Properties

Label 495.1.o.a.439.1
Level $495$
Weight $1$
Character 495.439
Analytic conductor $0.247$
Analytic rank $0$
Dimension $2$
Projective image $D_{6}$
CM discriminant -11
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [495,1,Mod(274,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3, 3]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.274");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 495.o (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: \(0.247037181253\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{6}\)
Projective field: Galois closure of 6.2.99235125.1

Embedding invariants

Embedding label 439.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 495.439
Dual form 495.1.o.a.274.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{20} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{31} -1.00000 q^{33} -1.00000 q^{36} +1.73205i q^{37} +1.00000 q^{44} +(0.500000 + 0.866025i) q^{45} +(-1.50000 - 0.866025i) q^{47} +1.00000 q^{48} +(0.500000 + 0.866025i) q^{49} +1.73205i q^{53} +(-0.500000 - 0.866025i) q^{55} +(0.500000 + 0.866025i) q^{59} +(-0.500000 - 0.866025i) q^{60} -1.00000 q^{64} +(-1.50000 + 0.866025i) q^{67} -1.00000 q^{71} +(-0.500000 + 0.866025i) q^{75} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.00000 q^{89} +(-0.500000 + 0.866025i) q^{93} +(1.50000 + 0.866025i) q^{97} +(0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} + q^{4} + q^{5} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} + q^{4} + q^{5} - q^{9} + q^{11} + q^{12} - 2 q^{15} - q^{16} + 2 q^{20} - q^{25} + 2 q^{27} - q^{31} - 2 q^{33} - 2 q^{36} + 2 q^{44} + q^{45} - 3 q^{47} + 2 q^{48} + q^{49} - q^{55} + q^{59} - q^{60} - 2 q^{64} - 3 q^{67} - 2 q^{71} - q^{75} + q^{80} - q^{81} - 4 q^{89} - q^{93} + 3 q^{97} + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) −0.500000 0.866025i −0.500000 0.866025i
\(4\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(5\) 0.500000 0.866025i 0.500000 0.866025i
\(6\) 0 0
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.500000 0.866025i
\(12\) 0.500000 0.866025i 0.500000 0.866025i
\(13\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 0 0
\(15\) −1.00000 −1.00000
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.00000 1.00000
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0 0
\(25\) −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 \(0.666667\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) −1.00000 −1.00000
\(34\) 0 0
\(35\) 0 0
\(36\) −1.00000 −1.00000
\(37\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(42\) 0 0
\(43\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(44\) 1.00000 1.00000
\(45\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(46\) 0 0
\(47\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(48\) 1.00000 1.00000
\(49\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0 0
\(55\) −0.500000 0.866025i −0.500000 0.866025i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) −0.500000 0.866025i −0.500000 0.866025i
\(61\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−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
\(83\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) 0 0
\(99\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(100\) 0.500000 0.866025i 0.500000 0.866025i
\(101\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 1.50000 0.866025i 1.50000 0.866025i
\(112\) 0 0
\(113\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.500000 0.866025i 0.500000 0.866025i
\(125\) −1.00000 −1.00000
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(132\) −0.500000 0.866025i −0.500000 0.866025i
\(133\) 0 0
\(134\) 0 0
\(135\) 0.500000 0.866025i 0.500000 0.866025i
\(136\) 0 0
\(137\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(140\) 0 0
\(141\) 1.73205i 1.73205i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.500000 0.866025i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.500000 0.866025i 0.500000 0.866025i
\(148\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.00000 −1.00000
\(156\) 0 0
\(157\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(158\) 0 0
\(159\) 1.50000 0.866025i 1.50000 0.866025i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(164\) 0 0
\(165\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(166\) 0 0
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 0.500000 0.866025i 0.500000 0.866025i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(177\) 0.500000 0.866025i 0.500000 0.866025i
\(178\) 0 0
\(179\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
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 \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(186\) 0 0
\(187\) 0 0
\(188\) 1.73205i 1.73205i
\(189\) 0 0
\(190\) 0 0
\(191\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(192\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(193\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 0 0
\(201\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(213\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.500000 0.866025i 0.500000 0.866025i
\(221\) 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
\(225\) 1.00000 1.00000
\(226\) 0 0
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(236\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0.500000 0.866025i 0.500000 0.866025i
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(244\) 0 0
\(245\) 1.00000 1.00000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(266\) 0 0
\(267\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(268\) −1.50000 0.866025i −1.50000 0.866025i
\(269\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 −1.00000
\(276\) 0 0
\(277\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(278\) 0 0
\(279\) 1.00000 1.00000
\(280\) 0 0
\(281\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 0 0
\(283\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) −0.500000 0.866025i −0.500000 0.866025i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 1.73205i 1.73205i
\(292\) 0 0
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) 0 0
\(295\) 1.00000 1.00000
\(296\) 0 0
\(297\) 0.500000 0.866025i 0.500000 0.866025i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.00000 −1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) −1.50000 0.866025i −1.50000 0.866025i
\(310\) 0 0
\(311\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 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 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 0.866025i 0.500000 0.866025i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −1.50000 0.866025i −1.50000 0.866025i
\(334\) 0 0
\(335\) 1.73205i 1.73205i
\(336\) 0 0
\(337\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(338\) 0 0
\(339\) −1.50000 0.866025i −1.50000 0.866025i
\(340\) 0 0
\(341\) −1.00000 −1.00000
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(356\) −1.00000 1.73205i −1.00000 1.73205i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.00000 −1.00000
\(373\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(376\) 0 0
\(377\) 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
\(383\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.73205i 1.73205i
\(389\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(397\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(408\) 0 0
\(409\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) 0 0
\(411\) 1.73205i 1.73205i
\(412\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 1.50000 0.866025i 1.50000 0.866025i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −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 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(445\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 0 0
\(463\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(464\) 0 0
\(465\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(466\) 0 0
\(467\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.50000 0.866025i −1.50000 0.866025i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.50000 0.866025i −1.50000 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
\(482\) 0 0
\(483\) 0 0
\(484\) 0.500000 0.866025i 0.500000 0.866025i
\(485\) 1.50000 0.866025i 1.50000 0.866025i
\(486\) 0 0
\(487\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(488\) 0 0
\(489\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(490\) 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
\(494\) 0 0
\(495\) 1.00000 1.00000
\(496\) 1.00000 1.00000
\(497\) 0 0
\(498\) 0 0
\(499\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −0.500000 0.866025i −0.500000 0.866025i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) 0 0
\(509\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.73205i 1.73205i
\(516\) 0 0
\(517\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.500000 0.866025i 0.500000 0.866025i
\(529\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) −1.00000 −1.00000
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.500000 0.866025i −0.500000 0.866025i
\(538\) 0 0
\(539\) 1.00000 1.00000
\(540\) 1.00000 1.00000
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −0.500000 0.866025i −0.500000 0.866025i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(548\) 1.73205i 1.73205i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.73205i 1.73205i
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(565\) 1.73205i 1.73205i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(572\) 0 0
\(573\) 1.00000 1.00000
\(574\) 0 0
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.500000 0.866025i
\(577\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 1.00000 1.00000
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.50000 0.866025i −1.50000 0.866025i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(598\) 0 0
\(599\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 1.73205i 1.73205i
\(604\) 0 0
\(605\) −1.00000 −1.00000
\(606\) 0 0
\(607\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(618\) 0 0
\(619\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(620\) −0.500000 0.866025i −0.500000 0.866025i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.50000 + 0.866025i 1.50000 + 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 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(637\) 0 0
\(638\) 0 0
\(639\) 0.500000 0.866025i 0.500000 0.866025i
\(640\) 0 0
\(641\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(642\) 0 0
\(643\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 1.00000 1.00000
\(650\) 0 0
\(651\) 0 0
\(652\) 1.50000 0.866025i 1.50000 0.866025i
\(653\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 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 \(0.666667\pi\)
\(660\) −1.00000 −1.00000
\(661\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 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 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(674\) 0 0
\(675\) −0.500000 0.866025i −0.500000 0.866025i
\(676\) 1.00000 1.00000
\(677\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(686\) 0 0
\(687\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(705\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(706\) 0 0
\(707\) 0 0
\(708\) 1.00000 1.00000
\(709\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(717\) 0 0
\(718\) 0 0
\(719\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) −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 0
\(727\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(734\) 0 0
\(735\) −0.500000 0.866025i −0.500000 0.866025i
\(736\) 0 0
\(737\) 1.73205i 1.73205i
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 1.73205i 1.73205i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 1.50000 0.866025i 1.50000 0.866025i
\(753\) −1.00000 1.73205i −1.00000 1.73205i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.00000 −1.00000
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(769\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 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
\(781\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(782\) 0 0
\(783\) 0 0
\(784\) −1.00000 −1.00000
\(785\) 1.73205i 1.73205i
\(786\) 0 0
\(787\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.73205i 1.73205i
\(796\) −0.500000 0.866025i −0.500000 0.866025i
\(797\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 1.00000 1.73205i 1.00000 1.73205i
\(802\) 0 0
\(803\) 0 0
\(804\) 1.73205i 1.73205i
\(805\) 0 0
\(806\) 0 0
\(807\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.50000 0.866025i −1.50000 0.866025i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) 0 0
\(823\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(824\) 0 0
\(825\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −0.500000 0.866025i −0.500000 0.866025i
\(838\) 0 0
\(839\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(840\) 0 0
\(841\) −0.500000 0.866025i −0.500000 0.866025i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.500000 0.866025i −0.500000 0.866025i
\(846\) 0 0
\(847\) 0 0
\(848\) −1.50000 0.866025i −1.50000 0.866025i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(853\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(858\) 0 0
\(859\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 1.00000 1.00000
\(881\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) 0 0
\(883\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 0 0
\(885\) −0.500000 0.866025i −0.500000 0.866025i
\(886\) 0 0
\(887\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.00000 −1.00000
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0.500000 0.866025i 0.500000 0.866025i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.500000 0.866025i 0.500000 0.866025i
\(906\) 0 0
\(907\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.00000 1.73205i 1.00000 1.73205i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.50000 0.866025i 1.50000 0.866025i
\(926\) 0 0
\(927\) 1.73205i 1.73205i
\(928\) 0 0
\(929\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.500000 0.866025i 0.500000 0.866025i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −1.50000 0.866025i −1.50000 0.866025i
\(941\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.00000 1.00000
\(961\) 0 0
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(972\) −1.00000 −1.00000
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(978\) 0 0
\(979\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(980\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(981\) 0 0
\(982\) 0 0
\(983\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 1.00000 1.00000
\(994\) 0 0
\(995\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(996\) 0 0
\(997\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(998\) 0 0
\(999\) 1.73205i 1.73205i
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 495.1.o.a.439.1 yes 2
3.2 odd 2 1485.1.o.a.1099.1 2
5.2 odd 4 2475.1.y.b.1726.1 4
5.3 odd 4 2475.1.y.b.1726.2 4
5.4 even 2 495.1.o.b.439.1 yes 2
9.4 even 3 495.1.o.b.274.1 yes 2
9.5 odd 6 1485.1.o.b.604.1 2
11.10 odd 2 CM 495.1.o.a.439.1 yes 2
15.14 odd 2 1485.1.o.b.1099.1 2
33.32 even 2 1485.1.o.a.1099.1 2
45.4 even 6 inner 495.1.o.a.274.1 2
45.13 odd 12 2475.1.y.b.76.2 4
45.14 odd 6 1485.1.o.a.604.1 2
45.22 odd 12 2475.1.y.b.76.1 4
55.32 even 4 2475.1.y.b.1726.1 4
55.43 even 4 2475.1.y.b.1726.2 4
55.54 odd 2 495.1.o.b.439.1 yes 2
99.32 even 6 1485.1.o.b.604.1 2
99.76 odd 6 495.1.o.b.274.1 yes 2
165.164 even 2 1485.1.o.b.1099.1 2
495.274 odd 6 inner 495.1.o.a.274.1 2
495.329 even 6 1485.1.o.a.604.1 2
495.373 even 12 2475.1.y.b.76.2 4
495.472 even 12 2475.1.y.b.76.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
495.1.o.a.274.1 2 45.4 even 6 inner
495.1.o.a.274.1 2 495.274 odd 6 inner
495.1.o.a.439.1 yes 2 1.1 even 1 trivial
495.1.o.a.439.1 yes 2 11.10 odd 2 CM
495.1.o.b.274.1 yes 2 9.4 even 3
495.1.o.b.274.1 yes 2 99.76 odd 6
495.1.o.b.439.1 yes 2 5.4 even 2
495.1.o.b.439.1 yes 2 55.54 odd 2
1485.1.o.a.604.1 2 45.14 odd 6
1485.1.o.a.604.1 2 495.329 even 6
1485.1.o.a.1099.1 2 3.2 odd 2
1485.1.o.a.1099.1 2 33.32 even 2
1485.1.o.b.604.1 2 9.5 odd 6
1485.1.o.b.604.1 2 99.32 even 6
1485.1.o.b.1099.1 2 15.14 odd 2
1485.1.o.b.1099.1 2 165.164 even 2
2475.1.y.b.76.1 4 45.22 odd 12
2475.1.y.b.76.1 4 495.472 even 12
2475.1.y.b.76.2 4 45.13 odd 12
2475.1.y.b.76.2 4 495.373 even 12
2475.1.y.b.1726.1 4 5.2 odd 4
2475.1.y.b.1726.1 4 55.32 even 4
2475.1.y.b.1726.2 4 5.3 odd 4
2475.1.y.b.1726.2 4 55.43 even 4