Properties

Label 2888.1.s.b.477.1
Level $2888$
Weight $1$
Character 2888.477
Analytic conductor $1.441$
Analytic rank $0$
Dimension $6$
Projective image $D_{3}$
CM discriminant -152
Inner twists $12$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2888,1,Mod(333,2888)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2888, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 17]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2888.333");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2888.s (of order \(18\), degree \(6\), not 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: \(1.44129975648\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.152.1
Artin image: $S_3\times C_{18}$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{54} - \cdots)\)

Embedding invariants

Embedding label 477.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 2888.477
Dual form 2888.1.s.b.333.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\) \(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 0.866025i) q^{12} +(0.766044 - 0.642788i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.173648 + 0.984808i) q^{17} +(-0.173648 + 0.984808i) q^{21} +(0.939693 + 0.342020i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(0.500000 + 0.866025i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.173648 - 0.984808i) q^{28} +(0.173648 + 0.984808i) q^{29} +(-0.766044 + 0.642788i) q^{32} +(-0.939693 - 0.342020i) q^{34} -2.00000 q^{37} +1.00000 q^{39} +(-0.939693 - 0.342020i) q^{42} +(-0.500000 + 0.866025i) q^{46} +(0.347296 + 1.96962i) q^{47} +(0.173648 + 0.984808i) q^{48} +(0.500000 + 0.866025i) q^{50} +(-0.766044 + 0.642788i) q^{51} +(-0.939693 + 0.342020i) q^{52} +(-0.939693 - 0.342020i) q^{53} +(0.766044 + 0.642788i) q^{54} +1.00000 q^{56} -1.00000 q^{58} +(0.173648 - 0.984808i) q^{59} +(-0.500000 - 0.866025i) q^{64} +(0.173648 + 0.984808i) q^{67} +(0.500000 - 0.866025i) q^{68} +(0.500000 + 0.866025i) q^{69} +(-0.766044 - 0.642788i) q^{73} +(0.347296 - 1.96962i) q^{74} +1.00000 q^{75} +(-0.173648 + 0.984808i) q^{78} +(0.939693 - 0.342020i) q^{81} +(0.500000 - 0.866025i) q^{84} +(-0.500000 + 0.866025i) q^{87} +(0.939693 + 0.342020i) q^{91} +(-0.766044 - 0.642788i) q^{92} -2.00000 q^{94} -1.00000 q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{7} + 3 q^{8} - 3 q^{12} + 3 q^{26} + 3 q^{27} - 12 q^{37} + 6 q^{39} - 3 q^{46} + 3 q^{50} + 6 q^{56} - 6 q^{58} - 3 q^{64} + 3 q^{68} + 3 q^{69} + 6 q^{75} + 3 q^{84} - 3 q^{87} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times\).

\(n\) \(1445\) \(2167\) \(2529\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(3\) 0.766044 + 0.642788i 0.766044 + 0.642788i 0.939693 0.342020i \(-0.111111\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(4\) −0.939693 0.342020i −0.939693 0.342020i
\(5\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(6\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(7\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 0.500000 0.866025i 0.500000 0.866025i
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) −0.500000 0.866025i −0.500000 0.866025i
\(13\) 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i \(-0.555556\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(14\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(15\) 0 0
\(16\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(17\) −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i \(0.222222\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(18\) 0 0
\(19\) 0 0
\(20\) 0 0
\(21\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(22\) 0 0
\(23\) 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i \(-0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(24\) 0.939693 0.342020i 0.939693 0.342020i
\(25\) 0.766044 0.642788i 0.766044 0.642788i
\(26\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(27\) 0.500000 0.866025i 0.500000 0.866025i
\(28\) −0.173648 0.984808i −0.173648 0.984808i
\(29\) 0.173648 + 0.984808i 0.173648 + 0.984808i 0.939693 + 0.342020i \(0.111111\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(30\) 0 0
\(31\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(33\) 0 0
\(34\) −0.939693 0.342020i −0.939693 0.342020i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 1.00000 1.00000
\(40\) 0 0
\(41\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(42\) −0.939693 0.342020i −0.939693 0.342020i
\(43\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(47\) 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i \(0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(48\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(49\) 0 0
\(50\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(51\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(52\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(53\) −0.939693 0.342020i −0.939693 0.342020i −0.173648 0.984808i \(-0.555556\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(54\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(55\) 0 0
\(56\) 1.00000 1.00000
\(57\) 0 0
\(58\) −1.00000 −1.00000
\(59\) 0.173648 0.984808i 0.173648 0.984808i −0.766044 0.642788i \(-0.777778\pi\)
0.939693 0.342020i \(-0.111111\pi\)
\(60\) 0 0
\(61\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.500000 0.866025i −0.500000 0.866025i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.173648 + 0.984808i 0.173648 + 0.984808i 0.939693 + 0.342020i \(0.111111\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(68\) 0.500000 0.866025i 0.500000 0.866025i
\(69\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(70\) 0 0
\(71\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(72\) 0 0
\(73\) −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i \(-0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(74\) 0.347296 1.96962i 0.347296 1.96962i
\(75\) 1.00000 1.00000
\(76\) 0 0
\(77\) 0 0
\(78\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(79\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(80\) 0 0
\(81\) 0.939693 0.342020i 0.939693 0.342020i
\(82\) 0 0
\(83\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(84\) 0.500000 0.866025i 0.500000 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(88\) 0 0
\(89\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(90\) 0 0
\(91\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(92\) −0.766044 0.642788i −0.766044 0.642788i
\(93\) 0 0
\(94\) −2.00000 −2.00000
\(95\) 0 0
\(96\) −1.00000 −1.00000
\(97\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(101\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(102\) −0.500000 0.866025i −0.500000 0.866025i
\(103\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) −0.173648 0.984808i −0.173648 0.984808i
\(105\) 0 0
\(106\) 0.500000 0.866025i 0.500000 0.866025i
\(107\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(108\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(109\) −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i \(-0.777778\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(110\) 0 0
\(111\) −1.53209 1.28558i −1.53209 1.28558i
\(112\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.173648 0.984808i 0.173648 0.984808i
\(117\) 0 0
\(118\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(119\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(128\) 0.939693 0.342020i 0.939693 0.342020i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.00000 −1.00000
\(135\) 0 0
\(136\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(137\) 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i \(-0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(138\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(139\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(140\) 0 0
\(141\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0.766044 0.642788i 0.766044 0.642788i
\(147\) 0 0
\(148\) 1.87939 + 0.684040i 1.87939 + 0.684040i
\(149\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(150\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.939693 0.342020i −0.939693 0.342020i
\(157\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(158\) 0 0
\(159\) −0.500000 0.866025i −0.500000 0.866025i
\(160\) 0 0
\(161\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(162\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(163\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(168\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.347296 + 1.96962i −0.347296 + 1.96962i −0.173648 + 0.984808i \(0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(174\) −0.766044 0.642788i −0.766044 0.642788i
\(175\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(176\) 0 0
\(177\) 0.766044 0.642788i 0.766044 0.642788i
\(178\) 0 0
\(179\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(180\) 0 0
\(181\) −0.347296 1.96962i −0.347296 1.96962i −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 0.984808i \(-0.555556\pi\)
\(182\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(183\) 0 0
\(184\) 0.766044 0.642788i 0.766044 0.642788i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0.347296 1.96962i 0.347296 1.96962i
\(189\) 1.00000 1.00000
\(190\) 0 0
\(191\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0.173648 0.984808i 0.173648 0.984808i
\(193\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(198\) 0 0
\(199\) −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i \(-0.888889\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(200\) −0.173648 0.984808i −0.173648 0.984808i
\(201\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(202\) 0 0
\(203\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(204\) 0.939693 0.342020i 0.939693 0.342020i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.00000 1.00000
\(209\) 0 0
\(210\) 0 0
\(211\) 0.173648 0.984808i 0.173648 0.984808i −0.766044 0.642788i \(-0.777778\pi\)
0.939693 0.342020i \(-0.111111\pi\)
\(212\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(213\) 0 0
\(214\) 0.939693 0.342020i 0.939693 0.342020i
\(215\) 0 0
\(216\) −0.500000 0.866025i −0.500000 0.866025i
\(217\) 0 0
\(218\) −0.173648 0.984808i −0.173648 0.984808i
\(219\) −0.173648 0.984808i −0.173648 0.984808i
\(220\) 0 0
\(221\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(222\) 1.53209 1.28558i 1.53209 1.28558i
\(223\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(224\) −0.939693 0.342020i −0.939693 0.342020i
\(225\) 0 0
\(226\) 0 0
\(227\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(233\) −1.87939 + 0.684040i −1.87939 + 0.684040i −0.939693 + 0.342020i \(0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(237\) 0 0
\(238\) −0.173648 0.984808i −0.173648 0.984808i
\(239\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(240\) 0 0
\(241\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(242\) 0.939693 0.342020i 0.939693 0.342020i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(257\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(258\) 0 0
\(259\) −1.00000 1.73205i −1.00000 1.73205i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.53209 + 1.28558i 1.53209 + 1.28558i 0.766044 + 0.642788i \(0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.173648 0.984808i 0.173648 0.984808i
\(269\) −1.53209 1.28558i −1.53209 1.28558i −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 0.642788i \(-0.777778\pi\)
\(270\) 0 0
\(271\) 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(272\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(273\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(274\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(275\) 0 0
\(276\) −0.173648 0.984808i −0.173648 0.984808i
\(277\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(282\) −1.53209 1.28558i −1.53209 1.28558i
\(283\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 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 0
\(296\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(297\) 0 0
\(298\) 0 0
\(299\) 0.939693 0.342020i 0.939693 0.342020i
\(300\) −0.939693 0.342020i −0.939693 0.342020i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.53209 1.28558i −1.53209 1.28558i −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 0.642788i \(-0.777778\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0.500000 0.866025i 0.500000 0.866025i
\(313\) −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i \(-0.888889\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i \(-0.555556\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(318\) 0.939693 0.342020i 0.939693 0.342020i
\(319\) 0 0
\(320\) 0 0
\(321\) 0.173648 0.984808i 0.173648 0.984808i
\(322\) −1.00000 −1.00000
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 0.173648 0.984808i 0.173648 0.984808i
\(326\) 0 0
\(327\) −0.939693 0.342020i −0.939693 0.342020i
\(328\) 0 0
\(329\) −1.53209 + 1.28558i −1.53209 + 1.28558i
\(330\) 0 0
\(331\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(337\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) −1.87939 0.684040i −1.87939 0.684040i
\(347\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(348\) 0.766044 0.642788i 0.766044 0.642788i
\(349\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(351\) −0.173648 0.984808i −0.173648 0.984808i
\(352\) 0 0
\(353\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(354\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(355\) 0 0
\(356\) 0 0
\(357\) −0.939693 0.342020i −0.939693 0.342020i
\(358\) 1.53209 + 1.28558i 1.53209 + 1.28558i
\(359\) −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i \(0.222222\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 2.00000 2.00000
\(363\) 0.173648 0.984808i 0.173648 0.984808i
\(364\) −0.766044 0.642788i −0.766044 0.642788i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.53209 1.28558i 1.53209 1.28558i 0.766044 0.642788i \(-0.222222\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(368\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.173648 0.984808i −0.173648 0.984808i
\(372\) 0 0
\(373\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.87939 + 0.684040i 1.87939 + 0.684040i
\(377\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(378\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(379\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.173648 0.984808i 0.173648 0.984808i
\(383\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(384\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(390\) 0 0
\(391\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(398\) 1.00000 1.00000
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(402\) −0.766044 0.642788i −0.766044 0.642788i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −0.500000 0.866025i −0.500000 0.866025i
\(407\) 0 0
\(408\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(409\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(410\) 0 0
\(411\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(412\) 0 0
\(413\) 0.939693 0.342020i 0.939693 0.342020i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0.766044 + 0.642788i 0.766044 + 0.642788i 0.939693 0.342020i \(-0.111111\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(422\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(423\) 0 0
\(424\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(425\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(432\) 0.939693 0.342020i 0.939693 0.342020i
\(433\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 1.00000
\(437\) 0 0
\(438\) 1.00000 1.00000
\(439\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(443\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(444\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.500000 0.866025i 0.500000 0.866025i
\(449\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(460\) 0 0
\(461\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(462\) 0 0
\(463\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(464\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(465\) 0 0
\(466\) −0.347296 1.96962i −0.347296 1.96962i
\(467\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 0 0
\(469\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(470\) 0 0
\(471\) 0 0
\(472\) −0.766044 0.642788i −0.766044 0.642788i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 1.00000 1.00000
\(477\) 0 0
\(478\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(479\) −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 0.342020i \(-0.888889\pi\)
\(480\) 0 0
\(481\) −1.53209 + 1.28558i −1.53209 + 1.28558i
\(482\) 0 0
\(483\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(484\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(492\) 0 0
\(493\) −1.00000 −1.00000
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i \(-0.888889\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.87939 + 0.684040i 1.87939 + 0.684040i 0.939693 + 0.342020i \(0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(510\) 0 0
\(511\) 0.173648 0.984808i 0.173648 0.984808i
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.87939 0.684040i 1.87939 0.684040i
\(519\) −1.53209 + 1.28558i −1.53209 + 1.28558i
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0.173648 + 0.984808i 0.173648 + 0.984808i 0.939693 + 0.342020i \(0.111111\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(524\) 0 0
\(525\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(526\) −1.53209 + 1.28558i −1.53209 + 1.28558i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(537\) 1.87939 0.684040i 1.87939 0.684040i
\(538\) 1.53209 1.28558i 1.53209 1.28558i
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(542\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(543\) 1.00000 1.73205i 1.00000 1.73205i
\(544\) −0.500000 0.866025i −0.500000 0.866025i
\(545\) 0 0
\(546\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(547\) 1.87939 + 0.684040i 1.87939 + 0.684040i 0.939693 + 0.342020i \(0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(548\) −0.766044 0.642788i −0.766044 0.642788i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 1.00000 1.00000
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(564\) 1.53209 1.28558i 1.53209 1.28558i
\(565\) 0 0
\(566\) 0 0
\(567\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) −0.766044 0.642788i −0.766044 0.642788i
\(574\) 0 0
\(575\) 0.939693 0.342020i 0.939693 0.342020i
\(576\) 0 0
\(577\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(585\) 0 0
\(586\) −0.766044 0.642788i −0.766044 0.642788i
\(587\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.53209 1.28558i −1.53209 1.28558i
\(593\) −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 0.342020i \(-0.888889\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.500000 0.866025i 0.500000 0.866025i
\(598\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(599\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(600\) 0.500000 0.866025i 0.500000 0.866025i
\(601\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) −1.00000 −1.00000
\(610\) 0 0
\(611\) 1.53209 + 1.28558i 1.53209 + 1.28558i
\(612\) 0 0
\(613\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(614\) 1.53209 1.28558i 1.53209 1.28558i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i \(0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(618\) 0 0
\(619\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0.766044 0.642788i 0.766044 0.642788i
\(622\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(623\) 0 0
\(624\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(625\) 0.173648 0.984808i 0.173648 0.984808i
\(626\) 1.00000 1.00000
\(627\) 0 0
\(628\) 0 0
\(629\) 0.347296 1.96962i 0.347296 1.96962i
\(630\) 0 0
\(631\) −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 0.342020i \(-0.888889\pi\)
\(632\) 0 0
\(633\) 0.766044 0.642788i 0.766044 0.642788i
\(634\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(635\) 0 0
\(636\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(642\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(643\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(644\) 0.173648 0.984808i 0.173648 0.984808i
\(645\) 0 0
\(646\) 0 0
\(647\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0.173648 0.984808i 0.173648 0.984808i
\(649\) 0 0
\(650\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) 0.500000 0.866025i 0.500000 0.866025i
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) −1.00000 1.73205i −1.00000 1.73205i
\(659\) 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i \(-0.555556\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(660\) 0 0
\(661\) −0.939693 0.342020i −0.939693 0.342020i −0.173648 0.984808i \(-0.555556\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(662\) −0.766044 0.642788i −0.766044 0.642788i
\(663\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.500000 0.866025i −0.500000 0.866025i
\(673\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0 0
\(675\) −0.173648 0.984808i −0.173648 0.984808i
\(676\) 0 0
\(677\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(682\) 0 0
\(683\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(687\) 0 0
\(688\) 0 0
\(689\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(690\) 0 0
\(691\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(692\) 1.00000 1.73205i 1.00000 1.73205i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(697\) 0 0
\(698\) 0 0
\(699\) −1.87939 0.684040i −1.87939 0.684040i
\(700\) −0.766044 0.642788i −0.766044 0.642788i
\(701\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(702\) 1.00000 1.00000
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(707\) 0 0
\(708\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(709\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0.500000 0.866025i 0.500000 0.866025i
\(715\) 0 0
\(716\) −1.53209 + 1.28558i −1.53209 + 1.28558i
\(717\) 0.939693 0.342020i 0.939693 0.342020i
\(718\) −0.939693 0.342020i −0.939693 0.342020i
\(719\) −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i \(-0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −0.347296 + 1.96962i −0.347296 + 1.96962i
\(725\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(726\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(727\) 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(728\) 0.766044 0.642788i 0.766044 0.642788i
\(729\) −0.500000 0.866025i −0.500000 0.866025i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(735\) 0 0
\(736\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.00000 1.00000
\(743\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.939693 0.342020i 0.939693 0.342020i
\(747\) 0 0
\(748\) 0 0
\(749\) 0.500000 0.866025i 0.500000 0.866025i
\(750\) 0 0
\(751\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(752\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(753\) 0 0
\(754\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(755\) 0 0
\(756\) −0.939693 0.342020i −0.939693 0.342020i
\(757\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(758\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(759\) 0 0
\(760\) 0 0
\(761\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) 0 0
\(763\) −0.766044 0.642788i −0.766044 0.642788i
\(764\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(765\) 0 0
\(766\) 0 0
\(767\) −0.500000 0.866025i −0.500000 0.866025i
\(768\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(769\) −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i \(-0.888889\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i \(-0.555556\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0.347296 1.96962i 0.347296 1.96962i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −0.766044 0.642788i −0.766044 0.642788i
\(783\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0.347296 + 1.96962i 0.347296 + 1.96962i
\(790\) 0 0
\(791\) 0 0
\(792\) 0