Properties

Label 1800.1.dg.a.1291.2
Level $1800$
Weight $1$
Character 1800.1291
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 1291.2
Root \(-0.994522 + 0.104528i\) of defining polynomial
Character \(\chi\) \(=\) 1800.1291
Dual form 1800.1.dg.a.1411.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.994522 + 0.104528i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.978148 + 0.207912i) q^{4} +(-0.207912 + 0.978148i) q^{5} +(-0.207912 - 0.978148i) q^{6} +(-0.866025 + 0.500000i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.994522 + 0.104528i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.978148 + 0.207912i) q^{4} +(-0.207912 + 0.978148i) q^{5} +(-0.207912 - 0.978148i) q^{6} +(-0.866025 + 0.500000i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(-0.169131 + 1.60917i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(0.614648 - 0.0646021i) q^{13} +(-0.913545 + 0.406737i) q^{14} +(0.994522 - 0.104528i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.309017 - 0.951057i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.743145 + 0.669131i) q^{21} +(-0.336408 + 1.58268i) q^{22} +(0.406737 + 0.913545i) q^{23} -1.00000i q^{24} +(-0.913545 - 0.406737i) q^{25} +0.618034 q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.951057 + 0.309017i) q^{28} +(1.20243 + 1.08268i) q^{29} +1.00000 q^{30} +(-0.743145 + 0.669131i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.58268 - 0.336408i) q^{33} +(0.406737 - 0.913545i) q^{34} +(-0.309017 - 0.951057i) q^{35} +(-0.913545 + 0.406737i) q^{36} +(0.406737 - 0.913545i) q^{38} +(-0.251377 - 0.564602i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.0646021 - 0.614648i) q^{41} +(0.669131 + 0.743145i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(-0.500000 + 1.53884i) q^{44} +(-0.406737 - 0.913545i) q^{45} +(0.309017 + 0.951057i) q^{46} +(-1.20243 - 1.08268i) q^{47} +(0.104528 - 0.994522i) q^{48} +(-0.866025 - 0.500000i) q^{50} -1.00000 q^{51} +(0.614648 + 0.0646021i) q^{52} +(0.587785 - 0.190983i) q^{53} +(0.743145 + 0.669131i) q^{54} +(-1.53884 - 0.500000i) q^{55} +(-0.978148 + 0.207912i) q^{56} -1.00000 q^{57} +(1.08268 + 1.20243i) q^{58} +(0.994522 + 0.104528i) q^{60} +(0.994522 + 0.104528i) q^{61} +(-0.809017 + 0.587785i) q^{62} +(0.406737 - 0.913545i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.0646021 + 0.614648i) q^{65} +(1.60917 - 0.169131i) q^{66} +(-0.413545 - 0.459289i) q^{67} +(0.500000 - 0.866025i) q^{68} +(0.743145 - 0.669131i) q^{69} +(-0.207912 - 0.978148i) q^{70} +(-0.951057 + 0.309017i) q^{72} +(-0.104528 + 0.994522i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-0.658114 - 1.47815i) q^{77} +(-0.190983 - 0.587785i) q^{78} +(-1.20243 - 1.08268i) q^{79} +(-0.587785 + 0.809017i) q^{80} +(0.309017 - 0.951057i) q^{81} -0.618034i q^{82} +(1.58268 - 0.336408i) q^{83} +(0.587785 + 0.809017i) q^{84} +(0.866025 + 0.500000i) q^{85} +(-0.406737 - 0.913545i) q^{86} +(0.658114 - 1.47815i) q^{87} +(-0.658114 + 1.47815i) q^{88} +(-0.809017 - 0.587785i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(-0.500000 + 0.363271i) q^{91} +(0.207912 + 0.978148i) q^{92} +(0.866025 + 0.500000i) q^{93} +(-1.08268 - 1.20243i) q^{94} +(0.866025 + 0.500000i) q^{95} +(0.207912 - 0.978148i) q^{96} +(-0.809017 - 1.40126i) 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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(3\) −0.309017 0.951057i −0.309017 0.951057i
\(4\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(5\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(6\) −0.207912 0.978148i −0.207912 0.978148i
\(7\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(8\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(9\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(10\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(11\) −0.169131 + 1.60917i −0.169131 + 1.60917i 0.500000 + 0.866025i \(0.333333\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(12\) −0.104528 0.994522i −0.104528 0.994522i
\(13\) 0.614648 0.0646021i 0.614648 0.0646021i 0.207912 0.978148i \(-0.433333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(14\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(15\) 0.994522 0.104528i 0.994522 0.104528i
\(16\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(17\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(18\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(19\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(20\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(21\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(22\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(23\) 0.406737 + 0.913545i 0.406737 + 0.913545i 0.994522 + 0.104528i \(0.0333333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(24\) 1.00000i 1.00000i
\(25\) −0.913545 0.406737i −0.913545 0.406737i
\(26\) 0.618034 0.618034
\(27\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(28\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(29\) 1.20243 + 1.08268i 1.20243 + 1.08268i 0.994522 + 0.104528i \(0.0333333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(30\) 1.00000 1.00000
\(31\) −0.743145 + 0.669131i −0.743145 + 0.669131i −0.951057 0.309017i \(-0.900000\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(32\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(33\) 1.58268 0.336408i 1.58268 0.336408i
\(34\) 0.406737 0.913545i 0.406737 0.913545i
\(35\) −0.309017 0.951057i −0.309017 0.951057i
\(36\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(37\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(38\) 0.406737 0.913545i 0.406737 0.913545i
\(39\) −0.251377 0.564602i −0.251377 0.564602i
\(40\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(41\) −0.0646021 0.614648i −0.0646021 0.614648i −0.978148 0.207912i \(-0.933333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(42\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(43\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(44\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(45\) −0.406737 0.913545i −0.406737 0.913545i
\(46\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(47\) −1.20243 1.08268i −1.20243 1.08268i −0.994522 0.104528i \(-0.966667\pi\)
−0.207912 0.978148i \(-0.566667\pi\)
\(48\) 0.104528 0.994522i 0.104528 0.994522i
\(49\) 0 0
\(50\) −0.866025 0.500000i −0.866025 0.500000i
\(51\) −1.00000 −1.00000
\(52\) 0.614648 + 0.0646021i 0.614648 + 0.0646021i
\(53\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(54\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(55\) −1.53884 0.500000i −1.53884 0.500000i
\(56\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(57\) −1.00000 −1.00000
\(58\) 1.08268 + 1.20243i 1.08268 + 1.20243i
\(59\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(60\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(61\) 0.994522 + 0.104528i 0.994522 + 0.104528i 0.587785 0.809017i \(-0.300000\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(62\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(63\) 0.406737 0.913545i 0.406737 0.913545i
\(64\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(65\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i
\(66\) 1.60917 0.169131i 1.60917 0.169131i
\(67\) −0.413545 0.459289i −0.413545 0.459289i 0.500000 0.866025i \(-0.333333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(68\) 0.500000 0.866025i 0.500000 0.866025i
\(69\) 0.743145 0.669131i 0.743145 0.669131i
\(70\) −0.207912 0.978148i −0.207912 0.978148i
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(73\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(74\) 0 0
\(75\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(76\) 0.500000 0.866025i 0.500000 0.866025i
\(77\) −0.658114 1.47815i −0.658114 1.47815i
\(78\) −0.190983 0.587785i −0.190983 0.587785i
\(79\) −1.20243 1.08268i −1.20243 1.08268i −0.994522 0.104528i \(-0.966667\pi\)
−0.207912 0.978148i \(-0.566667\pi\)
\(80\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(81\) 0.309017 0.951057i 0.309017 0.951057i
\(82\) 0.618034i 0.618034i
\(83\) 1.58268 0.336408i 1.58268 0.336408i 0.669131 0.743145i \(-0.266667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(84\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(85\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(86\) −0.406737 0.913545i −0.406737 0.913545i
\(87\) 0.658114 1.47815i 0.658114 1.47815i
\(88\) −0.658114 + 1.47815i −0.658114 + 1.47815i
\(89\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(90\) −0.309017 0.951057i −0.309017 0.951057i
\(91\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(92\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(93\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(94\) −1.08268 1.20243i −1.08268 1.20243i
\(95\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(96\) 0.207912 0.978148i 0.207912 0.978148i
\(97\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(98\) 0 0
\(99\) −0.809017 1.40126i −0.809017 1.40126i
\(100\) −0.809017 0.587785i −0.809017 0.587785i
\(101\) −0.535233 + 0.309017i −0.535233 + 0.309017i −0.743145 0.669131i \(-0.766667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(102\) −0.994522 0.104528i −0.994522 0.104528i
\(103\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(104\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(105\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(106\) 0.604528 0.128496i 0.604528 0.128496i
\(107\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(109\) −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(110\) −1.47815 0.658114i −1.47815 0.658114i
\(111\) 0 0
\(112\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(113\) −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i \(-0.866667\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(114\) −0.994522 0.104528i −0.994522 0.104528i
\(115\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(116\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(117\) −0.459289 + 0.413545i −0.459289 + 0.413545i
\(118\) 0 0
\(119\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(120\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(121\) −1.58268 0.336408i −1.58268 0.336408i
\(122\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(123\) −0.564602 + 0.251377i −0.564602 + 0.251377i
\(124\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(125\) 0.587785 0.809017i 0.587785 0.809017i
\(126\) 0.500000 0.866025i 0.500000 0.866025i
\(127\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(128\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(129\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(130\) −0.128496 + 0.604528i −0.128496 + 0.604528i
\(131\) 1.08268 + 1.20243i 1.08268 + 1.20243i 0.978148 + 0.207912i \(0.0666667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(132\) 1.61803 1.61803
\(133\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(134\) −0.363271 0.500000i −0.363271 0.500000i
\(135\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(136\) 0.587785 0.809017i 0.587785 0.809017i
\(137\) 1.47815 + 0.658114i 1.47815 + 0.658114i 0.978148 0.207912i \(-0.0666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 0.809017 0.587785i 0.809017 0.587785i
\(139\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(140\) −0.104528 0.994522i −0.104528 0.994522i
\(141\) −0.658114 + 1.47815i −0.658114 + 1.47815i
\(142\) 0 0
\(143\) 1.00000i 1.00000i
\(144\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(145\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −0.535233 0.309017i −0.535233 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(150\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(151\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(152\) 0.587785 0.809017i 0.587785 0.809017i
\(153\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(154\) −0.500000 1.53884i −0.500000 1.53884i
\(155\) −0.500000 0.866025i −0.500000 0.866025i
\(156\) −0.128496 0.604528i −0.128496 0.604528i
\(157\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) −1.08268 1.20243i −1.08268 1.20243i
\(159\) −0.363271 0.500000i −0.363271 0.500000i
\(160\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(161\) −0.809017 0.587785i −0.809017 0.587785i
\(162\) 0.406737 0.913545i 0.406737 0.913545i
\(163\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(164\) 0.0646021 0.614648i 0.0646021 0.614648i
\(165\) 1.61803i 1.61803i
\(166\) 1.60917 0.169131i 1.60917 0.169131i
\(167\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(168\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(169\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(170\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(171\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(172\) −0.309017 0.951057i −0.309017 0.951057i
\(173\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(174\) 0.809017 1.40126i 0.809017 1.40126i
\(175\) 0.994522 0.104528i 0.994522 0.104528i
\(176\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(177\) 0 0
\(178\) −0.743145 0.669131i −0.743145 0.669131i
\(179\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(180\) −0.207912 0.978148i −0.207912 0.978148i
\(181\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(182\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(183\) −0.207912 0.978148i −0.207912 0.978148i
\(184\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(185\) 0 0
\(186\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(187\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(188\) −0.951057 1.30902i −0.951057 1.30902i
\(189\) −0.994522 0.104528i −0.994522 0.104528i
\(190\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(191\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(192\) 0.309017 0.951057i 0.309017 0.951057i
\(193\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(194\) 0 0
\(195\) 0.604528 0.128496i 0.604528 0.128496i
\(196\) 0 0
\(197\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(198\) −0.658114 1.47815i −0.658114 1.47815i
\(199\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(200\) −0.743145 0.669131i −0.743145 0.669131i
\(201\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(202\) −0.564602 + 0.251377i −0.564602 + 0.251377i
\(203\) −1.58268 0.336408i −1.58268 0.336408i
\(204\) −0.978148 0.207912i −0.978148 0.207912i
\(205\) 0.614648 + 0.0646021i 0.614648 + 0.0646021i
\(206\) 0 0
\(207\) −0.866025 0.500000i −0.866025 0.500000i
\(208\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(209\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(210\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(211\) 1.47815 0.658114i 1.47815 0.658114i 0.500000 0.866025i \(-0.333333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(212\) 0.614648 0.0646021i 0.614648 0.0646021i
\(213\) 0 0
\(214\) −0.614648 0.0646021i −0.614648 0.0646021i
\(215\) 0.951057 0.309017i 0.951057 0.309017i
\(216\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(217\) 0.309017 0.951057i 0.309017 0.951057i
\(218\) −0.309017 0.535233i −0.309017 0.535233i
\(219\) 0 0
\(220\) −1.40126 0.809017i −1.40126 0.809017i
\(221\) 0.128496 0.604528i 0.128496 0.604528i
\(222\) 0 0
\(223\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(224\) −1.00000 −1.00000
\(225\) 0.978148 0.207912i 0.978148 0.207912i
\(226\) 1.00000i 1.00000i
\(227\) 0.104528 0.994522i 0.104528 0.994522i −0.809017 0.587785i \(-0.800000\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(228\) −0.978148 0.207912i −0.978148 0.207912i
\(229\) −0.128496 + 0.604528i −0.128496 + 0.604528i 0.866025 + 0.500000i \(0.166667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(230\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(231\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(232\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(233\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(234\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(235\) 1.30902 0.951057i 1.30902 0.951057i
\(236\) 0 0
\(237\) −0.658114 + 1.47815i −0.658114 + 1.47815i
\(238\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(239\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(240\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(241\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(242\) −1.53884 0.500000i −1.53884 0.500000i
\(243\) −1.00000 −1.00000
\(244\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(245\) 0 0
\(246\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(247\) 0.128496 0.604528i 0.128496 0.604528i
\(248\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(249\) −0.809017 1.40126i −0.809017 1.40126i
\(250\) 0.669131 0.743145i 0.669131 0.743145i
\(251\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(252\) 0.587785 0.809017i 0.587785 0.809017i
\(253\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(254\) 1.08268 1.20243i 1.08268 1.20243i
\(255\) 0.207912 0.978148i 0.207912 0.978148i
\(256\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(257\) 0.309017 0.535233i 0.309017 0.535233i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(258\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(259\) 0 0
\(260\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(261\) −1.60917 0.169131i −1.60917 0.169131i
\(262\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(263\) −0.406737 + 0.913545i −0.406737 + 0.913545i 0.587785 + 0.809017i \(0.300000\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(264\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(265\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(266\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(267\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(268\) −0.309017 0.535233i −0.309017 0.535233i
\(269\) −0.587785 0.190983i −0.587785 0.190983i 1.00000i \(-0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(270\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(271\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(272\) 0.669131 0.743145i 0.669131 0.743145i
\(273\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(274\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(275\) 0.809017 1.40126i 0.809017 1.40126i
\(276\) 0.866025 0.500000i 0.866025 0.500000i
\(277\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(278\) 0 0
\(279\) 0.207912 0.978148i 0.207912 0.978148i
\(280\) 1.00000i 1.00000i
\(281\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(282\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(283\) −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i \(-0.400000\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(284\) 0 0
\(285\) 0.207912 0.978148i 0.207912 0.978148i
\(286\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(287\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(288\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(289\) 0 0
\(290\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(291\) 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
\(297\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(298\) −0.500000 0.363271i −0.500000 0.363271i
\(299\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(300\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(301\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(302\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(303\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(304\) 0.669131 0.743145i 0.669131 0.743145i
\(305\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(306\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(307\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(308\) −0.336408 1.58268i −0.336408 1.58268i
\(309\) 0 0
\(310\) −0.406737 0.913545i −0.406737 0.913545i
\(311\) −0.406737 0.913545i −0.406737 0.913545i −0.994522 0.104528i \(-0.966667\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(312\) −0.0646021 0.614648i −0.0646021 0.614648i
\(313\) 0.913545 + 0.406737i 0.913545 + 0.406737i 0.809017 0.587785i \(-0.200000\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(314\) 0 0
\(315\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(316\) −0.951057 1.30902i −0.951057 1.30902i
\(317\) −0.207912 0.978148i −0.207912 0.978148i −0.951057 0.309017i \(-0.900000\pi\)
0.743145 0.669131i \(-0.233333\pi\)
\(318\) −0.309017 0.535233i −0.309017 0.535233i
\(319\) −1.94558 + 1.75181i −1.94558 + 1.75181i
\(320\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(321\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(322\) −0.743145 0.669131i −0.743145 0.669131i
\(323\) −0.809017 0.587785i −0.809017 0.587785i
\(324\) 0.500000 0.866025i 0.500000 0.866025i
\(325\) −0.587785 0.190983i −0.587785 0.190983i
\(326\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(327\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(328\) 0.128496 0.604528i 0.128496 0.604528i
\(329\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(330\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(331\) −0.604528 + 0.128496i −0.604528 + 0.128496i −0.500000 0.866025i \(-0.666667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(332\) 1.61803 1.61803
\(333\) 0 0
\(334\) 0 0
\(335\) 0.535233 0.309017i 0.535233 0.309017i
\(336\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(337\) −0.0646021 0.614648i −0.0646021 0.614648i −0.978148 0.207912i \(-0.933333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(338\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(339\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(340\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(341\) −0.951057 1.30902i −0.951057 1.30902i
\(342\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(343\) 1.00000i 1.00000i
\(344\) −0.207912 0.978148i −0.207912 0.978148i
\(345\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(346\) 0 0
\(347\) 0.978148 + 0.207912i 0.978148 + 0.207912i 0.669131 0.743145i \(-0.266667\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(348\) 0.951057 1.30902i 0.951057 1.30902i
\(349\) −1.40126 + 0.809017i −1.40126 + 0.809017i −0.994522 0.104528i \(-0.966667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(350\) 1.00000 1.00000
\(351\) 0.535233 + 0.309017i 0.535233 + 0.309017i
\(352\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(353\) −1.08268 + 1.20243i −1.08268 + 1.20243i −0.104528 + 0.994522i \(0.533333\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.669131 0.743145i −0.669131 0.743145i
\(357\) 0.866025 0.500000i 0.866025 0.500000i
\(358\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(359\) 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i \(0.100000\pi\)
1.00000i \(0.5\pi\)
\(360\) −0.104528 0.994522i −0.104528 0.994522i
\(361\) 0 0
\(362\) 0 0
\(363\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(364\) −0.564602 + 0.251377i −0.564602 + 0.251377i
\(365\) 0 0
\(366\) −0.104528 0.994522i −0.104528 0.994522i
\(367\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(368\) 1.00000i 1.00000i
\(369\) 0.413545 + 0.459289i 0.413545 + 0.459289i
\(370\) 0 0
\(371\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(372\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(373\) −0.658114 1.47815i −0.658114 1.47815i −0.866025 0.500000i \(-0.833333\pi\)
0.207912 0.978148i \(-0.433333\pi\)
\(374\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(375\) −0.951057 0.309017i −0.951057 0.309017i
\(376\) −0.809017 1.40126i −0.809017 1.40126i
\(377\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(378\) −0.978148 0.207912i −0.978148 0.207912i
\(379\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(380\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(381\) −1.53884 0.500000i −1.53884 0.500000i
\(382\) 0 0
\(383\) 1.20243 1.08268i 1.20243 1.08268i 0.207912 0.978148i \(-0.433333\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(384\) 0.406737 0.913545i 0.406737 0.913545i
\(385\) 1.58268 0.336408i 1.58268 0.336408i
\(386\) 0.587785 0.809017i 0.587785 0.809017i
\(387\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(388\) 0 0
\(389\) −0.994522 0.104528i −0.994522 0.104528i −0.406737 0.913545i \(-0.633333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(390\) 0.614648 0.0646021i 0.614648 0.0646021i
\(391\) 0.994522 0.104528i 0.994522 0.104528i
\(392\) 0 0
\(393\) 0.809017 1.40126i 0.809017 1.40126i
\(394\) 0 0
\(395\) 1.30902 0.951057i 1.30902 0.951057i
\(396\) −0.500000 1.53884i −0.500000 1.53884i
\(397\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(398\) 0.0646021 0.614648i 0.0646021 0.614648i
\(399\) 0.866025 0.500000i 0.866025 0.500000i
\(400\) −0.669131 0.743145i −0.669131 0.743145i
\(401\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(402\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(403\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(404\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(405\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(406\) −1.53884 0.500000i −1.53884 0.500000i
\(407\) 0 0
\(408\) −0.951057 0.309017i −0.951057 0.309017i
\(409\) −0.169131 1.60917i −0.169131 1.60917i −0.669131 0.743145i \(-0.733333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(410\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(411\) 0.169131 1.60917i 0.169131 1.60917i
\(412\) 0 0
\(413\) 0 0
\(414\) −0.809017 0.587785i −0.809017 0.587785i
\(415\) 1.61803i 1.61803i
\(416\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(417\) 0 0
\(418\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(419\) −0.413545 0.459289i −0.413545 0.459289i 0.500000 0.866025i \(-0.333333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(420\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(421\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(422\) 1.53884 0.500000i 1.53884 0.500000i
\(423\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(424\) 0.618034 0.618034
\(425\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(426\) 0 0
\(427\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(428\) −0.604528 0.128496i −0.604528 0.128496i
\(429\) 0.951057 0.309017i 0.951057 0.309017i
\(430\) 0.978148 0.207912i 0.978148 0.207912i
\(431\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(432\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(433\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(434\) 0.406737 0.913545i 0.406737 0.913545i
\(435\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(436\) −0.251377 0.564602i −0.251377 0.564602i
\(437\) 0.994522 0.104528i 0.994522 0.104528i
\(438\) 0 0
\(439\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(440\) −1.30902 0.951057i −1.30902 0.951057i
\(441\) 0 0
\(442\) 0.190983 0.587785i 0.190983 0.587785i
\(443\) 0.309017 + 0.535233i 0.309017 + 0.535233i 0.978148 0.207912i \(-0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(444\) 0 0
\(445\) 0.743145 0.669131i 0.743145 0.669131i
\(446\) 0 0
\(447\) −0.128496 + 0.604528i −0.128496 + 0.604528i
\(448\) −0.994522 0.104528i −0.994522 0.104528i
\(449\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) 0.994522 0.104528i 0.994522 0.104528i
\(451\) 1.00000 1.00000
\(452\) 0.104528 0.994522i 0.104528 0.994522i
\(453\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(454\) 0.207912 0.978148i 0.207912 0.978148i
\(455\) −0.251377 0.564602i −0.251377 0.564602i
\(456\) −0.951057 0.309017i −0.951057 0.309017i
\(457\) −0.809017 1.40126i −0.809017 1.40126i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 0.994522i \(-0.466667\pi\)
\(458\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(459\) 0.809017 0.587785i 0.809017 0.587785i
\(460\) −1.00000 −1.00000
\(461\) 1.60917 + 0.169131i 1.60917 + 0.169131i 0.866025 0.500000i \(-0.166667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(462\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(463\) −0.994522 + 0.104528i −0.994522 + 0.104528i −0.587785 0.809017i \(-0.700000\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(464\) 0.658114 + 1.47815i 0.658114 + 1.47815i
\(465\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(466\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(467\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(468\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(469\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(470\) 1.40126 0.809017i 1.40126 0.809017i
\(471\) 0 0
\(472\) 0 0
\(473\) 1.47815 0.658114i 1.47815 0.658114i
\(474\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(475\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(476\) 1.00000i 1.00000i
\(477\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(478\) 0 0
\(479\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(480\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(481\) 0 0
\(482\) 0 0
\(483\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(484\) −1.47815 0.658114i −1.47815 0.658114i
\(485\) 0 0
\(486\) −0.994522 0.104528i −0.994522 0.104528i
\(487\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(488\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(489\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(490\) 0 0
\(491\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(492\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(493\) 1.40126 0.809017i 1.40126 0.809017i
\(494\) 0.190983 0.587785i 0.190983 0.587785i
\(495\) 1.53884 0.500000i 1.53884 0.500000i
\(496\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(497\) 0 0
\(498\) −0.658114 1.47815i −0.658114 1.47815i
\(499\) 0.309017 0.535233i 0.309017 0.535233i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(500\) 0.743145 0.669131i 0.743145 0.669131i
\(501\) 0 0
\(502\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(503\) −1.53884 + 0.500000i −1.53884 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(504\) 0.669131 0.743145i 0.669131 0.743145i
\(505\) −0.190983 0.587785i −0.190983 0.587785i
\(506\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(507\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(508\) 1.20243 1.08268i 1.20243 1.08268i
\(509\) −1.60917 + 0.169131i −1.60917 + 0.169131i −0.866025 0.500000i \(-0.833333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(510\) 0.309017 0.951057i 0.309017 0.951057i
\(511\) 0 0
\(512\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(513\) 0.809017 0.587785i 0.809017 0.587785i
\(514\) 0.363271 0.500000i 0.363271 0.500000i
\(515\) 0 0
\(516\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(517\) 1.94558 1.75181i 1.94558 1.75181i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.251377 + 0.564602i −0.251377 + 0.564602i
\(521\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(522\) −1.58268 0.336408i −1.58268 0.336408i
\(523\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(524\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(525\) −0.406737 0.913545i −0.406737 0.913545i
\(526\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(527\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(528\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(529\) 0 0
\(530\) 0.618034i 0.618034i
\(531\) 0 0
\(532\) 1.00000i 1.00000i
\(533\) −0.0794152 0.373619i −0.0794152 0.373619i
\(534\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(535\) 0.128496 0.604528i 0.128496 0.604528i
\(536\) −0.251377 0.564602i −0.251377 0.564602i
\(537\) 0.809017 0.587785i 0.809017 0.587785i
\(538\) −0.564602 0.251377i −0.564602 0.251377i
\(539\) 0 0
\(540\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(541\) 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i \(0.100000\pi\)
1.00000i \(0.5\pi\)
\(542\) 0.978148 0.207912i 0.978148 0.207912i
\(543\) 0 0
\(544\) 0.743145 0.669131i 0.743145 0.669131i
\(545\) 0.564602 0.251377i 0.564602 0.251377i
\(546\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(547\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(548\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(549\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(550\) 0.951057 1.30902i 0.951057 1.30902i
\(551\) 1.40126 0.809017i 1.40126 0.809017i
\(552\) 0.913545 0.406737i 0.913545 0.406737i
\(553\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(558\) 0.309017 0.951057i 0.309017 0.951057i
\(559\) −0.363271 0.500000i −0.363271 0.500000i
\(560\) 0.104528 0.994522i 0.104528 0.994522i
\(561\) 0.169131 1.60917i 0.169131 1.60917i
\(562\) 0.994522 0.104528i 0.994522 0.104528i
\(563\) −0.0646021 0.614648i −0.0646021 0.614648i −0.978148 0.207912i \(-0.933333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(564\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(565\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(566\) −0.587785 0.809017i −0.587785 0.809017i
\(567\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(568\) 0 0
\(569\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(570\) 0.309017 0.951057i 0.309017 0.951057i
\(571\) 1.58268 + 0.336408i 1.58268 + 0.336408i 0.913545 0.406737i \(-0.133333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(572\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(573\) 0 0
\(574\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(575\) 1.00000i 1.00000i
\(576\) −1.00000 −1.00000
\(577\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(578\) 0 0
\(579\) −0.978148 0.207912i −0.978148 0.207912i
\(580\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(581\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(582\) 0 0
\(583\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(584\) 0 0
\(585\) −0.309017 0.535233i −0.309017 0.535233i
\(586\) 0 0
\(587\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(588\) 0 0
\(589\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(595\) −1.00000 −1.00000
\(596\) −0.459289 0.413545i −0.459289 0.413545i
\(597\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(598\) 0.251377 + 0.564602i 0.251377 + 0.564602i
\(599\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(600\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(601\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(602\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(603\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(604\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(605\) 0.658114 1.47815i 0.658114 1.47815i
\(606\) 0.413545 + 0.459289i 0.413545 + 0.459289i
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 0.743145 0.669131i 0.743145 0.669131i
\(609\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(610\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(611\) −0.809017 0.587785i −0.809017 0.587785i
\(612\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(613\) −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(614\) −0.614648 0.0646021i −0.614648 0.0646021i
\(615\) −0.128496 0.604528i −0.128496 0.604528i
\(616\) −0.169131 1.60917i −0.169131 1.60917i
\(617\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(618\) 0 0
\(619\) 0.604528 0.128496i 0.604528 0.128496i 0.104528 0.994522i \(-0.466667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) −0.309017 0.951057i −0.309017 0.951057i
\(621\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(622\) −0.309017 0.951057i −0.309017 0.951057i
\(623\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(624\) 0.618034i 0.618034i
\(625\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(626\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(627\) 0.169131 1.60917i 0.169131 1.60917i
\(628\) 0 0
\(629\) 0 0
\(630\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(631\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(632\) −0.809017 1.40126i −0.809017 1.40126i
\(633\) −1.08268 1.20243i −1.08268 1.20243i
\(634\) −0.104528 0.994522i −0.104528 0.994522i
\(635\) 1.08268 + 1.20243i 1.08268 + 1.20243i
\(636\) −0.251377 0.564602i −0.251377 0.564602i
\(637\) 0 0
\(638\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(639\) 0 0
\(640\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(641\) −1.47815 0.658114i −1.47815 0.658114i −0.500000 0.866025i \(-0.666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(642\) 0.128496 + 0.604528i 0.128496 + 0.604528i
\(643\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(644\) −0.669131 0.743145i −0.669131 0.743145i
\(645\) −0.587785 0.809017i −0.587785 0.809017i
\(646\) −0.743145 0.669131i −0.743145 0.669131i
\(647\) −0.951057 + 0.309017i −0.951057 + 0.309017i −0.743145 0.669131i \(-0.766667\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(648\) 0.587785 0.809017i 0.587785 0.809017i
\(649\) 0 0
\(650\) −0.564602 0.251377i −0.564602 0.251377i
\(651\) −1.00000 −1.00000
\(652\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(653\) −0.336408 + 1.58268i −0.336408 + 1.58268i 0.406737 + 0.913545i \(0.366667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(654\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(655\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(656\) 0.190983 0.587785i 0.190983 0.587785i
\(657\) 0 0
\(658\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(659\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(660\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(661\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(662\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(663\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(664\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(665\) −1.00000 −1.00000
\(666\) 0 0
\(667\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(668\) 0 0
\(669\) 0 0
\(670\) 0.564602 0.251377i 0.564602 0.251377i
\(671\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(672\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(673\) −0.104528 + 0.994522i −0.104528 + 0.994522i 0.809017 + 0.587785i \(0.200000\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(674\) 0.618034i 0.618034i
\(675\) −0.500000 0.866025i −0.500000 0.866025i
\(676\) −0.618034 −0.618034
\(677\) −0.994522 0.104528i −0.994522 0.104528i −0.406737 0.913545i \(-0.633333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(678\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(679\) 0 0
\(680\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(681\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(682\) −0.809017 1.40126i −0.809017 1.40126i
\(683\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(684\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(685\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(686\) 0.104528 0.994522i 0.104528 0.994522i
\(687\) 0.614648 0.0646021i 0.614648 0.0646021i
\(688\) −0.104528 0.994522i −0.104528 0.994522i
\(689\) 0.348943 0.155360i 0.348943 0.155360i
\(690\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(691\) −0.564602 0.251377i −0.564602 0.251377i 0.104528 0.994522i \(-0.466667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(692\) 0 0
\(693\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(694\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(695\) 0 0
\(696\) 1.08268 1.20243i 1.08268 1.20243i
\(697\) −0.604528 0.128496i −0.604528 0.128496i
\(698\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(699\) 1.00000 1.00000
\(700\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(703\) 0 0
\(704\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(705\) −1.30902 0.951057i −1.30902 0.951057i
\(706\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(707\) 0.309017 0.535233i 0.309017 0.535233i
\(708\) 0 0
\(709\) 0.406737 0.913545i 0.406737 0.913545i −0.587785 0.809017i \(-0.700000\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(710\) 0 0
\(711\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(712\) −0.587785 0.809017i −0.587785 0.809017i
\(713\) −0.913545 0.406737i −0.913545 0.406737i
\(714\) 0.913545 0.406737i 0.913545 0.406737i
\(715\) −0.978148 0.207912i −0.978148 0.207912i
\(716\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(717\) 0 0
\(718\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(719\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(720\) 1.00000i 1.00000i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.658114 1.47815i −0.658114 1.47815i
\(726\) 1.61803i 1.61803i
\(727\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(728\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(729\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(730\) 0 0
\(731\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(732\) 1.00000i 1.00000i
\(733\) −0.459289 + 0.413545i −0.459289 + 0.413545i −0.866025 0.500000i \(-0.833333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(737\) 0.809017 0.587785i 0.809017 0.587785i
\(738\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(739\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(742\) −0.459289 + 0.413545i −0.459289 + 0.413545i
\(743\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(745\) 0.413545 0.459289i 0.413545 0.459289i
\(746\) −0.500000 1.53884i −0.500000 1.53884i
\(747\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(748\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(749\) 0.535233 0.309017i 0.535233 0.309017i
\(750\) −0.913545 0.406737i −0.913545 0.406737i
\(751\) 0.535233 + 0.309017i 0.535233 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(752\) −0.658114 1.47815i −0.658114 1.47815i
\(753\) −0.500000 1.53884i −0.500000 1.53884i
\(754\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(755\) −0.309017 0.951057i −0.309017 0.951057i
\(756\) −0.951057 0.309017i −0.951057 0.309017i
\(757\) 1.61803i 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(758\) 0 0
\(759\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(760\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(761\) −1.47815 + 0.658114i −1.47815 + 0.658114i −0.978148 0.207912i \(-0.933333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) −1.47815 0.658114i −1.47815 0.658114i
\(763\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(764\) 0 0
\(765\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(766\) 1.30902 0.951057i 1.30902 0.951057i
\(767\) 0 0
\(768\) 0.500000 0.866025i 0.500000 0.866025i
\(769\) 0 0 0.743145 0.669131i \(-0.233333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(770\) 1.60917 0.169131i 1.60917 0.169131i
\(771\) −0.604528 0.128496i −0.604528 0.128496i
\(772\) 0.669131 0.743145i 0.669131 0.743145i
\(773\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(774\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(775\) 0.951057 0.309017i 0.951057 0.309017i
\(776\) 0 0
\(777\) 0 0
\(778\) −0.978148 0.207912i −0.978148 0.207912i
\(779\) −0.604528 0.128496i −0.604528 0.128496i
\(780\) 0.618034 0.618034
\(781\) 0 0
\(782\) 1.00000 1.00000
\(783\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(784\) 0 0
\(785\) 0 0
\(786\) 0.951057 1.30902i 0.951057 1.30902i
\(787\) 0.104528 + 0.994522i 0.104528 + 0.994522i 0.913545 + 0.406737i \(0.133333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(788\) 0 0
\(789\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(790\) 1.40126 0.809017i 1.40126 0.809017i
\(791\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(792\) −0.336408 1.58268i −0.336408 1.58268i
\(793\) 0.618034 0.618034
\(794\) 0.604528 0.128496i 0.604528 0.128496i
\(795\) 0.564602 0.251377i 0.564602 0.251377i
\(796\) 0.128496 0.604528i 0.128496 0.604528i
\(797\) −0.207912 + 0.978148i −0.207912 + 0.978148i 0.743145 + 0.669131i \(0.233333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(798\) 0.913545 0.406737i 0.913545 0.406737i
\(799\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(800\) −0.587785 0.809017i −0.587785 0.809017i
\(801\) 1.00000 1.00000
\(802\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(803\) 0 0
\(804\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(805\) 0.743145 0.669131i 0.743145 0.669131i
\(806\) −0.459289 + 0.413545i −0.459289 + 0.413545i
\(807\) 0.618034i 0.618034i
\(808\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(809\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(810\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(811\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(812\) −1.47815 0.658114i −1.47815 0.658114i
\(813\) −0.587785 0.809017i −0.587785 0.809017i
\(814\) 0 0
\(815\) −0.406737 0.913545i −0.406737 0.913545i
\(816\) −0.913545 0.406737i −0.913545 0.406737i
\(817\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(818\) 1.61803i 1.61803i
\(819\) 0.190983 0.587785i 0.190983 0.587785i
\(820\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(821\) −1.20243 1.08268i −1.20243 1.08268i −0.994522 0.104528i \(-0.966667\pi\)
−0.207912 0.978148i \(-0.566667\pi\)
\(822\) 0.336408 1.58268i 0.336408 1.58268i
\(823\) −0.251377 0.564602i −0.251377 0.564602i 0.743145 0.669131i \(-0.233333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(824\) 0 0
\(825\) −1.58268 0.336408i −1.58268 0.336408i
\(826\) 0 0
\(827\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(828\) −0.743145 0.669131i −0.743145 0.669131i
\(829\) −1.53884 + 0.500000i −1.53884 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(830\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(831\) 0 0
\(832\) 0.535233 + 0.309017i 0.535233 + 0.309017i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(837\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(838\) −0.363271 0.500000i −0.363271 0.500000i
\(839\) −0.994522 0.104528i −0.994522 0.104528i −0.406737 0.913545i \(-0.633333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(840\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(841\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(842\) 0 0
\(843\) −0.500000 0.866025i −0.500000 0.866025i
\(844\) 1.58268 0.336408i 1.58268 0.336408i
\(845\) 0.618034i 0.618034i
\(846\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(847\) 1.53884 0.500000i 1.53884 0.500000i
\(848\) 0.614648 + 0.0646021i 0.614648 + 0.0646021i
\(849\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(850\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(851\) 0 0
\(852\) 0 0
\(853\) 0.743145 + 0.669131i 0.743145 + 0.669131i 0.951057 0.309017i \(-0.100000\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(854\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(855\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(856\) −0.587785 0.190983i −0.587785 0.190983i
\(857\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(858\) 0.978148 0.207912i 0.978148 0.207912i
\(859\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(860\) 0.994522 0.104528i 0.994522 0.104528i
\(861\) 0.363271 0.500000i 0.363271 0.500000i
\(862\) −1.47815 0.658114i −1.47815 0.658114i
\(863\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(864\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(865\) 0 0
\(866\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(867\) 0 0
\(868\) 0.500000 0.866025i 0.500000 0.866025i
\(869\) 1.94558 1.75181i 1.94558 1.75181i
\(870\) 1.20243 + 1.08268i 1.20243 + 1.08268i
\(871\) −0.283856 0.255585i −0.283856 0.255585i
\(872\) −0.190983 0.587785i −0.190983 0.587785i
\(873\) 0 0
\(874\) 1.00000 1.00000
\(875\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(876\) 0 0
\(877\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −1.20243 1.08268i −1.20243 1.08268i
\(881\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(882\) 0 0
\(883\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(884\) 0.251377 0.564602i 0.251377 0.564602i
\(885\) 0 0
\(886\) 0.251377 + 0.564602i 0.251377 + 0.564602i
\(887\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(888\) 0 0
\(889\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(890\) 0.809017 0.587785i 0.809017 0.587785i
\(891\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(892\) 0 0
\(893\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(894\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(895\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(896\) −0.978148 0.207912i −0.978148 0.207912i
\(897\) 0.413545 0.459289i 0.413545 0.459289i
\(898\) −0.614648 0.0646021i −0.614648 0.0646021i
\(899\) −1.61803 −1.61803
\(900\) 1.00000 1.00000
\(901\) 0.618034i 0.618034i
\(902\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(903\) 0.207912 0.978148i 0.207912 0.978148i
\(904\) 0.207912 0.978148i 0.207912 0.978148i
\(905\) 0 0
\(906\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(907\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(908\) 0.309017 0.951057i 0.309017 0.951057i
\(909\) 0.251377 0.564602i 0.251377 0.564602i
\(910\) −0.190983 0.587785i −0.190983 0.587785i
\(911\) −0.994522 0.104528i −0.994522 0.104528i −0.406737 0.913545i \(-0.633333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(912\) −0.913545 0.406737i −0.913545 0.406737i
\(913\) 0.273659 + 2.60369i 0.273659 + 2.60369i
\(914\) −0.658114 1.47815i −0.658114 1.47815i
\(915\) 1.00000 1.00000
\(916\) −0.251377 + 0.564602i −0.251377 + 0.564602i
\(917\) −1.53884 0.500000i −1.53884 0.500000i
\(918\) 0.866025 0.500000i 0.866025 0.500000i
\(919\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(920\) −0.994522 0.104528i −0.994522 0.104528i
\(921\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(922\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(923\) 0 0
\(924\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(925\) 0 0
\(926\) −1.00000 −1.00000
\(927\) 0 0
\(928\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(929\) −0.413545 + 0.459289i −0.413545 + 0.459289i −0.913545 0.406737i \(-0.866667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(930\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(931\) 0 0
\(932\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(933\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(934\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(935\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(936\) −0.564602 + 0.251377i −0.564602 + 0.251377i
\(937\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(938\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(939\) 0.104528 0.994522i 0.104528 0.994522i
\(940\) 1.47815 0.658114i 1.47815 0.658114i
\(941\) 1.60917 0.169131i 1.60917 0.169131i 0.743145 0.669131i \(-0.233333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(942\) 0 0
\(943\) 0.535233 0.309017i 0.535233 0.309017i
\(944\) 0 0
\(945\) 0.309017 0.951057i 0.309017 0.951057i
\(946\) 1.53884 0.500000i 1.53884 0.500000i
\(947\) −0.669131 + 0.743145i −0.669131 + 0.743145i −0.978148 0.207912i \(-0.933333\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(948\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(949\) 0 0
\(950\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(951\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(952\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(953\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(954\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(955\) 0 0
\(956\) 0 0
\(957\) 2.26728 + 1.30902i 2.26728 + 1.30902i
\(958\) 0 0
\(959\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(960\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(961\) 0 0
\(962\) 0 0
\(963\) 0.500000 0.363271i 0.500000 0.363271i
\(964\) 0 0
\(965\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(966\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(967\) −0.743145 + 0.669131i −0.743145 + 0.669131i −0.951057 0.309017i \(-0.900000\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(968\) −1.40126 0.809017i −1.40126 0.809017i
\(969\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(970\) 0 0
\(971\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(972\) −0.978148 0.207912i −0.978148 0.207912i
\(973\) 0 0
\(974\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(975\) 0.618034i 0.618034i
\(976\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(977\) −1.47815 + 0.658114i −1.47815 + 0.658114i −0.978148 0.207912i \(-0.933333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(979\) 1.08268 1.20243i 1.08268 1.20243i
\(980\) 0 0
\(981\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(982\) 0 0
\(983\) −0.128496 0.604528i −0.128496 0.604528i −0.994522 0.104528i \(-0.966667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(984\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(985\) 0 0
\(986\) 1.47815 0.658114i 1.47815 0.658114i
\(987\) −0.169131 1.60917i −0.169131 1.60917i
\(988\) 0.251377 0.564602i 0.251377 0.564602i
\(989\) 0.587785 0.809017i 0.587785 0.809017i
\(990\) 1.58268 0.336408i 1.58268 0.336408i
\(991\) 0.363271 + 0.500000i 0.363271 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(992\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(993\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(994\) 0 0
\(995\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(996\) −0.500000 1.53884i −0.500000 1.53884i
\(997\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(998\) 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 1800.1.dg.a.1291.2 yes 16
8.3 odd 2 inner 1800.1.dg.a.1291.1 yes 16
9.7 even 3 inner 1800.1.dg.a.691.1 yes 16
25.11 even 5 inner 1800.1.dg.a.211.2 yes 16
72.43 odd 6 inner 1800.1.dg.a.691.2 yes 16
200.11 odd 10 inner 1800.1.dg.a.211.1 16
225.61 even 15 inner 1800.1.dg.a.1411.1 yes 16
1800.1411 odd 30 inner 1800.1.dg.a.1411.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1800.1.dg.a.211.1 16 200.11 odd 10 inner
1800.1.dg.a.211.2 yes 16 25.11 even 5 inner
1800.1.dg.a.691.1 yes 16 9.7 even 3 inner
1800.1.dg.a.691.2 yes 16 72.43 odd 6 inner
1800.1.dg.a.1291.1 yes 16 8.3 odd 2 inner
1800.1.dg.a.1291.2 yes 16 1.1 even 1 trivial
1800.1.dg.a.1411.1 yes 16 225.61 even 15 inner
1800.1.dg.a.1411.2 yes 16 1800.1411 odd 30 inner