Properties

Label 3528.1.cw.a.2077.1
Level $3528$
Weight $1$
Character 3528.2077
Analytic conductor $1.761$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -56
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3528,1,Mod(2077,3528)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3528, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4, 5]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3528.2077");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3528.cw (of order \(6\), degree \(2\), not 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: \(1.76070136457\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.4536.1
Artin image: $C_3\times S_3$
Artin field: Galois closure of 6.0.697019904.1

Embedding invariants

Embedding label 2077.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3528.2077
Dual form 3528.1.cw.a.2677.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +1.00000 q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.00000 q^{18} +(0.500000 - 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{20} -1.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{38} +(-1.00000 + 1.73205i) q^{39} -1.00000 q^{40} +(0.500000 - 0.866025i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-0.500000 + 0.866025i) q^{48} +2.00000 q^{52} +(-0.500000 - 0.866025i) q^{54} -1.00000 q^{57} +(-1.00000 + 1.73205i) q^{59} -1.00000 q^{60} +(0.500000 + 0.866025i) q^{61} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(0.500000 + 0.866025i) q^{69} -1.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(0.500000 + 0.866025i) q^{76} +2.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{83} -1.00000 q^{90} +(0.500000 - 0.866025i) q^{92} +(-0.500000 + 0.866025i) q^{95} +1.00000 q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{8} - q^{9} + q^{10} + 2 q^{12} - 2 q^{13} + q^{15} - q^{16} + 2 q^{18} + q^{19} + q^{20} - 2 q^{23} - q^{24} - 2 q^{26} + 2 q^{27} + q^{30} - q^{32} - q^{36} - 2 q^{38} - 2 q^{39} - 2 q^{40} + q^{45} + q^{46} - q^{48} + 4 q^{52} - q^{54} - 2 q^{57} - 2 q^{59} - 2 q^{60} + q^{61} + 2 q^{64} + 2 q^{65} + q^{69} - 2 q^{71} - q^{72} + q^{76} + 4 q^{78} + q^{79} + q^{80} - q^{81} - 2 q^{83} - 2 q^{90} + q^{92} - q^{95} + 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\) \(1765\) \(2647\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.500000 0.866025i
\(3\) −0.500000 0.866025i −0.500000 0.866025i
\(4\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(5\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(7\) 0 0
\(8\) 1.00000 1.00000
\(9\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(10\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000 1.00000
\(13\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(14\) 0 0
\(15\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 1.00000 1.00000
\(19\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(20\) 0.500000 0.866025i 0.500000 0.866025i
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.500000 0.866025i −0.500000 0.866025i
\(25\) 0 0
\(26\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0.500000 0.866025i 0.500000 0.866025i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.500000 0.866025i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) −1.00000 −1.00000
\(39\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(40\) −1.00000 −1.00000
\(41\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(42\) 0 0
\(43\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0 0
\(45\) 0.500000 0.866025i 0.500000 0.866025i
\(46\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(47\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 2.00000 2.00000
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −0.500000 0.866025i −0.500000 0.866025i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.00000 −1.00000
\(58\) 0 0
\(59\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) −1.00000 −1.00000
\(61\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(66\) 0 0
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(70\) 0 0
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(73\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(77\) 0 0
\(78\) 2.00000 2.00000
\(79\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(81\) −0.500000 0.866025i −0.500000 0.866025i
\(82\) 0 0
\(83\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) −1.00000 −1.00000
\(91\) 0 0
\(92\) 0.500000 0.866025i 0.500000 0.866025i
\(93\) 0 0
\(94\) 0 0
\(95\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(96\) 1.00000 1.00000
\(97\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −1.00000 1.73205i −1.00000 1.73205i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(115\) 1.00000 1.00000
\(116\) 0 0
\(117\) 2.00000 2.00000
\(118\) 2.00000 2.00000
\(119\) 0 0
\(120\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(121\) 1.00000 1.00000
\(122\) 0.500000 0.866025i 0.500000 0.866025i
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) −0.500000 0.866025i −0.500000 0.866025i
\(129\) 0 0
\(130\) 1.00000 1.73205i 1.00000 1.73205i
\(131\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.00000 −1.00000
\(136\) 0 0
\(137\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(138\) 0.500000 0.866025i 0.500000 0.866025i
\(139\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0.500000 0.866025i 0.500000 0.866025i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 1.73205i −1.00000 1.73205i
\(157\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(158\) 0.500000 0.866025i 0.500000 0.866025i
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.500000 0.866025i
\(161\) 0 0
\(162\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(163\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 2.00000 2.00000
\(167\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(170\) 0 0
\(171\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(172\) 0 0
\(173\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.00000 2.00000
\(178\) 0 0
\(179\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(181\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(182\) 0 0
\(183\) 0.500000 0.866025i 0.500000 0.866025i
\(184\) −1.00000 −1.00000
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 1.00000 1.00000
\(191\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) −0.500000 0.866025i −0.500000 0.866025i
\(193\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(194\) 0 0
\(195\) 1.00000 1.73205i 1.00000 1.73205i
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.500000 0.866025i 0.500000 0.866025i
\(208\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.500000 0.866025i 0.500000 0.866025i
\(227\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0.500000 0.866025i 0.500000 0.866025i
\(229\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) −0.500000 0.866025i −0.500000 0.866025i
\(231\) 0 0
\(232\) 0 0
\(233\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(234\) −1.00000 1.73205i −1.00000 1.73205i
\(235\) 0 0
\(236\) −1.00000 1.73205i −1.00000 1.73205i
\(237\) 0.500000 0.866025i 0.500000 0.866025i
\(238\) 0 0
\(239\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0.500000 0.866025i 0.500000 0.866025i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.500000 0.866025i −0.500000 0.866025i
\(243\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(244\) −1.00000 −1.00000
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 −2.00000
\(248\) 0 0
\(249\) 2.00000 2.00000
\(250\) −0.500000 0.866025i −0.500000 0.866025i
\(251\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.00000 −2.00000
\(261\) 0 0
\(262\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(263\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −1.00000 1.73205i −1.00000 1.73205i
\(275\) 0 0
\(276\) −1.00000 −1.00000
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0.500000 0.866025i 0.500000 0.866025i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(284\) 0.500000 0.866025i 0.500000 0.866025i
\(285\) 1.00000 1.00000
\(286\) 0 0
\(287\) 0 0
\(288\) −0.500000 0.866025i −0.500000 0.866025i
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 1.00000 1.73205i 1.00000 1.73205i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(303\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(304\) −1.00000 −1.00000
\(305\) −0.500000 0.866025i −0.500000 0.866025i
\(306\) 0 0
\(307\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) −1.00000 −1.00000
\(315\) 0 0
\(316\) −1.00000 −1.00000
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.00000 −1.00000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) −1.00000 1.73205i −1.00000 1.73205i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(338\) 3.00000 3.00000
\(339\) 0.500000 0.866025i 0.500000 0.866025i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.500000 0.866025i 0.500000 0.866025i
\(343\) 0 0
\(344\) 0 0
\(345\) −0.500000 0.866025i −0.500000 0.866025i
\(346\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(347\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) −1.00000 1.73205i −1.00000 1.73205i
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −1.00000 1.73205i −1.00000 1.73205i
\(355\) 1.00000 1.00000
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(360\) 0.500000 0.866025i 0.500000 0.866025i
\(361\) 0 0
\(362\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(363\) −0.500000 0.866025i −0.500000 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.00000 −1.00000
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −0.500000 0.866025i −0.500000 0.866025i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) −0.500000 0.866025i −0.500000 0.866025i
\(381\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(382\) 0.500000 0.866025i 0.500000 0.866025i
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −2.00000 −2.00000
\(391\) 0 0
\(392\) 0 0
\(393\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(394\) 0 0
\(395\) −0.500000 0.866025i −0.500000 0.866025i
\(396\) 0 0
\(397\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.500000 0.866025i 0.500000 0.866025i
\(405\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) −1.00000 1.73205i −1.00000 1.73205i
\(412\) 0 0
\(413\) 0 0
\(414\) −1.00000 −1.00000
\(415\) 1.00000 1.73205i 1.00000 1.73205i
\(416\) 2.00000 2.00000
\(417\) 0.500000 0.866025i 0.500000 0.866025i
\(418\) 0 0
\(419\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0.500000 0.866025i 0.500000 0.866025i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(432\) −0.500000 0.866025i −0.500000 0.866025i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(438\) 0 0
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −1.00000 −1.00000
\(453\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(454\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(455\) 0 0
\(456\) −1.00000 −1.00000
\(457\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(459\) 0 0
\(460\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(461\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.00000 −1.00000
\(467\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 −1.00000
\(472\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(473\) 0 0
\(474\) −1.00000 −1.00000
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.500000 0.866025i 0.500000 0.866025i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) −1.00000 −1.00000
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(485\) 0 0
\(486\) 1.00000 1.00000
\(487\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.00000 1.73205i −1.00000 1.73205i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(501\) 0 0
\(502\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 1.00000 1.00000
\(506\) 0 0
\(507\) 3.00000 3.00000
\(508\) 0.500000 0.866025i 0.500000 0.866025i
\(509\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 1.00000
\(513\) 0.500000 0.866025i 0.500000 0.866025i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(520\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(524\) 0.500000 0.866025i 0.500000 0.866025i
\(525\) 0 0
\(526\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) −1.00000 1.73205i −1.00000 1.73205i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.500000 0.866025i 0.500000 0.866025i
\(539\) 0 0
\(540\) 0.500000 0.866025i 0.500000 0.866025i
\(541\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(549\) −1.00000 −1.00000
\(550\) 0 0
\(551\) 0 0
\(552\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 −1.00000
\(557\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.00000 −1.00000
\(563\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(564\) 0 0
\(565\) −0.500000 0.866025i −0.500000 0.866025i
\(566\) −1.00000 −1.00000
\(567\) 0 0
\(568\) −1.00000 −1.00000
\(569\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(570\) −0.500000 0.866025i −0.500000 0.866025i
\(571\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0.500000 0.866025i 0.500000 0.866025i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(577\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 1.00000 1.00000
\(579\) −1.00000 −1.00000
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −2.00000 −2.00000
\(586\) 0.500000 0.866025i 0.500000 0.866025i
\(587\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(588\) 0 0
\(589\) 0 0
\(590\) −2.00000 −2.00000
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 1.00000 1.73205i 1.00000 1.73205i
\(599\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.500000 0.866025i 0.500000 0.866025i
\(605\) −1.00000 −1.00000
\(606\) 0.500000 0.866025i 0.500000 0.866025i
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(609\) 0 0
\(610\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(618\) 0 0
\(619\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) −1.00000 −1.00000
\(622\) 0 0
\(623\) 0 0
\(624\) 2.00000 2.00000
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(629\) 0 0
\(630\) 0 0
\(631\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(633\) 0 0
\(634\) 0 0
\(635\) 1.00000 1.00000
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.500000 0.866025i 0.500000 0.866025i
\(640\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(641\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) −0.500000 0.866025i −0.500000 0.866025i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 1.00000 1.00000
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 0 0
\(661\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(674\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(675\) 0 0
\(676\) −1.50000 2.59808i −1.50000 2.59808i
\(677\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(678\) −1.00000 −1.00000
\(679\) 0 0
\(680\) 0 0
\(681\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(682\) 0 0
\(683\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) −1.00000 −1.00000
\(685\) −2.00000 −2.00000
\(686\) 0 0
\(687\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(688\) 0 0
\(689\) 0 0
\(690\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(691\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 2.00000 2.00000
\(693\) 0 0
\(694\) 0 0
\(695\) −0.500000 0.866025i −0.500000 0.866025i
\(696\) 0 0
\(697\) 0 0
\(698\) 2.00000 2.00000
\(699\) −1.00000 −1.00000
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) −0.500000 0.866025i −0.500000 0.866025i
\(711\) −1.00000 −1.00000
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.500000 0.866025i 0.500000 0.866025i
\(718\) −1.00000 −1.00000
\(719\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) −1.00000 −1.00000
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0.500000 0.866025i 0.500000 0.866025i
\(725\) 0 0
\(726\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(727\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(733\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.500000 0.866025i 0.500000 0.866025i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(742\) 0 0
\(743\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.00000 1.73205i −1.00000 1.73205i
\(748\) 0 0
\(749\) 0 0
\(750\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(751\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0 0
\(753\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(754\) 0 0
\(755\) 1.00000 1.00000
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0.500000 0.866025i 0.500000 0.866025i
\(763\) 0 0
\(764\) −1.00000 −1.00000
\(765\) 0 0
\(766\) 0 0
\(767\) 4.00000 4.00000
\(768\) 1.00000 1.00000
\(769\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(773\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(786\) 0.500000 0.866025i 0.500000 0.866025i
\(787\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(788\) 0 0
\(789\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(790\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(791\) 0 0
\(792\) 0 0
\(793\) 1.00000 1.73205i 1.00000 1.73205i
\(794\) 2.00000 2.00000
\(795\) 0 0
\(796\) 0 0
\(797\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0.500000 0.866025i 0.500000 0.866025i
\(808\) −1.00000 −1.00000
\(809\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(810\) 0.500000 0.866025i 0.500000 0.866025i
\(811\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(822\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(823\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(829\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(830\) −2.00000 −2.00000
\(831\) 0 0
\(832\) −1.00000 1.73205i −1.00000 1.73205i
\(833\) 0 0
\(834\) −1.00000 −1.00000
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0.500000 0.866025i 0.500000 0.866025i
\(839\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(840\) 0 0
\(841\) −0.500000 0.866025i −0.500000 0.866025i
\(842\) 0 0
\(843\) −1.00000 −1.00000
\(844\) 0 0
\(845\) 1.50000 2.59808i 1.50000 2.59808i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −1.00000 −1.00000
\(850\) 0 0
\(851\) 0 0
\(852\) −1.00000 −1.00000
\(853\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(854\) 0 0
\(855\) −0.500000 0.866025i −0.500000 0.866025i
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 0 0
\(862\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(863\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(864\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(865\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(866\) 0 0
\(867\) 1.00000 1.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 1.00000 1.00000
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0.500000 0.866025i 0.500000 0.866025i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) −2.00000 −2.00000
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 1.00000 1.73205i 1.00000 1.73205i
\(898\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(905\) 1.00000 1.00000
\(906\) 0.500000 0.866025i 0.500000 0.866025i
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0.500000 0.866025i 0.500000 0.866025i
\(909\) 0.500000 0.866025i 0.500000 0.866025i
\(910\) 0 0
\(911\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(912\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(913\) 0 0
\(914\) 0.500000 0.866025i 0.500000 0.866025i
\(915\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(916\) 0.500000 0.866025i 0.500000 0.866025i
\(917\) 0 0
\(918\) 0 0
\(919\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(920\) 1.00000 1.00000
\(921\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(922\) −1.00000 −1.00000
\(923\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(924\) 0 0
\(925\) 0 0
\(926\) 0.500000 0.866025i 0.500000 0.866025i
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(933\) 0 0
\(934\) 2.00000 2.00000
\(935\) 0 0
\(936\) 2.00000 2.00000
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(942\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(943\) 0 0
\(944\) 2.00000 2.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(954\) 0 0
\(955\) −0.500000 0.866025i −0.500000 0.866025i
\(956\) −1.00000 −1.00000
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(961\) −0.500000 0.866025i −0.500000 0.866025i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(966\) 0 0
\(967\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 1.00000 1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(972\) −0.500000 0.866025i −0.500000 0.866025i
\(973\) 0 0
\(974\) 0.500000 0.866025i 0.500000 0.866025i
\(975\) 0 0
\(976\) 0.500000 0.866025i 0.500000 0.866025i
\(977\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1.00000 1.73205i 1.00000 1.73205i
\(989\) 0 0
\(990\) 0 0
\(991\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(997\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 3528.1.cw.a.2077.1 2
7.2 even 3 504.1.bn.b.349.1 yes 2
7.3 odd 6 3528.1.bp.b.1501.1 2
7.4 even 3 3528.1.bp.a.1501.1 2
7.5 odd 6 504.1.bn.a.349.1 yes 2
7.6 odd 2 3528.1.cw.b.2077.1 2
8.5 even 2 3528.1.cw.b.2077.1 2
9.4 even 3 3528.1.bp.a.3253.1 2
21.2 odd 6 1512.1.bn.a.181.1 2
21.5 even 6 1512.1.bn.b.181.1 2
28.19 even 6 2016.1.bv.b.1105.1 2
28.23 odd 6 2016.1.bv.a.1105.1 2
56.5 odd 6 504.1.bn.b.349.1 yes 2
56.13 odd 2 CM 3528.1.cw.a.2077.1 2
56.19 even 6 2016.1.bv.a.1105.1 2
56.37 even 6 504.1.bn.a.349.1 yes 2
56.45 odd 6 3528.1.bp.a.1501.1 2
56.51 odd 6 2016.1.bv.b.1105.1 2
56.53 even 6 3528.1.bp.b.1501.1 2
63.4 even 3 inner 3528.1.cw.a.2677.1 2
63.5 even 6 1512.1.bn.b.685.1 2
63.13 odd 6 3528.1.bp.b.3253.1 2
63.23 odd 6 1512.1.bn.a.685.1 2
63.31 odd 6 3528.1.cw.b.2677.1 2
63.40 odd 6 504.1.bn.a.13.1 2
63.58 even 3 504.1.bn.b.13.1 yes 2
72.13 even 6 3528.1.bp.b.3253.1 2
168.5 even 6 1512.1.bn.a.181.1 2
168.149 odd 6 1512.1.bn.b.181.1 2
252.103 even 6 2016.1.bv.b.1777.1 2
252.247 odd 6 2016.1.bv.a.1777.1 2
504.5 even 6 1512.1.bn.a.685.1 2
504.13 odd 6 3528.1.bp.a.3253.1 2
504.149 odd 6 1512.1.bn.b.685.1 2
504.157 odd 6 inner 3528.1.cw.a.2677.1 2
504.229 odd 6 504.1.bn.b.13.1 yes 2
504.355 even 6 2016.1.bv.a.1777.1 2
504.373 even 6 504.1.bn.a.13.1 2
504.445 even 6 3528.1.cw.b.2677.1 2
504.499 odd 6 2016.1.bv.b.1777.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.1.bn.a.13.1 2 63.40 odd 6
504.1.bn.a.13.1 2 504.373 even 6
504.1.bn.a.349.1 yes 2 7.5 odd 6
504.1.bn.a.349.1 yes 2 56.37 even 6
504.1.bn.b.13.1 yes 2 63.58 even 3
504.1.bn.b.13.1 yes 2 504.229 odd 6
504.1.bn.b.349.1 yes 2 7.2 even 3
504.1.bn.b.349.1 yes 2 56.5 odd 6
1512.1.bn.a.181.1 2 21.2 odd 6
1512.1.bn.a.181.1 2 168.5 even 6
1512.1.bn.a.685.1 2 63.23 odd 6
1512.1.bn.a.685.1 2 504.5 even 6
1512.1.bn.b.181.1 2 21.5 even 6
1512.1.bn.b.181.1 2 168.149 odd 6
1512.1.bn.b.685.1 2 63.5 even 6
1512.1.bn.b.685.1 2 504.149 odd 6
2016.1.bv.a.1105.1 2 28.23 odd 6
2016.1.bv.a.1105.1 2 56.19 even 6
2016.1.bv.a.1777.1 2 252.247 odd 6
2016.1.bv.a.1777.1 2 504.355 even 6
2016.1.bv.b.1105.1 2 28.19 even 6
2016.1.bv.b.1105.1 2 56.51 odd 6
2016.1.bv.b.1777.1 2 252.103 even 6
2016.1.bv.b.1777.1 2 504.499 odd 6
3528.1.bp.a.1501.1 2 7.4 even 3
3528.1.bp.a.1501.1 2 56.45 odd 6
3528.1.bp.a.3253.1 2 9.4 even 3
3528.1.bp.a.3253.1 2 504.13 odd 6
3528.1.bp.b.1501.1 2 7.3 odd 6
3528.1.bp.b.1501.1 2 56.53 even 6
3528.1.bp.b.3253.1 2 63.13 odd 6
3528.1.bp.b.3253.1 2 72.13 even 6
3528.1.cw.a.2077.1 2 1.1 even 1 trivial
3528.1.cw.a.2077.1 2 56.13 odd 2 CM
3528.1.cw.a.2677.1 2 63.4 even 3 inner
3528.1.cw.a.2677.1 2 504.157 odd 6 inner
3528.1.cw.b.2077.1 2 7.6 odd 2
3528.1.cw.b.2077.1 2 8.5 even 2
3528.1.cw.b.2677.1 2 63.31 odd 6
3528.1.cw.b.2677.1 2 504.445 even 6