Properties

Label 429.1.v.a.38.1
Level $429$
Weight $1$
Character 429.38
Analytic conductor $0.214$
Analytic rank $0$
Dimension $4$
Projective image $D_{5}$
CM discriminant -39
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,1,Mod(38,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4, 5]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.38");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 429.v (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: \(0.214098890420\)
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 5.1.22268961.1

Embedding invariants

Embedding label 38.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 429.38
Dual form 429.1.v.a.350.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.190983 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.500000 - 0.363271i) q^{4} +(0.500000 - 1.53884i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.190983 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.500000 - 0.363271i) q^{4} +(0.500000 - 1.53884i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{10} +(-0.309017 + 0.951057i) q^{11} -0.618034 q^{12} +(0.309017 + 0.951057i) q^{13} +(-1.30902 + 0.951057i) q^{15} +(0.500000 - 0.363271i) q^{18} +(-0.309017 - 0.951057i) q^{20} +0.618034 q^{22} +(0.309017 + 0.951057i) q^{24} +(-1.30902 - 0.951057i) q^{25} +(0.500000 - 0.363271i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.809017 + 0.587785i) q^{30} -1.00000 q^{32} +(0.809017 - 0.587785i) q^{33} +(0.500000 + 0.363271i) q^{36} +(0.309017 - 0.951057i) q^{39} +(-1.30902 + 0.951057i) q^{40} +(1.61803 + 1.17557i) q^{41} -1.61803 q^{43} +(0.190983 + 0.587785i) q^{44} +1.61803 q^{45} +(0.500000 + 0.363271i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(0.500000 + 0.363271i) q^{52} -0.618034 q^{54} +(1.30902 + 0.951057i) q^{55} +(0.500000 - 0.363271i) q^{59} +(-0.309017 + 0.951057i) q^{60} +(0.190983 - 0.587785i) q^{61} +(0.190983 + 0.587785i) q^{64} +1.61803 q^{65} +(-0.500000 - 0.363271i) q^{66} +(-0.618034 + 1.90211i) q^{71} +(0.309017 - 0.951057i) q^{72} +(0.500000 + 1.53884i) q^{75} -0.618034 q^{78} +(0.190983 + 0.587785i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.381966 - 1.17557i) q^{82} +(0.500000 - 1.53884i) q^{83} +(0.309017 + 0.951057i) q^{86} +(0.809017 - 0.587785i) q^{88} -2.00000 q^{89} +(-0.309017 - 0.951057i) q^{90} +(0.118034 - 0.363271i) q^{94} +(0.809017 + 0.587785i) q^{96} -0.618034 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} - q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} - q^{8} - q^{9} - 4 q^{10} + q^{11} + 2 q^{12} - q^{13} - 3 q^{15} + 2 q^{18} + q^{20} - 2 q^{22} - q^{24} - 3 q^{25} + 2 q^{26} - q^{27} + q^{30} - 4 q^{32} + q^{33} + 2 q^{36} - q^{39} - 3 q^{40} + 2 q^{41} - 2 q^{43} + 3 q^{44} + 2 q^{45} + 2 q^{47} - q^{49} + q^{50} + 2 q^{52} + 2 q^{54} + 3 q^{55} + 2 q^{59} + q^{60} + 3 q^{61} + 3 q^{64} + 2 q^{65} - 2 q^{66} + 2 q^{71} - q^{72} + 2 q^{75} + 2 q^{78} + 3 q^{79} - q^{81} + 6 q^{82} + 2 q^{83} - q^{86} + q^{88} - 8 q^{89} + q^{90} - 4 q^{94} + q^{96} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(3\) −0.809017 0.587785i −0.809017 0.587785i
\(4\) 0.500000 0.363271i 0.500000 0.363271i
\(5\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(6\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(7\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(8\) −0.809017 0.587785i −0.809017 0.587785i
\(9\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(10\) −1.00000 −1.00000
\(11\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(12\) −0.618034 −0.618034
\(13\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(14\) 0 0
\(15\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(16\) 0 0
\(17\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(18\) 0.500000 0.363271i 0.500000 0.363271i
\(19\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(20\) −0.309017 0.951057i −0.309017 0.951057i
\(21\) 0 0
\(22\) 0.618034 0.618034
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(25\) −1.30902 0.951057i −1.30902 0.951057i
\(26\) 0.500000 0.363271i 0.500000 0.363271i
\(27\) 0.309017 0.951057i 0.309017 0.951057i
\(28\) 0 0
\(29\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(31\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0.809017 0.587785i 0.809017 0.587785i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(37\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(38\) 0 0
\(39\) 0.309017 0.951057i 0.309017 0.951057i
\(40\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(41\) 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(42\) 0 0
\(43\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(44\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(45\) 1.61803 1.61803
\(46\) 0 0
\(47\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(48\) 0 0
\(49\) 0.309017 0.951057i 0.309017 0.951057i
\(50\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(51\) 0 0
\(52\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(53\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) −0.618034 −0.618034
\(55\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(60\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(61\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(65\) 1.61803 1.61803
\(66\) −0.500000 0.363271i −0.500000 0.363271i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i \(0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(72\) 0.309017 0.951057i 0.309017 0.951057i
\(73\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(74\) 0 0
\(75\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(76\) 0 0
\(77\) 0 0
\(78\) −0.618034 −0.618034
\(79\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(82\) 0.381966 1.17557i 0.381966 1.17557i
\(83\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(87\) 0 0
\(88\) 0.809017 0.587785i 0.809017 0.587785i
\(89\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(90\) −0.309017 0.951057i −0.309017 0.951057i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.118034 0.363271i 0.118034 0.363271i
\(95\) 0 0
\(96\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(97\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) −0.618034 −0.618034
\(99\) −1.00000 −1.00000
\(100\) −1.00000 −1.00000
\(101\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(102\) 0 0
\(103\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(104\) 0.309017 0.951057i 0.309017 0.951057i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(108\) −0.190983 0.587785i −0.190983 0.587785i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0.309017 0.951057i 0.309017 0.951057i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(118\) −0.309017 0.224514i −0.309017 0.224514i
\(119\) 0 0
\(120\) 1.61803 1.61803
\(121\) −0.809017 0.587785i −0.809017 0.587785i
\(122\) −0.381966 −0.381966
\(123\) −0.618034 1.90211i −0.618034 1.90211i
\(124\) 0 0
\(125\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(126\) 0 0
\(127\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(128\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(129\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(130\) −0.309017 0.951057i −0.309017 0.951057i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0.190983 0.587785i 0.190983 0.587785i
\(133\) 0 0
\(134\) 0 0
\(135\) −1.30902 0.951057i −1.30902 0.951057i
\(136\) 0 0
\(137\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) 0 0
\(141\) −0.190983 0.587785i −0.190983 0.587785i
\(142\) 1.23607 1.23607
\(143\) −1.00000 −1.00000
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(148\) 0 0
\(149\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(150\) 0.809017 0.587785i 0.809017 0.587785i
\(151\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.190983 0.587785i −0.190983 0.587785i
\(157\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0.309017 0.224514i 0.309017 0.224514i
\(159\) 0 0
\(160\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(161\) 0 0
\(162\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(163\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(164\) 1.23607 1.23607
\(165\) −0.500000 1.53884i −0.500000 1.53884i
\(166\) −1.00000 −1.00000
\(167\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(168\) 0 0
\(169\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(173\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.618034 −0.618034
\(178\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(179\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(180\) 0.809017 0.587785i 0.809017 0.587785i
\(181\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(182\) 0 0
\(183\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0.381966 0.381966
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(192\) 0.190983 0.587785i 0.190983 0.587785i
\(193\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(194\) 0 0
\(195\) −1.30902 0.951057i −1.30902 0.951057i
\(196\) −0.190983 0.587785i −0.190983 0.587785i
\(197\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(198\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(199\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(200\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.61803 1.90211i 2.61803 1.90211i
\(206\) −0.809017 0.587785i −0.809017 0.587785i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(212\) 0 0
\(213\) 1.61803 1.17557i 1.61803 1.17557i
\(214\) 0 0
\(215\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(216\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 1.00000 1.00000
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(224\) 0 0
\(225\) 0.500000 1.53884i 0.500000 1.53884i
\(226\) 0 0
\(227\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(234\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(235\) 0.809017 0.587785i 0.809017 0.587785i
\(236\) 0.118034 0.363271i 0.118034 0.363271i
\(237\) 0.190983 0.587785i 0.190983 0.587785i
\(238\) 0 0
\(239\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(243\) 1.00000 1.00000
\(244\) −0.118034 0.363271i −0.118034 0.363271i
\(245\) −1.30902 0.951057i −1.30902 0.951057i
\(246\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(250\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(251\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.00000 1.00000
\(255\) 0 0
\(256\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(257\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(258\) 0.309017 0.951057i 0.309017 0.951057i
\(259\) 0 0
\(260\) 0.809017 0.587785i 0.809017 0.587785i
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −1.00000 −1.00000
\(265\) 0 0
\(266\) 0 0
\(267\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(268\) 0 0
\(269\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(270\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(271\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0.381966 0.381966
\(275\) 1.30902 0.951057i 1.30902 0.951057i
\(276\) 0 0
\(277\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(278\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(282\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(283\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(284\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(285\) 0 0
\(286\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(287\) 0 0
\(288\) −0.309017 0.951057i −0.309017 0.951057i
\(289\) −0.809017 0.587785i −0.809017 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(294\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(295\) −0.309017 0.951057i −0.309017 0.951057i
\(296\) 0 0
\(297\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(298\) −1.00000 −1.00000
\(299\) 0 0
\(300\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.809017 0.587785i −0.809017 0.587785i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −1.61803 −1.61803
\(310\) 0 0
\(311\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(312\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(313\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(315\) 0 0
\(316\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(317\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.00000 1.00000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(325\) 0.500000 1.53884i 0.500000 1.53884i
\(326\) 0 0
\(327\) 0 0
\(328\) −0.618034 1.90211i −0.618034 1.90211i
\(329\) 0 0
\(330\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −0.309017 0.951057i −0.309017 0.951057i
\(333\) 0 0
\(334\) 0.809017 0.587785i 0.809017 0.587785i
\(335\) 0 0
\(336\) 0 0
\(337\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(338\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(350\) 0 0
\(351\) 1.00000 1.00000
\(352\) 0.309017 0.951057i 0.309017 0.951057i
\(353\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(354\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(355\) 2.61803 + 1.90211i 2.61803 + 1.90211i
\(356\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(357\) 0 0
\(358\) 0 0
\(359\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(360\) −1.30902 0.951057i −1.30902 0.951057i
\(361\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(362\) 1.00000 1.00000
\(363\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(367\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(374\) 0 0
\(375\) 1.00000 1.00000
\(376\) −0.190983 0.587785i −0.190983 0.587785i
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(380\) 0 0
\(381\) 1.30902 0.951057i 1.30902 0.951057i
\(382\) 0 0
\(383\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(384\) 0.618034 0.618034
\(385\) 0 0
\(386\) 0 0
\(387\) −0.500000 1.53884i −0.500000 1.53884i
\(388\) 0 0
\(389\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(391\) 0 0
\(392\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(393\) 0 0
\(394\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(395\) 1.00000 1.00000
\(396\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −0.118034 0.363271i −0.118034 0.363271i
\(399\) 0 0
\(400\) 0 0
\(401\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(410\) −1.61803 1.17557i −1.61803 1.17557i
\(411\) 0.500000 0.363271i 0.500000 0.363271i
\(412\) 0.309017 0.951057i 0.309017 0.951057i
\(413\) 0 0
\(414\) 0 0
\(415\) −2.11803 1.53884i −2.11803 1.53884i
\(416\) −0.309017 0.951057i −0.309017 0.951057i
\(417\) 0.618034 0.618034
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(423\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(424\) 0 0
\(425\) 0 0
\(426\) −1.00000 0.726543i −1.00000 0.726543i
\(427\) 0 0
\(428\) 0 0
\(429\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(430\) 1.61803 1.61803
\(431\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(440\) −0.500000 1.53884i −0.500000 1.53884i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(444\) 0 0
\(445\) −1.00000 + 3.07768i −1.00000 + 3.07768i
\(446\) 0 0
\(447\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(448\) 0 0
\(449\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(450\) −1.00000 −1.00000
\(451\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(452\) 0 0
\(453\) 0 0
\(454\) −0.309017 0.224514i −0.309017 0.224514i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(468\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(469\) 0 0
\(470\) −0.500000 0.363271i −0.500000 0.363271i
\(471\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(472\) −0.618034 −0.618034
\(473\) 0.500000 1.53884i 0.500000 1.53884i
\(474\) −0.381966 −0.381966
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(479\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(480\) 1.30902 0.951057i 1.30902 0.951057i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.618034 −0.618034
\(485\) 0 0
\(486\) −0.190983 0.587785i −0.190983 0.587785i
\(487\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(488\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(489\) 0 0
\(490\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(491\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) −1.00000 0.726543i −1.00000 0.726543i
\(493\) 0 0
\(494\) 0 0
\(495\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(496\) 0 0
\(497\) 0 0
\(498\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(499\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(500\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(501\) 0.500000 1.53884i 0.500000 1.53884i
\(502\) 0 0
\(503\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 1.00000
\(508\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(509\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.809017 2.48990i −0.809017 2.48990i
\(516\) 1.00000 1.00000
\(517\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(518\) 0 0
\(519\) 0 0
\(520\) −1.30902 0.951057i −1.30902 0.951057i
\(521\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(532\) 0 0
\(533\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(534\) 0.381966 1.17557i 0.381966 1.17557i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(540\) −1.00000 −1.00000
\(541\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) 0 0
\(543\) 1.30902 0.951057i 1.30902 0.951057i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(548\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(549\) 0.618034 0.618034
\(550\) −0.809017 0.587785i −0.809017 0.587785i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 1.00000 0.726543i 1.00000 0.726543i
\(555\) 0 0
\(556\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(557\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(558\) 0 0
\(559\) −0.500000 1.53884i −0.500000 1.53884i
\(560\) 0 0
\(561\) 0 0
\(562\) 0.381966 0.381966
\(563\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(564\) −0.309017 0.224514i −0.309017 0.224514i
\(565\) 0 0
\(566\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(567\) 0 0
\(568\) 1.61803 1.17557i 1.61803 1.17557i
\(569\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(570\) 0 0
\(571\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(572\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(577\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(578\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(586\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(587\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(588\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(589\) 0 0
\(590\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(591\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(592\) 0 0
\(593\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(594\) 0.190983 0.587785i 0.190983 0.587785i
\(595\) 0 0
\(596\) −0.309017 0.951057i −0.309017 0.951057i
\(597\) −0.500000 0.363271i −0.500000 0.363271i
\(598\) 0 0
\(599\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(600\) 0.500000 1.53884i 0.500000 1.53884i
\(601\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(606\) 0 0
\(607\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(611\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(612\) 0 0
\(613\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(614\) 0 0
\(615\) −3.23607 −3.23607
\(616\) 0 0
\(617\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(618\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(619\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 1.00000 1.00000
\(627\) 0 0
\(628\) −0.381966 −0.381966
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(632\) 0.190983 0.587785i 0.190983 0.587785i
\(633\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(634\) 0.809017 0.587785i 0.809017 0.587785i
\(635\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(636\) 0 0
\(637\) 1.00000 1.00000
\(638\) 0 0
\(639\) −2.00000 −2.00000
\(640\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(641\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(642\) 0 0
\(643\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(644\) 0 0
\(645\) 2.11803 1.53884i 2.11803 1.53884i
\(646\) 0 0
\(647\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(648\) 1.00000 1.00000
\(649\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(650\) −1.00000 −1.00000
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −0.809017 0.587785i −0.809017 0.587785i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(669\) 0 0
\(670\) 0 0
\(671\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(672\) 0 0
\(673\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(674\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(675\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(676\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(677\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.618034 −0.618034
\(682\) 0 0
\(683\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(684\) 0 0
\(685\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(702\) −0.190983 0.587785i −0.190983 0.587785i
\(703\) 0 0
\(704\) −0.618034 −0.618034
\(705\) −1.00000 −1.00000
\(706\) −0.309017 0.951057i −0.309017 0.951057i
\(707\) 0 0
\(708\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(709\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) 0.618034 1.90211i 0.618034 1.90211i
\(711\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(712\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(713\) 0 0
\(714\) 0 0
\(715\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(716\) 0 0
\(717\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(718\) −1.00000 0.726543i −1.00000 0.726543i
\(719\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.500000 0.363271i 0.500000 0.363271i
\(723\) 0 0
\(724\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(725\) 0 0
\(726\) 0.500000 0.363271i 0.500000 0.363271i
\(727\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(728\) 0 0
\(729\) −0.809017 0.587785i −0.809017 0.587785i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(733\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(735\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(736\) 0 0
\(737\) 0 0
\(738\) 1.23607 1.23607
\(739\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) −2.11803 1.53884i −2.11803 1.53884i
\(746\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(747\) 1.61803 1.61803
\(748\) 0 0
\(749\) 0 0
\(750\) −0.190983 0.587785i −0.190983 0.587785i
\(751\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(762\) −0.809017 0.587785i −0.809017 0.587785i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(767\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(768\) −0.309017 0.951057i −0.309017 0.951057i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(774\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.00000 −1.00000
\(781\) −1.61803 1.17557i −1.61803 1.17557i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(786\) 0 0
\(787\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(788\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(789\) 0 0
\(790\) −0.190983 0.587785i −0.190983 0.587785i
\(791\) 0 0
\(792\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(793\) 0.618034 0.618034
\(794\) 0 0
\(795\) 0 0
\(796\) 0.309017 0.224514i 0.309017 0.224514i
\(797\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(801\) −0.618034 1.90211i −0.618034 1.90211i
\(802\) −1.00000 −1.00000
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(810\) 0.809017 0.587785i 0.809017 0.587785i
\(811\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0.618034 1.90211i 0.618034 1.90211i
\(821\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(822\) −0.309017 0.224514i −0.309017 0.224514i
\(823\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(824\) −1.61803 −1.61803
\(825\) −1.61803 −1.61803
\(826\) 0 0
\(827\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(830\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(831\) 0.618034 1.90211i 0.618034 1.90211i
\(832\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(833\) 0 0
\(834\) −0.118034 0.363271i −0.118034 0.363271i
\(835\) 2.61803 2.61803
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(840\) 0 0
\(841\) 0.309017 0.951057i 0.309017 0.951057i
\(842\) 0 0
\(843\) 0.500000 0.363271i 0.500000 0.363271i
\(844\) −0.809017 0.587785i −0.809017 0.587785i
\(845\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(846\) 0.381966 0.381966
\(847\) 0 0
\(848\) 0 0
\(849\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(850\) 0 0
\(851\) 0 0
\(852\) 0.381966 1.17557i 0.381966 1.17557i
\(853\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0.190983 0.587785i 0.190983 0.587785i
\(859\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(860\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(861\) 0 0
\(862\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(863\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(864\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(865\) 0 0
\(866\) −0.809017 0.587785i −0.809017 0.587785i
\(867\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(868\) 0 0
\(869\) −0.618034 −0.618034
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(878\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(879\) 1.61803 1.61803
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −0.190983 0.587785i −0.190983 0.587785i
\(883\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(884\) 0 0
\(885\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(886\) 0 0
\(887\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 2.00000 2.00000
\(891\) −0.309017 0.951057i −0.309017 0.951057i
\(892\) 0 0
\(893\) 0 0
\(894\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(899\) 0 0
\(900\) −0.309017 0.951057i −0.309017 0.951057i
\(901\) 0 0
\(902\) 1.00000 + 0.726543i 1.00000 + 0.726543i
\(903\) 0 0
\(904\) 0 0
\(905\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(906\) 0 0
\(907\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(908\) 0.118034 0.363271i 0.118034 0.363271i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(912\) 0 0
\(913\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(914\) 0 0
\(915\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(923\) −2.00000 −2.00000
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(928\) 0 0
\(929\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 1.00000 1.00000
\(937\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(938\) 0 0
\(939\) 1.30902 0.951057i 1.30902 0.951057i
\(940\) 0.190983 0.587785i 0.190983 0.587785i
\(941\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(942\) 0.309017 0.224514i 0.309017 0.224514i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −1.00000 −1.00000
\(947\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(948\) −0.118034 0.363271i −0.118034 0.363271i
\(949\) 0 0
\(950\) 0 0
\(951\) 0.500000 1.53884i 0.500000 1.53884i
\(952\) 0 0
\(953\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −1.00000 −1.00000
\(957\) 0 0
\(958\) −1.00000 −1.00000
\(959\) 0 0
\(960\) −0.809017 0.587785i −0.809017 0.587785i
\(961\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(972\) 0.500000 0.363271i 0.500000 0.363271i
\(973\) 0 0
\(974\) 0 0
\(975\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(976\) 0 0
\(977\) −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(978\) 0 0
\(979\) 0.618034 1.90211i 0.618034 1.90211i
\(980\) −1.00000 −1.00000
\(981\) 0 0
\(982\) 0 0
\(983\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(984\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(985\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 1.00000 1.00000
\(991\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0.309017 0.951057i 0.309017 0.951057i
\(996\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(997\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(998\) 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 429.1.v.a.38.1 4
3.2 odd 2 429.1.v.b.38.1 yes 4
11.9 even 5 inner 429.1.v.a.350.1 yes 4
13.12 even 2 429.1.v.b.38.1 yes 4
33.20 odd 10 429.1.v.b.350.1 yes 4
39.38 odd 2 CM 429.1.v.a.38.1 4
143.64 even 10 429.1.v.b.350.1 yes 4
429.350 odd 10 inner 429.1.v.a.350.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.1.v.a.38.1 4 1.1 even 1 trivial
429.1.v.a.38.1 4 39.38 odd 2 CM
429.1.v.a.350.1 yes 4 11.9 even 5 inner
429.1.v.a.350.1 yes 4 429.350 odd 10 inner
429.1.v.b.38.1 yes 4 3.2 odd 2
429.1.v.b.38.1 yes 4 13.12 even 2
429.1.v.b.350.1 yes 4 33.20 odd 10
429.1.v.b.350.1 yes 4 143.64 even 10