Properties

Label 2023.1.c.e.1735.3
Level $2023$
Weight $1$
Character 2023.1735
Analytic conductor $1.010$
Analytic rank $0$
Dimension $4$
Projective image $D_{5}$
CM discriminant -119
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] = [2023,1,Mod(1735,2023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2023, 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("2023.1735");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2023.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: \(1.00960852056\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 119)
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.14161.1
Artin image: $C_4\times D_5$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{20} - \cdots)\)

Embedding invariants

Embedding label 1735.3
Root \(1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 2023.1735
Dual form 2023.1.c.e.1735.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.61803 q^{2} -1.61803i q^{3} +1.61803 q^{4} +0.618034i q^{5} -2.61803i q^{6} -1.00000i q^{7} +1.00000 q^{8} -1.61803 q^{9} +O(q^{10})\) \(q+1.61803 q^{2} -1.61803i q^{3} +1.61803 q^{4} +0.618034i q^{5} -2.61803i q^{6} -1.00000i q^{7} +1.00000 q^{8} -1.61803 q^{9} +1.00000i q^{10} -2.61803i q^{12} -1.61803i q^{14} +1.00000 q^{15} -2.61803 q^{18} +1.00000i q^{20} -1.61803 q^{21} -1.61803i q^{24} +0.618034 q^{25} +1.00000i q^{27} -1.61803i q^{28} +1.61803 q^{30} +0.618034i q^{31} -1.00000 q^{32} +0.618034 q^{35} -2.61803 q^{36} +0.618034i q^{40} +1.61803i q^{41} -2.61803 q^{42} +1.61803 q^{43} -1.00000i q^{45} -1.00000 q^{49} +1.00000 q^{50} -0.618034 q^{53} +1.61803i q^{54} -1.00000i q^{56} +1.61803 q^{60} +1.61803i q^{61} +1.00000i q^{62} +1.61803i q^{63} -1.61803 q^{64} +0.618034 q^{67} +1.00000 q^{70} -1.61803 q^{72} -1.61803i q^{73} -1.00000i q^{75} +2.61803i q^{82} -2.61803 q^{84} +2.61803 q^{86} -1.61803i q^{90} +1.00000 q^{93} +1.61803i q^{96} +0.618034i q^{97} -1.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 2 q^{4} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 2 q^{4} + 4 q^{8} - 2 q^{9} + 4 q^{15} - 6 q^{18} - 2 q^{21} - 2 q^{25} + 2 q^{30} - 4 q^{32} - 2 q^{35} - 6 q^{36} - 6 q^{42} + 2 q^{43} - 4 q^{49} + 4 q^{50} + 2 q^{53} + 2 q^{60} - 2 q^{64} - 2 q^{67} + 4 q^{70} - 2 q^{72} - 6 q^{84} + 6 q^{86} + 4 q^{93} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2023\mathbb{Z}\right)^\times\).

\(n\) \(290\) \(1737\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(3\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(4\) 1.61803 1.61803
\(5\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(6\) − 2.61803i − 2.61803i
\(7\) − 1.00000i − 1.00000i
\(8\) 1.00000 1.00000
\(9\) −1.61803 −1.61803
\(10\) 1.00000i 1.00000i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) − 2.61803i − 2.61803i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) − 1.61803i − 1.61803i
\(15\) 1.00000 1.00000
\(16\) 0 0
\(17\) 0 0
\(18\) −2.61803 −2.61803
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.00000i 1.00000i
\(21\) −1.61803 −1.61803
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) − 1.61803i − 1.61803i
\(25\) 0.618034 0.618034
\(26\) 0 0
\(27\) 1.00000i 1.00000i
\(28\) − 1.61803i − 1.61803i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.61803 1.61803
\(31\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 0.618034 0.618034
\(36\) −2.61803 −2.61803
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.618034i 0.618034i
\(41\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(42\) −2.61803 −2.61803
\(43\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(44\) 0 0
\(45\) − 1.00000i − 1.00000i
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −1.00000 −1.00000
\(50\) 1.00000 1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) 1.61803i 1.61803i
\(55\) 0 0
\(56\) − 1.00000i − 1.00000i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 1.61803 1.61803
\(61\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(62\) 1.00000i 1.00000i
\(63\) 1.61803i 1.61803i
\(64\) −1.61803 −1.61803
\(65\) 0 0
\(66\) 0 0
\(67\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.00000 1.00000
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.61803 −1.61803
\(73\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(74\) 0 0
\(75\) − 1.00000i − 1.00000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 2.61803i 2.61803i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −2.61803 −2.61803
\(85\) 0 0
\(86\) 2.61803 2.61803
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) − 1.61803i − 1.61803i
\(91\) 0 0
\(92\) 0 0
\(93\) 1.00000 1.00000
\(94\) 0 0
\(95\) 0 0
\(96\) 1.61803i 1.61803i
\(97\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(98\) −1.61803 −1.61803
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) − 1.00000i − 1.00000i
\(106\) −1.00000 −1.00000
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 1.61803i 1.61803i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 1.00000 1.00000
\(121\) −1.00000 −1.00000
\(122\) 2.61803i 2.61803i
\(123\) 2.61803 2.61803
\(124\) 1.00000i 1.00000i
\(125\) 1.00000i 1.00000i
\(126\) 2.61803i 2.61803i
\(127\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(128\) −1.61803 −1.61803
\(129\) − 2.61803i − 2.61803i
\(130\) 0 0
\(131\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.00000 1.00000
\(135\) −0.618034 −0.618034
\(136\) 0 0
\(137\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(138\) 0 0
\(139\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(140\) 1.00000 1.00000
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) − 2.61803i − 2.61803i
\(147\) 1.61803i 1.61803i
\(148\) 0 0
\(149\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) − 1.61803i − 1.61803i
\(151\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.381966 −0.381966
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 1.00000i 1.00000i
\(160\) − 0.618034i − 0.618034i
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 2.61803i 2.61803i
\(165\) 0 0
\(166\) 0 0
\(167\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(168\) −1.61803 −1.61803
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 2.61803 2.61803
\(173\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(174\) 0 0
\(175\) − 0.618034i − 0.618034i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(180\) − 1.61803i − 1.61803i
\(181\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(182\) 0 0
\(183\) 2.61803 2.61803
\(184\) 0 0
\(185\) 0 0
\(186\) 1.61803 1.61803
\(187\) 0 0
\(188\) 0 0
\(189\) 1.00000 1.00000
\(190\) 0 0
\(191\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(192\) 2.61803i 2.61803i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 1.00000i 1.00000i
\(195\) 0 0
\(196\) −1.61803 −1.61803
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(200\) 0.618034 0.618034
\(201\) − 1.00000i − 1.00000i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.00000 −1.00000
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) − 1.61803i − 1.61803i
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) −1.00000 −1.00000
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000i 1.00000i
\(216\) 1.00000i 1.00000i
\(217\) 0.618034 0.618034
\(218\) 0 0
\(219\) −2.61803 −2.61803
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 1.00000i 1.00000i
\(225\) −1.00000 −1.00000
\(226\) 0 0
\(227\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 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
\(239\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) 0 0
\(241\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(242\) −1.61803 −1.61803
\(243\) 1.00000i 1.00000i
\(244\) 2.61803i 2.61803i
\(245\) − 0.618034i − 0.618034i
\(246\) 4.23607 4.23607
\(247\) 0 0
\(248\) 0.618034i 0.618034i
\(249\) 0 0
\(250\) 1.61803i 1.61803i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 2.61803i 2.61803i
\(253\) 0 0
\(254\) −1.00000 −1.00000
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) − 4.23607i − 4.23607i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 3.23607i 3.23607i
\(263\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) − 0.381966i − 0.381966i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.00000 1.00000
\(269\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) −1.00000 −1.00000
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.61803 −2.61803
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 1.00000i 1.00000i
\(279\) − 1.00000i − 1.00000i
\(280\) 0.618034 0.618034
\(281\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(282\) 0 0
\(283\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.61803 1.61803
\(288\) 1.61803 1.61803
\(289\) 0 0
\(290\) 0 0
\(291\) 1.00000 1.00000
\(292\) − 2.61803i − 2.61803i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 2.61803i 2.61803i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −2.61803 −2.61803
\(299\) 0 0
\(300\) − 1.61803i − 1.61803i
\(301\) − 1.61803i − 1.61803i
\(302\) 2.61803 2.61803
\(303\) 0 0
\(304\) 0 0
\(305\) −1.00000 −1.00000
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.618034 −0.618034
\(311\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(312\) 0 0
\(313\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(314\) 0 0
\(315\) −1.00000 −1.00000
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 1.61803i 1.61803i
\(319\) 0 0
\(320\) − 1.00000i − 1.00000i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 1.61803i 1.61803i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) − 2.61803i − 2.61803i
\(335\) 0.381966i 0.381966i
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 1.61803 1.61803
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000i 1.00000i
\(344\) 1.61803 1.61803
\(345\) 0 0
\(346\) − 2.61803i − 2.61803i
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) − 1.00000i − 1.00000i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 2.61803 2.61803
\(359\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) − 1.00000i − 1.00000i
\(361\) 1.00000 1.00000
\(362\) − 3.23607i − 3.23607i
\(363\) 1.61803i 1.61803i
\(364\) 0 0
\(365\) 1.00000 1.00000
\(366\) 4.23607 4.23607
\(367\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(368\) 0 0
\(369\) − 2.61803i − 2.61803i
\(370\) 0 0
\(371\) 0.618034i 0.618034i
\(372\) 1.61803 1.61803
\(373\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(374\) 0 0
\(375\) 1.61803 1.61803
\(376\) 0 0
\(377\) 0 0
\(378\) 1.61803 1.61803
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 1.00000i 1.00000i
\(382\) 1.00000 1.00000
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 2.61803i 2.61803i
\(385\) 0 0
\(386\) 0 0
\(387\) −2.61803 −2.61803
\(388\) 1.00000i 1.00000i
\(389\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 −1.00000
\(393\) 3.23607 3.23607
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(398\) − 2.61803i − 2.61803i
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) − 1.61803i − 1.61803i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) −1.61803 −1.61803
\(411\) 2.61803i 2.61803i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.00000 1.00000
\(418\) 0 0
\(419\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(420\) − 1.61803i − 1.61803i
\(421\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.618034 −0.618034
\(425\) 0 0
\(426\) 0 0
\(427\) 1.61803 1.61803
\(428\) 0 0
\(429\) 0 0
\(430\) 1.61803i 1.61803i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 1.00000 1.00000
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −4.23607 −4.23607
\(439\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(440\) 0 0
\(441\) 1.61803 1.61803
\(442\) 0 0
\(443\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 2.61803i 2.61803i
\(448\) 1.61803i 1.61803i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) −1.61803 −1.61803
\(451\) 0 0
\(452\) 0 0
\(453\) − 2.61803i − 2.61803i
\(454\) − 1.00000i − 1.00000i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(464\) 0 0
\(465\) 0.618034i 0.618034i
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) − 0.618034i − 0.618034i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.00000 1.00000
\(478\) −2.61803 −2.61803
\(479\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(480\) −1.00000 −1.00000
\(481\) 0 0
\(482\) 1.00000i 1.00000i
\(483\) 0 0
\(484\) −1.61803 −1.61803
\(485\) −0.381966 −0.381966
\(486\) 1.61803i 1.61803i
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 1.61803i 1.61803i
\(489\) 0 0
\(490\) − 1.00000i − 1.00000i
\(491\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 4.23607 4.23607
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 1.61803i 1.61803i
\(501\) −2.61803 −2.61803
\(502\) 0 0
\(503\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(504\) 1.61803i 1.61803i
\(505\) 0 0
\(506\) 0 0
\(507\) − 1.61803i − 1.61803i
\(508\) −1.00000 −1.00000
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −1.61803 −1.61803
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) − 4.23607i − 4.23607i
\(517\) 0 0
\(518\) 0 0
\(519\) −2.61803 −2.61803
\(520\) 0 0
\(521\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 3.23607i 3.23607i
\(525\) −1.00000 −1.00000
\(526\) −3.23607 −3.23607
\(527\) 0 0
\(528\) 0 0
\(529\) −1.00000 −1.00000
\(530\) − 0.618034i − 0.618034i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.618034 0.618034
\(537\) − 2.61803i − 2.61803i
\(538\) 3.23607i 3.23607i
\(539\) 0 0
\(540\) −1.00000 −1.00000
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) −3.23607 −3.23607
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −2.61803 −2.61803
\(549\) − 2.61803i − 2.61803i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.00000i 1.00000i
\(557\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(558\) − 1.61803i − 1.61803i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.00000 −1.00000
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) − 1.00000i − 1.00000i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) − 1.00000i − 1.00000i
\(574\) 2.61803 2.61803
\(575\) 0 0
\(576\) 2.61803 2.61803
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 1.61803 1.61803
\(583\) 0 0
\(584\) − 1.61803i − 1.61803i
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 2.61803i 2.61803i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2.61803 −2.61803
\(597\) −2.61803 −2.61803
\(598\) 0 0
\(599\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(600\) − 1.00000i − 1.00000i
\(601\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(602\) − 2.61803i − 2.61803i
\(603\) −1.00000 −1.00000
\(604\) 2.61803 2.61803
\(605\) − 0.618034i − 0.618034i
\(606\) 0 0
\(607\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −1.61803 −1.61803
\(611\) 0 0
\(612\) 0 0
\(613\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 0 0
\(615\) 1.61803i 1.61803i
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(620\) −0.618034 −0.618034
\(621\) 0 0
\(622\) 1.00000i 1.00000i
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) − 1.00000i − 1.00000i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −1.61803 −1.61803
\(631\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 0.381966i − 0.381966i
\(636\) 1.61803i 1.61803i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) − 1.00000i − 1.00000i
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(644\) 0 0
\(645\) 1.61803 1.61803
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) − 1.00000i − 1.00000i
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) −1.23607 −1.23607
\(656\) 0 0
\(657\) 2.61803i 2.61803i
\(658\) 0 0
\(659\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −1.00000 −1.00000
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) − 2.61803i − 2.61803i
\(669\) 0 0
\(670\) 0.618034i 0.618034i
\(671\) 0 0
\(672\) 1.61803 1.61803
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0.618034i 0.618034i
\(676\) 1.61803 1.61803
\(677\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0.618034 0.618034
\(680\) 0 0
\(681\) −1.00000 −1.00000
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) − 1.00000i − 1.00000i
\(686\) 1.61803i 1.61803i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(692\) − 2.61803i − 2.61803i
\(693\) 0 0
\(694\) 0 0
\(695\) −0.381966 −0.381966
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) − 1.00000i − 1.00000i
\(701\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 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
\(716\) 2.61803 2.61803
\(717\) 2.61803i 2.61803i
\(718\) −1.00000 −1.00000
\(719\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.61803 1.61803
\(723\) 1.00000 1.00000
\(724\) − 3.23607i − 3.23607i
\(725\) 0 0
\(726\) 2.61803i 2.61803i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.61803 1.61803
\(730\) 1.61803 1.61803
\(731\) 0 0
\(732\) 4.23607 4.23607
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 2.61803i 2.61803i
\(735\) −1.00000 −1.00000
\(736\) 0 0
\(737\) 0 0
\(738\) − 4.23607i − 4.23607i
\(739\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.00000i 1.00000i
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 1.00000 1.00000
\(745\) − 1.00000i − 1.00000i
\(746\) −2.61803 −2.61803
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 2.61803 2.61803
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.00000i 1.00000i
\(756\) 1.61803 1.61803
\(757\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 1.61803i 1.61803i
\(763\) 0 0
\(764\) 1.00000 1.00000
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.61803i 1.61803i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −4.23607 −4.23607
\(775\) 0.381966i 0.381966i
\(776\) 0.618034i 0.618034i
\(777\) 0 0
\(778\) −1.00000 −1.00000
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 5.23607 5.23607
\(787\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 3.23607i 3.23607i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) − 1.00000i − 1.00000i
\(795\) −0.618034 −0.618034
\(796\) − 2.61803i − 2.61803i
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.618034 −0.618034
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) − 1.61803i − 1.61803i
\(805\) 0 0
\(806\) 0 0
\(807\) 3.23607 3.23607
\(808\) 0 0
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) − 1.61803i − 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) −1.61803 −1.61803
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 4.23607i 4.23607i
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 1.61803 1.61803
\(835\) 1.00000 1.00000
\(836\) 0 0
\(837\) −0.618034 −0.618034
\(838\) − 1.00000i − 1.00000i
\(839\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(840\) − 1.00000i − 1.00000i
\(841\) −1.00000 −1.00000
\(842\) −2.61803 −2.61803
\(843\) 1.00000i 1.00000i
\(844\) 0 0
\(845\) 0.618034i 0.618034i
\(846\) 0 0
\(847\) 1.00000i 1.00000i
\(848\) 0 0
\(849\) −1.00000 −1.00000
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 2.61803 2.61803
\(855\) 0 0
\(856\) 0 0
\(857\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 1.61803i 1.61803i
\(861\) − 2.61803i − 2.61803i
\(862\) 0 0
\(863\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(864\) − 1.00000i − 1.00000i
\(865\) 1.00000 1.00000
\(866\) 0 0
\(867\) 0 0
\(868\) 1.00000 1.00000
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) − 1.00000i − 1.00000i
\(874\) 0 0
\(875\) 1.00000 1.00000
\(876\) −4.23607 −4.23607
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) − 2.61803i − 2.61803i
\(879\) 0 0
\(880\) 0 0
\(881\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(882\) 2.61803 2.61803
\(883\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 3.23607 3.23607
\(887\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(888\) 0 0
\(889\) 0.618034i 0.618034i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 4.23607i 4.23607i
\(895\) 1.00000i 1.00000i
\(896\) 1.61803i 1.61803i
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −1.61803 −1.61803
\(901\) 0 0
\(902\) 0 0
\(903\) −2.61803 −2.61803
\(904\) 0 0
\(905\) 1.23607 1.23607
\(906\) − 4.23607i − 4.23607i
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) − 1.00000i − 1.00000i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −1.00000 −1.00000
\(915\) 1.61803i 1.61803i
\(916\) 0 0
\(917\) 2.00000 2.00000
\(918\) 0 0
\(919\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −2.61803 −2.61803
\(927\) 0 0
\(928\) 0 0
\(929\) − 0.618034i − 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(930\) 1.00000i 1.00000i
\(931\) 0 0
\(932\) 0 0
\(933\) 1.00000 1.00000
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) − 1.00000i − 1.00000i
\(939\) −1.00000 −1.00000
\(940\) 0 0
\(941\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0.618034i 0.618034i
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(954\) 1.61803 1.61803
\(955\) 0.381966i 0.381966i
\(956\) −2.61803 −2.61803
\(957\) 0 0
\(958\) − 2.61803i − 2.61803i
\(959\) 1.61803i 1.61803i
\(960\) −1.61803 −1.61803
\(961\) 0.618034 0.618034
\(962\) 0 0
\(963\) 0 0
\(964\) 1.00000i 1.00000i
\(965\) 0 0
\(966\) 0 0
\(967\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) −0.618034 −0.618034
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 1.61803i 1.61803i
\(973\) 0.618034 0.618034
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) − 1.00000i − 1.00000i
\(981\) 0 0
\(982\) −1.00000 −1.00000
\(983\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(984\) 2.61803 2.61803
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) − 0.618034i − 0.618034i
\(993\) 1.00000i 1.00000i
\(994\) 0 0
\(995\) 1.00000 1.00000
\(996\) 0 0
\(997\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(998\) 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 2023.1.c.e.1735.3 4
7.6 odd 2 inner 2023.1.c.e.1735.4 4
17.2 even 8 2023.1.f.b.1483.3 8
17.3 odd 16 2023.1.l.b.468.4 16
17.4 even 4 119.1.d.a.118.1 2
17.5 odd 16 2023.1.l.b.1266.2 16
17.6 odd 16 2023.1.l.b.1889.3 16
17.7 odd 16 2023.1.l.b.1868.1 16
17.8 even 8 2023.1.f.b.251.1 8
17.9 even 8 2023.1.f.b.251.2 8
17.10 odd 16 2023.1.l.b.1868.2 16
17.11 odd 16 2023.1.l.b.1889.4 16
17.12 odd 16 2023.1.l.b.1266.1 16
17.13 even 4 119.1.d.b.118.1 yes 2
17.14 odd 16 2023.1.l.b.468.3 16
17.15 even 8 2023.1.f.b.1483.4 8
17.16 even 2 inner 2023.1.c.e.1735.4 4
51.38 odd 4 1071.1.h.b.118.2 2
51.47 odd 4 1071.1.h.a.118.2 2
68.47 odd 4 1904.1.n.a.1665.1 2
68.55 odd 4 1904.1.n.b.1665.2 2
85.4 even 4 2975.1.h.d.951.2 2
85.13 odd 4 2975.1.b.a.2974.4 4
85.38 odd 4 2975.1.b.b.2974.4 4
85.47 odd 4 2975.1.b.a.2974.1 4
85.64 even 4 2975.1.h.c.951.2 2
85.72 odd 4 2975.1.b.b.2974.1 4
119.4 even 12 833.1.h.b.509.2 4
119.6 even 16 2023.1.l.b.1889.4 16
119.13 odd 4 119.1.d.a.118.1 2
119.20 even 16 2023.1.l.b.468.3 16
119.27 even 16 2023.1.l.b.1868.1 16
119.30 even 12 833.1.h.a.815.2 4
119.38 odd 12 833.1.h.a.509.2 4
119.41 even 16 2023.1.l.b.1868.2 16
119.47 odd 12 833.1.h.b.815.2 4
119.48 even 16 2023.1.l.b.468.4 16
119.55 odd 4 119.1.d.b.118.1 yes 2
119.62 even 16 2023.1.l.b.1889.3 16
119.72 even 12 833.1.h.b.815.2 4
119.76 odd 8 2023.1.f.b.251.2 8
119.81 even 12 833.1.h.a.509.2 4
119.83 odd 8 2023.1.f.b.1483.3 8
119.89 odd 12 833.1.h.a.815.2 4
119.90 even 16 2023.1.l.b.1266.1 16
119.97 even 16 2023.1.l.b.1266.2 16
119.104 odd 8 2023.1.f.b.1483.4 8
119.111 odd 8 2023.1.f.b.251.1 8
119.115 odd 12 833.1.h.b.509.2 4
119.118 odd 2 CM 2023.1.c.e.1735.3 4
357.251 even 4 1071.1.h.b.118.2 2
357.293 even 4 1071.1.h.a.118.2 2
476.55 even 4 1904.1.n.a.1665.1 2
476.251 even 4 1904.1.n.b.1665.2 2
595.13 even 4 2975.1.b.b.2974.4 4
595.132 even 4 2975.1.b.b.2974.1 4
595.174 odd 4 2975.1.h.c.951.2 2
595.293 even 4 2975.1.b.a.2974.4 4
595.412 even 4 2975.1.b.a.2974.1 4
595.489 odd 4 2975.1.h.d.951.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
119.1.d.a.118.1 2 17.4 even 4
119.1.d.a.118.1 2 119.13 odd 4
119.1.d.b.118.1 yes 2 17.13 even 4
119.1.d.b.118.1 yes 2 119.55 odd 4
833.1.h.a.509.2 4 119.38 odd 12
833.1.h.a.509.2 4 119.81 even 12
833.1.h.a.815.2 4 119.30 even 12
833.1.h.a.815.2 4 119.89 odd 12
833.1.h.b.509.2 4 119.4 even 12
833.1.h.b.509.2 4 119.115 odd 12
833.1.h.b.815.2 4 119.47 odd 12
833.1.h.b.815.2 4 119.72 even 12
1071.1.h.a.118.2 2 51.47 odd 4
1071.1.h.a.118.2 2 357.293 even 4
1071.1.h.b.118.2 2 51.38 odd 4
1071.1.h.b.118.2 2 357.251 even 4
1904.1.n.a.1665.1 2 68.47 odd 4
1904.1.n.a.1665.1 2 476.55 even 4
1904.1.n.b.1665.2 2 68.55 odd 4
1904.1.n.b.1665.2 2 476.251 even 4
2023.1.c.e.1735.3 4 1.1 even 1 trivial
2023.1.c.e.1735.3 4 119.118 odd 2 CM
2023.1.c.e.1735.4 4 7.6 odd 2 inner
2023.1.c.e.1735.4 4 17.16 even 2 inner
2023.1.f.b.251.1 8 17.8 even 8
2023.1.f.b.251.1 8 119.111 odd 8
2023.1.f.b.251.2 8 17.9 even 8
2023.1.f.b.251.2 8 119.76 odd 8
2023.1.f.b.1483.3 8 17.2 even 8
2023.1.f.b.1483.3 8 119.83 odd 8
2023.1.f.b.1483.4 8 17.15 even 8
2023.1.f.b.1483.4 8 119.104 odd 8
2023.1.l.b.468.3 16 17.14 odd 16
2023.1.l.b.468.3 16 119.20 even 16
2023.1.l.b.468.4 16 17.3 odd 16
2023.1.l.b.468.4 16 119.48 even 16
2023.1.l.b.1266.1 16 17.12 odd 16
2023.1.l.b.1266.1 16 119.90 even 16
2023.1.l.b.1266.2 16 17.5 odd 16
2023.1.l.b.1266.2 16 119.97 even 16
2023.1.l.b.1868.1 16 17.7 odd 16
2023.1.l.b.1868.1 16 119.27 even 16
2023.1.l.b.1868.2 16 17.10 odd 16
2023.1.l.b.1868.2 16 119.41 even 16
2023.1.l.b.1889.3 16 17.6 odd 16
2023.1.l.b.1889.3 16 119.62 even 16
2023.1.l.b.1889.4 16 17.11 odd 16
2023.1.l.b.1889.4 16 119.6 even 16
2975.1.b.a.2974.1 4 85.47 odd 4
2975.1.b.a.2974.1 4 595.412 even 4
2975.1.b.a.2974.4 4 85.13 odd 4
2975.1.b.a.2974.4 4 595.293 even 4
2975.1.b.b.2974.1 4 85.72 odd 4
2975.1.b.b.2974.1 4 595.132 even 4
2975.1.b.b.2974.4 4 85.38 odd 4
2975.1.b.b.2974.4 4 595.13 even 4
2975.1.h.c.951.2 2 85.64 even 4
2975.1.h.c.951.2 2 595.174 odd 4
2975.1.h.d.951.2 2 85.4 even 4
2975.1.h.d.951.2 2 595.489 odd 4