Properties

Label 684.1.x.a.391.1
Level $684$
Weight $1$
Character 684.391
Analytic conductor $0.341$
Analytic rank $0$
Dimension $4$
Projective image $A_{4}$
CM/RM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [684,1,Mod(7,684)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(684, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("684.7");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 684.x (of order \(6\), degree \(2\), 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: \(0.341360468641\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(A_{4}\)
Projective field: Galois closure of 4.0.467856.1
Artin image: $\SL(2,3):C_2$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\)

Embedding invariants

Embedding label 391.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 684.391
Dual form 684.1.x.a.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000i q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000i q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.866025 - 0.500000i) q^{11} -1.00000i q^{12} +(-0.866025 + 0.500000i) q^{14} +(0.866025 - 0.500000i) q^{15} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{17} +1.00000 q^{18} +1.00000i q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{21} +(-0.866025 + 0.500000i) q^{22} +1.00000i q^{24} +1.00000i q^{27} +(0.866025 - 0.500000i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.866025 + 0.500000i) q^{30} +(-0.866025 - 0.500000i) q^{31} -1.00000 q^{32} +(-0.500000 - 0.866025i) q^{33} +(0.500000 - 0.866025i) q^{34} +(0.866025 + 0.500000i) q^{35} -1.00000 q^{36} -1.00000i q^{38} +(-0.500000 - 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{41} +(0.500000 + 0.866025i) q^{42} -2.00000i q^{43} +(0.866025 - 0.500000i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.866025 - 0.500000i) q^{47} -1.00000i q^{48} +(0.866025 + 0.500000i) q^{51} +(-0.500000 - 0.866025i) q^{53} -1.00000i q^{54} +(0.866025 + 0.500000i) q^{55} +(-0.866025 + 0.500000i) q^{56} +1.00000 q^{57} +(-0.500000 + 0.866025i) q^{58} +(0.866025 - 0.500000i) q^{59} +(0.866025 - 0.500000i) q^{60} +(-0.500000 + 0.866025i) q^{61} +(0.866025 + 0.500000i) q^{62} +(-0.866025 + 0.500000i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(-0.500000 + 0.866025i) q^{68} +(-0.866025 - 0.500000i) q^{70} +(-0.866025 - 0.500000i) q^{71} +1.00000 q^{72} +(-0.500000 + 0.866025i) q^{73} +1.00000i q^{76} +(0.500000 - 0.866025i) q^{77} +2.00000i q^{79} +(0.500000 + 0.866025i) q^{80} +1.00000 q^{81} +(-0.500000 - 0.866025i) q^{82} +(-0.866025 + 0.500000i) q^{83} +(-0.500000 - 0.866025i) q^{84} -1.00000 q^{85} +2.00000i q^{86} +(-0.866025 - 0.500000i) q^{87} +(-0.866025 + 0.500000i) q^{88} +(0.500000 + 0.866025i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-0.500000 + 0.866025i) q^{93} +(0.866025 + 0.500000i) q^{94} +(-0.866025 + 0.500000i) q^{95} +1.00000i q^{96} +(-0.866025 + 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{20} - 2 q^{21} + 2 q^{29} - 4 q^{32} - 2 q^{33} + 2 q^{34} - 4 q^{36} - 2 q^{40} + 2 q^{41} + 2 q^{42} - 2 q^{45} - 2 q^{53} + 4 q^{57} - 2 q^{58} - 2 q^{61} + 4 q^{64} + 2 q^{66} - 2 q^{68} + 4 q^{72} - 2 q^{73} + 2 q^{77} + 2 q^{80} + 4 q^{81} - 2 q^{82} - 2 q^{84} - 4 q^{85} + 2 q^{89} + 2 q^{90} - 2 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000
\(3\) 1.00000i 1.00000i
\(4\) 1.00000 1.00000
\(5\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 1.00000i 1.00000i
\(7\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) −1.00000 −1.00000
\(9\) −1.00000 −1.00000
\(10\) −0.500000 0.866025i −0.500000 0.866025i
\(11\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 1.00000i 1.00000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(15\) 0.866025 0.500000i 0.866025 0.500000i
\(16\) 1.00000 1.00000
\(17\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(18\) 1.00000 1.00000
\(19\) 1.00000i 1.00000i
\(20\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(21\) −0.500000 0.866025i −0.500000 0.866025i
\(22\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.00000i 1.00000i
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000i 1.00000i
\(28\) 0.866025 0.500000i 0.866025 0.500000i
\(29\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(30\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(31\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) −1.00000 −1.00000
\(33\) −0.500000 0.866025i −0.500000 0.866025i
\(34\) 0.500000 0.866025i 0.500000 0.866025i
\(35\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(36\) −1.00000 −1.00000
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 1.00000i 1.00000i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.500000 0.866025i
\(41\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(43\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(44\) 0.866025 0.500000i 0.866025 0.500000i
\(45\) −0.500000 0.866025i −0.500000 0.866025i
\(46\) 0 0
\(47\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 1.00000i 1.00000i
\(49\) 0 0
\(50\) 0 0
\(51\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(52\) 0 0
\(53\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(54\) 1.00000i 1.00000i
\(55\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(56\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(57\) 1.00000 1.00000
\(58\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(59\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0.866025 0.500000i 0.866025 0.500000i
\(61\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(62\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(63\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(69\) 0 0
\(70\) −0.866025 0.500000i −0.866025 0.500000i
\(71\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) 1.00000 1.00000
\(73\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 1.00000i 1.00000i
\(77\) 0.500000 0.866025i 0.500000 0.866025i
\(78\) 0 0
\(79\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(81\) 1.00000 1.00000
\(82\) −0.500000 0.866025i −0.500000 0.866025i
\(83\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(84\) −0.500000 0.866025i −0.500000 0.866025i
\(85\) −1.00000 −1.00000
\(86\) 2.00000i 2.00000i
\(87\) −0.866025 0.500000i −0.866025 0.500000i
\(88\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(89\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(91\) 0 0
\(92\) 0 0
\(93\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(94\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(95\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(96\) 1.00000i 1.00000i
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(100\) 0 0
\(101\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(102\) −0.866025 0.500000i −0.866025 0.500000i
\(103\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) 0 0
\(105\) 0.500000 0.866025i 0.500000 0.866025i
\(106\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.00000i 1.00000i
\(109\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(110\) −0.866025 0.500000i −0.866025 0.500000i
\(111\) 0 0
\(112\) 0.866025 0.500000i 0.866025 0.500000i
\(113\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(114\) −1.00000 −1.00000
\(115\) 0 0
\(116\) 0.500000 0.866025i 0.500000 0.866025i
\(117\) 0 0
\(118\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(119\) 1.00000i 1.00000i
\(120\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(121\) 0 0
\(122\) 0.500000 0.866025i 0.500000 0.866025i
\(123\) 0.866025 0.500000i 0.866025 0.500000i
\(124\) −0.866025 0.500000i −0.866025 0.500000i
\(125\) 1.00000 1.00000
\(126\) 0.866025 0.500000i 0.866025 0.500000i
\(127\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(128\) −1.00000 −1.00000
\(129\) −2.00000 −2.00000
\(130\) 0 0
\(131\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(132\) −0.500000 0.866025i −0.500000 0.866025i
\(133\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(134\) 0 0
\(135\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(136\) 0.500000 0.866025i 0.500000 0.866025i
\(137\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(141\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(142\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 1.00000 1.00000
\(146\) 0.500000 0.866025i 0.500000 0.866025i
\(147\) 0 0
\(148\) 0 0
\(149\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(152\) 1.00000i 1.00000i
\(153\) 0.500000 0.866025i 0.500000 0.866025i
\(154\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(155\) 1.00000i 1.00000i
\(156\) 0 0
\(157\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 2.00000i 2.00000i
\(159\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(160\) −0.500000 0.866025i −0.500000 0.866025i
\(161\) 0 0
\(162\) −1.00000 −1.00000
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(165\) 0.500000 0.866025i 0.500000 0.866025i
\(166\) 0.866025 0.500000i 0.866025 0.500000i
\(167\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(169\) −1.00000 −1.00000
\(170\) 1.00000 1.00000
\(171\) 1.00000i 1.00000i
\(172\) 2.00000i 2.00000i
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(175\) 0 0
\(176\) 0.866025 0.500000i 0.866025 0.500000i
\(177\) −0.500000 0.866025i −0.500000 0.866025i
\(178\) −0.500000 0.866025i −0.500000 0.866025i
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −0.500000 0.866025i −0.500000 0.866025i
\(181\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(184\) 0 0
\(185\) 0 0
\(186\) 0.500000 0.866025i 0.500000 0.866025i
\(187\) 1.00000i 1.00000i
\(188\) −0.866025 0.500000i −0.866025 0.500000i
\(189\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(190\) 0.866025 0.500000i 0.866025 0.500000i
\(191\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000i 1.00000i
\(193\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0.866025 0.500000i 0.866025 0.500000i
\(199\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(203\) 1.00000i 1.00000i
\(204\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(205\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(206\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(207\) 0 0
\(208\) 0 0
\(209\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(210\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(211\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(212\) −0.500000 0.866025i −0.500000 0.866025i
\(213\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(214\) 0 0
\(215\) 1.73205 1.00000i 1.73205 1.00000i
\(216\) 1.00000i 1.00000i
\(217\) −1.00000 −1.00000
\(218\) 0.500000 0.866025i 0.500000 0.866025i
\(219\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(220\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(225\) 0 0
\(226\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(227\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 1.00000 1.00000
\(229\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(230\) 0 0
\(231\) −0.866025 0.500000i −0.866025 0.500000i
\(232\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(233\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(234\) 0 0
\(235\) 1.00000i 1.00000i
\(236\) 0.866025 0.500000i 0.866025 0.500000i
\(237\) 2.00000 2.00000
\(238\) 1.00000i 1.00000i
\(239\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(240\) 0.866025 0.500000i 0.866025 0.500000i
\(241\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(242\) 0 0
\(243\) 1.00000i 1.00000i
\(244\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(245\) 0 0
\(246\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(247\) 0 0
\(248\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(249\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(250\) −1.00000 −1.00000
\(251\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(253\) 0 0
\(254\) 0.866025 0.500000i 0.866025 0.500000i
\(255\) 1.00000i 1.00000i
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 2.00000 2.00000
\(259\) 0 0
\(260\) 0 0
\(261\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(262\) 0.866025 0.500000i 0.866025 0.500000i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(265\) 0.500000 0.866025i 0.500000 0.866025i
\(266\) −0.500000 0.866025i −0.500000 0.866025i
\(267\) 0.866025 0.500000i 0.866025 0.500000i
\(268\) 0 0
\(269\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(270\) 0.866025 0.500000i 0.866025 0.500000i
\(271\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(273\) 0 0
\(274\) 0.500000 0.866025i 0.500000 0.866025i
\(275\) 0 0
\(276\) 0 0
\(277\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(280\) −0.866025 0.500000i −0.866025 0.500000i
\(281\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(282\) 0.500000 0.866025i 0.500000 0.866025i
\(283\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(284\) −0.866025 0.500000i −0.866025 0.500000i
\(285\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(286\) 0 0
\(287\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(288\) 1.00000 1.00000
\(289\) 0 0
\(290\) −1.00000 −1.00000
\(291\) 0 0
\(292\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(293\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(296\) 0 0
\(297\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(298\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(299\) 0 0
\(300\) 0 0
\(301\) −1.00000 1.73205i −1.00000 1.73205i
\(302\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(303\) −0.866025 0.500000i −0.866025 0.500000i
\(304\) 1.00000i 1.00000i
\(305\) −1.00000 −1.00000
\(306\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(307\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(308\) 0.500000 0.866025i 0.500000 0.866025i
\(309\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(310\) 1.00000i 1.00000i
\(311\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(314\) −0.500000 0.866025i −0.500000 0.866025i
\(315\) −0.866025 0.500000i −0.866025 0.500000i
\(316\) 2.00000i 2.00000i
\(317\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(318\) 0.866025 0.500000i 0.866025 0.500000i
\(319\) 1.00000i 1.00000i
\(320\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(321\) 0 0
\(322\) 0 0
\(323\) −0.866025 0.500000i −0.866025 0.500000i
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(328\) −0.500000 0.866025i −0.500000 0.866025i
\(329\) −1.00000 −1.00000
\(330\) −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 \(0.166667\pi\)
\(332\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(333\) 0 0
\(334\) 2.00000i 2.00000i
\(335\) 0 0
\(336\) −0.500000 0.866025i −0.500000 0.866025i
\(337\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(338\) 1.00000 1.00000
\(339\) −0.866025 0.500000i −0.866025 0.500000i
\(340\) −1.00000 −1.00000
\(341\) −1.00000 −1.00000
\(342\) 1.00000i 1.00000i
\(343\) 1.00000i 1.00000i
\(344\) 2.00000i 2.00000i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(348\) −0.866025 0.500000i −0.866025 0.500000i
\(349\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(353\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(354\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(355\) 1.00000i 1.00000i
\(356\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(357\) 1.00000 1.00000
\(358\) 0 0
\(359\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(361\) −1.00000 −1.00000
\(362\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(363\) 0 0
\(364\) 0 0
\(365\) −1.00000 −1.00000
\(366\) −0.866025 0.500000i −0.866025 0.500000i
\(367\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 0 0
\(369\) −0.500000 0.866025i −0.500000 0.866025i
\(370\) 0 0
\(371\) −0.866025 0.500000i −0.866025 0.500000i
\(372\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(373\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(374\) 1.00000i 1.00000i
\(375\) 1.00000i 1.00000i
\(376\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(377\) 0 0
\(378\) −0.500000 0.866025i −0.500000 0.866025i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(381\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(382\) 0.866025 0.500000i 0.866025 0.500000i
\(383\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 1.00000i 1.00000i
\(385\) 1.00000 1.00000
\(386\) −0.500000 0.866025i −0.500000 0.866025i
\(387\) 2.00000i 2.00000i
\(388\) 0 0
\(389\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(394\) 0 0
\(395\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(396\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(397\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(398\) 0.866025 0.500000i 0.866025 0.500000i
\(399\) 0.866025 0.500000i 0.866025 0.500000i
\(400\) 0 0
\(401\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.500000 0.866025i 0.500000 0.866025i
\(405\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(406\) 1.00000i 1.00000i
\(407\) 0 0
\(408\) −0.866025 0.500000i −0.866025 0.500000i
\(409\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(410\) 0.500000 0.866025i 0.500000 0.866025i
\(411\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(412\) −0.866025 0.500000i −0.866025 0.500000i
\(413\) 0.500000 0.866025i 0.500000 0.866025i
\(414\) 0 0
\(415\) −0.866025 0.500000i −0.866025 0.500000i
\(416\) 0 0
\(417\) 0 0
\(418\) −0.500000 0.866025i −0.500000 0.866025i
\(419\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(420\) 0.500000 0.866025i 0.500000 0.866025i
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0.866025 0.500000i 0.866025 0.500000i
\(423\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(424\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(425\) 0 0
\(426\) 0.500000 0.866025i 0.500000 0.866025i
\(427\) 1.00000i 1.00000i
\(428\) 0 0
\(429\) 0 0
\(430\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(431\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 1.00000i 1.00000i
\(433\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(434\) 1.00000 1.00000
\(435\) 1.00000i 1.00000i
\(436\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(437\) 0 0
\(438\) −0.866025 0.500000i −0.866025 0.500000i
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) −0.866025 0.500000i −0.866025 0.500000i
\(441\) 0 0
\(442\) 0 0
\(443\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(446\) 0 0
\(447\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(448\) 0.866025 0.500000i 0.866025 0.500000i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(452\) 0.500000 0.866025i 0.500000 0.866025i
\(453\) −0.500000 0.866025i −0.500000 0.866025i
\(454\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(455\) 0 0
\(456\) −1.00000 −1.00000
\(457\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(458\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(459\) −0.866025 0.500000i −0.866025 0.500000i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(463\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(464\) 0.500000 0.866025i 0.500000 0.866025i
\(465\) −1.00000 −1.00000
\(466\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(467\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.00000i 1.00000i
\(471\) 0.866025 0.500000i 0.866025 0.500000i
\(472\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(473\) −1.00000 1.73205i −1.00000 1.73205i
\(474\) −2.00000 −2.00000
\(475\) 0 0
\(476\) 1.00000i 1.00000i
\(477\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(478\) −0.866025 0.500000i −0.866025 0.500000i
\(479\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(481\) 0 0
\(482\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 1.00000i 1.00000i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0.500000 0.866025i 0.500000 0.866025i
\(489\) 0 0
\(490\) 0 0
\(491\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 0.866025 0.500000i 0.866025 0.500000i
\(493\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(494\) 0 0
\(495\) −0.866025 0.500000i −0.866025 0.500000i
\(496\) −0.866025 0.500000i −0.866025 0.500000i
\(497\) −1.00000 −1.00000
\(498\) −0.500000 0.866025i −0.500000 0.866025i
\(499\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(500\) 1.00000 1.00000
\(501\) 2.00000 2.00000
\(502\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(503\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(504\) 0.866025 0.500000i 0.866025 0.500000i
\(505\) 1.00000 1.00000
\(506\) 0 0
\(507\) 1.00000i 1.00000i
\(508\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 1.00000i 1.00000i
\(511\) 1.00000i 1.00000i
\(512\) −1.00000 −1.00000
\(513\) −1.00000 −1.00000
\(514\) 0 0
\(515\) 1.00000i 1.00000i
\(516\) −2.00000 −2.00000
\(517\) −1.00000 −1.00000
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0.500000 0.866025i 0.500000 0.866025i
\(523\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(524\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(525\) 0 0
\(526\) 0 0
\(527\) 0.866025 0.500000i 0.866025 0.500000i
\(528\) −0.500000 0.866025i −0.500000 0.866025i
\(529\) 1.00000 1.00000
\(530\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(531\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(532\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(533\) 0 0
\(534\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(539\) 0 0
\(540\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(541\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(543\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(544\) 0.500000 0.866025i 0.500000 0.866025i
\(545\) −1.00000 −1.00000
\(546\) 0 0
\(547\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(548\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(549\) 0.500000 0.866025i 0.500000 0.866025i
\(550\) 0 0
\(551\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(552\) 0 0
\(553\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(554\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(555\) 0 0
\(556\) 0 0
\(557\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) −0.866025 0.500000i −0.866025 0.500000i
\(559\) 0 0
\(560\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(561\) 1.00000 1.00000
\(562\) 0.500000 0.866025i 0.500000 0.866025i
\(563\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(565\) 1.00000 1.00000
\(566\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(567\) 0.866025 0.500000i 0.866025 0.500000i
\(568\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(569\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) −0.500000 0.866025i −0.500000 0.866025i
\(571\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(572\) 0 0
\(573\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(574\) −0.866025 0.500000i −0.866025 0.500000i
\(575\) 0 0
\(576\) −1.00000 −1.00000
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0 0
\(579\) 0.866025 0.500000i 0.866025 0.500000i
\(580\) 1.00000 1.00000
\(581\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(582\) 0 0
\(583\) −0.866025 0.500000i −0.866025 0.500000i
\(584\) 0.500000 0.866025i 0.500000 0.866025i
\(585\) 0 0
\(586\) 0.500000 0.866025i 0.500000 0.866025i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0.500000 0.866025i 0.500000 0.866025i
\(590\) −0.866025 0.500000i −0.866025 0.500000i
\(591\) 0 0
\(592\) 0 0
\(593\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) −0.500000 0.866025i −0.500000 0.866025i
\(595\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(596\) −0.500000 0.866025i −0.500000 0.866025i
\(597\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(598\) 0 0
\(599\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(600\) 0 0
\(601\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(602\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(603\) 0 0
\(604\) 0.866025 0.500000i 0.866025 0.500000i
\(605\) 0 0
\(606\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(607\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(608\) 1.00000i 1.00000i
\(609\) −1.00000 −1.00000
\(610\) 1.00000 1.00000
\(611\) 0 0
\(612\) 0.500000 0.866025i 0.500000 0.866025i
\(613\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(614\) −0.866025 0.500000i −0.866025 0.500000i
\(615\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(616\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0.500000 0.866025i 0.500000 0.866025i
\(619\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(620\) 1.00000i 1.00000i
\(621\) 0 0
\(622\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(623\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(624\) 0 0
\(625\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(626\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(627\) 0.866025 0.500000i 0.866025 0.500000i
\(628\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(629\) 0 0
\(630\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(631\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(632\) 2.00000i 2.00000i
\(633\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(634\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(635\) −0.866025 0.500000i −0.866025 0.500000i
\(636\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(637\) 0 0
\(638\) 1.00000i 1.00000i
\(639\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(640\) −0.500000 0.866025i −0.500000 0.866025i
\(641\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) −1.00000 1.73205i −1.00000 1.73205i
\(646\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −1.00000 −1.00000
\(649\) 0.500000 0.866025i 0.500000 0.866025i
\(650\) 0 0
\(651\) 1.00000i 1.00000i
\(652\) 0 0
\(653\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(654\) −0.866025 0.500000i −0.866025 0.500000i
\(655\) −0.866025 0.500000i −0.866025 0.500000i
\(656\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(657\) 0.500000 0.866025i 0.500000 0.866025i
\(658\) 1.00000 1.00000
\(659\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(660\) 0.500000 0.866025i 0.500000 0.866025i
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(663\) 0 0
\(664\) 0.866025 0.500000i 0.866025 0.500000i
\(665\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(666\) 0 0
\(667\) 0 0
\(668\) 2.00000i 2.00000i
\(669\) 0 0
\(670\) 0 0
\(671\) 1.00000i 1.00000i
\(672\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(673\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(675\) 0 0
\(676\) −1.00000 −1.00000
\(677\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(679\) 0 0
\(680\) 1.00000 1.00000
\(681\) −0.500000 0.866025i −0.500000 0.866025i
\(682\) 1.00000 1.00000
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 1.00000i 1.00000i
\(685\) −1.00000 −1.00000
\(686\) 1.00000i 1.00000i
\(687\) −0.866025 0.500000i −0.866025 0.500000i
\(688\) 2.00000i 2.00000i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(692\) 0 0
\(693\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(694\) 0.866025 0.500000i 0.866025 0.500000i
\(695\) 0 0
\(696\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(697\) −1.00000 −1.00000
\(698\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(699\) −0.866025 0.500000i −0.866025 0.500000i
\(700\) 0 0
\(701\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.866025 0.500000i 0.866025 0.500000i
\(705\) −1.00000 −1.00000
\(706\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(707\) 1.00000i 1.00000i
\(708\) −0.500000 0.866025i −0.500000 0.866025i
\(709\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(710\) 1.00000i 1.00000i
\(711\) 2.00000i 2.00000i
\(712\) −0.500000 0.866025i −0.500000 0.866025i
\(713\) 0 0
\(714\) −1.00000 −1.00000
\(715\) 0 0
\(716\) 0 0
\(717\) 0.500000 0.866025i 0.500000 0.866025i
\(718\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(719\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) −0.500000 0.866025i −0.500000 0.866025i
\(721\) −1.00000 −1.00000
\(722\) 1.00000 1.00000
\(723\) −0.866025 0.500000i −0.866025 0.500000i
\(724\) −0.500000 0.866025i −0.500000 0.866025i
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −1.00000 −1.00000
\(730\) 1.00000 1.00000
\(731\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(732\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(733\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(734\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(739\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(743\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 0.500000 0.866025i 0.500000 0.866025i
\(745\) 0.500000 0.866025i 0.500000 0.866025i
\(746\) 0.500000 0.866025i 0.500000 0.866025i
\(747\) 0.866025 0.500000i 0.866025 0.500000i
\(748\) 1.00000i 1.00000i
\(749\) 0 0
\(750\) 1.00000i 1.00000i
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) −0.866025 0.500000i −0.866025 0.500000i
\(753\) −0.500000 0.866025i −0.500000 0.866025i
\(754\) 0 0
\(755\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(756\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(757\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0.866025 0.500000i 0.866025 0.500000i
\(761\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(762\) −0.500000 0.866025i −0.500000 0.866025i
\(763\) 1.00000i 1.00000i
\(764\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(765\) 1.00000 1.00000
\(766\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(767\) 0 0
\(768\) 1.00000i 1.00000i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) −1.00000 −1.00000
\(771\) 0 0
\(772\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(773\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(774\) 2.00000i 2.00000i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.500000 0.866025i 0.500000 0.866025i
\(779\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(780\) 0 0
\(781\) −1.00000 −1.00000
\(782\) 0 0
\(783\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(784\) 0 0
\(785\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(786\) −0.500000 0.866025i −0.500000 0.866025i
\(787\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 1.73205 1.00000i 1.73205 1.00000i
\(791\) 1.00000i 1.00000i
\(792\) 0.866025 0.500000i 0.866025 0.500000i
\(793\) 0 0
\(794\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(795\) −0.866025 0.500000i −0.866025 0.500000i
\(796\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(797\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(798\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(799\) 0.866025 0.500000i 0.866025 0.500000i
\(800\) 0 0
\(801\) −0.500000 0.866025i −0.500000 0.866025i
\(802\) −0.500000 0.866025i −0.500000 0.866025i
\(803\) 1.00000i 1.00000i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −0.866025 0.500000i −0.866025 0.500000i
\(808\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) −0.500000 0.866025i −0.500000 0.866025i
\(811\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(812\) 1.00000i 1.00000i
\(813\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(814\) 0 0
\(815\) 0 0
\(816\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(817\) 2.00000 2.00000
\(818\) −2.00000 −2.00000
\(819\) 0 0
\(820\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(821\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(822\) −0.866025 0.500000i −0.866025 0.500000i
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(825\) 0 0
\(826\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(827\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(831\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(836\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(837\) 0.500000 0.866025i 0.500000 0.866025i
\(838\) −0.866025 0.500000i −0.866025 0.500000i
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(841\) 0 0
\(842\) 0 0
\(843\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(844\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(845\) −0.500000 0.866025i −0.500000 0.866025i
\(846\) −0.866025 0.500000i −0.866025 0.500000i
\(847\) 0 0
\(848\) −0.500000 0.866025i −0.500000 0.866025i
\(849\) −0.500000 0.866025i −0.500000 0.866025i
\(850\) 0 0
\(851\) 0 0
\(852\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 1.00000i 1.00000i
\(855\) 0.866025 0.500000i 0.866025 0.500000i
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 1.73205 1.00000i 1.73205 1.00000i
\(861\) 0.500000 0.866025i 0.500000 0.866025i
\(862\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 1.00000i 1.00000i
\(865\) 0 0
\(866\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(867\) 0 0
\(868\) −1.00000 −1.00000
\(869\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(870\) 1.00000i 1.00000i
\(871\) 0 0
\(872\) 0.500000 0.866025i 0.500000 0.866025i
\(873\) 0 0
\(874\) 0 0
\(875\) 0.866025 0.500000i 0.866025 0.500000i
\(876\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(877\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(880\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(884\) 0 0
\(885\) 0.500000 0.866025i 0.500000 0.866025i
\(886\) −0.866025 0.500000i −0.866025 0.500000i
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(890\) 0.500000 0.866025i 0.500000 0.866025i
\(891\) 0.866025 0.500000i 0.866025 0.500000i
\(892\) 0 0
\(893\) 0.500000 0.866025i 0.500000 0.866025i
\(894\) 0.866025 0.500000i 0.866025 0.500000i
\(895\) 0 0
\(896\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(897\) 0 0
\(898\) 0 0
\(899\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(900\) 0 0
\(901\) 1.00000 1.00000
\(902\) −0.866025 0.500000i −0.866025 0.500000i
\(903\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(904\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(905\) 0.500000 0.866025i 0.500000 0.866025i
\(906\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(907\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0.866025 0.500000i 0.866025 0.500000i
\(909\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(910\) 0 0
\(911\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(912\) 1.00000 1.00000
\(913\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(914\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(915\) 1.00000i 1.00000i
\(916\) 0.500000 0.866025i 0.500000 0.866025i
\(917\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(918\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(919\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(920\) 0 0
\(921\) 0.500000 0.866025i 0.500000 0.866025i
\(922\) 0 0
\(923\) 0 0
\(924\) −0.866025 0.500000i −0.866025 0.500000i
\(925\) 0 0
\(926\) −0.866025 0.500000i −0.866025 0.500000i
\(927\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(928\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(929\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(930\) 1.00000 1.00000
\(931\) 0 0
\(932\) 0.500000 0.866025i 0.500000 0.866025i
\(933\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(934\) 2.00000i 2.00000i
\(935\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(936\) 0 0
\(937\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 0 0
\(939\) −0.866025 0.500000i −0.866025 0.500000i
\(940\) 1.00000i 1.00000i
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(943\) 0 0
\(944\) 0.866025 0.500000i 0.866025 0.500000i
\(945\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(946\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 2.00000 2.00000
\(949\) 0 0
\(950\) 0 0
\(951\) −0.866025 0.500000i −0.866025 0.500000i
\(952\) 1.00000i 1.00000i
\(953\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(954\) −0.500000 0.866025i −0.500000 0.866025i
\(955\) −0.866025 0.500000i −0.866025 0.500000i
\(956\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(957\) −1.00000 −1.00000
\(958\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(959\) 1.00000i 1.00000i
\(960\) 0.866025 0.500000i 0.866025 0.500000i
\(961\) 0 0
\(962\) 0 0
\(963\) 0 0
\(964\) 0.500000 0.866025i 0.500000 0.866025i
\(965\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(966\) 0 0
\(967\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(970\) 0 0
\(971\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(972\) 1.00000i 1.00000i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(977\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(980\) 0 0
\(981\) 0.500000 0.866025i 0.500000 0.866025i
\(982\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(985\) 0 0
\(986\) −0.500000 0.866025i −0.500000 0.866025i
\(987\) 1.00000i 1.00000i
\(988\) 0 0
\(989\) 0 0
\(990\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(991\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(992\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(993\) −0.500000 0.866025i −0.500000 0.866025i
\(994\) 1.00000 1.00000
\(995\) −0.866025 0.500000i −0.866025 0.500000i
\(996\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(997\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(998\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 684.1.x.a.391.1 yes 4
3.2 odd 2 2052.1.x.a.847.2 4
4.3 odd 2 inner 684.1.x.a.391.2 yes 4
9.2 odd 6 2052.1.bm.a.1531.1 4
9.7 even 3 684.1.bm.a.619.1 yes 4
12.11 even 2 2052.1.x.a.847.1 4
19.7 even 3 684.1.bm.a.463.2 yes 4
36.7 odd 6 684.1.bm.a.619.2 yes 4
36.11 even 6 2052.1.bm.a.1531.2 4
57.26 odd 6 2052.1.bm.a.1603.2 4
76.7 odd 6 684.1.bm.a.463.1 yes 4
171.7 even 3 inner 684.1.x.a.7.1 4
171.83 odd 6 2052.1.x.a.235.1 4
228.83 even 6 2052.1.bm.a.1603.1 4
684.7 odd 6 inner 684.1.x.a.7.2 yes 4
684.83 even 6 2052.1.x.a.235.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
684.1.x.a.7.1 4 171.7 even 3 inner
684.1.x.a.7.2 yes 4 684.7 odd 6 inner
684.1.x.a.391.1 yes 4 1.1 even 1 trivial
684.1.x.a.391.2 yes 4 4.3 odd 2 inner
684.1.bm.a.463.1 yes 4 76.7 odd 6
684.1.bm.a.463.2 yes 4 19.7 even 3
684.1.bm.a.619.1 yes 4 9.7 even 3
684.1.bm.a.619.2 yes 4 36.7 odd 6
2052.1.x.a.235.1 4 171.83 odd 6
2052.1.x.a.235.2 4 684.83 even 6
2052.1.x.a.847.1 4 12.11 even 2
2052.1.x.a.847.2 4 3.2 odd 2
2052.1.bm.a.1531.1 4 9.2 odd 6
2052.1.bm.a.1531.2 4 36.11 even 6
2052.1.bm.a.1603.1 4 228.83 even 6
2052.1.bm.a.1603.2 4 57.26 odd 6