Properties

Label 1148.1.o.a.655.1
Level $1148$
Weight $1$
Character 1148.655
Analytic conductor $0.573$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -164
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1148,1,Mod(163,1148)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1148.163");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1148.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: \(0.572926634503\)
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 3.1.8036.1

Embedding invariants

Embedding label 655.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1148.655
Dual form 1148.1.o.a.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{22} +(-0.500000 + 0.866025i) q^{24} -1.00000 q^{27} -1.00000 q^{28} +(0.500000 + 0.866025i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(-1.00000 - 1.73205i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(0.500000 + 0.866025i) q^{40} +1.00000 q^{41} +(0.500000 + 0.866025i) q^{42} +(-0.500000 - 0.866025i) q^{44} +(1.00000 + 1.73205i) q^{47} +1.00000 q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{54} -1.00000 q^{55} +(0.500000 + 0.866025i) q^{56} +1.00000 q^{57} +(0.500000 - 0.866025i) q^{60} +(0.500000 + 0.866025i) q^{61} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(1.00000 - 1.73205i) q^{67} +1.00000 q^{70} +1.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 + 1.73205i) q^{74} +1.00000 q^{76} -1.00000 q^{77} +(-0.500000 - 0.866025i) q^{79} +(0.500000 - 0.866025i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{82} +(0.500000 - 0.866025i) q^{84} +(-0.500000 + 0.866025i) q^{88} +(1.00000 - 1.73205i) q^{94} +(0.500000 - 0.866025i) q^{95} +(-0.500000 - 0.866025i) q^{96} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + q^{10} - q^{11} - q^{12} + q^{14} - 2 q^{15} - q^{16} - q^{19} - 2 q^{20} - 2 q^{21} + 2 q^{22} - q^{24} - 2 q^{27} - 2 q^{28} + q^{30} - q^{32} - q^{33} - q^{35} - 2 q^{37} - q^{38} + q^{40} + 2 q^{41} + q^{42} - q^{44} + 2 q^{47} + 2 q^{48} - q^{49} + q^{54} - 2 q^{55} + q^{56} + 2 q^{57} + q^{60} + q^{61} + 2 q^{64} - q^{66} + 2 q^{67} + 2 q^{70} + 2 q^{71} - 2 q^{73} - 2 q^{74} + 2 q^{76} - 2 q^{77} - q^{79} + q^{80} + q^{81} - q^{82} + q^{84} - q^{88} + 2 q^{94} + q^{95} - q^{96} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\)

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
\(3\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(4\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(5\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 1.00000 1.00000
\(7\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(8\) 1.00000 1.00000
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.500000 0.866025i
\(11\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(12\) −0.500000 0.866025i −0.500000 0.866025i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0.500000 0.866025i 0.500000 0.866025i
\(15\) −1.00000 −1.00000
\(16\) −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
\(21\) −1.00000 −1.00000
\(22\) 1.00000 1.00000
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) −1.00000 −1.00000
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(33\) −0.500000 0.866025i −0.500000 0.866025i
\(34\) 0 0
\(35\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(36\) 0 0
\(37\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(38\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(41\) 1.00000 1.00000
\(42\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −0.500000 0.866025i −0.500000 0.866025i
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 1.00000 1.00000
\(49\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(55\) −1.00000 −1.00000
\(56\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(57\) 1.00000 1.00000
\(58\) 0 0
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0.500000 0.866025i 0.500000 0.866025i
\(61\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(67\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.00000 1.00000
\(71\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(72\) 0 0
\(73\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(75\) 0 0
\(76\) 1.00000 1.00000
\(77\) −1.00000 −1.00000
\(78\) 0 0
\(79\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(80\) 0.500000 0.866025i 0.500000 0.866025i
\(81\) 0.500000 0.866025i 0.500000 0.866025i
\(82\) −0.500000 0.866025i −0.500000 0.866025i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0.500000 0.866025i 0.500000 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(89\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 1.00000 1.73205i 1.00000 1.73205i
\(95\) 0.500000 0.866025i 0.500000 0.866025i
\(96\) −0.500000 0.866025i −0.500000 0.866025i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000 1.00000
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) 0 0
\(105\) −0.500000 0.866025i −0.500000 0.866025i
\(106\) 0 0
\(107\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 0.500000 0.866025i 0.500000 0.866025i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(111\) 2.00000 2.00000
\(112\) 0.500000 0.866025i 0.500000 0.866025i
\(113\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −0.500000 0.866025i −0.500000 0.866025i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −1.00000 −1.00000
\(121\) 0 0
\(122\) 0.500000 0.866025i 0.500000 0.866025i
\(123\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −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 \(0.333333\pi\)
\(132\) 1.00000 1.00000
\(133\) 0.500000 0.866025i 0.500000 0.866025i
\(134\) −2.00000 −2.00000
\(135\) −0.500000 0.866025i −0.500000 0.866025i
\(136\) 0 0
\(137\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −0.500000 0.866025i −0.500000 0.866025i
\(141\) −2.00000 −2.00000
\(142\) −0.500000 0.866025i −0.500000 0.866025i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 2.00000 2.00000
\(147\) −0.500000 0.866025i −0.500000 0.866025i
\(148\) 2.00000 2.00000
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(152\) −0.500000 0.866025i −0.500000 0.866025i
\(153\) 0 0
\(154\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(159\) 0 0
\(160\) −1.00000 −1.00000
\(161\) 0 0
\(162\) −1.00000 −1.00000
\(163\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(164\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(165\) 0.500000 0.866025i 0.500000 0.866025i
\(166\) 0 0
\(167\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(168\) −1.00000 −1.00000
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 1.00000
\(177\) 0 0
\(178\) 0 0
\(179\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −1.00000 −1.00000
\(184\) 0 0
\(185\) 1.00000 1.73205i 1.00000 1.73205i
\(186\) 0 0
\(187\) 0 0
\(188\) −2.00000 −2.00000
\(189\) −0.500000 0.866025i −0.500000 0.866025i
\(190\) −1.00000 −1.00000
\(191\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(193\) 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
\(199\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(200\) 0 0
\(201\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.00000 1.00000
\(210\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(211\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(214\) 0 0
\(215\) 0 0
\(216\) −1.00000 −1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) −1.00000 1.73205i −1.00000 1.73205i
\(220\) 0.500000 0.866025i 0.500000 0.866025i
\(221\) 0 0
\(222\) −1.00000 1.73205i −1.00000 1.73205i
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −1.00000 −1.00000
\(225\) 0 0
\(226\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(227\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(228\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(229\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 0 0
\(231\) 0.500000 0.866025i 0.500000 0.866025i
\(232\) 0 0
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(236\) 0 0
\(237\) 1.00000 1.00000
\(238\) 0 0
\(239\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(241\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −1.00000 −1.00000
\(245\) −1.00000 −1.00000
\(246\) 1.00000 1.00000
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.500000 0.866025i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 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
\(259\) 1.00000 1.73205i 1.00000 1.73205i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(264\) −0.500000 0.866025i −0.500000 0.866025i
\(265\) 0 0
\(266\) −1.00000 −1.00000
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(269\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(270\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(271\) 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 0
\(276\) 0 0
\(277\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(278\) 0 0
\(279\) 0 0
\(280\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(283\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(285\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(286\) 0 0
\(287\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.500000 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 1.73205i −1.00000 1.73205i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(295\) 0 0
\(296\) −1.00000 1.73205i −1.00000 1.73205i
\(297\) 0.500000 0.866025i 0.500000 0.866025i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −2.00000 −2.00000
\(303\) 0 0
\(304\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(305\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0.500000 0.866025i 0.500000 0.866025i
\(309\) 0 0
\(310\) 0 0
\(311\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(312\) 0 0
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.00000 1.00000
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 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
\(328\) 1.00000 1.00000
\(329\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(330\) −1.00000 −1.00000
\(331\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(335\) 2.00000 2.00000
\(336\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(337\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) −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 0
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0.500000 0.866025i 0.500000 0.866025i
\(347\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.500000 0.866025i
\(353\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(354\) 0 0
\(355\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(356\) 0 0
\(357\) 0 0
\(358\) 1.00000 1.00000
\(359\) 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
\(364\) 0 0
\(365\) −2.00000 −2.00000
\(366\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(367\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −2.00000 −2.00000
\(371\) 0 0
\(372\) 0 0
\(373\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(376\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(377\) 0 0
\(378\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(381\) 0 0
\(382\) 1.00000 1.73205i 1.00000 1.73205i
\(383\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(384\) 1.00000 1.00000
\(385\) −0.500000 0.866025i −0.500000 0.866025i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(393\) 0 0
\(394\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(395\) 0.500000 0.866025i 0.500000 0.866025i
\(396\) 0 0
\(397\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(398\) −2.00000 −2.00000
\(399\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(400\) 0 0
\(401\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 1.00000 1.73205i 1.00000 1.73205i
\(403\) 0 0
\(404\) 0 0
\(405\) 1.00000 1.00000
\(406\) 0 0
\(407\) 2.00000 2.00000
\(408\) 0 0
\(409\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(410\) 0.500000 0.866025i 0.500000 0.866025i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −0.500000 0.866025i −0.500000 0.866025i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 1.00000 1.00000
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −0.500000 0.866025i −0.500000 0.866025i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 1.00000 1.00000
\(427\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(428\) 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
\(433\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(439\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(440\) −1.00000 −1.00000
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(452\) 0.500000 0.866025i 0.500000 0.866025i
\(453\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(454\) 1.00000 1.00000
\(455\) 0 0
\(456\) 1.00000 1.00000
\(457\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) −1.00000 −1.00000
\(463\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(464\) 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
\(469\) 2.00000 2.00000
\(470\) 2.00000 2.00000
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) −0.500000 0.866025i −0.500000 0.866025i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.500000 0.866025i −0.500000 0.866025i
\(479\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(480\) 0.500000 0.866025i 0.500000 0.866025i
\(481\) 0 0
\(482\) 2.00000 2.00000
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(489\) 0 0
\(490\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) −0.500000 0.866025i −0.500000 0.866025i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(498\) 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
\(501\) 1.00000 1.73205i 1.00000 1.73205i
\(502\) 0 0
\(503\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(504\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(510\) 0 0
\(511\) −2.00000 −2.00000
\(512\) 1.00000 1.00000
\(513\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2.00000 −2.00000
\(518\) −2.00000 −2.00000
\(519\) −1.00000 −1.00000
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −2.00000 −2.00000
\(527\) 0 0
\(528\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(529\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 1.00000 1.73205i 1.00000 1.73205i
\(537\) −0.500000 0.866025i −0.500000 0.866025i
\(538\) −1.00000 −1.00000
\(539\) −0.500000 0.866025i −0.500000 0.866025i
\(540\) 1.00000 1.00000
\(541\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0.500000 0.866025i 0.500000 0.866025i
\(554\) −1.00000 −1.00000
\(555\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(556\) 0 0
\(557\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.00000 1.00000
\(561\) 0 0
\(562\) 0 0
\(563\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(564\) 1.00000 1.73205i 1.00000 1.73205i
\(565\) −0.500000 0.866025i −0.500000 0.866025i
\(566\) 0 0
\(567\) 1.00000 1.00000
\(568\) 1.00000 1.00000
\(569\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(570\) 0.500000 0.866025i 0.500000 0.866025i
\(571\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) −2.00000 −2.00000
\(574\) 0.500000 0.866025i 0.500000 0.866025i
\(575\) 0 0
\(576\) 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 0
\(584\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 1.00000 1.00000
\(589\) 0 0
\(590\) 0 0
\(591\) 0.500000 0.866025i 0.500000 0.866025i
\(592\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(593\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(594\) −1.00000 −1.00000
\(595\) 0 0
\(596\) 0 0
\(597\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) 1.00000 1.00000
\(609\) 0 0
\(610\) 1.00000 1.00000
\(611\) 0 0
\(612\) 0 0
\(613\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(614\) 0 0
\(615\) −1.00000 −1.00000
\(616\) −1.00000 −1.00000
\(617\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 0 0
\(619\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −2.00000 −2.00000
\(623\) 0 0
\(624\) 0 0
\(625\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(626\) 0 0
\(627\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) −0.500000 0.866025i −0.500000 0.866025i
\(633\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(634\) 0 0
\(635\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−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
\(653\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.500000 0.866025i −0.500000 0.866025i
\(657\) 0 0
\(658\) 2.00000 2.00000
\(659\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(660\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(661\) 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
\(664\) 0 0
\(665\) 1.00000 1.00000
\(666\) 0 0
\(667\) 0 0
\(668\) 1.00000 1.73205i 1.00000 1.73205i
\(669\) 0 0
\(670\) −1.00000 1.73205i −1.00000 1.73205i
\(671\) −1.00000 −1.00000
\(672\) 0.500000 0.866025i 0.500000 0.866025i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(675\) 0 0
\(676\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(677\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) −1.00000 −1.00000
\(679\) 0 0
\(680\) 0 0
\(681\) −0.500000 0.866025i −0.500000 0.866025i
\(682\) 0 0
\(683\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(692\) −1.00000 −1.00000
\(693\) 0 0
\(694\) 1.00000 1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −1.00000 1.73205i −1.00000 1.73205i
\(699\) 0 0
\(700\) 0 0
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(704\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(705\) −1.00000 1.73205i −1.00000 1.73205i
\(706\) −1.00000 −1.00000
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0.500000 0.866025i 0.500000 0.866025i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.500000 0.866025i −0.500000 0.866025i
\(717\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(718\) 0 0
\(719\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −1.00000 1.73205i −1.00000 1.73205i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(731\) 0 0
\(732\) 0.500000 0.866025i 0.500000 0.866025i
\(733\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(734\) 0 0
\(735\) 0.500000 0.866025i 0.500000 0.866025i
\(736\) 0 0
\(737\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(738\) 0 0
\(739\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.500000 0.866025i 0.500000 0.866025i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 1.00000 1.00000
\(751\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(752\) 1.00000 1.73205i 1.00000 1.73205i
\(753\) 0 0
\(754\) 0 0
\(755\) 2.00000 2.00000
\(756\) 1.00000 1.00000
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0.500000 0.866025i 0.500000 0.866025i
\(761\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.00000 −2.00000
\(765\) 0 0
\(766\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(767\) 0 0
\(768\) −0.500000 0.866025i −0.500000 0.866025i
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(778\) −1.00000 −1.00000
\(779\) −0.500000 0.866025i −0.500000 0.866025i
\(780\) 0 0
\(781\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 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
\(789\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(790\) −1.00000 −1.00000
\(791\) −0.500000 0.866025i −0.500000 0.866025i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(797\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(798\) 0.500000 0.866025i 0.500000 0.866025i
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0.500000 0.866025i 0.500000 0.866025i
\(803\) −1.00000 1.73205i −1.00000 1.73205i
\(804\) −2.00000 −2.00000
\(805\) 0 0
\(806\) 0 0
\(807\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(808\) 0 0
\(809\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) −0.500000 0.866025i −0.500000 0.866025i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −1.00000 1.73205i −1.00000 1.73205i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −1.00000 −1.00000
\(819\) 0 0
\(820\) −1.00000 −1.00000
\(821\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) 0 0
\(823\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −1.00000 1.73205i −1.00000 1.73205i
\(836\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(837\) 0 0
\(838\) 0 0
\(839\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(840\) −0.500000 0.866025i −0.500000 0.866025i
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(845\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) −0.500000 0.866025i −0.500000 0.866025i
\(853\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(854\) 1.00000 1.00000
\(855\) 0 0
\(856\) 0 0
\(857\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(858\) 0 0
\(859\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(860\) 0 0
\(861\) −1.00000 −1.00000
\(862\) 0 0
\(863\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(864\) 0.500000 0.866025i 0.500000 0.866025i
\(865\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(866\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(867\) 1.00000 1.00000
\(868\) 0 0
\(869\) 1.00000 1.00000
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(876\) 2.00000 2.00000
\(877\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(878\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(879\) 0 0
\(880\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(881\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) 0 0
\(883\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(888\) 2.00000 2.00000
\(889\) 0 0
\(890\) 0 0
\(891\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(892\) 0 0
\(893\) 1.00000 1.73205i 1.00000 1.73205i
\(894\) 0 0
\(895\) −1.00000 −1.00000
\(896\) 0.500000 0.866025i 0.500000 0.866025i
\(897\) 0 0
\(898\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 1.00000 1.00000
\(903\) 0 0
\(904\) −1.00000 −1.00000
\(905\) 0 0
\(906\) 1.00000 1.73205i 1.00000 1.73205i
\(907\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(908\) −0.500000 0.866025i −0.500000 0.866025i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −0.500000 0.866025i −0.500000 0.866025i
\(913\) 0 0
\(914\) 0 0
\(915\) −0.500000 0.866025i −0.500000 0.866025i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(923\) 0 0
\(924\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(925\) 0 0
\(926\) −0.500000 0.866025i −0.500000 0.866025i
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(930\) 0 0
\(931\) 1.00000 1.00000
\(932\) 0 0
\(933\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) −1.00000 1.73205i −1.00000 1.73205i
\(939\) 0 0
\(940\) −1.00000 1.73205i −1.00000 1.73205i
\(941\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0.500000 0.866025i 0.500000 0.866025i
\(946\) 0 0
\(947\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(954\) 0 0
\(955\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(956\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(957\) 0 0
\(958\) 1.00000 1.00000
\(959\) 0 0
\(960\) −1.00000 −1.00000
\(961\) −0.500000 0.866025i −0.500000 0.866025i
\(962\) 0 0
\(963\) 0 0
\(964\) −1.00000 1.73205i −1.00000 1.73205i
\(965\) 0 0
\(966\) 0 0
\(967\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0.500000 0.866025i 0.500000 0.866025i
\(977\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.500000 0.866025i 0.500000 0.866025i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(984\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(985\) −0.500000 0.866025i −0.500000 0.866025i
\(986\) 0 0
\(987\) −1.00000 1.73205i −1.00000 1.73205i
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −2.00000 −2.00000
\(994\) 0.500000 0.866025i 0.500000 0.866025i
\(995\) 2.00000 2.00000
\(996\) 0 0
\(997\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 1.00000 1.73205i 1.00000 1.73205i
\(999\) 1.00000 + 1.73205i 1.00000 + 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 1148.1.o.a.655.1 yes 2
4.3 odd 2 1148.1.o.b.655.1 yes 2
7.2 even 3 inner 1148.1.o.a.163.1 2
28.23 odd 6 1148.1.o.b.163.1 yes 2
41.40 even 2 1148.1.o.b.655.1 yes 2
164.163 odd 2 CM 1148.1.o.a.655.1 yes 2
287.163 even 6 1148.1.o.b.163.1 yes 2
1148.163 odd 6 inner 1148.1.o.a.163.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1148.1.o.a.163.1 2 7.2 even 3 inner
1148.1.o.a.163.1 2 1148.163 odd 6 inner
1148.1.o.a.655.1 yes 2 1.1 even 1 trivial
1148.1.o.a.655.1 yes 2 164.163 odd 2 CM
1148.1.o.b.163.1 yes 2 28.23 odd 6
1148.1.o.b.163.1 yes 2 287.163 even 6
1148.1.o.b.655.1 yes 2 4.3 odd 2
1148.1.o.b.655.1 yes 2 41.40 even 2