Properties

Label 1859.1.c.c.846.2
Level $1859$
Weight $1$
Character 1859.846
Analytic conductor $0.928$
Analytic rank $0$
Dimension $4$
Projective image $D_{5}$
CM discriminant -143
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1859,1,Mod(846,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1859.846");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1859.c (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: \(0.927761858485\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 3x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 143)
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.20449.1
Artin image: $C_4\times D_5$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{20} - \cdots)\)

Embedding invariants

Embedding label 846.2
Root \(0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 1859.846
Dual form 1859.1.c.c.846.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.618034i q^{2} +0.618034 q^{3} +0.618034 q^{4} -0.381966i q^{6} -1.61803i q^{7} -1.00000i q^{8} -0.618034 q^{9} +O(q^{10})\) \(q-0.618034i q^{2} +0.618034 q^{3} +0.618034 q^{4} -0.381966i q^{6} -1.61803i q^{7} -1.00000i q^{8} -0.618034 q^{9} +1.00000i q^{11} +0.381966 q^{12} -1.00000 q^{14} +0.381966i q^{18} -0.618034i q^{19} -1.00000i q^{21} +0.618034 q^{22} +1.61803 q^{23} -0.618034i q^{24} -1.00000 q^{25} -1.00000 q^{27} -1.00000i q^{28} -1.00000i q^{32} +0.618034i q^{33} -0.381966 q^{36} -0.381966 q^{38} +1.61803i q^{41} -0.618034 q^{42} +0.618034i q^{44} -1.00000i q^{46} -1.61803 q^{49} +0.618034i q^{50} +0.618034 q^{53} +0.618034i q^{54} -1.61803 q^{56} -0.381966i q^{57} +1.00000i q^{63} -0.618034 q^{64} +0.381966 q^{66} +1.00000 q^{69} +0.618034i q^{72} +0.618034i q^{73} -0.618034 q^{75} -0.381966i q^{76} +1.61803 q^{77} +1.00000 q^{82} +1.61803i q^{83} -0.618034i q^{84} +1.00000 q^{88} +1.00000 q^{92} -0.618034i q^{96} +1.00000i q^{98} -0.618034i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} - 2 q^{4} + 2 q^{9} + 6 q^{12} - 4 q^{14} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 4 q^{27} - 6 q^{36} - 6 q^{38} + 2 q^{42} - 2 q^{49} - 2 q^{53} - 2 q^{56} + 2 q^{64} + 6 q^{66} + 4 q^{69} + 2 q^{75} + 2 q^{77} + 4 q^{82} + 4 q^{88} + 4 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1859\mathbb{Z}\right)^\times\).

\(n\) \(508\) \(1354\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(3\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(4\) 0.618034 0.618034
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) − 0.381966i − 0.381966i
\(7\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(8\) − 1.00000i − 1.00000i
\(9\) −0.618034 −0.618034
\(10\) 0 0
\(11\) 1.00000i 1.00000i
\(12\) 0.381966 0.381966
\(13\) 0 0
\(14\) −1.00000 −1.00000
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0.381966i 0.381966i
\(19\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(20\) 0 0
\(21\) − 1.00000i − 1.00000i
\(22\) 0.618034 0.618034
\(23\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(24\) − 0.618034i − 0.618034i
\(25\) −1.00000 −1.00000
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) − 1.00000i − 1.00000i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) − 1.00000i − 1.00000i
\(33\) 0.618034i 0.618034i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.381966 −0.381966
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) −0.381966 −0.381966
\(39\) 0 0
\(40\) 0 0
\(41\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(42\) −0.618034 −0.618034
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.618034i 0.618034i
\(45\) 0 0
\(46\) − 1.00000i − 1.00000i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −1.61803 −1.61803
\(50\) 0.618034i 0.618034i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) 0.618034i 0.618034i
\(55\) 0 0
\(56\) −1.61803 −1.61803
\(57\) − 0.381966i − 0.381966i
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 1.00000i 1.00000i
\(64\) −0.618034 −0.618034
\(65\) 0 0
\(66\) 0.381966 0.381966
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 1.00000 1.00000
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0.618034i 0.618034i
\(73\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(74\) 0 0
\(75\) −0.618034 −0.618034
\(76\) − 0.381966i − 0.381966i
\(77\) 1.61803 1.61803
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 1.00000 1.00000
\(83\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(84\) − 0.618034i − 0.618034i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 1.00000 1.00000
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.00000 1.00000
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) − 0.618034i − 0.618034i
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 1.00000i 1.00000i
\(99\) − 0.618034i − 0.618034i
\(100\) −0.618034 −0.618034
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) − 0.381966i − 0.381966i
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −0.618034 −0.618034
\(109\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(114\) −0.236068 −0.236068
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 0 0
\(123\) 1.00000i 1.00000i
\(124\) 0 0
\(125\) 0 0
\(126\) 0.618034 0.618034
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) − 0.618034i − 0.618034i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0.381966i 0.381966i
\(133\) −1.00000 −1.00000
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) − 0.618034i − 0.618034i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0.381966 0.381966
\(147\) −1.00000 −1.00000
\(148\) 0 0
\(149\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(150\) 0.381966i 0.381966i
\(151\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −0.618034 −0.618034
\(153\) 0 0
\(154\) − 1.00000i − 1.00000i
\(155\) 0 0
\(156\) 0 0
\(157\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) 0.381966 0.381966
\(160\) 0 0
\(161\) − 2.61803i − 2.61803i
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 1.00000i 1.00000i
\(165\) 0 0
\(166\) 1.00000 1.00000
\(167\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(168\) −1.00000 −1.00000
\(169\) 0 0
\(170\) 0 0
\(171\) 0.381966i 0.381966i
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 1.61803i 1.61803i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) − 1.61803i − 1.61803i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.61803i 1.61803i
\(190\) 0 0
\(191\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(192\) −0.381966 −0.381966
\(193\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.00000 −1.00000
\(197\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(198\) −0.381966 −0.381966
\(199\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(200\) 1.00000i 1.00000i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) − 1.00000i − 1.00000i
\(207\) −1.00000 −1.00000
\(208\) 0 0
\(209\) 0.618034 0.618034
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0.381966 0.381966
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000i 1.00000i
\(217\) 0 0
\(218\) −0.381966 −0.381966
\(219\) 0.381966i 0.381966i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) −1.61803 −1.61803
\(225\) 0.618034 0.618034
\(226\) − 0.381966i − 0.381966i
\(227\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(228\) − 0.236068i − 0.236068i
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 1.00000 1.00000
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(240\) 0 0
\(241\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(242\) 0.618034i 0.618034i
\(243\) 1.00000 1.00000
\(244\) 0 0
\(245\) 0 0
\(246\) 0.618034 0.618034
\(247\) 0 0
\(248\) 0 0
\(249\) 1.00000i 1.00000i
\(250\) 0 0
\(251\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(252\) 0.618034i 0.618034i
\(253\) 1.61803i 1.61803i
\(254\) 0 0
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0.618034 0.618034
\(265\) 0 0
\(266\) 0.618034i 0.618034i
\(267\) 0 0
\(268\) 0 0
\(269\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 0 0
\(271\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 1.00000i − 1.00000i
\(276\) 0.618034 0.618034
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.61803 2.61803
\(288\) 0.618034i 0.618034i
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0.381966i 0.381966i
\(293\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0.618034i 0.618034i
\(295\) 0 0
\(296\) 0 0
\(297\) − 1.00000i − 1.00000i
\(298\) 1.00000 1.00000
\(299\) 0 0
\(300\) −0.381966 −0.381966
\(301\) 0 0
\(302\) 1.23607 1.23607
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 1.00000 1.00000
\(309\) 1.00000 1.00000
\(310\) 0 0
\(311\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(312\) 0 0
\(313\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 1.00000i 1.00000i
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) − 0.236068i − 0.236068i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −1.61803 −1.61803
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 0.381966i − 0.381966i
\(328\) 1.61803 1.61803
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 1.00000i 1.00000i
\(333\) 0 0
\(334\) 0.381966 0.381966
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0.381966 0.381966
\(340\) 0 0
\(341\) 0 0
\(342\) 0.236068 0.236068
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(350\) 1.00000 1.00000
\(351\) 0 0
\(352\) 1.00000 1.00000
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.23607i 1.23607i
\(359\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(360\) 0 0
\(361\) 0.618034 0.618034
\(362\) 0.381966i 0.381966i
\(363\) −0.618034 −0.618034
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) − 1.00000i − 1.00000i
\(370\) 0 0
\(371\) − 1.00000i − 1.00000i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 1.00000 1.00000
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) − 0.381966i − 0.381966i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) − 0.381966i − 0.381966i
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.61803i 1.61803i
\(393\) 0 0
\(394\) −0.381966 −0.381966
\(395\) 0 0
\(396\) − 0.381966i − 0.381966i
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0.381966i 0.381966i
\(399\) −0.618034 −0.618034
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.00000 1.00000
\(413\) 0 0
\(414\) 0.618034i 0.618034i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) − 0.381966i − 0.381966i
\(419\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) − 0.618034i − 0.618034i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(432\) 0 0
\(433\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) − 0.381966i − 0.381966i
\(437\) − 1.00000i − 1.00000i
\(438\) 0.236068 0.236068
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.00000i 1.00000i
\(448\) 1.00000i 1.00000i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) − 0.381966i − 0.381966i
\(451\) −1.61803 −1.61803
\(452\) 0.381966 0.381966
\(453\) 1.23607i 1.23607i
\(454\) −0.381966 −0.381966
\(455\) 0 0
\(456\) −0.381966 −0.381966
\(457\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(462\) − 0.618034i − 0.618034i
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 −1.00000
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.618034i 0.618034i
\(476\) 0 0
\(477\) −0.381966 −0.381966
\(478\) −0.381966 −0.381966
\(479\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.00000 −1.00000
\(483\) − 1.61803i − 1.61803i
\(484\) −0.618034 −0.618034
\(485\) 0 0
\(486\) − 0.618034i − 0.618034i
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0.618034i 0.618034i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.618034 0.618034
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 0.381966i 0.381966i
\(502\) − 1.00000i − 1.00000i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 1.00000 1.00000
\(505\) 0 0
\(506\) 1.00000 1.00000
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 1.00000 1.00000
\(512\) 0 0
\(513\) 0.618034i 0.618034i
\(514\) − 1.00000i − 1.00000i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 1.00000i 1.00000i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.61803 1.61803
\(530\) 0 0
\(531\) 0 0
\(532\) −0.618034 −0.618034
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.23607 −1.23607
\(538\) 1.00000i 1.00000i
\(539\) − 1.61803i − 1.61803i
\(540\) 0 0
\(541\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(542\) 0.381966 0.381966
\(543\) −0.381966 −0.381966
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −0.618034 −0.618034
\(551\) 0 0
\(552\) − 1.00000i − 1.00000i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.381966 0.381966
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 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 \(\pi\)
\(572\) 0 0
\(573\) 0.381966 0.381966
\(574\) − 1.61803i − 1.61803i
\(575\) −1.61803 −1.61803
\(576\) 0.381966 0.381966
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) − 0.618034i − 0.618034i
\(579\) − 1.00000i − 1.00000i
\(580\) 0 0
\(581\) 2.61803 2.61803
\(582\) 0 0
\(583\) 0.618034i 0.618034i
\(584\) 0.618034 0.618034
\(585\) 0 0
\(586\) 1.23607 1.23607
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) −0.618034 −0.618034
\(589\) 0 0
\(590\) 0 0
\(591\) − 0.381966i − 0.381966i
\(592\) 0 0
\(593\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(594\) −0.618034 −0.618034
\(595\) 0 0
\(596\) 1.00000i 1.00000i
\(597\) −0.381966 −0.381966
\(598\) 0 0
\(599\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(600\) 0.618034i 0.618034i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.23607i 1.23607i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) −0.618034 −0.618034
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(614\) 1.23607 1.23607
\(615\) 0 0
\(616\) − 1.61803i − 1.61803i
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) − 0.618034i − 0.618034i
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) −1.61803 −1.61803
\(622\) 0.381966i 0.381966i
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 1.00000i 1.00000i
\(627\) 0.381966 0.381966
\(628\) −1.00000 −1.00000
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0.236068 0.236068
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) − 1.61803i − 1.61803i
\(645\) 0 0
\(646\) 0 0
\(647\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(654\) −0.236068 −0.236068
\(655\) 0 0
\(656\) 0 0
\(657\) − 0.381966i − 0.381966i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.61803 1.61803
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.381966i 0.381966i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −1.00000 −1.00000
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) − 0.236068i − 0.236068i
\(679\) 0 0
\(680\) 0 0
\(681\) − 0.381966i − 0.381966i
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0.236068i 0.236068i
\(685\) 0 0
\(686\) 0.618034 0.618034
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) −1.00000 −1.00000
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −1.00000 −1.00000
\(699\) 0 0
\(700\) 1.00000i 1.00000i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) − 0.618034i − 0.618034i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.23607 −1.23607
\(717\) − 0.381966i − 0.381966i
\(718\) −1.00000 −1.00000
\(719\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) − 2.61803i − 2.61803i
\(722\) − 0.381966i − 0.381966i
\(723\) − 1.00000i − 1.00000i
\(724\) −0.381966 −0.381966
\(725\) 0 0
\(726\) 0.381966i 0.381966i
\(727\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(728\) 0 0
\(729\) 0.618034 0.618034
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(734\) − 0.381966i − 0.381966i
\(735\) 0 0
\(736\) − 1.61803i − 1.61803i
\(737\) 0 0
\(738\) −0.618034 −0.618034
\(739\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.618034 −0.618034
\(743\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) − 1.00000i − 1.00000i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(752\) 0 0
\(753\) 1.00000 1.00000
\(754\) 0 0
\(755\) 0 0
\(756\) 1.00000i 1.00000i
\(757\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 1.00000i 1.00000i
\(760\) 0 0
\(761\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(762\) 0 0
\(763\) −1.00000 −1.00000
\(764\) 0.381966 0.381966
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.618034 −0.618034
\(769\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(770\) 0 0
\(771\) 1.00000 1.00000
\(772\) − 1.00000i − 1.00000i
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.381966i 0.381966i
\(779\) 1.00000 1.00000
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(788\) − 0.381966i − 0.381966i
\(789\) 0 0
\(790\) 0 0
\(791\) − 1.00000i − 1.00000i
\(792\) −0.618034 −0.618034
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −0.381966 −0.381966
\(797\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(798\) 0.381966i 0.381966i
\(799\) 0 0
\(800\) 1.00000i 1.00000i
\(801\) 0 0
\(802\) 0 0
\(803\) −0.618034 −0.618034
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.00000 −1.00000
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(812\) 0 0
\(813\) 0.381966i 0.381966i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −1.23607 −1.23607
\(819\) 0 0
\(820\) 0 0
\(821\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(822\) 0 0
\(823\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(824\) − 1.61803i − 1.61803i
\(825\) − 0.618034i − 0.618034i
\(826\) 0 0
\(827\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(828\) −0.618034 −0.618034
\(829\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0.381966 0.381966
\(837\) 0 0
\(838\) 1.00000i 1.00000i
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0.381966i 0.381966i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 1.61803i 1.61803i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(860\) 0 0
\(861\) 1.61803 1.61803
\(862\) 1.00000 1.00000
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 1.00000i 1.00000i
\(865\) 0 0
\(866\) 0.381966i 0.381966i
\(867\) 0.618034 0.618034
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −0.618034 −0.618034
\(873\) 0 0
\(874\) −0.618034 −0.618034
\(875\) 0 0
\(876\) 0.236068i 0.236068i
\(877\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(878\) 0 0
\(879\) 1.23607i 1.23607i
\(880\) 0 0
\(881\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(882\) − 0.618034i − 0.618034i
\(883\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.00000i 1.00000i
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0.618034 0.618034
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.381966 0.381966
\(901\) 0 0
\(902\) 1.00000i 1.00000i
\(903\) 0 0
\(904\) − 0.618034i − 0.618034i
\(905\) 0 0
\(906\) 0.763932 0.763932
\(907\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(908\) − 0.381966i − 0.381966i
\(909\) 0 0
\(910\) 0 0
\(911\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(912\) 0 0
\(913\) −1.61803 −1.61803
\(914\) −0.381966 −0.381966
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 1.23607i 1.23607i
\(922\) −0.381966 −0.381966
\(923\) 0 0
\(924\) 0.618034 0.618034
\(925\) 0 0
\(926\) 0 0
\(927\) −1.00000 −1.00000
\(928\) 0 0
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 1.00000i 1.00000i
\(932\) 0 0
\(933\) −0.381966 −0.381966
\(934\) 1.23607i 1.23607i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) −1.00000 −1.00000
\(940\) 0 0
\(941\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(942\) 0.618034i 0.618034i
\(943\) 2.61803i 2.61803i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.381966 0.381966
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0.236068i 0.236068i
\(955\) 0 0
\(956\) − 0.381966i − 0.381966i
\(957\) 0 0
\(958\) 1.23607 1.23607
\(959\) 0 0
\(960\) 0 0
\(961\) −1.00000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) − 1.00000i − 1.00000i
\(965\) 0 0
\(966\) −1.00000 −1.00000
\(967\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(968\) 1.00000i 1.00000i
\(969\) 0 0
\(970\) 0 0
\(971\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(972\) 0.618034 0.618034
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0.381966i 0.381966i
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 1.00000 1.00000
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0.618034i 0.618034i
\(997\) 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 1859.1.c.c.846.2 4
11.10 odd 2 inner 1859.1.c.c.846.3 4
13.2 odd 12 1859.1.i.a.1330.2 4
13.3 even 3 1859.1.k.c.1374.3 8
13.4 even 6 1859.1.k.c.1836.3 8
13.5 odd 4 143.1.d.b.142.1 yes 2
13.6 odd 12 1859.1.i.a.868.2 4
13.7 odd 12 1859.1.i.b.868.1 4
13.8 odd 4 143.1.d.a.142.2 2
13.9 even 3 1859.1.k.c.1836.2 8
13.10 even 6 1859.1.k.c.1374.2 8
13.11 odd 12 1859.1.i.b.1330.1 4
13.12 even 2 inner 1859.1.c.c.846.3 4
39.5 even 4 1287.1.g.a.1000.2 2
39.8 even 4 1287.1.g.b.1000.1 2
52.31 even 4 2288.1.m.a.2001.1 2
52.47 even 4 2288.1.m.b.2001.1 2
65.8 even 4 3575.1.c.d.3574.2 4
65.18 even 4 3575.1.c.c.3574.3 4
65.34 odd 4 3575.1.h.f.2001.1 2
65.44 odd 4 3575.1.h.e.2001.2 2
65.47 even 4 3575.1.c.d.3574.3 4
65.57 even 4 3575.1.c.c.3574.2 4
143.5 odd 20 1573.1.l.c.844.1 4
143.8 even 20 1573.1.l.a.233.1 4
143.10 odd 6 1859.1.k.c.1374.3 8
143.18 even 20 1573.1.l.d.1546.1 4
143.21 even 4 143.1.d.b.142.1 yes 2
143.31 odd 20 1573.1.l.c.766.1 4
143.32 even 12 1859.1.i.b.868.1 4
143.43 odd 6 1859.1.k.c.1836.2 8
143.47 odd 20 1573.1.l.d.233.1 4
143.54 even 12 1859.1.i.b.1330.1 4
143.57 even 20 1573.1.l.b.766.1 4
143.60 odd 20 1573.1.l.b.844.1 4
143.70 odd 20 1573.1.l.a.1546.1 4
143.73 even 20 1573.1.l.a.1546.1 4
143.76 even 12 1859.1.i.a.1330.2 4
143.83 even 20 1573.1.l.b.844.1 4
143.86 odd 20 1573.1.l.b.766.1 4
143.87 odd 6 1859.1.k.c.1836.3 8
143.96 even 20 1573.1.l.d.233.1 4
143.98 even 12 1859.1.i.a.868.2 4
143.109 even 4 143.1.d.a.142.2 2
143.112 even 20 1573.1.l.c.766.1 4
143.120 odd 6 1859.1.k.c.1374.2 8
143.125 odd 20 1573.1.l.d.1546.1 4
143.135 odd 20 1573.1.l.a.233.1 4
143.138 even 20 1573.1.l.c.844.1 4
143.142 odd 2 CM 1859.1.c.c.846.2 4
429.164 odd 4 1287.1.g.a.1000.2 2
429.395 odd 4 1287.1.g.b.1000.1 2
572.307 odd 4 2288.1.m.a.2001.1 2
572.395 odd 4 2288.1.m.b.2001.1 2
715.109 even 4 3575.1.h.f.2001.1 2
715.164 even 4 3575.1.h.e.2001.2 2
715.252 odd 4 3575.1.c.d.3574.3 4
715.307 odd 4 3575.1.c.c.3574.2 4
715.538 odd 4 3575.1.c.d.3574.2 4
715.593 odd 4 3575.1.c.c.3574.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.1.d.a.142.2 2 13.8 odd 4
143.1.d.a.142.2 2 143.109 even 4
143.1.d.b.142.1 yes 2 13.5 odd 4
143.1.d.b.142.1 yes 2 143.21 even 4
1287.1.g.a.1000.2 2 39.5 even 4
1287.1.g.a.1000.2 2 429.164 odd 4
1287.1.g.b.1000.1 2 39.8 even 4
1287.1.g.b.1000.1 2 429.395 odd 4
1573.1.l.a.233.1 4 143.8 even 20
1573.1.l.a.233.1 4 143.135 odd 20
1573.1.l.a.1546.1 4 143.70 odd 20
1573.1.l.a.1546.1 4 143.73 even 20
1573.1.l.b.766.1 4 143.57 even 20
1573.1.l.b.766.1 4 143.86 odd 20
1573.1.l.b.844.1 4 143.60 odd 20
1573.1.l.b.844.1 4 143.83 even 20
1573.1.l.c.766.1 4 143.31 odd 20
1573.1.l.c.766.1 4 143.112 even 20
1573.1.l.c.844.1 4 143.5 odd 20
1573.1.l.c.844.1 4 143.138 even 20
1573.1.l.d.233.1 4 143.47 odd 20
1573.1.l.d.233.1 4 143.96 even 20
1573.1.l.d.1546.1 4 143.18 even 20
1573.1.l.d.1546.1 4 143.125 odd 20
1859.1.c.c.846.2 4 1.1 even 1 trivial
1859.1.c.c.846.2 4 143.142 odd 2 CM
1859.1.c.c.846.3 4 11.10 odd 2 inner
1859.1.c.c.846.3 4 13.12 even 2 inner
1859.1.i.a.868.2 4 13.6 odd 12
1859.1.i.a.868.2 4 143.98 even 12
1859.1.i.a.1330.2 4 13.2 odd 12
1859.1.i.a.1330.2 4 143.76 even 12
1859.1.i.b.868.1 4 13.7 odd 12
1859.1.i.b.868.1 4 143.32 even 12
1859.1.i.b.1330.1 4 13.11 odd 12
1859.1.i.b.1330.1 4 143.54 even 12
1859.1.k.c.1374.2 8 13.10 even 6
1859.1.k.c.1374.2 8 143.120 odd 6
1859.1.k.c.1374.3 8 13.3 even 3
1859.1.k.c.1374.3 8 143.10 odd 6
1859.1.k.c.1836.2 8 13.9 even 3
1859.1.k.c.1836.2 8 143.43 odd 6
1859.1.k.c.1836.3 8 13.4 even 6
1859.1.k.c.1836.3 8 143.87 odd 6
2288.1.m.a.2001.1 2 52.31 even 4
2288.1.m.a.2001.1 2 572.307 odd 4
2288.1.m.b.2001.1 2 52.47 even 4
2288.1.m.b.2001.1 2 572.395 odd 4
3575.1.c.c.3574.2 4 65.57 even 4
3575.1.c.c.3574.2 4 715.307 odd 4
3575.1.c.c.3574.3 4 65.18 even 4
3575.1.c.c.3574.3 4 715.593 odd 4
3575.1.c.d.3574.2 4 65.8 even 4
3575.1.c.d.3574.2 4 715.538 odd 4
3575.1.c.d.3574.3 4 65.47 even 4
3575.1.c.d.3574.3 4 715.252 odd 4
3575.1.h.e.2001.2 2 65.44 odd 4
3575.1.h.e.2001.2 2 715.164 even 4
3575.1.h.f.2001.1 2 65.34 odd 4
3575.1.h.f.2001.1 2 715.109 even 4