Properties

Label 285.1.n.b.254.1
Level $285$
Weight $1$
Character 285.254
Analytic conductor $0.142$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -15
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [285,1,Mod(239,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.239");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 285.n (of order \(6\), degree \(2\), 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: \(0.142233528600\)
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: yes
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.5415.1
Artin image: $C_3\times S_3$
Artin field: Galois closure of 6.0.1218375.1

Embedding invariants

Embedding label 254.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 285.254
Dual form 285.1.n.b.239.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} -1.00000 q^{18} +(-0.500000 - 0.866025i) q^{19} +(-1.00000 + 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -1.00000 q^{30} -1.00000 q^{31} +(-0.500000 + 0.866025i) q^{34} +(0.500000 - 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{40} +1.00000 q^{45} -2.00000 q^{46} +(0.500000 - 0.866025i) q^{47} +(0.500000 - 0.866025i) q^{48} +1.00000 q^{49} -1.00000 q^{50} +(0.500000 - 0.866025i) q^{51} +(0.500000 - 0.866025i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.500000 + 0.866025i) q^{57} +(-1.00000 + 1.73205i) q^{61} +(-0.500000 - 0.866025i) q^{62} +1.00000 q^{64} +2.00000 q^{69} +(-0.500000 + 0.866025i) q^{72} +1.00000 q^{75} +(-1.00000 - 1.73205i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} -1.00000 q^{83} +(0.500000 - 0.866025i) q^{85} +(0.500000 + 0.866025i) q^{90} +(0.500000 + 0.866025i) q^{93} +1.00000 q^{94} +(-0.500000 + 0.866025i) q^{95} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{5} + q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{3} - q^{5} + q^{6} + 2 q^{8} - q^{9} + q^{10} - q^{15} + q^{16} + q^{17} - 2 q^{18} - q^{19} - 2 q^{23} - q^{24} - q^{25} + 2 q^{27} - 2 q^{30} - 2 q^{31} - q^{34} + q^{38} - q^{40} + 2 q^{45} - 4 q^{46} + q^{47} + q^{48} + 2 q^{49} - 2 q^{50} + q^{51} + q^{53} + q^{54} - q^{57} - 2 q^{61} - q^{62} + 2 q^{64} + 4 q^{69} - q^{72} + 2 q^{75} - 2 q^{79} + q^{80} - q^{81} - 2 q^{83} + q^{85} + q^{90} + q^{93} + 2 q^{94} - q^{95} + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(211\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



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 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) −0.500000 0.866025i −0.500000 0.866025i
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.500000 0.866025i
\(6\) 0.500000 0.866025i 0.500000 0.866025i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 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 \(\pi\)
\(12\) 0 0
\(13\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−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
\(17\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) −1.00000 −1.00000
\(19\) −0.500000 0.866025i −0.500000 0.866025i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.500000 0.866025i −0.500000 0.866025i
\(25\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(26\) 0 0
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) −1.00000 −1.00000
\(31\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0.500000 0.866025i 0.500000 0.866025i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.500000 0.866025i
\(41\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 0 0
\(45\) 1.00000 1.00000
\(46\) −2.00000 −2.00000
\(47\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(48\) 0.500000 0.866025i 0.500000 0.866025i
\(49\) 1.00000 1.00000
\(50\) −1.00000 −1.00000
\(51\) 0.500000 0.866025i 0.500000 0.866025i
\(52\) 0 0
\(53\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(54\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(58\) 0 0
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) 0 0
\(61\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) −0.500000 0.866025i −0.500000 0.866025i
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 2.00000 2.00000
\(70\) 0 0
\(71\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(72\) −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
\(75\) 1.00000 1.00000
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−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 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0 0
\(85\) 0.500000 0.866025i 0.500000 0.866025i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(91\) 0 0
\(92\) 0 0
\(93\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(94\) 1.00000 1.00000
\(95\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(96\) 0 0
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 1.00000 1.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.00000 1.00000
\(107\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −1.00000 −1.00000
\(115\) 2.00000 2.00000
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(121\) 1.00000 1.00000
\(122\) −2.00000 −2.00000
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.500000 0.866025i −0.500000 0.866025i
\(136\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(137\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(138\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(139\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(140\) 0 0
\(141\) −1.00000 −1.00000
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −0.500000 0.866025i −0.500000 0.866025i
\(148\) 0 0
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(151\) −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
\(153\) −1.00000 −1.00000
\(154\) 0 0
\(155\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(156\) 0 0
\(157\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) 1.00000 1.73205i 1.00000 1.73205i
\(159\) −1.00000 −1.00000
\(160\) 0 0
\(161\) 0 0
\(162\) 0.500000 0.866025i 0.500000 0.866025i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.500000 0.866025i −0.500000 0.866025i
\(167\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.500000 0.866025i
\(170\) 1.00000 1.00000
\(171\) 1.00000 1.00000
\(172\) 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
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(182\) 0 0
\(183\) 2.00000 2.00000
\(184\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(185\) 0 0
\(186\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −1.00000 −1.00000
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −0.500000 0.866025i −0.500000 0.866025i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) 0 0
\(199\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.00000 1.73205i −1.00000 1.73205i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.500000 0.866025i −0.500000 0.866025i
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(224\) 0 0
\(225\) −0.500000 0.866025i −0.500000 0.866025i
\(226\) −0.500000 0.866025i −0.500000 0.866025i
\(227\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(228\) 0 0
\(229\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(231\) 0 0
\(232\) 0 0
\(233\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) −1.00000 −1.00000
\(236\) 0 0
\(237\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −1.00000 −1.00000
\(241\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(242\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(243\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(244\) 0 0
\(245\) −0.500000 0.866025i −0.500000 0.866025i
\(246\) 0 0
\(247\) 0 0
\(248\) −1.00000 −1.00000
\(249\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(250\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(251\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −1.00000 −1.00000
\(256\) 0 0
\(257\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) −1.00000 −1.00000
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(270\) 0.500000 0.866025i 0.500000 0.866025i
\(271\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(273\) 0 0
\(274\) 1.00000 1.00000
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 1.00000 1.00000
\(279\) 0.500000 0.866025i 0.500000 0.866025i
\(280\) 0 0
\(281\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) −0.500000 0.866025i −0.500000 0.866025i
\(283\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(284\) 0 0
\(285\) 1.00000 1.00000
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0.500000 0.866025i 0.500000 0.866025i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −0.500000 0.866025i −0.500000 0.866025i
\(303\) 0 0
\(304\) 0.500000 0.866025i 0.500000 0.866025i
\(305\) 2.00000 2.00000
\(306\) −0.500000 0.866025i −0.500000 0.866025i
\(307\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(318\) −0.500000 0.866025i −0.500000 0.866025i
\(319\) 0 0
\(320\) −0.500000 0.866025i −0.500000 0.866025i
\(321\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(322\) 0 0
\(323\) 0.500000 0.866025i 0.500000 0.866025i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0.500000 0.866025i 0.500000 0.866025i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.00000 1.00000
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(338\) 0.500000 0.866025i 0.500000 0.866025i
\(339\) 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
\(345\) −1.00000 1.73205i −1.00000 1.73205i
\(346\) 1.00000 1.73205i 1.00000 1.73205i
\(347\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 1.00000 1.00000
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) 1.00000 1.00000
\(363\) −0.500000 0.866025i −0.500000 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(367\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) −2.00000 −2.00000
\(369\) 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
\(376\) 0.500000 0.866025i 0.500000 0.866025i
\(377\) 0 0
\(378\) 0 0
\(379\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 0.500000 0.866025i 0.500000 0.866025i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) −2.00000 −2.00000
\(392\) 1.00000 1.00000
\(393\) 0 0
\(394\) −0.500000 0.866025i −0.500000 0.866025i
\(395\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(396\) 0 0
\(397\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(398\) −2.00000 −2.00000
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(406\) 0 0
\(407\) 0 0
\(408\) 0.500000 0.866025i 0.500000 0.866025i
\(409\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) −1.00000 −1.00000
\(412\) 0 0
\(413\) 0 0
\(414\) 1.00000 1.73205i 1.00000 1.73205i
\(415\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(416\) 0 0
\(417\) −1.00000 −1.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(422\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(423\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(424\) 0.500000 0.866025i 0.500000 0.866025i
\(425\) −1.00000 −1.00000
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(433\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.00000 2.00000
\(438\) 0 0
\(439\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(442\) 0 0
\(443\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0.500000 0.866025i 0.500000 0.866025i
\(451\) 0 0
\(452\) 0 0
\(453\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(454\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(455\) 0 0
\(456\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −0.500000 0.866025i −0.500000 0.866025i
\(459\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(460\) 0 0
\(461\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0.500000 0.866025i 0.500000 0.866025i
\(466\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(467\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.500000 0.866025i −0.500000 0.866025i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) −2.00000 −2.00000
\(475\) 1.00000 1.00000
\(476\) 0 0
\(477\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.00000 1.00000
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) −1.00000 −1.00000
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(489\) 0 0
\(490\) 0.500000 0.866025i 0.500000 0.866025i
\(491\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.500000 0.866025i −0.500000 0.866025i
\(497\) 0 0
\(498\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(499\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) −1.00000 −1.00000
\(502\) 0 0
\(503\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) −0.500000 0.866025i −0.500000 0.866025i
\(511\) 0 0
\(512\) 1.00000 1.00000
\(513\) −0.500000 0.866025i −0.500000 0.866025i
\(514\) −2.00000 −2.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(527\) −0.500000 0.866025i −0.500000 0.866025i
\(528\) 0 0
\(529\) −1.50000 2.59808i −1.50000 2.59808i
\(530\) −0.500000 0.866025i −0.500000 0.866025i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(542\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(543\) −1.00000 −1.00000
\(544\) 0 0
\(545\) 0.500000 0.866025i 0.500000 0.866025i
\(546\) 0 0
\(547\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 0 0
\(549\) −1.00000 1.73205i −1.00000 1.73205i
\(550\) 0 0
\(551\) 0 0
\(552\) 2.00000 2.00000
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 1.00000 1.00000
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 1.73205i −1.00000 1.73205i
\(576\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −0.500000 0.866025i −0.500000 0.866025i
\(587\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 0 0
\(589\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(590\) 0 0
\(591\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(592\) 0 0
\(593\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.00000 2.00000
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 1.00000 1.00000
\(601\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.500000 0.866025i −0.500000 0.866025i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(618\) 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 + 1.73205i −1.00000 + 1.73205i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.500000 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(632\) −1.00000 1.73205i −1.00000 1.73205i
\(633\) 0.500000 0.866025i 0.500000 0.866025i
\(634\) 1.00000 1.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.500000 0.866025i
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(643\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.00000 1.00000
\(647\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) −0.500000 0.866025i −0.500000 0.866025i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(654\) 1.00000 1.00000
\(655\) 0 0
\(656\) 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 \(0\)
\(662\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(663\) 0 0
\(664\) −1.00000 −1.00000
\(665\) 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 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(676\) 0 0
\(677\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(679\) 0 0
\(680\) 0.500000 0.866025i 0.500000 0.866025i
\(681\) −1.00000 1.73205i −1.00000 1.73205i
\(682\) 0 0
\(683\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) −1.00000 −1.00000
\(686\) 0 0
\(687\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(688\) 0 0
\(689\) 0 0
\(690\) 1.00000 1.73205i 1.00000 1.73205i
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(695\) −1.00000 −1.00000
\(696\) 0 0
\(697\) 0 0
\(698\) −0.500000 0.866025i −0.500000 0.866025i
\(699\) 0.500000 0.866025i 0.500000 0.866025i
\(700\) 0 0
\(701\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(706\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(710\) 0 0
\(711\) 2.00000 2.00000
\(712\) 0 0
\(713\) 1.00000 1.73205i 1.00000 1.73205i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(721\) 0 0
\(722\) −1.00000 −1.00000
\(723\) −1.00000 −1.00000
\(724\) 0 0
\(725\) 0 0
\(726\) 0.500000 0.866025i 0.500000 0.866025i
\(727\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(745\) 0 0
\(746\) 0 0
\(747\) 0.500000 0.866025i 0.500000 0.866025i
\(748\) 0 0
\(749\) 0 0
\(750\) 0.500000 0.866025i 0.500000 0.866025i
\(751\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(752\) 1.00000 1.00000
\(753\) 0 0
\(754\) 0 0
\(755\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(756\) 0 0
\(757\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(758\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(759\) 0 0
\(760\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(766\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(767\) 0 0
\(768\) 0 0
\(769\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 2.00000 2.00000
\(772\) 0 0
\(773\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0 0
\(775\) 0.500000 0.866025i 0.500000 0.866025i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −1.00000 1.73205i −1.00000 1.73205i
\(783\) 0 0
\(784\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0.500000 0.866025i 0.500000 0.866025i
\(790\) −2.00000 −2.00000
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(796\) 0 0
\(797\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 0 0
\(799\) 1.00000 1.00000
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −1.00000 −1.00000
\(811\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(812\) 0 0
\(813\) 0.500000 0.866025i 0.500000 0.866025i
\(814\) 0 0
\(815\) 0 0
\(816\) 1.00000 1.00000
\(817\) 0 0
\(818\) −2.00000 −2.00000
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) −0.500000 0.866025i −0.500000 0.866025i
\(823\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(828\) 0 0
\(829\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(831\) 0 0
\(832\) 0 0
\(833\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(834\) −0.500000 0.866025i −0.500000 0.866025i
\(835\) −1.00000 −1.00000
\(836\) 0 0
\(837\) −1.00000 −1.00000
\(838\) 0 0
\(839\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(840\) 0 0
\(841\) −0.500000 0.866025i −0.500000 0.866025i
\(842\) 1.00000 1.73205i 1.00000 1.73205i
\(843\) 0 0
\(844\) 0 0
\(845\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(846\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(847\) 0 0
\(848\) 1.00000 1.00000
\(849\) 0 0
\(850\) −0.500000 0.866025i −0.500000 0.866025i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(854\) 0 0
\(855\) −0.500000 0.866025i −0.500000 0.866025i
\(856\) −1.00000 −1.00000
\(857\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(858\) 0 0
\(859\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(864\) 0 0
\(865\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(873\) 0 0
\(874\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(878\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(879\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −1.00000 −1.00000
\(883\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.00000 1.00000
\(887\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.00000 −1.00000
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 1.00000 1.00000
\(902\) 0 0
\(903\) 0 0
\(904\) −1.00000 −1.00000
\(905\) −1.00000 −1.00000
\(906\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(907\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −1.00000 −1.00000
\(913\) 0 0
\(914\) 0 0
\(915\) −1.00000 1.73205i −1.00000 1.73205i
\(916\) 0 0
\(917\) 0 0
\(918\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(919\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(920\) 2.00000 2.00000
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(930\) 1.00000 1.00000
\(931\) −0.500000 0.866025i −0.500000 0.866025i
\(932\) 0 0
\(933\) 0 0
\(934\) −0.500000 0.866025i −0.500000 0.866025i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(951\) −1.00000 −1.00000
\(952\) 0 0
\(953\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(954\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(961\) 0 0
\(962\) 0 0
\(963\) 0.500000 0.866025i 0.500000 0.866025i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(968\) 1.00000 1.00000
\(969\) −1.00000 −1.00000
\(970\) 0 0
\(971\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −2.00000 −2.00000
\(977\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1.00000 −1.00000
\(982\) 0 0
\(983\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(984\) 0 0
\(985\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) 0 0
\(993\) −1.00000 1.73205i −1.00000 1.73205i
\(994\) 0 0
\(995\) 2.00000 2.00000
\(996\) 0 0
\(997\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(999\) 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 285.1.n.b.254.1 yes 2
3.2 odd 2 285.1.n.a.254.1 yes 2
5.2 odd 4 1425.1.t.b.26.1 4
5.3 odd 4 1425.1.t.b.26.2 4
5.4 even 2 285.1.n.a.254.1 yes 2
15.2 even 4 1425.1.t.b.26.2 4
15.8 even 4 1425.1.t.b.26.1 4
15.14 odd 2 CM 285.1.n.b.254.1 yes 2
19.11 even 3 inner 285.1.n.b.239.1 yes 2
57.11 odd 6 285.1.n.a.239.1 2
95.49 even 6 285.1.n.a.239.1 2
95.68 odd 12 1425.1.t.b.1151.1 4
95.87 odd 12 1425.1.t.b.1151.2 4
285.68 even 12 1425.1.t.b.1151.2 4
285.182 even 12 1425.1.t.b.1151.1 4
285.239 odd 6 inner 285.1.n.b.239.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.1.n.a.239.1 2 57.11 odd 6
285.1.n.a.239.1 2 95.49 even 6
285.1.n.a.254.1 yes 2 3.2 odd 2
285.1.n.a.254.1 yes 2 5.4 even 2
285.1.n.b.239.1 yes 2 19.11 even 3 inner
285.1.n.b.239.1 yes 2 285.239 odd 6 inner
285.1.n.b.254.1 yes 2 1.1 even 1 trivial
285.1.n.b.254.1 yes 2 15.14 odd 2 CM
1425.1.t.b.26.1 4 5.2 odd 4
1425.1.t.b.26.1 4 15.8 even 4
1425.1.t.b.26.2 4 5.3 odd 4
1425.1.t.b.26.2 4 15.2 even 4
1425.1.t.b.1151.1 4 95.68 odd 12
1425.1.t.b.1151.1 4 285.182 even 12
1425.1.t.b.1151.2 4 95.87 odd 12
1425.1.t.b.1151.2 4 285.68 even 12