Properties

Label 2013.1.bm.b.1280.1
Level $2013$
Weight $1$
Character 2013.1280
Analytic conductor $1.005$
Analytic rank $0$
Dimension $4$
Projective image $D_{5}$
CM discriminant -183
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2013,1,Mod(548,2013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2013, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6, 5]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2013.548");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2013.bm (of order \(10\), degree \(4\), 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: \(1.00461787043\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.490312449.1

Embedding invariants

Embedding label 1280.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 2013.1280
Dual form 2013.1.bm.b.1829.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.30902 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.500000 + 1.53884i) q^{4} +(1.30902 - 0.951057i) q^{6} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(1.30902 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.500000 + 1.53884i) q^{4} +(1.30902 - 0.951057i) q^{6} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.309017 + 0.951057i) q^{11} +1.61803 q^{12} +(1.30902 + 0.951057i) q^{13} +(-0.500000 + 0.363271i) q^{17} +(-0.500000 - 1.53884i) q^{18} +(0.190983 - 0.587785i) q^{19} +(-0.500000 + 1.53884i) q^{22} -1.61803 q^{23} +(0.809017 + 0.587785i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.809017 + 2.48990i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.500000 - 1.53884i) q^{29} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} +(0.500000 - 1.53884i) q^{36} +(0.809017 - 0.587785i) q^{38} +(1.30902 - 0.951057i) q^{39} +(-1.30902 + 0.951057i) q^{44} +(-2.11803 - 1.53884i) q^{46} +(-0.809017 + 0.587785i) q^{49} +(1.30902 - 0.951057i) q^{50} +(0.190983 + 0.587785i) q^{51} +(-0.809017 + 2.48990i) q^{52} +(1.30902 + 0.951057i) q^{53} -1.61803 q^{54} +(-0.500000 - 0.363271i) q^{57} +(0.809017 - 2.48990i) q^{58} +(0.190983 + 0.587785i) q^{59} +(-0.809017 + 0.587785i) q^{61} +(1.30902 + 0.951057i) q^{64} +(1.30902 + 0.951057i) q^{66} +(-0.809017 - 0.587785i) q^{68} +(-0.500000 + 1.53884i) q^{69} +(-1.61803 + 1.17557i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-0.500000 - 1.53884i) q^{73} +(-0.809017 - 0.587785i) q^{75} +1.00000 q^{76} +2.61803 q^{78} +(0.309017 + 0.951057i) q^{81} -1.61803 q^{87} -1.00000 q^{88} +0.618034 q^{89} +(-0.809017 - 2.48990i) q^{92} +(0.309017 - 0.951057i) q^{96} +(-1.61803 - 1.17557i) q^{97} -1.61803 q^{98} +(0.309017 - 0.951057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - q^{3} + 2 q^{4} + 3 q^{6} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} - q^{3} + 2 q^{4} + 3 q^{6} + q^{8} - q^{9} - q^{11} + 2 q^{12} + 3 q^{13} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 2 q^{22} - 2 q^{23} + q^{24} - q^{25} + q^{26} - q^{27} - 2 q^{29} + 4 q^{32} + 4 q^{33} - 4 q^{34} + 2 q^{36} + q^{38} + 3 q^{39} - 3 q^{44} - 4 q^{46} - q^{49} + 3 q^{50} + 3 q^{51} - q^{52} + 3 q^{53} - 2 q^{54} - 2 q^{57} + q^{58} + 3 q^{59} - q^{61} + 3 q^{64} + 3 q^{66} - q^{68} - 2 q^{69} - 2 q^{71} + q^{72} - 2 q^{73} - q^{75} + 4 q^{76} + 6 q^{78} - q^{81} - 2 q^{87} - 4 q^{88} - 2 q^{89} - q^{92} - q^{96} - 2 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2013\mathbb{Z}\right)^\times\).

\(n\) \(1222\) \(1343\) \(1465\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(3\) 0.309017 0.951057i 0.309017 0.951057i
\(4\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(5\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(6\) 1.30902 0.951057i 1.30902 0.951057i
\(7\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(8\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(9\) −0.809017 0.587785i −0.809017 0.587785i
\(10\) 0 0
\(11\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(12\) 1.61803 1.61803
\(13\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) −0.500000 1.53884i −0.500000 1.53884i
\(19\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(23\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(25\) 0.309017 0.951057i 0.309017 0.951057i
\(26\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(27\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(28\) 0 0
\(29\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) 1.00000 1.00000
\(33\) 1.00000 1.00000
\(34\) −1.00000 −1.00000
\(35\) 0 0
\(36\) 0.500000 1.53884i 0.500000 1.53884i
\(37\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 0.809017 0.587785i 0.809017 0.587785i
\(39\) 1.30902 0.951057i 1.30902 0.951057i
\(40\) 0 0
\(41\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(45\) 0 0
\(46\) −2.11803 1.53884i −2.11803 1.53884i
\(47\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(48\) 0 0
\(49\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(50\) 1.30902 0.951057i 1.30902 0.951057i
\(51\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(52\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(53\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) −1.61803 −1.61803
\(55\) 0 0
\(56\) 0 0
\(57\) −0.500000 0.363271i −0.500000 0.363271i
\(58\) 0.809017 2.48990i 0.809017 2.48990i
\(59\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(60\) 0 0
\(61\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(62\) 0 0
\(63\) 0 0
\(64\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(65\) 0 0
\(66\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −0.809017 0.587785i −0.809017 0.587785i
\(69\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(70\) 0 0
\(71\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) 0.809017 0.587785i 0.809017 0.587785i
\(73\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(74\) 0 0
\(75\) −0.809017 0.587785i −0.809017 0.587785i
\(76\) 1.00000 1.00000
\(77\) 0 0
\(78\) 2.61803 2.61803
\(79\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(82\) 0 0
\(83\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.61803 −1.61803
\(88\) −1.00000 −1.00000
\(89\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.809017 2.48990i −0.809017 2.48990i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.309017 0.951057i 0.309017 0.951057i
\(97\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(98\) −1.61803 −1.61803
\(99\) 0.309017 0.951057i 0.309017 0.951057i
\(100\) 1.61803 1.61803
\(101\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(102\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(103\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(104\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(105\) 0 0
\(106\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(107\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) −1.30902 0.951057i −1.30902 0.951057i
\(109\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(114\) −0.309017 0.951057i −0.309017 0.951057i
\(115\) 0 0
\(116\) 2.11803 1.53884i 2.11803 1.53884i
\(117\) −0.500000 1.53884i −0.500000 1.53884i
\(118\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(122\) −1.61803 −1.61803
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(128\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.190983 0.587785i −0.190983 0.587785i
\(137\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(138\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(139\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.23607 −3.23607
\(143\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(144\) 0 0
\(145\) 0 0
\(146\) 0.809017 2.48990i 0.809017 2.48990i
\(147\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(148\) 0 0
\(149\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) −0.500000 1.53884i −0.500000 1.53884i
\(151\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(152\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(153\) 0.618034 0.618034
\(154\) 0 0
\(155\) 0 0
\(156\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(157\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(158\) 0 0
\(159\) 1.30902 0.951057i 1.30902 0.951057i
\(160\) 0 0
\(161\) 0 0
\(162\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(163\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(168\) 0 0
\(169\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(170\) 0 0
\(171\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(172\) 0 0
\(173\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(174\) −2.11803 1.53884i −2.11803 1.53884i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.618034 0.618034
\(178\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(179\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(180\) 0 0
\(181\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(182\) 0 0
\(183\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(184\) 0.500000 1.53884i 0.500000 1.53884i
\(185\) 0 0
\(186\) 0 0
\(187\) −0.500000 0.363271i −0.500000 0.363271i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(192\) 1.30902 0.951057i 1.30902 0.951057i
\(193\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(194\) −1.00000 3.07768i −1.00000 3.07768i
\(195\) 0 0
\(196\) −1.30902 0.951057i −1.30902 0.951057i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 1.30902 0.951057i 1.30902 0.951057i
\(199\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(200\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(201\) 0 0
\(202\) −1.00000 3.07768i −1.00000 3.07768i
\(203\) 0 0
\(204\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(205\) 0 0
\(206\) 0.809017 2.48990i 0.809017 2.48990i
\(207\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(208\) 0 0
\(209\) 0.618034 0.618034
\(210\) 0 0
\(211\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(212\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(213\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.309017 0.951057i −0.309017 0.951057i
\(217\) 0 0
\(218\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(219\) −1.61803 −1.61803
\(220\) 0 0
\(221\) −1.00000 −1.00000
\(222\) 0 0
\(223\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(224\) 0 0
\(225\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(226\) 0 0
\(227\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) 0.309017 0.951057i 0.309017 0.951057i
\(229\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.61803 1.61803
\(233\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 0.809017 2.48990i 0.809017 2.48990i
\(235\) 0 0
\(236\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(240\) 0 0
\(241\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(242\) −1.61803 −1.61803
\(243\) 1.00000 1.00000
\(244\) −1.30902 0.951057i −1.30902 0.951057i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.809017 0.587785i 0.809017 0.587785i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(252\) 0 0
\(253\) −0.500000 1.53884i −0.500000 1.53884i
\(254\) −3.23607 −3.23607
\(255\) 0 0
\(256\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(257\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.190983 0.587785i 0.190983 0.587785i
\(268\) 0 0
\(269\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 0 0
\(271\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 1.00000
\(276\) −2.61803 −2.61803
\(277\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(284\) −2.61803 1.90211i −2.61803 1.90211i
\(285\) 0 0
\(286\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(287\) 0 0
\(288\) −0.809017 0.587785i −0.809017 0.587785i
\(289\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(290\) 0 0
\(291\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(292\) 2.11803 1.53884i 2.11803 1.53884i
\(293\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(294\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.809017 0.587785i −0.809017 0.587785i
\(298\) 0 0
\(299\) −2.11803 1.53884i −2.11803 1.53884i
\(300\) 0.500000 1.53884i 0.500000 1.53884i
\(301\) 0 0
\(302\) 0 0
\(303\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(304\) 0 0
\(305\) 0 0
\(306\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −1.61803 −1.61803
\(310\) 0 0
\(311\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(312\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(313\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(318\) 2.61803 2.61803
\(319\) 1.30902 0.951057i 1.30902 0.951057i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(324\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(325\) 1.30902 0.951057i 1.30902 0.951057i
\(326\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(327\) 0.190983 0.587785i 0.190983 0.587785i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(338\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −1.00000 −1.00000
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 2.61803 1.90211i 2.61803 1.90211i
\(347\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) −0.809017 2.48990i −0.809017 2.48990i
\(349\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) 0 0
\(351\) −1.61803 −1.61803
\(352\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(355\) 0 0
\(356\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(357\) 0 0
\(358\) 0 0
\(359\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0 0
\(361\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(362\) 0 0
\(363\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(367\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −0.309017 0.951057i −0.309017 0.951057i
\(375\) 0 0
\(376\) 0 0
\(377\) 0.809017 2.48990i 0.809017 2.48990i
\(378\) 0 0
\(379\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(380\) 0 0
\(381\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(382\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(383\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(384\) 1.61803 1.61803
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.00000 3.07768i 1.00000 3.07768i
\(389\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0.809017 0.587785i 0.809017 0.587785i
\(392\) −0.309017 0.951057i −0.309017 0.951057i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 1.61803 1.61803
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(399\) 0 0
\(400\) 0 0
\(401\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.00000 3.07768i 1.00000 3.07768i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.618034 −0.618034
\(409\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 2.11803 1.53884i 2.11803 1.53884i
\(413\) 0 0
\(414\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(415\) 0 0
\(416\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(417\) 0 0
\(418\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(419\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(420\) 0 0
\(421\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(425\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(426\) −1.00000 + 3.07768i −1.00000 + 3.07768i
\(427\) 0 0
\(428\) 0 0
\(429\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(430\) 0 0
\(431\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(432\) 0 0
\(433\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(437\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(438\) −2.11803 1.53884i −2.11803 1.53884i
\(439\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) −1.30902 0.951057i −1.30902 0.951057i
\(443\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(450\) −1.61803 −1.61803
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −1.00000 + 3.07768i −1.00000 + 3.07768i
\(455\) 0 0
\(456\) 0.500000 0.363271i 0.500000 0.363271i
\(457\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(458\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(459\) 0.190983 0.587785i 0.190983 0.587785i
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.309017 0.951057i −0.309017 0.951057i
\(467\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(468\) 2.11803 1.53884i 2.11803 1.53884i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.618034 −0.618034
\(473\) 0 0
\(474\) 0 0
\(475\) −0.500000 0.363271i −0.500000 0.363271i
\(476\) 0 0
\(477\) −0.500000 1.53884i −0.500000 1.53884i
\(478\) 0 0
\(479\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 2.61803 + 1.90211i 2.61803 + 1.90211i
\(483\) 0 0
\(484\) −1.30902 0.951057i −1.30902 0.951057i
\(485\) 0 0
\(486\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(487\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(488\) −0.309017 0.951057i −0.309017 0.951057i
\(489\) 1.30902 0.951057i 1.30902 0.951057i
\(490\) 0 0
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(494\) 1.61803 1.61803
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.309017 0.951057i −0.309017 0.951057i
\(503\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0.809017 2.48990i 0.809017 2.48990i
\(507\) 1.61803 1.61803
\(508\) −2.61803 1.90211i −2.61803 1.90211i
\(509\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.61803 1.17557i −1.61803 1.17557i
\(520\) 0 0
\(521\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(523\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.61803 1.61803
\(530\) 0 0
\(531\) 0.190983 0.587785i 0.190983 0.587785i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.809017 0.587785i 0.809017 0.587785i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.809017 0.587785i −0.809017 0.587785i
\(540\) 0 0
\(541\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(542\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(543\) 0 0
\(544\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(548\) 0 0
\(549\) 1.00000 1.00000
\(550\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(551\) −1.00000 −1.00000
\(552\) −1.30902 0.951057i −1.30902 0.951057i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(562\) 2.61803 2.61803
\(563\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.809017 0.587785i 0.809017 0.587785i
\(567\) 0 0
\(568\) −0.618034 1.90211i −0.618034 1.90211i
\(569\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(570\) 0 0
\(571\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(572\) −2.61803 −2.61803
\(573\) 0.618034 0.618034
\(574\) 0 0
\(575\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(576\) −0.500000 1.53884i −0.500000 1.53884i
\(577\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) −3.23607 −3.23607
\(583\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(584\) 1.61803 1.61803
\(585\) 0 0
\(586\) 0 0
\(587\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(588\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(594\) −0.500000 1.53884i −0.500000 1.53884i
\(595\) 0 0
\(596\) 0 0
\(597\) 0.190983 0.587785i 0.190983 0.587785i
\(598\) −1.30902 4.02874i −1.30902 4.02874i
\(599\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(600\) 0.809017 0.587785i 0.809017 0.587785i
\(601\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −3.23607 −3.23607
\(607\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(608\) 0.190983 0.587785i 0.190983 0.587785i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(613\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(618\) −2.11803 1.53884i −2.11803 1.53884i
\(619\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(620\) 0 0
\(621\) 1.30902 0.951057i 1.30902 0.951057i
\(622\) 2.61803 1.90211i 2.61803 1.90211i
\(623\) 0 0
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.809017 0.587785i
\(626\) 0 0
\(627\) 0.190983 0.587785i 0.190983 0.587785i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(637\) −1.61803 −1.61803
\(638\) 2.61803 2.61803
\(639\) 2.00000 2.00000
\(640\) 0 0
\(641\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(642\) 0 0
\(643\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(647\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(648\) −1.00000 −1.00000
\(649\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(650\) 2.61803 2.61803
\(651\) 0 0
\(652\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(653\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(654\) 0.809017 0.587785i 0.809017 0.587785i
\(655\) 0 0
\(656\) 0 0
\(657\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.809017 0.587785i −0.809017 0.587785i
\(672\) 0 0
\(673\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(674\) 0 0
\(675\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(676\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(677\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 2.00000 2.00000
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −0.809017 0.587785i −0.809017 0.587785i
\(685\) 0 0
\(686\) 0 0
\(687\) 1.30902 0.951057i 1.30902 0.951057i
\(688\) 0 0
\(689\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(690\) 0 0
\(691\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(692\) 3.23607 3.23607
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0.500000 1.53884i 0.500000 1.53884i
\(697\) 0 0
\(698\) 0 0
\(699\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(700\) 0 0
\(701\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(702\) −2.11803 1.53884i −2.11803 1.53884i
\(703\) 0 0
\(704\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(709\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(719\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(723\) 0.618034 1.90211i 0.618034 1.90211i
\(724\) 0 0
\(725\) −1.61803 −1.61803
\(726\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(727\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(728\) 0 0
\(729\) 0.309017 0.951057i 0.309017 0.951057i
\(730\) 0 0
\(731\) 0 0
\(732\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(733\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(734\) −1.00000 + 3.07768i −1.00000 + 3.07768i
\(735\) 0 0
\(736\) −1.61803 −1.61803
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) 0 0
\(741\) −0.309017 0.951057i −0.309017 0.951057i
\(742\) 0 0
\(743\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0.309017 0.951057i 0.309017 0.951057i
\(749\) 0 0
\(750\) 0 0
\(751\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(752\) 0 0
\(753\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(754\) 3.42705 2.48990i 3.42705 2.48990i
\(755\) 0 0
\(756\) 0 0
\(757\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(758\) 2.61803 2.61803
\(759\) −1.61803 −1.61803
\(760\) 0 0
\(761\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) −1.00000 + 3.07768i −1.00000 + 3.07768i
\(763\) 0 0
\(764\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(765\) 0 0
\(766\) −0.309017 0.951057i −0.309017 0.951057i
\(767\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(768\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.61803 1.17557i 1.61803 1.17557i
\(777\) 0 0
\(778\) −1.00000 + 3.07768i −1.00000 + 3.07768i
\(779\) 0 0
\(780\) 0 0
\(781\) −1.61803 1.17557i −1.61803 1.17557i
\(782\) 1.61803 1.61803
\(783\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(793\) −1.61803 −1.61803
\(794\) 0 0
\(795\) 0 0
\(796\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(797\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.309017 0.951057i 0.309017 0.951057i
\(801\) −0.500000 0.363271i −0.500000 0.363271i
\(802\) 2.61803 2.61803
\(803\) 1.30902 0.951057i 1.30902 0.951057i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 1.61803 1.17557i 1.61803 1.17557i
\(809\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(810\) 0 0
\(811\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(812\) 0 0
\(813\) 0.618034 0.618034
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(822\) 0 0
\(823\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(824\) 1.61803 1.61803
\(825\) 0.309017 0.951057i 0.309017 0.951057i
\(826\) 0 0
\(827\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(828\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(829\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(833\) 0.190983 0.587785i 0.190983 0.587785i
\(834\) 0 0
\(835\) 0 0
\(836\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(837\) 0 0
\(838\) −2.11803 1.53884i −2.11803 1.53884i
\(839\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(840\) 0 0
\(841\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(842\) 0 0
\(843\) −0.500000 1.53884i −0.500000 1.53884i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −0.500000 0.363271i −0.500000 0.363271i
\(850\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(851\) 0 0
\(852\) −2.61803 + 1.90211i −2.61803 + 1.90211i
\(853\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(859\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(864\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(865\) 0 0
\(866\) 0 0
\(867\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(873\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(874\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(875\) 0 0
\(876\) −0.809017 2.48990i −0.809017 2.48990i
\(877\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(878\) −2.11803 1.53884i −2.11803 1.53884i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(883\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(884\) −0.500000 1.53884i −0.500000 1.53884i
\(885\) 0 0
\(886\) 0 0
\(887\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(898\) 0 0
\(899\) 0 0
\(900\) −1.30902 0.951057i −1.30902 0.951057i
\(901\) −1.00000 −1.00000
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(908\) −2.61803 + 1.90211i −2.61803 + 1.90211i
\(909\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(910\) 0 0
\(911\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(917\) 0 0
\(918\) 0.809017 0.587785i 0.809017 0.587785i
\(919\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.23607 −3.23607
\(924\) 0 0
\(925\) 0 0
\(926\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(927\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(928\) −0.500000 1.53884i −0.500000 1.53884i
\(929\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(930\) 0 0
\(931\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(932\) 0.309017 0.951057i 0.309017 0.951057i
\(933\) −1.61803 1.17557i −1.61803 1.17557i
\(934\) −1.00000 −1.00000
\(935\) 0 0
\(936\) 1.61803 1.61803
\(937\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(948\) 0 0
\(949\) 0.809017 2.48990i 0.809017 2.48990i
\(950\) −0.309017 0.951057i −0.309017 0.951057i
\(951\) 0 0
\(952\) 0 0
\(953\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(954\) 0.809017 2.48990i 0.809017 2.48990i
\(955\) 0 0
\(956\) 0 0
\(957\) −0.500000 1.53884i −0.500000 1.53884i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(962\) 0 0
\(963\) 0 0
\(964\) 1.00000 + 3.07768i 1.00000 + 3.07768i
\(965\) 0 0
\(966\) 0 0
\(967\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(968\) −0.309017 0.951057i −0.309017 0.951057i
\(969\) 0.381966 0.381966
\(970\) 0 0
\(971\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(972\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(973\) 0 0
\(974\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(975\) −0.500000 1.53884i −0.500000 1.53884i
\(976\) 0 0
\(977\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(978\) 2.61803 2.61803
\(979\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(980\) 0 0
\(981\) −0.500000 0.363271i −0.500000 0.363271i
\(982\) 0 0
\(983\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(987\) 0 0
\(988\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(989\) 0 0
\(990\) 0 0
\(991\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(998\) 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 2013.1.bm.b.1280.1 yes 4
3.2 odd 2 2013.1.bm.a.1280.1 4
11.3 even 5 inner 2013.1.bm.b.1829.1 yes 4
33.14 odd 10 2013.1.bm.a.1829.1 yes 4
61.60 even 2 2013.1.bm.a.1280.1 4
183.182 odd 2 CM 2013.1.bm.b.1280.1 yes 4
671.487 even 10 2013.1.bm.a.1829.1 yes 4
2013.1829 odd 10 inner 2013.1.bm.b.1829.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.1.bm.a.1280.1 4 3.2 odd 2
2013.1.bm.a.1280.1 4 61.60 even 2
2013.1.bm.a.1829.1 yes 4 33.14 odd 10
2013.1.bm.a.1829.1 yes 4 671.487 even 10
2013.1.bm.b.1280.1 yes 4 1.1 even 1 trivial
2013.1.bm.b.1280.1 yes 4 183.182 odd 2 CM
2013.1.bm.b.1829.1 yes 4 11.3 even 5 inner
2013.1.bm.b.1829.1 yes 4 2013.1829 odd 10 inner