Properties

Label 3192.1.fm.c.1133.1
Level $3192$
Weight $1$
Character 3192.1133
Analytic conductor $1.593$
Analytic rank $0$
Dimension $2$
Projective image $D_{6}$
CM discriminant -56
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3192,1,Mod(293,3192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3192, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 3, 3, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3192.293");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3192.fm (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: \(1.59301552032\)
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: \(D_{6}\)
Projective field: Galois closure of 6.2.209656254528.1

Embedding invariants

Embedding label 1133.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3192.1133
Dual form 3192.1.fm.c.293.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 0.866025i) q^{10} +1.00000 q^{12} +(-1.50000 - 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{18} +(-0.500000 - 0.866025i) q^{19} +1.73205i q^{20} +(0.500000 + 0.866025i) q^{21} +(-1.50000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 1.73205i) q^{25} -1.73205i q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} -1.73205i q^{30} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{38} +1.73205i q^{39} +(-1.50000 + 0.866025i) q^{40} +(-0.500000 + 0.866025i) q^{42} +1.73205i q^{45} -1.73205i q^{46} +(-0.500000 + 0.866025i) q^{48} +1.00000 q^{49} +2.00000 q^{50} +(1.50000 - 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{54} +1.00000 q^{56} +(-0.500000 + 0.866025i) q^{57} +(-0.500000 - 0.866025i) q^{59} +(1.50000 - 0.866025i) q^{60} +(0.500000 - 0.866025i) q^{61} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} -3.00000 q^{65} +1.73205i q^{69} +(-1.50000 - 0.866025i) q^{70} +(0.500000 + 0.866025i) q^{71} +(0.500000 - 0.866025i) q^{72} -2.00000 q^{75} +1.00000 q^{76} +(-1.50000 + 0.866025i) q^{78} +(-1.50000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +1.73205i q^{83} -1.00000 q^{84} +(-1.50000 + 0.866025i) q^{90} +(1.50000 + 0.866025i) q^{91} +(1.50000 - 0.866025i) q^{92} +(-1.50000 - 0.866025i) q^{95} -1.00000 q^{96} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9} + 3 q^{10} + 2 q^{12} - 3 q^{13} - q^{14} - 3 q^{15} - q^{16} - 2 q^{18} - q^{19} + q^{21} - 3 q^{23} + q^{24} + 2 q^{25}+ \cdots + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3192\mathbb{Z}\right)^\times\).

\(n\) \(799\) \(913\) \(1009\) \(1597\) \(2129\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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
\(4\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(5\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(6\) 0.500000 0.866025i 0.500000 0.866025i
\(7\) −1.00000 −1.00000
\(8\) −1.00000 −1.00000
\(9\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(10\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 1.00000
\(13\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(14\) −0.500000 0.866025i −0.500000 0.866025i
\(15\) −1.50000 0.866025i −1.50000 0.866025i
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) −1.00000 −1.00000
\(19\) −0.500000 0.866025i −0.500000 0.866025i
\(20\) 1.73205i 1.73205i
\(21\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(22\) 0 0
\(23\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(24\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(25\) 1.00000 1.73205i 1.00000 1.73205i
\(26\) 1.73205i 1.73205i
\(27\) 1.00000 1.00000
\(28\) 0.500000 0.866025i 0.500000 0.866025i
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 1.73205i 1.73205i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0.500000 0.866025i 0.500000 0.866025i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(36\) −0.500000 0.866025i −0.500000 0.866025i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0.500000 0.866025i 0.500000 0.866025i
\(39\) 1.73205i 1.73205i
\(40\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(41\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(42\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(43\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 0 0
\(45\) 1.73205i 1.73205i
\(46\) 1.73205i 1.73205i
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(49\) 1.00000 1.00000
\(50\) 2.00000 2.00000
\(51\) 0 0
\(52\) 1.50000 0.866025i 1.50000 0.866025i
\(53\) 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
\(55\) 0 0
\(56\) 1.00000 1.00000
\(57\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(58\) 0 0
\(59\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(60\) 1.50000 0.866025i 1.50000 0.866025i
\(61\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(62\) 0 0
\(63\) 0.500000 0.866025i 0.500000 0.866025i
\(64\) 1.00000 1.00000
\(65\) −3.00000 −3.00000
\(66\) 0 0
\(67\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(68\) 0 0
\(69\) 1.73205i 1.73205i
\(70\) −1.50000 0.866025i −1.50000 0.866025i
\(71\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0.500000 0.866025i 0.500000 0.866025i
\(73\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) −2.00000 −2.00000
\(76\) 1.00000 1.00000
\(77\) 0 0
\(78\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(79\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) −1.50000 0.866025i −1.50000 0.866025i
\(81\) −0.500000 0.866025i −0.500000 0.866025i
\(82\) 0 0
\(83\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) −1.00000 −1.00000
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(91\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(92\) 1.50000 0.866025i 1.50000 0.866025i
\(93\) 0 0
\(94\) 0 0
\(95\) −1.50000 0.866025i −1.50000 0.866025i
\(96\) −1.00000 −1.00000
\(97\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(98\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(101\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(105\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(109\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(113\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −1.00000 −1.00000
\(115\) −3.00000 −3.00000
\(116\) 0 0
\(117\) 1.50000 0.866025i 1.50000 0.866025i
\(118\) 0.500000 0.866025i 0.500000 0.866025i
\(119\) 0 0
\(120\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(121\) −1.00000 −1.00000
\(122\) 1.00000 1.00000
\(123\) 0 0
\(124\) 0 0
\(125\) 1.73205i 1.73205i
\(126\) 1.00000 1.00000
\(127\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(128\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(129\) 0 0
\(130\) −1.50000 2.59808i −1.50000 2.59808i
\(131\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(132\) 0 0
\(133\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(134\) 0 0
\(135\) 1.50000 0.866025i 1.50000 0.866025i
\(136\) 0 0
\(137\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(139\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(140\) 1.73205i 1.73205i
\(141\) 0 0
\(142\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −0.500000 0.866025i −0.500000 0.866025i
\(148\) 0 0
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) −1.00000 1.73205i −1.00000 1.73205i
\(151\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(152\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.50000 0.866025i −1.50000 0.866025i
\(157\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 1.73205i 1.73205i
\(161\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(162\) 0.500000 0.866025i 0.500000 0.866025i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(167\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) −0.500000 0.866025i −0.500000 0.866025i
\(169\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(170\) 0 0
\(171\) 1.00000 1.00000
\(172\) 0 0
\(173\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(176\) 0 0
\(177\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −1.50000 0.866025i −1.50000 0.866025i
\(181\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(182\) 1.73205i 1.73205i
\(183\) −1.00000 −1.00000
\(184\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.00000 −1.00000
\(190\) 1.73205i 1.73205i
\(191\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) −0.500000 0.866025i −0.500000 0.866025i
\(193\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(196\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.50000 0.866025i 1.50000 0.866025i
\(208\) 1.73205i 1.73205i
\(209\) 0 0
\(210\) 1.73205i 1.73205i
\(211\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(212\) 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
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(224\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(225\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(226\) −0.500000 0.866025i −0.500000 0.866025i
\(227\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) −0.500000 0.866025i −0.500000 0.866025i
\(229\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) −1.50000 2.59808i −1.50000 2.59808i
\(231\) 0 0
\(232\) 0 0
\(233\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(234\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(235\) 0 0
\(236\) 1.00000 1.00000
\(237\) 0 0
\(238\) 0 0
\(239\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 1.73205i 1.73205i
\(241\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) −0.500000 0.866025i −0.500000 0.866025i
\(243\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(244\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(245\) 1.50000 0.866025i 1.50000 0.866025i
\(246\) 0 0
\(247\) 1.73205i 1.73205i
\(248\) 0 0
\(249\) 1.50000 0.866025i 1.50000 0.866025i
\(250\) 1.50000 0.866025i 1.50000 0.866025i
\(251\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(253\) 0 0
\(254\) 1.73205i 1.73205i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.50000 2.59808i 1.50000 2.59808i
\(261\) 0 0
\(262\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(263\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(267\) 0 0
\(268\) 0 0
\(269\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(270\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0 0
\(273\) 1.73205i 1.73205i
\(274\) 1.73205i 1.73205i
\(275\) 0 0
\(276\) −1.50000 0.866025i −1.50000 0.866025i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 2.00000 2.00000
\(279\) 0 0
\(280\) 1.50000 0.866025i 1.50000 0.866025i
\(281\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 0 0
\(283\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(284\) −1.00000 −1.00000
\(285\) 1.73205i 1.73205i
\(286\) 0 0
\(287\) 0 0
\(288\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(289\) 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 \(0.666667\pi\)
\(294\) 0.500000 0.866025i 0.500000 0.866025i
\(295\) −1.50000 0.866025i −1.50000 0.866025i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(300\) 1.00000 1.73205i 1.00000 1.73205i
\(301\) 0 0
\(302\) 1.50000 0.866025i 1.50000 0.866025i
\(303\) 0 0
\(304\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(305\) 1.73205i 1.73205i
\(306\) 0 0
\(307\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 1.73205i 1.73205i
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0.500000 0.866025i 0.500000 0.866025i
\(315\) 1.73205i 1.73205i
\(316\) 0 0
\(317\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.50000 0.866025i 1.50000 0.866025i
\(321\) 0 0
\(322\) 1.73205i 1.73205i
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) −3.00000 + 1.73205i −3.00000 + 1.73205i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) −1.50000 0.866025i −1.50000 0.866025i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0.500000 0.866025i 0.500000 0.866025i
\(337\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(338\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(339\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(346\) 0.500000 0.866025i 0.500000 0.866025i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(350\) −2.00000 −2.00000
\(351\) −1.50000 0.866025i −1.50000 0.866025i
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) −1.00000 −1.00000
\(355\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 1.73205i 1.73205i
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) 1.73205i 1.73205i
\(363\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(364\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(365\) 0 0
\(366\) −0.500000 0.866025i −0.500000 0.866025i
\(367\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 1.73205i 1.73205i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.500000 0.866025i −0.500000 0.866025i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 1.50000 0.866025i 1.50000 0.866025i
\(381\) 1.73205i 1.73205i
\(382\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(383\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(384\) 0.500000 0.866025i 0.500000 0.866025i
\(385\) 0 0
\(386\) −1.50000 0.866025i −1.50000 0.866025i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(391\) 0 0
\(392\) −1.00000 −1.00000
\(393\) −1.50000 0.866025i −1.50000 0.866025i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(398\) 0 0
\(399\) 0.500000 0.866025i 0.500000 0.866025i
\(400\) −2.00000 −2.00000
\(401\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.50000 0.866025i −1.50000 0.866025i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(410\) 0 0
\(411\) 1.73205i 1.73205i
\(412\) 0 0
\(413\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(414\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(415\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(416\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(417\) −2.00000 −2.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(421\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(422\) 0 0
\(423\) 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
\(431\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(432\) −0.500000 0.866025i −0.500000 0.866025i
\(433\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.73205i 1.73205i
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(442\) 0 0
\(443\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.00000 −1.00000
\(449\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(450\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(451\) 0 0
\(452\) 0.500000 0.866025i 0.500000 0.866025i
\(453\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(454\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(455\) 3.00000 3.00000
\(456\) 0.500000 0.866025i 0.500000 0.866025i
\(457\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(459\) 0 0
\(460\) 1.50000 2.59808i 1.50000 2.59808i
\(461\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 1.73205i 1.73205i
\(469\) 0 0
\(470\) 0 0
\(471\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(472\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(473\) 0 0
\(474\) 0 0
\(475\) −2.00000 −2.00000
\(476\) 0 0
\(477\) 0 0
\(478\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(481\) 0 0
\(482\) 0 0
\(483\) 1.73205i 1.73205i
\(484\) 0.500000 0.866025i 0.500000 0.866025i
\(485\) 0 0
\(486\) −1.00000 −1.00000
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(489\) 0 0
\(490\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(495\) 0 0
\(496\) 0 0
\(497\) −0.500000 0.866025i −0.500000 0.866025i
\(498\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(501\) 0 0
\(502\) 1.73205i 1.73205i
\(503\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(504\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 1.73205i 1.00000 1.73205i
\(508\) 1.50000 0.866025i 1.50000 0.866025i
\(509\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) −0.500000 0.866025i −0.500000 0.866025i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(520\) 3.00000 3.00000
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 1.73205i 1.73205i
\(525\) 2.00000 2.00000
\(526\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(530\) 0 0
\(531\) 1.00000 1.00000
\(532\) −1.00000 −1.00000
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.00000 1.73205i 1.00000 1.73205i
\(539\) 0 0
\(540\) 1.73205i 1.73205i
\(541\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) 1.73205i 1.73205i
\(544\) 0 0
\(545\) 0 0
\(546\) 1.50000 0.866025i 1.50000 0.866025i
\(547\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(548\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(549\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(550\) 0 0
\(551\) 0 0
\(552\) 1.73205i 1.73205i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(557\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(561\) 0 0
\(562\) −2.00000 −2.00000
\(563\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(564\) 0 0
\(565\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(566\) 0.500000 0.866025i 0.500000 0.866025i
\(567\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(568\) −0.500000 0.866025i −0.500000 0.866025i
\(569\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 1.50000 0.866025i 1.50000 0.866025i
\(574\) 0 0
\(575\) −3.00000 + 1.73205i −3.00000 + 1.73205i
\(576\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 1.00000 1.00000
\(579\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(580\) 0 0
\(581\) 1.73205i 1.73205i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 1.50000 2.59808i 1.50000 2.59808i
\(586\) −0.500000 0.866025i −0.500000 0.866025i
\(587\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 1.00000 1.00000
\(589\) 0 0
\(590\) 1.73205i 1.73205i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(599\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(600\) 2.00000 2.00000
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(605\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) −1.00000 −1.00000
\(609\) 0 0
\(610\) 1.50000 0.866025i 1.50000 0.866025i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) −1.50000 0.866025i −1.50000 0.866025i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(618\) 0 0
\(619\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) −1.50000 0.866025i −1.50000 0.866025i
\(622\) 0 0
\(623\) 0 0
\(624\) 1.50000 0.866025i 1.50000 0.866025i
\(625\) −0.500000 0.866025i −0.500000 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.00000 1.00000
\(629\) 0 0
\(630\) 1.50000 0.866025i 1.50000 0.866025i
\(631\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.00000 −3.00000
\(636\) 0 0
\(637\) −1.50000 0.866025i −1.50000 0.866025i
\(638\) 0 0
\(639\) −1.00000 −1.00000
\(640\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(641\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(649\) 0 0
\(650\) −3.00000 1.73205i −3.00000 1.73205i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 1.50000 2.59808i 1.50000 2.59808i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 0 0
\(661\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.73205i 1.73205i
\(665\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 1.00000 1.00000
\(673\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(675\) 1.00000 1.73205i 1.00000 1.73205i
\(676\) −2.00000 −2.00000
\(677\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(678\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.500000 0.866025i −0.500000 0.866025i
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(685\) 3.00000 3.00000
\(686\) −0.500000 0.866025i −0.500000 0.866025i
\(687\) −0.500000 0.866025i −0.500000 0.866025i
\(688\) 0 0
\(689\) 0 0
\(690\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 1.00000 1.00000
\(693\) 0 0
\(694\) 0 0
\(695\) 3.46410i 3.46410i
\(696\) 0 0
\(697\) 0 0
\(698\) −1.00000 1.73205i −1.00000 1.73205i
\(699\) −1.50000 0.866025i −1.50000 0.866025i
\(700\) −1.00000 1.73205i −1.00000 1.73205i
\(701\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(702\) 1.73205i 1.73205i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) −0.500000 0.866025i −0.500000 0.866025i
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 1.73205i 1.73205i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.50000 0.866025i 1.50000 0.866025i
\(718\) 0 0
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 1.50000 0.866025i 1.50000 0.866025i
\(721\) 0 0
\(722\) −1.00000 −1.00000
\(723\) 0 0
\(724\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(725\) 0 0
\(726\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(727\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(728\) −1.50000 0.866025i −1.50000 0.866025i
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0.500000 0.866025i 0.500000 0.866025i
\(733\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(734\) 0 0
\(735\) −1.50000 0.866025i −1.50000 0.866025i
\(736\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 1.50000 0.866025i 1.50000 0.866025i
\(742\) 0 0
\(743\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.50000 0.866025i −1.50000 0.866025i
\(748\) 0 0
\(749\) 0 0
\(750\) −1.50000 0.866025i −1.50000 0.866025i
\(751\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0 0
\(753\) 1.73205i 1.73205i
\(754\) 0 0
\(755\) −1.50000 2.59808i −1.50000 2.59808i
\(756\) 0.500000 0.866025i 0.500000 0.866025i
\(757\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(763\) 0 0
\(764\) −1.50000 0.866025i −1.50000 0.866025i
\(765\) 0 0
\(766\) 0 0
\(767\) 1.73205i 1.73205i
\(768\) 1.00000 1.00000
\(769\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.73205i 1.73205i
\(773\) 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 0
\(780\) −3.00000 −3.00000
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.500000 0.866025i −0.500000 0.866025i
\(785\) −1.50000 0.866025i −1.50000 0.866025i
\(786\) 1.73205i 1.73205i
\(787\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(788\) 0 0
\(789\) −1.50000 0.866025i −1.50000 0.866025i
\(790\) 0 0
\(791\) 1.00000 1.00000
\(792\) 0 0
\(793\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(794\) 1.00000 1.73205i 1.00000 1.73205i
\(795\) 0 0
\(796\) 0 0
\(797\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(798\) 1.00000 1.00000
\(799\) 0 0
\(800\) −1.00000 1.73205i −1.00000 1.73205i
\(801\) 0 0
\(802\) 0.500000 0.866025i 0.500000 0.866025i
\(803\) 0 0
\(804\) 0 0
\(805\) 3.00000 3.00000
\(806\) 0 0
\(807\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(808\) 0 0
\(809\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) 1.73205i 1.73205i
\(811\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(820\) 0 0
\(821\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(822\) 1.50000 0.866025i 1.50000 0.866025i
\(823\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(824\) 0 0
\(825\) 0 0
\(826\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(827\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(828\) 1.73205i 1.73205i
\(829\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(830\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(831\) 0 0
\(832\) −1.50000 0.866025i −1.50000 0.866025i
\(833\) 0 0
\(834\) −1.00000 1.73205i −1.00000 1.73205i
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(840\) −1.50000 0.866025i −1.50000 0.866025i
\(841\) −0.500000 0.866025i −0.500000 0.866025i
\(842\) 0 0
\(843\) 2.00000 2.00000
\(844\) 0 0
\(845\) 3.00000 + 1.73205i 3.00000 + 1.73205i
\(846\) 0 0
\(847\) 1.00000 1.00000
\(848\) 0 0
\(849\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(850\) 0 0
\(851\) 0 0
\(852\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(853\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(854\) −1.00000 −1.00000
\(855\) 1.50000 0.866025i 1.50000 0.866025i
\(856\) 0 0
\(857\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(858\) 0 0
\(859\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 2.00000 2.00000
\(863\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(864\) 0.500000 0.866025i 0.500000 0.866025i
\(865\) −1.50000 0.866025i −1.50000 0.866025i
\(866\) 0 0
\(867\) −1.00000 −1.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(875\) 1.73205i 1.73205i
\(876\) 0 0
\(877\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(878\) 0 0
\(879\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) −1.00000 −1.00000
\(883\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 0 0
\(885\) 1.73205i 1.73205i
\(886\) 0 0
\(887\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(888\) 0 0
\(889\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −0.500000 0.866025i −0.500000 0.866025i
\(897\) 1.50000 2.59808i 1.50000 2.59808i
\(898\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(899\) 0 0
\(900\) −2.00000 −2.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 1.00000 1.00000
\(905\) 3.00000 3.00000
\(906\) −1.50000 0.866025i −1.50000 0.866025i
\(907\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(908\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(909\) 0 0
\(910\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(911\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(912\) 1.00000 1.00000
\(913\) 0 0
\(914\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(915\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(916\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(917\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(918\) 0 0
\(919\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(920\) 3.00000 3.00000
\(921\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(922\) −1.50000 0.866025i −1.50000 0.866025i
\(923\) 1.73205i 1.73205i
\(924\) 0 0
\(925\) 0 0
\(926\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(930\) 0 0
\(931\) −0.500000 0.866025i −0.500000 0.866025i
\(932\) 1.73205i 1.73205i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(937\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(942\) −1.00000 −1.00000
\(943\) 0 0
\(944\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(945\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(946\) 0 0
\(947\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −1.00000 1.73205i −1.00000 1.73205i
\(951\) 0 0
\(952\) 0 0
\(953\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(954\) 0 0
\(955\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(956\) −1.50000 0.866025i −1.50000 0.866025i
\(957\) 0 0
\(958\) 0 0
\(959\) −1.50000 0.866025i −1.50000 0.866025i
\(960\) −1.50000 0.866025i −1.50000 0.866025i
\(961\) −1.00000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(966\) 1.50000 0.866025i 1.50000 0.866025i
\(967\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 1.00000 1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(972\) −0.500000 0.866025i −0.500000 0.866025i
\(973\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(974\) 0 0
\(975\) 3.00000 + 1.73205i 3.00000 + 1.73205i
\(976\) −1.00000 −1.00000
\(977\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.73205i 1.73205i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −1.50000 0.866025i −1.50000 0.866025i
\(989\) 0 0
\(990\) 0 0
\(991\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0.500000 0.866025i 0.500000 0.866025i
\(995\) 0 0
\(996\) 1.73205i 1.73205i
\(997\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 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 3192.1.fm.c.1133.1 yes 2
3.2 odd 2 3192.1.fm.b.1133.1 yes 2
7.6 odd 2 3192.1.fm.d.1133.1 yes 2
8.5 even 2 3192.1.fm.d.1133.1 yes 2
19.8 odd 6 3192.1.fm.b.293.1 yes 2
21.20 even 2 3192.1.fm.a.1133.1 yes 2
24.5 odd 2 3192.1.fm.a.1133.1 yes 2
56.13 odd 2 CM 3192.1.fm.c.1133.1 yes 2
57.8 even 6 inner 3192.1.fm.c.293.1 yes 2
133.27 even 6 3192.1.fm.a.293.1 2
152.141 odd 6 3192.1.fm.a.293.1 2
168.125 even 2 3192.1.fm.b.1133.1 yes 2
399.293 odd 6 3192.1.fm.d.293.1 yes 2
456.293 even 6 3192.1.fm.d.293.1 yes 2
1064.293 even 6 3192.1.fm.b.293.1 yes 2
3192.293 odd 6 inner 3192.1.fm.c.293.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3192.1.fm.a.293.1 2 133.27 even 6
3192.1.fm.a.293.1 2 152.141 odd 6
3192.1.fm.a.1133.1 yes 2 21.20 even 2
3192.1.fm.a.1133.1 yes 2 24.5 odd 2
3192.1.fm.b.293.1 yes 2 19.8 odd 6
3192.1.fm.b.293.1 yes 2 1064.293 even 6
3192.1.fm.b.1133.1 yes 2 3.2 odd 2
3192.1.fm.b.1133.1 yes 2 168.125 even 2
3192.1.fm.c.293.1 yes 2 57.8 even 6 inner
3192.1.fm.c.293.1 yes 2 3192.293 odd 6 inner
3192.1.fm.c.1133.1 yes 2 1.1 even 1 trivial
3192.1.fm.c.1133.1 yes 2 56.13 odd 2 CM
3192.1.fm.d.293.1 yes 2 399.293 odd 6
3192.1.fm.d.293.1 yes 2 456.293 even 6
3192.1.fm.d.1133.1 yes 2 7.6 odd 2
3192.1.fm.d.1133.1 yes 2 8.5 even 2