Properties

Label 2205.1.v.a.2174.1
Level $2205$
Weight $1$
Character 2205.2174
Analytic conductor $1.100$
Analytic rank $0$
Dimension $2$
Projective image $D_{6}$
CM discriminant -35
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2205,1,Mod(569,2205)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2205, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2205.569");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2205.v (of order \(6\), degree \(2\), not 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: \(1.10043835286\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{6}\)
Projective field: Galois closure of 6.2.168781725.1

Embedding invariants

Embedding label 2174.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2205.2174
Dual form 2205.1.v.a.569.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{9} -1.73205i q^{11} -1.00000 q^{12} +(1.50000 + 0.866025i) q^{13} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{20} +1.00000 q^{25} +1.00000 q^{27} +(1.50000 + 0.866025i) q^{33} +(0.500000 - 0.866025i) q^{36} +(-1.50000 + 0.866025i) q^{39} +(1.50000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{51} +1.73205i q^{52} -1.73205i q^{55} -1.00000 q^{60} -1.00000 q^{64} +(1.50000 + 0.866025i) q^{65} -1.00000 q^{68} -1.73205i q^{71} +(-1.50000 - 0.866025i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{83} +(-0.500000 + 0.866025i) q^{85} +(-1.50000 + 0.866025i) q^{97} +(-1.50000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} + q^{4} + 2 q^{5} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} + q^{4} + 2 q^{5} - q^{9} - 2 q^{12} + 3 q^{13} - q^{15} - q^{16} - q^{17} + q^{20} + 2 q^{25} + 2 q^{27} + 3 q^{33} + q^{36} - 3 q^{39} + 3 q^{44} - q^{45} - q^{47} - q^{48} - q^{51} - 2 q^{60} - 2 q^{64} + 3 q^{65} - 2 q^{68} - 3 q^{73} - q^{75} - q^{79} - q^{80} - q^{81} - q^{83} - q^{85} - 3 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times\).

\(n\) \(442\) \(1081\) \(1226\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)

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 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(4\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(5\) 1.00000 1.00000
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.500000 0.866025i
\(10\) 0 0
\(11\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(12\) −1.00000 −1.00000
\(13\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) 0 0
\(15\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0 0
\(33\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.500000 0.866025i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(40\) 0 0
\(41\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 1.50000 0.866025i 1.50000 0.866025i
\(45\) −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 \(\pi\)
\(48\) −0.500000 0.866025i −0.500000 0.866025i
\(49\) 0 0
\(50\) 0 0
\(51\) −0.500000 0.866025i −0.500000 0.866025i
\(52\) 1.73205i 1.73205i
\(53\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) 0 0
\(55\) 1.73205i 1.73205i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) −1.00000 −1.00000
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(66\) 0 0
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) −1.00000 −1.00000
\(69\) 0 0
\(70\) 0 0
\(71\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(72\) 0 0
\(73\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(80\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(81\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(100\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(109\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.73205i 1.73205i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −2.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 1.73205i 1.73205i
\(133\) 0 0
\(134\) 0 0
\(135\) 1.00000 1.00000
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) 0 0
\(141\) −0.500000 0.866025i −0.500000 0.866025i
\(142\) 0 0
\(143\) 1.50000 2.59808i 1.50000 2.59808i
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) 1.00000 1.00000
\(154\) 0 0
\(155\) 0 0
\(156\) −1.50000 0.866025i −1.50000 0.866025i
\(157\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(164\) 0 0
\(165\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(166\) 0 0
\(167\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(168\) 0 0
\(169\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(177\) 0 0
\(178\) 0 0
\(179\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−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 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(188\) −1.00000 −1.00000
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0.500000 0.866025i 0.500000 0.866025i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0.500000 0.866025i 0.500000 0.866025i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(212\) 0 0
\(213\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.50000 0.866025i 1.50000 0.866025i
\(220\) 1.50000 0.866025i 1.50000 0.866025i
\(221\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(222\) 0 0
\(223\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −0.500000 0.866025i −0.500000 0.866025i
\(226\) 0 0
\(227\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0 0
\(235\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(236\) 0 0
\(237\) −0.500000 0.866025i −0.500000 0.866025i
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) −0.500000 0.866025i −0.500000 0.866025i
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.500000 0.866025i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 1.00000 1.00000
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −0.500000 0.866025i −0.500000 0.866025i
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.73205i 1.73205i
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) −0.500000 0.866025i −0.500000 0.866025i
\(273\) 0 0
\(274\) 0 0
\(275\) 1.73205i 1.73205i
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(282\) 0 0
\(283\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(284\) 1.50000 0.866025i 1.50000 0.866025i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 1.73205i 1.73205i
\(292\) 1.73205i 1.73205i
\(293\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.73205i 1.73205i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.00000 −1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(312\) 0 0
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.00000 −1.00000
\(317\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.00000 −1.00000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(326\) 0 0
\(327\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(332\) 0.500000 0.866025i 0.500000 0.866025i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −1.00000 −1.00000
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(350\) 0 0
\(351\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(352\) 0 0
\(353\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(354\) 0 0
\(355\) 1.73205i 1.73205i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0 0
\(361\) 0.500000 0.866025i 0.500000 0.866025i
\(362\) 0 0
\(363\) 1.00000 1.73205i 1.00000 1.73205i
\(364\) 0 0
\(365\) −1.50000 0.866025i −1.50000 0.866025i
\(366\) 0 0
\(367\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −1.50000 0.866025i −1.50000 0.866025i
\(389\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(396\) −1.50000 0.866025i −1.50000 0.866025i
\(397\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −0.500000 0.866025i −0.500000 0.866025i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 1.00000 1.00000
\(424\) 0 0
\(425\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(430\) 0 0
\(431\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 1.00000
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 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
\(447\) −1.50000 0.866025i −1.50000 0.866025i
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(460\) 0 0
\(461\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 1.50000 0.866025i 1.50000 0.866025i
\(469\) 0 0
\(470\) 0 0
\(471\) 1.73205i 1.73205i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.00000 1.73205i −1.00000 1.73205i
\(485\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(486\) 0 0
\(487\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(501\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(502\) 0 0
\(503\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.00000 −2.00000
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(518\) 0 0
\(519\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.50000 0.866025i 1.50000 0.866025i
\(538\) 0 0
\(539\) 0 0
\(540\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(541\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.500000 0.866025i 0.500000 0.866025i
\(546\) 0 0
\(547\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(562\) 0 0
\(563\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(564\) 0.500000 0.866025i 0.500000 0.866025i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 3.00000 3.00000
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(577\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 1.73205i 1.73205i
\(586\) 0 0
\(587\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(597\) 0 0
\(598\) 0 0
\(599\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(600\) 0 0
\(601\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(605\) −2.00000 −2.00000
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(612\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(613\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.73205i 1.73205i
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(632\) 0 0
\(633\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.73205i 1.73205i
\(658\) 0 0
\(659\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(660\) 1.73205i 1.73205i
\(661\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(662\) 0 0
\(663\) 1.73205i 1.73205i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.00000 1.00000
\(669\) 1.73205i 1.73205i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(677\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.500000 0.866025i 0.500000 0.866025i
\(682\) 0 0
\(683\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(692\) 2.00000 2.00000
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.73205i 1.73205i
\(705\) −0.500000 0.866025i −0.500000 0.866025i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(710\) 0 0
\(711\) 1.00000 1.00000
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 1.50000 2.59808i 1.50000 2.59808i
\(716\) 1.73205i 1.73205i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 1.00000 1.00000
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 0 0
\(745\) 1.73205i 1.73205i
\(746\) 0 0
\(747\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(748\) 1.73205i 1.73205i
\(749\) 0 0
\(750\) 0 0
\(751\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(752\) −0.500000 0.866025i −0.500000 0.866025i
\(753\) 0 0
\(754\) 0 0
\(755\) 1.00000 1.00000
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1.00000 1.00000
\(766\) 0 0
\(767\) 0 0
\(768\) 1.00000 1.00000
\(769\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(770\) 0 0
\(771\) 0.500000 0.866025i 0.500000 0.866025i
\(772\) 0 0
\(773\) −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 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.50000 0.866025i −1.50000 0.866025i
\(781\) −3.00000 −3.00000
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.50000 0.866025i 1.50000 0.866025i
\(786\) 0 0
\(787\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) −0.500000 0.866025i −0.500000 0.866025i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 1.00000 1.00000
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(824\) 0 0
\(825\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.50000 0.866025i −1.50000 0.866025i
\(833\) 0 0
\(834\) 0 0
\(835\) 0.500000 0.866025i 0.500000 0.866025i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(840\) 0 0
\(841\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(842\) 0 0
\(843\) 1.73205i 1.73205i
\(844\) 1.00000 1.00000
\(845\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 1.73205i 1.73205i
\(850\) 0 0
\(851\) 0 0
\(852\) 1.73205i 1.73205i
\(853\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(864\) 0 0
\(865\) 1.00000 1.73205i 1.00000 1.73205i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(874\) 0 0
\(875\) 0 0
\(876\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) −1.00000 1.73205i −1.00000 1.73205i
\(880\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) −1.50000 0.866025i −1.50000 0.866025i
\(885\) 0 0
\(886\) 0 0
\(887\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(892\) −1.50000 0.866025i −1.50000 0.866025i
\(893\) 0 0
\(894\) 0 0
\(895\) −1.50000 0.866025i −1.50000 0.866025i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.500000 0.866025i 0.500000 0.866025i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) −0.500000 0.866025i −0.500000 0.866025i
\(909\) 0 0
\(910\) 0 0
\(911\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(920\) 0 0
\(921\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(922\) 0 0
\(923\) 1.50000 2.59808i 1.50000 2.59808i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(936\) 0 0
\(937\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −1.00000 −1.00000
\(941\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(948\) 0.500000 0.866025i 0.500000 0.866025i
\(949\) −1.50000 2.59808i −1.50000 2.59808i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0.500000 0.866025i 0.500000 0.866025i
\(961\) 0.500000 0.866025i 0.500000 0.866025i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(972\) 0.500000 0.866025i 0.500000 0.866025i
\(973\) 0 0
\(974\) 0 0
\(975\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(976\) 0 0
\(977\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1.00000 −1.00000
\(982\) 0 0
\(983\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(992\) 0 0
\(993\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(994\) 0 0
\(995\) 0 0
\(996\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(997\) 0 0 1.00000 \(0\)
−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 2205.1.v.a.2174.1 2
5.4 even 2 2205.1.v.b.2174.1 2
7.2 even 3 2205.1.br.a.2039.1 2
7.3 odd 6 2205.1.ba.a.1814.1 yes 2
7.4 even 3 2205.1.ba.b.1814.1 yes 2
7.5 odd 6 2205.1.br.b.2039.1 2
7.6 odd 2 2205.1.v.b.2174.1 2
9.2 odd 6 2205.1.br.b.704.1 2
35.4 even 6 2205.1.ba.a.1814.1 yes 2
35.9 even 6 2205.1.br.b.2039.1 2
35.19 odd 6 2205.1.br.a.2039.1 2
35.24 odd 6 2205.1.ba.b.1814.1 yes 2
35.34 odd 2 CM 2205.1.v.a.2174.1 2
45.29 odd 6 2205.1.br.a.704.1 2
63.2 odd 6 2205.1.v.b.569.1 2
63.11 odd 6 2205.1.ba.a.344.1 2
63.20 even 6 2205.1.br.a.704.1 2
63.38 even 6 2205.1.ba.b.344.1 yes 2
63.47 even 6 inner 2205.1.v.a.569.1 2
315.74 odd 6 2205.1.ba.b.344.1 yes 2
315.164 even 6 2205.1.ba.a.344.1 2
315.209 even 6 2205.1.br.b.704.1 2
315.254 odd 6 inner 2205.1.v.a.569.1 2
315.299 even 6 2205.1.v.b.569.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2205.1.v.a.569.1 2 63.47 even 6 inner
2205.1.v.a.569.1 2 315.254 odd 6 inner
2205.1.v.a.2174.1 2 1.1 even 1 trivial
2205.1.v.a.2174.1 2 35.34 odd 2 CM
2205.1.v.b.569.1 2 63.2 odd 6
2205.1.v.b.569.1 2 315.299 even 6
2205.1.v.b.2174.1 2 5.4 even 2
2205.1.v.b.2174.1 2 7.6 odd 2
2205.1.ba.a.344.1 2 63.11 odd 6
2205.1.ba.a.344.1 2 315.164 even 6
2205.1.ba.a.1814.1 yes 2 7.3 odd 6
2205.1.ba.a.1814.1 yes 2 35.4 even 6
2205.1.ba.b.344.1 yes 2 63.38 even 6
2205.1.ba.b.344.1 yes 2 315.74 odd 6
2205.1.ba.b.1814.1 yes 2 7.4 even 3
2205.1.ba.b.1814.1 yes 2 35.24 odd 6
2205.1.br.a.704.1 2 45.29 odd 6
2205.1.br.a.704.1 2 63.20 even 6
2205.1.br.a.2039.1 2 7.2 even 3
2205.1.br.a.2039.1 2 35.19 odd 6
2205.1.br.b.704.1 2 9.2 odd 6
2205.1.br.b.704.1 2 315.209 even 6
2205.1.br.b.2039.1 2 7.5 odd 6
2205.1.br.b.2039.1 2 35.9 even 6