Properties

Label 2520.1.ef.d.739.1
Level $2520$
Weight $1$
Character 2520.739
Analytic conductor $1.258$
Analytic rank $0$
Dimension $4$
Projective image $D_{6}$
CM discriminant -40
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2520,1,Mod(739,2520)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 0, 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("2520.739");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2520.ef (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: \(1.25764383184\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{6}\)
Projective field: Galois closure of 6.2.829785600.1

Embedding invariants

Embedding label 739.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 2520.739
Dual form 2520.1.ef.d.2179.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000i q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000i q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-0.866025 + 1.50000i) q^{11} -1.73205 q^{13} +(0.866025 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{19} +1.00000 q^{20} -1.73205 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.866025 - 1.50000i) q^{26} +(0.866025 + 0.500000i) q^{28} +(0.500000 - 0.866025i) q^{32} +(-0.866025 + 0.500000i) q^{35} +(-0.866025 - 1.50000i) q^{37} +(0.500000 - 0.866025i) q^{38} +(0.500000 + 0.866025i) q^{40} -1.73205 q^{41} +(-0.866025 - 1.50000i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(-0.500000 - 0.866025i) q^{47} -1.00000 q^{49} -1.00000 q^{50} +(0.866025 - 1.50000i) q^{52} +(-0.500000 + 0.866025i) q^{53} +1.73205 q^{55} +1.00000i q^{56} +1.00000 q^{64} +(0.866025 + 1.50000i) q^{65} +(-0.866025 - 0.500000i) q^{70} +(0.866025 - 1.50000i) q^{74} +1.00000 q^{76} +(1.50000 + 0.866025i) q^{77} +(-0.500000 + 0.866025i) q^{80} +(-0.866025 - 1.50000i) q^{82} +(0.866025 - 1.50000i) q^{88} +1.73205i q^{91} -1.00000 q^{92} +(0.500000 - 0.866025i) q^{94} +(-0.500000 + 0.866025i) q^{95} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} + 2 q^{10} - 2 q^{16} - 2 q^{19} + 4 q^{20} + 2 q^{23} - 2 q^{25} + 2 q^{32} + 2 q^{38} + 2 q^{40} - 2 q^{46} - 2 q^{47} - 4 q^{49} - 4 q^{50} - 2 q^{53} + 4 q^{64} + 4 q^{76} + 6 q^{77} - 2 q^{80} - 4 q^{92} + 2 q^{94} - 2 q^{95} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\)

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 0
\(4\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(5\) −0.500000 0.866025i −0.500000 0.866025i
\(6\) 0 0
\(7\) 1.00000i 1.00000i
\(8\) −1.00000 −1.00000
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.500000 0.866025i
\(11\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 0.866025 0.500000i 0.866025 0.500000i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(20\) 1.00000 1.00000
\(21\) 0 0
\(22\) −1.73205 −1.73205
\(23\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(26\) −0.866025 1.50000i −0.866025 1.50000i
\(27\) 0 0
\(28\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 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
\(35\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(36\) 0 0
\(37\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(38\) 0.500000 0.866025i 0.500000 0.866025i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(41\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −0.866025 1.50000i −0.866025 1.50000i
\(45\) 0 0
\(46\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(47\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −1.00000 −1.00000
\(50\) −1.00000 −1.00000
\(51\) 0 0
\(52\) 0.866025 1.50000i 0.866025 1.50000i
\(53\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 1.73205 1.73205
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(66\) 0 0
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −0.866025 0.500000i −0.866025 0.500000i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0.866025 1.50000i 0.866025 1.50000i
\(75\) 0 0
\(76\) 1.00000 1.00000
\(77\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(78\) 0 0
\(79\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(81\) 0 0
\(82\) −0.866025 1.50000i −0.866025 1.50000i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0.866025 1.50000i 0.866025 1.50000i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 0 0
\(91\) 1.73205i 1.73205i
\(92\) −1.00000 −1.00000
\(93\) 0 0
\(94\) 0.500000 0.866025i 0.500000 0.866025i
\(95\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 0.866025i −0.500000 0.866025i
\(99\) 0 0
\(100\) −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
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) 1.73205 1.73205
\(105\) 0 0
\(106\) −1.00000 −1.00000
\(107\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 0 0
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(111\) 0 0
\(112\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0.500000 0.866025i 0.500000 0.866025i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 1.73205i −1.00000 1.73205i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(128\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(129\) 0 0
\(130\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(131\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(140\) 1.00000i 1.00000i
\(141\) 0 0
\(142\) 0 0
\(143\) 1.50000 2.59808i 1.50000 2.59808i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 1.73205 1.73205
\(149\) 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 \(0.666667\pi\)
\(152\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(153\) 0 0
\(154\) 1.73205i 1.73205i
\(155\) 0 0
\(156\) 0 0
\(157\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −1.00000 −1.00000
\(161\) 0.866025 0.500000i 0.866025 0.500000i
\(162\) 0 0
\(163\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(164\) 0.866025 1.50000i 0.866025 1.50000i
\(165\) 0 0
\(166\) 0 0
\(167\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) 0 0
\(169\) 2.00000 2.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(176\) 1.73205 1.73205
\(177\) 0 0
\(178\) 0 0
\(179\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(183\) 0 0
\(184\) −0.500000 0.866025i −0.500000 0.866025i
\(185\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(186\) 0 0
\(187\) 0 0
\(188\) 1.00000 1.00000
\(189\) 0 0
\(190\) −1.00000 −1.00000
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 0 0
\(193\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.500000 0.866025i 0.500000 0.866025i
\(197\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) 0 0
\(199\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−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
\(205\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(206\) 0 0
\(207\) 0 0
\(208\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(209\) 1.73205 1.73205
\(210\) 0 0
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) −0.500000 0.866025i −0.500000 0.866025i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) −0.866025 0.500000i −0.866025 0.500000i
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0 0
\(229\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 1.00000 1.00000
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(242\) 1.00000 1.73205i 1.00000 1.73205i
\(243\) 0 0
\(244\) 0 0
\(245\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(246\) 0 0
\(247\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(248\) 0 0
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(251\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 0 0
\(253\) −1.73205 −1.73205
\(254\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(255\) 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
\(259\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(260\) −1.73205 −1.73205
\(261\) 0 0
\(262\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(263\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 1.00000 1.00000
\(266\) −0.866025 0.500000i −0.866025 0.500000i
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.866025 1.50000i −0.866025 1.50000i
\(276\) 0 0
\(277\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(278\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(279\) 0 0
\(280\) 0.866025 0.500000i 0.866025 0.500000i
\(281\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(282\) 0 0
\(283\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 3.00000 3.00000
\(287\) 1.73205i 1.73205i
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.500000 0.866025i
\(290\) 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 0
\(295\) 0 0
\(296\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(297\) 0 0
\(298\) 0 0
\(299\) −0.866025 1.50000i −0.866025 1.50000i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) −1.73205 −1.73205
\(315\) 0 0
\(316\) 0 0
\(317\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−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
\(322\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(323\) 0 0
\(324\) 0 0
\(325\) 0.866025 1.50000i 0.866025 1.50000i
\(326\) 0 0
\(327\) 0 0
\(328\) 1.73205 1.73205
\(329\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(330\) 0 0
\(331\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.500000 0.866025i −0.500000 0.866025i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) 0.500000 0.866025i 0.500000 0.866025i
\(347\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.00000i 1.00000i
\(351\) 0 0
\(352\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(353\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.73205 1.73205
\(359\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) −1.50000 0.866025i −1.50000 0.866025i
\(365\) 0 0
\(366\) 0 0
\(367\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(368\) 0.500000 0.866025i 0.500000 0.866025i
\(369\) 0 0
\(370\) −1.73205 −1.73205
\(371\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(372\) 0 0
\(373\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(377\) 0 0
\(378\) 0 0
\(379\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) −0.500000 0.866025i −0.500000 0.866025i
\(381\) 0 0
\(382\) 0 0
\(383\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 1.73205i 1.73205i
\(386\) 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
\(391\) 0 0
\(392\) 1.00000 1.00000
\(393\) 0 0
\(394\) −0.500000 0.866025i −0.500000 0.866025i
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.00000 3.00000
\(408\) 0 0
\(409\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(417\) 0 0
\(418\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(419\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −0.500000 0.866025i −0.500000 0.866025i
\(423\) 0 0
\(424\) 0.500000 0.866025i 0.500000 0.866025i
\(425\) 0 0
\(426\) 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 0
\(433\) 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 \(0.333333\pi\)
\(440\) −1.73205 −1.73205
\(441\) 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
\(448\) 1.00000i 1.00000i
\(449\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(450\) 0 0
\(451\) 1.50000 2.59808i 1.50000 2.59808i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.50000 0.866025i 1.50000 0.866025i
\(456\) 0 0
\(457\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.00000 −1.00000
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.00000 1.00000
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(482\) −1.00000 −1.00000
\(483\) 0 0
\(484\) 2.00000 2.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(501\) 0 0
\(502\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(503\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.866025 1.50000i −0.866025 1.50000i
\(507\) 0 0
\(508\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(509\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.73205 1.73205
\(518\) −1.50000 0.866025i −1.50000 0.866025i
\(519\) 0 0
\(520\) −0.866025 1.50000i −0.866025 1.50000i
\(521\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(522\) 0 0
\(523\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) −1.73205 −1.73205
\(525\) 0 0
\(526\) −2.00000 −2.00000
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(531\) 0 0
\(532\) 1.00000i 1.00000i
\(533\) 3.00000 3.00000
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.866025 1.50000i 0.866025 1.50000i
\(540\) 0 0
\(541\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0.866025 1.50000i 0.866025 1.50000i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(557\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(561\) 0 0
\(562\) −0.866025 1.50000i −0.866025 1.50000i
\(563\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(570\) 0 0
\(571\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(572\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(573\) 0 0
\(574\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(575\) −1.00000 −1.00000
\(576\) 0 0
\(577\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) 0.500000 0.866025i 0.500000 0.866025i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.866025 1.50000i −0.866025 1.50000i
\(584\) 0 0
\(585\) 0 0
\(586\) −0.500000 0.866025i −0.500000 0.866025i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(593\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.866025 1.50000i 0.866025 1.50000i
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(606\) 0 0
\(607\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(608\) −1.00000 −1.00000
\(609\) 0 0
\(610\) 0 0
\(611\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(612\) 0 0
\(613\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.50000 0.866025i −1.50000 0.866025i
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(620\) 0 0
\(621\) 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
\(628\) −0.866025 1.50000i −0.866025 1.50000i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 1.00000 1.73205i 1.00000 1.73205i
\(635\) −0.866025 1.50000i −0.866025 1.50000i
\(636\) 0 0
\(637\) 1.73205 1.73205
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.500000 0.866025i
\(641\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 1.00000i 1.00000i
\(645\) 0 0
\(646\) 0 0
\(647\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 1.73205 1.73205
\(651\) 0 0
\(652\) 0 0
\(653\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 0 0
\(655\) 0.866025 1.50000i 0.866025 1.50000i
\(656\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(657\) 0 0
\(658\) −0.866025 0.500000i −0.866025 0.500000i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0.500000 0.866025i 0.500000 0.866025i
\(663\) 0 0
\(664\) 0 0
\(665\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(666\) 0 0
\(667\) 0 0
\(668\) 0.500000 0.866025i 0.500000 0.866025i
\(669\) 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 0
\(676\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(677\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(687\) 0 0
\(688\) 0 0
\(689\) 0.866025 1.50000i 0.866025 1.50000i
\(690\) 0 0
\(691\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(692\) 1.00000 1.00000
\(693\) 0 0
\(694\) 0 0
\(695\) −1.00000 1.73205i −1.00000 1.73205i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(704\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −3.00000 −3.00000
\(716\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(728\) 1.73205i 1.73205i
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(734\) 1.73205 1.73205
\(735\) 0 0
\(736\) 1.00000 1.00000
\(737\) 0 0
\(738\) 0 0
\(739\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(740\) −0.866025 1.50000i −0.866025 1.50000i
\(741\) 0 0
\(742\) 1.00000i 1.00000i
\(743\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) −0.500000 0.866025i −0.500000 0.866025i
\(759\) 0 0
\(760\) 0.500000 0.866025i 0.500000 0.866025i
\(761\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.500000 0.866025i 0.500000 0.866025i
\(767\) 0 0
\(768\) 0 0
\(769\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 1.50000 0.866025i 1.50000 0.866025i
\(771\) 0 0
\(772\) 0 0
\(773\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(785\) 1.73205 1.73205
\(786\) 0 0
\(787\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(788\) 0.500000 0.866025i 0.500000 0.866025i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(801\) 0 0
\(802\) 0.866025 1.50000i 0.866025 1.50000i
\(803\) 0 0
\(804\) 0 0
\(805\) −0.866025 0.500000i −0.866025 0.500000i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(810\) 0 0
\(811\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −2.00000 −2.00000
\(819\) 0 0
\(820\) −1.73205 −1.73205
\(821\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(822\) 0 0
\(823\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.73205 −1.73205
\(833\) 0 0
\(834\) 0 0
\(835\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(836\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(837\) 0 0
\(838\) −0.866025 1.50000i −0.866025 1.50000i
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0.500000 0.866025i 0.500000 0.866025i
\(845\) −1.00000 1.73205i −1.00000 1.73205i
\(846\) 0 0
\(847\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(848\) 1.00000 1.00000
\(849\) 0 0
\(850\) 0 0
\(851\) 0.866025 1.50000i 0.866025 1.50000i
\(852\) 0 0
\(853\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(858\) 0 0
\(859\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(864\) 0 0
\(865\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 1.00000 1.00000
\(875\) 1.00000i 1.00000i
\(876\) 0 0
\(877\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −0.866025 1.50000i −0.866025 1.50000i
\(881\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(888\) 0 0
\(889\) 1.73205i 1.73205i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(894\) 0 0
\(895\) −1.73205 −1.73205
\(896\) 0.866025 0.500000i 0.866025 0.500000i
\(897\) 0 0
\(898\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 3.00000 3.00000
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 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
\(910\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.50000 0.866025i 1.50000 0.866025i
\(918\) 0 0
\(919\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(920\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.73205 1.73205
\(926\) −0.866025 1.50000i −0.866025 1.50000i
\(927\) 0 0
\(928\) 0 0
\(929\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −0.500000 0.866025i −0.500000 0.866025i
\(941\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(942\) 0 0
\(943\) −0.866025 1.50000i −0.866025 1.50000i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.500000 0.866025i −0.500000 0.866025i
\(962\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(963\) 0 0
\(964\) −0.500000 0.866025i −0.500000 0.866025i
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(969\) 0 0
\(970\) 0 0
\(971\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 2.00000i 2.00000i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −1.00000 −1.00000
\(981\) 0 0
\(982\) 0 0
\(983\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(986\) 0 0
\(987\) 0 0
\(988\) −1.73205 −1.73205
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(998\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(999\) 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 2520.1.ef.d.739.1 yes 4
3.2 odd 2 2520.1.ef.c.739.1 4
5.4 even 2 2520.1.ef.c.739.2 yes 4
7.2 even 3 inner 2520.1.ef.d.2179.2 yes 4
8.3 odd 2 2520.1.ef.c.739.2 yes 4
15.14 odd 2 inner 2520.1.ef.d.739.2 yes 4
21.2 odd 6 2520.1.ef.c.2179.2 yes 4
24.11 even 2 inner 2520.1.ef.d.739.2 yes 4
35.9 even 6 2520.1.ef.c.2179.1 yes 4
40.19 odd 2 CM 2520.1.ef.d.739.1 yes 4
56.51 odd 6 2520.1.ef.c.2179.1 yes 4
105.44 odd 6 inner 2520.1.ef.d.2179.1 yes 4
120.59 even 2 2520.1.ef.c.739.1 4
168.107 even 6 inner 2520.1.ef.d.2179.1 yes 4
280.219 odd 6 inner 2520.1.ef.d.2179.2 yes 4
840.779 even 6 2520.1.ef.c.2179.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2520.1.ef.c.739.1 4 3.2 odd 2
2520.1.ef.c.739.1 4 120.59 even 2
2520.1.ef.c.739.2 yes 4 5.4 even 2
2520.1.ef.c.739.2 yes 4 8.3 odd 2
2520.1.ef.c.2179.1 yes 4 35.9 even 6
2520.1.ef.c.2179.1 yes 4 56.51 odd 6
2520.1.ef.c.2179.2 yes 4 21.2 odd 6
2520.1.ef.c.2179.2 yes 4 840.779 even 6
2520.1.ef.d.739.1 yes 4 1.1 even 1 trivial
2520.1.ef.d.739.1 yes 4 40.19 odd 2 CM
2520.1.ef.d.739.2 yes 4 15.14 odd 2 inner
2520.1.ef.d.739.2 yes 4 24.11 even 2 inner
2520.1.ef.d.2179.1 yes 4 105.44 odd 6 inner
2520.1.ef.d.2179.1 yes 4 168.107 even 6 inner
2520.1.ef.d.2179.2 yes 4 7.2 even 3 inner
2520.1.ef.d.2179.2 yes 4 280.219 odd 6 inner