Properties

Label 1260.1.eb.b.1147.1
Level $1260$
Weight $1$
Character 1260.1147
Analytic conductor $0.629$
Analytic rank $0$
Dimension $8$
Projective image $S_{4}$
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] = [1260,1,Mod(223,1260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1260, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 8, 9, 6]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1260.223");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1260.eb (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.628821915918\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(S_{4}\)
Projective field: Galois closure of 4.2.1134000.1

Embedding invariants

Embedding label 1147.1
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1260.1147
Dual form 1260.1.eb.b.223.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.258819 - 0.965926i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.258819 - 0.965926i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-0.707107 + 0.707107i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.258819 + 0.965926i) q^{12} +(0.965926 - 0.258819i) q^{13} +(-0.258819 - 0.965926i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.707107 - 0.707107i) q^{17} +(-0.500000 - 0.866025i) q^{18} -1.41421i q^{19} +(-0.258819 + 0.965926i) q^{20} +(0.500000 + 0.866025i) q^{21} +(-0.500000 + 0.866025i) q^{22} +(0.707107 + 0.707107i) q^{24} +(0.866025 - 0.500000i) q^{25} +(0.707107 - 0.707107i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.707107 - 0.707107i) q^{28} -1.00000i q^{30} +(-0.866025 - 0.500000i) q^{32} +(0.258819 - 0.965926i) q^{33} +(0.258819 - 0.965926i) q^{34} +1.00000i q^{35} +(-0.866025 - 0.500000i) q^{36} +(-0.707107 - 1.22474i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(0.258819 + 0.965926i) q^{40} +(0.866025 + 0.500000i) q^{42} +(-0.366025 + 1.36603i) q^{43} +1.00000i q^{44} +(0.258819 + 0.965926i) q^{45} +(-0.258819 + 0.965926i) q^{47} +(0.965926 + 0.258819i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.500000 - 0.866025i) q^{50} +1.00000i q^{51} +(0.258819 - 0.965926i) q^{52} +(1.00000 - 1.00000i) q^{53} +(0.965926 + 0.258819i) q^{54} +(0.707107 - 0.707107i) q^{55} +(-0.965926 - 0.258819i) q^{56} +(1.00000 + 1.00000i) q^{57} +(-0.500000 - 0.866025i) q^{60} +(-1.22474 + 0.707107i) q^{61} +(-0.965926 - 0.258819i) q^{63} -1.00000 q^{64} +(-0.866025 + 0.500000i) q^{65} +(-0.258819 - 0.965926i) q^{66} +(-0.258819 - 0.965926i) q^{68} +(0.500000 + 0.866025i) q^{70} -1.00000i q^{71} -1.00000 q^{72} +(0.707107 + 0.707107i) q^{73} +(-0.258819 + 0.965926i) q^{75} +(-1.22474 - 0.707107i) q^{76} +(0.258819 + 0.965926i) q^{77} +1.00000i q^{78} +(-0.500000 - 0.866025i) q^{79} +(0.707107 + 0.707107i) q^{80} -1.00000 q^{81} +(0.965926 + 0.258819i) q^{83} +1.00000 q^{84} +(-0.500000 + 0.866025i) q^{85} +(0.366025 + 1.36603i) q^{86} +(0.500000 + 0.866025i) q^{88} +(0.707107 + 0.707107i) q^{90} -1.00000i q^{91} +(0.258819 + 0.965926i) q^{94} +(0.366025 + 1.36603i) q^{95} +(0.965926 - 0.258819i) q^{96} +(0.965926 + 0.258819i) q^{97} -1.00000 q^{98} +(0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 4 q^{15} - 4 q^{16} - 4 q^{18} + 4 q^{21} - 4 q^{22} - 4 q^{39} + 4 q^{43} + 4 q^{50} + 8 q^{53} + 8 q^{57} - 4 q^{60} - 8 q^{64} + 4 q^{70} - 8 q^{72} - 4 q^{79} - 8 q^{81} + 8 q^{84} - 4 q^{85} - 4 q^{86} + 4 q^{88} - 4 q^{95} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.866025 0.500000i
\(3\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(4\) 0.500000 0.866025i 0.500000 0.866025i
\(5\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(6\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(7\) 0.258819 0.965926i 0.258819 0.965926i
\(8\) 1.00000i 1.00000i
\(9\) 1.00000i 1.00000i
\(10\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(11\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(12\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(13\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) −0.258819 0.965926i −0.258819 0.965926i
\(15\) 0.500000 0.866025i 0.500000 0.866025i
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(18\) −0.500000 0.866025i −0.500000 0.866025i
\(19\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(20\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(21\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(22\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(23\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(24\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(25\) 0.866025 0.500000i 0.866025 0.500000i
\(26\) 0.707107 0.707107i 0.707107 0.707107i
\(27\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(28\) −0.707107 0.707107i −0.707107 0.707107i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 1.00000i 1.00000i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −0.866025 0.500000i −0.866025 0.500000i
\(33\) 0.258819 0.965926i 0.258819 0.965926i
\(34\) 0.258819 0.965926i 0.258819 0.965926i
\(35\) 1.00000i 1.00000i
\(36\) −0.866025 0.500000i −0.866025 0.500000i
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) −0.707107 1.22474i −0.707107 1.22474i
\(39\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(40\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(41\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(43\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(44\) 1.00000i 1.00000i
\(45\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(46\) 0 0
\(47\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(48\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(49\) −0.866025 0.500000i −0.866025 0.500000i
\(50\) 0.500000 0.866025i 0.500000 0.866025i
\(51\) 1.00000i 1.00000i
\(52\) 0.258819 0.965926i 0.258819 0.965926i
\(53\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(54\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(55\) 0.707107 0.707107i 0.707107 0.707107i
\(56\) −0.965926 0.258819i −0.965926 0.258819i
\(57\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(58\) 0 0
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) −0.500000 0.866025i −0.500000 0.866025i
\(61\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(62\) 0 0
\(63\) −0.965926 0.258819i −0.965926 0.258819i
\(64\) −1.00000 −1.00000
\(65\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(66\) −0.258819 0.965926i −0.258819 0.965926i
\(67\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(68\) −0.258819 0.965926i −0.258819 0.965926i
\(69\) 0 0
\(70\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(71\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(72\) −1.00000 −1.00000
\(73\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(74\) 0 0
\(75\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(76\) −1.22474 0.707107i −1.22474 0.707107i
\(77\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(78\) 1.00000i 1.00000i
\(79\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(80\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(84\) 1.00000 1.00000
\(85\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(86\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(91\) 1.00000i 1.00000i
\(92\) 0 0
\(93\) 0 0
\(94\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(95\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(96\) 0.965926 0.258819i 0.965926 0.258819i
\(97\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(98\) −1.00000 −1.00000
\(99\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(100\) 1.00000i 1.00000i
\(101\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(102\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(103\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(104\) −0.258819 0.965926i −0.258819 0.965926i
\(105\) −0.707107 0.707107i −0.707107 0.707107i
\(106\) 0.366025 1.36603i 0.366025 1.36603i
\(107\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(108\) 0.965926 0.258819i 0.965926 0.258819i
\(109\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(110\) 0.258819 0.965926i 0.258819 0.965926i
\(111\) 0 0
\(112\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(113\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(115\) 0 0
\(116\) 0 0
\(117\) −0.258819 0.965926i −0.258819 0.965926i
\(118\) 0 0
\(119\) −0.500000 0.866025i −0.500000 0.866025i
\(120\) −0.866025 0.500000i −0.866025 0.500000i
\(121\) 0 0
\(122\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(123\) 0 0
\(124\) 0 0
\(125\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(126\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(127\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(128\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(129\) −0.707107 1.22474i −0.707107 1.22474i
\(130\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(131\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(132\) −0.707107 0.707107i −0.707107 0.707107i
\(133\) −1.36603 0.366025i −1.36603 0.366025i
\(134\) 0 0
\(135\) −0.866025 0.500000i −0.866025 0.500000i
\(136\) −0.707107 0.707107i −0.707107 0.707107i
\(137\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(138\) 0 0
\(139\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(141\) −0.500000 0.866025i −0.500000 0.866025i
\(142\) −0.500000 0.866025i −0.500000 0.866025i
\(143\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(144\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(145\) 0 0
\(146\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(147\) 0.965926 0.258819i 0.965926 0.258819i
\(148\) 0 0
\(149\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(150\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(151\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(152\) −1.41421 −1.41421
\(153\) −0.707107 0.707107i −0.707107 0.707107i
\(154\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(155\) 0 0
\(156\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(157\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(158\) −0.866025 0.500000i −0.866025 0.500000i
\(159\) 1.41421i 1.41421i
\(160\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(161\) 0 0
\(162\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(163\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 1.00000i 1.00000i
\(166\) 0.965926 0.258819i 0.965926 0.258819i
\(167\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 0.866025 0.500000i 0.866025 0.500000i
\(169\) 0 0
\(170\) 1.00000i 1.00000i
\(171\) −1.41421 −1.41421
\(172\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(173\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(174\) 0 0
\(175\) −0.258819 0.965926i −0.258819 0.965926i
\(176\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(177\) 0 0
\(178\) 0 0
\(179\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −0.500000 0.866025i −0.500000 0.866025i
\(183\) 0.366025 1.36603i 0.366025 1.36603i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(188\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(189\) 0.866025 0.500000i 0.866025 0.500000i
\(190\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 0.707107 0.707107i 0.707107 0.707107i
\(193\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0.965926 0.258819i 0.965926 0.258819i
\(195\) 0.258819 0.965926i 0.258819 0.965926i
\(196\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(197\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(198\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −0.500000 0.866025i −0.500000 0.866025i
\(201\) 0 0
\(202\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(203\) 0 0
\(204\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.707107 0.707107i −0.707107 0.707107i
\(209\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(210\) −0.965926 0.258819i −0.965926 0.258819i
\(211\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(212\) −0.366025 1.36603i −0.366025 1.36603i
\(213\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(214\) 0.366025 1.36603i 0.366025 1.36603i
\(215\) 1.41421i 1.41421i
\(216\) 0.707107 0.707107i 0.707107 0.707107i
\(217\) 0 0
\(218\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(219\) −1.00000 −1.00000
\(220\) −0.258819 0.965926i −0.258819 0.965926i
\(221\) 0.500000 0.866025i 0.500000 0.866025i
\(222\) 0 0
\(223\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(224\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(225\) −0.500000 0.866025i −0.500000 0.866025i
\(226\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(227\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(228\) 1.36603 0.366025i 1.36603 0.366025i
\(229\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(230\) 0 0
\(231\) −0.866025 0.500000i −0.866025 0.500000i
\(232\) 0 0
\(233\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(234\) −0.707107 0.707107i −0.707107 0.707107i
\(235\) 1.00000i 1.00000i
\(236\) 0 0
\(237\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(238\) −0.866025 0.500000i −0.866025 0.500000i
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) −1.00000 −1.00000
\(241\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(242\) 0 0
\(243\) 0.707107 0.707107i 0.707107 0.707107i
\(244\) 1.41421i 1.41421i
\(245\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(246\) 0 0
\(247\) −0.366025 1.36603i −0.366025 1.36603i
\(248\) 0 0
\(249\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(250\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(253\) 0 0
\(254\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(255\) −0.258819 0.965926i −0.258819 0.965926i
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(258\) −1.22474 0.707107i −1.22474 0.707107i
\(259\) 0 0
\(260\) 1.00000i 1.00000i
\(261\) 0 0
\(262\) 1.41421i 1.41421i
\(263\) 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i \(-0.666667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(264\) −0.965926 0.258819i −0.965926 0.258819i
\(265\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(266\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(267\) 0 0
\(268\) 0 0
\(269\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(270\) −1.00000 −1.00000
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) −0.965926 0.258819i −0.965926 0.258819i
\(273\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(274\) 0 0
\(275\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(276\) 0 0
\(277\) 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i \(-0.666667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 1.00000 1.00000
\(281\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(282\) −0.866025 0.500000i −0.866025 0.500000i
\(283\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(284\) −0.866025 0.500000i −0.866025 0.500000i
\(285\) −1.22474 0.707107i −1.22474 0.707107i
\(286\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(287\) 0 0
\(288\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(289\) 0 0
\(290\) 0 0
\(291\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(292\) 0.965926 0.258819i 0.965926 0.258819i
\(293\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(294\) 0.707107 0.707107i 0.707107 0.707107i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.965926 0.258819i −0.965926 0.258819i
\(298\) 1.00000 1.00000
\(299\) 0 0
\(300\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(301\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(302\) 0.500000 0.866025i 0.500000 0.866025i
\(303\) 0.366025 1.36603i 0.366025 1.36603i
\(304\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(305\) 1.00000 1.00000i 1.00000 1.00000i
\(306\) −0.965926 0.258819i −0.965926 0.258819i
\(307\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(308\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(313\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(314\) −0.707107 0.707107i −0.707107 0.707107i
\(315\) 1.00000 1.00000
\(316\) −1.00000 −1.00000
\(317\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(318\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(319\) 0 0
\(320\) 0.965926 0.258819i 0.965926 0.258819i
\(321\) 1.41421i 1.41421i
\(322\) 0 0
\(323\) −1.00000 1.00000i −1.00000 1.00000i
\(324\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(325\) 0.707107 0.707107i 0.707107 0.707107i
\(326\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(327\) −0.707107 0.707107i −0.707107 0.707107i
\(328\) 0 0
\(329\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(330\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(331\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) 0.707107 0.707107i 0.707107 0.707107i
\(333\) 0 0
\(334\) 0.707107 0.707107i 0.707107 0.707107i
\(335\) 0 0
\(336\) 0.500000 0.866025i 0.500000 0.866025i
\(337\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(338\) 0 0
\(339\) −1.22474 0.707107i −1.22474 0.707107i
\(340\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(341\) 0 0
\(342\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(343\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(344\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(348\) 0 0
\(349\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(350\) −0.707107 0.707107i −0.707107 0.707107i
\(351\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(352\) 1.00000 1.00000
\(353\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(354\) 0 0
\(355\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(356\) 0 0
\(357\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(358\) 0.866025 0.500000i 0.866025 0.500000i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0.965926 0.258819i 0.965926 0.258819i
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) −0.866025 0.500000i −0.866025 0.500000i
\(365\) −0.866025 0.500000i −0.866025 0.500000i
\(366\) −0.366025 1.36603i −0.366025 1.36603i
\(367\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.707107 1.22474i −0.707107 1.22474i
\(372\) 0 0
\(373\) −0.366025 1.36603i −0.366025 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(374\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(375\) 1.00000i 1.00000i
\(376\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(377\) 0 0
\(378\) 0.500000 0.866025i 0.500000 0.866025i
\(379\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(381\) 1.41421i 1.41421i
\(382\) 0 0
\(383\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(384\) 0.258819 0.965926i 0.258819 0.965926i
\(385\) −0.500000 0.866025i −0.500000 0.866025i
\(386\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(387\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(388\) 0.707107 0.707107i 0.707107 0.707107i
\(389\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(390\) −0.258819 0.965926i −0.258819 0.965926i
\(391\) 0 0
\(392\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(393\) −0.366025 1.36603i −0.366025 1.36603i
\(394\) −1.36603 0.366025i −1.36603 0.366025i
\(395\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(396\) 1.00000 1.00000
\(397\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(398\) 0 0
\(399\) 1.22474 0.707107i 1.22474 0.707107i
\(400\) −0.866025 0.500000i −0.866025 0.500000i
\(401\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.41421i 1.41421i
\(405\) 0.965926 0.258819i 0.965926 0.258819i
\(406\) 0 0
\(407\) 0 0
\(408\) 1.00000 1.00000
\(409\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.00000 −1.00000
\(416\) −0.965926 0.258819i −0.965926 0.258819i
\(417\) 0 0
\(418\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(419\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(421\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 1.00000 1.00000
\(423\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(424\) −1.00000 1.00000i −1.00000 1.00000i
\(425\) 0.258819 0.965926i 0.258819 0.965926i
\(426\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(427\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(428\) −0.366025 1.36603i −0.366025 1.36603i
\(429\) 1.00000i 1.00000i
\(430\) −0.707107 1.22474i −0.707107 1.22474i
\(431\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0.258819 0.965926i 0.258819 0.965926i
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(437\) 0 0
\(438\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(439\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(440\) −0.707107 0.707107i −0.707107 0.707107i
\(441\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(442\) 1.00000i 1.00000i
\(443\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.965926 0.258819i 0.965926 0.258819i
\(447\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(448\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −0.866025 0.500000i −0.866025 0.500000i
\(451\) 0 0
\(452\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(453\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(454\) −0.258819 0.965926i −0.258819 0.965926i
\(455\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(456\) 1.00000 1.00000i 1.00000 1.00000i
\(457\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(458\) 1.41421i 1.41421i
\(459\) 1.00000 1.00000
\(460\) 0 0
\(461\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(462\) −1.00000 −1.00000
\(463\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(467\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(468\) −0.965926 0.258819i −0.965926 0.258819i
\(469\) 0 0
\(470\) −0.500000 0.866025i −0.500000 0.866025i
\(471\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(472\) 0 0
\(473\) −0.366025 1.36603i −0.366025 1.36603i
\(474\) 0.965926 0.258819i 0.965926 0.258819i
\(475\) −0.707107 1.22474i −0.707107 1.22474i
\(476\) −1.00000 −1.00000
\(477\) −1.00000 1.00000i −1.00000 1.00000i
\(478\) 0 0
\(479\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(480\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(481\) 0 0
\(482\) 0.707107 1.22474i 0.707107 1.22474i
\(483\) 0 0
\(484\) 0 0
\(485\) −1.00000 −1.00000
\(486\) 0.258819 0.965926i 0.258819 0.965926i
\(487\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(488\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(489\) −1.41421 −1.41421
\(490\) 0.965926 0.258819i 0.965926 0.258819i
\(491\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.00000 1.00000i −1.00000 1.00000i
\(495\) −0.707107 0.707107i −0.707107 0.707107i
\(496\) 0 0
\(497\) −0.965926 0.258819i −0.965926 0.258819i
\(498\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(499\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(500\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(501\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(502\) 0 0
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(505\) 1.00000 1.00000i 1.00000 1.00000i
\(506\) 0 0
\(507\) 0 0
\(508\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) −0.707107 0.707107i −0.707107 0.707107i
\(511\) 0.866025 0.500000i 0.866025 0.500000i
\(512\) 1.00000i 1.00000i
\(513\) 1.00000 1.00000i 1.00000 1.00000i
\(514\) −0.707107 0.707107i −0.707107 0.707107i
\(515\) 0 0
\(516\) −1.41421 −1.41421
\(517\) −0.258819 0.965926i −0.258819 0.965926i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(524\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(525\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(526\) −0.366025 1.36603i −0.366025 1.36603i
\(527\) 0 0
\(528\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(529\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(530\) 1.41421i 1.41421i
\(531\) 0 0
\(532\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(533\) 0 0
\(534\) 0 0
\(535\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(536\) 0 0
\(537\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(538\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(539\) 1.00000 1.00000
\(540\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(541\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(545\) −0.258819 0.965926i −0.258819 0.965926i
\(546\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(547\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(548\) 0 0
\(549\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(550\) 1.00000i 1.00000i
\(551\) 0 0
\(552\) 0 0
\(553\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(554\) −0.366025 1.36603i −0.366025 1.36603i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 0 0
\(559\) 1.41421i 1.41421i
\(560\) 0.866025 0.500000i 0.866025 0.500000i
\(561\) −0.500000 0.866025i −0.500000 0.866025i
\(562\) −0.866025 0.500000i −0.866025 0.500000i
\(563\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(564\) −1.00000 −1.00000
\(565\) −0.707107 1.22474i −0.707107 1.22474i
\(566\) −0.707107 0.707107i −0.707107 0.707107i
\(567\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(568\) −1.00000 −1.00000
\(569\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) −1.41421 −1.41421
\(571\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(572\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000i 1.00000i
\(577\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(578\) 0 0
\(579\) −1.22474 0.707107i −1.22474 0.707107i
\(580\) 0 0
\(581\) 0.500000 0.866025i 0.500000 0.866025i
\(582\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(583\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(584\) 0.707107 0.707107i 0.707107 0.707107i
\(585\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(586\) 0 0
\(587\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(588\) 0.258819 0.965926i 0.258819 0.965926i
\(589\) 0 0
\(590\) 0 0
\(591\) 1.41421 1.41421
\(592\) 0 0
\(593\) 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(594\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(595\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(596\) 0.866025 0.500000i 0.866025 0.500000i
\(597\) 0 0
\(598\) 0 0
\(599\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(600\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(601\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(602\) 1.41421 1.41421
\(603\) 0 0
\(604\) 1.00000i 1.00000i
\(605\) 0 0
\(606\) −0.366025 1.36603i −0.366025 1.36603i
\(607\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(608\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(609\) 0 0
\(610\) 0.366025 1.36603i 0.366025 1.36603i
\(611\) 1.00000i 1.00000i
\(612\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(613\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(614\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(615\) 0 0
\(616\) 0.965926 0.258819i 0.965926 0.258819i
\(617\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(618\) 0 0
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.00000 1.00000
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) 0 0
\(627\) −1.36603 0.366025i −1.36603 0.366025i
\(628\) −0.965926 0.258819i −0.965926 0.258819i
\(629\) 0 0
\(630\) 0.866025 0.500000i 0.866025 0.500000i
\(631\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(632\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(633\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(634\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(635\) 0.707107 1.22474i 0.707107 1.22474i
\(636\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(637\) −0.965926 0.258819i −0.965926 0.258819i
\(638\) 0 0
\(639\) −1.00000 −1.00000
\(640\) 0.707107 0.707107i 0.707107 0.707107i
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(643\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(644\) 0 0
\(645\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(646\) −1.36603 0.366025i −1.36603 0.366025i
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 0.258819 0.965926i 0.258819 0.965926i
\(651\) 0 0
\(652\) 1.36603 0.366025i 1.36603 0.366025i
\(653\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) −0.965926 0.258819i −0.965926 0.258819i
\(655\) 0.366025 1.36603i 0.366025 1.36603i
\(656\) 0 0
\(657\) 0.707107 0.707107i 0.707107 0.707107i
\(658\) 1.00000 1.00000
\(659\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(660\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(661\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0.500000 0.866025i 0.500000 0.866025i
\(663\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(664\) 0.258819 0.965926i 0.258819 0.965926i
\(665\) 1.41421 1.41421
\(666\) 0 0
\(667\) 0 0
\(668\) 0.258819 0.965926i 0.258819 0.965926i
\(669\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(670\) 0 0
\(671\) 0.707107 1.22474i 0.707107 1.22474i
\(672\) 1.00000i 1.00000i
\(673\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 0 0
\(675\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(676\) 0 0
\(677\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) −1.41421 −1.41421
\(679\) 0.500000 0.866025i 0.500000 0.866025i
\(680\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(681\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(682\) 0 0
\(683\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(684\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(685\) 0 0
\(686\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(687\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(688\) 1.36603 0.366025i 1.36603 0.366025i
\(689\) 0.707107 1.22474i 0.707107 1.22474i
\(690\) 0 0
\(691\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(692\) 0 0
\(693\) 0.965926 0.258819i 0.965926 0.258819i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 1.41421i 1.41421i
\(700\) −0.965926 0.258819i −0.965926 0.258819i
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 1.00000 1.00000
\(703\) 0 0
\(704\) 0.866025 0.500000i 0.866025 0.500000i
\(705\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(706\) 0 0
\(707\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(708\) 0 0
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(711\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(712\) 0 0
\(713\) 0 0
\(714\) 0.965926 0.258819i 0.965926 0.258819i
\(715\) 0.500000 0.866025i 0.500000 0.866025i
\(716\) 0.500000 0.866025i 0.500000 0.866025i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0.707107 0.707107i 0.707107 0.707107i
\(721\) 0 0
\(722\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(723\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(728\) −1.00000 −1.00000
\(729\) 1.00000i 1.00000i
\(730\) −1.00000 −1.00000
\(731\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(732\) −1.00000 1.00000i −1.00000 1.00000i
\(733\) −1.93185 + 0.517638i −1.93185 + 0.517638i −0.965926 + 0.258819i \(0.916667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(734\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(735\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(742\) −1.22474 0.707107i −1.22474 0.707107i
\(743\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) −0.965926 0.258819i −0.965926 0.258819i
\(746\) −1.00000 1.00000i −1.00000 1.00000i
\(747\) 0.258819 0.965926i 0.258819 0.965926i
\(748\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(749\) −0.707107 1.22474i −0.707107 1.22474i
\(750\) −0.500000 0.866025i −0.500000 0.866025i
\(751\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0.965926 0.258819i 0.965926 0.258819i
\(753\) 0 0
\(754\) 0 0
\(755\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(756\) 1.00000i 1.00000i
\(757\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 0.866025 0.500000i 0.866025 0.500000i
\(759\) 0 0
\(760\) 1.36603 0.366025i 1.36603 0.366025i
\(761\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(762\) −0.707107 1.22474i −0.707107 1.22474i
\(763\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(764\) 0 0
\(765\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(766\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(767\) 0 0
\(768\) −0.258819 0.965926i −0.258819 0.965926i
\(769\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(770\) −0.866025 0.500000i −0.866025 0.500000i
\(771\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(772\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(773\) −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(774\) 1.36603 0.366025i 1.36603 0.366025i
\(775\) 0 0
\(776\) 0.258819 0.965926i 0.258819 0.965926i
\(777\) 0 0
\(778\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(779\) 0 0
\(780\) −0.707107 0.707107i −0.707107 0.707107i
\(781\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 1.00000i
\(785\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(786\) −1.00000 1.00000i −1.00000 1.00000i
\(787\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(788\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(789\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(790\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(791\) 1.41421 1.41421
\(792\) 0.866025 0.500000i 0.866025 0.500000i
\(793\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(794\) 0 0
\(795\) −0.366025 1.36603i −0.366025 1.36603i
\(796\) 0 0
\(797\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0.707107 1.22474i 0.707107 1.22474i
\(799\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(800\) −1.00000 −1.00000
\(801\) 0 0
\(802\) 0 0
\(803\) −0.965926 0.258819i −0.965926 0.258819i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.00000 1.00000i 1.00000 1.00000i
\(808\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(809\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(810\) 0.707107 0.707107i 0.707107 0.707107i
\(811\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.22474 0.707107i −1.22474 0.707107i
\(816\) 0.866025 0.500000i 0.866025 0.500000i
\(817\) 1.93185 + 0.517638i 1.93185 + 0.517638i
\(818\) 1.41421i 1.41421i
\(819\) −1.00000 −1.00000
\(820\) 0 0
\(821\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(824\) 0 0
\(825\) −0.258819 0.965926i −0.258819 0.965926i
\(826\) 0 0
\(827\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(828\) 0 0
\(829\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(830\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(831\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(832\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(833\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(834\) 0 0
\(835\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(836\) 1.41421 1.41421
\(837\) 0 0
\(838\) 0 0
\(839\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(840\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(841\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(842\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(843\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(844\) 0.866025 0.500000i 0.866025 0.500000i
\(845\) 0 0
\(846\) 0.965926 0.258819i 0.965926 0.258819i
\(847\) 0 0
\(848\) −1.36603 0.366025i −1.36603 0.366025i
\(849\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(850\) −0.258819 0.965926i −0.258819 0.965926i
\(851\) 0 0
\(852\) 0.965926 0.258819i 0.965926 0.258819i
\(853\) 0.517638 1.93185i 0.517638 1.93185i 0.258819 0.965926i \(-0.416667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(854\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(855\) 1.36603 0.366025i 1.36603 0.366025i
\(856\) −1.00000 1.00000i −1.00000 1.00000i
\(857\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(858\) −0.500000 0.866025i −0.500000 0.866025i
\(859\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(860\) −1.22474 0.707107i −1.22474 0.707107i
\(861\) 0 0
\(862\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(863\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(864\) −0.258819 0.965926i −0.258819 0.965926i
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(870\) 0 0
\(871\) 0 0
\(872\) 1.00000 1.00000
\(873\) 0.258819 0.965926i 0.258819 0.965926i
\(874\) 0 0
\(875\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(876\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(877\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(878\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(879\) 0 0
\(880\) −0.965926 0.258819i −0.965926 0.258819i
\(881\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(882\) 1.00000i 1.00000i
\(883\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(884\) −0.500000 0.866025i −0.500000 0.866025i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(888\) 0 0
\(889\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(890\) 0 0
\(891\) 0.866025 0.500000i 0.866025 0.500000i
\(892\) 0.707107 0.707107i 0.707107 0.707107i
\(893\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(894\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(895\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(896\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −1.00000 −1.00000
\(901\) 1.41421i 1.41421i
\(902\) 0 0
\(903\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(904\) 1.36603 0.366025i 1.36603 0.366025i
\(905\) 0 0
\(906\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(907\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(908\) −0.707107 0.707107i −0.707107 0.707107i
\(909\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(910\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(911\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(912\) 0.366025 1.36603i 0.366025 1.36603i
\(913\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(914\) 0 0
\(915\) 1.41421i 1.41421i
\(916\) −0.707107 1.22474i −0.707107 1.22474i
\(917\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(918\) 0.866025 0.500000i 0.866025 0.500000i
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) −1.00000 −1.00000
\(922\) 0.707107 1.22474i 0.707107 1.22474i
\(923\) −0.258819 0.965926i −0.258819 0.965926i
\(924\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(925\) 0 0
\(926\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(930\) 0 0
\(931\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(932\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(933\) 0 0
\(934\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(935\) 1.00000i 1.00000i
\(936\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(937\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −0.866025 0.500000i −0.866025 0.500000i
\(941\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(942\) 1.00000 1.00000
\(943\) 0 0
\(944\) 0 0
\(945\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(946\) −1.00000 1.00000i −1.00000 1.00000i
\(947\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(948\) 0.707107 0.707107i 0.707107 0.707107i
\(949\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(950\) −1.22474 0.707107i −1.22474 0.707107i
\(951\) −0.707107 1.22474i −0.707107 1.22474i
\(952\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(953\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(954\) −1.36603 0.366025i −1.36603 0.366025i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0.707107 1.22474i 0.707107 1.22474i
\(959\) 0 0
\(960\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(961\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(962\) 0 0
\(963\) −1.00000 1.00000i −1.00000 1.00000i
\(964\) 1.41421i 1.41421i
\(965\) −0.707107 1.22474i −0.707107 1.22474i
\(966\) 0 0
\(967\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(968\) 0 0
\(969\) 1.41421 1.41421
\(970\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(971\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(972\) −0.258819 0.965926i −0.258819 0.965926i
\(973\) 0 0
\(974\) 0 0
\(975\) 1.00000i 1.00000i
\(976\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(977\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(978\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(979\) 0 0
\(980\) 0.707107 0.707107i 0.707107 0.707107i
\(981\) 1.00000 1.00000
\(982\) −1.00000 −1.00000
\(983\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(984\) 0 0
\(985\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(986\) 0 0
\(987\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(988\) −1.36603 0.366025i −1.36603 0.366025i
\(989\) 0 0
\(990\) −0.965926 0.258819i −0.965926 0.258819i
\(991\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(992\) 0 0
\(993\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(994\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(995\) 0 0
\(996\) 1.00000i 1.00000i
\(997\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(998\) 1.00000i 1.00000i
\(999\) 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 1260.1.eb.b.1147.1 yes 8
3.2 odd 2 3780.1.ee.a.307.2 8
4.3 odd 2 1260.1.eb.a.1147.2 yes 8
5.3 odd 4 1260.1.eb.a.643.1 yes 8
7.6 odd 2 inner 1260.1.eb.b.1147.2 yes 8
9.2 odd 6 3780.1.ee.a.2827.1 8
9.7 even 3 inner 1260.1.eb.b.727.1 yes 8
12.11 even 2 3780.1.ee.b.307.2 8
15.8 even 4 3780.1.ee.b.1063.2 8
20.3 even 4 inner 1260.1.eb.b.643.2 yes 8
21.20 even 2 3780.1.ee.a.307.1 8
28.27 even 2 1260.1.eb.a.1147.1 yes 8
35.13 even 4 1260.1.eb.a.643.2 yes 8
36.7 odd 6 1260.1.eb.a.727.2 yes 8
36.11 even 6 3780.1.ee.b.2827.1 8
45.38 even 12 3780.1.ee.b.3583.1 8
45.43 odd 12 1260.1.eb.a.223.1 8
60.23 odd 4 3780.1.ee.a.1063.2 8
63.20 even 6 3780.1.ee.a.2827.2 8
63.34 odd 6 inner 1260.1.eb.b.727.2 yes 8
84.83 odd 2 3780.1.ee.b.307.1 8
105.83 odd 4 3780.1.ee.b.1063.1 8
140.83 odd 4 inner 1260.1.eb.b.643.1 yes 8
180.43 even 12 inner 1260.1.eb.b.223.2 yes 8
180.83 odd 12 3780.1.ee.a.3583.1 8
252.83 odd 6 3780.1.ee.b.2827.2 8
252.223 even 6 1260.1.eb.a.727.1 yes 8
315.83 odd 12 3780.1.ee.b.3583.2 8
315.223 even 12 1260.1.eb.a.223.2 yes 8
420.83 even 4 3780.1.ee.a.1063.1 8
1260.83 even 12 3780.1.ee.a.3583.2 8
1260.223 odd 12 inner 1260.1.eb.b.223.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1260.1.eb.a.223.1 8 45.43 odd 12
1260.1.eb.a.223.2 yes 8 315.223 even 12
1260.1.eb.a.643.1 yes 8 5.3 odd 4
1260.1.eb.a.643.2 yes 8 35.13 even 4
1260.1.eb.a.727.1 yes 8 252.223 even 6
1260.1.eb.a.727.2 yes 8 36.7 odd 6
1260.1.eb.a.1147.1 yes 8 28.27 even 2
1260.1.eb.a.1147.2 yes 8 4.3 odd 2
1260.1.eb.b.223.1 yes 8 1260.223 odd 12 inner
1260.1.eb.b.223.2 yes 8 180.43 even 12 inner
1260.1.eb.b.643.1 yes 8 140.83 odd 4 inner
1260.1.eb.b.643.2 yes 8 20.3 even 4 inner
1260.1.eb.b.727.1 yes 8 9.7 even 3 inner
1260.1.eb.b.727.2 yes 8 63.34 odd 6 inner
1260.1.eb.b.1147.1 yes 8 1.1 even 1 trivial
1260.1.eb.b.1147.2 yes 8 7.6 odd 2 inner
3780.1.ee.a.307.1 8 21.20 even 2
3780.1.ee.a.307.2 8 3.2 odd 2
3780.1.ee.a.1063.1 8 420.83 even 4
3780.1.ee.a.1063.2 8 60.23 odd 4
3780.1.ee.a.2827.1 8 9.2 odd 6
3780.1.ee.a.2827.2 8 63.20 even 6
3780.1.ee.a.3583.1 8 180.83 odd 12
3780.1.ee.a.3583.2 8 1260.83 even 12
3780.1.ee.b.307.1 8 84.83 odd 2
3780.1.ee.b.307.2 8 12.11 even 2
3780.1.ee.b.1063.1 8 105.83 odd 4
3780.1.ee.b.1063.2 8 15.8 even 4
3780.1.ee.b.2827.1 8 36.11 even 6
3780.1.ee.b.2827.2 8 252.83 odd 6
3780.1.ee.b.3583.1 8 45.38 even 12
3780.1.ee.b.3583.2 8 315.83 odd 12