
\(94\) | −0.0320330 | + | 0.202248i | −0.0320330 | + | 0.202248i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.31831 | − | 2.31831i | −2.31831 | − | 2.31831i | ||||
\(97\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(98\) | 0.604528 | − | 1.86055i | 0.604528 | − | 1.86055i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.873619 | + | 2.68872i | 0.873619 | + | 2.68872i | ||||
\(101\) | −1.76007 | + | 0.896802i | −1.76007 | + | 0.896802i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(104\) | 4.95003 | − | 2.52217i | 4.95003 | − | 2.52217i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(108\) | −2.97456 | − | 0.471124i | −2.97456 | − | 0.471124i | ||||
\(109\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.39645 | + | 4.70330i | 2.39645 | + | 4.70330i | ||||
\(117\) | 0.343142 | − | 0.673455i | 0.343142 | − | 0.673455i | ||||
\(118\) | 1.86055 | + | 2.56082i | 1.86055 | + | 2.56082i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.601105 | − | 0.390362i | 0.601105 | − | 0.390362i | ||||
\(124\) | 2.29976 | 2.29976 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(128\) | 2.81160 | + | 3.86984i | 2.81160 | + | 3.86984i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.122881 | − | 0.169131i | 0.122881 | − | 0.169131i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 1.38488 | + | 0.219344i | 1.38488 | + | 0.219344i | ||||
\(139\) | −0.128496 | + | 0.395472i | −0.128496 | + | 0.395472i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0231831 | + | 0.0713503i | 0.0231831 | + | 0.0713503i | ||||
\(142\) | 1.89869 | − | 0.967431i | 1.89869 | − | 0.967431i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.92643 | + | 0.625935i | 1.92643 | + | 0.625935i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.20243 | − | 3.70071i | −1.20243 | − | 3.70071i | ||||
\(147\) | −0.112122 | − | 0.707912i | −0.112122 | − | 0.707912i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(150\) | 0.991468 | + | 0.991468i | 0.991468 | + | 0.991468i | ||||
\(151\) | −1.12146 | − | 0.571411i | −1.12146 | − | 0.571411i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.85119 | − | 2.54794i | 1.85119 | − | 2.54794i | ||||
\(157\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.515805 | + | 0.167595i | −0.515805 | + | 0.167595i | ||||
\(163\) | 1.98904 | 1.98904 | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) | ||||
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(164\) | −2.58268 | + | 1.14988i | −2.58268 | + | 1.14988i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.832200 | + | 1.14543i | 0.832200 | + | 1.14543i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 0.618034i | − | 0.618034i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(174\) | 2.11803 | + | 1.53884i | 2.11803 | + | 1.53884i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.03330 | + | 0.526494i | 1.03330 | + | 0.526494i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.90807 | + | 0.302208i | 1.90807 | + | 0.302208i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.39939 | − | 1.10453i | −3.39939 | − | 1.10453i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.01629 | − | 0.517826i | 1.01629 | − | 0.517826i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.0462916 | − | 0.292274i | −0.0462916 | − | 0.292274i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(192\) | 3.05475 | + | 1.55647i | 3.05475 | + | 1.55647i | ||||
\(193\) | −0.243145 | + | 1.53516i | −0.243145 | + | 1.53516i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.82709i | 2.82709i | ||||||||
\(197\) | 0.873619 | − | 1.20243i | 0.873619 | − | 1.20243i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(200\) | −2.10094 | − | 2.89169i | −2.10094 | − | 2.89169i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.73256 | − | 2.73256i | 2.73256 | − | 2.73256i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.462489 | + | 0.150272i | −0.462489 | + | 0.150272i | ||||
\(208\) | −4.57793 | + | 4.57793i | −4.57793 | + | 4.57793i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.412215 | + | 0.809017i | −0.412215 | + | 0.809017i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.458898 | − | 0.631620i | 0.458898 | − | 0.631620i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.76077 | − | 0.595648i | 3.76077 | − | 0.595648i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00806 | − | 1.00806i | −1.00806 | − | 1.00806i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.363271 | + | 1.11803i | 0.363271 | + | 1.11803i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.462489 | − | 0.150272i | −0.462489 | − | 0.150272i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.71912 | − | 4.71912i | −4.71912 | − | 4.71912i | ||||
\(233\) | 1.72129 | + | 0.877042i | 1.72129 | + | 0.877042i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(234\) | −0.231310 | + | 1.46043i | −0.231310 | + | 1.46043i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.70071 | − | 2.68872i | −3.70071 | − | 2.68872i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.847673 | − | 1.66365i | −0.847673 | − | 1.66365i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(242\) | −1.58268 | + | 1.14988i | −1.58268 | + | 1.14988i | ||||
\(243\) | 0.612761 | − | 0.612761i | 0.612761 | − | 0.612761i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.882400 | + | 1.08967i | −0.882400 | + | 1.08967i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.76531 | + | 0.898504i | −2.76531 | + | 0.898504i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.14988 | − | 1.58268i | 1.14988 | − | 1.58268i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.70071 | − | 2.68872i | −3.70071 | − | 2.68872i | ||||
\(257\) | 1.24314 | − | 0.196895i | 1.24314 | − | 0.196895i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.896802 | − | 0.142040i | −0.896802 | − | 0.142040i | ||||
\(262\) | −0.126381 | + | 0.388960i | −0.126381 | + | 0.388960i | ||||
\(263\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.614648 | + | 1.89169i | 0.614648 | + | 1.89169i | 0.406737 | + | 0.913545i | \(0.366667\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.587785 | − | 1.80902i | 0.587785 | − | 1.80902i | − | 1.00000i | \(-0.5\pi\) | |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.00133 | + | 0.316980i | −2.00133 | + | 0.316980i | ||||
\(277\) | −0.658114 | − | 0.478148i | −0.658114 | − | 0.478148i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(278\) | − | 0.813473i | − | 0.813473i | ||||||
\(279\) | −0.232518 | + | 0.320034i | −0.232518 | + | 0.320034i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(282\) | −0.0862665 | − | 0.118736i | −0.0862665 | − | 0.118736i | ||||
\(283\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(284\) | −2.17753 | + | 2.17753i | −2.17753 | + | 2.17753i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.22445 | −2.22445 | ||||||||
\(289\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.30524 | + | 4.54927i | 3.30524 | + | 4.54927i | ||||
\(293\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(294\) | 0.636561 | + | 1.24932i | 0.636561 | + | 1.24932i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.243145 | − | 1.53516i | 0.243145 | − | 1.53516i | ||||
\(300\) | −1.80543 | − | 0.919911i | −1.80543 | − | 0.919911i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.43196 | + | 0.385184i | 2.43196 | + | 0.385184i | ||||
\(303\) | 0.437513 | − | 1.34653i | 0.437513 | − | 1.34653i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.80902 | + | 0.587785i | 1.80902 | + | 0.587785i | 1.00000 | \(0\) | ||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.262394 | + | 1.65669i | 0.262394 | + | 1.65669i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(312\) | −1.23046 | + | 3.78698i | −1.23046 | + | 3.78698i | ||||
\(313\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.896802 | + | 0.142040i | −0.896802 | + | 0.142040i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.634077 | − | 0.460684i | 0.634077 | − | 0.460684i | ||||
\(325\) | 1.09905 | − | 1.09905i | 1.09905 | − | 1.09905i | ||||
\(326\) | −3.70071 | + | 1.20243i | −3.70071 | + | 1.20243i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.65624 | − | 2.39169i | 2.65624 | − | 2.39169i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.41228 | − | 1.41228i | 1.41228 | − | 1.41228i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.743145 | − | 0.669131i | \(-0.233333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.75441 | + | 3.44322i | −1.75441 | + | 3.44322i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | −2.24079 | − | 1.62803i | −2.24079 | − | 1.62803i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.373619 | + | 1.14988i | 0.373619 | + | 1.14988i | ||||
\(347\) | 0.278768 | − | 0.142040i | 0.278768 | − | 0.142040i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(348\) | −3.59821 | − | 1.16913i | −3.59821 | − | 1.16913i | ||||
\(349\) | 0.198825 | + | 0.0646021i | 0.198825 | + | 0.0646021i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.511655 | + | 1.57471i | 0.511655 | + | 1.57471i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.128496 | − | 0.395472i | 0.128496 | − | 0.395472i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(354\) | −2.24079 | − | 0.354906i | −2.24079 | − | 0.354906i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.73274 | + | 0.591208i | −3.73274 | + | 0.591208i | ||||
\(359\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.325391 | + | 0.638616i | −0.325391 | + | 0.638616i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(368\) | 4.16535 | 4.16535 | ||||||||
\(369\) | 0.101105 | − | 0.475663i | 0.101105 | − | 0.475663i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.16554 | + | 1.16554i | −1.16554 | + | 1.16554i | ||||
\(373\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.169852 | + | 0.333354i | 0.169852 | + | 0.333354i | ||||
\(377\) | 1.70582 | − | 2.34786i | 1.70582 | − | 2.34786i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.112122 | − | 0.707912i | 0.112122 | − | 0.707912i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | −3.38621 | − | 0.536324i | −3.38621 | − | 0.536324i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.475663 | − | 3.00322i | −0.475663 | − | 3.00322i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.10453 | − | 3.39939i | −1.10453 | − | 3.39939i | ||||
\(393\) | 0.0234399 | + | 0.147994i | 0.0234399 | + | 0.147994i | ||||
\(394\) | −0.898504 | + | 2.76531i | −0.898504 | + | 2.76531i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.72129 | − | 0.877042i | −1.72129 | − | 0.877042i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.743145 | − | 0.669131i | \(-0.766667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.36984 | + | 2.44833i | 3.36984 | + | 2.44833i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.574014 | − | 1.12657i | −0.574014 | − | 1.12657i | ||||
\(404\) | −2.53534 | + | 4.97589i | −2.53534 | + | 4.97589i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.769639 | − | 0.559175i | 0.769639 | − | 0.559175i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.22780 | − | 6.33492i | 3.22780 | − | 6.33492i | ||||
\(417\) | −0.135305 | − | 0.265552i | −0.135305 | − | 0.265552i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(422\) | 0.277871 | − | 1.75441i | 0.277871 | − | 1.75441i | ||||
\(423\) | 0.0453530 | + | 0.0231085i | 0.0453530 | + | 0.0231085i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.471970 | + | 1.45258i | −0.471970 | + | 1.45258i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(432\) | −3.95362 | + | 2.01447i | −3.95362 | + | 2.01447i | ||||
\(433\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.48496 | + | 1.26615i | 2.48496 | + | 1.26615i | ||||
\(439\) | 0.262394 | − | 1.65669i | 0.262394 | − | 1.65669i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.393417 | − | 0.285834i | −0.393417 | − | 0.285834i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.14988 | + | 1.58268i | −1.14988 | + | 1.58268i | −0.406737 | + | 0.913545i | \(0.633333\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.35177 | − | 1.86055i | −1.35177 | − | 1.86055i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(450\) | 0.951326 | 0.951326 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.857960 | − | 0.278768i | 0.857960 | − | 0.278768i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.08268 | + | 0.786610i | 1.08268 | + | 0.786610i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.309017 | + | 1.95106i | −0.309017 | + | 1.95106i | 1.00000i | \(0.5\pi\) | ||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(464\) | 6.92970 | + | 3.53086i | 6.92970 | + | 3.53086i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.73274 | − | 0.591208i | −3.73274 | − | 0.591208i | ||||
\(467\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(468\) | −0.334272 | − | 2.11051i | −0.334272 | − | 2.11051i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.50033 | + | 1.78716i | 5.50033 | + | 1.78716i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.58286 | + | 2.58286i | 2.58286 | + | 2.58286i | ||||
\(479\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.66172 | − | 2.28716i | 1.66172 | − | 2.28716i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.769639 | + | 1.51050i | −0.769639 | + | 1.51050i | ||||
\(487\) | −0.122881 | − | 0.169131i | −0.122881 | − | 0.169131i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.00806 | + | 1.00806i | −1.00806 | + | 1.00806i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.813473 | 0.813473 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(492\) | 0.726153 | − | 1.89169i | 0.726153 | − | 1.89169i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.74128 | − | 1.99165i | 2.74128 | − | 1.99165i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.906737 | + | 1.77957i | 0.906737 | + | 1.77957i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.41582i | 1.41582i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00228 | − | 0.158745i | −1.00228 | − | 0.158745i | ||||
\(508\) | −0.873619 | + | 2.68872i | −0.873619 | + | 2.68872i | ||||
\(509\) | −0.0809764 | − | 0.511265i | −0.0809764 | − | 0.511265i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.96149 | + | 1.28716i | 3.96149 | + | 1.28716i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.19390 | + | 1.11785i | −2.19390 | + | 1.11785i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.313225 | + | 0.313225i | 0.313225 | + | 0.313225i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(522\) | 1.75441 | − | 0.277871i | 1.75441 | − | 0.277871i | ||||
\(523\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(524\) | − | 0.591023i | − | 0.591023i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.748323 | − | 0.243145i | 0.748323 | − | 0.243145i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.20791 | + | 0.978148i | 1.20791 | + | 0.978148i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.12019 | + | 0.813864i | −1.12019 | + | 0.813864i | ||||
\(538\) | −2.28716 | − | 3.14801i | −2.28716 | − | 3.14801i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.01807 | − | 1.40126i | 1.01807 | − | 1.40126i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(542\) | 3.72109i | 3.72109i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.889993 | − | 0.889993i | −0.889993 | − | 0.889993i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.28263 | − | 1.16306i | 2.28263 | − | 1.16306i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.51351 | + | 0.491768i | 1.51351 | + | 0.491768i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.363271 | + | 1.11803i | 0.363271 | + | 1.11803i | ||||
\(557\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(558\) | 0.239142 | − | 0.736002i | 0.239142 | − | 0.736002i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(564\) | 0.171588 | + | 0.124666i | 0.171588 | + | 0.124666i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.76758 | − | 3.46908i | 1.76758 | − | 3.46908i | ||||
\(569\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −1.00000 | ||||||||
\(576\) | 2.21226 | − | 0.718808i | 2.21226 | − | 0.718808i | ||||
\(577\) | 0.770236 | − | 0.770236i | 0.770236 | − | 0.770236i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(578\) | 1.58268 | − | 1.14988i | 1.58268 | − | 1.14988i | ||||
\(579\) | −0.654803 | − | 0.901259i | −0.654803 | − | 0.901259i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.75170 | − | 4.17886i | −5.75170 | − | 4.17886i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.49452 | − | 0.761497i | −1.49452 | − | 0.761497i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(588\) | −1.43279 | − | 1.43279i | −1.43279 | − | 1.43279i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.166646 | + | 1.05216i | 0.166646 | + | 1.05216i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.809017 | + | 0.412215i | −0.809017 | + | 0.412215i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.475663 | + | 3.00322i | 0.475663 | + | 3.00322i | ||||
\(599\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | 1.00000i | \(0.5\pi\) | ||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(600\) | 2.53031 | + | 0.400762i | 2.53031 | + | 0.400762i | ||||
\(601\) | 1.32028 | + | 1.32028i | 1.32028 | + | 1.32028i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.51448 | + | 0.556639i | −3.51448 | + | 0.556639i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.76977i | 2.76977i | ||||||||
\(607\) | −0.690983 | + | 0.951057i | −0.690983 | + | 0.951057i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.131620 | + | 0.0956272i | −0.131620 | + | 0.0956272i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(614\) | −3.72109 | −3.72109 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.483626 | − | 0.949169i | 0.483626 | − | 0.949169i | ||||
\(622\) | −1.48971 | − | 2.92373i | −1.48971 | − | 2.92373i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 4.64027i | − | 4.64027i | ||||||
\(625\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.201103 | − | 0.618931i | −0.201103 | − | 0.618931i | ||||
\(634\) | 1.58268 | − | 0.806414i | 1.58268 | − | 0.806414i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.38488 | − | 0.705634i | 1.38488 | − | 0.705634i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0828641 | − | 0.523183i | −0.0828641 | − | 0.523183i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(648\) | −0.582449 | + | 0.801672i | −0.582449 | + | 0.801672i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.38043 | + | 2.70924i | −1.38043 | + | 2.70924i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.54927 | − | 3.30524i | 4.54927 | − | 3.30524i | ||||
\(653\) | 1.18606 | − | 1.18606i | 1.18606 | − | 1.18606i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.08268 | + | 3.60730i | −2.08268 | + | 3.60730i | ||||
\(657\) | −0.967251 | −0.967251 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(662\) | −1.77384 | + | 3.48137i | −1.77384 | + | 3.48137i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.84417 | + | 0.292088i | −1.84417 | + | 0.292088i | ||||
\(668\) | 0.873619 | − | 5.51581i | 0.873619 | − | 5.51581i | ||||
\(669\) | −0.750739 | − | 0.382520i | −0.750739 | − | 0.382520i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.196895 | + | 1.24314i | 0.196895 | + | 1.24314i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.949169 | − | 0.483626i | 0.949169 | − | 0.483626i | ||||
\(676\) | 3.80676 | + | 1.23689i | 3.80676 | + | 1.23689i | ||||
\(677\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.506809 | − | 0.506809i | −0.506809 | − | 0.506809i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.642040 | − | 1.26007i | 0.642040 | − | 1.26007i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(692\) | −1.02700 | − | 1.41355i | −1.02700 | − | 1.41355i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.432795 | + | 0.432795i | −0.432795 | + | 0.432795i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.78339 | 4.78339 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.408977 | −0.408977 | ||||||||
\(699\) | −1.31686 | + | 0.427873i | −1.31686 | + | 0.427873i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(702\) | −1.90392 | − | 2.62052i | −1.90392 | − | 2.62052i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.813473i | 0.813473i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.23822 | − | 0.512884i | 3.23822 | − | 0.512884i | ||||
\(709\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.251377 | + | 0.773659i | −0.251377 | + | 0.773659i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.86625 | − | 2.47948i | 4.86625 | − | 2.47948i | ||||
\(717\) | 1.27276 | + | 0.413545i | 1.27276 | + | 0.413545i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.809017 | − | 0.412215i | 0.809017 | − | 0.412215i | − | 1.00000i | \(-0.5\pi\) | |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.604528 | + | 1.86055i | −0.604528 | + | 1.86055i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.66365 | − | 0.847673i | −1.66365 | − | 0.847673i | ||||
\(726\) | 0.219344 | − | 1.38488i | 0.219344 | − | 1.38488i | ||||
\(727\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.898338i | 0.898338i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.35045 | + | 1.41355i | −4.35045 | + | 1.41355i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.0994407 | + | 0.946115i | 0.0994407 | + | 0.946115i | ||||
\(739\) | −1.82709 | −1.82709 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(744\) | 0.946115 | − | 1.85685i | 0.946115 | − | 1.85685i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(752\) | −0.308295 | − | 0.308295i | −0.308295 | − | 0.308295i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.75441 | + | 5.39952i | −1.75441 | + | 5.39952i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.535233 | + | 1.64728i | 0.535233 | + | 1.64728i | 0.743145 | + | 0.669131i | \(0.233333\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(762\) | 0.219344 | + | 1.38488i | 0.219344 | + | 1.38488i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.393417 | + | 2.48393i | −0.393417 | + | 2.48393i | ||||
\(768\) | 3.23822 | − | 0.512884i | 3.23822 | − | 0.512884i | ||||
\(769\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.530249 | + | 0.729825i | −0.530249 | + | 0.729825i | ||||
\(772\) | 1.99489 | + | 3.91519i | 1.99489 | + | 3.91519i | ||||
\(773\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.658114 | + | 0.478148i | −0.658114 | + | 0.478148i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.60917 | − | 1.16913i | 1.60917 | − | 1.16913i | ||||
\(784\) | 2.44833 | + | 3.36984i | 2.44833 | + | 3.36984i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.133078 | − | 0.261179i | −0.133078 | − | 0.261179i | ||||
\(787\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(788\) | − | 4.20188i | − | 4.20188i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 3.73274 | + | 0.591208i | 3.73274 | + | 0.591208i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.35045 | − | 1.41355i | −4.35045 | − | 1.41355i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.74902 | + | 1.74902i | 1.74902 | + | 1.74902i | ||||
\(807\) | −1.27024 | − | 0.647218i | −1.27024 | − | 0.647218i | ||||
\(808\) | 1.10453 | − | 6.97372i | 1.10453 | − | 6.97372i | ||||
\(809\) | 1.39680 | − | 0.221232i | 1.39680 | − | 0.221232i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.48629i | 1.48629i | 0.669131 | + | 0.743145i | \(0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.618931 | + | 1.21472i | 0.618931 | + | 1.21472i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.86055 | − | 0.604528i | 1.86055 | − | 0.604528i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.17557 | −1.17557 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0740142 | − | 0.0740142i | 0.0740142 | − | 0.0740142i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(828\) | −0.808078 | + | 1.11222i | −0.808078 | + | 1.11222i | ||||
\(829\) | 1.17557i | 1.17557i | 0.809017 | + | 0.587785i | \(0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.575867 | − | 0.0912084i | 0.575867 | − | 0.0912084i | ||||
\(832\) | −1.16306 | + | 7.34324i | −1.16306 | + | 7.34324i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.412275 | + | 0.412275i | 0.412275 | + | 0.412275i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.135562 | − | 0.855906i | −0.135562 | − | 0.855906i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.36460 | − | 0.768306i | −2.36460 | − | 0.768306i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.401559 | + | 2.53534i | 0.401559 | + | 2.53534i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.0983512 | − | 0.0155773i | −0.0983512 | − | 0.0155773i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | − | 2.20718i | − | 2.20718i | ||||||
\(853\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | 1.00000i | \(0.5\pi\) | ||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.58268 | − | 1.14988i | 1.58268 | − | 1.14988i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.89169 | + | 0.614648i | −1.89169 | + | 0.614648i | −0.913545 | + | 0.406737i | \(0.866667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(864\) | 3.44568 | − | 3.44568i | 3.44568 | − | 3.44568i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.325391 | − | 0.638616i | 0.325391 | − | 0.638616i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.98073 | − | 0.630486i | −3.98073 | − | 0.630486i | ||||
\(877\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(878\) | 0.513320 | + | 3.24098i | 0.513320 | + | 3.24098i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(882\) | 0.904765 | + | 0.293976i | 0.904765 | + | 0.293976i | ||||
\(883\) | 1.26007 | − | 0.642040i | 1.26007 | − | 0.642040i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.18264 | − | 3.63978i | 1.18264 | − | 3.63978i | ||||
\(887\) | 0.511265 | + | 0.0809764i | 0.511265 | + | 0.0809764i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.68872 | + | 1.95347i | 2.68872 | + | 1.95347i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.654803 | + | 0.901259i | 0.654803 | + | 0.901259i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.07401 | + | 1.07401i | −1.07401 | + | 1.07401i | ||||
\(900\) | −1.30750 | + | 0.424832i | −1.30750 | + | 0.424832i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.42775 | + | 1.03732i | −1.42775 | + | 1.03732i | ||||
\(907\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.436106 | − | 0.855906i | −0.436106 | − | 0.855906i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.21472 | + | 0.618931i | −1.21472 | + | 0.618931i | ||||
\(922\) | −2.48990 | − | 0.809017i | −2.48990 | − | 0.809017i | ||||
\(923\) | 1.61019 | + | 0.523183i | 1.61019 | + | 0.523183i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.604528 | − | 3.81684i | −0.604528 | − | 3.81684i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.43585 | − | 1.33611i | −8.43585 | − | 1.33611i | ||||
\(929\) | −0.0740142 | − | 0.0740142i | −0.0740142 | − | 0.0740142i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.39428 | − | 0.854370i | 5.39428 | − | 0.854370i | ||||
\(933\) | −0.972609 | − | 0.706642i | −0.972609 | − | 0.706642i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.22650 | + | 2.40715i | 1.22650 | + | 2.40715i | ||||
\(937\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(944\) | −6.73968 | −6.73968 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.47815 | + | 1.07394i | −1.47815 | + | 1.07394i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.40354 | − | 2.75460i | 1.40354 | − | 2.75460i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.382520 | − | 0.526494i | 0.382520 | − | 0.526494i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.70330 | − | 2.39645i | −4.70330 | − | 2.39645i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.104528 | − | 0.321706i | −0.104528 | − | 0.321706i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.0809764 | − | 0.511265i | −0.0809764 | − | 0.511265i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(968\) | −1.10453 | + | 3.39939i | −1.10453 | + | 3.39939i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(972\) | 0.383246 | − | 2.41972i | 0.383246 | − | 2.41972i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.330869 | + | 0.240391i | 0.330869 | + | 0.240391i | ||||
\(975\) | 1.11402i | 1.11402i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(978\) | 1.26615 | − | 2.48496i | 1.26615 | − | 2.48496i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.51351 | + | 0.491768i | −1.51351 | + | 0.491768i | ||||
\(983\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(984\) | −0.134077 | + | 2.55834i | −0.134077 | + | 2.55834i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.142040 | − | 0.278768i | −0.142040 | − | 0.278768i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(992\) | −2.18720 | + | 3.01043i | −2.18720 | + | 3.01043i | ||||
\(993\) | 1.43151i | 1.43151i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.58779 | − | 0.809017i | −1.58779 | − | 0.809017i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(998\) | −2.76283 | − | 2.76283i | −2.76283 | − | 2.76283i | ||||
\(999\) | 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 | 943.1.n.b.781.1 | yes | 16 | |
23.22 | odd | 2 | CM | 943.1.n.b.781.1 | yes | 16 | |
41.21 | even | 20 | inner | 943.1.n.b.390.1 | ✓ | 16 | |
943.390 | odd | 20 | inner | 943.1.n.b.390.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
943.1.n.b.390.1 | ✓ | 16 | 41.21 | even | 20 | inner | |
943.1.n.b.390.1 | ✓ | 16 | 943.390 | odd | 20 | inner | |
943.1.n.b.781.1 | yes | 16 | 1.1 | even | 1 | trivial | |
943.1.n.b.781.1 | yes | 16 | 23.22 | odd | 2 | CM |