Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3660,1,Mod(59,3660)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3660, base_ring=CyclotomicField(60))
chi = DirichletCharacter(H, H._module([30, 30, 30, 31]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3660.59");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3660 = 2^{2} \cdot 3 \cdot 5 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3660.fu (of order \(60\), degree \(16\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.82657794624\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
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: | \(\Z[a_1, a_2]\) |
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 | 3239.1 | ||
Root | \(-0.406737 - 0.913545i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3660.3239 |
Dual form | 3660.1.fu.c.539.1 |
$q$-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 \(\left(\mathbb{Z}/3660\mathbb{Z}\right)^\times\).
\(n\) | \(1831\) | \(2197\) | \(2441\) | \(3601\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{60}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(3\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(4\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(5\) | −0.207912 | + | 0.978148i | −0.207912 | + | 0.978148i | ||||
\(6\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(7\) | 0 | 0 | −0.777146 | − | 0.629320i | \(-0.783333\pi\) | ||||
0.777146 | + | 0.629320i | \(0.216667\pi\) | |||||||
\(8\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(11\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(12\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(16\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(17\) | 0.0270911 | + | 0.516929i | 0.0270911 | + | 0.516929i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(19\) | −0.0850311 | + | 0.809017i | −0.0850311 | + | 0.809017i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(20\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.66365 | + | 0.847673i | 1.66365 | + | 0.847673i | 0.994522 | + | 0.104528i | \(0.0333333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(24\) | 1.00000i | 1.00000i | ||||||||
\(25\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(30\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(31\) | −0.601105 | − | 1.56593i | −0.601105 | − | 1.56593i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.207912 | − | 0.978148i | \(-0.433333\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.366025 | − | 0.366025i | −0.366025 | − | 0.366025i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(37\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(38\) | −0.478148 | − | 0.658114i | −0.478148 | − | 0.658114i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(41\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.0523360 | − | 0.998630i | \(-0.483333\pi\) | ||||
−0.0523360 | + | 0.998630i | \(0.516667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(46\) | −1.80354 | + | 0.483257i | −1.80354 | + | 0.483257i | ||||
\(47\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(49\) | 0.207912 | + | 0.978148i | 0.207912 | + | 0.978148i | ||||
\(50\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(51\) | −0.281926 | + | 0.434128i | −0.281926 | + | 0.434128i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.77957 | + | 0.906737i | −1.77957 | + | 0.906737i | −0.866025 | + | 0.500000i | \(0.833333\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(54\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.544320 | + | 0.604528i | −0.544320 | + | 0.604528i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.933580 | − | 0.358368i | \(-0.883333\pi\) | ||||
0.933580 | + | 0.358368i | \(0.116667\pi\) | |||||||
\(60\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(61\) | −0.743145 | − | 0.669131i | −0.743145 | − | 0.669131i | ||||
\(62\) | 1.49452 | + | 0.761497i | 1.49452 | + | 0.761497i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.544639 | − | 0.838671i | \(-0.683333\pi\) | ||||
0.544639 | + | 0.838671i | \(0.316667\pi\) | |||||||
\(68\) | 0.516929 | + | 0.0270911i | 0.516929 | + | 0.0270911i | ||||
\(69\) | 0.847673 | + | 1.66365i | 0.847673 | + | 1.66365i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.838671 | − | 0.544639i | \(-0.816667\pi\) | ||||
0.838671 | + | 0.544639i | \(0.183333\pi\) | |||||||
\(72\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(73\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(76\) | 0.795697 | + | 0.169131i | 0.795697 | + | 0.169131i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.25692 | + | 0.0658722i | 1.25692 | + | 0.0658722i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(80\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.169131 | + | 0.379874i | 0.169131 | + | 0.379874i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.511265 | − | 0.0809764i | −0.511265 | − | 0.0809764i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(90\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.01693 | − | 1.56593i | 1.01693 | − | 1.56593i | ||||
\(93\) | 0.434128 | − | 1.62019i | 0.434128 | − | 1.62019i | ||||
\(94\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(95\) | −0.773659 | − | 0.251377i | −0.773659 | − | 0.251377i | ||||
\(96\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(97\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(98\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(102\) | −0.0809764 | − | 0.511265i | −0.0809764 | − | 0.511265i | ||||
\(103\) | 0 | 0 | −0.994522 | − | 0.104528i | \(-0.966667\pi\) | ||||
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.715754 | − | 1.86460i | 0.715754 | − | 1.86460i | ||||
\(107\) | −1.33093 | − | 1.47815i | −1.33093 | − | 1.47815i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.587785 | − | 0.809017i | \(-0.700000\pi\) | |||||||
\(108\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(109\) | −0.181049 | − | 0.104528i | −0.181049 | − | 0.104528i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.41355 | + | 0.459289i | −1.41355 | + | 0.459289i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | − | 0.813473i | − | 0.813473i | ||||||
\(115\) | −1.17504 | + | 1.45106i | −1.17504 | + | 1.45106i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(121\) | 1.00000i | 1.00000i | ||||||||
\(122\) | 1.00000 | 1.00000 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.62019 | + | 0.434128i | −1.62019 | + | 0.434128i | ||||
\(125\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(128\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(136\) | −0.402280 | + | 0.325760i | −0.402280 | + | 0.325760i | ||||
\(137\) | 0.895472 | + | 0.994522i | 0.895472 | + | 0.994522i | 1.00000 | \(0\) | ||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(138\) | −1.74314 | − | 0.669131i | −1.74314 | − | 0.669131i | ||||
\(139\) | 1.55216 | − | 0.0813454i | 1.55216 | − | 0.0813454i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.406737 | + | 0.913545i | −0.406737 | + | 0.913545i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(150\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(151\) | 0.281926 | − | 1.05216i | 0.281926 | − | 1.05216i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(152\) | −0.704489 | + | 0.406737i | −0.704489 | + | 0.406737i | ||||
\(153\) | −0.483257 | + | 0.185505i | −0.483257 | + | 0.185505i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.65669 | − | 0.262394i | 1.65669 | − | 0.262394i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.629320 | − | 0.777146i | \(-0.716667\pi\) | ||||
0.629320 | + | 0.777146i | \(0.283333\pi\) | |||||||
\(158\) | −0.978148 | + | 0.792088i | −0.978148 | + | 0.792088i | ||||
\(159\) | −1.97267 | − | 0.312440i | −1.97267 | − | 0.312440i | ||||
\(160\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(163\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.379874 | − | 0.169131i | −0.379874 | − | 0.169131i | ||||
\(167\) | 0.204489 | + | 1.94558i | 0.204489 | + | 1.94558i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0.434128 | − | 0.281926i | 0.434128 | − | 0.281926i | ||||
\(171\) | −0.795697 | + | 0.169131i | −0.795697 | + | 0.169131i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.262394 | − | 0.170401i | −0.262394 | − | 0.170401i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(180\) | 1.00000i | 1.00000i | ||||||||
\(181\) | 0.506809 | − | 1.32028i | 0.506809 | − | 1.32028i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.207912 | − | 0.978148i | −0.207912 | − | 0.978148i | ||||
\(184\) | 0.292088 | + | 1.84417i | 0.292088 | + | 1.84417i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.761497 | + | 1.49452i | 0.761497 | + | 1.49452i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.743145 | − | 0.330869i | 0.743145 | − | 0.330869i | ||||
\(191\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(192\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(193\) | 0 | 0 | 0.544639 | − | 0.838671i | \(-0.316667\pi\) | ||||
−0.544639 | + | 0.838671i | \(0.683333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.994522 | − | 0.104528i | 0.994522 | − | 0.104528i | ||||
\(197\) | 0.535233 | − | 0.309017i | 0.535233 | − | 0.309017i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.81708 | − | 0.190983i | 1.81708 | − | 0.190983i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(200\) | −0.207912 | − | 0.978148i | −0.207912 | − | 0.978148i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.402280 | + | 0.325760i | 0.402280 | + | 0.325760i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.292088 | + | 1.84417i | −0.292088 | + | 1.84417i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0163743 | − | 0.103383i | −0.0163743 | − | 0.103383i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(212\) | 0.715754 | + | 1.86460i | 0.715754 | + | 1.86460i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.97815 | + | 0.207912i | 1.97815 | + | 0.207912i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.204489 | − | 0.0434654i | 0.204489 | − | 0.0434654i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(226\) | 0.743145 | − | 1.28716i | 0.743145 | − | 1.28716i | ||||
\(227\) | −0.0375111 | − | 0.715754i | −0.0375111 | − | 0.715754i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(228\) | 0.544320 | + | 0.604528i | 0.544320 | + | 0.604528i | ||||
\(229\) | −1.41355 | + | 1.27276i | −1.41355 | + | 1.27276i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(230\) | −0.0977196 | − | 1.86460i | −0.0977196 | − | 1.86460i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.36603 | + | 1.36603i | 1.36603 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.978148 | + | 0.792088i | 0.978148 | + | 0.792088i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(240\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(241\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(242\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(243\) | −1.00000 | −1.00000 | ||||||||
\(244\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(245\) | −1.00000 | −1.00000 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.913545 | − | 1.40674i | 0.913545 | − | 1.40674i | ||||
\(249\) | −0.0864545 | + | 0.406737i | −0.0864545 | + | 0.406737i | ||||
\(250\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(251\) | 0 | 0 | −0.777146 | − | 0.629320i | \(-0.783333\pi\) | ||||
0.777146 | + | 0.629320i | \(0.216667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.366025 | − | 0.366025i | −0.366025 | − | 0.366025i | ||||
\(256\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(257\) | −0.994522 | + | 1.72256i | −0.994522 | + | 1.72256i | −0.406737 | + | 0.913545i | \(0.633333\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.181049 | − | 1.72256i | 0.181049 | − | 1.72256i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.516929 | − | 1.92920i | −0.516929 | − | 1.92920i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(270\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(271\) | 0.604528 | − | 1.86055i | 0.604528 | − | 1.86055i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(272\) | 0.0809764 | − | 0.511265i | 0.0809764 | − | 0.511265i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.33093 | − | 0.139886i | −1.33093 | − | 0.139886i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.74314 | − | 0.669131i | 1.74314 | − | 0.669131i | ||||
\(277\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(278\) | −1.09905 | + | 1.09905i | −1.09905 | + | 1.09905i | ||||
\(279\) | 1.30354 | − | 1.05558i | 1.30354 | − | 1.05558i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(282\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(283\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.478148 | − | 0.658114i | −0.478148 | − | 0.658114i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.743145 | + | 0.669131i | 0.743145 | + | 0.669131i | ||||
\(289\) | 0.728041 | − | 0.0765201i | 0.728041 | − | 0.0765201i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.395472 | − | 1.86055i | −0.395472 | − | 1.86055i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.104528 | − | 0.994522i | \(-0.466667\pi\) | |||||||
\(294\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.494522 | + | 0.970554i | 0.494522 | + | 0.970554i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.251377 | − | 0.773659i | 0.251377 | − | 0.773659i | ||||
\(305\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(306\) | 0.235003 | − | 0.461219i | 0.235003 | − | 0.461219i | ||||
\(307\) | 0 | 0 | 0.358368 | − | 0.933580i | \(-0.383333\pi\) | ||||
−0.358368 | + | 0.933580i | \(0.616667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.05558 | + | 1.30354i | −1.05558 | + | 1.30354i | ||||
\(311\) | 0 | 0 | −0.544639 | − | 0.838671i | \(-0.683333\pi\) | ||||
0.544639 | + | 0.838671i | \(0.316667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.196895 | − | 1.24314i | 0.196895 | − | 1.24314i | ||||
\(317\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(318\) | 1.67504 | − | 1.08779i | 1.67504 | − | 1.08779i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(321\) | −0.207912 | − | 1.97815i | −0.207912 | − | 1.97815i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.420508 | − | 0.0220379i | −0.420508 | − | 0.0220379i | ||||
\(324\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.0850311 | − | 0.190983i | −0.0850311 | − | 0.190983i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.889993 | + | 1.09905i | 0.889993 | + | 1.09905i | 0.994522 | + | 0.104528i | \(0.0333333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(332\) | 0.395472 | − | 0.128496i | 0.395472 | − | 0.128496i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.45381 | − | 1.30902i | −1.45381 | − | 1.30902i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(338\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(339\) | −1.41355 | − | 0.459289i | −1.41355 | − | 0.459289i | ||||
\(340\) | −0.133975 | + | 0.500000i | −0.133975 | + | 0.500000i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.478148 | − | 0.658114i | 0.478148 | − | 0.658114i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.80354 | + | 0.483257i | −1.80354 | + | 0.483257i | ||||
\(346\) | 0.309017 | − | 0.0489435i | 0.309017 | − | 0.0489435i | ||||
\(347\) | −1.89169 | − | 0.198825i | −1.89169 | − | 0.198825i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.97267 | − | 0.103383i | 1.97267 | − | 0.103383i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.360114 | + | 0.207912i | 0.360114 | + | 0.207912i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.629320 | − | 0.777146i | \(-0.283333\pi\) | ||||
−0.629320 | + | 0.777146i | \(0.716667\pi\) | |||||||
\(360\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(361\) | 0.330869 | + | 0.0703285i | 0.330869 | + | 0.0703285i | ||||
\(362\) | 0.506809 | + | 1.32028i | 0.506809 | + | 1.32028i | ||||
\(363\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | −1.45106 | − | 1.17504i | −1.45106 | − | 1.17504i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.56593 | − | 0.601105i | −1.56593 | − | 0.601105i | ||||
\(373\) | 0 | 0 | 0.629320 | − | 0.777146i | \(-0.283333\pi\) | ||||
−0.629320 | + | 0.777146i | \(0.716667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(376\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.535233 | + | 0.309017i | 0.535233 | + | 0.309017i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(380\) | −0.330869 | + | 0.743145i | −0.330869 | + | 0.743145i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.99452 | − | 0.104528i | 1.99452 | − | 0.104528i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
1.00000 | \(0\) | |||||||||
\(384\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.393116 | + | 0.882954i | −0.393116 | + | 0.882954i | ||||
\(392\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(395\) | −0.325760 | + | 1.21575i | −0.325760 | + | 1.21575i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.933580 | − | 0.358368i | \(-0.116667\pi\) | ||||
−0.933580 | + | 0.358368i | \(0.883333\pi\) | |||||||
\(398\) | −1.22256 | + | 1.35779i | −1.22256 | + | 1.35779i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(401\) | 0 | 0 | −0.629320 | − | 0.777146i | \(-0.716667\pi\) | ||||
0.629320 | + | 0.777146i | \(0.283333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.516929 | + | 0.0270911i | −0.516929 | + | 0.0270911i | ||||
\(409\) | −0.104528 | − | 0.00547810i | −0.104528 | − | 0.00547810i | − | 1.00000i | \(-0.5\pi\) | |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.139886 | + | 1.33093i | 0.139886 | + | 1.33093i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.01693 | − | 1.56593i | −1.01693 | − | 1.56593i | ||||
\(415\) | −0.406737 | + | 0.0864545i | −0.406737 | + | 0.0864545i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.30354 | + | 0.846528i | 1.30354 | + | 0.846528i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.685505 | − | 1.05558i | −0.685505 | − | 1.05558i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(422\) | 0.0813454 | + | 0.0658722i | 0.0813454 | + | 0.0658722i | ||||
\(423\) | 0.743145 | + | 0.669131i | 0.743145 | + | 0.669131i | ||||
\(424\) | −1.77957 | − | 0.906737i | −1.77957 | − | 0.906737i | ||||
\(425\) | 0.185505 | − | 0.483257i | 0.185505 | − | 0.483257i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.60917 | + | 1.16913i | −1.60917 | + | 1.16913i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(433\) | 0 | 0 | 0.838671 | − | 0.544639i | \(-0.183333\pi\) | ||||
−0.838671 | + | 0.544639i | \(0.816667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.122881 | + | 0.169131i | −0.122881 | + | 0.169131i | ||||
\(437\) | −0.827244 | + | 1.27384i | −0.827244 | + | 1.27384i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.360114 | − | 1.69420i | −0.360114 | − | 1.69420i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.614648 | − | 0.0646021i | 0.614648 | − | 0.0646021i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(450\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.309017 | + | 1.45381i | 0.309017 | + | 1.45381i | ||||
\(453\) | 0.846528 | − | 0.685505i | 0.846528 | − | 0.685505i | ||||
\(454\) | 0.506809 | + | 0.506809i | 0.506809 | + | 0.506809i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.809017 | − | 0.0850311i | −0.809017 | − | 0.0850311i | ||||
\(457\) | 0 | 0 | −0.358368 | − | 0.933580i | \(-0.616667\pi\) | ||||
0.358368 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(458\) | 0.198825 | − | 1.89169i | 0.198825 | − | 1.89169i | ||||
\(459\) | −0.500000 | − | 0.133975i | −0.500000 | − | 0.133975i | ||||
\(460\) | 1.32028 | + | 1.32028i | 1.32028 | + | 1.32028i | ||||
\(461\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.49452 | + | 0.761497i | 1.49452 | + | 0.761497i | ||||
\(466\) | −1.92920 | − | 0.101105i | −1.92920 | − | 0.101105i | ||||
\(467\) | 0.235003 | + | 0.877042i | 0.235003 | + | 0.877042i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.25692 | + | 0.0658722i | −1.25692 | + | 0.0658722i | ||||
\(475\) | 0.406737 | − | 0.704489i | 0.406737 | − | 0.704489i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.41228 | − | 1.41228i | −1.41228 | − | 1.41228i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(480\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.60917 | − | 0.169131i | 1.60917 | − | 0.169131i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.743145 | − | 0.669131i | 0.743145 | − | 0.669131i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.743145 | − | 0.669131i | 0.743145 | − | 0.669131i | ||||
\(491\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.262394 | + | 1.65669i | 0.262394 | + | 1.65669i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.207912 | − | 0.360114i | −0.207912 | − | 0.360114i | ||||
\(499\) | −0.221232 | − | 0.221232i | −0.221232 | − | 0.221232i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(500\) | −0.743145 | − | 0.669131i | −0.743145 | − | 0.669131i | ||||
\(501\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.994522 | + | 0.895472i | −0.994522 | + | 0.895472i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(510\) | 0.516929 | + | 0.0270911i | 0.516929 | + | 0.0270911i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(513\) | −0.743145 | − | 0.330869i | −0.743145 | − | 0.330869i | ||||
\(514\) | −0.413545 | − | 1.94558i | −0.413545 | − | 1.94558i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.112122 | − | 0.292088i | −0.112122 | − | 0.292088i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.777146 | − | 0.629320i | \(-0.216667\pi\) | ||||
−0.777146 | + | 0.629320i | \(0.783333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.01807 | + | 1.40126i | 1.01807 | + | 1.40126i | ||||
\(527\) | 0.793191 | − | 0.353151i | 0.793191 | − | 0.353151i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.46140 | + | 2.01145i | 1.46140 | + | 2.01145i | ||||
\(530\) | 1.67504 | + | 1.08779i | 1.67504 | + | 1.08779i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.72256 | − | 0.994522i | 1.72256 | − | 0.994522i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(541\) | 0.638616 | − | 0.325391i | 0.638616 | − | 0.325391i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(542\) | 0.795697 | + | 1.78716i | 0.795697 | + | 1.78716i | ||||
\(543\) | 1.18606 | − | 0.770236i | 1.18606 | − | 0.770236i | ||||
\(544\) | 0.281926 | + | 0.434128i | 0.281926 | + | 0.434128i | ||||
\(545\) | 0.139886 | − | 0.155360i | 0.139886 | − | 0.155360i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.933580 | − | 0.358368i | \(-0.883333\pi\) | ||||
0.933580 | + | 0.358368i | \(0.116667\pi\) | |||||||
\(548\) | 1.08268 | − | 0.786610i | 1.08268 | − | 0.786610i | ||||
\(549\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.847673 | + | 1.66365i | −0.847673 | + | 1.66365i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0813454 | − | 1.55216i | 0.0813454 | − | 1.55216i | ||||
\(557\) | −0.809017 | − | 1.58779i | −0.809017 | − | 1.58779i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(558\) | −0.262394 | + | 1.65669i | −0.262394 | + | 1.65669i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.743145 | + | 1.28716i | 0.743145 | + | 1.28716i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(564\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(565\) | −0.155360 | − | 1.47815i | −0.155360 | − | 1.47815i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(570\) | 0.795697 | + | 0.169131i | 0.795697 | + | 0.169131i | ||||
\(571\) | 0.478148 | + | 1.07394i | 0.478148 | + | 1.07394i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.17504 | − | 1.45106i | −1.17504 | − | 1.45106i | ||||
\(576\) | −1.00000 | −1.00000 | ||||||||
\(577\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(578\) | −0.489838 | + | 0.544020i | −0.489838 | + | 0.544020i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.53884 | + | 1.11803i | 1.53884 | + | 1.11803i | ||||
\(587\) | 0.642040 | − | 1.26007i | 0.642040 | − | 1.26007i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(588\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(589\) | 1.31798 | − | 0.353151i | 1.31798 | − | 0.353151i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.614648 | + | 0.0646021i | 0.614648 | + | 0.0646021i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.08779 | − | 0.0570084i | 1.08779 | − | 0.0570084i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.58231 | + | 0.913545i | 1.58231 | + | 0.913545i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(600\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | ||||
\(601\) | 1.86055 | − | 0.604528i | 1.86055 | − | 0.604528i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.01693 | − | 0.390362i | −1.01693 | − | 0.390362i | ||||
\(605\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(608\) | 0.330869 | + | 0.743145i | 0.330869 | + | 0.743145i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.207912 | + | 0.978148i | −0.207912 | + | 0.978148i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.133975 | + | 0.500000i | 0.133975 | + | 0.500000i | ||||
\(613\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.12146 | − | 1.38488i | 1.12146 | − | 1.38488i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.198825 | − | 0.0646021i | 0.198825 | − | 0.0646021i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(620\) | −0.0877853 | − | 1.67504i | −0.0877853 | − | 1.67504i | ||||
\(621\) | −1.32028 | + | 1.32028i | −1.32028 | + | 1.32028i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.90807 | − | 0.511265i | 1.90807 | − | 0.511265i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(632\) | 0.685505 | + | 1.05558i | 0.685505 | + | 1.05558i | ||||
\(633\) | 0.0475201 | − | 0.0932634i | 0.0475201 | − | 0.0932634i | ||||
\(634\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.516929 | + | 1.92920i | −0.516929 | + | 1.92920i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(641\) | 0 | 0 | 0.933580 | − | 0.358368i | \(-0.116667\pi\) | ||||
−0.933580 | + | 0.358368i | \(0.883333\pi\) | |||||||
\(642\) | 1.47815 | + | 1.33093i | 1.47815 | + | 1.33093i | ||||
\(643\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.327244 | − | 0.264997i | 0.327244 | − | 0.264997i | ||||
\(647\) | 1.07587 | + | 0.170401i | 1.07587 | + | 0.170401i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(648\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.86460 | + | 0.0977196i | 1.86460 | + | 0.0977196i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(654\) | 0.190983 | + | 0.0850311i | 0.190983 | + | 0.0850311i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0877853 | − | 0.0570084i | −0.0877853 | − | 0.0570084i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(662\) | −1.39680 | − | 0.221232i | −1.39680 | − | 0.221232i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.207912 | + | 0.360114i | −0.207912 | + | 0.360114i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.95630 | 1.95630 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.933580 | − | 0.358368i | \(-0.883333\pi\) | ||||
0.933580 | + | 0.358368i | \(0.116667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(676\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(677\) | −1.30354 | + | 0.846528i | −1.30354 | + | 0.846528i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(678\) | 1.35779 | − | 0.604528i | 1.35779 | − | 0.604528i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.235003 | − | 0.461219i | −0.235003 | − | 0.461219i | ||||
\(681\) | 0.390362 | − | 0.601105i | 0.390362 | − | 0.601105i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.0434654 | + | 0.204489i | 0.0434654 | + | 0.204489i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(684\) | 0.0850311 | + | 0.809017i | 0.0850311 | + | 0.809017i | ||||
\(685\) | −1.15897 | + | 0.669131i | −1.15897 | + | 0.669131i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.89169 | + | 0.198825i | −1.89169 | + | 0.198825i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.01693 | − | 1.56593i | 1.01693 | − | 1.56593i | ||||
\(691\) | −1.01807 | − | 1.40126i | −1.01807 | − | 1.40126i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(692\) | −0.196895 | + | 0.243145i | −0.196895 | + | 0.243145i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.53884 | − | 1.11803i | 1.53884 | − | 1.11803i | ||||
\(695\) | −0.243145 | + | 1.53516i | −0.243145 | + | 1.53516i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.39680 | + | 1.39680i | −1.39680 | + | 1.39680i | ||||
\(699\) | 0.302208 | + | 1.90807i | 0.302208 | + | 1.90807i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.358368 | − | 0.933580i | \(-0.616667\pi\) | ||||
0.358368 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(706\) | −0.406737 | + | 0.0864545i | −0.406737 | + | 0.0864545i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.38488 | + | 0.705634i | 1.38488 | + | 0.705634i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.325760 | + | 1.21575i | 0.325760 | + | 1.21575i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.327369 | − | 3.11471i | 0.327369 | − | 3.11471i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.292943 | + | 0.169131i | −0.292943 | + | 0.169131i | ||||
\(723\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(724\) | −1.26007 | − | 0.642040i | −1.26007 | − | 0.642040i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(727\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(736\) | 1.86460 | − | 0.0977196i | 1.86460 | − | 0.0977196i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.53516 | + | 1.24314i | 1.53516 | + | 1.24314i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.889993 | − | 0.889993i | −0.889993 | − | 0.889993i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(744\) | 1.56593 | − | 0.601105i | 1.56593 | − | 0.601105i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.309017 | + | 0.278240i | −0.309017 | + | 0.278240i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(751\) | −0.155360 | + | 1.47815i | −0.155360 | + | 1.47815i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(752\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.970554 | + | 0.494522i | 0.970554 | + | 0.494522i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(758\) | −0.604528 | + | 0.128496i | −0.604528 | + | 0.128496i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.251377 | − | 0.773659i | −0.251377 | − | 0.773659i | ||||
\(761\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0809764 | − | 0.511265i | −0.0809764 | − | 0.511265i | ||||
\(766\) | −1.41228 | + | 1.41228i | −1.41228 | + | 1.41228i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(769\) | 0.196895 | − | 1.24314i | 0.196895 | − | 1.24314i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.81708 | + | 0.809017i | −1.81708 | + | 0.809017i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.122881 | + | 0.169131i | 0.122881 | + | 0.169131i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0877853 | + | 1.67504i | −0.0877853 | + | 1.67504i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.298669 | − | 0.919209i | −0.298669 | − | 0.919209i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 1.00000i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.838671 | − | 0.544639i | \(-0.183333\pi\) | ||||
−0.838671 | + | 0.544639i | \(0.816667\pi\) | |||||||
\(788\) | −0.251377 | − | 0.564602i | −0.251377 | − | 0.564602i | ||||
\(789\) | 1.15897 | − | 1.28716i | 1.15897 | − | 1.28716i | ||||
\(790\) | −0.571411 | − | 1.12146i | −0.571411 | − | 1.12146i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.715754 | − | 1.86460i | 0.715754 | − | 1.86460i | ||||
\(796\) | − | 1.82709i | − | 1.82709i | ||||||
\(797\) | −0.309017 | − | 0.278240i | −0.309017 | − | 0.278240i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.281926 | + | 0.434128i | 0.281926 | + | 0.434128i | ||||
\(800\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(810\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(811\) | −0.715754 | − | 0.0375111i | −0.715754 | − | 0.0375111i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.58268 | − | 1.14988i | 1.58268 | − | 1.14988i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.366025 | − | 0.366025i | 0.366025 | − | 0.366025i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.0813454 | − | 0.0658722i | 0.0813454 | − | 0.0658722i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(822\) | −0.994522 | − | 0.895472i | −0.994522 | − | 0.895472i | ||||
\(823\) | 0 | 0 | 0.933580 | − | 0.358368i | \(-0.116667\pi\) | ||||
−0.933580 | + | 0.358368i | \(0.883333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.27276 | − | 0.413545i | −1.27276 | − | 0.413545i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(828\) | 1.80354 | + | 0.483257i | 1.80354 | + | 0.483257i | ||||
\(829\) | −0.809017 | + | 1.81708i | −0.809017 | + | 1.81708i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0.244415 | − | 0.336408i | 0.244415 | − | 0.336408i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.500000 | + | 0.133975i | −0.500000 | + | 0.133975i | ||||
\(834\) | −1.53516 | + | 0.243145i | −1.53516 | + | 0.243145i | ||||
\(835\) | −1.94558 | − | 0.204489i | −1.94558 | − | 0.204489i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.67504 | − | 0.0877853i | 1.67504 | − | 0.0877853i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(842\) | 1.21575 | + | 0.325760i | 1.21575 | + | 0.325760i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.104528 | + | 0.00547810i | −0.104528 | + | 0.00547810i | ||||
\(845\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(846\) | −1.00000 | −1.00000 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.92920 | − | 0.516929i | 1.92920 | − | 0.516929i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.185505 | + | 0.483257i | 0.185505 | + | 0.483257i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.813473i | − | 0.813473i | ||||||
\(856\) | 0.413545 | − | 1.94558i | 0.413545 | − | 1.94558i | ||||
\(857\) | 1.07394 | − | 1.47815i | 1.07394 | − | 1.47815i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.406737 | − | 0.0864545i | −0.406737 | − | 0.0864545i | − | 1.00000i | \(-0.5\pi\) | |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(864\) | 0.207912 | + | 0.978148i | 0.207912 | + | 0.978148i | ||||
\(865\) | 0.221232 | − | 0.221232i | 0.221232 | − | 0.221232i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.633975 | + | 0.366025i | 0.633975 | + | 0.366025i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.0218524 | − | 0.207912i | −0.0218524 | − | 0.207912i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.237606 | − | 1.50019i | −0.237606 | − | 1.50019i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(878\) | 1.40126 | + | 1.01807i | 1.40126 | + | 1.01807i | ||||
\(879\) | 0.773659 | − | 1.73767i | 0.773659 | − | 1.73767i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(882\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(883\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.413545 | + | 0.459289i | −0.413545 | + | 0.459289i | ||||
\(887\) | 0.896802 | − | 0.142040i | 0.896802 | − | 0.142040i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.330869 | + | 0.743145i | 0.330869 | + | 0.743145i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(901\) | −0.516929 | − | 0.895347i | −0.516929 | − | 0.895347i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.20243 | − | 0.873619i | −1.20243 | − | 0.873619i | ||||
\(905\) | 1.18606 | + | 0.770236i | 1.18606 | + | 0.770236i | ||||
\(906\) | −0.170401 | + | 1.07587i | −0.170401 | + | 1.07587i | ||||
\(907\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(908\) | −0.715754 | − | 0.0375111i | −0.715754 | − | 0.0375111i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(912\) | 0.658114 | − | 0.478148i | 0.658114 | − | 0.478148i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.00000 | 1.00000 | ||||||||
\(916\) | 1.11803 | + | 1.53884i | 1.11803 | + | 1.53884i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.461219 | − | 0.235003i | 0.461219 | − | 0.235003i | ||||
\(919\) | −0.895472 | + | 0.994522i | −0.895472 | + | 0.994522i | 0.104528 | + | 0.994522i | \(0.466667\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(920\) | −1.86460 | − | 0.0977196i | −1.86460 | − | 0.0977196i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | −1.62019 | + | 0.434128i | −1.62019 | + | 0.434128i | ||||
\(931\) | −0.809017 | + | 0.0850311i | −0.809017 | + | 0.0850311i | ||||
\(932\) | 1.50133 | − | 1.21575i | 1.50133 | − | 1.21575i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.761497 | − | 0.494522i | −0.761497 | − | 0.494522i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(941\) | 0 | 0 | 0.777146 | − | 0.629320i | \(-0.216667\pi\) | ||||
−0.777146 | + | 0.629320i | \(0.783333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.500000 | + | 0.133975i | 0.500000 | + | 0.133975i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0.889993 | − | 0.889993i | 0.889993 | − | 0.889993i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.169131 | + | 0.795697i | 0.169131 | + | 0.795697i | ||||
\(951\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.12146 | + | 0.571411i | 1.12146 | + | 0.571411i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(954\) | 1.99452 | + | 0.104528i | 1.99452 | + | 0.104528i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | ||||
\(961\) | −1.34767 | + | 1.21345i | −1.34767 | + | 1.21345i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.994522 | − | 1.72256i | 0.994522 | − | 1.72256i | ||||
\(964\) | −1.08268 | + | 1.20243i | −1.08268 | + | 1.20243i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(968\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(969\) | −0.327244 | − | 0.264997i | −0.327244 | − | 0.264997i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(972\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(977\) | 1.90211 | 1.90211 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(981\) | 0.0434654 | − | 0.204489i | 0.0434654 | − | 0.204489i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.53516 | − | 1.24314i | −1.53516 | − | 1.24314i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.669131 | − | 0.743145i | \(-0.733333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.994522 | + | 0.895472i | −0.994522 | + | 0.895472i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | −1.30354 | − | 1.05558i | −1.30354 | − | 1.05558i | ||||
\(993\) | 0.0740142 | + | 1.41228i | 0.0740142 | + | 1.41228i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.190983 | + | 1.81708i | −0.190983 | + | 1.81708i | ||||
\(996\) | 0.395472 | + | 0.128496i | 0.395472 | + | 0.128496i | ||||
\(997\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(998\) | 0.312440 | + | 0.0163743i | 0.312440 | + | 0.0163743i | ||||
\(999\) | 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 | 3660.1.fu.c.3239.1 | yes | 16 | |
3.2 | odd | 2 | 3660.1.fu.b.3239.1 | yes | 16 | ||
4.3 | odd | 2 | 3660.1.fu.d.3239.1 | yes | 16 | ||
5.4 | even | 2 | 3660.1.fu.b.3239.1 | yes | 16 | ||
12.11 | even | 2 | 3660.1.fu.a.3239.1 | yes | 16 | ||
15.14 | odd | 2 | CM | 3660.1.fu.c.3239.1 | yes | 16 | |
20.19 | odd | 2 | 3660.1.fu.a.3239.1 | yes | 16 | ||
60.59 | even | 2 | 3660.1.fu.d.3239.1 | yes | 16 | ||
61.51 | odd | 60 | 3660.1.fu.d.539.1 | yes | 16 | ||
183.173 | even | 60 | 3660.1.fu.a.539.1 | ✓ | 16 | ||
244.51 | even | 60 | inner | 3660.1.fu.c.539.1 | yes | 16 | |
305.234 | odd | 60 | 3660.1.fu.a.539.1 | ✓ | 16 | ||
732.539 | odd | 60 | 3660.1.fu.b.539.1 | yes | 16 | ||
915.539 | even | 60 | 3660.1.fu.d.539.1 | yes | 16 | ||
1220.539 | even | 60 | 3660.1.fu.b.539.1 | yes | 16 | ||
3660.539 | odd | 60 | inner | 3660.1.fu.c.539.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3660.1.fu.a.539.1 | ✓ | 16 | 183.173 | even | 60 | ||
3660.1.fu.a.539.1 | ✓ | 16 | 305.234 | odd | 60 | ||
3660.1.fu.a.3239.1 | yes | 16 | 12.11 | even | 2 | ||
3660.1.fu.a.3239.1 | yes | 16 | 20.19 | odd | 2 | ||
3660.1.fu.b.539.1 | yes | 16 | 732.539 | odd | 60 | ||
3660.1.fu.b.539.1 | yes | 16 | 1220.539 | even | 60 | ||
3660.1.fu.b.3239.1 | yes | 16 | 3.2 | odd | 2 | ||
3660.1.fu.b.3239.1 | yes | 16 | 5.4 | even | 2 | ||
3660.1.fu.c.539.1 | yes | 16 | 244.51 | even | 60 | inner | |
3660.1.fu.c.539.1 | yes | 16 | 3660.539 | odd | 60 | inner | |
3660.1.fu.c.3239.1 | yes | 16 | 1.1 | even | 1 | trivial | |
3660.1.fu.c.3239.1 | yes | 16 | 15.14 | odd | 2 | CM | |
3660.1.fu.d.539.1 | yes | 16 | 61.51 | odd | 60 | ||
3660.1.fu.d.539.1 | yes | 16 | 915.539 | even | 60 | ||
3660.1.fu.d.3239.1 | yes | 16 | 4.3 | odd | 2 | ||
3660.1.fu.d.3239.1 | yes | 16 | 60.59 | even | 2 |