Properties

Label 1287.1.s.a.835.2
Level $1287$
Weight $1$
Character 1287.835
Analytic conductor $0.642$
Analytic rank $0$
Dimension $4$
Projective image $A_{4}$
CM/RM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1287,1,Mod(373,1287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1287, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 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("1287.373");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1287.s (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: \(0.642296671259\)
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: \(A_{4}\)
Projective field: Galois closure of 4.0.1656369.1
Artin image: $\SL(2,3):C_2$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\)

Embedding invariants

Embedding label 835.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1287.835
Dual form 1287.1.s.a.373.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.866025 - 0.500000i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.866025 - 0.500000i) q^{7} +1.00000 q^{9} +1.00000i q^{11} -1.00000 q^{12} +1.00000i q^{13} +(-0.500000 - 0.866025i) q^{15} +1.00000 q^{16} +(-0.866025 - 0.500000i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.866025 + 0.500000i) q^{21} +(-0.500000 + 0.866025i) q^{23} -1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} -2.00000i q^{29} +(-0.500000 - 0.866025i) q^{31} -1.00000i q^{33} +(0.866025 + 0.500000i) q^{35} +1.00000 q^{36} +(0.500000 + 0.866025i) q^{37} -1.00000i q^{39} +(0.866025 + 0.500000i) q^{41} +(-0.866025 + 0.500000i) q^{43} +1.00000i q^{44} +(0.500000 + 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{47} -1.00000 q^{48} +(0.866025 + 0.500000i) q^{51} +1.00000i q^{52} +(-0.866025 + 0.500000i) q^{55} +(0.866025 + 0.500000i) q^{57} +(-0.500000 - 0.866025i) q^{60} +(0.866025 - 0.500000i) q^{61} +(0.866025 - 0.500000i) q^{63} +1.00000 q^{64} +(-0.866025 + 0.500000i) q^{65} +(0.500000 - 0.866025i) q^{67} +(-0.866025 - 0.500000i) q^{68} +(0.500000 - 0.866025i) q^{69} +(0.500000 - 0.866025i) q^{71} +(-0.866025 - 0.500000i) q^{76} +(0.500000 + 0.866025i) q^{77} +(-0.866025 - 0.500000i) q^{79} +(0.500000 + 0.866025i) q^{80} +1.00000 q^{81} +(0.866025 + 0.500000i) q^{83} +(-0.866025 + 0.500000i) q^{84} -1.00000i q^{85} +2.00000i q^{87} +(-0.500000 - 0.866025i) q^{89} +(0.500000 + 0.866025i) q^{91} +(-0.500000 + 0.866025i) q^{92} +(0.500000 + 0.866025i) q^{93} -1.00000i q^{95} +(-0.500000 - 0.866025i) q^{97} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{9} - 4 q^{12} - 2 q^{15} + 4 q^{16} + 2 q^{20} - 2 q^{23} - 4 q^{27} - 2 q^{31} + 4 q^{36} + 2 q^{37} + 2 q^{45} - 2 q^{47} - 4 q^{48} - 2 q^{60} + 4 q^{64} + 2 q^{67} + 2 q^{69} + 2 q^{71} + 2 q^{77} + 2 q^{80} + 4 q^{81} - 2 q^{89} + 2 q^{91} - 2 q^{92} + 2 q^{93} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1287\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(937\) \(1145\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −1.00000 −1.00000
\(4\) 1.00000 1.00000
\(5\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) 0 0
\(9\) 1.00000 1.00000
\(10\) 0 0
\(11\) 1.00000i 1.00000i
\(12\) −1.00000 −1.00000
\(13\) 1.00000i 1.00000i
\(14\) 0 0
\(15\) −0.500000 0.866025i −0.500000 0.866025i
\(16\) 1.00000 1.00000
\(17\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(21\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(22\) 0 0
\(23\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) 0.866025 0.500000i 0.866025 0.500000i
\(29\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 1.00000i 1.00000i
\(34\) 0 0
\(35\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(36\) 1.00000 1.00000
\(37\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 1.00000i 1.00000i
\(40\) 0 0
\(41\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(44\) 1.00000i 1.00000i
\(45\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(46\) 0 0
\(47\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(48\) −1.00000 −1.00000
\(49\) 0 0
\(50\) 0 0
\(51\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(52\) 1.00000i 1.00000i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(56\) 0 0
\(57\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −0.500000 0.866025i −0.500000 0.866025i
\(61\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) 0.866025 0.500000i 0.866025 0.500000i
\(64\) 1.00000 1.00000
\(65\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(66\) 0 0
\(67\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(68\) −0.866025 0.500000i −0.866025 0.500000i
\(69\) 0.500000 0.866025i 0.500000 0.866025i
\(70\) 0 0
\(71\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −0.866025 0.500000i −0.866025 0.500000i
\(77\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(78\) 0 0
\(79\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(84\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(85\) 1.00000i 1.00000i
\(86\) 0 0
\(87\) 2.00000i 2.00000i
\(88\) 0 0
\(89\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(92\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(93\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(94\) 0 0
\(95\) 1.00000i 1.00000i
\(96\) 0 0
\(97\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 1.00000i 1.00000i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) −0.866025 0.500000i −0.866025 0.500000i
\(106\) 0 0
\(107\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) −1.00000 −1.00000
\(109\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −0.500000 0.866025i −0.500000 0.866025i
\(112\) 0.866025 0.500000i 0.866025 0.500000i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −1.00000 −1.00000
\(116\) 2.00000i 2.00000i
\(117\) 1.00000i 1.00000i
\(118\) 0 0
\(119\) −1.00000 −1.00000
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 0 0
\(123\) −0.866025 0.500000i −0.866025 0.500000i
\(124\) −0.500000 0.866025i −0.500000 0.866025i
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(128\) 0 0
\(129\) 0.866025 0.500000i 0.866025 0.500000i
\(130\) 0 0
\(131\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(132\) 1.00000i 1.00000i
\(133\) −1.00000 −1.00000
\(134\) 0 0
\(135\) −0.500000 0.866025i −0.500000 0.866025i
\(136\) 0 0
\(137\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(141\) 0.500000 0.866025i 0.500000 0.866025i
\(142\) 0 0
\(143\) −1.00000 −1.00000
\(144\) 1.00000 1.00000
\(145\) 1.73205 1.00000i 1.73205 1.00000i
\(146\) 0 0
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(152\) 0 0
\(153\) −0.866025 0.500000i −0.866025 0.500000i
\(154\) 0 0
\(155\) 0.500000 0.866025i 0.500000 0.866025i
\(156\) 1.00000i 1.00000i
\(157\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000i 1.00000i
\(162\) 0 0
\(163\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(164\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(165\) 0.866025 0.500000i 0.866025 0.500000i
\(166\) 0 0
\(167\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) −0.866025 0.500000i −0.866025 0.500000i
\(172\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(173\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000i 1.00000i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(180\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(184\) 0 0
\(185\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(186\) 0 0
\(187\) 0.500000 0.866025i 0.500000 0.866025i
\(188\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(189\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(190\) 0 0
\(191\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(192\) −1.00000 −1.00000
\(193\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0.866025 0.500000i 0.866025 0.500000i
\(196\) 0 0
\(197\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(202\) 0 0
\(203\) −1.00000 1.73205i −1.00000 1.73205i
\(204\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(205\) 1.00000i 1.00000i
\(206\) 0 0
\(207\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(208\) 1.00000i 1.00000i
\(209\) 0.500000 0.866025i 0.500000 0.866025i
\(210\) 0 0
\(211\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(214\) 0 0
\(215\) −0.866025 0.500000i −0.866025 0.500000i
\(216\) 0 0
\(217\) −0.866025 0.500000i −0.866025 0.500000i
\(218\) 0 0
\(219\) 0 0
\(220\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(221\) 0.500000 0.866025i 0.500000 0.866025i
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(229\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) −0.500000 0.866025i −0.500000 0.866025i
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −1.00000 −1.00000
\(236\) 0 0
\(237\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(238\) 0 0
\(239\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) −0.500000 0.866025i −0.500000 0.866025i
\(241\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) 0 0
\(243\) −1.00000 −1.00000
\(244\) 0.866025 0.500000i 0.866025 0.500000i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.500000 0.866025i 0.500000 0.866025i
\(248\) 0 0
\(249\) −0.866025 0.500000i −0.866025 0.500000i
\(250\) 0 0
\(251\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(252\) 0.866025 0.500000i 0.866025 0.500000i
\(253\) −0.866025 0.500000i −0.866025 0.500000i
\(254\) 0 0
\(255\) 1.00000i 1.00000i
\(256\) 1.00000 1.00000
\(257\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(258\) 0 0
\(259\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(260\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(261\) 2.00000i 2.00000i
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(268\) 0.500000 0.866025i 0.500000 0.866025i
\(269\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) −0.866025 0.500000i −0.866025 0.500000i
\(273\) −0.500000 0.866025i −0.500000 0.866025i
\(274\) 0 0
\(275\) 0 0
\(276\) 0.500000 0.866025i 0.500000 0.866025i
\(277\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) −0.500000 0.866025i −0.500000 0.866025i
\(280\) 0 0
\(281\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 0.500000 0.866025i 0.500000 0.866025i
\(285\) 1.00000i 1.00000i
\(286\) 0 0
\(287\) 1.00000 1.00000
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.00000i 1.00000i
\(298\) 0 0
\(299\) −0.866025 0.500000i −0.866025 0.500000i
\(300\) 0 0
\(301\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(302\) 0 0
\(303\) 0 0
\(304\) −0.866025 0.500000i −0.866025 0.500000i
\(305\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(309\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(310\) 0 0
\(311\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(316\) −0.866025 0.500000i −0.866025 0.500000i
\(317\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 2.00000 2.00000
\(320\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(321\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(322\) 0 0
\(323\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 2.00000i 2.00000i
\(328\) 0 0
\(329\) 1.00000i 1.00000i
\(330\) 0 0
\(331\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(333\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(334\) 0 0
\(335\) 1.00000 1.00000
\(336\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(337\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 1.00000i 1.00000i
\(341\) 0.866025 0.500000i 0.866025 0.500000i
\(342\) 0 0
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 1.00000 1.00000
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 2.00000i 2.00000i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 1.00000i 1.00000i
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 1.00000 1.00000
\(356\) −0.500000 0.866025i −0.500000 0.866025i
\(357\) 1.00000 1.00000
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 1.00000 1.00000
\(364\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(369\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(370\) 0 0
\(371\) 0 0
\(372\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(373\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(374\) 0 0
\(375\) −1.00000 −1.00000
\(376\) 0 0
\(377\) 2.00000 2.00000
\(378\) 0 0
\(379\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 1.00000i 1.00000i
\(381\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(386\) 0 0
\(387\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(388\) −0.500000 0.866025i −0.500000 0.866025i
\(389\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0.866025 0.500000i 0.866025 0.500000i
\(392\) 0 0
\(393\) 0.866025 0.500000i 0.866025 0.500000i
\(394\) 0 0
\(395\) 1.00000i 1.00000i
\(396\) 1.00000i 1.00000i
\(397\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 1.00000 1.00000
\(400\) 0 0
\(401\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0.866025 0.500000i 0.866025 0.500000i
\(404\) 0 0
\(405\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(406\) 0 0
\(407\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(412\) −0.500000 0.866025i −0.500000 0.866025i
\(413\) 0 0
\(414\) 0 0
\(415\) 1.00000i 1.00000i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(420\) −0.866025 0.500000i −0.866025 0.500000i
\(421\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.500000 0.866025i 0.500000 0.866025i
\(428\) 0.866025 0.500000i 0.866025 0.500000i
\(429\) 1.00000 1.00000
\(430\) 0 0
\(431\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(432\) −1.00000 −1.00000
\(433\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(434\) 0 0
\(435\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(436\) 2.00000i 2.00000i
\(437\) 0.866025 0.500000i 0.866025 0.500000i
\(438\) 0 0
\(439\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(444\) −0.500000 0.866025i −0.500000 0.866025i
\(445\) 0.500000 0.866025i 0.500000 0.866025i
\(446\) 0 0
\(447\) 0 0
\(448\) 0.866025 0.500000i 0.866025 0.500000i
\(449\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(450\) 0 0
\(451\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(452\) 0 0
\(453\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(454\) 0 0
\(455\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(460\) −1.00000 −1.00000
\(461\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(462\) 0 0
\(463\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(464\) 2.00000i 2.00000i
\(465\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 1.00000i 1.00000i
\(469\) 1.00000i 1.00000i
\(470\) 0 0
\(471\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(472\) 0 0
\(473\) −0.500000 0.866025i −0.500000 0.866025i
\(474\) 0 0
\(475\) 0 0
\(476\) −1.00000 −1.00000
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(482\) 0 0
\(483\) 1.00000i 1.00000i
\(484\) −1.00000 −1.00000
\(485\) 0.500000 0.866025i 0.500000 0.866025i
\(486\) 0 0
\(487\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0.500000 0.866025i 0.500000 0.866025i
\(490\) 0 0
\(491\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) −0.866025 0.500000i −0.866025 0.500000i
\(493\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(494\) 0 0
\(495\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(496\) −0.500000 0.866025i −0.500000 0.866025i
\(497\) 1.00000i 1.00000i
\(498\) 0 0
\(499\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 1.00000 1.00000
\(501\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(502\) 0 0
\(503\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 1.00000
\(508\) 0.866025 0.500000i 0.866025 0.500000i
\(509\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(514\) 0 0
\(515\) 0.500000 0.866025i 0.500000 0.866025i
\(516\) 0.866025 0.500000i 0.866025 0.500000i
\(517\) −0.866025 0.500000i −0.866025 0.500000i
\(518\) 0 0
\(519\) 0.866025 0.500000i 0.866025 0.500000i
\(520\) 0 0
\(521\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(524\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(525\) 0 0
\(526\) 0 0
\(527\) 1.00000i 1.00000i
\(528\) 1.00000i 1.00000i
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) −1.00000 −1.00000
\(533\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(534\) 0 0
\(535\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(536\) 0 0
\(537\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(538\) 0 0
\(539\) 0 0
\(540\) −0.500000 0.866025i −0.500000 0.866025i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(546\) 0 0
\(547\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(548\) −0.500000 0.866025i −0.500000 0.866025i
\(549\) 0.866025 0.500000i 0.866025 0.500000i
\(550\) 0 0
\(551\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(552\) 0 0
\(553\) −1.00000 −1.00000
\(554\) 0 0
\(555\) 0.500000 0.866025i 0.500000 0.866025i
\(556\) 0 0
\(557\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) −0.500000 0.866025i −0.500000 0.866025i
\(560\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(561\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0.500000 0.866025i 0.500000 0.866025i
\(565\) 0 0
\(566\) 0 0
\(567\) 0.866025 0.500000i 0.866025 0.500000i
\(568\) 0 0
\(569\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(572\) −1.00000 −1.00000
\(573\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0 0
\(579\) −0.866025 0.500000i −0.866025 0.500000i
\(580\) 1.73205 1.00000i 1.73205 1.00000i
\(581\) 1.00000 1.00000
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(586\) 0 0
\(587\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(588\) 0 0
\(589\) 1.00000i 1.00000i
\(590\) 0 0
\(591\) 0.866025 0.500000i 0.866025 0.500000i
\(592\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) −0.500000 0.866025i −0.500000 0.866025i
\(596\) 0 0
\(597\) 0.500000 0.866025i 0.500000 0.866025i
\(598\) 0 0
\(599\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0.500000 0.866025i 0.500000 0.866025i
\(604\) −0.866025 0.500000i −0.866025 0.500000i
\(605\) −0.500000 0.866025i −0.500000 0.866025i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(610\) 0 0
\(611\) −0.866025 0.500000i −0.866025 0.500000i
\(612\) −0.866025 0.500000i −0.866025 0.500000i
\(613\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(614\) 0 0
\(615\) 1.00000i 1.00000i
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 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
\(621\) 0.500000 0.866025i 0.500000 0.866025i
\(622\) 0 0
\(623\) −0.866025 0.500000i −0.866025 0.500000i
\(624\) 1.00000i 1.00000i
\(625\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(626\) 0 0
\(627\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(628\) −0.500000 0.866025i −0.500000 0.866025i
\(629\) 1.00000i 1.00000i
\(630\) 0 0
\(631\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(632\) 0 0
\(633\) −0.866025 0.500000i −0.866025 0.500000i
\(634\) 0 0
\(635\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.500000 0.866025i 0.500000 0.866025i
\(640\) 0 0
\(641\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 1.00000i 1.00000i
\(645\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(646\) 0 0
\(647\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(652\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(653\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(654\) 0 0
\(655\) −0.866025 0.500000i −0.866025 0.500000i
\(656\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(657\) 0 0
\(658\) 0 0
\(659\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0.866025 0.500000i 0.866025 0.500000i
\(661\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(664\) 0 0
\(665\) −0.500000 0.866025i −0.500000 0.866025i
\(666\) 0 0
\(667\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(668\) −0.866025 0.500000i −0.866025 0.500000i
\(669\) 0 0
\(670\) 0 0
\(671\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −1.00000 −1.00000
\(677\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) −0.866025 0.500000i −0.866025 0.500000i
\(680\) 0 0
\(681\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(682\) 0 0
\(683\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(684\) −0.866025 0.500000i −0.866025 0.500000i
\(685\) 0.500000 0.866025i 0.500000 0.866025i
\(686\) 0 0
\(687\) −0.500000 0.866025i −0.500000 0.866025i
\(688\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(693\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.500000 0.866025i −0.500000 0.866025i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 1.00000i 1.00000i
\(704\) 1.00000i 1.00000i
\(705\) 1.00000 1.00000
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) −0.866025 0.500000i −0.866025 0.500000i
\(712\) 0 0
\(713\) 1.00000 1.00000
\(714\) 0 0
\(715\) −0.500000 0.866025i −0.500000 0.866025i
\(716\) −0.500000 0.866025i −0.500000 0.866025i
\(717\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(718\) 0 0
\(719\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(720\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(721\) −0.866025 0.500000i −0.866025 0.500000i
\(722\) 0 0
\(723\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 1.00000 1.00000
\(732\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(733\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(738\) 0 0
\(739\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(740\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(741\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(742\) 0 0
\(743\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(748\) 0.500000 0.866025i 0.500000 0.866025i
\(749\) 0.500000 0.866025i 0.500000 0.866025i
\(750\) 0 0
\(751\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(752\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(753\) 0.500000 0.866025i 0.500000 0.866025i
\(754\) 0 0
\(755\) 1.00000i 1.00000i
\(756\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(757\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 0 0
\(759\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(760\) 0 0
\(761\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(762\) 0 0
\(763\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(764\) −0.500000 0.866025i −0.500000 0.866025i
\(765\) 1.00000i 1.00000i
\(766\) 0 0
\(767\) 0 0
\(768\) −1.00000 −1.00000
\(769\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(772\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(773\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −0.866025 0.500000i −0.866025 0.500000i
\(778\) 0 0
\(779\) −0.500000 0.866025i −0.500000 0.866025i
\(780\) 0.866025 0.500000i 0.866025 0.500000i
\(781\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(782\) 0 0
\(783\) 2.00000i 2.00000i
\(784\) 0 0
\(785\) 0.500000 0.866025i 0.500000 0.866025i
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(794\) 0 0
\(795\) 0 0
\(796\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0.866025 0.500000i 0.866025 0.500000i
\(800\) 0 0
\(801\) −0.500000 0.866025i −0.500000 0.866025i
\(802\) 0 0
\(803\) 0 0
\(804\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(805\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(806\) 0 0
\(807\) 0.500000 0.866025i 0.500000 0.866025i
\(808\) 0 0
\(809\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −1.00000 1.73205i −1.00000 1.73205i
\(813\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(814\) 0 0
\(815\) −1.00000 −1.00000
\(816\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(817\) 1.00000 1.00000
\(818\) 0 0
\(819\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(820\) 1.00000i 1.00000i
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(829\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 0.866025 0.500000i 0.866025 0.500000i
\(832\) 1.00000i 1.00000i
\(833\) 0 0
\(834\) 0 0
\(835\) 1.00000i 1.00000i
\(836\) 0.500000 0.866025i 0.500000 0.866025i
\(837\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(838\) 0 0
\(839\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(840\) 0 0
\(841\) −3.00000 −3.00000
\(842\) 0 0
\(843\) −0.866025 0.500000i −0.866025 0.500000i
\(844\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(845\) −0.500000 0.866025i −0.500000 0.866025i
\(846\) 0 0
\(847\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(848\) 0 0
\(849\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(850\) 0 0
\(851\) −1.00000 −1.00000
\(852\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(853\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(854\) 0 0
\(855\) 1.00000i 1.00000i
\(856\) 0 0
\(857\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(858\) 0 0
\(859\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(860\) −0.866025 0.500000i −0.866025 0.500000i
\(861\) −1.00000 −1.00000
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) −0.866025 0.500000i −0.866025 0.500000i
\(866\) 0 0
\(867\) 0 0
\(868\) −0.866025 0.500000i −0.866025 0.500000i
\(869\) 0.500000 0.866025i 0.500000 0.866025i
\(870\) 0 0
\(871\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(872\) 0 0
\(873\) −0.500000 0.866025i −0.500000 0.866025i
\(874\) 0 0
\(875\) 0.866025 0.500000i 0.866025 0.500000i
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(881\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0.500000 0.866025i 0.500000 0.866025i
\(885\) 0 0
\(886\) 0 0
\(887\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0.500000 0.866025i 0.500000 0.866025i
\(890\) 0 0
\(891\) 1.00000i 1.00000i
\(892\) 0 0
\(893\) 0.866025 0.500000i 0.866025 0.500000i
\(894\) 0 0
\(895\) 0.500000 0.866025i 0.500000 0.866025i
\(896\) 0 0
\(897\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(898\) 0 0
\(899\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0.500000 0.866025i 0.500000 0.866025i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0.866025 0.500000i 0.866025 0.500000i
\(909\) 0 0
\(910\) 0 0
\(911\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(912\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(913\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(914\) 0 0
\(915\) −0.866025 0.500000i −0.866025 0.500000i
\(916\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(917\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(918\) 0 0
\(919\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(924\) −0.500000 0.866025i −0.500000 0.866025i
\(925\) 0 0
\(926\) 0 0
\(927\) −0.500000 0.866025i −0.500000 0.866025i
\(928\) 0 0
\(929\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(934\) 0 0
\(935\) 1.00000 1.00000
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0.500000 0.866025i 0.500000 0.866025i
\(940\) −1.00000 −1.00000
\(941\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(944\) 0 0
\(945\) −0.866025 0.500000i −0.866025 0.500000i
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(949\) 0 0
\(950\) 0 0
\(951\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(952\) 0 0
\(953\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(954\) 0 0
\(955\) 0.500000 0.866025i 0.500000 0.866025i
\(956\) 0.866025 0.500000i 0.866025 0.500000i
\(957\) −2.00000 −2.00000
\(958\) 0 0
\(959\) −0.866025 0.500000i −0.866025 0.500000i
\(960\) −0.500000 0.866025i −0.500000 0.866025i
\(961\) 0 0
\(962\) 0 0
\(963\) 0.866025 0.500000i 0.866025 0.500000i
\(964\) 0.866025 0.500000i 0.866025 0.500000i
\(965\) 1.00000i 1.00000i
\(966\) 0 0
\(967\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(968\) 0 0
\(969\) −0.500000 0.866025i −0.500000 0.866025i
\(970\) 0 0
\(971\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(972\) −1.00000 −1.00000
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0.866025 0.500000i 0.866025 0.500000i
\(977\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0.866025 0.500000i 0.866025 0.500000i
\(980\) 0 0
\(981\) 2.00000i 2.00000i
\(982\) 0 0
\(983\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −0.866025 0.500000i −0.866025 0.500000i
\(986\) 0 0
\(987\) 1.00000i 1.00000i
\(988\) 0.500000 0.866025i 0.500000 0.866025i
\(989\) 1.00000i 1.00000i
\(990\) 0 0
\(991\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −0.500000 0.866025i −0.500000 0.866025i
\(994\) 0 0
\(995\) −1.00000 −1.00000
\(996\) −0.866025 0.500000i −0.866025 0.500000i
\(997\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(998\) 0 0
\(999\) −0.500000 0.866025i −0.500000 0.866025i
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 1287.1.s.a.835.2 yes 4
3.2 odd 2 3861.1.s.a.1693.2 4
9.4 even 3 1287.1.bg.a.1264.2 yes 4
9.5 odd 6 3861.1.bg.a.2980.2 4
11.10 odd 2 inner 1287.1.s.a.835.1 yes 4
13.9 even 3 1287.1.bg.a.1231.2 yes 4
33.32 even 2 3861.1.s.a.1693.1 4
39.35 odd 6 3861.1.bg.a.802.2 4
99.32 even 6 3861.1.bg.a.2980.1 4
99.76 odd 6 1287.1.bg.a.1264.1 yes 4
117.22 even 3 inner 1287.1.s.a.373.1 4
117.113 odd 6 3861.1.s.a.2089.1 4
143.87 odd 6 1287.1.bg.a.1231.1 yes 4
429.230 even 6 3861.1.bg.a.802.1 4
1287.230 even 6 3861.1.s.a.2089.2 4
1287.373 odd 6 inner 1287.1.s.a.373.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1287.1.s.a.373.1 4 117.22 even 3 inner
1287.1.s.a.373.2 yes 4 1287.373 odd 6 inner
1287.1.s.a.835.1 yes 4 11.10 odd 2 inner
1287.1.s.a.835.2 yes 4 1.1 even 1 trivial
1287.1.bg.a.1231.1 yes 4 143.87 odd 6
1287.1.bg.a.1231.2 yes 4 13.9 even 3
1287.1.bg.a.1264.1 yes 4 99.76 odd 6
1287.1.bg.a.1264.2 yes 4 9.4 even 3
3861.1.s.a.1693.1 4 33.32 even 2
3861.1.s.a.1693.2 4 3.2 odd 2
3861.1.s.a.2089.1 4 117.113 odd 6
3861.1.s.a.2089.2 4 1287.230 even 6
3861.1.bg.a.802.1 4 429.230 even 6
3861.1.bg.a.802.2 4 39.35 odd 6
3861.1.bg.a.2980.1 4 99.32 even 6
3861.1.bg.a.2980.2 4 9.5 odd 6