Properties

Label 633.1.m.b.266.1
Level $633$
Weight $1$
Character 633.266
Analytic conductor $0.316$
Analytic rank $0$
Dimension $8$
Projective image $A_{5}$
CM/RM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [633,1,Mod(71,633)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(633, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 8]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("633.71");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 633 = 3 \cdot 211 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 633.m (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: \(0.315908152997\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(A_{5}\)
Projective field: Galois closure of 5.1.17839074969.1

Embedding invariants

Embedding label 266.1
Root \(0.587785 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 633.266
Dual form 633.1.m.b.188.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 + 0.190983i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-0.587785 - 0.809017i) q^{5} +(-0.587785 - 0.190983i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.587785 + 0.190983i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-0.587785 - 0.809017i) q^{5} +(-0.587785 - 0.190983i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.500000 + 0.363271i) q^{10} +(0.951057 + 1.30902i) q^{11} -0.618034 q^{12} +(-0.309017 + 0.951057i) q^{13} +0.618034i q^{14} -1.00000i q^{15} +(1.53884 + 0.500000i) q^{17} +(-0.363271 - 0.500000i) q^{18} +(0.309017 - 0.951057i) q^{19} +(0.587785 + 0.190983i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-0.809017 - 0.587785i) q^{22} +(-0.951057 + 0.309017i) q^{23} +(0.951057 - 0.309017i) q^{24} -0.618034i q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.190983 + 0.587785i) q^{28} +(-0.587785 - 0.190983i) q^{29} +(0.190983 + 0.587785i) q^{30} +0.618034 q^{31} +1.00000i q^{32} +1.61803i q^{33} -1.00000 q^{34} +(-0.951057 + 0.309017i) q^{35} +(-0.500000 - 0.363271i) q^{36} +0.618034i q^{38} +(-0.809017 + 0.587785i) q^{39} -1.00000 q^{40} +(-0.951057 - 1.30902i) q^{41} +(-0.363271 + 0.500000i) q^{42} -1.00000 q^{43} +(-0.951057 - 0.309017i) q^{44} +(0.587785 - 0.809017i) q^{45} +(0.500000 - 0.363271i) q^{46} +(0.587785 + 0.190983i) q^{47} +(0.951057 + 1.30902i) q^{51} +(-0.190983 - 0.587785i) q^{52} -0.618034i q^{54} +(0.500000 - 1.53884i) q^{55} +(-0.587785 - 0.809017i) q^{56} +(0.809017 - 0.587785i) q^{57} +0.381966 q^{58} +(0.363271 + 0.500000i) q^{60} +(-1.30902 - 0.951057i) q^{61} +(-0.363271 + 0.118034i) q^{62} +1.00000 q^{63} +(-0.190983 - 0.587785i) q^{64} +(0.951057 - 0.309017i) q^{65} +(-0.309017 - 0.951057i) q^{66} +(-0.951057 + 0.309017i) q^{68} +(-0.951057 - 0.309017i) q^{69} +(0.500000 - 0.363271i) q^{70} +(0.363271 - 0.500000i) q^{71} +(0.951057 + 0.309017i) q^{72} -1.00000 q^{73} +(0.190983 + 0.587785i) q^{76} +(1.53884 - 0.500000i) q^{77} +(0.363271 - 0.500000i) q^{78} +(-0.809017 + 0.587785i) q^{81} +(0.809017 + 0.587785i) q^{82} +(0.363271 + 0.500000i) q^{83} +(-0.190983 + 0.587785i) q^{84} +(-0.500000 - 1.53884i) q^{85} +(0.587785 - 0.190983i) q^{86} +(-0.363271 - 0.500000i) q^{87} +1.61803 q^{88} +(0.951057 + 0.309017i) q^{89} +(-0.190983 + 0.587785i) q^{90} +(0.809017 + 0.587785i) q^{91} +(0.363271 - 0.500000i) q^{92} +(0.500000 + 0.363271i) q^{93} -0.381966 q^{94} +(-0.951057 + 0.309017i) q^{95} +(-0.587785 + 0.809017i) q^{96} +(-0.951057 + 1.30902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{3} - 4 q^{4} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{3} - 4 q^{4} - 2 q^{7} - 2 q^{9} + 4 q^{10} + 4 q^{12} + 2 q^{13} - 2 q^{19} + 2 q^{21} - 2 q^{22} + 2 q^{27} + 6 q^{28} + 6 q^{30} - 4 q^{31} - 8 q^{34} - 4 q^{36} - 2 q^{39} - 8 q^{40} - 8 q^{43} + 4 q^{46} - 6 q^{52} + 4 q^{55} + 2 q^{57} + 12 q^{58} - 6 q^{61} + 8 q^{63} - 6 q^{64} + 2 q^{66} + 4 q^{70} - 8 q^{73} + 6 q^{76} - 2 q^{81} + 2 q^{82} - 6 q^{84} - 4 q^{85} + 4 q^{88} - 6 q^{90} + 2 q^{91} + 4 q^{93} - 12 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/633\mathbb{Z}\right)^\times\).

\(n\) \(212\) \(424\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 + 0.190983i −0.587785 + 0.190983i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(0.5\pi\)
\(3\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(4\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(5\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(6\) −0.587785 0.190983i −0.587785 0.190983i
\(7\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(8\) 0.587785 0.809017i 0.587785 0.809017i
\(9\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(10\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(11\) 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i \(0.100000\pi\)
1.00000i \(0.5\pi\)
\(12\) −0.618034 −0.618034
\(13\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(14\) 0.618034i 0.618034i
\(15\) 1.00000i 1.00000i
\(16\) 0 0
\(17\) 1.53884 + 0.500000i 1.53884 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(18\) −0.363271 0.500000i −0.363271 0.500000i
\(19\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(20\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(21\) 0.809017 0.587785i 0.809017 0.587785i
\(22\) −0.809017 0.587785i −0.809017 0.587785i
\(23\) −0.951057 + 0.309017i −0.951057 + 0.309017i −0.743145 0.669131i \(-0.766667\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(24\) 0.951057 0.309017i 0.951057 0.309017i
\(25\) 0 0
\(26\) 0.618034i 0.618034i
\(27\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(28\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(29\) −0.587785 0.190983i −0.587785 0.190983i 1.00000i \(-0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(30\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(31\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 1.61803i 1.61803i
\(34\) −1.00000 −1.00000
\(35\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(36\) −0.500000 0.363271i −0.500000 0.363271i
\(37\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(38\) 0.618034i 0.618034i
\(39\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(40\) −1.00000 −1.00000
\(41\) −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(-0.5\pi\)
\(42\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(43\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) −0.951057 0.309017i −0.951057 0.309017i
\(45\) 0.587785 0.809017i 0.587785 0.809017i
\(46\) 0.500000 0.363271i 0.500000 0.363271i
\(47\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(52\) −0.190983 0.587785i −0.190983 0.587785i
\(53\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(54\) 0.618034i 0.618034i
\(55\) 0.500000 1.53884i 0.500000 1.53884i
\(56\) −0.587785 0.809017i −0.587785 0.809017i
\(57\) 0.809017 0.587785i 0.809017 0.587785i
\(58\) 0.381966 0.381966
\(59\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(60\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(61\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(62\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(63\) 1.00000 1.00000
\(64\) −0.190983 0.587785i −0.190983 0.587785i
\(65\) 0.951057 0.309017i 0.951057 0.309017i
\(66\) −0.309017 0.951057i −0.309017 0.951057i
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(69\) −0.951057 0.309017i −0.951057 0.309017i
\(70\) 0.500000 0.363271i 0.500000 0.363271i
\(71\) 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(72\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(73\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(77\) 1.53884 0.500000i 1.53884 0.500000i
\(78\) 0.363271 0.500000i 0.363271 0.500000i
\(79\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(82\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(83\) 0.363271 + 0.500000i 0.363271 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(84\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(85\) −0.500000 1.53884i −0.500000 1.53884i
\(86\) 0.587785 0.190983i 0.587785 0.190983i
\(87\) −0.363271 0.500000i −0.363271 0.500000i
\(88\) 1.61803 1.61803
\(89\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(90\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(91\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(92\) 0.363271 0.500000i 0.363271 0.500000i
\(93\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(94\) −0.381966 −0.381966
\(95\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(96\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(97\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(98\) 0 0
\(99\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −0.809017 0.587785i −0.809017 0.587785i
\(103\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(104\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(105\) −0.951057 0.309017i −0.951057 0.309017i
\(106\) 0 0
\(107\) −1.17557 1.61803i −1.17557 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(108\) −0.190983 0.587785i −0.190983 0.587785i
\(109\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(110\) 1.00000i 1.00000i
\(111\) 0 0
\(112\) 0 0
\(113\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(114\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(115\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(116\) 0.363271 0.118034i 0.363271 0.118034i
\(117\) −1.00000 −1.00000
\(118\) 0 0
\(119\) 0.951057 1.30902i 0.951057 1.30902i
\(120\) −0.809017 0.587785i −0.809017 0.587785i
\(121\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(122\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(123\) 1.61803i 1.61803i
\(124\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(125\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(126\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(127\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(128\) −0.363271 0.500000i −0.363271 0.500000i
\(129\) −0.809017 0.587785i −0.809017 0.587785i
\(130\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(131\) 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(132\) −0.587785 0.809017i −0.587785 0.809017i
\(133\) −0.809017 0.587785i −0.809017 0.587785i
\(134\) 0 0
\(135\) 0.951057 0.309017i 0.951057 0.309017i
\(136\) 1.30902 0.951057i 1.30902 0.951057i
\(137\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(138\) 0.618034 0.618034
\(139\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(140\) 0.363271 0.500000i 0.363271 0.500000i
\(141\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(142\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(143\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(144\) 0 0
\(145\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(146\) 0.587785 0.190983i 0.587785 0.190983i
\(147\) 0 0
\(148\) 0 0
\(149\) −0.587785 + 0.190983i −0.587785 + 0.190983i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(152\) −0.587785 0.809017i −0.587785 0.809017i
\(153\) 1.61803i 1.61803i
\(154\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(155\) −0.363271 0.500000i −0.363271 0.500000i
\(156\) 0.190983 0.587785i 0.190983 0.587785i
\(157\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.809017 0.587785i 0.809017 0.587785i
\(161\) 1.00000i 1.00000i
\(162\) 0.363271 0.500000i 0.363271 0.500000i
\(163\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(164\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(165\) 1.30902 0.951057i 1.30902 0.951057i
\(166\) −0.309017 0.224514i −0.309017 0.224514i
\(167\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(168\) 1.00000i 1.00000i
\(169\) 0 0
\(170\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(171\) 1.00000 1.00000
\(172\) 0.500000 0.363271i 0.500000 0.363271i
\(173\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −0.618034 −0.618034
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.618034i 0.618034i
\(181\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(182\) −0.587785 0.190983i −0.587785 0.190983i
\(183\) −0.500000 1.53884i −0.500000 1.53884i
\(184\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(185\) 0 0
\(186\) −0.363271 0.118034i −0.363271 0.118034i
\(187\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(188\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(189\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(190\) 0.500000 0.363271i 0.500000 0.363271i
\(191\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(192\) 0.190983 0.587785i 0.190983 0.587785i
\(193\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(194\) 0 0
\(195\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(196\) 0 0
\(197\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(198\) 0.309017 0.951057i 0.309017 0.951057i
\(199\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(204\) −0.951057 0.309017i −0.951057 0.309017i
\(205\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(206\) 0 0
\(207\) −0.587785 0.809017i −0.587785 0.809017i
\(208\) 0 0
\(209\) 1.53884 0.500000i 1.53884 0.500000i
\(210\) 0.618034 0.618034
\(211\) 0.309017 0.951057i 0.309017 0.951057i
\(212\) 0 0
\(213\) 0.587785 0.190983i 0.587785 0.190983i
\(214\) 1.00000 + 0.726543i 1.00000 + 0.726543i
\(215\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(216\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(217\) 0.190983 0.587785i 0.190983 0.587785i
\(218\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(219\) −0.809017 0.587785i −0.809017 0.587785i
\(220\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(221\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(222\) 0 0
\(223\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(224\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(225\) 0 0
\(226\) 0.618034 0.618034
\(227\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(228\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(229\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) −0.587785 0.190983i −0.587785 0.190983i
\(231\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(232\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(233\) 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(234\) 0.587785 0.190983i 0.587785 0.190983i
\(235\) −0.190983 0.587785i −0.190983 0.587785i
\(236\) 0 0
\(237\) 0 0
\(238\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(239\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(240\) 0 0
\(241\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(242\) 1.00000i 1.00000i
\(243\) −1.00000 −1.00000
\(244\) 1.00000 1.00000
\(245\) 0 0
\(246\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(247\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(248\) 0.363271 0.500000i 0.363271 0.500000i
\(249\) 0.618034i 0.618034i
\(250\) 0.500000 0.363271i 0.500000 0.363271i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(253\) −1.30902 0.951057i −1.30902 0.951057i
\(254\) 0.618034i 0.618034i
\(255\) 0.500000 1.53884i 0.500000 1.53884i
\(256\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(257\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(258\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(259\) 0 0
\(260\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(261\) 0.618034i 0.618034i
\(262\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(263\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(264\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(265\) 0 0
\(266\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(267\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(271\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(272\) 0 0
\(273\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(274\) 0.618034 0.618034
\(275\) 0 0
\(276\) 0.587785 0.190983i 0.587785 0.190983i
\(277\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(278\) 0.618034i 0.618034i
\(279\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(280\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(281\) −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(-0.5\pi\)
\(282\) −0.309017 0.224514i −0.309017 0.224514i
\(283\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(284\) 0.381966i 0.381966i
\(285\) −0.951057 0.309017i −0.951057 0.309017i
\(286\) 0.809017 0.587785i 0.809017 0.587785i
\(287\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(288\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(289\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(290\) −0.224514 0.309017i −0.224514 0.309017i
\(291\) 0 0
\(292\) 0.500000 0.363271i 0.500000 0.363271i
\(293\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(298\) 0.309017 0.224514i 0.309017 0.224514i
\(299\) 1.00000i 1.00000i
\(300\) 0 0
\(301\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(302\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(303\) 0 0
\(304\) 0 0
\(305\) 1.61803i 1.61803i
\(306\) −0.309017 0.951057i −0.309017 0.951057i
\(307\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(308\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(309\) 0 0
\(310\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(311\) −0.951057 + 0.309017i −0.951057 + 0.309017i −0.743145 0.669131i \(-0.766667\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(312\) 1.00000i 1.00000i
\(313\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 0.587785 0.190983i 0.587785 0.190983i
\(315\) −0.587785 0.809017i −0.587785 0.809017i
\(316\) 0 0
\(317\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(318\) 0 0
\(319\) −0.309017 0.951057i −0.309017 0.951057i
\(320\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(321\) 2.00000i 2.00000i
\(322\) −0.190983 0.587785i −0.190983 0.587785i
\(323\) 0.951057 1.30902i 0.951057 1.30902i
\(324\) 0.190983 0.587785i 0.190983 0.587785i
\(325\) 0 0
\(326\) 0.363271 0.500000i 0.363271 0.500000i
\(327\) −0.309017 0.951057i −0.309017 0.951057i
\(328\) −1.61803 −1.61803
\(329\) 0.363271 0.500000i 0.363271 0.500000i
\(330\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(331\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(332\) −0.363271 0.118034i −0.363271 0.118034i
\(333\) 0 0
\(334\) −0.381966 −0.381966
\(335\) 0 0
\(336\) 0 0
\(337\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(338\) 0 0
\(339\) −0.587785 0.809017i −0.587785 0.809017i
\(340\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(341\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(342\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(343\) 0.809017 0.587785i 0.809017 0.587785i
\(344\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(345\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(346\) −0.190983 0.587785i −0.190983 0.587785i
\(347\) 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i \(0.100000\pi\)
1.00000i \(0.5\pi\)
\(348\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(349\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) 0 0
\(351\) −0.809017 0.587785i −0.809017 0.587785i
\(352\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(353\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(354\) 0 0
\(355\) −0.618034 −0.618034
\(356\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(357\) 1.53884 0.500000i 1.53884 0.500000i
\(358\) 0 0
\(359\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(360\) −0.309017 0.951057i −0.309017 0.951057i
\(361\) 0 0
\(362\) 0 0
\(363\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(364\) −0.618034 −0.618034
\(365\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(366\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(367\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(368\) 0 0
\(369\) 0.951057 1.30902i 0.951057 1.30902i
\(370\) 0 0
\(371\) 0 0
\(372\) −0.381966 −0.381966
\(373\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(374\) −0.951057 1.30902i −0.951057 1.30902i
\(375\) −0.951057 0.309017i −0.951057 0.309017i
\(376\) 0.500000 0.363271i 0.500000 0.363271i
\(377\) 0.363271 0.500000i 0.363271 0.500000i
\(378\) −0.587785 0.190983i −0.587785 0.190983i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0.363271 0.500000i 0.363271 0.500000i
\(381\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(382\) 0.618034 0.618034
\(383\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(384\) 0.618034i 0.618034i
\(385\) −1.30902 0.951057i −1.30902 0.951057i
\(386\) 0 0
\(387\) −0.309017 0.951057i −0.309017 0.951057i
\(388\) 0 0
\(389\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(390\) −0.618034 −0.618034
\(391\) −1.61803 −1.61803
\(392\) 0 0
\(393\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(394\) −0.118034 0.363271i −0.118034 0.363271i
\(395\) 0 0
\(396\) 1.00000i 1.00000i
\(397\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0.363271 0.118034i 0.363271 0.118034i
\(399\) −0.309017 0.951057i −0.309017 0.951057i
\(400\) 0 0
\(401\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) 0 0
\(403\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(404\) 0 0
\(405\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(406\) 0.118034 0.363271i 0.118034 0.363271i
\(407\) 0 0
\(408\) 1.61803 1.61803
\(409\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(410\) 1.00000i 1.00000i
\(411\) −0.587785 0.809017i −0.587785 0.809017i
\(412\) 0 0
\(413\) 0 0
\(414\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(415\) 0.190983 0.587785i 0.190983 0.587785i
\(416\) −0.951057 0.309017i −0.951057 0.309017i
\(417\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(418\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(419\) 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(420\) 0.587785 0.190983i 0.587785 0.190983i
\(421\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) 0.618034i 0.618034i
\(423\) 0.618034i 0.618034i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(427\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(428\) 1.17557 + 0.381966i 1.17557 + 0.381966i
\(429\) −1.53884 0.500000i −1.53884 0.500000i
\(430\) −0.500000 0.363271i −0.500000 0.363271i
\(431\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(432\) 0 0
\(433\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(434\) 0.381966i 0.381966i
\(435\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(436\) 0.618034 0.618034
\(437\) 1.00000i 1.00000i
\(438\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(439\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(440\) −0.951057 1.30902i −0.951057 1.30902i
\(441\) 0 0
\(442\) 0.309017 0.951057i 0.309017 0.951057i
\(443\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(444\) 0 0
\(445\) −0.309017 0.951057i −0.309017 0.951057i
\(446\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(447\) −0.587785 0.190983i −0.587785 0.190983i
\(448\) −0.618034 −0.618034
\(449\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(450\) 0 0
\(451\) 0.809017 2.48990i 0.809017 2.48990i
\(452\) 0.587785 0.190983i 0.587785 0.190983i
\(453\) 1.61803 1.61803
\(454\) 0.618034 0.618034
\(455\) 1.00000i 1.00000i
\(456\) 1.00000i 1.00000i
\(457\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(458\) 0.224514 0.309017i 0.224514 0.309017i
\(459\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(460\) −0.618034 −0.618034
\(461\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(462\) −1.00000 −1.00000
\(463\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(464\) 0 0
\(465\) 0.618034i 0.618034i
\(466\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(467\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(468\) 0.500000 0.363271i 0.500000 0.363271i
\(469\) 0 0
\(470\) 0.224514 + 0.309017i 0.224514 + 0.309017i
\(471\) −0.809017 0.587785i −0.809017 0.587785i
\(472\) 0 0
\(473\) −0.951057 1.30902i −0.951057 1.30902i
\(474\) 0 0
\(475\) 0 0
\(476\) 1.00000i 1.00000i
\(477\) 0 0
\(478\) 0 0
\(479\) 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i \(0.100000\pi\)
1.00000i \(0.5\pi\)
\(480\) 1.00000 1.00000
\(481\) 0 0
\(482\) −0.587785 0.809017i −0.587785 0.809017i
\(483\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(484\) −0.309017 0.951057i −0.309017 0.951057i
\(485\) 0 0
\(486\) 0.587785 0.190983i 0.587785 0.190983i
\(487\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(488\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(489\) −1.00000 −1.00000
\(490\) 0 0
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(493\) −0.809017 0.587785i −0.809017 0.587785i
\(494\) −0.587785 0.190983i −0.587785 0.190983i
\(495\) 1.61803 1.61803
\(496\) 0 0
\(497\) −0.363271 0.500000i −0.363271 0.500000i
\(498\) −0.118034 0.363271i −0.118034 0.363271i
\(499\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(500\) 0.363271 0.500000i 0.363271 0.500000i
\(501\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(502\) 0 0
\(503\) 0.363271 + 0.500000i 0.363271 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(504\) 0.587785 0.809017i 0.587785 0.809017i
\(505\) 0 0
\(506\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(507\) 0 0
\(508\) −0.190983 0.587785i −0.190983 0.587785i
\(509\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(510\) 1.00000i 1.00000i
\(511\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(512\) 0 0
\(513\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(514\) 0 0
\(515\) 0 0
\(516\) 0.618034 0.618034
\(517\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(518\) 0 0
\(519\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(520\) 0.309017 0.951057i 0.309017 0.951057i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(523\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(525\) 0 0
\(526\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(527\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0.618034 0.618034
\(533\) 1.53884 0.500000i 1.53884 0.500000i
\(534\) −0.500000 0.363271i −0.500000 0.363271i
\(535\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(541\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(542\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(543\) 0 0
\(544\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(545\) 1.00000i 1.00000i
\(546\) −0.363271 0.500000i −0.363271 0.500000i
\(547\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(548\) 0.587785 0.190983i 0.587785 0.190983i
\(549\) 0.500000 1.53884i 0.500000 1.53884i
\(550\) 0 0
\(551\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(552\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.190983 0.587785i −0.190983 0.587785i
\(557\) −1.53884 + 0.500000i −1.53884 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(558\) −0.224514 0.309017i −0.224514 0.309017i
\(559\) 0.309017 0.951057i 0.309017 0.951057i
\(560\) 0 0
\(561\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(562\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(563\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(564\) −0.363271 0.118034i −0.363271 0.118034i
\(565\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(566\) 0.618034i 0.618034i
\(567\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(568\) −0.190983 0.587785i −0.190983 0.587785i
\(569\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(570\) 0.618034 0.618034
\(571\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(572\) 0.587785 0.809017i 0.587785 0.809017i
\(573\) −0.587785 0.809017i −0.587785 0.809017i
\(574\) 0.809017 0.587785i 0.809017 0.587785i
\(575\) 0 0
\(576\) 0.500000 0.363271i 0.500000 0.363271i
\(577\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(578\) −0.951057 0.309017i −0.951057 0.309017i
\(579\) 0 0
\(580\) −0.309017 0.224514i −0.309017 0.224514i
\(581\) 0.587785 0.190983i 0.587785 0.190983i
\(582\) 0 0
\(583\) 0 0
\(584\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(585\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(586\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(587\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(588\) 0 0
\(589\) 0.190983 0.587785i 0.190983 0.587785i
\(590\) 0 0
\(591\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0.809017 0.587785i 0.809017 0.587785i
\(595\) −1.61803 −1.61803
\(596\) 0.224514 0.309017i 0.224514 0.309017i
\(597\) −0.500000 0.363271i −0.500000 0.363271i
\(598\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(599\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0.618034i 0.618034i
\(603\) 0 0
\(604\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(605\) 1.53884 0.500000i 1.53884 0.500000i
\(606\) 0 0
\(607\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(609\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(610\) −0.309017 0.951057i −0.309017 0.951057i
\(611\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(612\) −0.587785 0.809017i −0.587785 0.809017i
\(613\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(614\) −0.587785 0.190983i −0.587785 0.190983i
\(615\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(616\) 0.500000 1.53884i 0.500000 1.53884i
\(617\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(618\) 0 0
\(619\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(621\) 1.00000i 1.00000i
\(622\) 0.500000 0.363271i 0.500000 0.363271i
\(623\) 0.587785 0.809017i 0.587785 0.809017i
\(624\) 0 0
\(625\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(626\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(627\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(628\) 0.500000 0.363271i 0.500000 0.363271i
\(629\) 0 0
\(630\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(631\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0.809017 0.587785i 0.809017 0.587785i
\(634\) −0.618034 −0.618034
\(635\) 0.951057 0.309017i 0.951057 0.309017i
\(636\) 0 0
\(637\) 0 0
\(638\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(639\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(640\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(641\) −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i \(-0.966667\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(642\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(643\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(644\) −0.363271 0.500000i −0.363271 0.500000i
\(645\) 1.00000i 1.00000i
\(646\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(647\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 0.500000 0.363271i 0.500000 0.363271i
\(652\) 0.190983 0.587785i 0.190983 0.587785i
\(653\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(654\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(655\) −1.30902 0.951057i −1.30902 0.951057i
\(656\) 0 0
\(657\) −0.309017 0.951057i −0.309017 0.951057i
\(658\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(661\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(662\) 0 0
\(663\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(664\) 0.618034 0.618034
\(665\) 1.00000i 1.00000i
\(666\) 0 0
\(667\) 0.618034 0.618034
\(668\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(669\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(670\) 0 0
\(671\) 2.61803i 2.61803i
\(672\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(673\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(675\) 0 0
\(676\) 0 0
\(677\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(678\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(679\) 0 0
\(680\) −1.53884 0.500000i −1.53884 0.500000i
\(681\) −0.587785 0.809017i −0.587785 0.809017i
\(682\) −0.500000 0.363271i −0.500000 0.363271i
\(683\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(684\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(685\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(686\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(687\) −0.618034 −0.618034
\(688\) 0 0
\(689\) 0 0
\(690\) −0.363271 0.500000i −0.363271 0.500000i
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) −0.363271 0.500000i −0.363271 0.500000i
\(693\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(694\) −0.809017 0.587785i −0.809017 0.587785i
\(695\) 0.951057 0.309017i 0.951057 0.309017i
\(696\) −0.618034 −0.618034
\(697\) −0.809017 2.48990i −0.809017 2.48990i
\(698\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(699\) 0.587785 0.190983i 0.587785 0.190983i
\(700\) 0 0
\(701\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(702\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(703\) 0 0
\(704\) 0.587785 0.809017i 0.587785 0.809017i
\(705\) 0.190983 0.587785i 0.190983 0.587785i
\(706\) 1.00000 1.00000
\(707\) 0 0
\(708\) 0 0
\(709\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(710\) 0.363271 0.118034i 0.363271 0.118034i
\(711\) 0 0
\(712\) 0.809017 0.587785i 0.809017 0.587785i
\(713\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(714\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(715\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(716\) 0 0
\(717\) 0 0
\(718\) −0.309017 0.951057i −0.309017 0.951057i
\(719\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.587785 0.809017i 0.587785 0.809017i
\(727\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(728\) 0.951057 0.309017i 0.951057 0.309017i
\(729\) −0.809017 0.587785i −0.809017 0.587785i
\(730\) −0.500000 0.363271i −0.500000 0.363271i
\(731\) −1.53884 0.500000i −1.53884 0.500000i
\(732\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(733\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(734\) 0.618034i 0.618034i
\(735\) 0 0
\(736\) −0.309017 0.951057i −0.309017 0.951057i
\(737\) 0 0
\(738\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(739\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(740\) 0 0
\(741\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0.587785 0.190983i 0.587785 0.190983i
\(745\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(746\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(747\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(748\) −1.30902 0.951057i −1.30902 0.951057i
\(749\) −1.90211 + 0.618034i −1.90211 + 0.618034i
\(750\) 0.618034 0.618034
\(751\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(755\) −1.53884 0.500000i −1.53884 0.500000i
\(756\) −0.618034 −0.618034
\(757\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(758\) 0 0
\(759\) −0.500000 1.53884i −0.500000 1.53884i
\(760\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(761\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) 0.363271 0.500000i 0.363271 0.500000i
\(763\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(764\) 0.587785 0.190983i 0.587785 0.190983i
\(765\) 1.30902 0.951057i 1.30902 0.951057i
\(766\) 0 0
\(767\) 0 0
\(768\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(769\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(770\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(774\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.190983 0.587785i −0.190983 0.587785i
\(779\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(780\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(781\) 1.00000 1.00000
\(782\) 0.951057 0.309017i 0.951057 0.309017i
\(783\) 0.363271 0.500000i 0.363271 0.500000i
\(784\) 0 0
\(785\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(786\) −1.00000 −1.00000
\(787\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(788\) −0.224514 0.309017i −0.224514 0.309017i
\(789\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(790\) 0 0
\(791\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(792\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(793\) 1.30902 0.951057i 1.30902 0.951057i
\(794\) 1.00000i 1.00000i
\(795\) 0 0
\(796\) 0.309017 0.224514i 0.309017 0.224514i
\(797\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(798\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(799\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(800\) 0 0
\(801\) 1.00000i 1.00000i
\(802\) 0 0
\(803\) −0.951057 1.30902i −0.951057 1.30902i
\(804\) 0 0
\(805\) 0.809017 0.587785i 0.809017 0.587785i
\(806\) 0.381966i 0.381966i
\(807\) 0 0
\(808\) 0 0
\(809\) −0.587785 + 0.190983i −0.587785 + 0.190983i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(0.5\pi\)
\(810\) −0.618034 −0.618034
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0.381966i 0.381966i
\(813\) 1.61803 1.61803
\(814\) 0 0
\(815\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(816\) 0 0
\(817\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(818\) 0.381966i 0.381966i
\(819\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(820\) −0.309017 0.951057i −0.309017 0.951057i
\(821\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(822\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(823\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(828\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(829\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(830\) 0.381966i 0.381966i
\(831\) 0 0
\(832\) 0.618034 0.618034
\(833\) 0 0
\(834\) 0.363271 0.500000i 0.363271 0.500000i
\(835\) −0.190983 0.587785i −0.190983 0.587785i
\(836\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(837\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(838\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(839\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(840\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(841\) −0.500000 0.363271i −0.500000 0.363271i
\(842\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(843\) 1.61803i 1.61803i
\(844\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(845\) 0 0
\(846\) −0.118034 0.363271i −0.118034 0.363271i
\(847\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(848\) 0 0
\(849\) 0.809017 0.587785i 0.809017 0.587785i
\(850\) 0 0
\(851\) 0 0
\(852\) −0.224514 + 0.309017i −0.224514 + 0.309017i
\(853\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(854\) 0.587785 0.809017i 0.587785 0.809017i
\(855\) −0.587785 0.809017i −0.587785 0.809017i
\(856\) −2.00000 −2.00000
\(857\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(858\) 1.00000 1.00000
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) −0.587785 0.190983i −0.587785 0.190983i
\(861\) −1.53884 0.500000i −1.53884 0.500000i
\(862\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(863\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(864\) −0.951057 0.309017i −0.951057 0.309017i
\(865\) 0.809017 0.587785i 0.809017 0.587785i
\(866\) 0.363271 0.500000i 0.363271 0.500000i
\(867\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(868\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(869\) 0 0
\(870\) 0.381966i 0.381966i
\(871\) 0 0
\(872\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(873\) 0 0
\(874\) −0.190983 0.587785i −0.190983 0.587785i
\(875\) 1.00000i 1.00000i
\(876\) 0.618034 0.618034
\(877\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(878\) 0 0
\(879\) 0.951057 0.309017i 0.951057 0.309017i
\(880\) 0 0
\(881\) −0.363271 + 0.500000i −0.363271 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(882\) 0 0
\(883\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(884\) 1.00000i 1.00000i
\(885\) 0 0
\(886\) −0.500000 0.363271i −0.500000 0.363271i
\(887\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(888\) 0 0
\(889\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(890\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(891\) −1.53884 0.500000i −1.53884 0.500000i
\(892\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(893\) 0.363271 0.500000i 0.363271 0.500000i
\(894\) 0.381966 0.381966
\(895\) 0 0
\(896\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(897\) 0.587785 0.809017i 0.587785 0.809017i
\(898\) 0.618034 0.618034
\(899\) −0.363271 0.118034i −0.363271 0.118034i
\(900\) 0 0
\(901\) 0 0
\(902\) 1.61803i 1.61803i
\(903\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(904\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(905\) 0 0
\(906\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(907\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(908\) 0.587785 0.190983i 0.587785 0.190983i
\(909\) 0 0
\(910\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(911\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(912\) 0 0
\(913\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(914\) 0.224514 + 0.309017i 0.224514 + 0.309017i
\(915\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(916\) 0.118034 0.363271i 0.118034 0.363271i
\(917\) 1.61803i 1.61803i
\(918\) 0.309017 0.951057i 0.309017 0.951057i
\(919\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(920\) 0.951057 0.309017i 0.951057 0.309017i
\(921\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(922\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(923\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(924\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(925\) 0 0
\(926\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(927\) 0 0
\(928\) 0.190983 0.587785i 0.190983 0.587785i
\(929\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(930\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(931\) 0 0
\(932\) 0.381966i 0.381966i
\(933\) −0.951057 0.309017i −0.951057 0.309017i
\(934\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(935\) 1.53884 2.11803i 1.53884 2.11803i
\(936\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(937\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(938\) 0 0
\(939\) −0.190983 0.587785i −0.190983 0.587785i
\(940\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(941\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(942\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(943\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(944\) 0 0
\(945\) 1.00000i 1.00000i
\(946\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(947\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(948\) 0 0
\(949\) 0.309017 0.951057i 0.309017 0.951057i
\(950\) 0 0
\(951\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(952\) −0.500000 1.53884i −0.500000 1.53884i
\(953\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(954\) 0 0
\(955\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(956\) 0 0
\(957\) 0.309017 0.951057i 0.309017 0.951057i
\(958\) −0.809017 0.587785i −0.809017 0.587785i
\(959\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(960\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(961\) −0.618034 −0.618034
\(962\) 0 0
\(963\) 1.17557 1.61803i 1.17557 1.61803i
\(964\) −0.809017 0.587785i −0.809017 0.587785i
\(965\) 0 0
\(966\) 0.190983 0.587785i 0.190983 0.587785i
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(969\) 1.53884 0.500000i 1.53884 0.500000i
\(970\) 0 0
\(971\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(972\) 0.500000 0.363271i 0.500000 0.363271i
\(973\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(974\) 0.224514 + 0.309017i 0.224514 + 0.309017i
\(975\) 0 0
\(976\) 0 0
\(977\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(978\) 0.587785 0.190983i 0.587785 0.190983i
\(979\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(980\) 0 0
\(981\) 0.309017 0.951057i 0.309017 0.951057i
\(982\) 0 0
\(983\) 1.53884 + 0.500000i 1.53884 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(984\) −1.30902 0.951057i −1.30902 0.951057i
\(985\) 0.500000 0.363271i 0.500000 0.363271i
\(986\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(987\) 0.587785 0.190983i 0.587785 0.190983i
\(988\) −0.618034 −0.618034
\(989\) 0.951057 0.309017i 0.951057 0.309017i
\(990\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(991\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(992\) 0.618034i 0.618034i
\(993\) 0 0
\(994\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(995\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(996\) −0.224514 0.309017i −0.224514 0.309017i
\(997\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(999\) 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 633.1.m.b.266.1 yes 8
3.2 odd 2 inner 633.1.m.b.266.2 yes 8
211.188 even 5 inner 633.1.m.b.188.2 yes 8
633.188 odd 10 inner 633.1.m.b.188.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
633.1.m.b.188.1 8 633.188 odd 10 inner
633.1.m.b.188.2 yes 8 211.188 even 5 inner
633.1.m.b.266.1 yes 8 1.1 even 1 trivial
633.1.m.b.266.2 yes 8 3.2 odd 2 inner