Properties

Label 2900.1.e.a.2899.2
Level $2900$
Weight $1$
Character 2900.2899
Analytic conductor $1.447$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -116
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2900,1,Mod(2899,2900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2900, 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("2900.2899");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2900.e (of order \(2\), degree \(1\), 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: \(1.44728853664\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 116)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.116.1
Artin image: $C_4\times D_6$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{24} - \cdots)\)

Embedding invariants

Embedding label 2899.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 2900.2899
Dual form 2900.1.e.a.2899.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{11} -1.00000i q^{12} +1.00000i q^{13} +1.00000 q^{16} -2.00000 q^{19} -1.00000i q^{22} +1.00000 q^{24} -1.00000 q^{26} +1.00000i q^{27} -1.00000 q^{29} -1.00000 q^{31} +1.00000i q^{32} -1.00000i q^{33} -2.00000i q^{38} -1.00000 q^{39} +1.00000i q^{43} +1.00000 q^{44} -1.00000i q^{47} +1.00000i q^{48} -1.00000 q^{49} -1.00000i q^{52} +1.00000i q^{53} -1.00000 q^{54} -2.00000i q^{57} -1.00000i q^{58} -1.00000i q^{62} -1.00000 q^{64} +1.00000 q^{66} +2.00000 q^{76} -1.00000i q^{78} +1.00000 q^{79} -1.00000 q^{81} -1.00000 q^{86} -1.00000i q^{87} +1.00000i q^{88} -1.00000i q^{93} +1.00000 q^{94} -1.00000 q^{96} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 2 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{11} + 2 q^{16} - 4 q^{19} + 2 q^{24} - 2 q^{26} - 2 q^{29} - 2 q^{31} - 2 q^{39} + 2 q^{44} - 2 q^{49} - 2 q^{54} - 2 q^{64} + 2 q^{66} + 4 q^{76} + 2 q^{79} - 2 q^{81} - 2 q^{86} + 2 q^{94} - 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times\).

\(n\) \(901\) \(1277\) \(1451\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 1.00000i
\(3\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −1.00000 −1.00000
\(5\) 0 0
\(6\) −1.00000 −1.00000
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) − 1.00000i − 1.00000i
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) − 1.00000i − 1.00000i
\(13\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) − 1.00000i − 1.00000i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 1.00000
\(25\) 0 0
\(26\) −1.00000 −1.00000
\(27\) 1.00000i 1.00000i
\(28\) 0 0
\(29\) −1.00000 −1.00000
\(30\) 0 0
\(31\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 1.00000i 1.00000i
\(33\) − 1.00000i − 1.00000i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) − 2.00000i − 2.00000i
\(39\) −1.00000 −1.00000
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(44\) 1.00000 1.00000
\(45\) 0 0
\(46\) 0 0
\(47\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(48\) 1.00000i 1.00000i
\(49\) −1.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) − 1.00000i − 1.00000i
\(53\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) −1.00000 −1.00000
\(55\) 0 0
\(56\) 0 0
\(57\) − 2.00000i − 2.00000i
\(58\) − 1.00000i − 1.00000i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) − 1.00000i − 1.00000i
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0 0
\(66\) 1.00000 1.00000
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 2.00000 2.00000
\(77\) 0 0
\(78\) − 1.00000i − 1.00000i
\(79\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) 0 0
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.00000 −1.00000
\(87\) − 1.00000i − 1.00000i
\(88\) 1.00000i 1.00000i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) − 1.00000i − 1.00000i
\(94\) 1.00000 1.00000
\(95\) 0 0
\(96\) −1.00000 −1.00000
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) − 1.00000i − 1.00000i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 1.00000 1.00000
\(105\) 0 0
\(106\) −1.00000 −1.00000
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) − 1.00000i − 1.00000i
\(109\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 2.00000 2.00000
\(115\) 0 0
\(116\) 1.00000 1.00000
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 1.00000 1.00000
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) − 1.00000i − 1.00000i
\(129\) −1.00000 −1.00000
\(130\) 0 0
\(131\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(132\) 1.00000i 1.00000i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 1.00000 1.00000
\(142\) 0 0
\(143\) − 1.00000i − 1.00000i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 1.00000i − 1.00000i
\(148\) 0 0
\(149\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 2.00000i 2.00000i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.00000 1.00000
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 1.00000i 1.00000i
\(159\) −1.00000 −1.00000
\(160\) 0 0
\(161\) 0 0
\(162\) − 1.00000i − 1.00000i
\(163\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(164\) 0 0
\(165\) 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
\(172\) − 1.00000i − 1.00000i
\(173\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(174\) 1.00000 1.00000
\(175\) 0 0
\(176\) −1.00000 −1.00000
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 1.00000 1.00000
\(187\) 0 0
\(188\) 1.00000i 1.00000i
\(189\) 0 0
\(190\) 0 0
\(191\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(192\) − 1.00000i − 1.00000i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) 2.00000i 2.00000i 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 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.00000i 1.00000i
\(209\) 2.00000 2.00000
\(210\) 0 0
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) − 1.00000i − 1.00000i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 1.00000i 1.00000i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 2.00000i 2.00000i
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000i 1.00000i
\(233\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.00000i 1.00000i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 2.00000i − 2.00000i
\(248\) 1.00000i 1.00000i
\(249\) 0 0
\(250\) 0 0
\(251\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −2.00000 −2.00000
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(258\) − 1.00000i − 1.00000i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 2.00000i 2.00000i
\(263\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) −1.00000 −1.00000
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 1.00000i 1.00000i
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.00000 1.00000
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 1.00000 1.00000
\(295\) 0 0
\(296\) 0 0
\(297\) − 1.00000i − 1.00000i
\(298\) 1.00000i 1.00000i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −2.00000 −2.00000
\(305\) 0 0
\(306\) 0 0
\(307\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(312\) 1.00000i 1.00000i
\(313\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.00000 −1.00000
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) − 1.00000i − 1.00000i
\(319\) 1.00000 1.00000
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) −1.00000 −1.00000
\(327\) 1.00000i 1.00000i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.00000 1.00000
\(342\) 0 0
\(343\) 0 0
\(344\) 1.00000 1.00000
\(345\) 0 0
\(346\) 2.00000 2.00000
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 1.00000i 1.00000i
\(349\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) 0 0
\(351\) −1.00000 −1.00000
\(352\) − 1.00000i − 1.00000i
\(353\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0 0
\(361\) 3.00000 3.00000
\(362\) − 1.00000i − 1.00000i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.00000i 1.00000i
\(373\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.00000 −1.00000
\(377\) − 1.00000i − 1.00000i
\(378\) 0 0
\(379\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −2.00000 −2.00000
\(382\) 2.00000i 2.00000i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 1.00000 1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.00000i 1.00000i
\(393\) 2.00000i 2.00000i
\(394\) −2.00000 −2.00000
\(395\) 0 0
\(396\) 0 0
\(397\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) − 1.00000i − 1.00000i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −1.00000 −1.00000
\(417\) 0 0
\(418\) 2.00000i 2.00000i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) − 1.00000i − 1.00000i
\(423\) 0 0
\(424\) 1.00000 1.00000
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.00000 1.00000
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.00000i 1.00000i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.00000 −1.00000
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.00000i 1.00000i
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) −2.00000 −2.00000
\(457\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) −1.00000 −1.00000
\(465\) 0 0
\(466\) −1.00000 −1.00000
\(467\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 1.00000i − 1.00000i
\(474\) −1.00000 −1.00000
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) − 1.00000i − 1.00000i
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) −1.00000 −1.00000
\(490\) 0 0
\(491\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 2.00000 2.00000
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) − 1.00000i − 1.00000i
\(503\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) − 2.00000i − 2.00000i
\(509\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) − 2.00000i − 2.00000i
\(514\) 1.00000 1.00000
\(515\) 0 0
\(516\) 1.00000 1.00000
\(517\) 1.00000i 1.00000i
\(518\) 0 0
\(519\) 2.00000 2.00000
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) −2.00000 −2.00000
\(525\) 0 0
\(526\) −1.00000 −1.00000
\(527\) 0 0
\(528\) − 1.00000i − 1.00000i
\(529\) −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
\(537\) 0 0
\(538\) 0 0
\(539\) 1.00000 1.00000
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) − 1.00000i − 1.00000i
\(543\) − 1.00000i − 1.00000i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.00000 2.00000
\(552\) 0 0
\(553\) 0 0
\(554\) −2.00000 −2.00000
\(555\) 0 0
\(556\) 0 0
\(557\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) −1.00000 −1.00000
\(560\) 0 0
\(561\) 0 0
\(562\) − 1.00000i − 1.00000i
\(563\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) −1.00000 −1.00000
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 1.00000i 1.00000i
\(573\) 2.00000i 2.00000i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) − 1.00000i − 1.00000i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) − 1.00000i − 1.00000i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 1.00000i 1.00000i
\(589\) 2.00000 2.00000
\(590\) 0 0
\(591\) −2.00000 −2.00000
\(592\) 0 0
\(593\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 1.00000 1.00000
\(595\) 0 0
\(596\) −1.00000 −1.00000
\(597\) 0 0
\(598\) 0 0
\(599\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(608\) − 2.00000i − 2.00000i
\(609\) 0 0
\(610\) 0 0
\(611\) 1.00000 1.00000
\(612\) 0 0
\(613\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(614\) 1.00000 1.00000
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 2.00000i 2.00000i
\(623\) 0 0
\(624\) −1.00000 −1.00000
\(625\) 0 0
\(626\) −1.00000 −1.00000
\(627\) 2.00000i 2.00000i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) − 1.00000i − 1.00000i
\(633\) − 1.00000i − 1.00000i
\(634\) 0 0
\(635\) 0 0
\(636\) 1.00000 1.00000
\(637\) − 1.00000i − 1.00000i
\(638\) 1.00000i 1.00000i
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) − 1.00000i − 1.00000i
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) −1.00000 −1.00000
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(662\) − 1.00000i − 1.00000i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 1.00000i 1.00000i
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.00000i 1.00000i
\(689\) −1.00000 −1.00000
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 2.00000i 2.00000i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) −1.00000 −1.00000
\(697\) 0 0
\(698\) 1.00000i 1.00000i
\(699\) −1.00000 −1.00000
\(700\) 0 0
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) − 1.00000i − 1.00000i
\(703\) 0 0
\(704\) 1.00000 1.00000
\(705\) 0 0
\(706\) 2.00000 2.00000
\(707\) 0 0
\(708\) 0 0
\(709\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 1.00000i 1.00000i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.00000i 3.00000i
\(723\) − 1.00000i − 1.00000i
\(724\) 1.00000 1.00000
\(725\) 0 0
\(726\) 0 0
\(727\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) −2.00000 −2.00000
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 2.00000 2.00000
\(742\) 0 0
\(743\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(744\) −1.00000 −1.00000
\(745\) 0 0
\(746\) −1.00000 −1.00000
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(752\) − 1.00000i − 1.00000i
\(753\) − 1.00000i − 1.00000i
\(754\) 1.00000 1.00000
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) − 2.00000i − 2.00000i
\(759\) 0 0
\(760\) 0 0
\(761\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(762\) − 2.00000i − 2.00000i
\(763\) 0 0
\(764\) −2.00000 −2.00000
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.00000i 1.00000i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.00000 1.00000
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) − 1.00000i − 1.00000i
\(784\) −1.00000 −1.00000
\(785\) 0 0
\(786\) −2.00000 −2.00000
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) − 2.00000i − 2.00000i
\(789\) −1.00000 −1.00000
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 1.00000 1.00000
\(795\) 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
\(802\) − 1.00000i − 1.00000i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 1.00000 1.00000
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) − 1.00000i − 1.00000i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) − 2.00000i − 2.00000i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) 0 0
\(823\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) −2.00000 −2.00000
\(832\) − 1.00000i − 1.00000i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) −2.00000 −2.00000
\(837\) − 1.00000i − 1.00000i
\(838\) 0 0
\(839\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) − 1.00000i − 1.00000i
\(844\) 1.00000 1.00000
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 1.00000i 1.00000i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(858\) 1.00000i 1.00000i
\(859\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) −1.00000 −1.00000
\(865\) 0 0
\(866\) 0 0
\(867\) − 1.00000i − 1.00000i
\(868\) 0 0
\(869\) −1.00000 −1.00000
\(870\) 0 0
\(871\) 0 0
\(872\) − 1.00000i − 1.00000i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 1.00000i − 1.00000i −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 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 2.00000 2.00000
\(887\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.00000 1.00000
\(892\) 0 0
\(893\) 2.00000i 2.00000i
\(894\) −1.00000 −1.00000
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.00000 1.00000
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(912\) − 2.00000i − 2.00000i
\(913\) 0 0
\(914\) −2.00000 −2.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 1.00000 1.00000
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) − 1.00000i − 1.00000i
\(929\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 2.00000 2.00000
\(932\) − 1.00000i − 1.00000i
\(933\) 2.00000i 2.00000i
\(934\) 1.00000 1.00000
\(935\) 0 0
\(936\) 0 0
\(937\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) −1.00000 −1.00000
\(940\) 0 0
\(941\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 1.00000 1.00000
\(947\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(948\) − 1.00000i − 1.00000i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.00000i 1.00000i
\(958\) 1.00000i 1.00000i
\(959\) 0 0
\(960\) 0 0
\(961\) 0 0
\(962\) 0 0
\(963\) 0 0
\(964\) 1.00000 1.00000
\(965\) 0 0
\(966\) 0 0
\(967\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(978\) − 1.00000i − 1.00000i
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) − 1.00000i − 1.00000i
\(983\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 2.00000i 2.00000i
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) − 1.00000i − 1.00000i
\(993\) − 1.00000i − 1.00000i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
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 2900.1.e.a.2899.2 2
4.3 odd 2 2900.1.e.b.2899.1 2
5.2 odd 4 2900.1.g.a.2551.1 1
5.3 odd 4 116.1.d.b.115.1 yes 1
5.4 even 2 inner 2900.1.e.a.2899.1 2
15.8 even 4 1044.1.g.a.811.1 1
20.3 even 4 116.1.d.a.115.1 1
20.7 even 4 2900.1.g.d.2551.1 1
20.19 odd 2 2900.1.e.b.2899.2 2
29.28 even 2 2900.1.e.b.2899.1 2
40.3 even 4 1856.1.h.a.1855.1 1
40.13 odd 4 1856.1.h.c.1855.1 1
60.23 odd 4 1044.1.g.b.811.1 1
116.115 odd 2 CM 2900.1.e.a.2899.2 2
145.3 even 28 3364.1.j.f.571.2 12
145.8 even 28 3364.1.j.f.1415.2 12
145.13 odd 28 3364.1.h.b.63.1 6
145.18 even 28 3364.1.j.f.1619.1 12
145.23 odd 28 3364.1.h.a.2719.1 6
145.28 odd 4 116.1.d.a.115.1 1
145.33 odd 28 3364.1.h.b.651.1 6
145.38 odd 28 3364.1.h.b.267.1 6
145.43 even 28 3364.1.j.f.2327.1 12
145.48 even 28 3364.1.j.f.1031.1 12
145.53 odd 28 3364.1.h.a.2759.1 6
145.57 odd 4 2900.1.g.d.2551.1 1
145.63 odd 28 3364.1.h.b.2759.1 6
145.68 even 28 3364.1.j.f.1031.2 12
145.73 even 28 3364.1.j.f.2327.2 12
145.78 odd 28 3364.1.h.a.267.1 6
145.83 odd 28 3364.1.h.a.651.1 6
145.93 odd 28 3364.1.h.b.2719.1 6
145.98 even 28 3364.1.j.f.1619.2 12
145.103 odd 28 3364.1.h.a.63.1 6
145.108 even 28 3364.1.j.f.1415.1 12
145.113 even 28 3364.1.j.f.571.1 12
145.118 even 28 3364.1.j.f.2287.2 12
145.123 odd 28 3364.1.h.a.1111.1 6
145.128 even 4 3364.1.b.a.1683.2 2
145.133 even 4 3364.1.b.a.1683.1 2
145.138 odd 28 3364.1.h.b.1111.1 6
145.143 even 28 3364.1.j.f.2287.1 12
145.144 even 2 2900.1.e.b.2899.2 2
435.173 even 4 1044.1.g.b.811.1 1
580.3 odd 28 3364.1.j.f.571.1 12
580.23 even 28 3364.1.h.b.2719.1 6
580.43 odd 28 3364.1.j.f.2327.2 12
580.63 even 28 3364.1.h.a.2759.1 6
580.83 even 28 3364.1.h.b.651.1 6
580.103 even 28 3364.1.h.b.63.1 6
580.123 even 28 3364.1.h.b.1111.1 6
580.143 odd 28 3364.1.j.f.2287.2 12
580.163 odd 28 3364.1.j.f.1619.2 12
580.183 even 28 3364.1.h.a.267.1 6
580.223 even 28 3364.1.h.b.267.1 6
580.243 odd 28 3364.1.j.f.1619.1 12
580.263 odd 28 3364.1.j.f.2287.1 12
580.283 even 28 3364.1.h.a.1111.1 6
580.303 even 28 3364.1.h.a.63.1 6
580.323 even 28 3364.1.h.a.651.1 6
580.343 even 28 3364.1.h.b.2759.1 6
580.347 even 4 2900.1.g.a.2551.1 1
580.363 odd 28 3364.1.j.f.2327.1 12
580.383 even 28 3364.1.h.a.2719.1 6
580.403 odd 28 3364.1.j.f.571.2 12
580.423 odd 4 3364.1.b.a.1683.2 2
580.443 odd 28 3364.1.j.f.1415.1 12
580.463 even 4 116.1.d.b.115.1 yes 1
580.483 odd 28 3364.1.j.f.1031.2 12
580.503 odd 28 3364.1.j.f.1031.1 12
580.543 odd 28 3364.1.j.f.1415.2 12
580.563 odd 4 3364.1.b.a.1683.1 2
580.579 odd 2 inner 2900.1.e.a.2899.1 2
1160.173 odd 4 1856.1.h.a.1855.1 1
1160.1043 even 4 1856.1.h.c.1855.1 1
1740.1043 odd 4 1044.1.g.a.811.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
116.1.d.a.115.1 1 20.3 even 4
116.1.d.a.115.1 1 145.28 odd 4
116.1.d.b.115.1 yes 1 5.3 odd 4
116.1.d.b.115.1 yes 1 580.463 even 4
1044.1.g.a.811.1 1 15.8 even 4
1044.1.g.a.811.1 1 1740.1043 odd 4
1044.1.g.b.811.1 1 60.23 odd 4
1044.1.g.b.811.1 1 435.173 even 4
1856.1.h.a.1855.1 1 40.3 even 4
1856.1.h.a.1855.1 1 1160.173 odd 4
1856.1.h.c.1855.1 1 40.13 odd 4
1856.1.h.c.1855.1 1 1160.1043 even 4
2900.1.e.a.2899.1 2 5.4 even 2 inner
2900.1.e.a.2899.1 2 580.579 odd 2 inner
2900.1.e.a.2899.2 2 1.1 even 1 trivial
2900.1.e.a.2899.2 2 116.115 odd 2 CM
2900.1.e.b.2899.1 2 4.3 odd 2
2900.1.e.b.2899.1 2 29.28 even 2
2900.1.e.b.2899.2 2 20.19 odd 2
2900.1.e.b.2899.2 2 145.144 even 2
2900.1.g.a.2551.1 1 5.2 odd 4
2900.1.g.a.2551.1 1 580.347 even 4
2900.1.g.d.2551.1 1 20.7 even 4
2900.1.g.d.2551.1 1 145.57 odd 4
3364.1.b.a.1683.1 2 145.133 even 4
3364.1.b.a.1683.1 2 580.563 odd 4
3364.1.b.a.1683.2 2 145.128 even 4
3364.1.b.a.1683.2 2 580.423 odd 4
3364.1.h.a.63.1 6 145.103 odd 28
3364.1.h.a.63.1 6 580.303 even 28
3364.1.h.a.267.1 6 145.78 odd 28
3364.1.h.a.267.1 6 580.183 even 28
3364.1.h.a.651.1 6 145.83 odd 28
3364.1.h.a.651.1 6 580.323 even 28
3364.1.h.a.1111.1 6 145.123 odd 28
3364.1.h.a.1111.1 6 580.283 even 28
3364.1.h.a.2719.1 6 145.23 odd 28
3364.1.h.a.2719.1 6 580.383 even 28
3364.1.h.a.2759.1 6 145.53 odd 28
3364.1.h.a.2759.1 6 580.63 even 28
3364.1.h.b.63.1 6 145.13 odd 28
3364.1.h.b.63.1 6 580.103 even 28
3364.1.h.b.267.1 6 145.38 odd 28
3364.1.h.b.267.1 6 580.223 even 28
3364.1.h.b.651.1 6 145.33 odd 28
3364.1.h.b.651.1 6 580.83 even 28
3364.1.h.b.1111.1 6 145.138 odd 28
3364.1.h.b.1111.1 6 580.123 even 28
3364.1.h.b.2719.1 6 145.93 odd 28
3364.1.h.b.2719.1 6 580.23 even 28
3364.1.h.b.2759.1 6 145.63 odd 28
3364.1.h.b.2759.1 6 580.343 even 28
3364.1.j.f.571.1 12 145.113 even 28
3364.1.j.f.571.1 12 580.3 odd 28
3364.1.j.f.571.2 12 145.3 even 28
3364.1.j.f.571.2 12 580.403 odd 28
3364.1.j.f.1031.1 12 145.48 even 28
3364.1.j.f.1031.1 12 580.503 odd 28
3364.1.j.f.1031.2 12 145.68 even 28
3364.1.j.f.1031.2 12 580.483 odd 28
3364.1.j.f.1415.1 12 145.108 even 28
3364.1.j.f.1415.1 12 580.443 odd 28
3364.1.j.f.1415.2 12 145.8 even 28
3364.1.j.f.1415.2 12 580.543 odd 28
3364.1.j.f.1619.1 12 145.18 even 28
3364.1.j.f.1619.1 12 580.243 odd 28
3364.1.j.f.1619.2 12 145.98 even 28
3364.1.j.f.1619.2 12 580.163 odd 28
3364.1.j.f.2287.1 12 145.143 even 28
3364.1.j.f.2287.1 12 580.263 odd 28
3364.1.j.f.2287.2 12 145.118 even 28
3364.1.j.f.2287.2 12 580.143 odd 28
3364.1.j.f.2327.1 12 145.43 even 28
3364.1.j.f.2327.1 12 580.363 odd 28
3364.1.j.f.2327.2 12 145.73 even 28
3364.1.j.f.2327.2 12 580.43 odd 28