Properties

Label 1800.1.dg.a.931.1
Level $1800$
Weight $1$
Character 1800.931
Analytic conductor $0.898$
Analytic rank $0$
Dimension $16$
Projective image $A_{5}$
CM/RM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1800,1,Mod(211,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 15, 10, 24]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1800.211");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1800.dg (of order \(30\), degree \(8\), 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: \(0.898317022739\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{30})\)
Coefficient field: \(\Q(\zeta_{60})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(A_{5}\)
Projective field: Galois closure of 5.1.2025000000.9

Embedding invariants

Embedding label 931.1
Root \(0.743145 - 0.669131i\) of defining polynomial
Character \(\chi\) \(=\) 1800.931
Dual form 1800.1.dg.a.1771.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.743145 - 0.669131i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.104528 + 0.994522i) q^{4} +(-0.994522 + 0.104528i) q^{5} +(-0.994522 - 0.104528i) q^{6} +(-0.866025 + 0.500000i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.743145 - 0.669131i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.104528 + 0.994522i) q^{4} +(-0.994522 + 0.104528i) q^{5} +(-0.994522 - 0.104528i) q^{6} +(-0.866025 + 0.500000i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.413545 + 0.459289i) q^{11} +(0.669131 + 0.743145i) q^{12} +(1.20243 - 1.08268i) q^{13} +(0.978148 + 0.207912i) q^{14} +(-0.743145 + 0.669131i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-0.207912 - 0.978148i) q^{20} +(-0.406737 + 0.913545i) q^{21} +(0.614648 - 0.0646021i) q^{22} +(0.207912 - 0.978148i) q^{23} -1.00000i q^{24} +(0.978148 - 0.207912i) q^{25} -1.61803 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(0.251377 - 0.564602i) q^{29} +1.00000 q^{30} +(0.406737 + 0.913545i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.0646021 + 0.614648i) q^{33} +(0.207912 + 0.978148i) q^{34} +(0.809017 - 0.587785i) q^{35} +(0.978148 + 0.207912i) q^{36} +(0.207912 + 0.978148i) q^{38} +(0.336408 - 1.58268i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-1.08268 - 1.20243i) q^{41} +(0.913545 - 0.406737i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(-0.500000 - 0.363271i) q^{44} +(-0.207912 + 0.978148i) q^{45} +(-0.809017 + 0.587785i) q^{46} +(-0.251377 + 0.564602i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(-0.866025 - 0.500000i) q^{50} -1.00000 q^{51} +(1.20243 + 1.08268i) q^{52} +(-0.951057 - 1.30902i) q^{53} +(-0.406737 + 0.913545i) q^{54} +(0.363271 - 0.500000i) q^{55} +(-0.104528 + 0.994522i) q^{56} -1.00000 q^{57} +(-0.564602 + 0.251377i) q^{58} +(-0.743145 - 0.669131i) q^{60} +(-0.743145 - 0.669131i) q^{61} +(0.309017 - 0.951057i) q^{62} +(0.207912 + 0.978148i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.08268 + 1.20243i) q^{65} +(0.459289 - 0.413545i) q^{66} +(1.47815 - 0.658114i) q^{67} +(0.500000 - 0.866025i) q^{68} +(-0.406737 - 0.913545i) q^{69} +(-0.994522 - 0.104528i) q^{70} +(-0.587785 - 0.809017i) q^{72} +(0.669131 - 0.743145i) q^{75} +(0.500000 - 0.866025i) q^{76} +(0.128496 - 0.604528i) q^{77} +(-1.30902 + 0.951057i) q^{78} +(-0.251377 + 0.564602i) q^{79} +(0.951057 - 0.309017i) q^{80} +(-0.809017 - 0.587785i) q^{81} +1.61803i q^{82} +(-0.0646021 + 0.614648i) q^{83} +(-0.951057 - 0.309017i) q^{84} +(0.866025 + 0.500000i) q^{85} +(-0.207912 + 0.978148i) q^{86} +(-0.128496 - 0.604528i) q^{87} +(0.128496 + 0.604528i) q^{88} +(0.309017 + 0.951057i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-0.500000 + 1.53884i) q^{91} +(0.994522 + 0.104528i) q^{92} +(0.866025 + 0.500000i) q^{93} +(0.564602 - 0.251377i) q^{94} +(0.866025 + 0.500000i) q^{95} +(0.994522 - 0.104528i) q^{96} +(0.309017 + 0.535233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} - 2 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} - 2 q^{4} - 4 q^{9} + 4 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{25} - 8 q^{26} + 4 q^{27} + 16 q^{30} + 4 q^{33} + 4 q^{35} - 2 q^{36} - 8 q^{40} + 4 q^{41} + 2 q^{42} - 8 q^{43} - 8 q^{44} - 4 q^{46} - 2 q^{48} - 16 q^{51} + 2 q^{56} - 16 q^{57} - 4 q^{58} - 4 q^{62} + 4 q^{64} + 4 q^{65} + 6 q^{67} + 8 q^{68} + 2 q^{75} + 8 q^{76} - 12 q^{78} - 4 q^{81} + 4 q^{83} - 4 q^{89} + 4 q^{90} - 8 q^{91} + 4 q^{94} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1001\) \(1351\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.743145 0.669131i −0.743145 0.669131i
\(3\) 0.809017 0.587785i 0.809017 0.587785i
\(4\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(5\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(6\) −0.994522 0.104528i −0.994522 0.104528i
\(7\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(8\) 0.587785 0.809017i 0.587785 0.809017i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(11\) −0.413545 + 0.459289i −0.413545 + 0.459289i −0.913545 0.406737i \(-0.866667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(13\) 1.20243 1.08268i 1.20243 1.08268i 0.207912 0.978148i \(-0.433333\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(14\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(15\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(16\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(17\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(18\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(19\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(20\) −0.207912 0.978148i −0.207912 0.978148i
\(21\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(22\) 0.614648 0.0646021i 0.614648 0.0646021i
\(23\) 0.207912 0.978148i 0.207912 0.978148i −0.743145 0.669131i \(-0.766667\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(24\) 1.00000i 1.00000i
\(25\) 0.978148 0.207912i 0.978148 0.207912i
\(26\) −1.61803 −1.61803
\(27\) −0.309017 0.951057i −0.309017 0.951057i
\(28\) −0.587785 0.809017i −0.587785 0.809017i
\(29\) 0.251377 0.564602i 0.251377 0.564602i −0.743145 0.669131i \(-0.766667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(30\) 1.00000 1.00000
\(31\) 0.406737 + 0.913545i 0.406737 + 0.913545i 0.994522 + 0.104528i \(0.0333333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(32\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(33\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i
\(34\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(35\) 0.809017 0.587785i 0.809017 0.587785i
\(36\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(37\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(39\) 0.336408 1.58268i 0.336408 1.58268i
\(40\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(41\) −1.08268 1.20243i −1.08268 1.20243i −0.978148 0.207912i \(-0.933333\pi\)
−0.104528 0.994522i \(-0.533333\pi\)
\(42\) 0.913545 0.406737i 0.913545 0.406737i
\(43\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(44\) −0.500000 0.363271i −0.500000 0.363271i
\(45\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(46\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(47\) −0.251377 + 0.564602i −0.251377 + 0.564602i −0.994522 0.104528i \(-0.966667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(48\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(49\) 0 0
\(50\) −0.866025 0.500000i −0.866025 0.500000i
\(51\) −1.00000 −1.00000
\(52\) 1.20243 + 1.08268i 1.20243 + 1.08268i
\(53\) −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(-0.5\pi\)
\(54\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(55\) 0.363271 0.500000i 0.363271 0.500000i
\(56\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(57\) −1.00000 −1.00000
\(58\) −0.564602 + 0.251377i −0.564602 + 0.251377i
\(59\) 0 0 0.743145 0.669131i \(-0.233333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(60\) −0.743145 0.669131i −0.743145 0.669131i
\(61\) −0.743145 0.669131i −0.743145 0.669131i 0.207912 0.978148i \(-0.433333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(62\) 0.309017 0.951057i 0.309017 0.951057i
\(63\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(64\) −0.309017 0.951057i −0.309017 0.951057i
\(65\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(66\) 0.459289 0.413545i 0.459289 0.413545i
\(67\) 1.47815 0.658114i 1.47815 0.658114i 0.500000 0.866025i \(-0.333333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(68\) 0.500000 0.866025i 0.500000 0.866025i
\(69\) −0.406737 0.913545i −0.406737 0.913545i
\(70\) −0.994522 0.104528i −0.994522 0.104528i
\(71\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) −0.587785 0.809017i −0.587785 0.809017i
\(73\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(74\) 0 0
\(75\) 0.669131 0.743145i 0.669131 0.743145i
\(76\) 0.500000 0.866025i 0.500000 0.866025i
\(77\) 0.128496 0.604528i 0.128496 0.604528i
\(78\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(79\) −0.251377 + 0.564602i −0.251377 + 0.564602i −0.994522 0.104528i \(-0.966667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(80\) 0.951057 0.309017i 0.951057 0.309017i
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 1.61803i 1.61803i
\(83\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i 0.913545 + 0.406737i \(0.133333\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(84\) −0.951057 0.309017i −0.951057 0.309017i
\(85\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(86\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(87\) −0.128496 0.604528i −0.128496 0.604528i
\(88\) 0.128496 + 0.604528i 0.128496 + 0.604528i
\(89\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(90\) 0.809017 0.587785i 0.809017 0.587785i
\(91\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(92\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(93\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(94\) 0.564602 0.251377i 0.564602 0.251377i
\(95\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(96\) 0.994522 0.104528i 0.994522 0.104528i
\(97\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(98\) 0 0
\(99\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(100\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(101\) 1.40126 0.809017i 1.40126 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(102\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(103\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(104\) −0.169131 1.60917i −0.169131 1.60917i
\(105\) 0.309017 0.951057i 0.309017 0.951057i
\(106\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(107\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(108\) 0.913545 0.406737i 0.913545 0.406737i
\(109\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(110\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(111\) 0 0
\(112\) 0.743145 0.669131i 0.743145 0.669131i
\(113\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(114\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(115\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(116\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(117\) −0.658114 1.47815i −0.658114 1.47815i
\(118\) 0 0
\(119\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(120\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(121\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(122\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(123\) −1.58268 0.336408i −1.58268 0.336408i
\(124\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(125\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(126\) 0.500000 0.866025i 0.500000 0.866025i
\(127\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(128\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(129\) −0.913545 0.406737i −0.913545 0.406737i
\(130\) 1.60917 0.169131i 1.60917 0.169131i
\(131\) −0.564602 + 0.251377i −0.564602 + 0.251377i −0.669131 0.743145i \(-0.733333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(132\) −0.618034 −0.618034
\(133\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(134\) −1.53884 0.500000i −1.53884 0.500000i
\(135\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(136\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(137\) 0.604528 0.128496i 0.604528 0.128496i 0.104528 0.994522i \(-0.466667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(139\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(140\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(141\) 0.128496 + 0.604528i 0.128496 + 0.604528i
\(142\) 0 0
\(143\) 1.00000i 1.00000i
\(144\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(145\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.40126 + 0.809017i 1.40126 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(150\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(151\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(152\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(153\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(154\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(155\) −0.500000 0.866025i −0.500000 0.866025i
\(156\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(157\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0.564602 0.251377i 0.564602 0.251377i
\(159\) −1.53884 0.500000i −1.53884 0.500000i
\(160\) −0.913545 0.406737i −0.913545 0.406737i
\(161\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(162\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(163\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(164\) 1.08268 1.20243i 1.08268 1.20243i
\(165\) 0.618034i 0.618034i
\(166\) 0.459289 0.413545i 0.459289 0.413545i
\(167\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(168\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(169\) 0.169131 1.60917i 0.169131 1.60917i
\(170\) −0.309017 0.951057i −0.309017 0.951057i
\(171\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(172\) 0.809017 0.587785i 0.809017 0.587785i
\(173\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(174\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(175\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(176\) 0.309017 0.535233i 0.309017 0.535233i
\(177\) 0 0
\(178\) 0.406737 0.913545i 0.406737 0.913545i
\(179\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(180\) −0.994522 0.104528i −0.994522 0.104528i
\(181\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(182\) 1.40126 0.809017i 1.40126 0.809017i
\(183\) −0.994522 0.104528i −0.994522 0.104528i
\(184\) −0.669131 0.743145i −0.669131 0.743145i
\(185\) 0 0
\(186\) −0.309017 0.951057i −0.309017 0.951057i
\(187\) 0.604528 0.128496i 0.604528 0.128496i
\(188\) −0.587785 0.190983i −0.587785 0.190983i
\(189\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(190\) −0.309017 0.951057i −0.309017 0.951057i
\(191\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(192\) −0.809017 0.587785i −0.809017 0.587785i
\(193\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(194\) 0 0
\(195\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(196\) 0 0
\(197\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(198\) 0.128496 0.604528i 0.128496 0.604528i
\(199\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(200\) 0.406737 0.913545i 0.406737 0.913545i
\(201\) 0.809017 1.40126i 0.809017 1.40126i
\(202\) −1.58268 0.336408i −1.58268 0.336408i
\(203\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(204\) −0.104528 0.994522i −0.104528 0.994522i
\(205\) 1.20243 + 1.08268i 1.20243 + 1.08268i
\(206\) 0 0
\(207\) −0.866025 0.500000i −0.866025 0.500000i
\(208\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(209\) 0.604528 0.128496i 0.604528 0.128496i
\(210\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(211\) 0.604528 + 0.128496i 0.604528 + 0.128496i 0.500000 0.866025i \(-0.333333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(212\) 1.20243 1.08268i 1.20243 1.08268i
\(213\) 0 0
\(214\) −1.20243 1.08268i −1.20243 1.08268i
\(215\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(216\) −0.951057 0.309017i −0.951057 0.309017i
\(217\) −0.809017 0.587785i −0.809017 0.587785i
\(218\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(219\) 0 0
\(220\) 0.535233 + 0.309017i 0.535233 + 0.309017i
\(221\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(222\) 0 0
\(223\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(224\) −1.00000 −1.00000
\(225\) 0.104528 0.994522i 0.104528 0.994522i
\(226\) 1.00000i 1.00000i
\(227\) −0.669131 + 0.743145i −0.669131 + 0.743145i −0.978148 0.207912i \(-0.933333\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) −0.104528 0.994522i −0.104528 0.994522i
\(229\) 1.60917 0.169131i 1.60917 0.169131i 0.743145 0.669131i \(-0.233333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(230\) 0.743145 0.669131i 0.743145 0.669131i
\(231\) −0.251377 0.564602i −0.251377 0.564602i
\(232\) −0.309017 0.535233i −0.309017 0.535233i
\(233\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(234\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(235\) 0.190983 0.587785i 0.190983 0.587785i
\(236\) 0 0
\(237\) 0.128496 + 0.604528i 0.128496 + 0.604528i
\(238\) −0.669131 0.743145i −0.669131 0.743145i
\(239\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(240\) 0.587785 0.809017i 0.587785 0.809017i
\(241\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(242\) 0.363271 0.500000i 0.363271 0.500000i
\(243\) −1.00000 −1.00000
\(244\) 0.587785 0.809017i 0.587785 0.809017i
\(245\) 0 0
\(246\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(247\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(248\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(249\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(250\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(251\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(253\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(254\) −0.564602 0.251377i −0.564602 0.251377i
\(255\) 0.994522 0.104528i 0.994522 0.104528i
\(256\) 0.913545 0.406737i 0.913545 0.406737i
\(257\) −0.809017 + 1.40126i −0.809017 + 1.40126i 0.104528 + 0.994522i \(0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(258\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(259\) 0 0
\(260\) −1.30902 0.951057i −1.30902 0.951057i
\(261\) −0.459289 0.413545i −0.459289 0.413545i
\(262\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(263\) −0.207912 0.978148i −0.207912 0.978148i −0.951057 0.309017i \(-0.900000\pi\)
0.743145 0.669131i \(-0.233333\pi\)
\(264\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(265\) 1.08268 + 1.20243i 1.08268 + 1.20243i
\(266\) −0.669131 0.743145i −0.669131 0.743145i
\(267\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(268\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(269\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(270\) 0.309017 0.951057i 0.309017 0.951057i
\(271\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(272\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(273\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(274\) −0.535233 0.309017i −0.535233 0.309017i
\(275\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(276\) 0.866025 0.500000i 0.866025 0.500000i
\(277\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(278\) 0 0
\(279\) 0.994522 0.104528i 0.994522 0.104528i
\(280\) 1.00000i 1.00000i
\(281\) 0.104528 0.994522i 0.104528 0.994522i −0.809017 0.587785i \(-0.800000\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(282\) 0.309017 0.535233i 0.309017 0.535233i
\(283\) −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i \(-0.800000\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(284\) 0 0
\(285\) 0.994522 0.104528i 0.994522 0.104528i
\(286\) 0.669131 0.743145i 0.669131 0.743145i
\(287\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(288\) 0.743145 0.669131i 0.743145 0.669131i
\(289\) 0 0
\(290\) 0.535233 0.309017i 0.535233 0.309017i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(298\) −0.500000 1.53884i −0.500000 1.53884i
\(299\) −0.809017 1.40126i −0.809017 1.40126i
\(300\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(301\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(302\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(303\) 0.658114 1.47815i 0.658114 1.47815i
\(304\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(305\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(306\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(307\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(308\) 0.614648 + 0.0646021i 0.614648 + 0.0646021i
\(309\) 0 0
\(310\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(311\) −0.207912 + 0.978148i −0.207912 + 0.978148i 0.743145 + 0.669131i \(0.233333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(312\) −1.08268 1.20243i −1.08268 1.20243i
\(313\) −0.978148 + 0.207912i −0.978148 + 0.207912i −0.669131 0.743145i \(-0.733333\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(314\) 0 0
\(315\) −0.309017 0.951057i −0.309017 0.951057i
\(316\) −0.587785 0.190983i −0.587785 0.190983i
\(317\) −0.994522 0.104528i −0.994522 0.104528i −0.406737 0.913545i \(-0.633333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(318\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(319\) 0.155360 + 0.348943i 0.155360 + 0.348943i
\(320\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(321\) 1.30902 0.951057i 1.30902 0.951057i
\(322\) 0.406737 0.913545i 0.406737 0.913545i
\(323\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(324\) 0.500000 0.866025i 0.500000 0.866025i
\(325\) 0.951057 1.30902i 0.951057 1.30902i
\(326\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(327\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(328\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(329\) −0.0646021 0.614648i −0.0646021 0.614648i
\(330\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(331\) 0.169131 1.60917i 0.169131 1.60917i −0.500000 0.866025i \(-0.666667\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(332\) −0.618034 −0.618034
\(333\) 0 0
\(334\) 0 0
\(335\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(336\) 0.207912 0.978148i 0.207912 0.978148i
\(337\) −1.08268 1.20243i −1.08268 1.20243i −0.978148 0.207912i \(-0.933333\pi\)
−0.104528 0.994522i \(-0.533333\pi\)
\(338\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(339\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(340\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(341\) −0.587785 0.190983i −0.587785 0.190983i
\(342\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(343\) 1.00000i 1.00000i
\(344\) −0.994522 0.104528i −0.994522 0.104528i
\(345\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(346\) 0 0
\(347\) 0.104528 + 0.994522i 0.104528 + 0.994522i 0.913545 + 0.406737i \(0.133333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0.587785 0.190983i 0.587785 0.190983i
\(349\) 0.535233 0.309017i 0.535233 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(350\) 1.00000 1.00000
\(351\) −1.40126 0.809017i −1.40126 0.809017i
\(352\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(353\) 0.564602 + 0.251377i 0.564602 + 0.251377i 0.669131 0.743145i \(-0.266667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(357\) 0.866025 0.500000i 0.866025 0.500000i
\(358\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(359\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(360\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(361\) 0 0
\(362\) 0 0
\(363\) 0.413545 + 0.459289i 0.413545 + 0.459289i
\(364\) −1.58268 0.336408i −1.58268 0.336408i
\(365\) 0 0
\(366\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(367\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(368\) 1.00000i 1.00000i
\(369\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(370\) 0 0
\(371\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(372\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(373\) 0.128496 0.604528i 0.128496 0.604528i −0.866025 0.500000i \(-0.833333\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(374\) −0.535233 0.309017i −0.535233 0.309017i
\(375\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(376\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(377\) −0.309017 0.951057i −0.309017 0.951057i
\(378\) −0.104528 0.994522i −0.104528 0.994522i
\(379\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(380\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(381\) 0.363271 0.500000i 0.363271 0.500000i
\(382\) 0 0
\(383\) 0.251377 + 0.564602i 0.251377 + 0.564602i 0.994522 0.104528i \(-0.0333333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(384\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(385\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i
\(386\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(387\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(388\) 0 0
\(389\) 0.743145 + 0.669131i 0.743145 + 0.669131i 0.951057 0.309017i \(-0.100000\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(390\) 1.20243 1.08268i 1.20243 1.08268i
\(391\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(392\) 0 0
\(393\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(394\) 0 0
\(395\) 0.190983 0.587785i 0.190983 0.587785i
\(396\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(397\) −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(-0.5\pi\)
\(398\) 1.08268 1.20243i 1.08268 1.20243i
\(399\) 0.866025 0.500000i 0.866025 0.500000i
\(400\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(401\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(402\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(403\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(404\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(405\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(406\) 0.363271 0.500000i 0.363271 0.500000i
\(407\) 0 0
\(408\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(409\) −0.413545 0.459289i −0.413545 0.459289i 0.500000 0.866025i \(-0.333333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(410\) −0.169131 1.60917i −0.169131 1.60917i
\(411\) 0.413545 0.459289i 0.413545 0.459289i
\(412\) 0 0
\(413\) 0 0
\(414\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(415\) 0.618034i 0.618034i
\(416\) 1.58268 0.336408i 1.58268 0.336408i
\(417\) 0 0
\(418\) −0.535233 0.309017i −0.535233 0.309017i
\(419\) 1.47815 0.658114i 1.47815 0.658114i 0.500000 0.866025i \(-0.333333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(420\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(421\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(422\) −0.363271 0.500000i −0.363271 0.500000i
\(423\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(424\) −1.61803 −1.61803
\(425\) −0.913545 0.406737i −0.913545 0.406737i
\(426\) 0 0
\(427\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(428\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(429\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(430\) 0.104528 0.994522i 0.104528 0.994522i
\(431\) 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(432\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(433\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(434\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(435\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(436\) 0.336408 1.58268i 0.336408 1.58268i
\(437\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(438\) 0 0
\(439\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(440\) −0.190983 0.587785i −0.190983 0.587785i
\(441\) 0 0
\(442\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(443\) −0.809017 1.40126i −0.809017 1.40126i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 0.994522i \(-0.466667\pi\)
\(444\) 0 0
\(445\) −0.406737 0.913545i −0.406737 0.913545i
\(446\) 0 0
\(447\) 1.60917 0.169131i 1.60917 0.169131i
\(448\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(449\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(450\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(451\) 1.00000 1.00000
\(452\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(453\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(454\) 0.994522 0.104528i 0.994522 0.104528i
\(455\) 0.336408 1.58268i 0.336408 1.58268i
\(456\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(457\) 0.309017 + 0.535233i 0.309017 + 0.535233i 0.978148 0.207912i \(-0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(458\) −1.30902 0.951057i −1.30902 0.951057i
\(459\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(460\) −1.00000 −1.00000
\(461\) 0.459289 + 0.413545i 0.459289 + 0.413545i 0.866025 0.500000i \(-0.166667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(462\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(463\) 0.743145 0.669131i 0.743145 0.669131i −0.207912 0.978148i \(-0.566667\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(464\) −0.128496 + 0.604528i −0.128496 + 0.604528i
\(465\) −0.913545 0.406737i −0.913545 0.406737i
\(466\) −0.207912 0.978148i −0.207912 0.978148i
\(467\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(468\) 1.40126 0.809017i 1.40126 0.809017i
\(469\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(470\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(471\) 0 0
\(472\) 0 0
\(473\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(474\) 0.309017 0.535233i 0.309017 0.535233i
\(475\) −0.913545 0.406737i −0.913545 0.406737i
\(476\) 1.00000i 1.00000i
\(477\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(478\) 0 0
\(479\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(480\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(481\) 0 0
\(482\) 0 0
\(483\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(484\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(485\) 0 0
\(486\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(487\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(488\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(489\) −0.309017 0.951057i −0.309017 0.951057i
\(490\) 0 0
\(491\) 0 0 0.743145 0.669131i \(-0.233333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(492\) 0.169131 1.60917i 0.169131 1.60917i
\(493\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(494\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(495\) −0.363271 0.500000i −0.363271 0.500000i
\(496\) −0.587785 0.809017i −0.587785 0.809017i
\(497\) 0 0
\(498\) 0.128496 0.604528i 0.128496 0.604528i
\(499\) −0.809017 + 1.40126i −0.809017 + 1.40126i 0.104528 + 0.994522i \(0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(500\) −0.406737 0.913545i −0.406737 0.913545i
\(501\) 0 0
\(502\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(503\) 0.363271 + 0.500000i 0.363271 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(504\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(505\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(506\) 0.0646021 0.614648i 0.0646021 0.614648i
\(507\) −0.809017 1.40126i −0.809017 1.40126i
\(508\) 0.251377 + 0.564602i 0.251377 + 0.564602i
\(509\) −0.459289 + 0.413545i −0.459289 + 0.413545i −0.866025 0.500000i \(-0.833333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(510\) −0.809017 0.587785i −0.809017 0.587785i
\(511\) 0 0
\(512\) −0.951057 0.309017i −0.951057 0.309017i
\(513\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(514\) 1.53884 0.500000i 1.53884 0.500000i
\(515\) 0 0
\(516\) 0.309017 0.951057i 0.309017 0.951057i
\(517\) −0.155360 0.348943i −0.155360 0.348943i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(521\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(522\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(523\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(524\) −0.309017 0.535233i −0.309017 0.535233i
\(525\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(526\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(527\) 0.207912 0.978148i 0.207912 0.978148i
\(528\) −0.0646021 0.614648i −0.0646021 0.614648i
\(529\) 0 0
\(530\) 1.61803i 1.61803i
\(531\) 0 0
\(532\) 1.00000i 1.00000i
\(533\) −2.60369 0.273659i −2.60369 0.273659i
\(534\) −0.207912 0.978148i −0.207912 0.978148i
\(535\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(536\) 0.336408 1.58268i 0.336408 1.58268i
\(537\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(538\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(539\) 0 0
\(540\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(541\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(542\) 0.104528 0.994522i 0.104528 0.994522i
\(543\) 0 0
\(544\) −0.406737 0.913545i −0.406737 0.913545i
\(545\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(546\) 0.658114 1.47815i 0.658114 1.47815i
\(547\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(548\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(549\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(550\) 0.587785 0.190983i 0.587785 0.190983i
\(551\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(552\) −0.978148 0.207912i −0.978148 0.207912i
\(553\) −0.0646021 0.614648i −0.0646021 0.614648i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(558\) −0.809017 0.587785i −0.809017 0.587785i
\(559\) −1.53884 0.500000i −1.53884 0.500000i
\(560\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(561\) 0.413545 0.459289i 0.413545 0.459289i
\(562\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(563\) −1.08268 1.20243i −1.08268 1.20243i −0.978148 0.207912i \(-0.933333\pi\)
−0.104528 0.994522i \(-0.533333\pi\)
\(564\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(565\) −0.743145 0.669131i −0.743145 0.669131i
\(566\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(567\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(568\) 0 0
\(569\) 0.104528 0.994522i 0.104528 0.994522i −0.809017 0.587785i \(-0.800000\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(570\) −0.809017 0.587785i −0.809017 0.587785i
\(571\) −0.0646021 0.614648i −0.0646021 0.614648i −0.978148 0.207912i \(-0.933333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(572\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(573\) 0 0
\(574\) −0.809017 1.40126i −0.809017 1.40126i
\(575\) 1.00000i 1.00000i
\(576\) −1.00000 −1.00000
\(577\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(578\) 0 0
\(579\) −0.104528 0.994522i −0.104528 0.994522i
\(580\) −0.604528 0.128496i −0.604528 0.128496i
\(581\) −0.251377 0.564602i −0.251377 0.564602i
\(582\) 0 0
\(583\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(584\) 0 0
\(585\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(586\) 0 0
\(587\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(588\) 0 0
\(589\) 0.207912 0.978148i 0.207912 0.978148i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) −0.251377 0.564602i −0.251377 0.564602i
\(595\) −1.00000 −1.00000
\(596\) −0.658114 + 1.47815i −0.658114 + 1.47815i
\(597\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(598\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(599\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(600\) −0.207912 0.978148i −0.207912 0.978148i
\(601\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(602\) −0.309017 0.951057i −0.309017 0.951057i
\(603\) −0.169131 1.60917i −0.169131 1.60917i
\(604\) −0.587785 0.809017i −0.587785 0.809017i
\(605\) −0.128496 0.604528i −0.128496 0.604528i
\(606\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) −0.406737 0.913545i −0.406737 0.913545i
\(609\) 0.413545 + 0.459289i 0.413545 + 0.459289i
\(610\) −0.207912 0.978148i −0.207912 0.978148i
\(611\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(612\) −0.669131 0.743145i −0.669131 0.743145i
\(613\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(614\) −1.20243 1.08268i −1.20243 1.08268i
\(615\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(616\) −0.413545 0.459289i −0.413545 0.459289i
\(617\) 0.913545 0.406737i 0.913545 0.406737i 0.104528 0.994522i \(-0.466667\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(618\) 0 0
\(619\) −0.169131 + 1.60917i −0.169131 + 1.60917i 0.500000 + 0.866025i \(0.333333\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(620\) 0.809017 0.587785i 0.809017 0.587785i
\(621\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(622\) 0.809017 0.587785i 0.809017 0.587785i
\(623\) −0.743145 0.669131i −0.743145 0.669131i
\(624\) 1.61803i 1.61803i
\(625\) 0.913545 0.406737i 0.913545 0.406737i
\(626\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(627\) 0.413545 0.459289i 0.413545 0.459289i
\(628\) 0 0
\(629\) 0 0
\(630\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(631\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(632\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(633\) 0.564602 0.251377i 0.564602 0.251377i
\(634\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(635\) −0.564602 + 0.251377i −0.564602 + 0.251377i
\(636\) 0.336408 1.58268i 0.336408 1.58268i
\(637\) 0 0
\(638\) 0.118034 0.363271i 0.118034 0.363271i
\(639\) 0 0
\(640\) 0.309017 0.951057i 0.309017 0.951057i
\(641\) −0.604528 + 0.128496i −0.604528 + 0.128496i −0.500000 0.866025i \(-0.666667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(642\) −1.60917 0.169131i −1.60917 0.169131i
\(643\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(644\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(645\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(646\) 0.406737 0.913545i 0.406737 0.913545i
\(647\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(648\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(649\) 0 0
\(650\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(651\) −1.00000 −1.00000
\(652\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(653\) 0.614648 0.0646021i 0.614648 0.0646021i 0.207912 0.978148i \(-0.433333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(654\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(655\) 0.535233 0.309017i 0.535233 0.309017i
\(656\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(657\) 0 0
\(658\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(659\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(660\) 0.614648 0.0646021i 0.614648 0.0646021i
\(661\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(662\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(663\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(664\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(665\) −1.00000 −1.00000
\(666\) 0 0
\(667\) −0.500000 0.363271i −0.500000 0.363271i
\(668\) 0 0
\(669\) 0 0
\(670\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(671\) 0.614648 0.0646021i 0.614648 0.0646021i
\(672\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(673\) 0.669131 0.743145i 0.669131 0.743145i −0.309017 0.951057i \(-0.600000\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(674\) 1.61803i 1.61803i
\(675\) −0.500000 0.866025i −0.500000 0.866025i
\(676\) 1.61803 1.61803
\(677\) 0.743145 + 0.669131i 0.743145 + 0.669131i 0.951057 0.309017i \(-0.100000\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(678\) −0.587785 0.809017i −0.587785 0.809017i
\(679\) 0 0
\(680\) 0.913545 0.406737i 0.913545 0.406737i
\(681\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(682\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(683\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(684\) −0.669131 0.743145i −0.669131 0.743145i
\(685\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(686\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(687\) 1.20243 1.08268i 1.20243 1.08268i
\(688\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(689\) −2.56082 0.544320i −2.56082 0.544320i
\(690\) 0.207912 0.978148i 0.207912 0.978148i
\(691\) −1.58268 + 0.336408i −1.58268 + 0.336408i −0.913545 0.406737i \(-0.866667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(692\) 0 0
\(693\) −0.535233 0.309017i −0.535233 0.309017i
\(694\) 0.587785 0.809017i 0.587785 0.809017i
\(695\) 0 0
\(696\) −0.564602 0.251377i −0.564602 0.251377i
\(697\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(698\) −0.604528 0.128496i −0.604528 0.128496i
\(699\) 1.00000 1.00000
\(700\) −0.743145 0.669131i −0.743145 0.669131i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(703\) 0 0
\(704\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(705\) −0.190983 0.587785i −0.190983 0.587785i
\(706\) −0.251377 0.564602i −0.251377 0.564602i
\(707\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(708\) 0 0
\(709\) 0.207912 + 0.978148i 0.207912 + 0.978148i 0.951057 + 0.309017i \(0.100000\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(710\) 0 0
\(711\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(712\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(713\) 0.978148 0.207912i 0.978148 0.207912i
\(714\) −0.978148 0.207912i −0.978148 0.207912i
\(715\) −0.104528 0.994522i −0.104528 0.994522i
\(716\) −0.669131 0.743145i −0.669131 0.743145i
\(717\) 0 0
\(718\) −0.309017 0.535233i −0.309017 0.535233i
\(719\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(720\) 1.00000i 1.00000i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.128496 0.604528i 0.128496 0.604528i
\(726\) 0.618034i 0.618034i
\(727\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(728\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(729\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(730\) 0 0
\(731\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(732\) 1.00000i 1.00000i
\(733\) −0.658114 1.47815i −0.658114 1.47815i −0.866025 0.500000i \(-0.833333\pi\)
0.207912 0.978148i \(-0.433333\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.669131 0.743145i 0.669131 0.743145i
\(737\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(738\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(739\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(742\) −0.658114 1.47815i −0.658114 1.47815i
\(743\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0.913545 0.406737i 0.913545 0.406737i
\(745\) −1.47815 0.658114i −1.47815 0.658114i
\(746\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(747\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(748\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(749\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(750\) 0.978148 0.207912i 0.978148 0.207912i
\(751\) −1.40126 0.809017i −1.40126 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(752\) 0.128496 0.604528i 0.128496 0.604528i
\(753\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(754\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(755\) 0.809017 0.587785i 0.809017 0.587785i
\(756\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(757\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(758\) 0 0
\(759\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(760\) 0.913545 0.406737i 0.913545 0.406737i
\(761\) −0.604528 0.128496i −0.604528 0.128496i −0.104528 0.994522i \(-0.533333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(763\) 1.58268 0.336408i 1.58268 0.336408i
\(764\) 0 0
\(765\) 0.743145 0.669131i 0.743145 0.669131i
\(766\) 0.190983 0.587785i 0.190983 0.587785i
\(767\) 0 0
\(768\) 0.500000 0.866025i 0.500000 0.866025i
\(769\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(770\) 0.459289 0.413545i 0.459289 0.413545i
\(771\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(772\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(773\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(774\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(775\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(776\) 0 0
\(777\) 0 0
\(778\) −0.104528 0.994522i −0.104528 0.994522i
\(779\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(780\) −1.61803 −1.61803
\(781\) 0 0
\(782\) 1.00000 1.00000
\(783\) −0.614648 0.0646021i −0.614648 0.0646021i
\(784\) 0 0
\(785\) 0 0
\(786\) 0.587785 0.190983i 0.587785 0.190983i
\(787\) −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i \(-0.400000\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(788\) 0 0
\(789\) −0.743145 0.669131i −0.743145 0.669131i
\(790\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(791\) −0.951057 0.309017i −0.951057 0.309017i
\(792\) 0.614648 + 0.0646021i 0.614648 + 0.0646021i
\(793\) −1.61803 −1.61803
\(794\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(795\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(796\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(797\) −0.994522 + 0.104528i −0.994522 + 0.104528i −0.587785 0.809017i \(-0.700000\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(798\) −0.978148 0.207912i −0.978148 0.207912i
\(799\) 0.535233 0.309017i 0.535233 0.309017i
\(800\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(801\) 1.00000 1.00000
\(802\) 0.951057 0.309017i 0.951057 0.309017i
\(803\) 0 0
\(804\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(805\) −0.406737 0.913545i −0.406737 0.913545i
\(806\) −0.658114 1.47815i −0.658114 1.47815i
\(807\) 1.61803i 1.61803i
\(808\) 0.169131 1.60917i 0.169131 1.60917i
\(809\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(810\) −0.309017 0.951057i −0.309017 0.951057i
\(811\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(812\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(813\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(814\) 0 0
\(815\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(816\) 0.978148 0.207912i 0.978148 0.207912i
\(817\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(818\) 0.618034i 0.618034i
\(819\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(820\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(821\) −0.251377 + 0.564602i −0.251377 + 0.564602i −0.994522 0.104528i \(-0.966667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(822\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(823\) 0.336408 1.58268i 0.336408 1.58268i −0.406737 0.913545i \(-0.633333\pi\)
0.743145 0.669131i \(-0.233333\pi\)
\(824\) 0 0
\(825\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(826\) 0 0
\(827\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(828\) 0.406737 0.913545i 0.406737 0.913545i
\(829\) 0.363271 + 0.500000i 0.363271 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(830\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(831\) 0 0
\(832\) −1.40126 0.809017i −1.40126 0.809017i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(837\) 0.743145 0.669131i 0.743145 0.669131i
\(838\) −1.53884 0.500000i −1.53884 0.500000i
\(839\) 0.743145 + 0.669131i 0.743145 + 0.669131i 0.951057 0.309017i \(-0.100000\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(840\) −0.587785 0.809017i −0.587785 0.809017i
\(841\) 0.413545 + 0.459289i 0.413545 + 0.459289i
\(842\) 0 0
\(843\) −0.500000 0.866025i −0.500000 0.866025i
\(844\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i
\(845\) 1.61803i 1.61803i
\(846\) −0.0646021 0.614648i −0.0646021 0.614648i
\(847\) −0.363271 0.500000i −0.363271 0.500000i
\(848\) 1.20243 + 1.08268i 1.20243 + 1.08268i
\(849\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(850\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(851\) 0 0
\(852\) 0 0
\(853\) −0.406737 + 0.913545i −0.406737 + 0.913545i 0.587785 + 0.809017i \(0.300000\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(854\) −0.587785 0.809017i −0.587785 0.809017i
\(855\) 0.743145 0.669131i 0.743145 0.669131i
\(856\) 0.951057 1.30902i 0.951057 1.30902i
\(857\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(858\) 0.104528 0.994522i 0.104528 0.994522i
\(859\) 1.08268 + 1.20243i 1.08268 + 1.20243i 0.978148 + 0.207912i \(0.0666667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(860\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(861\) 1.53884 0.500000i 1.53884 0.500000i
\(862\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(863\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(864\) 0.207912 0.978148i 0.207912 0.978148i
\(865\) 0 0
\(866\) −0.207912 0.978148i −0.207912 0.978148i
\(867\) 0 0
\(868\) 0.500000 0.866025i 0.500000 0.866025i
\(869\) −0.155360 0.348943i −0.155360 0.348943i
\(870\) 0.251377 0.564602i 0.251377 0.564602i
\(871\) 1.06485 2.39169i 1.06485 2.39169i
\(872\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(873\) 0 0
\(874\) 1.00000 1.00000
\(875\) 0.669131 0.743145i 0.669131 0.743145i
\(876\) 0 0
\(877\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −0.251377 + 0.564602i −0.251377 + 0.564602i
\(881\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(882\) 0 0
\(883\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(884\) −0.336408 1.58268i −0.336408 1.58268i
\(885\) 0 0
\(886\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(887\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(888\) 0 0
\(889\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(890\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(891\) 0.604528 0.128496i 0.604528 0.128496i
\(892\) 0 0
\(893\) 0.535233 0.309017i 0.535233 0.309017i
\(894\) −1.30902 0.951057i −1.30902 0.951057i
\(895\) 0.743145 0.669131i 0.743145 0.669131i
\(896\) −0.104528 0.994522i −0.104528 0.994522i
\(897\) −1.47815 0.658114i −1.47815 0.658114i
\(898\) −1.20243 1.08268i −1.20243 1.08268i
\(899\) 0.618034 0.618034
\(900\) 1.00000 1.00000
\(901\) 1.61803i 1.61803i
\(902\) −0.743145 0.669131i −0.743145 0.669131i
\(903\) 0.994522 0.104528i 0.994522 0.104528i
\(904\) 0.994522 0.104528i 0.994522 0.104528i
\(905\) 0 0
\(906\) 0.913545 0.406737i 0.913545 0.406737i
\(907\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(908\) −0.809017 0.587785i −0.809017 0.587785i
\(909\) −0.336408 1.58268i −0.336408 1.58268i
\(910\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(911\) 0.743145 + 0.669131i 0.743145 + 0.669131i 0.951057 0.309017i \(-0.100000\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(912\) 0.978148 0.207912i 0.978148 0.207912i
\(913\) −0.255585 0.283856i −0.255585 0.283856i
\(914\) 0.128496 0.604528i 0.128496 0.604528i
\(915\) 1.00000 1.00000
\(916\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(917\) 0.363271 0.500000i 0.363271 0.500000i
\(918\) 0.866025 0.500000i 0.866025 0.500000i
\(919\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(920\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(921\) 1.30902 0.951057i 1.30902 0.951057i
\(922\) −0.0646021 0.614648i −0.0646021 0.614648i
\(923\) 0 0
\(924\) 0.535233 0.309017i 0.535233 0.309017i
\(925\) 0 0
\(926\) −1.00000 −1.00000
\(927\) 0 0
\(928\) 0.500000 0.363271i 0.500000 0.363271i
\(929\) 1.47815 + 0.658114i 1.47815 + 0.658114i 0.978148 0.207912i \(-0.0666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(930\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(931\) 0 0
\(932\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(933\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(934\) −0.207912 0.978148i −0.207912 0.978148i
\(935\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(936\) −1.58268 0.336408i −1.58268 0.336408i
\(937\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(938\) 1.58268 0.336408i 1.58268 0.336408i
\(939\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(940\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(941\) 0.459289 0.413545i 0.459289 0.413545i −0.406737 0.913545i \(-0.633333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(942\) 0 0
\(943\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(944\) 0 0
\(945\) −0.809017 0.587785i −0.809017 0.587785i
\(946\) −0.363271 0.500000i −0.363271 0.500000i
\(947\) −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i \(-0.533333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(948\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(949\) 0 0
\(950\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(951\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(952\) 0.669131 0.743145i 0.669131 0.743145i
\(953\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(954\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(955\) 0 0
\(956\) 0 0
\(957\) 0.330792 + 0.190983i 0.330792 + 0.190983i
\(958\) 0 0
\(959\) −0.459289 + 0.413545i −0.459289 + 0.413545i
\(960\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(961\) 0 0
\(962\) 0 0
\(963\) 0.500000 1.53884i 0.500000 1.53884i
\(964\) 0 0
\(965\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(966\) −0.207912 0.978148i −0.207912 0.978148i
\(967\) 0.406737 + 0.913545i 0.406737 + 0.913545i 0.994522 + 0.104528i \(0.0333333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(968\) 0.535233 + 0.309017i 0.535233 + 0.309017i
\(969\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(970\) 0 0
\(971\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(972\) −0.104528 0.994522i −0.104528 0.994522i
\(973\) 0 0
\(974\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(975\) 1.61803i 1.61803i
\(976\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(977\) −0.604528 0.128496i −0.604528 0.128496i −0.104528 0.994522i \(-0.533333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(979\) −0.564602 0.251377i −0.564602 0.251377i
\(980\) 0 0
\(981\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(982\) 0 0
\(983\) 1.60917 + 0.169131i 1.60917 + 0.169131i 0.866025 0.500000i \(-0.166667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(984\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(985\) 0 0
\(986\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(987\) −0.413545 0.459289i −0.413545 0.459289i
\(988\) −0.336408 1.58268i −0.336408 1.58268i
\(989\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(990\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i
\(991\) 1.53884 + 0.500000i 1.53884 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(992\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(993\) −0.809017 1.40126i −0.809017 1.40126i
\(994\) 0 0
\(995\) −0.169131 1.60917i −0.169131 1.60917i
\(996\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(997\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(998\) 1.53884 0.500000i 1.53884 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 1800.1.dg.a.931.1 yes 16
8.3 odd 2 inner 1800.1.dg.a.931.2 yes 16
9.7 even 3 inner 1800.1.dg.a.331.1 16
25.21 even 5 inner 1800.1.dg.a.571.2 yes 16
72.43 odd 6 inner 1800.1.dg.a.331.2 yes 16
200.171 odd 10 inner 1800.1.dg.a.571.1 yes 16
225.196 even 15 inner 1800.1.dg.a.1771.2 yes 16
1800.1771 odd 30 inner 1800.1.dg.a.1771.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1800.1.dg.a.331.1 16 9.7 even 3 inner
1800.1.dg.a.331.2 yes 16 72.43 odd 6 inner
1800.1.dg.a.571.1 yes 16 200.171 odd 10 inner
1800.1.dg.a.571.2 yes 16 25.21 even 5 inner
1800.1.dg.a.931.1 yes 16 1.1 even 1 trivial
1800.1.dg.a.931.2 yes 16 8.3 odd 2 inner
1800.1.dg.a.1771.1 yes 16 1800.1771 odd 30 inner
1800.1.dg.a.1771.2 yes 16 225.196 even 15 inner