Properties

Label 3640.1.lw.a.1133.1
Level $3640$
Weight $1$
Character 3640.1133
Analytic conductor $1.817$
Analytic rank $0$
Dimension $4$
Projective image $D_{12}$
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] = [3640,1,Mod(1077,3640)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3640, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 3, 6, 7]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3640.1077");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3640.lw (of order \(12\), degree \(4\), 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: \(1.81659664598\)
Analytic rank: \(0\)
Dimension: \(4\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{12}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{12} - \cdots)\)

Embedding invariants

Embedding label 1133.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 3640.1133
Dual form 3640.1.lw.a.2477.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.133975 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.133975 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(0.633975 + 0.366025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.133975 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.133975 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(0.633975 + 0.366025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.366025 + 0.366025i) q^{12} +(0.500000 - 0.866025i) q^{13} +1.00000i q^{14} +(0.133975 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.732051 q^{18} +(-1.36603 + 0.366025i) q^{19} -1.00000i q^{20} +(-0.366025 - 0.366025i) q^{21} +(1.86603 + 0.500000i) q^{23} +(0.500000 + 0.133975i) q^{24} +(0.500000 - 0.866025i) q^{25} -1.00000i q^{26} +(-0.633975 + 0.633975i) q^{27} +(0.500000 + 0.866025i) q^{28} +(0.366025 + 0.366025i) q^{30} +(-0.866025 - 0.500000i) q^{32} +1.00000i q^{35} +(0.633975 - 0.366025i) q^{36} +(-1.00000 + 1.00000i) q^{38} +(0.366025 + 0.366025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.500000 - 0.133975i) q^{42} +0.732051 q^{45} +(1.86603 - 0.500000i) q^{46} +(0.500000 - 0.133975i) q^{48} +(-0.500000 - 0.866025i) q^{49} -1.00000i q^{50} +(-0.500000 - 0.866025i) q^{52} +(-0.232051 + 0.866025i) q^{54} +(0.866025 + 0.500000i) q^{56} -0.732051i q^{57} +(-0.500000 - 1.86603i) q^{59} +(0.500000 + 0.133975i) q^{60} +(-0.866025 + 1.50000i) q^{61} +(-0.633975 + 0.366025i) q^{63} -1.00000 q^{64} -1.00000i q^{65} +(-0.500000 + 0.866025i) q^{69} +(0.500000 + 0.866025i) q^{70} +(-0.133975 - 0.500000i) q^{71} +(0.366025 - 0.633975i) q^{72} +(0.366025 + 0.366025i) q^{75} +(-0.366025 + 1.36603i) q^{76} +(0.500000 + 0.133975i) q^{78} +2.00000i q^{79} +(-0.866025 - 0.500000i) q^{80} +(0.133975 + 0.232051i) q^{81} +2.00000 q^{83} +(-0.500000 + 0.133975i) q^{84} +(0.633975 - 0.366025i) q^{90} +(0.500000 + 0.866025i) q^{91} +(1.36603 - 1.36603i) q^{92} +(-1.00000 + 1.00000i) q^{95} +(0.366025 - 0.366025i) q^{96} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 2 q^{4} + 4 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 2 q^{4} + 4 q^{6} - 2 q^{7} + 6 q^{9} + 2 q^{10} - 2 q^{12} + 2 q^{13} + 4 q^{15} - 2 q^{16} - 4 q^{18} - 2 q^{19} + 2 q^{21} + 4 q^{23} + 2 q^{24} + 2 q^{25} - 6 q^{27} + 2 q^{28} - 2 q^{30} + 6 q^{36} - 4 q^{38} - 2 q^{39} - 2 q^{40} - 2 q^{42} - 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} - 2 q^{52} + 6 q^{54} - 2 q^{59} + 2 q^{60} - 6 q^{63} - 4 q^{64} - 2 q^{69} + 2 q^{70} - 4 q^{71} - 2 q^{72} - 2 q^{75} + 2 q^{76} + 2 q^{78} + 4 q^{81} + 8 q^{83} - 2 q^{84} + 6 q^{90} + 2 q^{91} + 2 q^{92} - 4 q^{95} - 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3640\mathbb{Z}\right)^\times\).

\(n\) \(521\) \(561\) \(911\) \(1457\) \(1821\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.866025 0.500000i
\(3\) −0.133975 + 0.500000i −0.133975 + 0.500000i 0.866025 + 0.500000i \(0.166667\pi\)
−1.00000 \(\pi\)
\(4\) 0.500000 0.866025i 0.500000 0.866025i
\(5\) 0.866025 0.500000i 0.866025 0.500000i
\(6\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(7\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(8\) 1.00000i 1.00000i
\(9\) 0.633975 + 0.366025i 0.633975 + 0.366025i
\(10\) 0.500000 0.866025i 0.500000 0.866025i
\(11\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(12\) 0.366025 + 0.366025i 0.366025 + 0.366025i
\(13\) 0.500000 0.866025i 0.500000 0.866025i
\(14\) 1.00000i 1.00000i
\(15\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(18\) 0.732051 0.732051
\(19\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 1.00000i 1.00000i
\(21\) −0.366025 0.366025i −0.366025 0.366025i
\(22\) 0 0
\(23\) 1.86603 + 0.500000i 1.86603 + 0.500000i 1.00000 \(0\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(25\) 0.500000 0.866025i 0.500000 0.866025i
\(26\) 1.00000i 1.00000i
\(27\) −0.633975 + 0.633975i −0.633975 + 0.633975i
\(28\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0.366025 + 0.366025i 0.366025 + 0.366025i
\(31\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(32\) −0.866025 0.500000i −0.866025 0.500000i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000i 1.00000i
\(36\) 0.633975 0.366025i 0.633975 0.366025i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(39\) 0.366025 + 0.366025i 0.366025 + 0.366025i
\(40\) −0.500000 0.866025i −0.500000 0.866025i
\(41\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(42\) −0.500000 0.133975i −0.500000 0.133975i
\(43\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(44\) 0 0
\(45\) 0.732051 0.732051
\(46\) 1.86603 0.500000i 1.86603 0.500000i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0.500000 0.133975i 0.500000 0.133975i
\(49\) −0.500000 0.866025i −0.500000 0.866025i
\(50\) 1.00000i 1.00000i
\(51\) 0 0
\(52\) −0.500000 0.866025i −0.500000 0.866025i
\(53\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) −0.232051 + 0.866025i −0.232051 + 0.866025i
\(55\) 0 0
\(56\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(57\) 0.732051i 0.732051i
\(58\) 0 0
\(59\) −0.500000 1.86603i −0.500000 1.86603i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(-0.5\pi\)
\(60\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(61\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 0 0
\(63\) −0.633975 + 0.366025i −0.633975 + 0.366025i
\(64\) −1.00000 −1.00000
\(65\) 1.00000i 1.00000i
\(66\) 0 0
\(67\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 0 0
\(69\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(70\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(71\) −0.133975 0.500000i −0.133975 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
−1.00000 \(\pi\)
\(72\) 0.366025 0.633975i 0.366025 0.633975i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0.366025 + 0.366025i 0.366025 + 0.366025i
\(76\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(77\) 0 0
\(78\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(79\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −0.866025 0.500000i −0.866025 0.500000i
\(81\) 0.133975 + 0.232051i 0.133975 + 0.232051i
\(82\) 0 0
\(83\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(84\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(90\) 0.633975 0.366025i 0.633975 0.366025i
\(91\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(92\) 1.36603 1.36603i 1.36603 1.36603i
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(96\) 0.366025 0.366025i 0.366025 0.366025i
\(97\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(98\) −0.866025 0.500000i −0.866025 0.500000i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.500000 0.866025i
\(101\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 0 0
\(103\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) −0.866025 0.500000i −0.866025 0.500000i
\(105\) −0.500000 0.133975i −0.500000 0.133975i
\(106\) 0 0
\(107\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(108\) 0.232051 + 0.866025i 0.232051 + 0.866025i
\(109\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 1.00000
\(113\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −0.366025 0.633975i −0.366025 0.633975i
\(115\) 1.86603 0.500000i 1.86603 0.500000i
\(116\) 0 0
\(117\) 0.633975 0.366025i 0.633975 0.366025i
\(118\) −1.36603 1.36603i −1.36603 1.36603i
\(119\) 0 0
\(120\) 0.500000 0.133975i 0.500000 0.133975i
\(121\) −0.866025 0.500000i −0.866025 0.500000i
\(122\) 1.73205i 1.73205i
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000i 1.00000i
\(126\) −0.366025 + 0.633975i −0.366025 + 0.633975i
\(127\) 0.133975 0.500000i 0.133975 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000 \(0\)
\(128\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(129\) 0 0
\(130\) −0.500000 0.866025i −0.500000 0.866025i
\(131\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0.366025 1.36603i 0.366025 1.36603i
\(134\) 0 0
\(135\) −0.232051 + 0.866025i −0.232051 + 0.866025i
\(136\) 0 0
\(137\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(138\) 1.00000i 1.00000i
\(139\) −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 0.500000i \(-0.833333\pi\)
\(140\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(141\) 0 0
\(142\) −0.366025 0.366025i −0.366025 0.366025i
\(143\) 0 0
\(144\) 0.732051i 0.732051i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.500000 0.133975i 0.500000 0.133975i
\(148\) 0 0
\(149\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(150\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(151\) −1.36603 1.36603i −1.36603 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(152\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.500000 0.133975i 0.500000 0.133975i
\(157\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(158\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(159\) 0 0
\(160\) −1.00000 −1.00000
\(161\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(162\) 0.232051 + 0.133975i 0.232051 + 0.133975i
\(163\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.73205 1.00000i 1.73205 1.00000i
\(167\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(168\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(169\) −0.500000 0.866025i −0.500000 0.866025i
\(170\) 0 0
\(171\) −1.00000 0.267949i −1.00000 0.267949i
\(172\) 0 0
\(173\) 0.500000 + 1.86603i 0.500000 + 1.86603i 0.500000 + 0.866025i \(0.333333\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(176\) 0 0
\(177\) 1.00000 1.00000
\(178\) 0 0
\(179\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 0.366025 0.633975i 0.366025 0.633975i
\(181\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(182\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(183\) −0.633975 0.633975i −0.633975 0.633975i
\(184\) 0.500000 1.86603i 0.500000 1.86603i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.232051 0.866025i −0.232051 0.866025i
\(190\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0.133975 0.500000i 0.133975 0.500000i
\(193\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(194\) 0 0
\(195\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(196\) −1.00000 −1.00000
\(197\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(198\) 0 0
\(199\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) −0.866025 0.500000i −0.866025 0.500000i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(208\) −1.00000 −1.00000
\(209\) 0 0
\(210\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) 0.267949 0.267949
\(214\) 0 0
\(215\) 0 0
\(216\) 0.633975 + 0.633975i 0.633975 + 0.633975i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(224\) 0.866025 0.500000i 0.866025 0.500000i
\(225\) 0.633975 0.366025i 0.633975 0.366025i
\(226\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(227\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) −0.633975 0.366025i −0.633975 0.366025i
\(229\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(230\) 1.36603 1.36603i 1.36603 1.36603i
\(231\) 0 0
\(232\) 0 0
\(233\) −1.36603 + 1.36603i −1.36603 + 1.36603i −0.500000 + 0.866025i \(0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0.366025 0.633975i 0.366025 0.633975i
\(235\) 0 0
\(236\) −1.86603 0.500000i −1.86603 0.500000i
\(237\) −1.00000 0.267949i −1.00000 0.267949i
\(238\) 0 0
\(239\) −0.366025 0.366025i −0.366025 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0.366025 0.366025i 0.366025 0.366025i
\(241\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(242\) −1.00000 −1.00000
\(243\) −1.00000 + 0.267949i −1.00000 + 0.267949i
\(244\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(245\) −0.866025 0.500000i −0.866025 0.500000i
\(246\) 0 0
\(247\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(248\) 0 0
\(249\) −0.267949 + 1.00000i −0.267949 + 1.00000i
\(250\) −0.500000 0.866025i −0.500000 0.866025i
\(251\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) 0.732051i 0.732051i
\(253\) 0 0
\(254\) −0.133975 0.500000i −0.133975 0.500000i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.866025 0.500000i −0.866025 0.500000i
\(261\) 0 0
\(262\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(263\) −0.133975 + 0.500000i −0.133975 + 0.500000i 0.866025 + 0.500000i \(0.166667\pi\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.366025 1.36603i −0.366025 1.36603i
\(267\) 0 0
\(268\) 0 0
\(269\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(270\) 0.232051 + 0.866025i 0.232051 + 0.866025i
\(271\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(272\) 0 0
\(273\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(274\) 1.00000i 1.00000i
\(275\) 0 0
\(276\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(277\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(278\) −2.00000 −2.00000
\(279\) 0 0
\(280\) 1.00000 1.00000
\(281\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −0.500000 0.133975i −0.500000 0.133975i 1.00000i \(-0.5\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) −0.500000 0.133975i −0.500000 0.133975i
\(285\) −0.366025 0.633975i −0.366025 0.633975i
\(286\) 0 0
\(287\) 0 0
\(288\) −0.366025 0.633975i −0.366025 0.633975i
\(289\) 0.866025 0.500000i 0.866025 0.500000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0.366025 0.366025i 0.366025 0.366025i
\(295\) −1.36603 1.36603i −1.36603 1.36603i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.36603 1.36603i 1.36603 1.36603i
\(300\) 0.500000 0.133975i 0.500000 0.133975i
\(301\) 0 0
\(302\) −1.86603 0.500000i −1.86603 0.500000i
\(303\) 0 0
\(304\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(305\) 1.73205i 1.73205i
\(306\) 0 0
\(307\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0.366025 0.366025i 0.366025 0.366025i
\(313\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(314\) 0.366025 1.36603i 0.366025 1.36603i
\(315\) −0.366025 + 0.633975i −0.366025 + 0.633975i
\(316\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(321\) 0 0
\(322\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(323\) 0 0
\(324\) 0.267949 0.267949
\(325\) −0.500000 0.866025i −0.500000 0.866025i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(332\) 1.00000 1.73205i 1.00000 1.73205i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(337\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(338\) −0.866025 0.500000i −0.866025 0.500000i
\(339\) 0.732051i 0.732051i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.00000 + 0.267949i −1.00000 + 0.267949i
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 1.00000i 1.00000i
\(346\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(347\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(348\) 0 0
\(349\) −0.500000 0.133975i −0.500000 0.133975i 1.00000i \(-0.5\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(351\) 0.232051 + 0.866025i 0.232051 + 0.866025i
\(352\) 0 0
\(353\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 0.866025 0.500000i 0.866025 0.500000i
\(355\) −0.366025 0.366025i −0.366025 0.366025i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.36603 + 1.36603i −1.36603 + 1.36603i −0.500000 + 0.866025i \(0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0.732051i 0.732051i
\(361\) 0.866025 0.500000i 0.866025 0.500000i
\(362\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(363\) 0.366025 0.366025i 0.366025 0.366025i
\(364\) 1.00000 1.00000
\(365\) 0 0
\(366\) −0.866025 0.232051i −0.866025 0.232051i
\(367\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(368\) −0.500000 1.86603i −0.500000 1.86603i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.633975 0.633975i −0.633975 0.633975i
\(379\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(380\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(381\) 0.232051 + 0.133975i 0.232051 + 0.133975i
\(382\) 0 0
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) −0.133975 0.500000i −0.133975 0.500000i
\(385\) 0 0
\(386\) 0.866025 1.50000i 0.866025 1.50000i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0.500000 0.133975i 0.500000 0.133975i
\(391\) 0 0
\(392\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(393\) 0.133975 0.500000i 0.133975 0.500000i
\(394\) 0 0
\(395\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(396\) 0 0
\(397\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0.633975 + 0.366025i 0.633975 + 0.366025i
\(400\) −1.00000 −1.00000
\(401\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.232051 + 0.133975i 0.232051 + 0.133975i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(410\) 0 0
\(411\) −0.366025 0.366025i −0.366025 0.366025i
\(412\) 0 0
\(413\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(414\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(415\) 1.73205 1.00000i 1.73205 1.00000i
\(416\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(417\) 0.732051 0.732051i 0.732051 0.732051i
\(418\) 0 0
\(419\) −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i \(0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(421\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0.232051 0.133975i 0.232051 0.133975i
\(427\) −0.866025 1.50000i −0.866025 1.50000i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.500000 0.133975i −0.500000 0.133975i 1.00000i \(-0.5\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0.866025 + 0.232051i 0.866025 + 0.232051i
\(433\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.73205 −2.73205
\(438\) 0 0
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0.732051i 0.732051i
\(442\) 0 0
\(443\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.500000 0.866025i 0.500000 0.866025i
\(449\) −0.500000 1.86603i −0.500000 1.86603i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(-0.5\pi\)
\(450\) 0.366025 0.633975i 0.366025 0.633975i
\(451\) 0 0
\(452\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(453\) 0.866025 0.500000i 0.866025 0.500000i
\(454\) −1.00000 −1.00000
\(455\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(456\) −0.732051 −0.732051
\(457\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(458\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(459\) 0 0
\(460\) 0.500000 1.86603i 0.500000 1.86603i
\(461\) 0.500000 + 1.86603i 0.500000 + 1.86603i 0.500000 + 0.866025i \(0.333333\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(467\) −0.366025 0.366025i −0.366025 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 0.732051i 0.732051i
\(469\) 0 0
\(470\) 0 0
\(471\) 0.366025 + 0.633975i 0.366025 + 0.633975i
\(472\) −1.86603 + 0.500000i −1.86603 + 0.500000i
\(473\) 0 0
\(474\) −1.00000 + 0.267949i −1.00000 + 0.267949i
\(475\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.500000 0.133975i −0.500000 0.133975i
\(479\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(480\) 0.133975 0.500000i 0.133975 0.500000i
\(481\) 0 0
\(482\) 0 0
\(483\) −0.500000 0.866025i −0.500000 0.866025i
\(484\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(485\) 0 0
\(486\) −0.732051 + 0.732051i −0.732051 + 0.732051i
\(487\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(488\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(489\) 0 0
\(490\) −1.00000 −1.00000
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(495\) 0 0
\(496\) 0 0
\(497\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(498\) 0.267949 + 1.00000i 0.267949 + 1.00000i
\(499\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(500\) −0.866025 0.500000i −0.866025 0.500000i
\(501\) 0 0
\(502\) 1.73205 1.73205
\(503\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(504\) 0.366025 + 0.633975i 0.366025 + 0.633975i
\(505\) 0 0
\(506\) 0 0
\(507\) 0.500000 0.133975i 0.500000 0.133975i
\(508\) −0.366025 0.366025i −0.366025 0.366025i
\(509\) 0.500000 1.86603i 0.500000 1.86603i 1.00000i \(-0.5\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) 0.633975 1.09808i 0.633975 1.09808i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.00000 −1.00000
\(520\) −1.00000 −1.00000
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0.500000 1.86603i 0.500000 1.86603i 1.00000i \(-0.5\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(524\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(525\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(526\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(527\) 0 0
\(528\) 0 0
\(529\) 2.36603 + 1.36603i 2.36603 + 1.36603i
\(530\) 0 0
\(531\) 0.366025 1.36603i 0.366025 1.36603i
\(532\) −1.00000 1.00000i −1.00000 1.00000i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.00000 1.00000
\(539\) 0 0
\(540\) 0.633975 + 0.633975i 0.633975 + 0.633975i
\(541\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(542\) 0 0
\(543\) −0.866025 0.232051i −0.866025 0.232051i
\(544\) 0 0
\(545\) 0 0
\(546\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(547\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(549\) −1.09808 + 0.633975i −1.09808 + 0.633975i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(553\) −1.73205 1.00000i −1.73205 1.00000i
\(554\) 0 0
\(555\) 0 0
\(556\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(557\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.866025 0.500000i 0.866025 0.500000i
\(561\) 0 0
\(562\) −1.36603 0.366025i −1.36603 0.366025i
\(563\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(566\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(567\) −0.267949 −0.267949
\(568\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(569\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(570\) −0.633975 0.366025i −0.633975 0.366025i
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.36603 1.36603i 1.36603 1.36603i
\(576\) −0.633975 0.366025i −0.633975 0.366025i
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0.500000 0.866025i 0.500000 0.866025i
\(579\) 0.232051 + 0.866025i 0.232051 + 0.866025i
\(580\) 0 0
\(581\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0.366025 0.633975i 0.366025 0.633975i
\(586\) 0 0
\(587\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(588\) 0.133975 0.500000i 0.133975 0.500000i
\(589\) 0 0
\(590\) −1.86603 0.500000i −1.86603 0.500000i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.500000 1.86603i 0.500000 1.86603i
\(599\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(600\) 0.366025 0.366025i 0.366025 0.366025i
\(601\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.86603 + 0.500000i −1.86603 + 0.500000i
\(605\) −1.00000 −1.00000
\(606\) 0 0
\(607\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(608\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(609\) 0 0
\(610\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(611\) 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
\(617\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(618\) 0 0
\(619\) −0.366025 + 0.366025i −0.366025 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
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
\(624\) 0.133975 0.500000i 0.133975 0.500000i
\(625\) −0.500000 0.866025i −0.500000 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.366025 1.36603i −0.366025 1.36603i
\(629\) 0 0
\(630\) 0.732051i 0.732051i
\(631\) 0.500000 0.133975i 0.500000 0.133975i 1.00000i \(-0.5\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(632\) 2.00000 2.00000
\(633\) 0 0
\(634\) 0 0
\(635\) −0.133975 0.500000i −0.133975 0.500000i
\(636\) 0 0
\(637\) −1.00000 −1.00000
\(638\) 0 0
\(639\) 0.0980762 0.366025i 0.0980762 0.366025i
\(640\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(641\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(644\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(648\) 0.232051 0.133975i 0.232051 0.133975i
\(649\) 0 0
\(650\) −0.866025 0.500000i −0.866025 0.500000i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(654\) 0 0
\(655\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) 0.500000 1.86603i 0.500000 1.86603i 1.00000i \(-0.5\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 2.00000i 2.00000i
\(665\) −0.366025 1.36603i −0.366025 1.36603i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(673\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) −1.36603 0.366025i −1.36603 0.366025i
\(675\) 0.232051 + 0.866025i 0.232051 + 0.866025i
\(676\) −1.00000 −1.00000
\(677\) 1.36603 1.36603i 1.36603 1.36603i 0.500000 0.866025i \(-0.333333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(678\) −0.366025 0.633975i −0.366025 0.633975i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.366025 0.366025i 0.366025 0.366025i
\(682\) 0 0
\(683\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(684\) −0.732051 + 0.732051i −0.732051 + 0.732051i
\(685\) 1.00000i 1.00000i
\(686\) 0.866025 0.500000i 0.866025 0.500000i
\(687\) −0.366025 0.633975i −0.366025 0.633975i
\(688\) 0 0
\(689\) 0 0
\(690\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(691\) 1.86603 + 0.500000i 1.86603 + 0.500000i 1.00000 \(0\)
0.866025 + 0.500000i \(0.166667\pi\)
\(692\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(693\) 0 0
\(694\) 0 0
\(695\) −2.00000 −2.00000
\(696\) 0 0
\(697\) 0 0
\(698\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(699\) −0.500000 0.866025i −0.500000 0.866025i
\(700\) 1.00000 1.00000
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0.633975 + 0.633975i 0.633975 + 0.633975i
\(703\) 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 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(710\) −0.500000 0.133975i −0.500000 0.133975i
\(711\) −0.732051 + 1.26795i −0.732051 + 1.26795i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.232051 0.133975i 0.232051 0.133975i
\(718\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(719\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) −0.366025 0.633975i −0.366025 0.633975i
\(721\) 0 0
\(722\) 0.500000 0.866025i 0.500000 0.866025i
\(723\) 0 0
\(724\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(725\) 0 0
\(726\) 0.133975 0.500000i 0.133975 0.500000i
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 0.866025 0.500000i 0.866025 0.500000i
\(729\) 0.267949i 0.267949i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.866025 + 0.232051i −0.866025 + 0.232051i
\(733\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(734\) 0 0
\(735\) 0.366025 0.366025i 0.366025 0.366025i
\(736\) −1.36603 1.36603i −1.36603 1.36603i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(740\) 0 0
\(741\) −0.633975 0.366025i −0.633975 0.366025i
\(742\) 0 0
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.26795 + 0.732051i 1.26795 + 0.732051i
\(748\) 0 0
\(749\) 0 0
\(750\) 0.500000 0.133975i 0.500000 0.133975i
\(751\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(752\) 0 0
\(753\) −0.633975 + 0.633975i −0.633975 + 0.633975i
\(754\) 0 0
\(755\) −1.86603 0.500000i −1.86603 0.500000i
\(756\) −0.866025 0.232051i −0.866025 0.232051i
\(757\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(761\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(762\) 0.267949 0.267949
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.86603 0.500000i −1.86603 0.500000i
\(768\) −0.366025 0.366025i −0.366025 0.366025i
\(769\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.73205i 1.73205i
\(773\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.366025 0.366025i 0.366025 0.366025i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(785\) 0.366025 1.36603i 0.366025 1.36603i
\(786\) −0.133975 0.500000i −0.133975 0.500000i
\(787\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(788\) 0 0
\(789\) −0.232051 0.133975i −0.232051 0.133975i
\(790\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(791\) 0.366025 1.36603i 0.366025 1.36603i
\(792\) 0 0
\(793\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(794\) 1.00000i 1.00000i
\(795\) 0 0
\(796\) 0 0
\(797\) 1.86603 0.500000i 1.86603 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000 \(0\)
\(798\) 0.732051 0.732051
\(799\) 0 0
\(800\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(801\) 0 0
\(802\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(803\) 0 0
\(804\) 0 0
\(805\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(806\) 0 0
\(807\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(808\) 0 0
\(809\) −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i \(0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(810\) 0.267949 0.267949
\(811\) 1.36603 1.36603i 1.36603 1.36603i 0.500000 0.866025i \(-0.333333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0.732051i 0.732051i
\(820\) 0 0
\(821\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(822\) −0.500000 0.133975i −0.500000 0.133975i
\(823\) −0.500000 1.86603i −0.500000 1.86603i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(-0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 1.86603 0.500000i 1.86603 0.500000i
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 1.36603 0.366025i 1.36603 0.366025i
\(829\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 1.00000 1.73205i 1.00000 1.73205i
\(831\) 0 0
\(832\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(833\) 0 0
\(834\) 0.267949 1.00000i 0.267949 1.00000i
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(839\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(840\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(841\) 0.500000 0.866025i 0.500000 0.866025i
\(842\) 0 0
\(843\) 0.633975 0.366025i 0.633975 0.366025i
\(844\) 0 0
\(845\) −0.866025 0.500000i −0.866025 0.500000i
\(846\) 0 0
\(847\) 0.866025 0.500000i 0.866025 0.500000i
\(848\) 0 0
\(849\) 0.133975 0.232051i 0.133975 0.232051i
\(850\) 0 0
\(851\) 0 0
\(852\) 0.133975 0.232051i 0.133975 0.232051i
\(853\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(854\) −1.50000 0.866025i −1.50000 0.866025i
\(855\) −1.00000 + 0.267949i −1.00000 + 0.267949i
\(856\) 0 0
\(857\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(863\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(864\) 0.866025 0.232051i 0.866025 0.232051i
\(865\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(866\) 0 0
\(867\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) −2.36603 + 1.36603i −2.36603 + 1.36603i
\(875\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(876\) 0 0
\(877\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(882\) −0.366025 0.633975i −0.366025 0.633975i
\(883\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(884\) 0 0
\(885\) 0.866025 0.500000i 0.866025 0.500000i
\(886\) 0 0
\(887\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(888\) 0 0
\(889\) 0.366025 + 0.366025i 0.366025 + 0.366025i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000i 1.00000i
\(897\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(898\) −1.36603 1.36603i −1.36603 1.36603i
\(899\) 0 0
\(900\) 0.732051i 0.732051i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(905\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(906\) 0.500000 0.866025i 0.500000 0.866025i
\(907\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(908\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(909\) 0 0
\(910\) 1.00000 1.00000
\(911\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(912\) −0.633975 + 0.366025i −0.633975 + 0.366025i
\(913\) 0 0
\(914\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(915\) −0.866025 0.232051i −0.866025 0.232051i
\(916\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(917\) 0.500000 0.866025i 0.500000 0.866025i
\(918\) 0 0
\(919\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(920\) −0.500000 1.86603i −0.500000 1.86603i
\(921\) −0.232051 + 0.866025i −0.232051 + 0.866025i
\(922\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(923\) −0.500000 0.133975i −0.500000 0.133975i
\(924\) 0 0
\(925\) 0 0
\(926\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(930\) 0 0
\(931\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(932\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(933\) 0 0
\(934\) −0.500000 0.133975i −0.500000 0.133975i
\(935\) 0 0
\(936\) −0.366025 0.633975i −0.366025 0.633975i
\(937\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0.366025 0.366025i 0.366025 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(942\) 0.633975 + 0.366025i 0.633975 + 0.366025i
\(943\) 0 0
\(944\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(945\) −0.633975 0.633975i −0.633975 0.633975i
\(946\) 0 0
\(947\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(948\) −0.732051 + 0.732051i −0.732051 + 0.732051i
\(949\) 0 0
\(950\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(951\) 0 0
\(952\) 0 0
\(953\) −0.133975 0.500000i −0.133975 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(957\) 0 0
\(958\) 0 0
\(959\) −0.500000 0.866025i −0.500000 0.866025i
\(960\) −0.133975 0.500000i −0.133975 0.500000i
\(961\) 1.00000i 1.00000i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0.866025 1.50000i 0.866025 1.50000i
\(966\) −0.866025 0.500000i −0.866025 0.500000i
\(967\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(968\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(969\) 0 0
\(970\) 0 0
\(971\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(972\) −0.267949 + 1.00000i −0.267949 + 1.00000i
\(973\) 1.73205 1.00000i 1.73205 1.00000i
\(974\) 1.00000 1.00000
\(975\) 0.500000 0.133975i 0.500000 0.133975i
\(976\) 1.73205 1.73205
\(977\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(978\) 0 0
\(979\) 0 0
\(980\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(989\) 0 0
\(990\) 0 0
\(991\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0.500000 0.133975i 0.500000 0.133975i
\(995\) 0 0
\(996\) 0.732051 + 0.732051i 0.732051 + 0.732051i
\(997\) 0.500000 + 1.86603i 0.500000 + 1.86603i 0.500000 + 0.866025i \(0.333333\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 3640.1.lw.a.1133.1 4
5.2 odd 4 3640.1.md.d.3317.1 yes 4
7.6 odd 2 3640.1.lw.d.1133.1 yes 4
8.5 even 2 3640.1.lw.d.1133.1 yes 4
13.7 odd 12 3640.1.md.d.293.1 yes 4
35.27 even 4 3640.1.md.c.3317.1 yes 4
40.37 odd 4 3640.1.md.c.3317.1 yes 4
56.13 odd 2 CM 3640.1.lw.a.1133.1 4
65.7 even 12 inner 3640.1.lw.a.2477.1 yes 4
91.20 even 12 3640.1.md.c.293.1 yes 4
104.85 odd 12 3640.1.md.c.293.1 yes 4
280.237 even 4 3640.1.md.d.3317.1 yes 4
455.202 odd 12 3640.1.lw.d.2477.1 yes 4
520.397 even 12 3640.1.lw.d.2477.1 yes 4
728.293 even 12 3640.1.md.d.293.1 yes 4
3640.2477 odd 12 inner 3640.1.lw.a.2477.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.1.lw.a.1133.1 4 1.1 even 1 trivial
3640.1.lw.a.1133.1 4 56.13 odd 2 CM
3640.1.lw.a.2477.1 yes 4 65.7 even 12 inner
3640.1.lw.a.2477.1 yes 4 3640.2477 odd 12 inner
3640.1.lw.d.1133.1 yes 4 7.6 odd 2
3640.1.lw.d.1133.1 yes 4 8.5 even 2
3640.1.lw.d.2477.1 yes 4 455.202 odd 12
3640.1.lw.d.2477.1 yes 4 520.397 even 12
3640.1.md.c.293.1 yes 4 91.20 even 12
3640.1.md.c.293.1 yes 4 104.85 odd 12
3640.1.md.c.3317.1 yes 4 35.27 even 4
3640.1.md.c.3317.1 yes 4 40.37 odd 4
3640.1.md.d.293.1 yes 4 13.7 odd 12
3640.1.md.d.293.1 yes 4 728.293 even 12
3640.1.md.d.3317.1 yes 4 5.2 odd 4
3640.1.md.d.3317.1 yes 4 280.237 even 4