Properties

Label 975.1.cj.a.146.2
Level $975$
Weight $1$
Character 975.146
Analytic conductor $0.487$
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] = [975,1,Mod(146,975)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(975, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 18, 10]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("975.146");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 975.cj (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: \(0.486588387317\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(A_{5}\)
Projective field: Galois closure of 5.1.594140625.2

Embedding invariants

Embedding label 146.2
Root \(0.207912 - 0.978148i\) of defining polynomial
Character \(\chi\) \(=\) 975.146
Dual form 975.1.cj.a.581.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.336408 + 1.58268i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-1.47815 + 0.658114i) q^{4} +(0.951057 + 0.309017i) q^{5} +(0.169131 + 1.60917i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\) \(q+(0.336408 + 1.58268i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-1.47815 + 0.658114i) q^{4} +(0.951057 + 0.309017i) q^{5} +(0.169131 + 1.60917i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(-0.169131 + 1.60917i) q^{10} +(-0.336408 - 1.58268i) q^{11} +(-1.53884 + 0.500000i) q^{12} +(-0.309017 - 0.951057i) q^{13} +(-1.53884 - 0.500000i) q^{14} +(0.913545 + 0.406737i) q^{15} +(-0.994522 + 0.104528i) q^{17} +1.61803i q^{18} +(-0.104528 - 0.994522i) q^{19} +(-1.60917 + 0.169131i) q^{20} +(-0.587785 + 0.809017i) q^{21} +(2.39169 - 1.06485i) q^{22} +(-0.207912 - 0.978148i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.809017 + 0.587785i) q^{25} +(1.40126 - 0.809017i) q^{26} +(0.951057 + 0.309017i) q^{27} +(0.169131 - 1.60917i) q^{28} +(-0.336408 + 1.58268i) q^{30} +(-0.866025 - 0.500000i) q^{32} +(-0.169131 - 1.60917i) q^{33} +(-0.500000 - 1.53884i) q^{34} +(-0.743145 + 0.669131i) q^{35} +(-1.58268 + 0.336408i) q^{36} +(-0.669131 + 0.743145i) q^{37} +(1.53884 - 0.500000i) q^{38} +(-0.207912 - 0.978148i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(-0.743145 - 0.669131i) q^{41} +(-1.47815 - 0.658114i) q^{42} +(-0.309017 + 0.535233i) q^{43} +(1.53884 + 2.11803i) q^{44} +(0.866025 + 0.500000i) q^{45} +(1.47815 - 0.658114i) q^{46} +(-0.363271 + 0.500000i) q^{47} +(-0.658114 + 1.47815i) q^{50} -1.00000 q^{51} +(1.08268 + 1.20243i) q^{52} +(-0.951057 + 1.30902i) q^{53} +(-0.169131 + 1.60917i) q^{54} +(0.169131 - 1.60917i) q^{55} +(0.994522 - 0.104528i) q^{56} -1.00000i q^{57} +(0.207912 - 0.978148i) q^{59} -1.61803 q^{60} +(0.669131 + 0.743145i) q^{61} +(-0.669131 + 0.743145i) q^{63} +(0.500000 - 1.53884i) q^{64} -1.00000i q^{65} +(2.48990 - 0.809017i) q^{66} +(0.564602 + 0.251377i) q^{67} +(1.40126 - 0.809017i) q^{68} +(-0.104528 - 0.994522i) q^{69} +(-1.30902 - 0.951057i) q^{70} +(-0.406737 - 0.913545i) q^{72} +(-0.309017 + 0.951057i) q^{73} +(-1.40126 - 0.809017i) q^{74} +(0.743145 + 0.669131i) q^{75} +(0.809017 + 1.40126i) q^{76} +(1.53884 + 0.500000i) q^{77} +(1.47815 - 0.658114i) q^{78} +(0.913545 + 0.406737i) q^{81} +(0.809017 - 1.40126i) q^{82} +(-0.587785 - 0.809017i) q^{83} +(0.336408 - 1.58268i) q^{84} +(-0.978148 - 0.207912i) q^{85} +(-0.951057 - 0.309017i) q^{86} +(-1.08268 + 1.20243i) q^{88} +(0.207912 + 0.978148i) q^{89} +(-0.500000 + 1.53884i) q^{90} +(0.978148 + 0.207912i) q^{91} +(0.951057 + 1.30902i) q^{92} +(-0.913545 - 0.406737i) q^{94} +(0.207912 - 0.978148i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-0.564602 + 0.251377i) q^{97} -1.61803i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{4} - 6 q^{6} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{4} - 6 q^{6} - 8 q^{7} - 2 q^{9} + 6 q^{10} + 4 q^{13} + 2 q^{15} + 2 q^{19} + 8 q^{22} - 8 q^{24} + 4 q^{25} - 6 q^{28} + 6 q^{33} - 8 q^{34} - 4 q^{36} - 2 q^{37} + 4 q^{40} - 6 q^{42} + 4 q^{43} + 6 q^{46} - 16 q^{51} - 4 q^{52} + 6 q^{54} - 6 q^{55} - 8 q^{60} + 2 q^{61} - 2 q^{63} + 8 q^{64} + 4 q^{67} + 2 q^{69} - 12 q^{70} + 4 q^{73} + 4 q^{76} + 6 q^{78} + 2 q^{81} + 4 q^{82} + 2 q^{85} + 4 q^{88} - 8 q^{90} - 2 q^{91} - 2 q^{94} - 4 q^{96} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.336408 + 1.58268i 0.336408 + 1.58268i 0.743145 + 0.669131i \(0.233333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(3\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(4\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(5\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(6\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(7\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(8\) −0.587785 0.809017i −0.587785 0.809017i
\(9\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(10\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(11\) −0.336408 1.58268i −0.336408 1.58268i −0.743145 0.669131i \(-0.766667\pi\)
0.406737 0.913545i \(-0.366667\pi\)
\(12\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(13\) −0.309017 0.951057i −0.309017 0.951057i
\(14\) −1.53884 0.500000i −1.53884 0.500000i
\(15\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(16\) 0 0
\(17\) −0.994522 + 0.104528i −0.994522 + 0.104528i −0.587785 0.809017i \(-0.700000\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(18\) 1.61803i 1.61803i
\(19\) −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i \(-0.866667\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(20\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(21\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(22\) 2.39169 1.06485i 2.39169 1.06485i
\(23\) −0.207912 0.978148i −0.207912 0.978148i −0.951057 0.309017i \(-0.900000\pi\)
0.743145 0.669131i \(-0.233333\pi\)
\(24\) −0.500000 0.866025i −0.500000 0.866025i
\(25\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(26\) 1.40126 0.809017i 1.40126 0.809017i
\(27\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(28\) 0.169131 1.60917i 0.169131 1.60917i
\(29\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(30\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(31\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(32\) −0.866025 0.500000i −0.866025 0.500000i
\(33\) −0.169131 1.60917i −0.169131 1.60917i
\(34\) −0.500000 1.53884i −0.500000 1.53884i
\(35\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(36\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(37\) −0.669131 + 0.743145i −0.669131 + 0.743145i −0.978148 0.207912i \(-0.933333\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 1.53884 0.500000i 1.53884 0.500000i
\(39\) −0.207912 0.978148i −0.207912 0.978148i
\(40\) −0.309017 0.951057i −0.309017 0.951057i
\(41\) −0.743145 0.669131i −0.743145 0.669131i 0.207912 0.978148i \(-0.433333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(42\) −1.47815 0.658114i −1.47815 0.658114i
\(43\) −0.309017 + 0.535233i −0.309017 + 0.535233i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(44\) 1.53884 + 2.11803i 1.53884 + 2.11803i
\(45\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(46\) 1.47815 0.658114i 1.47815 0.658114i
\(47\) −0.363271 + 0.500000i −0.363271 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.658114 + 1.47815i −0.658114 + 1.47815i
\(51\) −1.00000 −1.00000
\(52\) 1.08268 + 1.20243i 1.08268 + 1.20243i
\(53\) −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i \(0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(54\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(55\) 0.169131 1.60917i 0.169131 1.60917i
\(56\) 0.994522 0.104528i 0.994522 0.104528i
\(57\) 1.00000i 1.00000i
\(58\) 0 0
\(59\) 0.207912 0.978148i 0.207912 0.978148i −0.743145 0.669131i \(-0.766667\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(60\) −1.61803 −1.61803
\(61\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(62\) 0 0
\(63\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(64\) 0.500000 1.53884i 0.500000 1.53884i
\(65\) 1.00000i 1.00000i
\(66\) 2.48990 0.809017i 2.48990 0.809017i
\(67\) 0.564602 + 0.251377i 0.564602 + 0.251377i 0.669131 0.743145i \(-0.266667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(68\) 1.40126 0.809017i 1.40126 0.809017i
\(69\) −0.104528 0.994522i −0.104528 0.994522i
\(70\) −1.30902 0.951057i −1.30902 0.951057i
\(71\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(72\) −0.406737 0.913545i −0.406737 0.913545i
\(73\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(74\) −1.40126 0.809017i −1.40126 0.809017i
\(75\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(76\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(77\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(78\) 1.47815 0.658114i 1.47815 0.658114i
\(79\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(80\) 0 0
\(81\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(82\) 0.809017 1.40126i 0.809017 1.40126i
\(83\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(84\) 0.336408 1.58268i 0.336408 1.58268i
\(85\) −0.978148 0.207912i −0.978148 0.207912i
\(86\) −0.951057 0.309017i −0.951057 0.309017i
\(87\) 0 0
\(88\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(89\) 0.207912 + 0.978148i 0.207912 + 0.978148i 0.951057 + 0.309017i \(0.100000\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(90\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(91\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(92\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(93\) 0 0
\(94\) −0.913545 0.406737i −0.913545 0.406737i
\(95\) 0.207912 0.978148i 0.207912 0.978148i
\(96\) −0.809017 0.587785i −0.809017 0.587785i
\(97\) −0.564602 + 0.251377i −0.564602 + 0.251377i −0.669131 0.743145i \(-0.733333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(98\) 0 0
\(99\) 1.61803i 1.61803i
\(100\) −1.58268 0.336408i −1.58268 0.336408i
\(101\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) −0.336408 1.58268i −0.336408 1.58268i
\(103\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(104\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(105\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(106\) −2.39169 1.06485i −2.39169 1.06485i
\(107\) 1.40126 0.809017i 1.40126 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(108\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(109\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(110\) 2.60369 0.273659i 2.60369 0.273659i
\(111\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(112\) 0 0
\(113\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(114\) 1.58268 0.336408i 1.58268 0.336408i
\(115\) 0.104528 0.994522i 0.104528 0.994522i
\(116\) 0 0
\(117\) −0.104528 0.994522i −0.104528 0.994522i
\(118\) 1.61803 1.61803
\(119\) 0.406737 0.913545i 0.406737 0.913545i
\(120\) −0.207912 0.978148i −0.207912 0.978148i
\(121\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(122\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(123\) −0.669131 0.743145i −0.669131 0.743145i
\(124\) 0 0
\(125\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(126\) −1.40126 0.809017i −1.40126 0.809017i
\(127\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(128\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(129\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(130\) 1.58268 0.336408i 1.58268 0.336408i
\(131\) −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(132\) 1.30902 + 2.26728i 1.30902 + 2.26728i
\(133\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(134\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(135\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(136\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(137\) 0.207912 0.978148i 0.207912 0.978148i −0.743145 0.669131i \(-0.766667\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(138\) 1.53884 0.500000i 1.53884 0.500000i
\(139\) 0.413545 + 0.459289i 0.413545 + 0.459289i 0.913545 0.406737i \(-0.133333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0.658114 1.47815i 0.658114 1.47815i
\(141\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(142\) 0 0
\(143\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(144\) 0 0
\(145\) 0 0
\(146\) −1.60917 0.169131i −1.60917 0.169131i
\(147\) 0 0
\(148\) 0.500000 1.53884i 0.500000 1.53884i
\(149\) 0.535233 + 0.309017i 0.535233 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(150\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(151\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(152\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(153\) −0.994522 0.104528i −0.994522 0.104528i
\(154\) −0.273659 + 2.60369i −0.273659 + 2.60369i
\(155\) 0 0
\(156\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(160\) −0.669131 0.743145i −0.669131 0.743145i
\(161\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(162\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(163\) 0.978148 + 0.207912i 0.978148 + 0.207912i 0.669131 0.743145i \(-0.266667\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(164\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(165\) 0.336408 1.58268i 0.336408 1.58268i
\(166\) 1.08268 1.20243i 1.08268 1.20243i
\(167\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(168\) 1.00000 1.00000
\(169\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(170\) 1.61803i 1.61803i
\(171\) 0.104528 0.994522i 0.104528 0.994522i
\(172\) 0.104528 0.994522i 0.104528 0.994522i
\(173\) 0.459289 0.413545i 0.459289 0.413545i −0.406737 0.913545i \(-0.633333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(176\) 0 0
\(177\) 0.309017 0.951057i 0.309017 0.951057i
\(178\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(179\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(180\) −1.60917 0.169131i −1.60917 0.169131i
\(181\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(182\) 1.61803i 1.61803i
\(183\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(184\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(185\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(186\) 0 0
\(187\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(188\) 0.207912 0.978148i 0.207912 0.978148i
\(189\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(190\) 1.61803 1.61803
\(191\) −0.336408 + 1.58268i −0.336408 + 1.58268i 0.406737 + 0.913545i \(0.366667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(192\) 0.658114 1.47815i 0.658114 1.47815i
\(193\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) −0.587785 0.809017i −0.587785 0.809017i
\(195\) 0.104528 0.994522i 0.104528 0.994522i
\(196\) 0 0
\(197\) 0.614648 + 0.0646021i 0.614648 + 0.0646021i 0.406737 0.913545i \(-0.366667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(198\) 2.56082 0.544320i 2.56082 0.544320i
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 1.00000i 1.00000i
\(201\) 0.535233 + 0.309017i 0.535233 + 0.309017i
\(202\) 0 0
\(203\) 0 0
\(204\) 1.47815 0.658114i 1.47815 0.658114i
\(205\) −0.500000 0.866025i −0.500000 0.866025i
\(206\) −1.06485 + 2.39169i −1.06485 + 2.39169i
\(207\) 1.00000i 1.00000i
\(208\) 0 0
\(209\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(210\) −1.20243 1.08268i −1.20243 1.08268i
\(211\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(212\) 0.544320 2.56082i 0.544320 2.56082i
\(213\) 0 0
\(214\) 1.75181 + 1.94558i 1.75181 + 1.94558i
\(215\) −0.459289 + 0.413545i −0.459289 + 0.413545i
\(216\) −0.309017 0.951057i −0.309017 0.951057i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(220\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(221\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(222\) −1.30902 0.951057i −1.30902 0.951057i
\(223\) −0.604528 + 0.128496i −0.604528 + 0.128496i −0.500000 0.866025i \(-0.666667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(224\) 0.866025 0.500000i 0.866025 0.500000i
\(225\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(226\) 0 0
\(227\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(228\) 0.658114 + 1.47815i 0.658114 + 1.47815i
\(229\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(230\) 1.60917 0.169131i 1.60917 0.169131i
\(231\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(232\) 0 0
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 1.53884 0.500000i 1.53884 0.500000i
\(235\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(236\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(237\) 0 0
\(238\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(239\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(240\) 0 0
\(241\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(242\) −1.53884 2.11803i −1.53884 2.11803i
\(243\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(244\) −1.47815 0.658114i −1.47815 0.658114i
\(245\) 0 0
\(246\) 0.951057 1.30902i 0.951057 1.30902i
\(247\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(248\) 0 0
\(249\) −0.500000 0.866025i −0.500000 0.866025i
\(250\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(251\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(252\) 0.500000 1.53884i 0.500000 1.53884i
\(253\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(254\) 0.658114 + 1.47815i 0.658114 + 1.47815i
\(255\) −0.951057 0.309017i −0.951057 0.309017i
\(256\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) −0.913545 0.406737i −0.913545 0.406737i
\(259\) −0.309017 0.951057i −0.309017 0.951057i
\(260\) 0.658114 + 1.47815i 0.658114 + 1.47815i
\(261\) 0 0
\(262\) 0.669131 0.743145i 0.669131 0.743145i
\(263\) −0.459289 0.413545i −0.459289 0.413545i 0.406737 0.913545i \(-0.366667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(265\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(266\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(267\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(268\) −1.00000 −1.00000
\(269\) 0.994522 0.104528i 0.994522 0.104528i 0.406737 0.913545i \(-0.366667\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(270\) −0.658114 + 1.47815i −0.658114 + 1.47815i
\(271\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(272\) 0 0
\(273\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(274\) 1.61803 1.61803
\(275\) 0.658114 1.47815i 0.658114 1.47815i
\(276\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(277\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(278\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(279\) 0 0
\(280\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(281\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(282\) −0.866025 0.500000i −0.866025 0.500000i
\(283\) −1.47815 0.658114i −1.47815 0.658114i −0.500000 0.866025i \(-0.666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(284\) 0 0
\(285\) 0.309017 0.951057i 0.309017 0.951057i
\(286\) −1.75181 1.94558i −1.75181 1.94558i
\(287\) 0.951057 0.309017i 0.951057 0.309017i
\(288\) −0.743145 0.669131i −0.743145 0.669131i
\(289\) 0 0
\(290\) 0 0
\(291\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(292\) −0.169131 1.60917i −0.169131 1.60917i
\(293\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 0.500000 0.866025i 0.500000 0.866025i
\(296\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(297\) 0.169131 1.60917i 0.169131 1.60917i
\(298\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(299\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(300\) −1.53884 0.500000i −1.53884 0.500000i
\(301\) −0.309017 0.535233i −0.309017 0.535233i
\(302\) −0.544320 2.56082i −0.544320 2.56082i
\(303\) 0 0
\(304\) 0 0
\(305\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(306\) −0.169131 1.60917i −0.169131 1.60917i
\(307\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(308\) −2.60369 + 0.273659i −2.60369 + 0.273659i
\(309\) 1.20243 + 1.08268i 1.20243 + 1.08268i
\(310\) 0 0
\(311\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(312\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(313\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(314\) 0 0
\(315\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(316\) 0 0
\(317\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) −2.26728 1.30902i −2.26728 1.30902i
\(319\) 0 0
\(320\) 0.951057 1.30902i 0.951057 1.30902i
\(321\) 1.47815 0.658114i 1.47815 0.658114i
\(322\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(323\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(324\) −1.61803 −1.61803
\(325\) 0.309017 0.951057i 0.309017 0.951057i
\(326\) 1.61803i 1.61803i
\(327\) 0 0
\(328\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(329\) −0.251377 0.564602i −0.251377 0.564602i
\(330\) 2.61803 2.61803
\(331\) −0.169131 1.60917i −0.169131 1.60917i −0.669131 0.743145i \(-0.733333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(332\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(333\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(334\) 0 0
\(335\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(336\) 0 0
\(337\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(338\) −1.20243 1.08268i −1.20243 1.08268i
\(339\) 0 0
\(340\) 1.58268 0.336408i 1.58268 0.336408i
\(341\) 0 0
\(342\) 1.60917 0.169131i 1.60917 0.169131i
\(343\) −1.00000 −1.00000
\(344\) 0.614648 0.0646021i 0.614648 0.0646021i
\(345\) 0.207912 0.978148i 0.207912 0.978148i
\(346\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(347\) 0.251377 + 0.564602i 0.251377 + 0.564602i 0.994522 0.104528i \(-0.0333333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(348\) 0 0
\(349\) −0.809017 1.40126i −0.809017 1.40126i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 0.994522i \(-0.466667\pi\)
\(350\) −0.951057 1.30902i −0.951057 1.30902i
\(351\) 1.00000i 1.00000i
\(352\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(353\) 0.994522 + 0.104528i 0.994522 + 0.104528i 0.587785 0.809017i \(-0.300000\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(354\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(355\) 0 0
\(356\) −0.951057 1.30902i −0.951057 1.30902i
\(357\) 0.500000 0.866025i 0.500000 0.866025i
\(358\) 0 0
\(359\) 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(360\) −0.104528 0.994522i −0.104528 0.994522i
\(361\) 0 0
\(362\) 1.20243 + 1.08268i 1.20243 + 1.08268i
\(363\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(364\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(365\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(366\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(367\) −1.47815 0.658114i −1.47815 0.658114i −0.500000 0.866025i \(-0.666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(368\) 0 0
\(369\) −0.587785 0.809017i −0.587785 0.809017i
\(370\) −1.08268 1.20243i −1.08268 1.20243i
\(371\) −0.658114 1.47815i −0.658114 1.47815i
\(372\) 0 0
\(373\) 0.413545 + 0.459289i 0.413545 + 0.459289i 0.913545 0.406737i \(-0.133333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −2.26728 + 1.30902i −2.26728 + 1.30902i
\(375\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(376\) 0.618034 0.618034
\(377\) 0 0
\(378\) −1.30902 0.951057i −1.30902 0.951057i
\(379\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(380\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(381\) 0.994522 0.104528i 0.994522 0.104528i
\(382\) −2.61803 −2.61803
\(383\) −1.60917 + 0.169131i −1.60917 + 0.169131i −0.866025 0.500000i \(-0.833333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(384\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(385\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(386\) 0 0
\(387\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(388\) 0.669131 0.743145i 0.669131 0.743145i
\(389\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(390\) 1.60917 0.169131i 1.60917 0.169131i
\(391\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(392\) 0 0
\(393\) −0.309017 0.535233i −0.309017 0.535233i
\(394\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(395\) 0 0
\(396\) 1.06485 + 2.39169i 1.06485 + 2.39169i
\(397\) 0.564602 0.251377i 0.564602 0.251377i −0.104528 0.994522i \(-0.533333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(398\) 0 0
\(399\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(400\) 0 0
\(401\) −1.40126 + 0.809017i −1.40126 + 0.809017i −0.994522 0.104528i \(-0.966667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(402\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(403\) 0 0
\(404\) 0 0
\(405\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(406\) 0 0
\(407\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(408\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(409\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(410\) 1.20243 1.08268i 1.20243 1.08268i
\(411\) 0.309017 0.951057i 0.309017 0.951057i
\(412\) −2.56082 0.544320i −2.56082 0.544320i
\(413\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(414\) 1.58268 0.336408i 1.58268 0.336408i
\(415\) −0.309017 0.951057i −0.309017 0.951057i
\(416\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(417\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(418\) −1.30902 2.26728i −1.30902 2.26728i
\(419\) −0.406737 + 0.913545i −0.406737 + 0.913545i 0.587785 + 0.809017i \(0.300000\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(420\) 0.809017 1.40126i 0.809017 1.40126i
\(421\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(422\) 0 0
\(423\) −0.459289 + 0.413545i −0.459289 + 0.413545i
\(424\) 1.61803 1.61803
\(425\) −0.866025 0.500000i −0.866025 0.500000i
\(426\) 0 0
\(427\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(428\) −1.53884 + 2.11803i −1.53884 + 2.11803i
\(429\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(430\) −0.809017 0.587785i −0.809017 0.587785i
\(431\) −0.658114 + 1.47815i −0.658114 + 1.47815i 0.207912 + 0.978148i \(0.433333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(438\) −1.58268 0.336408i −1.58268 0.336408i
\(439\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(440\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(441\) 0 0
\(442\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(443\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(444\) 0.658114 1.47815i 0.658114 1.47815i
\(445\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(446\) −0.406737 0.913545i −0.406737 0.913545i
\(447\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(448\) 1.08268 + 1.20243i 1.08268 + 1.20243i
\(449\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(451\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(452\) 0 0
\(453\) −1.60917 0.169131i −1.60917 0.169131i
\(454\) 0 0
\(455\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(456\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(457\) 0.809017 + 1.40126i 0.809017 + 1.40126i 0.913545 + 0.406737i \(0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(458\) 0.658114 1.47815i 0.658114 1.47815i
\(459\) −0.978148 0.207912i −0.978148 0.207912i
\(460\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(461\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(462\) −0.544320 + 2.56082i −0.544320 + 2.56082i
\(463\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(468\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(469\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(470\) −0.743145 0.669131i −0.743145 0.669131i
\(471\) 0 0
\(472\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(473\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(474\) 0 0
\(475\) 0.500000 0.866025i 0.500000 0.866025i
\(476\) 1.61803i 1.61803i
\(477\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(478\) 0 0
\(479\) 1.60917 + 0.169131i 1.60917 + 0.169131i 0.866025 0.500000i \(-0.166667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(480\) −0.587785 0.809017i −0.587785 0.809017i
\(481\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(482\) 0 0
\(483\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(484\) 1.75181 1.94558i 1.75181 1.94558i
\(485\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(486\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(487\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(488\) 0.207912 0.978148i 0.207912 0.978148i
\(489\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(490\) 0 0
\(491\) −0.459289 0.413545i −0.459289 0.413545i 0.406737 0.913545i \(-0.366667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(493\) 0 0
\(494\) −0.951057 1.30902i −0.951057 1.30902i
\(495\) 0.500000 1.53884i 0.500000 1.53884i
\(496\) 0 0
\(497\) 0 0
\(498\) 1.20243 1.08268i 1.20243 1.08268i
\(499\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) −1.40126 0.809017i −1.40126 0.809017i
\(501\) 0 0
\(502\) 0.500000 1.53884i 0.500000 1.53884i
\(503\) −0.658114 1.47815i −0.658114 1.47815i −0.866025 0.500000i \(-0.833333\pi\)
0.207912 0.978148i \(-0.433333\pi\)
\(504\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(505\) 0 0
\(506\) −1.53884 2.11803i −1.53884 2.11803i
\(507\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(508\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(509\) −0.743145 0.669131i −0.743145 0.669131i 0.207912 0.978148i \(-0.433333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(510\) 0.169131 1.60917i 0.169131 1.60917i
\(511\) −0.669131 0.743145i −0.669131 0.743145i
\(512\) 0 0
\(513\) 0.207912 0.978148i 0.207912 0.978148i
\(514\) 0 0
\(515\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(516\) 0.207912 0.978148i 0.207912 0.978148i
\(517\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(518\) 1.40126 0.809017i 1.40126 0.809017i
\(519\) 0.500000 0.363271i 0.500000 0.363271i
\(520\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(521\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(522\) 0 0
\(523\) −0.978148 + 0.207912i −0.978148 + 0.207912i −0.669131 0.743145i \(-0.733333\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(524\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(525\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(526\) 0.500000 0.866025i 0.500000 0.866025i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) −1.94558 1.75181i −1.94558 1.75181i
\(531\) 0.406737 0.913545i 0.406737 0.913545i
\(532\) −1.61803 −1.61803
\(533\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(534\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(535\) 1.58268 0.336408i 1.58268 0.336408i
\(536\) −0.128496 0.604528i −0.128496 0.604528i
\(537\) 0 0
\(538\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(539\) 0 0
\(540\) −1.58268 0.336408i −1.58268 0.336408i
\(541\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(542\) 0 0
\(543\) 0.866025 0.500000i 0.866025 0.500000i
\(544\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(545\) 0 0
\(546\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(547\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(548\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(549\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(550\) 2.56082 + 0.544320i 2.56082 + 0.544320i
\(551\) 0 0
\(552\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(553\) 0 0
\(554\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(555\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(556\) −0.913545 0.406737i −0.913545 0.406737i
\(557\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(560\) 0 0
\(561\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(562\) 1.08268 1.20243i 1.08268 1.20243i
\(563\) −0.207912 + 0.978148i −0.207912 + 0.978148i 0.743145 + 0.669131i \(0.233333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(564\) 0.309017 0.951057i 0.309017 0.951057i
\(565\) 0 0
\(566\) 0.544320 2.56082i 0.544320 2.56082i
\(567\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(568\) 0 0
\(569\) 0.406737 0.913545i 0.406737 0.913545i −0.587785 0.809017i \(-0.700000\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(570\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(571\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) 1.53884 2.11803i 1.53884 2.11803i
\(573\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(574\) 0.809017 + 1.40126i 0.809017 + 1.40126i
\(575\) 0.406737 0.913545i 0.406737 0.913545i
\(576\) 0.809017 1.40126i 0.809017 1.40126i
\(577\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.994522 0.104528i 0.994522 0.104528i
\(582\) −0.500000 0.866025i −0.500000 0.866025i
\(583\) 2.39169 + 1.06485i 2.39169 + 1.06485i
\(584\) 0.951057 0.309017i 0.951057 0.309017i
\(585\) 0.207912 0.978148i 0.207912 0.978148i
\(586\) 0 0
\(587\) −0.459289 0.413545i −0.459289 0.413545i 0.406737 0.913545i \(-0.366667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(591\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(592\) 0 0
\(593\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(594\) 2.60369 0.273659i 2.60369 0.273659i
\(595\) 0.669131 0.743145i 0.669131 0.743145i
\(596\) −0.994522 0.104528i −0.994522 0.104528i
\(597\) 0 0
\(598\) −1.08268 1.20243i −1.08268 1.20243i
\(599\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(600\) 0.104528 0.994522i 0.104528 0.994522i
\(601\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(602\) 0.743145 0.669131i 0.743145 0.669131i
\(603\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(604\) 2.39169 1.06485i 2.39169 1.06485i
\(605\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(606\) 0 0
\(607\) −0.309017 + 0.535233i −0.309017 + 0.535233i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(608\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(609\) 0 0
\(610\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(611\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(612\) 1.53884 0.500000i 1.53884 0.500000i
\(613\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(614\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(615\) −0.406737 0.913545i −0.406737 0.913545i
\(616\) −0.500000 1.53884i −0.500000 1.53884i
\(617\) −1.60917 + 0.169131i −1.60917 + 0.169131i −0.866025 0.500000i \(-0.833333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(618\) −1.30902 + 2.26728i −1.30902 + 2.26728i
\(619\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(620\) 0 0
\(621\) 0.104528 0.994522i 0.104528 0.994522i
\(622\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(623\) −0.951057 0.309017i −0.951057 0.309017i
\(624\) 0 0
\(625\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(626\) 2.26728 1.30902i 2.26728 1.30902i
\(627\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(628\) 0 0
\(629\) 0.587785 0.809017i 0.587785 0.809017i
\(630\) −1.08268 1.20243i −1.08268 1.20243i
\(631\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(636\) 0.809017 2.48990i 0.809017 2.48990i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(641\) −0.128496 + 0.604528i −0.128496 + 0.604528i 0.866025 + 0.500000i \(0.166667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(642\) 1.53884 + 2.11803i 1.53884 + 2.11803i
\(643\) 0.309017 0.535233i 0.309017 0.535233i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(644\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(645\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(646\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(647\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(648\) −0.207912 0.978148i −0.207912 0.978148i
\(649\) −1.61803 −1.61803
\(650\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(651\) 0 0
\(652\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(653\) 1.60917 + 0.169131i 1.60917 + 0.169131i 0.866025 0.500000i \(-0.166667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(654\) 0 0
\(655\) −0.190983 0.587785i −0.190983 0.587785i
\(656\) 0 0
\(657\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(658\) 0.809017 0.587785i 0.809017 0.587785i
\(659\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(660\) 0.544320 + 2.56082i 0.544320 + 2.56082i
\(661\) 0.604528 0.128496i 0.604528 0.128496i 0.104528 0.994522i \(-0.466667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 2.48990 0.809017i 2.48990 0.809017i
\(663\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(664\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(665\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(666\) −1.20243 1.08268i −1.20243 1.08268i
\(667\) 0 0
\(668\) 0 0
\(669\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(670\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(671\) 0.951057 1.30902i 0.951057 1.30902i
\(672\) 0.913545 0.406737i 0.913545 0.406737i
\(673\) 1.58268 0.336408i 1.58268 0.336408i 0.669131 0.743145i \(-0.266667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(674\) 0.866025 0.500000i 0.866025 0.500000i
\(675\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(676\) 0.809017 1.40126i 0.809017 1.40126i
\(677\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(678\) 0 0
\(679\) 0.0646021 0.614648i 0.0646021 0.614648i
\(680\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(681\) 0 0
\(682\) 0 0
\(683\) 0.994522 0.104528i 0.994522 0.104528i 0.406737 0.913545i \(-0.366667\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(684\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(685\) 0.500000 0.866025i 0.500000 0.866025i
\(686\) −0.336408 1.58268i −0.336408 1.58268i
\(687\) −0.743145 0.669131i −0.743145 0.669131i
\(688\) 0 0
\(689\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(690\) 1.61803 1.61803
\(691\) −1.08268 + 1.20243i −1.08268 + 1.20243i −0.104528 + 0.994522i \(0.533333\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(692\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(693\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(694\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(695\) 0.251377 + 0.564602i 0.251377 + 0.564602i
\(696\) 0 0
\(697\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(698\) 1.94558 1.75181i 1.94558 1.75181i
\(699\) 0 0
\(700\) 1.08268 1.20243i 1.08268 1.20243i
\(701\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(702\) 1.58268 0.336408i 1.58268 0.336408i
\(703\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(704\) −2.60369 0.273659i −2.60369 0.273659i
\(705\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(706\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(707\) 0 0
\(708\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(709\) 0.978148 + 0.207912i 0.978148 + 0.207912i 0.669131 0.743145i \(-0.266667\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.669131 0.743145i 0.669131 0.743145i
\(713\) 0 0
\(714\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(715\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(716\) 0 0
\(717\) 0 0
\(718\) 1.30902 + 2.26728i 1.30902 + 2.26728i
\(719\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(720\) 0 0
\(721\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(722\) 0 0
\(723\) 0 0
\(724\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(725\) 0 0
\(726\) −1.30902 2.26728i −1.30902 2.26728i
\(727\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(728\) −0.406737 0.913545i −0.406737 0.913545i
\(729\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(730\) −1.47815 0.658114i −1.47815 0.658114i
\(731\) 0.251377 0.564602i 0.251377 0.564602i
\(732\) −1.40126 0.809017i −1.40126 0.809017i
\(733\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(734\) 0.544320 2.56082i 0.544320 2.56082i
\(735\) 0 0
\(736\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(737\) 0.207912 0.978148i 0.207912 0.978148i
\(738\) 1.08268 1.20243i 1.08268 1.20243i
\(739\) −1.58268 + 0.336408i −1.58268 + 0.336408i −0.913545 0.406737i \(-0.866667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(740\) 0.951057 1.30902i 0.951057 1.30902i
\(741\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(742\) 2.11803 1.53884i 2.11803 1.53884i
\(743\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0.413545 + 0.459289i 0.413545 + 0.459289i
\(746\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(747\) −0.406737 0.913545i −0.406737 0.913545i
\(748\) −1.75181 1.94558i −1.75181 1.94558i
\(749\) 1.61803i 1.61803i
\(750\) −1.20243 + 1.08268i −1.20243 + 1.08268i
\(751\) −0.309017 0.535233i −0.309017 0.535233i 0.669131 0.743145i \(-0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(752\) 0 0
\(753\) −0.809017 0.587785i −0.809017 0.587785i
\(754\) 0 0
\(755\) −1.53884 0.500000i −1.53884 0.500000i
\(756\) 0.658114 1.47815i 0.658114 1.47815i
\(757\) 0.809017 + 1.40126i 0.809017 + 1.40126i 0.913545 + 0.406737i \(0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(758\) 0 0
\(759\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(760\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(761\) −0.743145 + 0.669131i −0.743145 + 0.669131i −0.951057 0.309017i \(-0.900000\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(762\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(763\) 0 0
\(764\) −0.544320 2.56082i −0.544320 2.56082i
\(765\) −0.913545 0.406737i −0.913545 0.406737i
\(766\) −0.809017 2.48990i −0.809017 2.48990i
\(767\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(768\) 1.00000i 1.00000i
\(769\) −0.564602 0.251377i −0.564602 0.251377i 0.104528 0.994522i \(-0.466667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(770\) −1.06485 + 2.39169i −1.06485 + 2.39169i
\(771\) 0 0
\(772\) 0 0
\(773\) 0.459289 0.413545i 0.459289 0.413545i −0.406737 0.913545i \(-0.633333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(774\) −0.866025 0.500000i −0.866025 0.500000i
\(775\) 0 0
\(776\) 0.535233 + 0.309017i 0.535233 + 0.309017i
\(777\) −0.207912 0.978148i −0.207912 0.978148i
\(778\) 0.273659 2.60369i 0.273659 2.60369i
\(779\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(780\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(781\) 0 0
\(782\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0.743145 0.669131i 0.743145 0.669131i
\(787\) −0.978148 0.207912i −0.978148 0.207912i −0.309017 0.951057i \(-0.600000\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(788\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(789\) −0.413545 0.459289i −0.413545 0.459289i
\(790\) 0 0
\(791\) 0 0
\(792\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(793\) 0.500000 0.866025i 0.500000 0.866025i
\(794\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(795\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(796\) 0 0
\(797\) 0.658114 + 1.47815i 0.658114 + 1.47815i 0.866025 + 0.500000i \(0.166667\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(798\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(799\) 0.309017 0.535233i 0.309017 0.535233i
\(800\) −0.406737 0.913545i −0.406737 0.913545i
\(801\) 1.00000i 1.00000i
\(802\) −1.75181 1.94558i −1.75181 1.94558i
\(803\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(804\) −0.994522 0.104528i −0.994522 0.104528i
\(805\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(806\) 0 0
\(807\) 1.00000 1.00000
\(808\) 0 0
\(809\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(810\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(811\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(815\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(816\) 0 0
\(817\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(818\) 0 0
\(819\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(820\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(821\) 1.60917 + 0.169131i 1.60917 + 0.169131i 0.866025 0.500000i \(-0.166667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(822\) 1.60917 + 0.169131i 1.60917 + 0.169131i
\(823\) −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i \(-0.400000\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(824\) 1.61803i 1.61803i
\(825\) 0.809017 1.40126i 0.809017 1.40126i
\(826\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(827\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(828\) 0.658114 + 1.47815i 0.658114 + 1.47815i
\(829\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(830\) 1.40126 0.809017i 1.40126 0.809017i
\(831\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(832\) −1.61803 −1.61803
\(833\) 0 0
\(834\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(835\) 0 0
\(836\) 1.94558 1.75181i 1.94558 1.75181i
\(837\) 0 0
\(838\) −1.58268 0.336408i −1.58268 0.336408i
\(839\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(840\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(841\) −0.978148 0.207912i −0.978148 0.207912i
\(842\) −0.658114 + 1.47815i −0.658114 + 1.47815i
\(843\) −0.500000 0.866025i −0.500000 0.866025i
\(844\) 0 0
\(845\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(846\) −0.809017 0.587785i −0.809017 0.587785i
\(847\) 0.169131 1.60917i 0.169131 1.60917i
\(848\) 0 0
\(849\) −1.40126 0.809017i −1.40126 0.809017i
\(850\) 0.500000 1.53884i 0.500000 1.53884i
\(851\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(852\) 0 0
\(853\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(854\) −0.658114 1.47815i −0.658114 1.47815i
\(855\) 0.406737 0.913545i 0.406737 0.913545i
\(856\) −1.47815 0.658114i −1.47815 0.658114i
\(857\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(858\) −1.53884 2.11803i −1.53884 2.11803i
\(859\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(860\) 0.406737 0.913545i 0.406737 0.913545i
\(861\) 0.978148 0.207912i 0.978148 0.207912i
\(862\) −2.56082 0.544320i −2.56082 0.544320i
\(863\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(864\) −0.669131 0.743145i −0.669131 0.743145i
\(865\) 0.564602 0.251377i 0.564602 0.251377i
\(866\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0.0646021 0.614648i 0.0646021 0.614648i
\(872\) 0 0
\(873\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(874\) −0.809017 1.40126i −0.809017 1.40126i
\(875\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(876\) 1.61803i 1.61803i
\(877\) 0.669131 + 0.743145i 0.669131 + 0.743145i 0.978148 0.207912i \(-0.0666667\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(878\) 0.658114 + 1.47815i 0.658114 + 1.47815i
\(879\) 0 0
\(880\) 0 0
\(881\) 0.406737 0.913545i 0.406737 0.913545i −0.587785 0.809017i \(-0.700000\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(882\) 0 0
\(883\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(884\) −1.20243 1.08268i −1.20243 1.08268i
\(885\) 0.587785 0.809017i 0.587785 0.809017i
\(886\) 1.58268 0.336408i 1.58268 0.336408i
\(887\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(888\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(889\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(890\) −1.60917 + 0.169131i −1.60917 + 0.169131i
\(891\) 0.336408 1.58268i 0.336408 1.58268i
\(892\) 0.809017 0.587785i 0.809017 0.587785i
\(893\) 0.535233 + 0.309017i 0.535233 + 0.309017i
\(894\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(895\) 0 0
\(896\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(897\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(898\) 0 0
\(899\) 0 0
\(900\) −1.47815 0.658114i −1.47815 0.658114i
\(901\) 0.809017 1.40126i 0.809017 1.40126i
\(902\) −2.48990 0.809017i −2.48990 0.809017i
\(903\) −0.251377 0.564602i −0.251377 0.564602i
\(904\) 0 0
\(905\) 0.951057 0.309017i 0.951057 0.309017i
\(906\) −0.273659 2.60369i −0.273659 2.60369i
\(907\) −0.809017 1.40126i −0.809017 1.40126i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 0.994522i \(-0.466667\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(911\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(912\) 0 0
\(913\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(914\) −1.94558 + 1.75181i −1.94558 + 1.75181i
\(915\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(916\) 1.58268 + 0.336408i 1.58268 + 0.336408i
\(917\) 0.614648 0.0646021i 0.614648 0.0646021i
\(918\) 1.61803i 1.61803i
\(919\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(920\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(921\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(922\) 0 0
\(923\) 0 0
\(924\) −2.61803 −2.61803
\(925\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(926\) 0 0
\(927\) 1.08268 + 1.20243i 1.08268 + 1.20243i
\(928\) 0 0
\(929\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(934\) 0 0
\(935\) 1.61803i 1.61803i
\(936\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(937\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(938\) −0.743145 0.669131i −0.743145 0.669131i
\(939\) −0.336408 1.58268i −0.336408 1.58268i
\(940\) 0.500000 0.866025i 0.500000 0.866025i
\(941\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(942\) 0 0
\(943\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(944\) 0 0
\(945\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(946\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(947\) −0.614648 0.0646021i −0.614648 0.0646021i −0.207912 0.978148i \(-0.566667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(948\) 0 0
\(949\) 1.00000 1.00000
\(950\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(951\) 0 0
\(952\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(953\) −0.251377 0.564602i −0.251377 0.564602i 0.743145 0.669131i \(-0.233333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(954\) −2.11803 1.53884i −2.11803 1.53884i
\(955\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(956\) 0 0
\(957\) 0 0
\(958\) 0.273659 + 2.60369i 0.273659 + 2.60369i
\(959\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(960\) 1.08268 1.20243i 1.08268 1.20243i
\(961\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(962\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(963\) 1.53884 0.500000i 1.53884 0.500000i
\(964\) 0 0
\(965\) 0 0
\(966\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(967\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(968\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(969\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(970\) −0.309017 0.951057i −0.309017 0.951057i
\(971\) 0.406737 + 0.913545i 0.406737 + 0.913545i 0.994522 + 0.104528i \(0.0333333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(972\) −1.60917 0.169131i −1.60917 0.169131i
\(973\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(974\) 0 0
\(975\) 0.406737 0.913545i 0.406737 0.913545i
\(976\) 0 0
\(977\) 0.207912 + 0.978148i 0.207912 + 0.978148i 0.951057 + 0.309017i \(0.100000\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(978\) −0.169131 + 1.60917i −0.169131 + 1.60917i
\(979\) 1.47815 0.658114i 1.47815 0.658114i
\(980\) 0 0
\(981\) 0 0
\(982\) 0.500000 0.866025i 0.500000 0.866025i
\(983\) 0.363271 + 0.500000i 0.363271 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(984\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(985\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(986\) 0 0
\(987\) −0.190983 0.587785i −0.190983 0.587785i
\(988\) 1.08268 1.20243i 1.08268 1.20243i
\(989\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(990\) 2.60369 + 0.273659i 2.60369 + 0.273659i
\(991\) 0.413545 0.459289i 0.413545 0.459289i −0.500000 0.866025i \(-0.666667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(992\) 0 0
\(993\) 1.61803i 1.61803i
\(994\) 0 0
\(995\) 0 0
\(996\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(997\) −1.47815 + 0.658114i −1.47815 + 0.658114i −0.978148 0.207912i \(-0.933333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 0.336408 + 1.58268i 0.336408 + 1.58268i
\(999\) −0.866025 + 0.500000i −0.866025 + 0.500000i
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 975.1.cj.a.146.2 yes 16
3.2 odd 2 inner 975.1.cj.a.146.1 16
13.9 even 3 inner 975.1.cj.a.971.2 yes 16
25.6 even 5 inner 975.1.cj.a.731.1 yes 16
39.35 odd 6 inner 975.1.cj.a.971.1 yes 16
75.56 odd 10 inner 975.1.cj.a.731.2 yes 16
325.256 even 15 inner 975.1.cj.a.581.1 yes 16
975.581 odd 30 inner 975.1.cj.a.581.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
975.1.cj.a.146.1 16 3.2 odd 2 inner
975.1.cj.a.146.2 yes 16 1.1 even 1 trivial
975.1.cj.a.581.1 yes 16 325.256 even 15 inner
975.1.cj.a.581.2 yes 16 975.581 odd 30 inner
975.1.cj.a.731.1 yes 16 25.6 even 5 inner
975.1.cj.a.731.2 yes 16 75.56 odd 10 inner
975.1.cj.a.971.1 yes 16 39.35 odd 6 inner
975.1.cj.a.971.2 yes 16 13.9 even 3 inner