Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1925,1,Mod(118,1925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1925, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([15, 10, 6]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1925.118");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1925 = 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1925.dn (of order \(20\), degree \(8\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.960700149319\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{20})\) |
Coefficient field: | \(\Q(\zeta_{120})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{32} + x^{28} - x^{20} - x^{16} - x^{12} + x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{30}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{30} - \cdots)\) |
Embedding invariants
Embedding label | 118.1 | ||
Root | \(-0.998630 + 0.0523360i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1925.118 |
Dual form | 1925.1.dn.c.832.1 |
$q$-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 \(\left(\mathbb{Z}/1925\mathbb{Z}\right)^\times\).
\(n\) | \(276\) | \(1002\) | \(1751\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.93221 | − | 0.306032i | −1.93221 | − | 0.306032i | −0.933580 | − | 0.358368i | \(-0.883333\pi\) |
−0.998630 | + | 0.0523360i | \(0.983333\pi\) | |||||||
\(3\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(4\) | 2.68872 | + | 0.873619i | 2.68872 | + | 0.873619i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.891007 | − | 0.453990i | 0.891007 | − | 0.453990i | ||||
\(8\) | −3.18475 | − | 1.62271i | −3.18475 | − | 1.62271i | ||||
\(9\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(14\) | −1.86055 | + | 0.604528i | −1.86055 | + | 0.604528i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.36984 | + | 2.44833i | 3.36984 | + | 2.44833i | ||||
\(17\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(18\) | 0.888139 | + | 1.74307i | 0.888139 | + | 1.74307i | ||||
\(19\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.506326 | − | 1.88964i | 0.506326 | − | 1.88964i | ||||
\(23\) | 1.05097 | + | 1.05097i | 1.05097 | + | 1.05097i | 0.998630 | + | 0.0523360i | \(0.0166667\pi\) |
0.0523360 | + | 0.998630i | \(0.483333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.79228 | − | 0.442254i | 2.79228 | − | 0.442254i | ||||
\(29\) | 0.614648 | − | 1.89169i | 0.614648 | − | 1.89169i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.406737 | − | 0.913545i | \(-0.366667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(32\) | −3.23454 | − | 3.23454i | −3.23454 | − | 3.23454i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.873619 | − | 2.68872i | −0.873619 | − | 2.68872i | ||||
\(37\) | 0.188780 | + | 0.370501i | 0.188780 | + | 0.370501i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.777146 | + | 0.629320i | \(0.783333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.147826 | − | 0.147826i | 0.147826 | − | 0.147826i | −0.629320 | − | 0.777146i | \(-0.716667\pi\) |
0.777146 | + | 0.629320i | \(0.216667\pi\) | |||||||
\(44\) | −1.14988 | + | 2.58268i | −1.14988 | + | 2.58268i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.70906 | − | 2.35232i | −1.70906 | − | 2.35232i | ||||
\(47\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.16110 | + | 0.183900i | 1.16110 | + | 0.183900i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.57433 | −3.57433 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.76655 | + | 3.46705i | −1.76655 | + | 3.46705i | ||||
\(59\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.891007 | − | 0.453990i | −0.891007 | − | 0.453990i | ||||
\(64\) | 2.81160 | + | 3.86984i | 2.81160 | + | 3.86984i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.575212 | − | 0.575212i | 0.575212 | − | 0.575212i | −0.358368 | − | 0.933580i | \(-0.616667\pi\) |
0.933580 | + | 0.358368i | \(0.116667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.169131 | + | 0.122881i | 0.169131 | + | 0.122881i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(72\) | 0.559148 | + | 3.53032i | 0.559148 | + | 3.53032i | ||||
\(73\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(74\) | −0.251377 | − | 0.773659i | −0.251377 | − | 0.773659i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.358368 | + | 0.933580i | 0.358368 | + | 0.933580i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.658114 | + | 0.478148i | −0.658114 | + | 0.478148i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.330869 | + | 0.240391i | −0.330869 | + | 0.240391i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.94672 | − | 2.99768i | 1.94672 | − | 2.99768i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.90761 | + | 3.74390i | 1.90761 | + | 3.74390i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(98\) | −1.38331 | + | 1.38331i | −1.38331 | + | 1.38331i | ||||
\(99\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.18720 | − | 0.710666i | −2.18720 | − | 0.710666i | ||||
\(107\) | 0.280582 | − | 0.550672i | 0.280582 | − | 0.550672i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.415823 | −0.415823 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.11407 | + | 0.651605i | 4.11407 | + | 0.651605i | ||||
\(113\) | 0.903007 | − | 1.77225i | 0.903007 | − | 1.77225i | 0.358368 | − | 0.933580i | \(-0.383333\pi\) |
0.544639 | − | 0.838671i | \(-0.316667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.30524 | − | 4.54927i | 3.30524 | − | 4.54927i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.58268 | + | 1.14988i | 1.58268 | + | 1.14988i | ||||
\(127\) | −0.209350 | − | 1.32178i | −0.209350 | − | 1.32178i | −0.838671 | − | 0.544639i | \(-0.816667\pi\) |
0.629320 | − | 0.777146i | \(-0.283333\pi\) | |||||||
\(128\) | −2.17161 | − | 4.26203i | −2.17161 | − | 4.26203i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.28746 | + | 0.935398i | −1.28746 | + | 0.935398i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.87869 | + | 0.297556i | −1.87869 | + | 0.297556i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.289190 | − | 0.289190i | −0.289190 | − | 0.289190i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 4.16535i | − | 4.16535i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.183900 | + | 1.16110i | 0.183900 | + | 1.16110i | ||||
\(149\) | 1.40126 | + | 1.01807i | 1.40126 | + | 1.01807i | 0.994522 | + | 0.104528i | \(0.0333333\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.41355 | − | 0.459289i | 1.41355 | − | 0.459289i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.406737 | − | 1.91355i | −0.406737 | − | 1.91355i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(158\) | 1.41794 | − | 0.722478i | 1.41794 | − | 0.722478i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.41355 | + | 0.459289i | 1.41355 | + | 0.459289i | ||||
\(162\) | 0.888139 | − | 1.74307i | 0.888139 | − | 1.74307i | ||||
\(163\) | 1.87869 | + | 0.297556i | 1.87869 | + | 0.297556i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.526605 | − | 0.268319i | 0.526605 | − | 0.268319i | ||||
\(173\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.78716 | + | 3.09546i | −2.78716 | + | 3.09546i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.64165 | − | 5.05248i | −1.64165 | − | 5.05248i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.80460 | + | 0.285820i | −1.80460 | + | 0.285820i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.838671 | + | 0.544639i | \(0.816667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.28716 | − | 1.66172i | 2.28716 | − | 1.66172i | ||||
\(197\) | 0.946294 | + | 0.946294i | 0.946294 | + | 0.946294i | 0.998630 | − | 0.0523360i | \(-0.0166667\pi\) |
−0.0523360 | + | 0.998630i | \(0.516667\pi\) | |||||||
\(198\) | −1.82636 | + | 0.701074i | −1.82636 | + | 0.701074i | ||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.311155 | − | 1.96456i | −0.311155 | − | 1.96456i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.232507 | − | 1.46799i | 0.232507 | − | 1.46799i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.11803 | + | 1.53884i | 1.11803 | + | 1.53884i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(212\) | 2.96121 | + | 1.50881i | 2.96121 | + | 1.50881i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.710666 | + | 0.978148i | −0.710666 | + | 0.978148i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.803458 | + | 0.127255i | 0.803458 | + | 0.127255i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(224\) | −4.35045 | − | 1.41355i | −4.35045 | − | 1.41355i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.28716 | + | 3.14801i | −2.28716 | + | 3.14801i | ||||
\(227\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.02717 | + | 5.02717i | −5.02717 | + | 5.02717i | ||||
\(233\) | 0.156434 | − | 0.987688i | 0.156434 | − | 0.987688i | −0.777146 | − | 0.629320i | \(-0.783333\pi\) |
0.933580 | − | 0.358368i | \(-0.116667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.363271 | + | 1.11803i | 0.363271 | + | 1.11803i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 1.82636 | + | 0.701074i | 1.82636 | + | 0.701074i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(252\) | −1.99906 | − | 1.99906i | −1.99906 | − | 1.99906i | ||||
\(253\) | −1.15506 | + | 0.935352i | −1.15506 | + | 0.935352i | ||||
\(254\) | 2.61803i | 2.61803i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.41355 | + | 4.35045i | 1.41355 | + | 4.35045i | ||||
\(257\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.336408 | + | 0.244415i | 0.336408 | + | 0.244415i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.89169 | + | 0.614648i | −1.89169 | + | 0.614648i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.29195 | + | 1.29195i | −1.29195 | + | 1.29195i | −0.358368 | + | 0.933580i | \(0.616667\pi\) |
−0.933580 | + | 0.358368i | \(0.883333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.04910 | − | 1.04407i | 2.04910 | − | 1.04407i | ||||
\(269\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.72109 | 3.72109 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.610425 | − | 0.0966818i | −0.610425 | − | 0.0966818i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.478148 | − | 0.658114i | 0.478148 | − | 0.658114i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(284\) | 0.347395 | + | 0.478148i | 0.347395 | + | 0.478148i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.715583 | + | 4.51801i | −0.715583 | + | 4.51801i | ||||
\(289\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 1.48629i | − | 1.48629i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.39596 | − | 2.39596i | −2.39596 | − | 2.39596i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0646021 | − | 0.198825i | 0.0646021 | − | 0.198825i | ||||
\(302\) | −2.87182 | + | 0.454852i | −2.87182 | + | 0.454852i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0.147959 | + | 2.82322i | 0.147959 | + | 2.82322i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.18720 | + | 0.710666i | −2.18720 | + | 0.710666i | ||||
\(317\) | −0.127255 | + | 0.803458i | −0.127255 | + | 0.803458i | 0.838671 | + | 0.544639i | \(0.183333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.81708 | + | 0.809017i | 1.81708 | + | 0.809017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.59071 | − | 1.32003i | −2.59071 | − | 1.32003i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.66172 | + | 2.28716i | −1.66172 | + | 2.28716i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.53897 | − | 1.14988i | −3.53897 | − | 1.14988i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.33826 | −1.33826 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.188780 | − | 0.370501i | 0.188780 | − | 0.370501i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.550672 | − | 0.280582i | 0.550672 | − | 0.280582i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | 1.74307 | + | 0.888139i | 1.74307 | + | 0.888139i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.156434 | − | 0.987688i | 0.156434 | − | 0.987688i | ||||
\(344\) | −0.710666 | + | 0.230909i | −0.710666 | + | 0.230909i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.285820 | + | 1.80460i | 0.285820 | + | 1.80460i | 0.544639 | + | 0.838671i | \(0.316667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.55492 | − | 2.87872i | 3.55492 | − | 2.87872i | ||||
\(353\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.19417 | + | 0.189138i | −1.19417 | + | 0.189138i | ||||
\(359\) | −0.128496 | + | 0.395472i | −0.128496 | + | 0.395472i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(368\) | 0.968473 | + | 6.11470i | 0.968473 | + | 6.11470i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.11803 | − | 0.363271i | 1.11803 | − | 0.363271i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.14988 | + | 1.58268i | −1.14988 | + | 1.58268i | −0.406737 | + | 0.913545i | \(0.633333\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.43704 | + | 2.82035i | −1.43704 | + | 2.82035i | ||||
\(383\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.57433 | 3.57433 | ||||||||
\(387\) | −0.206483 | − | 0.0327037i | −0.206483 | − | 0.0327037i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.27276 | − | 0.413545i | −1.27276 | − | 0.413545i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.18475 | + | 1.62271i | −3.18475 | + | 1.62271i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.53884 | − | 2.11803i | −1.53884 | − | 2.11803i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.76531 | − | 0.587785i | 2.76531 | − | 0.587785i | ||||
\(397\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.08268 | − | 0.786610i | −1.08268 | − | 0.786610i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.89116i | 3.89116i | ||||||||
\(407\) | −0.388205 | + | 0.149018i | −0.388205 | + | 0.149018i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.898504 | + | 2.76531i | −0.898504 | + | 2.76531i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.604528 | + | 1.86055i | 0.604528 | + | 1.86055i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(422\) | −1.68934 | − | 3.31552i | −1.68934 | − | 3.31552i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.39939 | − | 2.46980i | −3.39939 | − | 2.46980i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.23548 | − | 1.23548i | 1.23548 | − | 1.23548i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.11803 | − | 1.53884i | −1.11803 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.11803 | − | 0.363271i | −1.11803 | − | 0.363271i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.533698 | − | 1.04744i | 0.533698 | − | 1.04744i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.26203 | + | 2.17161i | 4.26203 | + | 2.17161i | ||||
\(449\) | −1.14988 | − | 1.58268i | −1.14988 | − | 1.58268i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.406737 | − | 0.913545i | \(-0.633333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.97621 | − | 3.97621i | 3.97621 | − | 3.97621i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.209350 | + | 1.32178i | 0.209350 | + | 1.32178i | 0.838671 | + | 0.544639i | \(0.183333\pi\) |
−0.629320 | + | 0.777146i | \(0.716667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.831254 | − | 0.831254i | −0.831254 | − | 0.831254i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(464\) | 6.70276 | − | 4.86984i | 6.70276 | − | 4.86984i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.604528 | + | 1.86055i | −0.604528 | + | 1.86055i | ||||
\(467\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.251377 | − | 0.773659i | 0.251377 | − | 0.773659i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.131564 | + | 0.162468i | 0.131564 | + | 0.162468i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.533698 | − | 1.04744i | −0.533698 | − | 1.04744i | ||||
\(478\) | −0.359762 | − | 2.27145i | −0.359762 | − | 2.27145i | ||||
\(479\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.44833 | − | 1.41355i | −2.44833 | − | 1.41355i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.77225 | − | 0.903007i | −1.77225 | − | 0.903007i | −0.933580 | − | 0.358368i | \(-0.883333\pi\) |
−0.838671 | − | 0.544639i | \(-0.816667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.64728 | + | 0.535233i | 1.64728 | + | 0.535233i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.206483 | + | 0.0327037i | 0.206483 | + | 0.0327037i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(504\) | 2.10094 | + | 2.89169i | 2.10094 | + | 2.89169i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.51807 | − | 1.45381i | 2.51807 | − | 1.45381i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.591852 | − | 3.73681i | 0.591852 | − | 3.73681i | ||||
\(509\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.651605 | − | 4.11407i | −0.651605 | − | 4.11407i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.575212 | − | 0.575212i | −0.575212 | − | 0.575212i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(522\) | 3.84325 | − | 0.608711i | 3.84325 | − | 0.608711i | ||||
\(523\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.89169 | − | 2.10094i | 2.89169 | − | 2.10094i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.20906i | 1.20906i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.76531 | + | 0.898504i | −2.76531 | + | 0.898504i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.743145 | + | 0.669131i | 0.743145 | + | 0.669131i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.873619 | − | 1.20243i | −0.873619 | − | 1.20243i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.104528 | − | 0.994522i | \(-0.466667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.453990 | + | 0.891007i | −0.453990 | + | 0.891007i | 0.544639 | + | 0.838671i | \(0.316667\pi\) |
−0.998630 | + | 0.0523360i | \(0.983333\pi\) | |||||||
\(548\) | −5.31124 | − | 0.841218i | −5.31124 | − | 0.841218i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.369309 | + | 0.724810i | −0.369309 | + | 0.724810i | ||||
\(554\) | 1.14988 | + | 0.373619i | 1.14988 | + | 0.373619i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.62795 | + | 0.829482i | −1.62795 | + | 0.829482i | −0.629320 | + | 0.777146i | \(0.716667\pi\) |
−0.998630 | + | 0.0523360i | \(0.983333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.12529 | + | 1.12529i | −1.12529 | + | 1.12529i | ||||
\(563\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.156434 | + | 0.987688i | 0.156434 | + | 0.987688i | ||||
\(568\) | −0.339239 | − | 0.665794i | −0.339239 | − | 0.665794i | ||||
\(569\) | 0.535233 | + | 1.64728i | 0.535233 | + | 1.64728i | 0.743145 | + | 0.669131i | \(0.233333\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.48629i | 1.48629i | 0.669131 | + | 0.743145i | \(0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.47815 | − | 4.54927i | 1.47815 | − | 4.54927i | ||||
\(577\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(578\) | 1.93221 | − | 0.306032i | 1.93221 | − | 0.306032i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.304260 | + | 1.13551i | −0.304260 | + | 1.13551i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.270952 | + | 1.71073i | −0.270952 | + | 1.71073i | ||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.87819 | + | 3.96149i | 2.87819 | + | 3.96149i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.786610 | + | 1.08268i | −0.786610 | + | 1.08268i | 0.207912 | + | 0.978148i | \(0.433333\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(602\) | −0.185672 | + | 0.364401i | −0.185672 | + | 0.364401i | ||||
\(603\) | −0.803458 | − | 0.127255i | −0.803458 | − | 0.127255i | ||||
\(604\) | 4.20188 | 4.20188 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.186271 | − | 0.0949099i | −0.186271 | − | 0.0949099i | 0.358368 | − | 0.933580i | \(-0.383333\pi\) |
−0.544639 | + | 0.838671i | \(0.683333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.373619 | − | 3.55475i | 0.373619 | − | 3.55475i | ||||
\(617\) | −0.575212 | + | 0.575212i | −0.575212 | + | 0.575212i | −0.933580 | − | 0.358368i | \(-0.883333\pi\) |
0.358368 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.604528 | − | 1.86055i | 0.604528 | − | 1.86055i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(632\) | 2.87182 | − | 0.454852i | 2.87182 | − | 0.454852i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.491768 | − | 1.51351i | 0.491768 | − | 1.51351i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.26340 | − | 2.11928i | −3.26340 | − | 2.11928i | ||||
\(639\) | − | 0.209057i | − | 0.209057i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.0646021 | + | 0.198825i | 0.0646021 | + | 0.198825i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(644\) | 3.39939 | + | 2.46980i | 3.39939 | + | 2.46980i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(648\) | 2.52743 | − | 2.52743i | 2.52743 | − | 2.52743i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.79134 | + | 2.44131i | 4.79134 | + | 2.44131i | ||||
\(653\) | −1.69480 | + | 0.863541i | −1.69480 | + | 0.863541i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 2.58580 | + | 0.409551i | 2.58580 | + | 0.409551i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.478148 | + | 0.658114i | −0.478148 | + | 0.658114i | ||||
\(667\) | 2.63408 | − | 1.34213i | 2.63408 | − | 1.34213i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.253116 | − | 1.59811i | 0.253116 | − | 1.59811i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(674\) | −1.14988 | + | 0.373619i | −1.14988 | + | 0.373619i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.28716 | − | 1.66172i | −2.28716 | − | 1.66172i | ||||
\(677\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.294032 | + | 0.294032i | 0.294032 | + | 0.294032i | 0.838671 | − | 0.544639i | \(-0.183333\pi\) |
−0.544639 | + | 0.838671i | \(0.683333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.604528 | + | 1.86055i | −0.604528 | + | 1.86055i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.860075 | − | 0.136222i | 0.860075 | − | 0.136222i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.544639 | − | 0.838671i | 0.544639 | − | 0.838671i | ||||
\(694\) | − | 3.57433i | − | 3.57433i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.80902 | + | 0.587785i | −1.80902 | + | 0.587785i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.14253 | + | 2.39169i | −4.14253 | + | 2.39169i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | 1.00000i | \(0.5\pi\) | ||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.773659 | + | 0.251377i | 0.773659 | + | 0.251377i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.74724 | 1.74724 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.369309 | − | 0.724810i | 0.369309 | − | 0.724810i | ||||
\(719\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.74307 | − | 0.888139i | 1.74307 | − | 0.888139i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.79878i | − | 6.79878i | ||||||
\(737\) | 0.511935 | + | 0.632187i | 0.511935 | + | 0.632187i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.60917 | + | 1.16913i | −1.60917 | + | 1.16913i | −0.743145 | + | 0.669131i | \(0.766667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.27145 | + | 0.359762i | −2.27145 | + | 0.359762i | ||||
\(743\) | −1.59811 | + | 0.253116i | −1.59811 | + | 0.253116i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.58268 | − | 1.14988i | 1.58268 | − | 1.14988i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 0.618034i | − | 0.618034i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.311155 | − | 1.96456i | 0.311155 | − | 1.96456i | 0.0523360 | − | 0.998630i | \(-0.483333\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(758\) | 2.70616 | − | 2.70616i | 2.70616 | − | 2.70616i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.370501 | + | 0.188780i | −0.370501 | + | 0.188780i | ||||
\(764\) | 2.68872 | − | 3.70071i | 2.68872 | − | 3.70071i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.10176 | − | 0.808039i | −5.10176 | − | 0.808039i | ||||
\(773\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(774\) | 0.388960 | + | 0.126381i | 0.388960 | + | 0.126381i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.33269 | + | 1.18856i | 2.33269 | + | 1.18856i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.139886 | + | 0.155360i | −0.139886 | + | 0.155360i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.96149 | − | 1.28716i | 3.96149 | − | 1.28716i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(788\) | 1.71762 | + | 3.37102i | 1.71762 | + | 3.37102i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.98904i | − | 1.98904i | ||||||
\(792\) | −3.56943 | + | 0.187066i | −3.56943 | + | 0.187066i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.85123 | + | 1.85123i | 1.85123 | + | 1.85123i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.336408 | − | 0.244415i | −0.336408 | − | 0.244415i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(812\) | 0.879663 | − | 5.55398i | 0.879663 | − | 5.55398i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.795697 | − | 0.169131i | 0.795697 | − | 0.169131i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.96456 | + | 0.311155i | 1.96456 | + | 0.311155i | 0.998630 | + | 0.0523360i | \(0.0166667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.987688 | − | 0.156434i | −0.987688 | − | 0.156434i | −0.358368 | − | 0.933580i | \(-0.616667\pi\) |
−0.629320 | + | 0.777146i | \(0.716667\pi\) | |||||||
\(828\) | 1.90761 | − | 3.74390i | 1.90761 | − | 3.74390i | ||||
\(829\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.39169 | − | 1.73767i | −2.39169 | − | 1.73767i | ||||
\(842\) | −0.598689 | − | 3.77997i | −0.598689 | − | 3.77997i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.66172 | + | 5.11426i | 1.66172 | + | 5.11426i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(848\) | 3.46247 | + | 3.46247i | 3.46247 | + | 3.46247i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.78716 | + | 1.29845i | −1.78716 | + | 1.29845i | ||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.68934 | + | 3.31552i | 1.68934 | + | 3.31552i | ||||
\(863\) | 0.270952 | + | 1.71073i | 0.270952 | + | 1.71073i | 0.629320 | + | 0.777146i | \(0.283333\pi\) |
−0.358368 | + | 0.933580i | \(0.616667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.406737 | − | 0.704489i | −0.406737 | − | 0.704489i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.32429 | + | 0.674761i | 1.32429 | + | 0.674761i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.734572 | + | 1.44168i | −0.734572 | + | 1.44168i | 0.156434 | + | 0.987688i | \(0.450000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 1.93221 | + | 0.306032i | 1.93221 | + | 0.306032i | ||||
\(883\) | 0.786335 | − | 1.54327i | 0.786335 | − | 1.54327i | −0.0523360 | − | 0.998630i | \(-0.516667\pi\) |
0.838671 | − | 0.544639i | \(-0.183333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.35177 | + | 1.86055i | −1.35177 | + | 1.86055i | ||||
\(887\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.786610 | − | 1.08268i | −0.786610 | − | 1.08268i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.86984 | − | 2.81160i | −3.86984 | − | 2.81160i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.73746 | + | 3.40996i | 1.73746 | + | 3.40996i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.75170 | + | 4.17886i | −5.75170 | + | 4.17886i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.16110 | − | 0.183900i | 1.16110 | − | 0.183900i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 2.61803i | − | 2.61803i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.60917 | − | 1.16913i | −1.60917 | − | 1.16913i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.743145 | − | 0.669131i | \(-0.766667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.35177 | + | 1.86055i | 1.35177 | + | 1.86055i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.10686 | + | 4.13065i | −8.10686 | + | 4.13065i | ||||
\(929\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.28347 | − | 2.51896i | 1.28347 | − | 2.51896i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(938\) | −0.722478 | + | 1.41794i | −0.722478 | + | 1.41794i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.204489 | − | 0.354185i | −0.204489 | − | 0.354185i | ||||
\(947\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.607558 | + | 1.19240i | 0.607558 | + | 1.19240i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.358368 | + | 0.933580i | \(0.616667\pi\) | |||||||
\(954\) | 0.710666 | + | 2.18720i | 0.710666 | + | 2.18720i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.32344i | 3.32344i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.53884 | + | 1.11803i | −1.53884 | + | 1.11803i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.610425 | + | 0.0966818i | −0.610425 | + | 0.0966818i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.437016 | + | 0.437016i | 0.437016 | + | 0.437016i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(968\) | 2.77778 | + | 2.24940i | 2.77778 | + | 2.24940i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.14801 | + | 2.28716i | 3.14801 | + | 2.28716i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.232507 | + | 1.46799i | −0.232507 | + | 1.46799i | 0.544639 | + | 0.838671i | \(0.316667\pi\) |
−0.777146 | + | 0.629320i | \(0.783333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.244415 | + | 0.336408i | 0.244415 | + | 0.336408i | ||||
\(982\) | −3.01909 | − | 1.53830i | −3.01909 | − | 1.53830i | ||||
\(983\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.310719 | 0.310719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.388960 | − | 0.126381i | −0.388960 | − | 0.126381i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(998\) | −2.82035 | − | 1.43704i | −2.82035 | − | 1.43704i | ||||
\(999\) | 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 | 1925.1.dn.c.118.1 | ✓ | 32 | |
5.2 | odd | 4 | inner | 1925.1.dn.c.657.4 | yes | 32 | |
5.3 | odd | 4 | inner | 1925.1.dn.c.657.1 | yes | 32 | |
5.4 | even | 2 | inner | 1925.1.dn.c.118.4 | yes | 32 | |
7.6 | odd | 2 | CM | 1925.1.dn.c.118.1 | ✓ | 32 | |
11.7 | odd | 10 | inner | 1925.1.dn.c.293.4 | yes | 32 | |
35.13 | even | 4 | inner | 1925.1.dn.c.657.1 | yes | 32 | |
35.27 | even | 4 | inner | 1925.1.dn.c.657.4 | yes | 32 | |
35.34 | odd | 2 | inner | 1925.1.dn.c.118.4 | yes | 32 | |
55.7 | even | 20 | inner | 1925.1.dn.c.832.1 | yes | 32 | |
55.18 | even | 20 | inner | 1925.1.dn.c.832.4 | yes | 32 | |
55.29 | odd | 10 | inner | 1925.1.dn.c.293.1 | yes | 32 | |
77.62 | even | 10 | inner | 1925.1.dn.c.293.4 | yes | 32 | |
385.62 | odd | 20 | inner | 1925.1.dn.c.832.1 | yes | 32 | |
385.139 | even | 10 | inner | 1925.1.dn.c.293.1 | yes | 32 | |
385.293 | odd | 20 | inner | 1925.1.dn.c.832.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1925.1.dn.c.118.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1925.1.dn.c.118.1 | ✓ | 32 | 7.6 | odd | 2 | CM | |
1925.1.dn.c.118.4 | yes | 32 | 5.4 | even | 2 | inner | |
1925.1.dn.c.118.4 | yes | 32 | 35.34 | odd | 2 | inner | |
1925.1.dn.c.293.1 | yes | 32 | 55.29 | odd | 10 | inner | |
1925.1.dn.c.293.1 | yes | 32 | 385.139 | even | 10 | inner | |
1925.1.dn.c.293.4 | yes | 32 | 11.7 | odd | 10 | inner | |
1925.1.dn.c.293.4 | yes | 32 | 77.62 | even | 10 | inner | |
1925.1.dn.c.657.1 | yes | 32 | 5.3 | odd | 4 | inner | |
1925.1.dn.c.657.1 | yes | 32 | 35.13 | even | 4 | inner | |
1925.1.dn.c.657.4 | yes | 32 | 5.2 | odd | 4 | inner | |
1925.1.dn.c.657.4 | yes | 32 | 35.27 | even | 4 | inner | |
1925.1.dn.c.832.1 | yes | 32 | 55.7 | even | 20 | inner | |
1925.1.dn.c.832.1 | yes | 32 | 385.62 | odd | 20 | inner | |
1925.1.dn.c.832.4 | yes | 32 | 55.18 | even | 20 | inner | |
1925.1.dn.c.832.4 | yes | 32 | 385.293 | odd | 20 | inner |