Properties

Label 1407.1.g.i.1406.2
Level $1407$
Weight $1$
Character 1407.1406
Analytic conductor $0.702$
Analytic rank $0$
Dimension $2$
Projective image $D_{6}$
RM discriminant 469
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1407,1,Mod(1406,1407)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1407, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1407.1406");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1407 = 3 \cdot 7 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1407.g (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.702184472775\)
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 6.0.5938947.1

Embedding invariants

Embedding label 1406.2
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1407.1406
Dual form 1407.1.g.i.1406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +1.73205i q^{5} +1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +1.73205i q^{5} +1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-1.50000 + 0.866025i) q^{15} +1.00000 q^{16} -1.73205i q^{20} +(0.500000 + 0.866025i) q^{21} -1.73205i q^{23} -2.00000 q^{25} -1.00000 q^{27} -1.00000 q^{28} +1.73205i q^{29} -1.00000 q^{31} +1.73205i q^{35} +(0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(0.500000 + 0.866025i) q^{39} -1.73205i q^{41} +(-1.50000 - 0.866025i) q^{45} +(0.500000 + 0.866025i) q^{48} +1.00000 q^{49} -1.00000 q^{52} +(1.50000 - 0.866025i) q^{60} +2.00000 q^{61} +(-0.500000 + 0.866025i) q^{63} -1.00000 q^{64} +1.73205i q^{65} -1.00000 q^{67} +(1.50000 - 0.866025i) q^{69} -1.73205i q^{71} +(-1.00000 - 1.73205i) q^{75} +1.73205i q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{84} +(-1.50000 + 0.866025i) q^{87} +1.00000 q^{91} +1.73205i q^{92} +(-0.500000 - 0.866025i) q^{93} +2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} - 2 q^{4} + 2 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} - 2 q^{4} + 2 q^{7} - q^{9} - q^{12} + 2 q^{13} - 3 q^{15} + 2 q^{16} + q^{21} - 4 q^{25} - 2 q^{27} - 2 q^{28} - 2 q^{31} + q^{36} - 2 q^{37} + q^{39} - 3 q^{45} + q^{48} + 2 q^{49} - 2 q^{52} + 3 q^{60} + 4 q^{61} - q^{63} - 2 q^{64} - 2 q^{67} + 3 q^{69} - 2 q^{75} - q^{81} - q^{84} - 3 q^{87} + 2 q^{91} - q^{93} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1407\mathbb{Z}\right)^\times\).

\(n\) \(337\) \(470\) \(1207\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(4\) −1.00000 −1.00000
\(5\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 0 0
\(7\) 1.00000 1.00000
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −0.500000 0.866025i −0.500000 0.866025i
\(13\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) 0 0
\(15\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.73205i 1.73205i
\(21\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(22\) 0 0
\(23\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(24\) 0 0
\(25\) −2.00000 −2.00000
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) −1.00000 −1.00000
\(29\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.73205i 1.73205i
\(36\) 0.500000 0.866025i 0.500000 0.866025i
\(37\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(40\) 0 0
\(41\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) −1.50000 0.866025i −1.50000 0.866025i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(49\) 1.00000 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) −1.00000 −1.00000
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 1.50000 0.866025i 1.50000 0.866025i
\(61\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(62\) 0 0
\(63\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(64\) −1.00000 −1.00000
\(65\) 1.73205i 1.73205i
\(66\) 0 0
\(67\) −1.00000 −1.00000
\(68\) 0 0
\(69\) 1.50000 0.866025i 1.50000 0.866025i
\(70\) 0 0
\(71\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −1.00000 1.73205i −1.00000 1.73205i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 1.73205i 1.73205i
\(81\) −0.500000 0.866025i −0.500000 0.866025i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −0.500000 0.866025i −0.500000 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 1.00000 1.00000
\(92\) 1.73205i 1.73205i
\(93\) −0.500000 0.866025i −0.500000 0.866025i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.00000 2.00000
\(101\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.00000 1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −0.500000 0.866025i −0.500000 0.866025i
\(112\) 1.00000 1.00000
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 3.00000 3.00000
\(116\) 1.73205i 1.73205i
\(117\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 0 0
\(123\) 1.50000 0.866025i 1.50000 0.866025i
\(124\) 1.00000 1.00000
\(125\) 1.73205i 1.73205i
\(126\) 0 0
\(127\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.73205i 1.73205i
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(140\) 1.73205i 1.73205i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(145\) −3.00000 −3.00000
\(146\) 0 0
\(147\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(148\) 1.00000 1.00000
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.73205i 1.73205i
\(156\) −0.500000 0.866025i −0.500000 0.866025i
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.73205i 1.73205i
\(162\) 0 0
\(163\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 1.73205i 1.73205i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) −2.00000 −2.00000
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(184\) 0 0
\(185\) 1.73205i 1.73205i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.00000 −1.00000
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −0.500000 0.866025i −0.500000 0.866025i
\(193\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(196\) −1.00000 −1.00000
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) −0.500000 0.866025i −0.500000 0.866025i
\(202\) 0 0
\(203\) 1.73205i 1.73205i
\(204\) 0 0
\(205\) 3.00000 3.00000
\(206\) 0 0
\(207\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(208\) 1.00000 1.00000
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 1.50000 0.866025i 1.50000 0.866025i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.00000 −1.00000
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 1.00000 1.73205i 1.00000 1.73205i
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.500000 0.866025i
\(244\) −2.00000 −2.00000
\(245\) 1.73205i 1.73205i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0.500000 0.866025i 0.500000 0.866025i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) −1.00000 −1.00000
\(260\) 1.73205i 1.73205i
\(261\) −1.50000 0.866025i −1.50000 0.866025i
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 1.00000 1.00000
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0 0
\(273\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(274\) 0 0
\(275\) 0 0
\(276\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(277\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0.500000 0.866025i 0.500000 0.866025i
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 1.73205i 1.73205i
\(285\) 0 0
\(286\) 0 0
\(287\) 1.73205i 1.73205i
\(288\) 0 0
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.73205i 1.73205i
\(300\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(301\) 0 0
\(302\) 0 0
\(303\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(304\) 0 0
\(305\) 3.46410i 3.46410i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(312\) 0 0
\(313\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) −1.50000 0.866025i −1.50000 0.866025i
\(316\) 0 0
\(317\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.73205i 1.73205i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(325\) −2.00000 −2.00000
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0.500000 0.866025i 0.500000 0.866025i
\(334\) 0 0
\(335\) 1.73205i 1.73205i
\(336\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 1.50000 0.866025i 1.50000 0.866025i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −1.00000 −1.00000
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 3.00000 3.00000
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −0.500000 0.866025i −0.500000 0.866025i
\(364\) −1.00000 −1.00000
\(365\) 0 0
\(366\) 0 0
\(367\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 1.73205i 1.73205i
\(369\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(370\) 0 0
\(371\) 0 0
\(372\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.50000 0.866025i 1.50000 0.866025i
\(376\) 0 0
\(377\) 1.73205i 1.73205i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(382\) 0 0
\(383\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −2.00000 −2.00000
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.00000 −2.00000
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) −1.00000 −1.00000
\(404\) 1.73205i 1.73205i
\(405\) 1.50000 0.866025i 1.50000 0.866025i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 1.50000 0.866025i 1.50000 0.866025i
\(421\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.00000 2.00000
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −1.00000 −1.00000
\(433\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) −1.50000 2.59808i −1.50000 2.59808i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.00000 −1.00000
\(449\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(454\) 0 0
\(455\) 1.73205i 1.73205i
\(456\) 0 0
\(457\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −3.00000 −3.00000
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 1.73205i 1.73205i
\(465\) 1.50000 0.866025i 1.50000 0.866025i
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0.500000 0.866025i 0.500000 0.866025i
\(469\) −1.00000 −1.00000
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −1.00000 −1.00000
\(482\) 0 0
\(483\) 1.50000 0.866025i 1.50000 0.866025i
\(484\) 1.00000 1.00000
\(485\) 3.46410i 3.46410i
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −0.500000 0.866025i −0.500000 0.866025i
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) 1.73205i 1.73205i
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 1.73205i 1.73205i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) −3.00000 −3.00000
\(506\) 0 0
\(507\) 0 0
\(508\) −1.00000 −1.00000
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) −1.00000 1.73205i −1.00000 1.73205i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −2.00000 −2.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.73205i 1.73205i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 1.73205i 1.73205i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.50000 0.866025i 1.50000 0.866025i
\(556\) −1.00000 −1.00000
\(557\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.73205i 1.73205i
\(561\) 0 0
\(562\) 0 0
\(563\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.500000 0.866025i −0.500000 0.866025i
\(568\) 0 0
\(569\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3.46410i 3.46410i
\(576\) 0.500000 0.866025i 0.500000 0.866025i
\(577\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 0 0
\(579\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(580\) 3.00000 3.00000
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −1.50000 0.866025i −1.50000 0.866025i
\(586\) 0 0
\(587\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) −0.500000 0.866025i −0.500000 0.866025i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 −1.00000
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0.500000 0.866025i 0.500000 0.866025i
\(604\) −1.00000 −1.00000
\(605\) 1.73205i 1.73205i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) 0 0
\(615\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(616\) 0 0
\(617\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 1.73205i 1.73205i
\(621\) 1.73205i 1.73205i
\(622\) 0 0
\(623\) 0 0
\(624\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −0.500000 0.866025i −0.500000 0.866025i
\(634\) 0 0
\(635\) 1.73205i 1.73205i
\(636\) 0 0
\(637\) 1.00000 1.00000
\(638\) 0 0
\(639\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 1.73205i 1.73205i
\(645\) 0 0
\(646\) 0 0
\(647\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −0.500000 0.866025i −0.500000 0.866025i
\(652\) 1.00000 1.00000
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.73205i 1.73205i
\(657\) 0 0
\(658\) 0 0
\(659\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(660\) 0 0
\(661\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3.00000 3.00000
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 2.00000 2.00000
\(676\) 0 0
\(677\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(678\) 0 0
\(679\) 2.00000 2.00000
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.500000 0.866025i −0.500000 0.866025i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.73205i 1.73205i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 2.00000 2.00000
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.73205i 1.73205i
\(708\) 0 0
\(709\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.73205i 1.73205i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) −1.50000 0.866025i −1.50000 0.866025i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.46410i 3.46410i
\(726\) 0 0
\(727\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) −1.00000 1.73205i −1.00000 1.73205i
\(733\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) 0 0
\(735\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 1.73205i 1.73205i
\(741\) 0 0
\(742\) 0 0
\(743\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(754\) 0 0
\(755\) 1.73205i 1.73205i
\(756\) 1.00000 1.00000
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(769\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 −1.00000
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 2.00000 2.00000
\(776\) 0 0
\(777\) −0.500000 0.866025i −0.500000 0.866025i
\(778\) 0 0
\(779\) 0 0
\(780\) 1.50000 0.866025i 1.50000 0.866025i
\(781\) 0 0
\(782\) 0 0
\(783\) 1.73205i 1.73205i
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 2.00000 2.00000
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(805\) 3.00000 3.00000
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 1.73205i 1.73205i
\(813\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(814\) 0 0
\(815\) 1.73205i 1.73205i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(820\) −3.00000 −3.00000
\(821\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(822\) 0 0
\(823\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −1.50000 0.866025i −1.50000 0.866025i
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) −1.00000 1.73205i −1.00000 1.73205i
\(832\) −1.00000 −1.00000
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.00000 1.00000
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −2.00000 −2.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 1.00000 1.00000
\(845\) 0 0
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.73205i 1.73205i
\(852\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 1.50000 0.866025i 1.50000 0.866025i
\(862\) 0 0
\(863\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −0.500000 0.866025i −0.500000 0.866025i
\(868\) 1.00000 1.00000
\(869\) 0 0
\(870\) 0 0
\(871\) −1.00000 −1.00000
\(872\) 0 0
\(873\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(874\) 0 0
\(875\) 1.73205i 1.73205i
\(876\) 0 0
\(877\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 1.00000 1.00000
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 1.50000 0.866025i 1.50000 0.866025i
\(898\) 0 0
\(899\) 1.73205i 1.73205i
\(900\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(908\) 0 0
\(909\) −1.50000 0.866025i −1.50000 0.866025i
\(910\) 0 0
\(911\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −3.00000 + 1.73205i −3.00000 + 1.73205i
\(916\) 1.00000 1.00000
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.73205i 1.73205i
\(924\) 0 0
\(925\) 2.00000 2.00000
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.50000 0.866025i 1.50000 0.866025i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 0 0
\(939\) −0.500000 0.866025i −0.500000 0.866025i
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) −3.00000 −3.00000
\(944\) 0 0
\(945\) 1.73205i 1.73205i
\(946\) 0 0
\(947\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 1.50000 0.866025i 1.50000 0.866025i
\(952\) 0 0
\(953\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.50000 0.866025i 1.50000 0.866025i
\(961\) 0 0
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.73205i 1.73205i
\(966\) 0 0
\(967\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(973\) 1.00000 1.00000
\(974\) 0 0
\(975\) −1.00000 1.73205i −1.00000 1.73205i
\(976\) 2.00000 2.00000
\(977\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
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 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 1.00000 1.00000
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 1407.1.g.i.1406.2 yes 2
3.2 odd 2 inner 1407.1.g.i.1406.1 yes 2
7.6 odd 2 1407.1.g.h.1406.1 2
21.20 even 2 1407.1.g.h.1406.2 yes 2
67.66 odd 2 1407.1.g.h.1406.1 2
201.200 even 2 1407.1.g.h.1406.2 yes 2
469.468 even 2 RM 1407.1.g.i.1406.2 yes 2
1407.1406 odd 2 inner 1407.1.g.i.1406.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1407.1.g.h.1406.1 2 7.6 odd 2
1407.1.g.h.1406.1 2 67.66 odd 2
1407.1.g.h.1406.2 yes 2 21.20 even 2
1407.1.g.h.1406.2 yes 2 201.200 even 2
1407.1.g.i.1406.1 yes 2 3.2 odd 2 inner
1407.1.g.i.1406.1 yes 2 1407.1406 odd 2 inner
1407.1.g.i.1406.2 yes 2 1.1 even 1 trivial
1407.1.g.i.1406.2 yes 2 469.468 even 2 RM