Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3225,1,Mod(221,3225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3225, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([15, 18, 20]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3225.221");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3225 = 3 \cdot 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3225.cc (of order \(30\), 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: | \(1.60948466574\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{30})\) |
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: | \(A_{5}\) |
Projective field: | Galois closure of 5.1.6500390625.1 |
Embedding invariants
Embedding label | 2156.2 | ||
Root | \(-0.406737 + 0.913545i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3225.2156 |
Dual form | 3225.1.cc.a.896.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3225\mathbb{Z}\right)^\times\).
\(n\) | \(1076\) | \(2452\) | \(2626\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(3\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.406737 | + | 0.913545i | 0.406737 | + | 0.913545i | ||||
\(6\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(9\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(10\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(11\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58268 | + | 0.336408i | −1.58268 | + | 0.336408i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(14\) | 0.743145 | + | 0.669131i | 0.743145 | + | 0.669131i | ||||
\(15\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(16\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(17\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(19\) | 0 | 0 | −0.406737 | − | 0.913545i | \(-0.633333\pi\) | ||||
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(22\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(23\) | 0.336408 | − | 1.58268i | 0.336408 | − | 1.58268i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.743145 | − | 0.669131i | \(-0.233333\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(25\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(26\) | −1.40126 | + | 0.809017i | −1.40126 | + | 0.809017i | ||||
\(27\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.251377 | + | 0.564602i | −0.251377 | + | 0.564602i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(30\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(31\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.406737 | + | 0.913545i | 0.406737 | + | 0.913545i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.08268 | + | 1.20243i | 1.08268 | + | 1.20243i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(40\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(41\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(42\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(43\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(46\) | −0.169131 | − | 1.60917i | −0.169131 | − | 1.60917i | ||||
\(47\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(48\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.406737 | + | 0.913545i | −0.406737 | + | 0.913545i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(54\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(55\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(56\) | −0.994522 | − | 0.104528i | −0.994522 | − | 0.104528i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0646021 | + | 0.614648i | −0.0646021 | + | 0.614648i | ||||
\(59\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(62\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(63\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(64\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(65\) | −0.951057 | − | 1.30902i | −0.951057 | − | 1.30902i | ||||
\(66\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(67\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.60917 | − | 0.169131i | −1.60917 | − | 0.169131i | ||||
\(70\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(71\) | 0.251377 | − | 0.564602i | 0.251377 | − | 0.564602i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(72\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | ||||
\(73\) | 0.413545 | − | 0.459289i | 0.413545 | − | 0.459289i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(74\) | 1.40126 | + | 0.809017i | 1.40126 | + | 0.809017i | ||||
\(75\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.743145 | − | 0.669131i | −0.743145 | − | 0.669131i | ||||
\(78\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | ||||
\(79\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(80\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(81\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(82\) | 1.00000 | 1.00000 | ||||||||
\(83\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.207912 | + | 0.978148i | −0.207912 | + | 0.978148i | ||||
\(87\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(88\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(89\) | −0.207912 | + | 0.978148i | −0.207912 | + | 0.978148i | 0.743145 | + | 0.669131i | \(0.233333\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(90\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(91\) | −1.08268 | − | 1.20243i | −1.08268 | − | 1.20243i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.535233 | − | 0.309017i | 0.535233 | − | 0.309017i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(104\) | 0.658114 | − | 1.47815i | 0.658114 | − | 1.47815i | ||||
\(105\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.08268 | + | 1.20243i | 1.08268 | + | 1.20243i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(110\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(111\) | 1.08268 | − | 1.20243i | 1.08268 | − | 1.20243i | ||||
\(112\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(113\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.58268 | − | 0.336408i | 1.58268 | − | 0.336408i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.47815 | − | 0.658114i | 1.47815 | − | 0.658114i | ||||
\(118\) | 1.00000 | 1.00000 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(126\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(127\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(128\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(129\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(130\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(131\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(135\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(138\) | −1.58268 | + | 0.336408i | −1.58268 | + | 0.336408i | ||||
\(139\) | 1.58268 | + | 0.336408i | 1.58268 | + | 0.336408i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.0646021 | − | 0.614648i | 0.0646021 | − | 0.614648i | ||||
\(143\) | 1.40126 | − | 0.809017i | 1.40126 | − | 0.809017i | ||||
\(144\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(145\) | −0.618034 | −0.618034 | ||||||||
\(146\) | 0.251377 | − | 0.564602i | 0.251377 | − | 0.564602i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.40126 | − | 0.809017i | −1.40126 | − | 0.809017i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(150\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(155\) | −0.743145 | − | 0.669131i | −0.743145 | − | 0.669131i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.309017 | + | 0.535233i | 0.309017 | + | 0.535233i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | ||||
\(162\) | 0.743145 | − | 0.669131i | 0.743145 | − | 0.669131i | ||||
\(163\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(168\) | 1.00000i | 1.00000i | ||||||||
\(169\) | 1.47815 | − | 0.658114i | 1.47815 | − | 0.658114i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(174\) | 0.618034 | 0.618034 | ||||||||
\(175\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(176\) | − | 1.00000i | − | 1.00000i | ||||||
\(177\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(178\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(179\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.994522 | − | 0.104528i | \(-0.966667\pi\) | ||||
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(182\) | −1.40126 | − | 0.809017i | −1.40126 | − | 0.809017i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.08268 | + | 1.20243i | 1.08268 | + | 1.20243i | ||||
\(185\) | −0.658114 | + | 1.47815i | −0.658114 | + | 1.47815i | ||||
\(186\) | 0.743145 | + | 0.669131i | 0.743145 | + | 0.669131i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.20243 | + | 1.08268i | −1.20243 | + | 1.08268i | −0.207912 | + | 0.978148i | \(0.566667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(192\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(195\) | −1.20243 | + | 1.08268i | −1.20243 | + | 1.08268i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(198\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(199\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | −0.207912 | − | 0.978148i | −0.207912 | − | 0.978148i | ||||
\(201\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(202\) | 0.413545 | − | 0.459289i | 0.413545 | − | 0.459289i | ||||
\(203\) | −0.614648 | + | 0.0646021i | −0.614648 | + | 0.0646021i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(206\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(207\) | 1.61803i | 1.61803i | ||||||||
\(208\) | 0.169131 | − | 1.60917i | 0.169131 | − | 1.60917i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | ||||
\(211\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(214\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(215\) | −0.994522 | − | 0.104528i | −0.994522 | − | 0.104528i | ||||
\(216\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(217\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(218\) | 1.40126 | + | 0.809017i | 1.40126 | + | 0.809017i | ||||
\(219\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.658114 | − | 1.47815i | 0.658114 | − | 1.47815i | ||||
\(223\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(230\) | 1.40126 | − | 0.809017i | 1.40126 | − | 0.809017i | ||||
\(231\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(232\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | ||||
\(233\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(234\) | 1.20243 | − | 1.08268i | 1.20243 | − | 1.08268i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.336408 | + | 1.58268i | −0.336408 | + | 1.58268i | 0.406737 | + | 0.913545i | \(0.366667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(240\) | 0.207912 | + | 0.978148i | 0.207912 | + | 0.978148i | ||||
\(241\) | −1.58268 | + | 0.336408i | −1.58268 | + | 0.336408i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −1.00000 | ||||||||
\(251\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.169131 | + | 1.60917i | 0.169131 | + | 1.60917i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(259\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.128496 | − | 0.604528i | 0.128496 | − | 0.604528i | ||||
\(262\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(263\) | 0.743145 | − | 0.669131i | 0.743145 | − | 0.669131i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(264\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(271\) | 0.564602 | + | 0.251377i | 0.564602 | + | 0.251377i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.08268 | + | 1.20243i | −1.08268 | + | 1.20243i | ||||
\(274\) | 1.61803 | 1.61803 | ||||||||
\(275\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.58268 | − | 0.336408i | −1.58268 | − | 0.336408i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(278\) | 1.60917 | − | 0.169131i | 1.60917 | − | 0.169131i | ||||
\(279\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(280\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(281\) | 0.251377 | + | 0.564602i | 0.251377 | + | 0.564602i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0646021 | − | 0.614648i | 0.0646021 | − | 0.614648i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.08268 | − | 1.20243i | 1.08268 | − | 1.20243i | ||||
\(287\) | 0.207912 | + | 0.978148i | 0.207912 | + | 0.978148i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(290\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(291\) | 0.413545 | + | 0.459289i | 0.413545 | + | 0.459289i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.618034i | 0.618034i | 0.951057 | + | 0.309017i | \(0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(296\) | −1.60917 | + | 0.169131i | −1.60917 | + | 0.169131i | ||||
\(297\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(298\) | −1.58268 | − | 0.336408i | −1.58268 | − | 0.336408i | ||||
\(299\) | 2.61803i | 2.61803i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | −1.00000 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.309017 | − | 0.535233i | 0.309017 | − | 0.535233i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(310\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(311\) | −0.336408 | + | 1.58268i | −0.336408 | + | 1.58268i | 0.406737 | + | 0.913545i | \(0.366667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(312\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(313\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(314\) | 0.459289 | + | 0.413545i | 0.459289 | + | 0.413545i | ||||
\(315\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0646021 | − | 0.614648i | 0.0646021 | − | 0.614648i | ||||
\(320\) | 0.743145 | − | 0.669131i | 0.743145 | − | 0.669131i | ||||
\(321\) | −1.60917 | + | 0.169131i | −1.60917 | + | 0.169131i | ||||
\(322\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.08268 | − | 1.20243i | 1.08268 | − | 1.20243i | ||||
\(328\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.406737 | + | 0.913545i | −0.406737 | + | 0.913545i | ||||
\(331\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(334\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(335\) | −0.743145 | − | 0.669131i | −0.743145 | − | 0.669131i | ||||
\(336\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(337\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(338\) | 1.20243 | − | 1.08268i | 1.20243 | − | 1.08268i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.743145 | − | 0.669131i | 0.743145 | − | 0.669131i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 1.00000 | ||||||||
\(344\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | ||||
\(345\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(346\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(347\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.809017 | + | 1.40126i | −0.809017 | + | 1.40126i | 0.104528 | + | 0.994522i | \(0.466667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(350\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(351\) | −0.809017 | − | 1.40126i | −0.809017 | − | 1.40126i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(354\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(355\) | 0.618034 | 0.618034 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(359\) | 0.336408 | + | 1.58268i | 0.336408 | + | 1.58268i | 0.743145 | + | 0.669131i | \(0.233333\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(360\) | 1.00000 | 1.00000 | ||||||||
\(361\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.564602 | − | 0.251377i | 0.564602 | − | 0.251377i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(368\) | 1.40126 | + | 0.809017i | 1.40126 | + | 0.809017i | ||||
\(369\) | −0.994522 | − | 0.104528i | −0.994522 | − | 0.104528i | ||||
\(370\) | −0.169131 | + | 1.60917i | −0.169131 | + | 1.60917i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.413545 | − | 0.459289i | 0.413545 | − | 0.459289i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.207912 | + | 0.978148i | −0.207912 | + | 0.978148i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(378\) | −0.406737 | + | 0.913545i | −0.406737 | + | 0.913545i | ||||
\(379\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.809017 | + | 1.40126i | −0.809017 | + | 1.40126i | ||||
\(383\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(384\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(385\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(390\) | −0.809017 | + | 1.40126i | −0.809017 | + | 1.40126i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.169131 | + | 1.60917i | 0.169131 | + | 1.60917i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(398\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(401\) | 1.40126 | − | 0.809017i | 1.40126 | − | 0.809017i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(402\) | 0.743145 | + | 0.669131i | 0.743145 | + | 0.669131i | ||||
\(403\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.743145 | + | 0.669131i | 0.743145 | + | 0.669131i | ||||
\(406\) | −0.564602 | + | 0.251377i | −0.564602 | + | 0.251377i | ||||
\(407\) | −1.40126 | − | 0.809017i | −1.40126 | − | 0.809017i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(410\) | 0.406737 | + | 0.913545i | 0.406737 | + | 0.913545i | ||||
\(411\) | 0.336408 | − | 1.58268i | 0.336408 | − | 1.58268i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.207912 | + | 0.978148i | 0.207912 | + | 0.978148i | ||||
\(414\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.169131 | − | 1.60917i | 0.169131 | − | 1.60917i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.564602 | + | 0.251377i | 0.564602 | + | 0.251377i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(422\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.618034 | −0.618034 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.951057 | − | 1.30902i | −0.951057 | − | 1.30902i | ||||
\(430\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(431\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(432\) | −1.00000 | −1.00000 | ||||||||
\(433\) | 0.564602 | − | 0.251377i | 0.564602 | − | 0.251377i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(434\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(435\) | 0.0646021 | + | 0.614648i | 0.0646021 | + | 0.614648i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(439\) | −0.413545 | + | 0.459289i | −0.413545 | + | 0.459289i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0.994522 | − | 0.104528i | 0.994522 | − | 0.104528i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(446\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(447\) | −0.658114 | + | 1.47815i | −0.658114 | + | 1.47815i | ||||
\(448\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(449\) | 0.535233 | + | 0.309017i | 0.535233 | + | 0.309017i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(450\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(451\) | −1.00000 | −1.00000 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(455\) | 0.658114 | − | 1.47815i | 0.658114 | − | 1.47815i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(462\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(463\) | −0.413545 | − | 0.459289i | −0.413545 | − | 0.459289i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(464\) | −0.459289 | − | 0.413545i | −0.459289 | − | 0.413545i | ||||
\(465\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(466\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(467\) | 0.406737 | + | 0.913545i | 0.406737 | + | 0.913545i | 0.994522 | + | 0.104528i | \(0.0333333\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(472\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(473\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.169131 | + | 1.60917i | 0.169131 | + | 1.60917i | ||||
\(479\) | 1.60917 | − | 0.169131i | 1.60917 | − | 0.169131i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.11803 | − | 1.53884i | −2.11803 | − | 1.53884i | ||||
\(482\) | −1.40126 | + | 0.809017i | −1.40126 | + | 0.809017i | ||||
\(483\) | −0.658114 | − | 1.47815i | −0.658114 | − | 1.47815i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.535233 | − | 0.309017i | −0.535233 | − | 0.309017i | ||||
\(486\) | −0.743145 | − | 0.669131i | −0.743145 | − | 0.669131i | ||||
\(487\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.128496 | − | 0.604528i | −0.128496 | − | 0.604528i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(496\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(497\) | 0.614648 | − | 0.0646021i | 0.614648 | − | 0.0646021i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(502\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(503\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(504\) | 0.994522 | − | 0.104528i | 0.994522 | − | 0.104528i | ||||
\(505\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(506\) | 0.658114 | + | 1.47815i | 0.658114 | + | 1.47815i | ||||
\(507\) | −0.809017 | − | 1.40126i | −0.809017 | − | 1.40126i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.415823 | + | 1.95630i | 0.415823 | + | 1.95630i | 0.207912 | + | 0.978148i | \(0.433333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.604528 | + | 0.128496i | 0.604528 | + | 0.128496i | ||||
\(512\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.00000i | 1.00000i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.61803i | 1.61803i | ||||||||
\(519\) | 0.406737 | + | 0.913545i | 0.406737 | + | 0.913545i | ||||
\(520\) | 1.61803 | 1.61803 | ||||||||
\(521\) | 0.614648 | − | 0.0646021i | 0.614648 | − | 0.0646021i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(522\) | −0.0646021 | − | 0.614648i | −0.0646021 | − | 0.614648i | ||||
\(523\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(526\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(529\) | −1.47815 | − | 0.658114i | −1.47815 | − | 0.658114i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.994522 | − | 0.104528i | −0.994522 | − | 0.104528i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.60917 | − | 0.169131i | −1.60917 | − | 0.169131i | ||||
\(534\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(535\) | 1.47815 | − | 0.658114i | 1.47815 | − | 0.658114i | ||||
\(536\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | ||||
\(537\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(538\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(542\) | 0.614648 | + | 0.0646021i | 0.614648 | + | 0.0646021i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.658114 | + | 1.47815i | −0.658114 | + | 1.47815i | ||||
\(546\) | −0.658114 | + | 1.47815i | −0.658114 | + | 1.47815i | ||||
\(547\) | −0.0646021 | − | 0.614648i | −0.0646021 | − | 0.614648i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.08268 | − | 1.20243i | 1.08268 | − | 1.20243i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.60917 | + | 0.169131i | −1.60917 | + | 0.169131i | ||||
\(555\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(558\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(559\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | ||||
\(560\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.413545 | + | 0.459289i | 0.413545 | + | 0.459289i | ||||
\(563\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.128496 | − | 0.604528i | −0.128496 | − | 0.604528i | ||||
\(567\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(568\) | 0.309017 | + | 0.535233i | 0.309017 | + | 0.535233i | ||||
\(569\) | −0.406737 | − | 0.913545i | −0.406737 | − | 0.913545i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.20243 | + | 1.08268i | 1.20243 | + | 1.08268i | ||||
\(574\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(575\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(577\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(578\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.535233 | + | 0.309017i | 0.535233 | + | 0.309017i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.128496 | + | 0.604528i | 0.128496 | + | 0.604528i | ||||
\(585\) | 1.20243 | + | 1.08268i | 1.20243 | + | 1.08268i | ||||
\(586\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(587\) | −0.128496 | − | 0.604528i | −0.128496 | − | 0.604528i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0.406737 | + | 0.913545i | 0.406737 | + | 0.913545i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.47815 | + | 0.658114i | −1.47815 | + | 0.658114i | ||||
\(593\) | −0.535233 | + | 0.309017i | −0.535233 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(594\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(598\) | 0.809017 | + | 2.48990i | 0.809017 | + | 2.48990i | ||||
\(599\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(601\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(602\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(603\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(607\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.128496 | + | 0.604528i | 0.128496 | + | 0.604528i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
1.00000 | \(0\) | |||||||||
\(614\) | 0.128496 | − | 0.604528i | 0.128496 | − | 0.604528i | ||||
\(615\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(616\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(617\) | −0.994522 | − | 0.104528i | −0.994522 | − | 0.104528i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(618\) | − | 1.00000i | − | 1.00000i | ||||||
\(619\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.60917 | − | 0.169131i | 1.60917 | − | 0.169131i | ||||
\(622\) | 0.169131 | + | 1.60917i | 0.169131 | + | 1.60917i | ||||
\(623\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(624\) | −1.61803 | −1.61803 | ||||||||
\(625\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(626\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(631\) | −0.0646021 | + | 0.614648i | −0.0646021 | + | 0.614648i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(634\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.128496 | − | 0.604528i | −0.128496 | − | 0.604528i | ||||
\(639\) | −0.128496 | + | 0.604528i | −0.128496 | + | 0.604528i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(641\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(642\) | −1.47815 | + | 0.658114i | −1.47815 | + | 0.658114i | ||||
\(643\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.00000i | 1.00000i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(648\) | −0.207912 | + | 0.978148i | −0.207912 | + | 0.978148i | ||||
\(649\) | −1.00000 | −1.00000 | ||||||||
\(650\) | 0.336408 | − | 1.58268i | 0.336408 | − | 1.58268i | ||||
\(651\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(654\) | 0.658114 | − | 1.47815i | 0.658114 | − | 1.47815i | ||||
\(655\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | ||||
\(656\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(657\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.207912 | − | 0.978148i | −0.207912 | − | 0.978148i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.743145 | − | 0.669131i | \(-0.233333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(662\) | 0.207912 | + | 0.978148i | 0.207912 | + | 0.978148i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(667\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(670\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(674\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(675\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.564602 | − | 0.251377i | −0.564602 | − | 0.251377i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.994522 | − | 0.104528i | −0.994522 | − | 0.104528i | ||||
\(682\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(683\) | 0.251377 | + | 0.564602i | 0.251377 | + | 0.564602i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.169131 | + | 1.60917i | 0.169131 | + | 1.60917i | ||||
\(686\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.951057 | − | 1.30902i | −0.951057 | − | 1.30902i | ||||
\(691\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.336408 | + | 1.58268i | 0.336408 | + | 1.58268i | ||||
\(696\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.336408 | + | 1.58268i | −0.336408 | + | 1.58268i | ||||
\(699\) | − | 1.00000i | − | 1.00000i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | −1.20243 | − | 1.08268i | −1.20243 | − | 1.08268i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(707\) | 0.535233 | + | 0.309017i | 0.535233 | + | 0.309017i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
1.00000 | \(0\) | |||||||||
\(710\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(713\) | 0.336408 | + | 1.58268i | 0.336408 | + | 1.58268i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.60917 | + | 0.169131i | 1.60917 | + | 0.169131i | ||||
\(718\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | ||||
\(719\) | −0.251377 | − | 0.564602i | −0.251377 | − | 0.564602i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(720\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(721\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(722\) | −0.406737 | + | 0.913545i | −0.406737 | + | 0.913545i | ||||
\(723\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.251377 | − | 0.564602i | −0.251377 | − | 0.564602i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(728\) | 1.60917 | − | 0.169131i | 1.60917 | − | 0.169131i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(730\) | 0.618034 | 0.618034 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0.459289 | − | 0.413545i | 0.459289 | − | 0.413545i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.743145 | − | 0.669131i | 0.743145 | − | 0.669131i | ||||
\(738\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(739\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.40126 | − | 0.809017i | −1.40126 | − | 0.809017i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(744\) | −0.994522 | − | 0.104528i | −0.994522 | − | 0.104528i | ||||
\(745\) | 0.169131 | − | 1.60917i | 0.169131 | − | 1.60917i | ||||
\(746\) | 0.251377 | − | 0.564602i | 0.251377 | − | 0.564602i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.40126 | − | 0.809017i | 1.40126 | − | 0.809017i | ||||
\(750\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(751\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(754\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(758\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(759\) | 1.58268 | − | 0.336408i | 1.58268 | − | 0.336408i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | ||||
\(767\) | −1.60917 | − | 0.169131i | −1.60917 | − | 0.169131i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.47815 | − | 0.658114i | 1.47815 | − | 0.658114i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(770\) | − | 1.00000i | − | 1.00000i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(774\) | − | 1.00000i | − | 1.00000i | ||||||
\(775\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(776\) | − | 0.618034i | − | 0.618034i | ||||||
\(777\) | 1.58268 | + | 0.336408i | 1.58268 | + | 0.336408i | ||||
\(778\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0646021 | + | 0.614648i | −0.0646021 | + | 0.614648i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.614648 | − | 0.0646021i | −0.614648 | − | 0.0646021i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(786\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(787\) | 1.58268 | − | 0.336408i | 1.58268 | − | 0.336408i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.743145 | − | 0.669131i | −0.743145 | − | 0.669131i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.658114 | + | 1.47815i | 0.658114 | + | 1.47815i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.994522 | − | 0.104528i | 0.994522 | − | 0.104528i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.00000i | − | 1.00000i | ||||||
\(802\) | 1.08268 | − | 1.20243i | 1.08268 | − | 1.20243i | ||||
\(803\) | −0.251377 | + | 0.564602i | −0.251377 | + | 0.564602i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.08268 | + | 1.20243i | 1.08268 | + | 1.20243i | ||||
\(806\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | ||||
\(807\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(808\) | −0.0646021 | + | 0.614648i | −0.0646021 | + | 0.614648i | ||||
\(809\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(810\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(811\) | 0.604528 | + | 0.128496i | 0.604528 | + | 0.128496i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(814\) | −1.58268 | − | 0.336408i | −1.58268 | − | 0.336408i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 1.00000i | − | 1.00000i | ||||||
\(819\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(822\) | −0.169131 | − | 1.60917i | −0.169131 | − | 1.60917i | ||||
\(823\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(824\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(825\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(826\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(827\) | 0.128496 | − | 0.604528i | 0.128496 | − | 0.604528i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.169131 | + | 1.60917i | 0.169131 | + | 1.60917i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.169131 | + | 1.60917i | −0.169131 | + | 1.60917i | ||||
\(832\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.336408 | − | 1.58268i | −0.336408 | − | 1.58268i | ||||
\(835\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(838\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(839\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(840\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(841\) | 0.413545 | + | 0.459289i | 0.413545 | + | 0.459289i | ||||
\(842\) | 0.614648 | + | 0.0646021i | 0.614648 | + | 0.0646021i | ||||
\(843\) | 0.535233 | − | 0.309017i | 0.535233 | − | 0.309017i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.20243 | + | 1.08268i | 1.20243 | + | 1.08268i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.618034 | −0.618034 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.26728 | − | 1.30902i | 2.26728 | − | 1.30902i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(857\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(859\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(862\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | ||||
\(863\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(866\) | 0.459289 | − | 0.413545i | 0.459289 | − | 0.413545i | ||||
\(867\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.251377 | + | 0.564602i | 0.251377 | + | 0.564602i | ||||
\(871\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(872\) | −1.60917 | + | 0.169131i | −1.60917 | + | 0.169131i | ||||
\(873\) | 0.413545 | − | 0.459289i | 0.413545 | − | 0.459289i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.207912 | − | 0.978148i | −0.207912 | − | 0.978148i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.08268 | + | 1.20243i | −1.08268 | + | 1.20243i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(878\) | −0.251377 | + | 0.564602i | −0.251377 | + | 0.564602i | ||||
\(879\) | 0.614648 | − | 0.0646021i | 0.614648 | − | 0.0646021i | ||||
\(880\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(881\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.564602 | − | 0.251377i | 0.564602 | − | 0.251377i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(886\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(887\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(888\) | 0.336408 | + | 1.58268i | 0.336408 | + | 1.58268i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(891\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.169131 | + | 1.60917i | −0.169131 | + | 1.60917i | ||||
\(895\) | 1.00000 | 1.00000 | ||||||||
\(896\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | ||||
\(897\) | 2.60369 | − | 0.273659i | 2.60369 | − | 0.273659i | ||||
\(898\) | 0.604528 | + | 0.128496i | 0.604528 | + | 0.128496i | ||||
\(899\) | − | 0.618034i | − | 0.618034i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(903\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.459289 | + | 0.413545i | −0.459289 | + | 0.413545i | ||||
\(910\) | 0.169131 | − | 1.60917i | 0.169131 | − | 1.60917i | ||||
\(911\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(920\) | −0.658114 | + | 1.47815i | −0.658114 | + | 1.47815i | ||||
\(921\) | −0.564602 | − | 0.251377i | −0.564602 | − | 0.251377i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.207912 | + | 0.978148i | −0.207912 | + | 0.978148i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.61803 | −1.61803 | ||||||||
\(926\) | −0.535233 | − | 0.309017i | −0.535233 | − | 0.309017i | ||||
\(927\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.658114 | − | 1.47815i | 0.658114 | − | 1.47815i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(930\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.60917 | + | 0.169131i | 1.60917 | + | 0.169131i | ||||
\(934\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.336408 | + | 1.58268i | −0.336408 | + | 1.58268i | ||||
\(937\) | 0.604528 | − | 0.128496i | 0.604528 | − | 0.128496i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(938\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(939\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(942\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(943\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | ||||
\(944\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(945\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(946\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(947\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.535233 | + | 0.309017i | 0.535233 | + | 0.309017i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.251377 | + | 0.564602i | −0.251377 | + | 0.564602i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.47815 | − | 0.658114i | −1.47815 | − | 0.658114i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.618034 | −0.618034 | ||||||||
\(958\) | 1.47815 | − | 0.658114i | 1.47815 | − | 0.658114i | ||||
\(959\) | 0.336408 | + | 1.58268i | 0.336408 | + | 1.58268i | ||||
\(960\) | −0.743145 | − | 0.669131i | −0.743145 | − | 0.669131i | ||||
\(961\) | 0 | 0 | ||||||||
\(962\) | −2.48990 | − | 0.809017i | −2.48990 | − | 0.809017i | ||||
\(963\) | 0.336408 | + | 1.58268i | 0.336408 | + | 1.58268i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.08268 | − | 1.20243i | −1.08268 | − | 1.20243i | ||||
\(967\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.604528 | − | 0.128496i | −0.604528 | − | 0.128496i | ||||
\(971\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.47815 | − | 0.658114i | −1.47815 | − | 0.658114i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(982\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | ||||
\(983\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(984\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.20243 | + | 1.08268i | 1.20243 | + | 1.08268i | ||||
\(990\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(991\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.00000 | 1.00000 | ||||||||
\(994\) | 0.564602 | − | 0.251377i | 0.564602 | − | 0.251377i | ||||
\(995\) | 0.406737 | + | 0.913545i | 0.406737 | + | 0.913545i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(998\) | 1.20243 | + | 1.08268i | 1.20243 | + | 1.08268i | ||||
\(999\) | −0.809017 | + | 1.40126i | −0.809017 | + | 1.40126i |
(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 | 3225.1.cc.a.2156.2 | yes | 16 | |
3.2 | odd | 2 | inner | 3225.1.cc.a.2156.1 | yes | 16 | |
25.21 | even | 5 | inner | 3225.1.cc.a.221.1 | ✓ | 16 | |
43.36 | even | 3 | inner | 3225.1.cc.a.2831.2 | yes | 16 | |
75.71 | odd | 10 | inner | 3225.1.cc.a.221.2 | yes | 16 | |
129.122 | odd | 6 | inner | 3225.1.cc.a.2831.1 | yes | 16 | |
1075.896 | even | 15 | inner | 3225.1.cc.a.896.1 | yes | 16 | |
3225.896 | odd | 30 | inner | 3225.1.cc.a.896.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3225.1.cc.a.221.1 | ✓ | 16 | 25.21 | even | 5 | inner | |
3225.1.cc.a.221.2 | yes | 16 | 75.71 | odd | 10 | inner | |
3225.1.cc.a.896.1 | yes | 16 | 1075.896 | even | 15 | inner | |
3225.1.cc.a.896.2 | yes | 16 | 3225.896 | odd | 30 | inner | |
3225.1.cc.a.2156.1 | yes | 16 | 3.2 | odd | 2 | inner | |
3225.1.cc.a.2156.2 | yes | 16 | 1.1 | even | 1 | trivial | |
3225.1.cc.a.2831.1 | yes | 16 | 129.122 | odd | 6 | inner | |
3225.1.cc.a.2831.2 | yes | 16 | 43.36 | even | 3 | inner |